8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 1, 2, 2, 1, 2] 
dist 0=[45.352879229247123598  ,45.352879229247123598  ] 
dist 1=[45.119173677806426247  ,45.429976851966336411  ] 
dist 2=[44.653292667891980969  ,45.504172988304496756  ] 
dist 3=[43.747037262629561520  ,45.575045477027604051  ] 
dist 4=[42.623728186778614182  ,45.659843301953351526  ] 
dist 5=[41.290883952571578248  ,45.746748816563953115  ] 
dist 6=[39.545303903369464004  ,45.825910539805172849  ] 
dist 7=[36.773429444158422353  ,45.914012243626813800  ] 
dist 8=[33.938922157791251763  ,46.036370381150942854  ] 
dist 9=[31.943114933195993214  ,46.150122486725998621  ] 
dist 10=[30.173663908549578044  ,46.203890743072246082  ] 
dist 11=[28.243106957813899817  ,46.223353781749896784  ] 
dist 12=[26.349254649224049145  ,46.200461645544115828  ] 
dist 13=[24.726238483749496608  ,46.104138923082035948  ] 
dist 14=[22.985063934163586025  ,43.777499341944628386  ] 
dist 15=[20.618913593473347021  ,43.318012356614046487  ] 
dist 16=[18.254322791586792003  ,40.566046284697743608  ] 
dist 17=[16.519200243654426166  ,35.111353598364417735  ] 
dist 18=[14.905985228052081013  ,34.171072629805950137  ] 
dist 19=[13.028137081166256168  ,31.851947293948074996  ] 
dist 20=[11.113647984375127773  ,31.515782959870501420  ] 
dist 21=[9.3537266878407486117 ,27.967498575435645178  ] 
dist 22=[7.3612638822619340635 ,27.292261973084213601  ] 
dist 23=[4.5170751701960284585 ,26.552544659837432188  ] 
dist 24=[1.7117037177470087464 ,26.410242569817867633  ] 
dist 25=[-.1257570723008424619 ,20.091033307841581354  ] 
dist 26=[-1.6155579892569024822 ,19.299015412270866372  ] 
dist 27=[-3.0499332774638545706 ,17.724697014179404908  ] 
dist 28=[-4.5343814059030905983 ,17.324708173556739276  ] 
dist 29=[-5.9180814769243719608 ,15.936825071524842171  ] 
dist 30=[-7.1404740753788464800 ,15.632346610899377087  ] 
dist 31=[-7.9803835992102022380 ,15.257548350670524002  ] 
dist 32=[-8.7063031653474263560 ,15.157231193914427283  ] 
dist 33=[-9.4734495496500659825 ,3.7293986936287077289 ] 
dist 34=[-10.155897697365022381  ,2.7965417743429540587 ] 
dist 35=[-10.543353909412534398  ,.68977790164061933253] 
dist 36=[-10.792351402988756330  ,.34941954980380105867] 
dist 37=[-10.921230211571110503  ,-2.1865427572759809029 ] 
dist 38=[-10.988655052289332512  ,-2.6155457130225661116 ] 
dist 39=[-10.991975316929674292  ,-1.7568112994335656321 ] 
dist 40=[-10.954442046002840919  ,-.3161926190777757026 ] 
dist 41=[-10.923280585817751047  ,.6705815306176170802 ] 
dist 42=[-8.5483893709698461924 ,1.5127885537842301072 ] 
dist 43=[-9.0699711789070215438 ,2.3766916493492262741 ] 
dist 44=[-9.4957158137451675805 ,3.1875500909616839967 ] 
dist 45=[-9.8326900489257115783 ,3.8181610401713653736 ] 
dist 46=[-9.9996131290147510824 ,4.4371135898095567591 ] 
dist 47=[-10.084351441650575084  ,5.2015117993058470464 ] 
dist 48=[-10.093411821351896995  ,5.9254667786744450904 ] 
dist 49=[-6.2063004858121537902 ,6.3830343489266616040 ] 
dist 50=[-6.0057133471839472913 ,6.7328675366038923858 ] 
dist 51=[-5.5192971227344798971 ,7.0268614752124988529 ] 
dist 52=[-5.4320071358116781173 ,7.2621851764790658849 ] 
dist 53=[-4.7124667473808108330 ,7.3778493384686535076 ] 
dist 54=[-4.5751066372853008862 ,7.4299751068934636644 ] 
dist 55=[-4.3716093017164887781 ,7.4345936687285328983 ] 
dist 56=[-4.3133356614296338192 ,7.3418956089172299668 ] 
dist 57=[-3.1947086261394804122 ,7.2646517566040177284 ] 
dist 58=[-3.0493670872177808127 ,1.5235812841726746171 ] 
dist 59=[-2.7208927223847122694 ,2.0505725978179170117 ] 
dist 60=[-2.6548171870773245379 ,2.4769759568434339102 ] 
dist 61=[-2.2457467655677049531 ,2.8790183627491819703 ] 
dist 62=[-2.1721179185938021280 ,3.2358073945705755621 ] 
dist 63=[-2.0305377021926003547 ,3.4814943873110399634 ] 
dist 64=[-1.9958502261452362159 ,3.6934930642143416126 ] 
dist 65=[-.77686692725362815247,3.9157646529632496660 ] 
dist 66=[-.65136197144458966662,4.1141040216107964934 ] 
dist 67=[-.37338867677615682083,4.2305291714632053327 ] 
dist 68=[-.31770255145321241217,4.3096217623605034719 ] 
dist 69=[.0135132498418545170 ,4.3588562355356984667 ] 
dist 70=[.0729091919995728629 ,4.3867289121335640787 ] 
dist 71=[.1876818149912776697 ,4.3897278171700227154 ] 
dist 72=[.2159059933455405860 ,4.3650917890506070126 ] 
dist 73=[.5345417526291780450 ,4.3562706045829856975 ] 
dist 74=[.5809544178437664868 ,3.5466260231995550999 ] 
dist 75=[.6775737418959863596 ,3.5926310401222380404 ] 
dist 76=[.7033970687149791548 ,3.6225256739526887849 ] 
dist 77=[.60740467919062698245,3.6401932385594352681 ] 
dist 78=[.2523558718981698494 ,3.6395498046736562582 ] 
dist 79=[-.0472033372326149567 ,3.6258874109920646806 ] 
dist 80=[-.3638617040215872508 ,3.6132469000007089334 ] 
dist 81=[-.7872018132779813303 ,2.0433988525534326902 ] 
dist 82=[-1.2054140004823320895 ,1.4475832192334902049 ] 
dist 83=[-1.5016102311143217513 ,1.3290083816459134359 ] 
dist 84=[-1.7655709062705105203 ,1.1963862793623490666 ] 
dist 85=[-2.0550928995157505086 ,1.1701212135982316611 ] 
dist 86=[-2.3394457512037529968 ,1.1141069174581700198 ] 
dist 87=[-2.5827820899675248183 ,1.0977655250486355672 ] 
dist 88=[-2.8431072877874189042 ,.6157775412725628440 ] 
dist 89=[-3.1953181355558797462 ,.5934420234021232940 ] 
dist 90=[-3.5352876245742638680 ,.1729070128452540454 ] 
dist 91=[-3.7467394731647214096 ,.1598438397564606224 ] 
dist 92=[-3.9049381492885653634 ,.1889219372130422589 ] 
dist 93=[-4.0322653205274641562 ,.2415948215129557082 ] 
dist 94=[-4.1303197679075017033 ,.3245719499123749593 ] 
dist 95=[-4.1716350664770669377 ,.4456205161542760253 ] 
dist 96=[-4.1883888270700563539 ,.65026178360427967256] 
dist 97=[-4.1883488557342409708 ,.86306080304272555027] 
dist 98=[-4.0941110745672507185 ,1.0166777246074090334 ] 
dist 99=[-4.0678953205392834971 ,1.1563836654030046976 ] 
dist 100=[-4.0159382318309465387 ,1.3136704900229876526 ] 
dist 101=[-4.0149947172445620170 ,1.4702833620651365439 ] 
dist 102=[-4.0006254152596293724 ,1.6073084969650875431 ] 
dist 103=[-3.9904085137825420620 ,1.7562975865566166249 ] 
dist 104=[-3.9064229091614532759 ,1.9606786121452346089 ] 
dist 105=[-3.6836478358801424768 ,2.1647087498928568734 ] 
dist 106=[-2.6631169996096110915 ,2.3123029297436905002 ] 
dist 107=[-2.6324152342029489301 ,2.4469235884162276413 ] 
dist 108=[-2.3283115477738103673 ,2.5991726772557932156 ] 
dist 109=[-2.2661015130883435753 ,2.7512557744801671620 ] 
dist 110=[-2.1898953873643624531 ,2.8852206435316599508 ] 
dist 111=[-2.1609165588133503307 ,3.0317018279090341966 ] 
dist 112=[-1.5200476201207900919 ,3.2337611063259221196 ] 
dist 113=[-1.4349337690317575641 ,3.4284172614806432795 ] 
dist 114=[-1.2568632328773528322 ,3.5453449270543195466 ] 
dist 115=[-1.2084614463029930870 ,3.6278413163362806456 ] 
dist 116=[-1.0207891271371594305 ,3.6850360607089789412 ] 
dist 117=[-.98315012426047363865,3.7218962195942050825 ] 
dist 118=[-.9011485446065052896 ,3.7292945857608586758 ] 
dist 119=[-.87753958208175018933,3.7145098528331078011 ] 
dist 120=[.22783101290555866697,3.6936441477380041887 ] 
dist 121=[.30220707559958805762,3.5422929765034188861 ] 
dist 122=[.4446888307831753185 ,.72632996874169621954] 
dist 123=[.46419390267163812273,.92004279420462201156] 
dist 124=[.50172927938245492773,1.1035940547248166865 ] 
dist 125=[.50985537951957430818,1.2499929775810593990 ] 
dist 126=[.53004902246410100135,1.3974265317793121330 ] 
dist 127=[.52933412988886233397,1.5851089681579253413 ] 
dist 128=[.52054152766835592047,1.7662241348119495150 ] 
dist 129=[.49841742971816977745,1.8874364669011769360 ] 
dist 130=[.47180778715485361681,1.9881512950103783235 ] 
dist 131=[.44510292492372209592,2.0874256310894234400 ] 
dist 132=[.41316853038058915918,2.1783457455455189504 ] 
dist 133=[.36567493629382636659,2.2457047660088745688 ] 
dist 134=[.25420579266818644573,2.3088035752838468658 ] 
dist 135=[-.06989717085173388924,2.3827146767642700275 ] 
dist 136=[-.39931527042293132719,2.4482370410834601987 ] 
dist 137=[-.62689381967414175203,2.4778421409527546285 ] 
dist 138=[-.82375016282950969791,2.4913747627709491269 ] 
dist 139=[-1.0305069059425021018 ,2.4927227273371774642 ] 
dist 140=[-1.2281323072871785991 ,2.4476053100144776493 ] 
dist 141=[-1.3885312075655204882 ,2.4335170566181114890 ] 
dist 142=[-1.5525974076922912753 ,2.4228861127563393954 ] 
dist 143=[-1.7648658071653027486 ,2.4141765616369081815 ] 
dist 144=[-1.9713177350437217501 ,2.0453513232518566828 ] 
dist 145=[-2.1121612821830775938 ,1.9924975495211898736 ] 
dist 146=[-2.2321039623136272093 ,1.8935132114959910193 ] 
dist 147=[-2.3551067292851861065 ,1.8671514783252804889 ] 
dist 148=[-2.4708627015266460156 ,1.7730356903225114785 ] 
dist 149=[-2.5618720656669895670 ,1.7478460120680684583 ] 
dist 150=[-2.6523108293664734443 ,1.7111878079427583734 ] 
dist 151=[-2.7657896948805793358 ,1.6981894462627880685 ] 
dist 152=[-2.8710700804440010780 ,.27381152410178507692] 
dist 153=[-2.9287752772269169740 ,.15369545552446008424] 
dist 154=[-2.9627569556729152403 ,-.0870305956577918259 ] 
dist 155=[-2.9733168179808213218 ,-.1065783950872641714 ] 
dist 156=[-2.9725856846732552299 ,-.1491337809745612012 ] 
dist 157=[-2.9656536843854357738 ,-.1573082540227486713 ] 
dist 158=[-2.9452765168778143574 ,-.2029878309985951102 ] 
dist 159=[-2.9331686881397771008 ,-.2103625527072599044 ] 
dist 160=[-2.6838437276255601387 ,-.2260173574485124220 ] 
dist 161=[-2.6420827156614357069 ,-.2282967284742190574 ] 
dist 162=[-2.5478839573889170610 ,-.2413536228182556057 ] 
dist 163=[-2.5171471445131070216 ,-.24090096992072768004] 
dist 164=[-2.3735678871123524908 ,-.23595151909354191996] 
dist 165=[-2.3417549804089517883 ,-.22354506604835580529] 
dist 166=[-2.2621980829737711871 ,-.20724894233659133252] 
dist 167=[-2.2381431306990892782 ,.09820499939295234625] 
dist 168=[-2.0794041257780587244 ,.66905116703582645735] 
dist 169=[-2.1164434626603512036 ,1.0453266256689918060 ] 
dist 170=[-2.1364889666251061946 ,1.3516251638606829121 ] 
dist 171=[-2.1398238933204653991 ,1.6430780593602207711 ] 
dist 172=[-2.1334030342473596736 ,1.9031391619504979020 ] 
dist 173=[-2.1261640576916826549 ,2.0841012808875687121 ] 
dist 174=[-2.1112205201171453997 ,2.2420170081114747270 ] 
dist 175=[-2.1035134088328267944 ,2.4100619271308397798 ] 
dist 176=[-1.8946328417339930097 ,2.5628265848069749712 ] 
dist 177=[-1.8612122422055429308 ,2.6597335893224620935 ] 
dist 178=[-1.7893426404345210313 ,2.7344069897617643433 ] 
dist 179=[-1.7669586796500771158 ,2.7984006964923242011 ] 
dist 180=[-1.6662924464055498523 ,2.8507287867878460300 ] 
dist 181=[-1.6448202867021938142 ,2.8788254913462867050 ] 
dist 182=[-1.5832085702482339186 ,2.8945871701893154262 ] 
dist 183=[-1.5721655807735359127 ,2.8976658575478772759 ] 
dist 184=[-.21605003723449604774,.59670229436181219092] 
dist 185=[-.21406578330186914996,.59653281306550920119] 
dist 186=[.02545710597720454389,.28024307597604266692] 
dist 187=[.00410898297335139217,.34607308276769642974] 
dist 188=[-.01758432334433858551,.40635905720978569806] 
dist 189=[-.04545856332676252833,.45100482996678273246] 
dist 190=[-.07521888179725167409,.49280479544874453967] 
dist 191=[-.10444310897846537164,.54172849231584501134] 
dist 192=[-.13891351845405929936,.58687171668305230097] 
dist 193=[-.18962063541959227221,.61357756226085647845] 
dist 194=[-.24183503494795426657,.63192644415604504135] 
dist 195=[-.28232382943522095304,.64370315437627810375] 
dist 196=[-.322034640038643403  ,.65188543560586448124] 
dist 197=[-.37114318304347400848,.67313025904358539053] 
dist 198=[-.42262116633930938961,.72348494284750130642] 
dist 199=[-.47179280193221432236,.7684863962769996876 ] 
dist 200=[-.5287661828761389711 ,.81824391501201558068] 
dist 201=[-.61139486650048304531,.88758691640200605771] 
dist 202=[-.69278677321992538267,.95468334822336143389] 
dist 203=[-.74482218891194388332,.9954710426515815142 ] 
dist 204=[-.78539117292196272976,1.0248451122517485853 ] 
dist 205=[-.82100072431517526911,1.0463717479089517075 ] 
dist 206=[-.85075704521807674269,1.0616203104444888826 ] 
dist 207=[-.87234739072997427307,1.0659288187848704847 ] 
dist 208=[-.92279716503076014347,1.0660623266470278737 ] 
dist 209=[-.98320611726958724843,1.0646422050108810970 ] 
dist 210=[-1.0396648937472067616 ,1.0185633175313756636 ] 
dist 211=[-1.0743427868827733531 ,1.0089404784953244333 ] 
dist 212=[-1.0997538317971653210 ,.98639338062798964913] 
dist 213=[-1.1192127515899242318 ,.97815207077863567003] 
dist 214=[-1.1333871784026976432 ,.93642431263513636191] 
dist 215=[-1.1376988337038140229 ,.92648517100479351429] 
dist 216=[-1.1374442420100249075 ,.90179965972103937397] 
dist 217=[-1.1347527622861453760 ,.89280674671721331149] 
dist 218=[-1.1095639627928823975 ,.763396458503476874  ] 
dist 219=[-1.1028555150949021007 ,.75077465848168130837] 
dist 220=[-1.0809252049866736675 ,.71609938500497858068] 
dist 221=[-1.0750946723627161766 ,.71004860664095842563] 
dist 222=[-1.0180449367667409239 ,.64284939267611651614] 
dist 223=[-1.0043576433787483953 ,.62858020886887571198] 
dist 224=[-.98698981330930726408,.61280653929363097722] 
dist 225=[-.97971056569294167445,.60684223074028651466] 
dist 226=[-.79793336071019266917,.44350795918341351984] 
dist 227=[-.77232607639845037646,.42171340059531793419] 
dist 228=[-.72642816101867633271,.37747896591106826587] 
dist 229=[-.727403754785155315  ,.36563540254881693298] 
dist 230=[-.72592101592695172712,.32121047526151384705] 
dist 231=[-.72404603934516616728,.31163105024454840202] 
dist 232=[-.66961661539572133563,.29328285958407449496] 
dist 233=[-.66115183787148379987,.28838375881978882331] 
dist 234=[-.63575531805778365889,.28737120415437874264] 
dist 235=[-.64535192243392770903,.41063249547447493202] 
dist 236=[-.68233406290878450697,.51214321241934341393] 
dist 237=[-.71570080768075193798,.61070435337885055352] 
dist 238=[-.74423937325460579434,.6999855518140155209 ] 
dist 239=[-.76194430148699108216,.76444441541322866507] 
dist 240=[-.77512524874057790073,.82315311219394402404] 
dist 241=[-.78560101707232050981,.8894757546694857207 ] 
dist 242=[-.79283501105735623916,.94995673329468970729] 
dist 243=[-.79416818650957970745,.98534155957277581891] 
dist 244=[-.79122973291475814779,1.0091651720859093038 ] 
dist 245=[-.79015619287943376966,1.0234859737015366927 ] 
dist 246=[-.76130565285564706306,1.0326184236958908650 ] 
dist 247=[-.75341581460239870092,1.0357265543689770617 ] 
dist 248=[-.74782265165815053419,1.0350201897290945782 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[48.299862003443462886  ,48.299862003443462886  ] 
dist 1=[48.086046589378430575  ,48.410781264702755606  ] 
dist 2=[47.656079638282646153  ,48.639869139565274280  ] 
dist 3=[46.953200167804244810  ,48.823684927363117229  ] 
dist 4=[46.066735529921268697  ,48.914554197133766997  ] 
dist 5=[44.903155881671050426  ,48.954346004096133416  ] 
dist 6=[43.308271084113384455  ,48.934203794070850888  ] 
dist 7=[40.698700643063590437  ,48.884073361063265425  ] 
dist 8=[38.001262140691073258  ,48.804205231734746881  ] 
dist 9=[36.055294375448759518  ,48.686912524750769685  ] 
dist 10=[34.278971681698330066  ,48.611146614900140899  ] 
dist 11=[32.259155109612121234  ,48.250854564165065710  ] 
dist 12=[29.877054317670316593  ,48.132267432081247040  ] 
dist 13=[27.285613081319534984  ,47.745438555995215540  ] 
dist 14=[25.038909203169091766  ,47.374943373756016844  ] 
dist 15=[22.666928867544175936  ,37.160513941408648907  ] 
dist 16=[20.387601768302835986  ,36.185292680803353742  ] 
dist 17=[18.327216876013046734  ,33.812680480163403622  ] 
dist 18=[16.147724507514535497  ,33.433537151123350726  ] 
dist 19=[13.463322592659098031  ,29.879370698661577348  ] 
dist 20=[10.641218550738592824  ,29.199948764367788903  ] 
dist 21=[7.9110315794235944742 ,28.351394327554441581  ] 
dist 22=[4.7089200227684765037 ,28.094128388679796754  ] 
dist 23=[0                     ,22.048932541619348779  ] 
dist 24=[4.5305960382828427371 ,21.267124108195318360  ] 
dist 25=[2.9753725463545654815 ,19.647267432100542920  ] 
dist 26=[1.2687535833393564169 ,19.216429642232317884  ] 
dist 27=[-1.1049046833469412772 ,17.589368889885573646  ] 
dist 28=[-3.4189868581309991179 ,17.264119816530887250  ] 
dist 29=[-4.8877353154546027053 ,16.600136564721296351  ] 
dist 30=[-6.0285262953687870443 ,16.421870301594461171  ] 
dist 31=[-7.0317537445658535400 ,6.2014670652626481250 ] 
dist 32=[-7.8796060159142970295 ,5.2962563611058230774 ] 
dist 33=[-8.3995442970303330651 ,3.2726856035320527364 ] 
dist 34=[-8.7845510774566383743 ,2.9108713643259090188 ] 
dist 35=[-9.0936286843066046573 ,.5114901579869784910 ] 
dist 36=[-9.3377886953312636258 ,.0993695256346555446 ] 
dist 37=[-9.4632541103391297963 ,-.6485620040989544324 ] 
dist 38=[-10.367506358907485872  ,-.8091575068890294250 ] 
dist 39=[-11.430109538339959807  ,-2.7514422758942971283 ] 
dist 40=[-12.084122631248361106  ,-3.0220560753495200775 ] 
dist 41=[-12.566920965601350129  ,-3.4593082705741744506 ] 
dist 42=[-12.945484204371419743  ,-3.5554236566138510963 ] 
dist 43=[-13.230418797351769085  ,-3.1276992968754384895 ] 
dist 44=[-13.339194817895791025  ,-1.5088076468625447612 ] 
dist 45=[-13.375894396468632507  ,-.4209920110317362412 ] 
dist 46=[-13.372667845496118277  ,.4856963998971011768 ] 
dist 47=[-8.1298521694943706510 ,1.3818848231602037130 ] 
dist 48=[-7.7587377565327030187 ,2.2026915102002795256 ] 
dist 49=[-6.8513300557958272258 ,2.8086323284017756960 ] 
dist 50=[-6.7081796569361659014 ,3.3734460190442825557 ] 
dist 51=[-5.3592312070301344541 ,4.0302470980675073735 ] 
dist 52=[-5.1064203642248987779 ,4.6424236964890451387 ] 
dist 53=[-4.7825157875017164255 ,5.0291099451361291477 ] 
dist 54=[-4.6907634334638966740 ,5.3248999039780703164 ] 
dist 55=[-2.5949856307045877968 ,5.5740880090294791234 ] 
dist 56=[-2.3336061856589893044 ,5.7739752393573728870 ] 
dist 57=[-1.7686529914367003349 ,5.8728347944615051204 ] 
dist 58=[-1.6446217317879155418 ,5.9188853995022079944 ] 
dist 59=[-1.0369989471490868453 ,5.9231349542930657950 ] 
dist 60=[-.9326239076557410342 ,4.5663281255473209991 ] 
dist 61=[-.7028862703087122971 ,4.4414150140598033728 ] 
dist 62=[-.6638883910365523602 ,4.1454112006421927740 ] 
dist 63=[1.3243071322017211764 ,4.0727983368395638210 ] 
dist 64=[1.5096163713313819696 ,3.7237351693661245978 ] 
dist 65=[1.8586239042066680296 ,4.1490596765085798516 ] 
dist 66=[1.9358258057036216841 ,4.5510813897225686821 ] 
dist 67=[2.0297738606321832846 ,4.9090247368736107205 ] 
dist 68=[1.4557584491356944086 ,5.1583001474261382562 ] 
dist 69=[1.0205259715578697748 ,5.3766682735592859658 ] 
dist 70=[.6032747166953648520 ,5.6111967193219205279 ] 
dist 71=[.1009434818060055226 ,5.8178384915721970382 ] 
dist 72=[-.4183953155699617422 ,5.9248251332936815733 ] 
dist 73=[-.9036191910424896913 ,5.9810298311230312529 ] 
dist 74=[-1.4575587477326918446 ,5.9918695331172117169 ] 
dist 75=[-2.2513462597865539758 ,5.9594307041747019155 ] 
dist 76=[-3.0320443719911311797 ,5.9390910426704449512 ] 
dist 77=[-3.5337435769360382504 ,5.9144768116482785682 ] 
dist 78=[-3.9280441651121008098 ,5.8937473452387552479 ] 
dist 79=[-4.2799086995774182256 ,1.0471201103588675153 ] 
dist 80=[-4.5783995103768344070 ,1.0004592805027602672 ] 
dist 81=[-4.7595904440709398864 ,1.0077645844898884714 ] 
dist 82=[-4.8899823697637389306 ,1.0415884647211685137 ] 
dist 83=[-4.9856587240257123655 ,1.1200753853800807244 ] 
dist 84=[-5.0585685710488225625 ,1.2121183769788695569 ] 
dist 85=[-5.0980550055938801745 ,1.3000691731646332828 ] 
dist 86=[-5.1208425607003636496 ,1.4016833831847786286 ] 
dist 87=[-5.1270516606503192398 ,1.5483115990995340752 ] 
dist 88=[-5.1955104551576086853 ,1.7125254853333967474 ] 
dist 89=[-5.2941692549521977624 ,1.8843556479633315156 ] 
dist 90=[-5.3411838295385343803 ,2.0946465821433237644 ] 
dist 91=[-5.3619664959283303007 ,2.4123958836738285524 ] 
dist 92=[-5.3558661830209849759 ,2.7280561015654081972 ] 
dist 93=[-5.3948311611781934759 ,2.9300184464776983496 ] 
dist 94=[-5.4014799800850177888 ,3.0873911764342565927 ] 
dist 95=[-5.3853863382992186811 ,3.2250822498458134798 ] 
dist 96=[-5.3725191615607474007 ,3.3396044985232019518 ] 
dist 97=[-5.2954194482720740163 ,3.4045040171521243829 ] 
dist 98=[-5.2822811278334120126 ,3.4454954196506713933 ] 
dist 99=[-4.9940303927977093795 ,3.4680019843870053716 ] 
dist 100=[-4.9236887179845072618 ,3.8600335371284744068 ] 
dist 101=[-4.8729196191458053683 ,4.2300446984061565545 ] 
dist 102=[-4.8556146835820457890 ,4.6669365646830117950 ] 
dist 103=[-3.7825447337195197534 ,5.0713276328568765887 ] 
dist 104=[-3.6387490961064525006 ,5.3116018483087416468 ] 
dist 105=[-3.3635259806390656056 ,5.4777231546415332225 ] 
dist 106=[-3.2922151662110108044 ,5.5861136553049938829 ] 
dist 107=[-3.0449127948066160152 ,5.6603935337413899246 ] 
dist 108=[-2.9825439454011451354 ,5.6903592603816385049 ] 
dist 109=[-2.9100560766472929419 ,5.6935782269352396951 ] 
dist 110=[-2.8795864230685351692 ,5.6852755992008529365 ] 
dist 111=[-2.6809761136624448977 ,3.9534773129217142567 ] 
dist 112=[-3.0354508105979690006 ,3.9871267140260806943 ] 
dist 113=[-3.2784308060948288291 ,3.9910075370510998503 ] 
dist 114=[-3.4863435979115793771 ,3.9784198755039635807 ] 
dist 115=[-3.7008161976689872656 ,3.9639165461073873856 ] 
dist 116=[-3.8927889694432033061 ,3.7212972251955277577 ] 
dist 117=[-4.0108882966115817135 ,3.6757312280447324532 ] 
dist 118=[-4.0974830648562212335 ,3.5665925141655235735 ] 
dist 119=[-4.1637208620233125000 ,3.5282674223869129454 ] 
dist 120=[-4.2118110423572881365 ,3.3394063189089957295 ] 
dist 121=[-4.2259796902558331362 ,3.2955154804867334262 ] 
dist 122=[-4.2220211509276804004 ,3.1852175991523858831 ] 
dist 123=[-4.2123753550045808405 ,2.9818301127185682928 ] 
dist 124=[.64044779530814458348,1.6660751126048653278 ] 
dist 125=[.63552252543792728135,1.6806048931136510578 ] 
dist 126=[.62634214867800954483,1.6828524127573695049 ] 
dist 127=[.60899575422393303966,1.5559074161824807811 ] 
dist 128=[.58773622286179211003,1.5377948059360373459 ] 
dist 129=[.56292470971226381196,1.4996711288012548717 ] 
dist 130=[.53073583804495120635,1.4869650560240524364 ] 
dist 131=[.48001321110960380677,1.4267478381152511432 ] 
dist 132=[.42637539134752426668,1.4132542505231115372 ] 
dist 133=[.38254222348153693304,1.3698904529420472130 ] 
dist 134=[.28108194158507543239,1.3635172515004498790 ] 
dist 135=[.07177640836764226576,1.2573269237677764370 ] 
dist 136=[-.09018120304185594277,1.2373203161710658936 ] 
dist 137=[-.24864354553215361175,1.1909053427406581624 ] 
dist 138=[-.44400377924486491022,1.1757034005642237448 ] 
dist 139=[-.6484133466031351426 ,1.1045089592116349489 ] 
dist 140=[-.84301102175059074391,1.0887228758568922312 ] 
dist 141=[-1.0679423816027816430 ,1.0527834875366321900 ] 
dist 142=[-1.3934670252848447058 ,1.0409556431040716025 ] 
dist 143=[-1.7154859368622396240 ,.20383482325522688076] 
dist 144=[-1.9264228473500059824 ,.15176775945553232238] 
dist 145=[-2.0966510455420639546 ,.14215941055174744931] 
dist 146=[-2.2561390766228834767 ,.12342292259905401614] 
dist 147=[-2.3967657753345598497 ,.11866188508249526234] 
dist 148=[-2.4916904723789031451 ,.06223080866218797767] 
dist 149=[-2.5714479659647944026 ,.05398258512138428755] 
dist 150=[-2.6515220735779162250 ,.03695044829303470019] 
dist 151=[-2.7185343010151134684 ,.03245589290359675736] 
dist 152=[-2.7461411760486528020 ,.01568064623169841153] 
dist 153=[-2.7576463473141615033 ,.01231360879327223727] 
dist 154=[-2.7603666534035872207 ,.00569847367238658446] 
dist 155=[-2.6908429101223087660 ,.00398699949160576090] 
dist 156=[-2.6731165574098523724 ,-.0021951024938143299 ] 
dist 157=[-2.6627452206396026504 ,-.0034926757392703650 ] 
dist 158=[-2.6596975861753068007 ,-.0064241518312054299 ] 
dist 159=[-2.3175956358745294537 ,.35370375888158658866] 
dist 160=[-2.2760921646603570140 ,.7050164263822621432 ] 
dist 161=[-2.1646165304084119270 ,1.0000388790841035674 ] 
dist 162=[-2.1442268370659238819 ,1.2958516719156422678 ] 
dist 163=[-1.9358747974040623135 ,1.5699413066836091871 ] 
dist 164=[-1.8919440561185432276 ,1.7782349210479848440 ] 
dist 165=[-1.8393689867150946828 ,1.9784670157445435477 ] 
dist 166=[-1.8182632547352675615 ,2.2203712299160647890 ] 
dist 167=[-1.3352233860148917697 ,2.4474526759971401048 ] 
dist 168=[-1.2703034720681811734 ,2.5885052539472835377 ] 
dist 169=[-1.1357010514331381889 ,2.6937079891637248346 ] 
dist 170=[-1.0990369254504711150 ,2.7776598982909138918 ] 
dist 171=[-.95711661367110862699,2.8416305277849256052 ] 
dist 172=[-.92789430022243864125,2.8670582991005652842 ] 
dist 173=[-.86510039146457626994,2.8767350398036361115 ] 
dist 174=[-.84687407127178336907,2.8778211004628081205 ] 
dist 175=[-.10936523438529299639,.20596814789156184255] 
dist 176=[-.11354854224924788065,.34864986324164732969] 
dist 177=[-.11632963423054382396,.50650567026583547367] 
dist 178=[-.11859824313828085818,.67097822900974332567] 
dist 179=[-.12073783870909251166,.82738125269627750461] 
dist 180=[-.12240694979292053988,.95301904531600457447] 
dist 181=[-.1227995609037995952 ,1.0803557350750090331 ] 
dist 182=[-.12264324863009719896,1.2435430778894176982 ] 
dist 183=[-.1221881248906249178 ,1.4015297798776267420 ] 
dist 184=[-.11845629061601711856,1.5081027278218823388 ] 
dist 185=[-.1172865196767337133 ,1.5975686748304386457 ] 
dist 186=[-.11539092524467026441,1.6872536652767549257 ] 
dist 187=[-.11466957452191517118,1.7703681639138622616 ] 
dist 188=[.03255275219571944878,1.8336013272268005758 ] 
dist 189=[-.00443508594948826846,1.8944755670275507427 ] 
dist 190=[-.06722274016678043905,1.9681737991325748757 ] 
dist 191=[-.32827888395299110999,2.0347511938742348982 ] 
dist 192=[-.50914117162205931835,2.0671944976079315725 ] 
dist 193=[-.6661226793024734162 ,2.0836709468188809938 ] 
dist 194=[-.83183345835186480186,2.0864943860291394047 ] 
dist 195=[-.9907274157955788177 ,2.0587705739055114812 ] 
dist 196=[-1.1204925632576374719 ,2.0500454426244312384 ] 
dist 197=[-1.2539422774116144898 ,2.0434119569188870864 ] 
dist 198=[-1.4275476303321407768 ,2.0378901942835334227 ] 
dist 199=[-1.5968300644156945888 ,1.7339373509767551087 ] 
dist 200=[-1.7130203851667124443 ,1.6903837064174018065 ] 
dist 201=[-1.8127185519598074889 ,1.6100991826055257371 ] 
dist 202=[-1.9161548867258432117 ,1.5889200950957969870 ] 
dist 203=[-2.0142391386766649667 ,1.5150214653613289027 ] 
dist 204=[-2.0925689353300795797 ,1.4943762251987742323 ] 
dist 205=[-2.1715341454478376732 ,1.4684976030011059725 ] 
dist 206=[-2.2721559320483180145 ,1.4575378431283601763 ] 
dist 207=[-2.3661588177088075653 ,.6278646785065789292 ] 
dist 208=[-2.4186974398143039974 ,.64242584239360672001] 
dist 209=[-2.4509886618630668893 ,.64932644945828874735] 
dist 210=[-2.4641513038707789080 ,.67632453441339483034] 
dist 211=[-2.4673381942264920499 ,.71500287204254580093] 
dist 212=[-2.4631522395968060614 ,.75106726333488494362] 
dist 213=[-2.4475911398655270326 ,.77304255700262216917] 
dist 214=[-2.4374064366887366691 ,.78892902997615507183] 
dist 215=[-2.2450396573461068549 ,.80068386087016781599] 
dist 216=[-2.2120370337445139124 ,.80889571679019110939] 
dist 217=[-2.1364929518108109994 ,.81063676718723442662] 
dist 218=[-2.1114096173292771064 ,.80953446476443579533] 
dist 219=[-1.9926570714667444738 ,.80712029359927881261] 
dist 220=[-1.9660075138669943157 ,.78690548063982140126] 
dist 221=[-1.9015610032142589408 ,.78169277577541523347] 
dist 222=[-1.8797381290529404288 ,.76510550844046381094] 
dist 223=[-1.7668659336232218986 ,.76070161039622619136] 
dist 224=[-1.7978483982570913744 ,.88956876868564381471] 
dist 225=[-1.8143961282100762187 ,1.1465340936609945471 ] 
dist 226=[-1.8171625309223225641 ,1.3911727199639663847 ] 
dist 227=[-1.8106366705302486622 ,1.6095398212087627130 ] 
dist 228=[-1.8042407994179014686 ,1.7616127343091233412 ] 
dist 229=[-1.7913918867849645567 ,1.8944434391385960745 ] 
dist 230=[-1.7848867142163378754 ,2.0359833684845748589 ] 
dist 231=[-1.6044988179572750890 ,2.1646152443146695742 ] 
dist 232=[-1.5757632477773221064 ,2.2459089991144634980 ] 
dist 233=[-1.5141577646232321997 ,2.3081964192344635406 ] 
dist 234=[-1.4950475714365340298 ,2.3609435795789378116 ] 
dist 235=[-1.4094002691751678350 ,2.4035986798557308261 ] 
dist 236=[-1.3911989443035668391 ,2.4255925541087952194 ] 
dist 237=[-1.3384797752581522937 ,2.4366895026985476789 ] 
dist 238=[-1.3294815891522343299 ,2.4358376035822233192 ] 
dist 239=[-.46118317473310010953,.54421290570427602296] 
dist 240=[-.52542858352361987898,.56924017119441863701] 
dist 241=[-.57172347268160421751,.58545516334603914321] 
dist 242=[-.61379338468289425692,.59834362079994971829] 
dist 243=[-.66117025248452519171,.61008946047593272913] 
dist 244=[-.70426430783779294293,.61918531663334886003] 
dist 245=[-.72923471504210843602,.62149335372281549133] 
dist 246=[-.74574015204003867793,.62149928891699087264] 
dist 247=[-.75503702065503462148,.62140266384164559384] 
dist 248=[-.76064993175242555844,.60053168607045829739] 
dist 249=[-.76244699082528376818,.59514423302709523856] 
dist 250=[-.76179420415871436584,.59454501746782301817] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 2, 1, 0, 2] 
dist 0=[50.687323605712676298  ,50.687323605712676298  ] 
dist 1=[50.456331689414513966  ,50.742042932277371126  ] 
dist 2=[50.014460810151292396  ,50.699504445963307412  ] 
dist 3=[49.117030565704437269  ,50.641514192714867744  ] 
dist 4=[48.126937616560173120  ,50.372807676493517153  ] 
dist 5=[47.314908180099726399  ,50.283749248892624589  ] 
dist 6=[46.474247065406948104  ,50.236387857407321038  ] 
dist 7=[45.369937338022290193  ,50.115826813628088338  ] 
dist 8=[44.175275887059520140  ,46.133548632601685164  ] 
dist 9=[42.973737523528234409  ,45.559453403411306077  ] 
dist 10=[41.428287818292963696  ,44.555300922236963343  ] 
dist 11=[39.242615114556588706  ,44.299879001542779927  ] 
dist 12=[36.982778277652123107  ,43.504756315001635467  ] 
dist 13=[34.228374031246019102  ,43.258075689802855261  ] 
dist 14=[30.067033128034981219  ,43.127444408481510273  ] 
dist 15=[25.878739087401645187  ,42.979286935185319013  ] 
dist 16=[23.016608545666013382  ,33.336524190238141398  ] 
dist 17=[20.568616815506310007  ,33.005517086159712854  ] 
dist 18=[18.034533061478971828  ,32.712914524373506024  ] 
dist 19=[15.628650076725013499  ,32.644727173673223887  ] 
dist 20=[13.692643141396526614  ,15.842789865000275929  ] 
dist 21=[11.723013109179471488  ,15.085581596775004705  ] 
dist 22=[9.1825519129458055794 ,14.233843886490057363  ] 
dist 23=[6.7047356396431500490 ,13.636254464646036866  ] 
dist 24=[4.9852090831228610515 ,8.9156084072667333407 ] 
dist 25=[3.4848622017890145725 ,8.3224558546840139657 ] 
dist 26=[1.8824362365899720911 ,7.2734770093599325017 ] 
dist 27=[-.14003339110494263971,6.8237230855442748771 ] 
dist 28=[-2.0904557300186163361 ,5.7709890254261964894 ] 
dist 29=[-3.3715710308207224999 ,5.4898932765897667845 ] 
dist 30=[-4.4133470529491672798 ,5.3232989230501502632 ] 
dist 31=[-6.0434350416452515418 ,5.1882764514144593097 ] 
dist 32=[-7.1920684155765731007 ,-4.3967163653301666360 ] 
dist 33=[-8.0850520830131269643 ,-4.5865999821958647367 ] 
dist 34=[-8.8707498037339265341 ,-4.9284299798910318911 ] 
dist 35=[-9.5338969070035599948 ,-4.9833048415783681585 ] 
dist 36=[-10.072374893660148922  ,-8.5914905087860581902 ] 
dist 37=[-10.446741273822952772  ,-8.7878698763512416055 ] 
dist 38=[-10.706277944508248431  ,-9.1451984439078494824 ] 
dist 39=[-10.881381969907033662  ,-9.1757837381530884368 ] 
dist 40=[-11.002178417553320816  ,-8.8840853460508759678 ] 
dist 41=[-11.044650774545382512  ,-8.4734674112250259831 ] 
dist 42=[-11.039859247278634648  ,-7.7947144320103459657 ] 
dist 43=[-11.022105101897626191  ,-6.9961417795213401672 ] 
dist 44=[-10.872573526857612163  ,-6.1069520319494509164 ] 
dist 45=[-10.823427496532333120  ,-4.9807528694884136520 ] 
dist 46=[-10.633677878442990814  ,-3.2357972027895606394 ] 
dist 47=[-10.590710148992380015  ,-1.4733012157182656678 ] 
dist 48=[-7.9415184495812811697 ,-.27698852931726823131] 
dist 49=[-7.8657146578011784012 ,.73469714781839423408] 
dist 50=[-7.7144342592063028564 ,1.7601976302950893634 ] 
dist 51=[-7.6652411332652930724 ,2.7173124144639881913 ] 
dist 52=[-3.8498033089385521615 ,3.4560246673193156597 ] 
dist 53=[-3.5922350627519567444 ,4.1770499991069544845 ] 
dist 54=[-3.4395461927890561776 ,5.0635942954091172613 ] 
dist 55=[-3.1563719209687480736 ,5.9037461838171699604 ] 
dist 56=[-1.3476425910991593331 ,6.4395641150794923748 ] 
dist 57=[-1.0344357514186729101 ,6.8557005784359000588 ] 
dist 58=[-.72896404242681589553,7.2180245036353799407 ] 
dist 59=[-.40983824118397108342,7.5185432072442575417 ] 
dist 60=[-.04374996813417539890,7.6879185258814249285 ] 
dist 61=[.1641367952850218089 ,7.7938554317218040347 ] 
dist 62=[.20913346765252147878,7.8429388808737789173 ] 
dist 63=[.55563489634625232055,7.8572211774509094032 ] 
dist 64=[1.8561332802379960364 ,5.6139448474332526121 ] 
dist 65=[1.9819766132917150579 ,5.7202362619360891696 ] 
dist 66=[2.2496986061700509526 ,5.7777318384845652490 ] 
dist 67=[2.2514851261425085115 ,5.7883769431218474017 ] 
dist 68=[2.2264954313975452978 ,2.7727862375025465211 ] 
dist 69=[2.1933953174094298607 ,2.8718526896864531712 ] 
dist 70=[2.1483483507933134229 ,2.9675443998423797950 ] 
dist 71=[2.0755745087059592131 ,3.0486070188176079437 ] 
dist 72=[1.9907586490410742375 ,3.0892424259867661161 ] 
dist 73=[1.8975933180771361016 ,3.1082777941143364277 ] 
dist 74=[1.7804971882934279040 ,3.1108681278787526042 ] 
dist 75=[1.6001033454864643833 ,3.0886360385736935415 ] 
dist 76=[1.4111827391986597952 ,3.0763092839382771118 ] 
dist 77=[1.2600185428929582673 ,3.0500963805925399756 ] 
dist 78=[.99147576598219102458,3.0379314299888151991 ] 
dist 79=[.51612665271444933844,2.7294737282641075430 ] 
dist 80=[.18922856803833183752,2.2211883260787162775 ] 
dist 81=[-.09199912230781916522,2.0220818371779019141 ] 
dist 82=[-.38500774202605287154,1.9928041163827141509 ] 
dist 83=[-.66371046291280616026,1.6679060510031889380 ] 
dist 84=[-.88782584658832858518,1.6046607382742957863 ] 
dist 85=[-1.1152495876904177835 ,1.5367269829656887870 ] 
dist 86=[-1.4071746071493595540 ,1.5224236666097507367 ] 
dist 87=[-1.6902027926322777410 ,.8994183668574379234 ] 
dist 88=[-1.8821076079100787715 ,.82140163399063178821] 
dist 89=[-2.0443551346092637186 ,.6637101283568330821 ] 
dist 90=[-2.2089681321689739948 ,.62320661270245222987] 
dist 91=[-2.3628924212449827058 ,.47983020052091688656] 
dist 92=[-2.4824671588021076199 ,.44940271105374750457] 
dist 93=[-2.6000427059869338756 ,.40721203617664876292] 
dist 94=[-2.7459995180466221869 ,.39471522562963260723] 
dist 95=[-2.8818828465118757893 ,-.08341865759235795654] 
dist 96=[-2.9592353148952736070 ,-.09652346969064190706] 
dist 97=[-3.0087203196218552830 ,-.09184965099022627794] 
dist 98=[-3.0333146732848799172 ,-.07753807292962306478] 
dist 99=[-3.0450389670937712770 ,-.0464444991505985311 ] 
dist 100=[-3.0431251438445846383 ,-.01311187786255473422] 
dist 101=[-3.0330489274095671695 ,.01014650133495191104] 
dist 102=[-3.0246741552434146613 ,.03043733233414618006] 
dist 103=[-2.7812737987303033395 ,.05194496063075835284] 
dist 104=[-2.7406312687671486207 ,.07258101641293932549] 
dist 105=[-2.6549223167917228518 ,.08940551822043764196] 
dist 106=[-2.6279010896703489568 ,.10668242442531017201] 
dist 107=[-2.5051533407501952867 ,.12914162981272529945] 
dist 108=[-2.4786590791586159901 ,.15110570433521216727] 
dist 109=[-2.3967989537013381490 ,.16641502603051618974] 
dist 110=[-2.3849807707583471186 ,.1798510917077708377 ] 
dist 111=[-1.8646376376944297274 ,.24545400964316142353] 
dist 112=[-1.7730261796071099570 ,.60297123580256399627] 
dist 113=[-1.7125086022738593650 ,.89788676421757527081] 
dist 114=[-1.7031058990601175010 ,1.1851493026946003027 ] 
dist 115=[-1.5695511528468823335 ,1.4460686703152147014 ] 
dist 116=[-1.5403489783671873396 ,1.6357979577355399440 ] 
dist 117=[-1.5143305746214867871 ,1.8100303330059306497 ] 
dist 118=[-1.5070938740419532459 ,2.0090728959588459386 ] 
dist 119=[-1.1338403967956534402 ,2.1931050211402217956 ] 
dist 120=[-1.0846095801263036789 ,2.3074012229778116650 ] 
dist 121=[-.9893053307082975023 ,2.3926901760794588539 ] 
dist 122=[-.96469111442026454511,2.4608955212621277487 ] 
dist 123=[-.87894873807008161673,2.5130301412161871329 ] 
dist 124=[-.85816912769492135471,2.5341482408440167122 ] 
dist 125=[-.83270328195242718069,2.5420013357952214592 ] 
dist 126=[-.82289601953348977377,2.5411685766003503240 ] 
dist 127=[-.64445873790863948306,1.7787010953728491468 ] 
dist 128=[-.63990055214409369397,.98836707482109554664] 
dist 129=[-.63631037117018279508,.98199362616031513622] 
dist 130=[-.63064569846672862303,.97665590774964071654] 
dist 131=[-.62783775036810228981,.97200944153206031119] 
dist 132=[.23168295198321551729,.65300358861178155805] 
dist 133=[.16485488264528436142,.68688432178389316963] 
dist 134=[.10774586072061502556,.71461418777631122199] 
dist 135=[.04888227720771339838,.74125728084092073422] 
dist 136=[-.00668791639398273508,.76434113602405561954] 
dist 137=[-.05065103537015844737,.77785908631732087466] 
dist 138=[-.09459109171134304998,.78697519127242189787] 
dist 139=[-.15007351519535614693,.79248426097166381168] 
dist 140=[-.20340658939594993686,.7952603785696040842 ] 
dist 141=[-.23876744050256920214,.79486923917589255433] 
dist 142=[-.26779411766866954495,.7902200255433672524 ] 
dist 143=[-.29583985145134526567,.78720729761721275226] 
dist 144=[-.32118128987093897588,.51915565508511279582] 
dist 145=[-.33941403416941775572,.49409399633386378253] 
dist 146=[-.3559841174335192664 ,.43527578308820164871] 
dist 147=[-.37469434461406218906,.42360381067388573489] 
dist 148=[-.39177849871424277515,.34160718914996254779] 
dist 149=[-.4018565672213385606 ,.3259902837875007799 ] 
dist 150=[-.40878037365160222936,.29892144373841447358] 
dist 151=[-.41326442145672463222,.29244806010921306191] 
dist 152=[-.41587874051071535022,.17606653660301752948] 
dist 153=[-.41614335765051001058,.16060847360123868247] 
dist 154=[-.41390953996940616693,.12354541801557782491] 
dist 155=[-.41299589310790288027,.11784505476307755195] 
dist 156=[-.44995351481199240867,.06532051060650650618] 
dist 157=[-.5008627048614975407 ,.05911222800635141556] 
dist 158=[-.55617595997119539672,.09155270991224876707] 
dist 159=[-.63207713548613298945,.13211025410745117794] 
dist 160=[-.7058560579039049132 ,.17483289192435990822] 
dist 161=[-.75269518573333362975,.21591921168791900333] 
dist 162=[-.7888378105400884815 ,.2637245846668740694 ] 
dist 163=[-.81990720509465654075,.33327482348751103478] 
dist 164=[-.84538920444718918211,.40210987864992241773] 
dist 165=[-.85922210138477717295,.44706069390070463538] 
dist 166=[-.86718829497954884402,.48317773798495383637] 
dist 167=[-.86924513033345179169,.51674459397006932595] 
dist 168=[-.86818642174480066935,.54615368714380828034] 
dist 169=[-.86622603528304761728,.56567147231010106677] 
dist 170=[-.8583702236047080716 ,.58170846090127879589] 
dist 171=[-.85389474456518349105,.59722165635451603508] 
dist 172=[-.82600465946836375553,.6098612814448332379 ] 
dist 173=[-.81832731162271844808,.61442546284908338991] 
dist 174=[-.80447359347008092775,.61589759023569766165] 
dist 175=[-.79996198541093014832,.61619079886744568091] 
dist 176=[-.62153396399755468385,.59799119450026353926] 
dist 177=[-.60337609741037238536,.59330627963061401465] 
dist 178=[-.55682092038088425196,.59052486360298216533] 
dist 179=[-.5493418609096098156 ,.58961473796041940025] 
dist 180=[-.47116636572615869502,.55297218602129925211] 
dist 181=[-.45556588299026499809,.5499063996906237953 ] 
dist 182=[-.43763946961892427593,.59897378746786725398] 
dist 183=[-.43216181071078887568,.67142890289040889506] 
dist 184=[-.3866870159206949294 ,.73899984593152163834] 
dist 185=[-.43304158979990147926,.78026400918276763306] 
dist 186=[-.476928946122599368  ,.81021974596178044061] 
dist 187=[-.5289889986021773777 ,.83263845310849662002] 
dist 188=[-.57736313967783716678,.84947624658854690659] 
dist 189=[-.60653476034917488092,.85714836049011197502] 
dist 190=[-.62725520375956682813,.85989298864952095502] 
dist 191=[-.64188879684326982656,.85956749970160935919] 
dist 192=[-.65247363594080349311,.30938967512773473427] 
dist 193=[-.65703005008556462076,.30306871830014472782] 
dist 194=[-.65809220846159642955,.29180296337528913057] 
dist 195=[-.65758483044589182018,.28883712971306982738] 
dist 196=[.01181563949088881488,.16168068259008207059] 
dist 197=[-.01289529189755286261,.17499969259623197901] 
dist 198=[-.03401077132256030786,.18750802457951491855] 
dist 199=[-.05577876017791654047,.20220131442187784921] 
dist 200=[-.07633565620936357260,.21578103081106695534] 
dist 201=[-.09261615713907400167,.22384288651249623655] 
dist 202=[-.10890572359010247594,.22941373231992031731] 
dist 203=[-.12949959010111886969,.23304737515602892417] 
dist 204=[-.14930763748647815481,.23545865584019678393] 
dist 205=[-.16246006888978528829,.23614965218218811179] 
dist 206=[-.17327663731564074893,.235940218196621215  ] 
dist 207=[-.18375871235434735725,.23543365830401068145] 
dist 208=[-.19324654221119145376,.2193185656982799709 ] 
dist 209=[-.20009398844079498572,.21671836263512199885] 
dist 210=[-.20633379361795407772,.20924189488955245786] 
dist 211=[-.21339685006372689825,.20777390469638032357] 
dist 212=[-.21963335389730177822,.19189439503676591527] 
dist 213=[-.22257298405118871348,.18837450540792723736] 
dist 214=[-.22396942566242201939,.18435613059597343109] 
dist 215=[-.2240420524957591995 ,.18258208377286292397] 
dist 216=[-.22086450582574256016,.13984391804053728244] 
dist 217=[-.2196922288472890828 ,.13399478253670585834] 
dist 218=[-.2186737055624079046 ,.12208187755235119293] 
dist 219=[-.21770583900328679792,.11883532191595572768] 
dist 220=[-.21061452355146109262,.13157493601839631267] 
dist 221=[-.22290145459383902876,.14639834275713692868] 
dist 222=[-.23568703790894707921,.15983158668465544878] 
dist 223=[-.25252093882274969507,.17490265943900271829] 
dist 224=[-.26856199102957229568,.18989608962698671093] 
dist 225=[-.27818195639977857833,.20301947916573284278] 
dist 226=[-.2849535656803481568 ,.21730367695203243802] 
dist 227=[-.28962200715794627651,.23693189160816441852] 
dist 228=[-.29271283218671604123,.25591237985067315641] 
dist 229=[-.29330220366467550962,.26761050042879615554] 
dist 230=[-.2927395284096985811 ,.27622873983169910306] 
dist 231=[-.29216258617778849593,.28291245790910830368] 
dist 232=[-.27796470155743295724,.28785027558317579877] 
dist 233=[-.27513249354542826353,.28949779285554622208] 
dist 234=[-.26822185768318456467,.28986177645052053883] 
dist 235=[-.26570214403881675282,.28967503350181755001] 
dist 236=[-.25296520661366566708,.28132354458319912935] 
dist 237=[-.24993628824607923583,.27929551281642388051] 
dist 238=[-.24324175005938538608,.27386939866866320171] 
dist 239=[-.24097390591022610718,.27167487039222304027] 
dist 240=[-.14043790636597916899,.25987527119945551551] 
dist 241=[-.13009991836142490238,.25692917530920846601] 
dist 242=[-.10660851100049054002,.25102367297380207508] 
dist 243=[-.10174564387049392193,.2490907403059994946 ] 
dist 244=[-.07186466762292506365,.15683630483048296259] 
dist 245=[-.06638900219533030075,.14711562426974700967] 
dist 246=[-.05583018976043980303,.1247669672836595953 ] 
dist 247=[-.05320546271847099376,.12018815472983748729] 
dist 248=[-.02175541076743577485,.09075719204590612061] 
dist 249=[-.01717510240484725370,.08527875943272214631] 
dist 250=[-.00835397092004589288,.07507482359747465648] 
dist 251=[-.00623432082544888593,.07259022814122946176] 
dist 252=[.00030686083475393546,.03754274080071100703] 
dist 253=[.00168618436124309945,.03262745262585660809] 
dist 254=[.00174002658286459492,.02221714919578266511] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 1, 2, 0, 1] 
dist 0=[45.428047196246215816  ,45.428047196246215816  ] 
dist 1=[44.975312054985554476  ,45.723920726693605431  ] 
dist 2=[44.188593741147476449  ,45.883942012212990984  ] 
dist 3=[43.216608805238210933  ,45.984687585602607473  ] 
dist 4=[42.023818152506069194  ,46.043672877170131131  ] 
dist 5=[40.437138160513956126  ,46.082764437131822070  ] 
dist 6=[37.891849579539114539  ,46.103823235962410723  ] 
dist 7=[35.280942747079167317  ,46.110040223919565938  ] 
dist 8=[33.432116832861906750  ,46.089897865498956502  ] 
dist 9=[31.781958947294181720  ,46.045789570764732563  ] 
dist 10=[29.964441907723391283  ,45.977271273208995403  ] 
dist 11=[28.171253473013694286  ,45.845038957330257882  ] 
dist 12=[26.618116399793929060  ,45.754407977336667754  ] 
dist 13=[24.937830855680791526  ,45.557174139008141885  ] 
dist 14=[22.636458922055619025  ,45.362858360176263788  ] 
dist 15=[20.328459736868227200  ,34.799714552911254236  ] 
dist 16=[18.621541172484759292  ,33.855303192492072216  ] 
dist 17=[17.021270094501844187  ,31.540842787354563810  ] 
dist 18=[15.139082625729817142  ,31.195074775919743688  ] 
dist 19=[13.209609616219812744  ,27.696142298299690934  ] 
dist 20=[11.420138828873998396  ,27.031219311667093185  ] 
dist 21=[9.3818768442447775220 ,26.268541889066062003  ] 
dist 22=[6.4578478499347240240 ,26.094704721801610780  ] 
dist 23=[3.5663974217656814391 ,20.015012657430466802  ] 
dist 24=[1.6582250670121789977 ,19.246991798784940869  ] 
dist 25=[.0954578358929976103 ,18.187424541331505099  ] 
dist 26=[-1.4156478079127837596 ,17.794211798270096312  ] 
dist 27=[-2.7873061248573548674 ,16.125261834835169864  ] 
dist 28=[-3.7928656301066918616 ,15.575418792663336786  ] 
dist 29=[-4.7283928395420136448 ,15.109596612971400281  ] 
dist 30=[-5.8203742960817601399 ,14.985297755935783129  ] 
dist 31=[-6.8349993684541697473 ,4.3699127184060230054 ] 
dist 32=[-7.7694396958000147616 ,3.4809850286360654661 ] 
dist 33=[-8.9738930048345240070 ,1.4754954884781762189 ] 
dist 34=[-9.7968331140707877093 ,1.1447087665093554909 ] 
dist 35=[-10.503303495922961025  ,-1.2719779898048496210 ] 
dist 36=[-11.242585964097762151  ,-1.6833082797575265773 ] 
dist 37=[-11.894331695795631323  ,-2.1390282932671368392 ] 
dist 38=[-12.250995828680756435  ,-.79905489468748055702] 
dist 39=[-12.463221018906783331  ,.57144027335092267542] 
dist 40=[-12.537515288393705615  ,1.5161961646518733933 ] 
dist 41=[-12.554835290207713839  ,2.3288278523239882432 ] 
dist 42=[-12.539256568923762501  ,3.1722759344698962020 ] 
dist 43=[-12.497659628008245912  ,3.9699722043671768311 ] 
dist 44=[-12.457339062551615233  ,4.6001107412031560199 ] 
dist 45=[-10.400765074455963038  ,5.2276848509323251811 ] 
dist 46=[-10.405674550378440130  ,6.0151975789660342816 ] 
dist 47=[-8.9323426949055819657 ,6.7669215150776928557 ] 
dist 48=[-8.8099149620855791095 ,7.2516793454603002860 ] 
dist 49=[-7.6247344882036547325 ,7.6333273062179546666 ] 
dist 50=[-7.3904991171779081469 ,7.9735424645876494451 ] 
dist 51=[-7.0960575482107345200 ,8.2605445443193732074 ] 
dist 52=[-6.9932560965611957600 ,8.4297841594801076729 ] 
dist 53=[-4.7715595313255269236 ,8.5447112384249128446 ] 
dist 54=[-4.5355028390592436717 ,8.6148493256971201390 ] 
dist 55=[-3.8684162067216280577 ,8.6506763558721948716 ] 
dist 56=[-3.7024713544886226455 ,8.6420249221861977751 ] 
dist 57=[-3.0598513943066388328 ,8.5840466029682189164 ] 
dist 58=[-2.9353137882816423810 ,8.5396857399930510543 ] 
dist 59=[-2.6643420750944935082 ,8.2392128382530064812 ] 
dist 60=[-2.5950881030279383548 ,7.9727541157643643765 ] 
dist 61=[-1.6443617865701747267 ,1.9294968737821722991 ] 
dist 62=[-1.6117586885542518977 ,2.3819132321092892876 ] 
dist 63=[-1.2722530707331761995 ,2.8098692523126481218 ] 
dist 64=[-1.2484406101368367251 ,3.0824474162284726746 ] 
dist 65=[-1.1988608978190984257 ,3.2939972563249175317 ] 
dist 66=[-1.1835975915372426235 ,3.5810521881982253048 ] 
dist 67=[-1.1147664213001764810 ,3.8761544791856188743 ] 
dist 68=[-1.0989085871430313653 ,4.0659807781602485704 ] 
dist 69=[-1.0590565037473251666 ,4.2159477935574559205 ] 
dist 70=[-1.0455401414137302416 ,4.3519296016502410000 ] 
dist 71=[-.8900622264438905139 ,4.4654838172260659390 ] 
dist 72=[-.8634165122907588315 ,4.5258640251724687240 ] 
dist 73=[-.7963814524498088170 ,4.5594379741191595860 ] 
dist 74=[-.7789398821708669976 ,4.5658183020487965284 ] 
dist 75=[-.6590813103033264258 ,4.5561605808958300194 ] 
dist 76=[-.6324098185596591165 ,4.5465097561546596449 ] 
dist 77=[-.5870794693714519664 ,4.4941096293386150104 ] 
dist 78=[-.6376142638697753590 ,4.4802300316448123529 ] 
dist 79=[-1.0290319121993388074 ,3.1471699619770783492 ] 
dist 80=[-1.3187632417083629510 ,3.0829596882034921252 ] 
dist 81=[-1.5897462898578022005 ,2.9275772177323816992 ] 
dist 82=[-1.9063491873761537979 ,2.8880313485517105435 ] 
dist 83=[-2.2284807361079085582 ,2.6425708809926705310 ] 
dist 84=[-2.5215601921248024737 ,2.5908850322855134074 ] 
dist 85=[-2.8498829092513669918 ,2.4941426712234121726 ] 
dist 86=[-3.3127545924417648617 ,2.4674889568260256138 ] 
dist 87=[-3.7651895243818722284 ,.36496318951424921792] 
dist 88=[-4.0518516593478509899 ,.30247697476750326262] 
dist 89=[-4.2723917128406211238 ,.16952028838264838108] 
dist 90=[-4.4608270984816258650 ,.13979482022999780356] 
dist 91=[-4.6145637773646216881 ,.00610779532286144048] 
dist 92=[-4.6965696036485730406 ,-.01749518909721789028] 
dist 93=[-4.7419024648438922865 ,-.06246099986113522794] 
dist 94=[-4.7492306903759291548 ,-.07233084174039990952] 
dist 95=[-4.7380628131681300732 ,.24641684681293564433] 
dist 96=[-4.7242982024823146608 ,.48843620232145369167] 
dist 97=[-4.6763078646785232978 ,.70750347509512165147] 
dist 98=[-4.6502191110854561542 ,.9526182546161393825 ] 
dist 99=[-4.4903271328816217909 ,1.1958441843344385967 ] 
dist 100=[-4.4468404767108200932 ,1.4073849873963580226 ] 
dist 101=[-4.3609301240363140130 ,1.6363556453252297084 ] 
dist 102=[-4.3314363718309085467 ,1.9491746567374230263 ] 
dist 103=[-2.8319378738025682694 ,2.2609273966231708704 ] 
dist 104=[-2.6727287298284319242 ,2.4856500464651133868 ] 
dist 105=[-2.3017802330152001125 ,2.6898292229715474744 ] 
dist 106=[-2.2276437622902770914 ,2.9195846732858693810 ] 
dist 107=[-1.7226367622144174921 ,3.1484513083498274074 ] 
dist 108=[-1.6277112571317224885 ,3.3490927343910482154 ] 
dist 109=[-1.4578316379341898352 ,3.5676985306605662344 ] 
dist 110=[-1.4179155493494467339 ,3.8682975263530061448 ] 
dist 111=[-.76017854583922710667,4.1580827186255525377 ] 
dist 112=[-.67097359668734069425,4.3335200510612201114 ] 
dist 113=[-.4708473747290594124 ,4.4589846682386082691 ] 
dist 114=[-.43032265828178925097,4.5492609546022411834 ] 
dist 115=[-.18781622924941333492,4.6115024868762472964 ] 
dist 116=[-.1448427896171996518 ,4.6253108788770255972 ] 
dist 117=[-.05973535829219772624,4.6119223758404333175 ] 
dist 118=[-.03875248203301261465,4.5018733165502085286 ] 
dist 119=[.16552893220128196708,1.2919869433285832618 ] 
dist 120=[.19420516193155568212,1.3385800767008970778 ] 
dist 121=[.25752487836669350137,1.3702442448775173282 ] 
dist 122=[.26823047151435844249,1.3899315395305266244 ] 
dist 123=[.33812185007035733241,1.4019082657694444108 ] 
dist 124=[.3492202575037899334 ,1.4030878049403131784 ] 
dist 125=[.26658894113952988872,1.3991241081199998265 ] 
dist 126=[.01593643455425964502,1.3944589940047463514 ] 
dist 127=[-.23722542958744549077,1.3801458219170604792 ] 
dist 128=[-.40859882531765438095,1.3747844342922668239 ] 
dist 129=[-.55297309185958621034,1.3521692996488282961 ] 
dist 130=[-.69836001974497859576,1.3469907366204397676 ] 
dist 131=[-.83336759476787775335,1.2753856611566771086 ] 
dist 132=[-.93630952237886581576,1.2580017728403557339 ] 
dist 133=[-1.0355372004358894035 ,1.2408582697429403810 ] 
dist 134=[-1.1557180059265440999 ,1.2319753027936531456 ] 
dist 135=[-1.2685683413536052432 ,.98481221544765322543] 
dist 136=[-1.3385336157851562984 ,.95064939400146120007] 
dist 137=[-1.3905186395222853573 ,.88261240052016583505] 
dist 138=[-1.4315938110622418253 ,.86422418201077859966] 
dist 139=[-1.4625296818851859318 ,.79516120256154446432] 
dist 140=[-1.4740391407265028882 ,.7793571236336944012 ] 
dist 141=[-1.4776577171837426203 ,.74951373848258851461] 
dist 142=[-1.4770962371568890466 ,.74124363416063592877] 
dist 143=[-.18443555628209653911,.21913862734915282143] 
dist 144=[-.22232433599014774425,.20891768459300328274] 
dist 145=[-.2566502048916891838 ,.18522639067872740835] 
dist 146=[-.29745751054039030127,.18018555032868666937] 
dist 147=[-.40432978744014758072,.14793958900296627704] 
dist 148=[-.49104966639135413307,.14178141271656974182] 
dist 149=[-.57973732565714925452,.13032727840961465202] 
dist 150=[-.6944689794944315291 ,.12746384652774260812] 
dist 151=[-.80606922476076195207,-.24408355881376530416] 
dist 152=[-.88225564169963646914,-.2673149823416431173 ] 
dist 153=[-.9472018253522657661 ,-.31557207276074222037] 
dist 154=[-1.0139251238662178613 ,-.31813139987213014626] 
dist 155=[-1.0768117394361743687 ,-.26092360104683245657] 
dist 156=[-1.1264413935369538613 ,-.19165797976352343594] 
dist 157=[-1.1759520095563253453 ,-.10021534763080644385] 
dist 158=[-1.2383679265823826300 ,.04553220061495662408] 
dist 159=[-1.2960425914101537753 ,.19437936607460151742] 
dist 160=[-1.3266232423311010096 ,.298197498129321834  ] 
dist 161=[-1.3437380472486267438 ,.38902279581336640232] 
dist 162=[-1.3476399095882041948 ,.48599885724270085632] 
dist 163=[-1.3427748213482024748 ,.57963512162816439187] 
dist 164=[-1.3410273609775990458 ,.65712751016092921593] 
dist 165=[-1.3395426668309679749 ,.73772453258049506145] 
dist 166=[-1.3380341249111612108 ,.84375691534047955742] 
dist 167=[-1.1501821576869769542 ,.94768136902202436345] 
dist 168=[-1.1232148147453056471 ,1.0198632388469634217 ] 
dist 169=[-1.0750199534037133676 ,1.0826993774215008529 ] 
dist 170=[-1.0625333265224596224 ,1.1493123718014298400 ] 
dist 171=[-1.0209679771260388067 ,1.2133516171386203448 ] 
dist 172=[-1.0082785716808793817 ,1.2659129831901338103 ] 
dist 173=[-.99716594398206852149,1.3201997944199413020 ] 
dist 174=[-.99158324914613769983,1.3911292410050868390 ] 
dist 175=[-.25229477142746378671,1.4581101769855243324 ] 
dist 176=[-.23858965067497798182,1.4966327571649143329 ] 
dist 177=[-.21156331214058311622,1.5217331931851972811 ] 
dist 178=[-.20455945316527876381,1.5351254477317795890 ] 
dist 179=[-.17980015676799147595,1.5415554778173839551 ] 
dist 180=[-.17410300811330028637,1.5407320989187562880 ] 
dist 181=[-.16633527084767594573,1.5326919498879370220 ] 
dist 182=[-.16377305770951183556,1.5262322332906213525 ] 
dist 183=[.03147076722337230385,1.4215785450742514858 ] 
dist 184=[.03775589727969567817,1.4027133244502257096 ] 
dist 185=[.04910732947379950498,1.3583625895611524976 ] 
dist 186=[.05153411834112215606,1.3431635936814356035 ] 
dist 187=[.05697095018155289915,1.2695119690716939964 ] 
dist 188=[.05649317534969155574,1.2526286365246229065 ] 
dist 189=[.05346237471467126640,1.2139198384964407677 ] 
dist 190=[-.07399321770278839451,1.2008101439679154211 ] 
dist 191=[-.37845130379182451599,1.1527675413270153252 ] 
dist 192=[-.57923924309970617884,1.1732984375037730052 ] 
dist 193=[-.74278331090179013177,1.1843166038794567597 ] 
dist 194=[-.89854281718982457037,1.1861717144809989720 ] 
dist 195=[-1.0376039715534002996 ,1.1821390407314941307 ] 
dist 196=[-1.1344785846626138547 ,1.1779942036331488675 ] 
dist 197=[-1.2191208599741449620 ,1.1696818364499762418 ] 
dist 198=[-1.3093430299616688453 ,1.1654520692104930717 ] 
dist 199=[-1.3912733380190780095 ,1.0475015832108968741 ] 
dist 200=[-1.4428099151925616226 ,1.0287222934804050636 ] 
dist 201=[-1.4820115334844986530 ,.9884620167860426342 ] 
dist 202=[-1.5146945973455277490 ,.97597724692553771991] 
dist 203=[-1.5407304368671110156 ,.92004106484347552535] 
dist 204=[-1.5533930853271341321 ,.90815923527422080805] 
dist 205=[-1.5586982837272171238 ,.87372868816282260667] 
dist 206=[-1.5574272198254390619 ,.86787363073134978621] 
dist 207=[-.55879673055754810268,.56034192774007444436] 
dist 208=[-.58641976904526871813,.5507975185057657976 ] 
dist 209=[-.60864849910903898052,.53161808533676139008] 
dist 210=[-.62936927528743935305,.52584965071628026257] 
dist 211=[-.64756772373681880901,.50122713907937790433] 
dist 212=[-.65972567289872697074,.49549966985814054326] 
dist 213=[-.66980346132864444328,.480347761706338543  ] 
dist 214=[-.67969658290323878451,.47604026890801729694] 
dist 215=[-.68756148606675924553,.18200247466586133054] 
dist 216=[-.68954129492669352979,.15518879160935110382] 
dist 217=[-.68897761094492772267,.09380688585524834821] 
dist 218=[-.6870192818992298409 ,.08387394716946606255] 
dist 219=[-.67069856396247496271,.05167282915452144485] 
dist 220=[-.66554698674506591463,.04579192516119451711] 
dist 221=[-.6571649549989507282 ,.03673017010172842235] 
dist 222=[-.65397436143976135818,.03437783686663600251] 
dist 223=[-.56678237737393909841,-.00657457183702376236] 
dist 224=[-.55372255837327452992,-.01176441623465313820] 
dist 225=[-.52577719910738130131,-.02342240496137268613] 
dist 226=[-.51741533669833298006,-.02540686164905340202] 
dist 227=[-.48111777088228295521,-.03910544239519877934] 
dist 228=[-.47366686928705344539,-.04138272936839322587] 
dist 229=[-.45244931496112812225,-.02083001232070569527] 
dist 230=[-.44920358091641249646,.04420812305604644835] 
dist 231=[-.15805668510882287489,.16990976391546561984] 
dist 232=[-.1656997460086638721 ,.25311379985435696649] 
dist 233=[-.1744634615969605298 ,.32122922095347242898] 
dist 234=[-.18231274284249949169,.38668759067514964562] 
dist 235=[-.18898432925114144185,.44553036610392704482] 
dist 236=[-.1930460119401599997 ,.48723218482580845257] 
dist 237=[-.19597819457378980088,.52441935012093233205] 
dist 238=[-.19814012496449504141,.5652368538523635732 ] 
dist 239=[-.19950060945541098536,.6023971836931998353 ] 
dist 240=[-.19968778254368104321,.62498256526184433734] 
dist 241=[-.19855201789661003093,.64124543979977861093] 
dist 242=[-.1982626262807477897 ,.65316214664575379541] 
dist 243=[-.19033765212433597719,.66138979760298390359] 
dist 244=[-.18823202194409970078,.66327758690164769129] 
dist 245=[-.18679917607019615359,.66229384879669193513] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 2, 2, 1, 2] 
dist 0=[38.379701671114127960  ,38.379701671114127960  ] 
dist 1=[37.541869039270993051  ,39.003737398656580511  ] 
dist 2=[36.190713556570583515  ,39.500808487589540701  ] 
dist 3=[34.799382949104869709  ,39.886676871100717652  ] 
dist 4=[33.800951729157588652  ,40.066628735033241748  ] 
dist 5=[32.896301207106984239  ,40.147425957392058443  ] 
dist 6=[31.879293968281848198  ,40.144589438932081923  ] 
dist 7=[30.863563151435209414  ,39.921756192819397025  ] 
dist 8=[29.963780777731263618  ,39.686760051619488256  ] 
dist 9=[28.972861299018121486  ,39.279198279528402529  ] 
dist 10=[27.592678975585710069  ,39.201628181766893128  ] 
dist 11=[26.196173619819959874  ,38.884114291557382242  ] 
dist 12=[25.139840250032358337  ,38.782109318364235277  ] 
dist 13=[24.125067335317640275  ,38.524796766768619844  ] 
dist 14=[22.894347870462138829  ,38.420170218546840512  ] 
dist 15=[21.610376420714946192  ,37.886065877589215818  ] 
dist 16=[20.382498929100340201  ,37.333462014511860500  ] 
dist 17=[18.952823346814995842  ,27.493898261114562086  ] 
dist 18=[16.861833068256604586  ,27.223964454799736066  ] 
dist 19=[14.777001131421352047  ,24.366140767190542208  ] 
dist 20=[13.371869972793202773  ,23.819631483023831852  ] 
dist 21=[12.186567964502394743  ,23.226662646400547606  ] 
dist 22=[10.980616012998322157  ,23.111272280954386914  ] 
dist 23=[9.8441899528320746067 ,19.453086251716426266  ] 
dist 24=[8.9368399104998998765 ,19.298015922166432639  ] 
dist 25=[8.0174809972174614182 ,18.013709794886685082  ] 
dist 26=[6.8330042786570839259 ,17.413231712322314504  ] 
dist 27=[5.6727805411021688007 ,14.500220522886521782  ] 
dist 28=[4.8503778827987595291 ,14.245624297146992920  ] 
dist 29=[4.1124649967596595889 ,13.944009370961240322  ] 
dist 30=[3.2900500306483509085 ,13.862842853717043849  ] 
dist 31=[2.2669161068264681763 ,5.6963708998303524439 ] 
dist 32=[-.25356427481504249896,4.4473154805240299633 ] 
dist 33=[-2.7307829716143901514 ,4.1717332623517276479 ] 
dist 34=[-4.3209416452982271354 ,4.1170216141387039948 ] 
dist 35=[-5.5754081645702112036 ,1.8996832267096374885 ] 
dist 36=[-6.7108744847292180056 ,1.6857513726736547365 ] 
dist 37=[-7.6920382402643859035 ,1.2202791572655468054 ] 
dist 38=[-8.3298757943212587801 ,1.1296059123134075079 ] 
dist 39=[-8.8434014223950236828 ,.60972933023765360858] 
dist 40=[-9.3280308640532572944 ,.5204683748604406602 ] 
dist 41=[-9.7463059006956111435 ,.3423325166676201795 ] 
dist 42=[-9.9945914262862061528 ,.29882325831969251431] 
dist 43=[-10.169012498020128343  ,-.05912761031040643935] 
dist 44=[-10.291645122831362167  ,-.11542178275342220413] 
dist 45=[-10.373932499675776179  ,-.19348741771659397791] 
dist 46=[-10.386905152742908708  ,-.21341313311975936704] 
dist 47=[-10.363744603879181339  ,-.21253596142319463955] 
dist 48=[-10.335217723106111168  ,-.18004971138146529791] 
dist 49=[-6.7418046066142436330 ,-.11821121078046378442] 
dist 50=[-6.5703735524180920882 ,0                     ] 
dist 51=[-5.2210634471192410803 ,-2.9537795599488249362 ] 
dist 52=[-5.0833791082246795544 ,-2.1416572671442627910 ] 
dist 53=[-4.0549546115968753551 ,-1.3612670257327908734 ] 
dist 54=[-4.0096211499348733596 ,-.72225141721290642719] 
dist 55=[-3.3626497314229688740 ,-.06380495251911985292] 
dist 56=[-3.2721558489317345098 ,.79432007261915356336] 
dist 57=[-2.4051339558669203068 ,1.6319742447088924325 ] 
dist 58=[-2.3226662229091846216 ,2.2087722596847524149 ] 
dist 59=[-2.0099799472968426163 ,2.7058999948920123208 ] 
dist 60=[-1.9483579959314989481 ,3.2255582028427264181 ] 
dist 61=[-1.8230401658393022337 ,3.7213597668626825134 ] 
dist 62=[-1.7901413900789260499 ,4.1233299115010899513 ] 
dist 63=[-.0092407475236019298 ,4.5347433166856428047 ] 
dist 64=[.0252831825915111535 ,5.0684296704987880369 ] 
dist 65=[.50061627749725295771,5.5765426859042677773 ] 
dist 66=[.57381011859509926228,5.8858604819588807341 ] 
dist 67=[.90333462942752447445,6.1100024384266560903 ] 
dist 68=[.96096140892664342853,6.2778871578727713172 ] 
dist 69=[1.0661650300895105143 ,6.4021973530640261408 ] 
dist 70=[1.0877271899099997703 ,6.4522603408941338546 ] 
dist 71=[1.1294761230448901227 ,6.4681069631678392329 ] 
dist 72=[1.1102010120751392427 ,6.4585417968409749165 ] 
dist 73=[1.0589989292207389064 ,6.1701661075858687151 ] 
dist 74=[.9511670084126777174 ,6.1109157833476946375 ] 
dist 75=[.8153522787961811006 ,5.9875989414253661901 ] 
dist 76=[.6524017689468997705 ,5.9452335673118569613 ] 
dist 77=[.4383427196636422208 ,5.7399718424465109632 ] 
dist 78=[.0984640387813381232 ,5.6927452267032910875 ] 
dist 79=[-.2464022615355495757 ,5.5370346465305140603 ] 
dist 80=[-.4803919092214016082 ,5.5138039255736778883 ] 
dist 81=[-.6781365096834567281 ,3.4885797723461982442 ] 
dist 82=[-.8783333428722303031 ,3.3109937338054535719 ] 
dist 83=[-1.3317538089165576043 ,2.8713393703903237240 ] 
dist 84=[-1.9468548753191839660 ,2.8074393127147897491 ] 
dist 85=[-2.5107208785554811662 ,2.1355429686172536475 ] 
dist 86=[-2.9294294736394180636 ,2.0088413892677101822 ] 
dist 87=[-3.3226412540685870066 ,1.8663314671177727324 ] 
dist 88=[-3.7847132194200151016 ,1.8388631342359946454 ] 
dist 89=[-4.2143335785772173579 ,.69790219955009685772] 
dist 90=[-4.4779716187042364112 ,.5580636220077130180 ] 
dist 91=[-4.6709134896780976222 ,.2708756074901575710 ] 
dist 92=[-4.8182460773794690044 ,.1973841225721034560 ] 
dist 93=[-4.9307061190498195410 ,.25546681724039785264] 
dist 94=[-4.9844071031963804941 ,.4669744065966458885 ] 
dist 95=[-5.0061736366568048624 ,.68431539981510818289] 
dist 96=[-5.0067763781497088667 ,.87112042577419149243] 
dist 97=[-2.8541765956295173362 ,1.0778364173446896566 ] 
dist 98=[-2.9281429248007059544 ,1.2850445022981733794 ] 
dist 99=[-2.9828703368282632918 ,1.4767302672745091559 ] 
dist 100=[-3.0084443205320920189 ,1.6214881295440148116 ] 
dist 101=[-3.0177018185548210053 ,1.7595994119379476494 ] 
dist 102=[-3.0165309636895839399 ,1.9247497789231127900 ] 
dist 103=[-2.8264292282931781902 ,2.0785746871051635875 ] 
dist 104=[-2.7757177789808751938 ,2.1714778842609731394 ] 
dist 105=[-2.5345762034789033017 ,2.2375192747662886195 ] 
dist 106=[-2.5105498696204888617 ,2.2841234908289421730 ] 
dist 107=[-2.4783930531051469050 ,2.3163179609955530042 ] 
dist 108=[-2.3947332714565371314 ,2.3248481232418165150 ] 
dist 109=[-1.9645622688971085787 ,2.3236166135242222509 ] 
dist 110=[-1.6848649833819193553 ,2.3168511703745992067 ] 
dist 111=[-.71410611443580116486,-.30436949217806182401] 
dist 112=[-.7071809442604936513 ,-.15411260332737013176] 
dist 113=[-.29335747670397958342,-.00417958753703130075] 
dist 114=[-.25598529138541935522,.09529112897932425450] 
dist 115=[-.17037363333537185329,.17703868151733999231] 
dist 116=[-.1553949493040311861 ,.25620267802136130095] 
dist 117=[-.04688226856329217124,.32784844638259952041] 
dist 118=[-.02773207197091439071,.3795774213403862911 ] 
dist 119=[.00461351077802747584,.44386293333056369017] 
dist 120=[.01183388385906926808,.51634165590212201085] 
dist 121=[.12207557206532038296,.57436271829900887064] 
dist 122=[.13659846539472161574,.62797893541499247141] 
dist 123=[.16481256400611593054,.67480919951022944015] 
dist 124=[.17133948202649808096,.70574357934112703574] 
dist 125=[.19036485737112782889,.7310629451724962166 ] 
dist 126=[.19318171109858407277,.75549027746095193893] 
dist 127=[.19129874840856370841,.77661221929019842846] 
dist 128=[.18257376514008835411,.78873502525775392757] 
dist 129=[.1723194546883021662 ,.79668149733142377454] 
dist 130=[.1643282505377631963 ,.80111505478532861727] 
dist 131=[.15649417000949944031,.80303786554048665036] 
dist 132=[.14685685891198818428,.80207605397591218365] 
dist 133=[.13681366921329347626,.79729640305802184697] 
dist 134=[.12735371917156093361,.79396985854925141083] 
dist 135=[.07590339853820874912,.77153783860311605879] 
dist 136=[.00388101811642382957,.76584523132196233967] 
dist 137=[-.06824266509355220679,.7497632822446584331 ] 
dist 138=[-.15944943019398718717,.74446901329847285084] 
dist 139=[-.25605926760323334179,.70869739505748830249] 
dist 140=[-.34975898201088424549,.70010700535938086593] 
dist 141=[-.45938556240633442033,.68511616369680947007] 
dist 142=[-.61958812003500757726,.6806842479538412384 ] 
dist 143=[-.77846856367193033829,.16680314577058677478] 
dist 144=[-.88281856753323551826,.16458429823542289074] 
dist 145=[-.96733465934477600873,.10960284193903023426] 
dist 146=[-1.0470293313878069660 ,.10857460153360584998] 
dist 147=[-1.1176485457297978916 ,.10543335860738362711] 
dist 148=[-1.1659321966267610447 ,.10486293309331671204] 
dist 149=[-1.2071698106755220409 ,.09726169219289450007] 
dist 150=[-1.2496605484189521471 ,.09547953749022454444] 
dist 151=[-1.2858702004930406188 ,.09390409139295521851] 
dist 152=[-1.3020315744624291186 ,.09322425430370241751] 
dist 153=[-1.3094280904364850503 ,.06797210698311142771] 
dist 154=[-1.3106378174273291692 ,.06447094887195487590] 
dist 155=[-1.2837031081056588246 ,.05784433348117742318] 
dist 156=[-1.2760510289815311193 ,.05610282542362017432] 
dist 157=[-1.2708491618224755746 ,.04991427092927110215] 
dist 158=[-1.2676219834436173752 ,.04833295963558655626] 
dist 159=[-1.1529315439914778633 ,.19573698226983634232] 
dist 160=[-1.1387214643046525666 ,.36400150334866309972] 
dist 161=[-1.0975074676255799372 ,.50506321181549296226] 
dist 162=[-1.0899581030193219257 ,.64608563437074693561] 
dist 163=[-1.0024631491009382292 ,.77646379642275128135] 
dist 164=[-.98328950176648714472,.87503000485538771813] 
dist 165=[-.96259042500371534233,.96927333390684554833] 
dist 166=[-.95406988111065554452,1.0823928700923429139 ] 
dist 167=[-.72173842884393418382,1.1881826681429650137 ] 
dist 168=[-.69041166656594491629,1.2531630146871591881 ] 
dist 169=[-.62710858272517459074,1.3007564517625965065 ] 
dist 170=[-.61009981630293940706,1.3371315105460974373 ] 
dist 171=[-.54618403197076012607,1.3642124536867461284 ] 
dist 172=[-.53218881868115130063,1.3747006719810051903 ] 
dist 173=[-.50536928324614038403,1.3779892098626598830 ] 
dist 174=[-.49810429019915978735,1.3763268288770419337 ] 
dist 175=[-.24146881080248638783,.48142566660895665994] 
dist 176=[-.26194051347194837585,.54113942331256340405] 
dist 177=[-.29349883127630499925,.59918638166632769672] 
dist 178=[-.33811266851670045968,.63504816923542733682] 
dist 179=[-.37592053038789690561,.66158457019393372134] 
dist 180=[-.41437758135510887748,.6823966958444748411 ] 
dist 181=[-.45035423702713665471,.69823631050054736572] 
dist 182=[-.47825954503102674833,.70491779039023418935] 
dist 183=[-.50562463324759500561,.74538171490383071446] 
dist 184=[-.53944437820926258835,.80767582961612887346] 
dist 185=[-.57156607522298627504,.860978159415593347  ] 
dist 186=[-.59215194954359001026,.91605042341669505884] 
dist 187=[-.60824869017974737302,.96814175369874721875] 
dist 188=[-.62244832292390032643,1.0095429917426229470 ] 
dist 189=[-.63435568884588396934,1.0511062583741906439 ] 
dist 190=[-.64130081347542915503,1.1038462092625516529 ] 
dist 191=[-.64594539494584812653,1.1526959901032187587 ] 
dist 192=[-.64866780868029974578,1.1787272378559935052 ] 
dist 193=[-.64959360145446094833,1.1931034851960058748 ] 
dist 194=[-.64871821981906493855,1.1964113418430556220 ] 
dist 195=[-.64356554752660369045,1.1932625497725976730 ] 
dist 196=[-.6825662150610547493 ,1.1909964504811677828 ] 
dist 197=[-.75459348439191465104,1.1880891507967365393 ] 
dist 198=[-.84766550374997378539,1.1837962696644210665 ] 
dist 199=[-.93811921427080204696,1.0336560428334386757 ] 
dist 200=[-.999692910528536501  ,1.0112058186392782343 ] 
dist 201=[-1.0519795087426338223 ,.9693811501061069505 ] 
dist 202=[-1.1053541607809922284 ,.9579906572495446078 ] 
dist 203=[-1.1554245315172295641 ,.91618157030599700581] 
dist 204=[-1.1945188034363835266 ,.9048298692066101445 ] 
dist 205=[-1.2331111385188808187 ,.88560376557471690434] 
dist 206=[-1.2811778986329037757 ,.87965482360499389153] 
dist 207=[-1.3255327269306820579 ,.211559172884666242  ] 
dist 208=[-1.3493049275608170085 ,.15452965512810430239] 
dist 209=[-1.3625810289225826588 ,.1985716214467596919 ] 
dist 210=[-1.3650290797797202457 ,.27744333559724540834] 
dist 211=[-1.3625726806507147873 ,.3420327067829426473 ] 
dist 212=[-1.3585742894281086253 ,.40412540149906902997] 
dist 213=[-1.3479526711073926909 ,.45994809646305424891] 
dist 214=[-1.3421609536199332045 ,.4995043908513753417 ] 
dist 215=[-1.2217439266909991946 ,.53476728963777160963] 
dist 216=[-1.2018376094538487124 ,.57344841174200398262] 
dist 217=[-1.1568908050857191561 ,.60851287203164603357] 
dist 218=[-1.1423081430646353129 ,.62933614293130218669] 
dist 219=[-1.0744942389454021856 ,.64373771940119710808] 
dist 220=[-1.0595352265257466654 ,.65316344480742185566] 
dist 221=[-1.0224864069064466733 ,.65915564148851444019] 
dist 222=[-1.0111653019121049178 ,.66001784202460043797] 
dist 223=[-.96729250344333007175,.65851023131995453713] 
dist 224=[-.99106147793397463197,.65638973265109540943] 
dist 225=[-1.0059948824395642338 ,.64945316414589343036] 
dist 226=[-1.0128060094515334861 ,.78403254344986863189] 
dist 227=[-1.0153560384827136242 ,.9040649074540738547 ] 
dist 228=[-1.0139792051355951414 ,.98748870720627282152] 
dist 229=[-1.0089047182570580033 ,1.0601789535999200350 ] 
dist 230=[-1.0052056943324789462 ,1.1373562698057494136 ] 
dist 231=[-.92475140267923645756,1.2073956290859092236 ] 
dist 232=[-.91105980885337479822,1.2515867921437360818 ] 
dist 233=[-.88063472173977529206,1.2853609702274942469 ] 
dist 234=[-.8707029546256380086 ,1.3138095129990427702 ] 
dist 235=[-.82429477744887746676,1.3366981564708614189 ] 
dist 236=[-.81400948372947682576,1.3482738723557197593 ] 
dist 237=[-.78684936860705475882,1.3537922463247528221 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 0, 0, 2, 1, 2] 
dist 0=[42.542589181623437601  ,42.542589181623437601  ] 
dist 1=[42.242102784524657890  ,43.036453961786688015  ] 
dist 2=[41.535863707343036902  ,43.556788641023540319  ] 
dist 3=[40.413435185589337568  ,43.813518072685541756  ] 
dist 4=[38.601510055757683557  ,43.934615237635117296  ] 
dist 5=[36.732623356414641543  ,43.946946289347260565  ] 
dist 6=[35.382583066871235341  ,43.748729962008208328  ] 
dist 7=[34.149879784828725206  ,43.528624673819839166  ] 
dist 8=[32.749548276677348869  ,42.850450281772953698  ] 
dist 9=[31.342820586013346774  ,42.753169424378623258  ] 
dist 10=[30.084430094052246960  ,42.441395603502972572  ] 
dist 11=[28.689002210722061577  ,42.322673616913868675  ] 
dist 12=[26.734613167666059219  ,42.085643347648496055  ] 
dist 13=[24.754844018472826273  ,41.994069896429744520  ] 
dist 14=[23.257893285529275795  ,41.564334060195612369  ] 
dist 15=[21.821827555567202587  ,40.984781441260387431  ] 
dist 16=[20.085103207904746212  ,28.331896840581454329  ] 
dist 17=[18.278575769610632418  ,27.991145939389698666  ] 
dist 18=[16.563394299776360358  ,24.907500792228281250  ] 
dist 19=[14.578401299516607002  ,24.415160014067936183  ] 
dist 20=[11.693410977883323498  ,23.357078768442695829  ] 
dist 21=[8.8249057923741250967 ,23.130183437095377000  ] 
dist 22=[6.9057275464940304000 ,20.333190067812250804  ] 
dist 23=[5.3051880632753722513 ,20.117297942151024798  ] 
dist 24=[3.7100811873695043700 ,18.391631883596697698  ] 
dist 25=[2.2311112453386703474 ,18.094545273592701791  ] 
dist 26=[1.0946647291033702583 ,17.758885932082971384  ] 
dist 27=[-.0142810119254554179 ,16.946601912509742558  ] 
dist 28=[-1.3834425406529023435 ,15.232854161772252816  ] 
dist 29=[-2.6928991618244481511 ,12.974035566635124504  ] 
dist 30=[-3.5633069091802153728 ,9.6048825249048706104 ] 
dist 31=[-4.2835071741834395649 ,7.5528956251248279300 ] 
dist 32=[-4.9927755115059905323 ,1.6935518170483772738 ] 
dist 33=[-6.2353751591765813495 ,1.4053377359906644968 ] 
dist 34=[-7.6225082973529216741 ,-.0277232107035121229 ] 
dist 35=[-8.8931811089254589406 ,.4184083740036665935 ] 
dist 36=[-10.001210714850023703  ,1.1984504814706459815 ] 
dist 37=[-10.738434136063772052  ,2.0104769614060902006 ] 
dist 38=[-11.350546766635367673  ,2.5843937122206319570 ] 
dist 39=[-11.958894531495874345  ,3.0917644226573581675 ] 
dist 40=[-12.484125950687216764  ,3.6386180293644907779 ] 
dist 41=[-12.764076093726640589  ,4.1670905157376042180 ] 
dist 42=[-12.921300812027242323  ,4.6012556640039004997 ] 
dist 43=[-12.955769636405875729  ,5.0484157578119988076 ] 
dist 44=[-12.937985279413729957  ,5.6288018624422349321 ] 
dist 45=[-12.897010680285598112  ,6.1907720978952396640 ] 
dist 46=[-12.808969951481133175  ,6.5644775877714924647 ] 
dist 47=[-12.761153978366784849  ,6.8709834451324015329 ] 
dist 48=[-9.6407062190680412285 ,7.1648407253348983675 ] 
dist 49=[-9.3068378580498391616 ,7.4270101299489985702 ] 
dist 50=[-8.4818588719397805909 ,7.6070363765335609603 ] 
dist 51=[-8.3403612743210302824 ,7.7605563148402833545 ] 
dist 52=[-7.0670387199290062034 ,7.9168217376820550032 ] 
dist 53=[-6.8208240114546165459 ,8.0464948016638795131 ] 
dist 54=[-6.4886422717217416801 ,8.0938822232425930700 ] 
dist 55=[-6.3815364776777707234 ,8.0964674087655442341 ] 
dist 56=[-4.2234218552036886711 ,8.0799469817692554242 ] 
dist 57=[-3.9436429030887856534 ,7.9088990636577307108 ] 
dist 58=[-3.3348487122470844794 ,7.8501611091857720344 ] 
dist 59=[-3.1897636882506042978 ,7.7098184351312255350 ] 
dist 60=[-2.5007535741562668566 ,7.6505959114385493802 ] 
dist 61=[-2.3778828195944142708 ,6.6342649146784932841 ] 
dist 62=[-2.0873855491611061987 ,6.4698846878216317707 ] 
dist 63=[-2.0413277163360350758 ,5.8381667497206874387 ] 
dist 64=[-1.3787678399750926065 ,3.2612128933460117558 ] 
dist 65=[-1.4077573361680862048 ,3.5699109111586221173 ] 
dist 66=[-1.4284251267182234187 ,3.8364906345579872502 ] 
dist 67=[-1.4337990190816370551 ,4.0078689311071294514 ] 
dist 68=[-1.4328558261308593625 ,4.1431298461456589451 ] 
dist 69=[-1.4284398637561982691 ,4.2655287340350743508 ] 
dist 70=[-1.3362737261729683063 ,4.3663949794346260128 ] 
dist 71=[-1.3165046911836801287 ,4.4156475517397902017 ] 
dist 72=[-1.2772939851512354595 ,4.4370301033640158172 ] 
dist 73=[-1.2637211110403822638 ,4.4380199339765039268 ] 
dist 74=[-1.1974514901781062981 ,4.4026737115825096480 ] 
dist 75=[-1.1815982591156614287 ,4.3853776796359282862 ] 
dist 76=[-1.1282082883872588005 ,4.3374147913663286634 ] 
dist 77=[-1.1196316833447443291 ,4.3145984375023973221 ] 
dist 78=[-.4212753926162347961 ,3.7070719050315115371 ] 
dist 79=[-.7020122882507673241 ,3.6058550274533723488 ] 
dist 80=[-1.0512923182629700912 ,3.5880277820671459897 ] 
dist 81=[-1.4182828245252030200 ,3.3459128802819187083 ] 
dist 82=[-1.7697583376711127243 ,3.2914222912073657794 ] 
dist 83=[-2.1775895365916718829 ,3.2394278964004406475 ] 
dist 84=[-2.7696124516232144721 ,3.2199598533826320728 ] 
dist 85=[-3.3544470495212615170 ,.98540827048890013866] 
dist 86=[-3.7335921078052661435 ,.57769500634915012032] 
dist 87=[-4.0351515939209607885 ,.5275887961281915856 ] 
dist 88=[-4.3102327533770643062 ,.42576773285681213509] 
dist 89=[-4.5476994942858806166 ,.3998477655299139121 ] 
dist 90=[-4.6990917533649311663 ,.30901082203123336845] 
dist 91=[-4.8166763727736205557 ,.29018021481501204856] 
dist 92=[-4.9191841027690304343 ,.2663626816090583542 ] 
dist 93=[-4.9982379095775731570 ,.26165964542952633585] 
dist 94=[-5.0221832602176521126 ,.48088451798785656889] 
dist 95=[-5.0239749773866678951 ,.81155415665015991636] 
dist 96=[-5.0145532267868257200 ,1.1032355575500792247 ] 
dist 97=[-4.8744718742556182842 ,1.4181901243463321239 ] 
dist 98=[-4.8678521454287507831 ,1.7242298325331382149 ] 
dist 99=[-4.8513636910276304862 ,1.9803333701314672267 ] 
dist 100=[-4.7585880108617734446 ,2.2490877082718550268 ] 
dist 101=[-3.5703690969227077004 ,2.6056403217281546475 ] 
dist 102=[-3.4319191432855924471 ,2.9562611195851729310 ] 
dist 103=[-3.1012871212716953179 ,3.2013417125066253441 ] 
dist 104=[-3.0338901198408032639 ,3.4162431792031570313 ] 
dist 105=[-2.5503750377251844320 ,3.6463960005756751515 ] 
dist 106=[-2.4560772690520224504 ,3.8689922585217270925 ] 
dist 107=[-2.2956594346851983295 ,4.0537349480542581182 ] 
dist 108=[-2.2553824221528937632 ,4.2463238746052839997 ] 
dist 109=[-1.4966894499204781632 ,4.5002560784691965474 ] 
dist 110=[-1.3957781821584180252 ,4.7402465649062969326 ] 
dist 111=[-1.1520336734822909939 ,4.8771789888847977537 ] 
dist 112=[-1.1139474939679638525 ,4.9649909978716149129 ] 
dist 113=[-.76183672036211253299,5.0088756276943266973 ] 
dist 114=[-.69676451512957074231,5.0290934270738176350 ] 
dist 115=[-.61218788529127794625,5.0239364940560727996 ] 
dist 116=[-.589014594375388898  ,4.9007766510756578352 ] 
dist 117=[.05548807040878509217,.54177093943480773903] 
dist 118=[.1281928428395113989 ,.6086046463816252041 ] 
dist 119=[.2963284525849369059 ,.65142980311094161457] 
dist 120=[.32049490530189941976,.68495839876960921112] 
dist 121=[.28579987450863646198,.71467893737109382177] 
dist 122=[.23961559974303743498,.73978935759418363324] 
dist 123=[.18434338494055651448,.7549180469437295256 ] 
dist 124=[.11184165573564307472,.7662244304183125797 ] 
dist 125=[-.00474897679136570788,.82540037592534087161] 
dist 126=[-.12345717650431144996,.86948787346886163338] 
dist 127=[-.2044802565628971114 ,.90339762381245025715] 
dist 128=[-.27340956709746711176,.93235780210036904209] 
dist 129=[-.34385121587591904086,.95597164817000960832] 
dist 130=[-.40987202649826793576,.96853405638864289535] 
dist 131=[-.46115793514396865544,.97542487821540060408] 
dist 132=[-.51147451026625120029,.97639268962578749276] 
dist 133=[-.57362760336973993783,.73137745670289038569] 
dist 134=[-.63255128078468681565,.6727576344350617681 ] 
dist 135=[-.66997867489705375186,.61863648057530151891] 
dist 136=[-.69882932440419072415,.60290376924954222418] 
dist 137=[-.72352065508190650938,.54392093045325409445] 
dist 138=[-.74364944638410311207,.52327089914185838437] 
dist 139=[-.75428949654023466676,.49731561425321800961] 
dist 140=[-.76001613505288993891,.48366545263815845037] 
dist 141=[-.76053368080963667249,.47393061739208316812] 
dist 142=[-.01465689419987372500,.39803157474108278246] 
dist 143=[-.09771170734690790489,.3738716954367577568 ] 
dist 144=[-.19859116371352112536,.36760877206666573086] 
dist 145=[-.30336996393541089945,.34609269680882679197] 
dist 146=[-.40199467060264679933,.34037845407076209038] 
dist 147=[-.51513676253315060393,.33413029423932462549] 
dist 148=[-.67787966062072177978,.33130971383062753044] 
dist 149=[-.83870254033020866897,-.16159363198474378442] 
dist 150=[-.94417921913081803011,-.20336399314568672015] 
dist 151=[-1.0294516486717172470 ,-.20871594101147623729] 
dist 152=[-1.1096064026350240961 ,-.20673472103386081802] 
dist 153=[-1.1804649522311681047 ,-.19424005163558382882] 
dist 154=[-1.2286212828285131478 ,-.17593895374114085162] 
dist 155=[-1.2694363353381264222 ,-.15077655342961810821] 
dist 156=[-1.3109845262425955963 ,-.11575036560409810366] 
dist 157=[-1.3460892361698571535 ,-.05807094791566987261] 
dist 158=[-1.3611777732517910594 ,.00148357491000043290] 
dist 159=[-1.3678791712613412021 ,.04399625259970248574] 
dist 160=[-1.3694959211500010320 ,.08220090766449242770] 
dist 161=[-1.3380344274431931697 ,.12455889194712195278] 
dist 162=[-1.3300290831704596241 ,.16639057549504607892] 
dist 163=[-1.3253579748708146052 ,.2024953190806564471 ] 
dist 164=[-1.3240105628868104334 ,.24135559219587412691] 
dist 165=[-1.0953674630383231766 ,.29418947574952067772] 
dist 166=[-1.0666766941833252772 ,.34675818360101074221] 
dist 167=[-.99415779297727535941,.44644125707214886132] 
dist 168=[-.98065932629709129243,.5917034027492467025 ] 
dist 169=[-.86044060070631044894,.72698343062086786258] 
dist 170=[-.83609171599687584352,.83096756692594695415] 
dist 171=[-.8030093921187616325 ,.93207512264662074538] 
dist 172=[-.7918901955075746816 ,1.0558702597815837677 ] 
dist 173=[-.55448753453104958689,1.1729376198136168215 ] 
dist 174=[-.52286079020618261945,1.2471840065486231531 ] 
dist 175=[-.45442703074562655823,1.3043729698637604624 ] 
dist 176=[-.43618782364729116699,1.3533371764982258418 ] 
dist 177=[-.35780783809766538303,1.3933375878225872361 ] 
dist 178=[-.34315384231886195693,1.4147378575551938213 ] 
dist 179=[-.30642848038993685   ,1.4266361109886055972 ] 
dist 180=[-.30083815646447643471,1.4286989230524408411 ] 
dist 181=[.09223634519247952633,.74795773599682065422] 
dist 182=[.12806686377723542032,.72465410001789147988] 
dist 183=[.20585448191283879872,.71915344931182036549] 
dist 184=[.22103382351798352072,.704229211585977081  ] 
dist 185=[.27035420524613701671,.69847045149511850715] 
dist 186=[.24745278246516062155,.66600008456543071919] 
dist 187=[.21747697759272701242,.65797435312578099601] 
dist 188=[.12435558417438971744,.64250924256537296809] 
dist 189=[-.02410151753744232627,.63760873125399000176] 
dist 190=[-.17597690813846981078,.60756644507922153406] 
dist 191=[-.27667083332005141887,.61102562626923902098] 
dist 192=[-.35927528138510510107,.63364894104412283132] 
dist 193=[-.43892807099197468461,.6531945768689890218 ] 
dist 194=[-.51069941101604641714,.66472305461065823155] 
dist 195=[-.5618368898097006399 ,.67260286471786709341] 
dist 196=[-.60771320433939362511,.6775810047581570375 ] 
dist 197=[-.65847888061187784283,.6800497732903299477 ] 
dist 198=[-.70484089277389379464,.6798853393011254649 ] 
dist 199=[-.7331355122186128292 ,.6747383716671626208 ] 
dist 200=[-.75364486447392155218,.67308225066186153945] 
dist 201=[-.76892447094167223805,.64617687377971572689] 
dist 202=[-.77969120966832709651,.63907866389357913965] 
dist 203=[-.7822472625329420389 ,.63262741924101059646] 
dist 204=[-.78186467584908704162,.62866592465939773645] 
dist 205=[-.781411687426062691  ,.51621662993453650936] 
dist 206=[-.49086913781230718796,.50037276864729048091] 
dist 207=[-.53294756599645093326,.46936511642991431343] 
dist 208=[-.57882521874306413321,.46097657442485669615] 
dist 209=[-.62370794018574788945,.42965800888023842122] 
dist 210=[-.66181406696812439578,.42217472940547549367] 
dist 211=[-.7023065758135166104 ,.40833244205481455874] 
dist 212=[-.75671739976645436687,.40442827365810881315] 
dist 213=[-.80890921255775349169,-.08659233194738474909] 
dist 214=[-.84054204046875700861,-.12352696791453788379] 
dist 215=[-.86321315081395556982,-.20356283535010072837] 
dist 216=[-.87962400821479226265,-.21939179334448325729] 
dist 217=[-.89094765702192519167,-.30402579450796935691] 
dist 218=[-.89351892851027002872,-.27944602714006667867] 
dist 219=[-.89262960458443716097,-.24116650901077017853] 
dist 220=[-.89182592267764784616,-.190247283348563978  ] 
dist 221=[-.85450371900228865778,-.1086758541886329751 ] 
dist 222=[-.84667548784552274469,-.02516143416305319663] 
dist 223=[-.82705692235587513216,.03351546054741736063] 
dist 224=[-.81967306798552052527,.08531025337424559599] 
dist 225=[-.78159417637433973846,.14134738969134163736] 
dist 226=[-.77238919472039515153,.19591073367648853699] 
dist 227=[-.75271404783425835512,.24182138960382295892] 
dist 228=[-.74612628026519528715,.29024785024086971819] 
dist 229=[-.67053980319226489505,.35485597553818188082] 
dist 230=[-.66994333968558652181,.41861562427127423528] 
dist 231=[-.6641696312850051239 ,.46365453828373358662] 
dist 232=[-.66216800365356070844,.50366396855312528075] 
dist 233=[-.63562453685946883378,.56748378103554648702] 
dist 234=[-.62864470535177559934,.62747922134597545655] 
dist 235=[-.62141645801531307637,.68166990274962106885] 
dist 236=[-.61740985712012803223,.74220662975368081711] 
dist 237=[-.50961927030607667282,.79766557308845976443] 
dist 238=[-.49432883200664075437,.83158251166740207234] 
dist 239=[-.46384911990388007808,.85625754216642001578] 
dist 240=[-.45545487919835631067,.87481695217194078697] 
dist 241=[-.4231059432260432834 ,.888051267736187286  ] 
dist 242=[-.41568682602719877996,.8914651622758963096 ] 
dist 243=[-.400390193757398072  ,.89154447101549413442] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 1, 0, 2, 1, 2] 
dist 0=[53.318208530762621853  ,53.318208530762621853  ] 
dist 1=[53.199327173156747459  ,53.380284043273270996  ] 
dist 2=[52.786765590352032488  ,53.424851928213004574  ] 
dist 3=[52.061717319694707420  ,53.411258053835906282  ] 
dist 4=[50.751546740910880032  ,53.351855840544164785  ] 
dist 5=[49.289561937325548801  ,53.266459568920427674  ] 
dist 6=[47.958195162899406520  ,53.076762781165422932  ] 
dist 7=[46.464813723891255557  ,52.376076676781121304  ] 
dist 8=[44.355545253492028142  ,48.696073604713991426  ] 
dist 9=[42.005571719620673190  ,48.462523090984573441  ] 
dist 10=[39.550713464826123030  ,47.669841540783111389  ] 
dist 11=[36.542463307811829802  ,47.419280122225880829  ] 
dist 12=[31.982134710855453690  ,47.144607758843057188  ] 
dist 13=[27.393949404480219962  ,47.000797308719256932  ] 
dist 14=[24.274322785456859199  ,41.548481032632308944  ] 
dist 15=[21.624769731288989404  ,41.378482396679264636  ] 
dist 16=[18.913816828421836434  ,34.520195618840234010  ] 
dist 17=[16.361255630029592069  ,33.618767504396112713  ] 
dist 18=[14.344074899030539737  ,31.857942059836650139  ] 
dist 19=[12.326031549503505771  ,31.401676596749719013  ] 
dist 20=[9.7695397242740933828 ,29.790828767493854854  ] 
dist 21=[7.2984470205006650516 ,29.413208988930735112  ] 
dist 22=[5.6212445493564180743 ,28.883999928301333339  ] 
dist 23=[4.1973294835897209049 ,28.710731209304607071  ] 
dist 24=[2.7376269920061916285 ,11.776855384347182166  ] 
dist 25=[1.3570033835851618695 ,10.366378152569026608  ] 
dist 26=[.2484668729545758935 ,7.9533372389680027982 ] 
dist 27=[-.8807981546304620693 ,7.6886370075389794923 ] 
dist 28=[-2.3453517722079031778 ,7.2272391892855358984 ] 
dist 29=[-3.7501084492058555228 ,7.1440635590392045322 ] 
dist 30=[-4.7683060290764963102 ,.7422760022297218329 ] 
dist 31=[-6.6542117426586126713 ,.4762719290530606596 ] 
dist 32=[-8.4156502423999214734 ,-3.7036406314784783552 ] 
dist 33=[-9.5150500968636456641 ,-4.2186626919147397429 ] 
dist 34=[-10.343651520376536006  ,-5.2584812288250174940 ] 
dist 35=[-11.023494295952505966  ,-5.4840040384241434139 ] 
dist 36=[-11.563356258202040065  ,-5.5559750550175932738 ] 
dist 37=[-11.832753114076694299  ,-5.1708026610376237440 ] 
dist 38=[-11.971611134236513454  ,-4.7753709655510919612 ] 
dist 39=[-11.990048277635712995  ,-4.2989668726903217921 ] 
dist 40=[-9.1609112147118383471 ,-3.5899662524878427112 ] 
dist 41=[-8.9727343707272156545 ,-2.7873064474728223587 ] 
dist 42=[-8.6121161545296709831 ,-1.9367655960097148574 ] 
dist 43=[-8.6283211986524544274 ,-.88871662777078037056] 
dist 44=[-8.6293507161046356743 ,.70255136295625605371] 
dist 45=[-8.6105150526278539529 ,2.2940581590779336563 ] 
dist 46=[-7.1203843614545810226 ,3.3431832081575229326 ] 
dist 47=[-7.0399383203157822514 ,4.1961196751652394100 ] 
dist 48=[-5.8231070237547942724 ,5.0046531225176907683 ] 
dist 49=[-5.5808419006066387422 ,5.7232300419394756699 ] 
dist 50=[-5.5175536542893130795 ,6.2171737889854504695 ] 
dist 51=[-5.2139493750170509791 ,6.6415973270265380566 ] 
dist 52=[-4.6072571343370937968 ,7.0827818193772539010 ] 
dist 53=[-3.7709165897665366994 ,7.4768461695542664765 ] 
dist 54=[-3.5138807837317434832 ,7.7131509980173231960 ] 
dist 55=[-3.4664242117380820712 ,7.8794226704326936336 ] 
dist 56=[-.82547967798258285296,7.9937404080336414836 ] 
dist 57=[-.5715377793807881554 ,8.0656338393129034884 ] 
dist 58=[-.04769994298613270798,8.0758991224128126687 ] 
dist 59=[.08300902546839507437,8.0362033390904761446 ] 
dist 60=[.5532947160164654734 ,8.0166432690388628679 ] 
dist 61=[.6445039561689371648 ,5.4307897845516037996 ] 
dist 62=[.7738375192254017932 ,5.7540115410821620645 ] 
dist 63=[.8032034234961651684 ,6.0967161342074682052 ] 
dist 64=[.7967159489551352682 ,6.4018434393517569852 ] 
dist 65=[.7360477946521094834 ,6.5750056658611798673 ] 
dist 66=[.6246168609120441326 ,6.6852973633007449023 ] 
dist 67=[.4153712495272338979 ,6.7393343096521379188 ] 
dist 68=[.1596477357788626936 ,6.7634028773754708175 ] 
dist 69=[-.1373684242239544573 ,6.7564882791807116937 ] 
dist 70=[-.5214256704365493776 ,6.7276896008177949439 ] 
dist 71=[-1.1246377201787177438 ,6.7043745979106796839 ] 
dist 72=[-1.7324809391145060720 ,4.1248689985285780690 ] 
dist 73=[-2.1350534394576703373 ,4.0954180759102634200 ] 
dist 74=[-2.4644310997419585952 ,3.9640571427122057640 ] 
dist 75=[-2.7801417607042383290 ,3.9314278639713196620 ] 
dist 76=[-3.0630280384530285925 ,3.8408179095545079048 ] 
dist 77=[-3.2614026476437558636 ,3.8140558795018240562 ] 
dist 78=[-3.6073568697828111604 ,2.0190871314272997849 ] 
dist 79=[-3.9361096236349329538 ,1.8612670776723625172 ] 
dist 80=[-4.2395383844998171822 ,1.4869556482412689173 ] 
dist 81=[-4.5043815268125442252 ,1.4270843916115541486 ] 
dist 82=[-4.6790587342493968972 ,.90934121324880632896] 
dist 83=[-4.8216522344158407119 ,.81517954144076644324] 
dist 84=[-4.9584017039047560124 ,.68453125663864928492] 
dist 85=[-5.0706476271662243666 ,.64657556368681341394] 
dist 86=[-5.1153941532598176367 ,-.03943619533005739218] 
dist 87=[-5.1319364996524783415 ,.00603012411719701137] 
dist 88=[-5.1314873939160328705 ,.7855499448591715457 ] 
dist 89=[-5.0095348925365230664 ,1.3062315007504635015 ] 
dist 90=[-4.9726138784529747135 ,1.7370193970828011342 ] 
dist 91=[-4.9456743302212174137 ,2.1577419645851214539 ] 
dist 92=[-4.9253360803324482789 ,2.5397478766004181059 ] 
dist 93=[-4.5147742576774856150 ,2.8159973622224605695 ] 
dist 94=[-4.4971336125194633436 ,3.2171868555466573328 ] 
dist 95=[-4.4848994686672175193 ,3.5829439146490282863 ] 
dist 96=[-4.0265756818546891478 ,3.9326266618027569206 ] 
dist 97=[-3.9539655980158998390 ,4.2455842387015337615 ] 
dist 98=[-3.8039849374989470867 ,4.4647459310772959940 ] 
dist 99=[-3.7585948446253466828 ,4.6574099770932489584 ] 
dist 100=[-3.5621480302305762948 ,4.8646105756888582941 ] 
dist 101=[-3.5185517822091007547 ,5.0462685076652223734 ] 
dist 102=[-3.3982494303324384882 ,5.1369734716078605844 ] 
dist 103=[-3.3711990723681247965 ,5.1826635297807743171 ] 
dist 104=[-1.2108104640418657743 ,5.1881371788534330746 ] 
dist 105=[-1.2068714112595869311 ,5.1332410815599497405 ] 
dist 106=[-1.1649341804118169624 ,5.1074995968368680941 ] 
dist 107=[-1.1538463899291174943 ,5.1279254928699937098 ] 
dist 108=[-1.1403849753962920481 ,5.1306305889007178042 ] 
dist 109=[-1.2244159820781445417 ,5.0822880298577803838 ] 
dist 110=[-1.9189617060560146920 ,5.0633102595669858971 ] 
dist 111=[-2.4961329423501518252 ,4.9803185448507793059 ] 
dist 112=[-3.0645158427728506640 ,4.9615473115035110988 ] 
dist 113=[-3.5841469676647164162 ,4.6915862391328617515 ] 
dist 114=[-3.9667022159245283002 ,4.6257306416074057518 ] 
dist 115=[-4.3223290846843659549 ,4.5627953259291757108 ] 
dist 116=[-4.7344564282545511709 ,4.5266418014896121457 ] 
dist 117=[-5.1120743245461973448 ,3.5816710948826894509 ] 
dist 118=[-5.3299413411783613646 ,3.4508274130358678561 ] 
dist 119=[-5.4725958646296826329 ,2.9786524514262507747 ] 
dist 120=[-5.5499768010418529096 ,2.0625356066359405606 ] 
dist 121=[-5.5981018137284407058 ,1.7005668481566083202 ] 
dist 122=[-5.6239714436458575075 ,1.6310622693895694019 ] 
dist 123=[-5.6384778788711949405 ,1.5122207273055820554 ] 
dist 124=[-5.6412439016210507627 ,1.4830768218263757890 ] 
dist 125=[-.16931215836731391292,1.2175311989836618358 ] 
dist 126=[-.0358101473462316850 ,1.2165995185380790146 ] 
dist 127=[-.03403213386920683699,1.2146047474478272847 ] 
dist 128=[-.2274512766600568082 ,1.2022719523081479988 ] 
dist 129=[-.40652252454914351409,1.1987726918489475236 ] 
dist 130=[-.54238001233387264207,1.1500175072014878367 ] 
dist 131=[-.67277656662298785848,1.1375801088928514270 ] 
dist 132=[-.83005341618184811238,1.1252438649037105446 ] 
dist 133=[-.97763144400970694037,1.1182224369840172045 ] 
dist 134=[-1.0693094602620029936 ,.930981021126898366  ] 
dist 135=[-1.1377350909522761827 ,.90459564807397033096] 
dist 136=[-1.1924815006380554776 ,.85245101532578225135] 
dist 137=[-1.2359813036308358575 ,.83824934088218705161] 
dist 138=[-1.2594989633862253483 ,.78447226631864598611] 
dist 139=[-1.2729209261769467411 ,.771933407824396941  ] 
dist 140=[-1.2760926802646512555 ,.74746736445305315493] 
dist 141=[-1.2147108711254336818 ,.7403169941693672263 ] 
dist 142=[-1.2038177864571790034 ,.50256403459539155669] 
dist 143=[-1.1816344765115032484 ,.50503376917717261717] 
dist 144=[-1.1738330832028365454 ,.50543064691512167568] 
dist 145=[-1.1356699048853304622 ,.50454040958884083965] 
dist 146=[-1.1265014884360095956 ,.4954417479721397017 ] 
dist 147=[-1.0967503829276347583 ,.49233932670577199979] 
dist 148=[-1.0913473869449763845 ,.48699647011463935003] 
dist 149=[-1.0162764236010356042 ,.48498627010663323706] 
dist 150=[-1.0016702801396474590 ,.42846617893990071363] 
dist 151=[-.96703740992988256366,.41981006053133264618] 
dist 152=[-.95537219425832215402,.40146877214607322165] 
dist 153=[-.89956774577803421034,.51012846143073295759] 
dist 154=[-.89691312101601617744,.66297736733827174527] 
dist 155=[-.90432458503315644007,.83999535060006886778] 
dist 156=[-.90693794832277029628,1.0965753739802685048 ] 
dist 157=[-.90631784460393348407,1.3504911806113085670 ] 
dist 158=[-.03992886206829061067,1.5168738921758719527 ] 
dist 159=[-.00815882241938394008,1.6512026801503873256 ] 
dist 160=[.05609393043142707308,1.7771432891316417220 ] 
dist 161=[.07207979101749857646,1.8882425259852976968 ] 
dist 162=[.12599848236502992538,1.9633178436785767781 ] 
dist 163=[.13718415572411593305,2.0264822187088827267 ] 
dist 164=[.14604453472766377092,2.0900290440917593496 ] 
dist 165=[.14244067017895818862,2.1432609212466435900 ] 
dist 166=[.13359151752333446463,2.1652423832186655508 ] 
dist 167=[.11859876736227132918,2.1744569298513299759 ] 
dist 168=[.09621676283119922693,2.1767133436893822549 ] 
dist 169=[.05786625516481404422,2.1217937415895436516 ] 
dist 170=[.01213042361878502381,2.1078927488441670293 ] 
dist 171=[-.03973702730690188675,2.0998526149112295458 ] 
dist 172=[-.10609237030559773367,2.0977059210112653671 ] 
dist 173=[-.28301200539542814241,1.8372109079918898744 ] 
dist 174=[-.56026634547958036041,1.8059896443417106373 ] 
dist 175=[-.79305741194024159027,1.7213536964853603203 ] 
dist 176=[-1.0264054028101524736 ,1.7058406752258070180 ] 
dist 177=[-1.2425719154354103082 ,1.5449260973825474943 ] 
dist 178=[-1.4067667064896008236 ,1.5107980359175010246 ] 
dist 179=[-1.5645275493196877332 ,1.4704712285944213882 ] 
dist 180=[-1.7550066405492881034 ,1.4539687115641589688 ] 
dist 181=[-1.9337520208617772857 ,1.0733505387339014692 ] 
dist 182=[-2.0446664114327107918 ,1.0221172366825361680 ] 
dist 183=[-2.1272549107818840433 ,.91628250692081939238] 
dist 184=[-2.1929102151976048520 ,.88750130575754810438] 
dist 185=[-2.2427357877531537267 ,.85524730867407388895] 
dist 186=[-2.2621244514649790321 ,.82371960859128180334] 
dist 187=[-2.2693449947844552343 ,.81565140063711702018] 
dist 188=[-2.2705908235807370431 ,.79582987529035020771] 
dist 189=[-.9709355624059904248 ,.78852812424861480518] 
dist 190=[-.98738688707623013049,.31356998177397223661] 
dist 191=[-.99364300803178690286,.27095644544974847009] 
dist 192=[-.99504756940085837481,.17292716062040371605] 
dist 193=[-.99332982551254504539,.15570947046861253844] 
dist 194=[-.97428307465754586537,.03022710731230687116] 
dist 195=[-.9677024567249817593 ,.00802181219592368513] 
dist 196=[-.9966245882970377529 ,-.02949540233569808077] 
dist 197=[-1.1250707280668548407 ,-.03789936889980682404] 
dist 198=[-1.2119295911435003500 ,-.16638699845337749114] 
dist 199=[-1.2850770465160434623 ,-.18336302550872650608] 
dist 200=[-1.3587789664793697435 ,-.21535495179039291778] 
dist 201=[-1.4273221591943355477 ,-.22240639007954806258] 
dist 202=[-1.4798734674725496256 ,-.24030373427351752156] 
dist 203=[-1.5308535211246872024 ,-.13901783491628045683] 
dist 204=[-1.5931251217826600120 ,.06829177740385830814] 
dist 205=[-1.6496547966986567347 ,.27925512157627537542] 
dist 206=[-1.6777094547708624726 ,.42537452143386168235] 
dist 207=[-1.6922238975022041061 ,.5521606809891486396 ] 
dist 208=[-1.6946888436333694892 ,.68593482436236768139] 
dist 209=[-1.6752831591172748591 ,.81416825354054029245] 
dist 210=[-1.6688304175873404456 ,.91883286566985132911] 
dist 211=[-1.6636668938480817641 ,1.0264148147560697113 ] 
dist 212=[-1.6589063487571646360 ,1.1662962240437074295 ] 
dist 213=[-1.4174326130752642272 ,1.3026599377223117409 ] 
dist 214=[-1.3826214907174036695 ,1.3961973188518797098 ] 
dist 215=[-1.3183715952153513238 ,1.4763951535165477999 ] 
dist 216=[-1.3013474767831941836 ,1.5594997185500477892 ] 
dist 217=[-1.2415189498805600682 ,1.6382414350728028323 ] 
dist 218=[-1.2248654498500530487 ,1.7010203761962777589 ] 
dist 219=[-1.2029514583613635960 ,1.7642125789715468281 ] 
dist 220=[-1.1941239819197284780 ,1.8446045992394650962 ] 
dist 221=[-.20749613497080681898,1.9196239076720061003 ] 
dist 222=[-.12472018665950141175,1.9613650171905198032 ] 
dist 223=[-.10716571111207995642,1.9867732061025403245 ] 
dist 224=[-.1558763210244085975 ,1.9965813700341345797 ] 
dist 225=[-.21749869288669033166,1.9984247027967947480 ] 
dist 226=[-.28280833159630079571,1.9947081569271593946 ] 
dist 227=[-.34624067741492922106,1.9819141698325084659 ] 
dist 228=[-.42053556317597316528,1.9737349232346391406 ] 
dist 229=[-.52921515368640976483,1.8143009800345048221 ] 
dist 230=[-.64086046740141105401,1.7871478915117562662 ] 
dist 231=[-.72699627603194518141,1.7253562039958932994 ] 
dist 232=[-.81105702711600117721,1.7049584900565373810 ] 
dist 233=[-.9144172201972002792 ,1.6088171021813135245 ] 
dist 234=[-1.0224429311084911377 ,1.5873321212146967051 ] 
dist 235=[-1.1251312023648225537 ,1.5346287406898122345 ] 
dist 236=[-1.2437185844658745526 ,1.5175480513684190668 ] 
dist 237=[-1.4152232516138144170 ,1.4232649326070566231 ] 
dist 238=[-1.5838988953422665851 ,1.4496352427974298639 ] 
dist 239=[-1.6911909675074623153 ,1.4641768428406036249 ] 
dist 240=[-1.7742006245576800028 ,1.4666168222425050496 ] 
dist 241=[-1.8459256837058137004 ,1.4634819065265512680 ] 
dist 242=[-1.9050131778656128682 ,1.4587606066896806422 ] 
dist 243=[-1.9375656928701026508 ,1.4488144500344501693 ] 
dist 244=[-1.9569528316607884337 ,1.4435488560407166401 ] 
dist 245=[-1.9634756743502352106 ,1.3018777132135350588 ] 
dist 246=[-1.9626735779628646928 ,1.2791353884451634394 ] 
dist 247=[-1.9588919257901539138 ,1.2301635565498428212 ] 
dist 248=[-1.9408644517613963723 ,1.2148738145186508951 ] 
dist 249=[-1.9317096034253921248 ,1.1459707067275422557 ] 
dist 250=[-1.8041870573935621086 ,1.1312436696992131853 ] 
dist 251=[-1.7743471928937275980 ,1.0891132572225614815 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 2, 0, 1] 
dist 0=[46.713345340040138150  ,46.713345340040138150  ] 
dist 1=[46.266857835966026093  ,46.967411103892658803  ] 
dist 2=[45.348224540739784545  ,47.117387451365495816  ] 
dist 3=[44.216363506708237722  ,47.233862573165829175  ] 
dist 4=[42.918198059277758759  ,47.353796341178591702  ] 
dist 5=[41.245675308753031422  ,47.447427256832513245  ] 
dist 6=[38.618367491647022067  ,47.458892687735915443  ] 
dist 7=[35.935363404671721277  ,47.411778634982062368  ] 
dist 8=[34.040286340947681496  ,47.357376345965564503  ] 
dist 9=[32.353630227128227290  ,47.082249588850142855  ] 
dist 10=[30.503012943883570448  ,46.985232512798763196  ] 
dist 11=[28.681154251157743913  ,46.617386105379860177  ] 
dist 12=[27.109232168457114471  ,46.524171923840354229  ] 
dist 13=[25.413665008746031802  ,45.438342529975024826  ] 
dist 14=[23.097630782951405410  ,44.607688505060058652  ] 
dist 15=[20.777630549339756333  ,33.985258326709995630  ] 
dist 16=[19.066073065107495554  ,33.667458797318291856  ] 
dist 17=[17.465631982394091760  ,30.206968272328414776  ] 
dist 18=[15.589317767577709292  ,29.541661618006272380  ] 
dist 19=[13.669213997497496541  ,28.834667351799016806  ] 
dist 20=[11.893556390478745473  ,28.703938220807717790  ] 
dist 21=[9.8751227949523156646 ,22.255887517362818064  ] 
dist 22=[6.9845227215220506087 ,21.444536540655937865  ] 
dist 23=[4.1269038784513343631 ,19.846310291090522377  ] 
dist 24=[2.2401779514703413017 ,19.441641811894717936  ] 
dist 25=[.6940867517202166755 ,18.052293741634655503  ] 
dist 26=[-.8022460391422155334 ,17.739070858754285617  ] 
dist 27=[-2.1612376216625624151 ,17.389149661461993479  ] 
dist 28=[-3.1585248772243793887 ,17.312942604259708418  ] 
dist 29=[-4.0872245356358586811 ,11.495414504805563008  ] 
dist 30=[-5.1722798344982051663 ,9.5331147839058538349 ] 
dist 31=[-6.1805773369179484194 ,1.4620095122493175483 ] 
dist 32=[-7.6408909631805420260 ,1.1015634369595769404 ] 
dist 33=[-8.9580566493315951776 ,-1.7432644371378416036 ] 
dist 34=[-10.132214012136642669  ,-2.2278399172776764036 ] 
dist 35=[-11.133445571125688369  ,-2.9602387828122535099 ] 
dist 36=[-11.759664178987266628  ,-3.1366064143232009702 ] 
dist 37=[-12.235988542965782311  ,-2.7533429012885881708 ] 
dist 38=[-12.638578696090176347  ,-1.6680305585693278521 ] 
dist 39=[-12.964039447213533242  ,-.55065364353236798644] 
dist 40=[-13.132123405371166710  ,.2287302319866506309 ] 
dist 41=[-13.220097848242306035  ,.90841835971335714963] 
dist 42=[-13.225008765247102441  ,1.6282228766836408206 ] 
dist 43=[-13.178340517678834551  ,2.3175812154518855507 ] 
dist 44=[-13.144726144218514496  ,2.8758895324811125912 ] 
dist 45=[-12.945909467580339829  ,3.4445766088878145218 ] 
dist 46=[-12.915579897197260753  ,4.1754392965300939672 ] 
dist 47=[-7.9500473676078751762 ,4.8814670504543307255 ] 
dist 48=[-7.4819399769413101509 ,5.3510765148033219080 ] 
dist 49=[-6.3463806079554063859 ,5.7371111651413103091 ] 
dist 50=[-6.1682375143517644171 ,6.1096273948545261022 ] 
dist 51=[-4.5136976867510181855 ,6.4445821704655727008 ] 
dist 52=[-4.4089918920369789460 ,6.6807061564726815459 ] 
dist 53=[-3.8086006905616369720 ,6.8893940266010261238 ] 
dist 54=[-3.7558314693201660232 ,7.1148104387685760778 ] 
dist 55=[-2.9704981595510058287 ,7.3145088103302229462 ] 
dist 56=[-2.9153150720999009611 ,7.4205513300310177362 ] 
dist 57=[-2.5190078926502053875 ,7.4780082525980868934 ] 
dist 58=[-2.4459326708537799045 ,7.4838303272095608324 ] 
dist 59=[-2.3209120623007081385 ,7.4557491915087681506 ] 
dist 60=[-2.2917404555160064884 ,7.4344774610349706580 ] 
dist 61=[-1.2240676109494880121 ,7.3017773803360582812 ] 
dist 62=[-1.1083434041808195287 ,7.0126626473951336047 ] 
dist 63=[-.85346262734021791963,2.8588853852433033973 ] 
dist 64=[-.79837327290685077872,3.1906533210704012901 ] 
dist 65=[-.49571236398415915128,3.4532169418814771033 ] 
dist 66=[-.44045403529514195821,3.6912878948458010684 ] 
dist 67=[-.32738744890814642796,3.8964261486047507197 ] 
dist 68=[-.2973948683249021922 ,4.0274409764339822829 ] 
dist 69=[-.0036503535414749828 ,4.1297711794971369424 ] 
dist 70=[.0414765673203110420 ,4.2203436589632819706 ] 
dist 71=[.1354193255346706985 ,4.2921427374645360478 ] 
dist 72=[.1610660039553851073 ,4.3194896388152927316 ] 
dist 73=[.2619861603457875768 ,4.3265686547325773367 ] 
dist 74=[.2819870540289579569 ,4.3193189204821982875 ] 
dist 75=[.3298834436863968348 ,4.2382456227368108130 ] 
dist 76=[.3404259307177107112 ,4.2103466998569618589 ] 
dist 77=[1.6335000987091587245 ,4.1699543968622921692 ] 
dist 78=[.91878850254443264197,4.1518026217467140331 ] 
dist 79=[.19817659623721775044,3.1617067789365517950 ] 
dist 80=[-.29031458939422146261,3.0520352758955293983 ] 
dist 81=[-.7029778389083908778 ,2.7743249474332109599 ] 
dist 82=[-1.1208509528425501940 ,2.7315942855102144432 ] 
dist 83=[-1.5108256775164016307 ,2.2800120945927785152 ] 
dist 84=[-1.8121125588550913792 ,2.1915417932108730092 ] 
dist 85=[-2.1066165826476095768 ,2.0918654452559938822 ] 
dist 86=[-2.4695306513258638778 ,2.0659439690286781186 ] 
dist 87=[-2.8141691517359215607 ,1.1986867436603535247 ] 
dist 88=[-3.0357118488576171877 ,1.0882148702875818967 ] 
dist 89=[-3.2099144126549470452 ,.8629419179597365625 ] 
dist 90=[-3.3655393614238796237 ,.8041437787567611354 ] 
dist 91=[-3.4977291825604589380 ,.5902896712566133357 ] 
dist 92=[-3.5783716443471593403 ,.5456360726739957509 ] 
dist 93=[-3.6369495891657445374 ,.4705086629818958705 ] 
dist 94=[-3.6810690455073201794 ,.4524088105893949553 ] 
dist 95=[-3.7101698457893902874 ,-.4686518113838532605 ] 
dist 96=[-3.7143373466155067862 ,-.44847483210385383642] 
dist 97=[-3.6981712430629563237 ,-.41308552051226578189] 
dist 98=[-3.6903966408987799619 ,-.3584580628524723412 ] 
dist 99=[-3.5598096533531935140 ,-.2793128811738423042 ] 
dist 100=[-3.5239495722527566766 ,-.1460337963796096571 ] 
dist 101=[-3.4908327413317630806 ,-.0020388684502427749 ] 
dist 102=[-3.4695688223155067475 ,.1198963024043594873 ] 
dist 103=[-2.8813717528035736847 ,.2490948555612731979 ] 
dist 104=[-2.7979173484851122720 ,.4221067508443107480 ] 
dist 105=[-2.6337880394849509133 ,.6102340380126212233 ] 
dist 106=[-2.5890400744860281405 ,.7997891073987411844 ] 
dist 107=[-2.4199798978257413371 ,1.0269024335199700801 ] 
dist 108=[-2.3799436768103264327 ,1.3649877503161388800 ] 
dist 109=[-2.3030729764977234243 ,1.7023243879675906182 ] 
dist 110=[-2.2807254653207859802 ,1.9264525957379740068 ] 
dist 111=[-.3692586079407671869 ,2.1108244029823977421 ] 
dist 112=[-.2037222295006063824 ,2.2894387439123721783 ] 
dist 113=[.1629394122079990856 ,2.4509286950097270896 ] 
dist 114=[.2335057491349101690 ,2.5669343775209541852 ] 
dist 115=[.6541766518980147720 ,2.6719794731447754880 ] 
dist 116=[.7253222862552668933 ,2.7897131279614765923 ] 
dist 117=[.8678489903071317472 ,2.8956104587848644502 ] 
dist 118=[.90166315494713552666,2.9534009124058036285 ] 
dist 119=[1.1447125999358603984 ,2.9870955677988459391 ] 
dist 120=[1.1847039789240482829 ,2.9967922064987969342 ] 
dist 121=[1.0841807962915989950 ,2.9950002776160455049 ] 
dist 122=[.88357692469838332107,2.9875513825768008404 ] 
dist 123=[.57451135853284961953,2.9656599333020635682 ] 
dist 124=[.06027025640655521948,2.9439675909759118639 ] 
dist 125=[-.45747646112646125056,2.6955778358834451911 ] 
dist 126=[-.80614424792317389669,2.6113762421297483110 ] 
dist 127=[-1.0980445604148554185 ,2.3953002892873556486 ] 
dist 128=[-1.3891637908476708665 ,2.3839402344253309606 ] 
dist 129=[-1.6578160873797948375 ,2.2267301423541181682 ] 
dist 130=[-1.8600233445185459279 ,2.1906368759562537718 ] 
dist 131=[-2.0524693284885343661 ,2.1563425133898444386 ] 
dist 132=[-2.2821514381655127728 ,2.1423649545317545633 ] 
dist 133=[-2.4962304562420262182 ,1.6582134083122098670 ] 
dist 134=[-2.6263848618680588472 ,1.5927918339264056056 ] 
dist 135=[-2.7200942786297382434 ,1.4636762866088792891 ] 
dist 136=[-2.7886761690589902150 ,1.4294183122573362720 ] 
dist 137=[-2.8387643606071412036 ,1.3043514871768817343 ] 
dist 138=[-2.8586435238107844072 ,1.2752840033615662043 ] 
dist 139=[-2.8636097117445672193 ,1.2265300132189599256 ] 
dist 140=[-2.8593112703540101837 ,1.2132341522452060328 ] 
dist 141=[-1.0706645305115293174 ,.06058570081913558897] 
dist 142=[-1.1029252197610633409 ,-.00334652343442750485] 
dist 143=[-1.1306822635159166892 ,-.1487799541781004537 ] 
dist 144=[-1.1446494674752228885 ,-.17249695580489173277] 
dist 145=[-1.1512659336149612730 ,-.24188695377314026161] 
dist 146=[-1.1515738931908968395 ,-.16913225909321778627] 
dist 147=[-1.2455698991861000794 ,-.09344869120095138881] 
dist 148=[-1.4682747001298908055 ,-.02212779018444625821] 
dist 149=[-1.6860214258966624992 ,.05971644086734553903] 
dist 150=[-1.8365232825547770090 ,.17741582258116595496] 
dist 151=[-1.9667991484997327802 ,.29739620623999580194] 
dist 152=[-2.1037921681703534730 ,.38834963993974255691] 
dist 153=[-2.2348616507580031562 ,.47554881752904422737] 
dist 154=[-2.3414891405058827766 ,.58054573583873161746] 
dist 155=[-2.4508005208158919478 ,.68908946516099285137] 
dist 156=[-2.5925908800638613119 ,.79045216349400871081] 
dist 157=[-2.7253918825102943546 ,.90609109068624676977] 
dist 158=[-2.7988121489714106264 ,1.0716357866339980487 ] 
dist 159=[-2.8429115328722683079 ,1.2345004784031475228 ] 
dist 160=[-2.8586401924316617194 ,1.3394407996921454774 ] 
dist 161=[-2.8630241005441730146 ,1.5233803869719495788 ] 
dist 162=[-2.8618248011246642911 ,1.6854669203076769579 ] 
dist 163=[-2.8563131714449178552 ,1.8503758989548507752 ] 
dist 164=[-2.8476425978025219197 ,2.0625323644470474714 ] 
dist 165=[-2.5230144460124497437 ,2.2682685516615474136 ] 
dist 166=[-2.4733218901571617818 ,2.4075447798245970717 ] 
dist 167=[-2.3800467200292927245 ,2.5249791777894002930 ] 
dist 168=[-2.3540608721631503164 ,2.6435116502934251001 ] 
dist 169=[-2.2554285483788975964 ,2.7538548525403175283 ] 
dist 170=[-2.2291218555408205174 ,2.8385937935776780853 ] 
dist 171=[-2.1790053779789664775 ,2.9209144121627710989 ] 
dist 172=[-2.1632051049528107338 ,3.0216032823567680673 ] 
dist 173=[-.62069068285301113819,3.1135682926154906771 ] 
dist 174=[-.48725816976445301059,3.1610584734739028098 ] 
dist 175=[-.30441229198009508234,3.1851199237773951001 ] 
dist 176=[-.52656303496928507764,3.1883764772227292671 ] 
dist 177=[-.71117154386382303094,3.1714673374197422009 ] 
dist 178=[-.89310635630839608734,3.1595992289453151338 ] 
dist 179=[-1.0596442242574532252 ,3.1319052020790552135 ] 
dist 180=[-1.1827808713123469440 ,3.1182247758325952229 ] 
dist 181=[-1.2978476295595284798 ,2.8158986367119312242 ] 
dist 182=[-1.4321661624989449317 ,2.7669551662397715672 ] 
dist 183=[-1.5558726084997754912 ,2.6574357301407228157 ] 
dist 184=[-1.6285710245730665987 ,2.6224129575294250522 ] 
dist 185=[-1.6779024954229415999 ,2.4614196022083076126 ] 
dist 186=[-1.7083179559631836348 ,2.4263097878687962505 ] 
dist 187=[-1.7292067396337435326 ,2.3377315392380950090 ] 
dist 188=[-1.7405035249527281919 ,2.3127329836259153967 ] 
dist 189=[-1.7469467922385241223 ,2.2355378657022727652 ] 
dist 190=[-1.7484580663219474229 ,2.3010952496395414453 ] 
dist 191=[-1.5322254425678903879 ,2.3447703478285528283 ] 
dist 192=[-1.8457849117990178728 ,2.3700931139371180127 ] 
dist 193=[-2.1257611178784181691 ,2.3841984810658657628 ] 
dist 194=[-2.3208831474649769623 ,2.3843243498413384728 ] 
dist 195=[-2.4914629988848763937 ,2.3756530909914463074 ] 
dist 196=[-2.6734517153881773509 ,2.3668917220481961135 ] 
dist 197=[-2.8386230714734293494 ,2.2093856167861156690 ] 
dist 198=[-2.9420578796613703445 ,2.1809116349722914452 ] 
dist 199=[-3.0202038577472946546 ,2.1157227814544032380 ] 
dist 200=[-3.0844072763619595019 ,2.0935921911148913829 ] 
dist 201=[-3.1348243292174639539 ,1.9870780742359371928 ] 
dist 202=[-3.1579268852676799184 ,1.9628078948177134154 ] 
dist 203=[-3.1654686247717862560 ,1.9026782965957768664 ] 
dist 204=[-3.1629773001098393345 ,1.8826345244788535096 ] 
dist 205=[-1.7635003285193110211 ,.18461288498842556648] 
dist 206=[-1.8828966388434726790 ,.44247096808980547437] 
dist 207=[-1.9964015696000365727 ,.70328753748761865814] 
dist 208=[-2.0620324070309325370 ,.88136322419228012971] 
dist 209=[-2.1052527949887589035 ,1.0331575680921026358 ] 
dist 210=[-2.1292794274450102721 ,1.1890435296778297013 ] 
dist 211=[-2.1431963188402625818 ,1.3358692497954097541 ] 
dist 212=[-2.1460511754078590648 ,1.4514897966103213240 ] 
dist 213=[-2.1413538884342285401 ,1.5665463082768169148 ] 
dist 214=[-2.1371557630226585851 ,1.7111201470014116722 ] 
dist 215=[-1.9528849206165572191 ,1.8496915917333428784 ] 
dist 216=[-1.9224752966478368694 ,1.9407830028173356434 ] 
dist 217=[-1.8619886310007527577 ,2.0146533147636541838 ] 
dist 218=[-1.8436354375085898534 ,2.0844678860994686877 ] 
dist 219=[-1.7649167622996716970 ,2.1464375484964076494 ] 
dist 220=[-1.7461640891371209447 ,2.1889863237154070199 ] 
dist 221=[-1.6965796934648333785 ,2.2255115364757255644 ] 
dist 222=[-1.6816542641581968303 ,2.2634315765432011568 ] 
dist 223=[-.82739839563710981875,2.2947498715284296744 ] 
dist 224=[-.84599179160685531402,2.3049169100874953811 ] 
dist 225=[-.85935753987676332991,2.3053477293195063773 ] 
dist 226=[-.8639402221984460393 ,2.3001190904501502670 ] 
dist 227=[-.86468089779218037219,2.2514360756881481755 ] 
dist 228=[-.86272517321702481917,2.2354564747720377406 ] 
dist 229=[-.82132244775579527408,2.2074050497880401444 ] 
dist 230=[-.81290705533940597814,2.1972748560530054253 ] 
dist 231=[-.79475139537427926186,1.9182021316099644564 ] 
dist 232=[-.78844717990722608533,1.8759266124930025581 ] 
dist 233=[-.75761180542218823957,1.7844268349022798582 ] 
dist 234=[-.75048444452636198396,1.7566812119028546962 ] 
dist 235=[-.7290337166278442902 ,1.6347813689354256944 ] 
dist 236=[-.72455980355480855049,1.6094223982626580666 ] 
dist 237=[-.37574053644177061117,1.5399094776190878638 ] 
dist 238=[-.34226118062248419501,1.5269197068734057389 ] 
dist 239=[-.5943584175705109421 ,1.4985322643165767746 ] 
dist 240=[-.87657744706235452555,1.5649038996285426052 ] 
dist 241=[-1.1072743272954755311 ,1.6135931591861079266 ] 
dist 242=[-1.3283966580279055418 ,1.6509747263234658789 ] 
dist 243=[-1.5267824210729550550 ,1.6782838185100911268 ] 
dist 244=[-1.6667006259971582890 ,1.6867572075573452649 ] 
dist 245=[-1.7907680194590702095 ,1.6881592769340362686 ] 
dist 246=[-1.9258672792594880851 ,1.6872342936257544153 ] 
dist 247=[-2.0486809349108350179 ,1.6354408429378460368 ] 
dist 248=[-2.1236964762092684255 ,1.6232230481871768844 ] 
dist 249=[-2.1781581713747729873 ,1.5906601402321469928 ] 
dist 250=[-2.2189080615431779900 ,1.5776208437357246745 ] 
dist 251=[-2.2477818475252786693 ,1.5078964858968475653 ] 
dist 252=[-2.2548266880926960602 ,1.4905608948677493861 ] 
dist 253=[-2.2536631272580924504 ,1.4559963806330267701 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 1, 1, 0, 1] 
dist 0=[49.420736693616409772  ,49.420736693616409772  ] 
dist 1=[48.652126111611960510  ,49.817883341856938351  ] 
dist 2=[47.764188109540646249  ,50.019632893011094375  ] 
dist 3=[46.890419708119415559  ,50.055242805147841664  ] 
dist 4=[45.857501770137467245  ,49.916984893371966942  ] 
dist 5=[44.333678305374932794  ,49.818610712928120844  ] 
dist 6=[42.605398799686838219  ,49.645976395591061998  ] 
dist 7=[40.755694461036612393  ,49.564058442899484892  ] 
dist 8=[38.456954348926372995  ,49.010556034871754249  ] 
dist 9=[34.934902379221218910  ,46.546902674539006990  ] 
dist 10=[31.371383453156006599  ,45.913371085767323196  ] 
dist 11=[28.906928132621034617  ,45.705461038243133365  ] 
dist 12=[26.767869938858014481  ,45.306275079322585632  ] 
dist 13=[24.504022433516065676  ,44.590590413438532686  ] 
dist 14=[22.324019703192399444  ,41.003327563800605013  ] 
dist 15=[20.519739305128596918  ,38.603792565566252090  ] 
dist 16=[18.638593142554697724  ,37.025715887763440025  ] 
dist 17=[16.151258302952951454  ,30.547519100366525383  ] 
dist 18=[13.696341191397857337  ,29.712443403612739916  ] 
dist 19=[11.944537716638070499  ,28.102614617819168024  ] 
dist 20=[10.365214099207483024  ,27.694292248443024270  ] 
dist 21=[8.5991109365106078866 ,26.307161993963874548  ] 
dist 22=[6.8382713770618910447 ,25.971967539475191036  ] 
dist 23=[5.2796692294058514830 ,25.629292233849647722  ] 
dist 24=[3.5627155702251659809 ,25.543846325526556417  ] 
dist 25=[1.1685878637102998323 ,12.645404107650565620  ] 
dist 26=[-1.1775478087382574322 ,11.661237725028922416  ] 
dist 27=[-2.7028320937497765250 ,11.439341968526976283  ] 
dist 28=[-3.9272807939681371226 ,10.839086324849670866  ] 
dist 29=[-5.0710794153938777397 ,10.416274852631143436  ] 
dist 30=[-6.0835812494979862438 ,9.0510780096871573252 ] 
dist 31=[-6.7833619214872442121 ,8.3140127361117625595 ] 
dist 32=[-7.3926805916778514481 ,-.18023860716952574921] 
dist 33=[-8.0438723616885196159 ,-4.5205667523895546131 ] 
dist 34=[-8.6236357490424497984 ,-5.0193900020815798648 ] 
dist 35=[-9.5389960549044657743 ,-6.1109404718691788283 ] 
dist 36=[-10.374092309419479792  ,-6.2679295630780743951 ] 
dist 37=[-10.890493493724997579  ,-6.0914200286868668937 ] 
dist 38=[-11.276655169789481428  ,-5.5150072562114981873 ] 
dist 39=[-11.591579682629904777  ,-4.8184801720233602020 ] 
dist 40=[-11.839802213872072381  ,-3.9013396041149540808 ] 
dist 41=[-11.959376654931576630  ,-2.4441393178446640138 ] 
dist 42=[-12.010186940899532197  ,-.96232224097858288124] 
dist 43=[-12.003074474353049923  ,.05319517801949748623] 
dist 44=[-11.914787193012090318  ,.92149844899429047931] 
dist 45=[-11.873281534534976726  ,1.8158570192901346008 ] 
dist 46=[-11.690698613351210812  ,2.6586201820331016235 ] 
dist 47=[-11.645866027075442127  ,3.3210458666378417250 ] 
dist 48=[-8.0318344818253257951 ,3.9784162851605993277 ] 
dist 49=[-6.9792885819542952627 ,4.8010553980696247981 ] 
dist 50=[-6.4288508510369529111 ,5.5866997865283947242 ] 
dist 51=[-6.0731353194946283806 ,6.0964143209911676441 ] 
dist 52=[-5.9821280636750219519 ,6.5018128674169167591 ] 
dist 53=[-5.6751138269195270919 ,6.8710545967638332773 ] 
dist 54=[-5.5945680441036482233 ,7.1889185562917790241 ] 
dist 55=[-5.5210629545197367520 ,7.3892176933483893570 ] 
dist 56=[-5.5002736454178185461 ,7.5417551600121657977 ] 
dist 57=[-2.0436893876280541742 ,7.6689326792282039977 ] 
dist 58=[-1.0494365004210767988 ,7.7667851285793931967 ] 
dist 59=[-.61267886924453544   ,7.8022536749543107151 ] 
dist 60=[-.1808366144868347016 ,7.7986639031381662235 ] 
dist 61=[.17182004048381394293,7.7858901783054884302 ] 
dist 62=[.39698180776502958938,7.6587793943853109944 ] 
dist 63=[.44987891698655223801,7.5249047693180522536 ] 
dist 64=[1.2308272006106447612 ,2.7522578076019530625 ] 
dist 65=[2.1187399984417743729 ,3.1991925435372109463 ] 
dist 66=[2.2599651329609946791 ,3.4809996962025779570 ] 
dist 67=[2.4710060268003266848 ,3.6965645726822709683 ] 
dist 68=[2.4488965597909942418 ,3.8789522383499357998 ] 
dist 69=[2.3230782074746390813 ,4.0267329861575544613 ] 
dist 70=[2.1552399210295606274 ,4.1040998072176449002 ] 
dist 71=[1.9420233023446956928 ,4.1471383139979234501 ] 
dist 72=[1.6545841394426938490 ,4.1577409463169667173 ] 
dist 73=[1.1904079634559549551 ,3.6416226097254268019 ] 
dist 74=[.71428922225687892121,3.3887702503258975544 ] 
dist 75=[.37915826002541839033,3.3493835734066360928 ] 
dist 76=[.08281393910283816053,3.2372348006133659583 ] 
dist 77=[-.23847771036292975552,3.2145757109551386942 ] 
dist 78=[-.55163099330200775602,3.0834672626876075042 ] 
dist 79=[-.81549812575941653903,3.0758909552151045073 ] 
dist 80=[-1.0941175842923466511 ,2.8674120668592964357 ] 
dist 81=[-1.4661865158416641473 ,2.8417064646722482286 ] 
dist 82=[-1.8335220655575538227 ,2.2319902259265003117 ] 
dist 83=[-2.0932520316010098200 ,2.1486882898935900516 ] 
dist 84=[-2.3242493539885403103 ,1.9762496861287539365 ] 
dist 85=[-2.5768783602064471158 ,1.9287561556076140599 ] 
dist 86=[-2.8245360935783294082 ,1.7425590517996663271 ] 
dist 87=[-3.0356955660100719885 ,1.7037629446307263303 ] 
dist 88=[-3.2609096953686831215 ,1.6172658801577018972 ] 
dist 89=[-3.5647018755763867865 ,1.5909835622851107455 ] 
dist 90=[-3.8567797440280915303 ,.7203884354780191291 ] 
dist 91=[-4.0352239862665777261 ,.71637962224522149333] 
dist 92=[-4.1649068058041614457 ,.72248086290477104178] 
dist 93=[-4.2622820983574743838 ,.73435107691745771431] 
dist 94=[-4.3327055797566577880 ,.75338818851288245233] 
dist 95=[-4.3547699254374964490 ,.78117538843982117108] 
dist 96=[-4.3584406532724202728 ,.82797980562441954233] 
dist 97=[-4.3554146666738384861 ,.87826485503928478602] 
dist 98=[-4.1856818798746088280 ,.91995688580443480491] 
dist 99=[-4.1489140566249701128 ,.96325229298318167227] 
dist 100=[-4.0622006553120700437 ,1.0199641963896824294 ] 
dist 101=[-4.0299414650167313213 ,1.0809083260035260353 ] 
dist 102=[-3.8647867212989835795 ,1.1411109766855515078 ] 
dist 103=[-3.8251126034604461977 ,1.2122986971357687229 ] 
dist 104=[-3.7264312218021484157 ,1.3171051445331119986 ] 
dist 105=[-3.6902868871121355170 ,1.4199344997663196245 ] 
dist 106=[-3.0943329155245656413 ,1.4832361760729567168 ] 
dist 107=[-3.0737139471481105691 ,1.5297329087435754313 ] 
dist 108=[-3.0027881775175677000 ,1.5654863265329150117 ] 
dist 109=[-2.9898515479077626337 ,1.9797424014479537994 ] 
dist 110=[-2.8033528739840936700 ,2.3813523487579597314 ] 
dist 111=[-2.7602128921102884381 ,2.6734881422989822420 ] 
dist 112=[-2.7206919488964876219 ,2.9417725365985346222 ] 
dist 113=[-2.7048843748078684702 ,3.2481513613614710770 ] 
dist 114=[-2.1146929216906788115 ,3.5305818233336852481 ] 
dist 115=[-2.0348391927992555159 ,3.7032489288167926139 ] 
dist 116=[-1.8786977400915214325 ,3.8288018713799249011 ] 
dist 117=[-1.8374656798156909641 ,3.9231232760161952492 ] 
dist 118=[-1.6884988322496086659 ,3.9921473279192782326 ] 
dist 119=[-1.6531074599141466539 ,4.0166955849638738141 ] 
dist 120=[-1.5970597374608787181 ,4.0225892557930427294 ] 
dist 121=[-1.5805475363156449058 ,4.0171329373661386994 ] 
dist 122=[-1.0278426879156658116 ,2.0171252066312562837 ] 
dist 123=[-1.2257947737312425453 ,2.0752087473781876886 ] 
dist 124=[-1.4100816052699813519 ,2.1191493542711855554 ] 
dist 125=[-1.5715949825032095202 ,2.1367449445600515646 ] 
dist 126=[-1.6786341496251904217 ,2.1433098383179169086 ] 
dist 127=[-1.7663126876602040847 ,2.1432021596585666555 ] 
dist 128=[-1.8505331804700493789 ,1.9664661355892907772 ] 
dist 129=[-1.9245720607485700708 ,1.9204435554103546755 ] 
dist 130=[-1.9716060133736827232 ,1.9081158202561897706 ] 
dist 131=[-2.0078644322178537293 ,1.8736076012918183286 ] 
dist 132=[-2.0388939004078372738 ,1.8593880447515050733 ] 
dist 133=[-2.0641791883089109995 ,1.7797310826794057503 ] 
dist 134=[-2.0775095119958824931 ,1.7596526833352075162 ] 
dist 135=[-2.0846255584474007059 ,1.7209168411065764035 ] 
dist 136=[-2.0851048948663126156 ,1.7085010693757158017 ] 
dist 137=[.13464684030884075505,1.0894041273791312126 ] 
dist 138=[.01143934629913541971,1.1068252941773248864 ] 
dist 139=[-.09175138724987471313,1.1169370881220336386 ] 
dist 140=[-.19478307860869897365,1.1221083806386920491 ] 
dist 141=[-.28998540282123721675,1.1221649125949073618 ] 
dist 142=[-.36191934065271516601,1.1154430233895308150 ] 
dist 143=[-.43068483785824538876,1.1124159202144575153 ] 
dist 144=[-.51324090362706032027,.81918903829463182456] 
dist 145=[-.5905225138451751373 ,.78961100289283489547] 
dist 146=[-.63823116553181166723,.71905635222440027529] 
dist 147=[-.67348946039232683272,.70457215719611138606] 
dist 148=[-.70106350058376976903,.60108849889980775144] 
dist 149=[-.72266163435676193189,.58078064119804646941] 
dist 150=[-.73405752285113352667,.54633427296502164304] 
dist 151=[-.74018186184426153759,.53759615385342770047] 
dist 152=[-.74077877846929741659,.37076511792245432964] 
dist 153=[-.70104706716631600474,.34837720946161127389] 
dist 154=[-.69421411155234960098,.29495769460804622191] 
dist 155=[-.67884967841940456305,.28570557012540366476] 
dist 156=[-.69976426420634581285,.209637093410138232  ] 
dist 157=[-.77371734823378222165,.19539568701603316985] 
dist 158=[-.85418139852081890711,.17446243361891266088] 
dist 159=[-.96473298999283981529,.16855233666540638229] 
dist 160=[-1.0721602991004073110 ,-.02644201562672113816] 
dist 161=[-1.1401494444742278993 ,.06367273466379300283] 
dist 162=[-1.1923657414113125322 ,.13250103233519269114] 
dist 163=[-1.2368151515104047505 ,.19899466141048750705] 
dist 164=[-1.2729429729605700709 ,.27979124452360191422] 
dist 165=[-1.2919327266930627203 ,.36371785218397550547] 
dist 166=[-1.3020291886576487852 ,.44271004631340293515] 
dist 167=[-1.3031413152791678916 ,.5333194650918791315 ] 
dist 168=[-1.2986611002683314803 ,.66363060414348904276] 
dist 169=[-1.2948932183521481191 ,.79223477208464248049] 
dist 170=[-1.2812821468742017219 ,.87602976224847531911] 
dist 171=[-1.2741062900390082339 ,.9431537888292476064 ] 
dist 172=[-1.2302454911213175428 ,1.0051983142378946462 ] 
dist 173=[-1.2183652645885146529 ,1.0593251633447303144 ] 
dist 174=[-1.1968093194777276292 ,1.0948377909896031687 ] 
dist 175=[-1.1898419528559302417 ,1.1235644423338118006 ] 
dist 176=[-.95643635172381443017,1.1505988848647112989 ] 
dist 177=[-.93453841330023790068,1.1723123512648723836 ] 
dist 178=[-.87642862572773534313,1.1797944927052903504 ] 
dist 179=[-.86729103450163020355,1.1817692381131663176 ] 
dist 180=[-.76285550064443201241,1.1814925275307171297 ] 
dist 181=[-.74151086652908184331,1.1480173619423894349 ] 
dist 182=[-.71890806401127152291,1.1385569150567654200 ] 
dist 183=[-.71246554192435348844,1.1321671212683755743 ] 
dist 184=[-.48012209871669305631,1.1282912714327686536 ] 
dist 185=[-.44999938897463266393,1.1872253391917438977 ] 
dist 186=[-.38946110544629549222,1.2292013413601266437 ] 
dist 187=[-.4511031522928564468 ,1.2586436395755144662 ] 
dist 188=[-.57894323677568772917,1.2802520029742110072 ] 
dist 189=[-.69703511363712880263,1.2909487861914784551 ] 
dist 190=[-.78618539250844181108,1.2957154621953056673 ] 
dist 191=[-.87131738597339194385,1.2946987406494725517 ] 
dist 192=[-.97336602240812609168,.81178107951665753047] 
dist 193=[-1.0687627472603822587 ,.61312465543696112885] 
dist 194=[-1.1273367643826647039 ,.58622362607930553685] 
dist 195=[-1.1702213121149731685 ,.53114486030490118324] 
dist 196=[-1.2029774209943645324 ,.51619836088912482452] 
dist 197=[-1.2274609418033996489 ,.45894392231384967632] 
dist 198=[-1.2373171188382030734 ,.44678227104713284695] 
dist 199=[-1.2405858340317277463 ,.41966093852587087517] 
dist 200=[-1.2387688994924071793 ,.38189411841140638727] 
dist 201=[-.02610626502286055667,.33195393337622074587] 
dist 202=[-.07440947698040897114,.34847983916948450528] 
dist 203=[-.11446214005203594467,.36532898692833699367] 
dist 204=[-.15380128649392771615,.38111736933232590524] 
dist 205=[-.18973414058515709896,.39340743820275146007] 
dist 206=[-.2161871383527755306 ,.40549963136459714258] 
dist 207=[-.24079913820293563053,.42049664753195002742] 
dist 208=[-.26938229735709965063,.43418342421217783148] 
dist 209=[-.29582501708491442571,.44104424293326344631] 
dist 210=[-.31189097265061860311,.44446272548538091197] 
dist 211=[-.32345505966541399372,.4448940372223929006 ] 
dist 212=[-.3319225730952823344 ,.44084579762638392005] 
dist 213=[-.33818951567493681665,.43873471075967698343] 
dist 214=[-.34096754668805677703,.43638853745278449716] 
dist 215=[-.37065992545526133965,.43467357163785840979] 
dist 216=[-.40426792101516876688,.37996288821274790785] 
dist 217=[-.42635595621757157923,.37169420971706799814] 
dist 218=[-.4442659607730026581 ,.3553156333952510823 ] 
dist 219=[-.46119224176585304169,.350620893173671295  ] 
dist 220=[-.4762190850166632226 ,.33170083123449695779] 
dist 221=[-.4865451905260550188 ,.32723342571437634952] 
dist 222=[-.49542017210476771618,.31691395270316209821] 
dist 223=[-.50465316330367015508,.31340966013982853568] 
dist 224=[-.51235080850816296274,.08900513593955415891] 
dist 225=[-.51509563282298655183,.06899564589840398960] 
dist 226=[-.51551377364609018021,.09429222885562472373] 
dist 227=[-.5145063875489070194 ,.1225701722904820622 ] 
dist 228=[-.50430580106528590701,.1560876265819929967 ] 
dist 229=[-.50087002527354731016,.19046200466731672959] 
dist 230=[-.49481268030720299795,.22216148342106897995] 
dist 231=[-.49260172173364728175,.25801623072008122059] 
dist 232=[-.43116164946402199552,.30898122602834336228] 
dist 233=[-.42182895629784013883,.35908624586165131358] 
dist 234=[-.40165863964866319762,.39150747240927541092] 
dist 235=[-.39553780905418786503,.41722536245536012058] 
dist 236=[-.36862809185649375929,.44056640066781013136] 
dist 237=[-.36302581072278613025,.4606287026600367798 ] 
dist 238=[-.34756636988033288788,.47325577975340693805] 
dist 239=[-.34473091518702897769,.48287046681033786939] 
dist 240=[-.13217056084313298941,.49090535377040114952] 
dist 241=[-.11180458443055904093,.49685403087988274391] 
dist 242=[-.06707885265525082679,.49813923689106480296] 
dist 243=[-.05745038896897149060,.4977004403096221431 ] 
dist 244=[-.00643364251657109400,.49676587234505232778] 
dist 245=[.00244146695695314847,.48211463709984224905] 
dist 246=[.02179999527388224434,.47779469559012806925] 
dist 247=[.02571131240544359098,.47354679444065304535] 
dist 248=[.05698181418576125284,.47089278255916881958] 
dist 249=[.06251128923352357691,.36088592860576022519] 
dist 250=[.06497881220140318224,.34797499222084199508] 
dist 251=[.06141479183823820250,.31665573856363119685] 
dist 252=[.05464186593104834836,.310623216512384842  ] 
dist 253=[.04367046043074432021,.26325671424299816107] 
dist 254=[.02750617156643014881,.25396288933600173252] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 2, 0, 1, 2] 
dist 0=[28.952103667826091343  ,28.952103667826091343  ] 
dist 1=[28.662715890262365393  ,29.551032729606941504  ] 
dist 2=[28.105204073240565149  ,30.383388361223635929  ] 
dist 3=[27.179604859615580201  ,31.605290948127893398  ] 
dist 4=[25.890557945746594942  ,32.801051871627125887  ] 
dist 5=[24.628749428007506192  ,33.529045334137019556  ] 
dist 6=[23.138469574771074332  ,34.057917329331422348  ] 
dist 7=[20.936304544486703027  ,34.457956364952076634  ] 
dist 8=[18.650385893329531757  ,34.757365484453318172  ] 
dist 9=[16.825354650444801919  ,34.883988939784500406  ] 
dist 10=[14.978848043050713670  ,34.929834054563617510  ] 
dist 11=[12.607043465348168487  ,34.913632501466399771  ] 
dist 12=[10.063545395242504063  ,34.311823104789448834  ] 
dist 13=[7.5307507135877784629 ,34.185847941428441732  ] 
dist 14=[4.5067782009654778738 ,33.930683413205464100  ] 
dist 15=[0                     ,33.843098674615266857  ] 
dist 16=[21.130561935620467667  ,33.420714899904312110  ] 
dist 17=[20.706744750373253090  ,33.320058081579751250  ] 
dist 18=[20.116787732972666094  ,32.990936345870804797  ] 
dist 19=[19.464699898563342711  ,32.933855786964606875  ] 
dist 20=[18.792350465191596308  ,27.033612242474013498  ] 
dist 21=[17.793530832296553414  ,26.467735298945383262  ] 
dist 22=[16.144159054768743611  ,25.244144601258414109  ] 
dist 23=[14.421393407910459313  ,24.940546575457049926  ] 
dist 24=[12.774183727849572966  ,23.563888769002686565  ] 
dist 25=[11.426742084195721668  ,23.313584579025764432  ] 
dist 26=[10.034873544213108225  ,22.615980661794413053  ] 
dist 27=[8.2101407580051594033 ,21.606202134744169506  ] 
dist 28=[6.4148044079635867635 ,16.545516514762280401  ] 
dist 29=[5.1403819479062192857 ,15.932189164931008158  ] 
dist 30=[3.9978782527610890969 ,13.864328938033545363  ] 
dist 31=[2.4044119917672033498 ,6.3900517230008494725 ] 
dist 32=[.7647299047652561647 ,5.1616636436647887785 ] 
dist 33=[-.5515538887712300512 ,4.9504665216574632640 ] 
dist 34=[-1.7808593358584995098 ,4.5596440561415189770 ] 
dist 35=[-2.8687902086471560539 ,4.4727263061896245022 ] 
dist 36=[-4.1638108640258901962 ,1.7076160227985007810 ] 
dist 37=[-5.2168786563089619761 ,1.4198351877790636778 ] 
dist 38=[-6.0475577989284469287 ,.8216814869192132247 ] 
dist 39=[-6.7979364602542340931 ,.6784505113423526478 ] 
dist 40=[-7.4441764101912241923 ,.0983080600153418346 ] 
dist 41=[-7.8587925200529146665 ,-.0080488299245949794 ] 
dist 42=[-8.1858372857554250637 ,-.2249877575183151035 ] 
dist 43=[-8.4823374580720048431 ,-.2808992321729481841 ] 
dist 44=[-8.7340200817336723796 ,-.4785783397415617937 ] 
dist 45=[-8.8819633113480006199 ,-.51670116665174658814] 
dist 46=[-8.9838677456139896912 ,-.51601238010369694305] 
dist 47=[-9.0513516377688829369 ,-.46436516663654188142] 
dist 48=[-9.0927145156959714184 ,-.38566431388563747925] 
dist 49=[-9.0901295298593733531 ,-.27683345425901304472] 
dist 50=[-9.0643649854268958274 ,-.12601554826926991296] 
dist 51=[-9.0397340562269511982 ,.1203584796156820737 ] 
dist 52=[-4.3962095560814924731 ,.36940400251122201838] 
dist 53=[-4.0494619594519095546 ,.53096617893746310402] 
dist 54=[-3.2263862592407322213 ,.65884657760873817987] 
dist 55=[-3.0996064279790926994 ,.77361153473512044422] 
dist 56=[-1.9681125120309778583 ,.8707746028030734477 ] 
dist 57=[-1.7647701079078190655 ,.92847826181438140287] 
dist 58=[-1.4916101755939194084 ,.96821008852087657307] 
dist 59=[-1.4215936915275425707 ,.9937216191009536422 ] 
dist 60=[-.3995750619673552541 ,1.0063092471225780152 ] 
dist 61=[-.3078271526721250040 ,1.0030301104025236680 ] 
dist 62=[-.2891213714131468713 ,1.1666820910702644507 ] 
dist 63=[.6628896388304559769 ,1.5301823401602562914 ] 
dist 64=[1.1066613450566089432 ,1.8721175853191351240 ] 
dist 65=[1.1774193416143571585 ,2.1417749670826484753 ] 
dist 66=[1.3000723383575790598 ,2.4111106820475882889 ] 
dist 67=[1.3226343733968304398 ,2.7518973665215389920 ] 
dist 68=[1.6722266929294337300 ,3.0774429045322737419 ] 
dist 69=[1.6318590295373002073 ,3.2859281738764446547 ] 
dist 70=[1.5222528220021089335 ,3.4495815747675756339 ] 
dist 71=[1.3893600613749292308 ,3.5959999737514352808 ] 
dist 72=[1.2559943721537230335 ,3.7210895894700748841 ] 
dist 73=[1.0968832873309724322 ,3.7995346692612679111 ] 
dist 74=[.8611367912321053926 ,3.8593588687642259216 ] 
dist 75=[.5940947748223533164 ,3.9100827725397475699 ] 
dist 76=[.3100090663782735399 ,3.9475981198435281538 ] 
dist 77=[-.0411818170579880590 ,3.9546538583522295430 ] 
dist 78=[-.5761564881103050872 ,3.9494430941458988284 ] 
dist 79=[-1.1130326076775623341 ,3.9378736595986384071 ] 
dist 80=[-1.4718308228560967658 ,3.8449179218589465029 ] 
dist 81=[-1.7692357951200879618 ,3.8164754748204785290 ] 
dist 82=[-2.0610310930349928716 ,3.7735939579910582070 ] 
dist 83=[-2.3272706121543538655 ,3.7563012703584399190 ] 
dist 84=[-2.5226620237539883753 ,2.8637606260920004665 ] 
dist 85=[-2.9214348034042826851 ,2.8205038715557040571 ] 
dist 86=[-3.2816307908574160339 ,2.8022468211486276300 ] 
dist 87=[-3.6247011074848110660 ,2.5556018361092704716 ] 
dist 88=[-3.9310455375324580070 ,2.5148251385906833959 ] 
dist 89=[-4.1446255248446659476 ,2.4119716784542240320 ] 
dist 90=[-4.3314785981402636620 ,2.3864571725678910765 ] 
dist 91=[-4.5311376677746224075 ,2.2080352868256234722 ] 
dist 92=[-4.7055882328731571850 ,2.1694860568838117848 ] 
dist 93=[-4.7918049212404007018 ,2.1033948711166749893 ] 
dist 94=[-4.8362935032306289277 ,2.0851421324331739559 ] 
dist 95=[-4.8441040058046134431 ,1.2579595944258708148 ] 
dist 96=[-4.7817875030443549567 ,1.1695557735882829903 ] 
dist 97=[-4.7615677876934457873 ,.9565962961348286673 ] 
dist 98=[-4.7457539784175817623 ,.9230533842373347598 ] 
dist 99=[-4.7317974818651270913 ,.6157230181380587437 ] 
dist 100=[-4.4564605438728276000 ,.62983016318182707775] 
dist 101=[-4.4251275789880458510 ,1.2427863348942075278 ] 
dist 102=[-4.3180469301977923065 ,1.7571473330375831608 ] 
dist 103=[-4.2980793151889782616 ,2.2719849731779026623 ] 
dist 104=[-4.0192905990474651740 ,2.7481952717820883367 ] 
dist 105=[-3.9550397512135108640 ,3.1083534414411897642 ] 
dist 106=[-3.8940950295201690548 ,3.4527550548566955537 ] 
dist 107=[-3.8689819293091932912 ,3.8660619976518904661 ] 
dist 108=[-3.0027881775175676999 ,4.2523541456750565121 ] 
dist 109=[-2.8856896354339639392 ,4.4889091879212967060 ] 
dist 110=[-2.6543993095096506514 ,4.6612377934630598688 ] 
dist 111=[-2.5929866478069275274 ,4.7911309207262184951 ] 
dist 112=[-2.3685404318237438294 ,4.8873087158036048387 ] 
dist 113=[-2.3164414575277166680 ,4.9250452732707169670 ] 
dist 114=[-2.2287258685081444834 ,4.9361654655370083920 ] 
dist 115=[-2.2049227738113449610 ,4.9274174729417122491 ] 
dist 116=[-1.6760398051948327473 ,2.0779827629989948270 ] 
dist 117=[-1.7267745606467623008 ,2.2333044890619645379 ] 
dist 118=[-1.7827070832516647950 ,2.4129120411641313544 ] 
dist 119=[-1.8323802003337294324 ,2.5774670810313840680 ] 
dist 120=[-1.8581225965072573547 ,2.6726825964230008974 ] 
dist 121=[-1.8712394655904432423 ,2.7354335121647541339 ] 
dist 122=[-1.8726237444773178808 ,2.7703590028809642264 ] 
dist 123=[-1.8636939453662818914 ,2.7919069363853441778 ] 
dist 124=[-1.8572502465868145351 ,2.8012531408305461675 ] 
dist 125=[-1.8396074225742403718 ,2.8034580525252943033 ] 
dist 126=[-1.8306615022986679037 ,2.7973033127099131808 ] 
dist 127=[.56486417365753028788,2.5635085280365291173 ] 
dist 128=[.69053931328487169807,2.6161662967450662435 ] 
dist 129=[.97060614817024449627,2.6398007542633158537 ] 
dist 130=[1.0169939408431561689 ,2.6479252083314179519 ] 
dist 131=[1.3354045764650968905 ,2.6465139049658552717 ] 
dist 132=[1.3711009932876603846 ,2.2764269858016360712 ] 
dist 133=[1.1899529961784531713 ,2.2328267748525901358 ] 
dist 134=[1.0190983550784355967 ,2.1319977823371761576 ] 
dist 135=[.81737543196453185234,2.1002278545530156175 ] 
dist 136=[.61097527251761097316,1.9735423590637749337 ] 
dist 137=[.42144206977058228725,2.0223672948257284118 ] 
dist 138=[.20773552186635707316,2.0535115404259483284 ] 
dist 139=[-.09518159178449671154,2.0739408436452967553 ] 
dist 140=[-.40224142672812951182,2.0799831964806332269 ] 
dist 141=[-.63249086237285632796,2.0779854155773557759 ] 
dist 142=[-.85085532021342965197,2.0739113394235316026 ] 
dist 143=[-1.1104686298991622324 ,1.6954081553852671729 ] 
dist 144=[-1.3771386370754916525 ,1.6531155456638113194 ] 
dist 145=[-1.6236810026620826922 ,1.5512003369902981133 ] 
dist 146=[-1.9030343681964744347 ,1.5273199506019178341 ] 
dist 147=[-2.3007100439284373654 ,1.3700469883495168253 ] 
dist 148=[-2.6918849130932945893 ,1.3377116922581922562 ] 
dist 149=[-2.9452843796187831348 ,1.2793483225690598299 ] 
dist 150=[-3.1466166911365774570 ,1.2640969704745106400 ] 
dist 151=[-3.3299073977871113502 ,.97749865141169494325] 
dist 152=[-3.4878610468597248023 ,.93769986335409796249] 
dist 153=[-3.5880327839450792520 ,.84156757903670426023] 
dist 154=[-3.6651973959375756258 ,.82373514621133807198] 
dist 155=[-3.7312941311769476559 ,.68079963456954478633] 
dist 156=[-3.7811660327174339487 ,.65314928030467471081] 
dist 157=[-3.7935508496426578450 ,.61138304045794382014] 
dist 158=[-3.7919002782178952211 ,.5995010165405572165 ] 
dist 159=[-3.7857311998982636422 ,-1.1221136954453243750 ] 
dist 160=[-3.6746561750715336328 ,-1.2259425051125826486 ] 
dist 161=[-3.6416789862730159084 ,-1.3898430885249579642 ] 
dist 162=[-3.6113594253285066753 ,-.94754503458394303565] 
dist 163=[-3.5909555538169307335 ,-.22194332418945776444] 
dist 164=[-3.0732119706552714306 ,.50762705753919542942] 
dist 165=[-3.0179123309183190465 ,.9985296591495528677 ] 
dist 166=[-2.8681619806363546870 ,1.4092251758424528298 ] 
dist 167=[-2.8421528207489056655 ,1.8185627636742442830 ] 
dist 168=[-2.6489311434260149711 ,2.1963160779680862223 ] 
dist 169=[-2.6273503131673354728 ,2.4809089481639215964 ] 
dist 170=[-2.6154644877636990185 ,2.7521265840312331450 ] 
dist 171=[-2.5265500883661993387 ,3.0764780865191213939 ] 
dist 172=[-2.5021174528868908619 ,3.3793328067536453072 ] 
dist 173=[-2.4637046268518944660 ,3.5647227485356579826 ] 
dist 174=[-2.4497528447458154659 ,3.6997935721923021639 ] 
dist 175=[-2.0490707816092869370 ,3.8017451062533267013 ] 
dist 176=[-2.0130917717267040872 ,3.8778763939800707499 ] 
dist 177=[-1.9141132269231942947 ,3.9098579764841941195 ] 
dist 178=[-1.8980618794880556522 ,3.9205002597979143782 ] 
dist 179=[-1.7073692678218823632 ,3.9159708008442099499 ] 
dist 180=[-1.6672898768088410175 ,1.7505016973313919992 ] 
dist 181=[-1.6258947481459041229 ,1.9350141552647210751 ] 
dist 182=[-1.6128750998110224229 ,2.1529016956463281122 ] 
dist 183=[-1.1512467811807827078 ,2.3549691541965765866 ] 
dist 184=[-1.0906221704783166226 ,2.4763170561255547795 ] 
dist 185=[-.96947748892643757975,2.5619342137202173830 ] 
dist 186=[-.93764572432701488545,2.6213400157720933891 ] 
dist 187=[-.8221010134626070491 ,2.6646137485774070211 ] 
dist 188=[-.79634679787191087641,2.6858204234059821959 ] 
dist 189=[-.7540133776365493567 ,2.6949497459371016432 ] 
dist 190=[-.74274835476613343934,2.6925439814202810487 ] 
dist 191=[.12944196540931303831,2.5341835211165540855 ] 
dist 192=[.16421061215213485695,2.6690089295812361170 ] 
dist 193=[.23406887792618462441,2.7761643852181384108 ] 
dist 194=[.05639278370937514592,2.8837239149868834293 ] 
dist 195=[-.35476880491091615951,3.0201637131731974947 ] 
dist 196=[-.77184295405061906199,3.1464465913992803147 ] 
dist 197=[-1.0586285266131534754 ,3.2134531167738307117 ] 
dist 198=[-1.3052682420988802934 ,3.2499576364056773196 ] 
dist 199=[-1.5620552838608025655 ,3.2581183736184121045 ] 
dist 200=[-1.8061184306456053971 ,3.2477877360939556003 ] 
dist 201=[-2.0019565575908892661 ,3.2397096640437461458 ] 
dist 202=[-2.2002381198536384873 ,3.2290419693627456564 ] 
dist 203=[-2.4540571978573156650 ,3.2175759201919092351 ] 
dist 204=[-2.6996276271535391939 ,2.8233980869913361193 ] 
dist 205=[-2.8649755131307883151 ,2.7638868337987200505 ] 
dist 206=[-3.0034381608880269797 ,2.6503029679405531815 ] 
dist 207=[-3.1416659587935197302 ,2.6185922994767514566 ] 
dist 208=[-3.2693812172261517965 ,2.5520506933078651035 ] 
dist 209=[-3.3658713329938380358 ,2.5925572452510249760 ] 
dist 210=[-3.4580966253586037016 ,2.6091683618105739719 ] 
dist 211=[-3.5687842870491540834 ,2.6150816100605824898 ] 
dist 212=[-3.6690051549406884967 ,2.6128756271040918069 ] 
dist 213=[-3.7194404024772984312 ,2.6042934243591947722 ] 
dist 214=[-3.7431251757645486484 ,2.5973873970627545225 ] 
dist 215=[-3.7461904922544492048 ,2.3376970368955575310 ] 
dist 216=[-3.7183537662661629632 ,2.2964684217506512455 ] 
dist 217=[-3.7028022981402999554 ,2.2146326737175658791 ] 
dist 218=[-3.6690405927988837419 ,2.1903942905134474172 ] 
dist 219=[-3.6532299236427658185 ,2.0890669517594518700 ] 
dist 220=[-3.2842847627808618864 ,2.0649989741216766681 ] 
dist 221=[-3.2253071592688183525 ,2.0046043548338330278 ] 
dist 222=[-3.0945821315055194312 ,1.9843836413075117390 ] 
dist 223=[-3.0532392384684362297 ,.72625787329013163459] 
dist 224=[-2.9209644603797140102 ,.61236023025548108579] 
dist 225=[-2.9246456959686509966 ,.35339316357451944412] 
dist 226=[-2.9196405962919243109 ,.30590336652470275602] 
dist 227=[-2.8648873154605754173 ,.18820808896597746276] 
dist 228=[-2.8460391370625108061 ,.89943471725135589856] 
dist 229=[-2.8123561945530981235 ,1.3686869104425967938 ] 
dist 230=[-2.7998240151947773437 ,1.7511608052904492116 ] 
dist 231=[-2.7013189303449502537 ,2.1159129574587878714 ] 
dist 232=[-2.7150446451721230203 ,2.4419257615267515138 ] 
dist 233=[-2.7142489008608168342 ,2.6697273738071131907 ] 
dist 234=[-2.7033978554193889960 ,2.8695126914568886800 ] 
dist 235=[-2.6934148830967314615 ,3.0836664554665860070 ] 
dist 236=[-2.5059631066863192079 ,3.2782786730226018704 ] 
dist 237=[-2.4725887401094681019 ,3.4000416221442790473 ] 
dist 238=[-2.3967470245860041005 ,3.4919142547772492898 ] 
dist 239=[-2.3712399404475403263 ,3.5671852366019010250 ] 
dist 240=[-2.2493142283007379280 ,3.6261346913786362874 ] 
dist 241=[-2.2217044694033469216 ,3.6528413360267356881 ] 
dist 242=[-2.1522865315026940313 ,3.6610734332237410099 ] 
dist 243=[-2.1302815727094974783 ,3.6584656812300426596 ] 
dist 244=[-2.0903380506354595293 ,2.0773287133734935547 ] 
dist 245=[-2.0883773938915937296 ,2.2340746897973037323 ] 
dist 246=[-2.0865038797603972759 ,2.4045744595367723805 ] 
dist 247=[-1.9994534939962076689 ,2.5596825572811951950 ] 
dist 248=[-1.9811815833575598837 ,2.6549749087184804983 ] 
dist 249=[-1.9354670534036862470 ,2.7248224288617736623 ] 
dist 250=[-1.9182672365447812037 ,2.7783381008944785298 ] 
dist 251=[-1.8295843257957424074 ,2.8173381799434941971 ] 
dist 252=[-1.8081488263070340138 ,2.8292299675403889886 ] 
dist 253=[-1.7621483524655186495 ,2.8296048634200886915 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 2, 2, 1, 0, 2] 
dist 0=[39.433322533830120231  ,39.433322533830120231  ] 
dist 1=[38.798901730126829241  ,39.685062370107086715  ] 
dist 2=[37.804005356838251384  ,40.055995564536361749  ] 
dist 3=[36.171169976752368930  ,40.477326096950334390  ] 
dist 4=[34.488428379767817842  ,40.801996967226913713  ] 
dist 5=[33.294116655744181505  ,41.054082926340579300  ] 
dist 6=[32.225585703620471075  ,41.183516190357807319  ] 
dist 7=[31.044963602246625615  ,41.214276670114276974  ] 
dist 8=[29.877819010214040893  ,40.956182968630446405  ] 
dist 9=[28.862878980637029417  ,40.861503497675461804  ] 
dist 10=[27.760997720767332017  ,40.732683359475067642  ] 
dist 11=[26.246147374790879487  ,40.664601409689599414  ] 
dist 12=[24.722523939049328961  ,40.399355739168016769  ] 
dist 13=[23.585375257063507928  ,40.305299985134909679  ] 
dist 14=[22.507974851879392553  ,40.050470524532495974  ] 
dist 15=[21.222768310157596377  ,39.940821877729954904  ] 
dist 16=[19.893437223903959726  ,31.486649729389049125  ] 
dist 17=[18.639372977955778976  ,30.714495663979929608  ] 
dist 18=[17.192360511420505689  ,28.810498199842246710  ] 
dist 19=[15.091325767289982781  ,28.528402210676455556  ] 
dist 20=[13.002430025819084672  ,25.599680315442436220  ] 
dist 21=[11.603846234774301772  ,25.037846425314016855  ] 
dist 22=[10.433992005769044146  ,24.413565347798670773  ] 
dist 23=[9.2595483210163613205 ,24.276418088958405556  ] 
dist 24=[8.1624930106147633038 ,18.948645084043125006  ] 
dist 25=[7.3020009393384716910 ,18.271694572526026500  ] 
dist 26=[6.4439885672241406962 ,16.926986661073606407  ] 
dist 27=[5.3567484029035592476 ,16.582433439262507810  ] 
dist 28=[4.2995518941289665646 ,15.371569988407277512  ] 
dist 29=[2.6123207934143475643 ,15.104552835333931376  ] 
dist 30=[.07032852958711879039,14.736528081542444635  ] 
dist 31=[-2.4278025067647097090 ,14.621748069959639100  ] 
dist 32=[-4.0342891313472087547 ,4.2679697859597532494 ] 
dist 33=[-5.3048856375812238575 ,3.4100813112746033001 ] 
dist 34=[-6.4604743278498791873 ,2.9139775535730297062 ] 
dist 35=[-7.4628391026476866147 ,2.8595708296193808719 ] 
dist 36=[-8.1211146184397585441 ,1.2551903937306279878 ] 
dist 37=[-8.6584790535902522822 ,1.0961359692750925237 ] 
dist 38=[-9.1778913594740186039 ,.7550751710070818906 ] 
dist 39=[-9.6296338110495672212 ,.6866559796845997662 ] 
dist 40=[-9.8965057822747236795 ,.32009325273262100385] 
dist 41=[-10.082213216721938638  ,.25762298979332591465] 
dist 42=[-10.209162427174073766  ,.12705126571045658983] 
dist 43=[-10.290975240658258294  ,.09851093331813632233] 
dist 44=[-10.297661565369106047  ,-.12276223333118864777] 
dist 45=[-10.269175163124722191  ,-.15985198179260813409] 
dist 46=[-10.232073698272982981  ,-.20137645591451651074] 
dist 47=[-9.1464120226956648209 ,-.20533732164988261603] 
dist 48=[-6.3687642477795718296 ,-.1939490201844613424 ] 
dist 49=[-6.3089586028425895794 ,-.16022906196043214282] 
dist 50=[-6.1457844365834435930 ,-.1034881680268823895 ] 
dist 51=[-5.9506219502252630998 ,0                     ] 
dist 52=[-4.7758360227709146185 ,-.46607155436762179527] 
dist 53=[-4.6343619951337069638 ,.1920404062104629895 ] 
dist 54=[-4.4679498638725532754 ,1.0487847244182585509 ] 
dist 55=[-4.4205080077421250042 ,1.8845856156001847580 ] 
dist 56=[-3.0704607674045559490 ,2.4591635945974813522 ] 
dist 57=[-2.8984829714545142908 ,2.9533502018417647456 ] 
dist 58=[-2.5409526656879411373 ,3.4682798416632272925 ] 
dist 59=[-2.4464882732909991956 ,3.9585314092019367763 ] 
dist 60=[-2.0940354865963355001 ,4.3542818429109546400 ] 
dist 61=[-2.0237548531587016572 ,4.7577679339315962176 ] 
dist 62=[-1.8894910197528452562 ,5.2790858775971411269 ] 
dist 63=[-1.8565740284181430692 ,5.7743646198543854733 ] 
dist 64=[.22513390556907875222,6.0738960613582361031 ] 
dist 65=[.40663681143923891509,6.2885836978463423134 ] 
dist 66=[.78854007184112882325,6.4449633296105991175 ] 
dist 67=[.87165902569808634979,6.5586528299253866597 ] 
dist 68=[1.2368609935291553122 ,6.6027944583944366813 ] 
dist 69=[1.3011904626277894587 ,6.6138096858674528093 ] 
dist 70=[1.4101208918191706407 ,6.6032297871506914578 ] 
dist 71=[1.4316273572921198330 ,6.2636325758466701614 ] 
dist 72=[1.4514159083530885375 ,6.1976084390832366181 ] 
dist 73=[1.4174715656678212958 ,6.0607020238650430317 ] 
dist 74=[1.3466718622819121693 ,6.0147754523075524286 ] 
dist 75=[1.2074106325479909527 ,5.7966139454479083505 ] 
dist 76=[1.0349587577058099357 ,5.7465463904562051585 ] 
dist 77=[.8316149930458596310 ,5.5860963364751341515 ] 
dist 78=[.5666458856160759913 ,5.5600045137993695017 ] 
dist 79=[-.04398694793148584538,3.8596374021388679260 ] 
dist 80=[-.81214041968523520252,3.4064198201521006545 ] 
dist 81=[-1.4492768992130288437 ,2.9887693306283570386 ] 
dist 82=[-2.0754699459668893257 ,2.9254652612903831431 ] 
dist 83=[-2.6477943632820623727 ,2.2866377967920880421 ] 
dist 84=[-3.0698538994769089877 ,2.1653840066514250032 ] 
dist 85=[-3.4633096149954083933 ,2.0225129413588167650 ] 
dist 86=[-3.9214353066335147057 ,1.9879381726461947373 ] 
dist 87=[-4.3467746550859995047 ,.9028704731822651126 ] 
dist 88=[-4.6093210583469391766 ,.7677594009023020131 ] 
dist 89=[-4.8032909359950276688 ,.4862214940654298240 ] 
dist 90=[-4.9548077213724806130 ,.4127631219226686274 ] 
dist 91=[-5.0702152782904150628 ,.1427221772321076790 ] 
dist 92=[-5.1200075219489941230 ,.0899124064985731907 ] 
dist 93=[-5.1397654081947987956 ,-.0057968655539962664 ] 
dist 94=[-5.1352449148834274904 ,.17328391722242592464] 
dist 95=[-2.8094032999872821374 ,.4644990584251730258 ] 
dist 96=[-3.0351425418256249640 ,.76240165405640614962] 
dist 97=[-3.1685015943316033246 ,.97730060545957530505] 
dist 98=[-3.2602109259913820994 ,1.2242366609101487505 ] 
dist 99=[-3.3195960488862399109 ,1.4729564841218965367 ] 
dist 100=[-3.3602607141729282954 ,1.7038221762363155124 ] 
dist 101=[-3.3771906169897682385 ,1.8794933200652874855 ] 
dist 102=[-3.3801204004670331753 ,2.0483944111757966098 ] 
dist 103=[-3.3756987462067300653 ,2.2522328242210215505 ] 
dist 104=[-2.8883702027911424278 ,2.4430828486885166164 ] 
dist 105=[-2.8239365121239304782 ,2.5601385210094928622 ] 
dist 106=[-2.7305426956825974228 ,2.6455388775296812366 ] 
dist 107=[-2.7005910654089885396 ,2.7100347185794159962 ] 
dist 108=[-2.0803991085965759453 ,2.7561447715397449518 ] 
dist 109=[-1.9684380090077099220 ,2.7681619724815471286 ] 
dist 110=[-1.5525612066123814671 ,2.7686067180870011764 ] 
dist 111=[-1.5387401761786759907 ,2.7685296003512168934 ] 
dist 112=[-.52807364964618368572,.25217711596739293817] 
dist 113=[-.43349824960598462972,.32749964583661971899] 
dist 114=[-.21330192773662571937,.39912173600073005295] 
dist 115=[-.17909367320786966129,.46305906476253321427] 
dist 116=[-.02651824761809264459,.50769592162131982675] 
dist 117=[.00140587359993794793,.54684106914996027903] 
dist 118=[.00747693566340940168,.5888515666820614728 ] 
dist 119=[.05543399867709802558,.62693108984477652616] 
dist 120=[.06366090402294239803,.65625985891406451658] 
dist 121=[.07014070337217710794,.74383445360997502965] 
dist 122=[.06795607828584521042,.81274787164556155503] 
dist 123=[.0617239904452734917 ,.87439370621829174919] 
dist 124=[.05002606038652976911,.92681813237482840829] 
dist 125=[.03211187324287197089,.95892181543880556138] 
dist 126=[.00106433832450856310,.98240133747444681681] 
dist 127=[-.03096872754258480584,1.0004102557992372374 ] 
dist 128=[-.05281993694137940452,1.0141743509317650468 ] 
dist 129=[-.07138599310800682659,1.0207065731769493929 ] 
dist 130=[-.09031281622131267253,1.0232882136278795984 ] 
dist 131=[-.10802179214520927317,1.0218111976843769341 ] 
dist 132=[-.12173068894403047979,1.0165186936932383844 ] 
dist 133=[-.13514220534163542874,1.0132513322593723321 ] 
dist 134=[-.1516692838100712823 ,1.0000123544444669932 ] 
dist 135=[-.16735232026596792636,.99550587945318410822] 
dist 136=[-.17739739809329431622,.95148349452461140183] 
dist 137=[-.18525628290942783888,.94208121957618561982] 
dist 138=[-.1922156385781860267 ,.91644224276355088059] 
dist 139=[-.26178970042264703593,.90928350689164485406] 
dist 140=[-.38661909356667936052,.85690744058184833133] 
dist 141=[-.50671836705543501553,.84487165795799720619] 
dist 142=[-.64650212086259181873,.82518634568548503451] 
dist 143=[-.84992734064469790561,.81914339976672876222] 
dist 144=[-1.0514147775443347807 ,.17796843037894065319] 
dist 145=[-1.1834640635304704418 ,.20272610788557894737] 
dist 146=[-1.2900987010028964775 ,.22582646396091950156] 
dist 147=[-1.3901189402599362086 ,.24606535597906129145] 
dist 148=[-1.4783868977185834699 ,.25940212736721944112] 
dist 149=[-1.5381017995972907784 ,.27021631543896995237] 
dist 150=[-1.5884207884373749977 ,.28038455114189697326] 
dist 151=[-1.6391785063965504052 ,.28905256288630684186] 
dist 152=[-1.6817827477574875993 ,.29387993471783642053] 
dist 153=[-1.6995499315357432237 ,.29679949004500578395] 
dist 154=[-1.7070616705517926594 ,.29785816911162947005] 
dist 155=[-1.7087140105689061819 ,.29762586357150201333] 
dist 156=[-1.6664577888122960777 ,.29708027780660922774] 
dist 157=[-1.6554991113470215342 ,.29302483999662999127] 
dist 158=[-1.6489139690863096064 ,.29223189577064777212] 
dist 159=[-1.6465640833811804700 ,-.05872674136556496185] 
dist 160=[-1.4828632221585973913 ,.25134954611805432911] 
dist 161=[-1.4632643298080485526 ,.47117863282046210974] 
dist 162=[-1.4072229872532953594 ,.65539421400544308165] 
dist 163=[-1.3970710541177823316 ,.83944809894546708501] 
dist 164=[-1.2807727622354462391 ,1.0095479037976637234 ] 
dist 165=[-1.2554780935641256706 ,1.1380534410401661599 ] 
dist 166=[-1.2279760930633169155 ,1.2608408208097379180 ] 
dist 167=[-1.2168540382625490389 ,1.4081112802486663984 ] 
dist 168=[-.91451726777109500183,1.5457931748956916836 ] 
dist 169=[-.87384344021884765091,1.6302991264036475289 ] 
dist 170=[-.79153069800020832213,1.6921211453691932661 ] 
dist 171=[-.7694242876543099153 ,1.7392397713729152781 ] 
dist 172=[-.68633386181587148936,1.7743293103111975700 ] 
dist 173=[-.66822149395133902624,1.7881266896518450818 ] 
dist 174=[-.63343985356588306718,1.7924917736852970628 ] 
dist 175=[-.62403427076775503815,1.7899242433806084913 ] 
dist 176=[-.44674901155291109501,.89418242478422113971] 
dist 177=[-.50440391468069137969,.925251645705079841  ] 
dist 178=[-.56323396528087976907,.94819184390895847373] 
dist 179=[-.61839528321253107597,.9650118567262005219 ] 
dist 180=[-.66140301130724047791,.97164391219164147131] 
dist 181=[-.70379314867658740647,.97341071012366405897] 
dist 182=[-.75648864084197282817,.97192640543577272696] 
dist 183=[-.80670222380026535035,.92313242669214468229] 
dist 184=[-.83918346001388859723,.96825416143711259246] 
dist 185=[-.86493009629651713791,1.0481388851875692268 ] 
dist 186=[-.88825624348731903942,1.1165110716682752394 ] 
dist 187=[-.90826955623721887593,1.1871818870406325373 ] 
dist 188=[-.92078980305473483084,1.2540438135773932535 ] 
dist 189=[-.93023070011574364046,1.3072092649149089409 ] 
dist 190=[-.93794955690472450399,1.3606044712901485296 ] 
dist 191=[-.94302022365157297044,1.4283856361606222059 ] 
dist 192=[-.94299594285618234601,1.4911741332247310847 ] 
dist 193=[-.93851184686509953392,1.5246354427382403297 ] 
dist 194=[-.93462215854198970879,1.5430824558591042515 ] 
dist 195=[-.90678081356617552103,1.5473355287899598467 ] 
dist 196=[-.89866597279550062093,1.5432936629373236766 ] 
dist 197=[-.89509296965641200563,1.5402484876589155990 ] 
dist 198=[-.98835913492239852227,1.5362785353271389022 ] 
dist 199=[-1.1086717312113761965 ,1.5307597127382863207 ] 
dist 200=[-1.2255052592044392806 ,1.3380918370436357667 ] 
dist 201=[-1.3048811912697997095 ,1.3092249720570892281 ] 
dist 202=[-1.3721188140383280245 ,1.2552188832676972681 ] 
dist 203=[-1.4404895276205984749 ,1.2404420982121462488 ] 
dist 204=[-1.5044605696180809059 ,1.1857400290227471581 ] 
dist 205=[-1.5541324188112289832 ,1.1710437142736228078 ] 
dist 206=[-1.6029078807855854667 ,1.1450659807630073364 ] 
dist 207=[-1.6633004633499301498 ,1.1373730099688685422 ] 
dist 208=[-1.7188642087599526430 ,.38694376013730217118] 
dist 209=[-1.7483601624220688908 ,.4809217994727880774 ] 
dist 210=[-1.7644449277892154951 ,.57118841170655258677] 
dist 211=[-1.7667632280279004446 ,.65229226649325712339] 
dist 212=[-1.7622916276483536175 ,.70968745584895040563] 
dist 213=[-1.7567187164775695050 ,.7607776687882194203 ] 
dist 214=[-1.7425644699454924846 ,.81670840967103621828] 
dist 215=[-1.7350713379587054288 ,.86746476453130717314] 
dist 216=[-1.5758445986971203020 ,.89789590079390154987] 
dist 217=[-1.5496959704358504527 ,.91930090688986885661] 
dist 218=[-1.4908623134355584853 ,.93401992576476309646] 
dist 219=[-1.4718659223445336589 ,.94366410991665540808] 
dist 220=[-1.3838635238307440186 ,.94549254242753626564] 
dist 221=[-1.3645232662143018478 ,.94311804716335978393] 
dist 222=[-1.3162441598519335119 ,.94145068515812597701] 
dist 223=[-1.3019265761207966504 ,.09076791959487438144] 
dist 224=[-1.2441077673415204679 ,.43126239541443472412] 
dist 225=[-1.2754935729279278156 ,.6557118773518465654 ] 
dist 226=[-1.2954089878156162731 ,.83842476670243320224] 
dist 227=[-1.3049186704023375448 ,1.0122811024414949517 ] 
dist 228=[-1.3088425554593391076 ,1.1674036000093744154 ] 
dist 229=[-1.3073333902329666179 ,1.2753194299898445705 ] 
dist 230=[-1.3010434097143190139 ,1.3694607844708107591 ] 
dist 231=[-1.2962671603752592680 ,1.4695869365090072083 ] 
dist 232=[-1.1950950899324072699 ,1.5604743574828379033 ] 
dist 233=[-1.1777426072879134599 ,1.6177290085873588667 ] 
dist 234=[-1.1390287453400158883 ,1.6613825430387626486 ] 
dist 235=[-1.1263225321089599480 ,1.6979660904632914869 ] 
dist 236=[-1.0666992485132752719 ,1.7272577410407197876 ] 
dist 237=[-1.0534313028176478190 ,1.7417975843888534149 ] 
dist 238=[-1.0187140950387302738 ,1.7483319372957309404 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[43.980574866824478288  ,43.980574866824478288  ] 
dist 1=[43.751143808107342690  ,44.140681863717567742  ] 
dist 2=[43.445447954842198020  ,44.280580055121566478  ] 
dist 3=[42.980709303676714326  ,44.429238050175298634  ] 
dist 4=[42.309519851810516832  ,44.571652425354124824  ] 
dist 5=[41.179227018537603792  ,44.686518542867646805  ] 
dist 6=[39.836986455513149756  ,44.802574772353951588  ] 
dist 7=[38.319275797219440267  ,44.949515346443100521  ] 
dist 8=[36.255832210710392531  ,45.079993326548075879  ] 
dist 9=[33.346626741031977129  ,45.130373200124657826  ] 
dist 10=[30.265938213386584731  ,45.131043939853961397  ] 
dist 11=[28.130166132950295124  ,45.082026147072692995  ] 
dist 12=[26.272033952990146199  ,44.956992301831877807  ] 
dist 13=[24.299934894515963921  ,44.673728027717684111  ] 
dist 14=[22.398322654917323943  ,42.935215096044282947  ] 
dist 15=[20.821439425974298897  ,41.568832679837983248  ] 
dist 16=[19.174890331762341612  ,35.072071297613166208  ] 
dist 17=[16.994515758372012055  ,34.203241609124092916  ] 
dist 18=[14.840492788669616568  ,32.096023226826945191  ] 
dist 19=[13.298927946614496224  ,31.747035346612000917  ] 
dist 20=[11.903976336401522434  ,28.596740355849328855  ] 
dist 21=[10.335255496914651028  ,27.991321632727561799  ] 
dist 22=[8.7646493943971581576 ,27.203900071080111432  ] 
dist 23=[7.3616720474927320750 ,26.941323854506178474  ] 
dist 24=[5.8040065538970620576 ,21.594199090287158994  ] 
dist 25=[3.6143660613487252401 ,20.893107245025574905  ] 
dist 26=[1.4696089274637485256 ,19.422011304377602642  ] 
dist 27=[.0911538379452394520 ,19.024460699593733305  ] 
dist 28=[-.9995759412944172003 ,17.483682634240084450  ] 
dist 29=[-1.9941079358976597433 ,17.182579093575369486  ] 
dist 30=[-2.8601132990605822163 ,16.507711873682340225  ] 
dist 31=[-3.4371654195648049110 ,16.341457253052470860  ] 
dist 32=[-4.2068722480042802182 ,7.2333858753057144999 ] 
dist 33=[-5.0652266411749664446 ,6.4057683533796739981 ] 
dist 34=[-5.5900451521550987736 ,4.5555002435362842909 ] 
dist 35=[-5.9750529185024607641 ,4.2172230489482746349 ] 
dist 36=[-6.9620596185756633545 ,2.0126507127964151602 ] 
dist 37=[-8.0506765689920793395 ,1.6306696025871328870 ] 
dist 38=[-9.0186677933914871649 ,.92920859341259749918] 
dist 39=[-10.080478874237956354  ,.77432707485153084242] 
dist 40=[-11.052368879589439144  ,-1.0771045147292518174 ] 
dist 41=[-11.661148239384618242  ,-1.3374928144645187469 ] 
dist 42=[-12.123149400385500175  ,-1.3128719614853246068 ] 
dist 43=[-12.508624650550704498  ,-.83494269933163195366] 
dist 44=[-12.817703144755008712  ,-.31218049256195365414] 
dist 45=[-12.974518509633847063  ,.1985263124581964420 ] 
dist 46=[-13.050925484338763374  ,.6285238384561685921 ] 
dist 47=[-13.050659587073165982  ,1.0815137686636931699 ] 
dist 48=[-8.9531575110620583462 ,1.6841657486940954434 ] 
dist 49=[-8.6262496319500155709 ,2.2770156353493261411 ] 
dist 50=[-7.8039943953872755287 ,2.6909734263426681032 ] 
dist 51=[-7.6822403845279717414 ,3.0534122938250345607 ] 
dist 52=[-6.3842653037373965913 ,3.4407325878452085489 ] 
dist 53=[-6.1362741727963870114 ,3.8150656399690958124 ] 
dist 54=[-5.8565995171241090927 ,4.1257593989265642355 ] 
dist 55=[-5.7965857618471001145 ,4.4500279277319144950 ] 
dist 56=[-3.5016760801047810686 ,4.8787169308496692486 ] 
dist 57=[-3.2175871332320553230 ,5.2871209834890921502 ] 
dist 58=[-2.6326610114554889711 ,5.5304270914076731481 ] 
dist 59=[-2.4817569456321787239 ,5.7001892338435580315 ] 
dist 60=[-1.9393095272532219400 ,5.8148864578493014206 ] 
dist 61=[-1.8300917417256984789 ,5.8934128775595609035 ] 
dist 62=[-1.6603276401728477440 ,5.9187005412914110996 ] 
dist 63=[-1.6182769273224208815 ,5.9174208507954710631 ] 
dist 64=[1.5174379117393587806 ,5.9042622195392191695 ] 
dist 65=[1.7798268432862163062 ,5.5074574157761088548 ] 
dist 66=[2.3153514189874797474 ,5.4357067656011587408 ] 
dist 67=[2.4389598686920220474 ,5.2845890005609621599 ] 
dist 68=[2.8778209568373686283 ,5.2351475591285925646 ] 
dist 69=[2.8814775769737743296 ,5.0039340242022531413 ] 
dist 70=[2.2949602923183337292 ,4.9527511229976242064 ] 
dist 71=[1.5655888442502701930 ,4.9984284701635735786 ] 
dist 72=[.46736346103017075923,5.3196917679776169810 ] 
dist 73=[-.63051693851997044975,5.5153284595008713633 ] 
dist 74=[-1.3585212564498021749 ,5.6570990503765807327 ] 
dist 75=[-1.9557397236903655809 ,5.7631795066226806898 ] 
dist 76=[-2.5314844476961111958 ,5.8386931966820210511 ] 
dist 77=[-3.0500753890750216208 ,5.8583604285181333455 ] 
dist 78=[-3.4191183768222253144 ,5.8572441258474752344 ] 
dist 79=[-3.7496808700055740971 ,5.8497261535501064664 ] 
dist 80=[-4.1146448199429404141 ,2.9684858023646792516 ] 
dist 81=[-4.4496855267479165919 ,2.3942007357021933271 ] 
dist 82=[-4.6607838677785667663 ,2.3129309220178065327 ] 
dist 83=[-4.8217353917724225906 ,2.1202511541162135368 ] 
dist 84=[-4.9565718963104490387 ,2.0784164409818491190 ] 
dist 85=[-5.0644625608056688174 ,1.7979515995883956739 ] 
dist 86=[-5.1178357917749447503 ,1.7425074722497594868 ] 
dist 87=[-5.1415421530835523849 ,1.6430727846079260490 ] 
dist 88=[-5.1401370463863881658 ,1.6182883792486475363 ] 
dist 89=[-4.4264681270368721770 ,-.28543066657237374833] 
dist 90=[-4.6056890711271847135 ,-.1687955647094444288 ] 
dist 91=[-4.7556050995173995215 ,-.06772176383549991457] 
dist 92=[-4.8757606912209577739 ,.03860919940108421843] 
dist 93=[-4.9361984849154584791 ,.14025290199889717813] 
dist 94=[-5.0371500810727399518 ,.22262009168510681048] 
dist 95=[-5.1503924678478140684 ,.30669857610255202458] 
dist 96=[-5.2437995144418279839 ,.97582267957236189679] 
dist 97=[-5.2758053336363101872 ,1.5441320213610828447 ] 
dist 98=[-5.2826849363131167307 ,2.0252503929423035706 ] 
dist 99=[-5.2756281851454875604 ,2.5133570511451034412 ] 
dist 100=[-5.1394502250577678570 ,2.9687656812492682097 ] 
dist 101=[-5.0125403243997333624 ,3.3193695943195233132 ] 
dist 102=[-4.9605540938576986794 ,3.6604563645063797034 ] 
dist 103=[-4.6252541340783106870 ,4.0778760859638017093 ] 
dist 104=[-3.8611977569170487232 ,4.4718223205190601570 ] 
dist 105=[-3.5294741869892465975 ,4.7192114795745938299 ] 
dist 106=[-3.2942516407974525765 ,4.9066774002928821460 ] 
dist 107=[-3.2274493745334710243 ,5.0614320263091983380 ] 
dist 108=[-2.9554003031323160706 ,5.1833246722165114758 ] 
dist 109=[-2.8987746636284380113 ,5.2396143376000255050 ] 
dist 110=[-2.7592876481984725572 ,5.2609243837690009938 ] 
dist 111=[-2.7251973859739443175 ,5.2593177646357061911 ] 
dist 112=[-.56528189524734720797,1.0022350897932433619 ] 
dist 113=[-.38885894778579296024,.92636488761829451313] 
dist 114=[-.45931679341667395086,.91312850411213790107] 
dist 115=[-.52655865952143942628,.88342007241965858518] 
dist 116=[-.60708273259873869957,.87357173296125627761] 
dist 117=[-.69007983071429986059,1.0180826237504476811 ] 
dist 118=[-.76719478598607746601,1.2394738479167347821 ] 
dist 119=[-.85484987673389665034,1.5065587961816831566 ] 
dist 120=[-.97992608920256025189,1.7572371139516155288 ] 
dist 121=[-1.1027267305551265808 ,1.9131304867094908840 ] 
dist 122=[-1.1812971126064415022 ,2.0296949678563152324 ] 
dist 123=[-1.2425883860571931258 ,2.1233557683994973212 ] 
dist 124=[-1.2964060558848756786 ,2.1974690221842082240 ] 
dist 125=[-1.3413592340540279254 ,2.2359781870690256448 ] 
dist 126=[-1.3672608467098166140 ,2.2558470321378566005 ] 
dist 127=[-1.3841890978371405720 ,2.2590768750310409407 ] 
dist 128=[-1.3933176667806504301 ,2.1684201956509320280 ] 
dist 129=[-1.3969399977526786707 ,2.1506956173183943372 ] 
dist 130=[-1.3958512990409398816 ,2.1120589073677977230 ] 
dist 131=[-1.3847218285670308761 ,2.0977684961551903135 ] 
dist 132=[-1.3799266842286752878 ,2.0249537758864330302 ] 
dist 133=[-1.3269199424813240185 ,2.0076343306270659531 ] 
dist 134=[-1.3126829898568569544 ,1.9544951298016930080 ] 
dist 135=[-1.2958644353521300433 ,1.9430707102476097338 ] 
dist 136=[-1.2876567201762359048 ,1.7788966966494532722 ] 
dist 137=[-1.2204609971062042734 ,1.7500847500282117519 ] 
dist 138=[-1.2185687416561950372 ,1.6757890190227409082 ] 
dist 139=[-1.2041411866481967566 ,1.6587124727661452606 ] 
dist 140=[-1.2015202917359802721 ,1.5260748484435588195 ] 
dist 141=[-1.2921607614021885055 ,1.4975782890252781171 ] 
dist 142=[-1.5796106566556006992 ,1.4532732251521911429 ] 
dist 143=[-1.9942038212682435038 ,1.4396956094113963678 ] 
dist 144=[-2.4037304382368425466 ,1.2556517863002016904 ] 
dist 145=[-2.6709547944518403754 ,1.3559574224920856451 ] 
dist 146=[-2.8854483315202821829 ,1.4152887584494344632 ] 
dist 147=[-3.0844457543176668932 ,1.4560296856832855628 ] 
dist 148=[-3.2585592152154351106 ,1.4821145256023124112 ] 
dist 149=[-3.3737040627870088278 ,1.4999224791834976074 ] 
dist 150=[-3.4678622342745285543 ,1.5076182857954175674 ] 
dist 151=[-3.5581893929537457125 ,1.5093854943269311982 ] 
dist 152=[-3.6317029360475575787 ,1.5071370830792986033 ] 
dist 153=[-3.6587314770287909285 ,.10650588767438471711] 
dist 154=[-3.6673931235456192919 ,.23822458568630943625] 
dist 155=[-3.6675700037532762916 ,.35495794709150980555] 
dist 156=[-3.5671799386266779943 ,.48196990545791105769] 
dist 157=[-3.5392346651796015046 ,.60606945371117116103] 
dist 158=[-3.5207166428560413124 ,.71117544655873522537] 
dist 159=[-3.5102098696349378743 ,.82264073577352248869] 
dist 160=[-3.0897795876273673602 ,.97213157824804139072] 
dist 161=[-3.0417972385547136526 ,1.1200247644189782058 ] 
dist 162=[-2.9088198862024005820 ,1.3849948624020903612 ] 
dist 163=[-2.8851233585999248912 ,1.7805895482018720442 ] 
dist 164=[-2.6232130789852627527 ,2.1460693261808594927 ] 
dist 165=[-2.5672229467167879524 ,2.4220335545603941705 ] 
dist 166=[-2.5047562457104907713 ,2.6856012645633649066 ] 
dist 167=[-2.4801421909143133538 ,3.0015878703453611697 ] 
dist 168=[-1.8344953820884677839 ,3.2969789879165387741 ] 
dist 169=[-1.7479892351754223102 ,3.4783194742911142760 ] 
dist 170=[-1.5718863454764012650 ,3.6110425020539748283 ] 
dist 171=[-1.5245411494984669260 ,3.7123292880071751898 ] 
dist 172=[-1.3457995728340395342 ,3.7879855398937070910 ] 
dist 173=[-1.3780484301206595398 ,3.8183795127914337469 ] 
dist 174=[-1.4887413659665740926 ,3.8283820417196996394 ] 
dist 175=[-1.5981561225217502078 ,3.8226263527550862825 ] 
dist 176=[-1.7346282407336036423 ,2.1255642709123362792 ] 
dist 177=[-1.8649396561933243395 ,1.9666900354044729413 ] 
dist 178=[-1.9497571437977034944 ,1.9393035917205873905 ] 
dist 179=[-2.0175980759071572092 ,1.8837855669701230999 ] 
dist 180=[-2.0801288762806798240 ,1.8663530625274911517 ] 
dist 181=[-2.1345528782315387760 ,1.7885217786482434379 ] 
dist 182=[-2.1700265183469245490 ,1.7704626419418796910 ] 
dist 183=[-2.1984553843618347068 ,1.7990751285512507397 ] 
dist 184=[-2.2247521773289113352 ,2.0364581243037049760 ] 
dist 185=[-2.2445775336659229299 ,2.1988349762410948905 ] 
dist 186=[-2.2471684884585009595 ,2.3375850921299182626 ] 
dist 187=[-2.2427253694554715577 ,2.4806355858100052910 ] 
dist 188=[-2.2350847237650402822 ,2.6157441869586369940 ] 
dist 189=[-2.1767741749967109266 ,2.7227862844277650898 ] 
dist 190=[-2.1590113217382818190 ,2.8299267541595484320 ] 
dist 191=[-2.1299823431646967781 ,2.9654308370542347073 ] 
dist 192=[-2.1192256342130385818 ,3.0906916214047426510 ] 
dist 193=[-1.8299036310092896826 ,3.1569343019221020199 ] 
dist 194=[-1.7867344124928710183 ,3.1930819371240463375 ] 
dist 195=[-1.6939643209771297042 ,3.2009856969608139464 ] 
dist 196=[-1.6945565343110747538 ,3.1892217945543613051 ] 
dist 197=[-1.8858674403551012744 ,3.1816768631676878298 ] 
dist 198=[-2.0805884571267316790 ,3.1724132645530868054 ] 
dist 199=[-2.3312201387972675073 ,3.1608114593077906749 ] 
dist 200=[-2.5743496415138327106 ,2.7612449135616379052 ] 
dist 201=[-2.7391177479178651037 ,2.7013936150459800102 ] 
dist 202=[-2.8782478195661983864 ,2.5887210206267847460 ] 
dist 203=[-3.0190153380993560965 ,2.5577546867781103746 ] 
dist 204=[-3.1502800298370337523 ,2.4420647317498329913 ] 
dist 205=[-3.2514694552323106280 ,2.4114576600208208486 ] 
dist 206=[-3.3501412150754400696 ,2.3556772554412309292 ] 
dist 207=[-3.4713544536111295193 ,2.3388662162739335697 ] 
dist 208=[-3.5824476231067966050 ,1.8806269253829707868 ] 
dist 209=[-3.6407139835096231800 ,2.0010628940813662465 ] 
dist 210=[-3.6715116325417560107 ,2.0740257099905838881 ] 
dist 211=[-3.6758714300616217388 ,2.1262767035543944074 ] 
dist 212=[-3.6618761985108698294 ,2.1640181578974507157 ] 
dist 213=[-3.6493273441885478412 ,2.1895957384085265175 ] 
dist 214=[-3.6189931137326298974 ,2.1954044236507086733 ] 
dist 215=[-3.6034642753017287591 ,2.1903251318331296255 ] 
dist 216=[-3.2640772340348974589 ,2.1893881936322712534 ] 
dist 217=[-3.2087702351520001630 ,-.11961090999140460288] 
dist 218=[-3.0849150119559178356 ,-.15204423479559696677] 
dist 219=[-3.0451634235728587339 ,-.20930373567301009448] 
dist 220=[-2.8618922717103754490 ,-.2212431670266396765 ] 
dist 221=[-2.8218038756224630477 ,-.24532694569168152457] 
dist 222=[-2.7205972499872778995 ,-.24063613988325010437] 
dist 223=[-2.6918180356995940850 ,.18296029675357503525] 
dist 224=[-2.5620380989673881855 ,.8879353573031907017 ] 
dist 225=[-2.6275808722128137180 ,1.3527633999346155822 ] 
dist 226=[-2.6693977254134801991 ,1.7312919954433924678 ] 
dist 227=[-2.6898524862614604269 ,2.0917057060997871595 ] 
dist 228=[-2.6986861585388237507 ,2.4134457624812226517 ] 
dist 229=[-2.6958894376948627763 ,2.6375648742611951418 ] 
dist 230=[-2.6832059463465996010 ,2.8333860360127786855 ] 
dist 231=[-2.6733435946340105601 ,3.0421427633668227197 ] 
dist 232=[-2.4678696745232529601 ,3.2317196841744004142 ] 
dist 233=[-2.4324561393552403142 ,3.3509630460499055013 ] 
dist 234=[-2.3532574400631688442 ,3.4416710275757747568 ] 
dist 235=[-2.3271778947593325447 ,3.5173170310681397029 ] 
dist 236=[-2.2044884904381087564 ,3.5776017350367480037 ] 
dist 237=[-2.1771193336537073253 ,3.6069778366100276408 ] 
dist 238=[-2.1058953116225898435 ,3.6193711752489457700 ] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 1, 2, 1, 2] 
dist 0=[50.653811857455560675  ,50.653811857455560675  ] 
dist 1=[50.263131919551780701  ,50.858241007289741316  ] 
dist 2=[49.407501122664426956  ,50.970171895190077482  ] 
dist 3=[48.408237273701487433  ,51.020532542699416931  ] 
dist 4=[47.443750693992397924  ,50.979184033329030304  ] 
dist 5=[46.317422028442967328  ,50.900593323370537998  ] 
dist 6=[44.671548436026209395  ,50.802016285120012159  ] 
dist 7=[42.811568755015302906  ,50.669267785887146793  ] 
dist 8=[40.829921064453822319  ,50.368427183804667931  ] 
dist 9=[38.373317389594573571  ,47.747814461366059479  ] 
dist 10=[34.616038942986215309  ,47.284471958238468655  ] 
dist 11=[30.817073127554067556  ,46.586837358853764352  ] 
dist 12=[28.193882397560859888  ,46.366763291478620627  ] 
dist 13=[25.921396694515014333  ,45.901522502762771452  ] 
dist 14=[23.523208323867670676  ,45.150806628321396163  ] 
dist 15=[21.218095954080481962  ,41.437287249189206439  ] 
dist 16=[19.317272588914620294  ,38.943417439503987942  ] 
dist 17=[17.341767629557437887  ,29.411241203810182364  ] 
dist 18=[14.738065318347650010  ,28.996209108573414075  ] 
dist 19=[12.172508973449289775  ,27.562193629230278100  ] 
dist 20=[10.349235601417653506  ,27.221490034625591477  ] 
dist 21=[8.7133224757668406179 ,26.816204451858284340  ] 
dist 22=[6.8960245497462674676 ,26.670753504111362663  ] 
dist 23=[5.0913457413132917575 ,16.719761740103298212  ] 
dist 24=[3.5055471351547213197 ,16.447152005676623930  ] 
dist 25=[1.7684382579616743852 ,12.288842244286768075  ] 
dist 26=[-.64137304922668745908,11.739100516778309957  ] 
dist 27=[-2.9984097611020434520 ,10.671793197438931076  ] 
dist 28=[-4.5247455311822014661 ,10.424979191005210726  ] 
dist 29=[-5.7430716757415966269 ,9.7088855038724344842 ] 
dist 30=[-6.8691446086621446505 ,9.2724734094404243437 ] 
dist 31=[-7.8575866647826855736 ,7.9653854258416290668 ] 
dist 32=[-8.5259550382292311579 ,7.2522374738940550565 ] 
dist 33=[-9.0922659328884332192 ,-5.0423440236418736550 ] 
dist 34=[-9.6730848071301198025 ,-5.2025132976905054129 ] 
dist 35=[-10.181508568530592764  ,-6.4015245913270871462 ] 
dist 36=[-10.458513491847800399  ,-6.5807999318893045133 ] 
dist 37=[-11.249548697159682823  ,-6.8745487784631399992 ] 
dist 38=[-11.754088853652083690  ,-6.9190801085632552201 ] 
dist 39=[-12.125225278087016835  ,-6.5630429704005511520 ] 
dist 40=[-12.416671875113341137  ,-5.7358470870430164061 ] 
dist 41=[-12.640240778538895529  ,-4.6610171740617539350 ] 
dist 42=[-12.740103106769304185  ,-2.9674192476507534779 ] 
dist 43=[-12.770918169657897247  ,-1.2486916002088293709 ] 
dist 44=[-12.759818748765219974  ,-.07343839085100567734] 
dist 45=[-12.625378272674492578  ,.9290925770888163824 ] 
dist 46=[-12.572848923266988398  ,1.9584775508970877359 ] 
dist 47=[-12.374647552337087966  ,2.9268916052466395070 ] 
dist 48=[-12.314616894707514930  ,3.6860978805782990411 ] 
dist 49=[-7.8775357728645502925 ,4.4379048089174152327 ] 
dist 50=[-7.4453291779470769484 ,5.3768333821236849314 ] 
dist 51=[-6.4042940665059667618 ,6.2730725837859927147 ] 
dist 52=[-6.2324363084323061939 ,6.8544797031949774155 ] 
dist 53=[-5.4657758853238676171 ,7.3170040700624617052 ] 
dist 54=[-5.4291218111046751388 ,7.7386615459534533404 ] 
dist 55=[-4.0639393899075593475 ,8.1020927751766316634 ] 
dist 56=[-3.9478232825210992174 ,8.3321673767930095765 ] 
dist 57=[-1.7600472382502207781 ,8.5087191163848755598 ] 
dist 58=[-1.5773702268696003373 ,8.6584603880520249490 ] 
dist 59=[-.86911442240186434753,8.7748795289933437074 ] 
dist 60=[-.75477003902318779327,8.8183990390962894026 ] 
dist 61=[-.02736372460369792403,8.8173007250438833592 ] 
dist 62=[.09658885635707025130,8.8041871726231174538 ] 
dist 63=[.33304175443555040909,8.6630429324562786712 ] 
dist 64=[.38646907583151481712,8.5107021048700487009 ] 
dist 65=[1.9580696977056939100 ,3.9853775815348569884 ] 
dist 66=[2.1105386281229759656 ,4.1676896720616285546 ] 
dist 67=[2.4446003527540699430 ,4.3142204341177172705 ] 
dist 68=[2.4927784953963607147 ,4.3890492089939863850 ] 
dist 69=[2.4904402587799966990 ,4.4276970143371945564 ] 
dist 70=[2.3899559640324783121 ,4.4343199422917099380 ] 
dist 71=[2.1056298839832525065 ,3.9011941050506936639 ] 
dist 72=[1.8501239491366972881 ,3.9132009046213186891 ] 
dist 73=[1.6125668983264196445 ,3.9097644272714687838 ] 
dist 74=[1.3372735346925157753 ,3.9013009222041504710 ] 
dist 75=[1.0585622535793992597 ,3.0803200866454217991 ] 
dist 76=[.8073214381893867259 ,3.0868260597655848357 ] 
dist 77=[.5278178176524304286 ,3.0915072689459439692 ] 
dist 78=[.1362261318164897267 ,3.0930433042005665243 ] 
dist 79=[-.2588113192462353385 ,3.0926325056404088840 ] 
dist 80=[-.5520959032869808227 ,3.0895114853129166144 ] 
dist 81=[-.8274443656265696819 ,1.5114289385599161598 ] 
dist 82=[-1.1509012290665198290 ,1.4340348187155830434 ] 
dist 83=[-1.4812212952340101306 ,1.0775280693981935137 ] 
dist 84=[-1.7840010994890011495 ,1.0248355840604486663 ] 
dist 85=[-2.1251992575697714700 ,1.0162287332334522248 ] 
dist 86=[-2.6089642787604507894 ,1.1441987918731918591 ] 
dist 87=[-3.0818043067647127728 ,1.2788124745734933103 ] 
dist 88=[-3.3793872886418988796 ,1.3779201742424589825 ] 
dist 89=[-3.6062002847460743315 ,1.4699388810198743498 ] 
dist 90=[-3.7964400487240203528 ,1.5762753496087677666 ] 
dist 91=[-3.9495471194414057967 ,1.6836331256095828795 ] 
dist 92=[-4.0280731045304451015 ,1.7797368321105081130 ] 
dist 93=[-4.0705471310153606752 ,1.8859922206340956200 ] 
dist 94=[-4.0796810120369959628 ,2.0338768613614722873 ] 
dist 95=[-4.0301853420191739033 ,2.1823137074309460566 ] 
dist 96=[-4.0110295402756179387 ,2.2907782550539539830 ] 
dist 97=[-3.9911515705690632921 ,2.3907493725568607534 ] 
dist 98=[-3.9651574026433125270 ,2.5052931115900031426 ] 
dist 99=[-3.7835703855173089463 ,2.6204790269518483269 ] 
dist 100=[-3.7610981356818038868 ,2.7230187967731966727 ] 
dist 101=[-3.6044385028766315299 ,2.8359782051552031806 ] 
dist 102=[-3.4765642756017572400 ,2.9927616253679226673 ] 
dist 103=[-3.3680880541661451360 ,3.1429422290479434962 ] 
dist 104=[-3.3374227315421453877 ,3.2295436849746242265 ] 
dist 105=[-3.2815428295353443629 ,3.2861831938730895662 ] 
dist 106=[-3.2629005294223616625 ,3.3167548669876143779 ] 
dist 107=[-2.2891027094323650272 ,3.3317323050247097600 ] 
dist 108=[-2.2773928741373027247 ,3.3300750460783271168 ] 
dist 109=[-2.2089954237113930268 ,3.3125930858894349328 ] 
dist 110=[-2.1909121066943364384 ,3.2982828022653740319 ] 
dist 111=[-2.1493501439342820701 ,3.0637264545979169558 ] 
dist 112=[-2.1339817028780222709 ,3.0213629786107436381 ] 
dist 113=[-1.4254536018380069451 ,2.9223370112873977945 ] 
dist 114=[-1.3532383011177019059 ,2.8884519901957025037 ] 
dist 115=[-1.1793843020457888615 ,2.7244234579635015459 ] 
dist 116=[-1.1497372461952302082 ,2.6868619904667063982 ] 
dist 117=[-.89658932424946542879,2.5992904717776433028 ] 
dist 118=[-.84876424790179558855,2.5050276377757128569 ] 
dist 119=[-.78137576009067277985,1.3601552114359820889 ] 
dist 120=[-.76121318913193969796,1.5598575604462165812 ] 
dist 121=[-.37347969868098253833,1.7483192226797200985 ] 
dist 122=[-.32384150777093570939,1.8674181681930209198 ] 
dist 123=[-.36591332333937720228,1.9587151120586024714 ] 
dist 124=[-.40097157127929512149,2.0361617826948273613 ] 
dist 125=[-.43543026640794808491,2.0989319661990170320 ] 
dist 126=[-.47801695645691428802,2.1316248683929357732 ] 
dist 127=[-.51830408282732247926,2.1485991469072148100 ] 
dist 128=[-.54358809411278391542,2.1512077700970125973 ] 
dist 129=[-.56269060260267475284,.68607591579921089273] 
dist 130=[-.57831368356568904982,.67928637088476305276] 
dist 131=[-.59047540503843949241,.65497109462967780497] 
dist 132=[-.59576653461234721458,.64785021494149655144] 
dist 133=[-.59712206175916412007,.63776280321700788209] 
dist 134=[-.59658759029386684065,.66012654705759834103] 
dist 135=[.17909910284782409504,.69289670236579314454] 
dist 136=[.10039081515491990734,.72948649356465850465] 
dist 137=[.03201319656798691925,.76232749832930785654] 
dist 138=[-.04025551247439962930,.78012775175940629588] 
dist 139=[-.10960301354007254228,.79033787300939111317] 
dist 140=[-.16632004589507444428,.79287073399325735168] 
dist 141=[-.22472515758753171428,.79263610892553959463] 
dist 142=[-.30081605592492369912,.79179752387533732531] 
dist 143=[-.37508678652859413192,.79035263554114110817] 
dist 144=[-.42622652914938003888,.78776803202557669536] 
dist 145=[-.4702940747199684985 ,.69305486413312559558] 
dist 146=[-.51633022462661274278,.6802462844106637721 ] 
dist 147=[-.56020592079486163712,.64524056155345505254] 
dist 148=[-.59565024478845198437,.63972776552228616987] 
dist 149=[-.63177821836199841007,.57313912041213908047] 
dist 150=[-.67838932100801651876,.55922906616540396236] 
dist 151=[-.72220650266676476502,.54519069173289077972] 
dist 152=[-.74717972216768990696,.54114620146844288224] 
dist 153=[-.76319202275575618825,.3812583141614146444 ] 
dist 154=[-.77122673262096943362,.36036895042829370819] 
dist 155=[-.77568946458851875494,.31892801471585396163] 
dist 156=[-.7774366493616493795 ,.30812250456536335455] 
dist 157=[-.77754265402539765788,.31092064781704727421] 
dist 158=[-.77557998751417208136,.36806416606436965886] 
dist 159=[-.80196556364776067541,.42493552080986945556] 
dist 160=[-.84804188199285141954,.46583246453309538331] 
dist 161=[-.89133438090832529251,.50289786951185951281] 
dist 162=[-.91639588676303835982,.54447468725093058931] 
dist 163=[-.93294057873326857742,.58582219766494293751] 
dist 164=[-.94222611276962930632,.62197360777506477395] 
dist 165=[-.94724470993958124508,.66128477235274414328] 
dist 166=[-.94705639372216368332,.71524921398528650886] 
dist 167=[-.94379073454698613869,.76731859797045374799] 
dist 168=[-.94056466351759883594,.79906448006218633631] 
dist 169=[-.87586117570422275897,.82204005883640013599] 
dist 170=[-.86439430702805567636,.83909457928232215096] 
dist 171=[-.83872926784536195055,.85106345288996177748] 
dist 172=[-.83016955486978578917,.85392696490145359584] 
dist 173=[-.7895062086595219731 ,.85331868929717269913] 
dist 174=[-.78034844441680558825,.85295642182829796653] 
dist 175=[-.75633710655433009026,.82121300800705853032] 
dist 176=[-.74956717051638589568,.81421854642408813295] 
dist 177=[-.60909763846421851913,.79552817064957624253] 
dist 178=[-.6031990692431641487 ,.78868186321664129624] 
dist 179=[-.5858711547891768525 ,.74950102991612489974] 
dist 180=[-.5820485060813071414 ,.73997229930670417517] 
dist 181=[-.54348280478786949896,.72171110805361141468] 
dist 182=[-.53470695940565409443,.71600455199072510933] 
dist 183=[-.52399707272529849628,.70573853333670850833] 
dist 184=[-.51950154364421404113,.71391764323502745582] 
dist 185=[-.43836243422628907154,.76272831538459730669] 
dist 186=[-.52936435923272576068,.79730612118468520386] 
dist 187=[-.61095157107534088077,.82305853652162844245] 
dist 188=[-.66836296561476619871,.84355506059318315238] 
dist 189=[-.71912249711694058691,.85913951731743644666] 
dist 190=[-.77415175383098195315,.86527886117428090509] 
dist 191=[-.82418298394420364831,.86709771163528648018] 
dist 192=[-.85498818255978859687,.86571358083264144257] 
dist 193=[-.87763974781427416918,.56933129882428066654] 
dist 194=[-.89511884924509850314,.56129184584064363621] 
dist 195=[-.90795441784899844905,.52695527909118059505] 
dist 196=[-.91206734353443057075,.51959008153758573016] 
dist 197=[-.91227492836751677   ,.49940712447819975429] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 2, 0, 2, 0, 1] 
dist 0=[53.409134736526400454  ,53.409134736526400454  ] 
dist 1=[53.095001450467603332  ,53.498710193480174268  ] 
dist 2=[52.521914972856463368  ,53.488401026730053311  ] 
dist 3=[51.398362496671431692  ,53.410431555426658889  ] 
dist 4=[50.123398661543555182  ,53.306030926990282333  ] 
dist 5=[48.945469709713620162  ,53.242949045312193361  ] 
dist 6=[47.610175495251139254  ,53.192669152573751426  ] 
dist 7=[45.706502565109885098  ,53.076286643700744928  ] 
dist 8=[43.576769690644633558  ,49.088094463886107973  ] 
dist 9=[41.338452492608405749  ,48.492353873895954495  ] 
dist 10=[38.585397247313313556  ,47.553734804817501151  ] 
dist 11=[34.399573429665700073  ,47.281159334826821875  ] 
dist 12=[30.180068774719166657  ,46.665799217682473610  ] 
dist 13=[27.292394573278273975  ,46.531922245325654637  ] 
dist 14=[24.818937355439083830  ,45.266723462949912592  ] 
dist 15=[22.253749986438837684  ,42.985538842339470256  ] 
dist 16=[19.816174398715014086  ,34.101396536304384420  ] 
dist 17=[17.852247864690797146  ,32.352767865919968068  ] 
dist 18=[15.852363460548292903  ,31.897802197113988040  ] 
dist 19=[13.270787558925037576  ,30.279553215432809533  ] 
dist 20=[10.752234023112362103  ,29.902843207676090626  ] 
dist 21=[9.0038871892395703274 ,29.346506264368746541  ] 
dist 22=[7.4778096135064292003 ,29.174588439888317930  ] 
dist 23=[5.8468650173968237592 ,13.065368540915995598  ] 
dist 24=[4.2636908305956742754 ,11.020014340618995266  ] 
dist 25=[2.9280488035802999705 ,7.8284614335574704472 ] 
dist 26=[.9239315846555538221 ,7.3440571124781636721 ] 
dist 27=[-1.3669223896759293152 ,7.2501104003814545122 ] 
dist 28=[-3.0649410728560564689 ,5.5229797853519777330 ] 
dist 29=[-4.6592642820799525925 ,5.3611742629091353392 ] 
dist 30=[-6.5359084393976137756 ,4.7999042653743081028 ] 
dist 31=[-8.2876711072882976683 ,4.1726230672995709723 ] 
dist 32=[-9.3831965793386890769 ,-3.4656692355580447122 ] 
dist 33=[-10.211409560078410928  ,-4.4995828297049947221 ] 
dist 34=[-10.895511877368314734  ,-4.7264847975741365665 ] 
dist 35=[-11.437969902599583785  ,-5.5141742987270506985 ] 
dist 36=[-11.700335199989633259  ,-5.6630990895563142087 ] 
dist 37=[-11.835400372099937142  ,-5.6782274038528636472 ] 
dist 38=[-11.869163976235751822  ,-5.4935960700872803660 ] 
dist 39=[-9.1722644450805462455 ,-5.2481955548217096766 ] 
dist 40=[-8.9840615052267383553 ,-5.0139506329695883576 ] 
dist 41=[-8.9727641229958487106 ,-4.7461815734071565220 ] 
dist 42=[-8.9278075047662861586 ,-4.3661826427444804618 ] 
dist 43=[-8.9140132505574159035 ,-3.9456621343912981964 ] 
dist 44=[-8.5620136835643830701 ,-3.5157850737894933007 ] 
dist 45=[-8.4691341450166392033 ,-2.8751139269042294934 ] 
dist 46=[-8.3987336816375244641 ,-1.6840559519115807678 ] 
dist 47=[-8.3639471631525549903 ,.1183990124303402098 ] 
dist 48=[-6.6502820995922888074 ,1.9203521883211045233 ] 
dist 49=[-6.4363190157435863631 ,3.1095300224293235374 ] 
dist 50=[-5.9969184787781043595 ,4.0781805069153240434 ] 
dist 51=[-5.8785294091358188239 ,4.9999479996233766757 ] 
dist 52=[-4.6717894404004150902 ,5.8219137204188638905 ] 
dist 53=[-4.4486633059441666896 ,6.3922511572169530521 ] 
dist 54=[-3.4425407449636767374 ,6.8881742785013037926 ] 
dist 55=[-.81944246047458181814,7.4132084418716765706 ] 
dist 56=[-.56602435132936737168,7.8859675526543361868 ] 
dist 57=[-.04553361886097112512,8.1731804845031354125 ] 
dist 58=[.08580153593705428720,8.3799302819412506067 ] 
dist 59=[.5448041432031964980 ,8.5312692442619868250 ] 
dist 60=[.6351546060887861272 ,8.6352635889257042244 ] 
dist 61=[.7532988637278827973 ,8.6542018627360794493 ] 
dist 62=[.7723805214370563969 ,8.6383619682717089720 ] 
dist 63=[.7551248554361246625 ,8.6145445409418081635 ] 
dist 64=[.6858329780897713605 ,6.6917271156582891723 ] 
dist 65=[.5656902058474540977 ,6.8002267467276512661 ] 
dist 66=[.3453263510424898361 ,6.8511732831810722871 ] 
dist 67=[.0777819599230106200 ,6.8720790149654850548 ] 
dist 68=[-.2307496908963948696 ,6.8635832403606832419 ] 
dist 69=[-.6283078484520430263 ,6.8323793999010205754 ] 
dist 70=[-1.2512644746343196083 ,6.8084054892189574583 ] 
dist 71=[-1.8786428365944988445 ,3.6311450372253622471 ] 
dist 72=[-2.2938799285047174204 ,3.5171367310341323762 ] 
dist 73=[-2.6333155151155606327 ,3.4885502993879925072 ] 
dist 74=[-2.9581568134637577806 ,3.4089978419249661541 ] 
dist 75=[-3.2488777258561688117 ,3.3851553473878430454 ] 
dist 76=[-3.4521370319785723388 ,1.8063181099918336768 ] 
dist 77=[-3.6303604523040582811 ,1.6684123718121254978 ] 
dist 78=[-3.8211719244460770290 ,1.3406604559066273429 ] 
dist 79=[-3.9877884377064845273 ,1.2884724859300045110 ] 
dist 80=[-4.0694443343398100815 ,.83292931212689945143] 
dist 81=[-4.1118330373893447263 ,.74994401606054362499] 
dist 82=[-4.1216800550083975525 ,.63594143721671388373] 
dist 83=[-4.4001824577629825172 ,.60238191414726147122] 
dist 84=[-4.6942694293886332052 ,-.00823275525568024867] 
dist 85=[-4.8901058535962324240 ,-.08363720964290825098] 
dist 86=[-5.0520478697150943477 ,.00518829629174577219] 
dist 87=[-5.2108110430214084740 ,.8249886655528162529 ] 
dist 88=[-5.3432126765278392220 ,1.3725958200990108890 ] 
dist 89=[-5.3998876186610478972 ,1.8257093097886966530 ] 
dist 90=[-5.4236604933338305501 ,2.2683476134051783183 ] 
dist 91=[-5.4246013178375879386 ,2.6703535698773681961 ] 
dist 92=[-5.3113227427413755644 ,2.9612804716076643039 ] 
dist 93=[-5.2760159189123704218 ,3.2265151434081690677 ] 
dist 94=[-5.2494752826749855226 ,3.5259537293143825061 ] 
dist 95=[-5.2279878289385166316 ,3.7993814342962054999 ] 
dist 96=[-4.0497059486280946863 ,3.9608005962776928830 ] 
dist 97=[-3.8895857864805176419 ,4.0710174732798528697 ] 
dist 98=[-3.8414189637353025601 ,4.1401088392026178341 ] 
dist 99=[-3.6341707483767569106 ,4.1843660872212365708 ] 
dist 100=[-3.5883214981693697395 ,4.2712965307584699590 ] 
dist 101=[-3.4631182400797086587 ,4.5005279403093067259 ] 
dist 102=[-3.4344631351183661561 ,4.7032533408457394968 ] 
dist 103=[-1.1125493413759493486 ,4.9231527351724853904 ] 
dist 104=[-1.0721452651203983502 ,5.1170180597745681854 ] 
dist 105=[-1.0614757378498335349 ,5.2158240854839286700 ] 
dist 106=[-1.0539570167485946142 ,5.2664967569676308199 ] 
dist 107=[-1.0502274812723827599 ,5.2745982738721910610 ] 
dist 108=[-.84288263870664543547,5.2303633852679450117 ] 
dist 109=[-.81748908823921541379,5.2060285788874893004 ] 
dist 110=[-.75566087360028472478,5.2406949978446097120 ] 
dist 111=[-.74352571133638877234,5.2446129754951004677 ] 
dist 112=[-1.2719131300779529882 ,5.2269792164653759618 ] 
dist 113=[-1.9783638677514056299 ,5.2129417651424831883 ] 
dist 114=[-2.5653640629677759249 ,5.1404693393118604262 ] 
dist 115=[-3.1432907655549043976 ,5.1228124733817872623 ] 
dist 116=[-3.6715324508402673108 ,4.8620635082147951803 ] 
dist 117=[-4.0601927775946058671 ,4.7972107397799973586 ] 
dist 118=[-4.4212464048164522262 ,4.4426065702196606572 ] 
dist 119=[-4.8392767733285461472 ,3.3666317684459375423 ] 
dist 120=[-5.2221287505026884497 ,2.5788673044796456538 ] 
dist 121=[-5.4427533020511306240 ,2.4701032301261058067 ] 
dist 122=[-5.5868695521633829148 ,2.2122686545873393164 ] 
dist 123=[-5.6643149524992301381 ,2.1604105344112365781 ] 
dist 124=[-5.7120293336294112718 ,1.7917916395767915016 ] 
dist 125=[-5.7374654472062057761 ,1.7208369547566273770 ] 
dist 126=[-5.7514345333597569939 ,1.5986825381727000183 ] 
dist 127=[-5.7533761490551263339 ,1.5688745639185349425 ] 
dist 128=[-.0525234830904841175 ,1.0931462831629162018 ] 
dist 129=[-.0460503524883191578 ,1.0808187707900521034 ] 
dist 130=[-.0357515041938842412 ,1.0684464631995340598 ] 
dist 131=[-.20321397914528755382,1.0615602767731314036 ] 
dist 132=[-.38917842831548667247,.87947327807649301273] 
dist 133=[-.53057758701015170713,.85388241433163497218] 
dist 134=[-.66659465109512669604,.80320015412664808663] 
dist 135=[-.8310802334312275358 ,.78940259333501964785] 
dist 136=[-.98564278242109339086,.73713275957019956948] 
dist 137=[-1.0820465276913269186 ,.72501282548916543598] 
dist 138=[-1.1544567244644002835 ,.7013099767398312297 ] 
dist 139=[-1.2132289367184189980 ,.69439851112196235575] 
dist 140=[-1.2601243160576429775 ,.4856073996169822732 ] 
dist 141=[-1.2851098593708318464 ,.49225851267022361791] 
dist 142=[-1.2988712739771536178 ,.49563043838785693849] 
dist 143=[-1.3011688365569436023 ,.4960736615491906686 ] 
dist 144=[-1.2518607284220069477 ,.49365769082967025296] 
dist 145=[-1.2419678139269153717 ,.49195127380012558862] 
dist 146=[-1.2222648440678827926 ,.48796974148177210851] 
dist 147=[-1.2151228144332085785 ,.48599421372514205255] 
dist 148=[-1.1796478144370870581 ,.44218366673519887887] 
dist 149=[-1.1707793331675726642 ,.43501908499540421542] 
dist 150=[-1.1420547520842306849 ,.41923744759094474711] 
dist 151=[-1.1361936244551448878 ,.4142017397276571594 ] 
dist 152=[-1.0631008631303967476 ,.39108314838963598619] 
dist 153=[-1.0485811286808956857 ,.38603667093360846841] 
dist 154=[-1.0140688973996282389 ,.37268250608847976814] 
dist 155=[-1.0023400724088892576 ,.36934416461534355451] 
dist 156=[-.94586412910878451447,.51243157898410968651] 
dist 157=[-.933010635804554226  ,.67031450456708325878] 
dist 158=[-.90479626193669765446,.85335854128529650586] 
dist 159=[-.89558163909265660339,1.1189030461288759130 ] 
dist 160=[.15188653958045539464,1.3817605716048309048 ] 
dist 161=[.16343098759662979914,1.5540786290785362880 ] 
dist 162=[.17174981390203199963,1.6932841522889002687 ] 
dist 163=[.16707713861879627659,1.8239401728168180031 ] 
dist 164=[.15688381585521730374,1.9392974980104699767 ] 
dist 165=[.14046143293194350687,2.0174238504169104379 ] 
dist 166=[.11631079188677536595,2.0833438349910994713 ] 
dist 167=[.07526247604627341553,2.1499695510529223118 ] 
dist 168=[.02643212109541696799,2.2059540051662762528 ] 
dist 169=[-.02878805099470048927,2.2293893940961337532 ] 
dist 170=[-.09933339528379653622,2.2393996272113796574 ] 
dist 171=[-.20934879882306238112,2.2417780612869542394 ] 
dist 172=[-.32081676817982787618,2.1866895241219744138 ] 
dist 173=[-.39716147977695412616,2.1726354724999482612 ] 
dist 174=[-.46248431804035706625,2.1643999068480375541 ] 
dist 175=[-.52994815189446672661,2.1619369497352721730 ] 
dist 176=[-.59371767570037114483,1.8986503599509642253 ] 
dist 177=[-.64429122382032527484,1.8668808592182329491 ] 
dist 178=[-.81953137403022865236,1.7805392645578847462 ] 
dist 179=[-1.0598739298916802164 ,1.7646858794382574116 ] 
dist 180=[-1.2825220539949432313 ,1.5997503876293044094 ] 
dist 181=[-1.4516398843263808619 ,1.5647096397554504604 ] 
dist 182=[-1.6141291840480005240 ,1.5233983972485591171 ] 
dist 183=[-1.8103130774179037403 ,1.5064248738979991565 ] 
dist 184=[-1.9944068431834244726 ,1.1141867493370404998 ] 
dist 185=[-2.1086268120486437611 ,1.0613624244073542268 ] 
dist 186=[-2.1936601412088469082 ,.95231233154579355941] 
dist 187=[-2.2612275737283528568 ,.92266011987828155707] 
dist 188=[-2.3124780362952343103 ,.80836102687490206988] 
dist 189=[-2.3323663729003170964 ,.78457712620398729612] 
dist 190=[-2.3397385900506421091 ,.73430860164817612566] 
dist 191=[-2.3410201050336977564 ,.71983439256300171924] 
dist 192=[-1.0185146219559417807 ,.01932498536177262401] 
dist 193=[-1.0116367549541428936 ,-.00357322201446027220] 
dist 194=[-.99973634085048624722,-.04238877566837749825] 
dist 195=[-.99525072416175755343,-.05103125591771933481] 
dist 196=[-.86922603692454403356,-.18226352608734667588] 
dist 197=[-.85008105106733794008,-.19963572619425380999] 
dist 198=[-.89112893123882253196,-.23201280100665902328] 
dist 199=[-1.0285843155327552597 ,-.23903024273077689286] 
dist 200=[-1.1618084964230808341 ,-.25592529956241940167] 
dist 201=[-1.2519277156083805205 ,-.2542762555227590019 ] 
dist 202=[-1.3278527713599908774 ,-.1235980583440756324 ] 
dist 203=[-1.4044052985237500077 ,.07044171610359386992] 
dist 204=[-1.4756330268097511104 ,.26381129580308166708] 
dist 205=[-1.5302989284434245072 ,.3918137572644079753 ] 
dist 206=[-1.5833845040062273891 ,.49659878762328533314] 
dist 207=[-1.6483045552330075805 ,.59727258969983357869] 
dist 208=[-1.7072773582278920137 ,.68774337142194983299] 
dist 209=[-1.7366177635342053052 ,.7517928526080858627 ] 
dist 210=[-1.7518428134490127232 ,.80883279272484124573] 
dist 211=[-1.7544543127571234200 ,.87131820271833691396] 
dist 212=[-1.7347785659024553683 ,.92814947582393303802] 
dist 213=[-1.7282155998488805263 ,.96261495910581383242] 
dist 214=[-1.7229495875460710899 ,1.0609046577658851635 ] 
dist 215=[-1.7180703974317218222 ,1.2054878968873587936 ] 
dist 216=[-1.4683988071741663571 ,1.3464445413427319902 ] 
dist 217=[-1.4323996480781175644 ,1.4431468610068084106 ] 
dist 218=[-1.3659965916137658426 ,1.5260734660321781472 ] 
dist 219=[-1.3484064149352838717 ,1.6120295928964658689 ] 
dist 220=[-1.2866332178621597764 ,1.6934877924537012158 ] 
dist 221=[-1.2694104798861039597 ,1.7584562293397949049 ] 
dist 222=[-1.2468551921690502078 ,1.8238740546460967251 ] 
dist 223=[-1.2377162771805649489 ,1.9071268433336584088 ] 
dist 224=[-.289734608738594415  ,1.9848288099857943246 ] 
dist 225=[-.35548604632999072743,2.0280844411726141305 ] 
dist 226=[-.43250594487477218579,2.0544433840318826038 ] 
dist 227=[-.54518200199350774803,2.0646833266755147087 ] 
dist 228=[-.66093727770587551657,2.0666710299509237358 ] 
dist 229=[-.75025125282267153956,2.0628653376829289129 ] 
dist 230=[-.83742060232860010445,2.0496365875232389101 ] 
dist 231=[-.94461300498314249716,2.0411589552870262066 ] 
dist 232=[-1.0566492632889768507 ,1.8767461693778560662 ] 
dist 233=[-1.1631581822575137176 ,1.8487175679624032193 ] 
dist 234=[-1.2861642931439694594 ,1.7848701224812026372 ] 
dist 235=[-1.4640674536803961025 ,1.7637752054314793888 ] 
dist 236=[-1.6390402465966653152 ,1.6642806795624165588 ] 
dist 237=[-1.7503464175497109343 ,1.6420322434950933900 ] 
dist 238=[-1.8364717882397867136 ,1.5875954710708376352 ] 
dist 239=[-1.9109070472464045603 ,1.5698178048356347525 ] 
dist 240=[-1.9722408764215938558 ,1.4740671976853640604 ] 
dist 241=[-2.0060570518539243920 ,1.5014216879625932639 ] 
dist 242=[-2.0262316474827152084 ,1.5165187007788357089 ] 
dist 243=[-2.0330995131795066793 ,1.5190522487191089649 ] 
dist 244=[-2.0323773402737919377 ,1.5158675548031932926 ] 
dist 245=[-2.0284941349549819060 ,1.5109901340390437520 ] 
dist 246=[-2.0099234753947989940 ,1.5007012059322883678 ] 
dist 247=[-2.0004382095301606442 ,1.4952471574132272527 ] 
dist 248=[-1.9292946435927744971 ,1.3486173607559389216 ] 
dist 249=[-1.9099934409665618003 ,1.3250740354368733857 ] 
dist 250=[-1.8796719955828563548 ,1.2743717642744790812 ] 
dist 251=[-1.8549071367101124624 ,1.2585390489484848818 ] 
dist 252=[-1.3176629960199890308 ,1.1871787332850818128 ] 
dist 253=[-1.2574208646077340570 ,1.1719242345680996533 ] 
dist 254=[-1.1043947825840133689 ,1.1282979562953770005 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 1, 2, 0, 1] 
dist 0=[53.218448338329781595  ,53.218448338329781595  ] 
dist 1=[53.087183280968344973  ,53.261644263816131660  ] 
dist 2=[52.684075378458216016  ,53.313179353160710345  ] 
dist 3=[51.982651777992212664  ,53.352288526772244789  ] 
dist 4=[50.660326791229471320  ,53.345632952994684204  ] 
dist 5=[49.177124262013131113  ,53.303624167808541402  ] 
dist 6=[47.833076746375489215  ,53.214127892334813798  ] 
dist 7=[46.330758446811783535  ,49.859226914484479494  ] 
dist 8=[44.215230781521180851  ,49.343281028065125459  ] 
dist 9=[41.861119632987386862  ,48.438101701060865612  ] 
dist 10=[39.405798306653508639  ,48.198648947679390291  ] 
dist 11=[36.399643366261647791  ,47.396042306091430390  ] 
dist 12=[31.845390140978861551  ,47.141390471666932296  ] 
dist 13=[27.264288319007183643  ,46.884937866720374050  ] 
dist 14=[24.150785007265912673  ,46.370803090520485309  ] 
dist 15=[21.507799535834626044  ,34.946557760291126153  ] 
dist 16=[18.805714438170132600  ,34.047651386568147050  ] 
dist 17=[16.262815596397302180  ,32.296034923220457398  ] 
dist 18=[14.255380767532813170  ,31.842680063037533254  ] 
dist 19=[12.249023255529847896  ,30.247031559806957667  ] 
dist 20=[9.7099465904980768252 ,29.870399903219991530  ] 
dist 21=[7.2569063874595954453 ,29.354575736011136865  ] 
dist 22=[5.5939388454918909565 ,29.180700449235480064  ] 
dist 23=[4.1842294364997295797 ,12.089429895070198376  ] 
dist 24=[2.7424684518921677873 ,10.747214417416017981  ] 
dist 25=[1.3808968746315234774 ,9.2749599787770497104 ] 
dist 26=[.2910070406561364602 ,9.0376427083836224717 ] 
dist 27=[-1.0431572346714416057 ,7.4152300555717762819 ] 
dist 28=[-2.7482240654961225996 ,7.1608769503888749979 ] 
dist 29=[-4.3556662852924988366 ,6.6977361883862513903 ] 
dist 30=[-6.2572105958079085662 ,6.6111664685648179516 ] 
dist 31=[-8.0342621416394383997 ,-3.5808292428867776195 ] 
dist 32=[-9.1444559684700662064 ,-4.1044886364012570238 ] 
dist 33=[-9.9824048942655733230 ,-5.1703684005590605336 ] 
dist 34=[-10.672089964196032054  ,-5.3938284325184593451 ] 
dist 35=[-11.220949075884896273  ,-5.6626736837671671931 ] 
dist 36=[-11.496318032191155720  ,-5.3528747341437472813 ] 
dist 37=[-11.639587546229364946  ,-4.9666910772774425008 ] 
dist 38=[-11.660792588133952258  ,-4.5727506257223866067 ] 
dist 39=[-9.0813130351772329020 ,-4.0999267019144660736 ] 
dist 40=[-8.9094009050567407037 ,-3.3982602204828612132 ] 
dist 41=[-8.6916951443523461910 ,-2.6047640366529763396 ] 
dist 42=[-8.7352696087308942724 ,-1.7651091071674568722 ] 
dist 43=[-8.7663946517626383918 ,-.7312847834990450638 ] 
dist 44=[-8.7769971085654908617 ,.8374905069636885732 ] 
dist 45=[-8.7752414675567069742 ,2.4061596399526784916 ] 
dist 46=[-8.7567208473764953886 ,3.4396816446187037734 ] 
dist 47=[-5.9466767552295638856 ,4.2793261504736868772 ] 
dist 48=[-5.8842432665582228292 ,5.0742447670004841145 ] 
dist 49=[-5.6732977600615028904 ,5.7800374744044175753 ] 
dist 50=[-5.5037406241448606389 ,6.2640036935572774848 ] 
dist 51=[-4.8076702203423526832 ,6.6785903260409267814 ] 
dist 52=[-4.3416105057412080393 ,7.1075507652789234506 ] 
dist 53=[-3.6581593319146457027 ,7.4897825798170749469 ] 
dist 54=[-3.6089304700458829002 ,7.7178133369507996902 ] 
dist 55=[-.9782297362997601182 ,7.8768287127302844723 ] 
dist 56=[-.7242887978617692078 ,7.9833777514642637563 ] 
dist 57=[-.19834478645552117214,8.0477662125498036243 ] 
dist 58=[-.06802213941973801090,8.0560978657560320429 ] 
dist 59=[.4134378306961241682 ,8.0083342816665718497 ] 
dist 60=[.5058192462522278941 ,7.9908614789441775859 ] 
dist 61=[.6482388384937315338 ,5.7128676998542435093 ] 
dist 62=[.6817887434008777570 ,6.0565456228513715974 ] 
dist 63=[.6971658175943033420 ,6.3627105490748305918 ] 
dist 64=[.6473547284866462483 ,6.5378244348435398650 ] 
dist 65=[.5470250620826979653 ,6.6511051543527316473 ] 
dist 66=[.3521325363501895254 ,6.7103244270545120287 ] 
dist 67=[.1117781042236712730 ,6.7388283559146945803 ] 
dist 68=[-.1700785545762743982 ,6.7345681221723666182 ] 
dist 69=[-.5362012268758445304 ,6.7037098855617782256 ] 
dist 70=[-1.1129618106336937787 ,6.6780398264874216930 ] 
dist 71=[-1.6944216187067375985 ,4.2336570400703082210 ] 
dist 72=[-2.0793307753836716590 ,4.1832039095386646035 ] 
dist 73=[-2.3940193866429000199 ,4.0848086740561616025 ] 
dist 74=[-2.6952229768744003539 ,4.0542237240967480983 ] 
dist 75=[-2.9647978216026505610 ,3.9212561459833709005 ] 
dist 76=[-3.1532574043248778737 ,3.8879393224417891680 ] 
dist 77=[-3.3184786623699710349 ,3.7999618092106038308 ] 
dist 78=[-3.5797040045772527551 ,3.7704695425198524908 ] 
dist 79=[-3.9054945873155818618 ,1.9379991287767631799 ] 
dist 80=[-4.2065364533626326247 ,1.7777111061307909257 ] 
dist 81=[-4.4695403154012184559 ,1.3984730169220305856 ] 
dist 82=[-4.6434418304579050765 ,1.3378897256172841189 ] 
dist 83=[-4.7858884935566771175 ,.81697583638087770108] 
dist 84=[-4.9233094622232037639 ,.72260804248146479225] 
dist 85=[-5.0363262573851999404 ,.59089829464147905352] 
dist 86=[-5.0813227514662813831 ,.55307693823323930861] 
dist 87=[-5.0982140313411600929 ,.7920201741784520771 ] 
dist 88=[-5.0989311820807513754 ,1.2967634269035891594 ] 
dist 89=[-4.9744772131618450504 ,1.7137402615628198258 ] 
dist 90=[-4.9383674563871347536 ,2.1199260672491758274 ] 
dist 91=[-4.9132382629222085819 ,2.4880242794105591499 ] 
dist 92=[-4.8965502319765949605 ,2.7529737930546767618 ] 
dist 93=[-4.4339122853459470975 ,2.9930395058535492120 ] 
dist 94=[-4.4225039043531787102 ,3.2617977519410064390 ] 
dist 95=[-4.0122135162083522406 ,3.5633351470430555557 ] 
dist 96=[-3.9455109561095360423 ,3.9151498371487966651 ] 
dist 97=[-3.8061132132273852955 ,4.2302370456630073023 ] 
dist 98=[-3.7630306421815595696 ,4.4512776238398923987 ] 
dist 99=[-3.5719861598098703992 ,4.6459996052737978814 ] 
dist 100=[-3.5301466631279274438 ,4.8560446190291033424 ] 
dist 101=[-3.4082526665409261263 ,5.0405553095562447044 ] 
dist 102=[-3.3857343897409355365 ,5.1333514561317389392 ] 
dist 103=[-1.1747138986813509854 ,5.1804226826558057596 ] 
dist 104=[-1.1700284873624533608 ,5.1867319259973828192 ] 
dist 105=[-1.1548389390452225164 ,5.1357283324212099541 ] 
dist 106=[-1.1486442822644515856 ,5.1107349057772784801 ] 
dist 107=[-1.1067889406512057809 ,5.1303769082655716306 ] 
dist 108=[-1.0960576040731830092 ,5.1323102580696477547 ] 
dist 109=[-1.2137482959242795057 ,5.0742083562723828833 ] 
dist 110=[-1.9066929057527692669 ,5.0536513608867759390 ] 
dist 111=[-2.4827402741092093341 ,4.9667133261376959195 ] 
dist 112=[-3.0503560825798034289 ,4.9476780899619294842 ] 
dist 113=[-3.5695083715585830638 ,4.6719685967180691477 ] 
dist 114=[-3.9520905990577937874 ,4.6051435613775888197 ] 
dist 115=[-4.3081211004954361196 ,4.5418442869426116358 ] 
dist 116=[-4.7212734617056812763 ,4.4118236167159372930 ] 
dist 117=[-5.1000544089980430168 ,3.5525593846693189525 ] 
dist 118=[-5.3188737329870622151 ,3.2431926308760415181 ] 
dist 119=[-5.4625007610930145760 ,2.1289342186875900729 ] 
dist 120=[-5.5411181435028326235 ,2.0775392711636612261 ] 
dist 121=[-5.5903360652602488434 ,1.7173375946605029271 ] 
dist 122=[-5.6166098176481383377 ,1.6481423855836088949 ] 
dist 123=[-5.6310983155794600864 ,1.5272358526315433888 ] 
dist 124=[-5.6332933034473041618 ,1.4982957072727390672 ] 
dist 125=[-.13749420699427529479,1.1217619813943557147 ] 
dist 126=[-.13329723370132495848,1.1228335245111893258 ] 
dist 127=[-.0751187872857577320 ,1.1140255695981985154 ] 
dist 128=[-.24267691214021143015,1.1105693911322450195 ] 
dist 129=[-.42379633450943484833,1.0951253975078552744 ] 
dist 130=[-.56094977545128949324,1.0917168380788690971 ] 
dist 131=[-.69234121667123448295,1.0408461338822359513 ] 
dist 132=[-.85046416635632114696,1.0284090350575128430 ] 
dist 133=[-.99877327313408178198,1.0169168203135114460 ] 
dist 134=[-1.0909838382328192922 ,1.0111801621212258938 ] 
dist 135=[-1.1598867919905452700 ,.82973466193141720044] 
dist 136=[-1.2151346184885699023 ,.80463426895355764566] 
dist 137=[-1.2589761990652219752 ,.75557630738790949316] 
dist 138=[-1.2823399632025910382 ,.7424536647758438551 ] 
dist 139=[-1.2952209321071912346 ,.69418577411309575737] 
dist 140=[-1.2972163579108154355 ,.68267041195822439094] 
dist 141=[-1.2224140387160289334 ,.66234807416385859041] 
dist 142=[-1.2102746857246556916 ,.65691137844187577192] 
dist 143=[-1.1854529808609347835 ,.41701021981276848281] 
dist 144=[-1.1769534446702077308 ,.41746047250538027588] 
dist 145=[-1.1361575877023801738 ,.41675448633083522551] 
dist 146=[-1.1264909564478566710 ,.41551481184956528671] 
dist 147=[-1.0957378457114245592 ,.40598437602335280369] 
dist 148=[-1.0900543432116697867 ,.40304209305843838056] 
dist 149=[-1.0142347894233647634 ,.39828531488647262115] 
dist 150=[-.99940647041063762335,.39648709015852167676] 
dist 151=[-.96491935271018541784,.3475022919659379743 ] 
dist 152=[-.95344148297905882336,.3440762092425019318 ] 
dist 153=[-.89902255590647320212,.50696662882493727432] 
dist 154=[-.88681234622980981579,.66252690830700108472] 
dist 155=[-.85866678416603851111,.8427071186366420099 ] 
dist 156=[-.84924344210314615594,1.1038973779759274203 ] 
dist 157=[-.79678423459499208185,1.3623998975586257838 ] 
dist 158=[-.79666912857360511916,1.5318509111246648541 ] 
dist 159=[-.03677839071396709188,1.6687274122186417068 ] 
dist 160=[-.00257651009388227084,1.7971761853586742577 ] 
dist 161=[.06725493676301606677,1.9105702072018317318 ] 
dist 162=[.08478195444739199232,1.9873412778549638640 ] 
dist 163=[.14502935869946318909,2.0520896284372407650 ] 
dist 164=[.15721729744670240356,2.1174849352307854823 ] 
dist 165=[.16954946052815507911,2.1724055407524692536 ] 
dist 166=[.16822475368276343564,2.1953341394081481843 ] 
dist 167=[.16138542792624674552,2.2051087908813522578 ] 
dist 168=[.1474173630432959232 ,2.2075066528048892931 ] 
dist 169=[.12553610238770502953,2.1528815424764967862 ] 
dist 170=[.08710352858567573249,2.1390499642747432956 ] 
dist 171=[.04091732279794119468,2.1310406303833600683 ] 
dist 172=[-.01191987168699234641,2.1288686038637216258 ] 
dist 173=[-.28268542002483989857,1.8601312409233496679 ] 
dist 174=[-.5633585644603676562 ,1.8277019797107403083 ] 
dist 175=[-.79910485799075897559,1.7402459241223153042 ] 
dist 176=[-1.0355537010744932100 ,1.7241703232176041599 ] 
dist 177=[-1.2546824684661793409 ,1.5593880302604769509 ] 
dist 178=[-1.4212791084314400363 ,1.5245294932682511782 ] 
dist 179=[-1.5814946358833607721 ,1.4829018050525613015 ] 
dist 180=[-1.7751469339640021915 ,1.4661007187493831732 ] 
dist 181=[-1.9569774558207060532 ,1.0802685527917641256 ] 
dist 182=[-2.0699949123529677480 ,1.0283515680577204210 ] 
dist 183=[-2.1543726541772466951 ,.92079261501303715845] 
dist 184=[-2.2218601012404757629 ,.89252066632105433939] 
dist 185=[-2.2734081418131957019 ,.86541771771475939532] 
dist 186=[-2.2941481493483918448 ,.85748859082400496462] 
dist 187=[-2.3021153898850920545 ,.82547124050064781985] 
dist 188=[-2.3026695398507650142 ,.81704670768057280383] 
dist 189=[-.972783323420755207  ,.79820698336103715296] 
dist 190=[-.99736175016147155128,.79156813377930360195] 
dist 191=[-1.0190560274446824288 ,.28782348876634913192] 
dist 192=[-1.0287315895787395625 ,.24331614054482131046] 
dist 193=[-1.0323098073071374503 ,.14145112707253662788] 
dist 194=[-1.0316506112084102212 ,.12338961748186325124] 
dist 195=[-1.0167294460965564813 ,-.00511982568050737230] 
dist 196=[-1.0108876318168687016 ,-.02771167453520344511] 
dist 197=[-1.1247488960483261366 ,-.06696688440099237666] 
dist 198=[-1.2108115524729031438 ,-.07540109723692104363] 
dist 199=[-1.2830726993619360231 ,-.19946145996873159693] 
dist 200=[-1.3555319780682768974 ,-.21612274407956635632] 
dist 201=[-1.4226964325789604620 ,-.24572938426186472465] 
dist 202=[-1.4738180432861419933 ,-.25169417540875140062] 
dist 203=[-1.5230551965346924217 ,-.15432054664639961282] 
dist 204=[-1.5826975467783596059 ,.05114593673074833900] 
dist 205=[-1.6365959420784818450 ,.26030312699835495236] 
dist 206=[-1.6628995974408838413 ,.40528493669002768015] 
dist 207=[-1.6762958936614500614 ,.53120398057825793091] 
dist 208=[-1.6786563370432766321 ,.66425186989863954239] 
dist 209=[-1.6564645582543612420 ,.791904142385716965  ] 
dist 210=[-1.6495447725586151446 ,.89628095799885135687] 
dist 211=[-1.6443319694541190698 ,1.0037345845664917133 ] 
dist 212=[-1.6400792702353529673 ,1.1436715598088197856 ] 
dist 213=[-1.3949324514868011718 ,1.2801943171000286727 ] 
dist 214=[-1.3598498340865462969 ,1.3740165233534811302 ] 
dist 215=[-1.2952901054538445180 ,1.4546463327959297646 ] 
dist 216=[-1.2782898076699971018 ,1.5384974525118292012 ] 
dist 217=[-1.2191883699640559617 ,1.6181321528968010722 ] 
dist 218=[-1.2025985339702491385 ,1.6819277061989435765 ] 
dist 219=[-1.1823198402173116090 ,1.7464232703992929171 ] 
dist 220=[-1.1734878527553039297 ,1.8288531608109876567 ] 
dist 221=[-.18606943345520974559,1.9059561991505851976 ] 
dist 222=[-.10357123870201464843,1.9491837695509869462 ] 
dist 223=[-.05581486803121807469,1.9759275539185051228 ] 
dist 224=[-.1023086303393040847 ,1.9872170905069134400 ] 
dist 225=[-.14923262004732286742,1.9903790923916732936 ] 
dist 226=[-.20909935949051132767,1.9872095059926241062 ] 
dist 227=[-.27280486569311973321,1.9750794858979068373 ] 
dist 228=[-.33505547410446387343,1.9669704892048618958 ] 
dist 229=[-.4082501242239710994 ,1.8126948832081951209 ] 
dist 230=[-.51565098500291491679,1.7861820087737498463 ] 
dist 231=[-.62612110357201156074,1.7256291615290234165 ] 
dist 232=[-.7115700514206986928 ,1.7055281676999945986 ] 
dist 233=[-.79516923192667067976,1.6103802589734430608 ] 
dist 234=[-.89825373260537583252,1.5890313634319496228 ] 
dist 235=[-1.0061439362600372984 ,1.5370055031275871388 ] 
dist 236=[-1.1089303433365952626 ,1.5197012946067267709 ] 
dist 237=[-1.2278059631896046524 ,1.4222616380081784610 ] 
dist 238=[-1.3999341243860648731 ,1.4468296381014479969 ] 
dist 239=[-1.5693086749942477942 ,1.4598193236473588206 ] 
dist 240=[-1.6771900816566752109 ,1.4619912293904915924 ] 
dist 241=[-1.7608224409458691894 ,1.4561204648029164786 ] 
dist 242=[-1.8333796409822080511 ,1.4508423749475148143 ] 
dist 243=[-1.8933715869196453258 ,1.4403887881720462311 ] 
dist 244=[-1.9268355192121295390 ,1.4351640109292095529 ] 
dist 245=[-1.9473150015403121946 ,1.2887434942829521665 ] 
dist 246=[-1.9554646717420397702 ,1.2654764995500445275 ] 
dist 247=[-1.9562512724857302968 ,1.2156634720752456707 ] 
dist 248=[-1.9530707535456244894 ,1.2002435732370117653 ] 
dist 249=[-1.9360553612467148249 ,1.1312594618160481187 ] 
dist 250=[-1.9274232097180871752 ,1.1166272931894203392 ] 
dist 251=[-1.8035238580030717704 ,1.0740748603526502164 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 1, 2, 0, 1] 
dist 0=[50.979192790504863206  ,50.979192790504863206  ] 
dist 1=[50.868645072052558736  ,51.006086145662141649  ] 
dist 2=[50.518260350035493536  ,51.022523706528014276  ] 
dist 3=[49.902846246239156278  ,51.027752735991445921  ] 
dist 4=[48.734134757378236640  ,51.009655397009778957  ] 
dist 5=[47.420352358966151948  ,50.970441075656038714  ] 
dist 6=[46.225422929360365163  ,50.891048196653657628  ] 
dist 7=[44.886099827132956676  ,47.655280972310862737  ] 
dist 8=[42.995397274155661843  ,47.163221802711360392  ] 
dist 9=[40.889003459310998036  ,46.324680232019995143  ] 
dist 10=[38.688075284874139985  ,46.097155954797977215  ] 
dist 11=[35.990259667297328627  ,45.403120274945186672  ] 
dist 12=[31.899105484841240278  ,45.169195562650168272  ] 
dist 13=[27.780488104782577836  ,45.024575520774522844  ] 
dist 14=[24.972870118546570807  ,44.478162065348142089  ] 
dist 15=[22.580001998878837692  ,34.141985842071862138  ] 
dist 16=[20.117745482924130116  ,33.313161456434547501  ] 
dist 17=[17.790048405455526305  ,31.693223556793203037  ] 
dist 18=[15.934407020439131476  ,31.271598494596651378  ] 
dist 19=[14.062645919837906401  ,29.772599497628430679  ] 
dist 20=[11.670110137261272763  ,29.421449608399761547  ] 
dist 21=[9.3464868791467758360 ,28.902811999114583245  ] 
dist 22=[7.7497473602509221824 ,28.741539996423217849  ] 
dist 23=[6.3727270576901427577 ,12.875015841000748363  ] 
dist 24=[4.9264774685643662850 ,11.547303318908064226  ] 
dist 25=[3.5368280424717153820 ,9.9145702449970295786 ] 
dist 26=[1.9638975346180192815 ,9.6690999954240641465 ] 
dist 27=[-.2085152964792320973 ,8.4226759474580282234 ] 
dist 28=[-1.8226044560568864596 ,8.2170714673166260350 ] 
dist 29=[-3.3429454365587879314 ,7.8854313713232008476 ] 
dist 30=[-5.1411244988604614429 ,7.7669776843216652706 ] 
dist 31=[-6.8240404152321128919 ,-2.2452316075403528489 ] 
dist 32=[-7.8838934736164021191 ,-2.7700893440111030911 ] 
dist 33=[-8.6945253609495663382 ,-3.9026117154051331264 ] 
dist 34=[-9.3814755477702154436 ,-4.0906112420689898566 ] 
dist 35=[-9.9390555732078884752 ,-4.8078372723163599152 ] 
dist 36=[-10.232629713032684609  ,-4.6857497986897591448 ] 
dist 37=[-10.393909479137445684  ,-4.4881674500360142407 ] 
dist 38=[-10.427567826651796192  ,-4.2329738904554509575 ] 
dist 39=[-9.7039405197632981816 ,-3.8891214104609849321 ] 
dist 40=[-9.6286521490552417575 ,-3.3370258555329829940 ] 
dist 41=[-9.4429981631614953738 ,-2.6951195914244357630 ] 
dist 42=[-9.4570746238649282604 ,-1.9924957456340570835 ] 
dist 43=[-9.4351352176703452739 ,-1.1114533983536918742 ] 
dist 44=[-9.4126831505903667781 ,.2428481634106841346 ] 
dist 45=[-9.3013427118611068831 ,1.6033555652437506227 ] 
dist 46=[-9.2657653331353090123 ,2.5092970534664243149 ] 
dist 47=[-6.7333773471657101508 ,3.2558156197019240039 ] 
dist 48=[-6.6981393245874344580 ,3.9801331705218266902 ] 
dist 49=[-6.5619149532976060761 ,4.6351267961118743237 ] 
dist 50=[-6.4412325247155498530 ,5.1050275778281454814 ] 
dist 51=[-5.8919919115209222203 ,5.5297640760246097002 ] 
dist 52=[-5.5005855706695333234 ,6.0046074558050876055 ] 
dist 53=[-5.0268359004714044563 ,6.4346484256438836636 ] 
dist 54=[-4.9801637911789564224 ,6.6805189422182141392 ] 
dist 55=[-1.7566354674117597059 ,6.8388627074419581918 ] 
dist 56=[-1.5295854471812184668 ,6.9193102919490679412 ] 
dist 57=[-1.0612245215110727013 ,6.9633174895707885079 ] 
dist 58=[-.94085404862574770977,6.9762330886832228579 ] 
dist 59=[-.5101026914284832068 ,6.9690187652438232128 ] 
dist 60=[-.4241950723601174352 ,6.9493904400056574513 ] 
dist 61=[-.2964651527092690355 ,5.6913147937158427356 ] 
dist 62=[-.2638831625519299681 ,5.7537608751713251802 ] 
dist 63=[2.0937637006979991206 ,5.8892039193590545039 ] 
dist 64=[2.2855020042060059191 ,5.9477670435927965287 ] 
dist 65=[2.7053449125460154987 ,5.9700982351186171460 ] 
dist 66=[2.7721576362869977707 ,5.9645937270599586344 ] 
dist 67=[2.6474098804245197292 ,5.8643252987164908711 ] 
dist 68=[2.4377618094335490445 ,5.8268074777140885835 ] 
dist 69=[2.1380490073622855800 ,5.7751569255572929721 ] 
dist 70=[1.6372391063173719414 ,5.7497096706230085095 ] 
dist 71=[1.1216924321491907958 ,5.0083037975655739027 ] 
dist 72=[.7631150497958414886 ,4.8980983356134134267 ] 
dist 73=[.4508042624805847184 ,4.6677457988260415605 ] 
dist 74=[.1198741946688573375 ,4.6001554155468883693 ] 
dist 75=[-.1978977193827832146 ,4.3150961594451935453 ] 
dist 76=[-.5209577851855553164 ,4.2545156499301828342 ] 
dist 77=[-1.1630289778746059288 ,4.0930880579248373566 ] 
dist 78=[-1.5920845798124669584 ,4.0585300818681325161 ] 
dist 79=[-1.9482614095782090194 ,2.6659182237101187787 ] 
dist 80=[-2.2992871492368101542 ,2.5500053869204064036 ] 
dist 81=[-2.6211600259564741459 ,2.2806265308697080995 ] 
dist 82=[-2.8609161116445834289 ,2.2239841957414893685 ] 
dist 83=[-3.1142412666177544921 ,1.8537382860162278575 ] 
dist 84=[-3.4600775065982393202 ,1.7826260147662269086 ] 
dist 85=[-3.7714668727572122258 ,1.6529820787199013869 ] 
dist 86=[-4.1179001685460207683 ,1.6210015318945611592 ] 
dist 87=[-4.4355239914048827736 ,1.0995284142690565246 ] 
dist 88=[-4.6318850522781170260 ,1.2533409976595305252 ] 
dist 89=[-4.7773110336683146995 ,1.4023662748715952445 ] 
dist 90=[-4.8915789106897055091 ,1.5595379451028026804 ] 
dist 91=[-4.9773278338915985950 ,1.7226589749281749990 ] 
dist 92=[-5.0088983482262433645 ,1.8690820779682883203 ] 
dist 93=[-5.0166307406640703065 ,2.0126729063133605750 ] 
dist 94=[-5.0071613916843036060 ,2.1897231392205497017 ] 
dist 95=[-3.7811723413011525331 ,2.3570606435512020723 ] 
dist 96=[-3.7416222909024046333 ,2.4618944700558106309 ] 
dist 97=[-3.6725611649834016095 ,2.5408910870794028474 ] 
dist 98=[-3.6509416282686704970 ,2.6051293653639458699 ] 
dist 99=[-3.5637255344978434384 ,2.6548323779168063969 ] 
dist 100=[-3.5368452395528189165 ,2.6758239792326571807 ] 
dist 101=[-3.4788299254839054861 ,2.7354276700457963862 ] 
dist 102=[-3.4120358764824980547 ,2.9014178201092688542 ] 
dist 103=[-.92204067830638206028,3.0304213373376371684 ] 
dist 104=[-.78195350646767912356,3.1430288683204343341 ] 
dist 105=[-.4536388158310168023 ,3.2368372826660427476 ] 
dist 106=[-.4034120081792719112 ,3.2908130592650040149 ] 
dist 107=[.0309347195003985461 ,3.3565514823874783124 ] 
dist 108=[-.20840243855483754317,3.4403224136986048830 ] 
dist 109=[-.76553675539287236295,3.5103337014925548943 ] 
dist 110=[-1.1436974708546548714 ,3.5358461413540086113 ] 
dist 111=[-1.4632614907549406404 ,3.5431532991113685073 ] 
dist 112=[-1.7865101470920070741 ,3.5403843535029532700 ] 
dist 113=[-2.0874755446044442518 ,3.4480731702273183715 ] 
dist 114=[-2.3180967296674079360 ,3.4188415826914104596 ] 
dist 115=[-2.5414142412808599240 ,3.3959036793992079360 ] 
dist 116=[-2.8132264635152273640 ,3.3771068250913225009 ] 
dist 117=[-3.0689839073042587992 ,2.8278525548499794834 ] 
dist 118=[-3.2282178738414470000 ,2.7492729227716941704 ] 
dist 119=[-3.3472678976860334798 ,2.5960801043968478797 ] 
dist 120=[-3.4426291457808125242 ,2.5543498742523121104 ] 
dist 121=[-3.5154648963574921569 ,2.3978031466354799916 ] 
dist 122=[-3.5446016009216784947 ,2.3597633733215277393 ] 
dist 123=[-3.5534897043005478083 ,2.2891971174012600758 ] 
dist 124=[-3.5474699579794471379 ,2.2690012291932245314 ] 
dist 125=[.37591200751557287561,1.4664664149614558944 ] 
dist 126=[.04205185074529151513,1.4605714696140791122 ] 
dist 127=[-.24752066397258386692,1.4224351879976849355 ] 
dist 128=[-.55284068321245977788,1.4120845261590202133 ] 
dist 129=[-.84537033609424779281,1.3852930835368861363 ] 
dist 130=[-1.0838840747829743661 ,1.3746962486841810226 ] 
dist 131=[-1.3288269955163771810 ,1.3184584794108592897 ] 
dist 132=[-1.6470360494341478042 ,1.3045947228744147865 ] 
dist 133=[-1.9571670599917435515 ,1.2750311527976210338 ] 
dist 134=[-2.1698631071016398899 ,1.2650280601681480290 ] 
dist 135=[-2.3522218243821640740 ,-.8704252856586658977 ] 
dist 136=[-2.5412341622808077092 ,-.77569504782501844593] 
dist 137=[-2.7204197683011893174 ,-.65028268215161461685] 
dist 138=[-2.8635519685040777644 ,-.49190793019505983774] 
dist 139=[-3.0079427121110337602 ,-.27889686890086734869] 
dist 140=[-3.1921698665977910417 ,.0646396570290530968 ] 
dist 141=[-3.3636877172038720663 ,.4168741538581789364 ] 
dist 142=[-3.4573360637255882232 ,.6646117748705718966 ] 
dist 143=[-3.5120713430560140269 ,.8834808669606675885 ] 
dist 144=[-3.5282104889091898432 ,1.1204687855019968693 ] 
dist 145=[-3.5308157040378463253 ,1.3512499691779350626 ] 
dist 146=[-3.5315054510788435648 ,1.5453430107202971255 ] 
dist 147=[-3.5309568292843579424 ,1.7499384085067935216 ] 
dist 148=[-3.5286025963444667949 ,2.0226520865443222024 ] 
dist 149=[-3.0545615784037514160 ,2.2915558815830411756 ] 
dist 150=[-2.9860534948611677382 ,2.4809430348912088407 ] 
dist 151=[-2.8651427265086732754 ,2.6485543666310641638 ] 
dist 152=[-2.8339322011780647862 ,2.8305244010322754886 ] 
dist 153=[-2.7315307588054808397 ,3.0080461121558215643 ] 
dist 154=[-2.6991056399452844384 ,3.1579008374012693472 ] 
dist 155=[-2.6740023108402554080 ,3.3163695486874355942 ] 
dist 156=[-2.6620993165631276291 ,3.5282862467049596502 ] 
dist 157=[-1.8346425761935419272 ,3.7304842206522764874 ] 
dist 158=[-1.8165338472534733718 ,3.8501523336526783074 ] 
dist 159=[-1.3657252438132374964 ,3.9324212131621558585 ] 
dist 160=[-1.3048571040844574327 ,3.9853032826027753449 ] 
dist 161=[-1.1807133457952574368 ,4.0176269909220200091 ] 
dist 162=[-1.1471540873078363138 ,4.0218300429842973127 ] 
dist 163=[-1.0194876781525919581 ,4.0070707117259941763 ] 
dist 164=[-.9921340600477173482 ,3.9957407099653965072 ] 
dist 165=[-.9372191393676535667 ,3.7741200608093676154 ] 
dist 166=[-.92185897388076352271,3.7314896457346305834 ] 
dist 167=[.02720780009464282615,3.6269632527927194241 ] 
dist 168=[.08984496262646384173,3.5893872096278208763 ] 
dist 169=[.23370711781229634151,3.4012022861115794711 ] 
dist 170=[.25544546892339157437,3.3568095396581002791 ] 
dist 171=[.43395014927095572898,3.2619556149652884976 ] 
dist 172=[-.21118254606756161597,3.2307607360415399567 ] 
dist 173=[-1.0188481969130215563 ,3.1302331174433411935 ] 
dist 174=[-1.5521109641528218923 ,3.1771204099495729533 ] 
dist 175=[-1.9871195702756693369 ,3.1997043923163029372 ] 
dist 176=[-2.4025028878763044666 ,3.2029644926064993107 ] 
dist 177=[-2.7740632393958858172 ,3.1776775265377763030 ] 
dist 178=[-3.0341067834389477242 ,3.1634305929759532252 ] 
dist 179=[-3.2625671692085915463 ,3.1382772088161710754 ] 
dist 180=[-3.5080288393676586990 ,3.1270515015047963260 ] 
dist 181=[-3.7310745559045773925 ,2.7790932415103457484 ] 
dist 182=[-3.8700389915285380239 ,2.7249825834243114514 ] 
dist 183=[-3.9741767923975491477 ,2.6106281784948675431 ] 
dist 184=[-4.0581793511705509187 ,2.5759074908384803030 ] 
dist 185=[-4.1229161007940584183 ,2.4235299767566454905 ] 
dist 186=[-4.1501363885240525505 ,2.3913970048208669705 ] 
dist 187=[-4.1560430537624123839 ,2.2974429647064210672 ] 
dist 188=[-4.1522189699987909315 ,2.2826623977625158946 ] 
dist 189=[-1.2828751695718774353 ,2.1026546545555456072 ] 
dist 190=[-1.4555427700011623788 ,2.0971344612715873640 ] 
dist 191=[-1.6238262661325920805 ,1.7952925361809058321 ] 
dist 192=[-1.7391705017036131903 ,1.7517018224538777658 ] 
dist 193=[-1.8379670322390759966 ,1.6716640491343368331 ] 
dist 194=[-1.9401835320359091814 ,1.6505005931476350005 ] 
dist 195=[-2.0369307018914536619 ,1.5765803457386634333 ] 
dist 196=[-2.1138911422453988169 ,1.5557105623240743628 ] 
dist 197=[-2.1911971359873293255 ,1.5293561007573636821 ] 
dist 198=[-2.2893248379477104535 ,1.5181913863574454557 ] 
dist 199=[-2.3807674102293938658 ,.26208183029888600162] 
dist 200=[-2.4313826702666716827 ,.15698710124938797565] 
dist 201=[-2.4618455429439447106 ,-.07781943669483637873] 
dist 202=[-2.4728277550744306067 ,-.12155782218132293825] 
dist 203=[-2.4740469463359136797 ,-.39729825743654053736] 
dist 204=[-2.4689956132043479196 ,-.44419955699373436667] 
dist 205=[-2.4525275641135011951 ,-.53419296085060746681] 
dist 206=[-2.4422892103672319078 ,-.46656739658927801074] 
dist 207=[-2.2404276487972929615 ,-.33283430519872137678] 
dist 208=[-2.2062345695570240638 ,-.18195225897722583413] 
dist 209=[-2.1285017294339155264 ,-.03136320446280043514] 
dist 210=[-2.1029167106752918177 ,.1012010494619752986 ] 
dist 211=[-1.9825985635231144950 ,.24612446730843319402] 
dist 212=[-1.9557715674545166646 ,.44605951368395859116] 
dist 213=[-1.8899115071082521112 ,.64638404427586792131] 
dist 214=[-1.8687377060452551758 ,.7928631381461093724 ] 
dist 215=[-.98553508559421648869,.92814022924350678128] 
dist 216=[-.96388137160072816073,1.0837406935180337701 ] 
dist 217=[-.90726060069939770451,1.2407464616726018422 ] 
dist 218=[-.8972264238312430925 ,1.4046643041299560964 ] 
dist 219=[-.79706477578172947348,1.6227178914493215977 ] 
dist 220=[-.77642156184572757809,1.7740612384214167540 ] 
dist 221=[-.75131359964270897207,1.9694452133939296578 ] 
dist 222=[-.74162114627179513861,2.1049610087760630560 ] 
dist 223=[-.52526015493507042629,2.2097135156627017650 ] 
dist 224=[-.4964292815579629325 ,2.3000652017855565129 ] 
dist 225=[-.4362979739121535394 ,2.3743826253947792260 ] 
dist 226=[-.41995039788289475545,2.4151164674940051338 ] 
dist 227=[-.35663642079516372227,2.4391018635747158522 ] 
dist 228=[-.34383024996300687784,2.4465494315079556399 ] 
dist 229=[-.31609415083156086636,2.4448508765961231999 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 1, 2, 0, 2] 
dist 0=[51.314519902071417506  ,51.314519902071417506  ] 
dist 1=[51.199531437482651291  ,51.369370656245639246  ] 
dist 2=[50.795605829771275512  ,51.413923830191857853  ] 
dist 3=[50.091361274855661748  ,51.413791153830835810  ] 
dist 4=[48.818063818085399285  ,51.380687976941137113  ] 
dist 5=[47.406671688264271394  ,51.295509419096769776  ] 
dist 6=[46.150756969733316126  ,51.206585654638890980  ] 
dist 7=[44.765161017804129918  ,50.618433828190472951  ] 
dist 8=[42.835603842534839292  ,47.047788757436070542  ] 
dist 9=[40.697520343819127743  ,46.471471036853398488  ] 
dist 10=[38.478908244936571667  ,45.492263533616709102  ] 
dist 11=[35.769837641407490465  ,45.233896909711533116  ] 
dist 12=[31.672595207989159210  ,44.498638122864467940  ] 
dist 13=[27.550270052337289412  ,44.289882984288529806  ] 
dist 14=[24.740912960953987760  ,44.059678006321419129  ] 
dist 15=[22.346988131725170532  ,42.691081752032562493  ] 
dist 16=[19.883849738186204530  ,33.561724903953398064  ] 
dist 17=[17.555097093600120954  ,33.141651281833130046  ] 
dist 18=[15.697757289640420828  ,31.685542642338368397  ] 
dist 19=[13.823358878331454463  ,31.328216095190634270  ] 
dist 20=[11.426071441944877424  ,30.891444475936265737  ] 
dist 21=[9.0971178702406362476 ,30.720801281890619659  ] 
dist 22=[7.4954695169794371420 ,14.308569187542929916  ] 
dist 23=[6.1129583497389126418 ,14.015255292196340318  ] 
dist 24=[4.6591175963440100361 ,9.2310687050911755816 ] 
dist 25=[3.2613770492110849673 ,8.6425095314119938383 ] 
dist 26=[1.0418003427356579253 ,7.4251291832133127842 ] 
dist 27=[-.6629114267996856577 ,7.1780576954861640209 ] 
dist 28=[-2.2819792236937095371 ,6.3745564264720446965 ] 
dist 29=[-4.2143020148965528981 ,5.9714337702144293986 ] 
dist 30=[-6.0278478407387958599 ,5.7982790170999261760 ] 
dist 31=[-7.1723962497889999282 ,5.4447331817711930663 ] 
dist 32=[-8.0504343507154136737 ,-3.0411237439455773319 ] 
dist 33=[-8.7989623830362322642 ,-3.4669189243684704030 ] 
dist 34=[-9.4097327735016677486 ,-4.2964931948314233479 ] 
dist 35=[-9.7372081652125630333 ,-4.4816040676502055664 ] 
dist 36=[-9.9219733714769313141 ,-4.9959255643733649771 ] 
dist 37=[-9.9654304954728382185 ,-5.0493767981489517747 ] 
dist 38=[-9.7587652820098117592 ,-4.9626421006080381744 ] 
dist 39=[-9.7286525274401600231 ,-4.6667169361272010706 ] 
dist 40=[-9.5738084990433671330 ,-4.2990604676214475044 ] 
dist 41=[-9.5492184448248391276 ,-3.8411375101600556724 ] 
dist 42=[-9.0276813916290881704 ,-3.2330051018721195157 ] 
dist 43=[-8.9048397098274567585 ,-2.4594059054579901924 ] 
dist 44=[-8.8118407132369837630 ,-1.2580846441591437373 ] 
dist 45=[-8.7853009287709746041 ,-.0458384871066782532 ] 
dist 46=[-7.5210572931045424077 ,.7714860762871018573 ] 
dist 47=[-7.5107106620189279958 ,1.4562470384185725215 ] 
dist 48=[-7.4263244429316911482 ,2.6528497953421368202 ] 
dist 49=[-7.3916297946296177277 ,3.6296925964042684812 ] 
dist 50=[-7.3632127068759102319 ,4.4264706715310692111 ] 
dist 51=[-7.2645392594875004447 ,5.1864022081535378143 ] 
dist 52=[-6.5997582112190008387 ,5.8651783460420618245 ] 
dist 53=[-6.1610451595109751726 ,6.3380874884001610478 ] 
dist 54=[-3.1781061071798635338 ,6.7513529743254258281 ] 
dist 55=[-2.8729687704435189411 ,7.1921702063422397695 ] 
dist 56=[-2.8135680729588448194 ,7.5846206294958989007 ] 
dist 57=[-2.3917296541938758209 ,7.8047781867837397146 ] 
dist 58=[-2.3122894946409828620 ,7.9412733445267715630 ] 
dist 59=[-2.1749403909746612704 ,7.9995255657703190420 ] 
dist 60=[-2.1424381532198897826 ,8.0199434571910350587 ] 
dist 61=[-.9099007244281233860 ,8.0054335277272752374 ] 
dist 62=[-.7795249548654345669 ,7.9672811230168484017 ] 
dist 63=[-.4778647097053341203 ,7.9402833132810237676 ] 
dist 64=[-.4280009020155594351 ,6.0246320696644321248 ] 
dist 65=[-.0345556843803606237 ,5.8208565810759875122 ] 
dist 66=[.0355331816260019974 ,5.2987186068705377514 ] 
dist 67=[.1419987799105382558 ,5.3034529852943351906 ] 
dist 68=[.1691809416135611514 ,5.3379292096373794726 ] 
dist 69=[.6220129332001544394 ,5.3423403122071406688 ] 
dist 70=[.6788362531830641621 ,4.0187256259972684179 ] 
dist 71=[.8012261772781725961 ,3.9813868598601441224 ] 
dist 72=[.8243439972193264292 ,2.9998184762417494538 ] 
dist 73=[.9337174714064371057 ,2.7172395416256978056 ] 
dist 74=[.6495685508359654937 ,2.6552913344659108305 ] 
dist 75=[.4115357926052133340 ,2.5369271672441754440 ] 
dist 76=[-.27162674575801762694,2.5048822000346211556 ] 
dist 77=[-1.0628960081917665455 ,2.0757203985323032583 ] 
dist 78=[-1.5910235809062344781 ,2.1793492142716000655 ] 
dist 79=[-2.0284472771018878588 ,2.2611633414781295209 ] 
dist 80=[-2.4575192320443734010 ,2.3346447499898024683 ] 
dist 81=[-2.8492579351968323244 ,2.3971234867471438698 ] 
dist 82=[-3.1375977262671372564 ,2.4349963354312739913 ] 
dist 83=[-3.4058856014090222666 ,2.4620224115699249544 ] 
dist 84=[-3.7175380209928683198 ,2.4811684420859250179 ] 
dist 85=[-4.0039269857797100950 ,2.4919300041450340177 ] 
dist 86=[-4.1713261192720016832 ,2.4927226526947407885 ] 
dist 87=[-4.2838111866593446114 ,2.4756114991023648452 ] 
dist 88=[-4.3509127185047748094 ,2.4728353563388346165 ] 
dist 89=[-4.3957046843983587259 ,2.3732490422329801066 ] 
dist 90=[-4.4191274957913250841 ,2.3478556729915157792 ] 
dist 91=[-4.4314143822853296491 ,2.3329606568037864236 ] 
dist 92=[-4.4318151893331801956 ,2.3284600864838896845 ] 
dist 93=[-4.3951069222689888403 ,1.3709281667362299594 ] 
dist 94=[-4.4021809757639362320 ,1.4537111863746085250 ] 
dist 95=[-4.3979545763298360572 ,1.5043619334839230759 ] 
dist 96=[-2.6345488528081174331 ,1.7705444607706462542 ] 
dist 97=[-2.6161255794259263806 ,2.0838418499693517563 ] 
dist 98=[-2.5737118624480002827 ,2.3326539834903856038 ] 
dist 99=[-2.5572758234139684164 ,2.5820260548310183759 ] 
dist 100=[-2.5461595356182958444 ,2.8975379014339838311 ] 
dist 101=[-2.5395026436446202158 ,3.2005335758798957725 ] 
dist 102=[-.91129608321268087068,3.3999304065731967690 ] 
dist 103=[-.79090085308779316038,3.5616653940423839429 ] 
dist 104=[-.51736763390281401018,3.7143041935563608801 ] 
dist 105=[-.467278153031049345  ,3.8493518381644591583 ] 
dist 106=[-.1287949865720269228 ,3.9604193505569513118 ] 
dist 107=[-.0695913066331681073 ,4.0661374795139603361 ] 
dist 108=[-.1728643599734294285 ,4.1430708655537454831 ] 
dist 109=[-.77505320354586554082,4.1665507449006889385 ] 
dist 110=[-1.1862552392962944594 ,4.1704898571293850414 ] 
dist 111=[-1.5366362528968302033 ,4.1497611245884432222 ] 
dist 112=[-1.8960213421724153515 ,4.0546727955575255005 ] 
dist 113=[-2.2340407394485158724 ,4.0334800358532161992 ] 
dist 114=[-2.4991274409146775609 ,3.9587169698858150592 ] 
dist 115=[-2.7617790376239157885 ,3.9377942345125028968 ] 
dist 116=[-3.0900764084941567843 ,3.7284389544425436040 ] 
dist 117=[-3.4036335383955825480 ,3.6776301777535874063 ] 
dist 118=[-3.6074399539780695348 ,3.6131884185296271269 ] 
dist 119=[-3.7700387554761822195 ,3.5859397758749547224 ] 
dist 120=[-3.9190898433932110892 ,2.9663506683802581576 ] 
dist 121=[-4.0481532499028795946 ,3.0140248429399702717 ] 
dist 122=[-4.1309576891590941190 ,3.0456281526725924784 ] 
dist 123=[-4.1957872926675088846 ,3.0611981344195236185 ] 
dist 124=[-4.2530899287733888233 ,3.0680712868347925018 ] 
dist 125=[-4.2939884688639955553 ,3.0649287684567604438 ] 
dist 126=[-4.3012059974684786901 ,2.7550577911277877963 ] 
dist 127=[-4.2620753786625271589 ,2.7069916808682633472 ] 
dist 128=[-1.9804661752723702309 ,2.6247764717697937369 ] 
dist 129=[-2.1286995362403995321 ,2.6017013998080348278 ] 
dist 130=[-2.2758382348045708576 ,2.5264390978948884205 ] 
dist 131=[-2.4040300587873027680 ,2.5015723446561278734 ] 
dist 132=[-2.5430337787764018396 ,2.4750699432305084213 ] 
dist 133=[-2.7333440625117783672 ,2.4604412620806647091 ] 
dist 134=[-2.9165545788566067788 ,.4403887016980706799 ] 
dist 135=[-3.0272156134100381836 ,.2810082410854867758 ] 
dist 136=[-3.1060469279035520829 ,-.0737136721990200332 ] 
dist 137=[-3.1621815061010806446 ,-.1407724644571521511 ] 
dist 138=[-3.1999187611702589877 ,-.55281080606502405679] 
dist 139=[-3.2081439781051810652 ,-.62266294331672147566] 
dist 140=[-3.2005448499243890914 ,-.75944201260279245377] 
dist 141=[-3.1978187200642126333 ,-.79110037290942382793] 
dist 142=[-3.0577828920549617648 ,-1.0471004270682462724 ] 
dist 143=[-3.0286600286859443101 ,-1.0706286003922936750 ] 
dist 144=[-2.9528388043642131391 ,-1.0375967392217996823 ] 
dist 145=[-2.9255506872766002198 ,-.95909086917185540804] 
dist 146=[-2.7742197697456853041 ,-.8572835414894289752 ] 
dist 147=[-2.7378452174472553539 ,-.71191951452946435479] 
dist 148=[-2.6666621244066134995 ,-.38941339842847069146] 
dist 149=[-2.6442870373669384543 ,.23269288489185966051] 
dist 150=[-2.6537418577540001182 ,.89437096084541238094] 
dist 151=[-2.7001803036353517570 ,1.3311508314756041647 ] 
dist 152=[-2.7245103892985972746 ,1.6873072242856193324 ] 
dist 153=[-2.7286824844377994515 ,2.0271013218809341992 ] 
dist 154=[-2.7164928373694055647 ,2.3308062956089276556 ] 
dist 155=[-2.7062321962588809388 ,2.5428781580366080391 ] 
dist 156=[-2.6867710249918302599 ,2.7286639098270390484 ] 
dist 157=[-2.6772046486321176784 ,2.9274202071761146279 ] 
dist 158=[-2.3958193758787928058 ,3.1076463951439480790 ] 
dist 159=[-2.3514413324164430626 ,3.2194523436423026864 ] 
dist 160=[-2.2568842636086974979 ,3.3026561834721801642 ] 
dist 161=[-2.2278137959641396056 ,3.3686947696502565226 ] 
dist 162=[-2.0985447863032484246 ,3.4187162173991834552 ] 
dist 163=[-2.0713122879787963392 ,3.4379751220007822868 ] 
dist 164=[-1.9908248415239390643 ,3.4407043151413007197 ] 
dist 165=[-1.9785922708620069312 ,3.4357496465754959321 ] 
dist 166=[.18038201102456921163,2.8140422403632175673 ] 
dist 167=[.29337003614965007769,2.9057552978419004531 ] 
dist 168=[.54408966158902685369,2.9831344863087812777 ] 
dist 169=[.58877630494271439558,3.0161303699979233367 ] 
dist 170=[.87330918094601292743,3.0305679861722088483 ] 
dist 171=[.92003377446366962215,3.0338456213566411129 ] 
dist 172=[1.0095875545268517878 ,2.9626880159798403198 ] 
dist 173=[1.0289341448090559575 ,2.9443065112855200600 ] 
dist 174=[.76172952521783012325,2.9333246472348942406 ] 
dist 175=[.19762733512522931333,2.9295500480468818777 ] 
dist 176=[-.37062326681297746345,2.5253721875623371618 ] 
dist 177=[-.75450840022141460185,2.4747638482816902025 ] 
dist 178=[-1.0773046615174016636 ,2.3414387401123906069 ] 
dist 179=[-1.4016590509950646092 ,2.3169568823278392401 ] 
dist 180=[-1.7026479921973681219 ,2.0765887826245090313 ] 
dist 181=[-1.9321580968041916253 ,2.0264916755010255391 ] 
dist 182=[-2.1535375944328722333 ,1.9643714576519967273 ] 
dist 183=[-2.4220651691769429497 ,1.9406368611070043346 ] 
dist 184=[-2.6746943743531542441 ,1.6571022601290701753 ] 
dist 185=[-2.8325997403071126552 ,1.6447633722807297381 ] 
dist 186=[-2.9515364442129738639 ,1.5582381791085957552 ] 
dist 187=[-3.0485835196687235510 ,1.5375689611184360815 ] 
dist 188=[-3.1242578670504929737 ,1.5027457993138497447 ] 
dist 189=[-3.1578639289058742525 ,1.4920822465077640440 ] 
dist 190=[-3.1718820038638989564 ,1.2413366143453001407 ] 
dist 191=[-3.1694217664773025158 ,1.2052184520914539061 ] 
dist 192=[-1.0591257182787876148 ,1.1244359921695854490 ] 
dist 193=[-1.2061416101948980247 ,1.1010136176977646014 ] 
dist 194=[-1.3537190388697581128 ,.9946565609851888058 ] 
dist 195=[-1.4849633002370071407 ,.97293047068700723834] 
dist 196=[-1.6295573961541699726 ,.9222915205675124516 ] 
dist 197=[-1.8304367721740653416 ,.90786986863504466724] 
dist 198=[-2.0259758077518665581 ,-.6658634116984859718 ] 
dist 199=[-2.1492483583424660656 ,-.69046956340399084545] 
dist 200=[-2.2433488390710362342 ,-.80475538393023200654] 
dist 201=[-2.3224149566051027019 ,-.82116600474215876427] 
dist 202=[-2.3858850632243944441 ,-.78250910106334691469] 
dist 203=[-2.4177167939400360050 ,-.69913144203436811695] 
dist 204=[-2.4325081786923423209 ,-.59567935483595905282] 
dist 205=[-2.4341875957345810981 ,-.47309540757185020119] 
dist 206=[-2.4147823739984171181 ,-.31285336319263470112] 
dist 207=[-2.4057396606161880208 ,-.05904870436384266474] 
dist 208=[-2.3754409849111375515 ,.19968792276309256993] 
dist 209=[-2.3611422276868828854 ,.37962147969901795901] 
dist 210=[-2.2719079460724751345 ,.5365113090377157181 ] 
dist 211=[-2.2483112887822808625 ,.7032450977410374139 ] 
dist 212=[-2.2057989354714259668 ,.8637993616604266017 ] 
dist 213=[-2.1923206783950337906 ,.9960174971215925681 ] 
dist 214=[-1.4821603613916112878 ,1.1329724646887182558 ] 
dist 215=[-1.4053089888088026856 ,1.3124394662826036617 ] 
dist 216=[-1.2259249067992026655 ,1.4880472244913172617 ] 
dist 217=[-1.1898378125742436535 ,1.6095941965508587631 ] 
dist 218=[-.9436185477311960034 ,1.7149712795861739138 ] 
dist 219=[-.89702709554198865371,1.8260199235245302846 ] 
dist 220=[-.81392650029746204217,1.9323883212511173517 ] 
dist 221=[-.79430704079616935162,2.0229414683815179502 ] 
dist 222=[-.52089532385052216329,2.1943703830341086930 ] 
dist 223=[-.51391451266545251889,2.2968027248523283485 ] 
dist 224=[-.31466282749815200935,2.3684329628694429650 ] 
dist 225=[-.29557397936746035823,2.4168822222741493898 ] 
dist 226=[-.16192280838416262364,2.4511155351494287307 ] 
dist 227=[-.13783380143895196023,2.4659873338672641635 ] 
dist 228=[-.09539437250711086619,2.4695393512785701520 ] 
dist 229=[-.08610486294718417568,2.4527733305697515589 ] 
dist 230=[.05820809545071839989,1.5607467857633990691 ] 
dist 231=[.07912149165856088411,1.5689491492023118301 ] 
dist 232=[.10524933763920608998,1.5711606978993879821 ] 
dist 233=[.10956649740239008073,1.5691282666530137725 ] 
dist 234=[.10529950469286999331,1.5566623018710559210 ] 
dist 235=[.08818602932959953739,1.5498927793709660620 ] 
dist 236=[.05835796685448274400,1.4962573252586828773 ] 
dist 237=[.00332648859974326421,1.4815329905915388888 ] 
dist 238=[-.05797852274471321895,1.4593547741238657976 ] 
dist 239=[-.11285442098715682232,1.4509183658401167648 ] 
dist 240=[-.24444619468602503963,1.2525593796479011128 ] 
dist 241=[-.4515349200517163496 ,1.2361371805170519706 ] 
dist 242=[-.62374088353431943596,1.1877813743518174735 ] 
dist 243=[-.79367650883244902256,1.1803264580781691317 ] 
dist 244=[-.94940818154358730009,1.0769626130800255434 ] 
dist 245=[-1.0649032840177724701 ,1.0546257382489155069 ] 
dist 246=[-1.1731932624922840008 ,1.0343249489002945853 ] 
dist 247=[-1.3001575916161274740 ,1.0288545458911529303 ] 
dist 248=[-1.4174114847643659764 ,.74989959712489075173] 
dist 249=[-1.4869314395584621710 ,.71334487413094852116] 
dist 250=[-1.5348832822197449660 ,.64207874531002432368] 
dist 251=[-1.5660240924167139544 ,.62366509749970578681] 
dist 252=[-1.5880837737979994388 ,.55928406042452931961] 
dist 253=[-1.5997783437894816159 ,.54396897048204084066] 
dist 254=[-1.6061333551236287935 ,.52484908308797033549] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 0, 1, 1, 2] 
dist 0=[46.371556702240751482  ,46.371556702240751482  ] 
dist 1=[46.012087665744953583  ,46.790229932927208237  ] 
dist 2=[45.603397305907456591  ,47.434917904579312434  ] 
dist 3=[44.951969222730538102  ,48.057502782376892286  ] 
dist 4=[43.623007781406528208  ,48.387918250621893047  ] 
dist 5=[42.025431946946035126  ,48.567282884900865983  ] 
dist 6=[40.301229274006000654  ,48.587013710166393965  ] 
dist 7=[38.149879118302059542  ,48.523853078093986437  ] 
dist 8=[34.846160881455829870  ,48.459223047615497630  ] 
dist 9=[31.506310623681990735  ,48.205498647024139429  ] 
dist 10=[29.210516245499672302  ,48.083056586772354324  ] 
dist 11=[27.233892309910511558  ,46.421716420874643765  ] 
dist 12=[25.168526461214763288  ,46.086969216982263652  ] 
dist 13=[23.196726025653056144  ,44.899384885421304582  ] 
dist 14=[21.593542736976198296  ,42.937611662870927781  ] 
dist 15=[19.947786119746753510  ,34.724432283728401263  ] 
dist 16=[17.805456187112181374  ,34.101083100276985772  ] 
dist 17=[15.706239812736886661  ,33.442085823459821162  ] 
dist 18=[14.232429512787339299  ,33.284531027660059309  ] 
dist 19=[12.927997485937380568  ,26.817012164067734782  ] 
dist 20=[11.505025855080076554  ,25.982130950510274840  ] 
dist 21=[10.105246776310193426  ,24.340184390540832708  ] 
dist 22=[8.8929776145295708370 ,23.917815180765437423  ] 
dist 23=[7.5778760869492821251 ,22.435314561279370457  ] 
dist 24=[5.7662386652837508979 ,22.096517266382949624  ] 
dist 25=[3.9939629547600528646 ,21.639018545227683966  ] 
dist 26=[2.8360145591849089470 ,21.487716644635523996  ] 
dist 27=[1.8975171952741907958 ,13.423967592574581673  ] 
dist 28=[1.0027038147948395805 ,13.027428988585935160  ] 
dist 29=[.1955029104630939949 ,11.914268515066061776  ] 
dist 30=[-1.3638155520838911789 ,11.284255107151461218  ] 
dist 31=[-3.2398001958384653433 ,.0150739079962901600 ] 
dist 32=[-4.6353867038415674444 ,-.0566978099880561605 ] 
dist 33=[-5.9512119074417752531 ,-.4603245490701362346 ] 
dist 34=[-7.5085827038040855150 ,-.4937562415032924382 ] 
dist 35=[-8.9608784467442741651 ,-.4364372352771881487 ] 
dist 36=[-9.8569758002515321586 ,-.24437295267857683288] 
dist 37=[-10.520467616917820713  ,.01616754180302552972] 
dist 38=[-11.043609460788113231  ,.34701986091196991902] 
dist 39=[-11.455908441897560325  ,.79069462920092546785] 
dist 40=[-11.676571220961028681  ,1.5015576985548751413 ] 
dist 41=[-11.800019868653929672  ,2.2204542835494051986 ] 
dist 42=[-11.823805599714920822  ,2.6963246619613890588 ] 
dist 43=[-9.5181126833332815861 ,3.0837801409610742844 ] 
dist 44=[-9.5596691321822972103 ,3.4501653240676027686 ] 
dist 45=[-9.5745810627140848502 ,3.7736915426499418806 ] 
dist 46=[-9.5577108286314234756 ,3.9902491470649016633 ] 
dist 47=[-6.0974480290017467705 ,4.1693304336858480024 ] 
dist 48=[-5.9132216090903945956 ,4.3433959607221625276 ] 
dist 49=[-5.6836043747745190901 ,4.4934824481806714097 ] 
dist 50=[-5.6299444034906226629 ,4.5768842840817287786 ] 
dist 51=[-3.8921225472285778140 ,4.6270073379525630394 ] 
dist 52=[-3.6713696086095105898 ,4.6442366547869106988 ] 
dist 53=[-3.2018300713074370018 ,4.6405083096152938137 ] 
dist 54=[-3.0798123903089690515 ,4.6308399211965244414 ] 
dist 55=[-2.5870604033564122125 ,4.5700968686520698145 ] 
dist 56=[-2.4940989424014501023 ,4.5522719804094379039 ] 
dist 57=[-2.2917006966292678495 ,2.8363796111900765853 ] 
dist 58=[-2.2437594548953296059 ,2.6701254596262305143 ] 
dist 59=[.16966308639426744613,2.6702157532167144541 ] 
dist 60=[.38942167827624933841,3.0545522143389061894 ] 
dist 61=[.64447866109238698175,3.4532913336980569576 ] 
dist 62=[.66489124539716029183,3.9776878645398564201 ] 
dist 63=[.8646677164480726814 ,4.4803898230053737190 ] 
dist 64=[.4316577580873528927 ,4.7925180360412322415 ] 
dist 65=[.0016347563955183170 ,5.0259957284177312637 ] 
dist 66=[-.3056151448299108232 ,5.2145284104734159628 ] 
dist 67=[-.5819805164722664013 ,5.3607848792758922026 ] 
dist 68=[-.8887667151022019375 ,5.4254096598016188926 ] 
dist 69=[-1.1920424079428962299 ,5.4551001731548105890 ] 
dist 70=[-1.4544360939782479408 ,5.4617030379151561125 ] 
dist 71=[-1.7375335900078155070 ,5.3432887782408150087 ] 
dist 72=[-2.1235297789541188363 ,5.3378621871333247790 ] 
dist 73=[-2.4990066500756651028 ,5.3377035674019071549 ] 
dist 74=[-2.7401192248320599459 ,5.3337067788057699139 ] 
dist 75=[-2.9294310141360813042 ,5.0647984270724507642 ] 
dist 76=[-3.0980726827737948928 ,5.0287798567265236509 ] 
dist 77=[-3.2409525503600703153 ,4.9117203360672407898 ] 
dist 78=[-3.3274047229921831510 ,4.8885063648628351505 ] 
dist 79=[-3.3893089364584048193 ,2.9653285901935845540 ] 
dist 80=[-3.4341854031130025612 ,2.7872081480470825322 ] 
dist 81=[-3.4640896968295021822 ,2.3600026062102655543 ] 
dist 82=[-3.4678480923086309526 ,2.2904238355782953234 ] 
dist 83=[-3.4578498179193196297 ,1.6796869521122583401 ] 
dist 84=[-3.4458548915854089747 ,1.5663554798728735055 ] 
dist 85=[-3.4333239349377297827 ,1.4112908361641138945 ] 
dist 86=[-3.4610944950931033961 ,1.3643704213014278856 ] 
dist 87=[-3.4746745296321044680 ,1.5286566556133514234 ] 
dist 88=[-3.7323274106599740779 ,1.9823632810683447526 ] 
dist 89=[-3.9277025134539162961 ,2.4336575036364525653 ] 
dist 90=[-4.0896344077129596130 ,2.7293538683822072735 ] 
dist 91=[-4.2179926821120123079 ,2.9679196145202797960 ] 
dist 92=[-4.2793083028682293204 ,3.1911535744578704919 ] 
dist 93=[-4.3096830529586628856 ,3.3876673108105683997 ] 
dist 94=[-4.3144900714456504338 ,3.5195706115988815864 ] 
dist 95=[-3.6577149813944707607 ,3.6295343477104683427 ] 
dist 96=[-3.6356203316197616485 ,3.7384741869492663252 ] 
dist 97=[-3.6172004455370359792 ,3.8286499876151174358 ] 
dist 98=[-3.5993411477095681007 ,3.8637103761654189472 ] 
dist 99=[-3.0465910532977045588 ,3.8766370192376813311 ] 
dist 100=[-2.9668438363290798390 ,3.8784346433685968473 ] 
dist 101=[-2.8123984056221697630 ,3.7696282148066992934 ] 
dist 102=[-2.7702717822241124535 ,3.7402610224399580975 ] 
dist 103=[-2.6125947640685275896 ,3.7347870367092064456 ] 
dist 104=[-2.5735425516523595941 ,3.7326148363442069504 ] 
dist 105=[-2.5018311416328352048 ,3.6695345964073919192 ] 
dist 106=[-2.4811434165267547121 ,3.6509254135082490660 ] 
dist 107=[-1.8875011462484613299 ,3.5817468079362223339 ] 
dist 108=[-2.3156532644633053168 ,3.5651646240637259198 ] 
dist 109=[-2.7057825235423670395 ,3.3643667214718995551 ] 
dist 110=[-2.9908899637959347299 ,3.3159497621252740733 ] 
dist 111=[-3.2538684025850374199 ,3.2637354048242633090 ] 
dist 112=[-3.5556514943425084415 ,3.2375761991737551650 ] 
dist 113=[-3.8319585076452065997 ,2.5676734217409786008 ] 
dist 114=[-3.9932349845607419715 ,2.4745216374941332944 ] 
dist 115=[-4.1012223903723297204 ,2.2862118314691385555 ] 
dist 116=[-4.1648023643956008134 ,2.2345884919693136707 ] 
dist 117=[-4.2057219523329638969 ,2.0356379632522447313 ] 
dist 118=[-4.2232489383838529921 ,1.9274075744373539108 ] 
dist 119=[-4.2269880232169786552 ,1.5457774023923991690 ] 
dist 120=[-4.2181996304669582136 ,1.4741750699784904577 ] 
dist 121=[-.68864908965215836027,1.5581930746163936337 ] 
dist 122=[-.66581137324042033135,1.6385107678403873120 ] 
dist 123=[-.57842240979116285882,1.7104901237708477390 ] 
dist 124=[-.56026696719736956991,1.7612148389998617128 ] 
dist 125=[-.52259931237592680667,1.8061936906918603854 ] 
dist 126=[-.51196922989946544704,1.8552345969512548373 ] 
dist 127=[-.41442483510174018338,1.8978903562065047023 ] 
dist 128=[-.51395914245730898836,1.9173731117965770160 ] 
dist 129=[-.60803160014525698015,1.9254230987101963867 ] 
dist 130=[-.66763133716337407498,1.9246777269053041560 ] 
dist 131=[-.71347874456535233358,1.8989154093475564747 ] 
dist 132=[-.75264759821667153586,1.8884560614989874397 ] 
dist 133=[-.78461328652765953398,1.8727731455647130230 ] 
dist 134=[-.80170555728727707409,1.8654098582597533167 ] 
dist 135=[-.81122783210109814012,1.6465599220636283907 ] 
dist 136=[-.8131013124758349318 ,1.6133019386907388168 ] 
dist 137=[-.81147699885006485102,1.5441702955377186485 ] 
dist 138=[-.80888108517174522827,1.5236623770940858356 ] 
dist 139=[-.80313409402622886806,1.4361942057121516801 ] 
dist 140=[-.80007467628738963739,1.4173628377590674294 ] 
dist 141=[-.78148739109666217959,1.3658987182660659477 ] 
dist 142=[-.77648580269167025585,1.3551262030409860731 ] 
dist 143=[-.76003109786085524993,1.0678084963900239245 ] 
dist 144=[-.75603730238740894111,1.0695192638354589604 ] 
dist 145=[-.69649009691329590518,1.0679280112370831911 ] 
dist 146=[-.82612335502156957169,1.0649487930440224648 ] 
dist 147=[-.98317999920503530939,1.0369426275026295234 ] 
dist 148=[-1.0952465304596006744 ,1.0284755335403285038 ] 
dist 149=[-1.1960039716406923899 ,1.0172230053108142445 ] 
dist 150=[-1.3079045260731538922 ,1.0120546087075434780 ] 
dist 151=[-1.4107681858980367620 ,.86945067595769299753] 
dist 152=[-1.4754418112904500804 ,.84844937895364491737] 
dist 153=[-1.5246322069817624182 ,.90900223742615702245] 
dist 154=[-1.5656717227508536215 ,1.0040770743295750070 ] 
dist 155=[-1.5984131995899456616 ,1.0801154944621350394 ] 
dist 156=[-1.6144700337750236210 ,1.1501858818604354912 ] 
dist 157=[-1.6214085389799462424 ,1.2111596536568908110 ] 
dist 158=[-1.6212902204387939195 ,1.2508802931395632180 ] 
dist 159=[-.12230363503580848453,1.2826903953205058907 ] 
dist 160=[-.11755302006621300246,1.3120823877683560541 ] 
dist 161=[-.11395273369915312507,1.3354361203179216712 ] 
dist 162=[-.1144337468365812529 ,1.3431382935201278072 ] 
dist 163=[-.11695511214029325052,1.3447861270377153824 ] 
dist 164=[-.12236344762354833711,1.3439663722090947717 ] 
dist 165=[-.13093215281669332508,1.3056225737065792000 ] 
dist 166=[-.14606992151271796475,1.2943196657517127192 ] 
dist 167=[-.16270660239385577294,1.2862973551223908780 ] 
dist 168=[-.17725885012217134652,1.2806463416608520409 ] 
dist 169=[-.19736647592683934208,1.1380977714403205912 ] 
dist 170=[-.37203371591782224729,1.1231692942815102849 ] 
dist 171=[-.51808401412863267707,1.0801038555516095292 ] 
dist 172=[-.66350122301711240137,1.0725998167067893754 ] 
dist 173=[-.79758204700876150558,.98233133769770973463] 
dist 174=[-.89837211697977321301,.96271561663394544584] 
dist 175=[-.99419589032581351203,.94234168610057739529] 
dist 176=[-1.1084486527698784867 ,.93472709412163826893] 
dist 177=[-1.2149303758843293739 ,.6970837202796215083 ] 
dist 178=[-1.2797283908353934590 ,.66533102945634510843] 
dist 179=[-1.3264711412409166042 ,.6017263960285224127 ] 
dist 180=[-1.3608676922694622576 ,.58481417833796365843] 
dist 181=[-1.3862483280862000757 ,.59717442281804883853] 
dist 182=[-1.3969955974628363098 ,.60827677214493666201] 
dist 183=[-1.4001654775783691426 ,.61673766122695997932] 
dist 184=[-1.3987500255935259638 ,.61933689605357511926] 
dist 185=[-.52405228954519119742,.61940821609542921049] 
dist 186=[-.52328085749578703649,.6178353276362332683 ] 
dist 187=[-.51379513775771275757,.60367908032820453896] 
dist 188=[-.51042699787297410671,.59908893627879196839] 
dist 189=[-.50453275769080571766,.592558178949779329  ] 
dist 190=[-.53131669921090199862,.58966908881697586802] 
dist 191=[-.60628901668824146429,.43925978876600949061] 
dist 192=[-.70420216322853812214,.4226594548938918179 ] 
dist 193=[-.79986905345837407817,.3805469719251508844 ] 
dist 194=[-.86587322763131433187,.37435164946332378467] 
dist 195=[-.9228785924164031431 ,.30615541331180863712] 
dist 196=[-.98261681043241898078,.29293022032782281014] 
dist 197=[-1.0396408291466479504 ,.27860603838186757379] 
dist 198=[-1.0858098814329525220 ,.27560007507280837541] 
dist 199=[-1.1329374148535889376 ,.14681589580796388905] 
dist 200=[-1.1937894785940680936 ,.16621489627906488802] 
dist 201=[-1.2506323540246510412 ,.32836689012064629754] 
dist 202=[-1.2817526754153720077 ,.43985363814837286313] 
dist 203=[-1.3000344392740525110 ,.53571915206171247133] 
dist 204=[-1.3056165017354235866 ,.63550194136717513102] 
dist 205=[-1.3062233201664221228 ,.73032064316067280146] 
dist 206=[-1.3046399600238829707 ,.80636660571054200605] 
dist 207=[-1.3011484270869029776 ,.88332526062978841942] 
dist 208=[-1.2970785824634500793 ,.98178803489551167679] 
dist 209=[-1.1493917195894035609 ,1.0770217108963674266 ] 
dist 210=[-1.1267427706149395995 ,1.1410878972780285283 ] 
dist 211=[-1.0835019346068489484 ,1.1946735419384456913 ] 
dist 212=[-1.0712942149039342602 ,1.2480626371028572283 ] 
dist 213=[-1.0237878879964343606 ,1.2973213361317527839 ] 
dist 214=[-1.0116055596683274835 ,1.3344159811983042848 ] 
dist 215=[-.9865210223044715439 ,1.3697526779372771710 ] 
dist 216=[-.97830609432149764618,1.4119926222102043500 ] 
dist 217=[-.29328664749671031262,1.4501088543240320784 ] 
dist 218=[-.23336602091233055794,1.4689811514429108118 ] 
dist 219=[-.09824619907611407480,1.4774985626887584046 ] 
dist 220=[-.07316211151260748897,1.4784519924788316824 ] 
dist 221=[.05838086867449032314,1.4656461937495691805 ] 
dist 222=[-.00488461661967509017,1.4591133840502581317 ] 
dist 223=[-.07030047222231459735,1.4454814591167227187 ] 
dist 224=[-.11933201100216160942,1.4392857141538797177 ] 
dist 225=[-.16581840522772553204,1.2895447577441948631 ] 
dist 226=[-.22107209492972508131,1.2657824562374153111 ] 
dist 227=[-.27782459682552301252,1.2134239691712760348 ] 
dist 228=[-.33029502053928236534,1.1969779421188738456 ] 
dist 229=[-.38975101263929975539,1.1224855729824313552 ] 
dist 230=[-.47439413570817395591,1.1064796769768865834 ] 
dist 231=[-.5603713007829510089 ,1.0643817000528626350 ] 
dist 232=[-.62515350644357999203,1.0542477305835564612 ] 
dist 233=[-.68690257149638520619,1.0042934471344357092 ] 
dist 234=[-.76076933295153691907,1.0352176797486156612 ] 
dist 235=[-.83689276343231444383,1.0561250074588020054 ] 
dist 236=[-.90765169592213090071,1.0688705811238863454 ] 
dist 237=[-.98812985768494563222,1.0763861329747414140 ] 
dist 238=[-1.1030582441018941045 ,1.0769240790477951372 ] 
dist 239=[-1.2154814325978819925 ,1.0734580717235097433 ] 
dist 240=[-1.2859572029966383018 ,1.0694855978283442686 ] 
dist 241=[-1.3392900167721132507 ,1.0030353303574985407 ] 
dist 242=[-1.3832678659519735880 ,.99072538614679305477] 
dist 243=[-1.4179294146752808222 ,.9622224031468820233 ] 
dist 244=[-1.4340656863212591539 ,.95240771166052411224] 
dist 245=[-1.4409684950655081685 ,.9046837133546187811 ] 
dist 246=[-1.4406800283186258170 ,.89370802013715985185] 
dist 247=[-1.4206561365813130220 ,.86710499525360976849] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 1, 0, 0, 0, 1] 
dist 0=[43.246655402351022149  ,43.246655402351022149  ] 
dist 1=[43.048195883080062322  ,43.338955045613474755  ] 
dist 2=[42.703157254626308223  ,43.508953733168525132  ] 
dist 3=[42.087140213667333654  ,43.678210012001316334  ] 
dist 4=[41.143337694020098814  ,43.862327957555990932  ] 
dist 5=[39.982879893499743987  ,44.041559131207815156  ] 
dist 6=[38.437809756118616641  ,44.191189963671151438  ] 
dist 7=[35.957784900788209059  ,44.347255628692680208  ] 
dist 8=[33.418569885603806671  ,44.551943617538254541  ] 
dist 9=[31.637024375961595368  ,44.736639237656195260  ] 
dist 10=[29.383547892217465157  ,44.812925601870885967  ] 
dist 11=[27.241905422185938896  ,44.823749513184264887  ] 
dist 12=[25.382497234911382296  ,44.786228684983875886  ] 
dist 13=[23.414761159041945136  ,44.610417588382965142  ] 
dist 14=[21.520585045635759115  ,42.895705161944104059  ] 
dist 15=[19.954723696300474798  ,42.543459095324056293  ] 
dist 16=[18.323847859406119779  ,40.302213264535346822  ] 
dist 17=[16.169506345311508133  ,35.742991890818266767  ] 
dist 18=[14.043419491958731287  ,34.946747246658048821  ] 
dist 19=[12.525146608819393757  ,32.981363598944335766  ] 
dist 20=[11.154576930528293491  ,32.672404363469305988  ] 
dist 21=[9.6181791627332605449 ,29.621644146503467648  ] 
dist 22=[8.0826883955370705701 ,29.029412134950660200  ] 
dist 23=[6.7152715252854615531 ,28.330245002134777490  ] 
dist 24=[5.2005005038888859816 ,28.129856603796516672  ] 
dist 25=[3.0753113723710493159 ,22.520551328977643761  ] 
dist 26=[.99216323909569078979,21.793261848554924024  ] 
dist 27=[-.35475138597071631778,20.319709983357031616  ] 
dist 28=[-1.4297247076563240765 ,19.932441667050307804  ] 
dist 29=[-2.4257379688942551102 ,18.508235676303830673  ] 
dist 30=[-3.3041610791191755647 ,18.207242309060088115  ] 
dist 31=[-3.9091683189204290888 ,17.655326398695472387  ] 
dist 32=[-4.4353169894644015703 ,17.518057360470290700  ] 
dist 33=[-4.9988489085140515084 ,6.5876040314442941923 ] 
dist 34=[-5.5015678978784785530 ,5.6480706183535493060 ] 
dist 35=[-5.7845819503073372853 ,3.5081816775525244724 ] 
dist 36=[-5.9646011112703715862 ,3.1566711629705422899 ] 
dist 37=[-6.0551478763556022664 ,.4995609232839547484 ] 
dist 38=[-6.1073843523625852349 ,.0393267140325489343 ] 
dist 39=[-6.9497800567024232180 ,-.6916390913088643036 ] 
dist 40=[-8.1618980930608072352 ,-.86213763307337347987] 
dist 41=[-9.2846971090932271036 ,-.8848543036682976103 ] 
dist 42=[-9.9851884049347859122 ,-.2220726772539394153 ] 
dist 43=[-10.513312821827267121  ,.47404584170710787729] 
dist 44=[-10.947487977655832138  ,1.0589791784496280876 ] 
dist 45=[-11.290425885399960832  ,1.6441717926026644975 ] 
dist 46=[-11.454083299307178819  ,2.1842036487370312412 ] 
dist 47=[-11.531049806820013885  ,2.5890364880487364377 ] 
dist 48=[-11.533488170968088468  ,2.9722807747769813365 ] 
dist 49=[-8.4856982996918128696 ,3.4262964525250075226 ] 
dist 50=[-8.2586861316770773575 ,3.8475026136874935678 ] 
dist 51=[-7.6717191465747426404 ,4.0998664982383779594 ] 
dist 52=[-7.5839207869858684771 ,4.2771759361199358802 ] 
dist 53=[-6.5992212752654768402 ,4.3988854392976599087 ] 
dist 54=[-6.4058220272158564524 ,4.4876647990187908701 ] 
dist 55=[-6.1965889823183783198 ,4.5334467764549756977 ] 
dist 56=[-6.1488053794258257837 ,4.5564577952523995999 ] 
dist 57=[-4.2169546884170318545 ,4.6294441926145231904 ] 
dist 58=[-3.9736414116019949362 ,4.7752328879015189951 ] 
dist 59=[-3.4800821999085287938 ,4.8780129577799190544 ] 
dist 60=[-3.3525577057379415155 ,4.9489979256485129525 ] 
dist 61=[-2.8968069501757612976 ,4.9677817446241218950 ] 
dist 62=[-2.8005962507604800742 ,4.9658649257811681668 ] 
dist 63=[-2.6580966521676025702 ,4.9541392646268700768 ] 
dist 64=[-2.6187530594006186558 ,4.6930568878837328721 ] 
dist 65=[.6324023050423191381 ,4.6414238404710835387 ] 
dist 66=[.9033657422123811573 ,4.5193217543368613900 ] 
dist 67=[1.4817738026182440582 ,4.4757034596099449744 ] 
dist 68=[1.5987274922287322858 ,4.2583304492337760265 ] 
dist 69=[1.3678723026147257256 ,4.2074230439193168627 ] 
dist 70=[.92456367129794907397,4.0851631210094031366 ] 
dist 71=[-.06558745374456687996,4.0420124737522679694 ] 
dist 72=[-1.0542989988047138621 ,4.1463383257340403408 ] 
dist 73=[-1.7073387695961553374 ,4.4818797828985873584 ] 
dist 74=[-2.2402240073951340352 ,4.6873122625016609265 ] 
dist 75=[-2.7492397404486252968 ,4.8374637808393301315 ] 
dist 76=[-3.2045877293628988937 ,4.9521823983226298821 ] 
dist 77=[-3.5232122895348556526 ,5.0360627321285373700 ] 
dist 78=[-3.8030366219646570548 ,5.0630368181716887974 ] 
dist 79=[-4.1034771833917816278 ,5.0692009956521072260 ] 
dist 80=[-4.3769857212575685286 ,5.0699326106050988349 ] 
dist 81=[-4.5492859434304395139 ,3.1995112742816317047 ] 
dist 82=[-4.6806087698834641713 ,3.0566180041049717822 ] 
dist 83=[-4.7905188399563055251 ,3.0136512601414905753 ] 
dist 84=[-4.8783561035532279874 ,2.8263036207292275935 ] 
dist 85=[-4.9215528445298192561 ,2.7876310147509354592 ] 
dist 86=[-4.9403331217246558339 ,2.6761103781712020659 ] 
dist 87=[-4.9366659608475571658 ,2.6593450169687893426 ] 
dist 88=[-2.9629287008974657965 ,.62563380950954261246] 
dist 89=[-2.9638006793373460766 ,.74258929515222093967] 
dist 90=[-2.4799033669551350577 ,.84419305188737374477] 
dist 91=[-2.6376092074161654065 ,.95140074943392278062] 
dist 92=[-2.7845623000702290086 ,1.0539757421687040867 ] 
dist 93=[-2.9138953631533273039 ,1.1370808539185273105 ] 
dist 94=[-3.0012881509885950268 ,1.2218002244735946245 ] 
dist 95=[-3.1101138307095054682 ,1.3308021322878246846 ] 
dist 96=[-3.2590147491668942293 ,1.4361291191404922008 ] 
dist 97=[-3.3935080687393136979 ,1.5061731128674460984 ] 
dist 98=[-3.4615995233224179191 ,1.5672204371435063540 ] 
dist 99=[-3.4975415693703229748 ,1.6469578717808980806 ] 
dist 100=[-3.5035387982746536793 ,1.7052875654304079054 ] 
dist 101=[-3.4715865063032547986 ,1.8410327660908598026 ] 
dist 102=[-3.4593837801139416157 ,2.0390702706350785254 ] 
dist 103=[-3.4486065167177058883 ,2.2309109950174536134 ] 
dist 104=[-3.4370947797050892005 ,2.4643535834299330371 ] 
dist 105=[-2.9406304379488170235 ,2.6837401961120264039 ] 
dist 106=[-2.8688945093415806792 ,2.8194842572578164904 ] 
dist 107=[-2.7341028635244345875 ,2.9198922723515959553 ] 
dist 108=[-2.6979584679454027042 ,2.9982535169070751544 ] 
dist 109=[-2.5679045582888130689 ,3.0563732942202761241 ] 
dist 110=[-2.5331366441462819433 ,3.0759949897772895029 ] 
dist 111=[-2.4816318055528815472 ,3.0796669343763031783 ] 
dist 112=[-2.4637019015900501969 ,3.0741404346072125156 ] 
dist 113=[-1.9227780823856020801 ,2.2785937205875243854 ] 
dist 114=[-1.9651635248322867226 ,1.9680632989769761690 ] 
dist 115=[-1.9882828895866833422 ,1.9235188110435613846 ] 
dist 116=[-2.0010121094975109637 ,1.8444728496438149026 ] 
dist 117=[-2.0019276961752477128 ,1.8240853146132373044 ] 
dist 118=[-1.9957057680777897103 ,1.7572350817217592702 ] 
dist 119=[-1.9799373564464564241 ,1.7362562385751402136 ] 
dist 120=[-1.8020187369735905479 ,1.7206983017853317257 ] 
dist 121=[-1.7334684593707297533 ,1.9092890216725094669 ] 
dist 122=[.24964775339430299949,2.1318322451715882266 ] 
dist 123=[.01532796162030150269,2.3237570156130394300 ] 
dist 124=[-.1810046946460993274 ,2.5244932235869847613 ] 
dist 125=[-.3771499093977438197 ,2.7159374621232767334 ] 
dist 126=[-.5584479670391987274 ,2.8707719541761381031 ] 
dist 127=[-.6955075095184980379 ,3.0287363628266197198 ] 
dist 128=[-.8265894008719172753 ,3.2326975486166271595 ] 
dist 129=[-.9840282214933557197 ,3.4236387651090945394 ] 
dist 130=[-1.1314179113803572027 ,3.5296202304379516430 ] 
dist 131=[-1.2223815235577545060 ,3.5938958228511476876 ] 
dist 132=[-1.2895660109175399657 ,3.6183034848789209735 ] 
dist 133=[-1.3982791919785585746 ,3.6278368939766544477 ] 
dist 134=[-1.5904321336729992448 ,3.6327126237332927548 ] 
dist 135=[-1.7929116036404619023 ,3.6351565802667083558 ] 
dist 136=[-2.0626955666628700194 ,3.6349612472705067136 ] 
dist 137=[-2.3286357630533302021 ,3.1599823976197523391 ] 
dist 138=[-2.5157728484452623528 ,3.0912764016206634874 ] 
dist 139=[-2.6812152448113727244 ,2.9726520851520694310 ] 
dist 140=[-2.8605480289036455836 ,2.9411462695433326231 ] 
dist 141=[-3.0353243998140042637 ,2.8431892656402390595 ] 
dist 142=[-3.1825800133483932196 ,2.8107726192421909480 ] 
dist 143=[-3.3380551031526322974 ,2.7911238696335803877 ] 
dist 144=[-3.5456530341857762419 ,2.7839306366380759574 ] 
dist 145=[-3.7434924060578208600 ,.4835352066148851251 ] 
dist 146=[-3.8600084204177187311 ,.2974485758645049804 ] 
dist 147=[-3.9394045127115778421 ,.25288409985343454342] 
dist 148=[-3.9890431576651797273 ,.38060929592123792531] 
dist 149=[-4.0184818184313074129 ,.53587215153293281172] 
dist 150=[-4.0214693943323650422 ,.69718060731371016144] 
dist 151=[-4.0053672488172099344 ,.8490461488671571719 ] 
dist 152=[-3.9924541131346600549 ,1.0232751360579905869 ] 
dist 153=[-3.7604112963020436407 ,1.2738740752469715735 ] 
dist 154=[-3.7163320227636582159 ,1.5211816290505232170 ] 
dist 155=[-3.6090869246267517158 ,1.6822709696101686384 ] 
dist 156=[-3.5708948402396231961 ,1.8112519810566543096 ] 
dist 157=[-3.3808248533351819475 ,1.9303661944787437632 ] 
dist 158=[-3.3362301150139083774 ,2.0342019837518801488 ] 
dist 159=[-3.2398903167728843955 ,2.1021840383695644710 ] 
dist 160=[-3.2080811347120263208 ,2.1570119903873635488 ] 
dist 161=[-3.1351467754529378069 ,2.2083313283777055329 ] 
dist 162=[-3.1900815764851203617 ,2.2494454726265131054 ] 
dist 163=[-3.2191176170807399343 ,2.2635284874336119502 ] 
dist 164=[-3.2240384401384589431 ,2.4182231143755675193 ] 
dist 165=[-3.2109260149352359625 ,2.7882509827117857782 ] 
dist 166=[-3.1991590193464019013 ,3.0463317966889726466 ] 
dist 167=[-3.1762438693156678491 ,3.2721300330320263549 ] 
dist 168=[-3.1648264355238716063 ,3.5132668737482128959 ] 
dist 169=[-2.8381607982013779082 ,3.7321356106364378495 ] 
dist 170=[-2.7864151392885428546 ,3.8690286191015674182 ] 
dist 171=[-2.6758094825918474371 ,3.9722345800325715629 ] 
dist 172=[-2.6416617678537824547 ,4.0566111612278387223 ] 
dist 173=[-2.4892538530473454616 ,4.1225313713464773273 ] 
dist 174=[-2.4570146051224657477 ,4.1520521863271468296 ] 
dist 175=[-2.3627249584173735863 ,4.1605915665015779558 ] 
dist 176=[-2.3475152454309093934 ,4.1572951498371389256 ] 
dist 177=[-1.8586768258796869868 ,1.5168078168069297605 ] 
dist 178=[-2.0404319431615819835 ,1.1147193746141327834 ] 
dist 179=[-2.1517543857853435535 ,1.0610306756191988336 ] 
dist 180=[-2.2329268213566100508 ,.95207761136291553147] 
dist 181=[-2.2943079541709850164 ,.93917943620840652773] 
dist 182=[-2.3400416261178168189 ,1.0583604637063888084 ] 
dist 183=[-2.3587417987563241990 ,1.1696394405182345411 ] 
dist 184=[-2.3647743994520192225 ,1.2994380651629451908 ] 
dist 185=[-2.3614753722842709035 ,1.4192835712886259251 ] 
dist 186=[-.17021606069094782725,1.4908235054011711551 ] 
dist 187=[-.33037487887687451206,1.5407727504074104215 ] 
dist 188=[-.46896772246247701675,1.5744137334680844469 ] 
dist 189=[-.61461831489052816242,1.5985571815266682307 ] 
dist 190=[-.75389044063960941516,1.6105860975907997258 ] 
dist 191=[-.86701666531249675029,1.6160616403069332632 ] 
dist 192=[-.98280935418246972724,1.6141496919633564511 ] 
dist 193=[-1.1327280377977285702 ,1.4269978838985399981 ] 
dist 194=[-1.2785880323856992821 ,1.4025494961909971767 ] 
dist 195=[-1.3781760319260726449 ,1.3432928761975156530 ] 
dist 196=[-1.4630716117096000528 ,1.3263148282237465018 ] 
dist 197=[-1.5502703162951062927 ,1.2295416776150600494 ] 
dist 198=[-1.6324164351085901151 ,1.2083875932536236220 ] 
dist 199=[-1.6971391140988756209 ,1.1669009277953695190 ] 
dist 200=[-1.7615833899567006080 ,1.1546569224440553502 ] 
dist 201=[-1.8426184509097890520 ,.95433075484565356547] 
dist 202=[-1.9172768046175089988 ,.92533916516670364858] 
dist 203=[-1.9562612277996834630 ,.85319925140836372428] 
dist 204=[-1.9772738873937045773 ,.83992161443239925866] 
dist 205=[-1.9814185129084349336 ,.90548304894683878387] 
dist 206=[-1.9707987792694425706 ,1.0533302382949621440 ] 
dist 207=[-1.9652846686094087402 ,1.1724466615553407265 ] 
dist 208=[-1.9591785239250392417 ,1.2934854197935635981 ] 
dist 209=[-1.9516857394300072969 ,1.4490079830064591651 ] 
dist 210=[-1.8505737750825878503 ,1.5997451450913807910 ] 
dist 211=[-1.9537876822160229938 ,1.7016779219498986027 ] 
dist 212=[-2.0448483490959204798 ,1.7875100113770653440 ] 
dist 213=[-2.1212676965484254088 ,1.8739639374911434839 ] 
dist 214=[-2.1660244160188682795 ,1.9543341444452768088 ] 
dist 215=[-2.1962165966179401332 ,2.0158766269927867796 ] 
dist 216=[-2.2144856019278771377 ,2.0754946519884762299 ] 
dist 217=[-2.2240162849660627191 ,2.1481816452357757828 ] 
dist 218=[-2.2233819991207754404 ,2.2145317116642565352 ] 
dist 219=[-2.2101597470115306969 ,2.2488489659656076619 ] 
dist 220=[-2.2018697869526249622 ,2.2663142330337280731 ] 
dist 221=[-2.1293244048728671384 ,2.2687744424202904388 ] 
dist 222=[-2.1089863875103848676 ,2.2569695460418559288 ] 
dist 223=[-2.0804943699661586220 ,2.2485167028865594359 ] 
dist 224=[-2.0686241628283480512 ,2.2293200084418363863 ] 
dist 225=[-1.5005720005112424750 ,2.2198474841713381731 ] 
dist 226=[-1.4367092127381892723 ,2.0023738778364944949 ] 
dist 227=[-1.2847636606400379516 ,1.9672914836991123182 ] 
dist 228=[-1.2548614324018305472 ,1.8893887974786929958 ] 
dist 229=[-1.0356869543109436258 ,1.8646153994814102899 ] 
dist 230=[-.9934182262482421195 ,1.7512534131433749228 ] 
dist 231=[-.92324239188445001429,1.7266439660584931549 ] 
dist 232=[-.90535764278164785147,1.6630628007023667305 ] 
dist 233=[-.57080087122013457552,1.6464292569620090775 ] 
dist 234=[-.52665027406797589184,.7513589103861897602 ] 
dist 235=[-.42100412732458194448,.73830150044476469836] 
dist 236=[-.40421674968642994552,.70251612044730881239] 
dist 237=[-.45192230573081253687,.69648936155466030229] 
dist 238=[-.54522402363784695232,.62774721694536576129] 
dist 239=[-.61524368300562674292,.61325689886657861964] 
dist 240=[-.68170923911895719175,.5976654104642684459 ] 
dist 241=[-.76082079257811695429,.59224087592905256172] 
dist 242=[-.83449964176723835736,.42684463687531437923] 
dist 243=[-.87927455248484020082,.40496254233480437359] 
dist 244=[-.91150601530098693738,.36080469164024398879] 
dist 245=[-.93510385771859953192,.34908072847008663494] 
dist 246=[-.95256887161299703799,.30571356026315173153] 
dist 247=[-.96031446514118349211,.29625657488907193097] 
dist 248=[-.96272009505544234694,.27878276292979030701] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[45.148542954698766426  ,45.148542954698766426  ] 
dist 1=[44.797104474907535657  ,45.398659785521537873  ] 
dist 2=[44.360918915633140034  ,45.622577638385175360  ] 
dist 3=[43.772293719991969452  ,45.869310515633699777  ] 
dist 4=[42.958022878527152136  ,46.111582871576456859  ] 
dist 5=[41.620588553255890035  ,46.317581707478901339  ] 
dist 6=[40.045278029123357564  ,46.536013629770168571  ] 
dist 7=[38.280941062297039684  ,46.827698882330492269  ] 
dist 8=[36.035805251075861296  ,47.092843430557883290  ] 
dist 9=[32.540235383181955844  ,47.205351263413099136  ] 
dist 10=[28.996338793740336576  ,47.226995790722026851  ] 
dist 11=[26.558093904799325097  ,47.195575597455889198  ] 
dist 12=[24.456655698592448536  ,46.967091124518009744  ] 
dist 13=[22.257638040934181639  ,46.727695617425012675  ] 
dist 14=[20.156430509203774644  ,45.293361600060694030  ] 
dist 15=[18.445361760800627153  ,44.046719509241282017  ] 
dist 16=[16.686567755591213672  ,37.879031063458169473  ] 
dist 17=[14.394225202758087973  ,37.046710400330363919  ] 
dist 18=[12.146948403502409947  ,34.976749022067388478  ] 
dist 19=[10.567878299991847783  ,34.655126087850408701  ] 
dist 20=[9.1690392402770445350 ,31.390731708394633445  ] 
dist 21=[7.6413236898473054237 ,30.753963795458956812  ] 
dist 22=[6.1376398488953637384 ,30.021899861038030347  ] 
dist 23=[4.8342827011570471024 ,29.821280249674894736  ] 
dist 24=[3.4195702806841373714 ,23.658484954167168697  ] 
dist 25=[1.4699198207256193937 ,22.861711808395603153  ] 
dist 26=[-.4301799725332607435 ,21.257644703758577542  ] 
dist 27=[-1.6470528562932333366 ,20.838453394990366766  ] 
dist 28=[-2.6057315657145690075 ,19.314369632095779762  ] 
dist 29=[-3.4735857820283047145 ,18.986997450799974332  ] 
dist 30=[-4.2258215806068850226 ,18.417620768071868324  ] 
dist 31=[-4.7224078204230550097 ,18.279993094758145830  ] 
dist 32=[-5.1322370479474992560 ,6.0421034803755250431 ] 
dist 33=[-5.5380475928529660818 ,5.0008000932627900173 ] 
dist 34=[-5.8873980955759982604 ,2.6429009312111293013 ] 
dist 35=[-6.0714726319310824075 ,2.2484859550234422049 ] 
dist 36=[-6.1733514982792843914 ,-.6287189047224919028 ] 
dist 37=[-6.8588850513483837513 ,-1.1230439522815952303 ] 
dist 38=[-8.0333149532602410916 ,-1.9438373774038817770 ] 
dist 39=[-9.3936343075642745782 ,-2.1235643892883319989 ] 
dist 40=[-10.654021414524407441  ,-1.8072188262655559566 ] 
dist 41=[-11.429260247556987874  ,-.6090425748649336920 ] 
dist 42=[-12.000511898259424798  ,.5983937466797365586 ] 
dist 43=[-12.446025765936355964  ,1.4028913769474257206 ] 
dist 44=[-12.788499642776563836  ,2.0655100892443204317 ] 
dist 45=[-12.948090625787514515  ,2.7069293720870871960 ] 
dist 46=[-13.017433156954913581  ,3.2851477714050990095 ] 
dist 47=[-13.015276084184141721  ,3.6956397024123217205 ] 
dist 48=[-8.2255946099701589924 ,4.0617865342828209488 ] 
dist 49=[-7.9139209088037490465 ,4.4631305459124261605 ] 
dist 50=[-7.1439230155505647281 ,4.8296018613114898193 ] 
dist 51=[-7.0198923740668914376 ,5.0565586896690847019 ] 
dist 52=[-5.8430396970510652914 ,5.2247445320549060871 ] 
dist 53=[-5.6189072577691186931 ,5.3565187335506373468 ] 
dist 54=[-5.3327725391272224489 ,5.4543382804435028092 ] 
dist 55=[-5.2454525596185079629 ,5.4868838664103032656 ] 
dist 56=[-3.3077700602166449008 ,5.4904437379293349508 ] 
dist 57=[-3.0624032037306414587 ,5.4744059587793403862 ] 
dist 58=[-2.5349648863521730788 ,3.6810755427896864126 ] 
dist 59=[-2.4105401552783085159 ,3.5155790410589557213 ] 
dist 60=[-1.8455962270654264183 ,3.1267950302471353966 ] 
dist 61=[-1.7449203752910790973 ,3.0462895971915169088 ] 
dist 62=[-1.5214871672345490055 ,3.0762699681974961247 ] 
dist 63=[-1.4792023892712399477 ,3.1780305415851158855 ] 
dist 64=[.74081872016109308712,3.2694478322015128141 ] 
dist 65=[.94609986958463682069,3.3438685435438961834 ] 
dist 66=[.4616639069196432204 ,3.7354601259607907108 ] 
dist 67=[.0724774127011328104 ,4.1771955321412229117 ] 
dist 68=[-.2884370168049096996 ,4.5717184466295541572 ] 
dist 69=[-.7056047726991023809 ,4.8483911684197134970 ] 
dist 70=[-1.1276468858392520857 ,5.0926939913743080477 ] 
dist 71=[-1.5080812279473495847 ,5.3579620216601837796 ] 
dist 72=[-1.9315225172824328845 ,5.5931245645106823581 ] 
dist 73=[-2.5253566026967772687 ,5.7171876788332133209 ] 
dist 74=[-3.1060301574430698604 ,5.7858895397891745709 ] 
dist 75=[-3.4769434346524301226 ,5.8007551684226077330 ] 
dist 76=[-3.7659377923908174993 ,5.7797225389633031289 ] 
dist 77=[-4.0195091597742945862 ,5.7701975156511902486 ] 
dist 78=[-4.2315494234406434939 ,5.7606634016958597125 ] 
dist 79=[-4.3547161027707566490 ,5.7487434517134161265 ] 
dist 80=[-4.4366900572641758931 ,1.4721480921845521682 ] 
dist 81=[-4.4842660762735952066 ,.87179339554764634408] 
dist 82=[-4.5130185401063970160 ,.9564212559235041329 ] 
dist 83=[-4.5198306365530063372 ,1.1086400604565347271 ] 
dist 84=[-4.5120257398940398725 ,1.2694701921629672665 ] 
dist 85=[-4.5021151556535762331 ,1.4840669586391320296 ] 
dist 86=[-4.4411105292706767222 ,1.7168373682068045849 ] 
dist 87=[-4.4213923933052788194 ,1.9502294689739444708 ] 
dist 88=[-4.3392557710715137464 ,2.2288690415357841538 ] 
dist 89=[-4.3252725327695320963 ,2.6422733021708668851 ] 
dist 90=[-4.3655895654169085580 ,3.0516287947002350068 ] 
dist 91=[-4.4225688449486804863 ,3.3141125668405842024 ] 
dist 92=[-4.4549830038015135618 ,3.5193985441476216633 ] 
dist 93=[-4.4559169768555699428 ,3.7004348192943491675 ] 
dist 94=[-4.5410308735663873114 ,3.8521216199539529803 ] 
dist 95=[-4.6331189925392016201 ,3.9402507544144285420 ] 
dist 96=[-4.7050919404141919622 ,3.9987325993712853455 ] 
dist 97=[-4.7231977575180281729 ,4.0320717785971985757 ] 
dist 98=[-4.7224651194915273062 ,4.0481016959510680844 ] 
dist 99=[-4.7191013522893325286 ,4.0454777912734442226 ] 
dist 100=[-4.5581826117707897464 ,4.0181669059846059878 ] 
dist 101=[-4.5132694707945253807 ,3.9994464055081723847 ] 
dist 102=[-4.4834737644079390200 ,3.8596942026350251250 ] 
dist 103=[-4.4665786494103158451 ,4.0029497225580241522 ] 
dist 104=[-3.6425334187818376958 ,4.3287795918908840121 ] 
dist 105=[-3.5286600700607981575 ,4.5191436684641804818 ] 
dist 106=[-3.3113422090904128719 ,4.6467247091623189512 ] 
dist 107=[-3.2540490848001096323 ,4.7219479878738838738 ] 
dist 108=[-3.0507141403302300731 ,4.7703745706083767558 ] 
dist 109=[-2.9988033132134652901 ,4.7910013333356418727 ] 
dist 110=[-2.9270735532701364095 ,4.7951816276484145401 ] 
dist 111=[-3.0506707377717655448 ,4.7847434061831051444 ] 
dist 112=[-3.3045426114514242008 ,3.6828713613442282872 ] 
dist 113=[-3.5840602682331491375 ,3.6659850864984852592 ] 
dist 114=[-3.8387974113033291289 ,3.2079208340274706056 ] 
dist 115=[-3.9937488708721605338 ,3.1378759574539004880 ] 
dist 116=[-4.1053362344570052020 ,2.9845900184654503345 ] 
dist 117=[-4.1869865008989589394 ,2.9375825616891729995 ] 
dist 118=[-4.2431967247575848926 ,2.7290555167382428970 ] 
dist 119=[-4.2558992139636013068 ,2.6852720476826595427 ] 
dist 120=[-4.2483682415388121143 ,2.5687949917828993586 ] 
dist 121=[-4.2450026481119006912 ,2.5439209101998887424 ] 
dist 122=[.25639025336284200604,1.4611827424104975781 ] 
dist 123=[.37751218504972549819,1.4881823340390060295 ] 
dist 124=[.40080044200242427671,1.5032329137368045472 ] 
dist 125=[.52920637022353004064,1.5113705069168742048 ] 
dist 126=[.54999841319507869376,1.5109985426424187504 ] 
dist 127=[.59296281971254351811,1.5060673091160162238 ] 
dist 128=[.5999450896366357554 ,1.5010599149864796698 ] 
dist 129=[.63136388562835640901,1.3938404651923396241 ] 
dist 130=[.61333687574699768879,1.3750387956219706877 ] 
dist 131=[.57906285773800947534,1.3333639074353061526 ] 
dist 132=[.522620408673400786  ,1.3195893891616319709 ] 
dist 133=[.45614348196501584928,1.2546038370398585466 ] 
dist 134=[.38180305039176342169,1.2400689130573559396 ] 
dist 135=[.28734872705181258465,1.2009340715724764490 ] 
dist 136=[.05455154584921761120,1.1908428955086956769 ] 
dist 137=[-.2270124602221756793 ,1.0031730726905187323 ] 
dist 138=[-.41364800582191728914,.98153763625335448206] 
dist 139=[-.56674798241981863855,.97490304503570737405] 
dist 140=[-.71441367389463629413,.95736570219506308377] 
dist 141=[-.84753380367238692784,.93933895849560992795] 
dist 142=[-.94255748188103999793,.92107456732310990483] 
dist 143=[-1.0280090172427434758 ,.91425488265691102247] 
dist 144=[-1.2517594310691631787 ,.87534213850265257713] 
dist 145=[-1.4378071448698639668 ,.7145805323596512769 ] 
dist 146=[-1.5893201801956024430 ,.69190499507131654551] 
dist 147=[-1.7335896437715392835 ,.64521244727950662227] 
dist 148=[-1.8623869053527103122 ,.63210202096474403115] 
dist 149=[-1.9521282627113895263 ,.57961851309802311447] 
dist 150=[-2.0305724624359354460 ,.56841912643042066271] 
dist 151=[-2.1142691419310140323 ,.54208428034424804824] 
dist 152=[-2.1872826410275781463 ,.53430927690320979707] 
dist 153=[-2.2230751097320890501 ,-.23883766291368390692] 
dist 154=[-2.2411405123097233583 ,-.29433124026422638881] 
dist 155=[-2.2433694643189440626 ,-.41192376265263680831] 
dist 156=[-2.2156806541632761853 ,-.43687544510841375056] 
dist 157=[-2.2056275071668804931 ,-.55063979738877965037] 
dist 158=[-2.1969846561521567476 ,-.55664738437072060649] 
dist 159=[-2.1879914726095198001 ,-.14498278817666282081] 
dist 160=[-1.9113686440285172374 ,.27009733631486783164] 
dist 161=[-1.8742320806770077514 ,.55100307421317463954] 
dist 162=[-1.7765228046075373394 ,.7877247537633987864 ] 
dist 163=[-1.7579895280796793497 ,1.0264045699162226181 ] 
dist 164=[-1.5815988711105317021 ,1.2483921655564793922 ] 
dist 165=[-1.5446686601481878554 ,1.4184719044011202239 ] 
dist 166=[-1.4974000412030754502 ,1.5832927868382489762 ] 
dist 167=[-1.4798788164795148817 ,1.7842850633430721392 ] 
dist 168=[-1.1206616470087810242 ,1.9738950139261141691 ] 
dist 169=[-1.1229970588120628627 ,2.0932729467172982739 ] 
dist 170=[-1.1223063413989422686 ,2.1841938767481869075 ] 
dist 171=[-1.1116972546607644756 ,2.2601915187695361674 ] 
dist 172=[-1.1096258694292552221 ,2.3208737552039468273 ] 
dist 173=[-1.0591488913568750267 ,2.3506490398628548033 ] 
dist 174=[-1.0462867843529254066 ,2.3638292912435771187 ] 
dist 175=[-1.0374140210904102175 ,2.3650381616566419360 ] 
dist 176=[-1.0337873266597821072 ,.71529641653683084846] 
dist 177=[-.82665397571212243482,.82242448658814047205] 
dist 178=[-.79842012657590531635,.89662941593375462782] 
dist 179=[-.74500191372880091153,.96102901094724554414] 
dist 180=[-.73111661116407322693,1.0290075303221992625 ] 
dist 181=[-.68296512389083369484,1.0941969325249605635 ] 
dist 182=[-.67045993668241083012,1.1474605258816085766 ] 
dist 183=[-.65560351712105387554,1.2022642875855784526 ] 
dist 184=[-.64933651192840469275,1.2736032305732368451 ] 
dist 185=[.09093257765029041985,1.3410661160876264948 ] 
dist 186=[.14926299854931775267,1.3803940418598949628 ] 
dist 187=[.27735475619078474508,1.4066953887950105632 ] 
dist 188=[.3016020446124870682 ,1.4221472355865167400 ] 
dist 189=[.37848397848166347765,1.4308382421411770687 ] 
dist 190=[.2715305152179833658 ,1.4310656209104995655 ] 
dist 191=[.10092289121943489873,1.4257099708548825942 ] 
dist 192=[-.07344318769131132178,1.4203032981829923109 ] 
dist 193=[-.19540277167437984483,1.4120218253948636684 ] 
dist 194=[-.30247751210516129292,1.4163119139822096608 ] 
dist 195=[-.41741603808743484016,1.4166876123529896597 ] 
dist 196=[-.52878489598806500724,1.3809311220291973138 ] 
dist 197=[-.62160809606799491767,1.3709904588929447683 ] 
dist 198=[-.71874259023639761776,1.3644123805962285971 ] 
dist 199=[-.84732517519245219363,1.3606949120137813596 ] 
dist 200=[-.97374607249787654199,1.1327231324110211164 ] 
dist 201=[-1.0622502603057421134 ,1.0995571970909027109 ] 
dist 202=[-1.1400401878981198428 ,1.0400141046201485722 ] 
dist 203=[-1.2236842053767260841 ,1.0244615248666164323 ] 
dist 204=[-1.3048202118356869101 ,.97072682882442555987] 
dist 205=[-1.3725972144815306498 ,.95604124272871777968] 
dist 206=[-1.4436598950750440522 ,.93899180543513122072] 
dist 207=[-1.5379150864316916375 ,.93133446243682034896] 
dist 208=[-1.6277222976372513616 ,.16916156902588158912] 
dist 209=[-1.6810261631717993868 ,.02458272407594889615] 
dist 210=[-1.7178656921573439444 ,.00314498927324868726] 
dist 211=[-1.7419371731436728895 ,-.03527788132190043501] 
dist 212=[-1.7570002574815797223 ,-.04364879481482553764] 
dist 213=[-1.7591846840714184808 ,-.06323084242490954533] 
dist 214=[-1.7537707963500866937 ,-.06277763818985277962] 
dist 215=[-1.7489744890104436391 ,-.05411740452795388194] 
dist 216=[-1.6545283200892988374 ,-.03197799762577098011] 
dist 217=[-1.6362683084367913210 ,-.00581530309721405472] 
dist 218=[-1.5919616397657389379 ,.01890852398185410062] 
dist 219=[-1.5760709905280581162 ,.04734761616723103195] 
dist 220=[-1.4966088370140826078 ,.08834412625844984381] 
dist 221=[-1.4778837447764352737 ,.13434511468489792503] 
dist 222=[-1.4367178612558780841 ,.18276533216564212902] 
dist 223=[-1.4229107443628154369 ,.24230004973649062042] 
dist 224=[-1.3175016101533391476 ,.39239340817121647667] 
dist 225=[-1.3248121391882532107 ,.62203184995045740599] 
dist 226=[-1.3261546975232340574 ,.80995687887494639231] 
dist 227=[-1.3233418089896997287 ,.99042793895585903017] 
dist 228=[-1.2940449881724077024 ,1.1525703173108418087 ] 
dist 229=[-1.2843037850902597111 ,1.2673159657658001889 ] 
dist 230=[-1.2718863371148690890 ,1.3694647154178729970 ] 
dist 231=[-1.2656481305112011797 ,1.4813123421575323787 ] 
dist 232=[-1.0879879638822902508 ,1.5833913977710928514 ] 
dist 233=[-1.0617477320894791660 ,1.6465380508080155916 ] 
dist 234=[-1.0080154260080874502 ,1.6933362957622955723 ] 
dist 235=[-.99251030875996330447,1.7301427782810261311 ] 
dist 236=[-.92868228800777716245,1.7577609770609691918 ] 
dist 237=[-.91466477892328335299,1.7678740981131699572 ] 
dist 238=[-.87967587737569932855,1.7697680659520284104 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 0, 2, 1, 0, 2] 
dist 0=[46.338571186213068693  ,46.338571186213068693  ] 
dist 1=[46.091170378224568281  ,46.439735971247913407  ] 
dist 2=[45.629119586433686802  ,46.596248330750584528  ] 
dist 3=[44.841109856675362226  ,46.731611123063416507  ] 
dist 4=[43.865715722047535586  ,46.817537026376600335  ] 
dist 5=[42.655140116248625639  ,46.883204142809592889  ] 
dist 6=[41.036602968167696573  ,46.937442158851355827  ] 
dist 7=[38.431686013179188636  ,46.972636904911132770  ] 
dist 8=[35.758419480179988522  ,46.962291641896043616  ] 
dist 9=[33.866827436225372604  ,46.915877828743720571  ] 
dist 10=[32.179863214382311409  ,46.851077998792033132  ] 
dist 11=[30.323804547921343560  ,46.666858544469816562  ] 
dist 12=[28.493686838104107582  ,46.572551351050708588  ] 
dist 13=[26.910187503796530346  ,46.313523216944768679  ] 
dist 14=[25.198390330064746583  ,45.847535034608918782  ] 
dist 15=[22.855496897814778201  ,35.817070284276861757  ] 
dist 16=[20.506526263279799942  ,34.880066653855226175  ] 
dist 17=[18.770294943318196505  ,32.560016446660573138  ] 
dist 18=[17.143504023225023570  ,32.227344148271800280  ] 
dist 19=[15.231507601233292856  ,28.648771936217893890  ] 
dist 20=[12.772415509445327974  ,27.966175927771473698  ] 
dist 21=[10.904198193621885704  ,27.233195960409850862  ] 
dist 22=[9.1940277554731685297 ,27.101632595645601626  ] 
dist 23=[6.4238372077316032019 ,20.626417251061243514  ] 
dist 24=[3.4929700401350209386 ,19.816045548292146857  ] 
dist 25=[1.5613280059438599510 ,18.214732224846291900  ] 
dist 26=[-.0178043180040269841 ,17.809903056548488014  ] 
dist 27=[-1.5399315631216191947 ,16.420512080668550399  ] 
dist 28=[-4.0368693944938846962 ,16.110726198121498678  ] 
dist 29=[-5.8051189667167228547 ,15.766348296239250022  ] 
dist 30=[-7.2037042487849444465 ,15.699477408112461322  ] 
dist 31=[-8.4746201292057744906 ,3.6692824949988626740 ] 
dist 32=[-9.5753606031423697492 ,2.6977533583640922846 ] 
dist 33=[-10.293986619217864759  ,.49650583527791104801] 
dist 34=[-10.875458224922139891  ,.14727948185617974734] 
dist 35=[-11.428443788071510363  ,-2.5226478139775280078 ] 
dist 36=[-11.900156245355176144  ,-2.9746833434938224769 ] 
dist 37=[-12.156839590473636932  ,-3.6842131110420631782 ] 
dist 38=[-12.308377094429006225  ,-3.1439329684195024865 ] 
dist 39=[-12.359547215238973850  ,-1.9512192537193724468 ] 
dist 40=[-12.354665133623709042  ,-.72636737100972878387] 
dist 41=[-12.328992756874695508  ,.1240736131879104082 ] 
dist 42=[-12.196015792218039061  ,.8617875938741434194 ] 
dist 43=[-12.136794120573680956  ,1.6370567642585512068 ] 
dist 44=[-9.9826956780451393829 ,2.3760472582628602671 ] 
dist 45=[-10.092708477746358606  ,2.9691056695765719627 ] 
dist 46=[-10.115010169532040724  ,3.5683473425495726942 ] 
dist 47=[-7.0032267806536114063 ,4.3321060458483595797 ] 
dist 48=[-5.5918112568501004242 ,5.0670599159228675924 ] 
dist 49=[-5.1072758403856038870 ,5.5513823189505732972 ] 
dist 50=[-5.0147785860756542724 ,5.9446051066099947183 ] 
dist 51=[-4.4678424117292506035 ,6.3160147122242071273 ] 
dist 52=[-4.1936921613474900075 ,6.6447251522934331142 ] 
dist 53=[-3.9780206272851916595 ,6.8675385533298742976 ] 
dist 54=[-3.9237197673159156002 ,7.0552877047319004480 ] 
dist 55=[-3.6844409056483481706 ,7.2440350638620744417 ] 
dist 56=[-2.8069937439117016398 ,7.4044547381628967469 ] 
dist 57=[-2.4983009531745229633 ,7.4791397218055967778 ] 
dist 58=[-2.4521075611348052470 ,7.5051369631399679016 ] 
dist 59=[-2.0179892019904994932 ,7.4712425016395004529 ] 
dist 60=[-1.9393004944326149593 ,2.1992346749849353755 ] 
dist 61=[-1.8394108572563833180 ,2.5951877272457064333 ] 
dist 62=[-1.8159744444459613659 ,2.9149877546500482684 ] 
dist 63=[-1.0715642169048147273 ,3.2157944211989702088 ] 
dist 64=[-.98185215292931321388,3.4824448317280780487 ] 
dist 65=[-.79365257584419947049,3.6658222138322044512 ] 
dist 66=[-.74372312245270382138,3.8238946944273410141 ] 
dist 67=[-.54577511448022370261,3.9894851360483731034 ] 
dist 68=[-.50838519032040322851,4.1336125657557996544 ] 
dist 69=[-.4171266435260167817 ,4.2059666644327682066 ] 
dist 70=[-.4016619783465373071 ,4.2437551098059667560 ] 
dist 71=[-.2574355885960244311 ,4.2497880092132064778 ] 
dist 72=[-.2293111917668325767 ,4.2090765576522882360 ] 
dist 73=[-.1829232727853104168 ,4.1941754579763462523 ] 
dist 74=[-.1703951770048801354 ,4.1813056392548766318 ] 
dist 75=[-.1356120680822518434 ,4.1678386228643663836 ] 
dist 76=[-.1246974003129603654 ,3.9501968717817703886 ] 
dist 77=[-.13986591620168991041,3.9479568272833663895 ] 
dist 78=[-.53411931720889387164,3.9380529513450898941 ] 
dist 79=[-.93947833543322273714,3.0874033077009017263 ] 
dist 80=[-1.3215846788618494540 ,2.6741957090646849381 ] 
dist 81=[-1.6230143808982615438 ,2.5909660253007586328 ] 
dist 82=[-1.9235061599670256662 ,2.5095483877716804925 ] 
dist 83=[-2.3018882399351198715 ,2.4935720442868990975 ] 
dist 84=[-2.6651136374181375384 ,1.5874995711221473966 ] 
dist 85=[-2.9050991379342665812 ,1.4727336549038725129 ] 
dist 86=[-3.1011538820623784610 ,1.2458812932390514063 ] 
dist 87=[-3.2889857417587781535 ,1.1880190733474567885 ] 
dist 88=[-3.4575849103454946606 ,.9878263580763687293 ] 
dist 89=[-3.5768612087827454601 ,.9424484168342104221 ] 
dist 90=[-3.6831306556388832443 ,.8905744402203785230 ] 
dist 91=[-3.7998242524383493727 ,.8777210016541119150 ] 
dist 92=[-3.9017385016669150484 ,-.4270714489624768240 ] 
dist 93=[-3.9489989945172805863 ,-.44664612473264162889] 
dist 94=[-3.9698409390228854384 ,-.43687615829195939769] 
dist 95=[-3.9689147131011111812 ,-.41654819004678779777] 
dist 96=[-3.9129295138541080055 ,-.3868386763649537669 ] 
dist 97=[-3.8895857864805176135 ,-.34471619327808856896] 
dist 98=[-3.8621377216020197141 ,-.27479651586607969635] 
dist 99=[-3.8455249544905065229 ,-.1924433624231614440 ] 
dist 100=[-3.3420322147782614265 ,-.1006678304110119290 ] 
dist 101=[-3.2667786087481983967 ,.0155913943305314069 ] 
dist 102=[-3.1145823690897430800 ,.1956994685020897275 ] 
dist 103=[-3.0706913837773781130 ,.3846631934866762132 ] 
dist 104=[-2.8911824769252105229 ,.5362862757104044362 ] 
dist 105=[-2.8505814682537845912 ,.6896992705729570302 ] 
dist 106=[-2.7521808606950447542 ,.8858281653978043252 ] 
dist 107=[-2.7204713366017175386 ,1.0946333208818419708 ] 
dist 108=[-1.7750714247053460632 ,1.2986654462628520581 ] 
dist 109=[-1.7512749572254794349 ,1.5385074539879364566 ] 
dist 110=[-1.7412135647884313530 ,1.8902917473532619675 ] 
dist 111=[-.1945340693389996678 ,2.2392826871774380814 ] 
dist 112=[.2578737913977035308 ,2.4679764772644493576 ] 
dist 113=[.3360456676550723927 ,2.6526060920849066955 ] 
dist 114=[.4900518865699763027 ,2.8256752390054203140 ] 
dist 115=[.5267817508377807091 ,2.9783115473054894279 ] 
dist 116=[.84795183735942360366,3.0813659883010098038 ] 
dist 117=[.89796644733817990332,3.1679658168402537825 ] 
dist 118=[.94320630846541526887,3.2549114421334750314 ] 
dist 119=[.93142280951504461285,3.3276070372681847771 ] 
dist 120=[.89395218731224124573,3.3573155463177250988 ] 
dist 121=[.8209898636354536604 ,3.3681921989162212604 ] 
dist 122=[.70798124886563165511,3.3629497183716070325 ] 
dist 123=[.5106261642440578463 ,3.2814119994121337860 ] 
dist 124=[.30664316761724562343,2.6116958555011605608 ] 
dist 125=[.16717021476823300655,2.6003817721223974043 ] 
dist 126=[.04809603272757125976,2.5888417056400697834 ] 
dist 127=[-.43979735110580705961,2.4377551892497784026 ] 
dist 128=[-.78324664143329731118,2.4179651490947140954 ] 
dist 129=[-1.0709396067895992370 ,2.3535971141203065130 ] 
dist 130=[-1.3581265760977485328 ,2.3416580479985792392 ] 
dist 131=[-1.6233209576653347826 ,2.1827122490131284486 ] 
dist 132=[-1.8232146289232465932 ,2.1464911379636455200 ] 
dist 133=[-2.0137408274495530924 ,2.1111084117716325144 ] 
dist 134=[-2.2415373097744826062 ,2.0965195997655141455 ] 
dist 135=[-2.4540690381086271642 ,1.6188762002192966619 ] 
dist 136=[-2.5836544145439939773 ,1.5543061130609498602 ] 
dist 137=[-2.6774030637508031771 ,1.4262715875939091786 ] 
dist 138=[-2.7468659432647072369 ,1.3921968492921073304 ] 
dist 139=[-2.7978447675685971557 ,1.2669797756470175443 ] 
dist 140=[-2.8178014869512265069 ,1.2382177387493786398 ] 
dist 141=[-2.8230792383149472029 ,1.1879586389993889594 ] 
dist 142=[-2.8183940978395180074 ,1.1749398034996238660 ] 
dist 143=[-.9952681955503597619 ,.05116404895965834820] 
dist 144=[-.99310216748389909566,-.01294889823499997449] 
dist 145=[-.99025841943527895471,.03289930662268727179] 
dist 146=[-.98134786716341630864,.1007677661993322589 ] 
dist 147=[-.97652994961492840576,.19794656919811079234] 
dist 148=[-1.0451123147588872854 ,.29682700376699975406] 
dist 149=[-1.2094179609136435365 ,.37149109332308574958] 
dist 150=[-1.4238791465547881954 ,.44278803866991885197] 
dist 151=[-1.6333751684088707537 ,.52822963069716899515] 
dist 152=[-1.7778581277743005419 ,.6163383760495064913 ] 
dist 153=[-1.9025892998556803120 ,.69828625614283273314] 
dist 154=[-2.0332248273729729368 ,.79151446245463874972] 
dist 155=[-2.1578902170302311997 ,.9246623160060562727 ] 
dist 156=[-2.2587868645751786311 ,1.0554973604089939189 ] 
dist 157=[-2.3617546695040546965 ,1.1394927722820497745 ] 
dist 158=[-2.4946943630660599969 ,1.2053614957857603793 ] 
dist 159=[-2.6189221116150084406 ,1.2638265835797646432 ] 
dist 160=[-2.6871063846457695523 ,1.3131427913801851856 ] 
dist 161=[-2.7274044329643052490 ,1.3424853968436090701 ] 
dist 162=[-2.7402879909389047265 ,1.3628545372186444773 ] 
dist 163=[-2.7425899700601713499 ,1.4388725118927035365 ] 
dist 164=[-2.7406364812272990887 ,1.5954297534517670119 ] 
dist 165=[-2.7351978412060091092 ,1.7549770259131204952 ] 
dist 166=[-2.7265295656888111392 ,1.9605894924506300206 ] 
dist 167=[-2.4071042436948178400 ,2.1601482925145437603 ] 
dist 168=[-2.3585190511544531565 ,2.2955265482130152719 ] 
dist 169=[-2.2676389445546594927 ,2.4099816761981082796 ] 
dist 170=[-2.2424995580806922919 ,2.5260047452166245524 ] 
dist 171=[-2.1481116125839729340 ,2.6343293924035981161 ] 
dist 172=[-2.1227307314559209628 ,2.7180488268996309240 ] 
dist 173=[-2.0759363427386528570 ,2.7998856573315876694 ] 
dist 174=[-2.0615173475844547198 ,2.9006949158819506282 ] 
dist 175=[-.75827406896226912685,2.9931278047611607526 ] 
dist 176=[-.89688007793170950675,3.0415215787056115725 ] 
dist 177=[-.99886808678977463303,3.0669804945707175729 ] 
dist 178=[-1.0936800698117139408 ,3.0705375795598000727 ] 
dist 179=[-1.2036354838018441061 ,3.0582758912097766478 ] 
dist 180=[-1.3047948527856148590 ,3.0476640242314680108 ] 
dist 181=[-1.3644890084339267873 ,3.0219176165061162208 ] 
dist 182=[-1.4053023193199877029 ,3.0087838445137601285 ] 
dist 183=[-1.4310813683906793604 ,2.7242986176895348623 ] 
dist 184=[-1.4488051959345411763 ,2.6779304818723261397 ] 
dist 185=[-1.4574585256312865343 ,2.5738639526921603890 ] 
dist 186=[-1.4611311013301745280 ,2.5404254699138339501 ] 
dist 187=[-1.4589692780951013905 ,2.3861207301490292003 ] 
dist 188=[-.10922286564273879295,2.3523404339394560683 ] 
dist 189=[-.2318562230005046911 ,2.2676490056006126664 ] 
dist 190=[-.34012098829534582683,2.2430848213184073192 ] 
dist 191=[-.76515413041537441679,2.1632967006592923359 ] 
dist 192=[-1.1552430753735775436 ,2.2238571451411524918 ] 
dist 193=[-1.4728914770958990707 ,2.2636345629217986562 ] 
dist 194=[-1.7752985922556972660 ,2.2855332255962355641 ] 
dist 195=[-2.0452199971069051922 ,2.2969481159499066374 ] 
dist 196=[-2.2331658178933510589 ,2.2961684549163598645 ] 
dist 197=[-2.3972945773687728575 ,2.2869471026226874913 ] 
dist 198=[-2.5721236039937255196 ,2.2785276864322039467 ] 
dist 199=[-2.7307856539045920779 ,2.1183312581416114093 ] 
dist 200=[-2.8303660978498624127 ,2.0899105889360060277 ] 
dist 201=[-2.9058597458994324719 ,2.0254233887198764633 ] 
dist 202=[-2.9683531072346306241 ,2.0037818626656515727 ] 
dist 203=[-3.0177945862154317210 ,1.9005020046845138433 ] 
dist 204=[-3.0411773213673842912 ,1.8771516727550103847 ] 
dist 205=[-3.0499735736277168602 ,1.8182451346798657626 ] 
dist 206=[-3.0474962904561285671 ,1.7997984329352153870 ] 
dist 207=[-1.8978914151463039456 ,1.0886607245117004657 ] 
dist 208=[-1.9127046855147222154 ,1.2181389869294059905 ] 
dist 209=[-1.9162572326668752836 ,1.3196877377474882295 ] 
dist 210=[-1.9128469206127424622 ,1.4203585613197233156 ] 
dist 211=[-1.9089615912939260128 ,1.5463316612041880254 ] 
dist 212=[-1.7553754398536711466 ,1.6668190824054926805 ] 
dist 213=[-1.7295014962107760404 ,1.7455878156697133371 ] 
dist 214=[-1.6774723699962913854 ,1.8089802616492469320 ] 
dist 215=[-1.6614040057671806075 ,1.8680763597370404283 ] 
dist 216=[-1.5909852527289528165 ,1.9199765868496023757 ] 
dist 217=[-1.5744805714519546917 ,1.9546388123795733964 ] 
dist 218=[-1.5286332955539756452 ,1.9833556355640774875 ] 
dist 219=[-1.5167939586683142529 ,2.0115182507288279459 ] 
dist 220=[-.63977576158475159399,2.0338126689483730909 ] 
dist 221=[-.63086953022542107181,2.0391000790380374593 ] 
dist 222=[-.67601527675837567253,2.0370202932164739374 ] 
dist 223=[-.7190382110147189389 ,2.0311022174784184027 ] 
dist 224=[-.74409547618394006351,1.9825070179211861215 ] 
dist 225=[-.76082497930295669765,1.9672550026339804219 ] 
dist 226=[-.77059766329108370711,1.9416267679832781448 ] 
dist 227=[-.77656421178358484657,1.9322136048866010221 ] 
dist 228=[-.77809693441220286788,1.6764013460157208958 ] 
dist 229=[-.77673913565081703258,1.6379925455729598881 ] 
dist 230=[-.7752890243568790763 ,1.5552310259480378514 ] 
dist 231=[-.71076165367153604586,1.5303290888140213733 ] 
dist 232=[-.69999791143088845914,1.4216850256305325949 ] 
dist 233=[-.67864838773217887617,1.3992570764194082545 ] 
dist 234=[-.67214124926850878576,1.3370035199914149931 ] 
dist 235=[-.644137346861412263  ,1.3262470276848377742 ] 
dist 236=[-.63741972862796189333,1.3083325313811165455 ] 
dist 237=[-.77799940487312439148,1.3704616674756611958 ] 
dist 238=[-.98083346009602471055,1.4165855344179323570 ] 
dist 239=[-1.1754625379157376496 ,1.4530144924012356118 ] 
dist 240=[-1.3502223812338471547 ,1.4804793797211973004 ] 
dist 241=[-1.4737259481212697262 ,1.4908128484914915032 ] 
dist 242=[-1.5834963454434215871 ,1.4938317488192334445 ] 
dist 243=[-1.7034246500790446648 ,1.4920914722275758684 ] 
dist 244=[-1.8124655242255109904 ,1.4565105312264690477 ] 
dist 245=[-1.8787664507310677699 ,1.4471115840782164949 ] 
dist 246=[-1.9265389197521129931 ,1.4207356708441533279 ] 
dist 247=[-1.9616026257445290433 ,1.4101223313117786190 ] 
dist 248=[-1.9858618583142120830 ,1.3491115099799891993 ] 
dist 249=[-1.9912522120368159902 ,1.3337781396948957931 ] 
dist 250=[-1.9885608490586534458 ,1.3046599816822192164 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 1, 0, 0, 2] 
dist 0=[43.730974126579286953  ,43.730974126579286953  ] 
dist 1=[43.597008906065719642  ,43.835061120294981872  ] 
dist 2=[43.334704486580019864  ,43.977967714065629323  ] 
dist 3=[42.886537514361034322  ,44.134682825510897024  ] 
dist 4=[42.010317311492056878  ,44.293697933856084049  ] 
dist 5=[40.923437463599299522  ,44.484273693721487466  ] 
dist 6=[39.633881488182773181  ,44.766643331940011134  ] 
dist 7=[37.945596898534354872  ,45.035870772824082785  ] 
dist 8=[35.266198744437406560  ,45.173986383069980061  ] 
dist 9=[32.534228735820422634  ,45.241657361323838030  ] 
dist 10=[30.635877833123927706  ,45.230017339992129664  ] 
dist 11=[28.979644347061628811  ,45.167840616029998634  ] 
dist 12=[27.214405380084904117  ,45.108061104179966137  ] 
dist 13=[25.507603411597453366  ,44.743257262645736781  ] 
dist 14=[24.084502878940992824  ,43.929453386713744258  ] 
dist 15=[22.591525343228170296  ,35.947701446565245868  ] 
dist 16=[20.605131937163419822  ,35.128241834182070948  ] 
dist 17=[18.637986609510003827  ,33.111993002802147558  ] 
dist 18=[17.074425349450140289  ,32.791500429918240501  ] 
dist 19=[14.776308763320470125  ,29.682541675011433552  ] 
dist 20=[13.109750339077547396  ,29.080026195592018219  ] 
dist 21=[11.579528276693053973  ,28.354713769103326639  ] 
dist 22=[9.8257774588433290803 ,28.138388846445863438  ] 
dist 23=[8.0520492904195917216 ,22.504439316290390569  ] 
dist 24=[6.4416353300963980347 ,21.772358310867098441  ] 
dist 25=[4.6335428805301254074 ,20.278804366555526827  ] 
dist 26=[2.0692449440349292680 ,19.884099771905288198  ] 
dist 27=[-.45162681157750882462,18.416862771885704571  ] 
dist 28=[-2.0862964522827814061 ,18.111723965926497736  ] 
dist 29=[-3.3944169191397273783 ,17.527964006816645006  ] 
dist 30=[-4.6100733461322212065 ,17.377194674906538496  ] 
dist 31=[-5.6824703913565141172 ,6.6796191390736386364 ] 
dist 32=[-6.4180740081376380004 ,5.7506842206804692075 ] 
dist 33=[-7.0530495531278567521 ,3.6453165128265992805 ] 
dist 34=[-7.7235025623489946419 ,3.2902787958610242362 ] 
dist 35=[-8.3229615031600215022 ,.70605536205422552238] 
dist 36=[-8.6741767521284993944 ,.25907920580827304182] 
dist 37=[-8.9141167139334772568 ,-.4828759763101699050 ] 
dist 38=[-9.0685489852219794858 ,-.6470249396385216477 ] 
dist 39=[-9.8731888996655065379 ,-1.5334394672414202534 ] 
dist 40=[-10.563207700712406612  ,-1.3974817862197179810 ] 
dist 41=[-11.081690098526516832  ,-1.2444221639225659394 ] 
dist 42=[-11.504797880908883858  ,-1.1310045232808357706 ] 
dist 43=[-11.836575710257037335  ,-1.0270900685541606624 ] 
dist 44=[-11.990226971117481713  ,-.91139883925616494591] 
dist 45=[-12.058733829738057932  ,-.79871270881434700384] 
dist 46=[-12.055857082534444868  ,-.70652358282893863152] 
dist 47=[-8.4608474300739535267 ,-.1060015197014070022 ] 
dist 48=[-8.1951083670723922657 ,.48454715324754379139] 
dist 49=[-7.5179761984152000393 ,1.0913610238522462602 ] 
dist 50=[-7.4172700872499945785 ,1.8796641582863560841 ] 
dist 51=[-6.3168495837810215892 ,2.6475462661861726819 ] 
dist 52=[-6.1037927351080569837 ,3.1729174018819653580 ] 
dist 53=[-5.8683328366558400148 ,3.6219653348391748800 ] 
dist 54=[-5.8163428849883612309 ,4.0852388013210592803 ] 
dist 55=[-3.7687475600113861296 ,4.5233399697837257505 ] 
dist 56=[-3.5131444447152260014 ,4.8719822610534262902 ] 
dist 57=[-2.9906550252845853750 ,5.2228464270787254720 ] 
dist 58=[-2.8557576671700620924 ,5.6699906616254378526 ] 
dist 59=[-2.3722124145099867490 ,6.0912719949743533853 ] 
dist 60=[-2.2725658874682536799 ,6.3388909202516954685 ] 
dist 61=[-2.1213102979539415470 ,6.5077296982733633151 ] 
dist 62=[-2.0817614811352280036 ,6.6143470311377535748 ] 
dist 63=[1.0281358229364414292 ,6.6839046133891675173 ] 
dist 64=[1.2877982571499784394 ,6.7046916101341018112 ] 
dist 65=[1.8295399714761125978 ,6.6980745052972273645 ] 
dist 66=[1.9470241312977513218 ,6.6846723989368275420 ] 
dist 67=[2.4407040110865337783 ,6.1825477412807148024 ] 
dist 68=[2.5287264830204089061 ,6.0963226559756806201 ] 
dist 69=[2.6442012157004190118 ,5.9193733125638439944 ] 
dist 70=[2.6512199925091563168 ,5.8636158945641975046 ] 
dist 71=[2.6192582442441158189 ,5.6133762509445289379 ] 
dist 72=[2.5346764341788875019 ,5.5562504272333586358 ] 
dist 73=[2.0028339796477360840 ,5.3893339053259307063 ] 
dist 74=[.81902337946345770257,5.3541975943150387507 ] 
dist 75=[-.36468115671888131438,5.2964093647137514910 ] 
dist 76=[-1.1505373382007834483 ,5.3176486661353677924 ] 
dist 77=[-1.7964575249235217086 ,5.3193495871705173975 ] 
dist 78=[-2.4214620057037493085 ,5.3181875734444177793 ] 
dist 79=[-2.9861734681100394744 ,2.7272537616170400632 ] 
dist 80=[-3.3913725607788303457 ,2.6358900647194335152 ] 
dist 81=[-3.7578802471961812375 ,2.5014058842318394576 ] 
dist 82=[-4.1681189064015181734 ,2.4612525519222461637 ] 
dist 83=[-4.5465980251583930781 ,1.6518256677688944242 ] 
dist 84=[-4.7863008108861703193 ,1.5447401358593630630 ] 
dist 85=[-4.9705810502875404123 ,1.3049040951086594877 ] 
dist 86=[-5.1277687725844510189 ,1.2509310947388346020 ] 
dist 87=[-5.2557534278949937161 ,.9540245765750528464 ] 
dist 88=[-5.3234296168317768279 ,.8991317492253911310 ] 
dist 89=[-5.3599588468042946538 ,.7847761060754893349 ] 
dist 90=[-5.3635745800343898658 ,.7538410883023275913 ] 
dist 91=[-3.9497318282530938027 ,-.65862103694994917448] 
dist 92=[-4.0265476165170040160 ,-.5093833322258206095 ] 
dist 93=[-4.1254720222025773977 ,-.1460623944478189335 ] 
dist 94=[-4.3119553208080359914 ,.43095527447042544673] 
dist 95=[-4.4818553725620899359 ,1.0175208075880786853 ] 
dist 96=[-4.5700936600217511934 ,1.4189601061985393382 ] 
dist 97=[-4.6164121767520829409 ,1.7616381308464909051 ] 
dist 98=[-4.6256688960981796482 ,2.1136902040520170122 ] 
dist 99=[-4.6012927305026362404 ,2.4661986859911062172 ] 
dist 100=[-4.5844342483650329548 ,2.7482566958289034492 ] 
dist 101=[-4.5632511479138052946 ,3.0235909986912707446 ] 
dist 102=[-4.5307600468912554349 ,3.3618099017899117326 ] 
dist 103=[-3.6246529447742953157 ,3.6815791176755841698 ] 
dist 104=[-3.5077678683520960274 ,3.8832706270315173154 ] 
dist 105=[-3.1533510661288948346 ,4.0371152738462372748 ] 
dist 106=[-2.8859673014610081264 ,4.1659018667974815213 ] 
dist 107=[-2.6691186895892843174 ,4.2687100252982881684 ] 
dist 108=[-2.6228509358045979448 ,4.3188574176405777449 ] 
dist 109=[-2.5104832512945797571 ,4.3399970252003604579 ] 
dist 110=[-2.4797134729410999397 ,4.3400610451911029568 ] 
dist 111=[-.60359550315811277527,.96110802334909123527] 
dist 112=[-.4354074455932412238 ,.9763747222978006471 ] 
dist 113=[-.08791291792030507611,.98386530754125002854] 
dist 114=[-.14815492666642708086,.98483961536666254215] 
dist 115=[-.21132289725996292662,.97550852049834783803] 
dist 116=[-.26191734826222278337,.97123567918046870652] 
dist 117=[-.31301398562212751625,.97195762086046425361] 
dist 118=[-.37819184600089780738,1.2100558037345209467 ] 
dist 119=[-.44748592141922512476,1.4343979803734116628 ] 
dist 120=[-.51501756001799308818,1.5754323265059406138 ] 
dist 121=[-.59424656728925279797,1.6826785742232397150 ] 
dist 122=[-.71024041749454242693,1.7721254812736355677 ] 
dist 123=[-.82502746278804312615,1.8436617630555691168 ] 
dist 124=[-.8994399540901218516 ,1.8793887578093340408 ] 
dist 125=[-.95858808528799827217,1.8982522375285140813 ] 
dist 126=[-1.0124390264962352943 ,1.9024592743575249219 ] 
dist 127=[-1.0588180855424986613 ,1.8724555735573771397 ] 
dist 128=[-1.0881383055921695484 ,1.8625044928552625071 ] 
dist 129=[-1.1106048574267761620 ,1.8415216216400322139 ] 
dist 130=[-1.1296244167585111616 ,1.8326364593030853057 ] 
dist 131=[-1.1435668488224958036 ,1.7837710613632333941 ] 
dist 132=[-1.1465958152136375813 ,1.7714757439672594640 ] 
dist 133=[-1.1441792075007698955 ,1.7295805371937886862 ] 
dist 134=[-1.1430209068597303890 ,1.7219083206342621710 ] 
dist 135=[-1.1009268324003956079 ,1.5935962335700262826 ] 
dist 136=[-1.0893086763372956256 ,1.5704949729466257744 ] 
dist 137=[-1.0816948440816615945 ,1.5095752774289111851 ] 
dist 138=[-1.0775523120048921303 ,1.4956739929894729805 ] 
dist 139=[-1.0873179282551346631 ,1.3822198710431932522 ] 
dist 140=[-1.0926449494841898296 ,1.3575651833815444944 ] 
dist 141=[-1.3309833105322351367 ,1.3209774202169362891 ] 
dist 142=[-1.6895673433440691707 ,1.3090487471186360532 ] 
dist 143=[-2.0439560771352250958 ,.82013726352017939173] 
dist 144=[-2.2753534773005132813 ,.90532039722117714847] 
dist 145=[-2.4612582403170378036 ,.98378174838944188434] 
dist 146=[-2.6340171380259050561 ,1.0736843602360012728 ] 
dist 147=[-2.7853700429428477727 ,1.1560451032040916145 ] 
dist 148=[-2.8858123033530708962 ,1.2043971143941257514 ] 
dist 149=[-2.9683353548478387487 ,1.2371355318956439617 ] 
dist 150=[-3.0481490738265226048 ,1.2571636710795083810 ] 
dist 151=[-3.1134180575721561948 ,1.2703647741158812433 ] 
dist 152=[-3.1378702904550782036 ,1.2758479222441433105 ] 
dist 153=[-3.1461534982107542015 ,1.2767275230864771808 ] 
dist 154=[-3.1468613322388897065 ,1.2744465164166948883 ] 
dist 155=[-3.0609538864938368890 ,.05074057227562846655] 
dist 156=[-3.0374911785451319982 ,.17280329018741454483] 
dist 157=[-3.0223258322222251281 ,.28108196816253450602] 
dist 158=[-3.0145117823385663171 ,.39905051633278664683] 
dist 159=[-2.6719425357639927216 ,.51440470365111268383] 
dist 160=[-2.6327709389251752740 ,.85848610670178589226] 
dist 161=[-2.5229369941296407930 ,1.1986940727588777528 ] 
dist 162=[-2.5033608606909732102 ,1.5382700409965561042 ] 
dist 163=[-2.2827917259899103320 ,1.8519132817652458808 ] 
dist 164=[-2.2353579036096696042 ,2.0885860301573657485 ] 
dist 165=[-2.1832536459560651941 ,2.3144756645071788560 ] 
dist 166=[-2.1627590962394262146 ,2.5850674226954645951 ] 
dist 167=[-1.6075709515244734076 ,2.8378984773641812878 ] 
dist 168=[-1.5331517659978207637 ,2.9928790665837763969 ] 
dist 169=[-1.3822121830130506532 ,3.1060285004093231959 ] 
dist 170=[-1.3417080204083031051 ,3.1918502561697189113 ] 
dist 171=[-1.1894409190346850431 ,3.2557834199176177544 ] 
dist 172=[-1.1564763314150965128 ,3.2815438892946325273 ] 
dist 173=[-1.0930070290633544062 ,3.2897963801141351374 ] 
dist 174=[-1.1084132324519173623 ,3.2847537171615689607 ] 
dist 175=[-1.2349789809653448286 ,1.9450491611510478464 ] 
dist 176=[-1.3342269352566519457 ,1.9510572424965202656 ] 
dist 177=[-1.4325975119792989210 ,1.9492941117923624923 ] 
dist 178=[-1.5556601905551269314 ,1.9456500492152190873 ] 
dist 179=[-1.6733395987538588280 ,1.8021075033073930906 ] 
dist 180=[-1.7502171039372567492 ,1.7772921963145771118 ] 
dist 181=[-1.8120219280089189404 ,1.7275016963259169928 ] 
dist 182=[-1.8695227165665661120 ,1.7119286084597042648 ] 
dist 183=[-1.9199386708823641606 ,1.7741874139044103179 ] 
dist 184=[-1.9534567697288019490 ,1.9175807120535757761 ] 
dist 185=[-1.9810557149337635849 ,2.0403784403042105242 ] 
dist 186=[-2.0078388343123513433 ,2.1674123781480857612 ] 
dist 187=[-2.0288175040235123824 ,2.2876629958634939743 ] 
dist 188=[-2.0332417263617275695 ,2.3833784391384979435 ] 
dist 189=[-2.0305829611908036909 ,2.4795940880238645269 ] 
dist 190=[-2.0243921431428276415 ,2.6018444707195536595 ] 
dist 191=[-1.9747133956585037922 ,2.7151247461928508126 ] 
dist 192=[-1.9592613990610540987 ,2.7755260095437968058 ] 
dist 193=[-1.9332493277207810272 ,2.8088464764402646131 ] 
dist 194=[-1.9237663507167168228 ,2.8164442797524141509 ] 
dist 195=[-1.6671021467606566532 ,2.8093454183436021190 ] 
dist 196=[-1.6665060976261743524 ,2.8035013352658297320 ] 
dist 197=[-1.8365401243574547516 ,2.7956637120927647267 ] 
dist 198=[-2.0552675216301689776 ,2.7857318195144628686 ] 
dist 199=[-2.2673844231798742366 ,2.4398443839118824372 ] 
dist 200=[-2.4110256951198115418 ,2.3878375725739292399 ] 
dist 201=[-2.5321969538906154408 ,2.2898526271922293282 ] 
dist 202=[-2.6546006126084339567 ,2.2628319664654310850 ] 
dist 203=[-2.7686173422641486530 ,2.1613983166009907603 ] 
dist 204=[-2.8563033150323998899 ,2.1346104314365432471 ] 
dist 205=[-2.9416102011200460305 ,2.0850720524198787146 ] 
dist 206=[-3.0461287489235790013 ,2.0699595445242320634 ] 
dist 207=[-3.1417752607196596015 ,1.3619624039174859727 ] 
dist 208=[-3.1916596902238550174 ,1.4853670503044168919 ] 
dist 209=[-3.2176350498567582026 ,1.5950085127027262515 ] 
dist 210=[-3.2212644579665486778 ,1.7147299868702326785 ] 
dist 211=[-3.2072103280479153480 ,1.8235236940612397300 ] 
dist 212=[-3.1958488718926177331 ,1.8895348102334643930 ] 
dist 213=[-3.1688204049608528257 ,1.9369288219171125792 ] 
dist 214=[-3.1551742360362348473 ,1.9713917318732338559 ] 
dist 215=[-2.8548225462694944795 ,1.9949508000153710630 ] 
dist 216=[-2.8060120217182474797 ,2.0001834992259313748 ] 
dist 217=[-2.6968067789715124140 ,1.9963725918425400340 ] 
dist 218=[-2.6618205976903176706 ,1.9947924687344345183 ] 
dist 219=[-2.5007557283121820597 ,-.10772430753005118248] 
dist 220=[-2.4655760654913490107 ,-.13424651381774299872] 
dist 221=[-2.3766148364771976610 ,-.17955708818557269714] 
dist 222=[-2.3515353146476755865 ,.1651586377191704292 ] 
dist 223=[-2.2433497309547379384 ,.78266328866849614907] 
dist 224=[-2.3024806913216759873 ,1.1898474723336766253 ] 
dist 225=[-2.3405967567821350561 ,1.5214667843223540055 ] 
dist 226=[-2.3600757352453139166 ,1.8372693995010626097 ] 
dist 227=[-2.3691547686773904488 ,2.1192203298925834793 ] 
dist 228=[-2.3672471744478824204 ,2.3156825553200526346 ] 
dist 229=[-2.3566419346289722515 ,2.4874010208470983102 ] 
dist 230=[-2.3479717493730797891 ,2.6705592312557374320 ] 
dist 231=[-2.1727037962810843888 ,2.8368816375034496002 ] 
dist 232=[-2.1422133025501018327 ,2.9413810679267634088 ] 
dist 233=[-2.0737037837513342665 ,3.0207368380311954401 ] 
dist 234=[-2.0510026232629370228 ,3.0866702575674151366 ] 
dist 235=[-1.9436948193671051541 ,3.1390250922150375404 ] 
dist 236=[-1.9196482693128479663 ,3.1641667307391653899 ] 
dist 237=[-1.8577157033324459953 ,3.1742165757675646072 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 1, 1, 2] 
dist 0=[50.964529062310852447  ,50.964529062310852447  ] 
dist 1=[50.884089913676475654  ,50.986161581533091577  ] 
dist 2=[50.601430660277248812  ,50.968782422909713603  ] 
dist 3=[50.046582909814169447  ,50.893703785887137232  ] 
dist 4=[48.976317860475281557  ,50.811391487012839460  ] 
dist 5=[47.812630312982624881  ,50.765172303309285917  ] 
dist 6=[46.735508100655258604  ,50.736736385731213385  ] 
dist 7=[45.443342973872533164  ,50.230291423009623715  ] 
dist 8=[44.019086510230633553  ,46.905461449557730828  ] 
dist 9=[42.036486920967931713  ,46.360770872504448659  ] 
dist 10=[39.839140819333778679  ,45.411751733828533863  ] 
dist 11=[37.557018216493059867  ,45.166091872737663357  ] 
dist 12=[34.768340451762544842  ,44.392912901573988453  ] 
dist 13=[30.547469170593722550  ,44.142025238511825853  ] 
dist 14=[26.296817913091475152  ,43.990563313324538318  ] 
dist 15=[23.389122547578841228  ,43.416159833587202662  ] 
dist 16=[20.899153371972316678  ,33.739220284639678275  ] 
dist 17=[18.317015494833606599  ,32.409582754148339172  ] 
dist 18=[15.862824880743335429  ,32.074516336305838877  ] 
dist 19=[13.883817731355887554  ,31.734211575792583025  ] 
dist 20=[11.866795961747552331  ,31.627409807402610709  ] 
dist 21=[9.2604816916704015396 ,16.209617377034439809  ] 
dist 22=[6.7164524364676208893 ,15.046258916659239391  ] 
dist 23=[4.9480896125535006193 ,14.753639168937119830  ] 
dist 24=[3.4021938301420673526 ,9.9498484708557640083 ] 
dist 25=[1.7466692858473342898 ,9.3458293960963913782 ] 
dist 26=[.1381128766813975754 ,8.0627303531840546125 ] 
dist 27=[-1.2204535529302103153 ,7.8088645071906976311 ] 
dist 28=[-2.6632950569582786583 ,6.5626815263520270221 ] 
dist 29=[-4.6092003910130314661 ,6.3541948864009779092 ] 
dist 30=[-6.4935611271939549488 ,6.0142631324987404098 ] 
dist 31=[-7.6905957907168362836 ,5.8920645143532073593 ] 
dist 32=[-8.6205771256614383271 ,-3.4358971463725755139 ] 
dist 33=[-9.4375795090958531895 ,-4.7714261481000548416 ] 
dist 34=[-10.126138676722290779  ,-4.9702169377588110713 ] 
dist 35=[-10.542863623837962145  ,-5.3083983536234506990 ] 
dist 36=[-10.843891812380759253  ,-5.3636666382947508041 ] 
dist 37=[-11.070344343918863798  ,-7.9840793386243766158 ] 
dist 38=[-11.238682013634703013  ,-8.1480510376634601634 ] 
dist 39=[-11.307441331243347129  ,-8.4422594491338542013 ] 
dist 40=[-11.434753344332459816  ,-8.4913739336600709800 ] 
dist 41=[-11.517916861888210294  ,-8.1147496951354830015 ] 
dist 42=[-11.541905353946525226  ,-7.2451663906568011472 ] 
dist 43=[-11.531224243976679304  ,-6.2813326043566830039 ] 
dist 44=[-11.410493978216571605  ,-5.0635155147935996339 ] 
dist 45=[-11.364135886009534288  ,-3.1797917184926166795 ] 
dist 46=[-11.187638065613118813  ,-1.2785954441266114301 ] 
dist 47=[-11.136317139792406185  ,.00906578150651153359] 
dist 48=[-7.6462140975092722777 ,1.0949324710716074977 ] 
dist 49=[-7.3530783448129625494 ,2.1906070622110480519 ] 
dist 50=[-7.2732372469660280759 ,3.2099659445960223718 ] 
dist 51=[-7.1541966132506800300 ,3.9912042740924896701 ] 
dist 52=[-7.1124264284344315386 ,4.7484582058055024293 ] 
dist 53=[-4.1258582788613527412 ,5.6721055758155683666 ] 
dist 54=[-3.7949511774536912703 ,6.5436155128152132318 ] 
dist 55=[-3.6987721007160167622 ,7.0927279106716784227 ] 
dist 56=[-1.6269031427170087240 ,7.5114507260662512683 ] 
dist 57=[-1.3680328793685464218 ,7.8623875053606158158 ] 
dist 58=[-.80525778518028776899,8.1433526551507465533 ] 
dist 59=[-.68524817581402846806,8.2827127788889614837 ] 
dist 60=[-.0688662148305588304 ,8.3520829870633982209 ] 
dist 61=[.0352637103722249312 ,8.3593657497272271924 ] 
dist 62=[.27012927510023343359,8.2593499777241302012 ] 
dist 63=[.3043615685892070775 ,8.1876255600984333870 ] 
dist 64=[1.8777784137593529066 ,4.8098749464344004555 ] 
dist 65=[2.1427895326693700511 ,4.9865459737394751373 ] 
dist 66=[2.2300962846963555685 ,5.0803943511818247906 ] 
dist 67=[2.3032211113731206623 ,5.1317658005152090599 ] 
dist 68=[2.3104820189930057254 ,5.1423874651713578900 ] 
dist 69=[2.3021533578537679681 ,3.2543535409659201616 ] 
dist 70=[2.2126683798603127803 ,3.3255121935878278373 ] 
dist 71=[2.0935340990731820160 ,3.3669717623063714022 ] 
dist 72=[1.9371813234710879874 ,3.3948109186415893287 ] 
dist 73=[1.7688809176618467207 ,3.4115623332398426958 ] 
dist 74=[1.6020016394800935892 ,3.4236172868711030199 ] 
dist 75=[1.4040740472342272817 ,3.4326402055086698485 ] 
dist 76=[1.1117678915608036968 ,3.4391450345899808848 ] 
dist 77=[.8103710926887720708 ,3.4411081641234272536 ] 
dist 78=[.5761212298536419300 ,3.4401164728378116846 ] 
dist 79=[.3458491373150805904 ,3.4347755934429003822 ] 
dist 80=[.0602961939316498818 ,1.7276274860448596075 ] 
dist 81=[-.2395772489648193880 ,1.5865093546907355486 ] 
dist 82=[-.5270590842632752817 ,1.4399246081405773211 ] 
dist 83=[-.8611192170798847350 ,1.3945645965900221165 ] 
dist 84=[-1.3470233832501002555 ,1.3829603454832570376 ] 
dist 85=[-1.8272340921554094414 ,1.3041854505000596929 ] 
dist 86=[-2.1385677609293412056 ,1.2852629419683344806 ] 
dist 87=[-2.3864792174895765870 ,1.2697953842682739659 ] 
dist 88=[-2.6134238021786320224 ,1.2655888594921953753 ] 
dist 89=[-2.8101406285631481162 ,1.2670391373566026549 ] 
dist 90=[-2.9373462839091278035 ,1.2768609640153838579 ] 
dist 91=[-3.0383156947937821298 ,1.2945970559674310200 ] 
dist 92=[-3.1302738144010465571 ,1.3276375244292452971 ] 
dist 93=[-3.2077327394540562123 ,1.3642723884022017513 ] 
dist 94=[-3.2507987195765542097 ,1.3963608378596707859 ] 
dist 95=[-3.2770695306894838047 ,1.4311922354281325108 ] 
dist 96=[-3.2874387188719490398 ,1.4787908358819322518 ] 
dist 97=[-3.2868547884099915955 ,1.5308896862085105619 ] 
dist 98=[-3.2821705863626719667 ,1.5836897081706698416 ] 
dist 99=[-3.2498166193807547875 ,1.6470858566603779630 ] 
dist 100=[-3.2409409866973175354 ,1.7414811452147859078 ] 
dist 101=[-2.1817073471359857936 ,1.8336014685551762856 ] 
dist 102=[-2.1963309246587519740 ,1.8879175101118418196 ] 
dist 103=[-2.1981307945112368653 ,1.9249111265951067430 ] 
dist 104=[-2.1778123438542806998 ,1.9478882181558188684 ] 
dist 105=[-2.1688793023838417882 ,1.9611219102518890511 ] 
dist 106=[-2.1429406036791799850 ,1.9623043554849199066 ] 
dist 107=[-2.1305839627204499094 ,1.9525706572717552091 ] 
dist 108=[-2.0586910163255876899 ,1.9468091535736722471 ] 
dist 109=[-2.0397754885283588614 ,1.8340499789878042596 ] 
dist 110=[-1.9991015887347394620 ,1.8124001185509142525 ] 
dist 111=[-1.9846833876905176440 ,1.7587226925535645696 ] 
dist 112=[-1.2920420555080947566 ,1.7395256403963741445 ] 
dist 113=[-1.2199062699690827953 ,1.6418669052940522231 ] 
dist 114=[-1.0521182511100275717 ,1.6187875160520648978 ] 
dist 115=[-1.0191738051385601251 ,1.5710472216212155134 ] 
dist 116=[-.79248780860659059819,1.5556658047752095678 ] 
dist 117=[-.75016472463100731455,1.4485229104828737884 ] 
dist 118=[-.67496998605546793656,1.6240643213810842115 ] 
dist 119=[-.65759003182020315884,1.7353440469058537405 ] 
dist 120=[-.3682240621145898609 ,1.8210434574337469102 ] 
dist 121=[-.3291938440170193825 ,1.8944421329811242889 ] 
dist 122=[-.24169907747604943445,1.9544583012261186602 ] 
dist 123=[-.22420118999311880787,1.9867210388045224932 ] 
dist 124=[-.11832725611741902328,2.0048827071341664214 ] 
dist 125=[-.09955572573913993008,2.0085929287484197124 ] 
dist 126=[-.08738499882804115878,.54346010582557403248] 
dist 127=[-.08644078713315484165,.54415176508219569851] 
dist 128=[-.08557767630122159476,.54428157750453494564] 
dist 129=[-.08478013916459796817,.54408190437508154778] 
dist 130=[-.08410613172576257023,.55533043835033459446] 
dist 131=[-.08337402261687445150,.59042610179208987073] 
dist 132=[-.08249261583274791847,.62232369682044184965] 
dist 133=[.22816637313306834285,.65826493477942443618] 
dist 134=[.17900816802536789578,.69070589280964308462] 
dist 135=[.13591250971623249414,.70862630124541198668] 
dist 136=[.08872465410222843275,.71936343978429268736] 
dist 137=[.04155784817013883200,.72312133597120767026] 
dist 138=[.00197152995221098835,.72415992657269142172] 
dist 139=[-.03969760093938251241,.72404015479793541286] 
dist 140=[-.09518424432730160820,.72304714068353617568] 
dist 141=[-.14991247512109365714,.72088429985045560388] 
dist 142=[-.18855570284545994333,.63824890356964542504] 
dist 143=[-.2228795460698677294 ,.62697137646673887316] 
dist 144=[-.26036454386972722603,.59617731502279882442] 
dist 145=[-.29709932287440071895,.59112455966123459024] 
dist 146=[-.3284308572792996552 ,.53239519026688441544] 
dist 147=[-.36187386970433604229,.52006145379055961448] 
dist 148=[-.40704554607967398551,.50710995637319332442] 
dist 149=[-.45042221789712918465,.50288822550290625356] 
dist 150=[-.47669874261810758956,.36169947050123019652] 
dist 151=[-.52523898093484055707,.34308606826526841136] 
dist 152=[-.56902618825689837238,.30584236215572244608] 
dist 153=[-.61513093902411734997,.29602575656597136188] 
dist 154=[-.65928532382757353306,.26019725296096987297] 
dist 155=[-.69528462314034370925,.25223821750596309499] 
dist 156=[-.73226244687460800599,.2386310809371208556 ] 
dist 157=[-.78032363419941076191,.23515742198975302557] 
dist 158=[-.82588450406492315265,.25577180359943283902] 
dist 159=[-.85287871041713424846,.2776562768418293313 ] 
dist 160=[-.87148157775540204178,.30328084606898744966] 
dist 161=[-.88353672252370543298,.32937534121756068794] 
dist 162=[-.89116060405945447289,.35313742411214350972] 
dist 163=[-.89218797772172276952,.37976675779743755929] 
dist 164=[-.89032158918094733001,.41731002854039559975] 
dist 165=[-.88733204468567630075,.4538881985241768981 ] 
dist 166=[-.83776384334472337457,.47666515158813122473] 
dist 167=[-.82831497952567931637,.49371959856358549656] 
dist 168=[-.8065086322652067904 ,.50745171403980686465] 
dist 169=[-.79892359292311646114,.51801721395790487162] 
dist 170=[-.76177410815455639025,.52242974803327668114] 
dist 171=[-.75317156439567652403,.52388549341530880129] 
dist 172=[-.73191262332870399058,.52323059922181519016] 
dist 173=[-.72449431552699347729,.51333731215628622973] 
dist 174=[-.60112951822187790792,.51043592049765609444] 
dist 175=[-.59743746954289147041,.50115713134571356348] 
dist 176=[-.58446269653369089474,.498048153933367105  ] 
dist 177=[-.58202803741211314566,.47367136358686893296] 
dist 178=[-.54700205921531102514,.50513883579106883155] 
dist 179=[-.53882354171106254962,.56357788680186366919] 
dist 180=[-.53131493698835283488,.61692150522949960504] 
dist 181=[-.52817231477511461284,.67737089981601310615] 
dist 182=[-.41494642500532880158,.73300552725734957176] 
dist 183=[-.39954203831649734853,.76712467630351163784] 
dist 184=[-.36947181159677522598,.7920677035749432536 ] 
dist 185=[-.39900584164538057115,.81106342486399286558] 
dist 186=[-.43568632824700003205,.82493657046615662644] 
dist 187=[-.46828360624926178053,.82942602634872148925] 
dist 188=[-.50387706078577461361,.83038720335241646629] 
dist 189=[-.53622587171344172383,.8301722268049002451 ] 
dist 190=[-.55586922760342338846,.43354494506250701148] 
dist 191=[-.56998493654292139384,.41733563650365113813] 
dist 192=[-.58026578921440326106,.41268726420180493938] 
dist 193=[-.5873038406972782092 ,.39412931916720246041] 
dist 194=[-.58884706776955098709,.38953154378465698793] 
dist 195=[-.58773906756616809442,.37934601318829083923] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 2, 1, 2] 
dist 0=[52.461259735189050955  ,52.461259735189050955  ] 
dist 1=[52.137561317504208858  ,52.651506994705449810  ] 
dist 2=[51.555640106028070210  ,52.700596340874029463  ] 
dist 3=[50.672408494270091227  ,52.655499947326825786  ] 
dist 4=[49.145202410849309208  ,52.597737572815825286  ] 
dist 5=[47.476137073536688732  ,52.268234711484432401  ] 
dist 6=[46.026231178173621520  ,52.157041214387291412  ] 
dist 7=[44.455866827580336745  ,51.162329001454114346  ] 
dist 8=[42.305498192982858511  ,49.181956427070106766  ] 
dist 9=[39.940062431196788009  ,47.639071962803514466  ] 
dist 10=[37.510595696234881397  ,47.017503991202581618  ] 
dist 11=[34.562209398552250076  ,45.911390280245260820  ] 
dist 12=[30.124026991555008688  ,45.629982376389726866  ] 
dist 13=[25.669365651662971542  ,44.721104574067442566  ] 
dist 14=[22.655047971998185820  ,44.439955642867156976  ] 
dist 15=[20.110135171133109904  ,43.335463309775187367  ] 
dist 16=[17.530116620249200580  ,41.331591622229716076  ] 
dist 17=[15.115348109154536833  ,33.769761817617515282  ] 
dist 18=[13.230231465516892063  ,33.402218037402473782  ] 
dist 19=[11.365448332153966261  ,33.035706567575728434  ] 
dist 20=[9.0314199226184013141 ,32.918357775975329908  ] 
dist 21=[6.7881369936102503743 ,15.492374796520275633  ] 
dist 22=[5.2855695033998110695 ,14.678730985769190561  ] 
dist 23=[4.0310790223265025531 ,13.535548284853852762  ] 
dist 24=[2.7784265575641840076 ,13.232144591270306429  ] 
dist 25=[1.6137673189116197442 ,7.9405437245497531266 ] 
dist 26=[.5145082608069110886 ,7.2994704320961491614 ] 
dist 27=[-1.2107667580713308909 ,5.9241193611103115616 ] 
dist 28=[-3.2828901900657548537 ,5.6843850929335714699 ] 
dist 29=[-5.2303475677163476163 ,4.3323353683971789091 ] 
dist 30=[-6.4576908810714557327 ,4.1198435297621678385 ] 
dist 31=[-7.3963619178801364455 ,3.6894238545064426001 ] 
dist 32=[-8.1908963892513407107 ,3.4536214405747909855 ] 
dist 33=[-8.8358554465693018584 ,-3.8287532464011665566 ] 
dist 34=[-9.1770064059530700144 ,-3.8139551454739354888 ] 
dist 35=[-9.3684225321338487603 ,-3.6687466231229449857 ] 
dist 36=[-9.4153313468016970359 ,-3.3121401587883275822 ] 
dist 37=[-9.3593254529986730287 ,-2.8923545460018617235 ] 
dist 38=[-9.3544205877373880135 ,-2.4946643517152511000 ] 
dist 39=[-9.2620593414779796424 ,-2.0390207186084481994 ] 
dist 40=[-9.2432621369518912580 ,-1.3873354312958059758 ] 
dist 41=[-8.8147248608813486973 ,-.6608787011793169966 ] 
dist 42=[-8.7084976444369153651 ,.0934938794150412077 ] 
dist 43=[-8.6256873157239394517 ,1.0124450181506227076 ] 
dist 44=[-8.5922838606501059166 ,2.3960685168962751679 ] 
dist 45=[-7.5770499475079806646 ,3.7757207204366240562 ] 
dist 46=[-7.5231818982614656026 ,4.6789339629512761109 ] 
dist 47=[-7.4198595345238002729 ,5.4063898195190257774 ] 
dist 48=[-7.3856736066741898362 ,6.0845949817130667786 ] 
dist 49=[-6.6961634805764955232 ,6.6797560812857254201 ] 
dist 50=[-6.6069182059124332252 ,7.0758005541400956811 ] 
dist 51=[-6.0550713929968795596 ,7.4022889403050896895 ] 
dist 52=[-5.5525905985978077637 ,7.7199097372883557337 ] 
dist 53=[-2.1689030997730905288 ,7.9924334467189812431 ] 
dist 54=[-2.0040617755901213745 ,8.1388718336891838184 ] 
dist 55=[-1.7636216927556909763 ,8.2212647649500854081 ] 
dist 56=[-1.6976247517476524293 ,8.2379274985450018369 ] 
dist 57=[-.5303067912180111516 ,8.2207518186085705341 ] 
dist 58=[-.3857393290908019241 ,8.1967542611020783581 ] 
dist 59=[-.0520875706146207755 ,8.1064684501310005438 ] 
dist 60=[-.0043265205899120296 ,8.0565225725323763728 ] 
dist 61=[.4137698403132160893 ,5.4686083490024100998 ] 
dist 62=[.4837224664841531015 ,5.2083806684066315345 ] 
dist 63=[.5796366044920231513 ,4.9071035201271650732 ] 
dist 64=[.5955809714567366608 ,5.0733499747557123307 ] 
dist 65=[1.0176510940660529145 ,5.2005755850827894264 ] 
dist 66=[1.0656661593566390657 ,5.2619100583006138191 ] 
dist 67=[1.1635481982183753352 ,5.2874547335195208509 ] 
dist 68=[1.1816001320652551760 ,5.2888957526720104619 ] 
dist 69=[1.0154300355432875444 ,3.2062647600164289665 ] 
dist 70=[.5288233950727390681 ,3.1416911110496752969 ] 
dist 71=[.0891461386285279116 ,3.0839846560546747003 ] 
dist 72=[-.4021573461777036235 ,3.0700421647230228450 ] 
dist 73=[-.8899646943852860115 ,2.2662251349127416330 ] 
dist 74=[-1.3157681580606737524 ,2.1619560553282327809 ] 
dist 75=[-1.7785649555297722585 ,1.9579659192056439299 ] 
dist 76=[-2.4142057039561808901 ,1.9054922729117301345 ] 
dist 77=[-3.0355379672728388938 ,1.7232626256833552592 ] 
dist 78=[-3.4412265346932301037 ,1.6802293401884921466 ] 
dist 79=[-3.7676238411155054771 ,1.6310666082996068763 ] 
dist 80=[-4.0723030152012168426 ,1.6162066722622936559 ] 
dist 81=[-4.3406649931348403456 ,1.0392824187970007447 ] 
dist 82=[-4.5220345292854527436 ,1.0053846109314852036 ] 
dist 83=[-4.6749473392174656658 ,.9289339733728620325 ] 
dist 84=[-4.8296861565424049970 ,.9089042158086329804 ] 
dist 85=[-4.9603770181693511921 ,.84495015312138754392] 
dist 86=[-5.0172546383426965460 ,.97800737715911661842] 
dist 87=[-5.0425256555768124631 ,1.0907607761129142407 ] 
dist 88=[-5.0469470906917634989 ,1.2047796022155244020 ] 
dist 89=[-4.9389357099833604441 ,1.3104440803527064546 ] 
dist 90=[-4.9091400923983795603 ,1.3898792111205611282 ] 
dist 91=[-4.8896740766547701685 ,1.4650497120414208505 ] 
dist 92=[-4.8792830321167165920 ,2.0388010233116528021 ] 
dist 93=[-2.8759589275177935042 ,2.7725583660195960520 ] 
dist 94=[-2.8436510335015051580 ,3.2558964583949920726 ] 
dist 95=[-2.7987852780779723918 ,3.6486932009382167924 ] 
dist 96=[-2.7809229652431952012 ,4.0210208039576694881 ] 
dist 97=[-2.7383823570097421321 ,4.3520287090642665366 ] 
dist 98=[-2.7200273449022370650 ,4.5798847684297964629 ] 
dist 99=[-2.7053595229110714313 ,4.7760109337812032571 ] 
dist 100=[-2.6924288711276318423 ,4.9803644871054808631 ] 
dist 101=[-1.2383170488868143913 ,5.1564690952514272896 ] 
dist 102=[-1.2609165992052209771 ,5.2398257031765255070 ] 
dist 103=[-1.2747493928277593755 ,5.2808710637455627371 ] 
dist 104=[-1.2803218613137226543 ,5.2880571471455503063 ] 
dist 105=[-1.2814598141719585512 ,5.1943790859796939296 ] 
dist 106=[-1.2794186529813934415 ,5.1666319461536390673 ] 
dist 107=[-1.2716517289736128255 ,5.1468564831288169800 ] 
dist 108=[-1.2666981135257394925 ,5.1328105949914461841 ] 
dist 109=[-1.2347377700439358284 ,4.9035936977811422660 ] 
dist 110=[-1.2961161116295233190 ,4.8824031399274333164 ] 
dist 111=[-1.8578568367142503088 ,4.7911309207262184949 ] 
dist 112=[-2.4170338415107657258 ,4.7751697379429448914 ] 
dist 113=[-2.9321438792955904288 ,4.4878772698416129107 ] 
dist 114=[-3.3179709018469711346 ,4.4195279351889901038 ] 
dist 115=[-3.6831987939556401486 ,4.3647035296595211831 ] 
dist 116=[-4.1160709940618849578 ,4.3448375405157414148 ] 
dist 117=[-4.5176876119136534802 ,3.4560521031472518751 ] 
dist 118=[-4.7581427453615823715 ,3.6110687067567568758 ] 
dist 119=[-4.9266761361753722501 ,3.7163577005729588133 ] 
dist 120=[-5.0411859354964335744 ,3.7816463865362012418 ] 
dist 121=[-5.1229432411499808397 ,3.8261065671647740333 ] 
dist 122=[-5.1607422886181406789 ,3.8482210887210335506 ] 
dist 123=[-5.1735814855199891022 ,3.8582745211066396085 ] 
dist 124=[-5.1674421265732503662 ,3.8545564895971656854 ] 
dist 125=[-2.4976990009000715564 ,3.4798123548122770074 ] 
dist 126=[-2.6645736368315568883 ,3.4210447394446401194 ] 
dist 127=[-2.8107457998089123358 ,3.3216792644418730525 ] 
dist 128=[-2.9670698302082449582 ,3.2931954442416532599 ] 
dist 129=[-3.1181390067403429120 ,3.2017563315493243887 ] 
dist 130=[-3.2433360422574010185 ,3.1710215009892130626 ] 
dist 131=[-3.3736920607611972403 ,3.1382381760668816265 ] 
dist 132=[-3.5453623933435726095 ,3.1199870062432086387 ] 
dist 133=[-3.7075507577995104229 ,1.1432347296598676528 ] 
dist 134=[-3.8000527296101243834 ,1.1354999951365409910 ] 
dist 135=[-3.8593183726088676340 ,1.1246967524121949489 ] 
dist 136=[-3.8888148269803389820 ,1.1197158505962778999 ] 
dist 137=[-3.9009936205944206874 ,.9783624075552196871 ] 
dist 138=[-3.8974103479550688642 ,.9573113905299248385 ] 
dist 139=[-3.8732849066105497757 ,.9136706689782046927 ] 
dist 140=[-3.8556825236080372350 ,.9009073594713000352 ] 
dist 141=[-3.5820644663167258877 ,.8473197479132048544 ] 
dist 142=[-3.5329792559830604887 ,.8358025742912527618 ] 
dist 143=[-3.4160938253401662399 ,.8053773195256508422 ] 
dist 144=[-3.3759140098280617067 ,.7984428168969781338 ] 
dist 145=[-3.1807885286609588595 ,.5638065517455116043 ] 
dist 146=[-3.1359816117874418684 ,.5532165980734482365 ] 
dist 147=[-3.0371933998832173043 ,.5260416776815756608 ] 
dist 148=[-3.0046054004301765267 ,.5204514039176931901 ] 
dist 149=[-3.0511156036569381286 ,1.1141083248191595985 ] 
dist 150=[-3.1383914822243512434 ,1.6321557565288853480 ] 
dist 151=[-3.1957221054997621660 ,2.0524745931021227286 ] 
dist 152=[-3.2273300300188280760 ,2.4499863884864913378 ] 
dist 153=[-3.2439335700742383109 ,2.8029434391492182994 ] 
dist 154=[-3.2428760313982454091 ,3.0453781917126279497 ] 
dist 155=[-3.2302996307138188065 ,3.2535492698843856598 ] 
dist 156=[-3.2185657379727225346 ,3.4697075161279064535 ] 
dist 157=[-2.9887423126428667819 ,3.6647623056349274771 ] 
dist 158=[-2.9481713322602162299 ,3.7886784896516917040 ] 
dist 159=[-2.8564018246171980843 ,3.8843414488635065914 ] 
dist 160=[-2.8257133310847567936 ,3.9665982885896556296 ] 
dist 161=[-2.6796563882262273964 ,4.0340371235122446967 ] 
dist 162=[-2.6467281289428427904 ,4.0705404105067107894 ] 
dist 163=[-2.5629432516219307026 ,4.0914037949080695162 ] 
dist 164=[-2.5374358634716150972 ,4.0964008775223078100 ] 
dist 165=[-.5070881749845713869 ,.07088503197213657441] 
dist 166=[-.56504999133112393015,.18356709899272755499] 
dist 167=[-.62758416602397117515,.30549248812236414099] 
dist 168=[-.71281838541276928092,.42474265884540293707] 
dist 169=[-.79775227898433272691,.53333336154666332233] 
dist 170=[-.85908615165675035049,.61270057340719474646] 
dist 171=[-.91495169496505404273,.68596866236464295034] 
dist 172=[-.97805122811336168187,.77020957680922569507] 
dist 173=[-1.0410577956441203879 ,.84820612262928892999] 
dist 174=[-1.0965504086067783592 ,.89654305857595427579] 
dist 175=[-1.1572271336817772718 ,.9324772762363078409 ] 
dist 176=[-1.2409280836850922066 ,.9609534987869115873 ] 
dist 177=[-1.3214852297322649288 ,1.0217663922052794261 ] 
dist 178=[-1.3696096944785914978 ,1.1013430812937077535 ] 
dist 179=[-1.4032332447779121123 ,1.1633372002306193358 ] 
dist 180=[-1.4258968270038344286 ,1.2176737903196217778 ] 
dist 181=[-1.4408427759940353753 ,1.2630246461873312127 ] 
dist 182=[-1.4436551748058987421 ,1.2891413194176202123 ] 
dist 183=[-1.4416090192925196538 ,1.3062103389402077466 ] 
dist 184=[-1.4371588571048101295 ,1.3660730284419902301 ] 
dist 185=[-1.3579181978639891605 ,1.4464689592568889266 ] 
dist 186=[-1.3425547206375036491 ,1.4955744964031147080 ] 
dist 187=[-1.3073630315099254501 ,1.5312311735791946570 ] 
dist 188=[-1.2950638661034275840 ,1.5579295849104537473 ] 
dist 189=[-1.2409523238408175376 ,1.5768702083855430709 ] 
dist 190=[-1.2367053406591019602 ,1.5815524084506350402 ] 
dist 191=[-1.2257841336580965009 ,1.5804451725016543684 ] 
dist 192=[-1.2201837876368558300 ,1.5762693758165747985 ] 
dist 193=[-1.1066793373509279363 ,1.5335906760828246579 ] 
dist 194=[-1.0890536501958802081 ,1.5231725906824340153 ] 
dist 195=[-1.0406114290701640254 ,1.4895885646463600070 ] 
dist 196=[-1.0318076960688789914 ,1.4815211866934426803 ] 
dist 197=[-.93738928107489839204,1.3966653190996212488 ] 
dist 198=[-.91720489451295408715,1.3766559837424348886 ] 
dist 199=[-.9705758589057060927 ,1.3528055232427667177 ] 
dist 200=[-1.0634699920106415718 ,1.3422478586596908098 ] 
dist 201=[-1.1469746099982311164 ,1.0788157086069896111 ] 
dist 202=[-1.2061542673770482332 ,1.0420226372059437862 ] 
dist 203=[-1.2589285636511235927 ,.9665893194105281659 ] 
dist 204=[-1.3168595627218671340 ,.9456240919054465889 ] 
dist 205=[-1.3683085115426824098 ,.8628753946627134718 ] 
dist 206=[-1.3952026213973760895 ,.8451177432376973526 ] 
dist 207=[-1.4095257751220752965 ,.8051045973984071238 ] 
dist 208=[-1.4124161077173340659 ,.7925701484341714719 ] 
dist 209=[-1.4053194901482649881 ,.35739112290520982475] 
dist 210=[-1.4008286060083332215 ,.47148235815200216006] 
dist 211=[-1.3953434449162428104 ,.56608147617896023609] 
dist 212=[-1.3902197449886020415 ,.65897628005221413297] 
dist 213=[-1.2164509535655039854 ,.7438023161488153901 ] 
dist 214=[-1.1924153932408046635 ,.80618635845803932973] 
dist 215=[-1.1291050509282885438 ,.86415574614535953098] 
dist 216=[-1.1174560458898515217 ,.93135583122597319908] 
dist 217=[-1.0032467305576954477 ,.99300860220459244388] 
dist 218=[-.9794206007341621682 ,1.0288299457480932720 ] 
dist 219=[-.96356582740524025628,1.0526297571760574232 ] 
dist 220=[-.9680298822834016635 ,1.0662858425173989173 ] 
dist 221=[-.96869134525170927247,1.0746700530156804913 ] 
dist 222=[-.96672640251116857574,1.0774217039270429672 ] 
dist 223=[-.96083234946032950293,1.0765756638096547330 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[41.106837676344280260  ,41.106837676344280260  ] 
dist 1=[40.696133155772189216  ,41.379014713821743247  ] 
dist 2=[39.988059847660792629  ,41.533770528577402147  ] 
dist 3=[39.120969842135631078  ,41.643126096148479251  ] 
dist 4=[38.075144606297368305  ,41.733829356275836119  ] 
dist 5=[36.695520726535773766  ,41.827494734502868209  ] 
dist 6=[34.495249941161443946  ,41.948284572759337786  ] 
dist 7=[32.247318920435123911  ,42.057040580250144146  ] 
dist 8=[30.677247873777530340  ,42.102669210547362920  ] 
dist 9=[29.298962628091952124  ,42.109726582340130504  ] 
dist 10=[27.816737297559333845  ,42.065218963451060738  ] 
dist 11=[26.375514281898456966  ,41.989617634870329265  ] 
dist 12=[25.160731998407874405  ,41.923572904376083254  ] 
dist 13=[23.874643314233415682  ,41.745361332820570228  ] 
dist 14=[22.148132999675757988  ,41.607414011096981454  ] 
dist 15=[20.430818965841543458  ,33.074789064719020812  ] 
dist 16=[19.181211146960187099  ,32.296842223449680379  ] 
dist 17=[18.028979855167775372  ,30.400326534689590807  ] 
dist 18=[16.700333695147388339  ,30.095068490842903234  ] 
dist 19=[15.350744598772803047  ,27.232051347612047711  ] 
dist 20=[14.114398820634196380  ,26.681603148788778515  ] 
dist 21=[12.716137303115187856  ,25.995280327632358367  ] 
dist 22=[10.718711742850865796  ,25.781235927079409710  ] 
dist 23=[8.7409123012430730944 ,20.812141981524627110  ] 
dist 24=[7.4209756382427518161 ,20.166153145621195558  ] 
dist 25=[6.3209363888204759625 ,18.830229509133643078  ] 
dist 26=[5.2223683305772669233 ,18.474149454306584914  ] 
dist 27=[4.1991735168149611344 ,17.126349735587256890  ] 
dist 28=[2.7319280516931440048 ,16.855215680047691981  ] 
dist 29=[.25883205987943427932,16.296314386485392520  ] 
dist 30=[-1.3466319698032149965 ,16.143332937039517501  ] 
dist 31=[-2.6334805606895590014 ,7.4177706162208140991 ] 
dist 32=[-3.8330504045123493807 ,6.6440462127785111427 ] 
dist 33=[-4.8938795355637431967 ,4.9195812078656030374 ] 
dist 34=[-5.6262601676268755914 ,4.6058722206548050056 ] 
dist 35=[-6.2635062078030554936 ,2.5781117045577895948 ] 
dist 36=[-6.9443342853988701614 ,2.4090178486854008773 ] 
dist 37=[-7.5565743131749362502 ,2.5712725905382975960 ] 
dist 38=[-7.9307639772068721510 ,2.8742293522591414305 ] 
dist 39=[-8.9963374306259951816 ,3.1898011869030258800 ] 
dist 40=[-9.6558961190690744934 ,3.4025454037871698183 ] 
dist 41=[-10.147550249994441446  ,3.5784259654552815197 ] 
dist 42=[-10.541932282004230546  ,3.7473854821070747666 ] 
dist 43=[-10.851152702315898538  ,3.8969587340634686588 ] 
dist 44=[-11.002579863980127651  ,3.9956864002203337300 ] 
dist 45=[-11.075800905971950360  ,4.0750764409555143831 ] 
dist 46=[-11.082503496419668594  ,4.1476168883151285079 ] 
dist 47=[-10.159348917662210464  ,4.2022451248874504900 ] 
dist 48=[-10.054155961674490976  ,4.2146290450600434246 ] 
dist 49=[-9.7756956443185464648 ,4.2039284202681177849 ] 
dist 50=[-9.7095048076399821617 ,4.2014713762720361791 ] 
dist 51=[-8.9598501489767827955 ,4.0258516972598257589 ] 
dist 52=[-8.8039098898892986514 ,3.9804184215818476271 ] 
dist 53=[-8.2571217216664011329 ,3.9529474274661965489 ] 
dist 54=[-7.3519243713513506468 ,3.9422259019839430250 ] 
dist 55=[-2.5578721833340107275 ,3.0815749856895748122 ] 
dist 56=[-2.4672621487432169261 ,3.1790515353682262923 ] 
dist 57=[-2.0364685322062567414 ,3.6073740967343280446 ] 
dist 58=[-1.9607825404249620256 ,3.9580048545854501105 ] 
dist 59=[-1.7814936800357026510 ,4.3198824647150726979 ] 
dist 60=[-1.7556218352036581781 ,4.7932906330732342213 ] 
dist 61=[1.5489786679910858034 ,5.2447893418193971585 ] 
dist 62=[1.1485896762116354234 ,5.5192087773573362781 ] 
dist 63=[.74325209097440163224,5.7175500909154464095 ] 
dist 64=[.44080467330931134443,5.8651710625873252433 ] 
dist 65=[.1555380986016231404 ,5.9724944010458534861 ] 
dist 66=[-.18127382489732015463,6.0098509903874667262 ] 
dist 67=[-.52599962870540876004,6.0184346500703573222 ] 
dist 68=[-.84291086833892909347,6.0107869135822409319 ] 
dist 69=[-1.2006899943036054438 ,5.7538341821982314369 ] 
dist 70=[-1.7086554889529662998 ,5.6999472545198336069 ] 
dist 71=[-2.2073377683181850411 ,5.5764313640738298750 ] 
dist 72=[-2.5280645432735880863 ,5.5317641140058555765 ] 
dist 73=[-2.7804756659246349752 ,5.3073581612936422030 ] 
dist 74=[-3.0063653722597396597 ,5.2544424757209909858 ] 
dist 75=[-3.1984842339435926241 ,5.1140101547139359934 ] 
dist 76=[-3.3160477486231082089 ,5.0705816257888846300 ] 
dist 77=[-3.4017916651260975124 ,3.9013030317223472203 ] 
dist 78=[-3.4668615711932224966 ,3.8153886325117610985 ] 
dist 79=[-3.5165671885589971934 ,3.5888494380954927866 ] 
dist 80=[-3.5409618364057897722 ,3.5524111757235761129 ] 
dist 81=[-3.5516219369000236193 ,3.1500975264367376293 ] 
dist 82=[-3.5469288519854547110 ,3.0680995182035919311 ] 
dist 83=[-3.8595934231517785826 ,2.9780759958268375444 ] 
dist 84=[-4.2712416709258775732 ,2.9504859617007733192 ] 
dist 85=[-4.6508344389640665742 ,2.0740970093426172495 ] 
dist 86=[-4.8843676014747723752 ,1.9600070490761105471 ] 
dist 87=[-5.0559485598681353418 ,2.1376792035019987930 ] 
dist 88=[-5.1881737679615364637 ,2.3351726460330395260 ] 
dist 89=[-5.2857467990236986344 ,2.4900398507241349668 ] 
dist 90=[-5.3189732758990222314 ,2.6272914189560119379 ] 
dist 91=[-5.3277595857317257180 ,2.7427561173980147001 ] 
dist 92=[-5.3277443029225784565 ,2.8106572820121064634 ] 
dist 93=[-1.0452990424482395442 ,2.8567298021633563465 ] 
dist 94=[-1.3898148038557185138 ,2.8850593745689010664 ] 
dist 95=[-1.6700713942849100311 ,2.9007395054178681052 ] 
dist 96=[-1.9365860700951751150 ,2.8999780791268728690 ] 
dist 97=[-2.1744190566719782198 ,2.8843894848422975099 ] 
dist 98=[-2.3401490566205249786 ,2.8710472398827445034 ] 
dist 99=[-2.4850926029618803260 ,2.7785757496083758990 ] 
dist 100=[-2.6399267750192020754 ,2.7516499053898360072 ] 
dist 101=[-2.7791856503333267686 ,2.7044768509225278322 ] 
dist 102=[-2.8619367030162187329 ,2.7119952343220139835 ] 
dist 103=[-2.9192910225847119639 ,2.8688908370594778553 ] 
dist 104=[-2.9571382356034820260 ,2.9572455730230060568 ] 
dist 105=[-2.9802874060710177345 ,3.0126051846377179375 ] 
dist 106=[-2.9840032734426333044 ,3.0377404062444738144 ] 
dist 107=[-2.9706891717106503819 ,3.0492661934796633810 ] 
dist 108=[-2.9661815941164163662 ,3.0502656634892724083 ] 
dist 109=[-2.3388750202683676666 ,3.0438195364306666812 ] 
dist 110=[-2.5502249513714624938 ,3.0358143526404895698 ] 
dist 111=[-2.7436739942425004686 ,2.7204446723339393702 ] 
dist 112=[-2.8610203665562185543 ,2.6711668028078635986 ] 
dist 113=[-2.9451317168312916227 ,2.5752585012617021422 ] 
dist 114=[-3.0059248263874682870 ,2.5474990744512645329 ] 
dist 115=[-3.0480643879584921665 ,2.4355069499127711336 ] 
dist 116=[-3.0577099356874961590 ,2.4077805189318139052 ] 
dist 117=[-3.0557870692624704172 ,2.3449298814235136765 ] 
dist 118=[-3.0517590353211505037 ,2.3232905320475138972 ] 
dist 119=[-.86320636257254497426,1.2289982232319446616 ] 
dist 120=[-.8424579824606679454 ,1.4644491247112300059 ] 
dist 121=[-.70812597444686838715,1.7003057285124643759 ] 
dist 122=[-.99375826790994999696,1.9093852293546898761 ] 
dist 123=[-1.2556685848712275449 ,2.1392189529374481444 ] 
dist 124=[-1.4501645273714033284 ,2.4579450147265629748 ] 
dist 125=[-1.6327847853579463802 ,2.7687410961624174242 ] 
dist 126=[-1.8472851631308075306 ,2.9669122300944493286 ] 
dist 127=[-2.0462975127953742444 ,3.1208254487402811396 ] 
dist 128=[-2.1670808163976532075 ,3.2549072487262780139 ] 
dist 129=[-2.2538506566164981092 ,3.3662144196543311545 ] 
dist 130=[-2.3170575652556651715 ,3.4291927469808815429 ] 
dist 131=[-2.3643660043873418422 ,3.4689220499656035172 ] 
dist 132=[-2.3876598662230252861 ,3.4874007419819657693 ] 
dist 133=[-2.3978604095763546232 ,3.4927875113359057134 ] 
dist 134=[-2.3969280088499274051 ,3.4883643714624428183 ] 
dist 135=[-2.1249825316800303166 ,3.4624319727104303240 ] 
dist 136=[-2.0900660863510964229 ,3.4467845211064865414 ] 
dist 137=[-2.0084040577694331151 ,3.3349419476627514645 ] 
dist 138=[-1.9814739578268313796 ,3.3037909544958374201 ] 
dist 139=[-1.8546699252712538832 ,3.2531576832654258086 ] 
dist 140=[-1.8263977324887553041 ,3.2352835797956762185 ] 
dist 141=[-1.7635477174583119952 ,2.6248343548077392166 ] 
dist 142=[-1.7431365224705601805 ,2.5666769597499212888 ] 
dist 143=[-1.4941574178554603951 ,2.4133042230655641564 ] 
dist 144=[-1.6197692720647259735 ,2.3877876669012809476 ] 
dist 145=[-1.9639416218491861288 ,2.1138055129032434829 ] 
dist 146=[-2.2220282181718641743 ,2.0575657611910472214 ] 
dist 147=[-2.4668509520074612564 ,1.9940650162116001795 ] 
dist 148=[-2.7580648438068037500 ,1.9725744189666015566 ] 
dist 149=[-3.0292509641338177823 ,1.8134179998297003587 ] 
dist 150=[-3.1941083775464026655 ,2.1735768926980172759 ] 
dist 151=[-3.3128741069799339684 ,2.5276883660498622030 ] 
dist 152=[-3.4000285066199300496 ,2.7567382909275756498 ] 
dist 153=[-3.4649028022681125316 ,2.9383321254535467109 ] 
dist 154=[-3.4947096265981313723 ,3.1029709439317465012 ] 
dist 155=[-3.5046024341660245270 ,3.2443616513629248405 ] 
dist 156=[-3.5036237838627946472 ,3.3331357158269651169 ] 
dist 157=[-.39921373517214593147,3.4004836279566100778 ] 
dist 158=[-.61442932782466305938,3.4563296504905859101 ] 
dist 159=[-.80130076791700680461,3.4973682278774646058 ] 
dist 160=[-.99870524817638249595,3.5057103552428245039 ] 
dist 161=[-1.1880980795231955037 ,3.5018830135416108312 ] 
dist 162=[-1.3429808003219824042 ,3.4952466951166621033 ] 
dist 163=[-1.5024616897921627695 ,3.3891422524520806493 ] 
dist 164=[-1.7102124103102412694 ,3.3580970675685859784 ] 
dist 165=[-1.9129428622901950427 ,3.3279814274210589836 ] 
dist 166=[-2.0523789106543442880 ,3.3089707016694390608 ] 
dist 167=[-2.1723368879841302443 ,2.8541191543562750027 ] 
dist 168=[-2.2972972324748407682 ,2.8070350715057239452 ] 
dist 169=[-2.4161064059753014480 ,2.6772412563696624105 ] 
dist 170=[-2.5115040294406012073 ,2.6549540757825587968 ] 
dist 171=[-2.6081475415099251598 ,2.4025577423848954219 ] 
dist 172=[-2.7319294856715948463 ,2.3490269535740084951 ] 
dist 173=[-2.8470080220382707875 ,2.2908845512214709041 ] 
dist 174=[-2.9089016709145461561 ,2.2697076335174152421 ] 
dist 175=[-3.1496353509223944344 ,1.6544964383248712333 ] 
dist 176=[-3.3183327487552213298 ,1.5727200388634250667 ] 
dist 177=[-3.4401124999296985454 ,1.7797997299411587009 ] 
dist 178=[-3.5299157608558476030 ,1.9578632130006809984 ] 
dist 179=[-3.5964269953989603082 ,2.1362670591149667575 ] 
dist 180=[-3.6252117505608773100 ,2.3621182272742484966 ] 
dist 181=[-3.6341316218624031753 ,2.5794425128481978729 ] 
dist 182=[-3.6311251462597302746 ,2.7238012575880964837 ] 
dist 183=[-2.4381535465647772268 ,2.8425506795886804284 ] 
dist 184=[-2.4093220105717260652 ,2.9576250851829676240 ] 
dist 185=[-2.2926800392628740310 ,3.0617168022115711347 ] 
dist 186=[-2.2645297179794385653 ,3.1366159019832246066 ] 
dist 187=[-2.1993829053918355533 ,3.2045778303005577480 ] 
dist 188=[-2.1769502815063760875 ,3.2809718076150911218 ] 
dist 189=[-1.5465630730097937667 ,3.3476397568412716990 ] 
dist 190=[-1.7832685230861000424 ,3.3767687978022650458 ] 
dist 191=[-2.0143901219896506261 ,3.3869353134744678315 ] 
dist 192=[-2.1735852402847666403 ,3.3842373626871956151 ] 
dist 193=[-2.3107923416257952739 ,3.3341356443018803581 ] 
dist 194=[-2.4541238718696362250 ,3.3150073119275273660 ] 
dist 195=[-2.5906581849505958291 ,3.2791822784143300904 ] 
dist 196=[-2.7007268851886023845 ,3.2648759124575523079 ] 
dist 197=[-2.8126439145773563676 ,2.8893043935072811079 ] 
dist 198=[-2.9565590802322599036 ,2.8312244677350172802 ] 
dist 199=[-3.0906815476642178740 ,2.7047587879147741293 ] 
dist 200=[-3.1634998297150146630 ,2.6658290885406407214 ] 
dist 201=[-3.2054513857987741806 ,2.4925054219631940967 ] 
dist 202=[-3.2163329043671725861 ,2.4559248487954739499 ] 
dist 203=[-3.2153211819792578620 ,2.3568866370827919414 ] 
dist 204=[-3.2097865220778898172 ,2.3364109756946768349 ] 
dist 205=[-3.1998719711292494739 ,2.2187955429817513571 ] 
dist 206=[-3.1895583121576116614 ,2.4631484914854939088 ] 
dist 207=[-2.8229093765503218649 ,2.6991336567085653426 ] 
dist 208=[-2.7667437954698836987 ,2.8573058987115989126 ] 
dist 209=[-2.6587238174117643851 ,2.9889737644382804422 ] 
dist 210=[-2.6280962802185120063 ,3.1191369389846398954 ] 
dist 211=[-2.5676782573488543653 ,3.2385745383281740129 ] 
dist 212=[-2.7637409496074617295 ,3.3274192611611651469 ] 
dist 213=[-2.9421252344597433145 ,3.4109868403089841849 ] 
dist 214=[-3.0525191211086548115 ,3.5093549088361328953 ] 
dist 215=[-3.1343933160475629028 ,3.5974410013845816064 ] 
dist 216=[-3.1989079926847326699 ,3.6399564553515342597 ] 
dist 217=[-3.2474231498579590693 ,3.6582376233377527642 ] 
dist 218=[-3.2654166526003557479 ,3.6592060049473381647 ] 
dist 219=[-3.2683353046747976134 ,3.6217766792607191296 ] 
dist 220=[-3.2627637106528739545 ,3.6045024690669931808 ] 
dist 221=[.01559300235142892631,3.5691655809492680895 ] 
dist 222=[.02381794339342952427,3.5536136550207024610 ] 
dist 223=[.02407519979254719511,3.1761771062739672165 ] 
dist 224=[.01352617141191874480,3.1166041597134616242 ] 
dist 225=[-.00318381427183355152,2.9853051008175889678 ] 
dist 226=[-.02752490103066621571,2.9441737405740479227 ] 
dist 227=[-.06215408033494020487,2.7582868373463355346 ] 
dist 228=[-.11994053361421210299,2.7184370864085184894 ] 
dist 229=[-.18229015374341107544,2.6140084755587278151 ] 
dist 230=[-.23513831454838346601,2.5888169773600435789 ] 
dist 231=[-.89012539790488837567,2.4720314672583973091 ] 
dist 232=[-1.3464020418319749288 ,2.5489614023737199657 ] 
dist 233=[-1.7185223116268594386 ,2.6011632571891906952 ] 
dist 234=[-2.0737722402917831799 ,2.6333667079662885356 ] 
dist 235=[-2.3915422064464233187 ,2.6525905673887160127 ] 
dist 236=[-2.6140185191220472728 ,2.6542210087565987687 ] 
dist 237=[-2.8095887525609831444 ,2.6459405639480347476 ] 
dist 238=[-3.0199324117243247322 ,2.6361312524905763574 ] 
dist 239=[-3.2111055631325628435 ,2.4755602594236567528 ] 
dist 240=[-3.3301348715699105258 ,2.4455932876178444096 ] 
dist 241=[-3.4192632276570915652 ,2.3759910393378722444 ] 
dist 242=[-3.4910526933277895602 ,2.3519269205023172009 ] 
dist 243=[-3.5463071725923838654 ,2.2345766463067627387 ] 
dist 244=[-3.5694172764502864317 ,2.2075173538856654821 ] 
dist 245=[-3.5744828423173093899 ,2.1423073514143649834 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 0, 0, 2] 
dist 0=[51.055519923894639942  ,51.055519923894639942  ] 
dist 1=[50.370619565013357563  ,51.451287622163707226  ] 
dist 2=[49.111388950345682158  ,51.555640106028070195  ] 
dist 3=[47.709607437055719532  ,51.560702431607682035  ] 
dist 4=[46.455253613046871782  ,51.560142091492739672  ] 
dist 5=[45.066125747114637870  ,51.555001203413446990  ] 
dist 6=[43.125822705946448782  ,51.542558110135111787  ] 
dist 7=[40.973878041404371189  ,51.529891012806655982  ] 
dist 8=[38.739318943525318189  ,51.023121640597950736  ] 
dist 9=[36.010278264751669682  ,47.724040431484701390  ] 
dist 10=[31.883203165795754139  ,47.181884370666051698  ] 
dist 11=[27.733799328135336526  ,46.250799975931060296  ] 
dist 12=[24.915453560797203585  ,46.004660822717553659  ] 
dist 13=[22.524652700452290584  ,45.261358188425684305  ] 
dist 14=[20.082663252964770048  ,44.460559618621203201  ] 
dist 15=[17.785582176242173413  ,40.782588608815023062  ] 
dist 16=[15.973314346392187424  ,38.272788331084820165  ] 
dist 17=[14.162732099831251416  ,32.548009155237299026  ] 
dist 18=[11.871895387953534586  ,32.117920683148273951  ] 
dist 19=[9.6580168619796403717 ,30.648409650492686906  ] 
dist 20=[8.1545715804324707985 ,30.283905630244343480  ] 
dist 21=[6.8768414145962180037 ,29.889578324173919852  ] 
dist 22=[5.5642591203389462029 ,29.754021415987519879  ] 
dist 23=[4.3203992259742688914 ,15.629551342984387984  ] 
dist 24=[3.3166965828828088010 ,15.334377807097305063  ] 
dist 25=[2.2891422311642744294 ,10.463015399780185991  ] 
dist 26=[.9488864138022851072 ,9.8600540689970282120 ] 
dist 27=[-.34427875920395187187,8.5916423693932449583 ] 
dist 28=[-1.2922507870685742148 ,8.3428223415085223042 ] 
dist 29=[-2.9262905937284398800 ,7.1822989703979296980 ] 
dist 30=[-4.8829138757746801527 ,6.7751866816321023137 ] 
dist 31=[-6.7188237231960228902 ,6.0553542632729810807 ] 
dist 32=[-7.8707035445480250524 ,5.6605837909950988879 ] 
dist 33=[-8.7457814005943271066 ,-2.4824269987047226027 ] 
dist 34=[-9.4761265804353726298 ,-2.3017951633537719757 ] 
dist 35=[-10.065750361274824088  ,-2.0571420747654291530 ] 
dist 36=[-10.378668678247261582  ,-1.7866961078862080415 ] 
dist 37=[-10.550188795838734833  ,-1.4480523670952883950 ] 
dist 38=[-10.589129501103121035  ,-.9305818415593846807 ] 
dist 39=[-9.4791066399924989115 ,-.3397710823683896009 ] 
dist 40=[-9.4114928922361233034 ,.2918742919452598680 ] 
dist 41=[-9.1774484269703389319 ,1.0735479572483147982 ] 
dist 42=[-9.1385398445541649795 ,2.2633769725278022517 ] 
dist 43=[-8.5418662763822196124 ,3.4528844551586615617 ] 
dist 44=[-8.4081026773261766293 ,4.2333955902252754298 ] 
dist 45=[-8.2870552127214345356 ,4.8635306421325634054 ] 
dist 46=[-8.2480929662118177124 ,5.4529935304232867431 ] 
dist 47=[-7.7440668644517321490 ,5.9712058098202177153 ] 
dist 48=[-7.7058605201509183633 ,6.3170389100314976666 ] 
dist 49=[-7.0132511151215534732 ,6.6029934621780132862 ] 
dist 50=[-6.6628395016216228125 ,6.8823071798843402934 ] 
dist 51=[-5.2631206241599562812 ,7.1218738537285519313 ] 
dist 52=[-5.1642994877280740058 ,7.2491535173339939068 ] 
dist 53=[-5.0230633397496456404 ,7.3186351252706536141 ] 
dist 54=[-4.9781379984234845208 ,7.3273242847213468690 ] 
dist 55=[-2.1122651648819319729 ,7.3065988759099261776 ] 
dist 56=[-2.0536513159829754784 ,7.2820628823154502147 ] 
dist 57=[-.6631606460776579436 ,7.2023270722943960716 ] 
dist 58=[-.4935447204934335735 ,7.1595851186028401687 ] 
dist 59=[-.1244366901475686302 ,4.8903609838660321067 ] 
dist 60=[-.0519754815115078686 ,4.6593822426057403671 ] 
dist 61=[.3456077530182040283 ,4.1009677656973239888 ] 
dist 62=[.4104011143806955432 ,4.0835270178884676662 ] 
dist 63=[.5490388652105650097 ,4.5422614488365589289 ] 
dist 64=[.5696303038635885720 ,4.8232107111859815025 ] 
dist 65=[1.5185529947617835573 ,5.0284790220350133793 ] 
dist 66=[1.4574916929625950032 ,5.1849508765254671900 ] 
dist 67=[.8269802273454391296 ,5.3036621195877620270 ] 
dist 68=[.3721160138952005689 ,5.3581223693587639634 ] 
dist 69=[-.0416349026975332711 ,5.3794768870476815635 ] 
dist 70=[-.5081058833553269884 ,5.3777159917975815188 ] 
dist 71=[-.97360790130626033527,3.6756031178109740286 ] 
dist 72=[-1.3835668538900506701 ,3.6561743459786170952 ] 
dist 73=[-1.8321504827434057711 ,2.9916062476443946004 ] 
dist 74=[-2.4519843425761515438 ,2.9001622065995768481 ] 
dist 75=[-3.0578873619921766361 ,2.7201609795342985207 ] 
dist 76=[-3.4508690305498030490 ,2.6719395185996236203 ] 
dist 77=[-3.7640395200509707353 ,2.4941248570277869037 ] 
dist 78=[-4.0512239560853761416 ,2.4521810414145284448 ] 
dist 79=[-4.3005902909928727113 ,2.3782715237816008540 ] 
dist 80=[-4.4627442078180874062 ,2.3587615216352646761 ] 
dist 81=[-4.5925325466173588287 ,1.1960636957394700063 ] 
dist 82=[-4.7126698772670905706 ,1.1223361867886067277 ] 
dist 83=[-4.8101975433674358902 ,.9513047781642981899 ] 
dist 84=[-4.8497017722536853933 ,.9203135145326472351 ] 
dist 85=[-4.8630154744713576128 ,.6932765479273562596 ] 
dist 86=[-4.8558972217519288003 ,.6517821662097544401 ] 
dist 87=[-4.7618411560511038899 ,.8421997118155751097 ] 
dist 88=[-4.7283978860095001548 ,1.1915253519955986894 ] 
dist 89=[-4.6893905677547802769 ,1.6153772778568939396 ] 
dist 90=[-4.6672375696491875769 ,2.2520857268062021856 ] 
dist 91=[-3.1296642720048728335 ,2.8866636316962206202 ] 
dist 92=[-3.1638566877604030205 ,3.3020215561541058444 ] 
dist 93=[-3.1829392480667566410 ,3.6366021212777032336 ] 
dist 94=[-3.1865673707352379339 ,3.9487293070219197522 ] 
dist 95=[-2.9163710537588336604 ,4.2227847017705088588 ] 
dist 96=[-2.8733292921064394133 ,4.4053895556823705620 ] 
dist 97=[-2.8072753241086693141 ,4.5561111790735664650 ] 
dist 98=[-2.7854733067416907060 ,4.7028969074863721999 ] 
dist 99=[-2.7291348865449923471 ,4.8249721452290010248 ] 
dist 100=[-2.7085917193639877987 ,4.8770506951002096346 ] 
dist 101=[-2.6951700816011453921 ,4.8977516741171542278 ] 
dist 102=[-2.6879292160609725937 ,4.8945631962606533938 ] 
dist 103=[-1.4284491161754209280 ,4.7905539506453581436 ] 
dist 104=[-1.4502964282588270203 ,4.7531587763804604307 ] 
dist 105=[-1.4664076391451104720 ,4.7212648396895962377 ] 
dist 106=[-1.4721455734622110139 ,4.6958761800878363816 ] 
dist 107=[-1.4719770931784062767 ,4.5398727994132551160 ] 
dist 108=[-1.4698833224970058192 ,4.5352623294857088845 ] 
dist 109=[-1.8196765604597222742 ,4.4889091879212967015 ] 
dist 110=[-2.3429422919599409681 ,4.4768665848295810720 ] 
dist 111=[-2.8226144507315194712 ,4.2690787818529188068 ] 
dist 112=[-3.1779412524194567435 ,4.2159550803230329823 ] 
dist 113=[-3.5104308004196989444 ,4.1695512525947865170 ] 
dist 114=[-3.8989277719664777275 ,4.1444043655958231874 ] 
dist 115=[-4.2569851971070272797 ,3.3236646797837302482 ] 
dist 116=[-4.4679642356059034988 ,3.2101609287750226903 ] 
dist 117=[-4.6116982764369308125 ,3.0012984056848684546 ] 
dist 118=[-4.7013349637931269806 ,3.2685479721682442036 ] 
dist 119=[-4.7628969901258425210 ,3.5228456432073345815 ] 
dist 120=[-4.7945582515516540171 ,3.6709827126232598741 ] 
dist 121=[-4.8103680535093741873 ,3.7700242702927984657 ] 
dist 122=[-4.8086336097326172712 ,3.8282828067814153290 ] 
dist 123=[-1.6500425211664139110 ,3.8664999439735258044 ] 
dist 124=[-1.8325652645585541698 ,3.8855096700428697760 ] 
dist 125=[-2.0238157546273962442 ,3.8941586498717377710 ] 
dist 126=[-2.2772130777121332658 ,3.8909867521967164996 ] 
dist 127=[-2.5263038328905566863 ,3.4883467700549482861 ] 
dist 128=[-2.7003644610518290038 ,3.4263550277357503012 ] 
dist 129=[-2.8529593847177607702 ,3.3209610104709687034 ] 
dist 130=[-3.0163586517661816343 ,3.2912803421761486019 ] 
dist 131=[-3.1743956877858334774 ,3.1964460130666440869 ] 
dist 132=[-3.3055868656995554586 ,3.1647204220432528611 ] 
dist 133=[-3.4423825722427776750 ,3.1336702253752237853 ] 
dist 134=[-3.6228000580922369289 ,3.1149060073743509634 ] 
dist 135=[-3.7934549891411176492 ,1.3819167489172421271 ] 
dist 136=[-3.8912762899261534261 ,1.3773450419816407975 ] 
dist 137=[-3.9545838806862782413 ,1.2670437086832183659 ] 
dist 138=[-3.9874461600493340824 ,1.2485921869570911208 ] 
dist 139=[-4.0022326732383298409 ,1.2083604297611225788 ] 
dist 140=[-3.9994478736851269089 ,1.1954495540159190495 ] 
dist 141=[-3.9759976436403331802 ,1.1359270824248676725 ] 
dist 142=[-3.9581499278211558737 ,1.1229004444521853903 ] 
dist 143=[-3.6842298834811198499 ,1.0866649794477786463 ] 
dist 144=[-3.6347034313302493457 ,1.0787305817888625007 ] 
dist 145=[-3.5166106821862151454 ,.7977848572247935266 ] 
dist 146=[-3.4758713673964988143 ,.7804961743291679361 ] 
dist 147=[-3.2775277855897543204 ,.7348176185508975941 ] 
dist 148=[-3.2318782732021018087 ,.7273629084927041425 ] 
dist 149=[-3.1311800326572682578 ,.6454154583087923900 ] 
dist 150=[-3.0978946825611250969 ,.6285698521994428902 ] 
dist 151=[-3.1216870520957681632 ,1.1200108471590827494 ] 
dist 152=[-3.2050754071649370307 ,1.6508305380027939660 ] 
dist 153=[-3.2586662422940279192 ,2.0818142167512506592 ] 
dist 154=[-3.2857504071479788854 ,2.4899238895953615515 ] 
dist 155=[-3.2982421291997557449 ,2.8526400160939374979 ] 
dist 156=[-3.2953632294339059577 ,3.1023896004644456986 ] 
dist 157=[-3.2807985031652265848 ,3.3174924717180079869 ] 
dist 158=[-3.2688947446803596383 ,3.5418788679858253988 ] 
dist 159=[-3.0186988046721297347 ,3.7445705839397217520 ] 
dist 160=[-2.9755201613503590304 ,3.8730584411927779816 ] 
dist 161=[-2.8789174094588387081 ,3.9719262762748187268 ] 
dist 162=[-2.8470852854671683867 ,4.0563657591789670448 ] 
dist 163=[-2.6972683013569672635 ,4.1251706022973869909 ] 
dist 164=[-2.6638449955745211832 ,4.1616204192458252634 ] 
dist 165=[-2.5767842052120628811 ,4.1813881217328447639 ] 
dist 166=[-2.5525074140638143702 ,4.1835936697970988032 ] 
dist 167=[-.71128636513611868343,.06479272385860110435] 
dist 168=[-.80592704031522753732,.21975023845580320917] 
dist 169=[-.89963623744061736894,.35032730985912999591] 
dist 170=[-.96633233518455859764,.47699202558986839035] 
dist 171=[-1.0260943007130419660 ,.5916464252886592791 ] 
dist 172=[-1.0921166745029268252 ,.67427177050071801984] 
dist 173=[-1.1572016492202658026 ,.74937103767336466625] 
dist 174=[-1.2132191869580361377 ,.83397823649932175661] 
dist 175=[-1.2733844751809058318 ,.91211525105017502734] 
dist 176=[-1.3550261168913194881 ,.96138172630362345275] 
dist 177=[-1.4330127082546025815 ,.99900309818685352174] 
dist 178=[-1.4785844940971372561 ,1.0306446536800894770 ] 
dist 179=[-1.5091766780738614246 ,1.0560739933433810693 ] 
dist 180=[-1.5273583184766359045 ,1.0688920155543490451 ] 
dist 181=[-1.5380927048223886357 ,1.1442318122323906424 ] 
dist 182=[-1.5389531714031072044 ,1.2289004606522191344 ] 
dist 183=[-1.5350829816928208821 ,1.3105198970444799436 ] 
dist 184=[-1.5303301884685026299 ,1.4094778250741414514 ] 
dist 185=[-1.4218903751343456759 ,1.5025937225479663889 ] 
dist 186=[-1.4026804459554597010 ,1.5608877007779265189 ] 
dist 187=[-1.3608636073716642373 ,1.6049178083423480759 ] 
dist 188=[-1.3470897883350864694 ,1.6410821639517136728 ] 
dist 189=[-1.2822731842372174825 ,1.6694821262333056411 ] 
dist 190=[-1.2678067823883012495 ,1.6825114042696238892 ] 
dist 191=[-1.2266304562951391906 ,1.6867946775229649045 ] 
dist 192=[-1.2176063494357129093 ,1.6857664634388447275 ] 
dist 193=[-.90189840034755085908,1.6686074433848369119 ] 
dist 194=[-.88123867705452401303,1.6619759623994589184 ] 
dist 195=[-.82632628186237644516,1.6370621553739134982 ] 
dist 196=[-.81760344332596791652,1.6293606443279881819 ] 
dist 197=[-.71858995512802084496,1.5538966593001179655 ] 
dist 198=[-.7265296481455731588 ,1.5350449747731448892 ] 
dist 199=[-.9117397336968636546 ,1.5110116366744277659 ] 
dist 200=[-1.0337059212205718894 ,1.5006981038358847768 ] 
dist 201=[-1.1328597627523213058 ,1.2372957003526009432 ] 
dist 202=[-1.2269888348164897072 ,1.1998465004339267321 ] 
dist 203=[-1.3108314611150914683 ,1.1222746637684229368 ] 
dist 204=[-1.3689155993419326926 ,1.1002861204963432575 ] 
dist 205=[-1.4193325831007683049 ,1.0111106109249450630 ] 
dist 206=[-1.4725636547146637325 ,.9922338257583150335 ] 
dist 207=[-1.5186600016802925233 ,.9462138045819122122 ] 
dist 208=[-1.5405908766514622943 ,.9340152151003891601 ] 
dist 209=[-1.5513362770056125901 ,.30992048227634455517] 
dist 210=[-1.5527718667220215031 ,.39594294333859701804] 
dist 211=[-1.5296555407883171101 ,.46777433618114243197] 
dist 212=[-1.5221558334888011527 ,.53914102975891811703] 
dist 213=[-1.5162838892058252821 ,.60484996376873144424] 
dist 214=[-1.5110862969407189491 ,.65409257822042830982] 
dist 215=[-1.2833227214175551934 ,.70076396655485556101] 
dist 216=[-1.2532179944360410989 ,.75620711294019327546] 
dist 217=[-1.1762652385565178589 ,.80777986465823605811] 
dist 218=[-1.1617681577178102105 ,.83899855303871596122] 
dist 219=[-1.0307814254975708082 ,.86132146204267644924] 
dist 220=[-1.0039303892804127962 ,.87737754181403045723] 
dist 221=[-.9679409824613041263 ,.8883799743782166303 ] 
dist 222=[-.9313965503518276636 ,.89082944798155811428] 
dist 223=[-.8721449671019868168 ,.88969118348292105355] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 2, 2, 0, 1, 2] 
dist 0=[43.083322386778383647  ,43.083322386778383647  ] 
dist 1=[42.437830784083451122  ,43.360734382719082370  ] 
dist 2=[41.398584628628051662  ,43.823022872352710524  ] 
dist 3=[39.720143715372086555  ,44.293287613721474586  ] 
dist 4=[37.990406440469321045  ,44.496789485886802730  ] 
dist 5=[36.746166166418130518  ,44.582146365083755926  ] 
dist 6=[35.615779612087242446  ,44.580478370872387873  ] 
dist 7=[34.340584627594637054  ,44.139220049791668642  ] 
dist 8=[33.064816056337035784  ,43.780538198836586505  ] 
dist 9=[31.931944387862054701  ,43.480756875702929349  ] 
dist 10=[30.682545923504458504  ,43.373077731518047135  ] 
dist 11=[28.940978043483307074  ,42.844262241474191389  ] 
dist 12=[27.179975769353476574  ,42.705895882422392542  ] 
dist 13=[25.852762263381767277  ,42.267370033235043249  ] 
dist 14=[24.583385864527595018  ,42.161284961608205935  ] 
dist 15=[23.053195840041778743  ,40.982191731800349836  ] 
dist 16=[21.463364116179052049  ,31.713913988201077149  ] 
dist 17=[19.955399603871484583  ,29.543839064653023672  ] 
dist 18=[18.210567101283691841  ,29.192553656562327305  ] 
dist 19=[15.673739614507408288  ,25.986851846425727888  ] 
dist 20=[13.151762508496979833  ,25.376691704174531228  ] 
dist 21=[11.466203056517022794  ,24.593094832616161593  ] 
dist 22=[10.061421267533729851  ,24.344728733599564176  ] 
dist 23=[8.6616976553330770807 ,19.048904596149201714  ] 
dist 24=[7.3629817934953041260 ,18.362042374090051420  ] 
dist 25=[6.2208392899179569041 ,16.923736537578240700  ] 
dist 26=[4.7482265267121686559 ,16.538150662189099024  ] 
dist 27=[3.1258303783703875139 ,15.059875591320001824  ] 
dist 28=[1.5210731015632846910 ,14.771337532545666788  ] 
dist 29=[.1184102678459154528 ,14.146967873120581066  ] 
dist 30=[-1.4135202262557163838 ,13.980216096310475757  ] 
dist 31=[-3.5357775943552830796 ,5.4751583644511788980 ] 
dist 32=[-5.5983440500016045370 ,4.7073785638149741984 ] 
dist 33=[-6.8919401588771411614 ,3.0057335662608065082 ] 
dist 34=[-7.8793392073794604123 ,2.6880744812451567143 ] 
dist 35=[-8.7179608584895057780 ,.7129135364266051215 ] 
dist 36=[-9.4057908990875843883 ,.3744138142531868940 ] 
dist 37=[-9.7906317251948389882 ,-.2705471372112762232 ] 
dist 38=[-10.032332421753183112  ,-.4178321731436957435 ] 
dist 39=[-10.813211548363439073  ,-1.8658006369859598656 ] 
dist 40=[-11.363443661922095727  ,-2.0800597680675545504 ] 
dist 41=[-11.767580438516378075  ,-2.3671292012037377283 ] 
dist 42=[-12.080729591779830333  ,-2.3653714106276817944 ] 
dist 43=[-12.313435675311950129  ,-2.2954955981412435335 ] 
dist 44=[-12.396228038890452102  ,-2.1981933047952057025 ] 
dist 45=[-12.417574247884493947  ,-1.9951536267364388451 ] 
dist 46=[-12.404606762775562036  ,-1.5064553478378471476 ] 
dist 47=[-9.8594168189454585553 ,-.98957352505371947004] 
dist 48=[-6.7750102405015573034 ,-.6133128010000875320 ] 
dist 49=[-5.8580295209790273270 ,-.2693371825273489126 ] 
dist 50=[-5.7238167391035000282 ,.1634688610476015479 ] 
dist 51=[-4.3566586183512431976 ,1.1163197788422112043 ] 
dist 52=[-4.1028919879916876923 ,1.9904708413741932620 ] 
dist 53=[-3.8051273221819659534 ,2.6380709460836011824 ] 
dist 54=[-3.7461813518489123099 ,3.2436360575299386186 ] 
dist 55=[-1.5954478173584220830 ,3.9499499217289456526 ] 
dist 56=[-1.3353012912508343715 ,4.6091295048483525006 ] 
dist 57=[-.7898904959623953641 ,5.0265991362987911940 ] 
dist 58=[-.6604249693430227591 ,5.3469058850582989178 ] 
dist 59=[-.1430335552829939419 ,5.6184398469731667424 ] 
dist 60=[-.0470244235081869494 ,5.8382145284774189851 ] 
dist 61=[.1089491440583750357 ,5.9520571446919846784 ] 
dist 62=[.1427880045066724276 ,6.0106449248201164796 ] 
dist 63=[1.1052326202480046932 ,6.0170535191424814924 ] 
dist 64=[.99319159292062456592,4.4748791200397158628 ] 
dist 65=[.84485410679173191451,4.3496917975339594464 ] 
dist 66=[.60221089277281830287,4.0421122596965560280 ] 
dist 67=[.18596887501299423083,3.9784592648997796698 ] 
dist 68=[-.2361095568111374942 ,4.1587877473453410100 ] 
dist 69=[-.52266568597252071644,4.3510540803156239716 ] 
dist 70=[-.76470779360116078501,4.5752658072740981745 ] 
dist 71=[-1.0091485492292867333 ,4.7828061808961101734 ] 
dist 72=[-1.2363176324801508259 ,4.9084710313074948246 ] 
dist 73=[-1.4094354337451923002 ,4.9987689432406225105 ] 
dist 74=[-1.5760627668246899862 ,5.0650047181018343539 ] 
dist 75=[-1.7773317859728749168 ,5.1110999000068712069 ] 
dist 76=[-1.9657673814553012804 ,5.1209325222218187810 ] 
dist 77=[-2.0811762944352531666 ,5.1137617878370780431 ] 
dist 78=[-2.1651508247507962280 ,5.1003803385877789158 ] 
dist 79=[-2.2281281485434594227 ,1.6070537847688667630 ] 
dist 80=[-2.4399602531784513261 ,1.4968058957146266867 ] 
dist 81=[-2.9374263840149829525 ,1.4693802165317731997 ] 
dist 82=[-3.4237303938323717381 ,1.4343392248725831964 ] 
dist 83=[-3.8662563740436071476 ,1.4210719114788414762 ] 
dist 84=[-4.1889663364154174847 ,.17982472947449024162] 
dist 85=[-4.4861062424740168953 ,.10415489868541471512] 
dist 86=[-4.8265781005781721605 ,.0735206336568645926 ] 
dist 87=[-5.1369864928690118641 ,.1300917607318378723 ] 
dist 88=[-5.3141157693987506857 ,.2038013936793953811 ] 
dist 89=[-5.4278389711917789227 ,.2842614802273328812 ] 
dist 90=[-5.4851171659215525635 ,.3848905172132884174 ] 
dist 91=[-5.5147937246847702721 ,.5391613220736105280 ] 
dist 92=[-5.5183024678761812344 ,.7160085482118814467 ] 
dist 93=[-5.5033715136673763689 ,.9067815748279770077 ] 
dist 94=[-5.4895369100591733713 ,1.1443075052513308824 ] 
dist 95=[-5.0378382516666550512 ,1.5078012225313502575 ] 
dist 96=[-4.9756125930757558648 ,1.8716462276611303135 ] 
dist 97=[-4.7902570527526923213 ,2.1105871344465512562 ] 
dist 98=[-4.7585914112922984034 ,2.3038779413850548173 ] 
dist 99=[-4.3535775193354844753 ,2.6832070533797107350 ] 
dist 100=[-4.2649277035122796793 ,3.0824435475860947344 ] 
dist 101=[-4.1767588978462552878 ,3.4710839340690802495 ] 
dist 102=[-4.1455078889664567544 ,3.9471382485118245853 ] 
dist 103=[-3.0469019433996971108 ,4.3968019457733694128 ] 
dist 104=[-2.9009815701279990618 ,4.6800982848437056436 ] 
dist 105=[-2.6099282753827561695 ,4.8959092170451624459 ] 
dist 106=[-2.5463497381546990659 ,5.0761871673105240133 ] 
dist 107=[-2.5382650517083128469 ,5.2199131088965387829 ] 
dist 108=[-2.2234818652802159607 ,5.2898160634776041447 ] 
dist 109=[-2.1764468167196923587 ,5.3200096716860612828 ] 
dist 110=[-2.0897628739455467384 ,5.3221339803150069181 ] 
dist 111=[-2.0663299241472448681 ,3.1876304281631277835 ] 
dist 112=[-1.9817247057053228975 ,3.3134644737738930290 ] 
dist 113=[-1.9580894655703747272 ,3.3799148967294212633 ] 
dist 114=[-1.9216505206127809930 ,3.4158093518155550310 ] 
dist 115=[-2.1971758371662063846 ,3.4222423144531453366 ] 
dist 116=[-2.5100994682573152918 ,3.4107463893344893305 ] 
dist 117=[-2.7316925885101887076 ,3.3979666876301096050 ] 
dist 118=[-2.9288815105434347588 ,3.3743329971585993348 ] 
dist 119=[-3.1443761624205368905 ,3.3623476607017106965 ] 
dist 120=[-3.3392899144468519987 ,2.9919232886846066502 ] 
dist 121=[-3.4543257734629323602 ,2.9338499443664226809 ] 
dist 122=[-3.5328744198952180363 ,2.8100471036519237899 ] 
dist 123=[-3.5821561623665800530 ,2.7786974976183413445 ] 
dist 124=[-3.6118713442816436000 ,2.5362589921908443992 ] 
dist 125=[-3.6148783258421511039 ,2.4958103670084589968 ] 
dist 126=[-3.6018092007070978502 ,2.4045364271876136060 ] 
dist 127=[-3.5878205650969165999 ,2.3748051959191374011 ] 
dist 128=[.50289978832284330684,2.2361178329065874570 ] 
dist 129=[.42055642716230248688,2.2054391650101593952 ] 
dist 130=[.32300832803816314784,2.1288860618608168201 ] 
dist 131=[-.13454342314748265686,2.1057278182049740392 ] 
dist 132=[-.68153749678993195603,2.0235250606875029539 ] 
dist 133=[-1.0421539944610455489 ,2.0738550130892223913 ] 
dist 134=[-1.3357481147182690868 ,2.1056406725857569814 ] 
dist 135=[-1.6151506849276597872 ,2.1205075712762276043 ] 
dist 136=[-1.8644579674929121260 ,2.1263752015058414390 ] 
dist 137=[-2.0378943234899581666 ,2.1237381936364727375 ] 
dist 138=[-2.1891824727386815553 ,2.1132549929741752731 ] 
dist 139=[-2.3500608291738139524 ,2.1054652750326616000 ] 
dist 140=[-2.4961090308443113774 ,1.9401350976256465820 ] 
dist 141=[-2.5881866758705143200 ,1.9118661232779521766 ] 
dist 142=[-2.6584718227908193969 ,1.8487302024052770592 ] 
dist 143=[-2.7175124079910280459 ,1.8280279194533542554 ] 
dist 144=[-2.7648863052901140137 ,1.7309561192701062354 ] 
dist 145=[-2.7885914701595009991 ,1.7093709666063969921 ] 
dist 146=[-2.7995222747274851001 ,1.6531265063916464531 ] 
dist 147=[-2.7971485185963832577 ,1.6376083721602793130 ] 
dist 148=[-.75002066074272692149,.05445101003037875724] 
dist 149=[-.75988189870045006738,.07764238264103629625] 
dist 150=[-.76458142058840348757,.1060415258031846546 ] 
dist 151=[-.76565954619044679385,.14896856054881572364] 
dist 152=[-.74917049692524395522,.19355931119046004869] 
dist 153=[-.74445441906145532369,.22860294427425222871] 
dist 154=[-.73519227288534622174,.26337814756424547046] 
dist 155=[-.73163029531952799464,.30690304980193365055] 
dist 156=[-.71322589457241932007,.35275945692591842607] 
dist 157=[-.70852083215067375604,.39684574987738486682] 
dist 158=[-.69258306508107934199,.44812042978917888674] 
dist 159=[-.68954860537764348809,.52267818341875403371] 
dist 160=[-.55494916730832762157,.59620094523441740872] 
dist 161=[-.5722050544533353202 ,.64334498778252631166] 
dist 162=[-.58804019701367101579,.68024223683211346231] 
dist 163=[-.60611072012672385957,.71285761355533246224] 
dist 164=[-.6218912505079292404 ,.74026734726987545975] 
dist 165=[-.62858317835523866258,.75638295002473854092] 
dist 166=[-.6315013346387366325 ,.76733272897885695289] 
dist 167=[-.63221345139417272829,.77412057336693181533] 
dist 168=[-.61734739159352045845,.77764847493389643056] 
dist 169=[-.61357822755399271912,.77753682300378478325] 
dist 170=[-.61139159667295994906,.77203391072743982625] 
dist 171=[-.61079076692470564864,.76963403587573562838] 
dist 172=[-.50513263687959236896,.73946312455569315648] 
dist 173=[-.49055697945108767696,.73130767160831648943] 
dist 174=[-.46415165806348685029,.72244463161042572982] 
dist 175=[-.45742647114608991781,.71769856757708953887] 
dist 176=[-.43544518385803884078,.73433835035693062361] 
dist 177=[-.42896628389698114775,.74390577969860042428] 
dist 178=[-.42444049036588647382,.74832606505599240238] 
dist 179=[-.48228315103340477542,.74840993880320061161] 
dist 180=[-.56075755783982690494,.7367562669390818837 ] 
dist 181=[-.61725678785359943487,.73244360411686414004] 
dist 182=[-.66852861560212592315,.74207424541151726729] 
dist 183=[-.72613273932234449747,.74942195303925279456] 
dist 184=[-.77875357973864254727,.75326343611102981028] 
dist 185=[-.81013096539261928699,.75330457051416705665] 
dist 186=[-.83197906100460404952,.74902158644073500522] 
dist 187=[-.84655800091343716542,.74656790676087617451] 
dist 188=[-.85631610436331078119,.70272714899069240304] 
dist 189=[-.85891833868409595543,.69450223980772988255] 
dist 190=[-.85812901576075114338,.67385527112439210945] 
dist 191=[-.85585912968463118793,.66700906445422277522] 
dist 192=[-.04486368693597419986,.62930558144236046202] 
dist 193=[-.13312052172390841089,.62054722638851539727] 
dist 194=[-.21181866987848641671,.60322358697206751135] 
dist 195=[-.29819057429506833505,.59785854071564828273] 
dist 196=[-.38302413333436083146,.58470215929099350167] 
dist 197=[-.45558090296997846431,.59195801738136568792] 
dist 198=[-.5331412456820697613 ,.59523048830410872704] 
dist 199=[-.63795322757840779569,.59528456623870474367] 
dist 200=[-.74201239647984296053,.58808760500742222191] 
dist 201=[-.816567513547901445  ,.58489743864702592679] 
dist 202=[-.8838907029521798498 ,.58055886286779972389] 
dist 203=[-.95907587361676940578,.57823340433677364622] 
dist 204=[-1.0336901942973391602 ,.50737804647896197677] 
dist 205=[-1.0987348886963188178 ,.49662753103514547192] 
dist 206=[-1.1693234450407142120 ,.4746180096928127521 ] 
dist 207=[-1.2660740140993517879 ,.46815712343964401639] 
dist 208=[-1.3590522454847575799 ,.5735951576485933049 ] 
dist 209=[-1.4145792737842195501 ,.69251231688298266577] 
dist 210=[-1.4533843353744227862 ,.79328835806380333967] 
dist 211=[-1.4795963438587725512 ,.89583114515076632755] 
dist 212=[-1.4975194496065483834 ,.99181561148309638131] 
dist 213=[-1.5032289096418226662 ,1.0664071456739129344 ] 
dist 214=[-1.5027635589396859145 ,1.1397083534765807346 ] 
dist 215=[-1.4996515035546051910 ,1.2305410916400753533 ] 
dist 216=[-1.4041383266502973435 ,1.3169767619195561547 ] 
dist 217=[-1.3867793175984676034 ,1.3727223709602160073 ] 
dist 218=[-1.3509533519756875944 ,1.4167302241027187011 ] 
dist 219=[-1.3393034424622982435 ,1.4563021010031482426 ] 
dist 220=[-1.2853183459084328979 ,1.4900506571860135597 ] 
dist 221=[-1.2730408338976843868 ,1.5108084609373568514 ] 
dist 222=[-1.2348309498942201414 ,1.5260499051808054272 ] 
dist 223=[-1.2282171450783627885 ,1.5377738926870688187 ] 
dist 224=[-1.0066257069720209513 ,1.5450318596585201262 ] 
dist 225=[-1.0730970500767545582 ,1.5447095207010506791 ] 
dist 226=[-1.1462964546844233325 ,1.5364823832714998613 ] 
dist 227=[-1.2479499364532390741 ,1.5302838678770631898 ] 
dist 228=[-1.3461818433834871040 ,1.4830649493011459868 ] 
dist 229=[-1.4057201002249802103 ,1.4695294411823160058 ] 
dist 230=[-1.4483911441042556897 ,1.4485934201164886807 ] 
dist 231=[-1.4792783619731276502 ,1.4406613844886360545 ] 
dist 232=[-1.5012318057188280058 ,1.2311265938020751807 ] 
dist 233=[-1.5082336561080172349 ,1.2002451082863381792 ] 
dist 234=[-1.5088756093013376508 ,1.1342829381843584330 ] 
dist 235=[-1.5054362178865145854 ,1.0780481393983448699 ] 
dist 236=[-1.4325612965831734243 ,.86263719729371703823] 
dist 237=[-1.4178130632376481485 ,.84655490748668489707] 
dist 238=[-1.3853517047975601876 ,.78831784920308157346] 
dist 239=[-1.3739927937244769976 ,.87851672674308050831] 
dist 240=[-1.3181325616720560475 ,.9652543333307790016 ] 
dist 241=[-1.3051572888436947009 ,1.0198578135203668586 ] 
dist 242=[-1.2680822796659757327 ,1.0614519791674195414 ] 
dist 243=[-1.2589585735410799125 ,1.0962477051124053221 ] 
dist 244=[-.66368670108559217861,1.1240655993154800224 ] 
dist 245=[-.60604866012066786421,1.1377997167030455178 ] 
dist 246=[-.47138391765714490285,1.1438656701297461746 ] 
dist 247=[-.44771811949591989634,1.1444158742134886523 ] 
dist 248=[-.26689934356901930417,1.1342843730212754548 ] 
dist 249=[-.23401425202003671021,1.1299794051133681350 ] 
dist 250=[-.18146695855413953802,1.1147747637274028939 ] 
dist 251=[-.16066169138587117165,1.1087080524311218916 ] 
dist 252=[.22281412235339063707,1.0632349825917904543 ] 
dist 253=[.26607999505307699909,1.0515090439927544281 ] 
dist 254=[.22930133654557822844,1.0330046380164568444 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 0, 0, 0, 2] 
dist 0=[45.912963646701389041  ,45.912963646701389041  ] 
dist 1=[45.721821777902642139  ,46.042961550293282460  ] 
dist 2=[45.449934863246150155  ,46.153176592741246519  ] 
dist 3=[44.997386953019766182  ,46.265204654050035999  ] 
dist 4=[44.324535019794445634  ,46.369515039706921485  ] 
dist 5=[43.172691770593185827  ,46.448796905523392296  ] 
dist 6=[41.797006731785758397  ,46.524396522679760478  ] 
dist 7=[40.230075386864248066  ,46.613774291295874262  ] 
dist 8=[37.608682278752832927  ,46.690443645054782713  ] 
dist 9=[34.817321761586642728  ,46.715330781888417518  ] 
dist 10=[31.854474365913451833  ,46.706380053212832950  ] 
dist 11=[29.605769867085069079  ,46.648261283354289959  ] 
dist 12=[27.625307395359611620  ,46.562741511775991840  ] 
dist 13=[25.484945370498070238  ,46.232385574762168342  ] 
dist 14=[23.397431301816572226  ,44.197908793861816447  ] 
dist 15=[21.627872656684621672  ,42.660095333153130208  ] 
dist 16=[19.746178978378292196  ,35.468258599100685550  ] 
dist 17=[17.210408966721558474  ,34.519146201022493182  ] 
dist 18=[14.686100137157507900  ,32.177023113980920940  ] 
dist 19=[12.849998019171735223  ,31.837852415643804922  ] 
dist 20=[11.159150384074529423  ,28.250468203628555447  ] 
dist 21=[9.2148245003204954423 ,27.567545961291650154  ] 
dist 22=[7.2457572130129584809 ,26.820961398221576289  ] 
dist 23=[5.4557157412337901890 ,26.678226652958215300  ] 
dist 24=[3.4450563226688556634 ,20.276281339053727638  ] 
dist 25=[.5938768509270764638 ,19.473912377055067804  ] 
dist 26=[-2.2082149847127230558 ,17.880122927072740325  ] 
dist 27=[-4.0228537154787654410 ,17.475388692985708596  ] 
dist 28=[-5.4712587802260415807 ,16.072696269007288983  ] 
dist 29=[-6.8097546677428349718 ,15.764358646897280064  ] 
dist 30=[-7.9844299721463403679 ,15.389118788345495890  ] 
dist 31=[-8.7782620999595573958 ,15.291698908713231051  ] 
dist 32=[-9.4504090286187417210 ,3.6643810045936799819 ] 
dist 33=[-10.139112566446537915  ,2.7164073867653537892 ] 
dist 34=[-10.743810224250622591  ,.57259428977097525821] 
dist 35=[-11.080258861141166160  ,.22837753916027826291] 
dist 36=[-11.287999302603359221  ,-2.3614883830648728900 ] 
dist 37=[-11.378061365802628910  ,-2.8000717740415885378 ] 
dist 38=[-11.409763852829036772  ,-3.5014295644499929622 ] 
dist 39=[-11.389105408956522936  ,-3.6583333268873694525 ] 
dist 40=[-11.326745392373059647  ,-2.3227894298083154064 ] 
dist 41=[-11.282058262271824320  ,-.9188970854845376387 ] 
dist 42=[-9.1883405966519085622 ,.0493792635432192563 ] 
dist 43=[-9.6268684713187197836 ,.8829156747739093983 ] 
dist 44=[-9.9741526624902770292 ,1.7493279613888971379 ] 
dist 45=[-10.142444333844776918  ,2.5697566619176548937 ] 
dist 46=[-10.228519673492311849  ,3.2198917371751201987 ] 
dist 47=[-10.247260217130806064  ,3.8694771056982386547 ] 
dist 48=[-7.0520320235115464829 ,4.6878066972879057700 ] 
dist 49=[-5.7102339089292082310 ,5.4711209703962454960 ] 
dist 50=[-5.1887615219482941188 ,6.0661794193900439273 ] 
dist 51=[-5.0908490272293237326 ,6.5960845773590792057 ] 
dist 52=[-4.3499329590825454427 ,6.9936447432942011363 ] 
dist 53=[-4.2100399799850852184 ,7.3146523785301288341 ] 
dist 54=[-3.9829724931448199792 ,7.5635907131166339413 ] 
dist 55=[-3.9250611908229820060 ,7.6734817398561491758 ] 
dist 56=[-3.4279930321354583676 ,7.7225667340129313054 ] 
dist 57=[-2.7350683621700192083 ,7.7288065488482743926 ] 
dist 58=[-2.4093727010250397381 ,1.4354393251011719423 ] 
dist 59=[-2.3601062808159165340 ,1.8927431050794976924 ] 
dist 60=[-1.9084474499133395936 ,2.2673820903588663966 ] 
dist 61=[-1.8270643707129980125 ,2.6284632578212542888 ] 
dist 62=[-1.7209148320435179563 ,2.9542847919544499708 ] 
dist 63=[-1.6947589369460784875 ,3.1881093093569243936 ] 
dist 64=[-1.0469386205748821460 ,3.3999387819483415790 ] 
dist 65=[-.98349088247831711358,3.6379286404837692771 ] 
dist 66=[-.8531897952353784655 ,3.8528988218102464580 ] 
dist 67=[-.8181760740672079299 ,3.9727975072445596427 ] 
dist 68=[-.6821753142905327593 ,4.0463709389829512697 ] 
dist 69=[-.6552838964862926386 ,4.0763309960336536687 ] 
dist 70=[-.5891892217226156891 ,4.0890513498788465166 ] 
dist 71=[-.5756712649263323055 ,4.0937678668923569730 ] 
dist 72=[-.4640643720964612922 ,4.0935993296821047529 ] 
dist 73=[-.4415641267268969567 ,4.0867908324284306771 ] 
dist 74=[-.3965153526590763643 ,4.0986769687550174583 ] 
dist 75=[-.3828175848995492073 ,4.1139856448970970099 ] 
dist 76=[-.3225848381465828572 ,4.1211001101388302400 ] 
dist 77=[-.60545202344036454789,4.1151272779201451109 ] 
dist 78=[-.96571291396358408562,4.0990770385968924613 ] 
dist 79=[-1.2575501599847503070 ,4.0886258090708155792 ] 
dist 80=[-1.5555179416291678765 ,2.8145214451318233738 ] 
dist 81=[-1.9402755218637571315 ,2.7864045192404373570 ] 
dist 82=[-2.3141377786689888588 ,1.9999328067509767207 ] 
dist 83=[-2.5686158818254822792 ,1.8959746320602703170 ] 
dist 84=[-2.7847348545941015614 ,1.6840260441015507586 ] 
dist 85=[-3.0054573901830792074 ,1.6274274246379771828 ] 
dist 86=[-3.2126802875695118446 ,1.4153501111508136704 ] 
dist 87=[-3.3749137538089144376 ,1.3702649753053378442 ] 
dist 88=[-3.5355717999968562562 ,1.2837600883943944463 ] 
dist 89=[-3.7365310257346445656 ,1.2608810777741903436 ] 
dist 90=[-3.9235813222012439566 ,-.39990075092751181844] 
dist 91=[-4.0287080780529494723 ,-.42347973882871349198] 
dist 92=[-4.0942048418138175703 ,-.5152826474132705981 ] 
dist 93=[-4.1230066566416438327 ,-.5054669690754067170 ] 
dist 94=[-4.1339832445528844236 ,-.46647894080949362524] 
dist 95=[-4.1282973209361480980 ,-.37768659331027446921] 
dist 96=[-4.1114890118116278869 ,-.27777859199118780624] 
dist 97=[-4.0992871668759484212 ,-.19441257083456587593] 
dist 98=[-3.7233871301136404476 ,-.1072944234858773702 ] 
dist 99=[-3.6618878227754840350 ,.00762873708975960085] 
dist 100=[-3.5325542132568127391 ,.1316002692148879219 ] 
dist 101=[-3.4922881637255640194 ,.2548571707314224935 ] 
dist 102=[-3.3117773966524542684 ,.4012337111029610293 ] 
dist 103=[-3.2727762295693054082 ,.6175144991103143657 ] 
dist 104=[-3.1555906415618191455 ,.8403183841803617159 ] 
dist 105=[-3.1369113296378107828 ,1.0127464987385935297 ] 
dist 106=[-1.7549597411142846192 ,1.1814204405702441572 ] 
dist 107=[-1.7485006308985304926 ,1.3892557169258668506 ] 
dist 108=[-1.6994257929933203150 ,1.6065989045753080180 ] 
dist 109=[-1.6852472647282433409 ,1.8819084754977965480 ] 
dist 110=[-1.6630594770263569701 ,2.2396570170912537568 ] 
dist 111=[-1.6547232411513079055 ,2.4945300776348073199 ] 
dist 112=[.0256090998114431383 ,2.7370317925256151242 ] 
dist 113=[.0636514898029567496 ,2.9761587722349511142 ] 
dist 114=[.46904268323235589385,3.2079208340274706063 ] 
dist 115=[.52907563299424154934,3.3517830056982784442 ] 
dist 116=[.61765706786099546178,3.4589823132033866107 ] 
dist 117=[.64000007172398936704,3.5443623129682567332 ] 
dist 118=[.64213220767698166532,3.6092934367896478959 ] 
dist 119=[.60711793374057505373,3.6348466222576744800 ] 
dist 120=[.53917173697276321856,3.6415629862544404119 ] 
dist 121=[.40844103462758738407,3.6312934695761610766 ] 
dist 122=[.27100749043365502922,2.3986992933868841641 ] 
dist 123=[.17629870442480517811,2.4016435137861008021 ] 
dist 124=[.09465685553212963041,2.3785982493101848832 ] 
dist 125=[.00938623922399951863,2.3682396863408992489 ] 
dist 126=[-.07180398431416799943,2.3578017902736428447 ] 
dist 127=[-.13715892071984348706,2.3476661632533866009 ] 
dist 128=[-.39672342992903158529,2.2230903291077989826 ] 
dist 129=[-.70519370150156731381,2.2059349631199689911 ] 
dist 130=[-.96378381812487281634,2.1494040306600228045 ] 
dist 131=[-1.2222262122451411924 ,2.1387081848560810306 ] 
dist 132=[-1.4610625422407142876 ,1.9968083903722182824 ] 
dist 133=[-1.6413818017215670080 ,1.9642994099055837114 ] 
dist 134=[-1.8135288324232952438 ,1.9323415211399339688 ] 
dist 135=[-2.0197394192359536970 ,1.9187636843608393532 ] 
dist 136=[-2.2123173242277264085 ,1.4878186937087522763 ] 
dist 137=[-2.3300397477226457971 ,1.4294024589910373569 ] 
dist 138=[-2.4155661368887616397 ,1.3134034141157382890 ] 
dist 139=[-2.4796110089618974968 ,1.2824557962730530896 ] 
dist 140=[-2.5267380181220047185 ,1.1682803069950250246 ] 
dist 141=[-2.5447256211142821235 ,1.1421260308677177864 ] 
dist 142=[-2.5495761154097535083 ,1.0956052589019570394 ] 
dist 143=[-2.5447248912997666658 ,1.0835668568869962388 ] 
dist 144=[-.75621518158949541571,.1367795376648719091 ] 
dist 145=[-.75391065917671899619,.20121204124171474629] 
dist 146=[-.69680957101322049781,.26667869865610724857] 
dist 147=[-.68700667897043322555,.31594523815396800259] 
dist 148=[-.7859280265072765418 ,.36282395952415191162] 
dist 149=[-.92992191722873117765,.4187607776316936705 ] 
dist 150=[-1.0782615782137853712 ,.47630916843223047124] 
dist 151=[-1.2715975145488572067 ,.52962378364424022698] 
dist 152=[-1.4603251517545651565 ,.59010901505213546698] 
dist 153=[-1.5902669347665896392 ,.67628756945420625203] 
dist 154=[-1.7022143750798116534 ,.76081145512986151555] 
dist 155=[-1.8190983416338979811 ,.81469131347709763194] 
dist 156=[-1.9304199425479638333 ,.85650295293657297062] 
dist 157=[-2.0201609131860666462 ,.8928456419201052671 ] 
dist 158=[-2.1114237657281900269 ,.92294213432193757458] 
dist 159=[-2.2288265337548807589 ,.93981667131800417827] 
dist 160=[-2.3383489329676815771 ,.9502588954811906342 ] 
dist 161=[-2.3981484383854013499 ,.95467570553886592282] 
dist 162=[-2.4330751680798271535 ,.95535330367433707204] 
dist 163=[-2.4432850722779781394 ,1.0803724188909396987 ] 
dist 164=[-2.4442344824137887557 ,1.2529585717770565823 ] 
dist 165=[-2.4421843425537407799 ,1.3928922481911902550 ] 
dist 166=[-2.4375505698676453553 ,1.5358800786447312545 ] 
dist 167=[-2.4295612128731786767 ,1.7206608301054745245 ] 
dist 168=[-2.1376389402444113246 ,1.9002400003963297722 ] 
dist 169=[-2.0935064735725288362 ,2.0224608763069387590 ] 
dist 170=[-2.0114739710664231027 ,2.1262194085721797605 ] 
dist 171=[-1.9889878285367748031 ,2.2320878506049166928 ] 
dist 172=[-1.9058406252928748368 ,2.3313677356427824380 ] 
dist 173=[-1.8831338765962331323 ,2.4088218564186455153 ] 
dist 174=[-1.8433123222934765308 ,2.4852213570853149848 ] 
dist 175=[-1.8313475431711137800 ,2.5802916915455067641 ] 
dist 176=[-.77713703804377526269,2.6679247095204990294 ] 
dist 177=[-.85014227032035565089,2.7146304495827730283 ] 
dist 178=[-.9171241218987526186 ,2.7403559738040550621 ] 
dist 179=[-.95698965792837507647,2.7442236517504368513 ] 
dist 180=[-.98466581661711201365,2.7383455209583194973 ] 
dist 181=[-1.0029831759391149883 ,2.7299246950491629663 ] 
dist 182=[-1.0155612448840561118 ,2.7080601447935659436 ] 
dist 183=[-1.0203237855459927312 ,2.6963438679357995467 ] 
dist 184=[-1.0203833771349621306 ,2.4508586672509887402 ] 
dist 185=[-1.0190458260767838981 ,2.4104175183055074406 ] 
dist 186=[-.07767812485076954477,2.3191829152611822495 ] 
dist 187=[-.1700212158117772168 ,2.2896433579934128655 ] 
dist 188=[-.25201682747809966165,2.1524995486111837319 ] 
dist 189=[-.34147908910009321595,2.1222964704657605645 ] 
dist 190=[-.42903869520285754221,2.0474142368053896837 ] 
dist 191=[-.5034381286278458024 ,2.0246975932189852720 ] 
dist 192=[-.68265626951594966439,1.9511710743365859939 ] 
dist 193=[-1.0327309988332583911 ,2.0028610431421255050 ] 
dist 194=[-1.3176751743330714605 ,2.0361976703810986175 ] 
dist 195=[-1.5887430129357822610 ,2.0532752406129868557 ] 
dist 196=[-1.8305521351707065780 ,2.0612755077694390968 ] 
dist 197=[-1.9986779594962880919 ,2.0596432217975760707 ] 
dist 198=[-2.1452391596233991016 ,2.0504778333938030749 ] 
dist 199=[-2.3009490822616116871 ,2.0429473708670987421 ] 
dist 200=[-2.4422246482365317461 ,1.8903588448445447640 ] 
dist 201=[-2.5311552630657404603 ,1.8638216677996814895 ] 
dist 202=[-2.5988808489971231329 ,1.8041925664702306793 ] 
dist 203=[-2.6554935826689545246 ,1.7844365894891021237 ] 
dist 204=[-2.7007093584083335931 ,1.6910613847934358892 ] 
dist 205=[-2.7229315498809330357 ,1.6701404544650238566 ] 
dist 206=[-2.7325894581043103182 ,1.6162553045465692436 ] 
dist 207=[-2.7302581955296706185 ,1.6006055526383261987 ] 
dist 208=[-1.5311415546150084949 ,1.1633335218434227569 ] 
dist 209=[-1.5278697714126517685 ,1.2595422580720138383 ] 
dist 210=[-1.4205386262118249320 ,1.3512111367103662029 ] 
dist 211=[-1.4016585457426239196 ,1.4105410384779923912 ] 
dist 212=[-1.3629143612533254821 ,1.4576179756919826778 ] 
dist 213=[-1.3505462123712445687 ,1.5003657104033790014 ] 
dist 214=[-1.2942540290464187202 ,1.5371222340746109732 ] 
dist 215=[-1.2814096420630389679 ,1.5602786628333679091 ] 
dist 216=[-1.2426975792633152572 ,1.5779357736807319306 ] 
dist 217=[-1.2352354589698099330 ,1.5927356815996797611 ] 
dist 218=[-.56249274307140588663,1.6028908963238433342 ] 
dist 219=[-.50609761236034771811,1.6034250081031614206 ] 
dist 220=[-.53244603805615681897,1.5970208272136721803 ] 
dist 221=[-.55284411761377707488,1.5908247333574733026 ] 
dist 222=[-.57281978547186945965,1.5449206461140191914 ] 
dist 223=[-.59748214870977348878,1.5314216526142686220 ] 
dist 224=[-.61999441417057380337,1.5101587918228966194 ] 
dist 225=[-.63138550704756242634,1.5021499663922386430 ] 
dist 226=[-.63739719421351215358,1.2890687631124122782 ] 
dist 227=[-.63843051920417923572,1.2575227862980910369 ] 
dist 228=[-.63244900050430497894,1.1900208028533051133 ] 
dist 229=[-.63031111530507853694,1.1699640100976162831 ] 
dist 230=[-.62849524725627375683,1.0834634686097569775 ] 
dist 231=[-.62664208913978621015,1.0658370280857583798 ] 
dist 232=[-.53736659431867780218,1.0159026983000108561 ] 
dist 233=[-.52441711285544043396,1.0084162387587561684 ] 
dist 234=[-.50052877055583782614,1.0053670236472967680 ] 
dist 235=[-.61586130163476357108,1.0590288725999376778 ] 
dist 236=[-.77357751651646169116,1.0995871888128988095 ] 
dist 237=[-.92519935338852337643,1.1329445864960330563 ] 
dist 238=[-1.0615336723697982607 ,1.1591719094162403026 ] 
dist 239=[-1.1582125078337807085 ,1.1712623326096924741 ] 
dist 240=[-1.2444838440711134816 ,1.1761191857901273963 ] 
dist 241=[-1.3392648165364476741 ,1.1757688476927211032 ] 
dist 242=[-1.4254609320729411378 ,1.1597384816924902102 ] 
dist 243=[-1.4774561259315265124 ,1.1543071826775874024 ] 
dist 244=[-1.5144202085892246549 ,1.1369398505196447179 ] 
dist 245=[-1.5406027567557099763 ,1.1299850115263791876 ] 
dist 246=[-1.5581970863700161132 ,1.0827964612603384537 ] 
dist 247=[-1.5619462358140162409 ,1.0707336680640379511 ] 
dist 248=[-1.5587129065753923266 ,1.0500704862291553040 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 2, 0, 1] 
dist 0=[48.104438179226666881  ,48.104438179226666881  ] 
dist 1=[48.051817463861011974  ,48.066247362991083055  ] 
dist 2=[47.842406431798644572  ,48.104438179226666881  ] 
dist 3=[47.509915810558909327  ,47.797924559687686525  ] 
dist 4=[46.886415051652807025  ,47.493009497125002589  ] 
dist 5=[46.083895572532156114  ,47.422095138507934149  ] 
dist 6=[44.785287521147007782  ,47.404103768821530618  ] 
dist 7=[43.287218998855000110  ,44.961330614781459878  ] 
dist 8=[41.990658409426850759  ,44.781045854786200183  ] 
dist 9=[40.589781001951867733  ,43.078993206422163970  ] 
dist 10=[38.674945412574770033  ,42.699500174303161404  ] 
dist 11=[36.569346691274304681  ,42.216005559841545004  ] 
dist 12=[34.406434311128116758  ,42.025518981067795446  ] 
dist 13=[31.780630864107660228  ,40.371594462941256754  ] 
dist 14=[27.825989054492199806  ,40.331624377208886167  ] 
dist 15=[23.852929932209002966  ,35.545370658366042824  ] 
dist 16=[21.153484523996682405  ,35.182446389110593887  ] 
dist 17=[18.861814647781702666  ,33.740529041202114045  ] 
dist 18=[16.517418121427116695  ,33.433537151123350713  ] 
dist 19=[14.309213698193487375  ,32.717215284221155054  ] 
dist 20=[12.561375442044640510  ,32.503001927714862844  ] 
dist 21=[10.809660133382749316  ,20.044215223123398196  ] 
dist 22=[8.0592217129685886549 ,18.919526545297227206  ] 
dist 23=[5.5065615992014622018 ,16.295412005389003183  ] 
dist 24=[2.9776660059867950167 ,15.877532658183979490  ] 
dist 25=[.6471550658083018788 ,12.387540074849758572  ] 
dist 26=[-1.1132319448913376470 ,11.761916013265643349  ] 
dist 27=[-2.7998186664701126236 ,10.876567290851267716  ] 
dist 28=[-4.8359145024281525131 ,10.629673694273658276  ] 
dist 29=[-6.7572152258846543070 ,6.2922387316021100051 ] 
dist 30=[-7.9854340824427539291 ,5.7519174806693914658 ] 
dist 31=[-8.9471251894166196991 ,4.5540316532017351280 ] 
dist 32=[-9.8039385253596304711 ,4.3365448983290488206 ] 
dist 33=[-10.534897405059899981  ,2.9538515027013809313 ] 
dist 34=[-10.994203440140160087  ,2.7213458376654303922 ] 
dist 35=[-11.347630146548097057  ,2.2801186514906309249 ] 
dist 36=[-11.656509037777612409  ,2.1811382853124793358 ] 
dist 37=[-11.907169922350577382  ,-1.9711105964567976726 ] 
dist 38=[-12.028035774608441645  ,-1.5840055274864388342 ] 
dist 39=[-12.081680946673008351  ,-1.1349129735196990930 ] 
dist 40=[-12.078755270390717212  ,-.7175220805777932418 ] 
dist 41=[-12.007098085870637814  ,-.2453456682098782585 ] 
dist 42=[-11.972708830823595461  ,.4229835732203277936 ] 
dist 43=[-11.821667825822397274  ,1.1649744284029612521 ] 
dist 44=[-11.784271670028176313  ,1.9314434999764561317 ] 
dist 45=[-11.129136583187562170  ,2.8623447317693524071 ] 
dist 46=[-11.014725660246709577  ,4.2609173076259397406 ] 
dist 47=[-10.679383356288665908  ,5.6543925001679899501 ] 
dist 48=[-10.627785654744081414  ,6.5650593050053201836 ] 
dist 49=[-9.9191762664561342285 ,7.2967759042166022252 ] 
dist 50=[-9.7364852160267537049 ,7.9760553896220090764 ] 
dist 51=[-9.6090558464358539613 ,8.5702160708930729591 ] 
dist 52=[-9.3196976248759353034 ,8.9622412271242191192 ] 
dist 53=[-3.6606865801426351509 ,9.2817732219316307989 ] 
dist 54=[-3.6101370594418018258 ,9.5866783920659876322 ] 
dist 55=[-2.6641469523054574302 ,9.8401492864588075200 ] 
dist 56=[-2.5380516011880834727 ,9.9543190733884200002 ] 
dist 57=[-2.2366599702123986810 ,10.000878928682937290  ] 
dist 58=[-2.1865929001261416230 ,9.9945548677379098303 ] 
dist 59=[-1.7581358228204627844 ,9.8290323540935200956 ] 
dist 60=[-1.6787114896085098168 ,9.7628290490874713167 ] 
dist 61=[-1.5663720326927835200 ,9.6740036675771367657 ] 
dist 62=[-1.5336507218973435085 ,9.6276737128852459796 ] 
dist 63=[-.6097556950841488567 ,7.1570861757537572721 ] 
dist 64=[-.5067616330178481470 ,6.8850293023311185350 ] 
dist 65=[-.2637842613001695956 ,6.1998908539288053498 ] 
dist 66=[-.2279583488781669078 ,6.0963897816445948676 ] 
dist 67=[.1027431804648001871 ,5.0100192865036107895 ] 
dist 68=[.1619790953051920191 ,4.8017012418875793399 ] 
dist 69=[.2366981407562911992 ,4.5617926405281572109 ] 
dist 70=[.2520265696778543993 ,4.5049275284432426517 ] 
dist 71=[.6918273615706425479 ,2.8101918541753034741 ] 
dist 72=[.7442398166900842091 ,2.6708073607502338148 ] 
dist 73=[.8566121024958217687 ,2.3925707348698402686 ] 
dist 74=[.7582895369013885745 ,2.3199253818714763709 ] 
dist 75=[.1992535822240883942 ,2.0591085683833130320 ] 
dist 76=[-.2955014527999440156 ,2.0007563893683320392 ] 
dist 77=[-.83903528016795853205,1.9125172049564261268 ] 
dist 78=[-1.5929999746794872652 ,1.8869676937664674156 ] 
dist 79=[-2.3343313697024844784 ,1.3789943426091889982 ] 
dist 80=[-2.8274471648387815794 ,1.4262196157883915589 ] 
dist 81=[-3.2344591467434741615 ,1.4670998683436658890 ] 
dist 82=[-3.6319024676115414270 ,1.5097418369007848549 ] 
dist 83=[-3.9940766938160975588 ,1.5500392070543911222 ] 
dist 84=[-4.2602311283283788348 ,1.5815845166997187793 ] 
dist 85=[-4.5077750475111969978 ,1.6126577057787009672 ] 
dist 86=[-4.7956305285677258201 ,1.6510906238123459936 ] 
dist 87=[-5.0610323309981707876 ,1.6874127049236294531 ] 
dist 88=[-5.2188965670490793355 ,1.7100786277042973882 ] 
dist 89=[-5.3286847234315381015 ,1.7270641022554494376 ] 
dist 90=[-5.4020604083906986832 ,1.7407462845590504503 ] 
dist 91=[-5.4478265138629049795 ,1.7513286897429590906 ] 
dist 92=[-5.4557601213317050485 ,1.7559683743396842450 ] 
dist 93=[-5.4334960381887299097 ,1.7572550966779787912 ] 
dist 94=[-5.4257832901662974305 ,1.7545003626157674483 ] 
dist 95=[-1.1086705977965352168 ,1.6594530662502947261 ] 
dist 96=[-1.3660327373428596009 ,2.2359631644749662429 ] 
dist 97=[-1.5745556232964560474 ,2.7149045701903477775 ] 
dist 98=[-1.7714675532909969588 ,3.1864366823234177929 ] 
dist 99=[-1.9462585644063013615 ,3.6175990994248982295 ] 
dist 100=[-2.0664489782836319265 ,3.9353993589749205037 ] 
dist 101=[-2.1698708735622688937 ,4.2313446680461816789 ] 
dist 102=[-2.2777022245540249006 ,4.5752883284426323766 ] 
dist 103=[-2.3733379331759604954 ,4.8913177422387368316 ] 
dist 104=[-2.4280618033575696536 ,5.0758385061378540936 ] 
dist 105=[-2.4633893944758949321 ,5.1996318141783772036 ] 
dist 106=[-2.4815762476341025625 ,5.2732383342625468371 ] 
dist 107=[-2.4893931720071886440 ,5.3175676735799555151 ] 
dist 108=[-2.4877401880839924855 ,5.3244618552536468212 ] 
dist 109=[-2.4727356773744718848 ,5.3116398389670764431 ] 
dist 110=[-2.4626039454251122903 ,5.2958341284516922100 ] 
dist 111=[-1.8390145526404065997 ,5.2535454730912616490 ] 
dist 112=[-2.1201998385363227546 ,5.2466786854134360272 ] 
dist 113=[-2.5510586708937241951 ,5.1920534490951724769 ] 
dist 114=[-2.9859010184565413963 ,5.1761106497221685256 ] 
dist 115=[-3.3904468601897404927 ,4.9429632982992398484 ] 
dist 116=[-3.7003566896275983376 ,4.8832280033325198842 ] 
dist 117=[-4.0005486637771303089 ,4.8248244460388735390 ] 
dist 118=[-4.3662958634496030456 ,4.7909778928028931031 ] 
dist 119=[-4.7109569219453529806 ,3.8876931243465105841 ] 
dist 120=[-4.9269685911154269823 ,3.7612360215275336189 ] 
dist 121=[-5.0902597126710717072 ,3.5093452874457154338 ] 
dist 122=[-5.2244522006475988044 ,3.4407322968936351401 ] 
dist 123=[-5.3297510227160973537 ,3.1805184699157762984 ] 
dist 124=[-5.3776915853449972235 ,3.1207524695435711256 ] 
dist 125=[-5.3927904860186277286 ,3.0045311472381334886 ] 
dist 126=[-5.3669726909595077778 ,2.9712125441650110572 ] 
dist 127=[.29363631337150638878,2.3817213841017671757 ] 
dist 128=[-.16640372708288136856,2.5181958193095444637 ] 
dist 129=[-.5505731355768025841 ,2.6218044326474278002 ] 
dist 130=[-.93229667158052987597,2.7078756721481776249 ] 
dist 131=[-1.2838036835273993750 ,2.7762384975608334359 ] 
dist 132=[-1.5473392399780483580 ,2.8091396291472325758 ] 
dist 133=[-1.7972553086027452216 ,2.8235804443729544379 ] 
dist 134=[-2.0943968142521285404 ,2.8242325617520496945 ] 
dist 135=[-2.3715161242854815192 ,2.7929381232096918968 ] 
dist 136=[-2.5414933590752499788 ,2.7809903817248910937 ] 
dist 137=[-2.6657721216949722600 ,2.7444769248202558005 ] 
dist 138=[-2.7604293707273892783 ,2.7273226226883332312 ] 
dist 139=[-2.8334596072828483190 ,2.6280534830292516756 ] 
dist 140=[-2.8713913646834757084 ,2.6019554879462398558 ] 
dist 141=[-2.8909445881596798679 ,2.5517932640197415841 ] 
dist 142=[-2.8916840803342632772 ,2.5352544472450701224 ] 
dist 143=[-2.6396864483389582656 ,2.0433603822061855798 ] 
dist 144=[-2.6044014978220704958 ,2.0017644442415935700 ] 
dist 145=[-2.5246472877616302144 ,1.8896588364188266136 ] 
dist 146=[-2.4978895874073796158 ,1.8719906193292711787 ] 
dist 147=[-2.3702858951065154661 ,1.6644167018796754514 ] 
dist 148=[-2.3415430141862622650 ,1.6215108254854332039 ] 
dist 149=[-2.2673391155952903821 ,1.5770909137834107966 ] 
dist 150=[-2.2456076234072036175 ,1.5643088428868807034 ] 
dist 151=[-2.4299210260939497476 ,1.0841325133447349566 ] 
dist 152=[-2.5542045825132625787 ,1.0216376855337262713 ] 
dist 153=[-2.6410774545112826830 ,.89676178531398607912] 
dist 154=[-2.6997939220047640255 ,1.1145393082212781491 ] 
dist 155=[-2.7423758511475238914 ,1.4330873508374863502 ] 
dist 156=[-2.7648261674364449242 ,1.7315443253067551424 ] 
dist 157=[-2.7768607133779253948 ,2.0728357271465699974 ] 
dist 158=[-2.7778523285956951674 ,2.5624088525927520809 ] 
dist 159=[-.35976312995102562842,3.0451797906550996471 ] 
dist 160=[-.53920136783931301145,3.3593152546910714319 ] 
dist 161=[-.69626238954712388216,3.6104733809495746931 ] 
dist 162=[-.86414841167592497072,3.8418039982953284918 ] 
dist 163=[-1.0264209671854879541 ,4.0430380611645309260 ] 
dist 164=[-1.1610683328990803614 ,4.1740350338768392274 ] 
dist 165=[-1.3014532782491992557 ,4.2788433254611822626 ] 
dist 166=[-1.4866327952466872090 ,4.3755204525877150075 ] 
dist 167=[-1.6684176591098320727 ,4.4522560051576218563 ] 
dist 168=[-1.7952482300483162884 ,4.4774458125042453486 ] 
dist 169=[-1.9062782788809989371 ,4.4827097871689189591 ] 
dist 170=[-2.0249762585318072605 ,4.4798855410347207530 ] 
dist 171=[-2.1397045001866708233 ,4.3530492500901186809 ] 
dist 172=[-2.2348837959707977394 ,4.3155747162090105655 ] 
dist 173=[-2.3340951935473291959 ,4.2889061100540371336 ] 
dist 174=[-2.4649202313972560964 ,4.2699802812001158877 ] 
dist 175=[-2.5883000049027208680 ,3.7148212943061644702 ] 
dist 176=[-2.6577848945640388036 ,3.6529891782521318281 ] 
dist 177=[-2.7011742366282065268 ,3.4836534740601131682 ] 
dist 178=[-2.7203650816217998009 ,3.4537397662592860240 ] 
dist 179=[-2.7281419645291482578 ,3.1272242786038482218 ] 
dist 180=[-2.9533374076521578610 ,3.0579496890792162075 ] 
dist 181=[-3.2752072680021862816 ,2.9799914173151173862 ] 
dist 182=[-3.6608164187992354093 ,2.9497476491746203253 ] 
dist 183=[-4.0211841565136424262 ,2.4676741547536739734 ] 
dist 184=[-4.2422767884783184965 ,2.5896370287972246461 ] 
dist 185=[-4.4039422319120165129 ,2.6878009442318531375 ] 
dist 186=[-4.5270450998490353353 ,2.7793408804932923535 ] 
dist 187=[-4.6190525454283508070 ,2.8597653047091435059 ] 
dist 188=[-4.6565689534384874170 ,2.9135484401703677394 ] 
dist 189=[-4.6690505177717732618 ,2.9581897450537257802 ] 
dist 190=[-4.6622968235234393322 ,3.0021138201718580984 ] 
dist 191=[-.82094195715088225328,3.0371296254690353751 ] 
dist 192=[-.7050482947559080963 ,3.0462030085209207252 ] 
dist 193=[-.90346029379301481565,3.0439585246939187502 ] 
dist 194=[-1.1852375549457123365 ,3.0355314661006376748 ] 
dist 195=[-1.4548838346357268492 ,2.9647207287853504471 ] 
dist 196=[-1.6742555830596421612 ,2.9422990410748911400 ] 
dist 197=[-1.8991149651563618680 ,2.9051660842270000796 ] 
dist 198=[-2.1906728457512164870 ,2.8912524867319666281 ] 
dist 199=[-2.4745522990799001108 ,2.5111632626533761286 ] 
dist 200=[-2.6687551436703803555 ,2.4541081071479805982 ] 
dist 201=[-2.8347205059659797863 ,2.3316637350356879725 ] 
dist 202=[-3.0058583586447491356 ,2.2949134069350981617 ] 
dist 203=[-3.1675084929202220564 ,2.1349365447202868836 ] 
dist 204=[-3.2955937918788142934 ,2.1019907945178386970 ] 
dist 205=[-3.4238069423071456003 ,2.0091581467072454548 ] 
dist 206=[-3.5859699536922725858 ,1.9941335602959083524 ] 
dist 207=[-3.7358585362877222341 ,1.9159425252369920250 ] 
dist 208=[-3.8150643182413139988 ,1.9985819238121393104 ] 
dist 209=[-3.8581601739778245844 ,2.0589903503018359928 ] 
dist 210=[-3.8675451077256028944 ,2.1049625542653970665 ] 
dist 211=[-3.8529959370320880404 ,2.1381991961348875798 ] 
dist 212=[-3.8434635317933991525 ,2.3123652635686509701 ] 
dist 213=[-3.8316544259499975271 ,2.5481541085769544894 ] 
dist 214=[-3.8176910852582619218 ,2.8511069397819937765 ] 
dist 215=[-3.3382885080127477190 ,3.1447418053016397293 ] 
dist 216=[-3.2663446266533138762 ,3.3433278405553978648 ] 
dist 217=[-3.1302863289382742900 ,3.5105734211369357499 ] 
dist 218=[-3.0927152819387906487 ,3.6790783159316524598 ] 
dist 219=[-2.9511501911240938820 ,3.8357589826092312649 ] 
dist 220=[-2.9233347673353645599 ,3.9557952521842401586 ] 
dist 221=[-2.9218454883574581364 ,4.0721366510040355451 ] 
dist 222=[-2.9181151851644125612 ,4.2140655539466087339 ] 
dist 223=[-.72205102952164069002,4.3436830410918837932 ] 
dist 224=[-.54072620183809881102,4.4108696988230990835 ] 
dist 225=[-.13382823948980834677,4.4452709194176450393 ] 
dist 226=[-.05766674173156194061,4.4500379534132975891 ] 
dist 227=[.22060426557829379024,4.4280226799859095139 ] 
dist 228=[.21155446499836740366,4.4117991007110847179 ] 
dist 229=[.18677244790384143574,4.3740478118719570943 ] 
dist 230=[.13399715352295285836,4.3552742058762845198 ] 
dist 231=[.07286275684133343970,3.9357479361874522631 ] 
dist 232=[.01470598180459087558,3.8678166721755761838 ] 
dist 233=[-.05248808173424561502,3.7162353855855734047 ] 
dist 234=[-.14970500866884031538,3.6678230476055979643 ] 
dist 235=[-.25894548387820532942,3.4455049544601731207 ] 
dist 236=[-.37414505135493315575,3.3970660568711986467 ] 
dist 237=[-.51593518314548468656,3.2737331892437821422 ] 
dist 238=[-.73134173605265215304,3.2398245122199516754 ] 
dist 239=[-1.0702079868759179108 ,3.0786160022484709212 ] 
dist 240=[-1.6310447375343304075 ,3.1593740292996167915 ] 
dist 241=[-2.0878925271510269473 ,3.2113617212927899088 ] 
dist 242=[-2.5231081445237104348 ,3.2377808914064289182 ] 
dist 243=[-2.9117828483696488543 ,3.2499774872972464098 ] 
dist 244=[-3.1828098857837260228 ,3.2472593199149440712 ] 
dist 245=[-3.4199151276734890255 ,3.2326005023716317576 ] 
dist 246=[-3.6731524541560836588 ,3.2207041923845390830 ] 
dist 247=[-3.9031860285396803788 ,2.9794551984911042961 ] 
dist 248=[-4.0476472197642176213 ,2.9375314696299307777 ] 
dist 249=[-4.1572724797630662629 ,2.8433899398145646993 ] 
dist 250=[-4.2482191114384641321 ,2.8122185338638616816 ] 
dist 251=[-4.3203316630430029090 ,2.6649545915848634850 ] 
dist 252=[-4.3547593738044361928 ,2.6319712479692842929 ] 
dist 253=[-4.3682136087132094960 ,2.5469098267509066086 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 1, 0, 1] 
dist 0=[50.832709699615490830  ,50.832709699615490830  ] 
dist 1=[50.397654321150609360  ,51.060486608282616281  ] 
dist 2=[49.564750268085922985  ,51.101405559681272548  ] 
dist 3=[48.606100368947542086  ,50.986018158739032392  ] 
dist 4=[47.668781926919835244  ,50.889063063433500648  ] 
dist 5=[46.565101828492777976  ,50.719435231304718010  ] 
dist 6=[44.941783806859516314  ,50.636342808216712162  ] 
dist 7=[43.102711828552945288  ,50.230291423009623712  ] 
dist 8=[41.137130197027300565  ,49.385210534167217542  ] 
dist 9=[38.696213304338651110  ,46.863616816635664060  ] 
dist 10=[34.958332121281455883  ,46.649214815278947315  ] 
dist 11=[31.177333815347841306  ,46.208266653091558092  ] 
dist 12=[28.564117352249812458  ,46.101283738894863215  ] 
dist 13=[26.297728395875320656  ,45.053838228102420376  ] 
dist 14=[23.902010090568666890  ,43.114153653841932033  ] 
dist 15=[21.596887729951622380  ,37.923884121470487542  ] 
dist 16=[19.692250443361832146  ,37.786438554372566276  ] 
dist 17=[17.709416649517496120  ,31.291491079081975464  ] 
dist 18=[15.091660489970743877  ,30.450308446808613345  ] 
dist 19=[12.510245865234772494  ,28.814522516494638552  ] 
dist 20=[10.672432897179694878  ,28.395908665343368751  ] 
dist 21=[9.0201165816555526520 ,26.947345306941104769  ] 
dist 22=[7.1795109255384832225 ,26.605373095665371754  ] 
dist 23=[5.3487642200628556997 ,26.193524180378368813  ] 
dist 24=[3.7355322305064005934 ,26.045325898072682730  ] 
dist 25=[1.9646253826944716357 ,11.261720032384678571  ] 
dist 26=[-.49668593014515977639,11.168455969471930322  ] 
dist 27=[-2.9053316260488438847 ,10.277487222671507423  ] 
dist 28=[-4.4659021017298182733 ,10.171065745271251954  ] 
dist 29=[-5.7124293967523283751 ,9.6312019860063192096 ] 
dist 30=[-6.8660057458588981639 ,8.9440611624316799998 ] 
dist 31=[-7.8795382116400931334 ,.75557941928379249142] 
dist 32=[-8.5664683905300868031 ,.57287708317191838375] 
dist 33=[-9.2264199765795285842 ,-3.6843352447464221177 ] 
dist 34=[-10.231226606360210275  ,-4.1806498865440069530 ] 
dist 35=[-11.084772802063603272  ,-5.2619524594821826789 ] 
dist 36=[-11.612997380195993170  ,-5.4250601889447595018 ] 
dist 37=[-12.008339728936017366  ,-6.5531043346849640194 ] 
dist 38=[-12.331164911230730578  ,-6.7222658348088520540 ] 
dist 39=[-12.584519968578566376  ,-6.6422219810718061273 ] 
dist 40=[-12.702227079052577364  ,-5.8106091549874180187 ] 
dist 41=[-12.745630988333712449  ,-4.7285451201913492991 ] 
dist 42=[-12.738210978955234703  ,-3.0220510357057415595 ] 
dist 43=[-12.616303227944770336  ,-1.2898712838889522578 ] 
dist 44=[-12.564990911865913765  ,-.10516269606701886644] 
dist 45=[-12.376643148335989939  ,.90566168239287643322] 
dist 46=[-12.311245017629710414  ,1.9438712093633074490 ] 
dist 47=[-8.0376756635504696855 ,2.9207359647822438234 ] 
dist 48=[-8.0089808425142950034 ,3.6867479283711873788 ] 
dist 49=[-6.5400199093627468000 ,4.4454393168382545236 ] 
dist 50=[-6.3704241148589561719 ,5.3931360652377260372 ] 
dist 51=[-5.9322223220135249855 ,6.2977889444528367711 ] 
dist 52=[-5.8317812922625108389 ,6.8846680589353793405 ] 
dist 53=[-5.4792975674295919288 ,7.3515497348464674123 ] 
dist 54=[-5.3924913597824207398 ,7.7771760905661721602 ] 
dist 55=[-5.2830095108307282495 ,8.1440232371014907153 ] 
dist 56=[-5.2414061096688760416 ,8.3762509802998857206 ] 
dist 57=[-1.7018478774393294409 ,8.5544500065481097826 ] 
dist 58=[-1.6460748004757457786 ,8.7055925456176943380 ] 
dist 59=[-.4775185794730537087 ,8.8229001400974019935 ] 
dist 60=[-.3791356276230693184 ,8.8660205299251556484 ] 
dist 61=[.17428164460497001245,8.8644953951988760990 ] 
dist 62=[.22952586090860905542,8.7959518842084524235 ] 
dist 63=[.8775271629267025451 ,2.9074593290114339167 ] 
dist 64=[.9167896604051709214 ,3.1622767392463336041 ] 
dist 65=[2.0044686995106482583 ,3.6007815244115004237 ] 
dist 66=[2.1305111542179413474 ,3.8736710651239409975 ] 
dist 67=[2.4070214257163019754 ,4.0784387658611977053 ] 
dist 68=[2.4487405069054083969 ,4.2448772578611794294 ] 
dist 69=[2.5805388501838568926 ,4.3754678594541432580 ] 
dist 70=[2.5745094914771928195 ,4.4370209169948128720 ] 
dist 71=[2.5262397416924403225 ,4.4672136789785994494 ] 
dist 72=[2.4081459085870910337 ,4.4725386152577782775 ] 
dist 73=[2.1013855959676381807 ,4.0060565087683523660 ] 
dist 74=[1.8301937658953357124 ,3.9948538294412223439 ] 
dist 75=[1.5796179251568625921 ,3.1088869938110923510 ] 
dist 76=[1.2915070714449623326 ,3.1125458513381797679 ] 
dist 77=[1.0010586467496925573 ,3.1134683218079711724 ] 
dist 78=[.7411128091486238080 ,3.1109552433884849086 ] 
dist 79=[.4534400609417242957 ,1.8060480737190596686 ] 
dist 80=[.0522506190968636352 ,1.7602587095321267607 ] 
dist 81=[-.3516761673239111723 ,1.5912662458405459265 ] 
dist 82=[-.6503012455457908995 ,1.5558092642775312781 ] 
dist 83=[-.9294260452101415142 ,1.0686098953054005764 ] 
dist 84=[-1.2555263984936644772 ,1.0363047127754587906 ] 
dist 85=[-1.5875702188597976325 ,.9239293077397896899 ] 
dist 86=[-1.8904540789453349847 ,.89859435113541229681] 
dist 87=[-2.2305945010139994828 ,.9519647249267408135 ] 
dist 88=[-2.7114450747580374461 ,1.0908123818036762647 ] 
dist 89=[-3.1808627019126621580 ,1.2367486805414382891 ] 
dist 90=[-3.4753596396914899338 ,1.3440830262716906748 ] 
dist 91=[-3.6987420266482784448 ,1.4436422221595020703 ] 
dist 92=[-3.8841825590493245830 ,1.5585627885154955181 ] 
dist 93=[-4.0328544015970936615 ,1.6745284310190006126 ] 
dist 94=[-4.1094026115290060327 ,1.7782680040299994262 ] 
dist 95=[-4.1500706145217235818 ,1.8929182305888942178 ] 
dist 96=[-4.1571790664483070629 ,2.0524414021928276302 ] 
dist 97=[-4.0804959058068667155 ,2.2125631659153866808 ] 
dist 98=[-4.0554948832262989200 ,2.3296080345311114988 ] 
dist 99=[-3.8312880334639084341 ,2.4375393405807360350 ] 
dist 100=[-3.8138701750071245694 ,2.5612924942339998909 ] 
dist 101=[-3.8056386501173654337 ,2.6858015969296820876 ] 
dist 102=[-3.7083099640931825461 ,2.7967561387049102142 ] 
dist 103=[-3.4802907242004311258 ,2.9190892348929958875 ] 
dist 104=[-3.4480911738575633814 ,3.0890249692549946507 ] 
dist 105=[-3.3883029666115797816 ,3.2520667111596712345 ] 
dist 106=[-3.3682823062812324978 ,3.3468793743520181932 ] 
dist 107=[-2.3021784504922414491 ,3.4099087462485020506 ] 
dist 108=[-2.2719716978017732431 ,3.4460693045438519582 ] 
dist 109=[-2.2309861970057478089 ,3.4654619618201915895 ] 
dist 110=[-2.2160006115524288584 ,3.4652716364850494029 ] 
dist 111=[-1.5039443436695886018 ,3.4489057176674331207 ] 
dist 112=[-1.4306307976653911540 ,3.4341633754306753644 ] 
dist 113=[-1.2969751174628465382 ,3.2033421503836944181 ] 
dist 114=[-1.2678449400922641862 ,3.1608495407347721541 ] 
dist 115=[-.9643931178346701326 ,3.0608211992443618012 ] 
dist 116=[-.91527312899295406914,3.0262438587366417265 ] 
dist 117=[-.8461724954673442027 ,2.8576482372995950623 ] 
dist 118=[-.82537430392014249429,2.7861581152908170516 ] 
dist 119=[-.4229678444814566846 ,2.5693592698399678897 ] 
dist 120=[-.37132212218564504231,2.3718641982852067046 ] 
dist 121=[-.25627325500989579107,2.0388275990454003135 ] 
dist 122=[-.24268852009997476366,2.1194828822898297074 ] 
dist 123=[-.2980268465789228502 ,2.1849457369066738337 ] 
dist 124=[-.35487911182241811426,2.2192125364895525136 ] 
dist 125=[-.40828166797308999146,2.2372437957082399417 ] 
dist 126=[-.44985686243982795026,2.2398842391074386883 ] 
dist 127=[-.49069088071783488681,.86447294451673615761] 
dist 128=[-.54113747135088923515,.86169595424677679032] 
dist 129=[-.58888407287943621707,.75665282240564848548] 
dist 130=[-.61894469788319798136,.74088501128783808238] 
dist 131=[-.64177910645341424606,.71149626969148143334] 
dist 132=[-.66069058936884954547,.70347770850107885026] 
dist 133=[-.67560868246498371934,.71846107193471636512] 
dist 134=[-.68250755293093140242,.75946955561655576834] 
dist 135=[-.68484223863346795922,.79651815416749417262] 
dist 136=[-.68446883955244189667,.81703976222729842056] 
dist 137=[.17292191801359219008,.82940785445504847577] 
dist 138=[.09008278558980127503,.83389896746666136816] 
dist 139=[.01826026857243704035,.83522158746017840199] 
dist 140=[-.05742477855169408499,.83493978768584133676] 
dist 141=[-.12991464294082032029,.83342623800594946677] 
dist 142=[-.18898266999317152375,.83101312491230311623] 
dist 143=[-.24961276040609398583,.73885723192387840361] 
dist 144=[-.32834288961339767284,.72614242094268407712] 
dist 145=[-.40506775234949614534,.69111372068272328062] 
dist 146=[-.45769343003263658771,.68546443638249096405] 
dist 147=[-.50282437704592186439,.61771077756978544512] 
dist 148=[-.54962759788351932451,.60343961485087284324] 
dist 149=[-.59402253124464266633,.58888178969884569836] 
dist 150=[-.62954073637048687522,.58436230282881897696] 
dist 151=[-.66543068344196624457,.41863816578060526152] 
dist 152=[-.7113156972432095237 ,.39685023349189918265] 
dist 153=[-.75428753448751956465,.35352169892193220769] 
dist 154=[-.77854657426204853912,.34216290396170079618] 
dist 155=[-.79380317497837167794,.3011446223297832623 ] 
dist 156=[-.80496297918148350086,.29189557270746303152] 
dist 157=[-.84456875134131646237,.27714179279279094277] 
dist 158=[-.89540431485244402213,.27534015066992947155] 
dist 159=[-.94332358870082138526,.32003205275157853558] 
dist 160=[-.9712849055208714566 ,.38085225665561473672] 
dist 161=[-.99002340836772011624,.44138054721336242585] 
dist 162=[-1.0011169541438206216 ,.48490822312642952444] 
dist 163=[-1.0075063271082483419 ,.52435997922708314513] 
dist 164=[-1.0077359946150067280 ,.56861801893135373904] 
dist 165=[-1.0046659077598551432 ,.61263555745845558217] 
dist 166=[-1.0012145286408958192 ,.6511286382118895392 ] 
dist 167=[-.9362728241965818257 ,.69299274685635531749] 
dist 168=[-.92452088217860420601,.75047078097882809459] 
dist 169=[-.89795718322861408193,.80594877997480972019] 
dist 170=[-.88898184316100333175,.83982846949434872913] 
dist 171=[-.84593020890101840209,.86441551054661248943] 
dist 172=[-.83614778508368683854,.88279308621364014351] 
dist 173=[-.81102459424560210296,.89580043851912394021] 
dist 174=[-.80338271523302615702,.89894739642873673144] 
dist 175=[-.65877868885982848799,.89872594418838400279] 
dist 176=[-.65272091673933481564,.89828334712558594794] 
dist 177=[-.63464734903135132968,.86594147177928395153] 
dist 178=[-.63067260958682938861,.85872635766926824825] 
dist 179=[-.58958986068014130302,.83937675285616430795] 
dist 180=[-.58019956973239535821,.83223247262698817628] 
dist 181=[-.56896391717526018533,.79135015532469366636] 
dist 182=[-.5641288079533065059 ,.78137924276929492464] 
dist 183=[-.44592195775215798473,.81975418054872726677] 
dist 184=[-.4295254654650403547 ,.85682917040492317502] 
dist 185=[-.39588557450121072248,.88434269089301599345] 
dist 186=[-.38657626851234123841,.9060592125401693325 ] 
dist 187=[-.45688085736380422584,.92242396119412839553] 
dist 188=[-.55271355709993287443,.92856886312642890966] 
dist 189=[-.63870317216118758264,.93025881541738746621] 
dist 190=[-.69933812847710892822,.92883576799911987295] 
dist 191=[-.75307935607285321829,.72781921070719671107] 
dist 192=[-.8115453306043072781 ,.7246756198025861333 ] 
dist 193=[-.86474133499294539695,.63191452158378381668] 
dist 194=[-.89744245513123539666,.61794869326664066376] 
dist 195=[-.92142596026155211781,.58899590734698038704] 
dist 196=[-.93981805750197160437,.58047210745590087764] 
dist 197=[-.95322871312390455338,.54445965696331130271] 
dist 198=[-.95732442914632365326,.53668131398644646701] 
dist 199=[-.95743373370999791028,.51593121757872085598] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 1, 1, 2, 0, 2] 
dist 0=[43.255055117757733074  ,43.255055117757733074  ] 
dist 1=[42.975110612228056954  ,43.708504032670816531  ] 
dist 2=[42.310502044263215992  ,44.180974747214861981  ] 
dist 3=[41.246686011004636678  ,44.405095078040762350  ] 
dist 4=[39.520274296847454083  ,44.502314559216911823  ] 
dist 5=[37.736196703983347234  ,44.503377363216100603  ] 
dist 6=[36.441957740342604991  ,44.264602006158878975  ] 
dist 7=[35.254657068845711457  ,43.978827906960043532  ] 
dist 8=[33.897600693785961401  ,43.209359399134584501  ] 
dist 9=[32.529630862642952119  ,43.106190615873742553  ] 
dist 10=[31.298601292931719664  ,42.706526463338410422  ] 
dist 11=[29.927518096489620883  ,42.575979793794394090  ] 
dist 12=[27.999842502617010050  ,42.277352722292429181  ] 
dist 13=[26.043901102099711098  ,42.160535125743527880  ] 
dist 14=[24.559769687133548721  ,41.588634621981666193  ] 
dist 15=[23.130969473083031244  ,40.933762140376268483  ] 
dist 16=[21.395888927144456976  ,28.514402587633776322  ] 
dist 17=[19.587298251249756489  ,28.170313430591463166  ] 
dist 18=[17.864576512883863021  ,24.826792033580600634  ] 
dist 19=[15.866587662002939981  ,24.196983071300238362  ] 
dist 20=[12.957746980120195840  ,24.066826968537512755  ] 
dist 21=[10.063638979297141185  ,23.257321861066331840  ] 
dist 22=[8.1244646180484086089 ,18.987007840631903646  ] 
dist 23=[6.5041749666261032095 ,18.786473988176200989  ] 
dist 24=[4.8844422886741600970 ,17.172898114182442466  ] 
dist 25=[3.3795336899876895146 ,16.884713833014131388  ] 
dist 26=[2.2180907046278250285 ,16.626409391596144224  ] 
dist 27=[1.0799895645748395395 ,15.737334013985155134  ] 
dist 28=[-.3317242450819992806 ,13.957330184628117306  ] 
dist 29=[-1.6849467127210808618 ,12.991399449170775456  ] 
dist 30=[-2.5893586465622090835 ,7.9722385338950345254 ] 
dist 31=[-3.4692380960798035602 ,5.8458087516207869940 ] 
dist 32=[-6.1223284891502241903 ,1.6563257543371520677 ] 
dist 33=[-7.8135140490542335729 ,1.3642604041195002928 ] 
dist 34=[-9.1335229576534912440 ,.0060576187146294147 ] 
dist 35=[-10.303227653894848927  ,.2811660396371784034 ] 
dist 36=[-11.295854530933897908  ,.8082940388977503147 ] 
dist 37=[-11.908326967020231522  ,1.3684208901024025578 ] 
dist 38=[-12.364612168695388235  ,1.7753682228603054787 ] 
dist 39=[-12.733471393267376344  ,2.1456125539356518329 ] 
dist 40=[-13.026022286896556794  ,2.5597606710281910919 ] 
dist 41=[-13.177337932475452833  ,2.9681688460069132180 ] 
dist 42=[-13.257233203693319327  ,3.3157005888093545528 ] 
dist 43=[-13.263905355916998720  ,3.6839494562667117263 ] 
dist 44=[-13.225280994604950230  ,4.1751246531608592803 ] 
dist 45=[-13.189679699769374863  ,4.6563934028779611999 ] 
dist 46=[-13.018834006687718944  ,4.9851786967871652832 ] 
dist 47=[-12.964567077831111758  ,5.2643373906142528941 ] 
dist 48=[-7.6182162084926675431 ,5.5476818218579427737 ] 
dist 49=[-7.1259789720510879932 ,5.8110660232624826396 ] 
dist 50=[-6.5911986985310839851 ,6.0105932646386364075 ] 
dist 51=[-6.4913447417402890100 ,6.2009122757934676475 ] 
dist 52=[-6.4556829879662746236 ,6.4275025083608283233 ] 
dist 53=[-3.9000190218922905393 ,6.6360144756988091250 ] 
dist 54=[-3.3171029050336947407 ,6.7542016922988022705 ] 
dist 55=[-3.2083379555462903380 ,6.8282672967125745724 ] 
dist 56=[-2.0754577671829106261 ,6.8607907795814589382 ] 
dist 57=[-2.0028587929468403068 ,6.8635300986127517077 ] 
dist 58=[-1.5534970037832074472 ,6.8494107540466495437 ] 
dist 59=[-1.4744481478368898227 ,6.7645019578892473397 ] 
dist 60=[-1.3217060989565156354 ,6.7295030858979977265 ] 
dist 61=[-1.2850940445856272437 ,6.3639325291835467854 ] 
dist 62=[-.3758662395432277900 ,6.2865414912910338893 ] 
dist 63=[-.4085201826362304533 ,5.9822194984593682870 ] 
dist 64=[-.4340843415062963752 ,3.0356113598681354601 ] 
dist 65=[-.4553319714666025934 ,3.3069225529946856102 ] 
dist 66=[-.4721494110780866400 ,3.5136026737047668895 ] 
dist 67=[-.4801737172907312201 ,3.6906408749062438027 ] 
dist 68=[-.4830537093561491440 ,3.8346681745272803564 ] 
dist 69=[-.4827855444714411667 ,3.9724775503154236024 ] 
dist 70=[-.4257443884197050627 ,4.0890513498788465193 ] 
dist 71=[-.4135289877284049873 ,4.1482520740785652372 ] 
dist 72=[-.3988853363515792229 ,4.1773350828554282093 ] 
dist 73=[-.3916996623082351855 ,4.1813078037260654151 ] 
dist 74=[-.3747872480340127569 ,4.1566047671833647769 ] 
dist 75=[-.3667103357169949961 ,4.1410761361868901691 ] 
dist 76=[-.3549189145049885753 ,4.1057430433331619782 ] 
dist 77=[-.3493210029886954519 ,4.0888387347758679003 ] 
dist 78=[-.2247616869687322724 ,3.6324051126162854923 ] 
dist 79=[-.5222632517175819810 ,3.6179230747815776161 ] 
dist 80=[-.8914068476975917738 ,3.1939855608745755746 ] 
dist 81=[-1.2787908275941962373 ,2.9777361222734186518 ] 
dist 82=[-1.6491453518455641886 ,2.9295477908594105516 ] 
dist 83=[-2.0784036791935114844 ,2.8706936999040773878 ] 
dist 84=[-2.7009936345144542731 ,2.8464298284501354394 ] 
dist 85=[-3.3163252720283525774 ,.35977585056750559636] 
dist 86=[-3.7166167636903062226 ,.22925376622653434265] 
dist 87=[-4.0365611157520399482 ,.19551614704433131   ] 
dist 88=[-4.3311099389392576472 ,-.48059014568008018107] 
dist 89=[-4.5872875340341743380 ,-.56154385083668404903] 
dist 90=[-4.7540409699217351129 ,-.6264833311403194929 ] 
dist 91=[-4.8874956364331323001 ,-.3985578227841384182 ] 
dist 92=[-5.0107433865278758189 ,-.0947035629786710011 ] 
dist 93=[-5.1095376509889867580 ,.3924587336683083640 ] 
dist 94=[-5.1453613399935575049 ,.89042340787325227165] 
dist 95=[-5.1550687100483017069 ,1.2374050620615153763 ] 
dist 96=[-5.1495668684184403503 ,1.5404551261288400506 ] 
dist 97=[-5.0857593845693878048 ,1.8630567002976921644 ] 
dist 98=[-5.0826829252424762828 ,2.1738031313990432160 ] 
dist 99=[-5.0618984534350817062 ,2.4295341264999257792 ] 
dist 100=[-4.9100670947550692001 ,2.6941379463683801074 ] 
dist 101=[-3.7745849420963892941 ,3.0403126695936173197 ] 
dist 102=[-3.6398931930212161070 ,3.3784999127992986339 ] 
dist 103=[-3.3144200797364223230 ,3.6112213899295740113 ] 
dist 104=[-3.2494847331171644894 ,3.8114449275992183824 ] 
dist 105=[-2.7603727297731868277 ,4.0199033497852781590 ] 
dist 106=[-2.6642229104753166803 ,4.2179271137017159116 ] 
dist 107=[-2.5088603847749288296 ,4.3764993491721593236 ] 
dist 108=[-2.4671463382371025634 ,4.5367014845281040707 ] 
dist 109=[-1.9929915248948722251 ,4.7412403137619940134 ] 
dist 110=[-1.9365113890358375297 ,4.9313194953727531739 ] 
dist 111=[-1.9262307264838935608 ,5.0337964241313470712 ] 
dist 112=[-1.2482737179709825408 ,5.0918305510139400391 ] 
dist 113=[-1.0061640480995866553 ,5.1044788247664761644 ] 
dist 114=[-.83852964574697635891,5.0973559958127821973 ] 
dist 115=[-.80076463792860338522,5.0813776147541433427 ] 
dist 116=[-.70736957397222959595,4.9176220672601503044 ] 
dist 117=[-.50598616401893350954,1.0531443665276815308 ] 
dist 118=[-.4431352740054181469 ,1.1997853923246883210 ] 
dist 119=[-.42435206775336926684,1.3756882649769302424 ] 
dist 120=[-.07533750324944403178,1.5404488818972733295 ] 
dist 121=[-.03170604552061823656,1.6425953251195740878 ] 
dist 122=[.06528196916681097889,1.7186461828849244928 ] 
dist 123=[.08337786511418101880,1.7791968895138071530 ] 
dist 124=[.19570799170429016432,1.8265784630575519141 ] 
dist 125=[.21470801811560879295,1.8500380889110082176 ] 
dist 126=[.25151155119104077828,1.8611321557522425190 ] 
dist 127=[.25991208282837174741,1.8623327957184382258 ] 
dist 128=[.45284948224438831911,1.2408594174731826286 ] 
dist 129=[.45912195675042396241,1.2639653976961844979 ] 
dist 130=[.46275771816860908275,1.2715794915884314737 ] 
dist 131=[.45711855188472300931,1.2734763674992398170 ] 
dist 132=[.44704188174194946007,1.2737534083205907984 ] 
dist 133=[.43128290083278434466,1.0089100089682239060 ] 
dist 134=[.4083304232766220433 ,.98172213209170103289] 
dist 135=[.36952747501920341181,.9197649039199595333 ] 
dist 136=[.32747630909132465419,.90237661209157681976] 
dist 137=[.29155147774492100942,.81687446456016306709] 
dist 138=[.25275785178452607747,.79928074380865767575] 
dist 139=[.1510505077361796548 ,.78252375321492906849] 
dist 140=[.00707090719175928617,.7839809414750650931 ] 
dist 141=[-.13881275043413587538,.78348218089280300181] 
dist 142=[-.2481231565900342811 ,.7767494219571288846 ] 
dist 143=[-.3517179223697045556 ,.77521174749803645166] 
dist 144=[-.47478286786495157977,.73638348459029582487] 
dist 145=[-.60114511461261149549,.72890293532964790184] 
dist 146=[-.71790586165089443592,.70844033323413250547] 
dist 147=[-.8501581991058705668 ,.70295770184729473929] 
dist 148=[-1.0383741109004547747 ,.66080359299698726459] 
dist 149=[-1.2235754807959755729 ,.6511016742386376422 ] 
dist 150=[-1.3437922344972930960 ,.63610996078753407912] 
dist 151=[-1.4395865230981884212 ,.63120265548191169142] 
dist 152=[-1.5272776409888530503 ,.51633505893386026896] 
dist 153=[-1.6031873944678485372 ,.49999237938073509435] 
dist 154=[-1.6519430330240605105 ,.46440264555660220489] 
dist 155=[-1.6902104427122477490 ,.45396871957892123611] 
dist 156=[-1.7242449061078897703 ,.4095217363298975186 ] 
dist 157=[-1.7506748771098621256 ,.4005796829000923872 ] 
dist 158=[-1.7585802221543171093 ,.37768588836603460345] 
dist 159=[-1.7593035620091854811 ,.37311182635259220973] 
dist 160=[-1.7570574127847189130 ,.08863957553337970073] 
dist 161=[-1.7082535762092511231 ,.07460191909163069208] 
dist 162=[-1.6934375103856020583 ,.04996236498495335692] 
dist 163=[-1.6807826656230985673 ,.04634163612285233892] 
dist 164=[-1.6714793741365644985 ,.01078574294699698326] 
dist 165=[-1.4020975427012182381 ,.20827223804001881155] 
dist 166=[-1.3721190421788366936 ,.43343557635001838571] 
dist 167=[-1.2934722113941070767 ,.62222789348184295648] 
dist 168=[-1.2795345201210902192 ,.81108510890508322036] 
dist 169=[-1.1394799127384097230 ,.98582167301373965831] 
dist 170=[-1.1105429079064347245 ,1.1182357980956223214 ] 
dist 171=[-1.0755633944796660809 ,1.2451802855954269579 ] 
dist 172=[-1.0619367348865847165 ,1.3980787302407707705 ] 
dist 173=[-.75658504749783224046,1.5414072802839019753 ] 
dist 174=[-.71585968483828348004,1.6301429079391301096 ] 
dist 175=[-.63110632173100875807,1.6959915603515890895 ] 
dist 176=[-.60808712570855304456,1.7479413288998324646 ] 
dist 177=[-.51912376426014112436,1.7873272609428690078 ] 
dist 178=[-.51854226300986454755,1.8030134461437926972 ] 
dist 179=[-.52390374442301713966,1.8089516796171251448 ] 
dist 180=[-.52687697068930965566,1.8094178717218423480 ] 
dist 181=[-.52693126439393717792,.57236900367151004018] 
dist 182=[-.52481706843967205622,.62314094685489374442] 
dist 183=[-.52279319343278900395,.68040179452877099427] 
dist 184=[-.49043433013865063147,.73299019470191302108] 
dist 185=[-.48443659138143206895,.76510536791410637393] 
dist 186=[-.4705074760281670967 ,.78842623526767983856] 
dist 187=[-.46570310387221251384,.80589954504992995664] 
dist 188=[-.44230800271958182686,.8185035062261927316 ] 
dist 189=[-.43691524930871944997,.88562455720407288066] 
dist 190=[-.42401268059443335948,.94933279590167307524] 
dist 191=[-.41949871256643638772,1.0028778161165705195 ] 
dist 192=[.00692504869798058863,1.0566534619098521531 ] 
dist 193=[-.03180542397624772075,1.1065490221456175266 ] 
dist 194=[-.06668581891269026255,1.1446023142376716004 ] 
dist 195=[-.10549344911429265472,1.1813214278732744676 ] 
dist 196=[-.1439175076376859496 ,1.2258903500847004267 ] 
dist 197=[-.24074341429499143017,1.2661882575743260236 ] 
dist 198=[-.35717931098313503779,1.2858546999247196989 ] 
dist 199=[-.45777768098336461181,1.2957259617315835565 ] 
dist 200=[-.5632496006417624044 ,1.2969145721892491937 ] 
dist 201=[-.66395092602315532851,1.2808509605253099716 ] 
dist 202=[-.74550207471700506602,1.2750912447569629586 ] 
dist 203=[-.82875448738673328126,1.2701850157457370749 ] 
dist 204=[-.93624839845589935229,1.2651521601098134410 ] 
dist 205=[-1.0406927637131612042 ,1.0847819069509178055 ] 
dist 206=[-1.1117694626663847903 ,1.0584701505927893951 ] 
dist 207=[-1.1721084424143449102 ,1.0090753982716171231 ] 
dist 208=[-1.2336809836310515246 ,.99576495740207895379] 
dist 209=[-1.2914322686567817378 ,.94739707253759460517] 
dist 210=[-1.3365143766398569075 ,.93452654234953659737] 
dist 211=[-1.3810109929635584940 ,.91376035459643381712] 
dist 212=[-1.4364246826597450515 ,.90712899225574469962] 
dist 213=[-1.4876136297077953745 ,.50255689849016985312] 
dist 214=[-1.5152423501404895199 ,.53430198577085243252] 
dist 215=[-1.5309374792849894176 ,.57339914429353670201] 
dist 216=[-1.5344797731027796524 ,.61048103363872529545] 
dist 217=[-1.5324462737420510231 ,.63418010391055967328] 
dist 218=[-1.5282164808777108080 ,.65264177044010033914] 
dist 219=[-1.5169089151140813347 ,.66881322384112311149] 
dist 220=[-1.5105971972666757652 ,.6822963587623062326 ] 
dist 221=[-1.3767119293003284716 ,.69002481054503562398] 
dist 222=[-1.3545486524191939875 ,.69502585700568127829] 
dist 223=[-1.3047690292525613047 ,.69761962280549810688] 
dist 224=[-1.2886477443487520889 ,.69820052075949476716] 
dist 225=[-1.2137850876135405581 ,.69717272119328995127] 
dist 226=[-1.1972924464345638666 ,.69123489939718947234] 
dist 227=[-1.1557305768057549103 ,.68824381454486287916] 
dist 228=[-1.1436009383096674093 ,.66355476376355618242] 
dist 229=[-1.0683902381040717224 ,.65684781227661565309] 
dist 230=[-1.0904005339777718135 ,.64705058685254164236] 
dist 231=[-1.1032540714501479160 ,.70292190714682829398] 
dist 232=[-1.1069968593970116325 ,.85307439774201989403] 
dist 233=[-1.1065791838975626905 ,.98705875162244161779] 
dist 234=[-1.1037629887286347597 ,1.0802979742464833331 ] 
dist 235=[-1.0969438566086798516 ,1.1616698395753566027 ] 
dist 236=[-1.0929351193921464437 ,1.2482721225722528946 ] 
dist 237=[-.99312649313812231435,1.3269743064613968942 ] 
dist 238=[-.97678550677187223999,1.3768038654555498046 ] 
dist 239=[-.94121323794026192478,1.4150905078018354226 ] 
dist 240=[-.92992959340356057171,1.4477058047251271040 ] 
dist 241=[-.87840197650105681596,1.4742284117875140072 ] 
dist 242=[-.8672375992921583758 ,1.4881890189650065127 ] 
dist 243=[-.83623096982172811259,1.4956377662248223036 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 2, 0, 1, 0, 2] 
dist 0=[53.270711665047291144  ,53.270711665047291144  ] 
dist 1=[52.848441268570818810  ,53.387536191501512197  ] 
dist 2=[52.110908131048407824  ,53.431684244979352295  ] 
dist 3=[50.770513537427802993  ,53.466123113549301526  ] 
dist 4=[49.277007950202483479  ,53.462456025933621138  ] 
dist 5=[47.927980623624738570  ,53.429579866009049898  ] 
dist 6=[46.423719192622766717  ,53.347057030127485540  ] 
dist 7=[44.310000233720577778  ,53.144627388439097920  ] 
dist 8=[41.960088662361446835  ,49.356386254285179358  ] 
dist 9=[39.512368056489703962  ,48.433492825502644457  ] 
dist 10=[36.517851756018813840  ,48.190473254209393814  ] 
dist 11=[31.983926558727035820  ,47.382293733963084117  ] 
dist 12=[27.424578471466030438  ,47.125333553700540911  ] 
dist 13=[24.328402534356777151  ,46.806543102346452639  ] 
dist 14=[21.702913287644742860  ,45.617172571187907727  ] 
dist 15=[19.023238825857704873  ,42.076696870318451491  ] 
dist 16=[16.504287863665126225  ,35.105898228208082971  ] 
dist 17=[14.520478320042994440  ,34.190849169750487122  ] 
dist 18=[12.542089570296738390  ,32.417868663471813002  ] 
dist 19=[10.044294285087184540  ,31.961203958067125348  ] 
dist 20=[7.6338270795505343298 ,30.370338554448643242  ] 
dist 21=[6.0039793496109556832 ,29.989136065540305111  ] 
dist 22=[4.6268441513410537949 ,29.506282807881951534  ] 
dist 23=[3.2254685400280704436 ,29.328091105726593838  ] 
dist 24=[1.9062382340515692950 ,11.646385533704150111  ] 
dist 25=[.8567230099294354533 ,10.184718508845676887  ] 
dist 26=[-.2038677536980263268 ,8.9186045104482914095 ] 
dist 27=[-1.5684889181488428252 ,7.3320023374719773294 ] 
dist 28=[-2.8758855219253602002 ,7.0855380254328284510 ] 
dist 29=[-3.7079660321506091628 ,6.6282982892688758538 ] 
dist 30=[-4.4891430724215388285 ,6.5414034852355844645 ] 
dist 31=[-6.4494046294985990770 ,-.0787826074326410077 ] 
dist 32=[-8.2831849532786640410 ,-4.1720117604981324025 ] 
dist 33=[-9.4270253008047747406 ,-4.8652659849661513310 ] 
dist 34=[-10.288193123433914790  ,-4.7692388392162771321 ] 
dist 35=[-10.992968375544847897  ,-4.4577268525263190486 ] 
dist 36=[-11.555269998316540002  ,-4.0736697738707160525 ] 
dist 37=[-11.847280348236478211  ,-3.6877641123817592480 ] 
dist 38=[-11.999976680860833915  ,-3.2289133900716332575 ] 
dist 39=[-12.029925360804774248  ,-2.5530795761585341285 ] 
dist 40=[-9.3323373066881291413 ,-1.7911889582165573254 ] 
dist 41=[-9.1642408377684259306 ,-.98855830437685885408] 
dist 42=[-8.7149046931902849724 ,-.00293623063431043328] 
dist 43=[-8.6307652324962559895 ,1.4895941641847116791 ] 
dist 44=[-8.1307439677919812564 ,2.9802769172719886332 ] 
dist 45=[-8.1234655308210104876 ,3.9586444387777084556 ] 
dist 46=[-8.0992856612603687744 ,4.7491563994977435205 ] 
dist 47=[-7.3458280459766393360 ,5.4901444206676846464 ] 
dist 48=[-5.9560685245640216855 ,6.1428945067646738528 ] 
dist 49=[-5.9305343352107307949 ,6.5812781300050118698 ] 
dist 50=[-5.7170026271307786930 ,6.9469144144332413391 ] 
dist 51=[-5.3372982430818697936 ,7.3093873435944048331 ] 
dist 52=[-4.1809747021588019155 ,7.6271495725539130633 ] 
dist 53=[-4.0755963978141047120 ,7.8142896645709673205 ] 
dist 54=[-3.8220374331986327820 ,7.9417759018910245640 ] 
dist 55=[-3.7750164517146440335 ,8.0212396776623169091 ] 
dist 56=[-.76898651046532956014,8.0634105825935298828 ] 
dist 57=[-.48979909564323075345,8.0631190639287936534 ] 
dist 58=[.09950296003903113847,8.0031721969319558624 ] 
dist 59=[.23387697298228201827,7.9769584652945528942 ] 
dist 60=[.8134170405080196978 ,4.9956723769402068797 ] 
dist 61=[.9172390848912314609 ,5.0278178668492106529 ] 
dist 62=[1.1117371550325648622 ,5.3731727919127949660 ] 
dist 63=[1.1542904159879185851 ,5.7503769286711703436 ] 
dist 64=[1.2558779391154311402 ,6.0896613765735525814 ] 
dist 65=[1.2350546390692300708 ,6.2835891249851346779 ] 
dist 66=[1.1588428269327420161 ,6.4088540124917034002 ] 
dist 67=[.9877779638712418753 ,6.4739121748617280682 ] 
dist 68=[.4786053464288869588 ,6.5086244798394498079 ] 
dist 69=[.0051745442586209014 ,6.5126715607534358950 ] 
dist 70=[-.4172579969478626503 ,6.4951713352431863175 ] 
dist 71=[-.8811878764506724924 ,6.4811030161679087346 ] 
dist 72=[-1.3371039971434164560 ,3.4182519158195057420 ] 
dist 73=[-1.7276182332779258105 ,3.3141084661567996691 ] 
dist 74=[-2.1457715475035672792 ,3.2845685606956380229 ] 
dist 75=[-2.7121580813405918173 ,3.1703133678619499145 ] 
dist 76=[-3.2636035777838773818 ,3.1395689192839134760 ] 
dist 77=[-3.6221231527220639070 ,3.0785978004357423949 ] 
dist 78=[-3.9088315259437577023 ,3.0586243631447154916 ] 
dist 79=[-4.1735040392898794782 ,1.3638091576911932600 ] 
dist 80=[-4.4045956508856432417 ,1.2243903159280453145 ] 
dist 81=[-4.5572085879856739619 ,.89565131210925354691] 
dist 82=[-4.6820294451429219305 ,.84477992738749089221] 
dist 83=[-4.8021582801045528511 ,.3997949909513620778 ] 
dist 84=[-4.8999832715287417454 ,.32029148289409650355] 
dist 85=[-4.9357376862126052774 ,.21159568153720837145] 
dist 86=[-4.9468561731428023635 ,.18310370317716802182] 
dist 87=[-4.9462433398788683130 ,.58344887856764249614] 
dist 88=[-4.8133643220144214356 ,1.2962118161497445241 ] 
dist 89=[-4.7753065015770547550 ,1.7717159593956196087 ] 
dist 90=[-4.7492240723730813854 ,2.1644340313462570987 ] 
dist 91=[-4.7327029024396790511 ,2.5467772636444021725 ] 
dist 92=[-4.5226185735636428261 ,3.0384714789006717643 ] 
dist 93=[-4.5232482595363820730 ,3.5312552623461801688 ] 
dist 94=[-4.5112609714260908877 ,3.9315529427317284124 ] 
dist 95=[-4.4993773876429783251 ,4.3107445935993903671 ] 
dist 96=[-4.0323120240267855865 ,4.6477291763608406383 ] 
dist 97=[-3.9588276200093123226 ,4.8795410923290761443 ] 
dist 98=[-3.8123911288002237927 ,5.0789277263225808720 ] 
dist 99=[-3.7691927374311946637 ,5.2864811194753489361 ] 
dist 100=[-3.5895911731267598454 ,5.4646040555650610766 ] 
dist 101=[-3.5470617823558504875 ,5.5465022367074908459 ] 
dist 102=[-3.4422937157860355170 ,5.5861103887992555556 ] 
dist 103=[-3.4061233451328190516 ,5.5953934876895101767 ] 
dist 104=[-.95624698452487124786,5.4787917971937421363 ] 
dist 105=[-.93088344541627034482,5.4485505701155166196 ] 
dist 106=[-.92350889208414734435,5.4304055568162591283 ] 
dist 107=[-.8746992170002865925 ,5.4240526957430284469 ] 
dist 108=[-.86354537007385853449,5.0896204579313846250 ] 
dist 109=[-1.5108781145483628248 ,5.0438499238494754142 ] 
dist 110=[-2.1096532047770581196 ,4.8965516972054500978 ] 
dist 111=[-2.7037851692641680203 ,4.8699893032355537435 ] 
dist 112=[-3.2498973852683609481 ,4.5115555140435516137 ] 
dist 113=[-3.6569785493773577755 ,4.4303941103698914177 ] 
dist 114=[-4.0404257451351763186 ,4.3521310302526306240 ] 
dist 115=[-4.4921862169126381544 ,4.3212999053458958420 ] 
dist 116=[-4.9099846037549839119 ,3.2572105728479249808 ] 
dist 117=[-5.1578543864694182109 ,3.1143146863596312492 ] 
dist 118=[-5.3288243739479287564 ,2.7139827041568982821 ] 
dist 119=[-5.4396415361830517889 ,2.2203407008859348871 ] 
dist 120=[-5.5168846643683058426 ,1.3220217878821613107 ] 
dist 121=[-5.5538369191393964672 ,1.3301895412684600082 ] 
dist 122=[-5.5683566143636262887 ,1.3317942121990808110 ] 
dist 123=[-5.5594772995946851556 ,1.3290855506593879615 ] 
dist 124=[-.64918342754884780676,1.3261925541825656384 ] 
dist 125=[-.64868848958758133436,1.3105484477735839345 ] 
dist 126=[-.6474279985470923825 ,1.3061774244627020218 ] 
dist 127=[-.64519312322787664654,1.1047373817301533664 ] 
dist 128=[-.64292503747504640051,1.0979339070447587503 ] 
dist 129=[-.63578254030872620218,1.0943913281149547834 ] 
dist 130=[-.63201031241571004274,1.0800640335987161685 ] 
dist 131=[-.60910793195566272396,1.0754481775876604805 ] 
dist 132=[-.60288764090545232769,1.0295943430730093901 ] 
dist 133=[-.58980267233237427471,1.0180467688066961174 ] 
dist 134=[-.58512702762021018225,1.0033508986474164800 ] 
dist 135=[-.73539139486852636108,.99699771266881425777] 
dist 136=[-.93641441111996709941,.48067404081165552363] 
dist 137=[-1.0687373541491815183 ,.43586379143371037469] 
dist 138=[-1.1762301879012041287 ,.42394913843798567091] 
dist 139=[-1.2781226898146088807 ,.37972606855186446559] 
dist 140=[-1.3687693140928043450 ,.37013590070533414994] 
dist 141=[-1.4313659229431261517 ,.35243493287773203816] 
dist 142=[-1.4854907677207490047 ,.34789279392890573652] 
dist 143=[-1.5423189317215631884 ,.39327249415440784854] 
dist 144=[-1.5913775560680692092 ,.4866121379916810751 ] 
dist 145=[-1.6144846374212961626 ,.56236391987284880832] 
dist 146=[-1.6255761833103763007 ,.63397600441992220304] 
dist 147=[-1.6266538504596186579 ,.69748804091099518741] 
dist 148=[-1.6007591507899367614 ,.74090468759615468304] 
dist 149=[-1.5919500905243788124 ,.77793381965061030244] 
dist 150=[-1.5847610409838385330 ,.81594580126260383192] 
dist 151=[-1.5778901673243716740 ,.84941279915949735636] 
dist 152=[-1.4829999130237007462 ,.86829828672273548356] 
dist 153=[-1.4703461395522363127 ,.88011750235487385307] 
dist 154=[-1.4298363608941048753 ,.88537684592942446026] 
dist 155=[-1.4223520566430905972 ,.88678647545531614949] 
dist 156=[-1.3241515083721746084 ,1.0054949582280225905 ] 
dist 157=[-1.3018707948007641561 ,1.1278649543500707871 ] 
dist 158=[-1.2799118733822719903 ,1.2443845564644397567 ] 
dist 159=[-1.2708906614734578324 ,1.3835392131322918706 ] 
dist 160=[-.97945894401406291138,1.5132991076790504113 ] 
dist 161=[-.94007632034867845552,1.5923119836611906733 ] 
dist 162=[-.8618931511663296078 ,1.6493520262918230905 ] 
dist 163=[-.84107566346026397902,1.6913900849290013404 ] 
dist 164=[-.76447169957977272543,1.7221782574326911397 ] 
dist 165=[-.74693364477794314856,1.7343059936893575373 ] 
dist 166=[-.71600027428928678463,1.7374413219928601913 ] 
dist 167=[-.70808234763677253438,1.7346969020096228174 ] 
dist 168=[-.48947485569198056603,.05155972217883564197] 
dist 169=[-.51423440537596364104,.18500880291193500174] 
dist 170=[-.54190069920054895289,.30110458703187418781] 
dist 171=[-.56934590182069840983,.42408278064820762964] 
dist 172=[-.59322086400213174114,.54227010337431712452] 
dist 173=[-.619069137641018131  ,.63923876931271954865] 
dist 174=[-.65438897702518572219,.73936967213135461117] 
dist 175=[-.68818352054063116909,.870184275402511661  ] 
dist 176=[-.70794162934029636177,.99802356364008528136] 
dist 177=[-.7212055522667173421 ,1.0862758983191930347 ] 
dist 178=[-.72907461790543038255,1.1625533393456618735 ] 
dist 179=[-.73346595602672957103,1.2425819389941388393 ] 
dist 180=[-.73361858553774600446,1.3190376278179406869 ] 
dist 181=[-.7304086294362400564 ,1.3810508836001730086 ] 
dist 182=[-.72753648713851785887,1.4444573818068371394 ] 
dist 183=[-.68229925170159766835,1.5264784849166012348 ] 
dist 184=[-.67384011005523275156,1.6031899829544992843 ] 
dist 185=[-.65380755912926973192,1.6453972247559274353 ] 
dist 186=[-.64681492106364392412,1.6704779398236751385 ] 
dist 187=[-.7705340610513661018 ,1.6788069375847099159 ] 
dist 188=[-.88897398362476428149,1.6805914723908172417 ] 
dist 189=[-.98458769167568770003,1.6795408423633249890 ] 
dist 190=[-1.0819119162333905568 ,1.6762155522088567157 ] 
dist 191=[-1.2071815941073082402 ,1.6709743136708118220 ] 
dist 192=[-1.3286901437974611178 ,1.4768878141518240478 ] 
dist 193=[-1.4109981940045009762 ,1.4472988176257091885 ] 
dist 194=[-1.4804538222786964137 ,1.3918730931927693840 ] 
dist 195=[-1.5506489477260288107 ,1.3764997111673224205 ] 
dist 196=[-1.6160521069595480360 ,1.3185350739753829337 ] 
dist 197=[-1.6663759467220998236 ,1.3030012917518119916 ] 
dist 198=[-1.7153564207737250903 ,1.2739907725973113983 ] 
dist 199=[-1.7753967311288483333 ,1.2649710145381732220 ] 
dist 200=[-1.8303204656605562194 ,.52195683487488193824] 
dist 201=[-1.8588727892465574337 ,.479902120561222976  ] 
dist 202=[-1.8736092313644509917 ,.46848996064986476869] 
dist 203=[-1.8755952701074693656 ,.42505589755933076719] 
dist 204=[-1.8668583676626768726 ,.41547937702052162488] 
dist 205=[-1.8601499498180982935 ,.39630552358806864456] 
dist 206=[-1.8439283005438645852 ,.3908195965489527267 ] 
dist 207=[-1.8357748371206023688 ,-.00179423234238687659] 
dist 208=[-1.6612724202190910078 ,-.03619819969209510713] 
dist 209=[-1.6328625610182480195 ,-.1101603350934197975 ] 
dist 210=[-1.5689076991819433679 ,-.12592934428461667078] 
dist 211=[-1.5483389408069202615 ,-.20290523438194018666] 
dist 212=[-1.4533527822774052178 ,-.21605479071131047365] 
dist 213=[-1.4325432680067004317 ,-.24277964531030000221] 
dist 214=[-1.3809181615558184789 ,-.24636746487928412903] 
dist 215=[-1.3655182354221960056 ,.11708347246252428234] 
dist 216=[-1.3252655976299061048 ,.47928850249596721299] 
dist 217=[-1.3629888127521452880 ,.71805135638891681537] 
dist 218=[-1.3878996828505257907 ,.91241511554401597233] 
dist 219=[-1.4018897807067976832 ,1.0973521509988579859 ] 
dist 220=[-1.4093771190447364726 ,1.2623541800970391428 ] 
dist 221=[-1.4090997385931902069 ,1.3771252270666888080 ] 
dist 222=[-1.4036344411408351621 ,1.4772258282606242811 ] 
dist 223=[-1.3984634050946231857 ,1.5836541993831292897 ] 
dist 224=[-1.3020660592960165414 ,1.6801815771647056243 ] 
dist 225=[-1.2848473782046760362 ,1.7407514720112768022 ] 
dist 226=[-1.2456594002579946921 ,1.7866546261126052266 ] 
dist 227=[-1.2324536434921785107 ,1.8246240129348270499 ] 
dist 228=[-1.1692380261955783193 ,1.8546408940660929283 ] 
dist 229=[-1.1549049473269775534 ,1.8687930933993305873 ] 
dist 230=[-1.1189658044200405433 ,1.8740494183943233297 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 1, 1, 0, 1] 
dist 0=[44.292538963442050979  ,44.292538963442050979  ] 
dist 1=[44.101884970806112908  ,44.367758431278398628  ] 
dist 2=[43.682317386551151564  ,44.477509063134702232  ] 
dist 3=[42.839002356546264649  ,44.581641105208796582  ] 
dist 4=[41.784586535614582675  ,44.705319956161129949  ] 
dist 5=[40.521820719790219446  ,44.831810059924117017  ] 
dist 6=[38.860683590818348777  ,44.947042621589130308  ] 
dist 7=[36.215048654750492718  ,45.075605965351145730  ] 
dist 8=[33.509042968944657770  ,45.255083034395592364  ] 
dist 9=[31.606710074619192305  ,45.421943412823686493  ] 
dist 10=[29.923070738310411687  ,45.500160357146251004  ] 
dist 11=[28.090426488871688800  ,45.527797500761182244  ] 
dist 12=[26.294901508798273297  ,45.493032123450062853  ] 
dist 13=[24.759354485267303565  ,45.389965952611753868  ] 
dist 14=[23.114550319854656231  ,43.383044503751470880  ] 
dist 15=[20.882267417429102946  ,42.979286935185319012  ] 
dist 16=[18.652188113833125538  ,40.504662617266824498  ] 
dist 17=[17.016008695214483301  ,35.545052640151113006  ] 
dist 18=[15.192698662064997732  ,34.686895212985149317  ] 
dist 19=[13.481245611269130926  ,32.553704062755315882  ] 
dist 20=[11.904955503881241166  ,32.245528012166619999  ] 
dist 21=[10.091585392408285508  ,28.916822684674190235  ] 
dist 22=[8.2542091787505516645 ,28.277163771222192842  ] 
dist 23=[5.6799899607148296751 ,27.593231579174025670  ] 
dist 24=[3.0241170432356091181 ,27.463389712710431986  ] 
dist 25=[1.2819624123355925103 ,21.282778401314503965  ] 
dist 26=[-.59575851169350378506,20.503597565207043570  ] 
dist 27=[-2.2986523305010036455 ,18.968452937791266937  ] 
dist 28=[-3.6609404436312449773 ,18.579218602085204299  ] 
dist 29=[-4.9256331737318683364 ,17.239422478569295867  ] 
dist 30=[-6.0399744855771400848 ,16.937598142625125822  ] 
dist 31=[-6.8014682172661362829 ,16.590544740650413189  ] 
dist 32=[-7.4555664757396888031 ,16.505443638676325892  ] 
dist 33=[-8.1409925908712073762 ,4.4173870704574065817 ] 
dist 34=[-8.7498113447193206045 ,3.4354236154138459980 ] 
dist 35=[-9.0977495284161619815 ,1.1928984214012546355 ] 
dist 36=[-9.3246064724221563972 ,.8455484584380326947 ] 
dist 37=[-9.4492342880501970668 ,-1.9347595384423256255 ] 
dist 38=[-9.5176337141953116624 ,-2.4097329513426038567 ] 
dist 39=[-9.5196774723730731763 ,-1.7045320865617410137 ] 
dist 40=[-9.4871204424508795376 ,-.59321676641749379984] 
dist 41=[-9.4540065757025339169 ,.17341770312294408209] 
dist 42=[-8.1470829387394127042 ,.83303334173895043634] 
dist 43=[-8.7077447880010470785 ,1.5175446976302157389 ] 
dist 44=[-9.1743719558813838046 ,2.1645439178143402183 ] 
dist 45=[-9.5477778319259337015 ,2.6745771689970763432 ] 
dist 46=[-9.7359955263471430798 ,3.1814202162691376262 ] 
dist 47=[-9.8364039909364055334 ,3.8157687271143523809 ] 
dist 48=[-9.8589374460988100946 ,4.4203708263870210342 ] 
dist 49=[-6.8840582553439731080 ,4.8085361137701482224 ] 
dist 50=[-6.7326142461936776858 ,5.1121896018912552274 ] 
dist 51=[-6.3458491150675108719 ,5.3795470695442341956 ] 
dist 52=[-6.2792501091688784961 ,5.6028087326289790166 ] 
dist 53=[-5.6374118084988846671 ,5.7304819388081301904 ] 
dist 54=[-5.5095311173985577022 ,5.8123913834029892846 ] 
dist 55=[-5.3474694287039106435 ,5.8529901187577300027 ] 
dist 56=[-5.2896526742481746101 ,5.8680565007946394086 ] 
dist 57=[-4.0583443528634066808 ,5.8480585316507697092 ] 
dist 58=[-3.8962133686969353462 ,1.1320299306625920914 ] 
dist 59=[-3.5543888795009280238 ,1.5406403380223736584 ] 
dist 60=[-3.4615276532006399952 ,1.8794147145206908620 ] 
dist 61=[-3.1001675302992486623 ,2.2127474571419226044 ] 
dist 62=[-3.0293917275983011594 ,2.5181822261355018701 ] 
dist 63=[-2.8719740179587899706 ,2.7455383491866695726 ] 
dist 64=[-2.8321786864509912808 ,2.9599038679678454953 ] 
dist 65=[-.84779033614956616808,3.2134688515183803562 ] 
dist 66=[-.67377863172224669764,3.4495654578317224007 ] 
dist 67=[-.27530669396057286383,3.5941678861492058550 ] 
dist 68=[-.20903547284788798109,3.6999072583415649081 ] 
dist 69=[.2975145309577762556 ,3.7807871621820472819 ] 
dist 70=[.3870390813339569587 ,3.8399017743135837457 ] 
dist 71=[.5263637644412123195 ,3.8587221787196161399 ] 
dist 72=[.5605928224383149549 ,3.8613443427369372790 ] 
dist 73=[.42004613256592747976,3.8557122939556287565 ] 
dist 74=[-.18251259808556331145,3.7519109196346262849 ] 
dist 75=[-.59620806508979275257,3.7278980670843718217 ] 
dist 76=[-.95122154476920099974,3.6464681049490020919 ] 
dist 77=[-1.3195169359329028819 ,3.6456906348551229135 ] 
dist 78=[-1.6686877133014245301 ,3.6582773254415789778 ] 
dist 79=[-1.9473607518407602972 ,3.6572754972762826303 ] 
dist 80=[-2.2281308157904146346 ,3.6489271786912464010 ] 
dist 81=[-2.5856931817546006296 ,3.2967477995341035262 ] 
dist 82=[-2.9308162318031050623 ,2.6318330687007985801 ] 
dist 83=[-3.1619302312435739863 ,2.5406814959350970599 ] 
dist 84=[-3.3541344953580854055 ,2.3601574170023508733 ] 
dist 85=[-3.5439149302423234589 ,2.3117607272846676981 ] 
dist 86=[-3.7180093250359352458 ,2.1321354912015578596 ] 
dist 87=[-3.8475962228797749338 ,2.0906950697953783754 ] 
dist 88=[-3.9696677549363727888 ,2.0152161701822399818 ] 
dist 89=[-4.1137799929474803919 ,1.9949730527653604424 ] 
dist 90=[-4.2440684075424471829 ,.3841295062687705059 ] 
dist 91=[-4.3109467922293894611 ,.278640883829636796  ] 
dist 92=[-4.3443790745865326986 ,.26755032734032768661] 
dist 93=[-4.3497799184919747476 ,.27395824143630333092] 
dist 94=[-4.3238748807360344751 ,.30649022134089426898] 
dist 95=[-4.3066539805693049184 ,.36424233124619783027] 
dist 96=[-4.2730627604916611055 ,.47129425017163258577] 
dist 97=[-4.2571424285745030022 ,.58530241270812317217] 
dist 98=[-3.8162984702979628861 ,.67082501125376539858] 
dist 99=[-3.7467483216946620847 ,.75172418926049466582] 
dist 100=[-3.5970441108750791158 ,.84731376266067173391] 
dist 101=[-3.5507512556465839284 ,.9449236508483397762 ] 
dist 102=[-3.3438520515038444088 ,1.0339036626040787422 ] 
dist 103=[-3.3000214291972124722 ,1.1335658038024407175 ] 
dist 104=[-3.1750985575819556226 ,1.2738272997840468026 ] 
dist 105=[-3.1528732188182631478 ,1.4152703786040289892 ] 
dist 106=[-2.9208269817757381818 ,1.5196591056195593227 ] 
dist 107=[-2.8803808886638117970 ,1.6169116542700718049 ] 
dist 108=[-2.8624770128501083686 ,1.7564471491927886783 ] 
dist 109=[-2.8262951936764224181 ,2.1693589423622285194 ] 
dist 110=[-2.8107528963911679995 ,2.5397502420132503385 ] 
dist 111=[-2.7991595583219477412 ,2.8009589929851297164 ] 
dist 112=[-2.7899317697881881695 ,3.0325837972829644723 ] 
dist 113=[-2.7307760683563629592 ,3.2848523720118737746 ] 
dist 114=[-2.4341326103218006291 ,3.5154292501286852851 ] 
dist 115=[-2.3879180651408823372 ,3.6604448791572916595 ] 
dist 116=[-2.2891510444517328682 ,3.7707562854810934765 ] 
dist 117=[-2.2589335759244253826 ,3.8627703754880915385 ] 
dist 118=[-2.1251028015994239652 ,3.9361361668252140095 ] 
dist 119=[-2.0969969611463146150 ,3.9719915364754013142 ] 
dist 120=[-2.0155194365577326131 ,3.9872910253704224686 ] 
dist 121=[-2.0024070569958315193 ,3.9854582917558470057 ] 
dist 122=[.6627078269343955687 ,2.4920278971587072142 ] 
dist 123=[.67407013877861948316,2.4285405765719720418 ] 
dist 124=[.62172171562421686748,2.4073420647260687244 ] 
dist 125=[.55144672880808534587,2.2735521430743352504 ] 
dist 126=[.393352078563365888  ,2.2415849891015830597 ] 
dist 127=[.17639982805270419686,2.1834878111495237731 ] 
dist 128=[-.33832701632170080176,2.2407426406276809432 ] 
dist 129=[-.90470406661387769153,2.3718477815603143048 ] 
dist 130=[-1.2771285709398812439 ,2.4486800970433137426 ] 
dist 131=[-1.5791312737797761377 ,2.5006313145187775874 ] 
dist 132=[-1.8643662845099794842 ,2.5323879705227183790 ] 
dist 133=[-2.1172815107173812303 ,2.5513392762214815341 ] 
dist 134=[-2.2902532579179969765 ,2.5528091400472954663 ] 
dist 135=[-2.4379264728896941412 ,2.5454793325122989685 ] 
dist 136=[-2.5898375034496272873 ,2.5363299122578520034 ] 
dist 137=[-2.7262356747647258193 ,2.3736997267218550038 ] 
dist 138=[-2.8119785086179229656 ,2.3439206207893848984 ] 
dist 139=[-2.8770856414707879436 ,2.2753360834197910516 ] 
dist 140=[-2.9311095762497568724 ,2.2518817482368823002 ] 
dist 141=[-2.9739131417715268175 ,2.1384185059447543490 ] 
dist 142=[-2.9942306265793172908 ,2.1124636136866433629 ] 
dist 143=[-3.0019811145635466020 ,2.0486731697663676061 ] 
dist 144=[-2.9980229946667896623 ,2.0268062904786103028 ] 
dist 145=[-.41807032884567137764,.66290145740872209753] 
dist 146=[-.5377947972387248829 ,.59834632766901578994] 
dist 147=[-.67758407605905037769,.58671798066139081442] 
dist 148=[-.81980838048912387191,.48861327233610298213] 
dist 149=[-.94925563443389566347,.46955289836369362441] 
dist 150=[-1.0943206172273752751 ,.44223967608388026212] 
dist 151=[-1.2989022237138122526 ,.43395851469459195956] 
dist 152=[-1.4995632948070385040 ,-.67908299167767936654] 
dist 153=[-1.6289750094430701897 ,-.84880559915196671522] 
dist 154=[-1.7311515443745368919 ,-.87159136129085762259] 
dist 155=[-1.8230710730170231112 ,-.88921431679037706865] 
dist 156=[-1.9015094681363558176 ,-.87713538049393074189] 
dist 157=[-1.9498601586315788534 ,-.85128235273114145873] 
dist 158=[-1.9854953541555372879 ,-.80707089987673078613] 
dist 159=[-2.0131650553405175960 ,-.74090086373824680965] 
dist 160=[-2.0324946716162259126 ,-.62738050445455995015] 
dist 161=[-2.0356920701007784379 ,-.50844233061867059237] 
dist 162=[-2.0310158939661473859 ,-.42064106328370854568] 
dist 163=[-2.0257872903502860607 ,-.33874477567257962464] 
dist 164=[-1.9651714380493403337 ,-.24337812749739707588] 
dist 165=[-1.9474854755343137466 ,-.14652397516787977143] 
dist 166=[-1.9268384982912528502 ,-.05868678915439053876] 
dist 167=[-1.9161435303437793478 ,.03947235312564727506] 
dist 168=[-1.5908692773790118647 ,.25044489100866017409] 
dist 169=[-1.5562640682242546739 ,.51282073792159830232] 
dist 170=[-1.4649712207713445104 ,.73232185930418538513] 
dist 171=[-1.4494743101153797821 ,.95110793974442810104] 
dist 172=[-1.2859270735363779414 ,1.1530371646655175240 ] 
dist 173=[-1.2522438971678461186 ,1.3052348763725287888 ] 
dist 174=[-1.2134950335169470728 ,1.4503558977795123854 ] 
dist 175=[-1.1996863311117045305 ,1.6240304669150560120 ] 
dist 176=[-.83930364064064008349,1.7862781693985064760 ] 
dist 177=[-.79173082243071962042,1.8857757598160626726 ] 
dist 178=[-.69405106148065463005,1.9584890012755245144 ] 
dist 179=[-.66788557558482617929,2.0137962269191706048 ] 
dist 180=[-.56911830412014378964,2.0553056815295558133 ] 
dist 181=[-.54849312991000059017,2.0729292640752907333 ] 
dist 182=[-.50781871433751350277,2.0790965273625974587 ] 
dist 183=[-.49692346111741777909,2.0768379560414004694 ] 
dist 184=[.12095173456708654305,1.7446943477142061161 ] 
dist 185=[.15659045037175671691,1.7576651230139158901 ] 
dist 186=[.23612761701840316214,1.7591378966868449201 ] 
dist 187=[.24949899663736661005,1.7520135075205992028 ] 
dist 188=[.34062111660153625656,1.7469577171205322693 ] 
dist 189=[.35546058870119697884,1.6901837805044938615 ] 
dist 190=[.38247490890139792303,1.6740805689917312294 ] 
dist 191=[.38781531747164279472,1.6550157779152964653 ] 
dist 192=[.07412931429734722654,1.6454353945930179992 ] 
dist 193=[-.27032526765376896585,1.4374104085014676371 ] 
dist 194=[-.50142016571981997613,1.4183196006266120491 ] 
dist 195=[-.69401877689904222544,1.3629372480905255869 ] 
dist 196=[-.88477421905075951776,1.3538048595126631611 ] 
dist 197=[-1.0600306701698390883 ,1.2265883053989145401 ] 
dist 198=[-1.1907483895598950056 ,1.1993392876702037087 ] 
dist 199=[-1.3140399315761113624 ,1.0667856391567793509 ] 
dist 200=[-1.4596466244389425370 ,.76720280131764476761] 
dist 201=[-1.5946579462077212595 ,.50292382185426260588] 
dist 202=[-1.6756466006789042221 ,.46786751598984765409] 
dist 203=[-1.7326677213081361923 ,.45241928438551795268] 
dist 204=[-1.7719868408207339330 ,.41394820366734219264] 
dist 205=[-1.8004225712002917981 ,.40575800556103177233] 
dist 206=[-1.8139911899200096312 ,.39071841111678050418] 
dist 207=[-1.8192818460548811338 ,.3865958353791605767 ] 
dist 208=[-1.8175482870626188473 ,.30919611157955243048] 
dist 209=[-.23797888634753458113,.29825492205627664332] 
dist 210=[-.28035634020798301097,.27193351387304055487] 
dist 211=[-.32894967115651508477,.2666273733531270557 ] 
dist 212=[-.37790021889577485175,.22734603749448674881] 
dist 213=[-.42170394751287180877,.21961620877267595686] 
dist 214=[-.47018829019556614411,.20695253592169091527] 
dist 215=[-.53782697549228441519,.20360114847492139517] 
dist 216=[-.60385738502703785958,-.21296609068551781442] 
dist 217=[-.64592045992230973473,-.20898270380546702983] 
dist 218=[-.6785371827396200287 ,-.19908377702103895568] 
dist 219=[-.706851573945145224  ,-.18294164782112112579] 
dist 220=[-.73027719811711381609,-.15403148170314748258] 
dist 221=[-.74337479441384463102,-.1190774924783127819 ] 
dist 222=[-.7514318855314912856 ,-.07880473781728291532] 
dist 223=[-.75473260466484401269,-.02686672134651853624] 
dist 224=[-.75518901602698475612,.05466199089190892144] 
dist 225=[-.75400157866157561173,.13750455921651821435] 
dist 226=[-.74762982536769541468,.19468832515374667969] 
dist 227=[-.74425029109894934081,.24410009433913382808] 
dist 228=[-.71832677177009530647,.29591233067665471089] 
dist 229=[-.71124295710235780608,.34538257069706280308] 
dist 230=[-.70030882644515645078,.38544376104265789773] 
dist 231=[-.69627035523277645065,.42633786219299665139] 
dist 232=[-.49450934982203988599,.47913366495930812738] 
dist 233=[-.47212742746890637022,.53042570197990408994] 
dist 234=[-.41922974091941984293,.56531591038029328423] 
dist 235=[-.40874522523265188394,.59491767906769973107] 
dist 236=[-.33372079221265975432,.62509513484323036997] 
dist 237=[-.3193427415780468619 ,.65338006658067441375] 
dist 238=[-.29484860953202785598,.67542579084908251066] 
dist 239=[-.2888303542204090918 ,.69715253721263059227] 
dist 240=[-.17864030449827868982,.72416401484331952389] 
dist 241=[-.16410550347091147094,.74907005173902354086] 
dist 242=[-.12881226675342905994,.76239058053857122948] 
dist 243=[-.12372583741443819412,.76979137723719313367] 
dist 244=[-.07250106108067374615,.77106209178709281001] 
dist 245=[-.06311598926507410883,.76959224493650222101] 
dist 246=[-.05209377922245947297,.76729051701441970771] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 0, 1] 
dist 0=[38.298429263378736584  ,38.298429263378736584  ] 
dist 1=[37.504932123498676418  ,38.856624023096519262  ] 
dist 2=[36.180250998177054705  ,39.241482430639712297  ] 
dist 3=[34.807165389820179348  ,39.532811622412701706  ] 
dist 4=[33.820252493368483050  ,39.717409699109645011  ] 
dist 5=[32.924438361008377839  ,39.859320016853394221  ] 
dist 6=[31.914962314721382542  ,39.983500703014507005  ] 
dist 7=[30.905379866115333313  ,40.061492083622555795  ] 
dist 8=[30.008909998973323312  ,40.042691675281079253  ] 
dist 9=[29.019873510520855981  ,39.471632311153605557  ] 
dist 10=[27.640129566373876484  ,39.337377971030543669  ] 
dist 11=[26.243114156946650287  ,39.125875088295039894  ] 
dist 12=[25.184875172742546544  ,39.045852262174239317  ] 
dist 13=[24.166806463389674210  ,38.739537514306170316  ] 
dist 14=[22.930023363123883333  ,38.637328950355574826  ] 
dist 15=[21.638652986435412936  ,38.397620342137415700  ] 
dist 16=[20.402145677309702033  ,38.252087312128036482  ] 
dist 17=[18.961260252883095788  ,29.823152285568137127  ] 
dist 18=[16.852565007230646212  ,29.060973343928145574  ] 
dist 19=[14.750067873264044486  ,27.184360145865621696  ] 
dist 20=[13.333885026171865572  ,26.911630503485162096  ] 
dist 21=[12.140226040903324635  ,24.041317296552295278  ] 
dist 22=[10.927370940445840273  ,23.493461802418300424  ] 
dist 23=[9.7854734128990514903 ,22.895500339777105663  ] 
dist 24=[8.8754833922512046908 ,22.778188479173506117  ] 
dist 25=[7.9550362643041547382 ,17.600389466128627892  ] 
dist 26=[6.7712830901881628194 ,16.947152288800130596  ] 
dist 27=[5.6127408506643573621 ,15.657479856444055724  ] 
dist 28=[4.3538387911721684742 ,15.329914871454770943  ] 
dist 29=[2.5796471201114947919 ,14.197148168034463423  ] 
dist 30=[.03991778772103770321,13.943911170359838141  ] 
dist 31=[-2.4573297682600327300 ,13.638216657511625026  ] 
dist 32=[-4.0618681302782111548 ,13.553037681230176897  ] 
dist 33=[-5.3293654603032789646 ,4.0811153991803057398 ] 
dist 34=[-6.4794743875759902951 ,4.0285401749833627701 ] 
dist 35=[-7.4752436276496211253 ,1.8204769791832014375 ] 
dist 36=[-8.1259646487080222094 ,1.6083363767067518550 ] 
dist 37=[-8.6536169718392355092 ,1.1475220333507208589 ] 
dist 38=[-9.1578189190664696056 ,1.0577756005406785561 ] 
dist 39=[-9.5951381437873068629 ,.54612735784472294868] 
dist 40=[-9.8554404041259845755 ,.45858177816204611119] 
dist 41=[-10.039066555645749993  ,.28305189207390008266] 
dist 42=[-10.169512455509189767  ,.24010840260629676469] 
dist 43=[-10.258147339505795580  ,-.10007047927475552735] 
dist 44=[-10.274470220583579220  ,-.15415691762491777801] 
dist 45=[-10.253873170934112457  ,-.22459775112504863806] 
dist 46=[-10.225743406499307879  ,-.23887552503590958106] 
dist 47=[-8.3597698183373894507 ,-.23222028447162203095] 
dist 48=[-8.3795796098661186731 ,-.19443755923359820866] 
dist 49=[-6.8380614650436528095 ,-.12663880883719046196] 
dist 50=[-6.7328797006003709773 ,0                     ] 
dist 51=[-4.9400671534945445764 ,-1.4010821735154669227 ] 
dist 52=[-4.8775075327257234571 ,-.76904170128605106317] 
dist 53=[-4.2548944750726322635 ,-.11648973788182876883] 
dist 54=[-4.1330682383689928152 ,.73563113745281683293] 
dist 55=[-3.9842717165800460571 ,1.5681647810816813146 ] 
dist 56=[-3.9374055514199281825 ,2.1425975146722267290 ] 
dist 57=[-2.7913442451323617568 ,2.6389039016956000146 ] 
dist 58=[-2.6440098126660792714 ,3.1596092790916528228 ] 
dist 59=[-2.3342956686649092003 ,3.6575623805224668870 ] 
dist 60=[-2.2514761959666897312 ,4.0631217026374550859 ] 
dist 61=[-1.9359641292301838939 ,4.4798587673873375774 ] 
dist 62=[-1.8744253591844298836 ,5.0226219950067413967 ] 
dist 63=[-1.7467686920837121881 ,5.5401210035949946258 ] 
dist 64=[-1.7127992051822083000 ,5.8559974958200132455 ] 
dist 65=[.02189189133352620644,6.0858838262859463916 ] 
dist 66=[.17704951171673196486,6.2599055509191102248 ] 
dist 67=[.5034414631824360627 ,6.3895493754948900375 ] 
dist 68=[.57563565240930365755,6.4421502893579322522 ] 
dist 69=[.88927378041011667866,6.4598697295360357924 ] 
dist 70=[.94490826950574193015,6.4503208421910351262 ] 
dist 71=[1.0425479072325559085 ,6.1811006498070780179 ] 
dist 72=[1.0613985617392217106 ,6.1240758504519636840 ] 
dist 73=[1.0886471920261527818 ,6.0046504618135622720 ] 
dist 74=[1.0644554672373066542 ,5.9630487084122662970 ] 
dist 75=[1.0091521732501583793 ,5.7592705319274480158 ] 
dist 76=[.8972490222529123422 ,5.7122679474667344782 ] 
dist 77=[.7576834639645795099 ,5.5569640430380096593 ] 
dist 78=[.5919105610527455825 ,5.5336214539056621151 ] 
dist 79=[.02827488520975116599,3.5357316666818230313 ] 
dist 80=[-.72356687815581412432,3.4577119322982262870 ] 
dist 81=[-1.3487965957500382198 ,2.9242098152909137460 ] 
dist 82=[-1.9659657210954940162 ,2.8609126502015324147 ] 
dist 83=[-2.5318024974609428981 ,2.1919338835539520350 ] 
dist 84=[-2.9520813099563521499 ,2.0655303422986314633 ] 
dist 85=[-3.3468649225620091030 ,1.9240388580302989848 ] 
dist 86=[-3.8109143455835271526 ,1.8968489147026651702 ] 
dist 87=[-4.2423212613196578698 ,.75079243405319448391] 
dist 88=[-4.5067695487392954480 ,.6101833271706052561 ] 
dist 89=[-4.6999574272450759404 ,.3218765512568994376 ] 
dist 90=[-4.8468253499790335879 ,.2481258069531571605 ] 
dist 91=[-4.9587711481311027805 ,-.0134593899057414114 ] 
dist 92=[-5.0125208165507574196 ,-.0663455348103901658 ] 
dist 93=[-5.0341006643311365023 ,-.0030216372960043241 ] 
dist 94=[-5.0350307613353479769 ,.09133870271739815243] 
dist 95=[-2.1685695532692714590 ,.22319507211913801046] 
dist 96=[-2.4119412703629126469 ,.44047532632482940596] 
dist 97=[-2.6453196369327541078 ,.66375293112179824242] 
dist 98=[-2.7857531704178686030 ,.88695419290667292732] 
dist 99=[-2.8854540188305425387 ,1.1005149366630822876 ] 
dist 100=[-2.9561450923952883248 ,1.3142527682458850323 ] 
dist 101=[-3.0079371953740293871 ,1.5117764566434227842 ] 
dist 102=[-3.0321497184773494523 ,1.6606169189643240424 ] 
dist 103=[-3.0409352593439355874 ,1.8023124800713768259 ] 
dist 104=[-3.0391416834301550522 ,1.9713112247334912099 ] 
dist 105=[-2.6689110774205634418 ,2.1285062820748876087 ] 
dist 106=[-2.6183225914507265410 ,2.2230843786205884397 ] 
dist 107=[-2.5486108807255571152 ,2.2898819524056434597 ] 
dist 108=[-2.4771884497660326764 ,2.3361881898459100551 ] 
dist 109=[-1.9967807240656909690 ,2.3679723814654435927 ] 
dist 110=[-1.7035730438284115245 ,2.3768102941531654011 ] 
dist 111=[-1.2696213209084865588 ,2.3754738316132838776 ] 
dist 112=[-1.2523310383705219460 ,2.3684718000834396488 ] 
dist 113=[-.49595059287134255563,.15219237823542089232] 
dist 114=[-.42274524974388261361,.23189445755118640309] 
dist 115=[-.25154003972556620259,.30432495532538646838] 
dist 116=[-.22507853281397193992,.35712658902793103105] 
dist 117=[-.00601988172538201671,.40578429160939641089] 
dist 118=[.00149814101225114878,.46167352184037193977] 
dist 119=[.09592777687062094550,.51353763548565739662] 
dist 120=[.11043087488796226812,.5461212529330514662 ] 
dist 121=[.16688413192663852723,.57090519388935640345] 
dist 122=[.17434018801141953092,.59161446973171605783] 
dist 123=[.199128119122287351  ,.60817460030568931113] 
dist 124=[.2040234051724335499 ,.61890794713079971122] 
dist 125=[.20640169569885297563,.66490560222624934972] 
dist 126=[.20266667033312323773,.69519905980007007666] 
dist 127=[.19735932195006651802,.71989380922493898903] 
dist 128=[.1926133983926612579 ,.74355346723264564322] 
dist 129=[.1874034617826532084 ,.76395850863888015175] 
dist 130=[.18023327213442915924,.77565940205154822659] 
dist 131=[.17237120147677641579,.78331802236954855312] 
dist 132=[.16439357699714334116,.78757005138663874141] 
dist 133=[.15480353883950593022,.789392599587844178  ] 
dist 134=[.14049828785095265762,.78840698243233532166] 
dist 135=[.12568779991857845528,.78374255797660846629] 
dist 136=[.11407702636042139902,.78051028074271346709] 
dist 137=[.07982609891167845757,.75878341548122661005] 
dist 138=[.00872495266167376773,.75321951867836908418] 
dist 139=[-.06250881507240675180,.73765052964149828233] 
dist 140=[-.15263465569601573548,.73233992319456671714] 
dist 141=[-.24812222502938366164,.69795977989653280824] 
dist 142=[-.34076693244463553568,.68966234812843957136] 
dist 143=[-.44918456889095675095,.67478533280444997328] 
dist 144=[-.60765025012156619242,.67036979309502889761] 
dist 145=[-.76482137943223186073,.09065114032066702052] 
dist 146=[-.86807246313471556567,.08901130962189206990] 
dist 147=[-.95172513729141204036,.07492047870312672133] 
dist 148=[-1.0306507010962084391 ,.07208393736345264731] 
dist 149=[-1.1006192789391616127 ,.06826196480596680555] 
dist 150=[-1.1485124877440282079 ,.06697349350012035069] 
dist 151=[-1.1894750223962675612 ,.03931190694582543200] 
dist 152=[-1.2317756788769571092 ,.03556823132530235616] 
dist 153=[-1.2678788426826829512 ,.02768386716927783312] 
dist 154=[-1.2840988669379360857 ,.02549520945315453514] 
dist 155=[-1.2915773794152775676 ,.01671686686403246109] 
dist 156=[-1.2927738633989981393 ,.01498201044254042321] 
dist 157=[-1.2668058313127740692 ,.01066591026170909079] 
dist 158=[-1.2593521509358001327 ,.00982476763181893733] 
dist 159=[-1.2542221488880622448 ,-.08767791655832600544] 
dist 160=[-1.2509130845898674004 ,-.05325153794422061241] 
dist 161=[-1.1370156593765513411 ,.19196539322404593493] 
dist 162=[-1.1228326394465190841 ,.35778616997634787722] 
dist 163=[-1.0818279167932060690 ,.4968231171825855527 ] 
dist 164=[-1.0743025184116247851 ,.63586009574024996524] 
dist 165=[-.98765167289777293124,.7644274813829073693 ] 
dist 166=[-.9686837351523757795 ,.86166627829499047753] 
dist 167=[-.94809491604072841151,.95468062242578247365] 
dist 168=[-.93958538287209030973,1.0663823536351445872 ] 
dist 169=[-.7105316647167916299 ,1.1708754358178682638 ] 
dist 170=[-.67963724525658869196,1.2351102397970472885 ] 
dist 171=[-.61713252281688433424,1.2822184115312773136 ] 
dist 172=[-.60032359066300982665,1.3183358904521824720 ] 
dist 173=[-.53705028827803289058,1.3452535968676101141 ] 
dist 174=[-.52323452762667832923,1.3556331942762020135 ] 
dist 175=[-.49658666212783579227,1.3589210809479733416 ] 
dist 176=[-.48933346977267592063,1.3575265192888519373 ] 
dist 177=[-.36098658288859527197,.62232213262145673826] 
dist 178=[-.3964614269797929567 ,.64301139018632612658] 
dist 179=[-.42959393926914851648,.65887204454844457861] 
dist 180=[-.45520159927556612235,.66561041194187833933] 
dist 181=[-.48022638658066820457,.66842483024893515546] 
dist 182=[-.51103168516781725527,.66861704921739510066] 
dist 183=[-.54022829376590573567,.64855637719186844815] 
dist 184=[-.55883062939006169734,.64364566059150899503] 
dist 185=[-.57325121502248906344,.7311362516439241495 ] 
dist 186=[-.58575300158214647311,.79209652050527510356] 
dist 187=[-.5960759409567919039 ,.84420838796343357348] 
dist 188=[-.60179773978815375121,.89797235086934132252] 
dist 189=[-.60524763030808732307,.94877754527787551765] 
dist 190=[-.60649993307099431004,.98907680865560828958] 
dist 191=[-.60607789608417644419,1.0294603480564227773 ] 
dist 192=[-.60483720236443894301,1.0806037028133554808 ] 
dist 193=[-.5989959397263238449 ,1.1279281710013776657 ] 
dist 194=[-.59612939331966628938,1.1530642997996467465 ] 
dist 195=[-.57407476224539424238,1.1669117270501148367 ] 
dist 196=[-.56812695330344087939,1.1700237745517294523 ] 
dist 197=[-.59486046845167379482,1.1663863861940811305 ] 
dist 198=[-.66395292042027805466,1.1640568630055695949 ] 
dist 199=[-.73458951789346866149,1.1612000112479821873 ] 
dist 200=[-.82592365482960752571,1.1569486836586608858 ] 
dist 201=[-.91471632926303723122,1.0088722343353622334 ] 
dist 202=[-.97520616942233365618,.98677449605251677033] 
dist 203=[-1.0266227970948769857 ,.94566065603135958697] 
dist 204=[-1.0791903699925358276 ,.93449166514577298317] 
dist 205=[-1.1285546627720570626 ,.89366263087288455382] 
dist 206=[-1.1671822207137008573 ,.88254003242874080191] 
dist 207=[-1.2053932244938948568 ,.864101618292837785  ] 
dist 208=[-1.2530948057741615639 ,.85826204034020019544] 
dist 209=[-1.2971661832409137493 ,.32078676171760420375] 
dist 210=[-1.3208833598497594854 ,.37849074234401828947] 
dist 211=[-1.3342612193447793629 ,.43039601170611966012] 
dist 212=[-1.3370517876996452166 ,.46722423453067292796] 
dist 213=[-1.3349866557994590841 ,.50010434322468775253] 
dist 214=[-1.3312064487231182785 ,.53624661865926670322] 
dist 215=[-1.3209551687287762017 ,.56900635807110763368] 
dist 216=[-1.3152888519698515272 ,.58838161259709174619] 
dist 217=[-1.1984810955067224350 ,.60168363411853195896] 
dist 218=[-1.1791151669860637127 ,.61019590668362815743] 
dist 219=[-1.1353316246712119560 ,.6155430386056756806 ] 
dist 220=[-1.1210981909242386183 ,.61620834925441294429] 
dist 221=[-1.0548048233040558444 ,.61493200709399484488] 
dist 222=[-1.0401589889272068719 ,.612833287953549788  ] 
dist 223=[-1.0039815799183987569 ,-.07337429132392085161] 
dist 224=[-.99280810814452130041,.06801129745091490057] 
dist 225=[-.94909643022275953869,.32661844169432645058] 
dist 226=[-.9719717566767605736 ,.49704223231001577707] 
dist 227=[-.98623823563279691356,.63572282159910921163] 
dist 228=[-.99251619275137416675,.76759175172352215891] 
dist 229=[-.99467080600749385958,.88518981281966927602] 
dist 230=[-.99317955869635550305,.96689233856912270831] 
dist 231=[-.98807168946679384176,1.0380517434411234917 ] 
dist 232=[-.98445155439059285673,1.1135550833661543303 ] 
dist 233=[-.90429552046145559225,1.1820725703153844776 ] 
dist 234=[-.89072600609154027745,1.2253401858544225991 ] 
dist 235=[-.86065375602820175396,1.2584510950745624292 ] 
dist 236=[-.85087347850315827871,1.2864169593309687728 ] 
dist 237=[-.80530570490442595511,1.3089752924339368205 ] 
dist 238=[-.7952350343307151465 ,1.3204960883114870973 ] 
dist 239=[-.76847278691837791349,1.3261507576963613867 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 1, 1, 2] 
dist 0=[44.164342803093681965  ,44.164342803093681965  ] 
dist 1=[43.379984096817578841  ,44.762956908147323095  ] 
dist 2=[42.135995885485645450  ,45.264738342658177132  ] 
dist 3=[40.688870535535445482  ,45.682243557349539408  ] 
dist 4=[39.093016353277804671  ,45.944289406639290552  ] 
dist 5=[37.078754331243007973  ,46.141930725524650560  ] 
dist 6=[33.960353183963563514  ,46.302638136626714109  ] 
dist 7=[30.797787928144662345  ,46.426962164898305748  ] 
dist 8=[28.606983501850367555  ,46.479537726848264136  ] 
dist 9=[26.702664391765885226  ,46.489702792292139252  ] 
dist 10=[24.684025192957182230  ,46.444949114170186090  ] 
dist 11=[22.738871145964083201  ,46.378314899514039086  ] 
dist 12=[21.127773012000263581  ,46.301199241566643032  ] 
dist 13=[19.447052273058615746  ,46.202057775999999087  ] 
dist 14=[17.223291139812184107  ,45.946742333947110757  ] 
dist 15=[15.026985304971559655  ,43.878711295825182971  ] 
dist 16=[13.455657122595778489  ,42.421888942743836452  ] 
dist 17=[12.034177743530429952  ,35.835337344140117187  ] 
dist 18=[10.436115293859649759  ,34.956079153506191005  ] 
dist 19=[8.8363220608767335191 ,32.933855786964606876  ] 
dist 20=[7.4074397228091310327 ,32.520900946944337487  ] 
dist 21=[5.8211215304759140357 ,29.826612187147426998  ] 
dist 22=[3.5913193368668736806 ,29.318530086609280534  ] 
dist 23=[1.4060585175151163889 ,28.392102078919168422  ] 
dist 24=[-.0024238386292048995 ,28.166764243467128707  ] 
dist 25=[-1.1214922118752993304 ,24.656844877799694063  ] 
dist 26=[-2.1498090042746564081 ,24.175081190834747554  ] 
dist 27=[-3.0509432695584188273 ,23.066356493058104348  ] 
dist 28=[-3.6617334182462898192 ,22.854433709616200132  ] 
dist 29=[-4.1826472820756229079 ,20.919212632370037900  ] 
dist 30=[-4.7249096374460495827 ,19.967873775957127048  ] 
dist 31=[-5.2043346754040371556 ,16.587903558277811762  ] 
dist 32=[-5.4740193497380945807 ,15.181562899086213632  ] 
dist 33=[-5.9132945986838932069 ,-.4350868172189316970 ] 
dist 34=[-7.0993433131913103388 ,-.5974796006694761239 ] 
dist 35=[-8.1981076822114195079 ,-2.9910754153392598521 ] 
dist 36=[-8.8781604015337715032 ,-2.6097354916553389156 ] 
dist 37=[-9.3845574562745487448 ,-1.9440198644053074232 ] 
dist 38=[-9.7895562017686052582 ,-.88374404676871363935] 
dist 39=[-10.102816081316773245  ,.1904822818910447926 ] 
dist 40=[-10.242670344434150561  ,.9120339112150342307 ] 
dist 41=[-10.306191853649119450  ,1.5121994434777378321 ] 
dist 42=[-10.314449152303501057  ,2.1022925732058025429 ] 
dist 43=[-6.8985007393244923871 ,2.6398563493547610667 ] 
dist 44=[-6.6650145440894749136 ,3.0305262047469208689 ] 
dist 45=[-6.0853988808709355693 ,3.3880979566068913269 ] 
dist 46=[-5.9874961037679557462 ,3.7936992404527722630 ] 
dist 47=[-5.0884584321796149719 ,4.1673093286022489919 ] 
dist 48=[-4.9151968793234978242 ,4.3972138673233473645 ] 
dist 49=[-4.6846302425183372419 ,4.5657288532233302452 ] 
dist 50=[-4.6094289301575216151 ,4.6942339416400330356 ] 
dist 51=[-3.0987699946434672112 ,4.7870636857690441816 ] 
dist 52=[-2.9046988451972396874 ,4.8132476695231175008 ] 
dist 53=[-2.4810512525868132154 ,4.8159549861093534484 ] 
dist 54=[-2.3841441655518568399 ,4.8150291676382228473 ] 
dist 55=[-1.9050715337725736783 ,3.5558396899567423507 ] 
dist 56=[-1.8206689844874205689 ,3.4322176298511896586 ] 
dist 57=[-1.6268750934623767224 ,3.1355761083394412443 ] 
dist 58=[-1.5936311477179138554 ,3.0732659869887486596 ] 
dist 59=[.16387987789150131565,2.6356685829202599789 ] 
dist 60=[.3321986225354506091 ,2.7887412163281089597 ] 
dist 61=[.66671676116220039071,3.2028928146800203575 ] 
dist 62=[.74731092186836175345,3.5929135376540089636 ] 
dist 63=[.8981133109697098047 ,3.9389993171987607099 ] 
dist 64=[.5550895367319807770 ,4.1776900667587000838 ] 
dist 65=[.2322150130479860627 ,4.3842346633208866662 ] 
dist 66=[-.1479555615993866214 ,4.6019647751082169921 ] 
dist 67=[-.5364008953533744895 ,4.7932399911405423566 ] 
dist 68=[-.8923653639246898709 ,4.8941303332635733525 ] 
dist 69=[-1.2932575361093268188 ,4.9487607576625714260 ] 
dist 70=[-1.8611511207721384094 ,4.9608459558677674050 ] 
dist 71=[-2.4187532822178034501 ,4.9437482775212775301 ] 
dist 72=[-2.7785724113795325906 ,4.9310724109842866376 ] 
dist 73=[-3.0630520289795244986 ,4.9147286999203231548 ] 
dist 74=[-3.3198327257453521779 ,4.8975539987711557989 ] 
dist 75=[-3.5397570752126922214 ,.73623597621946610126] 
dist 76=[-3.6770788394757562879 ,.4856762463980109416 ] 
dist 77=[-3.7805069081166925640 ,.2591132977360183785 ] 
dist 78=[-3.8651132902768506010 ,.3588261803612422700 ] 
dist 79=[-3.9315962352705643472 ,.4725960471989746499 ] 
dist 80=[-3.9626597095172872252 ,.5774653199744975212 ] 
dist 81=[-3.9738914802560096637 ,.6958086122284897836 ] 
dist 82=[-3.9705715684241152798 ,.8633986805731656433 ] 
dist 83=[-3.9360240505369044551 ,1.0498081354012955516 ] 
dist 84=[-3.9214057931606378908 ,1.2432914418182357142 ] 
dist 85=[-3.8614563745073329073 ,1.4790721606863269694 ] 
dist 86=[-3.8453812454369744927 ,1.8343391972572785760 ] 
dist 87=[-3.5112494803223783787 ,2.1883544834481987220 ] 
dist 88=[-3.5039675878297743091 ,2.4191469406450577164 ] 
dist 89=[-3.5878186207434421098 ,2.6039802045500166978 ] 
dist 90=[-3.6945178430409905400 ,2.7745458628689254026 ] 
dist 91=[-3.7849958975551317517 ,2.9229985355378207649 ] 
dist 92=[-3.8226100058759954511 ,3.0195679566894768607 ] 
dist 93=[-3.8369779423920127855 ,3.0966965548929897026 ] 
dist 94=[-3.8345481145950503836 ,3.1675553099006947317 ] 
dist 95=[-3.7518650338631551150 ,3.2227705864464137678 ] 
dist 96=[-3.7230863025532490054 ,3.2374574783268251632 ] 
dist 97=[-3.6986811046166862162 ,3.2382867306981530800 ] 
dist 98=[-3.6794688804760133720 ,3.3102340338198905396 ] 
dist 99=[-3.1087302936945955114 ,3.5561083221508488534 ] 
dist 100=[-3.0262788538663037888 ,3.6971544814894548171 ] 
dist 101=[-2.8636108803512038194 ,3.7884027371466468282 ] 
dist 102=[-2.8185790559922183074 ,3.8355129622421773329 ] 
dist 103=[-2.6451436416904491593 ,3.8626991363298945903 ] 
dist 104=[-2.6040445306866587501 ,3.8744224142895215805 ] 
dist 105=[-2.5207115599828692243 ,3.8770261478690209296 ] 
dist 106=[-2.4951674095380584163 ,3.8678131499388141459 ] 
dist 107=[-2.5788648716876429860 ,3.3664066266469285499 ] 
dist 108=[-2.8136352885958731214 ,3.3480000412859284812 ] 
dist 109=[-3.0231634981590332584 ,3.3171309478065407854 ] 
dist 110=[-3.2531426738915990503 ,3.3035909270039153305 ] 
dist 111=[-3.4616295226107976423 ,2.8963353016463322032 ] 
dist 112=[-3.5853633241268114958 ,2.8340385262548632035 ] 
dist 113=[-3.6707354430689569346 ,2.7013892594303149388 ] 
dist 114=[-3.7261001196337202879 ,2.6613329666305947382 ] 
dist 115=[-3.7607489948051335158 ,2.4861610261574279559 ] 
dist 116=[-3.7654199528914214191 ,2.4498159329608048178 ] 
dist 117=[-3.7542127038598625811 ,2.3430792878755931267 ] 
dist 118=[-3.7414043749541226484 ,2.2071001911725122240 ] 
dist 119=[.43260449624848619706,.74265245395385118387] 
dist 120=[.35950059823314308732,.76462443148214845653] 
dist 121=[.2962501936277984249 ,.77780788369048777623] 
dist 122=[.22983989987368789946,.78257715723023829806] 
dist 123=[.16640638979150478558,.7839667015523720184 ] 
dist 124=[.11503519440231485979,.78365684804534552145] 
dist 125=[.06260147355690239048,.78212419706700592258] 
dist 126=[-.00508085035530292951,.77965921843939596381] 
dist 127=[-.07084087808450958828,.77418769869554024517] 
dist 128=[-.11560364219543250621,.77077178982719011886] 
dist 129=[-.15362797163288707961,.76310423642287010952] 
dist 130=[-.1924894307200385157 ,.75962820402737552565] 
dist 131=[-.22901167861679737897,.74058462625634043563] 
dist 132=[-.25770194561062319617,.73481168048949339822] 
dist 133=[-.28622672088433468842,.72380107497927379595] 
dist 134=[-.3220991584755620494 ,.719952872721378743  ] 
dist 135=[-.35637659332492192039,.70156626473338001067] 
dist 136=[-.37853393351448744179,.69670795511700803822] 
dist 137=[-.42236387730817316145,.68213292639282265175] 
dist 138=[-.61096455845687041052,.67804537053636249013] 
dist 139=[-.79827980277504708742,-.22290500297611803995] 
dist 140=[-.92190304941555232245,-.20870378923917045836] 
dist 141=[-1.0226970455251180295 ,-.18819373441160903942] 
dist 142=[-1.1188673611405989400 ,-.1537220535073160123 ] 
dist 143=[-1.2048542775753090943 ,-.11651284201086971745] 
dist 144=[-1.2649923061863452672 ,-.08507127677002558694] 
dist 145=[-1.3177969477164228205 ,-.05181889612081308195] 
dist 146=[-1.3745082035111157240 ,-.00737478580679580425] 
dist 147=[-1.4241962889956641090 ,.04090729304953975795] 
dist 148=[-1.4489618656140510231 ,.08948513394346045876] 
dist 149=[-1.4616469236290447619 ,.1476341748398001922 ] 
dist 150=[-1.4630967634526091608 ,.23413107057389038942] 
dist 151=[-1.4477094466261157123 ,.32038781753961297519] 
dist 152=[-1.4415162778208775816 ,.37757948838504148102] 
dist 153=[-1.4358000240265170983 ,.42449560404161312487] 
dist 154=[-1.4295339528250484711 ,.46972961879998703645] 
dist 155=[-1.2672714940815109994 ,.51048482763954739221] 
dist 156=[-1.2453810086509376321 ,.53952096830599669614] 
dist 157=[-1.1866231375837844809 ,.5655722163363543837 ] 
dist 158=[-1.1754425727887606039 ,.67696606665302880812] 
dist 159=[-1.0652647586022664379 ,.82168219607059846783] 
dist 160=[-1.0418996470340957507 ,.93238134754838875893] 
dist 161=[-1.0128877606236051368 ,1.0394818595757735329 ] 
dist 162=[-1.0016386092320577281 ,1.1698310300331831326 ] 
dist 163=[-.74476460628399496072,1.2926583308757740492 ] 
dist 164=[-.71008792333563244341,1.3697288110846247359 ] 
dist 165=[-.63747538018587510303,1.4281191192193726579 ] 
dist 166=[-.61748584628084608131,1.4763682967147380156 ] 
dist 167=[-.53878059112240844116,1.5144615995757336068 ] 
dist 168=[-.52286481842975284474,1.5323057905172158815 ] 
dist 169=[-.48664247995252160663,1.5399297329861409486 ] 
dist 170=[-.47691938893856805858,1.5397333343208888158 ] 
dist 171=[-.3903748286804755454 ,.53939656155335630536] 
dist 172=[-.43880997080250190234,.5305989685099503553 ] 
dist 173=[-.48529022596266685736,.521361254426413242  ] 
dist 174=[-.54131133220787335913,.51709855258367906407] 
dist 175=[-.59380497554392114637,.4058149489165615414 ] 
dist 176=[-.62620288099062882279,.47074802602371060647] 
dist 177=[-.65011058164507521343,.5359384960745852223 ] 
dist 178=[-.6687096963529122546 ,.61864814247653704883] 
dist 179=[-.68255381210680261941,.69832552231741750005] 
dist 180=[-.68747872782947414751,.75140972559525378438] 
dist 181=[-.68896729162077777361,.79525356307185026434] 
dist 182=[-.68909313530251615476,.83803788883643357863] 
dist 183=[-.00569110916511215684,.87694240495937641153] 
dist 184=[-.05833041452303901179,.90529627822505929872] 
dist 185=[-.1039134588919944289 ,.93139724050980368195] 
dist 186=[-.15186610057838271241,.96130843010997708596] 
dist 187=[-.19774769992647641367,.98756290590776544443] 
dist 188=[-.23506241854933349573,.99906396915176325883] 
dist 189=[-.27329936897190702615,1.0042684711324511613 ] 
dist 190=[-.32317292228606126619,1.0053797051092434676 ] 
dist 191=[-.40047617205495860935,.98379631045297960179] 
dist 192=[-.46464236361878229786,.97810162575100204361] 
dist 193=[-.53155589194589798327,.97459231968667763186] 
dist 194=[-.61982845933665967293,.97314447914200102418] 
dist 195=[-.70647440558816753994,.81050387092055231873] 
dist 196=[-.7668938221863615771 ,.78788871198389555318] 
dist 197=[-.81974780914065221319,.74666587276649736201] 
dist 198=[-.87618871742001739722,.73606865395469083104] 
dist 199=[-.93070293504254215577,.70076890671116732109] 
dist 200=[-.97586483113093466731,.69056356809291624029] 
dist 201=[-1.0228853325966989087 ,.68183282874521549018] 
dist 202=[-1.0848207517298722578 ,.67839010223734098947] 
dist 203=[-1.1436199680186913302 ,.28716988805910719159] 
dist 204=[-1.1781190132595680113 ,.3225987826668369655 ] 
dist 205=[-1.2014674468202877075 ,.35912599433088360605] 
dist 206=[-1.2157466354698123813 ,.40676278934412007687] 
dist 207=[-1.2240684026916174239 ,.45326274619936858742] 
dist 208=[-1.2247017507411639244 ,.48525126207775043882] 
dist 209=[-1.2199949169974088749 ,.51277416500587022783] 
dist 210=[-1.2155450087334827839 ,.54144531263881289189] 
dist 211=[-1.1428101162481428970 ,.56870273034879524993] 
dist 212=[-1.1291443715346895804 ,.59058147206238910531] 
dist 213=[-1.0965987987032588141 ,.61273834779447993401] 
dist 214=[-1.0851855848761815677 ,.64110652729994807666] 
dist 215=[-1.0289745230187856020 ,.6676388970980871123 ] 
dist 216=[-1.0159008865109235961 ,.68246626769936904378] 
dist 217=[-.98631955261671876701,.69157664116809987044] 
dist 218=[-.97629096533222122646,.69528348614998777123] 
dist 219=[-.90872139872296145901,.69615915955586723901] 
dist 220=[-.91700520988902696226,.69497296134783211991] 
dist 221=[-.92006572552621510578,.69046942052253172532] 
dist 222=[-.91917309770585502691,.68945668353757229354] 
dist 223=[-.90401626453637842603,.80118020567742194815] 
dist 224=[-.89830889559335542394,.87989744466831771906] 
dist 225=[-.89019377493310482654,.9496123721130284563 ] 
dist 226=[-.88630764593548737196,1.0253929990619781454 ] 
dist 227=[-.77248994664289928307,1.0944783267413445426 ] 
dist 228=[-.75536410771397776898,1.1374615891385871200 ] 
dist 229=[-.71987548373439979066,1.1696085593983831832 ] 
dist 230=[-.70943340007922906438,1.1954291361828929442 ] 
dist 231=[-.66533832406725443398,1.2152433147197048248 ] 
dist 232=[-.65581416294746959446,1.2234092703265499639 ] 
dist 233=[-.63041960528450810106,1.2253580467430601303 ] 
dist 234=[-.62467939449632965647,1.2240020393617180846 ] 
dist 235=[-.46400038770142118678,.52599870877620926409] 
dist 236=[-.50679965233818225842,.52468400883183390995] 
dist 237=[-.54398242112047820674,.5214622432637361916 ] 
dist 238=[-.58328641621582581014,.51955143991864427132] 
dist 239=[-.61893741195548136444,.47220909088474861113] 
dist 240=[-.64153530205095909948,.46445181477911218519] 
dist 241=[-.6589260826009016246 ,.44753590730143199051] 
dist 242=[-.67378755887016487243,.44216341299155725434] 
dist 243=[-.68590677842865719243,.41760506769901258929] 
dist 244=[-.69234905147503654956,.41227931001479020273] 
dist 245=[-.6958741075314360217 ,.39755968828403265393] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 0, 2, 2, 0, 1] 
dist 0=[44.589056413357606803  ,44.589056413357606803  ] 
dist 1=[44.397837512581863963  ,44.749801310529073859  ] 
dist 2=[44.058369230024785040  ,44.901060409461410640  ] 
dist 3=[43.305377914848111638  ,45.054219965134044893  ] 
dist 4=[42.341138087979602960  ,45.196648224628322035  ] 
dist 5=[41.157881625502034651  ,45.304932137187272288  ] 
dist 6=[39.583810816265178702  ,45.408437060766427273  ] 
dist 7=[37.058527540451807250  ,45.531540131574694696  ] 
dist 8=[34.470310613489252062  ,45.637242810413657838  ] 
dist 9=[32.644810916161115400  ,45.671299317015427263  ] 
dist 10=[31.022851387751129040  ,45.658698398633523851  ] 
dist 11=[29.247489324742236669  ,45.607222137760998353  ] 
dist 12=[27.502163639526028734  ,45.460500989983081427  ] 
dist 13=[26.000016075023865235  ,45.379436709974067284  ] 
dist 14=[24.137231336062328776  ,44.771875265728220670  ] 
dist 15=[22.114473423527839131  ,43.193465730913996477  ] 
dist 16=[19.969355636285981357  ,35.584072595680968570  ] 
dist 17=[18.341468984260327260  ,34.722121888570171413  ] 
dist 18=[16.200680134258183841  ,32.580641912529010946  ] 
dist 19=[13.805167555659371672  ,32.270657986920930126  ] 
dist 20=[12.070810408011242468  ,28.932713127839232025  ] 
dist 21=[10.481492920472921310  ,28.291472388594912441  ] 
dist 22=[8.6651062168961765625 ,27.603505059433024782  ] 
dist 23=[6.8313433156386464065 ,27.471310416848834324  ] 
dist 24=[4.1300303425695316146 ,21.288106359413995757  ] 
dist 25=[2.3380879467197339674 ,20.508391302793543408  ] 
dist 26=[.6866309159913572112 ,18.970584776772109585  ] 
dist 27=[-1.8929748769846078170 ,18.580332140442626837  ] 
dist 28=[-3.5577571947902095720 ,17.234458081377684068  ] 
dist 29=[-4.8806432781809285460 ,16.932119047806960802  ] 
dist 30=[-6.0938159987622792224 ,16.578429050529373050  ] 
dist 31=[-7.1527087705578063650 ,16.487491735277046083  ] 
dist 32=[-7.8591102451769925006 ,4.4464806554622061154 ] 
dist 33=[-8.4477405023599993820 ,3.4666498264196581723 ] 
dist 34=[-9.0362844339651886113 ,1.2300436400437560562 ] 
dist 35=[-9.5495515116344554440 ,.8826556688907237445 ] 
dist 36=[-9.8373332966392938652 ,-1.8874377040139466420 ] 
dist 37=[-10.018349049973687190  ,-2.3606362768359548383 ] 
dist 38=[-10.104585785751361566  ,-2.5751158957734166878 ] 
dist 39=[-10.137359873944298461  ,-1.6019439114409928091 ] 
dist 40=[-10.125587136992614397  ,-.59982914950505520961] 
dist 41=[-10.049334572320888084  ,.09773054427336321857] 
dist 42=[-9.9959925702549076658 ,.70430842823710613113] 
dist 43=[-9.2191208495799783304 ,1.3436534962005727840 ] 
dist 44=[-9.5874653783986628142 ,1.9538866463779604309 ] 
dist 45=[-9.7740525426690995554 ,2.4444213562442776751 ] 
dist 46=[-9.8728215844347938268 ,2.9406216499587399499 ] 
dist 47=[-9.8902578610224439125 ,3.5735583119462023386 ] 
dist 48=[-6.8813905052544714794 ,4.1825484653488639678 ] 
dist 49=[-6.7257432643893241416 ,4.5832271653063262952 ] 
dist 50=[-6.3298107865134405109 ,4.9077210750913790923 ] 
dist 51=[-6.2613523379062193123 ,5.2127148082608051151 ] 
dist 52=[-5.6095252758686192739 ,5.4815355688247102911 ] 
dist 53=[-5.4799959587795388448 ,5.6616797009892234995 ] 
dist 54=[-5.3139032202757868190 ,5.8111978877336040781 ] 
dist 55=[-5.2555681017470088378 ,6.0048540668605193548 ] 
dist 56=[-4.0207368280422518681 ,6.1023749128424888279 ] 
dist 57=[-3.8582587340992494726 ,6.1458239763144824083 ] 
dist 58=[-3.5141823216724562269 ,6.1469741027148794909 ] 
dist 59=[-3.4204473163120164554 ,1.2870556006031957718 ] 
dist 60=[-3.0537361162998107306 ,1.6150156118387648243 ] 
dist 61=[-2.9826004807767910825 ,1.8836433485751272640 ] 
dist 62=[-2.8211877051595809811 ,2.2079542486786068176 ] 
dist 63=[-2.7838684274972893299 ,2.6047734908179396671 ] 
dist 64=[-.87470400391797950621,2.9806195245597256015 ] 
dist 65=[-.70777026995119069405,3.2211917865568139182 ] 
dist 66=[-.32572637515569614664,3.4093481596983378691 ] 
dist 67=[-.26164331903612190054,3.5758919249639993750 ] 
dist 68=[.2242107163642485538 ,3.7164357349746521970 ] 
dist 69=[.3103035193238307291 ,3.8007876989795053942 ] 
dist 70=[.4453716551574816842 ,3.8605313846131566931 ] 
dist 71=[.4783713446651056926 ,3.9028602350666534133 ] 
dist 72=[.61184658813104034606,3.9295068677485070707 ] 
dist 73=[.30044242474545571816,3.9321405945843550194 ] 
dist 74=[.02049234056868266702,3.9143703409736777182 ] 
dist 75=[-.28992778268952341673,3.9034445393666128039 ] 
dist 76=[-.59642972466788562121,3.7756937375275608797 ] 
dist 77=[-.86076044834799617239,3.7401716931412212175 ] 
dist 78=[-1.1450570297508443308 ,3.7119666305205686769 ] 
dist 79=[-1.5312914439162193006 ,3.7024888954824825726 ] 
dist 80=[-1.9154494418311577827 ,3.1114329862745920421 ] 
dist 81=[-2.1914697920711498516 ,3.0302341807121359527 ] 
dist 82=[-2.4414419275685569657 ,2.8643501980270171029 ] 
dist 83=[-2.7216249415340469270 ,2.8175112043771179381 ] 
dist 84=[-3.0002244312477860026 ,2.6296773742787577524 ] 
dist 85=[-3.2438905333630114648 ,2.5885647628691677432 ] 
dist 86=[-3.5089943163889036115 ,2.4926682668440274232 ] 
dist 87=[-3.8732094517837000314 ,2.4617852133558270330 ] 
dist 88=[-4.2254869710309449133 ,.44474456387556047569] 
dist 89=[-4.4429330438214950165 ,.38479825415184076556] 
dist 90=[-4.6035916653532039799 ,.36886546876331495844] 
dist 91=[-4.7291292572384376573 ,.26490664838261515334] 
dist 92=[-4.8227356238362088569 ,.28280265505924195451] 
dist 93=[-4.8559023526878440234 ,.32775691298158730378] 
dist 94=[-4.8656266724443586513 ,.40101265824665001239] 
dist 95=[-4.8656187843396039209 ,.53185539905583094725] 
dist 96=[-4.7210136434153506946 ,.66983226716757294339] 
dist 97=[-4.6858864297101897445 ,.77156871105989253778] 
dist 98=[-4.5975533195895615504 ,.86612741407694128651] 
dist 99=[-4.5625148808363932103 ,.97548718649527583044] 
dist 100=[-4.3761715793764296964 ,1.0859063373730984790 ] 
dist 101=[-4.3300622454939658401 ,1.1847091855080238690 ] 
dist 102=[-4.2253748083596819184 ,1.2939009059015650323 ] 
dist 103=[-4.1883818046915711096 ,1.4458007717707274831 ] 
dist 104=[-3.6989709658998391837 ,1.5982358057286463188 ] 
dist 105=[-3.6886261286749789047 ,1.7095732014495033110 ] 
dist 106=[-3.6391606847382341190 ,1.9048912454690841895 ] 
dist 107=[-3.6266014149470278492 ,2.4095811395843899542 ] 
dist 108=[-3.4544856744692565714 ,2.8670174238655143262 ] 
dist 109=[-3.4116076783786093893 ,3.1975938794709241432 ] 
dist 110=[-3.3690369377682954727 ,3.4989502156938623961 ] 
dist 111=[-3.3452098088252992645 ,3.8397218416435360781 ] 
dist 112=[-2.7175158510555103657 ,4.1529375815893873043 ] 
dist 113=[-2.6297104778485934615 ,4.3442766387079264151 ] 
dist 114=[-2.4554563964563057556 ,4.4831979519137756202 ] 
dist 115=[-2.4081223189384006937 ,4.5871380538167911715 ] 
dist 116=[-2.2292517567082562980 ,4.6620195138170730895 ] 
dist 117=[-2.1879683858648435181 ,4.6849224518739532243 ] 
dist 118=[-2.1080065224883405191 ,4.6881032851081964466 ] 
dist 119=[-2.0850134125230276965 ,4.6842465938993789697 ] 
dist 120=[-.60984138796660215838,2.6723106885812809900 ] 
dist 121=[-.57640128106144370164,2.6445586015057414685 ] 
dist 122=[-.5673282374252256407 ,2.5718373991954084232 ] 
dist 123=[.44906696074102565405,2.5473538058149329766 ] 
dist 124=[.52606953327541006163,2.4028973602873156894 ] 
dist 125=[.38791356173480217209,2.3686948554597393776 ] 
dist 126=[.18035587057267987144,2.3039695762510454842 ] 
dist 127=[-.35710159623332675614,2.3494830752420317109 ] 
dist 128=[-.95934778937425559876,2.4929866569938577090 ] 
dist 129=[-1.3551108760149394998 ,2.5777182130057821912 ] 
dist 130=[-1.6757729034209540063 ,2.6357958961014289785 ] 
dist 131=[-1.9781944554529643572 ,2.6728729266533225561 ] 
dist 132=[-2.2460606463728677927 ,2.6959759863418129590 ] 
dist 133=[-2.4287658584859168372 ,2.6988213826342106559 ] 
dist 134=[-2.5842271788608902885 ,2.6922769144230561148 ] 
dist 135=[-2.7433220426129541247 ,2.6825614018058060507 ] 
dist 136=[-2.8860782963297312970 ,2.5232680591881791726 ] 
dist 137=[-2.9763123100075380048 ,2.4932695161767193373 ] 
dist 138=[-3.0454090729980240776 ,2.4232978133261491020 ] 
dist 139=[-3.1037885942907742091 ,2.3989899314194731608 ] 
dist 140=[-3.1508566711992114784 ,2.2800756177581362527 ] 
dist 141=[-3.1748001630265891239 ,2.2525995303381151374 ] 
dist 142=[-3.1864083642359037573 ,2.1866547520488621850 ] 
dist 143=[-3.1842368331605632829 ,2.1635466495157299162 ] 
dist 144=[-.03591777667091993069,.78651385863644497114] 
dist 145=[-.14973837992759455118,.74711522139694801711] 
dist 146=[-.28588776705085800919,.73725504744850142833] 
dist 147=[-.4273238159953630985 ,.5470652861979249321 ] 
dist 148=[-.54336748338905233489,.5210523267417309252 ] 
dist 149=[-.63470139794155167781,.45844948683191944294] 
dist 150=[-.73193858857069378847,.44727387503872214543] 
dist 151=[-.83892535309488784209,.35563861508426588113] 
dist 152=[-.93359452478852094361,.3381590242092522968 ] 
dist 153=[-1.0375132030885765899 ,.31238182668273457683] 
dist 154=[-1.1814306713918477520 ,.30496867692240757454] 
dist 155=[-1.3216375940686669952 ,-.74009417451164659525] 
dist 156=[-1.4107408673166652335 ,-.80278127141436435331] 
dist 157=[-1.4795966916167408127 ,-.81872982190177945224] 
dist 158=[-1.5389605112416524099 ,-.7686452773440327964 ] 
dist 159=[-1.5877758742201070603 ,-.67985552806354878226] 
dist 160=[-1.6145142882576191321 ,-.58585013012439122365] 
dist 161=[-1.6302363084056953272 ,-.51494153122694837697] 
dist 162=[-1.6350658835177627485 ,-.44730528059320786628] 
dist 163=[-1.6339025186497642186 ,-.36636029832095225787] 
dist 164=[-1.6305405751237352373 ,-.28295061739102042137] 
dist 165=[-1.6157665528917350575 ,-.20547189773053838117] 
dist 166=[-1.6077208370822038157 ,-.11740825357340776958] 
dist 167=[-1.5529943778800187350 ,.00826371181918960388] 
dist 168=[-1.5380234635241241804 ,.13601338350809633098] 
dist 169=[-1.5126916996093480987 ,.2323736838777632812 ] 
dist 170=[-1.5042271037377470883 ,.32431143071819093953] 
dist 171=[-1.2363890951624731178 ,.43440627893825909958] 
dist 172=[-1.2115823982466630318 ,.54791822465988904809] 
dist 173=[-1.1445543871397310097 ,.65350058375923989589] 
dist 174=[-1.1339170831098466159 ,.78261137973512506294] 
dist 175=[-1.0091591912810446523 ,.94526460995198622477] 
dist 176=[-.983308928881019463  ,1.1142977029574329559 ] 
dist 177=[-.95645512370608201188,1.2240812092530769248 ] 
dist 178=[-.94855291171025707151,1.3116282248521691337 ] 
dist 179=[-.65841189241477924985,1.4349642753793899406 ] 
dist 180=[-.62058888978016105061,1.5095485692573854690 ] 
dist 181=[-.54491554238849713603,1.5622354878956945000 ] 
dist 182=[-.52510728930641726975,1.5989184166988225404 ] 
dist 183=[-.45352978490605355762,1.6257157582090550007 ] 
dist 184=[-.43766719770410725045,1.6389322216509199375 ] 
dist 185=[-.41231623892543541783,1.6447482454294722387 ] 
dist 186=[-.40542897800352042102,1.6433325864596767693 ] 
dist 187=[.09711679516938088932,1.6043437688420353515 ] 
dist 188=[.11781598956367582659,1.5580302407003702934 ] 
dist 189=[.15921924180760049703,1.5441305943589753919 ] 
dist 190=[.16921606150319385365,1.5335639011452277835 ] 
dist 191=[.08943579941926220766,1.5255682497145162224 ] 
dist 192=[-.21892123053321021819,1.3197895289577595656 ] 
dist 193=[-.42653225636458822808,1.2976460525677763450 ] 
dist 194=[-.60036049688809707605,1.2374162718501881718 ] 
dist 195=[-.77383745504898654368,1.2265422139122866744 ] 
dist 196=[-.93407152863619825644,1.1114904961735229002 ] 
dist 197=[-1.0550266011923826758 ,1.0870880892755006584 ] 
dist 198=[-1.1705269275843663733 ,1.0588179662215959833 ] 
dist 199=[-1.3089824165165533818 ,1.0309463568321414356 ] 
dist 200=[-1.4384270428845467575 ,.68625293271839420089] 
dist 201=[-1.5179507917556281268 ,.64139675123938404821] 
dist 202=[-1.5762305673261892626 ,.54530886586578889569] 
dist 203=[-1.6208570451056672496 ,.56582288660999736834] 
dist 204=[-1.6543047986809942797 ,.57653720516832454675] 
dist 205=[-1.6679528202927524560 ,.58217729790817147894] 
dist 206=[-1.6726220353562679988 ,.58331373636851183561] 
dist 207=[-1.6702213584589054959 ,.58036750243096919753] 
dist 208=[-.39345276922396790662,.57830489775706324771] 
dist 209=[-.42928880008549617853,.57568058624361131227] 
dist 210=[-.47447090785454997811,.57360962287309750849] 
dist 211=[-.51785881707127644005,.50481535387100127861] 
dist 212=[-.54653117988702568391,.49433152676000650516] 
dist 213=[-.56995389259258832906,.47370319723739111755] 
dist 214=[-.59238157012547285109,.46778402458567509523] 
dist 215=[-.61248991849989942313,.44397239293643904874] 
dist 216=[-.62665229266985760095,.43826073757376838476] 
dist 217=[-.63919109577950576591,.42519684008202929505] 
dist 218=[-.652817105427309946  ,.42075136740631348931] 
dist 219=[-.66448192252401288206,.12601040137551521346] 
dist 220=[-.66919032828295651061,.09977309109940092073] 
dist 221=[-.67049163263824115481,.04026554253760253080] 
dist 222=[-.66958276530072567263,.02947700449964059552] 
dist 223=[-.65804487005899805493,-.04371597274575443575] 
dist 224=[-.65392792343498815425,-.05645124679779507074] 
dist 225=[-.64643209409525733854,-.07950305995567374650] 
dist 226=[-.64356564106618460193,-.08448736919035323574] 
dist 227=[-.56655005820316367809,-.11780571760010720596] 
dist 228=[-.5547413873713586158 ,-.08083227527129328495] 
dist 229=[-.52909842215797896412,-.04738979352950883288] 
dist 230=[-.52125424727095341163,-.01008392404692411150] 
dist 231=[-.48652203003520058159,.04231469827344066776] 
dist 232=[-.47923519428685384442,.09523106311110961881] 
dist 233=[-.45938910565011849502,.13460419595243771693] 
dist 234=[-.45545981087871142125,.17164866167746860368] 
dist 235=[-.18156568168099666487,.21526774182305654787] 
dist 236=[-.1552022567544692986 ,.25984588545675578186] 
dist 237=[-.09719449972735193374,.31388320138408146584] 
dist 238=[-.08473024430610677994,.37820227358165836631] 
dist 239=[-.01866915120892187050,.43586458044721631488] 
dist 240=[-.00649569276317204472,.47646049951974003053] 
dist 241=[.01867576544258226815,.51740063355788816292] 
dist 242=[.02401059359690463610,.55138729671097113697] 
dist 243=[.06653779054667553841,.58686384744536097421] 
dist 244=[.07395138531099049629,.60870262037864830351] 
dist 245=[.07828863255864409397,.62476160391817588071] 
dist 246=[.07460280758218716648,.63716151465363723021] 
dist 247=[.06683302703402662419,.64627850482942942783] 
dist 248=[.05362041104479907935,.6492299648942430656 ] 
dist 249=[.03387056168575010788,.64943984165585366658] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 1, 0, 1] 
dist 0=[44.716033898527725397  ,44.716033898527725397  ] 
dist 1=[44.550594629281413039  ,44.861111225731716988  ] 
dist 2=[44.313804428327869786  ,45.016458566537445361  ] 
dist 3=[43.987282379540933685  ,45.166327139625405035  ] 
dist 4=[43.203009400582716126  ,45.289401427698597709  ] 
dist 5=[42.205350585357629482  ,45.415962016374245043  ] 
dist 6=[40.989242641732993439  ,45.579509492915842459  ] 
dist 7=[39.376386741891350899  ,45.726088003285862400  ] 
dist 8=[36.793985809064229967  ,45.784919812671511779  ] 
dist 9=[34.149404217168386625  ,45.790092912947507333  ] 
dist 10=[32.288125112746003256  ,45.743786435656177864  ] 
dist 11=[30.465767238239715968  ,45.613606962739502795  ] 
dist 12=[28.253227051735683559  ,45.536853300199571491  ] 
dist 13=[26.313303788959890632  ,45.128329868007730225  ] 
dist 14=[24.230007826263130816  ,44.267405284495675590  ] 
dist 15=[22.205811006377433591  ,35.915073648101527775  ] 
dist 16=[20.501755835392186571  ,35.064966991717592806  ] 
dist 17=[18.699742163168950902  ,32.948112087012660176  ] 
dist 18=[16.283891054186190362  ,32.642434206836118054  ] 
dist 19=[13.884048921991731289  ,29.325673783737301230  ] 
dist 20=[12.145787015934363727  ,28.687132021914269666  ] 
dist 21=[10.552091796135764354  ,28.007289714337522893  ] 
dist 22=[8.7294940562821092885 ,27.878402855959633606  ] 
dist 23=[6.8887792487426377217 ,21.673587018828201464  ] 
dist 24=[5.2223404499877174591 ,20.890677824588537268  ] 
dist 25=[3.3556094143560874904 ,19.349994836017052720  ] 
dist 26=[.7139330413424679141 ,18.959435914518207701  ] 
dist 27=[-1.8796716983504988282 ,17.616456074094380642  ] 
dist 28=[-3.5544354512494022084 ,17.312798026935868405  ] 
dist 29=[-4.8862863167621836536 ,16.966866314646210831  ] 
dist 30=[-6.1093946366639308006 ,16.883055996322944642  ] 
dist 31=[-7.1780922792324068692 ,4.6187322089956267806 ] 
dist 32=[-7.8929331722926480220 ,3.6230284795759557923 ] 
dist 33=[-8.4906151002621141706 ,1.3468492521512461713 ] 
dist 34=[-9.0914024611068361803 ,.9955494820639582418 ] 
dist 35=[-9.6168302865087160924 ,-1.8337422298274954633 ] 
dist 36=[-9.9133334396822653943 ,-2.3174891256173659324 ] 
dist 37=[-10.102212377619063046  ,-3.0313123175633570778 ] 
dist 38=[-10.197188829291700733  ,-2.9695942855141666808 ] 
dist 39=[-10.237739284843782654  ,-2.3674162063958599897 ] 
dist 40=[-10.229186436485645558  ,-1.3675760473180587667 ] 
dist 41=[-10.156795009153381370  ,-.3403166851898893389 ] 
dist 42=[-10.103820962655468422  ,.37143513458970352506] 
dist 43=[-9.5177499914246073209 ,.98691928076097432257] 
dist 44=[-9.7102022645809868099 ,1.6303018833157482553 ] 
dist 45=[-9.8133355361087004566 ,2.2411329843389232898 ] 
dist 46=[-9.8371838432264892980 ,2.7268388822719479446 ] 
dist 47=[-6.9756714033878180334 ,3.2132936157144917844 ] 
dist 48=[-6.8305397683480690762 ,3.8271938038257763225 ] 
dist 49=[-6.4567605596227188980 ,4.4145924429690294087 ] 
dist 50=[-6.3925740619354091298 ,4.7953223757963002694 ] 
dist 51=[-5.7615860591240601166 ,5.0972037991010144946 ] 
dist 52=[-5.6350953479236949314 ,5.3699688373062037874 ] 
dist 53=[-5.4776581533522173821 ,5.6027556436517249584 ] 
dist 54=[-5.4203636618657482499 ,5.7450908836107017385 ] 
dist 55=[-4.1783441569770645744 ,5.8481711030205634415 ] 
dist 56=[-4.0145498971818740480 ,5.9242648645259481273 ] 
dist 57=[-3.6713853325271665134 ,5.9762756509614928925 ] 
dist 58=[-3.5784788923190128994 ,5.9832362136991692294 ] 
dist 59=[-3.2195045326998433954 ,1.5105200164252053958 ] 
dist 60=[-3.1481603404938628602 ,1.8842129948252723038 ] 
dist 61=[-2.9938303154904647749 ,2.1923410399014872855 ] 
dist 62=[-2.9501239045437294503 ,2.4928534129044483665 ] 
dist 63=[-.85446074604931716552,2.7665767939258602232 ] 
dist 64=[-.67159834119681409758,2.9677070090965830787 ] 
dist 65=[-.25200433838313196495,3.1548250942562772219 ] 
dist 66=[-.18316399204944781224,3.3725932203551216530 ] 
dist 67=[.3519905171502911487 ,3.5736268708392688704 ] 
dist 68=[.4464207140285147790 ,3.6939076504897749848 ] 
dist 69=[.5907481525490444399 ,3.7784995889033069173 ] 
dist 70=[.6268634055234752361 ,3.8369837573844402317 ] 
dist 71=[1.2174827150961375297 ,3.8750346370933772133 ] 
dist 72=[1.2913843450538169744 ,3.8827574276205278816 ] 
dist 73=[.9220578445033581084 ,3.8705364416206266360 ] 
dist 74=[.2862713991620202071 ,3.8668738161878430247 ] 
dist 75=[-.356745163213448663  ,3.7030083595111019836 ] 
dist 76=[-.79537297596771894193,3.6709098558714320233 ] 
dist 77=[-1.1687956385329953403 ,3.6588069169972870384 ] 
dist 78=[-1.5514978594466163145 ,3.6520660078774945748 ] 
dist 79=[-1.9114689945685584311 ,3.3350545450366740308 ] 
dist 80=[-2.1941499226972393211 ,3.2851617059066947440 ] 
dist 81=[-2.4747544360982445380 ,3.2247025630040104102 ] 
dist 82=[-2.8264547325921572368 ,3.1990573758942855568 ] 
dist 83=[-3.1632692367498466345 ,2.5740765561201800991 ] 
dist 84=[-3.3844485820897045872 ,2.4873284842146478075 ] 
dist 85=[-3.5636361021814554522 ,2.3089529451997000101 ] 
dist 86=[-3.7327981480372040152 ,2.2594943216153232244 ] 
dist 87=[-3.8829579136642256685 ,2.0645387137733396348 ] 
dist 88=[-3.9862861544358292369 ,2.0230956001173598865 ] 
dist 89=[-4.0753474808151540300 ,1.9297953155184700705 ] 
dist 90=[-4.1685687441045191697 ,1.9008107877558222443 ] 
dist 91=[-4.2475130365203211998 ,.29493172844644097901] 
dist 92=[-4.2795708055705007290 ,.32168919764833846121] 
dist 93=[-4.2894145597369365228 ,.37217445223606086898] 
dist 94=[-4.2835904105196573539 ,.46800880727163010974] 
dist 95=[-4.2078502181223161597 ,.57068529905333083138] 
dist 96=[-4.1807835337037142314 ,.64848534840099368301] 
dist 97=[-4.1382667409797456664 ,.72281566424847046551] 
dist 98=[-4.1203041190097345957 ,.81167989139758086698] 
dist 99=[-3.6064089866384457568 ,.90296644885774603167] 
dist 100=[-3.5792067223274306579 ,.98698268718455839308] 
dist 101=[-3.4980612901953267212 ,1.0817185689520013514 ] 
dist 102=[-3.4711187494904181808 ,1.2158064000367272131 ] 
dist 103=[-3.4370856599627338332 ,1.3513370080928409242 ] 
dist 104=[-3.4198322367045686336 ,1.4518423269098608235 ] 
dist 105=[-2.9372646190251624710 ,1.5459479230540984283 ] 
dist 106=[-2.9165368224544198007 ,1.6559516490690360681 ] 
dist 107=[-2.7866903501190905478 ,1.7678179343069354892 ] 
dist 108=[-2.7713772298427087752 ,1.8693707799149445000 ] 
dist 109=[-2.7593773969528824880 ,1.9828960290334545964 ] 
dist 110=[-2.7487691663939369052 ,2.1425706598978062825 ] 
dist 111=[-2.6124012611609635472 ,2.4769966766048965037 ] 
dist 112=[-2.6055837085964324976 ,2.7314790000244685572 ] 
dist 113=[-2.5877651102942764460 ,2.9591729199147931843 ] 
dist 114=[-2.5776943550505409052 ,3.2103066690935208705 ] 
dist 115=[-2.3555001402035950124 ,3.4400933145717812608 ] 
dist 116=[-2.3187011815579036219 ,3.5825528823771960462 ] 
dist 117=[-2.2371197223565287129 ,3.6885287538608735912 ] 
dist 118=[-2.2108515042230210096 ,3.7726470878560329560 ] 
dist 119=[-2.0894067435887644537 ,3.8364284817028361729 ] 
dist 120=[-2.0627419992022509051 ,3.8612061844506871949 ] 
dist 121=[-1.9928871060526751040 ,3.8673759404112012364 ] 
dist 122=[-1.9746068345822172046 ,3.8613317818743944953 ] 
dist 123=[.53693814938581488646,2.2134216272988462728 ] 
dist 124=[.38228863916430947925,2.1823014886612189902 ] 
dist 125=[.16638450203800386207,2.1267424944808784923 ] 
dist 126=[-.33709481446552773613,2.1932387507744653333 ] 
dist 127=[-.88861641848733818418,2.3220374292225876654 ] 
dist 128=[-1.2512817941301793374 ,2.3975373786578541852 ] 
dist 129=[-1.5453755639036529356 ,2.4486133567363291904 ] 
dist 130=[-1.8231425381872194260 ,2.4798886759111981666 ] 
dist 131=[-2.0694316756435514163 ,2.4985929504634894102 ] 
dist 132=[-2.2378561809346062871 ,2.5000810826820754143 ] 
dist 133=[-2.3816273474663944680 ,2.4929792224838309613 ] 
dist 134=[-2.5294883572352994960 ,2.4840293295744241694 ] 
dist 135=[-2.6622099798623496758 ,2.3249269117918704576 ] 
dist 136=[-2.7455419680297263742 ,2.2957812682657987277 ] 
dist 137=[-2.8087000690166401390 ,2.2286495214585595780 ] 
dist 138=[-2.8608914555425247933 ,2.2056874628185518141 ] 
dist 139=[-2.9020743766892520055 ,2.0945906152851720645 ] 
dist 140=[-2.9212889654006818699 ,2.0691746335613869128 ] 
dist 141=[-2.9281030666456599804 ,2.0067054620828641879 ] 
dist 142=[-2.9242325536710729954 ,1.9852890226693110503 ] 
dist 143=[-.00504735131279540768,.91032157065181799392] 
dist 144=[-.18161220080470309429,.89608152614837552676] 
dist 145=[-.32924739001641987434,.7163383828502779658 ] 
dist 146=[-.47626933389739552324,.68971659552005264482] 
dist 147=[-.61187755000672279815,.62575895003744557712] 
dist 148=[-.71394404752346456777,.61316369802747636693] 
dist 149=[-.81301981011724869614,.51848058271258386583] 
dist 150=[-.94980911484864948078,.50000328373376659488] 
dist 151=[-1.1035726787951884943 ,.47015920607865833938] 
dist 152=[-1.3209930753980506529 ,.46220702068700455582] 
dist 153=[-1.5344554746034462365 ,-.88563035994357836455] 
dist 154=[-1.6724163099084292921 ,-.87155551155599086531] 
dist 155=[-1.7816749832090516673 ,-.84346117144279958015] 
dist 156=[-1.8805389248184025878 ,-.79688848276212448862] 
dist 157=[-1.9653125341671833557 ,-.72781402681837093341] 
dist 158=[-2.0183131930720422584 ,-.60988368828304752904] 
dist 159=[-2.0582608331922891929 ,-.48652239170058470856] 
dist 160=[-2.0909183402727635308 ,-.39576423380265400657] 
dist 161=[-2.1147413416480618374 ,-.31141532444093334474] 
dist 162=[-2.1194157225845451457 ,-.21363886546571141283] 
dist 163=[-2.1169741739669389119 ,-.11458342895965194976] 
dist 164=[-2.1123848343311251690 ,-.02512617618740488164] 
dist 165=[-2.0506785573502305930 ,.07453946775388461468] 
dist 166=[-2.0324506755852576364 ,.21435383003675429339] 
dist 167=[-2.0129022528766334888 ,.35544634914195485644] 
dist 168=[-2.0017485446790865053 ,.46021635536050372743] 
dist 169=[-1.6639315619486499230 ,.55857116917988775548] 
dist 170=[-1.6271452624463677245 ,.67405302902150333766] 
dist 171=[-1.5305004639235939110 ,.79188535393489603416] 
dist 172=[-1.5139301603278196372 ,.9849989801205034989 ] 
dist 173=[-1.3420094503930887945 ,1.1953743117639737368 ] 
dist 174=[-1.3066492696108035611 ,1.3542345987581811233 ] 
dist 175=[-1.2652935731371517001 ,1.5059951717766320588 ] 
dist 176=[-1.2501836783136858603 ,1.6880239816687143565 ] 
dist 177=[-.87525590445004140954,1.8582821742701110457 ] 
dist 178=[-.82565994941641119406,1.9630469533766189467 ] 
dist 179=[-.72335790257414014113,2.0400323333212248507 ] 
dist 180=[-.69584831820869592932,2.0993774379633133242 ] 
dist 181=[-.59126937265167135461,2.1440900861587972942 ] 
dist 182=[-.56964802463778960522,2.1626533599777296073 ] 
dist 183=[-.52585284209354996738,2.1693477237391314641 ] 
dist 184=[-.51386961192002613364,2.1666721037229255527 ] 
dist 185=[.1265028459196763236 ,1.7737214352689587853 ] 
dist 186=[.16537555988449803028,1.7679428459684104488 ] 
dist 187=[.25323030608564728824,1.7091584979152801228 ] 
dist 188=[.2670630478786776714 ,1.6926567255785138270 ] 
dist 189=[.37105688297696790534,1.6718339765882730898 ] 
dist 190=[.06971695870747821625,1.6621171508621893693 ] 
dist 191=[-.28072834279369604925,1.4556966405738861648 ] 
dist 192=[-.51567312397857047829,1.4375353895738676178 ] 
dist 193=[-.71129514973546305993,1.3838619286640160170 ] 
dist 194=[-.90474160769178083662,1.3752234721943144039 ] 
dist 195=[-1.0822730570086669372 ,1.2594385476617028861 ] 
dist 196=[-1.2143532162926437963 ,1.2290859058952765706 ] 
dist 197=[-1.3386010696473412887 ,1.2046592166922671922 ] 
dist 198=[-1.4848612485011134056 ,1.1530688126518795924 ] 
dist 199=[-1.6202311422638989215 ,.85189880785249954839] 
dist 200=[-1.7009986444173924949 ,.74747594577873478767] 
dist 201=[-1.7573309446836107254 ,.47205927343256343575] 
dist 202=[-1.7951414577702758836 ,.45869127174105861569] 
dist 203=[-1.8222110345542636896 ,.42766707099482968205] 
dist 204=[-1.8356596264281672248 ,.41969084140097371224] 
dist 205=[-1.8417202005205187130 ,.3754840926692068699 ] 
dist 206=[-1.8394891463993267554 ,.36647736747565613129] 
dist 207=[-.04447966124304877583,.34822205196592589437] 
dist 208=[-.09704352131676279903,.34298488056500821498] 
dist 209=[-.143062289877209019  ,.27313805717086270139] 
dist 210=[-.19226590070323194124,.26293509868703088831] 
dist 211=[-.23983118193034783247,.23788724870187342714] 
dist 212=[-.27930893622067122746,.23341042549828036963] 
dist 213=[-.32180784487696639802,.19485533577819320098] 
dist 214=[-.3747976181339979144 ,.18733256555446904184] 
dist 215=[-.42866189126703612802,.17677694025199896308] 
dist 216=[-.50833746467050161475,.17348538062592547633] 
dist 217=[-.58649426641890726913,-.1383662395229188194 ] 
dist 218=[-.63690810171049935155,-.10434193962636622198] 
dist 219=[-.67672006676963370013,-.06409588520728153740] 
dist 220=[-.71254729105567720238,-.01887117029094749544] 
dist 221=[-.74312699451095013263,.03872494124439399280] 
dist 222=[-.76198746730077189562,.12836504709084037779] 
dist 223=[-.77589991932873960478,.21915569315960844494] 
dist 224=[-.78672399266272674252,.28134549102542261929] 
dist 225=[-.79428214038764548062,.33457320251316066471] 
dist 226=[-.79554360182754650187,.38958192582328658443] 
dist 227=[-.79363925689710108929,.44161051776450210817] 
dist 228=[-.79166121600395350099,.4829398086617279522 ] 
dist 229=[-.76755521108764027516,.5244011525312858776 ] 
dist 230=[-.76055845726340592125,.57695703085129105138] 
dist 231=[-.75264890919846873481,.62755445502974583175] 
dist 232=[-.74842081618251240935,.66119649978674754872] 
dist 233=[-.56366318757764982505,.68890360894390864561] 
dist 234=[-.54232377028695900889,.7158052320336672609 ] 
dist 235=[-.49090119162590947694,.74017134421654973421] 
dist 236=[-.48093149792115623482,.7577551942246392269 ] 
dist 237=[-.40439706506328799308,.77376123050519726891] 
dist 238=[-.38946822037772985281,.7918278059354261404 ] 
dist 239=[-.36587935986886837211,.80758741619168035166] 
dist 240=[-.35943971257761382582,.81438262360044361368] 
dist 241=[-.23444649113765256633,.81666831953233883156] 
dist 242=[-.21791465236141366143,.81592790549102022222] 
dist 243=[-.17951843883075151224,.80343141376344336297] 
dist 244=[-.17225651605773135534,.79872765080940295212] 
dist 245=[-.12092722892548559806,.78992875722645818359] 
dist 246=[-.11146991660887916938,.78091283078381175191] 
dist 247=[-.09504415966024456845,.69503688707981457357] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 2, 0, 0, 1] 
dist 0=[49.858769264244696313  ,49.858769264244696313  ] 
dist 1=[49.665024286958667222  ,50.022334790698956825  ] 
dist 2=[49.379457411289561446  ,50.187431378717473002  ] 
dist 3=[48.945435793543951428  ,50.313712531719557456  ] 
dist 4=[47.951404269298714655  ,50.322354412731537939  ] 
dist 5=[46.720345722130471519  ,50.252239656208599736  ] 
dist 6=[45.309726353443916862  ,50.194697918210292899  ] 
dist 7=[43.491728576637628231  ,49.767051473277777320  ] 
dist 8=[40.632957079709370618  ,49.638624279231806622  ] 
dist 9=[37.705733781455848291  ,49.198411045599014712  ] 
dist 10=[35.614144884321720842  ,49.079589751093411301  ] 
dist 11=[33.725658394834597533  ,47.362293379301075920  ] 
dist 12=[31.609687198840396402  ,46.996008816367858478  ] 
dist 13=[29.498090882187308665  ,45.668960433355408336  ] 
dist 14=[27.626840169620232656  ,43.421842259846955836  ] 
dist 15=[25.564295193934974874  ,32.916457528859214652  ] 
dist 16=[22.687899159830769528  ,32.248783856861370715  ] 
dist 17=[19.774122572005907465  ,31.431822601388704737  ] 
dist 18=[17.561962264200862180  ,31.178737766817621378  ] 
dist 19=[15.428490202519829353  ,24.985094754925291226  ] 
dist 20=[12.828816054790428950  ,24.178822912631631159  ] 
dist 21=[10.110334251947752682  ,22.521541487108221257  ] 
dist 22=[7.5016464349794003081 ,22.081104133015395581  ] 
dist 23=[4.4579229807931404967 ,20.426436266038855706  ] 
dist 24=[0                     ,20.087938208907093283  ] 
dist 25=[5.1466378021248769486 ,19.414074780614213891  ] 
dist 26=[3.3824573539303117418 ,19.234440876203251114  ] 
dist 27=[1.6515957502593892504 ,13.611052862744694095  ] 
dist 28=[-.3689100086996257121 ,13.185593632847335793  ] 
dist 29=[-2.3970436002139977354 ,10.970376203399318420  ] 
dist 30=[-4.3465164085775260228 ,9.8908929161956646870 ] 
dist 31=[-6.1046327831559565383 ,1.4822337844360699432 ] 
dist 32=[-7.3683294695613956791 ,1.0158795454359995391 ] 
dist 33=[-8.5165563082906840662 ,.1906684886408632641 ] 
dist 34=[-9.8134548463086344564 ,.0191606961484710272 ] 
dist 35=[-11.008200238982676274  ,-2.3019447980147032968 ] 
dist 36=[-11.748362163946634022  ,-2.6165304073499190782 ] 
dist 37=[-12.300269493686164016  ,-3.1685247375541823931 ] 
dist 38=[-12.742961251432649747  ,-3.2792256254552739934 ] 
dist 39=[-13.084141568283130897  ,-3.4806842761253678921 ] 
dist 40=[-13.230574339305927638  ,-3.4201463414065918107 ] 
dist 41=[-13.289518372653821867  ,-3.2296257542718361703 ] 
dist 42=[-13.280943621898062053  ,-2.8154598562692137695 ] 
dist 43=[-10.678958619156606517  ,-2.3619272377709936443 ] 
dist 44=[-10.630851454354275739  ,-2.0141260395643159967 ] 
dist 45=[-10.427401581055891482  ,-1.6791376916850551976 ] 
dist 46=[-10.393499677406224278  ,-1.2762159802945649008 ] 
dist 47=[-6.0966537952978454997 ,-.8619471084169698899 ] 
dist 48=[-5.6914910459936654119 ,.0998179190983839933 ] 
dist 49=[-5.3636059633313054685 ,1.1468769971114336275 ] 
dist 50=[-5.2613011258306774217 ,2.1733120610971799284 ] 
dist 51=[-3.5296548172297236019 ,3.1084522073347424594 ] 
dist 52=[-3.3419995200340530537 ,3.7912092354578689284 ] 
dist 53=[-2.9423309147658664786 ,4.4203921262819157821 ] 
dist 54=[-2.6558286993178403586 ,5.1418310780323804513 ] 
dist 55=[-1.6421903292426757253 ,5.8113308230489801820 ] 
dist 56=[-1.5334260773214429853 ,6.2331660105132349392 ] 
dist 57=[-1.2876632740726361561 ,6.5548007413438150739 ] 
dist 58=[-1.2471861428980658046 ,6.8241177339293039321 ] 
dist 59=[.83185321915192340514,7.0390625263997465873 ] 
dist 60=[1.0306045263467809091 ,7.1434938991430144380 ] 
dist 61=[1.4110434038087104364 ,7.1893996247459042697 ] 
dist 62=[1.4978662104434629514 ,7.1919285533626297041 ] 
dist 63=[1.7419464403267134501 ,5.3835076684166411048 ] 
dist 64=[1.7721928825537120097 ,5.5065453209792497950 ] 
dist 65=[1.7366016929101084233 ,5.7484183404439187947 ] 
dist 66=[1.6027903482002818827 ,6.0034676635819153004 ] 
dist 67=[1.4326601397050949386 ,6.2253829966556401674 ] 
dist 68=[1.2520302939940864709 ,6.3349255325274084622 ] 
dist 69=[1.0294640643920738287 ,6.3924995995115520612 ] 
dist 70=[.6917959872931399063 ,6.4067525918573817523 ] 
dist 71=[.3060357562012818728 ,6.3247466349107299885 ] 
dist 72=[-.1085803352019039883 ,6.3037451182735414431 ] 
dist 73=[-.6239447144753962186 ,6.2914579644744128463 ] 
dist 74=[-1.4119593925032274477 ,6.2879701788752683943 ] 
dist 75=[-2.2027311858707859209 ,1.9131711758223663959 ] 
dist 76=[-2.7291327410901859119 ,1.8270458702399601716 ] 
dist 77=[-3.1631006506094219253 ,1.7244645399771571492 ] 
dist 78=[-3.5849013288098292177 ,1.7013869317340982970 ] 
dist 79=[-3.9670907926339502007 ,.96075726393798769739] 
dist 80=[-4.2429519200942707199 ,.86477433639305655557] 
dist 81=[-4.4941006966358183183 ,.69904054781719795142] 
dist 82=[-4.7776778830353409200 ,.66212346601962077388] 
dist 83=[-5.0340873579056205793 ,.5828439397241886779 ] 
dist 84=[-5.1767961026386144051 ,.5858987774200091068 ] 
dist 85=[-5.3123239402933568452 ,.6238598859254435694 ] 
dist 86=[-5.4404735245168189868 ,.7189266919478791760 ] 
dist 87=[-5.5427956479349209740 ,.8322656126720048985 ] 
dist 88=[-5.5960779953102099077 ,.9431861117401674595 ] 
dist 89=[-5.6239233040608286161 ,1.0733721650264042691 ] 
dist 90=[-5.6246470647316066320 ,1.2636732501089369473 ] 
dist 91=[-5.6080953893862837943 ,1.4779424439439434049 ] 
dist 92=[-5.5935672060858721042 ,1.9522509916086925360 ] 
dist 93=[-5.5245267308520985608 ,2.5324263363268213801 ] 
dist 94=[-5.5028089877227142576 ,3.1057627112874926148 ] 
dist 95=[-5.2085739885543648161 ,3.6310603073795871989 ] 
dist 96=[-5.1490698072877303472 ,4.0194776456631560651 ] 
dist 97=[-5.1022792038898289040 ,4.3821416936673773711 ] 
dist 98=[-5.0761293722665014184 ,4.8046310196236391368 ] 
dist 99=[-4.1017473515097024192 ,5.1926551706752833187 ] 
dist 100=[-3.9669516150501247038 ,5.4177406118988282642 ] 
dist 101=[-3.7051536966649463750 ,5.5665920136723717865 ] 
dist 102=[-3.6353625742057527466 ,5.6503100663359320307 ] 
dist 103=[-3.3813130430320402912 ,5.7030916270833278790 ] 
dist 104=[-3.3193800454111331616 ,5.7284627076650907553 ] 
dist 105=[-3.2183384876969678889 ,5.7385843727723650706 ] 
dist 106=[-3.1887063706409323100 ,5.7305241118036195204 ] 
dist 107=[-.5530749413480729585 ,3.8092004501813900104 ] 
dist 108=[-.41749408922352020019,3.7648035166848933639 ] 
dist 109=[-.10128182927714661321,3.8397036147640352219 ] 
dist 110=[-.53335857201540628093,4.0505278194725862675 ] 
dist 111=[-1.4188872765339160080 ,4.2439489342331487976 ] 
dist 112=[-2.0044698959500948425 ,4.3519439574791025260 ] 
dist 113=[-2.4827698215455574304 ,4.4183384374966198525 ] 
dist 114=[-2.9400381971363159670 ,4.4456553479103965409 ] 
dist 115=[-3.3490205571595889044 ,4.4535067127194415374 ] 
dist 116=[-3.6345625597049896815 ,4.4453044050519640818 ] 
dist 117=[-3.8844568375787473357 ,4.4204793310546652301 ] 
dist 118=[-4.1511209549138004204 ,4.4035902996282361153 ] 
dist 119=[-4.3914224700564032276 ,4.0108437268273980619 ] 
dist 120=[-4.5360837690256001777 ,3.9456031890228419820 ] 
dist 121=[-4.6383903665892118170 ,3.7372882663636439539 ] 
dist 122=[-4.7096438797376302509 ,3.4349100489757394031 ] 
dist 123=[-4.7554784252251685865 ,1.5559980181057676555 ] 
dist 124=[-4.7634697201855477805 ,1.3809159062588417193 ] 
dist 125=[-4.7436263551973278736 ,1.3247245588154197418 ] 
dist 126=[-4.7353318851273113230 ,1.3167584719265002316 ] 
dist 127=[.66435687668217907141,1.2788441536689798787 ] 
dist 128=[.60933088279464703139,1.2690088521826615516 ] 
dist 129=[.5264761672053128929 ,1.2396896282338190652 ] 
dist 130=[.35015019971265044511,1.2316491141782379952 ] 
dist 131=[.16761359342368863303,1.1624910306966453035 ] 
dist 132=[.02477934786124917791,1.1476478955155010554 ] 
dist 133=[-.11646866305984882499,1.1149172172563582778 ] 
dist 134=[-.29268252488575249693,1.1040894707906765575 ] 
dist 135=[-.47813336139114644877,1.0529973307359505864 ] 
dist 136=[-.65626597038942238515,1.0415961385638280233 ] 
dist 137=[-.86337966746083072139,1.0100441723327084757 ] 
dist 138=[-1.1645449202554844989 ,1.0025568111083248771 ] 
dist 139=[-1.4629430442455600707 ,.1515297839859574139 ] 
dist 140=[-1.6590114310510683765 ,.1421696146009204245 ] 
dist 141=[-1.8179131790509888883 ,.1244301781878762661 ] 
dist 142=[-1.9679233547788556325 ,.1202290652859106891 ] 
dist 143=[-2.1009696358241308239 ,-.01869524217195014089] 
dist 144=[-2.1921440385616820838 ,-.03324691389770060765] 
dist 145=[-2.2702336007955875562 ,-.06054533353047812662] 
dist 146=[-2.3510418074479863335 ,-.06673377380880382478] 
dist 147=[-2.4200943844356331104 ,-.08359189716670351485] 
dist 148=[-2.4512503876166854093 ,-.08543427115610467980] 
dist 149=[-2.4657603589916956828 ,-.08242084513179936078] 
dist 150=[-2.4683447373092101166 ,-.07205476423974871193] 
dist 151=[-2.4193947660620880269 ,-.05901564147943008667] 
dist 152=[-2.4056522645632058965 ,-.04532748384412119758] 
dist 153=[-2.3964446919842080912 ,-.02856306944203685683] 
dist 154=[-2.3910023453290915127 ,-.00323451061724522309] 
dist 155=[-2.0962592258122223074 ,.31338661914151654861] 
dist 156=[-2.0590031896909769135 ,.62574584505049781035] 
dist 157=[-1.9590882327798779761 ,.88837063180052039029] 
dist 158=[-1.9405180517735650046 ,1.1521966823632718095 ] 
dist 159=[-1.7539576869428206356 ,1.3969566385145900738 ] 
dist 160=[-1.7145591071774775022 ,1.5834615822133468528 ] 
dist 161=[-1.6666026340278006977 ,1.7632242644831522772 ] 
dist 162=[-1.6476740153518341774 ,1.9810662151825211562 ] 
dist 163=[-1.2153048058279100607 ,2.1858858582062463543 ] 
dist 164=[-1.1570995077473634927 ,2.3136578118970394622 ] 
dist 165=[-1.0358676555910400256 ,2.4095968730278320318 ] 
dist 166=[-1.0026924851854551406 ,2.4873257095775079239 ] 
dist 167=[-.873294619389110561  ,2.5474940787471244310 ] 
dist 168=[-.84688090631593140193,2.5733238689720089910 ] 
dist 169=[-.78861347088825653878,2.5837501230663229877 ] 
dist 170=[-.77138095109521338562,2.5824216289094238544 ] 
dist 171=[.07329212795961321143,.4293545646073927588 ] 
dist 172=[.09917296354436172438,.4275647706673205222 ] 
dist 173=[.05305247322498018449,.43230304375430378075] 
dist 174=[-.03463962040999513421,.57835748921801867837] 
dist 175=[-.12276650406746601046,.71694941155013153671] 
dist 176=[-.18165753239981814506,.82779422986162859624] 
dist 177=[-.23043715910269704401,.93969523890002629706] 
dist 178=[-.27820159273003661266,1.0825054845809274109 ] 
dist 179=[-.32168129406227201317,1.2204811123574045808 ] 
dist 180=[-.35335682904404027427,1.3130798441725163695 ] 
dist 181=[-.38246347764737582423,1.3902992336664875898 ] 
dist 182=[-.41568759945174784101,1.4668711676405563909 ] 
dist 183=[-.4459926934821031845 ,1.5372985553397890789 ] 
dist 184=[-.46344715931325741525,1.5899858995273924498 ] 
dist 185=[-.4748328776501792134 ,1.6398493012666019700 ] 
dist 186=[-.4809138413559471229 ,1.6990039410882051393 ] 
dist 187=[-.4844998618046273291 ,1.7518535722201553062 ] 
dist 188=[-.4859265840412367918 ,1.7765433712547613309 ] 
dist 189=[-.51791509374336165226,1.7886175218343806283 ] 
dist 190=[-.66036973847742259258,1.7910930952173318354 ] 
dist 191=[-.79740714908495968797,1.7600762550498454489 ] 
dist 192=[-.91003632476248230651,1.7515296585045599732 ] 
dist 193=[-1.0265022743578394464 ,1.7459392503216962282 ] 
dist 194=[-1.1788587909696217318 ,1.7429153227846549561 ] 
dist 195=[-1.3278163724540950058 ,1.4649337235290009451 ] 
dist 196=[-1.4307121040113043735 ,1.4258690465934815056 ] 
dist 197=[-1.5197016775903088324 ,1.3546613840791351638 ] 
dist 198=[-1.6131382304983403007 ,1.3362311017793720222 ] 
dist 199=[-1.7024275571554651966 ,1.2741758203052867857 ] 
dist 200=[-1.7748593695223935615 ,1.2562571474146939097 ] 
dist 201=[-1.8489111469402072424 ,1.2392291107542811289 ] 
dist 202=[-1.9446689979171631098 ,1.2311600255359039107 ] 
dist 203=[-2.0347781089455349602 ,.14366270927396471406] 
dist 204=[-2.0862768397984247626 ,.07139861199896950069] 
dist 205=[-2.1194186414051884210 ,.09907510449770217331] 
dist 206=[-2.1362355608351308330 ,.19268898290616315089] 
dist 207=[-2.1436860087963867496 ,.28747151012661331094] 
dist 208=[-2.1419319776310969671 ,.35228667000496916607] 
dist 209=[-2.1305062103868819292 ,.40763700980055812786] 
dist 210=[-2.1217482292210204490 ,.4646316876468165394 ] 
dist 211=[-1.9707326537183389173 ,.51840112841554909289] 
dist 212=[-1.9439428275714828252 ,.56087489133981569208] 
dist 213=[-1.8817422167077251087 ,.60325943672131224463] 
dist 214=[-1.8606677347520820940 ,.65667277412243842974] 
dist 215=[-1.7593816986984512369 ,.70793415383617196561] 
dist 216=[-1.7363327762812265109 ,.74172709828819705336] 
dist 217=[-1.6820061592197824547 ,.76923441427264435301] 
dist 218=[-1.6633539140028542125 ,.79540059344453540873] 
dist 219=[-1.5571299558683607429 ,.81873822981717596439] 
dist 220=[-1.5790489614705895948 ,.83495266879035057048] 
dist 221=[-1.5893856535596129472 ,.99315389606636825612] 
dist 222=[-1.5906042823807464560 ,1.2079268171384589781 ] 
dist 223=[-1.5765477223368673161 ,1.4000050882182247419 ] 
dist 224=[-1.5692093492642087716 ,1.5344113950068885273 ] 
dist 225=[-1.5563613137233087444 ,1.6524845862571454473 ] 
dist 226=[-1.5507120120495898033 ,1.7793506891174146426 ] 
dist 227=[-1.3769272322136482851 ,1.8947992305416287578 ] 
dist 228=[-1.3499508011501762692 ,1.9672865157666166971 ] 
dist 229=[-1.2929810398809005710 ,2.0222753083394908651 ] 
dist 230=[-1.2757076831727651941 ,2.0678594965832571502 ] 
dist 231=[-1.2000074387701107026 ,2.1039755150462134905 ] 
dist 232=[-1.1840405428511732200 ,2.1211617807575749587 ] 
dist 233=[-1.1374719925777221940 ,2.1277922720301139057 ] 
dist 234=[-1.1300762490887225434 ,2.1263297795756492663 ] 
dist 235=[.03422984242989190258,.62550698856088749013] 
dist 236=[.03721701660703588524,.61567206622815769246] 
dist 237=[.02918703230579227713,.58912122002056334004] 
dist 238=[-.07340212418302990404,.5838121581416356765 ] 
dist 239=[-.23820829753195352482,.58677913299972198796] 
dist 240=[-.34716045708094315457,.6147462547091063601 ] 
dist 241=[-.4361981337151925784 ,.63550344831823951413] 
dist 242=[-.5214942187029983085 ,.65189053504626513853] 
dist 243=[-.59798378253805749625,.66424203037291444837] 
dist 244=[-.6518607184514407714 ,.66888652986795795373] 
dist 245=[-.69955880913993182966,.67024202723341295808] 
dist 246=[-.75137876337013160592,.6694606655320434235 ] 
dist 247=[-.79843114264314801088,.65345216011772979624] 
dist 248=[-.8270942781218577036 ,.64922996489424308443] 
dist 249=[-.84780999536729464828,.63202558377522656317] 
dist 250=[-.86313165779757355632,.60115547032104238462] 
dist 251=[-.87383290087813263096,.37714723722337018844] 
dist 252=[-.87611155507778060402,.35504623532226651234] 
dist 253=[-.87534229413761022938,.29723547258783991867] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 2, 0, 2] 
dist 0=[50.838863685571428838  ,50.838863685571428838  ] 
dist 1=[50.572131927794954625  ,50.909600247230845842  ] 
dist 2=[50.044907569949970734  ,50.925590076313598597  ] 
dist 3=[49.020951530004816484  ,50.892175033588412953  ] 
dist 4=[47.904413609294671959  ,50.819847165520934194  ] 
dist 5=[47.007353705952937428  ,50.667097528680509935  ] 
dist 6=[46.095497860299891864  ,50.609737523771608032  ] 
dist 7=[44.920004430581676077  ,50.472863740862509760  ] 
dist 8=[43.659396541215943892  ,49.302036351190794624  ] 
dist 9=[42.075405279358317380  ,46.563886905465872072  ] 
dist 10=[39.913809894180294890  ,45.998270289896550302  ] 
dist 11=[37.669563998883847332  ,45.027777385813798215  ] 
dist 12=[34.927581264952995947  ,44.774043150924816485  ] 
dist 13=[30.777665709283533681  ,44.021882087758582616  ] 
dist 14=[26.598044376533732066  ,43.794764517325841873  ] 
dist 15=[23.737342830226083709  ,43.554117105214073710  ] 
dist 16=[21.285781685281619050  ,42.242644311359139119  ] 
dist 17=[18.740404736982044068  ,32.369780742050065292  ] 
dist 18=[16.319132042654222418  ,32.030170629185393750  ] 
dist 19=[14.363195099781777883  ,31.921459617733652570  ] 
dist 20=[12.366471089248280105  ,20.342047649509688873  ] 
dist 21=[9.7820120816921917322 ,16.028484002887321889  ] 
dist 22=[7.2571654812820761397 ,15.266405859402958408  ] 
dist 23=[5.4984339758903746995 ,14.080906570098327368  ] 
dist 24=[3.9570438986534637242 ,13.789641305270460950  ] 
dist 25=[2.3002434487238985972 ,9.0989073542381699901 ] 
dist 26=[.68683041100606193343,8.5053133597929655559 ] 
dist 27=[-.84057564217973238667,7.2761546739202320346 ] 
dist 28=[-2.7372732515131710601 ,7.0096310167990487864 ] 
dist 29=[-4.1121111482826341793 ,5.9409595049208495097 ] 
dist 30=[-6.0247835071564354345 ,5.7475114030669652155 ] 
dist 31=[-7.2438517944023559848 ,5.5146519099705484554 ] 
dist 32=[-8.1954535629620930655 ,5.1551941566400964206 ] 
dist 33=[-9.0391267730462205363 ,-4.7151122723079163169 ] 
dist 34=[-9.7555336461770419331 ,-5.0535628130585739781 ] 
dist 35=[-10.198579786308372082  ,-5.1094335387825896627 ] 
dist 36=[-10.529839265126909432  ,-7.9157275463684782006 ] 
dist 37=[-10.799747911747303312  ,-8.0902920293369480835 ] 
dist 38=[-11.049904223901847976  ,-8.4081908858596553668 ] 
dist 39=[-11.316549317641328171  ,-8.4621448704579367344 ] 
dist 40=[-11.493565860811584122  ,-8.5180717078029533650 ] 
dist 41=[-11.613757627246982201  ,-8.0772513290309654703 ] 
dist 42=[-11.653286075809744532  ,-7.2611703730916629514 ] 
dist 43=[-11.643299371813292336  ,-6.3476178217421870658 ] 
dist 44=[-11.623897648559351347  ,-5.1873747426115004480 ] 
dist 45=[-11.455908795331429448  ,-3.3862642612266344414 ] 
dist 46=[-11.401711509763990825  ,-1.5658474740173151025 ] 
dist 47=[-11.200426342089108747  ,-.328439557090934158  ] 
dist 48=[-11.151092885024994519  ,.71989514651618368854] 
dist 49=[-7.3513732551246038610 ,1.7855721299310338069 ] 
dist 50=[-7.2274998273613897526 ,2.7820736957129827243 ] 
dist 51=[-7.1859744174984269498 ,3.5542845170239136790 ] 
dist 52=[-5.4262210255942578517 ,4.3109274897642499693 ] 
dist 53=[-4.0429198597100195442 ,5.2453192490290344133 ] 
dist 54=[-3.7865630519877983122 ,6.1327813441816762568 ] 
dist 55=[-3.4291320541478423633 ,6.7020730233104700886 ] 
dist 56=[-3.3233966972849835317 ,7.1479780106754462193 ] 
dist 57=[-1.3514488258737599466 ,7.5428220433250824068 ] 
dist 58=[-1.1041594144022682542 ,7.8751658538315383167 ] 
dist 59=[-.5487351811545354587 ,8.0715356390645075767 ] 
dist 60=[-.44876281684507485105,8.2061169107566008936 ] 
dist 61=[.0787054043987911620 ,8.2917601849815663938 ] 
dist 62=[.32356120643175276577,8.3447968285114348291 ] 
dist 63=[.5314772301322073708 ,8.3491901191719852902 ] 
dist 64=[.57654652611737486001,8.3187431819944667203 ] 
dist 65=[1.8858519733574379424 ,5.1497281644713803892 ] 
dist 66=[2.0141156560308317734 ,5.2013233447063277818 ] 
dist 67=[2.2817646779549854352 ,5.2116340478968295912 ] 
dist 68=[2.2925415318398217873 ,3.1936341577460935314 ] 
dist 69=[2.1820411714628682202 ,3.2541172582604176364 ] 
dist 70=[2.0660135746937121951 ,3.3004988948099158480 ] 
dist 71=[1.9122836011328653198 ,3.3281996860015820507 ] 
dist 72=[1.7461075118426155800 ,3.3477477666934076837 ] 
dist 73=[1.5803449895144987085 ,3.3615151019636520092 ] 
dist 74=[1.3830189440395975774 ,3.3706377334927144018 ] 
dist 75=[1.0907812873702776837 ,3.3716039848121325863 ] 
dist 76=[.7891363263398492242 ,3.3667739610914223143 ] 
dist 77=[.5542240167972882852 ,3.3577567531064060863 ] 
dist 78=[.3228679378869167235 ,2.7568153292913345196 ] 
dist 79=[.0353835029679651000 ,2.7565291440526753479 ] 
dist 80=[-.2668072819751531831 ,2.7560365466271142259 ] 
dist 81=[-.5569130889746279187 ,1.4820469669146570131 ] 
dist 82=[-.8943161504504852873 ,1.4460531304093217437 ] 
dist 83=[-1.3854062087272005877 ,1.4342404876607440845 ] 
dist 84=[-1.8708079611991627852 ,1.3815285505575867919 ] 
dist 85=[-2.1855053782748245344 ,1.3667134218020852504 ] 
dist 86=[-2.4360781466421642620 ,1.3590713625909726190 ] 
dist 87=[-2.6654119334929920164 ,1.3590355842560032594 ] 
dist 88=[-2.8641528234286656257 ,1.3637290212795045835 ] 
dist 89=[-2.9925632218818825890 ,1.3749711119862463108 ] 
dist 90=[-3.0943642884480495011 ,1.3930643995170603959 ] 
dist 91=[-3.1868579908594946428 ,1.4251035178452819938 ] 
dist 92=[-3.2645547171438160176 ,1.4600684390486186905 ] 
dist 93=[-3.3072641085362974937 ,1.4898446842772250649 ] 
dist 94=[-3.3326724570928967765 ,1.5214459845588681369 ] 
dist 95=[-3.3412605984402156226 ,1.5637100314113671851 ] 
dist 96=[-3.3384386862440845872 ,1.6095192896976009308 ] 
dist 97=[-3.3332160745627975266 ,1.6552761782991106782 ] 
dist 98=[-3.2968943966523690935 ,1.7097175062280737548 ] 
dist 99=[-3.2892391103289409490 ,1.7901905792272990153 ] 
dist 100=[-2.1723753758605010808 ,1.8681384959884564655 ] 
dist 101=[-2.1819278816516332627 ,1.9125009558901293185 ] 
dist 102=[-2.1830363437404411250 ,1.9407121038142157171 ] 
dist 103=[-2.1790349343606564433 ,1.9541930448173012475 ] 
dist 104=[-2.1624888926920821037 ,1.9591189966166723371 ] 
dist 105=[-2.1522832057144308839 ,1.9568943268613807135 ] 
dist 106=[-2.0871014926204026208 ,1.9435084397033174008 ] 
dist 107=[-2.0689601462175380125 ,1.9341771682928160135 ] 
dist 108=[-2.0330415337953829885 ,1.7938613097361425268 ] 
dist 109=[-2.0205158476753577403 ,1.7685440399528298003 ] 
dist 110=[-1.8943449385024229519 ,1.7082430303410458229 ] 
dist 111=[-1.8574742684925853123 ,1.6874605782404771759 ] 
dist 112=[-1.8437022426916224844 ,1.5863258517803718835 ] 
dist 113=[-1.2033802018675037892 ,1.5630397943707745344 ] 
dist 114=[-1.1381489038309832426 ,1.5117935588972779416 ] 
dist 115=[-.98187355965164659854,1.4948656799424235902 ] 
dist 116=[-.95518489494867191017,.76462511133226584286] 
dist 117=[-.76030341581407472181,.87592720298715014608] 
dist 118=[-.68829276263131346805,1.0226798089419760184 ] 
dist 119=[-.62794503320234578063,1.1648393950691780654 ] 
dist 120=[-.61030612420643503108,1.3382473239446108528 ] 
dist 121=[-.30037921081119670125,1.5020515840126970227 ] 
dist 122=[-.23333356892463164435,1.6058628467782055199 ] 
dist 123=[-.14692664001543922036,1.6857874309360903529 ] 
dist 124=[-.11952565809864258761,1.7542094156842161405 ] 
dist 125=[-.10386826183803467422,1.8101406154689885071 ] 
dist 126=[-.01748920834525837050,1.8401880187671767162 ] 
dist 127=[-.01589956011711808201,1.8570789570500682956 ] 
dist 128=[-.01079005274002566317,1.8604748200763782956 ] 
dist 129=[-.00914981557211031353,.52409420729365061921] 
dist 130=[-.00745022375159670860,.52253877098784910463] 
dist 131=[-.00650012968114568634,.52125187374946884257] 
dist 132=[.23088877963271955087,.49150907993877173562] 
dist 133=[.18422190994243583074,.52943343909927960442] 
dist 134=[.14308359559574158364,.55564754940102978653] 
dist 135=[.09867699246475864707,.57834549089024202948] 
dist 136=[.05550756009522028076,.60222773749955706343] 
dist 137=[.01930587212114569706,.62312592727837618366] 
dist 138=[-.01877303612563147815,.63390847031921544733] 
dist 139=[-.06944106019600387434,.63956175348860030995] 
dist 140=[-.11939556691520689649,.64057521519616406164] 
dist 141=[-.15462767743370018941,.63667028216270092033] 
dist 142=[-.18587830832032700845,.63450401197309256021] 
dist 143=[-.21993867304593156681,.63201224793781141932] 
dist 144=[-.25327548328444134358,.62976691694152831519] 
dist 145=[-.28164002892852445936,.51174934267594587133] 
dist 146=[-.31185597704939865511,.49800180220501850745] 
dist 147=[-.35259063333476633958,.46264903824875127403] 
dist 148=[-.39173979419546862017,.4568321297098399951 ] 
dist 149=[-.41562586968307835955,.39682602830574997807] 
dist 150=[-.43296451046314811392,.38474876303787169003] 
dist 151=[-.44596756781282803281,.37068737830776886259] 
dist 152=[-.45579069234289043953,.3660545969895220774 ] 
dist 153=[-.46042962536861781826,.2428049745994174207 ] 
dist 154=[-.46220239650271286896,.22670806309826038665] 
dist 155=[-.46345673523904288518,.19357578614075203235] 
dist 156=[-.50231585919787758566,.18474330779136500946] 
dist 157=[-.53933366110364916597,.1975000680630145185 ] 
dist 158=[-.5691985833177643924 ,.21662296739761028866] 
dist 159=[-.59959337519605167555,.23934154639321629015] 
dist 160=[-.63872668105333487947,.26265431430950980326] 
dist 161=[-.67571385694503338471,.28415107239958794462] 
dist 162=[-.69753917517270221975,.30845620323663951768] 
dist 163=[-.71247135960295687838,.34298278687385455043] 
dist 164=[-.72193458790772956174,.37672235876239120735] 
dist 165=[-.72783573610726443974,.39788624456044600834] 
dist 166=[-.72854490150414124855,.41391467546466080398] 
dist 167=[-.72706274357368143637,.42715222597376991365] 
dist 168=[-.72471984439852437426,.4376029054118460136 ] 
dist 169=[-.68517715173002934768,.44250575157125099461] 
dist 170=[-.67764839738858564306,.44520497135841817706] 
dist 171=[-.66041770695916658938,.44536821451525803857] 
dist 172=[-.65442575151693709794,.44240156532204084132] 
dist 173=[-.62508294438792740219,.44090120787627092911] 
dist 174=[-.6182877950521009649 ,.4346790619262658357 ] 
dist 175=[-.60107342943944960672,.43270452637991575429] 
dist 176=[-.5953934440624847435 ,.41236400771510928556] 
dist 177=[-.47625027704477027598,.40722448418675680627] 
dist 178=[-.47142161600181515774,.40090173415662786128] 
dist 179=[-.45637799982573785324,.40356859544110504637] 
dist 180=[-.45408151733732014353,.42284779921578736264] 
dist 181=[-.41928201581911420882,.43334031670795590532] 
dist 182=[-.41158467866664198057,.44258904119829400088] 
dist 183=[-.40504865710069611154,.48564013304093412777] 
dist 184=[-.40332606709867401471,.53625958773320836012] 
dist 185=[-.37942636838458072118,.5830340804189188736 ] 
dist 186=[-.40694284078059725203,.61159725039530223389] 
dist 187=[-.43847752732855837675,.6323343902492564338 ] 
dist 188=[-.46723319769823740449,.64786017238802924103] 
dist 189=[-.48451937533360539161,.65928642312996442526] 
dist 190=[-.49672890756754574093,.66365453469454340797] 
dist 191=[-.50521726857177288005,.66485115674248964864] 
dist 192=[-.51086576144693286758,.66368714438293787603] 
dist 193=[-.51197659807098025955,.3410084944675963916 ] 
dist 194=[-.51096280511995048575,.33307446993215538394] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 1, 1, 2] 
dist 0=[39.966821520719369741  ,39.966821520719369741  ] 
dist 1=[39.685062370107086709  ,40.394759712761006953  ] 
dist 2=[38.987755595773490776  ,40.878766998049594563  ] 
dist 3=[37.898323154419995918  ,41.173961075181050524  ] 
dist 4=[36.121785246601981787  ,41.387782793016740319  ] 
dist 5=[34.294785985011440570  ,41.546704949630284201  ] 
dist 6=[33.003720269778450068  ,41.690772762879735457  ] 
dist 7=[31.854470512049989053  ,41.718631553496403615  ] 
dist 8=[30.593630146657041026  ,41.594315461635106005  ] 
dist 9=[29.352485138680233858  ,41.519865484365316130  ] 
dist 10=[28.281656717294273658  ,41.428094540562427928  ] 
dist 11=[27.126300813336212540  ,41.365240245848022672  ] 
dist 12=[25.547084854741726923  ,41.124686094505445593  ] 
dist 13=[23.962973138078439671  ,41.034789281518505716  ] 
dist 14=[22.787832276920311610  ,40.778908377417957444  ] 
dist 15=[21.681523818795545022  ,40.655055872142929259  ] 
dist 16=[20.372106042742909930  ,32.183101509720818249  ] 
dist 17=[19.023311955428872416  ,31.404724614896099894  ] 
dist 18=[17.759297647953494636  ,29.485119413971476239  ] 
dist 19=[16.307321235183400944  ,29.197978514096223526  ] 
dist 20=[14.206723832982099624  ,26.241257299687890919  ] 
dist 21=[12.121184105232393314  ,25.673016537045879265  ] 
dist 22=[10.729292549319780520  ,25.035200003265981296  ] 
dist 23=[9.5698080504298293646 ,24.887893729284654866  ] 
dist 24=[8.4134195787772785623 ,19.501651314390592103  ] 
dist 25=[7.3379683271756968454 ,18.815090841604178107  ] 
dist 26=[6.1240400686967130357 ,17.446695616693508452  ] 
dist 27=[4.5417705504797621978 ,17.094573614694382266  ] 
dist 28=[2.7553993427205787133 ,15.847288072527418236  ] 
dist 29=[.20964921932120390604,15.574334970976968155  ] 
dist 30=[-2.2919248674317809172 ,15.174907340541205350  ] 
dist 31=[-3.9018762522137870748 ,15.058369040532577789  ] 
dist 32=[-5.1766177467420239788 ,4.5974554907471666036 ] 
dist 33=[-6.3383672620082353555 ,3.7254487684968189010 ] 
dist 34=[-7.3477269925944554245 ,2.5198664219951786318 ] 
dist 35=[-8.0134790741394544515 ,2.3095418011950420025 ] 
dist 36=[-8.5601175430636268828 ,2.2635544770039402829 ] 
dist 37=[-9.0937031386026798058 ,.9520303863601540966 ] 
dist 38=[-9.5591604279071715066 ,.8198314416228079208 ] 
dist 39=[-9.8334762697081813004 ,.5395059982150411102 ] 
dist 40=[-10.023472946286414069  ,.4819663240702717781 ] 
dist 41=[-10.151540816714245831  ,.1896927234833993176 ] 
dist 42=[-10.232353102820577785  ,.14015349322080899641] 
dist 43=[-10.240165853537445576  ,.03268974813837198784] 
dist 44=[-10.204359452125255493  ,.01314853308960501197] 
dist 45=[-10.165447325477640889  ,-.14575666203965962824] 
dist 46=[-9.5298366218883599794 ,-.17376726847835208766] 
dist 47=[-9.5402895553422530648 ,-.19874938233841099484] 
dist 48=[-6.5142270158612449409 ,-.1959604863806415925 ] 
dist 49=[-6.3275917969931980481 ,-.18055853989579834602] 
dist 50=[-5.8524892602234145706 ,-.14733703642658436426] 
dist 51=[-5.7898171657027939149 ,-.09438517086321634132] 
dist 52=[-5.4669786364232299984 ,.32494831580104634818] 
dist 53=[-4.8524595815657871371 ,1.1790423020655335298 ] 
dist 54=[-4.6768643153648122902 ,2.0118995024372363962 ] 
dist 55=[-4.6288627394658899351 ,2.5838107822047725711 ] 
dist 56=[-3.1823209667149081730 ,3.0750081536803399452 ] 
dist 57=[-2.9987290739558814745 ,3.5857078020330965125 ] 
dist 58=[-2.6183989961344478402 ,4.0712355699441735823 ] 
dist 59=[-2.5183496516407346745 ,4.4620254536221133957 ] 
dist 60=[-2.1478631039795059323 ,4.8594116656663328132 ] 
dist 61=[-2.0734760892404916081 ,5.3714562394428023512 ] 
dist 62=[-1.9356824386316431101 ,5.8572678768071457173 ] 
dist 63=[-1.9030843839762569665 ,6.1499263315285323254 ] 
dist 64=[.32881245533125198625,6.3583082502888121226 ] 
dist 65=[.52175971575667599082,6.5074875249900281882 ] 
dist 66=[.92736918525766727734,6.6146870813257193645 ] 
dist 67=[1.0154080186356302417 ,6.6553604663348717364 ] 
dist 68=[1.4009678102795680937 ,6.6636568409282065442 ] 
dist 69=[1.4689037834334222426 ,6.6526257527099505818 ] 
dist 70=[1.5805067005950882226 ,6.2855655751798049681 ] 
dist 71=[1.6032063639487630066 ,6.2160361338779092205 ] 
dist 72=[1.6154772462022024229 ,6.0722366673098267207 ] 
dist 73=[1.5755241961416360729 ,6.0245883536072639482 ] 
dist 74=[1.4961889520846039555 ,5.8006798015202545630 ] 
dist 75=[1.3427226911381890620 ,5.7493000991263809625 ] 
dist 76=[1.1535069345259152428 ,5.5874012661347826996 ] 
dist 77=[.9314099588727522523 ,5.5596257565253403680 ] 
dist 78=[-.08322522851412935705,4.0670584843246895563 ] 
dist 79=[-.85741882784658703768,4.0603583710955828926 ] 
dist 80=[-1.4987884856251357990 ,3.0266907958195777922 ] 
dist 81=[-2.1278541567203871413 ,2.9637853323051916834 ] 
dist 82=[-2.7019527210373264996 ,2.3431544806417786864 ] 
dist 83=[-3.1238601285110210098 ,2.2249902892447738784 ] 
dist 84=[-3.5157181769078225131 ,2.0822301753102131893 ] 
dist 85=[-3.9698466971022188357 ,2.0441603040096570670 ] 
dist 86=[-4.3911777970084960683 ,.9918701401289417031 ] 
dist 87=[-4.6520826985018272278 ,.8597507881331156331 ] 
dist 88=[-4.8458257437159989977 ,.5822418454658656389 ] 
dist 89=[-4.9989835111867006730 ,.5104979928254617999 ] 
dist 90=[-5.1155533043483187487 ,.2355978713752444290 ] 
dist 91=[-5.1632076356569584532 ,.1828987965075514049 ] 
dist 92=[-5.1819295221542629019 ,.0802819135105858200 ] 
dist 93=[-5.1829712647316798535 ,.0554345456483756632 ] 
dist 94=[-2.7769254656280691963 ,.13879809903246706942] 
dist 95=[-3.0091777312972449145 ,.46732270844496938879] 
dist 96=[-3.2293992522317058622 ,.80290373536181241102] 
dist 97=[-3.3580501223880545268 ,1.0345264535413212579 ] 
dist 98=[-3.4447510560167919963 ,1.2883652934004873729 ] 
dist 99=[-3.4974174779605754538 ,1.5554588087360908737 ] 
dist 100=[-3.5316057989254061952 ,1.8037466643668939500 ] 
dist 101=[-3.5444932813726995674 ,1.9932941722368267678 ] 
dist 102=[-3.5443907228205816863 ,2.1761361709420880353 ] 
dist 103=[-3.5384994601886349933 ,2.3976549676867999754 ] 
dist 104=[-2.9934255928949034730 ,2.6055037660259227734 ] 
dist 105=[-2.9220751260274633568 ,2.7337799512310709621 ] 
dist 106=[-2.8164412801480570241 ,2.8283216190291519986 ] 
dist 107=[-2.7268809644432433967 ,2.9015172579191535087 ] 
dist 108=[-2.1186715209298799479 ,2.9553351794694288229 ] 
dist 109=[-1.7690740091979897074 ,2.9725252549719908365 ] 
dist 110=[-1.6828566177332187079 ,2.9755842645041949098 ] 
dist 111=[-1.6703641712092914395 ,2.9730195172314199302 ] 
dist 112=[-.54093788846147243835,.4065042510532674702 ] 
dist 113=[-.43629587812603145268,.47426131294196256654] 
dist 114=[-.19302746689562276545,.53429002859597509359] 
dist 115=[-.15518076072709792388,.57540532297015895901] 
dist 116=[-.00231053713218739008,.61063283742593401464] 
dist 117=[.00292469043131396125,.64715335356040176846] 
dist 118=[.02221840393204333397,.67975534867949938216] 
dist 119=[.02430035990068652991,.69933588169289194165] 
dist 120=[.02124368170100990968,.76080573303620229947] 
dist 121=[.01043580542850941583,.85583491842769773681] 
dist 122=[-.00448366228132428846,.93013987622345321022] 
dist 123=[-.02395716724541141836,.99578414487315881328] 
dist 124=[-.05047931625855778808,1.0510149338505247040 ] 
dist 125=[-.09353768914182345091,1.0837510626276918927 ] 
dist 126=[-.13729852948534870394,1.1063957522583482883 ] 
dist 127=[-.16662751619138326533,1.1213536305025833410 ] 
dist 128=[-.19100010408682956664,1.1316027952187833010 ] 
dist 129=[-.21498194187390375237,1.1354480785842687773 ] 
dist 130=[-.23688389600548098593,1.1354356360131549052 ] 
dist 131=[-.25295748522245183793,1.1332431583249723826 ] 
dist 132=[-.2678503167958502947 ,1.1222621625949194411 ] 
dist 133=[-.2850433310366819703 ,1.1178697086698721728 ] 
dist 134=[-.30078194704966828236,1.1004624807710257455 ] 
dist 135=[-.30987138305946235663,1.0959128276374383331 ] 
dist 136=[-.31584924126083734314,1.0406415881643911232 ] 
dist 137=[-.31916941094159017342,1.0294037601702986654 ] 
dist 138=[-.32071877226026278674,.99900053961735382466] 
dist 139=[-.32064756909267627291,.99094281978245032851] 
dist 140=[-.45184186481432179028,.93020153852998883448] 
dist 141=[-.58489909294903198838,.91643202030003614627] 
dist 142=[-.73947939428779615014,.89448351732780923472] 
dist 143=[-.96410474005808718705,.88762742561202842452] 
dist 144=[-1.1864872789461847376 ,.25441684424008262801] 
dist 145=[-1.3321153845290975057 ,.29193041847314216039] 
dist 146=[-1.4495869988048724191 ,.32539918136342507639] 
dist 147=[-1.5595553746676978803 ,.3485853012685519161 ] 
dist 148=[-1.6564540216240777468 ,.36867220422849688165] 
dist 149=[-1.7217459582081656866 ,.38976801094901042105] 
dist 150=[-1.7764806415696390797 ,.40853189943671780002] 
dist 151=[-1.8312324554242270337 ,.41931130955942879235] 
dist 152=[-1.8769089035517732267 ,.42629491174481167853] 
dist 153=[-1.8954111188068802944 ,.42991134529295782303] 
dist 154=[-1.9029428599352516550 ,.43143430024981452848] 
dist 155=[-1.9048122652821754984 ,.43110720940531371208] 
dist 156=[-1.8548889229758105418 ,.42783311132538905962] 
dist 157=[-1.8422822798660999204 ,.42593673935623691977] 
dist 158=[-1.8350150285726912980 ,-.04467606822001355498] 
dist 159=[-1.8331215474862907033 ,.02026664046859799760] 
dist 160=[-1.6454616459366948952 ,.27899607379207009029] 
dist 161=[-1.6232452906982234756 ,.52425899393313033104] 
dist 162=[-1.5599784655538305700 ,.72975490169046506175] 
dist 163=[-1.5485617536917770662 ,.93502062610473679918] 
dist 164=[-1.4181523642546384346 ,1.1246955124212958050 ] 
dist 165=[-1.3898547368944990839 ,1.2679465735479256285 ] 
dist 166=[-1.3590389236317795538 ,1.4047837656323865803 ] 
dist 167=[-1.3466577053242248053 ,1.5688516407314036980 ] 
dist 168=[-1.0098113004230135134 ,1.7222136987230962438 ] 
dist 169=[-.96453162504490320932,1.8163087917276201383 ] 
dist 170=[-.87286793863372547777,1.8851055369362444012 ] 
dist 171=[-.84825708238207885679,1.9374661901230499593 ] 
dist 172=[-.7557693146172684577 ,1.9764572270555462772 ] 
dist 173=[-.73563098817406184169,1.9918772468134785952 ] 
dist 174=[-.69696805253135229152,1.9967630929185659381 ] 
dist 175=[-.68652642099338195426,1.9936977954961483438 ] 
dist 176=[-.56978917536157600136,1.0615239057827005529 ] 
dist 177=[-.63917985726727606473,1.0854742008941716396 ] 
dist 178=[-.70429386145683683756,1.1027234388597984512 ] 
dist 179=[-.75514973489617467003,1.1092977377268091894 ] 
dist 180=[-.80536014365596550059,1.1105883742839098486 ] 
dist 181=[-.86789703178895732565,1.1088104615657819539 ] 
dist 182=[-.92755154950491148678,1.0467422591781289586 ] 
dist 183=[-.96625415458304675324,1.0349559287636848577 ] 
dist 184=[-.99706334000834569744,1.0789262120881647157 ] 
dist 185=[-1.0252036565662053364 ,1.1675821823861885736 ] 
dist 186=[-1.0495106110710590005 ,1.2434791001678698608 ] 
dist 187=[-1.0650151212851775274 ,1.3219552137612786964 ] 
dist 188=[-1.0770566140405913570 ,1.3962184310769005557 ] 
dist 189=[-1.0875372620951238353 ,1.4552955988212131228 ] 
dist 190=[-1.0949294020956686986 ,1.5146520664638749407 ] 
dist 191=[-1.0954032410726547133 ,1.5900324407220302042 ] 
dist 192=[-1.0914065677402406439 ,1.6598730077240139431 ] 
dist 193=[-1.0871425811982593572 ,1.6971110471901218905 ] 
dist 194=[-1.0564154636928462361 ,1.7176540689613514149 ] 
dist 195=[-1.0472929727025664349 ,1.7223863013967073193 ] 
dist 196=[-1.0323839405047001401 ,1.7180183316862114045 ] 
dist 197=[-1.0269533841887520774 ,1.7146097220403414685 ] 
dist 198=[-1.1055952117058871265 ,1.7101142370169839766 ] 
dist 199=[-1.2394292668301721067 ,1.7039950092759479622 ] 
dist 200=[-1.3693515018368518776 ,1.4903688142869865168 ] 
dist 201=[-1.4575510006791902063 ,1.4583304125858094594 ] 
dist 202=[-1.5321889553696945235 ,1.3982925546255052240 ] 
dist 203=[-1.6079659625459459899 ,1.3818333028477454779 ] 
dist 204=[-1.6787918291699071853 ,1.3206922565955525592 ] 
dist 205=[-1.7336622184063683161 ,1.3043322186059613971 ] 
dist 206=[-1.7874254381183829609 ,1.2750868560763688678 ] 
dist 207=[-1.8538312912091740622 ,1.2663589195912167687 ] 
dist 208=[-1.9148514048035645200 ,.55284823243466225382] 
dist 209=[-1.9471116189183121925 ,.65774439287694153567] 
dist 210=[-1.9645212500925817690 ,.75197110979551694411] 
dist 211=[-1.9670131835518056892 ,.81861807868619053808] 
dist 212=[-1.9611572741617103178 ,.87790851831125016463] 
dist 213=[-1.9547741752942899546 ,.94276363774979290673] 
dist 214=[-1.9388317843272345246 ,1.0016378483299807443 ] 
dist 215=[-1.9304904481300453259 ,1.0370490475656705663 ] 
dist 216=[-1.7517266468768971787 ,1.0620956955626536272 ] 
dist 217=[-1.7224455255777198026 ,1.0795887234276294646 ] 
dist 218=[-1.6566531955009104915 ,1.0911514547581981672 ] 
dist 219=[-1.6354502187838293639 ,1.0934989104397379664 ] 
dist 220=[-1.5373740588107561211 ,1.0906494720719540025 ] 
dist 221=[-1.5158518225341996792 ,1.0892713278274199006 ] 
dist 222=[-1.4619618135163794179 ,-.08465946968886855297] 
dist 223=[-1.4461688578814176213 ,.10115106118617272478] 
dist 224=[-1.3815733393010088706 ,.47976793032868237074] 
dist 225=[-1.4168328087095599165 ,.72936670128065931537] 
dist 226=[-1.4393010619749616991 ,.93257446489054228698] 
dist 227=[-1.4502334727617058416 ,1.1259698289948779927 ] 
dist 228=[-1.4549104858510097326 ,1.2985517793053959175 ] 
dist 229=[-1.4533642167549490619 ,1.4186595009315503533 ] 
dist 230=[-1.4464969242341740134 ,1.5234849215109629269 ] 
dist 231=[-1.4411838403573422116 ,1.6350503264045573017 ] 
dist 232=[-1.3299708947307617546 ,1.7363302578768525779 ] 
dist 233=[-1.3108280170093162081 ,1.8000897169174619226 ] 
dist 234=[-1.2680426746473161399 ,1.8486541573202768669 ] 
dist 235=[-1.2539658745406599972 ,1.8892663552770883168 ] 
dist 236=[-1.1877866296280478469 ,1.9217170871108997338 ] 
dist 237=[-1.1730331975864429663 ,1.9376959660376461081 ] 
dist 238=[-1.1345861680619505751 ,1.9446865351490947441 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 1, 1, 1, 0, 1] 
dist 0=[49.974440779119129897  ,49.974440779119129897  ] 
dist 1=[49.538313006278395220  ,50.107558555291566987  ] 
dist 2=[49.007950863431952785  ,50.132769610233074069  ] 
dist 3=[48.498397100190794476  ,50.137710477903009656  ] 
dist 4=[47.904413609294671969  ,50.046971974363045534  ] 
dist 5=[47.036849279824336292  ,49.303635636230187645  ] 
dist 6=[46.055863548275133402  ,49.095687936631404977  ] 
dist 7=[45.008817695915664364  ,48.978105522711535605  ] 
dist 8=[43.709050100965961044  ,48.826285319624915125  ] 
dist 9=[41.718512943759248169  ,45.451640369783661335  ] 
dist 10=[39.629195533018601153  ,43.672693000738328873  ] 
dist 11=[37.934828037252588641  ,42.527086781761093227  ] 
dist 12=[36.199444188943368691  ,42.237831135557485087  ] 
dist 13=[33.946274673840547275  ,41.307403940438911982  ] 
dist 14=[31.523126761244371910  ,41.027836970658311288  ] 
dist 15=[27.451664494551651584  ,40.856294760768462317  ] 
dist 16=[23.180594899593006194  ,40.702067224566800898  ] 
dist 17=[20.274060009195394586  ,35.504890704899128329  ] 
dist 18=[17.669246107580302430  ,21.547071533294624347  ] 
dist 19=[14.781369560273271753  ,18.197329390670429550  ] 
dist 20=[12.351314723403861133  ,17.660892648736025056  ] 
dist 21=[9.8988314838715730436 ,13.311212175897564631  ] 
dist 22=[7.6090348258157758702 ,12.544358710892012540  ] 
dist 23=[5.8287835277382146618 ,11.411812882502631951  ] 
dist 24=[4.0740617898763707056 ,11.117511812022167651  ] 
dist 25=[1.8860285125754671156 ,6.5357299937458491862 ] 
dist 26=[-.21302916012338048817,5.6729063169607747430 ] 
dist 27=[-1.6124222036575365798 ,4.4018475691576076455 ] 
dist 28=[-2.7732832182455515862 ,4.1598513445545825620 ] 
dist 29=[-3.9195621283931960757 ,2.9480636758664280138 ] 
dist 30=[-4.9758422342726108776 ,2.7483035008181545107 ] 
dist 31=[-5.7774021185375404718 ,2.4611805805166923948 ] 
dist 32=[-7.2206854920597911312 ,2.3996468794366614555 ] 
dist 33=[-8.1780590311026087331 ,-2.4569947701582486385 ] 
dist 34=[-8.9095875966329809996 ,-7.8512468002002930122 ] 
dist 35=[-9.5313118187829430270 ,-8.1447879429336015230 ] 
dist 36=[-10.040547843476829597  ,-8.7205401748641432057 ] 
dist 37=[-10.322554320857326314  ,-8.8200276766291640681 ] 
dist 38=[-10.495092435031039497  ,-9.1469422648438481396 ] 
dist 39=[-10.580630884211955546  ,-9.1336279506854981341 ] 
dist 40=[-10.634310383227874540  ,-9.0018030184815891229 ] 
dist 41=[-10.642025615903617051  ,-8.6758510388364371712 ] 
dist 42=[-10.617047491540724254  ,-8.2882186133206090206 ] 
dist 43=[-10.565939487686552781  ,-7.8662642392249424512 ] 
dist 44=[-10.535165521673838335  ,-7.0475295730845573306 ] 
dist 45=[-10.340155359866447442  ,-6.1529218664709870999 ] 
dist 46=[-10.285989998007407147  ,-5.0306972629454628158 ] 
dist 47=[-10.077100535758083968  ,-3.3030343984339854588 ] 
dist 48=[-10.044435538462308926  ,-1.5608188186419230056 ] 
dist 49=[-8.3522718154844394727 ,-.38041742917821774196] 
dist 50=[-5.5207359200419354272 ,.61585498472178467196] 
dist 51=[-4.5940876798603060483 ,1.6229925821594299236 ] 
dist 52=[-4.4432451474510315414 ,2.5615802117189674952 ] 
dist 53=[-3.1432300804545937156 ,3.2841955639526192668 ] 
dist 54=[-2.9047112057866055551 ,3.9880006252659807915 ] 
dist 55=[-2.5709431190065825131 ,4.8515205610328480435 ] 
dist 56=[-2.4738212749941890418 ,5.6693007361871188888 ] 
dist 57=[-.90726748561194004357,6.1904892254191800070 ] 
dist 58=[-.47535137678631641408,6.5949789405307188511 ] 
dist 59=[.02345437221572981057,6.9468072980923275889 ] 
dist 60=[.10760400980274503854,7.2384641785190426515 ] 
dist 61=[.70292939020679064856,7.4026995967491832574 ] 
dist 62=[.8028661225825058279 ,7.5052747434097001062 ] 
dist 63=[.9788818973528722813 ,7.5528265862298204007 ] 
dist 64=[1.0136426029830910239 ,7.5668205794769572570 ] 
dist 65=[1.8700673119690753231 ,6.1246478206760364292 ] 
dist 66=[2.0672938034407325064 ,2.5604990097855753302 ] 
dist 67=[2.2315424749012949769 ,2.7009221308899242352 ] 
dist 68=[2.2884656474897393671 ,2.8159552453648662694 ] 
dist 69=[2.2379720716490375481 ,2.8788047474438987801 ] 
dist 70=[2.1680230442776826823 ,2.9158064757945210512 ] 
dist 71=[2.0764556814792408351 ,2.9276235424949044234 ] 
dist 72=[1.9515286415034892880 ,2.9287798764183014110 ] 
dist 73=[1.7483480404111253028 ,2.9231936663800726330 ] 
dist 74=[1.5312111247665874143 ,2.9117477294154372604 ] 
dist 75=[1.3505344217358182780 ,2.9039328206814906606 ] 
dist 76=[1.1617260561445245184 ,2.8619344520657884278 ] 
dist 77=[.9120802833137658537 ,2.8487395631349556977 ] 
dist 78=[.64189976001533818722,2.8012416707224244888 ] 
dist 79=[.37107036537107916415,2.7896510083824149892 ] 
dist 80=[.04735761433818748349,2.4113156401965271683 ] 
dist 81=[-.43402336399326603207,1.8787348564568659896 ] 
dist 82=[-.91396876916725749489,1.4886592435706175564 ] 
dist 83=[-1.2319566409463418734 ,1.4376447826238837265 ] 
dist 84=[-1.4928413461876255452 ,1.3284813222765086301 ] 
dist 85=[-1.7447585092790562982 ,1.2975963520137966970 ] 
dist 86=[-1.9722648221524263058 ,1.1706466273677286816 ] 
dist 87=[-2.1356724365720766191 ,1.1459697394582981090 ] 
dist 88=[-2.2837811426549558270 ,1.0808909128813115251 ] 
dist 89=[-2.4502009625862271420 ,1.0711761446944066610 ] 
dist 90=[-2.6014547645327482113 ,.95455020781834366732] 
dist 91=[-2.6889986087819195041 ,.93223147615036078887] 
dist 92=[-2.7468387453458684180 ,.89475160188267983476] 
dist 93=[-2.7794631471040301777 ,.88485515556619763308] 
dist 94=[-2.7994098626649188926 ,.85780625306313043253] 
dist 95=[-2.8066214519402309474 ,.85032555931487089815] 
dist 96=[-2.8059141805975247558 ,.84768489773305157665] 
dist 97=[-2.8005579359182949279 ,.85079197874936422517] 
dist 98=[-1.5083892467832533159 ,.85431472022552620891] 
dist 99=[-1.5560789519517897184 ,.85371960071745883548] 
dist 100=[-1.5920473413510551438 ,.85022378626584664791] 
dist 101=[-1.6184302835625117904 ,.84714692767519688265] 
dist 102=[-1.6278345510573050892 ,.82562798722741821282] 
dist 103=[-1.6302596591444990595 ,.81923254449619145534] 
dist 104=[-1.6287643134353006896 ,.80541189705698243827] 
dist 105=[-1.5694431739981390011 ,.80012891514099109409] 
dist 106=[-1.5566339554823940115 ,.70289910528128676787] 
dist 107=[-1.5280966426555121206 ,.68754742965119062225] 
dist 108=[-1.5177457360810965840 ,.65190568446552262948] 
dist 109=[-1.4656002171984310852 ,.64092845679472544655] 
dist 110=[-1.4532289225930360509 ,.58741169313167606177] 
dist 111=[-1.4182896147852802959 ,.57576082148428904177] 
dist 112=[-1.4088767675576500730 ,.55047690092319983181] 
dist 113=[-.83594101878126256791,.5424930781781721459 ] 
dist 114=[-.78035388743787391033,.21241581305175907874] 
dist 115=[-.64859103170889244599,.33816590364616508953] 
dist 116=[-.62633875140140235705,.4967100891674214884 ] 
dist 117=[-.50056495437765082193,.64386863507788344535] 
dist 118=[-.47012088576669185241,.7563572730932058306 ] 
dist 119=[-.46148637988663531969,.86521436422322439235] 
dist 120=[-.34531392879848610988,.99787164634151268859] 
dist 121=[-.27442738114240380444,1.1231599970199741887 ] 
dist 122=[-.22546313472100198862,1.2025907997635027543 ] 
dist 123=[-.21590569336059417123,1.2637932167606035541 ] 
dist 124=[-.15402915558688743644,1.3162897890537517893 ] 
dist 125=[-.13525585635757268616,1.3592914067815609137 ] 
dist 126=[-.10551844933588055687,1.3825773905719371379 ] 
dist 127=[-.07902124888166913801,1.3959234058623957925 ] 
dist 128=[.16249873044601450263,1.3992314637388371546 ] 
dist 129=[.28743457250921117857,.52507545255196733442] 
dist 130=[.26390994907356092175,.34848077358451278136] 
dist 131=[.24639117256472698603,.37213734750822448969] 
dist 132=[.22991308258733370318,.39309846305603992094] 
dist 133=[.21053802622547127002,.41077156446870205029] 
dist 134=[.1907656283806747115 ,.42129709799932111244] 
dist 135=[.17269810100559375168,.42862111228841315506] 
dist 136=[.15239752393854398623,.43350826881658555142] 
dist 137=[.12370598483185306701,.43702539668004289816] 
dist 138=[.09423173152037054246,.43884400499964461844] 
dist 139=[.07083809327811617212,.43890578145207610914] 
dist 140=[.04850631297948982818,.43826005249190244232] 
dist 141=[.02172810964283518435,.43165799226662394951] 
dist 142=[-.00592633216646084643,.42942607049676942207] 
dist 143=[-.03175963629888947907,.42387458008947164151] 
dist 144=[-.06126636968777319639,.42151444040315838294] 
dist 145=[-.10359375284604315093,.30024799385525723852] 
dist 146=[-.14525549949302030204,.28779714836149441464] 
dist 147=[-.17210495025464208644,.25668306128774969249] 
dist 148=[-.19331033885121675881,.2520141055792529114 ] 
dist 149=[-.21243220075183218254,.20307149880626984519] 
dist 150=[-.22881128920912337534,.19365630439642454273] 
dist 151=[-.23906380185037108374,.1830163685312656953 ] 
dist 152=[-.24682302539118317821,.18054514363254281685] 
dist 153=[-.26062405367809740645,.09192155154689846323] 
dist 154=[-.28857761405662004038,.08080919072537348516] 
dist 155=[-.31224750576864139668,.05806612727053433116] 
dist 156=[-.33632213619383152293,.05217342484433960683] 
dist 157=[-.35886842084514454191,.04459156316982341071] 
dist 158=[-.37643510179750670466,.05108056929324374657] 
dist 159=[-.39375120953698434396,.05826063967792225944] 
dist 160=[-.41529663255678842789,.06732385735170373715] 
dist 161=[-.43539937072624757059,.08133223418276590977] 
dist 162=[-.44695447908678129449,.09536737755491242562] 
dist 163=[-.45448074065151772474,.10453833652820839219] 
dist 164=[-.45849555307802091422,.11190981264915170839] 
dist 165=[-.46056475583222243196,.11876221427223586568] 
dist 166=[-.46032202341623391268,.12476599379695973221] 
dist 167=[-.45889759585234243267,.12875048736686111188] 
dist 168=[-.45752253813468331358,.13202606386450444123] 
dist 169=[-.4245647258137049781 ,.13520118926604783428] 
dist 170=[-.41888446030171222404,.13779786748800227531] 
dist 171=[-.4065957509247111482 ,.13876481994913708739] 
dist 172=[-.40260958613071280769,.13897058573406556747] 
dist 173=[-.38407201894858006981,.13868309771857421374] 
dist 174=[-.37997812832740770594,.13559223133460686055] 
dist 175=[-.36822093409859657277,.13454583726521363327] 
dist 176=[-.36580454230471138712,.13972242301647928697] 
dist 177=[-.27121959797975695251,.16153292514092643354] 
dist 178=[-.26728739275567437511,.18260644772672199705] 
dist 179=[-.25602308840114042912,.19564517057657456716] 
dist 180=[-.25432227388437340554,.20532849930282696212] 
dist 181=[-.23123054329972603227,.22509220638901395774] 
dist 182=[-.2263061839039862435 ,.25456984160548629795] 
dist 183=[-.22180698886238159924,.28186579460789096327] 
dist 184=[-.22068223104466749536,.31338759460726283493] 
dist 185=[-.1769225570300531612 ,.34255711114753351319] 
dist 186=[-.18518479877251793976,.36046029824503870964] 
dist 187=[-.19005087332039710432,.37357004266143824538] 
dist 188=[-.19336018063434607922,.38359883657672988887] 
dist 189=[-.19540866029466841518,.3911190709625939022 ] 
dist 190=[-.19648733657311776373,.39421195387952982051] 
dist 191=[-.196587448726825879  ,.39528333088616567434] 
dist 192=[-.19503407433066421637,.39476334678905335452] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 0, 2, 0, 1] 
dist 0=[51.206105695291233847  ,51.206105695291233847  ] 
dist 1=[51.087660687671088517  ,51.260952556914936043  ] 
dist 2=[50.850300308080587626  ,51.244050848247792578  ] 
dist 3=[50.413270982596516840  ,51.192875639428751639  ] 
dist 4=[49.484896055893973267  ,51.110660665728775549  ] 
dist 5=[48.409597194608683184  ,50.989383879799394865  ] 
dist 6=[47.189845148041611357  ,50.905159956475720736  ] 
dist 7=[45.424331984802464875  ,48.081387011230061901  ] 
dist 8=[44.102688153297308619  ,47.620896016644101111  ] 
dist 9=[42.522709157217933606  ,46.905151057523224470  ] 
dist 10=[40.455651461010597201  ,46.686478513667727779  ] 
dist 11=[37.897613399626286975  ,46.170857241961603944  ] 
dist 12=[33.990130787233868810  ,46.042448708444344835  ] 
dist 13=[30.041419458164507836  ,45.967471114766563972  ] 
dist 14=[27.318628846979139228  ,45.331296815077433503  ] 
dist 15=[24.963943076813600995  ,32.395620711024591970  ] 
dist 16=[22.485507167962434513  ,31.564668504170989426  ] 
dist 17=[20.107297442105569305  ,29.946771338920885446  ] 
dist 18=[18.152833622319557719  ,29.531075180783160147  ] 
dist 19=[16.127533623042890768  ,28.083166293045926408  ] 
dist 20=[13.466094858334186312  ,27.742031580226294197  ] 
dist 21=[10.847450696058632438  ,27.308409422704341804  ] 
dist 22=[8.9929497013711040153 ,27.151525646262663250  ] 
dist 23=[7.3357739846576577688 ,12.522302304325520014  ] 
dist 24=[5.5051886112518880942 ,12.038960774373304007  ] 
dist 25=[3.6933451107548489521 ,10.806641479400736066  ] 
dist 26=[2.1107389853180284670 ,10.529668565256350589  ] 
dist 27=[.38504630630443590591,9.9361030395736263114 ] 
dist 28=[-1.9990817638465171842 ,9.8577572737835804184 ] 
dist 29=[-4.3269376929654040475 ,9.4081590126988874773 ] 
dist 30=[-5.8278887340900029373 ,9.0968228968712181764 ] 
dist 31=[-7.0186693481432891992 ,-2.6855223387052020787 ] 
dist 32=[-8.1069355968794889399 ,-3.1898756867057360971 ] 
dist 33=[-9.0995449166790638681 ,-4.2971708847947871323 ] 
dist 34=[-10.101166321781870881  ,-4.4599339838420687845 ] 
dist 35=[-10.954786089787791305  ,-5.6460587164785424150 ] 
dist 36=[-11.487872628189579475  ,-5.8269479293987014570 ] 
dist 37=[-11.892414281228393705  ,-6.1260968431410591025 ] 
dist 38=[-12.232631168057366252  ,-6.1793978887949263374 ] 
dist 39=[-12.503627938760759551  ,-6.5667775877983525161 ] 
dist 40=[-12.631539084549011554  ,-6.6055584127089450139 ] 
dist 41=[-12.681583142053730964  ,-6.5938146601299015139 ] 
dist 42=[-12.677355840558476108  ,-6.2604619626538959744 ] 
dist 43=[-12.559382193496603674  ,-5.0793101780155149921 ] 
dist 44=[-12.507699734499175396  ,-3.2292536918875519004 ] 
dist 45=[-12.331997909163566349  ,-1.3550865830601417163 ] 
dist 46=[-12.257803233414075009  ,-.07758016438153915710] 
dist 47=[-8.1483066568560450202 ,1.0080654650837912157 ] 
dist 48=[-7.7396648628475279917 ,2.1164595767256295073 ] 
dist 49=[-6.7494048125054405513 ,3.1554351298202140271 ] 
dist 50=[-6.5860184594099085569 ,3.9640225539823041387 ] 
dist 51=[-6.2056489862689249379 ,4.7592910845062163947 ] 
dist 52=[-6.1177605390356929480 ,5.7451482586593233465 ] 
dist 53=[-6.0176378769056976304 ,6.6827872225282912447 ] 
dist 54=[-5.9744224170312349460 ,7.2855792502514611260 ] 
dist 55=[-2.3964680407200751753 ,7.7590145895272509435 ] 
dist 56=[-2.1847765189712885134 ,8.1802454215099897213 ] 
dist 57=[-1.7073352935276150433 ,8.5360695227875205534 ] 
dist 58=[-1.6188241966410422855 ,8.7483853634993704507 ] 
dist 59=[-1.1300728246070492400 ,8.8963714681271749723 ] 
dist 60=[-1.0779375111365822610 ,8.9953635290857590473 ] 
dist 61=[-.74722109607893316047,9.0585556141236891232 ] 
dist 62=[-.70544351848032813416,9.0636141438173935149 ] 
dist 63=[-.18558517122086978572,3.7893107658636544841 ] 
dist 64=[-.11270914580632110106,4.0970259694776229552 ] 
dist 65=[.01766207817184146173,4.3333550658225366847 ] 
dist 66=[.04529867744049251614,4.5350253989086209087 ] 
dist 67=[.1068987433488499026 ,4.6995957098977406701 ] 
dist 68=[.10347963794174482852,4.7877047815786339380 ] 
dist 69=[.07339747857749411540,4.8367997055417055062 ] 
dist 70=[0                     ,4.8480989275641752398 ] 
dist 71=[1.9871905753762669297 ,3.7872598011703903339 ] 
dist 72=[1.7783948189422186302 ,3.8330014602396962202 ] 
dist 73=[1.5809338006562855068 ,3.8660110248898598575 ] 
dist 74=[1.3472597079416134245 ,3.8756349433656239921 ] 
dist 75=[1.1080262327410243145 ,3.8703126042221710179 ] 
dist 76=[.8883336880086524580 ,3.8636569873401182359 ] 
dist 77=[.6406584354314773299 ,3.3519066347795897186 ] 
dist 78=[.2896662198745602840 ,3.3436730816434704112 ] 
dist 79=[-.0661369554415605306 ,1.9304225262302848249 ] 
dist 80=[-.3330422132172816504 ,1.8678746358616813259 ] 
dist 81=[-.5863284429482558069 ,1.4568484720198771913 ] 
dist 82=[-.8877859450302509813 ,1.3878671691049227784 ] 
dist 83=[-1.1977701980291920121 ,1.2381915867382927662 ] 
dist 84=[-1.4851272021896340633 ,1.2040273195358659893 ] 
dist 85=[-1.8115024317654511299 ,1.0980240390136417932 ] 
dist 86=[-2.2773209141576746007 ,1.1984481359889823704 ] 
dist 87=[-2.7338340594127651567 ,1.3041623852175825314 ] 
dist 88=[-3.0230604735102594868 ,1.3819575932522279088 ] 
dist 89=[-3.2457147724147143416 ,1.4541310555441614463 ] 
dist 90=[-3.4363930137649154346 ,1.5374235779130192640 ] 
dist 91=[-3.5924255477433685885 ,1.6214294458939348369 ] 
dist 92=[-3.6767373716357655942 ,1.6964576881886992548 ] 
dist 93=[-3.7248843375216502994 ,1.7792546092927177580 ] 
dist 94=[-3.7365168396064235424 ,1.8942736726694262972 ] 
dist 95=[-3.7344828098049525168 ,2.0095900496628115863 ] 
dist 96=[-3.7280548120439142393 ,2.0935782086419681579 ] 
dist 97=[-3.7172473139963524271 ,2.1706994833689665012 ] 
dist 98=[-3.7052549923009445060 ,2.2586154775939609102 ] 
dist 99=[-3.6740734027378224160 ,2.3467577606981557336 ] 
dist 100=[-3.6469157230894404591 ,2.4247871856247269208 ] 
dist 101=[-3.5039264491036332727 ,2.5103772573644584380 ] 
dist 102=[-3.3926020070836686972 ,2.6287035710927305404 ] 
dist 103=[-3.3101254309201200417 ,2.7418407778462941885 ] 
dist 104=[-3.2942031372561040663 ,2.8067174338536598421 ] 
dist 105=[-3.1986354933724785297 ,2.8486808297535136345 ] 
dist 106=[-3.1729762388418910401 ,2.8703508260270638659 ] 
dist 107=[-3.1089845820473215527 ,2.8790344942345919850 ] 
dist 108=[-3.0841745257151923274 ,2.8770551201027152689 ] 
dist 109=[-2.6290529919383919237 ,2.8545534814179683892 ] 
dist 110=[-2.6117429711567270344 ,2.8443755195114418195 ] 
dist 111=[-1.8675965876538966650 ,2.6642720013702429195 ] 
dist 112=[-1.7937116685282355394 ,2.6308473554357133023 ] 
dist 113=[-1.6121079377985327914 ,2.5447298684357714705 ] 
dist 114=[-1.5813654251088626773 ,2.5188609409807718854 ] 
dist 115=[-1.3028742462206038895 ,2.3568947634981585470 ] 
dist 116=[-1.2490342098845582813 ,2.3197969437517760353 ] 
dist 117=[-1.1776545292554738069 ,2.2517265807802766585 ] 
dist 118=[-1.1541941488245998676 ,2.2319426213152716957 ] 
dist 119=[-.67847480513940783588,2.2323011885217207078 ] 
dist 120=[-.61685971061736019875,2.3732376920236524122 ] 
dist 121=[-.4835742693603683282 ,2.4790581227594869069 ] 
dist 122=[-.45110669185434862253,2.5648653835305070018 ] 
dist 123=[-.30239698150100916366,2.6314011261319905750 ] 
dist 124=[-.27579047792034550782,2.6602718130441217592 ] 
dist 125=[-.21140020101663488056,2.6731698896284974837 ] 
dist 126=[-.20217204149705368488,2.6759262207830465161 ] 
dist 127=[.36759098941807760931,.64110850826530530324] 
dist 128=[.40549723797092634509,.68818829608517713387] 
dist 129=[.49021383869794896487,.72870152753526577107] 
dist 130=[.5027422528681537925 ,.7543253846430694277 ] 
dist 131=[.59817612674152264843,.82877825610240648   ] 
dist 132=[.61306275364306930213,.90150795303737929469] 
dist 133=[.6372419877396704937 ,.9729480195075335237 ] 
dist 134=[.64184944608261668426,1.0614498387478536550 ] 
dist 135=[.67089173089412969827,1.1456770582476436959 ] 
dist 136=[.62808039826400296712,1.2000481468606541719 ] 
dist 137=[.57702088477691086852,1.2430319691829648016 ] 
dist 138=[.51904108158171626461,1.2817906753100210472 ] 
dist 139=[.44477345766478781682,1.3149173202172457291 ] 
dist 140=[.32867363215152506348,1.3354117037275171038 ] 
dist 141=[.21011586719066609509,1.3505909325500804003 ] 
dist 142=[.00084111167418809638,1.3624914886990592850 ] 
dist 143=[-.21121275288103569671,1.3699416439546116806 ] 
dist 144=[-.35683723300372461358,1.3704921025180668962 ] 
dist 145=[-.4819048279534571601 ,1.3621703401422631279 ] 
dist 146=[-.61187880402175764787,1.3592835165126349334 ] 
dist 147=[-.7352946664405410779 ,1.3077378460859589272 ] 
dist 148=[-.83417697116596790601,1.2939119693681953478 ] 
dist 149=[-.93417730506264886812,1.2820027037639037527 ] 
dist 150=[-1.0620574428711872615 ,1.2746270336003134229 ] 
dist 151=[-1.1857610368243822007 ,1.0496174788277336902 ] 
dist 152=[-1.2690852335808656229 ,1.0179004553910881224 ] 
dist 153=[-1.3389117463037463146 ,.95637109488191836798] 
dist 154=[-1.4087214882800692283 ,.93980543124281247414] 
dist 155=[-1.4733042435898622636 ,.87859795030540648897] 
dist 156=[-1.5222604383448678466 ,.86366614732387993536] 
dist 157=[-1.5692212313578980077 ,.83703118364925158986] 
dist 158=[-1.6258370372218161027 ,.82967584705235522281] 
dist 159=[-1.6774451195591688497 ,.08820176914984658618] 
dist 160=[-1.7044110566480566854 ,.02476174177318711147] 
dist 161=[-1.7185291565831508063 ,-.11575874942890597163] 
dist 162=[-1.7206568770567570512 ,-.14263404214185847451] 
dist 163=[-1.7134798616944232240 ,-.30355622977282953581] 
dist 164=[-1.7074662072596762423 ,-.33067284293216799937] 
dist 165=[-1.6940871866705098133 ,-.38489376865690374098] 
dist 166=[-1.6873589835582412056 ,-.39767296155567506394] 
dist 167=[-1.5254640797781100810 ,-.45789413716079638561] 
dist 168=[-1.4993692625313711737 ,-.41352752113959820723] 
dist 169=[-1.4420378394578126641 ,-.36181450140581662744] 
dist 170=[-1.4239103237349149256 ,-.30466532244961471645] 
dist 171=[-1.3413452615162572732 ,-.21482272096819550967] 
dist 172=[-1.3234995575750901451 ,-.05738148880669372694] 
dist 173=[-1.2757800662924436602 ,.10035528361817213224] 
dist 174=[-1.2645803037489156977 ,.20580945067745092631] 
dist 175=[-1.1273553117724053910 ,.34642238491299314851] 
dist 176=[-1.1440881696708517815 ,.55816164501281752058] 
dist 177=[-1.1521708314532922197 ,.73078978216605507769] 
dist 178=[-1.1534627049378722831 ,.89552023133685928252] 
dist 179=[-1.1453483388166273128 ,1.0428438235423852078 ] 
dist 180=[-1.1405133617866426133 ,1.1459710165020538363 ] 
dist 181=[-1.1314764518405954425 ,1.2366202601951601701 ] 
dist 182=[-1.1273219656133634032 ,1.3341229730226224057 ] 
dist 183=[-1.0072773146453883024 ,1.4230150458199251819 ] 
dist 184=[-.98841211905869547216,1.4792842585539457043 ] 
dist 185=[-.94825175219203861866,1.5225116918767141332 ] 
dist 186=[-.93593307102284860729,1.5593310481556694219 ] 
dist 187=[-.88125418736196487953,1.5892749715279701534 ] 
dist 188=[-.86974883633101904911,1.6050505160933255436 ] 
dist 189=[-.83578759949350044547,1.6134903940868459004 ] 
dist 190=[-.83063107375189079759,1.6141449732338379168 ] 
dist 191=[.08258327878959732399,.2171996306202812875 ] 
dist 192=[.08176722380391613682,.2633280214352077041 ] 
dist 193=[.07849810820494869959,.30806007618250225436] 
dist 194=[.07179654385485948099,.34541146701705243525] 
dist 195=[.06128576473726624269,.38456104313742971054] 
dist 196=[.04280694966832336091,.43647199724454265801] 
dist 197=[.02251793532743492634,.48755411722011004637] 
dist 198=[.00477924116295140871,.52339410882735927064] 
dist 199=[-.01451651792944884227,.55497813260086771778] 
dist 200=[-.04102276521831291822,.58906727825487940073] 
dist 201=[-.07018725460076250198,.62220885418473458723] 
dist 202=[-.10009706308627595509,.65000907784389645728] 
dist 203=[-.1363300732051364953 ,.67925490945582474769] 
dist 204=[-.19074231390416709173,.71816723374059594272] 
dist 205=[-.29114509746847414593,.75501263893427728344] 
dist 206=[-.36469092750490409305,.77600592242519175799] 
dist 207=[-.42696751537943906244,.78942837101940611314] 
dist 208=[-.49027089295081809839,.79604695118921528447] 
dist 209=[-.5494975570669090031 ,.79918765710007240423] 
dist 210=[-.59549686317384270053,.79872479391595500415] 
dist 211=[-.64068291662524203659,.79599101179451900254] 
dist 212=[-.69666247893738900994,.79379558076198215693] 
dist 213=[-.74994153250506779359,.72566654597954286986] 
dist 214=[-.78434515621324666881,.71435362756563167208] 
dist 215=[-.81155839005160066109,.69077233759830212593] 
dist 216=[-.83612807973618072861,.68340414673214730355] 
dist 217=[-.85715882391009773398,.6503289988565050828 ] 
dist 218=[-.87024198874588666176,.64306527233858149553] 
dist 219=[-.8800270851305754336 ,.62128861248818316099] 
dist 220=[-.8878895654386616376 ,.61755710099820950384] 
dist 221=[-.8930990233775469167 ,.26650477134015929622] 
dist 222=[-.89329016461747120748,.23647833444812665494] 
dist 223=[-.88934711947051512065,.20705833307677908626] 
dist 224=[-.88602592280439466882,.20242671252532596288] 
dist 225=[-.85970898608742122704,.15750625661686352818] 
dist 226=[-.85208415651045136971,.14894702605649559925] 
dist 227=[-.84062770705675120111,.13838608426165687895] 
dist 228=[-.83612142894130770033,.13539573078181543403] 
dist 229=[-.71599265403940680235,.05988976354313760060] 
dist 230=[-.69829721498763814975,.05038262972645032255] 
dist 231=[-.66078864709978351599,.03020160581341184528] 
dist 232=[-.64974213011068120245,.02519805535256834106] 
dist 233=[-.60263821205313959648,.00449589328944359062] 
dist 234=[-.59295571052064763338,.00065937248694506641] 
dist 235=[-.56598285704124671154,-.00723574537688096489] 
dist 236=[-.56154558712597991042,.05606631348350397781] 
dist 237=[-.53778707126775227987,.21522881097249590491] 
dist 238=[-.5641552635344024877 ,.32066702816701843704] 
dist 239=[-.58386014476852461489,.40708529330114055659] 
dist 240=[-.59965819794128641598,.49030701178613582302] 
dist 241=[-.61175724102288073312,.56524001052041467191] 
dist 242=[-.61669328471364572785,.61856401709997702032] 
dist 243=[-.61835811647608707461,.66634447505122014015] 
dist 244=[-.61747237213092001064,.71914389623854901334] 
dist 245=[-.60522406328973694598,.76726630198289798308] 
dist 246=[-.60168587577055955925,.79637289753628037609] 
dist 247=[-.59137639148922914907,.81716274199383593699] 
dist 248=[-.5872361259846048299 ,.83207887501596128325] 
dist 249=[-.56212549152221506477,.84227766369579155063] 
dist 250=[-.55577767557662773986,.84453443580017036745] 
dist 251=[-.54409353954850306888,.84341554265329126222] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 0, 0, 0, 1] 
dist 0=[50.644176599269100040  ,50.644176599269100040  ] 
dist 1=[50.306312090262976376  ,50.723942613592300622  ] 
dist 2=[49.867194183299608430  ,50.705001007341103524  ] 
dist 3=[49.405500386163099886  ,50.678030584555566157  ] 
dist 4=[48.836860683069326828  ,50.565978200892801592  ] 
dist 5=[47.970665237537745572  ,49.688220780385469254  ] 
dist 6=[46.975659963655168526  ,49.437958050369064309  ] 
dist 7=[45.892540631572195392  ,49.290995678530503944  ] 
dist 8=[44.095382138640717538  ,49.125761735552722599  ] 
dist 9=[42.437516596655914616  ,46.421690226317031347  ] 
dist 10=[40.232060981611946251  ,43.656363607945102324  ] 
dist 11=[38.436904682796795924  ,42.427334463941410023  ] 
dist 12=[36.230824182606451840  ,42.114249784355116960  ] 
dist 13=[33.773351795537140314  ,41.082832221630903052  ] 
dist 14=[30.810509674973975209  ,40.786385792135020467  ] 
dist 15=[26.371131090229139988  ,40.552613730449069891  ] 
dist 16=[21.919488489349773258  ,40.393379223545400133  ] 
dist 17=[18.907588158781983699  ,36.104441990396099252  ] 
dist 18=[16.364254951980348401  ,21.023993300678775257  ] 
dist 19=[13.746355551002605568  ,17.604874529579584828  ] 
dist 20=[11.176334866171456081  ,17.093033563886742576  ] 
dist 21=[8.6051761796986192594 ,13.109322780745029178  ] 
dist 22=[6.2196595185781075768 ,11.781579470587195914  ] 
dist 23=[4.3910543425061495274 ,10.717444909175245159  ] 
dist 24=[2.6135329164894343450 ,10.479397010765168026  ] 
dist 25=[.43177360325069429245,6.5993187377076047564 ] 
dist 26=[-1.6440206037394109142 ,4.5475898311403426885 ] 
dist 27=[-2.9984097611020434625 ,3.1810551783001878675 ] 
dist 28=[-4.0896234098471978426 ,2.9721376812134839696 ] 
dist 29=[-5.1142988216668551238 ,1.5336682942520071998 ] 
dist 30=[-6.0247835071564354471 ,1.3187636215023264221 ] 
dist 31=[-6.6601490070816193142 ,.92929275229601090584] 
dist 32=[-7.2206854920597911410 ,.86337372184776029995] 
dist 33=[-7.8329845530747740370 ,-3.2368391688663907012 ] 
dist 34=[-8.3798589646558216248 ,-4.7183527112854590329 ] 
dist 35=[-8.6790751168488141453 ,-5.3050372765148316862 ] 
dist 36=[-8.8587354228687239536 ,-5.4237543291320738912 ] 
dist 37=[-8.9273796348912483744 ,-5.6661030856125157084 ] 
dist 38=[-8.9537947768271833687 ,-5.6163905079845339296 ] 
dist 39=[-8.9643279524670841362 ,-5.4362166295937817206 ] 
dist 40=[-8.9666777723621146484 ,-5.0345673592476417197 ] 
dist 41=[-8.9597450307365082824 ,-4.5697651419668048803 ] 
dist 42=[-8.1816395975623704972 ,-4.1372223690669137398 ] 
dist 43=[-8.1414496232585724338 ,-3.6468954482719729421 ] 
dist 44=[-7.9241609914268450930 ,-2.9509173672521654830 ] 
dist 45=[-7.8708038073057641922 ,-2.1765837464976265526 ] 
dist 46=[-7.8332025610324881687 ,-1.3732086859511728566 ] 
dist 47=[-7.8389841211109465150 ,-.39441939076885160829] 
dist 48=[-7.8266419901528943592 ,1.0804191254538798172 ] 
dist 49=[-7.7774734786683609474 ,2.5540873486920035271 ] 
dist 50=[-3.4456871845557032238 ,3.5283115304294978243 ] 
dist 51=[-3.3242080891833002504 ,4.3241897751874128968 ] 
dist 52=[-2.3461177647299795462 ,5.0859688985588071367 ] 
dist 53=[-2.1673605434177534627 ,5.7687496776290061566 ] 
dist 54=[-1.8986021783952756154 ,6.2493291062955010602 ] 
dist 55=[-1.8268082413805282641 ,6.6747272554217011867 ] 
dist 56=[-.55663034863045299166,7.1373470400996493432 ] 
dist 57=[-.39743329226979768631,7.5500708570868180553 ] 
dist 58=[-.02673106632512231634,7.7762397932747202186 ] 
dist 59=[.02664360972934181741,7.9096733031606203955 ] 
dist 60=[.50534266638613553428,7.9519448175359171571 ] 
dist 61=[.58724278005341829784,7.9591058261277832869 ] 
dist 62=[.69619503729490321906,7.8614064666031288063 ] 
dist 63=[.71533787671149405329,7.8128061748024387758 ] 
dist 64=[1.2663427054528347034 ,7.3884948197066573689 ] 
dist 65=[1.3300252873904737056 ,6.4229589244760563549 ] 
dist 66=[1.4588275451381297154 ,6.2490344362952566618 ] 
dist 67=[1.4866123079961341603 ,5.7961454429432398154 ] 
dist 68=[1.5859269527596880651 ,5.7268097555657904586 ] 
dist 69=[1.6044631681801058561 ,4.9546632541095633433 ] 
dist 70=[1.6058510972408274749 ,4.8017841614746389224 ] 
dist 71=[1.5811916955541899582 ,4.6338948797360440817 ] 
dist 72=[1.4584491702168002874 ,4.5913996669839177569 ] 
dist 73=[1.1399037890343621765 ,3.0504229222893502463 ] 
dist 74=[.8181335069659443639 ,2.8554119773139702430 ] 
dist 75=[.5789088455976137956 ,2.4559870338489048171 ] 
dist 76=[.3540415930805439274 ,2.3518252609286736039 ] 
dist 77=[.0895356353146734929 ,1.9733358689070999542 ] 
dist 78=[-.18078571523350383833,1.9549348649424268754 ] 
dist 79=[-.42891841860453475935,1.9500214621873744200 ] 
dist 80=[-.70887376706839843185,1.7734027435667695996 ] 
dist 81=[-1.4271644042774412466 ,1.7467893020679399617 ] 
dist 82=[-1.9080433312564123971 ,1.6839697789963748055 ] 
dist 83=[-2.3063520211045566233 ,1.6634874509819465128 ] 
dist 84=[-2.6974723820332882810 ,1.5607340600983159518 ] 
dist 85=[-3.0552076080408576288 ,1.5370798691530263478 ] 
dist 86=[-3.3201926390645139000 ,1.4883545538422272106 ] 
dist 87=[-3.5686756350432629966 ,1.4728380075850798304 ] 
dist 88=[-3.8605193848063546870 ,1.2324339607918537693 ] 
dist 89=[-4.1310204605142317321 ,1.1960173519801880429 ] 
dist 90=[-4.2942677933195429558 ,1.1069623327579216236 ] 
dist 91=[-4.4106635303195987643 ,1.0868369122731574946 ] 
dist 92=[-4.4940427923850116619 ,.94422614228971915419] 
dist 93=[-4.5514581357868449898 ,.91457875012910753711] 
dist 94=[-4.5641662871480776796 ,.86467196795105173267] 
dist 95=[-4.5610559264907653229 ,.85110969116097836323] 
dist 96=[-4.5553053813388905439 ,.78876315092118443964] 
dist 97=[-2.7295099003005026875 ,.77753653119234389579] 
dist 98=[-.97653389491465657178,1.0319948973168684910 ] 
dist 99=[-.86160313951266155767,1.3862406780623044348 ] 
dist 100=[-.5924599275559644206 ,1.7440674677086463982 ] 
dist 101=[-.5494839932709646060 ,2.0771816142921722967 ] 
dist 102=[-.1921209620725460991 ,2.3327961844451719036 ] 
dist 103=[-.1288259494583172207 ,2.5808780549350541927 ] 
dist 104=[-.0364936844051497420 ,2.8839574388718295367 ] 
dist 105=[-.0120095076726583887 ,3.1703039250417708922 ] 
dist 106=[.3949075575756915301 ,3.3516024593910427831 ] 
dist 107=[.4451568292163391717 ,3.4909750235745550369 ] 
dist 108=[.5495572128590546584 ,3.6099601121770702716 ] 
dist 109=[.5708131363007226170 ,3.7071280900820709882 ] 
dist 110=[.6605018752254341568 ,3.7594266386867891604 ] 
dist 111=[.40943942141722561627,3.8305951969940027196 ] 
dist 112=[-.22928958194103009746,3.9262826714132734508 ] 
dist 113=[-.87542109757586885401,4.0061885249701889161 ] 
dist 114=[-1.3135363644670326304 ,4.0351572309911613914 ] 
dist 115=[-1.6832889629485323441 ,4.0434540200320111868 ] 
dist 116=[-2.0565517182599164856 ,4.0407189943973765346 ] 
dist 117=[-2.4036171315848784480 ,3.9336741915084394818 ] 
dist 118=[-2.6688027337111048919 ,3.9001757518643129274 ] 
dist 119=[-2.9248689810495277618 ,3.8749257652846449798 ] 
dist 120=[-3.2355329158934266766 ,3.8544114551779354816 ] 
dist 121=[-3.5273492302875032756 ,3.2201887861812605957 ] 
dist 122=[-3.7081833049090516531 ,3.1298112934486187856 ] 
dist 123=[-3.8423841117172424516 ,2.9545255958624895672 ] 
dist 124=[-3.9480598186918265372 ,2.9070420266260546264 ] 
dist 125=[-4.0273086391236254627 ,2.7306569610354999329 ] 
dist 126=[-4.0560221052553247384 ,2.6872870310627842054 ] 
dist 127=[-4.0634987166964191692 ,2.6095285705744502442 ] 
dist 128=[-4.0579865130320707486 ,2.5878479659793572703 ] 
dist 129=[-1.0436041404996954528 ,1.2420936604206060358 ] 
dist 130=[-1.2977796103275585030 ,.37623439420695702622] 
dist 131=[-1.4645637856068566700 ,.03834854109981067537] 
dist 132=[-1.5994605922266362845 ,-.01992324328798160126] 
dist 133=[-1.7263306133287705012 ,-.43258119738438080982] 
dist 134=[-1.8385134719096600084 ,-.50319250359330678076] 
dist 135=[-1.9147752739373494115 ,-.62721356678595396929] 
dist 136=[-1.9794303148809393609 ,-.65249874923448282156] 
dist 137=[-2.3039487362159361459 ,-.98796297968758503428] 
dist 138=[-2.5525736648602200383 ,-1.0318152247174660646 ] 
dist 139=[-2.7664157195994603925 ,-.98297712037744783776] 
dist 140=[-2.9891398432399499031 ,-.86416905687271330952] 
dist 141=[-3.2009519176440766400 ,-.70933912049475881126] 
dist 142=[-3.3712350648414876600 ,-.5166885855468895257 ] 
dist 143=[-3.5440106715801838216 ,-.25923763043043769286] 
dist 144=[-3.7657928195876008046 ,.1542959553600223545 ] 
dist 145=[-3.9726372592669286256 ,.5777100714021859271 ] 
dist 146=[-4.0857734039401574349 ,.8746090087011231140 ] 
dist 147=[-4.1521599939118847831 ,1.1359789748976276046 ] 
dist 148=[-4.1723359671441100352 ,1.4175555793892977630 ] 
dist 149=[-4.1764034149536427635 ,1.6909149632351757551 ] 
dist 150=[-4.1784637940865682300 ,1.9194823795889894140 ] 
dist 151=[-4.1794868861981335147 ,2.1592582379986046593 ] 
dist 152=[-4.1793955123500019982 ,2.4773693655713271265 ] 
dist 153=[-3.6085009405930427060 ,2.7903556654385458230 ] 
dist 154=[-3.5266427251105256264 ,3.0096735789104567758 ] 
dist 155=[-3.3845546584785588759 ,3.2026150657733141200 ] 
dist 156=[-3.3473065309653278165 ,3.4103001296780518025 ] 
dist 157=[-3.2310370650055963869 ,3.6118521786096999893 ] 
dist 158=[-3.1931653671140274010 ,3.7803111773085678769 ] 
dist 159=[-3.1710075031836560166 ,3.9569950193624543007 ] 
dist 160=[-3.1644697486125742593 ,4.1913887046846644215 ] 
dist 161=[-.90720958285095698504,4.4141814013355860191 ] 
dist 162=[-.3182110297573768709 ,4.5445497528786513060 ] 
dist 163=[.02417052540457336695,4.6323319444496908740 ] 
dist 164=[.13049993850048619421,4.6850997784627388614 ] 
dist 165=[.148893030359269598  ,4.7149540486267543838 ] 
dist 166=[.27430469456086492087,4.7166273932496589256 ] 
dist 167=[.29529621423658200102,4.6957614472562919860 ] 
dist 168=[.33335790328708208424,4.6785429805419362462 ] 
dist 169=[.34116029300924358354,4.3940953049255760534 ] 
dist 170=[.42393263796824334061,4.3407812238074120306 ] 
dist 171=[.43571497339908917553,4.2122018344909537888 ] 
dist 172=[.44174096190763816357,4.1668914101085340913 ] 
dist 173=[.41606676539148166955,3.9429948509801831007 ] 
dist 174=[.3005840967729582918 ,3.8907803085225440276 ] 
dist 175=[.16821963367161110092,3.7765283061079734397 ] 
dist 176=[-.25885713013291964232,3.7386196420572778371 ] 
dist 177=[-1.2023128777024966862 ,3.6312426698985357631 ] 
dist 178=[-1.8247495118021991898 ,3.6941584842203801145 ] 
dist 179=[-2.3319706706549689315 ,3.7272018735026437922 ] 
dist 180=[-2.8154248548712305857 ,3.7327967467457726006 ] 
dist 181=[-3.2472828046249167258 ,3.7166454997707394990 ] 
dist 182=[-3.5485034879598942274 ,3.7028227620374639959 ] 
dist 183=[-3.8120703953127883276 ,3.6761063764142483967 ] 
dist 184=[-4.0935920142117577541 ,3.6628970149593551758 ] 
dist 185=[-4.3491700370392602532 ,3.2828865705462249619 ] 
dist 186=[-4.5091566991948762046 ,3.2227545588462572969 ] 
dist 187=[-4.6299355953731284495 ,3.0943715740002737271 ] 
dist 188=[-4.7289789633351263232 ,3.0547831060301500091 ] 
dist 189=[-4.8065978869577208869 ,2.8782741885274499203 ] 
dist 190=[-4.8418410539635957330 ,2.8409763576650750400 ] 
dist 191=[-4.8528276741893227802 ,2.7315093894157550530 ] 
dist 192=[-4.8490123923111794654 ,2.7141669277219068982 ] 
dist 193=[-2.3797344454788252779 ,1.6820925365902844924 ] 
dist 194=[-2.4477199225100145760 ,.46730482439949254989] 
dist 195=[-2.4820072632819643494 ,.36228915275330328436] 
dist 196=[-2.4982155977470621669 ,.12504695434936182191] 
dist 197=[-2.5003381210035898722 ,.08168706277808299348] 
dist 198=[-2.4819760317306864233 ,-.20669957241705076548] 
dist 199=[-2.4715721942789572757 ,-.25660880000188792845] 
dist 200=[-2.4489796245783859698 ,-.3483439725615007546 ] 
dist 201=[-2.4383684104627880589 ,-.36844938441957007981] 
dist 202=[-2.1901512256146985327 ,-.53224882733395490743] 
dist 203=[-2.1504738371735828729 ,-.51706693044393677412] 
dist 204=[-2.0625370625297672551 ,-.49189168320843972027] 
dist 205=[-2.0347293643585098649 ,-.44645962357965087529] 
dist 206=[-1.9080701605240795233 ,-.39141393101939829138] 
dist 207=[-1.8807035529027216535 ,-.327855815265958874  ] 
dist 208=[-1.8117097145809595755 ,-.23058229528645619315] 
dist 209=[-1.7917067679533494218 ,.14214173334337853083] 
dist 210=[-.80011624089107049831,.61956304808958311889] 
dist 211=[-.78801440798239073537,.93465930370102714951] 
dist 212=[-.76429742599856181338,1.1915829212460399142 ] 
dist 213=[-.760767601257887764  ,1.4367454622053927520 ] 
dist 214=[-.70334850857647283469,1.6559502852779931948 ] 
dist 215=[-.69054219429834035526,1.8092356859503264040 ] 
dist 216=[-.68016487416289617931,1.9437824167021280583 ] 
dist 217=[-.67765105632393900304,2.0881716177106402016 ] 
dist 218=[-.50578753717716949207,2.2193049983493557817 ] 
dist 219=[-.48320721319665489744,2.3009266617869385246 ] 
dist 220=[-.43991650470388170908,2.3620098781126182592 ] 
dist 221=[-.4288329123148598104 ,2.4111414268126463177 ] 
dist 222=[-.39098318924457183543,2.4488968376527952988 ] 
dist 223=[-.38154099387712466154,2.4645594824102225759 ] 
dist 224=[-.37191216261988785914,2.4678007724244190076 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 0, 0, 1, 2] 
dist 0=[31.113829689561327973  ,31.113829689561327973  ] 
dist 1=[30.466971564882690091  ,31.640315325630929142  ] 
dist 2=[29.365388277985907292  ,33.097612742820142833  ] 
dist 3=[28.017679901965135234  ,34.522698087090718926  ] 
dist 4=[26.606485722600345513  ,35.390156119543263754  ] 
dist 5=[25.251162892715046455  ,36.019751144507050830  ] 
dist 6=[23.670105686827946535  ,36.494378406812092241  ] 
dist 7=[21.356701660688617493  ,36.855070567393323486  ] 
dist 8=[18.965024903909123563  ,37.029272068901303271  ] 
dist 9=[17.071095908526343406  ,37.101264110423373359  ] 
dist 10=[15.169177771439426554  ,37.105352955181556316  ] 
dist 11=[12.745469240572256740  ,36.280911239310035941  ] 
dist 12=[10.155876977579500546  ,36.124457636415535761  ] 
dist 13=[7.5908530521247941956 ,35.856060517832715145  ] 
dist 14=[4.5383109994790471364 ,35.770766510679172421  ] 
dist 15=[0                     ,35.435721041023830558  ] 
dist 16=[20.631318007910681722  ,35.330935276981579340  ] 
dist 17=[20.156688789221728390  ,35.102112371015124024  ] 
dist 18=[19.657769793940130298  ,35.015085625499497304  ] 
dist 19=[18.995928952449774677  ,27.305837728294716613  ] 
dist 20=[18.279309367543963558  ,26.615386731609175579  ] 
dist 21=[17.561205539475116786  ,25.108923012060266540  ] 
dist 22=[16.702707288077153091  ,24.760557112993800897  ] 
dist 23=[15.344927906197066276  ,23.041551264187402078  ] 
dist 24=[13.925928996226379571  ,22.733872419364158488  ] 
dist 25=[12.443461564240430793  ,22.034511842834976701  ] 
dist 26=[10.478149553249559914  ,21.835589906032842442  ] 
dist 27=[8.5347426916735181482 ,15.410671634232025274  ] 
dist 28=[7.1398012164515102856 ,14.751533194942119276  ] 
dist 29=[5.8735711019103224587 ,13.687231446406530796  ] 
dist 30=[4.4444281864501281464 ,12.427191820383256253  ] 
dist 31=[3.0123668212881283836 ,9.3744663835820237173 ] 
dist 32=[1.0911914865587999231 ,6.8316807730320976858 ] 
dist 33=[-.5163188781651436965 ,6.3643483246405878612 ] 
dist 34=[-1.7953940607998325736 ,6.2473202200275996860 ] 
dist 35=[-3.6053788376029838682 ,2.4021925913089547340 ] 
dist 36=[-4.8615102980772268671 ,2.0195806964975624193 ] 
dist 37=[-5.8613392000963489333 ,1.2044367189512217769 ] 
dist 38=[-6.7794123532015532366 ,1.0260656353434701322 ] 
dist 39=[-7.5800785201853607148 ,.1691234923371828177 ] 
dist 40=[-8.1108479641872802898 ,.0223630649742064732 ] 
dist 41=[-8.5485380490967738000 ,-.3140676264759328464 ] 
dist 42=[-8.9774603980721498075 ,-.3629228638166052327 ] 
dist 43=[-9.3532124918338310334 ,-.7913189116058815620 ] 
dist 44=[-9.5784444672587311001 ,-.8731001460269934005 ] 
dist 45=[-9.7383584429031805449 ,-.91974541422215411466] 
dist 46=[-9.8529279096798521071 ,-.88986324206269779663] 
dist 47=[-9.9309319466778859419 ,-.82206831279185380552] 
dist 48=[-9.9446559023846593125 ,-.7063809831510114977 ] 
dist 49=[-9.9273825198071212251 ,-.53456544469950887712] 
dist 50=[-9.9016805055988958168 ,-.2426676562032326747 ] 
dist 51=[-5.0560905946101628899 ,.05663819483164691077] 
dist 52=[-4.6973928408010953048 ,.2581135865713917256 ] 
dist 53=[-3.8370744687801320444 ,.4258225096423792978 ] 
dist 54=[-3.7083384265080689147 ,.5905529600227193436 ] 
dist 55=[-2.4968387891198674792 ,.7402710680965644013 ] 
dist 56=[-2.2773804799517824415 ,.8481608032388558586 ] 
dist 57=[-1.9991408562707909813 ,.9459288123520064903 ] 
dist 58=[-1.9372075235415646690 ,1.0553497314391906807 ] 
dist 59=[-.2668578324077468986 ,1.1535701574602178588 ] 
dist 60=[-.0668269908397424618 ,1.2066933391570557782 ] 
dist 61=[.3667185003128479458 ,1.2371210586807711025 ] 
dist 62=[.4487368042881077350 ,1.2966659361899719578 ] 
dist 63=[.7776256744708600741 ,1.5459329668528975908 ] 
dist 64=[.9772472719763988164 ,1.8402296799405878766 ] 
dist 65=[1.1250207440021354105 ,2.1367401390410479775 ] 
dist 66=[1.1504392692634526784 ,2.5153880329921900462 ] 
dist 67=[2.0029574659079595055 ,2.8790497090648498235 ] 
dist 68=[1.9979204216305022594 ,3.1157299124663397586 ] 
dist 69=[1.9432007816902982349 ,3.3058099916278464767 ] 
dist 70=[1.8426462166074129005 ,3.4832743611214977465 ] 
dist 71=[1.6536689743063888792 ,3.6401197093149306540 ] 
dist 72=[1.4428751277668010062 ,3.7478213979856886599 ] 
dist 73=[1.2551851379674086646 ,3.8407542732383378479 ] 
dist 74=[1.0485345111551154560 ,3.9386125257348581342 ] 
dist 75=[.7619670545541676287 ,4.0240819648347829110 ] 
dist 76=[.4457584426612110487 ,4.0675163860460810902 ] 
dist 77=[.1207302601339231854 ,4.0888369828069182999 ] 
dist 78=[-.2733265228845287999 ,4.0889877629770808295 ] 
dist 79=[-.8651627663186434672 ,4.0706503726955263244 ] 
dist 80=[-1.4561235567093438404 ,4.0591869497308171737 ] 
dist 81=[-1.8467022334422652570 ,4.0138321829431749124 ] 
dist 82=[-2.1657442086248145014 ,3.9963262135983190841 ] 
dist 83=[-2.4711147263488784453 ,2.6892025658181908634 ] 
dist 84=[-2.7448022586978812823 ,2.6325741047390022297 ] 
dist 85=[-3.0881759026029057775 ,2.6177319322001720322 ] 
dist 86=[-3.4780204052459355611 ,2.5636300210015452065 ] 
dist 87=[-3.8295718115230580788 ,2.5546960427209013608 ] 
dist 88=[-4.0806183955589616177 ,2.3874492969601456556 ] 
dist 89=[-4.3064835861899380578 ,2.3571529711665113984 ] 
dist 90=[-4.5575234703326567521 ,2.2721471302077708901 ] 
dist 91=[-4.7823657251748999217 ,2.2558205971356843333 ] 
dist 92=[-4.9036474939004354782 ,2.0822012520796469991 ] 
dist 93=[-4.9725516556470454222 ,2.0441169548974137460 ] 
dist 94=[-4.9882827841199639003 ,2.0005232727489029903 ] 
dist 95=[-4.9842293944124061826 ,1.9815035903133321487 ] 
dist 96=[-4.9741245831864146164 ,1.5224723729967250383 ] 
dist 97=[-4.9576884938912838528 ,1.4631842491066573110 ] 
dist 98=[-4.9398752268715213755 ,1.3133277852146925964 ] 
dist 99=[-4.6244705885498900861 ,1.2903458338264327078 ] 
dist 100=[-4.5840147617843498079 ,1.1733162836304441700 ] 
dist 101=[-4.4569892255287449135 ,1.6923022660562276938 ] 
dist 102=[-4.4316069273241030168 ,2.2154782442600684919 ] 
dist 103=[-4.1291682066989011074 ,2.7017451865686564019 ] 
dist 104=[-4.0604236134605952993 ,3.0733916359304847232 ] 
dist 105=[-3.9865466722124423177 ,3.4325200210831733524 ] 
dist 106=[-3.9522661293513637671 ,3.8688144560997503151 ] 
dist 107=[-3.0737139471481105695 ,4.2792727553305009371 ] 
dist 108=[-2.9536772225133324650 ,4.5352623294857088877 ] 
dist 109=[-2.7109716255642534552 ,4.7272886102062720495 ] 
dist 110=[-2.6452446894406863113 ,4.8824031399274333139 ] 
dist 111=[-2.3958572860880708604 ,5.0020133954067851774 ] 
dist 112=[-2.3410210391823816906 ,5.0523032611476204815 ] 
dist 113=[-2.2328975071246621999 ,5.0717951104059773090 ] 
dist 114=[-2.2025792200914486586 ,5.0684679606308620372 ] 
dist 115=[-1.2857951812471901433 ,1.5124007391380963368 ] 
dist 116=[-1.3997267543921373221 ,1.7046836994729448904 ] 
dist 117=[-1.4859591185321563181 ,1.8508563451543830039 ] 
dist 118=[-1.5684621646115563733 ,1.9914742716357654550 ] 
dist 119=[-1.6675143436740362361 ,2.1615652488436054192 ] 
dist 120=[-1.7601077284541369946 ,2.3213955297979269644 ] 
dist 121=[-1.8168329102952788317 ,2.4210361839943596449 ] 
dist 122=[-1.8581970912576063524 ,2.4957766307669579026 ] 
dist 123=[-1.8894780345547583038 ,2.5561737213605365653 ] 
dist 124=[-1.9119508626940898271 ,2.6027398825004485194 ] 
dist 125=[-1.9181613714576589587 ,2.6222435240684704720 ] 
dist 126=[-1.9166938538405118820 ,2.6281056805767795761 ] 
dist 127=[-1.9117656947037654115 ,2.6251875044989910536 ] 
dist 128=[.59125283898556047198,2.5465124601945420183 ] 
dist 129=[.69934723453874499263,2.5557183024443271866 ] 
dist 130=[.93888240336461039216,2.5549051626832642652 ] 
dist 131=[.97906462834657554502,2.2137557834410626134 ] 
dist 132=[1.1962391584478883212 ,2.1731076255272928534 ] 
dist 133=[1.0349606759889339472 ,2.0797109392774722494 ] 
dist 134=[.84298857843784580795,2.0496863063948663702 ] 
dist 135=[.64572913039239660037,1.9111244430153152852 ] 
dist 136=[.46333570989141833742,1.8808444419002853703 ] 
dist 137=[.25668543939956745431,1.8111338797255276923 ] 
dist 138=[-.03742435435808252720,1.8238079878107361285 ] 
dist 139=[-.33605974276273658092,1.8474530963582849789 ] 
dist 140=[-.56078183040600196197,1.8620654494338708412 ] 
dist 141=[-.77467125233152111854,1.8652902548081778065 ] 
dist 142=[-1.0300623839587199739 ,1.8620278623793900061 ] 
dist 143=[-1.2929851243454039389 ,1.8578767369735929269 ] 
dist 144=[-1.5369489062042559839 ,1.5037483420781912159 ] 
dist 145=[-1.8140801664115205113 ,1.4644679639327636822 ] 
dist 146=[-2.2094319956258169082 ,1.3691919716155324933 ] 
dist 147=[-2.5986085045777150655 ,1.3480100831220675232 ] 
dist 148=[-2.8510856322587287881 ,1.2000484766718563405 ] 
dist 149=[-3.0521047063225950663 ,1.1698691481511271601 ] 
dist 150=[-3.2358294881362384624 ,1.1177495169755247751 ] 
dist 151=[-3.3946647273744057771 ,1.1042497817291533120 ] 
dist 152=[-3.4963103047198491408 ,.8338417391331072999 ] 
dist 153=[-3.5756673092406303503 ,.79670998674247776315] 
dist 154=[-3.6455149675302685231 ,.70902171347469327725] 
dist 155=[-3.6992676014504076108 ,.69150591974613904751] 
dist 156=[-3.7143631962040503669 ,.56715575319301492946] 
dist 157=[-3.7147704451786666025 ,.54327695626630744576] 
dist 158=[-3.7098748812908755625 ,.50230657148874265783] 
dist 159=[-3.6028590855556883669 ,.49229819519412635098] 
dist 160=[-3.5707894510556110438 ,-.96675016100156873745] 
dist 161=[-3.5437093601794752271 ,-.92755543780019200352] 
dist 162=[-3.5236908980315185492 ,-.21845728565406187316] 
dist 163=[-3.0235442739551276104 ,.49464721085129442645] 
dist 164=[-2.9691197417453462376 ,.97464093128426059821] 
dist 165=[-2.8219113045661794701 ,1.3763897510514742430 ] 
dist 166=[-2.7961775720639747918 ,1.7770966505478137818 ] 
dist 167=[-2.5188642584254813578 ,2.1470641642612206734 ] 
dist 168=[-2.4605449390764154473 ,2.4260840126510943936 ] 
dist 169=[-2.3943206142195650863 ,2.6922717672040017494 ] 
dist 170=[-2.3691442104275988363 ,3.0110061481080972547 ] 
dist 171=[-2.2789123733600259348 ,3.3088133558830143796 ] 
dist 172=[-2.1989535205185384678 ,3.4914478802336472068 ] 
dist 173=[-2.1773286946896019088 ,3.6249091380714798949 ] 
dist 174=[-2.1402428056353003803 ,3.7263886700569051996 ] 
dist 175=[-2.1281181912419848488 ,3.8023196160666607540 ] 
dist 176=[-1.7702443505046402035 ,3.8337765826157014792 ] 
dist 177=[-1.7393802022502702048 ,3.8444063977285142276 ] 
dist 178=[-1.6541150791844824410 ,3.8393924863966199514 ] 
dist 179=[-1.6405376240829288546 ,1.1333960098915499125 ] 
dist 180=[-1.4753540048187004200 ,1.3623256788148463184 ] 
dist 181=[-1.4406362964131081588 ,1.5326025926946956818 ] 
dist 182=[-1.4055942260679254354 ,1.6927648862596981137 ] 
dist 183=[-1.3951569817125313769 ,1.8813100928520029611 ] 
dist 184=[-.99229998638194580691,2.0558692403895575739 ] 
dist 185=[-.93956185039916622334,2.1601893553660371531 ] 
dist 186=[-.83472535986273194586,2.2331754569019676988 ] 
dist 187=[-.80732108692992598714,2.2826269863596156676 ] 
dist 188=[-.708825523114137894  ,2.3183795171342441874 ] 
dist 189=[-.68659802243701666137,2.3366692065528878442 ] 
dist 190=[-.65240831491038748702,2.4567383186383090143 ] 
dist 191=[-.64257725151130282187,2.5863265477468600405 ] 
dist 192=[.11672562947340324899,2.6888562113696421930 ] 
dist 193=[.07942028478938045735,2.7913462069730481274 ] 
dist 194=[-.31638839161975548816,2.9207773021793777051 ] 
dist 195=[-.71802827721466009623,3.0403046734252481752 ] 
dist 196=[-.99442040523005722908,3.1032525966092365948 ] 
dist 197=[-1.2323540447939305554 ,3.1373035246078564351 ] 
dist 198=[-1.4804440756182708299 ,3.1445436625631815424 ] 
dist 199=[-1.7164666928061156270 ,3.1313869937323814289 ] 
dist 200=[-1.9062199090120858898 ,3.1230016161459630810 ] 
dist 201=[-2.0986748695900656170 ,3.1127299956632313880 ] 
dist 202=[-2.3454847681064321393 ,3.1013452493290792651 ] 
dist 203=[-2.5844872984153171536 ,2.7130714633876323637 ] 
dist 204=[-2.7457705014595635356 ,2.6547402906267618323 ] 
dist 205=[-2.8812180057673448879 ,2.5438679124852744463 ] 
dist 206=[-3.0170684552083447369 ,2.5131148904663510023 ] 
dist 207=[-3.1429943408033256752 ,2.3962782107074484601 ] 
dist 208=[-3.2388169429640906328 ,2.3660683523069913597 ] 
dist 209=[-3.3310677768750612358 ,2.3079603529233409847 ] 
dist 210=[-3.4427332309324434467 ,2.3317930973625342661 ] 
dist 211=[-3.5443086826831061365 ,2.3490920418370142416 ] 
dist 212=[-3.5962738988232167404 ,2.3564449316371334249 ] 
dist 213=[-3.6219122854176587375 ,2.3552292894428378095 ] 
dist 214=[-3.6253737636566666534 ,2.3474988768226807499 ] 
dist 215=[-3.6032234328600226367 ,2.3416931208743288484 ] 
dist 216=[-3.5891479023604200324 ,2.1180313746931626561 ] 
dist 217=[-3.5575414374254367930 ,2.0820798954281441007 ] 
dist 218=[-3.5422703957735790804 ,2.0100644891657710330 ] 
dist 219=[-3.1932531613221811618 ,1.9884562733194625640 ] 
dist 220=[-3.1370961536812194689 ,1.8965594487343966521 ] 
dist 221=[-3.0122356801052965594 ,1.8750588354248120461 ] 
dist 222=[-2.9725544083732524119 ,1.8187453233660879845 ] 
dist 223=[-2.7910650499129691878 ,1.8021385971396566573 ] 
dist 224=[-2.7516811888636016877 ,.69082254526225250919] 
dist 225=[-2.6505307291803484826 ,.58954970534545602801] 
dist 226=[-2.6236853432042850406 ,.35873168827246107856] 
dist 227=[-2.6134163456333080821 ,.86780518525949872064] 
dist 228=[-2.5582912558614131232 ,1.3231275823444405233 ] 
dist 229=[-2.5986297352267345601 ,1.6941377629189957814 ] 
dist 230=[-2.6213190889975586823 ,2.0477723211286533354 ] 
dist 231=[-2.6323267568157588282 ,2.3637226741347689539 ] 
dist 232=[-2.6306002018047812251 ,2.5842734433028357103 ] 
dist 233=[-2.6191657550617956904 ,2.7774688188254965358 ] 
dist 234=[-2.6095117039277071989 ,2.9841989091667189841 ] 
dist 235=[-2.4187544428162410218 ,3.1720402395543187243 ] 
dist 236=[-2.3853420498377615682 ,3.2898196216003352601 ] 
dist 237=[-2.3100155418572481505 ,3.3789823258287750855 ] 
dist 238=[-2.2849436995242778774 ,3.4525676631152218437 ] 
dist 239=[-2.1660266613848731853 ,3.5106164606855116624 ] 
dist 240=[-2.1392924914410365647 ,3.5377473786904713380 ] 
dist 241=[-2.0709432937962378271 ,3.5474563768492886525 ] 
dist 242=[-2.0505330459673825631 ,3.5448298068268899391 ] 
dist 243=[-1.8331354885895620832 ,1.4764690446017876718 ] 
dist 244=[-1.8598636056034853236 ,1.7005898957008863972 ] 
dist 245=[-1.8664957608986885514 ,1.8588315348784016697 ] 
dist 246=[-1.8660277658883503788 ,1.9993316362612911202 ] 
dist 247=[-1.8659127617224376943 ,2.1526166241236428675 ] 
dist 248=[-1.7983753474932147390 ,2.2920942020651512291 ] 
dist 249=[-1.7834530350928353699 ,2.3774660508019720436 ] 
dist 250=[-1.7450132007737666449 ,2.4396633981809672964 ] 
dist 251=[-1.7301133233451964930 ,2.4866131264479575068 ] 
dist 252=[-1.6519045680497073524 ,2.5202370117435159186 ] 
dist 253=[-1.6327321326450418882 ,2.5292288559316931540 ] 
dist 254=[-1.5930564856217424485 ,2.5286316124719433344 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 1, 1, 1, 2] 
dist 0=[41.077409675767387612  ,41.077409675767387612  ] 
dist 1=[40.433167448726208537  ,41.522031276683798066  ] 
dist 2=[39.345444960396001455  ,41.812216094544103966  ] 
dist 3=[38.204854616748918288  ,42.009281913240531563  ] 
dist 4=[37.349344505616109024  ,42.081983498657718857  ] 
dist 5=[36.535867972905230905  ,42.078948856182483969  ] 
dist 6=[35.563071890210676675  ,42.056017352412392615  ] 
dist 7=[34.557779867357736786  ,41.835229190607693507  ] 
dist 8=[33.614372586629279569  ,41.449564898006470567  ] 
dist 9=[32.531708579354026261  ,40.104035956583757152  ] 
dist 10=[30.969886792004121026  ,39.975790246090967758  ] 
dist 11=[29.366928384560864171  ,39.440058299376917282  ] 
dist 12=[28.119811083222255810  ,39.295662049695081322  ] 
dist 13=[26.889006047471968315  ,38.948992519055786298  ] 
dist 14=[25.351076463278661916  ,38.820331003878629367  ] 
dist 15=[23.724546697811985824  ,38.203360522647091880  ] 
dist 16=[22.139554321130891712  ,37.556130149862556386  ] 
dist 17=[20.273514968589373369  ,27.009699033952504941  ] 
dist 18=[17.523652263506161528  ,26.906402876151103414  ] 
dist 19=[14.774871473890216462  ,22.985427274088870876  ] 
dist 20=[12.913130374022432912  ,22.397977655735333796  ] 
dist 21=[11.335535106393634582  ,21.741658683822075344  ] 
dist 22=[9.7223952335520747280 ,21.615824019518199005  ] 
dist 23=[8.2003707317298785419 ,17.301529050630834127  ] 
dist 24=[6.9869392191393856135 ,17.134071296031753436  ] 
dist 25=[5.7612208838579687840 ,16.244054887692219655  ] 
dist 26=[4.1901060145903575624 ,15.671871739165051904  ] 
dist 27=[2.6598173930673421875 ,12.784380907678984848  ] 
dist 28=[1.5972417123854121886 ,12.530534480606540546  ] 
dist 29=[.66862084860904209888,12.209458773408230983  ] 
dist 30=[-.32638777977403326855,12.121847858319400296  ] 
dist 31=[-1.2940635231485293765 ,2.8957004006833368971 ] 
dist 32=[-3.3384960886860207610 ,2.4176638037592175223 ] 
dist 33=[-5.7194789365938056968 ,2.1455451194072614628 ] 
dist 34=[-7.2248996152622196225 ,2.0929512856273452918 ] 
dist 35=[-8.3866421462334292559 ,1.7176615161565677398 ] 
dist 36=[-9.3940178741169044399 ,1.6522930805322727504 ] 
dist 37=[-10.233937916517105908  ,1.6112831819137229690 ] 
dist 38=[-10.726556706365708685  ,1.6331566524933713975 ] 
dist 39=[-11.063977717963670480  ,1.6834525356195845820 ] 
dist 40=[-11.284078835615412553  ,1.7672296769465403067 ] 
dist 41=[-11.439074515425953776  ,1.8897744693870901952 ] 
dist 42=[-11.516253355729634339  ,2.0948995235539344035 ] 
dist 43=[-11.554210725122224869  ,2.3125747978598148465 ] 
dist 44=[-11.551882898568970603  ,2.4853222321254752590 ] 
dist 45=[-11.526158918747018795  ,2.6569614049024097754 ] 
dist 46=[-11.486420370312147536  ,2.8704499649141499900 ] 
dist 47=[-11.394483256505644976  ,3.0932084916663178830 ] 
dist 48=[-11.346169542510226744  ,3.3019231755120738299 ] 
dist 49=[-7.5277920740780339899 ,3.5395342889052172418 ] 
dist 50=[-7.5018976919085445419 ,3.8776193699340324030 ] 
dist 51=[-3.9233872824553499785 ,4.2103588043422958626 ] 
dist 52=[-3.7401139752800353183 ,4.4266809546111045710 ] 
dist 53=[-3.5307656747622600767 ,4.5985370824150871663 ] 
dist 54=[-3.4820199045017951694 ,4.7539486173524543869 ] 
dist 55=[-2.5396929942205578429 ,4.8863707905161777843 ] 
dist 56=[-2.4175403116924146334 ,4.9665356194906829393 ] 
dist 57=[-2.1437075896420715519 ,5.0235269095862672434 ] 
dist 58=[-2.0868895244417354870 ,5.0635061118701911423 ] 
dist 59=[-1.7527864466326348109 ,5.0860131104870512487 ] 
dist 60=[-1.6928521248591248390 ,5.0765823293399991424 ] 
dist 61=[-1.5731130908727742804 ,5.0423096618406117927 ] 
dist 62=[-1.5426939817104443522 ,5.0159741163334326485 ] 
dist 63=[-.71443189645675597262,4.8376784776681477429 ] 
dist 64=[-.63664729045493385727,4.6866981419113998051 ] 
dist 65=[-.46453848186917136323,3.1133611109708236470 ] 
dist 66=[-.4289063455319995114 ,3.3426158298249196791 ] 
dist 67=[-.22183719566022341052,3.5555982427184828452 ] 
dist 68=[-.18399873832252239074,3.6853630720344981316 ] 
dist 69=[-.1102209970949286013 ,3.7797457777119968166 ] 
dist 70=[-.09149987655184955983,3.8513596243471685480 ] 
dist 71=[.1272180875740184280 ,3.9035288307603305905 ] 
dist 72=[.1590075451177811444 ,3.9202372498914542027 ] 
dist 73=[.2311240847432883742 ,3.9205811321983415619 ] 
dist 74=[.2468552889167747759 ,3.9119131538498698578 ] 
dist 75=[.0690146880806599406 ,3.8273206249121442190 ] 
dist 76=[-.2210444674921977603 ,3.8061063208567399117 ] 
dist 77=[-.5123167034708846564 ,3.7263961122959786550 ] 
dist 78=[-.8816472817502268109 ,3.7143312413233863139 ] 
dist 79=[-1.2732807791288668168 ,3.4911094340505803864 ] 
dist 80=[-1.6536245625648037717 ,3.4396469261918946334 ] 
dist 81=[-2.0989642404587306882 ,3.4004786530970173155 ] 
dist 82=[-2.7501207438401181755 ,3.3902673363337932932 ] 
dist 83=[-3.3948836210615899940 ,1.2883235969213640145 ] 
dist 84=[-3.8147086955373624066 ,1.2403874861139071020 ] 
dist 85=[-4.1506559890099419637 ,.95802000107386860098] 
dist 86=[-4.4605454509631811375 ,.9060801863752609693 ] 
dist 87=[-4.7304332618110822275 ,.8033379585114000370 ] 
dist 88=[-4.9066810522961535505 ,.7769792881388122994 ] 
dist 89=[-5.0483348747915287551 ,.4827253134927891777 ] 
dist 90=[-5.1801189120444744387 ,.4390036916092848679 ] 
dist 91=[-5.2866392729987019123 ,.3519092444839321905 ] 
dist 92=[-5.3274292459998012776 ,.3297319646542699109 ] 
dist 93=[-5.3398720137122770558 ,.28049466799259204427] 
dist 94=[-5.3331999501770423947 ,.4671972398728620977 ] 
dist 95=[-5.2083585247797913754 ,.66060462740725654527] 
dist 96=[-5.1665542182158773289 ,.79880082623340243428] 
dist 97=[-5.1260694759598640130 ,.92300380784041422592] 
dist 98=[-5.0987782220685955678 ,1.0605744371361231791 ] 
dist 99=[-4.5786607113919550396 ,1.1962239615694447166 ] 
dist 100=[-4.5314012413342179505 ,1.3127685108917956667 ] 
dist 101=[-4.3814053834058180117 ,1.8613272250702442221 ] 
dist 102=[-4.3593591074674672258 ,2.4290995115228342428 ] 
dist 103=[-4.0068397943700811941 ,2.9517699134079533121 ] 
dist 104=[-3.9290186739858660536 ,3.3429948750147994372 ] 
dist 105=[-3.8652425223407646422 ,3.7132105944737806716 ] 
dist 106=[-3.8506764108538740557 ,4.1520040373879740007 ] 
dist 107=[-2.8238239540295744768 ,4.5594014302128966839 ] 
dist 108=[-2.7564030534856789075 ,4.8042753300673765724 ] 
dist 109=[-2.7406522999460576868 ,4.9771803732854141808 ] 
dist 110=[-2.7284044590996833608 ,5.0972602248172875721 ] 
dist 111=[-2.1406312727526640953 ,5.1843019429618243172 ] 
dist 112=[-2.0849396646351158321 ,5.2253162851018637829 ] 
dist 113=[-2.0296789218668836666 ,5.2404922070248589903 ] 
dist 114=[-2.0156735000148457570 ,5.2355820893073693056 ] 
dist 115=[-.7342707335372331593 ,2.9115985434657082353 ] 
dist 116=[-.7855301027568181217 ,2.9123613054897434345 ] 
dist 117=[-.8298615080978808660 ,2.8973963689169906582 ] 
dist 118=[-.8579555098783142786 ,2.8869159026283008888 ] 
dist 119=[-.8794636478417346395 ,2.7073007716148040365 ] 
dist 120=[-.8975136308921217411 ,2.6736433048885027881 ] 
dist 121=[-.9113002221994896159 ,2.5908346260816679322 ] 
dist 122=[-.9157939160160657391 ,2.5618595383555864879 ] 
dist 123=[-.9158674927274495989 ,2.4149797836995036405 ] 
dist 124=[-.9135269136163918037 ,2.3806726843022240034 ] 
dist 125=[-.8916985371604831413 ,2.3092366761197388669 ] 
dist 126=[-.8844633455261171924 ,2.2863190734966800675 ] 
dist 127=[-.90850787969956758593,2.4165284927808075568 ] 
dist 128=[-1.3052800500281453004 ,2.4959462732447618661 ] 
dist 129=[-1.6268523645034740302 ,2.5500774007437377699 ] 
dist 130=[-1.9303347392039703258 ,2.5840167389029207959 ] 
dist 131=[-2.1993210408072825479 ,2.6047500947587582712 ] 
dist 132=[-2.3831717541727096002 ,2.6069154821112775707 ] 
dist 133=[-2.5400455716311865137 ,2.5998373686235593858 ] 
dist 134=[-2.7013274811114023398 ,2.5903891831856408244 ] 
dist 135=[-2.8463980031654906837 ,2.4329103634886616139 ] 
dist 136=[-2.9385501493643043885 ,2.4035175643396389018 ] 
dist 137=[-3.0096634811832381079 ,2.3351905423367748379 ] 
dist 138=[-3.0707424954728099298 ,2.3115630528489268110 ] 
dist 139=[-3.1207522455545255332 ,2.1963458351824541746 ] 
dist 140=[-3.1476741709070625450 ,2.1697945934482738860 ] 
dist 141=[-3.1628547136303649019 ,2.1057673283317886799 ] 
dist 142=[-3.1659888584620223299 ,2.0832983164836002608 ] 
dist 143=[.00790674735840860299,.79326977806649493632] 
dist 144=[-.11844360290355673998,.78974742576076086752] 
dist 145=[-.22287131373023832739,.63828019889575359593] 
dist 146=[-.32487444135465682351,.62041271201484553153] 
dist 147=[-.41767381661917883379,.57373152325346679998] 
dist 148=[-.48535576711767647585,.5669337860453379113 ] 
dist 149=[-.54769482792240536552,.48614866514757889463] 
dist 150=[-.61916431028388971123,.47000082301866909476] 
dist 151=[-.68542592208307858528,.45380174893832904335] 
dist 152=[-.72697210387909246839,.45050681093523542551] 
dist 153=[-.75843029487005306501,.2783948921951928023 ] 
dist 154=[-.78441266432612496329,.25654656377565147937] 
dist 155=[-.80493172601416656555,.21335584873741385331] 
dist 156=[-.8145761840044417791 ,.20232691102718946149] 
dist 157=[-.81872982190177945104,.16408291241451393006] 
dist 158=[-.81866634753456636416,.15542604888364881449] 
dist 159=[-.79817958045220743298,.14534893786528226751] 
dist 160=[-.83002541325944122472,.1427466607362187035 ] 
dist 161=[-.85904264938326357105,-.19980100418035064733] 
dist 162=[-.87465060888060660914,-.22756187613128731072] 
dist 163=[-.8834551121273424463 ,-.28708226292191061312] 
dist 164=[-.8853051202543722955 ,-.28919432205596790113] 
dist 165=[-.8840939339578305947 ,-.22423248971250811611] 
dist 166=[-.8816220439448953829 ,-.13015793981240239388] 
dist 167=[-.8758059593931187001 ,-.03394232498570139500] 
dist 168=[-.8726019600046309498 ,.03956904904991865058] 
dist 169=[-.7946886952422571768 ,.11061625240787666543] 
dist 170=[-.7819880807909263731 ,.19699582846311660261] 
dist 171=[-.7542230383737244652 ,.28675585085276272518] 
dist 172=[-.7454152397842129617 ,.37130125697577933353] 
dist 173=[-.7051880984026190740 ,.46833442519318777189] 
dist 174=[-.6964661708348331256 ,.60795492951971332209] 
dist 175=[-.6726566920656928713 ,.74595177393358275764] 
dist 176=[-.6673303131398193190 ,.8365029885923686100 ] 
dist 177=[-.5275737027154700542 ,.9097587939653362947 ] 
dist 178=[-.5216042377599842409 ,.9787021371331323573 ] 
dist 179=[-.5047668977576958756 ,1.0397082765973427515 ] 
dist 180=[-.5011154069506586958 ,1.0812744825465459600 ] 
dist 181=[-.46589070584529318083,1.1166201231335596321 ] 
dist 182=[-.45800557348750661595,1.1527913122415805996 ] 
dist 183=[-.44805197434383140243,1.1834614864752878515 ] 
dist 184=[-.4440777621672320808 ,1.1968441755319648440 ] 
dist 185=[-.34918559520552180705,1.2027463864325734063 ] 
dist 186=[-.3360328077870700544 ,1.2035466593491238328 ] 
dist 187=[-.30874347397349335629,1.1783780549114316714 ] 
dist 188=[-.3011335094833002554 ,1.1730846892421229588 ] 
dist 189=[-.27079564587131260379,1.1686988169264875733 ] 
dist 190=[-.26447737771226253445,1.1638407534185777377 ] 
dist 191=[-.24964224303620692449,.99891921637997114899] 
dist 192=[-.3196676824619077992 ,.97673371062966386398] 
dist 193=[-.44865120543043189335,.91941898341959219541] 
dist 194=[-.57830704947796267556,.90875073580803753616] 
dist 195=[-.69866576273797348608,.80918383269487922872] 
dist 196=[-.79053001941069671415,.78865985775737790128] 
dist 197=[-.87923144239986627653,.76198789809151868432] 
dist 198=[-.9869624602897080953 ,.75240831141576929387] 
dist 199=[-1.0883987275212904875 ,.54162430686504974258] 
dist 200=[-1.1519680025865505128 ,.51339841599441012037] 
dist 201=[-1.2000497849853399554 ,.45338007922915260683] 
dist 202=[-1.2396512692880345452 ,.43676731972267652947] 
dist 203=[-1.2708265882668981944 ,.37047335303449251422] 
dist 204=[-1.2852663957734311063 ,.35755015211606384966] 
dist 205=[-1.2914378752697989565 ,.32650165339432993513] 
dist 206=[-1.2910964217397611627 ,.36418822228045173607] 
dist 207=[-.52881381719444950585,.42551092868848668723] 
dist 208=[-.62187468323691997013,.51715212070571686996] 
dist 209=[-.71379462623686845285,.60848258713325424741] 
dist 210=[-.77297971114972480583,.66856460549947041112] 
dist 211=[-.81960203928179991534,.71733289816443315988] 
dist 212=[-.86136247120929518274,.7634929822537470145 ] 
dist 213=[-.8968713714407506028 ,.80450755764348883926] 
dist 214=[-.91853324710793678689,.83273212937949100468] 
dist 215=[-.93423132232064824028,.85702518516735927254] 
dist 216=[-.94592886136357812217,.8823426955345335531 ] 
dist 217=[-.95375408251657114225,.90406170357245940444] 
dist 218=[-.95484937934123100854,.91398750812036031076] 
dist 219=[-.95163403152031475936,.91815383070685780323] 
dist 220=[-.94910045555608606509,.91776212558434327201] 
dist 221=[-.91913214979669149347,.9045233626856947272 ] 
dist 222=[-.91057015693432032026,.8991446642967479046 ] 
dist 223=[-.90074684448804399019,.89186527588005514842] 
dist 224=[-.89562182588377215229,.88807714623605908426] 
dist 225=[-.75219119391647602515,.77353823051721278019] 
dist 226=[-.75264927180649204436,.75754136746467233022] 
dist 227=[-.73296593472388165152,.714655812994232465  ] 
dist 228=[-.72781231961066485328,.70763311791147159396] 
dist 229=[-.72467015647938472732,.62874451044372080859] 
dist 230=[-.72344588835793186175,.61241659344612169617] 
dist 231=[-.5970776836732188318 ,.59470658493686089781] 
dist 232=[-.57961024819115793169,.58897965021888956076] 
dist 233=[-.54759064536972193347,.37462790884001559193] 
dist 234=[-.53936073053567644802,.34785882262559011696] 
dist 235=[-.51185136103233153128,.29727504912069715521] 
dist 236=[-.50402734037944573563,.27722473871870413966] 
dist 237=[-.49714356566387688412,.12789874014064215642] 
dist 238=[-.49446021078704493833,.08756798741674170824] 
dist 239=[-.06958754751506343084,.15020160685875392955] 
dist 240=[-.06550836782406145533,.23827460849426142071] 
dist 241=[.11811332041780186778,.32525232067089692606] 
dist 242=[.13477399096675746536,.38351287546774869158] 
dist 243=[.23064973292238536497,.43197220220294675874] 
dist 244=[.24657153683540014699,.47981695278764675234] 
dist 245=[.27953104761644629641,.52368208045995217574] 
dist 246=[.28605547987311310102,.55625217116324971827] 
dist 247=[.32954927064461148221,.58683068424863382546] 
dist 248=[.34983256285489855345,.6227442440741312656 ] 
dist 249=[.43555465866291845735,.65594849200089509754] 
dist 250=[.41076850146957259614,.67570968308153149353] 
dist 251=[.37868910276281810036,.68943399751957869896] 
dist 252=[.32821112984108724355,.69853504152274432176] 
dist 253=[.26968195435023872835,.7040926139383099216 ] 
dist 254=[.20545692356227089446,.70500975416214129837] 
dist 255=[.12466698265972814598,.70162072664789149675] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 2, 2, 1, 2] 
dist 0=[40.288264126791640165  ,40.288264126791640165  ] 
dist 1=[39.544411012023714712  ,40.791146473349053032  ] 
dist 2=[38.274230576561831192  ,41.098828469430431671  ] 
dist 3=[36.945079192783014607  ,41.315820353630535758  ] 
dist 4=[35.965633203118132500  ,41.456398559640469187  ] 
dist 5=[35.051697978072466818  ,41.568156161850322108  ] 
dist 6=[33.984069033262415659  ,41.686669720111715928  ] 
dist 7=[32.894698786054926952  ,41.732144793508801062  ] 
dist 8=[31.893768429102111336  ,41.638541796085522116  ] 
dist 9=[30.761954021459679858  ,40.579221410521176259  ] 
dist 10=[29.149479587703542487  ,40.372631808863560497  ] 
dist 11=[27.503393989987194513  ,40.025940733242655455  ] 
dist 12=[26.237170119283964903  ,39.917078203184080545  ] 
dist 13=[25.001172674739212948  ,39.519040516653882447  ] 
dist 14=[23.475665862590035644  ,39.390138399594139264  ] 
dist 15=[21.871943799482936814  ,39.141517097339395252  ] 
dist 16=[20.323218484495380177  ,38.943417439503987942  ] 
dist 17=[18.510286173381202205  ,29.116092584243783380  ] 
dist 18=[15.850460028878302306  ,28.245421997022970495  ] 
dist 19=[13.196654456889262496  ,26.120271641949476323  ] 
dist 20=[11.407737725326512470  ,25.814358370208080338  ] 
dist 21=[9.9007565893902899202 ,22.644660337299274508  ] 
dist 22=[8.3737715350688452733 ,22.048851793793631383  ] 
dist 23=[6.9414086949361637289 ,21.387600154128551687  ] 
dist 24=[5.8125939347343289168 ,21.267083669475721595  ] 
dist 25=[4.6840995391065801622 ,17.021064656741756202  ] 
dist 26=[3.2529811812195130165 ,15.993475506808888787  ] 
dist 27=[1.8655295919850381821 ,13.866300972818453888  ] 
dist 28=[.9115192590155767207 ,13.528129445636147811  ] 
dist 29=[.0872748933815270725 ,12.359332892710711079  ] 
dist 30=[-1.5815078712787428550 ,12.105468747889092725  ] 
dist 31=[-4.1198217449528508488 ,11.802149294636503879  ] 
dist 32=[-5.7397202430725749425 ,11.734405831915950018  ] 
dist 33=[-7.0066422302298090316 ,2.4816229559854280729 ] 
dist 34=[-8.1342216261908353501 ,2.1631975835060764602 ] 
dist 35=[-9.0950191686851035050 ,2.2179899733131309109 ] 
dist 36=[-9.6955072663797317782 ,2.2798647529246660375 ] 
dist 37=[-10.152090105892977157  ,2.3555872656291993434 ] 
dist 38=[-10.538156492925210070  ,2.4662794882130480537 ] 
dist 39=[-10.854801371967301450  ,2.5878928347695033083 ] 
dist 40=[-11.033909092494528049  ,2.7074386567589794733 ] 
dist 41=[-11.149711046484699357  ,2.8465929358231413973 ] 
dist 42=[-11.212870399900454099  ,3.0465414155774721523 ] 
dist 43=[-11.239788008158958607  ,3.2465390076385991429 ] 
dist 44=[-11.221866763899341449  ,3.3859850307529562211 ] 
dist 45=[-11.154890230297192782  ,3.5064456370242984754 ] 
dist 46=[-11.108454443896844470  ,3.6308822925159189441 ] 
dist 47=[-8.2578950392384894564 ,3.7469044598978528549 ] 
dist 48=[-8.2685282062664828886 ,3.8338350719094628474 ] 
dist 49=[-6.5462271839273191164 ,3.9151464938918435016 ] 
dist 50=[-6.5141099208194212046 ,4.0086903838612512402 ] 
dist 51=[-4.2152748486061048342 ,4.0938685265836320558 ] 
dist 52=[-4.1388817710408551906 ,4.1418334599879999436 ] 
dist 53=[-3.5561978985453195273 ,4.1709019024011512666 ] 
dist 54=[-3.4461068193182342714 ,4.1808403999403188350 ] 
dist 55=[-3.2692875550463440209 ,4.1769804832052391590 ] 
dist 56=[-3.2236123275435062754 ,4.1609200369847187894 ] 
dist 57=[-2.3875369452918691149 ,4.1142597472062218710 ] 
dist 58=[-2.2787656726440706619 ,4.0868221142904429804 ] 
dist 59=[-2.0221083245657682708 ,3.9129989462165122572 ] 
dist 60=[-1.9809744790761696565 ,3.8656918474508974776 ] 
dist 61=[-1.6304810656762905200 ,3.7401962864622638282 ] 
dist 62=[-1.5671726529062173539 ,3.5687530224037618668 ] 
dist 63=[-1.4776269618839641315 ,3.3822872260468863140 ] 
dist 64=[-1.4523836055810108377 ,3.6416498022596718721 ] 
dist 65=[-.77973831532971357978,3.8416363440076375141 ] 
dist 66=[-.70145174752409125125,4.0142054501182505654 ] 
dist 67=[-.53604526394622928565,4.1569783411354270487 ] 
dist 68=[-.49419961826765404188,4.2379267566338740929 ] 
dist 69=[-.3186744956874056405 ,4.2895957044256711587 ] 
dist 70=[-.2924672524836885675 ,4.3154182043808390721 ] 
dist 71=[-.2278316961730485634 ,4.3250249436432411741 ] 
dist 72=[-.2176592064029821433 ,4.3210307355223022942 ] 
dist 73=[-.1129644009829955042 ,4.2921188937265405088 ] 
dist 74=[-.0930393322463350463 ,4.2749133601014495646 ] 
dist 75=[-.0573531574110250310 ,4.1433982111608865450 ] 
dist 76=[-.0479913052608306558 ,4.1070273501925085661 ] 
dist 77=[-.0151855955804102501 ,4.0500889895083965965 ] 
dist 78=[-.0058464721572821402 ,4.0292311978562967679 ] 
dist 79=[-.15399798972709958196,3.2139707641832649294 ] 
dist 80=[-.66663554746704897389,3.2066065988322866443 ] 
dist 81=[-1.0942970119077690110 ,2.7203762452864697708 ] 
dist 82=[-1.5186939527037766501 ,2.7106934848533927025 ] 
dist 83=[-1.9093126258471447332 ,2.0693167986201198070 ] 
dist 84=[-2.2021211367009902409 ,1.9849142572544325022 ] 
dist 85=[-2.4798696545476923852 ,1.8690796906117608528 ] 
dist 86=[-2.8103838727644160844 ,1.8323901968000299481 ] 
dist 87=[-3.1185410616601527671 ,1.0933115623341949502 ] 
dist 88=[-3.3070323506024670829 ,.99678090411030886245] 
dist 89=[-3.4443657579733093527 ,.78668169185194415578] 
dist 90=[-3.5482624345115832253 ,.73561182369886494412] 
dist 91=[-3.6263126043502580573 ,.49531505001356766801] 
dist 92=[-3.6604238609093819085 ,.45175454990975563296] 
dist 93=[-3.6727617595318308146 ,.34896716144689599702] 
dist 94=[-3.6696540701475891441 ,.33099930669984417509] 
dist 95=[-3.6507015388635863292 ,-.52478721227055581859] 
dist 96=[-3.6463199956693687716 ,-.53396832512742842107] 
dist 97=[-3.6311369441904248596 ,-.70753134885692449076] 
dist 98=[-3.6212433652417659803 ,-.17539257955093456533] 
dist 99=[-3.3743127101265279443 ,.48713019603379752704] 
dist 100=[-3.3361866310649594252 ,.93598888633822194963] 
dist 101=[-3.2249540691583884989 ,1.3146244800004139290 ] 
dist 102=[-3.2026785936257877898 ,1.6968170806913886159 ] 
dist 103=[-2.9625374398361510843 ,2.0523909323743597032 ] 
dist 104=[-2.9092204395591809264 ,2.3247647616189262491 ] 
dist 105=[-2.8473181138608743491 ,2.5885699217769486760 ] 
dist 106=[-2.8204451669935766341 ,2.9099382093399582106 ] 
dist 107=[-2.1755297716905515045 ,3.2127584950545412757 ] 
dist 108=[-2.0875110774307680787 ,3.4025189816917445134 ] 
dist 109=[-1.9065328908175385791 ,3.5459396512422678266 ] 
dist 110=[-1.8569889110588997512 ,3.6637678168681554039 ] 
dist 111=[-1.6649111098551178928 ,3.7562196612153956557 ] 
dist 112=[-1.6242724542618773166 ,3.7983353300018245729 ] 
dist 113=[-1.5374729708856584730 ,3.8155065989428677756 ] 
dist 114=[-1.5118885657761899708 ,3.8136742795285271053 ] 
dist 115=[-.05308663804040801662,2.0166500629781214792 ] 
dist 116=[.06002722889909960927,2.2051041166684037576 ] 
dist 117=[.31304003338737996159,2.3754639971165361775 ] 
dist 118=[.35765470342336325822,2.4977529108941711490 ] 
dist 119=[.65262083126248527205,2.6765270637895711549 ] 
dist 120=[.7018504739753274685 ,2.7848548487950685976 ] 
dist 121=[.79323574567894218009,2.8564425556576883502 ] 
dist 122=[.77980098092558093141,2.9031073536654994914 ] 
dist 123=[.65921956144307385671,2.9371444736488622399 ] 
dist 124=[.51118550194350775332,2.9446971421553545544 ] 
dist 125=[.31456279837957227725,2.9416428954629293681 ] 
dist 126=[0                     ,2.8980210981892065084 ] 
dist 127=[.40727942560071081443,2.3778865739732908981 ] 
dist 128=[.06550309670478163862,2.4665958958931476382 ] 
dist 129=[-.2790359536440922748 ,2.5507794508606780109 ] 
dist 130=[-.51168272305491488819,2.6510131897913155771 ] 
dist 131=[-.70711638121871591982,2.7410091046274201867 ] 
dist 132=[-.90309567678826581231,2.7843168549942023023 ] 
dist 133=[-1.0846275426799084576 ,2.8063220678192117287 ] 
dist 134=[-1.2223849625346010590 ,2.8112482983078900872 ] 
dist 135=[-1.3545797258012119094 ,2.7684005428035487145 ] 
dist 136=[-1.5139043190264076767 ,2.7568138498224320678 ] 
dist 137=[-1.6631922067255362045 ,2.7494291353209359922 ] 
dist 138=[-1.7553185363890445856 ,2.7458493963736463985 ] 
dist 139=[-1.9174850959391712370 ,2.3128575118923747562 ] 
dist 140=[-2.0814783071039691051 ,2.2520907249010858435 ] 
dist 141=[-2.2254049867372447581 ,2.1420579320077111381 ] 
dist 142=[-2.3798194970998780412 ,2.1137232797450942112 ] 
dist 143=[-2.5293899571408016248 ,2.0195045459482193430 ] 
dist 144=[-2.6539785673973766930 ,1.9917437210184515294 ] 
dist 145=[-2.7842919216570956079 ,1.9681796094569979248 ] 
dist 146=[-2.9567216516015543105 ,1.9582691578731957438 ] 
dist 147=[-3.1206732103741371311 ,.1486004348692211773 ] 
dist 148=[-3.2171376033021830709 ,.0034072797491995066 ] 
dist 149=[-3.2827608787488434154 ,-.2949930997892546912 ] 
dist 150=[-3.3235764636155785257 ,-.31912221102062754777] 
dist 151=[-3.3478091351598380601 ,-.35441687979524150267] 
dist 152=[-3.3501163892867457266 ,-.36256691913922936994] 
dist 153=[-3.3376936556201617122 ,-.48968234110164872211] 
dist 154=[-3.3262191460733863875 ,-.49490298472874038685] 
dist 155=[-3.1309544231318321717 ,-.46109287512014817609] 
dist 156=[-3.0940403071459525756 ,-.39605388151085317915] 
dist 157=[-3.0056221759674123442 ,-.31582128269515509301] 
dist 158=[-2.9744366514335697412 ,-.22135024649586818273] 
dist 159=[-2.8202408023596143036 ,-.09823722297907394001] 
dist 160=[-2.7842581500453002511 ,.09634848252106009676] 
dist 161=[-2.7036870839502543647 ,.29451373019066669727] 
dist 162=[-2.6765058242396010160 ,.43191848872394546488] 
dist 163=[-2.5169592182577254314 ,.77359597704403842431] 
dist 164=[-2.5437747507388536824 ,1.2109249271170198738 ] 
dist 165=[-2.5547925134576860233 ,1.5681616539840190836 ] 
dist 166=[-2.5536680770670016830 ,1.9101250023601335074 ] 
dist 167=[-2.5174534097837324466 ,2.2166052449166249306 ] 
dist 168=[-2.5028148866925052337 ,2.4321724548791582597 ] 
dist 169=[-2.4808852716960770289 ,2.6226951575029513549 ] 
dist 170=[-2.4705985216750067710 ,2.8291822271011702319 ] 
dist 171=[-2.1652239445999212724 ,3.0172836369695565115 ] 
dist 172=[-2.1188945666570827979 ,3.1344002310505080653 ] 
dist 173=[-2.0223636042086955432 ,3.2220859933310340761 ] 
dist 174=[-1.9937197806087927622 ,3.2926837590555681934 ] 
dist 175=[-1.8714571566393539145 ,3.3469906306601121925 ] 
dist 176=[-1.8452399391491870398 ,3.3696344294297140034 ] 
dist 177=[-1.7734432597424816094 ,3.3749992459056028111 ] 
dist 178=[-1.7587152590282506801 ,3.3715776549527273834 ] 
dist 179=[.02039830042243400525,1.9143885696028191261 ] 
dist 180=[.05489147877733033310,1.9235868660494557900 ] 
dist 181=[.27093972307768610069,1.9250939729726489974 ] 
dist 182=[.30779016846765318019,1.9214178207312363626 ] 
dist 183=[.37880639391762307946,1.9086837105800017069 ] 
dist 184=[.39504697816356961292,1.9006254708524973557 ] 
dist 185=[.54073175523974795488,1.7465724450726608868 ] 
dist 186=[.56299936562050289655,1.7203099798492734576 ] 
dist 187=[.57827567856708955043,1.6602544473320319727 ] 
dist 188=[.51602970114031925825,1.6403789085349884504 ] 
dist 189=[.4396655886601452175 ,1.5465169004240816729 ] 
dist 190=[.34725760265722957289,1.5255050559157250500 ] 
dist 191=[.23214101872224343446,1.4746838543123791805 ] 
dist 192=[-.09061308946712539157,1.4575928345319573702 ] 
dist 193=[-.46572336820429073233,1.4381402423556817049 ] 
dist 194=[-.7127979480175090957 ,1.4390640721415152944 ] 
dist 195=[-.91370698971765513483,.7101337484499480069 ] 
dist 196=[-1.1044974833637561899 ,.70258370926379282241] 
dist 197=[-1.2744659060841471922 ,.62568836733953797037] 
dist 198=[-1.3922410010313905825 ,.6097814751937211159 ] 
dist 199=[-1.4944859638363184094 ,.5907914781142156552 ] 
dist 200=[-1.6024487987784999031 ,.58343434958427309828] 
dist 201=[-1.7003768114043074894 ,.41443291602667967504] 
dist 202=[-1.7625568456464056727 ,.39192449909065971113] 
dist 203=[-1.8105337983832409360 ,.34523305935510565321] 
dist 204=[-1.8517548793118550459 ,.33258803999317212258] 
dist 205=[-1.8855361160585586764 ,.28396836830054694891] 
dist 206=[-1.9038088036066382474 ,.27401641985286460056] 
dist 207=[-1.9142401901492747083 ,.25303970132795361275] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 1, 0, 0, 2] 
dist 0=[47.721722035091150758  ,47.721722035091150758  ] 
dist 1=[47.639678371833484809  ,47.737125131046066171  ] 
dist 2=[47.327551131364328391  ,47.736908394947706300  ] 
dist 3=[46.771427675317368656  ,47.708721223920257565  ] 
dist 4=[45.749444132643012744  ,47.654083841987696420  ] 
dist 5=[44.603779014131193325  ,47.576614970259668704  ] 
dist 6=[43.553687457346148231  ,47.448739643584775530  ] 
dist 7=[42.370370402794343967  ,46.866344803733940799  ] 
dist 8=[40.692420388805476947  ,43.619370262785989123  ] 
dist 9=[38.819913212404567638  ,43.417305759475079909  ] 
dist 10=[36.859431950159320733  ,42.816203867486114263  ] 
dist 11=[34.453820010147371751  ,42.614328816671004833  ] 
dist 12=[30.803331910010499585  ,42.491887046164548361  ] 
dist 13=[27.128556898512686739  ,42.367933717768529955  ] 
dist 14=[24.625828877377750707  ,37.919022566708691654  ] 
dist 15=[22.495528643919649044  ,37.694907542547725817  ] 
dist 16=[20.308017800032815270  ,32.654403851673180810  ] 
dist 17=[18.242993157440703596  ,31.968292725029191146  ] 
dist 18=[16.601668519759658770  ,30.557346716332124968  ] 
dist 19=[14.950535599864994307  ,30.171114671833990354  ] 
dist 20=[12.845851876968577108  ,28.665850654663164295  ] 
dist 21=[10.804081920032048002  ,28.351394327554441572  ] 
dist 22=[9.4039879065711510402 ,27.651271786988819063  ] 
dist 23=[8.1993673124696350110 ,27.437723697089913908  ] 
dist 24=[6.9380916103724743966 ,15.607471781862531635  ] 
dist 25=[4.7350378992331129769 ,14.545486018941568366  ] 
dist 26=[2.3725155892172988688 ,12.108830034893978989  ] 
dist 27=[.0531279710903614772 ,11.699603122533586777  ] 
dist 28=[-2.0710950334670222739 ,9.0941175117524933912 ] 
dist 29=[-3.6541447229988627736 ,9.0364931669489271442 ] 
dist 30=[-5.1502504802022619622 ,7.1784482329702984450 ] 
dist 31=[-6.9274943146268167338 ,6.9692145301785985174 ] 
dist 32=[-8.5904977359474317135 ,3.5987466990861814178 ] 
dist 33=[-9.6304057775192244457 ,3.1710772894204348739 ] 
dist 34=[-10.418351011916430419  ,2.2361517485971762968 ] 
dist 35=[-11.074972570559376896  ,2.0654729848948998037 ] 
dist 36=[-11.602980753550589995  ,1.0246281076985167668 ] 
dist 37=[-11.877449918929044008  ,.84858317013685951705] 
dist 38=[-12.025780244659275215  ,.51547712759274018785] 
dist 39=[-12.057174833352977209  ,.44157163596341777107] 
dist 40=[-11.997016465977002168  ,.3432931202657482088 ] 
dist 41=[-11.958327672665566858  ,.9727483447938184595 ] 
dist 42=[-11.855239809950860240  ,1.6460144673412501779 ] 
dist 43=[-11.805703475921630237  ,2.4794318197709423504 ] 
dist 44=[-11.518547202385717038  ,3.7483087361951723708 ] 
dist 45=[-11.445586028733064633  ,5.0169026182805455455 ] 
dist 46=[-11.241634972624164188  ,5.8493141994134886328 ] 
dist 47=[-11.176026073112456615  ,6.5213560522860957104 ] 
dist 48=[-10.378863197260342788  ,7.1500272285348354542 ] 
dist 49=[-10.247710236105935987  ,7.7027096365985719482 ] 
dist 50=[-9.8874109716114561802 ,8.0715445457069412600 ] 
dist 51=[-9.7438258103058692578 ,8.3765178744773077365 ] 
dist 52=[-9.0344919405948639627 ,8.6744139367847376260 ] 
dist 53=[-6.9597309036283579987 ,8.9255533115942878906 ] 
dist 54=[-6.7012004459748703301 ,9.0438576127238584011 ] 
dist 55=[-5.6153648005792143065 ,9.0959518627483192293 ] 
dist 56=[-2.5988454674801498735 ,9.0953285751635750325 ] 
dist 57=[-2.5081692743198281063 ,8.9666631853348087124 ] 
dist 58=[-2.1171789112596914078 ,8.9106359940498646837 ] 
dist 59=[-2.0451217460660497292 ,8.8338338817992187751 ] 
dist 60=[-1.8729786183900420700 ,8.7932452605411440648 ] 
dist 61=[-1.8440839312648778929 ,6.5541235373403744417 ] 
dist 62=[.0242490096604485134 ,6.3072748046062661392 ] 
dist 63=[.1956014478502874163 ,5.6929878756459188640 ] 
dist 64=[.5823756333294562408 ,5.5931996420499874277 ] 
dist 65=[.6456825630233100232 ,5.2652894233443895728 ] 
dist 66=[1.1091138876793656406 ,5.0654016674763955441 ] 
dist 67=[1.1871076434413413693 ,5.0117351271000009561 ] 
dist 68=[1.3173326336294814612 ,4.9484665865162051111 ] 
dist 69=[1.3447782610915548289 ,4.9175296965845538745 ] 
dist 70=[1.5219195717888718383 ,4.0944568835877356700 ] 
dist 71=[1.0414030232246371027 ,3.9775693515288204952 ] 
dist 72=[.4919844944428509022 ,3.7366589023754981148 ] 
dist 73=[-.0608053109257293825 ,3.6686949772748708232 ] 
dist 74=[-.5548780708334554337 ,3.3956260430842375311 ] 
dist 75=[-1.1016299210357234613 ,3.3370146185333315641 ] 
dist 76=[-1.8649054739994183653 ,3.1990058137213739436 ] 
dist 77=[-2.6149924834634553167 ,3.1577365851120381258 ] 
dist 78=[-3.1091078284716598782 ,2.4571491436467726687 ] 
dist 79=[-3.5115658316763218228 ,2.4484144567572513373 ] 
dist 80=[-3.8956022760821045739 ,2.4291397565375290799 ] 
dist 81=[-4.2396146557110929680 ,2.4199532427678106897 ] 
dist 82=[-4.4822343945678213660 ,2.3663945776944425452 ] 
dist 83=[-4.6977277285166652309 ,2.3521333084217140246 ] 
dist 84=[-4.9334220479384481983 ,2.3078823553318933166 ] 
dist 85=[-5.1429545426658017521 ,2.2955562708250949875 ] 
dist 86=[-5.2539658611078319158 ,2.1244583969609287075 ] 
dist 87=[-5.3145980519185114940 ,2.0953566104027332423 ] 
dist 88=[-5.3282398742471805169 ,2.0127806190060155700 ] 
dist 89=[-5.3116813237142060066 ,1.9993523112528516376 ] 
dist 90=[-5.2996072531133708697 ,1.8310279279654033865 ] 
dist 91=[-5.2841169577670901986 ,1.7949086843694694394 ] 
dist 92=[-5.2653950305531352203 ,1.7592901589595692948 ] 
dist 93=[-4.6205616317925642122 ,2.0398523375388472472 ] 
dist 94=[-1.1336251356529623640 ,2.5341678292756208913 ] 
dist 95=[-1.4646165059393784268 ,2.9413705414958728266 ] 
dist 96=[-1.7339712419720343565 ,3.3365680552033486071 ] 
dist 97=[-1.9902796734207086459 ,3.6941781889929000818 ] 
dist 98=[-2.2191047644291783049 ,3.9513460479750204087 ] 
dist 99=[-2.3787170198542917193 ,4.1844353348731289386 ] 
dist 100=[-2.5184689712317456418 ,4.4459462926692959585 ] 
dist 101=[-2.6679912939084649371 ,4.6812823418525658493 ] 
dist 102=[-2.8021589147699771315 ,4.8098901152680471823 ] 
dist 103=[-2.8805994892498294347 ,4.8851405820196385677 ] 
dist 104=[-2.9333726564998929943 ,4.9074778800962526365 ] 
dist 105=[-2.9650507088633762410 ,4.9087919580144396829 ] 
dist 106=[-2.9829487367343885379 ,4.9000982117247022362 ] 
dist 107=[-2.9839440964624425772 ,4.8824344220579859799 ] 
dist 108=[-2.9713758371871897059 ,4.9025366814354445509 ] 
dist 109=[-2.9610431475042936645 ,4.9761077556361888046 ] 
dist 110=[-2.2457292427296331068 ,4.9938610255702670136 ] 
dist 111=[-2.4680078698094006381 ,4.9923900859171140988 ] 
dist 112=[-2.8542156292242366965 ,4.9890862830693128770 ] 
dist 113=[-3.2376609611570269457 ,4.8181043920847959682 ] 
dist 114=[-3.5903524939918171602 ,4.7710008074921172285 ] 
dist 115=[-3.8537832285030753834 ,4.7402824452456806636 ] 
dist 116=[-4.1024843632052137918 ,4.7239861268652247156 ] 
dist 117=[-4.4061349689902711302 ,3.8523111469597566277 ] 
dist 118=[-4.6686784990744438315 ,3.7320006591756594199 ] 
dist 119=[-4.8312684016532941366 ,3.5039564227122881788 ] 
dist 120=[-4.9447105432726932937 ,3.4441496614071187686 ] 
dist 121=[-5.0332925438675805968 ,3.2342985309430730219 ] 
dist 122=[-5.0684793836184828136 ,3.1797649397418546724 ] 
dist 123=[-5.0766208185815808298 ,3.1106154508805837458 ] 
dist 124=[-5.0165722799284420967 ,3.0832328140353538303 ] 
dist 125=[-.55624438230290723789,2.5657491537044765397 ] 
dist 126=[-.28926455417960169738,2.8568881703940729791 ] 
dist 127=[-.68812328120636856191,3.0413204615119412836 ] 
dist 128=[-1.0837949028427396561 ,3.1831779179627525412 ] 
dist 129=[-1.4477316977767943740 ,3.3043227251361604875 ] 
dist 130=[-1.7198936620853304005 ,3.4030915265143352579 ] 
dist 131=[-1.9773143904154043968 ,3.4556055306620030553 ] 
dist 132=[-2.2824059475165888592 ,3.4843680518138988678 ] 
dist 133=[-2.5665276435689760306 ,3.4883017396957109787 ] 
dist 134=[-2.7402255842952559716 ,3.4797711266519817644 ] 
dist 135=[-2.8665372964527682275 ,3.4704593793255257422 ] 
dist 136=[-2.9614585287496967376 ,3.4352396559221252060 ] 
dist 137=[-3.0340994457813884665 ,3.4166386538948956590 ] 
dist 138=[-3.0714555362836988640 ,3.2990559541500635244 ] 
dist 139=[-3.0901838815006984779 ,3.2671573731521043674 ] 
dist 140=[-3.0902905584080451389 ,3.2102782071779926932 ] 
dist 141=[-2.7997109127627567766 ,3.1920690281712799542 ] 
dist 142=[-2.7600168543055824536 ,2.5982049123713150812 ] 
dist 143=[-2.6690868399632501052 ,2.5451885212010922701 ] 
dist 144=[-2.6387032838538532016 ,2.4029338873122827050 ] 
dist 145=[-2.4942327451508491033 ,2.3799364065619851932 ] 
dist 146=[-2.4617606854198442971 ,2.1180360430192264089 ] 
dist 147=[-2.3821616104813336050 ,2.0638635459232806832 ] 
dist 148=[-2.4867677943644657400 ,2.0059975739806802296 ] 
dist 149=[-2.7714580566396757223 ,1.9879571789499033367 ] 
dist 150=[-3.0356203643430334566 ,1.3875115292368834962 ] 
dist 151=[-3.1945596476946596280 ,1.3089738931082076404 ] 
dist 152=[-3.3070784629325641819 ,1.2657747344035315233 ] 
dist 153=[-3.3858956055742091050 ,1.5969346272121783394 ] 
dist 154=[-3.4436787919759468708 ,1.9058181588106131215 ] 
dist 155=[-3.4722137240310878643 ,2.2579489795019162930 ] 
dist 156=[-3.4848258674405772398 ,2.7617822465536645838 ] 
dist 157=[-3.4820464507696861747 ,3.2581668195165182654 ] 
dist 158=[-.41678384042074302794,3.5805602103838476680 ] 
dist 159=[-.63983244463385241621,3.8376465237855077456 ] 
dist 160=[-.83446915574377093556,4.0732884181237482735 ] 
dist 161=[-1.0415901410623299094 ,4.2774712772998708076 ] 
dist 162=[-1.2412254452738470836 ,4.4089562122441169375 ] 
dist 163=[-1.4059734200880876630 ,4.5125431834443527956 ] 
dist 164=[-1.5769457949797159188 ,4.6053441225474428457 ] 
dist 165=[-1.8014318493984749782 ,4.6775634899614381807 ] 
dist 166=[-2.0213214154128899364 ,4.6989765864398790363 ] 
dist 167=[-2.1739409289222190491 ,4.7010745981470998123 ] 
dist 168=[-2.3067117994850237075 ,4.6961728590467384478 ] 
dist 169=[-2.4473517280924387927 ,4.5600626600270897880 ] 
dist 170=[-2.5825080308036271947 ,4.5192205285090389271 ] 
dist 171=[-2.6933837673118595161 ,4.4879430657613165991 ] 
dist 172=[-2.8078538334517527739 ,4.4642251089174465606 ] 
dist 173=[-2.9573592145566278476 ,3.8765748071300679003 ] 
dist 174=[-3.0977096178711508415 ,3.8125078348313425762 ] 
dist 175=[-3.1756268773019922711 ,3.6365278196462804904 ] 
dist 176=[-3.2228199036985772556 ,3.6057338002943515438 ] 
dist 177=[-3.2405004705138186787 ,3.2649782606570758944 ] 
dist 178=[-3.2452798373354499979 ,3.1926603058688753366 ] 
dist 179=[-3.4429384492388268957 ,3.1123265791855781898 ] 
dist 180=[-3.8455082062817674533 ,3.0817970113579725497 ] 
dist 181=[-4.2213582341387091793 ,2.6597501513974477428 ] 
dist 182=[-4.4513220212303624048 ,2.8879004284703482036 ] 
dist 183=[-4.6187279453959810701 ,3.0381236481551272656 ] 
dist 184=[-4.7448128730383707654 ,3.1602337557597998783 ] 
dist 185=[-4.8387539583361682562 ,3.2761372735146348999 ] 
dist 186=[-4.8778245572975337522 ,3.3793677098701872867 ] 
dist 187=[-4.8904999729427886210 ,3.4508782747680826235 ] 
dist 188=[-4.8844671117495515213 ,3.5129459429280827893 ] 
dist 189=[-2.4488441883509495727 ,3.5784740616113507581 ] 
dist 190=[-.89737481757114037555,3.6334002842815040833 ] 
dist 191=[-.96750809836036948987,3.6531380026512594118 ] 
dist 192=[-1.2652108473402751310 ,3.6563169780095617057 ] 
dist 193=[-1.5504357734033730322 ,3.6492963356573788510 ] 
dist 194=[-1.7830321514369264316 ,3.5775638740192426113 ] 
dist 195=[-2.0219427243525452062 ,3.5533344648762582830 ] 
dist 196=[-2.3323793074514165272 ,3.5106571992081427586 ] 
dist 197=[-2.6349507432514704743 ,3.4950466363523473847 ] 
dist 198=[-2.8424592117989557645 ,3.0605537096526087752 ] 
dist 199=[-3.0203500337882894219 ,2.9945317429391970270 ] 
dist 200=[-3.2046692939661817185 ,2.8519508461022493150 ] 
dist 201=[-3.3793200704908464298 ,2.8086933016859789412 ] 
dist 202=[-3.5186090111077464297 ,2.6185506241137273195 ] 
dist 203=[-3.6588698779151366493 ,2.5789704381483090726 ] 
dist 204=[-3.8374034342336405513 ,2.4694455974898734725 ] 
dist 205=[-4.0029521470273621664 ,2.4495547078468337869 ] 
dist 206=[-4.0913691987475154838 ,2.3436669953573904297 ] 
dist 207=[-4.1403368857726178610 ,2.4355930409755525155 ] 
dist 208=[-4.1512792746807887224 ,2.5015585798692505943 ] 
dist 209=[-4.1418819367254278661 ,2.5494618352060445838 ] 
dist 210=[-4.1328205427640732528 ,2.5826065153810483266 ] 
dist 211=[-4.1201342476586816231 ,2.7813948235508871807 ] 
dist 212=[-4.1057629671896466313 ,3.1029917874684319446 ] 
dist 213=[-3.6062453462260307179 ,3.4143034678016338958 ] 
dist 214=[-3.5307428296692324630 ,3.6241851923527392178 ] 
dist 215=[-3.3871278850964764816 ,3.8002304823754824944 ] 
dist 216=[-3.3918471596130527140 ,3.9764465078638112810 ] 
dist 217=[-3.4584800645354977104 ,4.1395606548176261423 ] 
dist 218=[-3.5068561434614987380 ,4.2632953725904933283 ] 
dist 219=[-3.5212178994929415340 ,4.3820448820233264347 ] 
dist 220=[-3.5214714629713226850 ,4.5252553597786277948 ] 
dist 221=[-3.5135179079414619662 ,4.6552326631642278641 ] 
dist 222=[-.63899133037140870119,4.7211471405448351112 ] 
dist 223=[-.20545872547716024645,4.7528349099213721194 ] 
dist 224=[-.12454221951828874737,4.7570041396458265615 ] 
dist 225=[.15318200070668974427,4.7245022954500377068 ] 
dist 226=[.15224904014967915531,4.7053341732421656661 ] 
dist 227=[.13465335188975279554,4.6629798661301560523 ] 
dist 228=[.10145316567215747974,4.6428545717482071390 ] 
dist 229=[.03821730974345962034,4.1793322746972531074 ] 
dist 230=[-.03288732577276434827,4.1049916975822712769 ] 
dist 231=[-.09750459414902799259,3.9398589962700731603 ] 
dist 232=[-.16983395015697517354,3.8874897606910766008 ] 
dist 233=[-.27173005985286723684,3.6483852971534027405 ] 
dist 234=[-.38500589971014994952,3.5965900864423959848 ] 
dist 235=[-.50277023725847469685,3.4633524640906801838 ] 
dist 236=[-.64654260091533562264,3.4283394416017541316 ] 
dist 237=[-1.1491850166568587582 ,3.2638467908077094998 ] 
dist 238=[-1.7464765345459448112 ,3.3551408984076998371 ] 
dist 239=[-2.2332251921844525799 ,3.4151691004851721427 ] 
dist 240=[-2.6972716548861267763 ,3.4483398535036345128 ] 
dist 241=[-3.1119289589211577950 ,3.4656997262703549134 ] 
dist 242=[-3.4014847631992221337 ,3.4646088732622704366 ] 
dist 243=[-3.6552321796260869744 ,3.4507075110755270265 ] 
dist 244=[-3.9269195731305304162 ,3.4379748380399931846 ] 
dist 245=[-4.1737582199326327461 ,3.1977744946168241044 ] 
dist 246=[-4.3282936704799822731 ,3.1550641853016645923 ] 
dist 247=[-4.4450050258178428258 ,3.0580711910636000829 ] 
dist 248=[-4.5408259856025728435 ,3.0254775852720811768 ] 
dist 249=[-4.6160250582308305393 ,2.8697743248438065587 ] 
dist 250=[-4.6504007532179789389 ,2.8345364685433233810 ] 
dist 251=[-4.6614932049551481654 ,2.7458094392406990355 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 0, 1, 2] 
dist 0=[47.781564195062785799  ,47.781564195062785799  ] 
dist 1=[47.694342526878180138  ,47.791048529632581769  ] 
dist 2=[47.418691294501179728  ,47.781564195062785799  ] 
dist 3=[46.922293203851353607  ,47.708721223920257566  ] 
dist 4=[45.953641925133875918  ,47.666050361676004634  ] 
dist 5=[44.855789188836434979  ,47.618435783373536974  ] 
dist 6=[43.843258969376217074  ,47.550676172977020728  ] 
dist 7=[42.696800603703316539  ,44.439301962823971139  ] 
dist 8=[41.063859529145970179  ,43.970987407797477180  ] 
dist 9=[39.237552686592282128  ,43.212351361018246286  ] 
dist 10=[37.318653022233663089  ,42.996764751794425488  ] 
dist 11=[34.958686763504676477  ,42.493252330256427434  ] 
dist 12=[31.370523142398463116  ,42.372235080643970488  ] 
dist 13=[27.752774535141340936  ,42.254810921252272997  ] 
dist 14=[25.274549985345103635  ,41.646974571217128729  ] 
dist 15=[23.149044956521119625  ,32.879057262524551113  ] 
dist 16=[20.940007884075005609  ,32.192439173410334459  ] 
dist 17=[18.837611504529655806  ,30.784183466487490100  ] 
dist 18=[17.137882940120347892  ,30.399535523518289164  ] 
dist 19=[15.401430611672876103  ,28.906398869656553934  ] 
dist 20=[13.151972839999063865  ,28.592669677320091393  ] 
dist 21=[10.952875386594672853  ,27.903955569602529264  ] 
dist 22=[9.4173895796478118370 ,27.695701784843865475  ] 
dist 23=[8.0089130791015537343 ,15.760422512863335568  ] 
dist 24=[5.1688117587555913880 ,14.693244124113581286  ] 
dist 25=[2.8189451376301831605 ,12.243035935686391636  ] 
dist 26=[.5123235209863183368 ,11.833693091923214154  ] 
dist 27=[-1.6000010603318887562 ,9.0342901755881061331 ] 
dist 28=[-3.1738699581072456344 ,8.9591980219715825375 ] 
dist 29=[-4.6610267093945564322 ,8.4734051000322170898 ] 
dist 30=[-6.4273130545264046725 ,8.2302006409350702500 ] 
dist 31=[-8.0800429920944427119 ,3.6738168466034568849 ] 
dist 32=[-9.1137419697625989923 ,3.2433381295541722415 ] 
dist 33=[-9.8973179141475849168 ,2.2985968781439725353 ] 
dist 34=[-10.551022773349956581  ,2.1299699242218642766 ] 
dist 35=[-11.077395012290303960  ,1.0672334701948141298 ] 
dist 36=[-11.352623696363509980  ,.88722712363715634513] 
dist 37=[-11.502114717075027717  ,.55561786767320065967] 
dist 38=[-11.535354779251197833  ,.48453843208625299495] 
dist 39=[-11.490208410917094746  ,-2.1071874841343270588 ] 
dist 40=[-11.453455197411218915  ,-1.7428912743579038684 ] 
dist 41=[-11.368010791793980236  ,-1.3046356741258224757 ] 
dist 42=[-11.327069148374115786  ,-.6534182288005929851 ] 
dist 43=[-11.090552041272682635  ,.0831373935555666167 ] 
dist 44=[-11.031239995100744696  ,.8623065803946478757 ] 
dist 45=[-10.826681252627964772  ,1.8213377461664270537 ] 
dist 46=[-10.791589462950874527  ,3.2760454952236680712 ] 
dist 47=[-10.193171608138655792  ,4.7299012828405989141 ] 
dist 48=[-10.083859039534225826  ,5.6856561853650955099 ] 
dist 49=[-9.8080406661849269378 ,6.4596498714167968606 ] 
dist 50=[-9.7352177293357083833 ,7.1881450107383325686 ] 
dist 51=[-8.9576818296340304708 ,7.8319977775033478660 ] 
dist 52=[-8.8033837494618231721 ,8.2682244959860980455 ] 
dist 53=[-8.2286094007984958130 ,8.6362919302987404397 ] 
dist 54=[-7.2822380793442129781 ,9.0082009722043002358 ] 
dist 55=[-3.0030392550687277987 ,9.3286723117408177292 ] 
dist 56=[-2.9214620334187711533 ,9.4913726702754846552 ] 
dist 57=[-2.5684510029664438977 ,9.5716308223905268085 ] 
dist 58=[-2.5023721615105516759 ,9.5841606444377630710 ] 
dist 59=[-2.3373424544458845599 ,9.5048761257727062889 ] 
dist 60=[-2.3116494638048417191 ,9.4572583495356217870 ] 
dist 61=[-.5029092577381192086 ,9.3864497436110395371 ] 
dist 62=[-.3341439156009261395 ,9.3483390392754383505 ] 
dist 63=[.0518002404563741277 ,7.0315566379533817066 ] 
dist 64=[.1142334853716838259 ,6.7779747324965952018 ] 
dist 65=[.5959699177225287683 ,6.1444584124466018038 ] 
dist 66=[.6789765802430832136 ,6.0418008956457177004 ] 
dist 67=[.8091013559937145252 ,5.0473052037856435035 ] 
dist 68=[.8396763664551730781 ,4.8556028229288899540 ] 
dist 69=[1.2946940517745708327 ,4.6149615616756886825 ] 
dist 70=[1.3524078856113828819 ,4.5401489741766498170 ] 
dist 71=[1.4558372034027012998 ,3.3661466350359978603 ] 
dist 72=[1.4761598308813036416 ,3.3004610051240943451 ] 
dist 73=[1.2780320412338353263 ,3.0364316892566288743 ] 
dist 74=[.6956254193463417306 ,2.9804346354951449621 ] 
dist 75=[.1083756501226496213 ,2.8478956890177484925 ] 
dist 76=[-.4184738818910278631 ,2.8100667125949664437 ] 
dist 77=[-1.0906355643733594679 ,2.3367338121683049870 ] 
dist 78=[-1.8213197115371250992 ,2.3672706153507934027 ] 
dist 79=[-2.6259955682753551921 ,2.3868889349070881487 ] 
dist 80=[-3.1566888701343951731 ,2.3967089977733584655 ] 
dist 81=[-3.5896284527291254842 ,2.3994004187073846951 ] 
dist 82=[-4.0039062432622945836 ,2.3966158499623392318 ] 
dist 83=[-4.3757869625862961674 ,2.3788215211116869970 ] 
dist 84=[-4.6394113980258666537 ,2.3700738871378877693 ] 
dist 85=[-4.8749624125681598336 ,2.2892940719956404358 ] 
dist 86=[-5.1347439844854084380 ,2.2717828376278963479 ] 
dist 87=[-5.3668843942966292759 ,2.2147048718157762974 ] 
dist 88=[-5.4920453378226054673 ,2.2049140339249170332 ] 
dist 89=[-5.5632280858231716389 ,2.0632300912979421127 ] 
dist 90=[-5.5797798293046277311 ,2.0308769813518987621 ] 
dist 91=[-5.5761613313638194120 ,2.0021344188734583987 ] 
dist 92=[-5.5667841279173196083 ,1.9918627332984187275 ] 
dist 93=[-5.5514788451849661486 ,.87092604161983634523] 
dist 94=[-5.5331900724183003420 ,1.1913604657864804773 ] 
dist 95=[-1.6586829495500320874 ,1.9490838923977879068 ] 
dist 96=[-1.9248280608744180815 ,2.4596948350959372961 ] 
dist 97=[-2.1633297420848110102 ,2.8815093295543206134 ] 
dist 98=[-2.3312297191340647825 ,3.2928572319136923440 ] 
dist 99=[-2.4798473711762085552 ,3.6663927457540929568 ] 
dist 100=[-2.6413554400283615632 ,3.9372766970913344948 ] 
dist 101=[-2.7870565165478135007 ,4.1851123938026899890 ] 
dist 102=[-2.8725574762693783934 ,4.4666660629545268518 ] 
dist 103=[-2.9304753809446800986 ,4.7219734337559543974 ] 
dist 104=[-2.9660384457679128531 ,4.8650444297933441546 ] 
dist 105=[-2.9873080225614296832 ,4.9535254622215514342 ] 
dist 106=[-2.9890104694436470402 ,4.9909143628794475877 ] 
dist 107=[-2.9806434517853115108 ,5.0048211901583436705 ] 
dist 108=[-2.9702718727687870944 ,4.9995383841664623713 ] 
dist 109=[-2.3021496991310892110 ,4.9792204727512783931 ] 
dist 110=[-2.4831772438425589827 ,5.0507690666227790579 ] 
dist 111=[-2.8894607853594280105 ,5.1376531489474214456 ] 
dist 112=[-3.2927958830693065641 ,5.1632344172473340791 ] 
dist 113=[-3.6637674077269519379 ,5.1665322174939388273 ] 
dist 114=[-3.9408468815486084569 ,5.1643204403818982043 ] 
dist 115=[-4.2024373458388084617 ,4.9985021050591288150 ] 
dist 116=[-4.5115674065799683306 ,4.9525548797488615572 ] 
dist 117=[-4.7980373466137066978 ,4.9223709204377858904 ] 
dist 118=[-4.9691619304091640954 ,4.9059078838279730701 ] 
dist 119=[-5.0886668270879346533 ,4.0166955849638738142 ] 
dist 120=[-5.1690605308008656872 ,3.8936371961706821165 ] 
dist 121=[-5.2198996157759316957 ,3.6608328079859914728 ] 
dist 122=[-5.2286541414929297626 ,3.5997494941655484161 ] 
dist 123=[-5.2077343467443006207 ,3.3855239789781913064 ] 
dist 124=[-5.1977845898998232464 ,3.3295460984257622304 ] 
dist 125=[-4.9178766196536321251 ,3.2588098347919648559 ] 
dist 126=[-4.7928097866699958066 ,3.2305775232726882574 ] 
dist 127=[.23324025111475610638,3.2419124975022181034 ] 
dist 128=[-.26210294056558167372,3.3686410213140991771 ] 
dist 129=[-.67556065052806768026,3.4724015600269501485 ] 
dist 130=[-1.0860779066975756451 ,3.5284033153012558936 ] 
dist 131=[-1.4639042386097049959 ,3.5602242983759788872 ] 
dist 132=[-1.7468485461785688226 ,3.5674363240716797779 ] 
dist 133=[-2.0148551356230978929 ,3.5617318619710597365 ] 
dist 134=[-2.3330526493097448116 ,3.5532803163246136058 ] 
dist 135=[-2.6295265389586928688 ,3.5190787893889102079 ] 
dist 136=[-2.8108010157598904168 ,3.5007962588180626993 ] 
dist 137=[-2.9426530488258360052 ,3.3808174246449582352 ] 
dist 138=[-3.0417962322993499850 ,3.3481481836356283392 ] 
dist 139=[-3.1178358482554111491 ,3.2912545279956231587 ] 
dist 140=[-3.1574454290545054053 ,3.2728905474992038518 ] 
dist 141=[-3.1780245691786582494 ,2.6839137166227871336 ] 
dist 142=[-3.1781658211368719858 ,2.6313655214293634738 ] 
dist 143=[-2.8969360279644482667 ,2.4894094830701915308 ] 
dist 144=[-2.8575090886685356825 ,2.4664722954495867639 ] 
dist 145=[-2.7672557486096248430 ,2.2018432145729046961 ] 
dist 146=[-2.7368936614964341922 ,2.1468693917429357474 ] 
dist 147=[-2.5918007062701069683 ,2.0887752634103054455 ] 
dist 148=[-2.8492577509327986114 ,2.0706940007161996998 ] 
dist 149=[-3.1196690147600084880 ,1.4545256389361232848 ] 
dist 150=[-3.2822370566396865070 ,1.3738624999476579476 ] 
dist 151=[-3.3971617570882827601 ,1.2118529154806255097 ] 
dist 152=[-3.4773461034884007208 ,1.1692339911309186116 ] 
dist 153=[-3.5360053353688499123 ,1.0138584241509563249 ] 
dist 154=[-3.5649855653229476805 ,1.2979031791849126678 ] 
dist 155=[-3.5778126015048400498 ,1.6403182503686369435 ] 
dist 156=[-3.5748117163657522519 ,1.9599559419353671612 ] 
dist 157=[-1.6682097499664364209 ,2.3245467676454316769 ] 
dist 158=[-1.6481128634741258473 ,2.8464462456973031899 ] 
dist 159=[-.85168554179972847698,3.3606984485132660037 ] 
dist 160=[-1.0676319235740013041 ,3.6947591845417519478 ] 
dist 161=[-1.2758538316562428939 ,3.9612195646858822623 ] 
dist 162=[-1.4478163791438517120 ,4.2055732491817165989 ] 
dist 163=[-1.6263899548418724337 ,4.4173887178415285213 ] 
dist 164=[-1.8610064413618992979 ,4.5539391968280673566 ] 
dist 165=[-2.0908897670681287734 ,4.6616883866167701440 ] 
dist 166=[-2.2505648832686794685 ,4.7585156507185765962 ] 
dist 167=[-2.3896001602344204355 ,4.8340249435079579555 ] 
dist 168=[-2.5370749796151693266 ,4.8566601539852543737 ] 
dist 169=[-2.6789219809759291338 ,4.8591681140822645778 ] 
dist 170=[-2.7954865384154834184 ,4.8543133771051511664 ] 
dist 171=[-2.9160099510738220886 ,4.7137769626121549547 ] 
dist 172=[-3.0736617188510340230 ,4.6715661257995508029 ] 
dist 173=[-3.2217776968411701697 ,4.6397164705945896772 ] 
dist 174=[-3.3042278712424620669 ,4.6156474437092141756 ] 
dist 175=[-3.3544609124444012998 ,4.0136485345575821164 ] 
dist 176=[-3.3739462131588893654 ,3.9479873962329761967 ] 
dist 177=[-3.3798582052115703794 ,3.7672844152443342181 ] 
dist 178=[-3.3758986225558695090 ,3.7356597404595470984 ] 
dist 179=[-3.3639385552113390503 ,3.3846001115065182372 ] 
dist 180=[-3.3548112323768333369 ,3.3100158679254302522 ] 
dist 181=[-3.5614968189875671451 ,3.2273777540387202969 ] 
dist 182=[-3.9775063605752570310 ,3.1959736329843408718 ] 
dist 183=[-4.3658771843634201925 ,3.2808814265054509278 ] 
dist 184=[-4.6034496549398991740 ,3.4012707200910663709 ] 
dist 185=[-4.7763308560750262664 ,3.5085544293946631151 ] 
dist 186=[-4.9064191316409859902 ,3.5829726562511004768 ] 
dist 187=[-5.0033000409607618703 ,3.6476691636989566845 ] 
dist 188=[-5.0435999244279778412 ,3.7161373658291468184 ] 
dist 189=[-5.0566163481239255093 ,3.7736084120781393035 ] 
dist 190=[-5.0504018916827599023 ,3.7943968821834788148 ] 
dist 191=[-.45884579079666857574,3.7978828766132494019 ] 
dist 192=[-.7063636131635779828 ,3.7906902073254454012 ] 
dist 193=[-.99936425294059348861,3.7166066627944986103 ] 
dist 194=[-1.3082853303343767915 ,3.6915250897080220761 ] 
dist 195=[-1.6042947886901466557 ,3.6472360653749810208 ] 
dist 196=[-1.8457448592757762606 ,3.6310088415166094081 ] 
dist 197=[-2.0938026218643892050 ,3.1804504333298878389 ] 
dist 198=[-2.4161956660409147357 ,3.1119511379785171271 ] 
dist 199=[-2.7304543299022098170 ,2.9639442638942198380 ] 
dist 200=[-2.9460350848202279959 ,2.9190137644966704346 ] 
dist 201=[-3.1309071256205642969 ,2.7214125612523037630 ] 
dist 202=[-3.3225574136966588617 ,2.6802562418641168749 ] 
dist 203=[-3.5042155792451819124 ,2.5665572430574282163 ] 
dist 204=[-3.6491936352810817824 ,2.5457398096592572757 ] 
dist 205=[-3.7952760105078154139 ,2.4392350431311460909 ] 
dist 206=[-3.9813457219157878897 ,2.5352157639211977148 ] 
dist 207=[-4.1539436589302078815 ,2.6041292416751691055 ] 
dist 208=[-4.2462380823108972303 ,2.6542468326135439276 ] 
dist 209=[-4.2975078625714899448 ,2.6889648826171206357 ] 
dist 210=[-4.3089494564614937762 ,2.6969565393080773036 ] 
dist 211=[-4.2999589921818019908 ,2.6945918453078130741 ] 
dist 212=[-4.2907520516821620372 ,2.6924552582675333622 ] 
dist 213=[-4.2776784439060163996 ,2.8871873950196874047 ] 
dist 214=[-4.2628231936332792554 ,3.2205806765128525695 ] 
dist 215=[-3.7455242094573569387 ,3.5433049254641695043 ] 
dist 216=[-3.6672918654109157499 ,3.7608688284737430343 ] 
dist 217=[-3.6469943616588065198 ,3.9433445077779643828 ] 
dist 218=[-3.6619058034268953372 ,4.1259752514126412171 ] 
dist 219=[-3.6621446837784117338 ,4.2950128811761688697 ] 
dist 220=[-3.6538018169757374599 ,4.4232167072713416639 ] 
dist 221=[-3.1967936537666134011 ,4.5462316829055641412 ] 
dist 222=[-3.1713358338834313504 ,4.6945526139907288056 ] 
dist 223=[-.86728714096745695226,4.8291481774758995380 ] 
dist 224=[-.66716775072868858876,4.8973629965024402551 ] 
dist 225=[-.21722886751132026538,4.9300963847767418583 ] 
dist 226=[-.13326565864978423069,4.9343943252644817615 ] 
dist 227=[.10473769994025935779,4.9004396237791169861 ] 
dist 228=[.03879085283465369375,4.8805076002527541068 ] 
dist 229=[-.03529318676366867413,4.8365060501555912434 ] 
dist 230=[-.10251821685890631961,4.8156207443566198955 ] 
dist 231=[-.17768617459801676113,4.3344290613735051108 ] 
dist 232=[-.28348335586034024516,4.2572700963093461333 ] 
dist 233=[-.40105140174596130395,4.0858812368438212186 ] 
dist 234=[-.5232160089247364184 ,4.0315341905924479658 ] 
dist 235=[-.67231687690885383349,3.7834230345484912023 ] 
dist 236=[-.89743130228769927271,3.7296820045413736673 ] 
dist 237=[-1.1227749242876891810 ,3.5914406907935114386 ] 
dist 238=[-1.2727908704043877961 ,3.5551231666268725513 ] 
dist 239=[-1.3965496164938840388 ,3.3859110458672253257 ] 
dist 240=[-1.8128316368337585407 ,3.4809539852735061444 ] 
dist 241=[-2.3177564782635657639 ,3.5435149810342962138 ] 
dist 242=[-2.7991359103141379511 ,3.5782262613776169970 ] 
dist 243=[-3.2292841313024085871 ,3.5964922588645969228 ] 
dist 244=[-3.5296615022390287400 ,3.5954638339392695534 ] 
dist 245=[-3.7928964733097663882 ,3.5811385239992785105 ] 
dist 246=[-4.0747485686702916545 ,3.5679232385805332292 ] 
dist 247=[-4.3308183152219072808 ,3.3196206046502071017 ] 
dist 248=[-4.4911138021677813666 ,3.2754111538634636445 ] 
dist 249=[-4.6121527996865915484 ,3.1749493020087325594 ] 
dist 250=[-4.7114858662204022535 ,3.1411620999544403921 ] 
dist 251=[-4.7894090254243513629 ,2.9796579596704553352 ] 
dist 252=[-4.8249661007718259063 ,2.9430866100307027847 ] 
dist 253=[-4.8363373179969290973 ,2.8511231434666682506 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 0, 2, 0, 2] 
dist 0=[41.884715586996907055  ,41.884715586996907055  ] 
dist 1=[41.161057254138527790  ,42.402568793838531690  ] 
dist 2=[40.145769996908734130  ,42.798799460628561114  ] 
dist 3=[38.463083440780569291  ,43.036612587663853570  ] 
dist 4=[36.718460744057593287  ,43.204408010502242609  ] 
dist 5=[35.455737116306499166  ,43.320801496654902344  ] 
dist 6=[34.300373090177612810  ,43.383274910034016126  ] 
dist 7=[32.984421738076041272  ,43.372926878171179018  ] 
dist 8=[31.660524074679202038  ,43.196949160159161038  ] 
dist 9=[30.473264287685752936  ,42.573813739064981758  ] 
dist 10=[29.154254105953742292  ,42.402733067758487040  ] 
dist 11=[27.303793971473500334  ,42.152665197635616614  ] 
dist 12=[25.427745738828587287  ,42.052574518780507121  ] 
dist 13=[24.006369884378032475  ,41.733352279663644776  ] 
dist 14=[22.639913927354537419  ,41.613342994741027395  ] 
dist 15=[20.983067323529121140  ,41.384301005199153010  ] 
dist 16=[19.257076656980463061  ,40.818088031932851081  ] 
dist 17=[17.614120054106170999  ,30.851249541007675697  ] 
dist 18=[15.709189257663522867  ,29.936731183557382467  ] 
dist 19=[12.936005928872060814  ,27.705697326940694622  ] 
dist 20=[10.177544429450595496  ,27.379580713840627216  ] 
dist 21=[8.3313803882498176422 ,24.052380290676863321  ] 
dist 22=[6.7907539970847229841 ,23.425966273346082356  ] 
dist 23=[5.2533811919358092842 ,22.717080482536155790  ] 
dist 24=[3.8263272194869668966 ,22.574542475618237926  ] 
dist 25=[2.7265582104217785905 ,17.535436993053405024  ] 
dist 26=[1.6501206570312571363 ,16.228789324153183230  ] 
dist 27=[.3162123068393870304 ,14.815069011366098063  ] 
dist 28=[-.9624160852591579329 ,14.454486350107969423  ] 
dist 29=[-1.8179884930203982384 ,13.189320113501707912  ] 
dist 30=[-4.2683910547646431285 ,12.919084187053663886  ] 
dist 31=[-5.9840050044321512763 ,12.552326436480185670  ] 
dist 32=[-7.3329322131486469044 ,12.440478017790605168  ] 
dist 33=[-8.5453528665315691126 ,2.9243762808677947695 ] 
dist 34=[-9.5864235613836257374 ,2.1393644777440365833 ] 
dist 35=[-10.250682852684723668  ,1.2296149123502238246 ] 
dist 36=[-10.771234460340349524  ,1.7183461256745603528 ] 
dist 37=[-11.238367262959440434  ,2.0709972174843089553 ] 
dist 38=[-11.629925115346863215  ,2.3889010463257488853 ] 
dist 39=[-11.848434027703891118  ,2.7394802175900516096 ] 
dist 40=[-11.985209897815000332  ,3.0817625601739979011 ] 
dist 41=[-12.049707048485266331  ,3.3667520922914823941 ] 
dist 42=[-12.065214941673188619  ,3.6629613159011194874 ] 
dist 43=[-12.049014490430207864  ,4.0500936066969122301 ] 
dist 44=[-11.931512571304900339  ,4.4249308683691247928 ] 
dist 45=[-11.885365182830788911  ,4.6721439560428793248 ] 
dist 46=[-8.8988972499721724919 ,4.8721707773376198168 ] 
dist 47=[-8.9601854683879978719 ,5.0588367909707097993 ] 
dist 48=[-8.9656252120786234654 ,5.2214724464239636699 ] 
dist 49=[-6.0861149011947199550 ,5.3256222879103493650 ] 
dist 50=[-5.9559179730710889146 ,5.4060878279977290142 ] 
dist 51=[-5.9088958432616995828 ,5.4741370421102518655 ] 
dist 52=[-3.8952985103168518789 ,5.5261767649085378665 ] 
dist 53=[-3.3746632112216523182 ,5.5427726067366470070 ] 
dist 54=[-3.0555371827070046099 ,5.5358643161881251376 ] 
dist 55=[-2.8847661555849045916 ,5.5200085141823505865 ] 
dist 56=[-2.8446707643484646061 ,5.4327756546905149491 ] 
dist 57=[-2.1565521921276695205 ,5.4017787843822983264 ] 
dist 58=[-2.0656580925493609189 ,5.2699239299866168361 ] 
dist 59=[-1.8561213964491360227 ,5.2451319839013941465 ] 
dist 60=[-1.8199149346171188868 ,4.8091980502876338388 ] 
dist 61=[-1.5466997533789655518 ,4.6257596685528941231 ] 
dist 62=[-1.4969651248521894760 ,3.1818391388095942509 ] 
dist 63=[-1.4199519555476780215 ,3.5262865086861114956 ] 
dist 64=[-1.4001630593913580259 ,3.7918082484894895172 ] 
dist 65=[-1.0468986928806948142 ,4.0204413986848750754 ] 
dist 66=[-.99960970333463017582,4.2089534785922095366 ] 
dist 67=[-.89368574000755259024,4.3142204341177172876 ] 
dist 68=[-.86889999418671204243,4.3791961220933136732 ] 
dist 69=[-.72813329914831276437,4.4067992613416175765 ] 
dist 70=[-.6996949331025683062 ,4.4177133792367105262 ] 
dist 71=[-.64553121538583293512,4.4160239334165168318 ] 
dist 72=[-.63063418145955045269,4.4050129729472406487 ] 
dist 73=[-.3940765265732090790 ,4.3936911942627357008 ] 
dist 74=[-.3590892232611556450 ,4.3446113265998347055 ] 
dist 75=[-.2768676244197882140 ,4.3260122731321846453 ] 
dist 76=[-.2567961636417610909 ,4.2640621758812586982 ] 
dist 77=[-.1338964683848781195 ,4.2415521746098115107 ] 
dist 78=[-.1084200836976303182 ,2.7768962920287676912 ] 
dist 79=[-.0608607654447338150 ,2.7632277529166710357 ] 
dist 80=[-.27062945240116679527,2.7529625879727873025 ] 
dist 81=[-.58048393548979452158,2.5414344734674458115 ] 
dist 82=[-.94771814372236279976,2.4965400389479836173 ] 
dist 83=[-1.4898720381378805196 ,2.4813081255454416507 ] 
dist 84=[-2.0292902008994348672 ,1.3773133180006288911 ] 
dist 85=[-2.3856136195314060696 ,1.1251535701682178369 ] 
dist 86=[-2.6765105006805589473 ,1.0784350992811763635 ] 
dist 87=[-2.9547174124044659354 ,.9810966111615208959 ] 
dist 88=[-3.2039395845653185779 ,.9547130057339769645 ] 
dist 89=[-3.3791211010706569132 ,.7047607094604218306 ] 
dist 90=[-3.5338912254165230045 ,.6654423223871054109 ] 
dist 91=[-3.7016353283317875809 ,.5930849690786712249 ] 
dist 92=[-3.8495612106185961711 ,.5761121645871274309 ] 
dist 93=[-3.9252116194545563293 ,.5275995931582360626 ] 
dist 94=[-3.9649859431301899938 ,.5189911511886720417 ] 
dist 95=[-3.9714803606465260131 ,.52205647456382999878] 
dist 96=[-3.9397477311433479125 ,.54171408731205262418] 
dist 97=[-3.9250771958243770545 ,.56689768196687528862] 
dist 98=[-3.9100033666704266753 ,.5920246302160469768 ] 
dist 99=[-3.8936400044968208960 ,.62184455575364772295] 
dist 100=[-3.5550179122166030125 ,.66578367244676177625] 
dist 101=[-3.5089222139273265754 ,1.0216252429158835662 ] 
dist 102=[-3.3774489917421178339 ,1.4417125962760297833 ] 
dist 103=[-3.3526046375483550045 ,1.8638583781004520657 ] 
dist 104=[-3.0799438735244551657 ,2.2554703632428950680 ] 
dist 105=[-3.0204278532539200767 ,2.5536618668132689358 ] 
dist 106=[-2.9528869526536778526 ,2.8408022781815245243 ] 
dist 107=[-2.9234735623635500829 ,3.1882964488682573628 ] 
dist 108=[-2.4285146380859994054 ,3.5146523171148460358 ] 
dist 109=[-2.3567667907096464685 ,3.7174041245780444517 ] 
dist 110=[-1.9278915922992338223 ,3.8686138820250624806 ] 
dist 111=[-1.8748771346238283834 ,3.9892025021262349200 ] 
dist 112=[-1.6720129764905132162 ,4.0809873284693803559 ] 
dist 113=[-1.6287558628532198199 ,4.1172050738921728524 ] 
dist 114=[-1.5402226603271016775 ,4.1304831489506593595 ] 
dist 115=[-1.5150604969328616643 ,4.1306909162526863243 ] 
dist 116=[.00986351195405424853,2.2512765957611530758 ] 
dist 117=[.11628750049823591444,2.3173752893507915029 ] 
dist 118=[.35824932930579746638,2.3570766745277291337 ] 
dist 119=[.39704384206732687673,2.3850795992177700673 ] 
dist 120=[.66445163522926701796,2.4044717401550277299 ] 
dist 121=[.68155304021944769893,2.4153324467229288946 ] 
dist 122=[.70853340894202090801,2.4153860094009960367 ] 
dist 123=[.69504447409728771721,2.3989972164751377160 ] 
dist 124=[.6590389153208741554 ,2.3863844203412428254 ] 
dist 125=[.58289894412635715152,2.2909566681246880644 ] 
dist 126=[.50101286000622657155,2.4189953969039613914 ] 
dist 127=[.44206237417656547141,2.5653693194188757219 ] 
dist 128=[.38858752896391422044,2.7016167183133176080 ] 
dist 129=[.32855175740355231146,2.8063063063203117628 ] 
dist 130=[.2688254458983218584 ,2.9081023473500929169 ] 
dist 131=[-.08446435890991857914,3.0328035167925933274 ] 
dist 132=[-.47267902824990823603,3.1462592699604047811 ] 
dist 133=[-.74235053644696126261,3.2031563372727436352 ] 
dist 134=[-.97714577978712665157,3.2331463161720051997 ] 
dist 135=[-1.2261192407319426056 ,3.2391582816554688075 ] 
dist 136=[-1.4655116054925789758 ,3.2041926723910591680 ] 
dist 137=[-1.6620557447929073497 ,3.1933731794046396319 ] 
dist 138=[-1.8650987079017951769 ,3.1852910985208350948 ] 
dist 139=[-2.1304395832387029409 ,3.1788298563203825994 ] 
dist 140=[-2.3897146111870498035 ,2.7091900447352951602 ] 
dist 141=[-2.5685405246215800712 ,2.6420856990042341456 ] 
dist 142=[-2.7229014202495713585 ,2.5197853312231664327 ] 
dist 143=[-2.8845004277525940221 ,2.4878016477657450183 ] 
dist 144=[-3.0386309757181336315 ,2.3784092893764780020 ] 
dist 145=[-3.1631750704037738038 ,2.3468496138515816383 ] 
dist 146=[-3.2900635580616326751 ,2.3125969879685762267 ] 
dist 147=[-3.4535565807106505240 ,2.2955119586799224531 ] 
dist 148=[-3.6070513635293474110 ,.36574373824160236188] 
dist 149=[-3.6940215216405805157 ,.20533280029846199129] 
dist 150=[-3.7490251610180280629 ,.20958079285178850592] 
dist 151=[-3.7748900838286313657 ,.23038524230011439808] 
dist 152=[-3.7846616117458821685 ,.25126870936606721376] 
dist 153=[-3.7801817603549824142 ,.27772092633676458309] 
dist 154=[-3.7583447843731346753 ,.30574055558970272379] 
dist 155=[-3.7427264327334561400 ,.33288434295936014756] 
dist 156=[-3.4636490093136066378 ,.3646047567325442984 ] 
dist 157=[-3.4148445949985483968 ,.4108980635997380889 ] 
dist 158=[-3.3020970832631508225 ,.4564420789687974205 ] 
dist 159=[-3.2642027020602171110 ,.4851724672596462221 ] 
dist 160=[-3.0831572639560011251 ,.5071139934767510547 ] 
dist 161=[-3.0421850013748114416 ,.5255564919892811683 ] 
dist 162=[-2.9448503176327741453 ,.5403603100921878818 ] 
dist 163=[-2.9113827020151753419 ,.5477762880751592583 ] 
dist 164=[-2.7538023604033916380 ,.89102160793909903296] 
dist 165=[-2.8010035926125640908 ,1.3782019158202903230 ] 
dist 166=[-2.8258234406487397789 ,1.7750252702898966981 ] 
dist 167=[-2.8299728607957729170 ,2.1529980004705556977 ] 
dist 168=[-2.8179812898234563469 ,2.4904942252601250728 ] 
dist 169=[-2.8076327118546734871 ,2.7257107435372941826 ] 
dist 170=[-2.7872711642463063727 ,2.9313484170100345431 ] 
dist 171=[-2.7771620097013826761 ,3.1507472904246899309 ] 
dist 172=[-2.4925440681536170934 ,3.3501336643837792725 ] 
dist 173=[-2.4473768758906016684 ,3.4758695425708995182 ] 
dist 174=[-2.3507150402751432713 ,3.5718866840823606640 ] 
dist 175=[-2.3208210460379846593 ,3.6526192202143084937 ] 
dist 176=[-2.1871936257318143027 ,3.7174630337429045605 ] 
dist 177=[-2.1588751029917299122 ,3.7500435543097458539 ] 
dist 178=[-2.0764339031855138102 ,3.7652671130978954565 ] 
dist 179=[-2.0627921348297822865 ,3.7622608817029227871 ] 
dist 180=[-.5023292850161402454 ,.58673353196584812962] 
dist 181=[-.5384435961103368469 ,.58550111223643941507] 
dist 182=[-.5711200645079773364 ,.53989061184527989351] 
dist 183=[-.5911232951789419136 ,.54577581553677971954] 
dist 184=[-.6056837028083476558 ,.6432504734916516776 ] 
dist 185=[-.6166338235009154184 ,.71198612682391843074] 
dist 186=[-.6244316130655145764 ,.77292623133910149459] 
dist 187=[-.6264087641347240915 ,.83927659405700035849] 
dist 188=[-.6259262427331400916 ,.89996879082872583485] 
dist 189=[-.6240003332589567776 ,.93831775718982227043] 
dist 190=[-.03428974992546323180,.9676950979366633217 ] 
dist 191=[-.10931253116705630823,.99256594761931151152] 
dist 192=[-.17676000945456554024,1.0126744143278174653 ] 
dist 193=[-.25162585992301761981,1.0230367058758913187 ] 
dist 194=[-.32565137928472726078,1.0282556373884252063 ] 
dist 195=[-.38974428176626575403,1.0278277074179570252 ] 
dist 196=[-.45892518398163988727,.70103304014362723818] 
dist 197=[-.55326602633317658642,.67222380153784198   ] 
dist 198=[-.64731484586701766338,.6081931009308909784 ] 
dist 199=[-.71533020371447312487,.5913492280959153    ] 
dist 200=[-.77739420674414949498,.51102509102318076081] 
dist 201=[-.84768181810483338398,.49540949005145274193] 
dist 202=[-.91799673203147356188,.45972408852199084759] 
dist 203=[-.98017031386179953563,.45035379261270937383] 
dist 204=[-1.0483789946648404642 ,.47049683047728511591] 
dist 205=[-1.1427911679265777351 ,.54604005731843461386] 
dist 206=[-1.2339206205082054441 ,.62092095576302678821] 
dist 207=[-1.2890226289108650955 ,.68063381082124020058] 
dist 208=[-1.3283622495503701711 ,.77167845507766683731] 
dist 209=[-1.3565570281560936639 ,.86369015366227301882] 
dist 210=[-1.3765929678537715267 ,.9494186860574005848 ] 
dist 211=[-1.3833565211833546342 ,1.0153774131809576999 ] 
dist 212=[-1.3841022575864296530 ,1.0795697934779294828 ] 
dist 213=[-1.3810516109375599835 ,1.1582460313867389304 ] 
dist 214=[-1.3089090313399946150 ,1.2326828925499908799 ] 
dist 215=[-1.2947682228835918600 ,1.2799492765677329047 ] 
dist 216=[-1.2646680352584883962 ,1.3164211967736282010 ] 
dist 217=[-1.2544164348261720648 ,1.3477604741287945846 ] 
dist 218=[-1.2595899468762796053 ,1.3734455548373874935 ] 
dist 219=[-1.2985301257426699944 ,1.3873426769174599606 ] 
dist 220=[-1.3312070520993773829 ,1.3952813037198560525 ] 
dist 221=[-1.3450145096702091725 ,1.3971765423064752790 ] 
dist 222=[-1.3508728076302170641 ,1.3949995399466855311 ] 
dist 223=[-1.3518111640279446314 ,1.3918542667836939261 ] 
dist 224=[-1.3211088896332684716 ,1.3773412385723052984 ] 
dist 225=[-1.3126711269293366561 ,1.3710999589397578221 ] 
dist 226=[-1.3071684786058961685 ,1.3180945185654233722 ] 
dist 227=[-1.3042232941225494231 ,1.3040705810656537726 ] 
dist 228=[-1.0622655679959220863 ,1.2840198220413732469 ] 
dist 229=[-1.0323017976118856779 ,1.2761281092573788043 ] 
dist 230=[-.95696884043544516833,1.0723295272696008417 ] 
dist 231=[-.94318256340575100924,1.0428133752710275751 ] 
dist 232=[-.82006206445211369602,.9804213567425772548 ] 
dist 233=[-.79532563907304529386,.9622748577510253736 ] 
dist 234=[-.76184551683297327572,.8859801857908644349 ] 
dist 235=[-.75063757462727224241,.87032373889727728211] 
dist 236=[-.51333219524427819078,.82808302260074957103] 
dist 237=[-.48185911738411842363,.82045963479474536392] 
dist 238=[-.41374039326569858161,.21805616033956766011] 
dist 239=[-.39584866042236433399,.26759328942272916777] 
dist 240=[-.32106264262723358265,.31906958867801022008] 
dist 241=[-.36814801215093982092,.37094127023898548734] 
dist 242=[-.41191821043005593646,.41918533114446331755] 
dist 243=[-.44543053047647056442,.4561773446413625152 ] 
dist 244=[-.4778898829650261806 ,.49206442495135299944] 
dist 245=[-.51745574880464790832,.53589658451420664229] 
dist 246=[-.55478139418145292096,.5773023564155510309 ] 
dist 247=[-.57829632604960205424,.60350141186680800233] 
dist 248=[-.59622574925764115342,.62361373954362062145] 
dist 249=[-.6112506018648453452 ,.64071671265863368954] 
dist 250=[-.62327787447157597979,.65460248993282097006] 
dist 251=[-.62923897097224843051,.66186926948190211655] 
dist 252=[-.63190264117477041319,.66568719720843132061] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 1, 0, 0, 2] 
dist 0=[51.572620446586037127  ,51.572620446586037127  ] 
dist 1=[51.474277834510126296  ,51.602602319044033178  ] 
dist 2=[51.111571824827496770  ,51.627040048257732471  ] 
dist 3=[50.451702087536404751  ,51.650859444470583148  ] 
dist 4=[49.212725368789559941  ,51.666483962560535367  ] 
dist 5=[47.824246153931832132  ,51.657994198311817654  ] 
dist 6=[46.567174135760280012  ,51.629725148335868917  ] 
dist 7=[45.162791804114689188  ,51.204497444333486053  ] 
dist 8=[43.185766041292944348  ,48.175524891999742156  ] 
dist 9=[40.985699650012428301  ,47.666318089416913880  ] 
dist 10=[38.690373358049442031  ,46.788756534013440728  ] 
dist 11=[35.879320618772982921  ,46.553876432680783602  ] 
dist 12=[31.619271228459020885  ,45.814477348143642340  ] 
dist 13=[27.332055921829181462  ,45.570704973230870365  ] 
dist 14=[24.412393078777338610  ,45.302143180522047052  ] 
dist 15=[21.927226615969114207  ,44.110928631005921541  ] 
dist 16=[19.375234097130891920  ,32.274934735663732708  ] 
dist 17=[16.966119731994367200  ,31.847487814206541491  ] 
dist 18=[15.051404887475142194  ,30.325044975828701193  ] 
dist 19=[13.125530417174643925  ,29.969156489525468867  ] 
dist 20=[10.671393622795460531  ,29.437738323037636228  ] 
dist 21=[8.2918600485466086914 ,29.274580620074075851  ] 
dist 22=[6.6637360419443969842 ,16.490697685217458934  ] 
dist 23=[5.2672739783904298154 ,16.191222211308183304  ] 
dist 24=[3.8128085241792884431 ,11.180682066128788414  ] 
dist 25=[2.1177101567698992859 ,10.558576381651346210  ] 
dist 26=[-.0751371765145496327 ,9.2188936765922719157 ] 
dist 27=[-1.6978367951161923656 ,8.9728052269178852188 ] 
dist 28=[-3.2213681994179552718 ,7.6137331905379452936 ] 
dist 29=[-5.0195818459382283078 ,7.3962998839720377190 ] 
dist 30=[-6.7015342957231453839 ,6.9993583579781757250 ] 
dist 31=[-7.7627322679796600697 ,6.8362662479533958945 ] 
dist 32=[-8.5766948080325496493 ,-3.5895915279350194017 ] 
dist 33=[-9.2705921348926199464 ,-3.7843503049351651572 ] 
dist 34=[-9.8369249474236608627 ,-4.8936545357788679004 ] 
dist 35=[-10.141026878153374895  ,-5.0664774694355073323 ] 
dist 36=[-10.311656418041345204  ,-5.3609320255060926733 ] 
dist 37=[-10.348217445050283542  ,-5.0959227404803217692 ] 
dist 38=[-9.3470061065921331418 ,-4.7889379872000445226 ] 
dist 39=[-9.2525790302757806412 ,-4.3946899120881443578 ] 
dist 40=[-9.3760955649442806770 ,-3.7807466962211567316 ] 
dist 41=[-9.4714476171438741961 ,-3.0741745440889596662 ] 
dist 42=[-9.5285423773757931317 ,-2.3099026890168028766 ] 
dist 43=[-9.5509240814776429780 ,-1.3574643737632822974 ] 
dist 44=[-9.5510257529242258197 ,.1004310569050839809 ] 
dist 45=[-9.5286120642172186769 ,1.5632380654270223713 ] 
dist 46=[-9.4687055697843549604 ,2.5354065260332951300 ] 
dist 47=[-9.4330051393009837699 ,3.3345615290953344352 ] 
dist 48=[-6.4169737770059428792 ,4.1069042756094419842 ] 
dist 49=[-6.1668449225046716484 ,4.8034217217883677812 ] 
dist 50=[-5.4487248944149866709 ,5.2999966918005780419 ] 
dist 51=[-5.3270400035854097680 ,5.7457097387017466118 ] 
dist 52=[-4.6192078652622551762 ,6.2393268609712485651 ] 
dist 53=[-4.5606034143639150702 ,6.6864859842540791835 ] 
dist 54=[-2.1959217662275825451 ,6.9467205822910373115 ] 
dist 55=[-2.1261056957542979776 ,7.1202086799053736432 ] 
dist 56=[-.3781893924272720169 ,7.2208842774913830274 ] 
dist 57=[-.1673941890384107470 ,7.2811589443931878207 ] 
dist 58=[.2933974788762880671 ,7.2934025400923757094 ] 
dist 59=[.3787563940751238044 ,7.2759603934117989200 ] 
dist 60=[.8766841831577610756 ,7.2578269597952868100 ] 
dist 61=[.9565713013971685267 ,5.7128638788536177263 ] 
dist 62=[1.1211913335797217441 ,5.5462726534858207487 ] 
dist 63=[1.1481423773896544978 ,5.5876595368576568229 ] 
dist 64=[1.9505788239346429709 ,5.7438334973659184611 ] 
dist 65=[1.8645203325611618557 ,5.8357612827925437294 ] 
dist 66=[1.7305555183952693585 ,5.8958813022643924828 ] 
dist 67=[1.5388505810530492860 ,5.9250064621938122509 ] 
dist 68=[1.2683411915082411518 ,5.9371969316893043636 ] 
dist 69=[.8197630867834495221 ,5.9296338425021554491 ] 
dist 70=[.35922163209020816964,5.4482912533961927992 ] 
dist 71=[.04091737703219455985,5.4338718379719448353 ] 
dist 72=[-.2341799734150430766 ,4.8792730031031869800 ] 
dist 73=[-.52232357265420076481,4.7931964285364788828 ] 
dist 74=[-.79699262838401636088,4.6257470388749589821 ] 
dist 75=[-1.0183516843107510264 ,4.5775140621670220220 ] 
dist 76=[-1.2432918686720343070 ,4.3840608098951226694 ] 
dist 77=[-1.5323276106474679951 ,4.3361507088514566621 ] 
dist 78=[-1.9505456361935362445 ,4.2291857631959777890 ] 
dist 79=[-2.3067600729144221390 ,4.1927570566065814000 ] 
dist 80=[-2.6545205631936005999 ,2.1387376428988416622 ] 
dist 81=[-2.9712571096565335440 ,1.9639281597908202211 ] 
dist 82=[-3.2035797002221324197 ,1.5489916287457399333 ] 
dist 83=[-3.4191625807568183354 ,1.4826916152908760679 ] 
dist 84=[-3.6690598970919390479 ,.9067367928340695868 ] 
dist 85=[-3.8989687970824414693 ,1.1082789842267630786 ] 
dist 86=[-4.0347261093038631764 ,1.5965908686027549709 ] 
dist 87=[-4.1278976205822651834 ,1.9207378298965611841 ] 
dist 88=[-4.1877242656064306977 ,2.1864322235817099528 ] 
dist 89=[-4.2257248256978570828 ,2.4414867696201081418 ] 
dist 90=[-4.2317294933237800218 ,2.6698705479301454849 ] 
dist 91=[-4.2240531629906081372 ,2.8291262360685617568 ] 
dist 92=[-4.2106525374677944067 ,2.9680418593186208089 ] 
dist 93=[-3.7554737075890129147 ,3.1152347796163565813 ] 
dist 94=[-3.7883313919451568930 ,3.2441659420919720260 ] 
dist 95=[-3.7963449724460726322 ,3.3102011836902984123 ] 
dist 96=[-3.1725741253945345198 ,3.3442136840898325903 ] 
dist 97=[-3.1356347832935302432 ,3.3496815665963664172 ] 
dist 98=[-2.9667238676426322881 ,3.3200565375284520086 ] 
dist 99=[-2.9302027013373442019 ,3.3039324155904156168 ] 
dist 100=[-2.8231244525689706471 ,3.2855455768832914537 ] 
dist 101=[-2.8042304306041785569 ,3.2705757683663935340 ] 
dist 102=[-.6046779963818045627 ,3.3632743660872104462 ] 
dist 103=[-.5938250232186513272 ,3.4819659439248419356 ] 
dist 104=[-.4012826130149060115 ,3.5776117687380880557 ] 
dist 105=[-.3756246695772006917 ,3.6514551106188976419 ] 
dist 106=[-.3157884085423529705 ,3.6831279197735110246 ] 
dist 107=[-.3055136441433209618 ,3.7404619772268243141 ] 
dist 108=[-.2258941943935646718 ,3.8250341109883587522 ] 
dist 109=[-.86185991790047806308,3.8942969745291895372 ] 
dist 110=[-1.3038952079815949364 ,3.9167598123001298500 ] 
dist 111=[-1.6761255540647811303 ,3.9211214091550948355 ] 
dist 112=[-2.0506056701826662038 ,3.9180181431312993729 ] 
dist 113=[-2.3980344334308081550 ,3.8041417034048567204 ] 
dist 114=[-2.6622849810914712621 ,3.7697595256395168610 ] 
dist 115=[-2.9163126217756492215 ,3.7447740558443095222 ] 
dist 116=[-3.2229328516051135874 ,3.7261479461413437749 ] 
dist 117=[-3.5102060716771927247 ,3.0930987767662509371 ] 
dist 118=[-3.6870056774289327276 ,3.0036168511006255857 ] 
dist 119=[-3.8167858758373380366 ,2.8308095753253789499 ] 
dist 120=[-3.9163718671546642152 ,2.7843265998767671249 ] 
dist 121=[-3.9889292232234387528 ,2.6136191326630282044 ] 
dist 122=[-4.0108169551297890649 ,2.5712587612752446269 ] 
dist 123=[-4.0145245082725708270 ,2.4992129974660021824 ] 
dist 124=[-4.0145221156047616983 ,2.4785892339326178114 ] 
dist 125=[-.3578182775172944877 ,1.0551336826995140967 ] 
dist 126=[-.4202523130853576662 ,1.0388037815425532647 ] 
dist 127=[-.5137893437762835617 ,1.0356217419292578106 ] 
dist 128=[-.72833996973537125083,.2497830633170612223 ] 
dist 129=[-1.0623759102275523560 ,.1949256714478425581 ] 
dist 130=[-1.3363312435718546779 ,.0734362944856797627 ] 
dist 131=[-1.6191099401252574240 ,.0495914783050353891 ] 
dist 132=[-1.9883845250864184208 ,-.0900062650304585719 ] 
dist 133=[-2.3491834587064417200 ,-.1137335503456114920 ] 
dist 134=[-2.5981278371595659840 ,-.1619587193216862683 ] 
dist 135=[-2.8131627955731824314 ,-.1734841556884407480 ] 
dist 136=[-3.0385810277348825736 ,-.2547881491062289269 ] 
dist 137=[-3.2538441208791900148 ,-.2683805384970954087 ] 
dist 138=[-3.4283414395695651281 ,-.2723185528460679887 ] 
dist 139=[-3.6066966810384867113 ,-.16541626811860751388] 
dist 140=[-3.8373799311170929433 ,.2696120805796959472 ] 
dist 141=[-4.0532886780046059162 ,.7141347196601991648 ] 
dist 142=[-4.1726559642424718670 ,1.0244809070863270143 ] 
dist 143=[-4.2443912895304789483 ,1.2962887648041908673 ] 
dist 144=[-4.2701098241072982804 ,1.5869569079420444146 ] 
dist 145=[-4.2786500892794046574 ,1.8678710532770309682 ] 
dist 146=[-4.2817891093866228306 ,2.1007399570970148710 ] 
dist 147=[-4.2816083525967093049 ,2.3432697784222111153 ] 
dist 148=[-4.2768782422671887902 ,2.6627568607369500094 ] 
dist 149=[-3.7296388344756811763 ,2.9760590050231995362 ] 
dist 150=[-3.6494382980511263777 ,3.1938978656932001750 ] 
dist 151=[-3.5074019746423742691 ,3.3837645691771337858 ] 
dist 152=[-3.4703319167147037026 ,3.5853932806721691064 ] 
dist 153=[-3.3462470563210694616 ,3.7794295054712712737 ] 
dist 154=[-3.3074878333473390374 ,3.9389861162238770212 ] 
dist 155=[-3.2713564075187216628 ,4.1040362248843210618 ] 
dist 156=[-3.2504210514905431721 ,4.3200084639111533690 ] 
dist 157=[-.74409477706767925366,4.5239406137503492821 ] 
dist 158=[-.72492483175687495581,4.6409217635795373738 ] 
dist 159=[-.71855658595284769506,4.7167454463911459260 ] 
dist 160=[-.12195071199164014417,4.7563564488096606554 ] 
dist 161=[-.11153199211293938768,4.7745772516705514416 ] 
dist 162=[-.10042232150267905777,4.7714350430116917967 ] 
dist 163=[-.09922456322032199559,4.7450387514289279964 ] 
dist 164=[-.10227950875656992245,4.7245532297354716303 ] 
dist 165=[-.11159696602683636877,4.3978129604007247317 ] 
dist 166=[-.12730201839028992192,4.3389840692824442268 ] 
dist 167=[-.15585863557815649307,4.2000752788764939638 ] 
dist 168=[-.18752793937284174712,4.1524120788270967509 ] 
dist 169=[-.21565984295154351266,3.9212398574095662129 ] 
dist 170=[-.24662291713450937022,3.8682069034506530354 ] 
dist 171=[-.28959483474214258964,3.7482136128316942894 ] 
dist 172=[-.33706017242714431101,3.7079204145461416214 ] 
dist 173=[-1.2257101353976852302 ,3.6119108156241920937 ] 
dist 174=[-1.8508676982286713996 ,3.6866825136766624218 ] 
dist 175=[-2.3595441739368630756 ,3.7301159561474874927 ] 
dist 176=[-2.8431176952331647530 ,3.7422528708506206995 ] 
dist 177=[-3.2742334845397270574 ,3.7402965993365229121 ] 
dist 178=[-3.5734693662319789747 ,3.7304167857355623111 ] 
dist 179=[-3.8337619090372572681 ,3.7073687106146457347 ] 
dist 180=[-4.1093924222774175577 ,3.6939632269623299699 ] 
dist 181=[-4.3592862672946550501 ,3.3497799818943186662 ] 
dist 182=[-4.5168244492679218410 ,3.2937399581952499887 ] 
dist 183=[-4.6370560919315485432 ,3.1721552772940190801 ] 
dist 184=[-4.7380054779435018000 ,3.1337646642873848343 ] 
dist 185=[-4.8189674845713942634 ,2.9591241688016947808 ] 
dist 186=[-4.8594006854957984630 ,2.9214415728180405485 ] 
dist 187=[-4.8779325291434171517 ,2.8157217946057370631 ] 
dist 188=[-4.8734798393195175948 ,2.7943413452157175725 ] 
dist 189=[-1.9154272400647816068 ,1.6314878139779924609 ] 
dist 190=[-1.9365887256822061033 ,1.5846503727026513625 ] 
dist 191=[-1.9541897164716764852 ,1.5743723566193784572 ] 
dist 192=[-1.9660944628540172249 ,.71573133404499181056] 
dist 193=[-1.9665569661785280551 ,.68684546385071811443] 
dist 194=[-1.9580395701842045007 ,.61496379596386829058] 
dist 195=[-1.9504101342403175375 ,.60355443382419749648] 
dist 196=[-1.8924779250774415883 ,.49114736512599829768] 
dist 197=[-1.8755754278533715593 ,.46946152225627013027] 
dist 198=[-1.8494001135017238583 ,.44308841184317877413] 
dist 199=[-1.8393992881278344668 ,.43538483996806751403] 
dist 200=[-1.5734070278408231440 ,.23703124936859607839] 
dist 201=[-1.5341234810828465790 ,.21182666802676159404] 
dist 202=[-1.4502928057509930262 ,.15877795946881177457] 
dist 203=[-1.4301055934280201234 ,.14476207762961691044] 
dist 204=[-1.4298798078202086148 ,.09136349286223177661] 
dist 205=[-1.2970197476628779964 ,.08105584929541258940] 
dist 206=[-1.2351993579087657000 ,.06022057244774653695] 
dist 207=[-1.2262271598755824436 ,.17140260248564218199] 
dist 208=[-.75661605781159103812,.52879711307013615572] 
dist 209=[-.64703717242356258579,.7655529838878310412 ] 
dist 210=[-.62601549039194908441,.95956975013074854637] 
dist 211=[-.57482017362014008373,1.1463257665418441314 ] 
dist 212=[-.58436697741735956774,1.3143979326100342680 ] 
dist 213=[-.61759033390963646889,1.4338183054448252835 ] 
dist 214=[-.64822502641228273121,1.5406202392720267314 ] 
dist 215=[-.68340171300349007012,1.6583125948733911326 ] 
dist 216=[-.71551706496492554808,1.7653208660755469035 ] 
dist 217=[-.73392875722697477505,1.8294656978196691435 ] 
dist 218=[-.74585663790683492832,1.8745723060935327568 ] 
dist 219=[-.75208368386910348457,1.9055685144884785877 ] 
dist 220=[-.75500297993854439318,1.9261066480872529801 ] 
dist 221=[-.75451144672892525891,1.9299449296132137335 ] 
dist 222=[-.75075851512250357313,1.9265999367564691741 ]