8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 0, 2, 1, 2] 
dist 0=[52.786205200740615420  ,52.786205200740615420  ] 
dist 1=[52.401091808302666639  ,52.871013087058819078  ] 
dist 2=[51.793323834190367797  ,52.823373274866886676  ] 
dist 3=[50.940546683067236560  ,52.725993836015881576  ] 
dist 4=[49.748833893601710238  ,52.537144349225513602  ] 
dist 5=[47.789404847103602528  ,51.060608621814501968  ] 
dist 6=[45.722408397118381654  ,50.716752240388453605  ] 
dist 7=[43.250764038359201069  ,49.681062674745048166  ] 
dist 8=[39.524924757419809473  ,49.423638232060171008  ] 
dist 9=[36.265308910748566184  ,46.998369123543873254  ] 
dist 10=[32.714142055955232645  ,46.430396476206994650  ] 
dist 11=[27.824593088037186132  ,45.698366084473486521  ] 
dist 12=[22.434894970871561827  ,45.402181256219664418  ] 
dist 13=[16.886651977812845078  ,38.227517342739288795  ] 
dist 14=[10.147084093109046777  ,37.073908724468617272  ] 
dist 15=[0                     ,32.261758364858162073  ] 
dist 16=[22.568206131613365572  ,30.611161448070047107  ] 
dist 17=[19.619992556507541493  ,30.337961584657936111  ] 
dist 18=[16.564608935246315181  ,27.963222328614749858  ] 
dist 19=[13.693968389740135186  ,27.521296070884926805  ] 
dist 20=[10.401166013090187304  ,26.906270409241992924  ] 
dist 21=[5.6587855335022862334 ,26.723039409116744839  ] 
dist 22=[.97351370737216176791,21.962576859369138852  ] 
dist 23=[-2.0914705248389181232 ,21.384433187401192700  ] 
dist 24=[-4.5660436053289964911 ,20.556700920417602717  ] 
dist 25=[-6.8931422154644029167 ,20.333496254023728097  ] 
dist 26=[-8.9569858613335996127 ,16.739128643279119395  ] 
dist 27=[-10.380233265683148088  ,16.154421474392683595  ] 
dist 28=[-11.612585950798368474  ,13.426874963480459838  ] 
dist 29=[-12.914402542342408920  ,-10.101388325168817552  ] 
dist 30=[-14.449747140932423267  ,-11.416737141982928431  ] 
dist 31=[-16.263941288800127522  ,-11.486236889421355557  ] 
dist 32=[-17.796440700527852260  ,-11.260761902929728766  ] 
dist 33=[-19.040254193927943154  ,-10.581159994681083479  ] 
dist 34=[-19.701511993204420063  ,-9.6686497092000314277 ] 
dist 35=[-20.070509289056836545  ,-8.5134684110726984643 ] 
dist 36=[-20.157076449776095060  ,-6.9641566347147919997 ] 
dist 37=[-20.097505893457310432  ,-4.4789892921508752614 ] 
dist 38=[-20.038873426822090981  ,-1.9575872614778987407 ] 
dist 39=[-19.958147548031839319  ,-.2634441189808943646 ] 
dist 40=[-19.867637980248241385  ,1.1447354296499070195 ] 
dist 41=[-19.685890671335963475  ,2.5258245509459386626 ] 
dist 42=[-19.569649848725000924  ,3.7800173626633413822 ] 
dist 43=[-19.359466500258523641  ,4.6822108433628478226 ] 
dist 44=[-19.270320124356554012  ,5.4976583113369841585 ] 
dist 45=[-6.8251852332200277804 ,6.4060406344424263048 ] 
dist 46=[-5.7597579828315890760 ,7.2388924465356072510 ] 
dist 47=[-3.3115199564112739285 ,7.7531036621818296826 ] 
dist 48=[-2.8802598464530220857 ,8.1318895955187514555 ] 
dist 49=[.22011379258509510781,8.4244805718812411285 ] 
dist 50=[.762382956525762429  ,8.6392603354036846783 ] 
dist 51=[1.5945606572870332637 ,8.7076441085165351781 ] 
dist 52=[1.9049956198334813664 ,9.4373845050880776558 ] 
dist 53=[2.0401665258887480365 ,11.012871104371199336  ] 
dist 54=[2.6455578275654807566 ,11.979613011794530169  ] 
dist 55=[1.7870539777446186270 ,12.685747279417234842  ] 
dist 56=[1.0494165536260983130 ,13.221279207033724286  ] 
dist 57=[.2877676443425279662 ,13.623914427841412237  ] 
dist 58=[-.42778506019132088263,13.799619357455078330  ] 
dist 59=[-.98172400293524130345,13.862568611364864430  ] 
dist 60=[-1.5216631569481417162 ,13.846093766513305786  ] 
dist 61=[-2.1815401857141354432 ,1.2070637520841579258 ] 
dist 62=[-2.8011905001310849594 ,.58144966362209114149] 
dist 63=[-3.1807364737536027971 ,-.85606639887833357234] 
dist 64=[-3.4561642677844907053 ,-1.0801538058602643291 ] 
dist 65=[-3.6605284346682191573 ,-2.3415149698592086981 ] 
dist 66=[-3.8167974586262051025 ,-2.2749523492450200918 ] 
dist 67=[-4.3408398369656222427 ,-2.1056659094998547862 ] 
dist 68=[-5.0238676966871528019 ,-1.8298617036469832148 ] 
dist 69=[-5.6504002886084980300 ,-1.3386618931021020195 ] 
dist 70=[-6.0357616067804898237 ,-.82783101251672789515] 
dist 71=[-6.3177047128201337990 ,-.47373722701416856304] 
dist 72=[-6.5316509800401635255 ,-.16843885633446017747] 
dist 73=[-6.6851920052336605967 ,.14795332840298133285] 
dist 74=[-6.7261504180814035772 ,.44543572610386822422] 
dist 75=[-6.7249623510703157184 ,.67539773736695265285] 
dist 76=[-6.7103823350056350091 ,.89893530572579461627] 
dist 77=[-3.9527565335569076342 ,1.1708631936789890412 ] 
dist 78=[-3.6959742987674514368 ,1.4258530608850720097 ] 
dist 79=[-3.0631640417560277441 ,1.5818598378318237550 ] 
dist 80=[-2.9594101569756307798 ,1.6945806424084133594 ] 
dist 81=[-2.0069135927136010058 ,1.7769332127889248039 ] 
dist 82=[-1.8283569046582825011 ,1.8385347605502132140 ] 
dist 83=[-1.5863724965407553929 ,1.8685524937576731384 ] 
dist 84=[-1.5114606709557084381 ,2.0785786964539138447 ] 
dist 85=[-.51927295610138182009,2.5456559733500551102 ] 
dist 86=[.08474818504887849002,2.8376521318666628162 ] 
dist 87=[.48586588668060655744,3.0563469954109268398 ] 
dist 88=[.54482607925848418583,3.2311717984800721254 ] 
dist 89=[1.0322424144353525816 ,3.3648396326852887152 ] 
dist 90=[.98922071689872992122,3.4194023683979603509 ] 
dist 91=[.83315474116296730334,3.4408763614346803070 ] 
dist 92=[.64964127489683220854,3.4426217405927531727 ] 
dist 93=[.3815262642116468782 ,3.4911813857248132797 ] 
dist 94=[.10823362163248420006,3.7488713066787776424 ] 
dist 95=[-.09596697512529513518,3.9145484932222325846 ] 
dist 96=[-.28813585477856040469,4.0442964602986864604 ] 
dist 97=[-.51350130696505624269,4.1585995650968372516 ] 
dist 98=[-.74242568015543197582,4.2538711591597747544 ] 
dist 99=[-.94883910220664741992,4.3076545347260085436 ] 
dist 100=[-1.4447740551246033103 ,4.3410786356679652401 ] 
dist 101=[-2.4012036784697869670 ,4.3550613358081685636 ] 
dist 102=[-3.3485269833718516084 ,4.3531610338211013759 ] 
dist 103=[-3.9524692603508317137 ,4.3405593345598432397 ] 
dist 104=[-4.4195174454683099783 ,4.2855018873957355358 ] 
dist 105=[-4.8207444851436135292 ,4.2527091051859932046 ] 
dist 106=[-5.1482140930439861565 ,4.0449816235560145250 ] 
dist 107=[-5.3210376558811818953 ,3.9875293464657890447 ] 
dist 108=[-5.4164157601593306110 ,3.8849782883163380051 ] 
dist 109=[-5.4363170026179517851 ,3.8518929297548956092 ] 
dist 110=[-5.3979767279660160200 ,3.5083360970176865798 ] 
dist 111=[-5.3733361674471006044 ,3.5354197304662293137 ] 
dist 112=[-5.3425561151229031279 ,3.5377524192213267260 ] 
dist 113=[-5.3137227523767291996 ,3.4938028282175230031 ] 
dist 114=[-5.2420407836429916478 ,3.4715892895564966137 ] 
dist 115=[-5.2042180786511133572 ,3.4188717247169261446 ] 
dist 116=[-5.1227736127193152493 ,3.3942544462647900206 ] 
dist 117=[-5.0872458118869277501 ,2.8979763520223943842 ] 
dist 118=[-4.6596052381905830888 ,2.8185057399935539352 ] 
dist 119=[-4.5783101838834591801 ,2.6336623883221091231 ] 
dist 120=[-4.5444223120051630387 ,2.5745978117399177222 ] 
dist 121=[-4.4285916609620899241 ,2.2967945754175266443 ] 
dist 122=[-4.3862328085680387626 ,2.7830849363392447776 ] 
dist 123=[-4.2988513934354010836 ,3.1775928393247862777 ] 
dist 124=[-4.2650859183957240202 ,3.5279283879981922533 ] 
dist 125=[.50462562884414198769,3.9086173886837362182 ] 
dist 126=[.85138656229098082967,4.2541686595438683628 ] 
dist 127=[1.6340240601983175362 ,4.4643401387274020554 ] 
dist 128=[1.7592166974781426559 ,4.6152007838890450813 ] 
dist 129=[2.6689589160470918466 ,4.7241488806106431920 ] 
dist 130=[2.8149304698232073416 ,4.7975718645008571816 ] 
dist 131=[3.0531765535624588251 ,4.8113734448314089349 ] 
dist 132=[2.6066815573940575501 ,4.7940850533027553488 ] 
dist 133=[1.8757243813355186840 ,4.7806549102085296064 ] 
dist 134=[1.1294575468626828537 ,4.2396313611488026696 ] 
dist 135=[.62189320442523992648,4.3621435673231885684 ] 
dist 136=[.19309820234388281349,4.4464371701632485202 ] 
dist 137=[-.23896697205478598552,4.4995409680460715032 ] 
dist 138=[-.63888925660523413694,4.5075064404165509926 ] 
dist 139=[-.93946847080827139029,4.4790883710722946046 ] 
dist 140=[-1.2241632811157252814 ,4.4658693152398316963 ] 
dist 141=[-1.5607199452673927061 ,2.5094506525981729743 ] 
dist 142=[-1.8765852516277786236 ,2.3272990569750566137 ] 
dist 143=[-2.0787475703228957507 ,1.8814601776499615180 ] 
dist 144=[-2.2358823033617744264 ,1.8100698456993462898 ] 
dist 145=[-2.3721510500933562316 ,1.1488108979398746145 ] 
dist 146=[-2.4842339758451795900 ,1.0256922613069333313 ] 
dist 147=[-2.5449039972360848089 ,.86208621450530003896] 
dist 148=[-2.5794338141926740060 ,.81378330173393249003] 
dist 149=[-2.5872619497609911569 ,-.16120274924378904356] 
dist 150=[-2.2272838848663578446 ,-.28012120779085975274] 
dist 151=[-2.3718829806099866301 ,-.55036429351762036588] 
dist 152=[-2.4912092243409025126 ,-.59200532944499453852] 
dist 153=[-2.5848731658938785362 ,-.91159670240360063703] 
dist 154=[-2.6271113115440433725 ,-.96305777106409419296] 
dist 155=[-2.6449073895436252017 ,-.88906484430080284882] 
dist 156=[-2.6425016666075181770 ,-.69452455948114005458] 
dist 157=[-2.4940957453820434688 ,-.41954414984274777664] 
dist 158=[-2.6409506586353883818 ,-.14268042669079432702] 
dist 159=[-2.7444516812224291631 ,.05937821281521166208] 
dist 160=[-2.8358356109080196475 ,.28579943918575583227] 
dist 161=[-2.9343408369470391754 ,.73584137390359231779] 
dist 162=[-3.0296405071231965019 ,1.2184284167049099536 ] 
dist 163=[-3.1082276758611259763 ,1.6924747053894323329 ] 
dist 164=[-3.1894424060287991636 ,2.2501814047291687345 ] 
dist 165=[-3.2952091438887980391 ,3.0665192748241897784 ] 
dist 166=[-3.3931026858322121361 ,3.8705552517332500082 ] 
dist 167=[-3.4429071900129330854 ,4.3791898807486106164 ] 
dist 168=[-3.4668764682589698913 ,4.7679344407472128304 ] 
dist 169=[-3.4646552080109039372 ,5.0937000260535190417 ] 
dist 170=[-3.4398076637554290090 ,5.3533578208325832787 ] 
dist 171=[-3.4252057241067230327 ,5.4783840412924369516 ] 
dist 172=[-3.3555005777098588103 ,5.5421085221648253546 ] 
dist 173=[-3.3390109874781716332 ,5.5572088799858566629 ] 
dist 174=[-3.0893273565025375855 ,5.4230772910439833722 ] 
dist 175=[-3.1348891728180385678 ,5.3775347994760973922 ] 
dist 176=[-3.1521916347875303921 ,5.2991583288504733346 ] 
dist 177=[-3.1515462791820959456 ,5.2674233360297801605 ] 
dist 178=[-3.1445735350845863325 ,5.1113660374604612475 ] 
dist 179=[-3.0962819569451657314 ,5.0647284145752923945 ] 
dist 180=[-3.0828633880840341924 ,4.9243661284578931001 ] 
dist 181=[-2.8143402275674971626 ,4.8766151162275702665 ] 
dist 182=[-2.7654093260558565226 ,4.6261049833131068092 ] 
dist 183=[-2.6268049817818173081 ,4.5420205049222998140 ] 
dist 184=[-2.7063894408548351655 ,4.5108136305305861456 ] 
dist 185=[-3.1441587386927563670 ,4.3722060358477970034 ] 
dist 186=[-3.7061321849710342207 ,4.3294953349638874147 ] 
dist 187=[-4.0908964276924838784 ,4.2162862560596738717 ] 
dist 188=[-4.4188167469482896455 ,4.1699898189716706701 ] 
dist 189=[-4.7540320840555736818 ,-.84236222085914302378] 
dist 190=[-5.0519279682435178024 ,-1.1940962711717343640 ] 
dist 191=[-5.2309743890551559098 ,-1.9867605000441470290 ] 
dist 192=[-5.3569215714034998157 ,-2.1117075707375204532 ] 
dist 193=[-5.4429928573030023406 ,-2.4299338205270590524 ] 
dist 194=[-5.4966574473496584686 ,-2.0690738936564016052 ] 
dist 195=[-5.5004053945281938372 ,-1.6699859317060881284 ] 
dist 196=[-5.4690794563336408036 ,-1.1672445286135150718 ] 
dist 197=[-5.4392980777251585603 ,-.39289783859167877256] 
dist 198=[-4.4808565868990044572 ,.3881960062117055627 ] 
dist 199=[-4.5923620470257561800 ,.9178525571242770088 ] 
dist 200=[-4.6699679929117174777 ,1.3637305736562352251 ] 
dist 201=[-4.7196759732757075052 ,1.8106208544998418688 ] 
dist 202=[-4.7239289100242244089 ,2.2228915488854146914 ] 
dist 203=[-4.7010694025125847309 ,2.5306671601386799687 ] 
dist 204=[-4.6748631871064315035 ,2.8202381688706123321 ] 
dist 205=[-2.4109097274753663594 ,3.1598873440555678663 ] 
dist 206=[-2.2055592180571164063 ,3.4717773244610132425 ] 
dist 207=[-1.7091147918430564288 ,3.6506129689642749802 ] 
dist 208=[-1.6287981143663818606 ,3.7658794350820809596 ] 
dist 209=[-.91423313100065221684,3.8241837361314366243 ] 
dist 210=[-.78290772608951551111,3.8567210515812322943 ] 
dist 211=[-.60108437489244840687,3.8692008118037929680 ] 
dist 212=[-.54743176612696528628,3.8693519096237833952 ] 
dist 213=[-.3328643799007826683 ,3.8550548406765742640 ] 
dist 214=[-.65461801546401316336,3.1291411663690925014 ] 
dist 215=[-1.0834245139409044107 ,3.2219182524606792652 ] 
dist 216=[-1.4902985047304527543 ,3.2676855375016058881 ] 
dist 217=[-1.8997640712243247247 ,3.2919394861191269528 ] 
dist 218=[-2.2785929881874070237 ,3.2988970828955025386 ] 
dist 219=[-2.5632537903019134729 ,3.2945029605268532004 ] 
dist 220=[-2.8329052174978536426 ,3.2824208084243333635 ] 
dist 221=[-3.1518609558033352661 ,1.9429322130532541366 ] 
dist 222=[-3.4461762417446929044 ,2.0744275840696064333 ] 
dist 223=[-3.6175338405002577411 ,2.1773028558183825498 ] 
dist 224=[-3.7313164491858606545 ,2.2787205569628062161 ] 
dist 225=[-3.7959568636429489435 ,2.4043985208621456048 ] 
dist 226=[-3.8339030811061654570 ,2.5357499917555937893 ] 
dist 227=[-3.8411969473931413184 ,2.6597979558050875029 ] 
dist 228=[-3.8288521927719349832 ,2.8020059005391637229 ] 
dist 229=[-3.8168490872572572529 ,3.0057966879485827940 ] 
dist 230=[-4.1300185827643223945 ,3.2033623726554500855 ] 
dist 231=[-4.5755377553052980455 ,3.3207367662325790314 ] 
dist 232=[-4.9094296583918287736 ,3.4016094512059328510 ] 
dist 233=[-5.1773913740168709310 ,3.4535659040029477500 ] 
dist 234=[-5.3861529369604347761 ,3.4828235677346834973 ] 
dist 235=[-5.4838813098218220121 ,3.4854307132372036415 ] 
dist 236=[-5.5280448323461136950 ,3.4536776204557987332 ] 
dist 237=[-5.5266799816275350743 ,3.4438679348076416795 ] 
dist 238=[-5.2507263568737507717 ,3.2350261658438934137 ] 
dist 239=[-5.1869465765381261108 ,3.2982215207258789326 ] 
dist 240=[-5.0704575743797466778 ,3.3490223463354732970 ] 
dist 241=[-5.0306950190890668594 ,3.3915207701492907079 ] 
dist 242=[-4.8934978275162290666 ,3.4253241736455757850 ] 
dist 243=[-4.9366056088182558549 ,3.4414395904156113317 ] 
dist 244=[-4.9381663487770968748 ,3.4476496769865371698 ] 
dist 245=[-4.7320493366798474294 ,3.4419392897566960378 ] 
dist 246=[-4.6801124857080685583 ,3.1992941622932074027 ] 
dist 247=[-4.5849062700122330066 ,3.2432907261568960790 ] 
dist 248=[-4.5511354490051855610 ,3.2758009524831769199 ] 
dist 249=[-4.3900829858959723588 ,3.2983609189402455380 ] 
dist 250=[-4.3448933608572336285 ,3.3026646431218517730 ] 
dist 251=[-4.2144243131388739109 ,3.2944095022154794788 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 2, 1, 1, 0, 1] 
dist 0=[62.484306018911220161  ,62.484306018911220161  ] 
dist 1=[62.241184562990866050  ,62.774553958417024025  ] 
dist 2=[61.651181844604262514  ,63.022568354424776041  ] 
dist 3=[60.573617916829718385  ,63.097074549023979725  ] 
dist 4=[58.717260932542663251  ,63.058679193315482882  ] 
dist 5=[56.498429016911184552  ,62.966128623630497173  ] 
dist 6=[53.973463816007441892  ,62.562817148664233942  ] 
dist 7=[50.736151040480996917  ,62.397945214442565264  ] 
dist 8=[45.672853998161591462  ,61.789065302128547306  ] 
dist 9=[40.529761937782192710  ,61.597551505917400132  ] 
dist 10=[36.973742564100618847  ,59.794712214242171823  ] 
dist 11=[33.893049370648756309  ,59.321156085083145015  ] 
dist 12=[30.647738760077319131  ,58.950084289269973902  ] 
dist 13=[27.537243875633245343  ,57.947180456494342227  ] 
dist 14=[24.994643736702426247  ,51.739254919307414109  ] 
dist 15=[22.375324431496391028  ,47.746270460527453076  ] 
dist 16=[18.958011959671731840  ,30.635533662667182480  ] 
dist 17=[15.613931651109295210  ,30.260104873317194264  ] 
dist 18=[13.286774482309160277  ,23.391041750625917417  ] 
dist 19=[11.252206624748922245  ,22.546634492969801677  ] 
dist 20=[9.0761560754919321146 ,17.839299783848438595  ] 
dist 21=[6.9660100263186435149 ,17.243418096419399155  ] 
dist 22=[5.1940849339553833105 ,14.929210935198564124  ] 
dist 23=[3.3224162475218025434 ,14.489629133544309568  ] 
dist 24=[.8127394965161420369 ,13.642392148717746032  ] 
dist 25=[-1.6151365403922925790 ,13.441880193710755373  ] 
dist 26=[-3.1602373999326476222 ,4.3940173810908162604 ] 
dist 27=[-4.9218939342966494600 ,4.1106029135377740508 ] 
dist 28=[-6.8129129960505209972 ,3.4577038181359960465 ] 
dist 29=[-8.6268174289250338514 ,.76573304897733005594] 
dist 30=[-10.260914223270304915  ,.40986267469623369347] 
dist 31=[-11.433730822844789889  ,-1.1266348319125639130 ] 
dist 32=[-12.791860383415585084  ,-4.3493992423009192218 ] 
dist 33=[-13.761731770732095944  ,-4.4991610343006111181 ] 
dist 34=[-14.794748206104426869  ,-4.8836856247370744602 ] 
dist 35=[-15.427101257889235143  ,-4.8382662991479959972 ] 
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dist 172=[-.05579739730198582932,.3394681521659175584 ] 
dist 173=[-.07569644914079054397,.37148133614986123027] 
dist 174=[-.10217422360742087788,.40515161857796272697] 
dist 175=[-.14448703621011616288,.44981988786570191075] 
dist 176=[-.18734920137721723026,.49227878043605673069] 
dist 177=[-.21601821994432588366,.51713512941593795932] 
dist 178=[-.2397258109970623949 ,.53382386630679417049] 
dist 179=[-.26279552891165648535,.54369731021146125907] 
dist 180=[-.28363355483908020671,.54972067877798801106] 
dist 181=[-.29843808850213120663,.55104894110771031378] 
dist 182=[-.31162727534451867615,.5495573586315717024 ] 
dist 183=[-.32602052967009979887,.54784651297233772212] 
dist 184=[-.33866786011834655815,.48548449615325259698] 
dist 185=[-.34489191116634213329,.47507251012367360698] 
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dist 188=[-.34323362939775809399,.41636459270514104991] 
dist 189=[-.34093876616574532437,.40963238172532190261] 
dist 190=[-.33627807490409958284,.39017014481759413328] 
dist 191=[-.33420518532799029725,.38628697100286331676] 
dist 192=[-.31916531915863098182,.15709128074052976829] 
dist 193=[-.38254206282885408392,.15669503591055625577] 
dist 194=[-.43290451540155880909,.1543064833323376105 ] 
dist 195=[-.47660782812413070116,.15329364005951023864] 
dist 196=[-.51258844826697694934,.1501934545627012979 ] 
dist 197=[-.53214264326903229453,.14873899683199913813] 
dist 198=[-.54337209138925667945,.14033357889985980454] 
dist 199=[-.55462166073195932813,.13814223546835146868] 
dist 200=[-.57434868530537449931,.13388941358989673374] 
dist 201=[-.58575513889145877243,.13249274369403307456] 
dist 202=[-.59323369769544819907,.104984194751841906  ] 
dist 203=[-.59729056717696740644,.13060095619033981903] 
dist 204=[-.59883167484894162464,.17361317751173014456] 
dist 205=[-.59759484755026648313,.21897285987102640785] 
dist 206=[-.59209947089145452788,.26227924275469823685] 
dist 207=[-.58840902871273062753,.29709962601870522829] 
dist 208=[-.25542261648354194137,.33231513584093610168] 
dist 209=[-.22563164469512128244,.37719743888544435122] 
dist 210=[-.15662243646306706393,.42029936406502008524] 
dist 211=[-.14387716572454291127,.44841190140873112827] 
dist 212=[-.09893283285289269297,.47088068140933323182] 
dist 213=[-.1271113953618244203 ,.49146682173160769764] 
dist 214=[-.15617623296616259633,.50922285936188456831] 
dist 215=[-.1830627844924658998 ,.52040074249088799092] 
dist 216=[-.21345721287313088281,.52887933792617498122] 
dist 217=[-.2565170540072741711 ,.53586599290902461344] 
dist 218=[-.29842595990314772738,.54047231763962407972] 
dist 219=[-.32422897639857354566,.54076269388126702565] 
dist 220=[-.34313282341899117123,.53670740497706251317] 
dist 221=[-.35751788270113058096,.53441408622844504502] 
dist 222=[-.36836594266421241011,.50802693720034525757] 
dist 223=[-.37315930658833368821,.48515747855230101884] 
dist 224=[-.37487470591298324851,.22952117281792621512] 
dist 225=[-.37448493968248658727,.22998883875979597089] 
dist 226=[-.347857518523483822  ,.22937956877481561363] 
dist 227=[-.34262451403338875144,.22869693492421171442] 
dist 228=[-.33258969896538791923,.22484413351291619352] 
dist 229=[-.32932698479733355672,.22382690084380485201] 
dist 230=[-.31465612089075683317,.20922087952003907503] 
dist 231=[-.3108295641124696835 ,.20554646612255701359] 
dist 232=[-.30040321020009394806,.20195902179413098559] 
dist 233=[-.29688338223578398098,.19993264595658138608] 
dist 234=[-.2011985117573205065 ,.14522883682712984885] 
dist 235=[-.2110658236745094552 ,.13805529356086353511] 
dist 236=[-.22580041628512871841,.12049416762680112194] 
dist 237=[-.25102856704113348562,.13047790266505240935] 
dist 238=[-.27883737373468151162,.15380219947842131934] 
dist 239=[-.31737947261621128927,.18915559176474079899] 
dist 240=[-.35441242428484733559,.22424746897460095915] 
dist 241=[-.37620076750694750615,.24652851031175886417] 
dist 242=[-.39096146782311637111,.26364998005195641   ] 
dist 243=[-.39995796833065394156,.27815937847185180908] 
dist 244=[-.40593113680013173012,.28984539171508950429] 
dist 245=[-.4086300892756282539 ,.29570383062534303558] 
dist 246=[-.40944425995045675353,.29843727545035254261] 
dist 247=[-.40838130422411496844,.29879544685896044272] 
dist 248=[-.3533371083127449628 ,.29506061036123873554] 
dist 249=[-.3446580368630049293 ,.29336434382779050838] 
dist 250=[-.32884103967802920902,.28824815182191429592] 
dist 251=[-.32444278984425346472,.2857794159938688235 ] 
dist 252=[-.30814104865219530447,.2713416636764484655 ] 
dist 253=[-.30341954442592140028,.2675472356164313794 ] 
dist 254=[-.29546593903867421637,.25968473377694851917] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 2, 0, 1, 0, 1] 
dist 0=[60.295592302913354004  ,60.295592302913354004  ] 
dist 1=[59.788729461167991624  ,60.559664914554669578  ] 
dist 2=[58.527840882623059628  ,60.850929917326227024  ] 
dist 3=[56.875642439885102102  ,61.117827303946048430  ] 
dist 4=[54.806422361405307227  ,61.284379256254879709  ] 
dist 5=[52.031817553037087982  ,61.373275372221473536  ] 
dist 6=[47.563203845787053697  ,61.330151092516474156  ] 
dist 7=[42.985781533242313104  ,61.181566085367436236  ] 
dist 8=[39.776689582257766570  ,61.079398170052074456  ] 
dist 9=[36.950286846964916648  ,60.489753840276118420  ] 
dist 10=[33.900709175357609274  ,60.233276423419705558  ] 
dist 11=[30.934515313390698660  ,59.998077550337145037  ] 
dist 12=[28.440856743887584206  ,59.820394905071851465  ] 
dist 13=[25.508597278258852046  ,59.476548422718008282  ] 
dist 14=[21.902995609837036469  ,58.710414425953309090  ] 
dist 15=[18.482168934760735130  ,54.431756762107899069  ] 
dist 16=[15.744336434630832179  ,51.348485337421171473  ] 
dist 17=[12.976664981696882422  ,37.327726849559276186  ] 
dist 18=[9.4359356429213610155 ,35.504975459452877586  ] 
dist 19=[6.0035962174302231193 ,31.110575957241303909  ] 
dist 20=[3.6682991516581841123 ,30.478286597234394208  ] 
dist 21=[1.6820952107216772652 ,24.202986253002522018  ] 
dist 22=[-.3568269487708237441 ,23.060164914456287392  ] 
dist 23=[-2.2846641303513671303 ,21.708301709340565631  ] 
dist 24=[-3.8280633345201511532 ,21.470564212884297087  ] 
dist 25=[-5.3949621204761407608 ,12.263217327071249923  ] 
dist 26=[-7.4183756357489870701 ,11.162092248217187640  ] 
dist 27=[-9.3392260699670821585 ,8.8668885211882615535 ] 
dist 28=[-10.496682775876358362  ,8.3302197554190785274 ] 
dist 29=[-11.326995428137074875  ,6.2094700217681362970 ] 
dist 30=[-11.940090178939208210  ,5.8164347786583877644 ] 
dist 31=[-12.407895126360870754  ,5.2410665968430670138 ] 
dist 32=[-12.657042466346216898  ,5.1228855344247905685 ] 
dist 33=[-12.797437438330839868  ,-3.3507617101046626090 ] 
dist 34=[-12.829411448877018801  ,-4.0446724859674038980 ] 
dist 35=[-11.828678232750617793  ,-4.9290091386089335167 ] 
dist 36=[-11.781361660042387847  ,-3.6973445571705172876 ] 
dist 37=[-11.730331141002810355  ,-2.1329809912718057542 ] 
dist 38=[-11.664090955868768377  ,.2888209597913227278 ] 
dist 39=[-10.823827162221368051  ,2.7216071657283559003 ] 
dist 40=[-10.952153819269603019  ,4.3299803798099648382 ] 
dist 41=[-11.696627897603487365  ,5.6389693876490196665 ] 
dist 42=[-12.155564890390800530  ,6.8776946586619462454 ] 
dist 43=[-12.496194077207369576  ,7.9735409087822663936 ] 
dist 44=[-12.767671154394009036  ,8.7126716600225482721 ] 
dist 45=[-12.976094828123543417  ,9.3308227059886656813 ] 
dist 46=[-13.064639416337255395  ,9.9441679560152229654 ] 
dist 47=[-13.082977481137357669  ,10.480241039311102357  ] 
dist 48=[-13.071404376330565675  ,10.790114696925879159  ] 
dist 49=[-2.0922968960618095633 ,10.993200863359631004  ] 
dist 50=[-1.9837645397089159418 ,11.103104611563052429  ] 
dist 51=[-1.0506941463195468299 ,11.144140775838248342  ] 
dist 52=[-.88084490157561494311,11.135135571006629182  ] 
dist 53=[-.63803936222063101564,10.981893964297175163  ] 
dist 54=[-.56974304989496375756,10.948627010329555694  ] 
dist 55=[.63748979505480989318,8.8021877622713422668 ] 
dist 56=[.78720095963332462134,9.1587085998725552926 ] 
dist 57=[1.1082095598841200621 ,9.4513943636203820352 ] 
dist 58=[1.1695413464666917617 ,9.6255428030876821423 ] 
dist 59=[.07708702138645988105,9.7469231387301452054 ] 
dist 60=[-.65185938858555852177,9.8288520661933697572 ] 
dist 61=[-1.2615239327773605290 ,9.8798041604119279765 ] 
dist 62=[-1.8513968934871110683 ,9.8774766456668034024 ] 
dist 63=[-2.3788743836548133125 ,9.8359833277358929022 ] 
dist 64=[-2.7448114460037349998 ,9.8018594449035892182 ] 
dist 65=[-3.0619691728450155250 ,3.6926832366579894092 ] 
dist 66=[-3.3949006231470523234 ,3.1724142009900551268 ] 
dist 67=[-3.6957297178164863050 ,2.3005127464167211482 ] 
dist 68=[-3.8848297546761847114 ,2.2909296488310525730 ] 
dist 69=[-4.0281571135541269077 ,2.2759214738738565168 ] 
dist 70=[-4.1463613799476819460 ,2.2651977682012073667 ] 
dist 71=[-4.2393394317853220117 ,1.5861690921077699391 ] 
dist 72=[-4.4683327971352059682 ,1.5095009727177534544 ] 
dist 73=[-5.3135837379710894544 ,1.3242916741479307465 ] 
dist 74=[-5.8357192132926223631 ,1.2869685651086935290 ] 
dist 75=[-6.2203254501621741997 ,1.0111243165167538833 ] 
dist 76=[-6.5169149525089919577 ,.95748641502832298763] 
dist 77=[-6.7431580303104590353 ,.86752533756421755795] 
dist 78=[-6.8471258276237961393 ,.84464870489202050578] 
dist 79=[-6.8880785999439609603 ,.41734105453697309952] 
dist 80=[-6.8844752005147830688 ,.36102050454980580433] 
dist 81=[-1.9962228859217036440 ,.4399338411705305547 ] 
dist 82=[-2.0293641058236436874 ,.7874376590325736478 ] 
dist 83=[-2.0489840214961294327 ,1.1172306137991890160 ] 
dist 84=[-2.0511771097179053204 ,1.3251864751502724560 ] 
dist 85=[-2.0348207996141847768 ,1.4833058732441378651 ] 
dist 86=[-2.0286097780940365535 ,1.6143330048594450400 ] 
dist 87=[-.34833981426183559218,1.7195545956587046416 ] 
dist 88=[-.32353109785167142546,2.0626960745134645652 ] 
dist 89=[-.38901607595644656128,2.4165112840239601176 ] 
dist 90=[-.47458447469155483683,2.6356503944069140400 ] 
dist 91=[-.56632806624452217009,2.7976832705942080266 ] 
dist 92=[-.65644621564955522217,2.9237074039394483894 ] 
dist 93=[-.76247069159786557168,3.0179756866667049477 ] 
dist 94=[-.91766745628672467568,3.0533376907295439225 ] 
dist 95=[-1.0762979102388289661 ,3.0645708275463671946 ] 
dist 96=[-1.1960193798191656027 ,3.2157956292459526067 ] 
dist 97=[-1.3771195339812166858 ,3.3761138301924463904 ] 
dist 98=[-1.6650643760740618872 ,3.4531152368844944490 ] 
dist 99=[-1.8967794583394200589 ,3.4924049934011000917 ] 
dist 100=[-2.1114364746977841125 ,3.5021434700072115802 ] 
dist 101=[-2.2979562367940148792 ,3.4243807736997284936 ] 
dist 102=[-2.4174389104406114841 ,3.4044883744039793346 ] 
dist 103=[-2.5103190802555985311 ,3.3929085419306460203 ] 
dist 104=[-2.5907174984543546896 ,3.3898218336650261902 ] 
dist 105=[-2.6549209038634575865 ,2.6317704044759723941 ] 
dist 106=[-2.6832011173173161910 ,2.6243204729620221607 ] 
dist 107=[-2.6906232908608434574 ,2.7098298453509857009 ] 
dist 108=[-2.6880897317090790080 ,2.7561620330023692857 ] 
dist 109=[-2.6398305016119539153 ,2.7825773026288419345 ] 
dist 110=[-2.6212923081229900439 ,2.7886417356388479745 ] 
dist 111=[-2.5687931646068033058 ,2.4667222229885179661 ] 
dist 112=[-2.5448810827672495375 ,2.4145769682174964059 ] 
dist 113=[-2.0090205931726116492 ,2.3385923792549288337 ] 
dist 114=[-1.9771647194823342320 ,2.3116352084364776563 ] 
dist 115=[-1.8400081068361100184 ,2.2488685049739351942 ] 
dist 116=[-1.8083324496353551694 ,2.2263533360484601613 ] 
dist 117=[-1.7245757946515978421 ,2.2128678313868726992 ] 
dist 118=[-1.7012331273324005599 ,2.2082482334567596414 ] 
dist 119=[-.8013202901457841178 ,.0426867635032979560 ] 
dist 120=[-.7953449398850221826 ,.1012974585494144220 ] 
dist 121=[-.79126953628601518584,.17240801954037669839] 
dist 122=[-1.0780343944468959437 ,.27914243088404813654] 
dist 123=[-1.3340302441821821906 ,.46331375348606881365] 
dist 124=[-1.5106663543362972308 ,.59207961653956601808] 
dist 125=[-1.6626421076943887916 ,.69886114706036752484] 
dist 126=[-1.8202717636816923664 ,.80337084953096463768] 
dist 127=[-1.9623676954363957538 ,.89825826350263377846] 
dist 128=[-2.0523795109871071823 ,.96664587729439015449] 
dist 129=[-2.1213034266003465543 ,1.0286262241194508362 ] 
dist 130=[-2.1792760249314309844 ,1.0979456493138489406 ] 
dist 131=[-2.2256342537883832959 ,1.1598890082730632800 ] 
dist 132=[-2.2482262060517137179 ,1.1924379782613043792 ] 
dist 133=[-2.2576891670578772319 ,1.2096734339623236649 ] 
dist 134=[-2.2532893800721602429 ,1.2132546306614628380 ] 
dist 135=[-1.0044045206678165810 ,1.2051589012320886782 ] 
dist 136=[-.9008545227258668066 ,1.1991834247412688535 ] 
dist 137=[-.64901734486741782029,1.1914668178782866942 ] 
dist 138=[-.61176283266609970635,1.1853154486339549868 ] 
dist 139=[-.5017798365394925907 ,.97909102336222533899] 
dist 140=[-.6715843956889136047 ,.94982607056790652628] 
dist 141=[-.8078222542737897865 ,.87670908453209087843] 
dist 142=[-.9335219697073992762 ,.85989051358477289469] 
dist 143=[-1.0425681681276309153 ,.73842896507281703664] 
dist 144=[-1.1123764980796332238 ,.71309657771070354329] 
dist 145=[-1.1667116370970336881 ,.79707047016988280743] 
dist 146=[-1.2140408790930689936 ,.87108465550321445315] 
dist 147=[-1.2530022245574258770 ,.93135505633315327226] 
dist 148=[-1.2739559267514389179 ,.96299733229625548921] 
dist 149=[-1.2857289105071806764 ,.98052945231568592605] 
dist 150=[-1.2880572016437394707 ,.98451755041902435972] 
dist 151=[-1.2841601668571451576 ,.85194249852848692462] 
dist 152=[-1.2799905882770376622 ,.83932210763322143035] 
dist 153=[-1.2574267878766955139 ,.8316174730425291081 ] 
dist 154=[-1.2511312356936184527 ,.83525990332917116227] 
dist 155=[.01399728093281366184,.83918359037941426275] 
dist 156=[.10094120785618269947,.84311700912203122858] 
dist 157=[.29055364196869728975,.84782318294293068799] 
dist 158=[.27542461989118049342,.85482765976835219034] 
dist 159=[.10875200839318464427,.86206865339876345033] 
dist 160=[-.02129381120049204140,.8677160959128687046 ] 
dist 161=[-.14915442679119453211,.87327641741100885551] 
dist 162=[-.31816008979256176006,.9581080892399452121 ] 
dist 163=[-.49966611469986227051,1.0694068156702300495 ] 
dist 164=[-.67333805154549713901,1.1349832896206227927 ] 
dist 165=[-.87420995922695358289,1.1795018707601349780 ] 
dist 166=[-1.1642264479931105303 ,1.2068039802842969240 ] 
dist 167=[-1.4494686762850078510 ,1.2246348186118244226 ] 
dist 168=[-1.6312960988467148239 ,1.2313700925382014968 ] 
dist 169=[-1.7718629748545833459 ,1.2312572419008665998 ] 
dist 170=[-1.8925072221952908738 ,1.2281387445289252566 ] 
dist 171=[-1.9908505103538807322 ,1.0668734023626719330 ] 
dist 172=[-2.0424540612367296526 ,1.0435401223502112458 ] 
dist 173=[-2.0696152463902572324 ,.97768113819204960081] 
dist 174=[-2.0743692797689502627 ,.96656027892642134016] 
dist 175=[-2.0603380047376301877 ,.91268638392339695017] 
dist 176=[-2.0497273757797143945 ,.90559827727720070801] 
dist 177=[-2.0235967758392913280 ,.89469310517044229953] 
dist 178=[-2.0104245473544965170 ,.88949683437569131058] 
dist 179=[-1.9320128757814988737 ,.8662055111683582799 ] 
dist 180=[-1.9111943506154465236 ,.8586789582753714754 ] 
dist 181=[-1.8520956070086108389 ,.83673303196617104196] 
dist 182=[-1.8319698450686533807 ,.82795451301391693277] 
dist 183=[-.96447591156204922999,.8526962191828991101 ] 
dist 184=[-.96896576563790244063,1.1521608978167667274 ] 
dist 185=[-.96839555898401479935,1.3922618776970842902 ] 
dist 186=[-.96574119732530655363,1.6134459672822891922 ] 
dist 187=[-.38893495018876555337,1.8050082037531458998 ] 
dist 188=[-.47761436565733762745,1.9269441381371961578 ] 
dist 189=[-.56790120631140818026,2.0209865414781420261 ] 
dist 190=[-.66924613462706287364,2.1052577781548162777 ] 
dist 191=[-.76971634843248489245,2.1990546711517573064 ] 
dist 192=[-.85651229007726785   ,2.2535205671042232485 ] 
dist 193=[-.94975307904765123571,2.2895072388545630386 ] 
dist 194=[-1.0759313369605671480 ,2.3095867931882255456 ] 
dist 195=[-1.2005800037164481430 ,2.3178641409454148194 ] 
dist 196=[-1.2877178513376068847 ,2.3146691901652298831 ] 
dist 197=[-1.3638990404432731317 ,2.2900873073980790033 ] 
dist 198=[-1.4448379191267294275 ,2.2760731186295026317 ] 
dist 199=[-1.5224437126534410414 ,1.0674781496417927747 ] 
dist 200=[-1.5853270646952430977 ,.95692693555286414532] 
dist 201=[-1.6493399819673224022 ,.93606630120792605081] 
dist 202=[-1.7314489266120033928 ,1.0188803670826844998 ] 
dist 203=[-1.8069989407411634828 ,1.0965769897553624478 ] 
dist 204=[-1.8448470067953279967 ,1.1410852873328790457 ] 
dist 205=[-1.8626877330574295145 ,1.1697282521044676303 ] 
dist 206=[-1.8649651037357590475 ,1.1841341006763067006 ] 
dist 207=[-1.8418313762416056815 ,1.1908813395122974089 ] 
dist 208=[-1.8295139329844601173 ,1.1892293588427271967 ] 
dist 209=[-1.8066357476699091524 ,1.1825093395323915584 ] 
dist 210=[-1.7964784616531675712 ,1.1767795015753845896 ] 
dist 211=[-1.7382254543696947720 ,1.0384659747273837040 ] 
dist 212=[-1.7552490402341949600 ,1.0152919720649976274 ] 
dist 213=[-1.7626305034365472877 ,.96357904884202534692] 
dist 214=[-1.7589875694743286929 ,.94682931355355911765] 
dist 215=[-.75141109031939496997,.86915049084456970927] 
dist 216=[-.75117692283400109369,.85222490320987783243] 
dist 217=[-.74237776867356141987,.80725219337206399088] 
dist 218=[-.74002217264053156408,.79625356782220118527] 
dist 219=[-.68176705708554692909,.32157729548144640185] 
dist 220=[-.6708366473866874801 ,.42972931080199976746] 
dist 221=[-.63956921074906100625,.53485091316394702451] 
dist 222=[-.63263752808014898797,.66303189489195232048] 
dist 223=[-.5663750011106737100 ,.78327662534077328687] 
dist 224=[-.5516229207804557565 ,.85674037585371282438] 
dist 225=[-.5323240876600810962 ,.90986059554224461977] 
dist 226=[-.5249462330308302668 ,.94895403362295843034] 
dist 227=[-.54522401366048794353,.97845307789070203696] 
dist 228=[-.62294466465211159909,.99330046004489715405] 
dist 229=[-.7171570394141491439 ,1.1008275444890984507 ] 
dist 230=[-.8582536749653727606 ,1.2678004128432659416 ] 
dist 231=[-.9975713834404890788 ,1.4287888323239747257 ] 
dist 232=[-1.0846871922331340804 ,1.5241763563651098024 ] 
dist 233=[-1.1500700017342352773 ,1.5896092206459558139 ] 
dist 234=[-1.2026935120347086811 ,1.6311014618198138273 ] 
dist 235=[-1.2429552035853758546 ,1.6595131250163368951 ] 
dist 236=[-1.2590257700570042528 ,1.6727635958549702595 ] 
dist 237=[-1.2651127692559620306 ,1.6774250882441964249 ] 
dist 238=[-1.2655504234915298238 ,1.6735001245033656089 ] 
dist 239=[-1.2179381763066115856 ,1.4523279410987411052 ] 
dist 240=[-1.2056464920409143038 ,1.4171317975945649066 ] 
dist 241=[-1.1756846766630067090 ,1.3535565133620990624 ] 
dist 242=[-1.1637263604483201198 ,1.3358758217364251870 ] 
dist 243=[-1.0999695200738100711 ,1.2706659428315962699 ] 
dist 244=[-1.0842787943607028668 ,1.2513661899568635522 ] 
dist 245=[-1.0451081025666435993 ,1.2197985305438878462 ] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 1, 2, 0, 0, 0, 2] 
dist 0=[60.182835538258732973  ,60.182835538258732973  ] 
dist 1=[59.901659671368438468  ,60.310665834556703298  ] 
dist 2=[59.254009768877169222  ,60.539604086168660864  ] 
dist 3=[57.797837460876243993  ,60.698707510492604885  ] 
dist 4=[55.951911061532995159  ,60.794351280397179331  ] 
dist 5=[53.713738968871427646  ,60.841506435413469174  ] 
dist 6=[50.755561268131328992  ,60.807042023383332830  ] 
dist 7=[46.034770416651545660  ,60.705810262295107437  ] 
dist 8=[41.209670075907712590  ,60.590002120543297522  ] 
dist 9=[37.834963198357308111  ,60.250648179996031811  ] 
dist 10=[34.870871592315377856  ,60.084389350751620451  ] 
dist 11=[31.405346739456764162  ,59.936855897365620506  ] 
dist 12=[28.071706956367213318  ,59.776051405311479142  ] 
dist 13=[24.581335779783641098  ,59.496641802706073713  ] 
dist 14=[21.249977892157766029  ,54.522403145936482920  ] 
dist 15=[18.550891305985839251  ,53.582403857650839626  ] 
dist 16=[15.792273685609542007  ,48.101126967238716650  ] 
dist 17=[12.222547855425593519  ,37.455738859428700449  ] 
dist 18=[8.7430900213317664750 ,35.641670972414963930  ] 
dist 19=[6.3445399836394734796 ,31.270113246395408864  ] 
dist 20=[4.2713118960350610408 ,30.640380641871356241  ] 
dist 21=[2.0904170634832642633 ,24.402826704826270152  ] 
dist 22=[-.00352982605795071904,23.266876920462444202  ] 
dist 23=[-1.7302583655323960601 ,21.921143697417232747  ] 
dist 24=[-4.3761410235811134874 ,21.682766775329624571  ] 
dist 25=[-6.3566444550112253704 ,12.535050530175550542  ] 
dist 26=[-8.1869586291261331184 ,11.439518859622799912  ] 
dist 27=[-9.5915915366846674088 ,9.1581860932978473610 ] 
dist 28=[-10.633837870318775120  ,8.6206553652559985504 ] 
dist 29=[-11.465804931035047642  ,6.5166157603679033406 ] 
dist 30=[-12.123394534774262563  ,6.1247763052040711495 ] 
dist 31=[-12.468428055415930542  ,5.5522251661716096146 ] 
dist 32=[-12.688819622298840228  ,5.4336906057099314810 ] 
dist 33=[-12.876111111476157856  ,-3.1945860375162530392 ] 
dist 34=[-12.955538948569496810  ,-3.9014513170786250804 ] 
dist 35=[-12.950554213865952754  ,-5.3229636934204661553 ] 
dist 36=[-12.810274564858559316  ,-5.6427065506873217810 ] 
dist 37=[-12.744747877246589860  ,-5.7446015096060177599 ] 
dist 38=[-12.500821168454683414  ,-4.0637137358364187427 ] 
dist 39=[-12.411632383708330255  ,-1.4679721332983642853 ] 
dist 40=[-11.366520694753053204  ,1.1458999308997733153 ] 
dist 41=[-11.304697633444094642  ,2.8992968117570173839 ] 
dist 42=[-11.730009094806753941  ,4.3549734109266735115 ] 
dist 43=[-12.077714083039628821  ,5.7813081713944893666 ] 
dist 44=[-12.364285676949574585  ,7.0768299118258588919 ] 
dist 45=[-12.592407792953284372  ,8.0107334872708351313 ] 
dist 46=[-12.706443340197271800  ,8.8572998458772561530 ] 
dist 47=[-12.759926166998193848  ,9.8044975842566583408 ] 
dist 48=[-12.747779925807652631  ,10.663097717988803886  ] 
dist 49=[-.05871935135548796368,11.156179303170978226  ] 
dist 50=[.35109972320400968446,11.475325595114921504  ] 
dist 51=[.44173988418360927247,11.639837084585361721  ] 
dist 52=[.59460446728352316001,11.726509942728495044  ] 
dist 53=[.54693887752117347902,11.735122484789745881  ] 
dist 54=[.39492623108087791618,11.688250752781174258  ] 
dist 55=[.06146848206519482597,11.649995901383051311  ] 
dist 56=[-.29367469934755165647,9.0247571383870098559 ] 
dist 57=[-.53222074091703905072,9.0339078812255928088 ] 
dist 58=[-.73043605152822904977,8.4931733728632192841 ] 
dist 59=[-.92473787780380722514,8.6062544129772116319 ] 
dist 60=[-1.1010985693950625534 ,8.6945173178717141704 ] 
dist 61=[-1.7368153091405266361 ,8.7607074607319195182 ] 
dist 62=[-2.3333543303409387673 ,8.7856004176808675753 ] 
dist 63=[-2.7627889626779937917 ,8.7852649578437546095 ] 
dist 64=[-3.1513580403597413858 ,8.7532234012139771015 ] 
dist 65=[-3.5849282310268620853 ,2.9873574021826587509 ] 
dist 66=[-3.9815832464832778988 ,2.5102277379252548973 ] 
dist 67=[-4.2228995147783653595 ,1.4139154878930794687 ] 
dist 68=[-4.3963709971171896821 ,1.2183459226083759316 ] 
dist 69=[-4.5223558362219570052 ,-.16419691095419825201] 
dist 70=[-4.6082797435520249556 ,-.40484523929343984386] 
dist 71=[-4.6280424536395634974 ,-.11106956900232650574] 
dist 72=[-4.6133294886377459662 ,.2220134847721484154 ] 
dist 73=[-4.6104906689355502126 ,.4434513236604973588 ] 
dist 74=[-4.6666964687007994974 ,.62507974402062710388] 
dist 75=[-5.0408459241354465741 ,.79935648008667258154] 
dist 76=[-5.3517938038991799374 ,.95514299072738682216] 
dist 77=[-5.5977406115442309472 ,1.0630094009390818586 ] 
dist 78=[-5.7125677522164430539 ,1.1562068713772959748 ] 
dist 79=[-5.7675043315804489965 ,1.3105205403075892307 ] 
dist 80=[-5.7745186068421058102 ,1.5260213933383725369 ] 
dist 81=[-1.3301330117826958958 ,1.7719142490122630925 ] 
dist 82=[-.89294565729354356745,2.0004083423430983479 ] 
dist 83=[-.65694197545602563547,2.1470333076879368223 ] 
dist 84=[-.47961582273692322699,2.2613370960263689972 ] 
dist 85=[-.44545265690040995073,2.3609018305431450454 ] 
dist 86=[-.23183245756544165119,2.4429205779739362138 ] 
dist 87=[-.19446295382172857606,2.4872229537248198931 ] 
dist 88=[-.12300192779664433692,2.5121194303795058018 ] 
dist 89=[-.10645486432869615602,2.5166978876100039470 ] 
dist 90=[.13749938487003520743,1.7727164392070966354 ] 
dist 91=[-.01077059214555378914,1.9083969633329647130 ] 
dist 92=[-.15287102140723144424,2.0818679547843586402 ] 
dist 93=[-.26813449213327048493,2.2361993625194646417 ] 
dist 94=[-.38567665022438073368,2.3422237667550476677 ] 
dist 95=[-.53686713361795373779,2.4332131530807073985 ] 
dist 96=[-.68283858166155559405,2.5276303142430504142 ] 
dist 97=[-.77955572250303597652,2.6074174413537781234 ] 
dist 98=[-.85859219839868150931,2.6400471066554904227 ] 
dist 99=[-.93401659760894904629,2.6517802820315916196 ] 
dist 100=[-1.0694083875885262688 ,2.6480959269718122492 ] 
dist 101=[-1.2321367366374438570 ,2.5720537731709342284 ] 
dist 102=[-1.3519608323332447283 ,2.5457069428923975314 ] 
dist 103=[-1.4640801978493019122 ,2.5194190972633014537 ] 
dist 104=[-1.7608010863373691840 ,2.5019983987516599945 ] 
dist 105=[-1.9433497143677826912 ,1.9935232085797192048 ] 
dist 106=[-2.0768372216872403637 ,1.9207377665540904234 ] 
dist 107=[-2.1778485252902039841 ,1.9539583052799141901 ] 
dist 108=[-2.2556050317855513498 ,1.9735424266229131969 ] 
dist 109=[-2.2963313630973895212 ,1.9752831494174183151 ] 
dist 110=[-2.3176416308069526018 ,1.9682102276661879599 ] 
dist 111=[-2.3179587782032203884 ,1.9597593933479711350 ] 
dist 112=[-2.0981857250224893925 ,1.7568301610767300253 ] 
dist 113=[-2.0595171190879764940 ,1.7216212672541629524 ] 
dist 114=[-2.0023297908131390147 ,1.6438345273922576391 ] 
dist 115=[-1.9816412978359038991 ,1.6183489191690134686 ] 
dist 116=[-1.9267787728700535071 ,1.4990789867043325224 ] 
dist 117=[-2.1131933815362576296 ,1.4728625303873339629 ] 
dist 118=[-2.2488261606041632763 ,1.4001298101988003231 ] 
dist 119=[-2.3528402063576106293 ,1.3839138339219057071 ] 
dist 120=[-2.4407425166724998901 ,.16956485934210753682] 
dist 121=[-2.5129830807999195030 ,.48174886946886745186] 
dist 122=[-2.5545100422429724693 ,.73862803637149862916] 
dist 123=[-2.5814683814043663069 ,.98645420441498622487] 
dist 124=[-2.5955769089445923795 ,1.2088868629798707831 ] 
dist 125=[-2.6003540807157242280 ,1.3644726480506138563 ] 
dist 126=[-2.5938546548756508517 ,1.5005829330602644381 ] 
dist 127=[-2.5724436273681049054 ,1.6453308304949632047 ] 
dist 128=[-2.5583756560127383779 ,1.7759495769463579294 ] 
dist 129=[-1.0689654414575363307 ,1.8556980133977721977 ] 
dist 130=[-.93764997249768776494,1.9133065819720372684 ] 
dist 131=[-.63335623052894264086,1.9556044430679941040 ] 
dist 132=[-.5782061730151631026 ,1.9847266735547761692 ] 
dist 133=[-.18237868821690748098,1.9897745849029146011 ] 
dist 134=[-.11191736509398605889,1.9850549341204012654 ] 
dist 135=[.01128965218621597903,1.9752246479662783613 ] 
dist 136=[.03803363475658146295,1.6507375310376643670 ] 
dist 137=[.28089066242646018979,1.8456531045674489442 ] 
dist 138=[.10093678616071290241,1.9634279282477736033 ] 
dist 139=[-.08140638494949114084,2.0470807994650136430 ] 
dist 140=[-.25085598257632321123,2.1058625136390473817 ] 
dist 141=[-.3793770340900075421 ,2.1471277890996756595 ] 
dist 142=[-.50225456402106798688,2.1608968562312099843 ] 
dist 143=[-.64919064217336206195,2.1614847681056898053 ] 
dist 144=[-.78729642297033751928,2.1549945030688186687 ] 
dist 145=[-.87495087379077381167,.4515772785482753196 ] 
dist 146=[-.94224741774585033421,.36959436619128669443] 
dist 147=[-.99914990751865388165,.2810291624149947169 ] 
dist 148=[-1.0448753186605781424 ,.26580981551297895759] 
dist 149=[-1.1418703459092991951 ,.22403823687551561712] 
dist 150=[-1.2732810593570599377 ,.21809147069007787496] 
dist 151=[-1.3928145218973428534 ,.22376456147924436714] 
dist 152=[-1.5271208070123016989 ,.24677033756457110505] 
dist 153=[-1.6484688208335257816 ,.2764315046436124614 ] 
dist 154=[-1.7163066300798533068 ,.30865519745975367945] 
dist 155=[-1.7578325832570624748 ,.34887114687066983348] 
dist 156=[-1.7742101447593060166 ,.41041618648892480784] 
dist 157=[-1.7801114258103618438 ,.48082827731833447167] 
dist 158=[-1.7798427825650883567 ,.55641793050278109092] 
dist 159=[-1.7750086211327622689 ,.65014497373806346376] 
dist 160=[-1.7675735662776702198 ,.79291325678829891314] 
dist 161=[-1.5405822334718219631 ,.93498329151059637739] 
dist 162=[-1.6407122340943879949 ,1.0259244493301996682 ] 
dist 163=[-1.7098489447511273394 ,1.0966689376803329953 ] 
dist 164=[-1.7546192583274978788 ,1.1581666174071053155 ] 
dist 165=[-1.7855260756624779556 ,1.2088779887520168922 ] 
dist 166=[-1.7993522876100608763 ,1.2365912439948101955 ] 
dist 167=[-1.8032972446119003154 ,1.2527110449805567987 ] 
dist 168=[-1.7996265320862057882 ,1.5167500501212250854 ] 
dist 169=[-1.5823741347454326621 ,1.7051983781852705467 ] 
dist 170=[-1.5471226234976894558 ,1.8488002163431681505 ] 
dist 171=[-1.4824255219319183285 ,1.9683719522432595475 ] 
dist 172=[-1.4639835567000053825 ,2.0631171055081849577 ] 
dist 173=[-1.3931558755654573074 ,2.1076792248461798228 ] 
dist 174=[-1.3730420985808223036 ,2.1298586058350420213 ] 
dist 175=[-1.3347999850709002963 ,2.1353125694387128015 ] 
dist 176=[-1.3223383361254855572 ,2.0762285963702819512 ] 
dist 177=[-1.1415083790845616805 ,2.0577899726053031000 ] 
dist 178=[-1.0870269608993488343 ,2.0241610420174558747 ] 
dist 179=[-1.0783847986707101606 ,2.0111786809214320882 ] 
dist 180=[-.95387793485155366083,1.9453558911930758276 ] 
dist 181=[-.92660620343295497945,1.9268309323096935918 ] 
dist 182=[-.90172205053019015435,1.8689920455703773946 ] 
dist 183=[-.89449637231548966944,1.8524314905967306206 ] 
dist 184=[-.82333510426438244112,.10239464275702731073] 
dist 185=[-1.0066745304951675748 ,.13334228174235103303] 
dist 186=[-1.1513183831587290010 ,.16119444746097577073] 
dist 187=[-1.2805620477134679564 ,.19206161693992751779] 
dist 188=[-1.4843875094390149880 ,.23503205535647924037] 
dist 189=[-1.6307677059956761126 ,.28238080290432242175] 
dist 190=[-1.7544243553609276490 ,.33071013327291869387] 
dist 191=[-1.8790747417841446799 ,.38890460148090187493] 
dist 192=[-1.9892653535446581136 ,.47560084417583661968] 
dist 193=[-2.0552393578135342720 ,.56093951071149753622] 
dist 194=[-2.1013381608831446472 ,.61371767381110347788] 
dist 195=[-2.1322421609993817877 ,.65262782383124321892] 
dist 196=[-2.1509478451423244756 ,.68264877230764574412] 
dist 197=[-2.1515456034952626039 ,.70555451995643501665] 
dist 198=[-2.1380093420867765935 ,.71608367048997724518] 
dist 199=[-2.1255478013935623063 ,.72020060688099233903] 
dist 200=[-1.0650444473864978396 ,.71982384153358785115] 
dist 201=[-.9687040912335676521 ,.66878693779162630209] 
dist 202=[-.73850160579125069203,.65865771889500116688] 
dist 203=[-.69957752500793491482,.64471506115116090441] 
dist 204=[-.61266860719876318941,.82114865385393286975] 
dist 205=[-.58150291227851175838,.95503300656370036712] 
dist 206=[-.57178825765017413895,1.0831289522181372718 ] 
dist 207=[-.5621347439687217753 ,1.2364721656591989428 ] 
dist 208=[-.55661736020675983265,1.3789029140815939026 ] 
dist 209=[.07162227160383223085,1.4634678001840488481 ] 
dist 210=[.00421443591681350508,1.5216764080220949818 ] 
dist 211=[-.08057795122448451006,1.5589687456741755749 ] 
dist 212=[-.17710314821007484789,1.5839478177529146110 ] 
dist 213=[-.27354896037559589733,1.5930369442818048970 ] 
dist 214=[-.3580251409586148666 ,1.5922090097812703946 ] 
dist 215=[-.44974615816123265986,1.5888943607728037293 ] 
dist 216=[-.57509307421948365205,.53527922964282628297] 
dist 217=[-.69946301842144698697,.52791338820464936698] 
dist 218=[-.78728711049935604853,.53307020645815902843] 
dist 219=[-.86499013843957927803,.54609553347098416326] 
dist 220=[-.94898633971469983693,.56315875390045276817] 
dist 221=[-1.0304013781340676990 ,.58442237343737765384] 
dist 222=[-1.0978082642095426557 ,.61279801949677634084] 
dist 223=[-1.1956109061838613976 ,.65823130962099002305] 
dist 224=[-1.3007158251440011981 ,.70629487004604991097] 
dist 225=[-1.3597582270380156350 ,.80820993525278362632] 
dist 226=[-1.3962515952475561245 ,.92398772225775509795] 
dist 227=[-1.4140271314509633693 ,1.0137252875551955939 ] 
dist 228=[-1.4199041396701428408 ,1.0911460378450673606 ] 
dist 229=[-1.4079818403114862872 ,1.1545458194191293080 ] 
dist 230=[-1.3982721302392103815 ,1.1883498578516815097 ] 
dist 231=[-1.3084954650085106944 ,1.2068813391347141287 ] 
dist 232=[-1.5499113271493696149 ,1.2105256324945481658 ] 
dist 233=[-1.7068557424995487784 ,1.2270204684855848507 ] 
dist 234=[-1.8234571200484426319 ,1.2636834395021312964 ] 
dist 235=[-1.9151818185280193359 ,1.2892165493949203284 ] 
dist 236=[-1.9859759094549586541 ,1.3055749939873612402 ] 
dist 237=[-2.0190795351363176136 ,1.3083115367994842374 ] 
dist 238=[-2.0331894111175845302 ,1.3007762631496265211 ] 
dist 239=[-2.0326856334067756860 ,1.2974805264600583616 ] 
dist 240=[-1.9084258371164482802 ,1.2257870695682024456 ] 
dist 241=[-1.8823553471484063818 ,1.2106672467861975421 ] 
dist 242=[-1.8347961110523179722 ,1.1644590624554101111 ] 
dist 243=[-1.8192226687648057699 ,1.1540792976471752460 ] 
dist 244=[-1.7500305215888463584 ,1.0464509623808923977 ] 
dist 245=[-1.7303620233214982639 ,1.0219078759078140986 ] 
dist 246=[-1.6797327706223963023 ,.99183649902617188896] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 0, 0, 2, 0, 2] 
dist 0=[54.321448782605677208  ,54.321448782605677208  ] 
dist 1=[53.075050417957671740  ,55.197690841456801743  ] 
dist 2=[51.316892215394410954  ,55.856842659849212451  ] 
dist 3=[48.397291546915894772  ,56.236431833393986311  ] 
dist 4=[45.375218191251816137  ,56.484256619278012151  ] 
dist 5=[43.207830445381758668  ,56.617263771509973398  ] 
dist 6=[41.248085563385254677  ,56.642064019848074406  ] 
dist 7=[39.054861878064063340  ,56.604683758835734761  ] 
dist 8=[36.874472556750750131  ,56.018613147307807622  ] 
dist 9=[34.965745047492386717  ,54.379778769717770172  ] 
dist 10=[32.886280093190377646  ,53.977942418455188175  ] 
dist 11=[30.023716221506797066  ,53.380297755474289887  ] 
dist 12=[27.152826959492639400  ,53.165127058190414822  ] 
dist 13=[25.039874284717479932  ,52.570396629157167741  ] 
dist 14=[23.071753946920451017  ,52.333785712144390302  ] 
dist 15=[20.778869603206237080  ,52.012997890704789469  ] 
dist 16=[18.443576348689625244  ,50.748572436374465370  ] 
dist 17=[16.305627969138876072  ,31.926259071274827172  ] 
dist 18=[13.894660970316642333  ,30.244703270912754353  ] 
dist 19=[10.468052664744366316  ,26.265580682125547323  ] 
dist 20=[7.0921246998491946771 ,25.651921350957219179  ] 
dist 21=[4.8834284473497863876 ,20.194947411357714774  ] 
dist 22=[3.0975425715581824396 ,19.210400158644012402  ] 
dist 23=[.75651801744368338307,17.897522025875024712  ] 
dist 24=[-1.3198234441963243108 ,17.557643901874638230  ] 
dist 25=[-3.5283282671456718658 ,10.355237417008894432  ] 
dist 26=[-5.6625565536683139111 ,9.4751324967244907219 ] 
dist 27=[-7.4428772354564764526 ,7.5510735478838747991 ] 
dist 28=[-9.3132284611522398927 ,7.1888766590113188356 ] 
dist 29=[-11.808298313653880623  ,5.0800464251594830543 ] 
dist 30=[-14.197379371067213467  ,4.7350990730284982430 ] 
dist 31=[-15.644611814207097241  ,4.0289985350457198226 ] 
dist 32=[-16.688022699656380114  ,3.8944773444545064358 ] 
dist 33=[-17.463574295448228744  ,-.75426971208969366763] 
dist 34=[-18.051714610365581147  ,-1.2053364083606795407 ] 
dist 35=[-18.346023805831483406  ,-2.0872067296746489019 ] 
dist 36=[-18.484634520543954371  ,-2.2933213632556240187 ] 
dist 37=[-18.488317450246037650  ,-2.3082392369986278487 ] 
dist 38=[-17.033303859144057865  ,-1.8620547830282594490 ] 
dist 39=[-16.775985510902490242  ,-1.3819473504582481598 ] 
dist 40=[-16.332888640579298624  ,-.92030202705634201612] 
dist 41=[-16.197249128578533163  ,-.54751041488671820155] 
dist 42=[-15.703335484884658216  ,-.17035298977489387188] 
dist 43=[-15.543639512007601600  ,.30885840030236444709] 
dist 44=[-15.267823598774001031  ,.76619045219456167311] 
dist 45=[-15.174034828692288446  ,1.0561778665407551560 ] 
dist 46=[-11.869949273246952869  ,1.2778948547862990814 ] 
dist 47=[-11.785255990120181702  ,1.7702925323430010890 ] 
dist 48=[-11.723987590799113835  ,3.6553387958360742772 ] 
dist 49=[-.23705791336874766847,5.5566207166198868201 ] 
dist 50=[.84648396130723419378,7.3217328117154707960 ] 
dist 51=[.83575435199882619424,8.6634411637498313822 ] 
dist 52=[.81074722452684383378,9.9514936866059808141 ] 
dist 53=[.78195150540179344305,11.502563388418568949  ] 
dist 54=[.71552534434940439178,12.952484041222789107  ] 
dist 55=[.62911265522918320704,13.836896723639484415  ] 
dist 56=[.54176551925240383085,14.476291815455998306  ] 
dist 57=[.46499540186262099866,14.948390061933269866  ] 
dist 58=[.38188370413537934927,15.291645118687515767  ] 
dist 59=[.26917935013481006948,15.416816029294145247  ] 
dist 60=[.1584730261504305049 ,15.443848021187450479  ] 
dist 61=[0                     ,15.401914223988128268  ] 
dist 62=[.02002949848208723621,5.5438269907563665253 ] 
dist 63=[-.04310956725296891506,5.5224010330859612196 ] 
dist 64=[-.10121142882244382826,5.4972497720157751263 ] 
dist 65=[-.14805674720592402574,1.6282233251469903262 ] 
dist 66=[-.23760959926487576947,1.3057539976363591055 ] 
dist 67=[-.36250480437913988759,.58001427699551568739] 
dist 68=[-.81303674078074104907,.45701214279193557001] 
dist 69=[-1.3884080002142543686 ,.4563230582488937631 ] 
dist 70=[-1.8361023135996291216 ,.4546277858052719849 ] 
dist 71=[-2.2754291657047114529 ,.4532459377660936399 ] 
dist 72=[-2.8174472159419063881 ,.44354448271302622316] 
dist 73=[-3.3298469381482112464 ,.44039872006755061969] 
dist 74=[-3.6510113227575036162 ,.43322015197515414821] 
dist 75=[-3.8932393610754766122 ,.430224261229732213  ] 
dist 76=[-4.0906943909319763364 ,.37611846697764304103] 
dist 77=[-4.2440241997911371622 ,.36697874551883740032] 
dist 78=[-4.3101994402831523879 ,.34722440991995970309] 
dist 79=[-4.3382696205108740466 ,.34085967290343183333] 
dist 80=[-4.3395512018341140200 ,.3113352637229621    ] 
dist 81=[-.70229925764305535996,.30474147186143062613] 
dist 82=[-.6901318875723376032 ,.30928486717110005429] 
dist 83=[-.6850417047368169591 ,.63452005832973399641] 
dist 84=[-.26700515736857768185,.95427052186509328416] 
dist 85=[-.22737003918371948842,1.2451655106284014905 ] 
dist 86=[-.15522483957186617779,1.4553114490746618938 ] 
dist 87=[-.13861429354924848893,1.6461134758197821158 ] 
dist 88=[-.09344549904365569952,1.8598621999471962010 ] 
dist 89=[-.08728240858960934237,2.0550898267917911033 ] 
dist 90=[-.09367481681132004375,2.1720177847608265626 ] 
dist 91=[-.1187054927297301124 ,2.2537756395548976618 ] 
dist 92=[-.1506059769708526293 ,2.3087128334861583932 ] 
dist 93=[-.1844140812030972486 ,2.3444221916787474359 ] 
dist 94=[-.22595895593281922011,2.3502985493306246506 ] 
dist 95=[-.28874905109991661806,2.3430324289305409542 ] 
dist 96=[-.36021200461586163099,2.3328552161013818050 ] 
dist 97=[-.43637110957507116297,1.5028044006661038932 ] 
dist 98=[-.53042660892638920662,1.4198184184634385128 ] 
dist 99=[-.67330402631796744827,1.2088379108311142043 ] 
dist 100=[-.81553112550454432402,1.1770030573118615154 ] 
dist 101=[-.90699880226044219628,.83726651486046798538] 
dist 102=[-.97868615485089064081,.77213705191441254863] 
dist 103=[-1.0420022937181643718 ,.69696869476298076075] 
dist 104=[-1.0950241205744937053 ,.67946579061912755931] 
dist 105=[-1.1256462229337725589 ,.08284504749940369811] 
dist 106=[-1.1457245011435888443 ,.01030190882664659429] 
dist 107=[-1.2041600952769131552 ,-.01710995943969349191] 
dist 108=[-1.2578008732727255826 ,-.02067432392260915391] 
dist 109=[-1.2994001015011870397 ,-.01801696796765019769] 
dist 110=[-1.3171619860605307914 ,-.01162242878006535458] 
dist 111=[-1.3231164831827651545 ,.00151099573164149239] 
dist 112=[-1.3209412621651664865 ,.01791971149057812893] 
dist 113=[-.56057929980420150232,.03737932031942674757] 
dist 114=[-.505295957593259226  ,.06274752525944262428] 
dist 115=[-.38135066804040523175,.10272440784407814932] 
dist 116=[-.35109468866949005029,.14272912708258958729] 
dist 117=[-.16166205295341181298,.19306055896776525438] 
dist 118=[-.12757372461055480144,.23916563852599619228] 
dist 119=[-.08155229239951703621,.28561048941457302511] 
dist 120=[-.06990760875102241140,.32859744066017907889] 
dist 121=[.1705895919966338646 ,.36091005495198540208] 
dist 122=[.1995043556596274467 ,.39152425403140731744] 
dist 123=[.21454577675386175654,.4277374694537324159 ] 
dist 124=[.20736231455881055661,.46114760032711987252] 
dist 125=[.19811661858277798435,.48058094322793311167] 
dist 126=[.1806123173168052869 ,.49346050689520733834] 
dist 127=[.13322851876588165442,.50072829130033043747] 
dist 128=[.07882320329379860642,.50452230631095118736] 
dist 129=[.02019962465181044379,.50438551314119685625] 
dist 130=[-.05261128972637372922,.50078562318442688957] 
dist 131=[-.16360808061534345196,.49767072995925168569] 
dist 132=[-.27443918738981934853,.47760469804527723622] 
dist 133=[-.34658915879010552096,.46956586331133537507] 
dist 134=[-.40406368848757942201,.46661800783575801406] 
dist 135=[-.45635617156971847261,.4554753299577710365 ] 
dist 136=[-.50117429436376670693,.4525258252822905658 ] 
dist 137=[-.5288343140097176826 ,.41933662794289955018] 
dist 138=[-.54916042956077893346,.41240278890502991294] 
dist 139=[-.56472399418289054522,.3959333938449582855 ] 
dist 140=[-.57668365029601129666,.39029000543153800238] 
dist 141=[-.582634385784371147  ,.36301945538568494324] 
dist 142=[-.58530812056296242092,.35688232414196757023] 
dist 143=[-.58419723682950576536,.34249135673811621389] 
dist 144=[-.58074191281649521377,.33764155698564832041] 
dist 145=[-.5781069265259932502 ,.14498599520416775746] 
dist 146=[-.60923067631014245284,.13174281680168550159] 
dist 147=[-.67944300528552364956,.12765439111039355032] 
dist 148=[-.74788158432005851129,.12664079082389877514] 
dist 149=[-.8098194233100893599 ,.16245376498183949434] 
dist 150=[-.85409646082414664953,.19120569252257421758] 
dist 151=[-.89385220530739164748,.24042189235966211602] 
dist 152=[-.93775206935957366017,.29876547105812502928] 
dist 153=[-.97668023926007041411,.33986510268338464179] 
dist 154=[-.99660075464668340216,.37611566147123045048] 
dist 155=[-1.0063846897520511612 ,.41511712973058997464] 
dist 156=[-1.0074389613171845546 ,.4504527763197722076 ] 
dist 157=[-.99861609685901304768,.47208086031779848474] 
dist 158=[-.99313208550655753931,.48776415717215752122] 
dist 159=[-.97901179746268675496,.49938664288281949485] 
dist 160=[-.97209252140693630195,.50748038460769536146] 
dist 161=[-.84086997216040694677,.71454853569026857842] 
dist 162=[-.81937554713065764391,.87552338064038642112] 
dist 163=[-.77051782755845488723,1.0038608224668200602 ] 
dist 164=[-.75485909742882708758,1.1208573549940821908 ] 
dist 165=[-.68283701638769825626,1.2213389948969238226 ] 
dist 166=[-.66725116562828938645,1.2837979006266099093 ] 
dist 167=[-.62920821248938565585,1.3302527223876068929 ] 
dist 168=[-.61786616379869708079,1.3668945723417854509 ] 
dist 169=[-.49834600263766782965,1.3948575205781376094 ] 
dist 170=[-.4786228991435551952 ,1.4066914240019941615 ] 
dist 171=[-.43296782078235267996,1.4089651183243042763 ] 
dist 172=[-.42076550397200396639,1.4066630318749816601 ] 
dist 173=[-.35636649383487496628,1.3827545908077378705 ] 
dist 174=[-.34330301403932305114,1.3739845114407139655 ] 
dist 175=[-.31559590919841026543,1.3421006181657540975 ] 
dist 176=[-.31127328390170692292,1.3322423237639253658 ] 
dist 177=[-.35112200972373584338,-.00297417880976952031] 
dist 178=[-.50872294593042501921,.01051189453684464892] 
dist 179=[-.63655411607954740304,.03322866958193592480] 
dist 180=[-.77947860742953889045,.06475222476882485901] 
dist 181=[-.92067773912238332642,.10606789004838976158] 
dist 182=[-1.0175653288618483992 ,.14114989074751297016] 
dist 183=[-1.1003513810531272450 ,.17679033701789433388] 
dist 184=[-1.1853011930221703082 ,.20996804220250765336] 
dist 185=[-1.2607727131017542588 ,.23522638131504029382] 
dist 186=[-1.3057500640591578522 ,.25946637261051685461] 
dist 187=[-1.3369152584538936864 ,.28858194670229159493] 
dist 188=[-1.3572889831192072988 ,.31566477418545531779] 
dist 189=[-1.3691198591436465528 ,.33179631901941334481] 
dist 190=[-1.3698174133516623796 ,.34296042161406639731] 
dist 191=[-1.3588443471061549743 ,.35022859218440115913] 
dist 192=[-1.3529250135149758859 ,.35481509144002853204] 
dist 193=[-.70110507449472834957,.35543029118434563597] 
dist 194=[-.64092172659511412455,.35415572638560829147] 
dist 195=[-.4973645072735397075 ,.35238644996527332116] 
dist 196=[-.47237619323166820224,.42848998548315887868] 
dist 197=[-.35197823697801391138,.48262988749837960403] 
dist 198=[-.35468223388662688065,.56669456588231683082] 
dist 199=[-.35456764573743984968,.6487296941093014125 ] 
dist 200=[-.35264727625602674793,.74508028917076272877] 
dist 201=[-.35134316486890134295,.83389297204562753695] 
dist 202=[-.34384408329832203592,.88586021376151588598] 
dist 203=[-.34269908316849949905,.9206755367082287386 ] 
dist 204=[-.34351689109021296697,.941071913599541826  ] 
dist 205=[-.34794022790295440909,.95427377693807777116] 
dist 206=[-.35097480158732772657,.96039093822793779132] 
dist 207=[-.35289679491654659171,.96247505434278661201] 
dist 208=[-.3539495453296670619 ,.95958862507858055   ] 
dist 209=[-.35351639113033461157,.55046527996096041804] 
dist 210=[-.35191039177791217314,.53181348311986874683] 
dist 211=[-.3504805557979781168 ,.52835799831336105155] 
dist 212=[-.24525866576950301168,.30496967139794435395] 
dist 213=[-.33268826497798956347,.3171765935954070369 ] 
dist 214=[-.40029757309729138735,.33243603908918003226] 
dist 215=[-.46619456889736219918,.35282890466065371932] 
dist 216=[-.54679464455288804954,.385512153366565315  ] 
dist 217=[-.62251814082295870596,.42009861589441284734] 
dist 218=[-.66896305723144495578,.4480824984996900519 ] 
dist 219=[-.70276113571553363519,.47653366118849159768] 
dist 220=[-.72803726151767456037,.51298233006261773671] 
dist 221=[-.74645398784180036511,.55168742948340744726] 
dist 222=[-.75288945029574702525,.58913818830138903259] 
dist 223=[-.75421894307000139461,.63276062987996736739] 
dist 224=[-.81379041023201266231,.69608250014842236796] 
dist 225=[-.96492790969109775059,.75776290863099107977] 
dist 226=[-1.0582025695323616500 ,.79483715501257553809] 
dist 227=[-1.1267794910619874628 ,.82090340336843139026] 
dist 228=[-1.1793943508949434144 ,.83867378961684378132] 
dist 229=[-1.2195629846110996681 ,.84996636330885021525] 
dist 230=[-1.2384896084665323282 ,.85200842742964145552] 
dist 231=[-1.2459849317872782163 ,.8471467956540183976 ] 
dist 232=[-1.2458599854368227164 ,.84538334388740461977] 
dist 233=[-1.1520366720776931835 ,.78709098237779613359] 
dist 234=[-1.1339624916894100503 ,.77551172221308704493] 
dist 235=[-1.1013223438038490990 ,.74460382039692291623] 
dist 236=[-1.0911218964433686171 ,.73499006012890218328] 
dist 237=[-1.0480157799720029330 ,.67309608135324695362] 
dist 238=[-1.0354729565925407004 ,.65876017384705414522] 
dist 239=[-1.0062317720329837780 ,.6326381091255206051 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 1, 2, 1, 2] 
dist 0=[47.296870463322859507  ,47.296870463322859507  ] 
dist 1=[46.017317167327369814  ,48.061565436907962964  ] 
dist 2=[44.109325093607488265  ,48.599861835343853799  ] 
dist 3=[40.835457819585440681  ,48.974795102553083189  ] 
dist 4=[37.260800295168470674  ,49.303836785382054855  ] 
dist 5=[34.151964652065369303  ,49.656876914808768255  ] 
dist 6=[30.780763327789293274  ,49.906435832571697612  ] 
dist 7=[26.158908419687552427  ,49.937025885754659981  ] 
dist 8=[21.073840347718250793  ,49.442625722536320141  ] 
dist 9=[15.853061598781579425  ,47.663521656868729345  ] 
dist 10=[9.5213564817277074889 ,47.275941638431800361  ] 
dist 11=[0                     ,46.193928067108589706  ] 
dist 12=[33.602565682925042275  ,45.901490373824484117  ] 
dist 13=[30.550196430610387491  ,43.601593685253422554  ] 
dist 14=[27.428762542500699103  ,43.067780491592223497  ] 
dist 15=[25.048181068839120645  ,42.261915295279649006  ] 
dist 16=[22.751549315084028857  ,41.034422026683806063  ] 
dist 17=[19.964424912631937960  ,30.592734450648254273  ] 
dist 18=[17.068570418959396414  ,29.331192000497645852  ] 
dist 19=[14.337079240067753161  ,26.772824040506118511  ] 
dist 20=[11.195755862247199047  ,26.048091443202780171  ] 
dist 21=[6.6622602140137827987 ,25.878405288614505362  ] 
dist 22=[2.1781950507833817274 ,22.011900158100107146  ] 
dist 23=[-.76595335330985013728,20.692529995375780217  ] 
dist 24=[-3.1547078219280807268 ,20.420380837638997741  ] 
dist 25=[-5.4205002656294523240 ,18.111959656430983677  ] 
dist 26=[-7.4427924026125096372 ,17.701803638838921894  ] 
dist 27=[-8.8591210694936883393 ,17.276128610754956023  ] 
dist 28=[-10.108208800332466614  ,16.066886583437918252  ] 
dist 29=[-11.462905139928560756  ,13.561373734703856017  ] 
dist 30=[-12.682239844353347640  ,6.1948859203393079627 ] 
dist 31=[-13.390755727326199849  ,5.3614955387353307472 ] 
dist 32=[-13.864794243742165253  ,2.4883150126088494766 ] 
dist 33=[-14.147441366025954391  ,-9.3573592659004883218 ] 
dist 34=[-15.288608361001642735  ,-8.5617591358885097718 ] 
dist 35=[-16.896594241132801515  ,-7.5318100377518562749 ] 
dist 36=[-18.223439581624444599  ,-6.1377089964874684082 ] 
dist 37=[-19.286063618670488506  ,-3.8891239559042685423 ] 
dist 38=[-19.838382980896199296  ,-1.6066640864756073092 ] 
dist 39=[-20.134953596746261752  ,-.07716257889018511412] 
dist 40=[-20.193483478524173171  ,1.1893169551991813375 ] 
dist 41=[-19.722358829797142555  ,2.4230138987605056762 ] 
dist 42=[-19.572601112181844988  ,3.5374631283164200061 ] 
dist 43=[-19.419892458280293889  ,4.3284767466285480126 ] 
dist 44=[-19.312778681758656598  ,5.0323779891525234400 ] 
dist 45=[-19.067011872676302132  ,5.7995481864954052171 ] 
dist 46=[-18.937888742298906299  ,6.4999538198322442344 ] 
dist 47=[-18.750153297078566843  ,6.9376007231644729890 ] 
dist 48=[-18.658207870608452561  ,7.2660778762164149442 ] 
dist 49=[-6.0385945044093775281 ,7.5310057745638112238 ] 
dist 50=[-4.9694900664085137893 ,7.7347458449429932861 ] 
dist 51=[-2.5274134361321166850 ,7.8191603626082194719 ] 
dist 52=[-2.0934478345489183340 ,7.8366413064300952271 ] 
dist 53=[.94691976353737073842,7.8234020179272311635 ] 
dist 54=[1.4745114240772001031 ,6.3116068369178638532 ] 
dist 55=[1.8892619062171422735 ,7.6955494617473186674 ] 
dist 56=[1.2178560167074925763 ,9.3745429487260475793 ] 
dist 57=[.51931025339353274727,10.951063076279395376  ] 
dist 58=[-.14011134195130596745,11.926137402967039576  ] 
dist 59=[-.65562719136275796695,12.647610579582839026  ] 
dist 60=[-1.1628095137803466324 ,13.212096146640358338  ] 
dist 61=[-1.7891525273377185044 ,13.640465780886059749  ] 
dist 62=[-2.3800659581800785621 ,13.818655064273058338  ] 
dist 63=[-2.7460365994561220440 ,13.887093341964019588  ] 
dist 64=[-3.0165786064379030756 ,13.877404382188660049  ] 
dist 65=[-3.2270086951725143922 ,.94580698789369164012] 
dist 66=[-3.3908099527389214170 ,.32407421187719250806] 
dist 67=[-3.4753270431864289073 ,-1.1022271204611158092 ] 
dist 68=[-3.5178334992841439154 ,-1.3235385449315144624 ] 
dist 69=[-3.5213982863804048780 ,-1.1288326129164541757 ] 
dist 70=[-3.9196167865019101921 ,-.69296093571218596143] 
dist 71=[-4.5092913022065156214 ,-.38934228420020553539] 
dist 72=[-5.1613358248002287782 ,-.12611033371117050824] 
dist 73=[-5.7575010958949059602 ,.1488556461249160337 ] 
dist 74=[-6.1242960684058295216 ,.40862629415012848816] 
dist 75=[-6.3928401879069941210 ,.61133396239179849057] 
dist 76=[-6.5970214871295808222 ,.81012366525559322357] 
dist 77=[-6.7439367914306341625 ,1.0543330544870551588 ] 
dist 78=[-6.7840133858595850394 ,1.2834827833593415088 ] 
dist 79=[-6.7816018512597930816 ,1.4222674600550674596 ] 
dist 80=[-6.7590247186928323752 ,1.5209558605512655885 ] 
dist 81=[-3.8380802106696624353 ,1.5902940880401791667 ] 
dist 82=[-3.5693720443600305050 ,1.6417331199915164674 ] 
dist 83=[-2.9127495174355902236 ,1.6690244434444276445 ] 
dist 84=[-2.8038178623925772906 ,1.6837108280367249863 ] 
dist 85=[-1.8341658998359351295 ,1.6847448685427517408 ] 
dist 86=[-1.6536590641868578288 ,1.5556412947932031445 ] 
dist 87=[-1.4013033501456641692 ,1.8847812185639268925 ] 
dist 88=[-1.3264704356441812616 ,2.1673611929229847870 ] 
dist 89=[.06117379662987871979,2.6254265724897284502 ] 
dist 90=[.23249368405128962928,2.9259240377547792526 ] 
dist 91=[.61958804530574808924,3.1492039403328900191 ] 
dist 92=[.68066583453094265635,3.3244934696103869230 ] 
dist 93=[.43425317765381706435,3.4583750131335019345 ] 
dist 94=[.17756785109287302159,3.6988753207621163760 ] 
dist 95=[-.01628485774566918916,3.8633330677905390521 ] 
dist 96=[-.20073534070633325127,3.9907659837508300360 ] 
dist 97=[-.41997845728397511038,4.1006617706255422114 ] 
dist 98=[-.64428527828876399685,4.1905390936947855380 ] 
dist 99=[-.84897988217050044727,4.2380732957330723827 ] 
dist 100=[-1.3222763631089636280 ,4.2634512463755829196 ] 
dist 101=[-2.2574770625685615855 ,4.2648763644091478210 ] 
dist 102=[-3.1843592292993252032 ,4.2504674875743566390 ] 
dist 103=[-3.7760615949509030092 ,4.2340218203400112402 ] 
dist 104=[-4.2345378709058557523 ,4.1701680932804707415 ] 
dist 105=[-4.6299586184358220159 ,4.1370663737091937776 ] 
dist 106=[-4.9538359815850765090 ,3.9202189542391591404 ] 
dist 107=[-5.1269206394546675942 ,3.8617623447083961700 ] 
dist 108=[-5.2230007326731727241 ,3.7589647771458527066 ] 
dist 109=[-5.2450940576831441388 ,3.7263455937422231455 ] 
dist 110=[-5.2232727741457463278 ,2.9129080627820715394 ] 
dist 111=[-5.2044364388446729823 ,2.8966985439002429908 ] 
dist 112=[-5.1785888674521979566 ,3.0394322759412503343 ] 
dist 113=[-5.1515637286841374814 ,3.1739587297077078611 ] 
dist 114=[-5.0877388376501117232 ,3.2446199498450058076 ] 
dist 115=[-5.0520927241449786714 ,3.2815684458371750417 ] 
dist 116=[-4.9750579336438143764 ,3.2859911424918269243 ] 
dist 117=[-4.9410149509755277348 ,3.2656130782775105816 ] 
dist 118=[-4.6075692159965075953 ,3.2490303406775297710 ] 
dist 119=[-4.6552963642373623349 ,3.2053074153280586448 ] 
dist 120=[-4.6613207886232569406 ,3.1829434907722409050 ] 
dist 121=[-4.4098940751397028124 ,2.7506595735534469184 ] 
dist 122=[-4.3546101428882155789 ,2.6799944010567882034 ] 
dist 123=[-4.2692455119983026643 ,3.0344512509939430163 ] 
dist 124=[-4.2362120967565521396 ,3.3738685763613586346 ] 
dist 125=[-4.1199933507852779300 ,3.7433882763971814006 ] 
dist 126=[-4.0789645881134374636 ,4.0790538561653181710 ] 
dist 127=[-3.9949534733778970661 ,4.2834278433719327052 ] 
dist 128=[-3.9630421308411770290 ,4.4303839346010446642 ] 
dist 129=[.51965391049306532638,4.5369982199762603337 ] 
dist 130=[.84562644537144423655,4.6092790175592770378 ] 
dist 131=[1.5805913731599821580 ,4.6230699738195132906 ] 
dist 132=[1.6983292355098325266 ,4.6079013476353440450 ] 
dist 133=[1.8196537326500042249 ,4.5949663456346512488 ] 
dist 134=[1.1060450954568371570 ,3.0062483634057479213 ] 
dist 135=[.62044758631102672432,3.2876074850512475922 ] 
dist 136=[.20994350522034619866,3.5858977470475850276 ] 
dist 137=[-.20413397809902695275,3.8540418546308611634 ] 
dist 138=[-.58771709508441808606,4.0151438449215013434 ] 
dist 139=[-.87658785207739696216,4.1284110401488214974 ] 
dist 140=[-1.1507857710058578454 ,4.2057264547196340404 ] 
dist 141=[-1.4758480780201020373 ,4.2538604368441448424 ] 
dist 142=[-1.7811300701896869089 ,4.2607226814879588293 ] 
dist 143=[-1.9764251878293649949 ,4.2323278678816109665 ] 
dist 144=[-2.1281420810150157962 ,4.2196707096819062954 ] 
dist 145=[-2.2595839916806745337 ,2.3609277051954346979 ] 
dist 146=[-2.3675687880740396661 ,2.1878256713509851952 ] 
dist 147=[-2.4257090384123388905 ,1.7650090314302449282 ] 
dist 148=[-2.4583125433776020990 ,1.6968280187229773364 ] 
dist 149=[-2.4644195224514273019 ,1.0723454378534736536 ] 
dist 150=[-1.6938179549506460616 ,.95617887894085610537] 
dist 151=[-1.7563001760744321875 ,.79998166643616586075] 
dist 152=[-1.8580850804533081731 ,.75272438988179241793] 
dist 153=[-1.9721849366212786789 ,-.15836762332551871628] 
dist 154=[-2.1417026903798480546 ,-.26972855545012424159] 
dist 155=[-2.2780853041243236482 ,-.52413844695374122451] 
dist 156=[-2.3898077369795464846 ,-.56211130220186513619] 
dist 157=[-2.4768642308563424137 ,-.43437580036789317246] 
dist 158=[-2.5718682015395219539 ,-.16513231913450984328] 
dist 159=[-2.6708117331916133280 ,.03225594904926421675] 
dist 160=[-2.7577227026881257019 ,.25332128378669395212] 
dist 161=[-2.8507125992894520676 ,.68940773520012514426] 
dist 162=[-2.9402625139925717965 ,1.1572234518681335119 ] 
dist 163=[-3.0134417631522737948 ,1.6170376205451568944 ] 
dist 164=[-3.0884744570922145118 ,2.1582063220201969516 ] 
dist 165=[-3.1854037013948560887 ,2.9505737383452909879 ] 
dist 166=[-3.2747416516747431996 ,3.7311406397233270170 ] 
dist 167=[-3.3194887336048147126 ,4.2252373501591922880 ] 
dist 168=[-3.3400054758270391545 ,4.6032268945563074594 ] 
dist 169=[-3.3372537448576058369 ,4.9206146245871009712 ] 
dist 170=[-3.3095401701482300411 ,5.1740804562285659794 ] 
dist 171=[-3.2948207083595943754 ,5.2970718304145196866 ] 
dist 172=[-3.2260337519141306817 ,5.3599896547681861782 ] 
dist 173=[-3.2100569574012428799 ,5.3737980737829268605 ] 
dist 174=[-2.9079425796789217086 ,5.2519637363526349584 ] 
dist 175=[-2.8543971717249288053 ,5.2089878147449599797 ] 
dist 176=[-2.6956965738376578969 ,5.1348524464588557744 ] 
dist 177=[-2.8253693302806397013 ,5.1045457175748221110 ] 
dist 178=[-2.8998252401494264547 ,4.9537432844691714290 ] 
dist 179=[-2.9459417570503911513 ,4.9088446656369466537 ] 
dist 180=[-2.9652587359974153834 ,4.7719499718148626751 ] 
dist 181=[-2.9673183119970451505 ,4.7268693148077410865 ] 
dist 182=[-2.9616434226355732206 ,4.5054998301089979949 ] 
dist 183=[-2.9182621605715732306 ,4.5501464746545569100 ] 
dist 184=[-2.9059174304183055161 ,4.5519528664083069635 ] 
dist 185=[-3.0516121139206278232 ,4.3645473008365718325 ] 
dist 186=[-3.5956403924119018364 ,4.3168825644127144633 ] 
dist 187=[-3.9680117862032296410 ,4.2359987878352639447 ] 
dist 188=[-4.2852553443365486431 ,4.2063231235893622448 ] 
dist 189=[-4.6093714435256468611 ,4.0762610632999626976 ] 
dist 190=[-4.8973288530457778654 ,4.0360288367038658180 ] 
dist 191=[-5.0703291195331770457 ,3.9313777082329806736 ] 
dist 192=[-5.1919342518831346525 ,3.8888684092924922641 ] 
dist 193=[-5.2748652287338634214 ,-.78017981391438167597] 
dist 194=[-5.3264090783923589941 ,-1.1085994452222663927 ] 
dist 195=[-5.3299075318445806542 ,-1.6431868826046323446 ] 
dist 196=[-5.2990611422364369046 ,-1.1540454255568046283 ] 
dist 197=[-5.2702684816975149123 ,-.4001590745032549987 ] 
dist 198=[-3.2471185049014278192 ,.36040187588720810305] 
dist 199=[-3.5138751329113814808 ,.87616901690884190841] 
dist 200=[-3.7880113587493553408 ,1.3103892818029392495 ] 
dist 201=[-4.0322310452046175721 ,1.7456493646483974898 ] 
dist 202=[-4.1796441435594626431 ,2.1472235168453537679 ] 
dist 203=[-4.2841079049911402682 ,2.4470659910896444364 ] 
dist 204=[-4.3569920333387464366 ,2.7292232361601914310 ] 
dist 205=[-4.4038411276374077187 ,3.0602478082602213211 ] 
dist 206=[-4.4079407679320692260 ,3.3642531489030051119 ] 
dist 207=[-4.3871467141784016521 ,3.5386269531980706792 ] 
dist 208=[-4.3628990858455844399 ,3.6510925314706021157 ] 
dist 209=[-2.2514651685370070222 ,3.7081381906944163909 ] 
dist 210=[-2.0600651175077170382 ,3.7401353548767012640 ] 
dist 211=[-1.5970424335778622659 ,3.7526804455139857017 ] 
dist 212=[-1.5223611091739094878 ,3.7533527565623553826 ] 
dist 213=[-.85501937933032572444,3.7394814219587684636 ] 
dist 214=[-.73234970711459234378,2.0770522391008612000 ] 
dist 215=[-1.0274319543688436191 ,2.2954432621539267428 ] 
dist 216=[-1.4207883812351910370 ,2.5510290350741672117 ] 
dist 217=[-1.8167956796845951927 ,2.7854485033041483493 ] 
dist 218=[-2.1832647291347843676 ,2.9194030993393429556 ] 
dist 219=[-2.4587897092118921180 ,3.0051610655235690385 ] 
dist 220=[-2.7199340481817808735 ,3.0473154908592122790 ] 
dist 221=[-3.0290380249115592205 ,3.0694729793864959955 ] 
dist 222=[-3.3143700335371064024 ,3.0754604249883866636 ] 
dist 223=[-3.4806851099987615010 ,3.0707374659831405244 ] 
dist 224=[-3.5913551608723559572 ,3.0594951387353101114 ] 
dist 225=[-3.6547113760917787506 ,2.3118311533833145600 ] 
dist 226=[-3.6922198297569235800 ,2.4399935746141480196 ] 
dist 227=[-3.6997778236965464867 ,2.5612423765540448569 ] 
dist 228=[-3.6882613367558087802 ,2.7004058207489527526 ] 
dist 229=[-3.6767876055601093086 ,2.9000288467570260107 ] 
dist 230=[-3.9911424547846438459 ,3.0936331179025918611 ] 
dist 231=[-4.4195965329909112467 ,3.2087861873676248053 ] 
dist 232=[-4.7404713362534287329 ,3.2882908792977677457 ] 
dist 233=[-4.9975713435992973111 ,3.3396900746981675018 ] 
dist 234=[-5.1977258382181708423 ,3.3689555057538435901 ] 
dist 235=[-5.2914314394032739541 ,3.3718249449007742877 ] 
dist 236=[-5.3335909620770185822 ,3.3417221217278726896 ] 
dist 237=[-5.3322897296800879791 ,3.3324806145411933310 ] 
dist 238=[-5.0607707210178757101 ,3.1306836743319512652 ] 
dist 239=[-4.9986226529027368557 ,3.1525085339263464369 ] 
dist 240=[-4.8851546887255200079 ,3.2017176719899119436 ] 
dist 241=[-4.8465784646373603018 ,3.2433919906029120662 ] 
dist 242=[-4.6692491569990083902 ,3.2769295904247638848 ] 
dist 243=[-4.6190520237576140005 ,3.2936804603021015338 ] 
dist 244=[-4.4823353237670747849 ,3.3013066115976628049 ] 
dist 245=[-4.5036683578952208680 ,3.2984443838884321163 ] 
dist 246=[-4.5906128739955180271 ,2.8401021245284314166 ] 
dist 247=[-4.6315227813913565130 ,2.8091623633485739234 ] 
dist 248=[-4.6337472209451788884 ,2.8838546275226017965 ] 
dist 249=[-4.4451099764675685283 ,2.9778219103647774178 ] 
dist 250=[-4.3970240284675600386 ,3.0350312721898968785 ] 
dist 251=[-4.3088271413056392638 ,3.0761582968191323142 ] 
dist 252=[-4.2773649144632212034 ,3.1059712326501352460 ] 
dist 253=[-4.1266156985567190158 ,3.1261579444175395665 ] 
dist 254=[-4.0843648158915009297 ,3.1288847313102026958 ] 
dist 255=[-3.9615055509280338737 ,3.1193373386722388912 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 1, 1, 0, 1, 2] 
dist 0=[63.540247032669620812  ,63.540247032669620812  ] 
dist 1=[62.800421287758502691  ,63.762646017706081159  ] 
dist 2=[61.541528638263204311  ,63.910693683288563000  ] 
dist 3=[59.296780634090269177  ,64.063991872041918142  ] 
dist 4=[56.914597873338524552  ,64.135206890895470877  ] 
dist 5=[55.106847217421590164  ,64.159865901571208459  ] 
dist 6=[53.370515470420014517  ,64.127441321077479108  ] 
dist 7=[51.273368079717837114  ,63.933130063601163801  ] 
dist 8=[49.099789764360035495  ,58.360013615222626010  ] 
dist 9=[47.058111021848757635  ,57.536499212156203757  ] 
dist 10=[44.717602857635066355  ,56.407639547233013948  ] 
dist 11=[41.350470955124095601  ,55.801584569226863964  ] 
dist 12=[37.909972642801343245  ,54.884618185408675015  ] 
dist 13=[35.276330089677383458  ,54.580779354429698703  ] 
dist 14=[32.723072840049490230  ,54.407732478616942375  ] 
dist 15=[27.680876427490321132  ,54.106658633619959025  ] 
dist 16=[23.273696285509256185  ,32.374585207483497692  ] 
dist 17=[19.559182062075008009  ,31.898407951912639438  ] 
dist 18=[15.808609650412631824  ,31.317992140217202133  ] 
dist 19=[12.313400396763014818  ,31.123463427694615377  ] 
dist 20=[9.3332119302692511670 ,11.410298676248260275  ] 
dist 21=[5.8843443050322368891 ,9.8529380758353341340 ] 
dist 22=[3.0150041433055785624 ,9.5704441192968330634 ] 
dist 23=[.1747351093344638269 ,7.6892421098742917660 ] 
dist 24=[-2.4393118288082139916 ,.48307288467039337501] 
dist 25=[-4.4050591171903755376 ,-.2570087378762821222 ] 
dist 26=[-6.2781367106818958170 ,-1.5731379340219123438 ] 
dist 27=[-8.5220676595827803267 ,-1.8390401537007753277 ] 
dist 28=[-10.625607119588215443  ,-5.0610187918504106281 ] 
dist 29=[-11.937947957736910681  ,-5.5029693697117999819 ] 
dist 30=[-12.925924549311376717  ,-5.7949320897784456647 ] 
dist 31=[-13.733904490885298152  ,-6.0615307773331038083 ] 
dist 32=[-14.367498161483558744  ,-5.8777233052594162445 ] 
dist 33=[-14.658985978132173787  ,-5.4124658511525698458 ] 
dist 34=[-14.795672576916627746  ,-4.6562289411720713838 ] 
dist 35=[-14.810874507901872355  ,-3.3113177217149414997 ] 
dist 36=[-8.2208715545958196651 ,-1.8651593853310573722 ] 
dist 37=[-8.1820155975597984097 ,-.65355419130066194659] 
dist 38=[-8.1414890834085468762 ,.38320186194789059042] 
dist 39=[-6.7814960212122461324 ,1.4480401639969613520 ] 
dist 40=[-6.5834616382867752158 ,2.4462275015730030762 ] 
dist 41=[-6.1834039442683937278 ,3.2174084887949274050 ] 
dist 42=[-6.0706310793237835403 ,3.9686193485512738333 ] 
dist 43=[-5.6266470662053261549 ,4.8874731359290551832 ] 
dist 44=[-5.5243721828221977550 ,5.7526227760230581062 ] 
dist 45=[-5.3120933978757957414 ,6.2897252475300689319 ] 
dist 46=[-5.2480279348993757474 ,6.6892193620021215101 ] 
dist 47=[-3.7380262780621603660 ,7.0054780482071242615 ] 
dist 48=[-.54046374310481858884,7.2447695326830391079 ] 
dist 49=[-.26368892150198610289,7.3373164671990073515 ] 
dist 50=[.32632247537518606736,7.3720574832929252232 ] 
dist 51=[.45091120505901937432,7.3801985560748445792 ] 
dist 52=[1.0435328239281584944 ,7.0724745365703325802 ] 
dist 53=[1.1450106355329695868 ,7.0064366979258466037 ] 
dist 54=[.89402297801797175299,6.7876155240465872771 ] 
dist 55=[.51037468471336690552,6.7415392879930915094 ] 
dist 56=[.14222994704305438859,6.1921788062893782722 ] 
dist 57=[-.15467830418759329493,6.0665287166078752316 ] 
dist 58=[-.45494301781253362598,5.9269194739245170063 ] 
dist 59=[-.83651011296129705431,5.8618219023388532610 ] 
dist 60=[-1.2007831787695475836 ,4.6663440862628398247 ] 
dist 61=[-1.4321154191200243305 ,4.6795210008696454762 ] 
dist 62=[-1.6094242171835590159 ,4.6721322753176496608 ] 
dist 63=[-1.7583224114006426697 ,4.6552824503315910299 ] 
dist 64=[-1.8770308413724787496 ,-.63614979303998354452] 
dist 65=[-1.9339848649760858041 ,-.81379172934855147501] 
dist 66=[-1.9627976604561865772 ,-.88765614009266911249] 
dist 67=[-2.0946100446820431141 ,-.74504552964232946002] 
dist 68=[-2.4875801873266060652 ,-.56960768457849906736] 
dist 69=[-2.7706064029323802656 ,-.44593266930264018092] 
dist 70=[-3.0270010852050080761 ,-.33724447143882282758] 
dist 71=[-3.3137387489980885670 ,-.22149983680780993744] 
dist 72=[-3.5714124494411960447 ,-.11087429042059127381] 
dist 73=[-3.7118564770660181801 ,-.02256721299441213348] 
dist 74=[-3.7932630948748547964 ,.06584400841591146992] 
dist 75=[-3.8153938928408496410 ,.176909935126515225  ] 
dist 76=[-3.8162669884380465281 ,.28223945742559814974] 
dist 77=[-3.8128433164770911550 ,.34779837293003421659] 
dist 78=[-3.8056848372340657521 ,.39650909546102524024] 
dist 79=[-3.7916049965992524194 ,.43469502345621685731] 
dist 80=[-2.9005778982439548943 ,.58198226615458073572] 
dist 81=[-2.7912849177934564352 ,1.0636830950491253900 ] 
dist 82=[-2.5141807670163813463 ,1.4561781630091914903 ] 
dist 83=[-2.4626873674943567709 ,1.8283523516472155795 ] 
dist 84=[-2.0051248989283965254 ,2.1580428054133672201 ] 
dist 85=[-1.9134994568395100407 ,2.3810874304020041185 ] 
dist 86=[-1.7861127275917046131 ,2.5683036502657239563 ] 
dist 87=[-1.7448573070954604972 ,2.7550973864689259969 ] 
dist 88=[-.88790584284626321826,2.9195418474969321811 ] 
dist 89=[-.7765053040155259626 ,3.0176112114230513647 ] 
dist 90=[-.54623889715228410268,3.0857096408132111995 ] 
dist 91=[-.54649235827548440851,3.1305905344741248866 ] 
dist 92=[-.54374103992177792552,3.1570816095196720158 ] 
dist 93=[-.54133520813695885105,3.1571601204240886327 ] 
dist 94=[-.53088834359310621738,3.1349493012638044290 ] 
dist 95=[-.52698464543930629237,3.1151210831990089493 ] 
dist 96=[-.49052880917709420392,.8429194659836571871 ] 
dist 97=[-.48106741438148746087,.8306474476970754179 ] 
dist 98=[-.468548992913474563  ,.7985796145178326850 ] 
dist 99=[-.53890265940929796066,.7887541260325446716 ] 
dist 100=[-.82562190016808411037,-.31243911259922273183] 
dist 101=[-1.0365590172181892630 ,-.3887266099629055195 ] 
dist 102=[-1.2318837086982445315 ,-.55604095980797231644] 
dist 103=[-1.4563481051770611381 ,-.58477291519346376336] 
dist 104=[-1.6642093621565520983 ,-.76174089379093866692] 
dist 105=[-1.7933126223302851297 ,-.7891024888453201262 ] 
dist 106=[-1.8891723397708489029 ,-.8411811154350250468 ] 
dist 107=[-1.9644270562742318726 ,-.8500748054360100166 ] 
dist 108=[-2.0204789680670858070 ,-.8658821343180514626 ] 
dist 109=[-2.0397393174563411514 ,-.8500972901963547543 ] 
dist 110=[-2.0443264168013399310 ,-.8159138180507565399 ] 
dist 111=[-2.0418568422852092437 ,-.7477906872328632855 ] 
dist 112=[-1.3147550826009936046 ,-.6632461686363646915 ] 
dist 113=[-1.2462127035737699477 ,-.53021181402232058632] 
dist 114=[-1.0926364859442727831 ,-.36490807603255075682] 
dist 115=[-1.0872120853882249016 ,-.18959635494640083975] 
dist 116=[-.77474160424283086238,-.02185555748107125719] 
dist 117=[-.7227174097999603222 ,.11607897188279787585] 
dist 118=[-.65515721159125574789,.25000601271816679237] 
dist 119=[-.63336247590504324511,.42424943191384090973] 
dist 120=[-.2917127228017367397 ,.59133815111822165867] 
dist 121=[-.26362665789942007934,.69955288957287462843] 
dist 122=[-.21624348497252587309,.78512036099968511527] 
dist 123=[-.20491806089826496833,.86188864695806866127] 
dist 124=[-.01200719110358172635,.92695760128518132267] 
dist 125=[.01351943676957401607,.9658709129905466573 ] 
dist 126=[.06716672821305392173,.99304759786369462298] 
dist 127=[.07975062651532795063,1.0113222662108900438 ] 
dist 128=[.12996034909755189656,1.0235979079275107717 ] 
dist 129=[.13928432529157336993,1.1036181788662698133 ] 
dist 130=[.15232534840685750999,1.1868643196028622531 ] 
dist 131=[.15435675917956396811,1.2718903208854100745 ] 
dist 132=[.15242371199174916328,1.3514340810214030541 ] 
dist 133=[.08318864466578880038,1.4128038383189315194 ] 
dist 134=[.00510539190208679200,1.4725391014680904844 ] 
dist 135=[-.07683011565937978515,1.5455576275307500578 ] 
dist 136=[-.15476938367992866119,1.6142243015637008314 ] 
dist 137=[-.21691249433102902359,1.6565939216131747682 ] 
dist 138=[-.27926341257724642289,1.6877509156078084855 ] 
dist 139=[-.35803321682233982722,1.7116776953983850798 ] 
dist 140=[-.43331063573989328875,1.7290636442889926796 ] 
dist 141=[-.5734804023626974757 ,1.7341204027175402746 ] 
dist 142=[-.88276286925588889151,1.7310821418117036124 ] 
dist 143=[-1.3394184393038296579 ,1.7259788620742934310 ] 
dist 144=[-1.7911654082893647582 ,1.6970894396934240709 ] 
dist 145=[-2.0808692347068757425 ,1.6843635427649022532 ] 
dist 146=[-2.3068269426678786158 ,1.6566604405605377492 ] 
dist 147=[-2.5042783760870141489 ,1.6447500185951138755 ] 
dist 148=[-2.6678685296942500497 ,1.5786723021429360147 ] 
dist 149=[-2.7587482115021004582 ,1.5618905324062375137 ] 
dist 150=[-2.8136216634326447345 ,1.5083897052014708706 ] 
dist 151=[-2.8335794096709985989 ,1.4960406391030440124 ] 
dist 152=[-2.8377914753680664343 ,1.3154764799713144240 ] 
dist 153=[-2.8298520171455724013 ,1.2839880041218380579 ] 
dist 154=[-2.8115289794424189753 ,1.2006266532369683209 ] 
dist 155=[-2.8001464224091764612 ,1.1830279878108964328 ] 
dist 156=[-2.7279149849020604555 ,1.0294984319018684355 ] 
dist 157=[-2.7072482602914932457 ,.99689414878811210518] 
dist 158=[-2.6263606568091886546 ,.95068319264434045237] 
dist 159=[-2.6133788518968153493 ,.93516219223473714859] 
dist 160=[-.80954005548049825108,.90175464998276832738] 
dist 161=[-.80040907225360000591,1.1773929439230500687 ] 
dist 162=[-.79440252615467073051,1.3985171716485415802 ] 
dist 163=[-.79110067624847612711,1.6595745944474735030 ] 
dist 164=[.05052052419641976175,1.9504118518004993138 ] 
dist 165=[.11649235260159583913,2.1490516854213008642 ] 
dist 166=[.26744913066168268313,2.3178130299593826885 ] 
dist 167=[.29046780456224281096,2.4894641282420380491 ] 
dist 168=[.30254345363078758142,2.6416050675845321905 ] 
dist 169=[.2756922333313952814 ,2.7325384322498785910 ] 
dist 170=[.2432152691747331369 ,2.7958807729737353260 ] 
dist 171=[.1946581140748233061 ,2.8379562339265430244 ] 
dist 172=[.1446127346033418209 ,2.8630491278526777448 ] 
dist 173=[.1061975538079707826 ,2.8642282896211503173 ] 
dist 174=[.0690167051826280806 ,2.8442666563157445719 ] 
dist 175=[.0238930080341011645 ,2.8295696524454250216 ] 
dist 176=[-.04918641902342234364,1.4418102852365871656 ] 
dist 177=[-.34615672114213587296,1.3148622959354885191 ] 
dist 178=[-.5964472416424569144 ,1.0115593165117178888 ] 
dist 179=[-.8477496632502281529 ,.95974334290253996444] 
dist 180=[-1.0798403565800414622 ,.53361056915062161834] 
dist 181=[-1.2534943218423559866 ,.45555957455738207803] 
dist 182=[-1.4172423716130478908 ,.34221436423993023757] 
dist 183=[-1.6098172125507074570 ,.32944974186938093549] 
dist 184=[-1.7868857127568890273 ,.20681366598986998353] 
dist 185=[-1.8887781638821204614 ,.18396825139445625149] 
dist 186=[-1.9549044726335624049 ,.15486414262722743578] 
dist 187=[-1.9893006215423051214 ,.1471455414443722488 ] 
dist 188=[-2.0097732806141030180 ,-.03583354359822929913] 
dist 189=[-2.0203592516719072856 ,-.01059720544752273296] 
dist 190=[-2.0257073114043560048 ,.01807324671146254728] 
dist 191=[-2.0252885282612576749 ,.05884757455890574199] 
dist 192=[-.67083467307498003965,.11894620129923427633] 
dist 193=[-.67047344525208628487,.34178189972891961646] 
dist 194=[-.67859946862829875411,.54298014946761178063] 
dist 195=[-.69771912057854732901,.74714095231151308002] 
dist 196=[-.72241305723714464212,.93708071143092389798] 
dist 197=[-.75277363869606711377,1.0815509987246452821 ] 
dist 198=[-.79304864386152996663,1.2200943603738662751 ] 
dist 199=[-.85729070544303921662,1.3863922963577039480 ] 
dist 200=[-.92515998551602748847,1.5410765243967164445 ] 
dist 201=[-.97990294015711692561,1.6332924870083345445 ] 
dist 202=[-1.0354089647901746471 ,1.6972300177399901793 ] 
dist 203=[-1.1063196194675179455 ,1.7391099653623914302 ] 
dist 204=[-1.1815283012422969418 ,1.7671211153483800175 ] 
dist 205=[-1.2541776038069934397 ,1.7757339011785817655 ] 
dist 206=[-1.3387143185059949537 ,1.7738245544118158504 ] 
dist 207=[-1.4613398221827674322 ,1.7685877989641521006 ] 
dist 208=[-1.5807978885964414216 ,2.0497238159514718910 ] 
dist 209=[-1.6526988377511325971 ,2.2545734871427784106 ] 
dist 210=[-1.7033796160447442775 ,2.4062585949018040186 ] 
dist 211=[-1.7381899576921178025 ,2.5246433867825933403 ] 
dist 212=[-1.7600386528562977104 ,2.6157123424875686250 ] 
dist 213=[-1.7640088401145501820 ,2.6584283184691866726 ] 
dist 214=[-1.7518723333070479082 ,2.6762419203528644348 ] 
dist 215=[-1.7493176329445554204 ,2.6757412388370048334 ] 
dist 216=[-1.6421100922621962731 ,2.4993232994433614005 ] 
dist 217=[-1.6201695189886301491 ,2.4634686554479385043 ] 
dist 218=[-1.5568779970166079921 ,2.3983525233819170502 ] 
dist 219=[-1.5405194601690930580 ,2.3773890166275208450 ] 
dist 220=[-1.4671837802950843950 ,2.2859061124699776928 ] 
dist 221=[-1.4691464269591473382 ,2.2596540683021577888 ] 
dist 222=[-1.4638896213120815388 ,2.1943924091412455263 ] 
dist 223=[-1.4588708122964132010 ,2.1691201147360331234 ] 
dist 224=[-1.0524146551825497511 ,1.1102270684110180629 ] 
dist 225=[-1.0484314546111150035 ,1.1011739346382918684 ] 
dist 226=[-1.0280512063793758160 ,1.0670309747202374366 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 2, 1, 2] 
dist 0=[64.761517966541636556  ,64.761517966541636556  ] 
dist 1=[64.033050379109755399  ,65.257756470272588738  ] 
dist 2=[62.858311368742665410  ,65.505238986889909056  ] 
dist 3=[61.129770280653870166  ,65.618121195960101764  ] 
dist 4=[58.189871550431811034  ,65.577089258544391465  ] 
dist 5=[55.117241051806869384  ,65.463930103972998459  ] 
dist 6=[52.858620209443809635  ,65.305851804622183989  ] 
dist 7=[50.759836862804071242  ,64.331043469537401809  ] 
dist 8=[48.325291811901594564  ,62.118116911327315436  ] 
dist 9=[45.855561963266733805  ,60.366164202339881689  ] 
dist 10=[43.616115255380086719  ,59.608204557764455124  ] 
dist 11=[41.111657078758894793  ,58.459803802658408496  ] 
dist 12=[37.378469422688897478  ,58.096999692660645489  ] 
dist 13=[30.875548375957151332  ,57.294526416596706441  ] 
dist 14=[26.465140033307112602  ,57.078941758430447969  ] 
dist 15=[22.734233084418387217  ,55.340112981148297715  ] 
dist 16=[18.944587621769952160  ,52.110751730805277922  ] 
dist 17=[15.397447279395356654  ,28.279540709924737162  ] 
dist 18=[12.634732914507315128  ,27.799228888424270561  ] 
dist 19=[9.9109063062384104416 ,27.167828242200473311  ] 
dist 20=[6.5186295687297059026 ,26.960341379402097279  ] 
dist 21=[3.2739690347823568361 ,12.012850707850499901  ] 
dist 22=[1.1393780205863897993 ,10.753239065531642957  ] 
dist 23=[-.59738902732177973618,9.1249129147832893819 ] 
dist 24=[-2.2537079377214727800 ,8.8318466504560272375 ] 
dist 25=[-4.2411275199626333473 ,.4225624867527456227 ] 
dist 26=[-6.0405489555308371948 ,-.5437815921127564269 ] 
dist 27=[-7.7477175590022377529 ,-2.5788037122484488567 ] 
dist 28=[-9.7829953150882142340 ,-2.9224851259334052379 ] 
dist 29=[-11.687039962640602824  ,-4.7113009998985724531 ] 
dist 30=[-12.870028438904432624  ,-4.9945302220007922309 ] 
dist 31=[-13.755327076479356258  ,-5.5618507799798949576 ] 
dist 32=[-14.470275846124964564  ,-5.8819424996423305898 ] 
dist 33=[-15.024263042404112935  ,-5.6535856913743303554 ] 
dist 34=[-15.266658600888724610  ,-5.0443803110652550798 ] 
dist 35=[-15.371898019734886601  ,-4.1377567750774093909 ] 
dist 36=[-15.377878071687124862  ,-2.5935374116840872376 ] 
dist 37=[-8.3877805825764012550 ,-.76367361613593329867] 
dist 38=[-8.3166642487176736714 ,.60798233573885288013] 
dist 39=[-8.2626425304505163498 ,1.7666786349986843140 ] 
dist 40=[-8.2203522684636547750 ,2.9337805430476886838 ] 
dist 41=[-7.3089394947580338834 ,4.0141342852709140282 ] 
dist 42=[-7.2087499964661919074 ,4.8270170957831763825 ] 
dist 43=[-6.9310044115164274889 ,5.5984992965395945024 ] 
dist 44=[-6.8668534444492561667 ,6.5139810194700239904 ] 
dist 45=[-5.4159750448878168887 ,7.3623129483374625932 ] 
dist 46=[-5.3148312398371630753 ,7.8660125484083165132 ] 
dist 47=[-5.1314695142975679367 ,8.2137382495271893372 ] 
dist 48=[-5.0842684111801865523 ,8.4398539431416961064 ] 
dist 49=[-.88216871072529368348,8.5946493602582540096 ] 
dist 50=[-.52194315047712917505,8.6576639326824096313 ] 
dist 51=[.2535380587498498121 ,8.6655387977604183194 ] 
dist 52=[.41403117612263348006,8.6488305393975649529 ] 
dist 53=[1.2217709519796137200 ,7.6371714705647795472 ] 
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dist 55=[.93014130019927868139,7.0805137206355397255 ] 
dist 56=[.4219052521309966506 ,6.9938547626879984355 ] 
dist 57=[-.06451158078046431948,6.2252593318349607645 ] 
dist 58=[-.45567343682747839954,6.0611407641854526960 ] 
dist 59=[-.85060584724760612788,5.5560665828138515290 ] 
dist 60=[-1.3520999602571022655 ,5.6965034560353059790 ] 
dist 61=[-1.8314499276830370346 ,5.7938046326140989401 ] 
dist 62=[-2.1380942877523384081 ,5.8210283267768979556 ] 
dist 63=[-2.3759748408297897052 ,5.8192468705479402274 ] 
dist 64=[-2.5811227723101775309 ,5.8006782642909918655 ] 
dist 65=[-2.7487668838680465255 ,-.65397062628481672447] 
dist 66=[-2.8370962537425670441 ,-.87532469128563890562] 
dist 67=[-2.8839931268721682002 ,-1.0826704670022153685 ] 
dist 68=[-2.8923815678135203225 ,-.81288774656932480973] 
dist 69=[-2.8483068469731172394 ,-.53119352638994798908] 
dist 70=[-3.1865783623841517569 ,-.33787852440622373565] 
dist 71=[-3.4925618605498215577 ,-.17318291697570854324] 
dist 72=[-3.8340235539594631344 ,-.00555841054136488446] 
dist 73=[-4.1414089314415901218 ,.15019813798858131867] 
dist 74=[-4.3114477168706236676 ,.2675936437960083190 ] 
dist 75=[-4.4133446905857917178 ,.3788609216632446106 ] 
dist 76=[-4.4488658235095093203 ,.5101999216400754778 ] 
dist 77=[-4.4580940023011583048 ,.6329806236679721150 ] 
dist 78=[-4.4550726827160410029 ,.7101368604357212103 ] 
dist 79=[-4.4425796863410596505 ,.7683555310184859468 ] 
dist 80=[-4.4222284694471369637 ,.8156488094059829240 ] 
dist 81=[-3.3023806160186497455 ,.8521395163829806270 ] 
dist 82=[-3.1697060054368166983 ,1.0438614468130201931 ] 
dist 83=[-2.8342097837831859886 ,1.4956431124049470308 ] 
dist 84=[-2.7733618370387717857 ,1.9267900038529720476 ] 
dist 85=[-2.2248946189120064545 ,2.3105511010246287518 ] 
dist 86=[-2.1159589774511135855 ,2.5733323316083055739 ] 
dist 87=[-1.9665958266055288746 ,2.7972950815459509348 ] 
dist 88=[-1.9178927625987719218 ,3.0262356010409619259 ] 
dist 89=[-.91293718274888617817,3.2296885915514817636 ] 
dist 90=[-.78315152293388673088,3.3519885183589432524 ] 
dist 91=[-.49152300361433826165,3.4380776376573838646 ] 
dist 92=[-.43085969174577037161,3.4970801394307468318 ] 
dist 93=[-.45516832290664492862,3.5340935510045216148 ] 
dist 94=[-.48316803524242207754,3.5367810556383747102 ] 
dist 95=[-.50108661424390061876,3.5164340188382682569 ] 
dist 96=[-.50981620815353534062,3.4959599689645659249 ] 
dist 97=[-.51468376222274597481,.601431021595349248  ] 
dist 98=[-.51720122180999351383,.4135088550930564872 ] 
dist 99=[-.51844832714259557709,.3810439809170737200 ] 
dist 100=[-.51823121757723732909,.3735643925336702868 ] 
dist 101=[-.8101780851781800609 ,-.42732019814293058185] 
dist 102=[-1.0431759776265920017 ,-.48224079930811584994] 
dist 103=[-1.2600449451930123538 ,-.59864295059282218314] 
dist 104=[-1.5109001986823725254 ,-.62002062807091924822] 
dist 105=[-1.7437825248731958321 ,-.7260248437253794685 ] 
dist 106=[-1.8889679882493686563 ,-.7434491304372350389 ] 
dist 107=[-1.9974022273335518920 ,-.7577840621177277000 ] 
dist 108=[-2.0836875251713898532 ,-.7465644865343856169 ] 
dist 109=[-2.1489004873416242096 ,-.7255791522355778359 ] 
dist 110=[-2.1732786708693277276 ,-.6946576621306167050 ] 
dist 111=[-2.1806106452021058449 ,-.6506199384969817939 ] 
dist 112=[-2.1778386407884567813 ,-.5773006375693941930 ] 
dist 113=[-1.4199204069133273690 ,-.4909494640340379364 ] 
dist 114=[-1.3484945463284275918 ,-.3949180206738265214 ] 
dist 115=[-1.1700860063342928711 ,-.2735746972238463119 ] 
dist 116=[-1.1393632539891951393 ,-.0862396146983930721 ] 
dist 117=[-.85955845240348659818,.10239999827662494642] 
dist 118=[-.80565361200017310362,.22894967402167029029] 
dist 119=[-.73185876853028671688,.33404231038676808978] 
dist 120=[-.70854196968277099378,.43708255241421053203] 
dist 121=[-.24842642616436946729,.57640261546236750184] 
dist 122=[-.19357447161930097133,.69971318486367780356] 
dist 123=[-.1510824213358038732 ,.79970542833478189722] 
dist 124=[-.14048933785197371974,.89370831732653355387] 
dist 125=[-.01664554167454140514,.97645759534461670418] 
dist 126=[.00159382931841268867,1.0315765279357534081 ] 
dist 127=[.03426132144418995455,1.0769568752788475927 ] 
dist 128=[.04132106084415707922,1.1208864743947000706 ] 
dist 129=[.05734084113492745997,1.1584286474319564474 ] 
dist 130=[.05637575373391203299,1.2543017252689608738 ] 
dist 131=[.04818902030507021401,1.3500532784821557634 ] 
dist 132=[.02803587368523558142,1.4466888106198376675 ] 
dist 133=[.00516112458229466443,1.5363620542325023946 ] 
dist 134=[-.07826090906013412954,1.6043321525975070503 ] 
dist 135=[-.16689864252800240098,1.6693402017247601668 ] 
dist 136=[-.25858419624826415311,1.7471917328051013807 ] 
dist 137=[-.34499869032915199173,1.8196024556585869733 ] 
dist 138=[-.41260988108555741843,1.8629000892781604964 ] 
dist 139=[-.47926883833267181217,1.8931009347895928539 ] 
dist 140=[-.56188560037688503797,1.9132539792436408654 ] 
dist 141=[-.64007689234238514113,1.9253523783022715334 ] 
dist 142=[-.68908219756386064083,1.9234130403616186095 ] 
dist 143=[-.9239837047926933344 ,1.9138510369265347642 ] 
dist 144=[-1.4332788194737362128 ,1.9052129213719416624 ] 
dist 145=[-1.9374255878616815977 ,1.8453028594798398486 ] 
dist 146=[-2.2614744985446053803 ,1.8265811224987483587 ] 
dist 147=[-2.5150640156013206237 ,1.7859707524110624592 ] 
dist 148=[-2.7381354413338755894 ,1.7702840998901144582 ] 
dist 149=[-2.9240339050016454866 ,1.6881772950286758212 ] 
dist 150=[-3.0293350026177877316 ,1.6682162379023031926 ] 
dist 151=[-3.0955893796624537038 ,1.6058257442418371989 ] 
dist 152=[-3.1257272024805011862 ,1.5922878309055061091 ] 
dist 153=[-3.1381695652436740562 ,1.3951932079611182633 ] 
dist 154=[-3.1338331295873037171 ,1.3605011006115965767 ] 
dist 155=[-3.1164101139681470406 ,1.2717305687190727188 ] 
dist 156=[-3.1049142869022753211 ,1.2507153496159877247 ] 
dist 157=[-3.0261522154206311222 ,1.0949879167822281764 ] 
dist 158=[-3.0034882195655093199 ,1.0618027031838613380 ] 
dist 159=[-2.9147421185822677470 ,1.0070152323548664007 ] 
dist 160=[-2.9001248952348164790 ,.99143261476681241936] 
dist 161=[-.53966013018639341864,.97770799048927150957] 
dist 162=[-.53146601466236537454,1.2994570639362943245 ] 
dist 163=[-.51295136453363839165,1.5581524922853075328 ] 
dist 164=[-.50649686572169341272,1.8545949011242449462 ] 
dist 165=[-.04232319780562515740,2.1756717543838455709 ] 
dist 166=[-.00219802889108926641,2.3946571564044082184 ] 
dist 167=[.09124623048336750276,2.5803711867372310796 ] 
dist 168=[.10492677988870574249,2.7687281123682267229 ] 
dist 169=[.0546523389274937740 ,2.9354607567221949472 ] 
dist 170=[.0102477114210422642 ,3.0349136489189747056 ] 
dist 171=[-.0345052197027459967 ,3.1039424311196638298 ] 
dist 172=[-.0913097082482129926 ,3.1493082017348413012 ] 
dist 173=[-.1457221247292963462 ,3.1758919895269822790 ] 
dist 174=[-.1809348307585654059 ,3.1768303388770967851 ] 
dist 175=[-.2087630053319875083 ,3.1533869533013962805 ] 
dist 176=[-.2337205695281056007 ,3.1372311671583324206 ] 
dist 177=[-.2548796765982022978 ,1.5931382265396550417 ] 
dist 178=[-.34950762097587295536,1.4517097409514995819 ] 
dist 179=[-.63284592471652385912,1.1145800963623325199 ] 
dist 180=[-.91745919779206744598,1.0564301802217769815 ] 
dist 181=[-1.1803929546346485723 ,.58506157411063401402] 
dist 182=[-1.3772508592739454616 ,.49879512780774964144] 
dist 183=[-1.5630009041689699690 ,.36659216349526772091] 
dist 184=[-1.7816242624246895428 ,.33197042426173000532] 
dist 185=[-1.9827296947311835304 ,.16233271015345959891] 
dist 186=[-2.0986000518554575176 ,.15176927151532745005] 
dist 187=[-2.1739824680691480948 ,.13237343600229922748] 
dist 188=[-2.2135806527420240347 ,.12764604399627836058] 
dist 189=[-2.2375219462155873192 ,.05432571659600279952] 
dist 190=[-2.2504497568005478237 ,.04417074809576719840] 
dist 191=[-2.2577577227293326095 ,.07057841421285866806] 
dist 192=[-2.2592844810286383348 ,.1173905445826144905 ] 
dist 193=[-.70634842657953753003,.16636483751006667467] 
dist 194=[-.70387792611113553285,.32040765362286239422] 
dist 195=[-.70951326975058738786,.54124096228923194342] 
dist 196=[-.72769861127609359736,.7657216273304874149 ] 
dist 197=[-.75253487212416896564,.9748127484658341933 ] 
dist 198=[-.78469923478704617784,1.1342572035057783609 ] 
dist 199=[-.82833805660089282202,1.2875506826993570924 ] 
dist 200=[-.89894524196151719774,1.4721064796065455168 ] 
dist 201=[-.97392193846427385213,1.6440512306128064237 ] 
dist 202=[-1.0349895338009482794 ,1.7470391148079041534 ] 
dist 203=[-1.0974454025865765775 ,1.8190362581396850717 ] 
dist 204=[-1.1779570576250909140 ,1.8673576388893967340 ] 
dist 205=[-1.2637111205111366450 ,1.9003477741978087591 ] 
dist 206=[-1.3470771398304905613 ,1.9111864409472669811 ] 
dist 207=[-1.4444853780149712227 ,1.9102345131198564575 ] 
dist 208=[-1.5862513667247203734 ,1.9048469638665809759 ] 
dist 209=[-1.7245451875443316322 ,2.2440118153369157987 ] 
dist 210=[-1.8081020080513060920 ,2.4624128686349268668 ] 
dist 211=[-1.8673859759020402748 ,2.6234414484304997098 ] 
dist 212=[-1.9088551039864662649 ,2.7478445439863731071 ] 
dist 213=[-1.9355847243400641353 ,2.8430852676592484912 ] 
dist 214=[-1.9409184898494445807 ,2.8877785413602509115 ] 
dist 215=[-1.9293189068003671472 ,2.9058224355477979771 ] 
dist 216=[-1.9271691956936220059 ,2.9053220970090979942 ] 
dist 217=[-1.8100600490898074453 ,2.6986298300299912070 ] 
dist 218=[-1.7859434446764195601 ,2.6579430970818315350 ] 
dist 219=[-1.7177438168794537858 ,2.5841480023227831398 ] 
dist 220=[-1.6987115819298859691 ,2.5607756475959769776 ] 
dist 221=[-1.5516846129461786635 ,2.4604618888415254195 ] 
dist 222=[-1.5444018091823850714 ,2.4315584552784232609 ] 
dist 223=[-1.5370925199590646255 ,2.3619230757777940967 ] 
dist 224=[-1.5293097675151305892 ,2.3353427623990016078 ] 
dist 225=[-.98289683543399962774,.89793604226141364344] 
dist 226=[-.97730328378895432509,.89103443567934763117] 
dist 227=[-.95675188567973302806,.86898431452506812066] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 0, 2, 2, 0, 2] 
dist 0=[62.602365069988996810  ,62.602365069988996810  ] 
dist 1=[61.856762412293246072  ,63.043626402706564586  ] 
dist 2=[60.744406550076238152  ,63.321554766346562861  ] 
dist 3=[58.838656761496806560  ,63.415001818945060540  ] 
dist 4=[56.565034123340671423  ,63.391075730760002804  ] 
dist 5=[53.983752880519884330  ,63.300146755561626409  ] 
dist 6=[50.678416145253338629  ,62.916886012065780024  ] 
dist 7=[45.513644212718819260  ,62.753606269000385994  ] 
dist 8=[40.270956176180574453  ,62.148661444684657778  ] 
dist 9=[36.654409045743763778  ,61.952787805451312896  ] 
dist 10=[33.530435690284701589  ,60.149704243088235953  ] 
dist 11=[30.254314621941289051  ,59.673674101766901510  ] 
dist 12=[27.123563617169202248  ,59.293569020935316843  ] 
dist 13=[24.579779702905559369  ,59.024725817514035034  ] 
dist 14=[21.973088577842223067  ,52.031079006772698331  ] 
dist 15=[18.590616530931235918  ,50.751505219092069259  ] 
dist 16=[15.289108507295803151  ,43.792705707377032170  ] 
dist 17=[13.005418961175011493  ,30.743360837362337491  ] 
dist 18=[11.023263346199079030  ,28.528429895432350974  ] 
dist 19=[8.9254557493576616429 ,23.427266610805553904  ] 
dist 20=[6.9040233365037184621 ,22.583153889959251273  ] 
dist 21=[5.2262744413455208665 ,17.156848581487977214  ] 
dist 22=[3.4706568063604305218 ,14.961023638472500059  ] 
dist 23=[1.1369512001555055789 ,14.351157999506744990  ] 
dist 24=[-1.1150881894775660095 ,13.477955181361354577  ] 
dist 25=[-2.5446776925838293737 ,13.266866078259134588  ] 
dist 26=[-3.6545784936225806185 ,5.5188024208018723744 ] 
dist 27=[-5.3360353090108449533 ,4.0321905112007415566 ] 
dist 28=[-7.2354222655917071258 ,3.7319937958485719532 ] 
dist 29=[-9.0539638257043919489 ,.71765479929307875873] 
dist 30=[-10.689892501530799577  ,.26314180531931102963] 
dist 31=[-11.859895607739297282  ,-1.3679624473860383096 ] 
dist 32=[-12.917797987074044063  ,-3.6801312369933810584 ] 
dist 33=[-14.106195828116572455  ,-4.4058731334572981219 ] 
dist 34=[-15.184400612521164287  ,-4.7490870081372392753 ] 
dist 35=[-15.802203742970822619  ,-4.6891943984239353616 ] 
dist 36=[-16.204888136234291809  ,-4.4549730430888245149 ] 
dist 37=[-16.423738964094805059  ,-3.9259133696209798021 ] 
dist 38=[-16.543785861007612998  ,-3.2511258656267538546 ] 
dist 39=[-16.551606594880472386  ,-2.4348967900210269172 ] 
dist 40=[-16.495526744942510214  ,-1.3603259916169670746 ] 
dist 41=[-16.441447433316979480  ,.34582373634872152098] 
dist 42=[-14.115588594468594542  ,3.3107823612897578795 ] 
dist 43=[-13.718017726759394021  ,5.3314967419480507106 ] 
dist 44=[-13.570479715838511118  ,6.9944499462365007202 ] 
dist 45=[-12.818391662545237730  ,8.6011060905293101837 ] 
dist 46=[-12.641123393076103670  ,10.046632111880747854  ] 
dist 47=[-12.243964542578044717  ,11.066821739955717535  ] 
dist 48=[-12.109694240142447607  ,11.970150058103843400  ] 
dist 49=[-6.2306702086931581904 ,12.949596365621108715  ] 
dist 50=[-5.6258745530887126539 ,13.823454426201757192  ] 
dist 51=[-4.2866592072216241470 ,14.305442355831275485  ] 
dist 52=[-3.9843110866972468042 ,14.592581275715888050  ] 
dist 53=[-2.3968036204738442096 ,14.688672766264831970  ] 
dist 54=[-2.1108369502858688803 ,14.703670312775747316  ] 
dist 55=[-1.4876391194601222886 ,14.667259018545609813  ] 
dist 56=[-1.3401890594510927198 ,14.586535080829109736  ] 
dist 57=[-.0991121357112870476 ,14.526284506238426541  ] 
dist 58=[.02402568062770701444,10.462525174115545031  ] 
dist 59=[-.24906739172182428213,10.006984236511554916  ] 
dist 60=[-.49943046370102534953,8.8996873008307695421 ] 
dist 61=[-.68324493593321969846,8.6811549552439508367 ] 
dist 62=[-1.2711632479175932885 ,7.0138103148023832433 ] 
dist 63=[-1.8326368890528451629 ,6.6893658283954321793 ] 
dist 64=[-2.3864683436368181675 ,5.4330020293828966379 ] 
dist 65=[-3.0732650740910819044 ,-.735849782404725807  ] 
dist 66=[-3.7235454001456499226 ,-.75710834947162573039] 
dist 67=[-4.1317129481374553311 ,-.72098530076385226063] 
dist 68=[-4.4399778535550919038 ,-.66010252762028116058] 
dist 69=[-4.6917192765718050246 ,-.56839459819427219726] 
dist 70=[-4.8873337300538125966 ,-.43687754227016788152] 
dist 71=[-4.9716905057534347281 ,-.21724144925315165557] 
dist 72=[-5.0092518750573555128 ,.00777262060404857306] 
dist 73=[-5.0181892914173526567 ,.16073789355133681403] 
dist 74=[-2.5966856014008106926 ,.28971018396235329895] 
dist 75=[-2.6101578505005942986 ,.41904775828062692775] 
dist 76=[-2.6065621530379175878 ,.53818717271712165313] 
dist 77=[-2.5877929886586403059 ,.62649043977980094052] 
dist 78=[-2.5770355865386495514 ,.85962004151274440395] 
dist 79=[-2.5247758106233545625 ,1.0903902575294481672 ] 
dist 80=[-2.5137268755348827766 ,1.3034523285146555239 ] 
dist 81=[-1.1784005280954661554 ,1.5473620219715610597 ] 
dist 82=[-1.0527813079953507446 ,1.7729832198297131910 ] 
dist 83=[-.77047969770881347911,1.9131074371686143875 ] 
dist 84=[-.71067435173210005611,2.0171524653490188446 ] 
dist 85=[-.36783074457102731287,2.0988691631968779769 ] 
dist 86=[-.33213579933778423649,2.1598252159919504156 ] 
dist 87=[-.32801278322474329648,2.1810681172586688855 ] 
dist 88=[-.14869887912632612832,2.1860272944002084393 ] 
dist 89=[.11737403975325520672,2.1820114259941054467 ] 
dist 90=[-.12298407414990403139,2.1651464796486570518 ] 
dist 91=[-.32791265984240333084,2.2375597936941658742 ] 
dist 92=[-.49874222758301316445,2.2730850101456598423 ] 
dist 93=[-.66699814397332868033,2.2929678418268083073 ] 
dist 94=[-.8201118260720641765 ,2.3029720402833062151 ] 
dist 95=[-.93054615735106536084,2.3076541148540174679 ] 
dist 96=[-1.0305193210924349290 ,2.3062811119034795289 ] 
dist 97=[-1.1419010810908874153 ,1.2894282480897653204 ] 
dist 98=[-1.2436661678240357460 ,.93954516604776310424] 
dist 99=[-1.3052802040237671508 ,.94294776803203974089] 
dist 100=[-1.3490420256169815500 ,.94418250863649067688] 
dist 101=[-1.3796022656162892715 ,.9419378549863132486 ] 
dist 102=[-1.3994647458921408488 ,.93672718828640718436] 
dist 103=[-1.4262620310526924400 ,.93324080969498045454] 
dist 104=[-1.6329485393891204816 ,.50090043581836287305] 
dist 105=[-1.8270858288153426191 ,.49052903038266764612] 
dist 106=[-1.9461800662293259662 ,.18942424384235621357] 
dist 107=[-2.0329034936982820721 ,.16962244886129342326] 
dist 108=[-2.0979208164987607806 ,.02032745092034116834] 
dist 109=[-2.1439271907675409351 ,-.00602442018199286126] 
dist 110=[-2.1550752453142277272 ,.07581064972476523977] 
dist 111=[-2.1538967752868784771 ,.21269644827157060373] 
dist 112=[-2.1527053327605678862 ,.45008313330371972889] 
dist 113=[-2.0355422991539417059 ,.86408659702662879148] 
dist 114=[-2.0109970487141255348 ,1.1328261613334503595 ] 
dist 115=[-1.9361901483583614380 ,1.3459608843888828413 ] 
dist 116=[-1.9182219923023185761 ,1.5381751581895464527 ] 
dist 117=[-1.7437344713964885560 ,1.7016346520065890252 ] 
dist 118=[-1.7037031339600683520 ,1.8000739048911187748 ] 
dist 119=[-1.6515158691169473561 ,1.8694682705790341221 ] 
dist 120=[-1.6309905871153521637 ,1.9170708439856961642 ] 
dist 121=[-1.1397063132244170528 ,1.9525060593421503799 ] 
dist 122=[-1.0726123092347405983 ,1.9733716554193880034 ] 
dist 123=[-.92743786570157251543,1.9874817606347459257 ] 
dist 124=[-.88629271958959603059,1.9959863060813230024 ] 
dist 125=[-.71759594762382431158,2.0002118005119408658 ] 
dist 126=[-.68497685076955699379,1.9972641692187524810 ] 
dist 127=[-.60257979084629479666,1.9885264549452281685 ] 
dist 128=[-.58888742804530232   ,1.9795005379456685266 ] 
dist 129=[-.13477033786384519474,.8376415507091762286 ] 
dist 130=[-.14427396616952140603,.84795093539731864119] 
dist 131=[-.2280462421595382829 ,.84960902865561268975] 
dist 132=[-.44619036456717307681,.84054297745416271024] 
dist 133=[-.6457920928766415152 ,.83535257614966058726] 
dist 134=[-.79187407826242987256,.82931749520262469104] 
dist 135=[-.92639292308040791555,.82482574434563984341] 
dist 136=[-1.0798797717043222082 ,.57937063026463729905] 
dist 137=[-1.2217269463949982375 ,.60807394562517492589] 
dist 138=[-1.3098192060660340790 ,.63870289264823357975] 
dist 139=[-1.3752146394305020058 ,.66099289938328520511] 
dist 140=[-1.4265256849970764078 ,.67742810577699661045] 
dist 141=[-1.4647180967136782563 ,.68469720784399598884] 
dist 142=[-1.4777838317429961903 ,.68681235514195837214] 
dist 143=[-1.4805509939436514389 ,.68623150800473164612] 
dist 144=[-1.4776685718632531531 ,.6278477868170325431 ] 
dist 145=[-.93372621995421382365,.61730041605199313536] 
dist 146=[-.8828507311997637487 ,.59748009624848897673] 
dist 147=[-.80935451076364690025,.59136329381122043696] 
dist 148=[-.8145521428983858613 ,.56538641361133816454] 
dist 149=[-.81475373927417138395,.55838858862131047479] 
dist 150=[-.80567663186447742179,.54138269325728622638] 
dist 151=[-.80387087542983369558,.53503814210076084068] 
dist 152=[-.43381278081508975433,.31394403077688948492] 
dist 153=[-.11385891831700543097,.43758611292854465308] 
dist 154=[-.07396353916224653212,.51809451031120694806] 
dist 155=[.01637101066899345841,.58224705423493261045] 
dist 156=[.03207837336501438888,.64065472858417062757] 
dist 157=[.13969868394157431836,.69076182403604945174] 
dist 158=[.15760753921427754652,.72181001024207615419] 
dist 159=[.19051187410246648065,.74480094895294567808] 
dist 160=[.19726246103495455133,.76277816745043226792] 
dist 161=[.32511940198706268431,.77648695755433912173] 
dist 162=[.28625580771943876041,.8276452240014461056 ] 
dist 163=[.22112616625808371972,.88769972136074278285] 
dist 164=[.14426504040131354539,.94913882120059680268] 
dist 165=[.05860564691504919805,1.0066617344755902288 ] 
dist 166=[-.04972350280514203970,1.0510908161250486591 ] 
dist 167=[-.21701265994013565151,1.0943739993361574722 ] 
dist 168=[-.38421397257113247533,1.1473236812153045895 ] 
dist 169=[-.4921922578114062158 ,1.1971258013732795005 ] 
dist 170=[-.57723981986088739314,1.2278503373230177010 ] 
dist 171=[-.65297076833680034083,1.2504357720431589540 ] 
dist 172=[-.71671950323620903078,1.2677643637264834431 ] 
dist 173=[-.75396986088319104074,1.2803470990990680883 ] 
dist 174=[-.77886110452837532311,1.2839968521764580477 ] 
dist 175=[-.79330859049522714481,1.2817863817559179222 ] 
dist 176=[-1.0303219142454378578 ,1.2778929302243584933 ] 
dist 177=[-1.3701687848892303683 ,1.2572418394086969602 ] 
dist 178=[-1.5881929052400284344 ,1.2477946139321556794 ] 
dist 179=[-1.7583248187874283959 ,1.2281710450037951413 ] 
dist 180=[-1.9071218715996866568 ,1.2198012761611865680 ] 
dist 181=[-2.0304825344486323973 ,1.1735600457540222986 ] 
dist 182=[-2.0991450335298733763 ,1.1618607096550635472 ] 
dist 183=[-2.1407683007660101956 ,1.1215140084843784671 ] 
dist 184=[-2.1562665170153895540 ,1.1142974312955006085 ] 
dist 185=[-2.1597731040522834296 ,.99161456156970941575] 
dist 186=[-2.1535597871925169751 ,.96936324063040469802] 
dist 187=[-2.1393700016967527699 ,.91190105011170896152] 
dist 188=[-2.1305389633160494000 ,.8977986838629423365 ] 
dist 189=[-2.0728695014031130728 ,.79444006067332279344] 
dist 190=[-2.0567062492529068272 ,.77210598609894311503] 
dist 191=[-1.9940597273305573838 ,.73491321857773378689] 
dist 192=[-1.9840772313477172570 ,.72558514904300290437] 
dist 193=[-.99223600971638634556,.81329975968479041701] 
dist 194=[-1.0667053294028221120 ,.94982203769089637723] 
dist 195=[-1.1478668875787982276 ,1.1318517077301701076 ] 
dist 196=[-1.2269192367491627229 ,1.3058880474729863502 ] 
dist 197=[-1.2929747369137546348 ,1.5275975431049462321 ] 
dist 198=[-1.3620278951378986632 ,1.6784857570441650713 ] 
dist 199=[-1.4530380477515086204 ,1.8060994031829023725 ] 
dist 200=[-1.5379529421656571495 ,1.9349658029645571735 ] 
dist 201=[-1.5826916798062203102 ,2.0488397460862038048 ] 
dist 202=[-1.6064793182400558825 ,2.1166470926064233805 ] 
dist 203=[-1.6114189308530593472 ,2.1635674894503129951 ] 
dist 204=[-1.6011315964816480954 ,2.1941201459777092911 ] 
dist 205=[-1.5929000458932408335 ,2.2117459552831798567 ] 
dist 206=[-1.5819780731202951526 ,2.2120976538583572389 ] 
dist 207=[-1.5737183257342473754 ,2.1951768258103036434 ] 
dist 208=[-1.2998620436165337248 ,2.1837785344814094308 ] 
dist 209=[-1.2586556679533888179 ,1.1029375028660230272 ] 
dist 210=[-1.1746050625884392106 ,1.0039459093063530685 ] 
dist 211=[-1.1501753665701774007 ,.87399964641596495305] 
dist 212=[-1.0495968062115168887 ,.79838243519550908064] 
dist 213=[-1.0269376360839606049 ,.7795758531629459416 ] 
dist 214=[-.98810975376718690129,.74624970145320490219] 
dist 215=[-.97815552894701590292,.73703097531536634566] 
dist 216=[-1.0289233769857977456 ,.22244204484120798568] 
dist 217=[-1.1916845173148123619 ,-.19054899641769781003] 
dist 218=[-1.2912134178387747115 ,-.24325051345064901554] 
dist 219=[-1.3632846166097608929 ,-.22603505500634091468] 
dist 220=[-1.4165166139389809370 ,-.13827240099842401277] 
dist 221=[-1.4560136287093208534 ,-.06678702184213670475] 
dist 222=[-1.4732950135870530076 ,.00632733820791005531] 
dist 223=[-1.4785959548744139896 ,.10058576673345621622] 
dist 224=[-1.4769781274371760076 ,.1915682297979487077 ] 
dist 225=[-.47995019104580537764,.25161293013654030879] 
dist 226=[-.47606511424958681741,.30037140703191122359] 
dist 227=[-.47826930119296064638,.34632995134929386543] 
dist 228=[-.48937247073727799307,.38684707391684099504] 
dist 229=[-.50533089643004351011,.41389713288125872476] 
dist 230=[-.52690183163375746651,.43619489284888015037] 
dist 231=[-.55667849588746057355,.45775064528407544691] 
dist 232=[-.60536920726624317974,.47700444314575965756] 
dist 233=[-.65726497174118704119,.49011929062312240072] 
dist 234=[-.69982588651400244726,.50120483286071204656] 
dist 235=[-.74361682510755848904,.51236695656268093082] 
dist 236=[-.80041743982500610052,.58893839761426677432] 
dist 237=[-.8610909533183235894 ,.74681327075496651814] 
dist 238=[-.92032981578240727263,.89649404894363926199] 
dist 239=[-.98973948612790349659,1.0685579772553573161 ] 
dist 240=[-1.0909829146626590060 ,1.3157253369424517704 ] 
dist 241=[-1.1898441355532047121 ,1.5571098118133704356 ] 
dist 242=[-1.2497506048849847874 ,1.7061053259016343421 ] 
dist 243=[-1.2924675155918017750 ,1.8156839718342135106 ] 
dist 244=[-1.3227593319863968914 ,1.8998270267126976576 ] 
dist 245=[-1.3426641265526617234 ,1.9640544057998470522 ] 
dist 246=[-1.3468043176204767444 ,1.9941848754327062263 ] 
dist 247=[-1.3398833519049219446 ,2.0060998628766161887 ] 
dist 248=[-1.3384647767434561724 ,2.0057520365055676401 ] 
dist 249=[-1.2590252274352508103 ,1.8573418875608146157 ] 
dist 250=[-1.2425115568836299565 ,1.8285965931101977417 ] 
dist 251=[-1.1960213410251609374 ,1.7764677806178064495 ] 
dist 252=[-1.1826317589095591678 ,1.7600943530539979222 ] 
dist 253=[-1.0825435348636759362 ,1.6904102966088469721 ] 
dist 254=[-1.0593218577902791533 ,1.6703090039843963807 ] 
dist 255=[-.94791055100340199639,1.6226489695598142101 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 2, 2, 1, 1, 2] 
dist 0=[52.590108807639541292  ,52.590108807639541292  ] 
dist 1=[51.517712961054317683  ,53.298381306601573080  ] 
dist 2=[49.970700629377689482  ,53.820993314960819421  ] 
dist 3=[47.367194229930770931  ,54.151921114791122776  ] 
dist 4=[44.663357856902284332  ,54.406345593364096217  ] 
dist 5=[42.715671822312974894  ,54.623194512213456004  ] 
dist 6=[40.944838432732806399  ,54.751536801667466783  ] 
dist 7=[38.947094831449342440  ,54.752945361594505754  ] 
dist 8=[36.950788594513974064  ,54.366457801307125849  ] 
dist 9=[35.185546818648216740  ,53.086353923673608200  ] 
dist 10=[33.246975834069666592  ,52.762361034027184390  ] 
dist 11=[30.558199853914061242  ,52.211563439780600965  ] 
dist 12=[27.851421802166729698  ,52.033382952689635076  ] 
dist 13=[25.840788029422853019  ,51.333127829122469195  ] 
dist 14=[23.949204887404386990  ,51.112495230364339366  ] 
dist 15=[21.717619496119077613  ,50.632617930616218977  ] 
dist 16=[19.429232410892208034  ,49.787272171755230050  ] 
dist 17=[17.310440645246999176  ,33.803583102611236426  ] 
dist 18=[14.320896006626469622  ,32.337819040538161155  ] 
dist 19=[11.456941503086552764  ,28.808316075036294737  ] 
dist 20=[8.0546206428151224676 ,28.283327409460724962  ] 
dist 21=[5.8176861968038620900 ,23.216183353036012368  ] 
dist 22=[3.0378126019952463640 ,22.282984533848871430  ] 
dist 23=[.8752720837850243504 ,21.149841711554282923  ] 
dist 24=[-.99670032584703865479,20.902053918952979994  ] 
dist 25=[-2.9711414591142582093 ,13.247842354424971980  ] 
dist 26=[-4.8708787644567222905 ,12.309596249478775320  ] 
dist 27=[-6.4451375788494570379 ,10.349708573640397106  ] 
dist 28=[-8.0913523537832260006 ,9.8668424935860057846 ] 
dist 29=[-10.279860629688654228  ,7.9927312270236889196 ] 
dist 30=[-12.375675900421235397  ,7.6392612192507266520 ] 
dist 31=[-13.651812438734986827  ,7.0075869636966703340 ] 
dist 32=[-14.581377779055718642  ,6.8752047393038447545 ] 
dist 33=[-15.292016809133817867  ,-1.5851966056983390249 ] 
dist 34=[-15.833471326853024256  ,-2.3116859587361117362 ] 
dist 35=[-16.086617493808214788  ,-3.3401729095244926510 ] 
dist 36=[-16.195358679682522713  ,-2.7181331746194299115 ] 
dist 37=[-16.194744586401829870  ,-2.2761796008692916409 ] 
dist 38=[-15.305841687110144469  ,-1.8851764698433463936 ] 
dist 39=[-15.126764948160747445  ,-1.4656746123112148515 ] 
dist 40=[-14.779847645377539921  ,-1.0632225129331264441 ] 
dist 41=[-14.665670379563805157  ,-.73990717283560349578] 
dist 42=[-14.149925618363657503  ,-.41424008663087552047] 
dist 43=[-14.402252486996220666  ,-.00213926767340183558] 
dist 44=[-14.614963139147662951  ,.39141540854899964694] 
dist 45=[-14.744836498655522645  ,.64319690134800222706] 
dist 46=[-14.760139265326369412  ,.83848037767676429015] 
dist 47=[-14.711602890396516965  ,2.4408638272892007452 ] 
dist 48=[-14.656983358597390464  ,4.0867571743933153984 ] 
dist 49=[-2.3931416103083611468 ,5.7115730973468344276 ] 
dist 50=[-.40355628742985347616,7.1981229273593250416 ] 
dist 51=[-.05858767879875220460,8.2922970778613029913 ] 
dist 52=[.64243427901494774395,9.3086281082570098430 ] 
dist 53=[.81563128868288978723,10.484627834114653536  ] 
dist 54=[1.1970649765008558733 ,11.561267390049884992  ] 
dist 55=[1.1408865798263535645 ,12.181052479356493651  ] 
dist 56=[1.0746861012523537794 ,12.585066813814795051  ] 
dist 57=[1.0024354428508709661 ,12.800449954056925363  ] 
dist 58=[.91256494581907152698,12.931960448360136095  ] 
dist 59=[.77601635033156258756,13.001224081352647130  ] 
dist 60=[.6352072293557131492 ,13.041594031115759882  ] 
dist 61=[.52828222139787373642,12.979287270751424143  ] 
dist 62=[-.29058826322315800596,1.9846864266224474151 ] 
dist 63=[-.88421345084097193459,1.9869428061895109803 ] 
dist 64=[-1.3676681612077945400 ,1.9806403383609629278 ] 
dist 65=[-1.8260612597726339187 ,1.9751949045303345040 ] 
dist 66=[-2.2324704056232379798 ,1.9427997912688654324 ] 
dist 67=[-2.5085768359305039728 ,1.9366390502883345740 ] 
dist 68=[-2.7418333887444338444 ,1.8080918180553291676 ] 
dist 69=[-2.9773545990024481965 ,1.7819366607597382103 ] 
dist 70=[-3.1865156379276492648 ,1.7140024854357176380 ] 
dist 71=[-3.3146125437683736246 ,1.6922673690155164458 ] 
dist 72=[-3.4078812143735958278 ,1.5596987298512621432 ] 
dist 73=[-3.4780469268675585590 ,1.5286230706478038069 ] 
dist 74=[-3.5280585853609372268 ,1.4710928207428524072 ] 
dist 75=[-3.5408976513029025011 ,1.4539843699938329602 ] 
dist 76=[-3.5333851433795088594 ,1.1051615511626450874 ] 
dist 77=[-3.5212690555861291210 ,1.0546785726731242123 ] 
dist 78=[-2.4182567990644118498 ,.93552858777184935403] 
dist 79=[-2.4086977399191908030 ,.90717324433770002677] 
dist 80=[-2.3795715151882934390 ,.73357053168194001535] 
dist 81=[-2.3648758315962351605 ,.69880074262277537755] 
dist 82=[-2.3225056345196352467 ,.63212934684178575725] 
dist 83=[-2.3026247683582576417 ,.8172496853079276816 ] 
dist 84=[-.19525159204210577056,1.0661707588689531952 ] 
dist 85=[-.15874156370760535463,1.3706714108852147765 ] 
dist 86=[.41675911670820235911,1.6565485548298512117 ] 
dist 87=[.49281903469086831081,1.8311927174264566114 ] 
dist 88=[.63359923968849858898,1.9573716113124317129 ] 
dist 89=[.66363739053978795484,2.0499438174767334409 ] 
dist 90=[.65648211619148373312,2.1198072795596419387 ] 
dist 91=[.61939679421291118119,2.1554147875765072952 ] 
dist 92=[.57444850955496571881,2.1726763640165742865 ] 
dist 93=[.52963937767212401365,2.1712649256442533889 ] 
dist 94=[.40664377846113711845,1.9730124127485652918 ] 
dist 95=[.21765427298177925309,2.0215703399357567289 ] 
dist 96=[.05441896551264346295,2.0564647455467302904 ] 
dist 97=[-.11559792388799743295,2.0658488770171132930 ] 
dist 98=[-.2763104778687643653 ,2.0633566879087033549 ] 
dist 99=[-.40245329063676473302,2.0553309350621848224 ] 
dist 100=[-.52705993095019709229,1.0804297387113129911 ] 
dist 101=[-.68166263961249622867,.99355325776321969834] 
dist 102=[-.82785072659302335484,.78114103236467750099] 
dist 103=[-.91890732107992635217,.74812796446457737546] 
dist 104=[-.98679708280012403627,.43560134150508468339] 
dist 105=[-1.0406016095749209074 ,.40498809559149696397] 
dist 106=[-1.0815896742700990637 ,.4596198049874663885 ] 
dist 107=[-1.0983580027865932190 ,.52036097036595709527] 
dist 108=[-1.1048364572560378833 ,.59698336216864955196] 
dist 109=[-1.1122159658295646585 ,.71493015983940893821] 
dist 110=[-1.2514487432778401082 ,.83196704120127284729] 
dist 111=[-1.3329971628646632220 ,.90495616651181500712] 
dist 112=[-1.3878858139857344608 ,.9593662689392283637 ] 
dist 113=[-1.4207508222696029002 ,1.0023158664504458028 ] 
dist 114=[-1.4424777923559446044 ,1.0348993783443418252 ] 
dist 115=[-1.4529183294792445680 ,1.0479751899002473797 ] 
dist 116=[-1.4571237713496208173 ,1.0526658398561338330 ] 
dist 117=[-1.4539464649797526440 ,1.0518207357595843450 ] 
dist 118=[-1.2429348931656862367 ,.99446358848686007015] 
dist 119=[-1.2105452812137410547 ,.9814502599040877201 ] 
dist 120=[-1.1520406573389661224 ,.95389951844017564128] 
dist 121=[-1.1361509888133673625 ,.94392715163276661476] 
dist 122=[-1.0795435937165734523 ,.8937814073187159262 ] 
dist 123=[-1.0626315899823235537 ,.86432941935943701022] 
dist 124=[-1.0399333517178058390 ,.73310515548026600599] 
dist 125=[-1.0305236149007391145 ,.66348478823104471639] 
dist 126=[-.93899037525001682068,.253078029549814006  ] 
dist 127=[-.96887696241419963896,.44603534110613384985] 
dist 128=[-.99880789175838847869,.6039027903622870081 ] 
dist 129=[-1.0251139691198893301 ,.75476014217428940695] 
dist 130=[-1.0537327959144506883 ,.88924398827217806533] 
dist 131=[-1.0928807176757626466 ,1.1247797240011389793 ] 
dist 132=[-1.1299150880973009939 ,1.4025209744386606818 ] 
dist 133=[-1.1501010681217603137 ,1.5779393258641286608 ] 
dist 134=[-1.1617402217237275554 ,1.7117006510588703693 ] 
dist 135=[-1.1646842901535986479 ,1.8232593876131215984 ] 
dist 136=[-1.1617708715500426211 ,1.9117888260366159650 ] 
dist 137=[-1.1584472477494033929 ,1.9536802845010900730 ] 
dist 138=[-1.1379188018947560842 ,1.9746041770401288751 ] 
dist 139=[-1.1334184062658838967 ,1.9794812767748107246 ] 
dist 140=[-1.0502507023840395510 ,1.9277652319166116353 ] 
dist 141=[-1.0342003657835439070 ,1.9111289913057949453 ] 
dist 142=[-.98500913210818585362,1.8804916298990674459 ] 
dist 143=[-.97673140340268408881,1.8685050837109250626 ] 
dist 144=[-.86533448998525852996,1.8070282143700960795 ] 
dist 145=[-.84086120249045934794,1.7899352676610698594 ] 
dist 146=[-.81715919547033680714,1.7355027054631047448 ] 
dist 147=[-.8091300002381922453 ,1.7209320866349852233 ] 
dist 148=[-.71907648488679650754,.22031240577437578451] 
dist 149=[-.8871297976154720529 ,.20573419071452188119] 
dist 150=[-1.0204710208275592002 ,-.05918680111928326500] 
dist 151=[-1.1810039736296683514 ,-.09216843135537562421] 
dist 152=[-1.3805596515862707604 ,-.16579625826263196114] 
dist 153=[-1.5161912339624602290 ,-.17817815562526178656] 
dist 154=[-1.6307217111179571424 ,-.26131117873283272731] 
dist 155=[-1.7461020259768131994 ,-.27454302462217590219] 
dist 156=[-1.8480616753747162849 ,-.2993359847261457401 ] 
dist 157=[-1.9090544677166359461 ,-.30423739852721719973] 
dist 158=[-1.9516096894440668485 ,-.33378258802325537961] 
dist 159=[-1.9800171235420920572 ,-.28681873176034895446] 
dist 160=[-1.9970968430222827453 ,-.22757570554205043475] 
dist 161=[-1.9975888507576223622 ,-.1646713501478055437 ] 
dist 162=[-1.9846810150134336432 ,-.10438338194275130835] 
dist 163=[-1.9732446468330466081 ,-.05557618054786987233] 
dist 164=[-.99027343129160559449,.08940223315384144166] 
dist 165=[-.90090672710563972156,.29117742652780305812] 
dist 166=[-.68740822421229709717,.4612796671552152392 ] 
dist 167=[-.65126254654748336621,.63216506286342863164] 
dist 168=[-.58869388270162959979,.79006997015802887664] 
dist 169=[-.6239613059906480662 ,.90839116925168954977] 
dist 170=[-.660378353380098158  ,1.0201468881363032059 ] 
dist 171=[-.69410884139308798676,1.1518609786110479993 ] 
dist 172=[-.73226124797031873916,1.2731445074265979801 ] 
dist 173=[-.78631572746028178522,1.3432911505742940765 ] 
dist 174=[-.83843894679201483158,1.3892762167238593363 ] 
dist 175=[-.86888680250628706644,1.4141757258700673348 ] 
dist 176=[-.88922119001789100697,1.4291258978646133193 ] 
dist 177=[-.90100116026475434934,1.4354219461165582877 ] 
dist 178=[-.90680933836364375444,1.4365720358260428443 ] 
dist 179=[-.9068091987672309075 ,1.4316843990732149983 ] 
dist 180=[-.89758106463108167166,1.3374196534497136980 ] 
dist 181=[-.89439977690508040959,1.3381052588622343508 ] 
dist 182=[-.82345905448299088137,1.2605015123469939369 ] 
dist 183=[-.81009566713363754501,1.2439173443543671322 ] 
dist 184=[-.77380250331318783484,1.2159216395119188060 ] 
dist 185=[-.86904512330235619295,1.2062956553846880520 ] 
dist 186=[-.96587329056554534823,1.1674059755213730091 ] 
dist 187=[-1.0804568738420664805 ,1.1550809665815173774 ] 
dist 188=[-1.1862151376774196343 ,1.1268203992983164586 ] 
dist 189=[-1.2478380300945664211 ,1.1159010223493959788 ] 
dist 190=[-1.2888163971469389164 ,.7268630057884994054 ] 
dist 191=[-1.3122207038734338859 ,.77425114316080261463] 
dist 192=[-1.3262846097249337023 ,.82457870018422840388] 
dist 193=[-1.3300021328401707140 ,.87329898039767832407] 
dist 194=[-1.3268456899563859638 ,.9300754860037486432 ] 
dist 195=[-1.3231005258571897268 ,1.0125391480764453732 ] 
dist 196=[-1.4397845685943275248 ,1.0929443438484430562 ] 
dist 197=[-1.5851899020426150315 ,1.1415090467731366953 ] 
dist 198=[-1.6931720791344443438 ,1.1759522014790483668 ] 
dist 199=[-1.7780301442292062683 ,1.2000250083423711628 ] 
dist 200=[-1.8434946731223569958 ,1.2155274890938197100 ] 
dist 201=[-1.8741110291147850385 ,1.2181655935251862686 ] 
dist 202=[-1.8871208495858155023 ,1.2113868495312467693 ] 
dist 203=[-1.8866601482723269965 ,1.2083390552997954743 ] 
dist 204=[-1.7702014924101050728 ,1.1419943111885094735 ] 
dist 205=[-1.7458685757505750253 ,1.1279666216169478383 ] 
dist 206=[-1.7015032567103030396 ,1.1014458939727480740 ] 
dist 207=[-1.6870066288760726228 ,1.1179845415224975304 ] 
dist 208=[-1.6227392367712741539 ,1.1310750707345715500 ] 
dist 209=[-1.6044511811451204771 ,1.1371915217545887838 ] 
dist 210=[-1.5575678442625841052 ,1.1393588788204000479 ] 
dist 211=[-1.5391942590111678154 ,1.1366965223098700458 ] 
dist 212=[-.16721026773846314907,.66964384472255789227] 
dist 213=[-.15382509275629227476,.7402281155863568736 ] 
dist 214=[.08836923179753472854,.80498728138003137356] 
dist 215=[.09488092781289109456,.84203866281706755566] 
dist 216=[.08362659887124281807,.86581995290574647417] 
dist 217=[.05660142167182402955,.87764170252790799922] 
dist 218=[.02157345049664245798,.88373638043546441401] 
dist 219=[-.02160553883168946005,.88467127684181800623] 
dist 220=[-.07894126791554660778,.88200384715573730798] 
dist 221=[-.17044298625840470572,.8789529637230279489 ] 
dist 222=[-.26245550730126773599,.41874456121304841559] 
dist 223=[-.36218243734229749774,.41897126983327171321] 
dist 224=[-.46074933634477155707,.43224718158594290401] 
dist 225=[-.5590884204855937586 ,.44933217571707618644] 
dist 226=[-.64953083956319433799,.46752032862376264851] 
dist 227=[-.71659644765036720082,.4851968077517820591 ] 
dist 228=[-.77925775954656967222,.50585156474532570031] 
dist 229=[-.85213081879668352879,.5359205668875870815 ] 
dist 230=[-.91873802776577604828,.56658480050026650056] 
dist 231=[-.95640364186488877512,.58961393924272157251] 
dist 232=[-.98001378683571722173,.6114178455022618051 ] 
dist 233=[-.99055075667095592156,.63719413640639325255] 
dist 234=[-.99496207675811747437,.6634915008812259405 ] 
dist 235=[-.99413537128466123683,.68737390428815143123] 
dist 236=[-.98931522273271462858,.71401583925114482444] 
dist 237=[-.98569383331613999578,.75132127080883745408] 
dist 238=[-1.0047129673415443282 ,.78713561668042172138] 
dist 239=[-1.1225299266699913532 ,.80782922947338013532] 
dist 240=[-1.2118680921833266990 ,.82136998433982599463] 
dist 241=[-1.2854620934740367870 ,.82865016030059365818] 
dist 242=[-1.3434583641591413284 ,.83133137296089164609] 
dist 243=[-1.3705732953324672622 ,.8405294179423977815 ] 
dist 244=[-1.3836752483394604842 ,.88279457149946043184] 
dist 245=[-1.3857702614803676267 ,.91906721728038110788] 
dist 246=[-1.3383357767005024006 ,.94922439883478951497] 
dist 247=[-1.3251760023778269591 ,.96709365219862926483] 
dist 248=[-1.3009455527356929903 ,.97934954674360814797] 
dist 249=[-1.2919634474528993172 ,.98711416283438154637] 
dist 250=[-1.2475893935202808117 ,.99137951059580688599] 
dist 251=[-1.2352414816830580771 ,.98967626278875920544] 
dist 252=[-1.1976874875904482762 ,.9841034507206984786 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 2, 1, 2] 
dist 0=[57.399979228423989473  ,57.399979228423989473  ] 
dist 1=[56.373899549337216521  ,58.179179071384769133  ] 
dist 2=[54.933264837970120222  ,58.633972833050161853  ] 
dist 3=[52.910084357732755789  ,58.939052438004195127  ] 
dist 4=[49.558014457749754994  ,59.120176121861041092  ] 
dist 5=[46.090337076037818482  ,59.181200305511233930  ] 
dist 6=[43.605550324765510219  ,59.149351992593440029  ] 
dist 7=[41.360598262833359112  ,58.794972186521098720  ] 
dist 8=[38.850503244836621984  ,57.861463322235376905  ] 
dist 9=[36.356439034808701308  ,57.057066778419478260  ] 
dist 10=[34.175394901323127710  ,56.659912784474996192  ] 
dist 11=[31.801532608663044340  ,56.059885812595546687  ] 
dist 12=[28.537309370332604364  ,55.841366056340472976  ] 
dist 13=[25.267007709839088743  ,55.183780875373995819  ] 
dist 14=[22.868712690638503982  ,54.934259960330253193  ] 
dist 15=[20.644405817575878295  ,53.828375435640038903  ] 
dist 16=[18.068588238575201478  ,51.679040873019549634  ] 
dist 17=[15.049130720710405565  ,33.673746142706948563  ] 
dist 18=[12.394958089130939025  ,31.914860152163950008  ] 
dist 19=[9.7139762095215442063 ,27.721195898009656099  ] 
dist 20=[6.2867668560790495526 ,27.098457458248627884  ] 
dist 21=[2.9652384594262737511 ,21.261733939592301855  ] 
dist 22=[.55002986628379547938,20.207861698466245951  ] 
dist 23=[-1.4032335646876502382 ,18.881036953388670675  ] 
dist 24=[-3.2421451447806656804 ,18.597186290928393431  ] 
dist 25=[-5.0531972264694383242 ,10.591843163122665999  ] 
dist 26=[-6.5477916136506705288 ,9.6297720393397406684 ] 
dist 27=[-8.0666982147403555042 ,7.5737381637628470070 ] 
dist 28=[-10.030796851798101726  ,7.1508528893816891470 ] 
dist 29=[-11.891446769855151966  ,5.0703848626624286752 ] 
dist 30=[-12.997372770952542982  ,4.7192045406234127387 ] 
dist 31=[-13.772705307813980527  ,4.0488736356937816513 ] 
dist 32=[-14.311798574534148185  ,3.9068903545131423540 ] 
dist 33=[-14.707985889745674679  ,-1.8349041675830361858 ] 
dist 34=[-14.911658798646116420  ,-2.3442890703573183943 ] 
dist 35=[-15.017031984368512299  ,-3.3367158270452108568 ] 
dist 36=[-15.019114567369618418  ,-1.9236550165221311865 ] 
dist 37=[-13.487565950676921030  ,-.03824801997337674902] 
dist 38=[-13.244405427119240959  ,1.2337904528464515244 ] 
dist 39=[-12.822719939536873505  ,2.2958150976926432955 ] 
dist 40=[-12.702580781276502919  ,3.3439194363934752165 ] 
dist 41=[-12.300606710617360602  ,4.2988706956100201945 ] 
dist 42=[-12.168099919689130833  ,4.9894900641182119512 ] 
dist 43=[-12.030334370556103791  ,5.6166876108628656270 ] 
dist 44=[-11.952580925654011210  ,6.3187620620610470221 ] 
dist 45=[-11.172073704547279840  ,6.9597512263123293778 ] 
dist 46=[-11.146432482456342313  ,7.3433156801422957902 ] 
dist 47=[-11.061333405944897889  ,7.6105798889164665203 ] 
dist 48=[-11.010979405985949381  ,7.7876494143178782405 ] 
dist 49=[.03296139963256071259,7.9003820540533039650 ] 
dist 50=[.12435537182182235453,7.9168882179197208636 ] 
dist 51=[.30633774980035615375,7.8840236470551387074 ] 
dist 52=[.34921222112334773322,7.8462738331708323090 ] 
dist 53=[.48362448760522603694,8.4489963353731934234 ] 
dist 54=[.50826414672349426783,9.1450902843178340069 ] 
dist 55=[.53673000874692860284,9.6680227285029203066 ] 
dist 56=[.5328581848078245696 ,10.091721080729129971  ] 
dist 57=[.51639101544501732057,10.419511922213689246  ] 
dist 58=[.48314978856753792594,10.559635226132120082  ] 
dist 59=[.43162478459306848395,10.616133970361089730  ] 
dist 60=[.34220096625560152211,10.610111211790666828  ] 
dist 61=[-.17453412444056406928,8.7737919103464942107 ] 
dist 62=[-.98672314321619851186,8.7991966826304193839 ] 
dist 63=[-1.7378297458033799486 ,8.7922058913645303183 ] 
dist 64=[-2.5164469154093804706 ,8.7629932411038717449 ] 
dist 65=[-3.2188821852143095628 ,3.2466884295783013421 ] 
dist 66=[-3.7171123745359845202 ,2.7857205895672914412 ] 
dist 67=[-4.1605055004173612481 ,1.7186514886773589294 ] 
dist 68=[-4.6442339999463887050 ,1.5311382639604874213 ] 
dist 69=[-5.0832354421816880589 ,.75732364893504052975] 
dist 70=[-5.3482037602954954637 ,.75785655538683731723] 
dist 71=[-5.5362401175583280585 ,.75743417054645179604] 
dist 72=[-5.6682977486467890839 ,.75558591605803694264] 
dist 73=[-5.7542933465027204233 ,.75290311195970051915] 
dist 74=[-5.7717590224288868374 ,.74948629520470531843] 
dist 75=[-5.7395161743891237051 ,.74375735611331080873] 
dist 76=[-5.7324524113747261371 ,.74080317000633254442] 
dist 77=[-5.3980090703050521316 ,.72448782571353498201] 
dist 78=[-5.5028295138355568899 ,.71874694002395086487] 
dist 79=[-5.5514076065136832572 ,.70559426066944126476] 
dist 80=[-5.5528515196899344060 ,.70010024879216922308] 
dist 81=[-1.7151348347419360096 ,.83229302879308261194] 
dist 82=[-1.5551844237386517631 ,1.1863589059053885237 ] 
dist 83=[-1.3625704053340930989 ,1.5198644838687862717 ] 
dist 84=[-1.3165827551661445022 ,1.9114190047307297672 ] 
dist 85=[-.43972416221470619626,2.2766956814026029570 ] 
dist 86=[-.37798105995734273611,2.5054028484666791125 ] 
dist 87=[-.24528482572018263331,2.6773980057766317076 ] 
dist 88=[-.21466488630312324813,2.8164816018919080502 ] 
dist 89=[-.08500744418741958524,2.9235099011395100678 ] 
dist 90=[-.07147664259107595451,2.9676608759992635845 ] 
dist 91=[-.09211062070100485877,2.9845299235524734612 ] 
dist 92=[-.16467819871361422471,2.9826943108791508546 ] 
dist 93=[-.26478427678574716717,2.1939484949023713614 ] 
dist 94=[-.39524694219248118272,2.3866149798438256198 ] 
dist 95=[-.57253747146133720254,2.5837627377259629160 ] 
dist 96=[-.85939981771179116776,2.8384359362199100422 ] 
dist 97=[-1.1503646452551121450 ,3.0777395673840612417 ] 
dist 98=[-1.3440152258204314890 ,3.2135781372988794248 ] 
dist 99=[-1.5028965788274248232 ,3.2996703192593411268 ] 
dist 100=[-1.6551928648870364580 ,3.3404738312596846643 ] 
dist 101=[-1.7910280429889902375 ,3.3601623857550302625 ] 
dist 102=[-1.9883214442646963626 ,3.3619859134802447082 ] 
dist 103=[-2.2065660405068675515 ,3.3511651484531664234 ] 
dist 104=[-2.3917710634349627612 ,3.3394064917464718733 ] 
dist 105=[-2.5418697164150930650 ,2.8721431571639548493 ] 
dist 106=[-2.6200862761176090580 ,2.7992458777958915663 ] 
dist 107=[-2.6625161343635495583 ,2.6528276421470069878 ] 
dist 108=[-2.6704188661572232419 ,2.6097153954692063389 ] 
dist 109=[-2.6116532562955837124 ,2.4309478650562268810 ] 
dist 110=[-2.5918868691854178069 ,2.3890240427768141399 ] 
dist 111=[-2.5728026844513267299 ,2.2876221303430449816 ] 
dist 112=[-2.5562232740807339264 ,2.2523923001444286654 ] 
dist 113=[-2.5257084385014123969 ,1.4183981866488363078 ] 
dist 114=[-2.5060999843489352092 ,1.3801470258345158032 ] 
dist 115=[-2.4782542153452785631 ,1.2920342127343979685 ] 
dist 116=[-2.4635581581128763214 ,1.2640273730832906697 ] 
dist 117=[-2.6013908280284384431 ,.03350384610458762074] 
dist 118=[-2.7998942571369263898 ,.40727073632215179444] 
dist 119=[-2.9591056170061357441 ,.71705853636998265435] 
dist 120=[-3.1060070501417293931 ,1.0195867855142821963 ] 
dist 121=[-3.2315203860205829063 ,1.2935122704967370322 ] 
dist 122=[-3.3054023672464361760 ,1.4892095195171022259 ] 
dist 123=[-3.3555248634229626655 ,1.6646765084996991766 ] 
dist 124=[-3.3862432274680568893 ,1.8579108085425524563 ] 
dist 125=[-3.4021061533943511569 ,2.0339876017609754460 ] 
dist 126=[-3.3973833216204682916 ,2.1410144734723018207 ] 
dist 127=[-3.3728909141193719150 ,2.2177465358839280771 ] 
dist 128=[-3.3541911173822688744 ,2.2729734949429639064 ] 
dist 129=[-1.5093755490666904435 ,2.3100157097409629488 ] 
dist 130=[-1.3452683209275880105 ,2.3177164453876488588 ] 
dist 131=[-.96034553725106869759,2.3082049324551838393 ] 
dist 132=[-.89266453837006263935,2.3045957040061930662 ] 
dist 133=[-.37637011241269045596,1.4063946661363974682 ] 
dist 134=[-.28350672294255698209,1.6251129556252741744 ] 
dist 135=[-.1316865891796176159 ,1.8341994515293127309 ] 
dist 136=[-.11780966783740448161,2.0843430565387904860 ] 
dist 137=[-.31072557209789011808,2.3167542332062747278 ] 
dist 138=[-.45662717473400985146,2.4550983129017290598 ] 
dist 139=[-.59571597412020851773,2.5508114176215132406 ] 
dist 140=[-.76145892722949512528,2.6131474046716865248 ] 
dist 141=[-.91709556491731098481,2.6550689529252789557 ] 
dist 142=[-1.0158708086599693009 ,2.6693392310896958830 ] 
dist 143=[-1.0916972057053639436 ,2.6674289857882215749 ] 
dist 144=[-1.1557891570264072230 ,2.6611505762938571878 ] 
dist 145=[-1.2072518315155236525 ,.71790818246640495835] 
dist 146=[-1.2326978722356533102 ,.62207390877447375906] 
dist 147=[-1.2446962952480636777 ,.57652215410199448351] 
dist 148=[-1.2458568801235274311 ,.56233736930248327106] 
dist 149=[-1.4668212922035944785 ,.55221004830505701547] 
dist 150=[-1.6399906322350510591 ,.56084248236144918947] 
dist 151=[-1.7998236434700779238 ,.58279855650665317171] 
dist 152=[-1.9828618718865659887 ,.6286306541592182012 ] 
dist 153=[-2.1487096179512534908 ,.68120060353873182018] 
dist 154=[-2.2399650487561561606 ,.73003563870348488928] 
dist 155=[-2.2939051356828431422 ,.78539913269501684529] 
dist 156=[-2.3108901391729672579 ,.86401265768915537506] 
dist 157=[-2.3148881733500594464 ,.95137808321842774137] 
dist 158=[-2.3170175489568520972 ,1.0416551001468870752 ] 
dist 159=[-2.3181857437146472304 ,1.1511899671015974455 ] 
dist 160=[-2.3183447023410211473 ,1.3153798205379619957 ] 
dist 161=[-2.1947514922985281747 ,1.4776797538056666845 ] 
dist 162=[-2.3756842022660102169 ,1.5796748627391650761 ] 
dist 163=[-2.5063170338389991150 ,1.6568417628676524153 ] 
dist 164=[-2.6021467842000932705 ,1.7200945456376269104 ] 
dist 165=[-2.6734590484343689961 ,1.9833552364367538874 ] 
dist 166=[-2.7062806604469811404 ,2.2527709965009453663 ] 
dist 167=[-2.7171405841795123072 ,2.4592994173764203326 ] 
dist 168=[-2.7157641805404422854 ,2.6334587314459479577 ] 
dist 169=[-2.4733270978825111321 ,2.7731011895910413554 ] 
dist 170=[-2.4298509100801379011 ,2.8419349202122608644 ] 
dist 171=[-2.3501377621206652840 ,2.8775076164081983978 ] 
dist 172=[-2.3259789442986194536 ,2.8844610649311729953 ] 
dist 173=[-2.2264377202040461620 ,2.8272063060809900853 ] 
dist 174=[-2.1982480243722043544 ,2.8051845887869208304 ] 
dist 175=[-2.1350714504980680928 ,2.7681529203567127397 ] 
dist 176=[-2.1120753134690103160 ,2.7521985832835511713 ] 
dist 177=[-1.2430487897698242173 ,2.6737388987891686682 ] 
dist 178=[-1.2033875006427965598 ,2.6499945323099230130 ] 
dist 179=[-1.1649715514196604903 ,2.5773509755071867929 ] 
dist 180=[-1.1538176532282577355 ,2.5530480434483528393 ] 
dist 181=[-1.0378293912859829444 ,.06225784341344448750] 
dist 182=[-1.2611709729428942119 ,.08205342756172152039] 
dist 183=[-1.4374499129677961090 ,.11093034856478951157] 
dist 184=[-1.6213419536651786387 ,.15969562780312061315] 
dist 185=[-1.9137927322856708065 ,.21226431921762792646] 
dist 186=[-2.1141610581907673554 ,.25631123883580312082] 
dist 187=[-2.2850711603650411293 ,.3024693069216578715 ] 
dist 188=[-2.4600097610075002632 ,.36345541679298579762] 
dist 189=[-2.6155600065406536219 ,.42915156918167096891] 
dist 190=[-2.7091269224163984084 ,.49409537370242108064] 
dist 191=[-2.7750358887091583922 ,.57078661543693402377] 
dist 192=[-2.8202529526717038877 ,.68333951552781299434] 
dist 193=[-2.8486101071621943945 ,.79349240685165529264] 
dist 194=[-2.8507009799035018932 ,.86060891275089103429] 
dist 195=[-2.8349153922910591394 ,.90890418447013846781] 
dist 196=[-2.8194001818566452563 ,.94397970659505614027] 
dist 197=[-1.4452588561135239334 ,.97005916179295064067] 
dist 198=[-1.3202799441323193252 ,.98247022697962899231] 
dist 199=[-1.0248851789901717283 ,.98721351903320981855] 
dist 200=[-1.0221937300924105890 ,.98649521226336339134] 
dist 201=[-.88071525153276443826,1.1117434248985204788 ] 
dist 202=[-.8584608803621419054 ,1.2775882359824548742 ] 
dist 203=[-.81808220502192093267,1.4351272190038918281 ] 
dist 204=[-.80691172929548308258,1.6220879924374493192 ] 
dist 205=[-.76592228125111346288,1.7948984014685446194 ] 
dist 206=[-.75389747014649941347,1.8959901860499438059 ] 
dist 207=[-.73476174540357333755,1.9637063203240884021 ] 
dist 208=[-.72812058576010201126,2.0033780871446702289 ] 
dist 209=[.02620833578956482558,2.0282989371989884177 ] 
dist 210=[-.08210170182515185444,2.0371722988221394969 ] 
dist 211=[-.20179031484721836176,2.0359712794792818332 ] 
dist 212=[-.33651644777111606043,2.0302666107839524930 ] 
dist 213=[-.47027437404370949379,.78235927430931207284] 
dist 214=[-.58610075558766824263,.78688161968979818219] 
dist 215=[-.79273618970123086654,.80403570166055659855] 
dist 216=[-1.0019540404117082104 ,.83102608528411149984] 
dist 217=[-1.1947768235166155699 ,.86222147436599373743] 
dist 218=[-1.3384158611381310900 ,.89614852533135871643] 
dist 219=[-1.4732571045157968304 ,.93851445891932095589] 
dist 220=[-1.6309843418116858207 ,1.0033725196121835775 ] 
dist 221=[-1.7756028532507591234 ,1.0708490895023527532 ] 
dist 222=[-1.8581516372181888032 ,1.1236595765779207609 ] 
dist 223=[-1.9108827107936581449 ,1.1757396232997840841 ] 
dist 224=[-1.9365543625937050595 ,1.2403004929634015029 ] 
dist 225=[-1.9496252515368433790 ,1.3077847006972974161 ] 
dist 226=[-1.9520898072497297346 ,1.3715248713258886274 ] 
dist 227=[-1.9472509728403463666 ,1.4590762134888370814 ] 
dist 228=[-1.9311865372584806276 ,1.5729369013525478763 ] 
dist 229=[-2.1275604320740298893 ,1.6655215695037987438 ] 
dist 230=[-2.3571879603994886586 ,1.7136422344093104531 ] 
dist 231=[-2.5292716467278307494 ,1.7524857234185463421 ] 
dist 232=[-2.6673608212329399476 ,1.7789357913154208862 ] 
dist 233=[-2.7749390984210727845 ,1.7936639630348671370 ] 
dist 234=[-2.8253073288813955748 ,1.7949322711646285827 ] 
dist 235=[-2.8480669540416139719 ,1.7780824040450479250 ] 
dist 236=[-2.8473723542215223629 ,1.7732143465711512991 ] 
dist 237=[-2.7050102331354833868 ,1.6640052523690674785 ] 
dist 238=[-2.6721313944808589993 ,1.6419463508943657131 ] 
dist 239=[-2.6120762489624119895 ,1.5820756213749721154 ] 
dist 240=[-2.5915825630276334679 ,1.5604746478432023876 ] 
dist 241=[-2.4970595898931704684 ,1.4017886629084635242 ] 
dist 242=[-2.4703261856163387341 ,1.3662085402804575836 ] 
dist 243=[-2.3971147046958460869 ,1.3278444038809610422 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 2, 0, 0, 0, 2] 
dist 0=[59.902902385730611791  ,59.902902385730611791  ] 
dist 1=[59.558664329178791689  ,60.028631084679500723  ] 
dist 2=[58.792124223794674398  ,60.186370365709742076  ] 
dist 3=[57.247547887737673124  ,60.294313509963247957  ] 
dist 4=[55.318202406981528828  ,60.362712621852450630  ] 
dist 5=[53.015346657535599513  ,60.400304859638371412  ] 
dist 6=[49.994269063112734920  ,60.385145050073560624  ] 
dist 7=[45.197189105987531629  ,60.327982267948395336  ] 
dist 8=[40.303954374524359992  ,60.206015561692033053  ] 
dist 9=[36.898855806250500136  ,60.056420035862165133  ] 
dist 10=[33.926501000850893379  ,59.955492672098835143  ] 
dist 11=[30.760860938840662725  ,59.864119501641926065  ] 
dist 12=[27.706347827549772182  ,59.761216676230510394  ] 
dist 13=[25.177425861993149100  ,59.532832773072654688  ] 
dist 14=[22.046250220619974251  ,54.611759555785344928  ] 
dist 15=[19.070546019921933731  ,53.677052037772365376  ] 
dist 16=[15.654846933427679783  ,48.248143867419924513  ] 
dist 17=[12.782137070558209555  ,37.714965529908042491  ] 
dist 18=[9.1671409413885961238 ,35.915956383312994979  ] 
dist 19=[6.6525105309949701749 ,31.603336564389721760  ] 
dist 20=[4.4556498809104986066 ,30.958758105946475567  ] 
dist 21=[2.1091521431882232701 ,24.859728457553362337  ] 
dist 22=[-.16380167590293600488,23.747478958380789998  ] 
dist 23=[-2.0675655509810475603 ,22.360178141885101188  ] 
dist 24=[-4.0738528727400880139 ,22.051537957753596536  ] 
dist 25=[-6.7575113216159015366 ,13.311059924558937272  ] 
dist 26=[-9.3450937189661838124 ,12.248996256532908869  ] 
dist 27=[-10.967825243298035514  ,9.9949140220647241955 ] 
dist 28=[-12.203541383953947859  ,9.4956017258106843637 ] 
dist 29=[-13.244667547211046458  ,7.2442987454880169370 ] 
dist 30=[-14.089645383341185858  ,6.8483586575185490864 ] 
dist 31=[-14.541790291698738903  ,6.0994796949503637651 ] 
dist 32=[-14.797608715165658675  ,5.9376002048893065883 ] 
dist 33=[-14.858705257999501232  ,-1.7821590777385094780 ] 
dist 34=[-14.836486669067930072  ,-2.4607560339249291370 ] 
dist 35=[-14.779048637593237592  ,-3.8259166083336540423 ] 
dist 36=[-14.646252016365588010  ,-4.1456167854511812852 ] 
dist 37=[-14.574292663364586817  ,-5.2078597249499159573 ] 
dist 38=[-14.135855772829757587  ,-5.4151840113194946072 ] 
dist 39=[-14.019584329887357340  ,-4.1729485980038320630 ] 
dist 40=[-13.633711606367774428  ,-2.4086512959487275804 ] 
dist 41=[-13.545806200552635509  ,-1.1365907114128642395 ] 
dist 42=[-13.488202669000760832  ,1.8984593369650929150 ] 
dist 43=[-13.737115190184327872  ,3.9302196217822340714 ] 
dist 44=[-13.869751406021345208  ,5.6138577358808993469 ] 
dist 45=[-13.930493113262093007  ,7.2600542709730619858 ] 
dist 46=[-13.924979919183127893  ,8.7543521702677126938 ] 
dist 47=[-13.824975881833391519  ,9.8320061666839321240 ] 
dist 48=[-13.771538408562726024  ,10.810123985038433617  ] 
dist 49=[-.89338724263157715097,11.907400561814623302  ] 
dist 50=[.55921738797618288648,12.899639616992339956  ] 
dist 51=[.79569213982094815239,13.458622838192606260  ] 
dist 52=[1.0752576585070088402 ,13.807098457001425713  ] 
dist 53=[1.1066175434009062546 ,13.959186944690950553  ] 
dist 54=[1.0379441633812109983 ,14.026604122262621781  ] 
dist 55=[.82297314418819669335,14.037221108284764862  ] 
dist 56=[.46027391438439312253,14.008457551292555943  ] 
dist 57=[-.19785931868573452625,13.953349162077189779  ] 
dist 58=[-.87698332150454024232,7.7107843570083855227 ] 
dist 59=[-1.3234709975676801003 ,7.7863740467608831735 ] 
dist 60=[-1.6843308075150272771 ,7.8463056469834044958 ] 
dist 61=[-2.0218784235025003012 ,7.8922880621923221788 ] 
dist 62=[-2.3180351514322161436 ,7.9120956747636474536 ] 
dist 63=[-2.5137891682941395698 ,7.9167888811653894841 ] 
dist 64=[-2.6732824673089819664 ,7.9023315597239927241 ] 
dist 65=[-2.8248109905308323024 ,2.4254811538788876784 ] 
dist 66=[-2.9550808695941774478 ,1.9779756433758100976 ] 
dist 67=[-3.0297634036852481319 ,.95832929321700671693] 
dist 68=[-3.0780475926792277308 ,.77322735015791993553] 
dist 69=[-3.1029699346068931391 ,-.48260496486916146776] 
dist 70=[-3.1110370531133975761 ,-.31519020890032746673] 
dist 71=[-3.1064221196442179196 ,.10159991816818548643] 
dist 72=[-3.1971698817825652227 ,.52441112804201034253] 
dist 73=[-3.9250924145759920590 ,.8062326094877631348 ] 
dist 74=[-4.3873460639173671401 ,1.0379509110471383041 ] 
dist 75=[-4.7428437027987214707 ,1.2609318985024846817 ] 
dist 76=[-5.0448524278284022104 ,1.4604268651384992107 ] 
dist 77=[-5.2888394669425693369 ,1.5984687104211103348 ] 
dist 78=[-5.4128517285171352824 ,1.7174907744758304722 ] 
dist 79=[-5.4737385604952844946 ,1.8411118652413160141 ] 
dist 80=[-5.4831820651348599834 ,1.9510541767671388701 ] 
dist 81=[-1.4582971612535093665 ,2.0155151928555697437 ] 
dist 82=[-1.2983135155568213656 ,2.0907544173399654656 ] 
dist 83=[-1.2544102735429906141 ,2.2322254724393269363 ] 
dist 84=[-1.0840603893119163750 ,2.3292695271031307954 ] 
dist 85=[-1.0482840430068342324 ,2.3907716021843373338 ] 
dist 86=[-.97371277353661015047,2.4328345366953866136 ] 
dist 87=[-.95260088630476299124,2.4523329080959577094 ] 
dist 88=[.39030127299657351486,2.4589930357019336454 ] 
dist 89=[.29164759202721549413,2.4531325452862507121 ] 
dist 90=[.18386995074386989846,1.8676962461991873139 ] 
dist 91=[.03943077511233270420,1.9814594221786580767 ] 
dist 92=[-.17668465663807690887,2.0700176867454976687 ] 
dist 93=[-.39787904279229170202,2.1362269231447261380 ] 
dist 94=[-.6049019089139557997 ,2.1608440246899483568 ] 
dist 95=[-.76448955662855943592,2.1685735648274533843 ] 
dist 96=[-.9196056642050734307 ,2.1673934170839392056 ] 
dist 97=[-1.1087978974977398869 ,1.8784927757337635594 ] 
dist 98=[-1.2863945900764518508 ,1.8431263625585477308 ] 
dist 99=[-1.3952563794635356401 ,1.7410227455336926534 ] 
dist 100=[-1.4744409156545264642 ,1.7234668961710654071 ] 
dist 101=[-1.5336496440505134193 ,1.5130886612846870082 ] 
dist 102=[-1.5780807129571633746 ,1.4683231256504046015 ] 
dist 103=[-1.5983060246894340785 ,1.4200090019700723609 ] 
dist 104=[-1.6053222417145036242 ,1.4028560391810371419 ] 
dist 105=[-1.6043801725255302114 ,.99561076499665922976] 
dist 106=[-1.6514866196909593240 ,1.2017054308450917461 ] 
dist 107=[-1.7350765898441986410 ,1.3311483939159638459 ] 
dist 108=[-1.7875568809995563904 ,1.4289642667434552906 ] 
dist 109=[-1.8111933786415817223 ,1.5088913989622505077 ] 
dist 110=[-1.8232320543677315670 ,1.5714244904704645144 ] 
dist 111=[-1.8294419846659054007 ,1.5998554149079115590 ] 
dist 112=[-1.8325715057648993834 ,1.6130184041631559272 ] 
dist 113=[-1.8323138776808473116 ,1.6146464678016095875 ] 
dist 114=[-1.4997492382476916661 ,1.5529964894290736884 ] 
dist 115=[-1.4517888370167154942 ,1.5368053099701144689 ] 
dist 116=[-1.3666349377158032208 ,1.5058493434570310466 ] 
dist 117=[-1.3939472500897259696 ,1.4944437915077985502 ] 
dist 118=[-1.4493423438876751363 ,1.4376770228944537162 ] 
dist 119=[-1.4864943676334542972 ,1.4227051366399670453 ] 
dist 120=[-1.5054718694398226318 ,1.3754032854976564962 ] 
dist 121=[-1.5162684491689795612 ,1.3637443654842892317 ] 
dist 122=[-1.5207753990952711461 ,.25436787357776762924] 
dist 123=[-1.5215831434579710067 ,.48726563965951186677] 
dist 124=[-1.5176080823076764455 ,.67704708106846647612] 
dist 125=[-1.5109102995222416015 ,.85709657883672986768] 
dist 126=[-1.5033737300025791916 ,1.0167004975384500987 ] 
dist 127=[-1.4877286825912355509 ,1.1249222878813488722 ] 
dist 128=[-1.4800039211653483325 ,1.2160345745473588417 ] 
dist 129=[-.50989101905125183464,1.3073881115038026665 ] 
dist 130=[-.42593110247984636152,1.3884676307841554128 ] 
dist 131=[-.23586673381836161259,1.4385948997739812941 ] 
dist 132=[-.19948446151700707135,1.4755636874870864138 ] 
dist 133=[.03258984937461634358,1.5041488353222767042 ] 
dist 134=[.07294878823794774202,1.5250980514814733472 ] 
dist 135=[.15020441008225689942,1.5316040644588971132 ] 
dist 136=[.16803563023280681955,1.5291173204959119944 ] 
dist 137=[.34782298246526051201,1.5252746521622350110 ] 
dist 138=[.3747013126981925239 ,1.2568137160244158294 ] 
dist 139=[.2641577819154889995 ,1.3186058009639246332 ] 
dist 140=[.12199852422664466757,1.3669885529972857259 ] 
dist 141=[-.02393360138657588819,1.4029785616116856026 ] 
dist 142=[-.16076705497438453291,1.4153239778899292754 ] 
dist 143=[-.26663061956751452238,1.4186230449807507484 ] 
dist 144=[-.3698710952519321288 ,1.4185198944428055181 ] 
dist 145=[-.49624022005393916177,.14634029004130436137] 
dist 146=[-.61533532065050727321,.08817077799870185429] 
dist 147=[-.6895593331255990726 ,-.03013098560214894847] 
dist 148=[-.7449816608421138304 ,-.04872414316506235345] 
dist 149=[-.78907656028237575089,-.11720509339875589643] 
dist 150=[-.82373313678346321071,-.13044827732165475805] 
dist 151=[-.85703654495606546286,-.14801965834362009767] 
dist 152=[-.92771312194373481726,-.15043846118329743329] 
dist 153=[-.99097849215055694115,-.14709687682952247687] 
dist 154=[-1.0276046337690324432 ,-.13526720290720998482] 
dist 155=[-1.0516857473179507693 ,-.11497152781162329255] 
dist 156=[-1.0648987672364380203 ,-.07785528288295540332] 
dist 157=[-1.0712935573585302168 ,-.03284012274487707322] 
dist 158=[-1.0707529794897165064 ,.01896797774978083554] 
dist 159=[-1.0619354125837202564 ,.08559151368929936510] 
dist 160=[-1.0558983584284232362 ,.18971238537064983585] 
dist 161=[-.72389715460544381217,.29440902774852351504] 
dist 162=[-.73453354475519593404,.36332910216931522511] 
dist 163=[-.73914109146553420295,.41912840406967366787] 
dist 164=[-.74005974365345505701,.47147871470265425327] 
dist 165=[-.71711747722921439137,.51749597757566794626] 
dist 166=[-.71100072729782318565,.54802847662653667275] 
dist 167=[-.70719013955117566894,.57300887551778856638] 
dist 168=[-.7055501865989619635 ,.64119842041904161693] 
dist 169=[-.60648752878201005419,.80840525905752723739] 
dist 170=[-.64430058217263533806,.97211635631806902291] 
dist 171=[-.66773265847550836989,1.0747591979600140120 ] 
dist 172=[-.68506567336534261169,1.1521465407194147542 ] 
dist 173=[-.69854891005167428246,1.2151058107599972748 ] 
dist 174=[-.70848378221151757205,1.2641252612971926823 ] 
dist 175=[-.7116615197197402884 ,1.2859022679735168025 ] 
dist 176=[-.71066358534318059817,1.2957446092721644624 ] 
dist 177=[-.70893699694698524057,1.2971524317533025822 ] 
dist 178=[-.69302640066150804561,1.2470895061562400431 ] 
dist 179=[-.6878577671984169395 ,1.2341243546477607267 ] 
dist 180=[-.67117091079470342675,1.2080461370487834496 ] 
dist 181=[-.66532127406389890933,1.1983047332295223484 ] 
dist 182=[-.62087171296338598089,1.1487212814665000610 ] 
dist 183=[-.60984891127127351662,1.1364532666780872922 ] 
dist 184=[-.59234494227977778984,1.0952386170734791408 ] 
dist 185=[-.58646340620554764506,1.0879052119701484131 ] 
dist 186=[-.56360956499234147626,.01102593291745028214] 
dist 187=[-.70327146659915477263,.02624766755849053464] 
dist 188=[-.81366792555702159539,.05174643537006246777] 
dist 189=[-.91268238963786409644,.08182687217787878329] 
dist 190=[-.99656789748810506757,.11532204490288158166] 
dist 191=[-1.0832427026872926166 ,.15765225372592905338] 
dist 192=[-1.1549123462388822279 ,.22297093625463819207] 
dist 193=[-1.2245489210672031474 ,.28814206158443794821] 
dist 194=[-1.2852064716306198000 ,.32988299474251827528] 
dist 195=[-1.3210568455190606479 ,.36235098207864188804] 
dist 196=[-1.3455376190061335348 ,.3905350632570836345 ] 
dist 197=[-1.3608388824525403549 ,.4137185184526421783 ] 
dist 198=[-1.3690377479694088890 ,.42624000392132575447] 
dist 199=[-1.3681054393416245605 ,.43331194045564888758] 
dist 200=[-1.3570783864411594342 ,.43475733834880924084] 
dist 201=[-1.3483929602312288816 ,.43385430975488605457] 
dist 202=[-.64418842874821037471,.43184884382792545717] 
dist 203=[-.58029123719930028868,.42798480864721722397] 
dist 204=[-.42979439058949751655,.42588001134437308775] 
dist 205=[-.40311037372067798551,.41297158003650410136] 
dist 206=[-.34772632551307820141,.4957626643869127361 ] 
dist 207=[-.34030566530623663222,.59268673331496777767] 
dist 208=[-.33671841721426065618,.68643608706597878568] 
dist 209=[-.08673213631687916884,.80011883505873454156] 
dist 210=[.09285293591663315352,.90646594796739181861] 
dist 211=[.04473299809053975453,.97095250148009965938] 
dist 212=[-.01117754122762768358,1.0170046989269844224 ] 
dist 213=[-.06767800793802708569,1.0498142654763788304 ] 
dist 214=[-.11815204388588779554,1.0733365430399691244 ] 
dist 215=[-.17377799149088101552,1.0823396277170957886 ] 
dist 216=[-.25083097205251213883,1.0838473630093434615 ] 
dist 217=[-.32774604961022456572,1.0814380579996845200 ] 
dist 218=[-.38282247096179029332,.26113142470964246016] 
dist 219=[-.43234367088555027114,.24494462743552664289] 
dist 220=[-.48709910534663880695,.23534703143135232606] 
dist 221=[-.54090216436330835814,.2337637402945680744 ] 
dist 222=[-.586625003976584436  ,.2359505730159336169 ] 
dist 223=[-.63510151565361259927,.24374126313259193176] 
dist 224=[-.69989079440256311629,.32340357116596830491] 
dist 225=[-.76124263914299488932,.40732787209940145369] 
dist 226=[-.79600663247013275092,.46155132030278214931] 
dist 227=[-.81789033703011697987,.50430237402856785581] 
dist 228=[-.82785913715052754617,.54245968918992684248] 
dist 229=[-.83260177366020092072,.57465466359468108607] 
dist 230=[-.83363699048741257132,.59361976841112441006] 
dist 231=[-.83025773702039728565,.60648664098474613584] 
dist 232=[-.79376905452408103875,.61435296864368477578] 
dist 233=[-.78237288725724820344,.61872972182265951297] 
dist 234=[-.90867213091949044346,.65269965207414392158] 
dist 235=[-.98578376855501040918,.69452456099680279203] 
dist 236=[-1.0414965216969782462 ,.72541035542443491182] 
dist 237=[-1.0824297376708233540 ,.74935164528092932084] 
dist 238=[-1.1129627883730301451 ,.76693702446629253664] 
dist 239=[-1.1271859822146582878 ,.77246835197071688548] 
dist 240=[-1.1321618866162186703 ,.77323779803195792888] 
dist 241=[-1.1316023856713267053 ,.77182801763089638152] 
dist 242=[-1.0285213888611927500 ,.73978929404242830148] 
dist 243=[-1.0101085152287577477 ,.73209079550328425691] 
dist 244=[-.976623764978495141  ,.70977138857658694807] 
dist 245=[-.96654724362653442952,.70238510298163532648] 
dist 246=[-.92551249325390156494,.65090742532688229807] 
dist 247=[-.91368528777254467409,.63852967222089546249] 
dist 248=[-.88799144662920963992,.6172899591168162527 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 0, 2] 
dist 0=[57.364285831462424421  ,57.364285831462424421  ] 
dist 1=[56.019710286858426794  ,58.536260972731202965  ] 
dist 2=[54.655353984419412877  ,59.211472460376285592  ] 
dist 3=[53.013859368648434222  ,59.652295217550034580  ] 
dist 4=[50.562409219403594475  ,59.888758131216486114  ] 
dist 5=[47.773504057052948492  ,59.976000814920753253  ] 
dist 6=[44.784411296396073883  ,59.955405003089391809  ] 
dist 7=[41.071184591456323156  ,59.625766661119625851  ] 
dist 8=[35.390647081398066448  ,59.550098977440166239  ] 
dist 9=[29.669714651048114380  ,57.939972264442432035  ] 
dist 10=[25.795022745726389992  ,57.559826592442085597  ] 
dist 11=[22.523851877720566784  ,56.943986337398332148  ] 
dist 12=[19.212440864424483735  ,56.736920816473294224  ] 
dist 13=[16.120145671839643644  ,51.802077797726672857  ] 
dist 14=[13.723546018723806774  ,51.232215123153379074  ] 
dist 15=[11.371327678410725202  ,47.292922387310095048  ] 
dist 16=[8.4555202822097144917 ,40.958198021761828003  ] 
dist 17=[5.6706531532321136375 ,36.121906975114506906  ] 
dist 18=[3.8409237135747148884 ,34.489515253841961639  ] 
dist 19=[2.3532835275682451417 ,30.583318212714273646  ] 
dist 20=[.93404730678618961842,30.015038168073947867  ] 
dist 21=[-.34297082295585872271,24.546441919873954796  ] 
dist 22=[-1.2634005167704214478 ,23.561209930694825557  ] 
dist 23=[-2.1075600992592593380 ,22.350416544970693323  ] 
dist 24=[-3.0816851543367960680 ,22.117378981908337760  ] 
dist 25=[-3.9827398795447428199 ,14.598979018958908937  ] 
dist 26=[-4.5351184524704281521 ,13.712889349212387664  ] 
dist 27=[-4.9470544182703588479 ,11.808283190141816196  ] 
dist 28=[-5.2856359027888444556 ,11.448642495734423388  ] 
dist 29=[-7.2417675750234831574 ,9.5140828712505064680 ] 
dist 30=[-8.8274710227823444911 ,9.2015637270898553386 ] 
dist 31=[-10.337530513766250466  ,8.5982546565192742928 ] 
dist 32=[-12.145363169448175852  ,8.3049178426911288244 ] 
dist 33=[-13.839492731616123328  ,-2.6959031766965343897 ] 
dist 34=[-14.895401614109141651  ,-2.0674786555825116272 ] 
dist 35=[-15.689149306693838175  ,-1.4110775581528591098 ] 
dist 36=[-16.336168193272043274  ,-.54966731855956335412] 
dist 37=[-16.841900220305079963  ,.37348856948846642342] 
dist 38=[-17.071361379790874207  ,1.2765735896357809546 ] 
dist 39=[-17.165106491534622431  ,2.3354273974889446985 ] 
dist 40=[-17.154876911281376365  ,3.8802896503752198580 ] 
dist 41=[-4.7036741595012267055 ,5.4064604440052155573 ] 
dist 42=[-4.5855911329032876891 ,6.3909067887539354166 ] 
dist 43=[-4.3294766530613201358 ,7.1652979543005959469 ] 
dist 44=[-4.2493303007515890621 ,7.8536725604403031700 ] 
dist 45=[-3.8873809758593497591 ,8.4330703703263743787 ] 
dist 46=[-3.8097897749285640336 ,8.7728322034963375343 ] 
dist 47=[-3.5944051020011839084 ,9.0020956107036719102 ] 
dist 48=[-3.5505316515106046101 ,9.1408464652361555076 ] 
dist 49=[-2.9856134052788420266 ,9.2218147912687649689 ] 
dist 50=[-2.8855616734163569500 ,9.2205216048035665408 ] 
dist 51=[-2.6589526362537546368 ,9.1780892834875654739 ] 
dist 52=[-2.5881652076000177859 ,9.1340037412942394675 ] 
dist 53=[-2.2694530974092985390 ,8.1301051606050255235 ] 
dist 54=[-2.2022155744086237396 ,7.9830611575523775541 ] 
dist 55=[-2.0406157815635872650 ,7.8918245356352694694 ] 
dist 56=[-1.9945777722964491014 ,7.8727398988717387046 ] 
dist 57=[-1.5238435932632320059 ,3.2464038229345675428 ] 
dist 58=[-1.4482702961364078180 ,2.8561531183596863558 ] 
dist 59=[-1.2704044286280914527 ,1.9450812059198238653 ] 
dist 60=[-1.2304823265563414083 ,1.7841792379739873941 ] 
dist 61=[-.98227266918032912738,.58429483729753467589] 
dist 62=[-1.3825218137567464492 ,.37124595785806101137] 
dist 63=[-1.9541627228008514945 ,.01134423023811685922] 
dist 64=[-2.6643926451381734787 ,-.06966373426474842053] 
dist 65=[-3.3366654697477586508 ,.04570189539775247939] 
dist 66=[-3.7569239769344307074 ,.23098394646049593277] 
dist 67=[-4.0720257162872738364 ,.39657104714962757473] 
dist 68=[-4.3248780816337810873 ,.57806904475417432953] 
dist 69=[-4.5220461770744320621 ,.75557555213831819213] 
dist 70=[-4.6150559758903848698 ,.90530465049763464533] 
dist 71=[-4.6571266807561885545 ,1.0632919948684583422 ] 
dist 72=[-4.6566160890285180347 ,1.2738446735903959455 ] 
dist 73=[-1.0703847219298499514 ,1.4761450600778572762 ] 
dist 74=[-.96205687552672228191,1.6012317861473462254 ] 
dist 75=[-.72761651144404017007,1.6938447179524366722 ] 
dist 76=[-.66852494727002500619,1.7665552865068575823 ] 
dist 77=[-.41400312847483384858,1.8211716739852586755 ] 
dist 78=[-.42806768151569925857,1.8415904993881377879 ] 
dist 79=[-.45762191478828166816,1.8485156216661858746 ] 
dist 80=[-.49965361701472202631,1.8491926879454434984 ] 
dist 81=[-.54171004997049622312,1.7751970857893582884 ] 
dist 82=[-.57138649756230470245,1.7575948546767566279 ] 
dist 83=[-.59751398332655239205,1.7112952945814362154 ] 
dist 84=[-.62546525905798771934,1.6929257438111230218 ] 
dist 85=[-.65237781269647956782,1.6347358533762478453 ] 
dist 86=[-.67439759555811063677,1.7241138812163837600 ] 
dist 87=[-.69708514988771449043,1.8674028450463146794 ] 
dist 88=[-.73967298763859365246,2.0506192699098486320 ] 
dist 89=[-.96373499176586319781,2.2217148041679896758 ] 
dist 90=[-1.1101847477383190440 ,2.3166622341419028083 ] 
dist 91=[-1.3418138989071334985 ,2.3741457298254770202 ] 
dist 92=[-1.6017329639436981715 ,2.3957446026873683789 ] 
dist 93=[-1.8462445267104629812 ,2.4028930840292494037 ] 
dist 94=[-2.0369458035989013116 ,2.4026921656493210468 ] 
dist 95=[-2.2244459763801622645 ,2.3971889465935305838 ] 
dist 96=[-2.4561785312664508145 ,2.3866830790094693182 ] 
dist 97=[-2.6752357997402830269 ,1.9911167845721682503 ] 
dist 98=[-2.8121630711401471215 ,1.9320915852169323685 ] 
dist 99=[-2.9149055309824274633 ,1.8176921650855646344 ] 
dist 100=[-2.9975765010742246628 ,1.7857557867405721675 ] 
dist 101=[-3.0607970120953637887 ,1.6633252031400519953 ] 
dist 102=[-3.0859348960317542962 ,1.6325386797387363840 ] 
dist 103=[-3.0895282772047743857 ,1.5733643843784789465 ] 
dist 104=[-3.0840597158309355974 ,1.5554308942415782375 ] 
dist 105=[-3.0164151668921804438 ,1.8857691283983531607 ] 
dist 106=[-2.9944578527126700011 ,2.2987120229725892803 ] 
dist 107=[-2.9216520522069195290 ,2.6214094703527813379 ] 
dist 108=[-2.8969749524604327196 ,2.9044247303357658106 ] 
dist 109=[-2.6983801245659209151 ,3.1396291859249075453 ] 
dist 110=[-2.6491918942055032740 ,3.2716103767730215981 ] 
dist 111=[-2.5747312324883042210 ,3.3530336102441017198 ] 
dist 112=[-2.5483833691783501277 ,3.3865681282385661532 ] 
dist 113=[-2.1718912405809077728 ,3.4006140601663797185 ] 
dist 114=[-2.2296366443159845897 ,3.4042959885035837562 ] 
dist 115=[-2.2679571991194770867 ,3.4011329887248968140 ] 
dist 116=[-2.2897289406777781467 ,3.3878648441403298214 ] 
dist 117=[-2.2991835075721396373 ,3.3691982875912612378 ] 
dist 118=[-2.2969274880241516084 ,3.3492850744537282733 ] 
dist 119=[-2.2723081590271279540 ,3.3119155160905448326 ] 
dist 120=[-2.2608783044341648494 ,3.2941435209978026167 ] 
dist 121=[-1.1279915780479907747 ,.08766102267388219609] 
dist 122=[-1.0236290416339521374 ,-.00473010462089423011] 
dist 123=[-.78055662708045399928,.22890186879542238835] 
dist 124=[-1.1647713308674450540 ,.46359007653591720127] 
dist 125=[-1.5129953918258013642 ,.68047688849001950012] 
dist 126=[-1.7623300916541130019 ,.84309550991935246578] 
dist 127=[-1.9864559340656192298 ,.9968144597001818762 ] 
dist 128=[-2.2341333191161638153 ,1.1781996443186164854 ] 
dist 129=[-2.4605292011467088521 ,1.3466418763784076176 ] 
dist 130=[-2.5997655760188236623 ,1.4487285088617661460 ] 
dist 131=[-2.7015463971099263515 ,1.5215819265871415720 ] 
dist 132=[-2.7785278487469701559 ,1.5734052679642539171 ] 
dist 133=[-2.8334905928449291207 ,1.6110077551764608050 ] 
dist 134=[-2.8474360717445022017 ,1.6271292685136840295 ] 
dist 135=[-2.8453477938471602750 ,1.6309104909357278972 ] 
dist 136=[-2.8363562486773329537 ,1.6290044405401021086 ] 
dist 137=[-1.6654265571315939782 ,.4431426851321707307 ] 
dist 138=[-1.5578153416533154853 ,.40188673116242156445] 
dist 139=[-1.2873518304320558643 ,.39754083068423940192] 
dist 140=[-1.2480038284360214581 ,.40330570417077149968] 
dist 141=[-.82573742603464912631,.41513164852823030804] 
dist 142=[-.74633834253296866385,.43496213406891239635] 
dist 143=[-.65574173825579092651,.56028877532854092239] 
dist 144=[-.63842496725033512408,.77820637665140681291] 
dist 145=[-.51079149524117958973,.98395314385688951392] 
dist 146=[-.5821520883643238866 ,1.1135691754715127924 ] 
dist 147=[-.63634155734718755249,1.2119580273842790074 ] 
dist 148=[-.68112504799694923829,1.2931369044335778842 ] 
dist 149=[-.78188731007379230281,1.3575369528586031364 ] 
dist 150=[-.91958829190244979709,1.3890002087166248560 ] 
dist 151=[-1.0771659958207933791 ,1.4046119672416942505 ] 
dist 152=[-1.3027206194759940927 ,1.4057780760838406597 ] 
dist 153=[-1.5223855518740173466 ,1.1961589123647889104 ] 
dist 154=[-1.6564679930306548935 ,1.2553236137533125305 ] 
dist 155=[-1.7533214672214515977 ,1.3318584685859456656 ] 
dist 156=[-1.8244654290839217111 ,1.4138523954784658272 ] 
dist 157=[-1.8778924291116776317 ,1.4929487083981678881 ] 
dist 158=[-1.9040646500667849046 ,1.5579190545657739439 ] 
dist 159=[-1.9152459561837150125 ,1.6248921187894758275 ] 
dist 160=[-1.9142816452088417577 ,1.7119734959084438478 ] 
dist 161=[-1.7315199651112947366 ,1.7964420910738269843 ] 
dist 162=[-1.6995854342665025372 ,1.8529881132145438262 ] 
dist 163=[-1.6445682253078490102 ,1.8998132859680163036 ] 
dist 164=[-1.6279948028255283454 ,1.9454954799714507500 ] 
dist 165=[-1.5670713500035832599 ,1.9868326795787288526 ] 
dist 166=[-1.5476285090226451864 ,2.0163188855078299989 ] 
dist 167=[-1.5125195369399820627 ,2.0426956342476142232 ] 
dist 168=[-1.8492178744352318250 ,2.0716191583924987202 ] 
dist 169=[-2.3808447711849011442 ,2.0958056781992456580 ] 
dist 170=[-2.7193752323080933009 ,2.1032839262611039552 ] 
dist 171=[-2.9806728391926324428 ,2.0999076852678312991 ] 
dist 172=[-3.2042017508886384337 ,2.0941910322174876855 ] 
dist 173=[-3.3858588715343955192 ,2.0535591333432800451 ] 
dist 174=[-3.4801221025651670868 ,2.0404112968057365328 ] 
dist 175=[-3.5297638941870244393 ,1.9863259596652731987 ] 
dist 176=[-3.5389423262720481909 ,1.9765217975774282890 ] 
dist 177=[-3.5050925283306784566 ,1.7849118636067777011 ] 
dist 178=[-3.4838496485723904282 ,1.7503081442585539831 ] 
dist 179=[-3.4457258941033657844 ,1.7051132415697543198 ] 
dist 180=[-3.4280351308323078271 ,1.7366230221297240004 ] 
dist 181=[-3.3282539070561796341 ,1.7579443884621426298 ] 
dist 182=[-3.2999508174529635774 ,1.7608044606440708869 ] 
dist 183=[-3.2011216834925080457 ,1.7555829442974225671 ] 
dist 184=[-3.1793245757149431055 ,1.7474492005556153549 ] 
dist 185=[-.31150001040432691809,1.2189843857820431128 ] 
dist 186=[-.45324377618689692109,1.5392150652725770460 ] 
dist 187=[-.57226281516231153852,1.7947204212286613986 ] 
dist 188=[-.69109638083406470717,2.0977912724186302055 ] 
dist 189=[-.80046520316630380605,2.4596252572942501849 ] 
dist 190=[-.88172599248573962592,2.7063826821415185713 ] 
dist 191=[-.9578198263339800388 ,2.9156312475357460958 ] 
dist 192=[-1.0465758561088109380 ,3.1278388273556248144 ] 
dist 193=[-1.1278561276685539264 ,3.3157453465354277714 ] 
dist 194=[-1.1741264214371856339 ,3.4280535285050780023 ] 
dist 195=[-1.2035330155392096376 ,3.5062838202440690574 ] 
dist 196=[-1.2175377244268688643 ,3.5582470369992296128 ] 
dist 197=[-1.2239069948893882001 ,3.5892351794247360824 ] 
dist 198=[-1.2228533340856554770 ,3.5904912442715919380 ] 
dist 199=[-1.2166603923504077313 ,3.5658313458736526356 ] 
dist 200=[-1.2120897110848149467 ,3.5468849236547201973 ] 
dist 201=[-.64601078616045242699,1.8025018817937460817 ] 
dist 202=[-.64084638230195689123,1.6431947320479291949 ] 
dist 203=[-.80277565704811167686,1.2622769120340841683 ] 
dist 204=[-1.1130763839028666899 ,1.1975967857531034604 ] 
dist 205=[-1.3996361076829227976 ,1.0406772391223561088 ] 
dist 206=[-1.6140456106769763776 ,1.1357096180504472387 ] 
dist 207=[-1.8162384068172129992 ,1.2235687941109054167 ] 
dist 208=[-2.0540639320134870755 ,1.3243928739676237080 ] 
dist 209=[-2.2727858037620216325 ,1.4158493823884255758 ] 
dist 210=[-2.3987721664775606569 ,1.4663389355745222929 ] 
dist 211=[-2.4807029101234818675 ,1.4964012108675104327 ] 
dist 212=[-2.5236829054853089604 ,1.5063676186491231920 ] 
dist 213=[-2.5491004585196784003 ,1.5078276864855995239 ] 
dist 214=[-2.5609737088664331478 ,1.5039552808512115793 ] 
dist 215=[-2.5651745282035922434 ,1.4954435610168378540 ] 
dist 216=[-2.5599880925724584075 ,1.4891210780768269766 ] 
dist 217=[-1.1195540544970550513 ,1.4330184989454127876 ] 
dist 218=[-1.1424894033554140474 ,1.6085587607177996242 ] 
dist 219=[-1.1568512637546610270 ,1.7424937808339754226 ] 
dist 220=[-1.1632311404948086869 ,1.8543153420130955673 ] 
dist 221=[-1.2827049787106610756 ,1.9431163141509501470 ] 
dist 222=[-1.3692484117547926870 ,1.9852158063941415594 ] 
dist 223=[-1.4364989089855522648 ,2.0062014229332044806 ] 
dist 224=[-1.4948232186816621628 ,2.0107739966325402098 ] 
dist 225=[-1.5432178928093753396 ,2.0539422419430192725 ] 
dist 226=[-1.5708567915785084767 ,2.1676937908008578045 ] 
dist 227=[-1.5885332871191089947 ,2.2449368704965353876 ] 
dist 228=[-1.5971862886731278216 ,2.2923328683470345014 ] 
dist 229=[-1.5993591872678139548 ,2.3225236202121036222 ] 
dist 230=[-1.6024337503464525745 ,2.3311319887842956037 ] 
dist 231=[-1.7068179685023724072 ,2.3265301545179226663 ] 
dist 232=[-1.8580552330372841182 ,2.3201288213743013969 ] 
dist 233=[-2.0053459459464768335 ,2.6091479206918586748 ] 
dist 234=[-2.0939863727557581441 ,2.8730597262376337080 ] 
dist 235=[-2.1564572438534474032 ,3.0689434589343211639 ] 
dist 236=[-2.1993556687679124468 ,3.2226796822549867899 ] 
dist 237=[-2.2262774570179801855 ,3.3412373177242028465 ] 
dist 238=[-2.2308827806011219503 ,3.3967855475472288219 ] 
dist 239=[-2.2159292400901061310 ,3.4203295394368224792 ] 
dist 240=[-2.2116384531462533276 ,3.4196079973123681644 ] 
dist 241=[-2.0807079257428018980 ,3.2048602052933759968 ] 
dist 242=[-2.0536822127646816393 ,3.1602931181859835051 ] 
dist 243=[-1.9737040108069486332 ,3.0792276004278616317 ] 
dist 244=[-1.9544259410896423458 ,3.0528507003932449468 ] 
dist 245=[-1.9597408486054974826 ,2.9364905417003148816 ] 
dist 246=[-1.9666555583005813062 ,2.9032285430221440289 ] 
dist 247=[-1.9649700317076046030 ,2.8188360630558963744 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 2, 1, 1, 2] 
dist 0=[66.066060305724967402  ,66.066060305724967402  ] 
dist 1=[65.819328885441053405  ,66.143199762005548769  ] 
dist 2=[64.879313234031915845  ,66.405829862966256485  ] 
dist 3=[63.669046489911092728  ,66.633049635952990571  ] 
dist 4=[61.990683953406800122  ,66.568784988391062064  ] 
dist 5=[59.648841109518661816  ,66.363497753296871578  ] 
dist 6=[55.811479247416348700  ,66.210850023184879760  ] 
dist 7=[51.851194225708924709  ,65.679971863207787133  ] 
dist 8=[49.018436005485864583  ,65.427317749762907808  ] 
dist 9=[46.464241133877528551  ,62.159140178856347499  ] 
dist 10=[41.600427357836903820  ,61.500576354601486470  ] 
dist 11=[35.290129699008762211  ,60.658854397075327110  ] 
dist 12=[30.979534842950679668  ,60.324171931830096724  ] 
dist 13=[27.300295841084666013  ,59.866574318593124488  ] 
dist 14=[23.510951986126154633  ,58.656221413234636594  ] 
dist 15=[19.931707679467007429  ,52.294347810809396227  ] 
dist 16=[17.091247702806516111  ,48.062290829690099408  ] 
dist 17=[14.241646396667602528  ,29.613335465073400258  ] 
dist 18=[10.625507395712232423  ,27.249491791943324922  ] 
dist 19=[7.1350706701998925969 ,22.365412033972858636  ] 
dist 20=[4.7871896521296941178 ,21.888675925799432173  ] 
dist 21=[2.8201208968695960180 ,21.209327777148544300  ] 
dist 22=[.85003697542746174948,21.015129030141838127  ] 
dist 23=[-.98001534494553352663,10.638096892341579232  ] 
dist 24=[-2.3884023778578911723 ,10.235848534821987613  ] 
dist 25=[-3.7647189610203751718 ,2.2484734058892494847 ] 
dist 26=[-5.4678707710150107320 ,1.2971806758098824975 ] 
dist 27=[-7.0754724507600925164 ,-.6220532172152195139 ] 
dist 28=[-8.0702840325369218055 ,-1.0196802217123137903 ] 
dist 29=[-9.3078497528070837952 ,-2.3855182018311289980 ] 
dist 30=[-11.023480407494417955  ,-2.9912156633064403959 ] 
dist 31=[-12.623560904354055576  ,-4.1951448265698596254 ] 
dist 32=[-13.611974999102888183  ,-4.6610513621834588219 ] 
dist 33=[-14.345593637885527393  ,-6.1654911491707206026 ] 
dist 34=[-14.927791440640168569  ,-5.7719634536087385225 ] 
dist 35=[-15.371435240252861616  ,-5.1961806412837757854 ] 
dist 36=[-15.551595731415963895  ,-4.4132544074662384511 ] 
dist 37=[-15.618078717925701424  ,-3.3317233082429466559 ] 
dist 38=[-15.607383770980257292  ,-1.5270098223262713246 ] 
dist 39=[-10.319441236789476601  ,.74858627840045324322] 
dist 40=[-10.281027980266612843  ,2.2787267675482780540 ] 
dist 41=[-8.9272668257558912013 ,3.5528596279866083792 ] 
dist 42=[-8.8456945653615144246 ,4.8074477480102162977 ] 
dist 43=[-7.8928433526257935186 ,5.9511335904756914495 ] 
dist 44=[-7.7650975120190434316 ,6.7830101786684229810 ] 
dist 45=[-7.2892020998696917241 ,7.5449386118798225924 ] 
dist 46=[-7.1735010403766052503 ,8.4098022325569383943 ] 
dist 47=[-6.9780077462078756256 ,9.1932864224278814155 ] 
dist 48=[-6.9227719091981451165 ,9.6305323449731477744 ] 
dist 49=[-1.3429790932464895171 ,9.8977571377122652414 ] 
dist 50=[-.86870340962782103532,10.002656830185448996  ] 
dist 51=[.16044211197338002637,10.044804414648641562  ] 
dist 52=[.36985139773155500954,10.061673627501628627  ] 
dist 53=[1.1165878716031749446 ,10.063566169902339255  ] 
dist 54=[1.1092579601568826043 ,10.046236971375338115  ] 
dist 55=[1.0275862460251739162 ,7.9373532497367907564 ] 
dist 56=[.83954507784386123252,7.6720094928178245874 ] 
dist 57=[.53733749878075210019,7.0160628361313197151 ] 
dist 58=[0                     ,6.6743640514814565313 ] 
dist 59=[-.49102996293833180518,6.9567868277511751521 ] 
dist 60=[-.99820664080824654948,7.1654708370321423853 ] 
dist 61=[-1.5071627983247917807 ,7.3151767390495830185 ] 
dist 62=[-2.1497200668060098155 ,7.3621282908816460787 ] 
dist 63=[-2.7627889626779937825 ,7.3685226535561128445 ] 
dist 64=[-3.1541422343154653926 ,7.3562538084158445102 ] 
dist 65=[-3.4570000243308975974 ,-.67000334857189084057] 
dist 66=[-3.7171123745359845197 ,-.95115029314603068058] 
dist 67=[-3.9289909036286122157 ,-1.5786720617806133696 ] 
dist 68=[-4.0394668597237876176 ,-1.5066110234336131959 ] 
dist 69=[-4.0964981187485311757 ,-1.2797440647996890905 ] 
dist 70=[-4.1063371503627486245 ,-.87667470456040262111] 
dist 71=[-4.1007302355784260636 ,-.45989206928264283007] 
dist 72=[-4.5137220454267419638 ,-.1783272094548406809 ] 
dist 73=[-4.8860782270764615891 ,.0570339840493606155 ] 
dist 74=[-5.0951234910007577076 ,.28960594661455449433] 
dist 75=[-5.2244303401965320281 ,.50151851107921479545] 
dist 76=[-5.2786583180025007486 ,.6545124348391681163 ] 
dist 77=[-5.2998124145421655890 ,.7930799914098699105 ] 
dist 78=[-5.2971487660750968696 ,.9474768422218783410 ] 
dist 79=[-5.2766240617355847681 ,1.0937665895443291975 ] 
dist 80=[-5.2553123955165125080 ,1.2025807673143401500 ] 
dist 81=[-3.8103094515621586497 ,1.2850558089942406770 ] 
dist 82=[-3.6458293813627574091 ,1.3528508261630703362 ] 
dist 83=[-3.2311969044010399618 ,1.5138258328202032598 ] 
dist 84=[-3.1578368494861985831 ,2.0219514694053230075 ] 
dist 85=[-2.4874928478241978215 ,2.4766340308239582463 ] 
dist 86=[-2.3555149052716139244 ,2.7921112660592027541 ] 
dist 87=[-2.1769957992995543204 ,3.0653774021670876821 ] 
dist 88=[-2.1184570396727697134 ,3.3517109945640679873 ] 
dist 89=[-.91996149442209210367,3.6085190365564194433 ] 
dist 90=[-.76628928303231159274,3.7640181349505627453 ] 
dist 91=[-.4216064155255106402 ,3.8748237817773751576 ] 
dist 92=[-.35121470065263940765,3.9533495269289998874 ] 
dist 93=[-.15418054771706263511,4.0050096253405887906 ] 
dist 94=[-.29000856409941344228,4.0115485967275695014 ] 
dist 95=[-.42005567128683253212,3.9941815178981548502 ] 
dist 96=[-.50308187269370491919,3.9735754103321769250 ] 
dist 97=[-.56715769865492124875,.78806243430093148953] 
dist 98=[-.62168647812472301318,.5653506966969797215 ] 
dist 99=[-.66612312200581138904,.0445021757517873318 ] 
dist 100=[-.68995799633065574232,-.0347007208098170610 ] 
dist 101=[-.7692092990416871507 ,-.1834900245564514419 ] 
dist 102=[-1.0290538624267383727 ,-.2098935435765497910 ] 
dist 103=[-1.2724035688721393700 ,-.57197798263657984793] 
dist 104=[-1.5560610523432984235 ,-.5956293345328795465 ] 
dist 105=[-1.8201538176687250495 ,-.6379068031871718330 ] 
dist 106=[-1.9854730753654027464 ,-.6454489856162413794 ] 
dist 107=[-2.1097325114583923109 ,-.6527302385337876056 ] 
dist 108=[-2.2100435577952254883 ,-.6401821647077879461 ] 
dist 109=[-2.2870097798301452195 ,-.6143408904946050639 ] 
dist 110=[-2.3181494233479879899 ,-.5637524061920152028 ] 
dist 111=[-2.3292323019777678377 ,-.5068340839761644536 ] 
dist 112=[-2.3262074687950389226 ,-.4557326677792538259 ] 
dist 113=[-1.5421747219186255110 ,-.3992304615803602928 ] 
dist 114=[-1.4682591407226015892 ,-.3207488319402447953 ] 
dist 115=[-1.2847194777180365051 ,-.2343160548484700426 ] 
dist 116=[-1.2512497573745189244 ,-.1460819560471124957 ] 
dist 117=[-.96522398142060091673,-.0397580679542714765 ] 
dist 118=[-.90979919800919600722,.1188587372787569073 ] 
dist 119=[-.8287055185076408623 ,.27723449276010877578] 
dist 120=[-.80475340299290880982,.38260063371044015731] 
dist 121=[-.3381468127109498425 ,.54376824753142090013] 
dist 122=[-.2791129108639562644 ,.68598555206366676901] 
dist 123=[-.1400492578579527957 ,.80441348631827195443] 
dist 124=[-.1193630319823314034 ,.92097046997673933082] 
dist 125=[-.06683623295005441243,1.0271405374706526185 ] 
dist 126=[-.06034974511633890575,1.1041562251852972590 ] 
dist 127=[-.0274114098949439665 ,1.1744759011860817772 ] 
dist 128=[-.0217799685531769399 ,1.2539689787369134569 ] 
dist 129=[-.0227604938479982787 ,1.3266477351097746607 ] 
dist 130=[-.0329892960831203627 ,1.4434613214740803564 ] 
dist 131=[-.0483366207438816394 ,1.5553674721402031384 ] 
dist 132=[-.0697413030254117542 ,1.6668747649866979788 ] 
dist 133=[-.09964039121302843552,1.7694371016539475415 ] 
dist 134=[-.1488802535892731702 ,1.8456514256556645190 ] 
dist 135=[-.19904993828251012985,1.9170723796668322902 ] 
dist 136=[-.29993329447395324607,2.0005067390312533160 ] 
dist 137=[-.40102026451387527449,2.0770469303583441061 ] 
dist 138=[-.50402608145236216709,2.1209588122243880338 ] 
dist 139=[-.60015774085470274925,2.1493189122429119859 ] 
dist 140=[-.67382184309743567135,2.1638060408277684800 ] 
dist 141=[-.74500538051543716561,2.1682262494182116815 ] 
dist 142=[-.83124158660999990243,2.1640451964718682207 ] 
dist 143=[-.96341543326746327991,2.1399324812157414865 ] 
dist 144=[-1.5376598755958821505 ,2.1257097447726007524 ] 
dist 145=[-2.1065206406340804877 ,2.0214332466612637912 ] 
dist 146=[-2.4731087754781646333 ,1.9945496044275870355 ] 
dist 147=[-2.7610595898399700322 ,1.9363269149376042494 ] 
dist 148=[-3.0162227115666310754 ,1.9155484252303034965 ] 
dist 149=[-3.2302254025705337713 ,1.8120766306458545492 ] 
dist 150=[-3.3539817564770209086 ,1.7879367481723310483 ] 
dist 151=[-3.4351255981977790070 ,1.7141200439429630875 ] 
dist 152=[-3.4791441783217242847 ,1.6990511359799519170 ] 
dist 153=[-3.5030456482410405558 ,1.4816122446717484098 ] 
dist 154=[-3.5039384501755603560 ,1.4429644703419624840 ] 
dist 155=[-3.4884304335370669061 ,1.3479606458369280364 ] 
dist 156=[-3.4767425566294784942 ,1.3225354433759372073 ] 
dist 157=[-3.3908833507622764368 ,1.1661006027085487455 ] 
dist 158=[-3.3653695232655078795 ,1.1326240349890107727 ] 
dist 159=[-3.2706289572773077743 ,1.0692053333047494319 ] 
dist 160=[-3.2506158536913456033 ,1.0513980128960542152 ] 
dist 161=[-.43738580006686421416,1.0655615690873632818 ] 
dist 162=[-.41760538978598880725,1.4458201783993049792 ] 
dist 163=[-.335750125813581868  ,1.7522574251937410033 ] 
dist 164=[-.32004437573721872417,2.0930554889381355510 ] 
dist 165=[-.27948039229659339372,2.4507512142528021942 ] 
dist 166=[-.27346319011164183274,2.6943419356256609739 ] 
dist 167=[-.17246055424565128113,2.9005224092636014541 ] 
dist 168=[-.16855246027152548662,3.1089888767692732063 ] 
dist 169=[-.1585935259981709753 ,3.2932603234337803385 ] 
dist 170=[-.2030674075444434978 ,3.4029251259023845926 ] 
dist 171=[-.3020360248457060676 ,3.4787342880900366694 ] 
dist 172=[-.3744278653660716859 ,3.5279502762150426531 ] 
dist 173=[-.4410632380713181456 ,3.5561974493504808111 ] 
dist 174=[-.5170716247327862731 ,3.5568010209575192975 ] 
dist 175=[-.5874632202918076357 ,3.5289524684296348601 ] 
dist 176=[-.6316940749324643031 ,3.5110538633672937470 ] 
dist 177=[-.6651435581746767768 ,1.7764512884444181733 ] 
dist 178=[-.6925284861495034682 ,1.6173488029743507887 ] 
dist 179=[-.7138550193681377524 ,1.2390294749164728767 ] 
dist 180=[-.9984915058223852166 ,1.1730915319186266415 ] 
dist 181=[-1.2996783926645959076 ,.64693275936986429734] 
dist 182=[-1.5253253898581930812 ,.55072405933948725578] 
dist 183=[-1.7383829266459037972 ,.40073917966886027581] 
dist 184=[-1.9893493432517630902 ,.36225791981344392725] 
dist 185=[-2.2204641448552315492 ,.23522638131504030929] 
dist 186=[-2.3543336692495286788 ,.256517635723006361  ] 
dist 187=[-2.4423276457090674804 ,.27589328242322489389] 
dist 188=[-2.4904462463341360032 ,.28985277425819159736] 
dist 189=[-2.5204621448643662052 ,.3024688089355231072 ] 
dist 190=[-2.5362444261676206715 ,.3164860704903454323 ] 
dist 191=[-2.5445875278376117702 ,.3289074047346370680 ] 
dist 192=[-2.5449271437480553269 ,.3351589122697311110 ] 
dist 193=[-.7470199052808254355 ,.3380617773029199365 ] 
dist 194=[-.73900617680093647808,.3382357141744606322 ] 
dist 195=[-.74117327850028629891,.52945993479666040167] 
dist 196=[-.75783010724026817717,.7782971169163143224 ] 
dist 197=[-.78250852058194666009,1.0103928626116465204 ] 
dist 198=[-.81667191339695876419,1.1879036052635397198 ] 
dist 199=[-.86427000258744086493,1.3590669389577926852 ] 
dist 200=[-.94253847468174202995,1.5658441130235925977 ] 
dist 201=[-1.0261246343342654363 ,1.7588460208439637770 ] 
dist 202=[-1.0949335329504909779 ,1.8750599556148615088 ] 
dist 203=[-1.1659617681386623958 ,1.9570521621823093500 ] 
dist 204=[-1.2583975423792019831 ,2.0135427659262050266 ] 
dist 205=[-1.3572864281534570299 ,2.0529256902872444010 ] 
dist 206=[-1.4540539658059857150 ,2.0666732235182863020 ] 
dist 207=[-1.5675966101405968585 ,2.0670734306043876116 ] 
dist 208=[-1.7333983490315196018 ,2.0967183876741379432 ] 
dist 209=[-1.8953617268826022191 ,2.4758767386620827989 ] 
dist 210=[-1.9935921100654861341 ,2.7095333842971339992 ] 
dist 211=[-2.0637377768439669663 ,2.8809238884055089333 ] 
dist 212=[-2.1136712082413385192 ,3.0116912501052624164 ] 
dist 213=[-2.1466528182382985985 ,3.1112088113327857030 ] 
dist 214=[-2.1537666418141326418 ,3.1579368883909134567 ] 
dist 215=[-2.1430432819452920188 ,3.1760260461782548757 ] 
dist 216=[-2.1414920140820628121 ,3.1755347960629117692 ] 
dist 217=[-2.0124915822526620254 ,2.9305434477220241617 ] 
dist 218=[-1.9857457044860640125 ,2.8838598387528470846 ] 
dist 219=[-1.9118351567135281052 ,2.7993058495013327572 ] 
dist 220=[-1.8894174640771028583 ,2.7729912178459882693 ] 
dist 221=[-1.7333667494202962078 ,2.6621138594870564202 ] 
dist 222=[-1.6969916077071139010 ,2.6300193700529622137 ] 
dist 223=[-1.6341760767048783676 ,2.5554547327318561750 ] 
dist 224=[-1.6158176537206131247 ,2.5274876697244210302 ] 
dist 225=[-1.2297429720641429675 ,.95402708246529875294] 
dist 226=[-1.2252330071322776094 ,.95213178914386672643] 
dist 227=[-1.1917751118178887966 ,.93937840387763754005] 
dist 228=[-1.1817807600845532010 ,.93450098240982568482] 
dist 229=[-1.1500450639725377555 ,.91153906853280845451] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 2, 2, 1, 2, 0, 2] 
dist 0=[66.059476443832656118  ,66.059476443832656118  ] 
dist 1=[65.422878199606256214  ,66.394526290273927536  ] 
dist 2=[64.530706747136269125  ,66.573351892290622886  ] 
dist 3=[63.175109608176681265  ,66.586108955719309166  ] 
dist 4=[61.217730369347219227  ,66.502139965753472278  ] 
dist 5=[57.922539358369880958  ,66.370569653068075898  ] 
dist 6=[54.491131547671258111  ,66.022671044991680648  ] 
dist 7=[51.989790638892227840  ,65.680475108678616834  ] 
dist 8=[49.686102415316976571  ,61.952680722955169004  ] 
dist 9=[47.043879842371157312  ,61.251608687273471997  ] 
dist 10=[44.379987567739243514  ,60.203574209717311292  ] 
dist 11=[41.989659782146981620  ,59.858870616956907736  ] 
dist 12=[38.199950464365638837  ,59.075917402632720403  ] 
dist 13=[31.584557067020791619  ,58.833873412104812372  ] 
dist 14=[27.103884908164695207  ,58.515813439630941266  ] 
dist 15=[23.321282544169947346  ,56.392051964162453776  ] 
dist 16=[19.493401628510179376  ,29.765590087900919292  ] 
dist 17=[15.921722737760211584  ,28.605845966104526511  ] 
dist 18=[13.162186760334261011  ,26.309895909670415167  ] 
dist 19=[10.464491711937087273  ,25.817697921866640138  ] 
dist 20=[7.1397840605684657329 ,25.065089426190554801  ] 
dist 21=[3.9830507481199785827 ,24.859728457553362338  ] 
dist 22=[1.9128382771167396979 ,10.988426616223235077  ] 
dist 23=[.2426217845099007461 ,10.650317550885796718  ] 
dist 24=[-1.7585728966465583426 ,2.4212386492554444704 ] 
dist 25=[-4.3549392747365940031 ,1.8207415792040504373 ] 
dist 26=[-6.7310582727596934785 ,-1.0837756122471531370 ] 
dist 27=[-8.4961110795963164872 ,-1.4394857853638723286 ] 
dist 28=[-10.157235737779929437  ,-2.9413596789502000230 ] 
dist 29=[-12.118358932128406731  ,-3.7246695498060789979 ] 
dist 30=[-13.943458612880099140  ,-4.1039996144870494508 ] 
dist 31=[-15.061316587220184788  ,-4.4597924787628948256 ] 
dist 32=[-15.879163129850331198  ,-6.1840349632262077244 ] 
dist 33=[-16.505952988183873394  ,-5.8883519492211908349 ] 
dist 34=[-16.971394620504374073  ,-5.3941786789019858216 ] 
dist 35=[-17.144765072332614248  ,-4.6583202209314992716 ] 
dist 36=[-17.199503378525482694  ,-3.6078221716131847678 ] 
dist 37=[-17.190919155008100604  ,-1.8579073593090770288 ] 
dist 38=[-10.370512464027665526  ,.64501487685279462582] 
dist 39=[-10.323613023440657857  ,2.3582337370049735271 ] 
dist 40=[-9.5283424000736421791 ,3.7769323861558241116 ] 
dist 41=[-9.3851185942737838515 ,5.1606544244607742182 ] 
dist 42=[-9.0097415136348511428 ,6.4131629325490232187 ] 
dist 43=[-8.9080471514261412198 ,7.3086041070637748290 ] 
dist 44=[-8.2110715568537012595 ,8.1128925297880661562 ] 
dist 45=[-8.0577543067045031612 ,9.0020045395231546935 ] 
dist 46=[-7.7839040497795488195 ,9.8072438165107495674 ] 
dist 47=[-7.7088537044338802183 ,10.276901198395603634  ] 
dist 48=[-4.1935614501153721445 ,10.590385345223983152  ] 
dist 49=[-3.8111426529262579452 ,10.772260706544054760  ] 
dist 50=[-2.9761484099308834230 ,10.877221981008424465  ] 
dist 51=[-2.7726624072150869121 ,10.883876132735500752  ] 
dist 52=[-1.8090931552540024202 ,10.840671459704140496  ] 
dist 53=[-1.6334978525825336592 ,10.792591483243788110  ] 
dist 54=[-1.2218504624570516456 ,7.4498658109432503505 ] 
dist 55=[-1.1456981656211192175 ,7.0984055168806402848 ] 
dist 56=[-.4241417806406118897 ,6.2381134676130188846 ] 
dist 57=[-.2936928489225223710 ,6.0790872894194820632 ] 
dist 58=[-.69692721753581364533,4.8382268830695341977 ] 
dist 59=[-1.1775931430057717163 ,4.8811805065560152146 ] 
dist 60=[-1.6530133843904845302 ,4.8847720735266241068 ] 
dist 61=[-2.2437750516460028349 ,3.8752427900764202547 ] 
dist 62=[-2.8028171454882803863 ,2.0189903442240648520 ] 
dist 63=[-3.1517379515646009280 ,1.4971460982894420449 ] 
dist 64=[-3.4126357372615399825 ,-1.0458660242613295004 ] 
dist 65=[-3.6206105046625907365 ,-1.2597289134388919792 ] 
dist 66=[-3.7825286447127823467 ,-1.4942752681124510003 ] 
dist 67=[-3.8597427212501698688 ,-1.4813915161852601609 ] 
dist 68=[-3.8942604970152547237 ,-1.3654353833147044986 ] 
dist 69=[-3.8947589330232136040 ,-1.1277367866745808517 ] 
dist 70=[-2.6144849219698634931 ,-.84868395646265090061] 
dist 71=[-2.6874651081550367065 ,-.55017748809771885684] 
dist 72=[-2.7364069088162876274 ,-.29561477883816637726] 
dist 73=[-2.7662143092250266236 ,-.03564991567210973600] 
dist 74=[-2.7699084582012491707 ,.20687631541381360315] 
dist 75=[-2.7497035224575308003 ,.39191160284519014862] 
dist 76=[-2.7404263465833055900 ,.56970737381271473933] 
dist 77=[-1.9234081200694187619 ,.78338295996612567113] 
dist 78=[-1.8792996384391841734 ,.98417991295628653806] 
dist 79=[-1.8610506514834424162 ,1.1106232367628162375 ] 
dist 80=[-1.0292285946798575390 ,1.2064786099302336529 ] 
dist 81=[-.92175604972087773436,1.2852926441622706882 ] 
dist 82=[-.72743191588220501897,1.4015540116894140028 ] 
dist 83=[-.68389443142737088354,1.5329937574746227485 ] 
dist 84=[-.52495390088069322827,1.6687479520385294544 ] 
dist 85=[-.7262234596306103742 ,1.8458868524260325149 ] 
dist 86=[-.92926546335998888257,2.0125051921250116010 ] 
dist 87=[-1.0619869632089255932 ,2.1062980209263224072 ] 
dist 88=[-1.1681552632002536367 ,2.1648177426792146991 ] 
dist 89=[-1.2653033278905125039 ,2.1906768287230008801 ] 
dist 90=[-1.3487662564745362971 ,2.2029644648127852413 ] 
dist 91=[-1.4003536824594314877 ,2.2073066922133629332 ] 
dist 92=[-1.4382353781818530716 ,2.2067485070140580527 ] 
dist 93=[-1.4670261890724937647 ,2.1994227511258190381 ] 
dist 94=[-1.4872144075895104811 ,1.9622448309581483712 ] 
dist 95=[-1.4907848091092575779 ,1.9539595776529887662 ] 
dist 96=[-1.4869991586382627228 ,1.6941281052673992745 ] 
dist 97=[-1.4801651709340925346 ,1.6674476949518334060 ] 
dist 98=[-1.4265796469368857256 ,1.5705181944458387226 ] 
dist 99=[-1.4100658259388749326 ,1.5439322217120304640 ] 
dist 100=[-1.3796408374019600571 ,1.5034273136574330876 ] 
dist 101=[-1.3688604553104109838 ,1.4894393389315174703 ] 
dist 102=[-1.4129524036310205265 ,-.17696420776283025084] 
dist 103=[-1.6175149330341748141 ,-.10485046640005354515] 
dist 104=[-1.8110909592816825018 ,-.02523312321465925309] 
dist 105=[-1.9323559054937489826 ,.04428674299956250815] 
dist 106=[-2.0236587334768244469 ,.11958262043843444204] 
dist 107=[-2.0977159574459651798 ,.2222348484420262546 ] 
dist 108=[-2.1548866793952882455 ,.33433947281352604926] 
dist 109=[-2.1788314776382524421 ,.44733657673447669166] 
dist 110=[-2.1855240406760460190 ,.58237426529897452501] 
dist 111=[-2.1820197156412291536 ,.78239130712131975722] 
dist 112=[-2.1290630394723994948 ,1.0248913507210566652 ] 
dist 113=[-2.1132155604644826203 ,1.2942642593280653538 ] 
dist 114=[-2.0567283926225590557 ,1.5058628553687114553 ] 
dist 115=[-2.0419463104920955344 ,1.6932219326045364524 ] 
dist 116=[-1.8833746466690226208 ,1.8501170450981475905 ] 
dist 117=[-1.8452861573582390569 ,1.9402020734305951843 ] 
dist 118=[-1.7992728422701181740 ,1.9983771376417835966 ] 
dist 119=[-1.7789212317634924224 ,2.0279889102991561957 ] 
dist 120=[-1.2702015416461455951 ,2.0454712978281943753 ] 
dist 121=[-1.2001821122386848037 ,2.0552672880765159526 ] 
dist 122=[-1.0518940239160078004 ,2.0612758478696081470 ] 
dist 123=[-1.0102563805518093525 ,2.0636595545673922275 ] 
dist 124=[-.84274498120567847185,2.0635337529339304950 ] 
dist 125=[-.80885940952725337657,2.0595386184112972212 ] 
dist 126=[-.7289575644514831854 ,2.0519736440818568642 ] 
dist 127=[-.70933240251312529556,2.0415624334447297456 ] 
dist 128=[.04132106084415707911,.52842734741539709074] 
dist 129=[-.04081126752838521977,.57704115258749956508] 
dist 130=[-.27188364125797040126,.61512982181526930383] 
dist 131=[-.49868170091262410641,.65275450659909994849] 
dist 132=[-.70472473173090375227,.6995118528267347488 ] 
dist 133=[-.85301576890872591075,.74384928004007888258] 
dist 134=[-.987063206256282444  ,.77181590898321783619] 
dist 135=[-1.1362989472882063619 ,.79309468733429545659] 
dist 136=[-1.2737619610884798335 ,.81074519991258259144] 
dist 137=[-1.3608520699425592398 ,.82464959379095490922] 
dist 138=[-1.4275339855013335079 ,.83097799611530353441] 
dist 139=[-1.4835903070156590222 ,.83292609479037195188] 
dist 140=[-1.5283777495376032765 ,.83104895333950708453] 
dist 141=[-1.5501087831548726544 ,.82299220265272756564] 
dist 142=[-1.5590631679331630629 ,.81832963358889865138] 
dist 143=[-1.5579961715073825396 ,.80428075402477149975] 
dist 144=[-1.0128993653758805265 ,.79739173700948266964] 
dist 145=[-1.0818852121293754881 ,.75680730191061315797] 
dist 146=[-1.1194202066030618374 ,.74606403650879971373] 
dist 147=[-1.1410560958753432697 ,.7235989813652741558 ] 
dist 148=[-1.1466228059789977865 ,.71576541383771662009] 
dist 149=[-1.1458128848339594066 ,.57778429759976035308] 
dist 150=[-1.1420108589651835526 ,.55700835797545296778] 
dist 151=[-1.1353203586582475770 ,.50593777389268577465] 
dist 152=[-1.1300185700726704900 ,.49447765872118926603] 
dist 153=[-1.1080033066863492032 ,.41458215945832162069] 
dist 154=[-1.0998422873382539774 ,.490295722793757375  ] 
dist 155=[-1.0747050813384297811 ,.56338276710341364178] 
dist 156=[-1.0642984428554459083 ,.62901694533540804995] 
dist 157=[.1433958658281561466 ,.67500808616668999486] 
dist 158=[.22819569248219940554,.71534886025002068957] 
dist 159=[.3467310382581214250 ,.75845509511221455277] 
dist 160=[.44810192021346354875,.79761331907467483167] 
dist 161=[.64080609212833399704,.82955097209760941639] 
dist 162=[.67219733833524839887,.86775460254677745242] 
dist 163=[.7314634633863080518 ,.9147109954300225073 ] 
dist 164=[.72853253760352848867,1.0163389521469472899 ] 
dist 165=[.6720358641962673862 ,1.1087421550774869760 ] 
dist 166=[.59408890037568549523,1.1603928324267471690 ] 
dist 167=[.46672003353627407374,1.1919797669379527757 ] 
dist 168=[.33106513789830181789,1.2043476542260622626 ] 
dist 169=[.22006231275107987952,1.2093070065604736760 ] 
dist 170=[.10552975376370575112,1.2113414416749726073 ] 
dist 171=[-.05966255464650535679,1.2116213193471855556 ] 
dist 172=[-.2373775693997288208 ,1.2095832297506054719 ] 
dist 173=[-.41275364259823738475,1.0412762447952614614 ] 
dist 174=[-.61966673810075964994,1.0261993528083363060 ] 
dist 175=[-.9231921610022331624 ,1.0180134055550885997 ] 
dist 176=[-1.2233272422109741201 ,.96791328964916005453] 
dist 177=[-1.4167170998468268376 ,.95429929652040898009] 
dist 178=[-1.5685891257836390480 ,.9289145758620097131 ] 
dist 179=[-1.7031028086082578475 ,.92057308264117734704] 
dist 180=[-1.8158631656411731621 ,.88303439965008295581] 
dist 181=[-1.8809581549168875341 ,.87278357805587310036] 
dist 182=[-1.9234897671431502914 ,.84524953730476593832] 
dist 183=[-1.9462426953703118701 ,.83491941387696096475] 
dist 184=[-1.9578185664300919523 ,.77664679171568714766] 
dist 185=[-1.9557630418465571109 ,.76255932715127916392] 
dist 186=[-1.9456737284753822481 ,.73454128347232864889] 
dist 187=[-1.9372170969036835772 ,.72562004033195888894] 
dist 188=[-1.8779119855086962230 ,.68572377620055776908] 
dist 189=[-1.8606656389099725585 ,.6760110945731247019 ] 
dist 190=[-1.8102693363841785025 ,.64891021311242000084] 
dist 191=[-1.7915033821086920030 ,.64134812605462463427] 
dist 192=[-.52409477581304611565,.67885161494440073766] 
dist 193=[-.60099675979328889535,.94809746533117057666] 
dist 194=[-.66975671529021607619,1.1651861870714569737 ] 
dist 195=[-.74558440738826816579,1.3672282905650485909 ] 
dist 196=[-.85067954668007393707,1.5436381360996846738 ] 
dist 197=[-.95560289315367988072,1.6708176310340121043 ] 
dist 198=[-1.0307449099486098948 ,1.7820575530488040642 ] 
dist 199=[-1.0983112793956223334 ,1.8905843803179243436 ] 
dist 200=[-1.1730142548636247564 ,1.9850916404782513985 ] 
dist 201=[-1.2464008922327356370 ,2.0404063442759828452 ] 
dist 202=[-1.3087157579417717944 ,2.0775006941161840630 ] 
dist 203=[-1.3747263546163014556 ,2.0993242619146120073 ] 
dist 204=[-1.4628545180889091560 ,2.1096146035392803626 ] 
dist 205=[-1.5455721980304520176 ,2.1078167703594273067 ] 
dist 206=[-1.5899999479816316179 ,2.0863643025719858830 ] 
dist 207=[-1.6147953083584150771 ,2.0750184018484182044 ] 
dist 208=[-1.6191988719006859210 ,1.0785464865740035715 ] 
dist 209=[-1.6150397951676859005 ,1.0714702697167694773 ] 
dist 210=[-1.6074354598464934689 ,1.0655207293130912249 ] 
dist 211=[-1.5919079077300625619 ,1.0542632884178804818 ] 
dist 212=[-1.5836126875750446935 ,1.0487498758245960733 ] 
dist 213=[-1.3502297628861883917 ,.88625966925250643214] 
dist 214=[-1.3134592487284136287 ,.86100682135578393106] 
dist 215=[-1.2327660514973262248 ,.80591103645173018692] 
dist 216=[-1.2957659895310490792 ,.7889274827474196035 ] 
dist 217=[-1.3922733597607786782 ,.71333665925251428239] 
dist 218=[-1.4599115605271842237 ,.69755092445971934726] 
dist 219=[-1.5056358999740930854 ,.65376132852717483351] 
dist 220=[-1.5382212525421165155 ,.64580164261519444808] 
dist 221=[-1.5534472412257403331 ,-.40867815160690264059] 
dist 222=[-1.5588425444643228860 ,-.39377164366012637609] 
dist 223=[-1.5561760347543479595 ,-.35080161352642078791] 
dist 224=[-.5458585617110771935 ,-.30053645525990320623] 
dist 225=[-.46902067461906699101,-.15204840248545644832] 
dist 226=[-.45287200872423267857,-.02445476878035824595] 
dist 227=[-.4332175359084378663 ,.10695449885736431856] 
dist 228=[-.4254940106821327406 ,.23042825070021048293] 
dist 229=[-.27331999886308868167,.32636761255031498139] 
dist 230=[-.29521053280797854464,.42031496547212853568] 
dist 231=[-.33627467500399008931,.5358434044925896616 ] 
dist 232=[-.3820114026120710262 ,.64469996286879858954] 
dist 233=[-.42254039787570259302,.71203348107479267632] 
dist 234=[-.46693665887410168855,.76171099239482861352] 
dist 235=[-.52809866868175219388,.80013780694915865937] 
dist 236=[-.59520267512834988356,.82974316266213098835] 
dist 237=[-.66330081569967994526,.88492160619576411519] 
dist 238=[-.745027880195225527  ,1.0088327861676864539 ] 
dist 239=[-.86649670725672268658,1.1840321538888095738 ] 
dist 240=[-.98604386357815918086,1.3537461221371660005 ] 
dist 241=[-1.0601049221145018720 ,1.4557756592062807077 ] 
dist 242=[-1.1148752071434202554 ,1.5275783875943315694 ] 
dist 243=[-1.1574710660693976572 ,1.5767120450755883755 ] 
dist 244=[-1.1888873119203572140 ,1.6119984848894210807 ] 
dist 245=[-1.1990619123406012285 ,1.6285613484023996792 ] 
dist 246=[-1.2014976327510204676 ,1.6345527938269376628 ] 
dist 247=[-1.2020441219310838138 ,1.6320304932405344073 ] 
dist 248=[-1.1436223531132432590 ,1.4436237804371116269 ] 
dist 249=[-1.1302329256654174767 ,1.4124176123225733985 ] 
dist 250=[-1.0969349363576787182 ,1.3561078205477201207 ] 
dist 251=[-1.0840699903070674251 ,1.3400215476358138378 ] 
dist 252=[-1.0167494214363990544 ,1.2786432189834741853 ] 
dist 253=[-1.0004221701102112112 ,1.2605183542266692890 ] 
dist 254=[-.96274518009187702731,1.2269794123389829082 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 1, 2, 0, 2] 
dist 0=[57.713696568860087276  ,57.713696568860087276  ] 
dist 1=[56.659217273278465522  ,58.516158778947273102  ] 
dist 2=[55.192531342531800105  ,58.976511234798167818  ] 
dist 3=[53.140092254195163206  ,59.275226916227381362  ] 
dist 4=[49.746822463257597529  ,59.432059540962049503  ] 
dist 5=[46.237433361955191289  ,59.463502760908577887  ] 
dist 6=[43.721343313490592125  ,59.423593598547046993  ] 
dist 7=[41.446772986740634789  ,59.031785248956112199  ] 
dist 8=[38.901684985785579600  ,58.040947119070673631  ] 
dist 9=[36.371917353210184751  ,57.195259198448828182  ] 
dist 10=[34.158417996575084923  ,56.780548108804868003  ] 
dist 11=[31.748308108648909089  ,56.171426891215079578  ] 
dist 12=[28.433247646650943168  ,55.945087961616377878  ] 
dist 13=[25.111857985536464646  ,55.319587931484878589  ] 
dist 14=[22.676313133335450595  ,55.068084482734570834  ] 
dist 15=[20.417800829263164336  ,53.930661986692308432  ] 
dist 16=[17.803039831861934731  ,51.686668368325009433  ] 
dist 17=[15.151030312439938383  ,33.202320102170882690  ] 
dist 18=[12.743391376229240839  ,31.406057596059455492  ] 
dist 19=[10.046312464818241010  ,27.116292278517914212  ] 
dist 20=[6.2376512394857972760 ,26.492869812413521899  ] 
dist 21=[2.4921336695683178391 ,20.515279170453670276  ] 
dist 22=[.04708947160777363128,19.439396084052402206  ] 
dist 23=[-1.9217788282100496840 ,18.119591615517281619  ] 
dist 24=[-3.7652982747344918573 ,17.872915107611145857  ] 
dist 25=[-5.3955013893710553473 ,9.6520078843568649300 ] 
dist 26=[-6.8296611390328376752 ,8.6751701184931538955 ] 
dist 27=[-8.4615764884455309928 ,6.6072858191142696258 ] 
dist 28=[-10.588805945145332177  ,6.1734566996442885221 ] 
dist 29=[-12.608458258284398276  ,4.1669968070221495356 ] 
dist 30=[-13.810921982400076855  ,3.8211882899444234508 ] 
dist 31=[-14.655254236799220831  ,3.2351640722311313623 ] 
dist 32=[-15.243508550810771776  ,3.1222991093788591184 ] 
dist 33=[-15.678370652698942562  ,-2.7362242731684449696 ] 
dist 34=[-15.909223419114120301  ,-3.2303602064486833104 ] 
dist 35=[-16.038480122240129570  ,-4.0984146099912648270 ] 
dist 36=[-16.066109642223394942  ,-2.1671380378453035064 ] 
dist 37=[-14.323541444230051128  ,-.20446811585710518618] 
dist 38=[-14.053569214366899522  ,1.1238095040780945301 ] 
dist 39=[-13.611617422076093785  ,2.2373597149940220577 ] 
dist 40=[-13.477846346027336807  ,3.3439194363934752133 ] 
dist 41=[-13.093941634794129095  ,4.3571930348937505583 ] 
dist 42=[-12.960899468358928586  ,5.0988053616362600057 ] 
dist 43=[-12.878776147722510005  ,5.7813081713944893552 ] 
dist 44=[-12.845560495333296308  ,6.5589062208274490505 ] 
dist 45=[-10.003140501497943422  ,7.2713320233364371165 ] 
dist 46=[-10.009570285857207707  ,7.6938973523474527595 ] 
dist 47=[-9.9562062507471196054 ,7.9838060505012825273 ] 
dist 48=[-9.9335556823438444715 ,8.1670626848952912794 ] 
dist 49=[.25687814680537113086,8.2838850175890649488 ] 
dist 50=[.33379276038836217521,8.3088456876300832889 ] 
dist 51=[.3454165844754703446 ,8.2869842481952979690 ] 
dist 52=[.27161447519830150952,8.2527214718746181098 ] 
dist 53=[.17727930309806542876,8.9978873373266630333 ] 
dist 54=[.10700362027084736227,9.8066263420692930975 ] 
dist 55=[.04158110652937141809,10.429601568988388588  ] 
dist 56=[-.0334932384907745953 ,10.962059230126751303  ] 
dist 57=[-.1082908617857204703 ,11.395676366726023292  ] 
dist 58=[-.1726500076979513477 ,11.624148754208689211  ] 
dist 59=[-.2412487729226681005 ,11.746152869463438431  ] 
dist 60=[-.3329786936134791275 ,11.756725507374442097  ] 
dist 61=[-.52901301711392404187,7.5369369325206095248 ] 
dist 62=[-1.5767395020056076269 ,7.5609792501374256706 ] 
dist 63=[-2.4374396071934100988 ,7.5632609374958505268 ] 
dist 64=[-3.2611142504451858451 ,7.5366748862938798684 ] 
dist 65=[-3.9963222369580907047 ,2.5691016904605590644 ] 
dist 66=[-4.5041349509296721418 ,2.1587327315735043209 ] 
dist 67=[-4.9419092808995654988 ,1.2157220382800851913 ] 
dist 68=[-5.3977628262363281495 ,1.0476295327072497763 ] 
dist 69=[-5.8061995502682249706 ,.31307750044212221374] 
dist 70=[-6.0548198656657869001 ,.38620907445690805445] 
dist 71=[-6.2337891629115147113 ,.44663748414471465712] 
dist 72=[-6.3643361265302882322 ,.50531237840742671768] 
dist 73=[-6.4537728289609218336 ,.55814245267093498437] 
dist 74=[-6.4687309393204778694 ,.59524078010744379231] 
dist 75=[-6.4513873477778817984 ,.62775333045561036088] 
dist 76=[-6.4207586682843719880 ,.66226419855249133006] 
dist 77=[-4.7709514180606850305 ,.69257705998785231526] 
dist 78=[-4.8729626770935624193 ,.70834700756660363385] 
dist 79=[-4.9221864848054070351 ,.71635522305925842136] 
dist 80=[-4.9261641584866364717 ,.71771912713912929187] 
dist 81=[-1.1762311939223872163 ,.89269357861089111691] 
dist 82=[-.99333574763437301093,1.3250744104909214544 ] 
dist 83=[-.74360642105738879114,1.7413814463987495064 ] 
dist 84=[-.67004103587377120333,2.2433462938659193868 ] 
dist 85=[.03929031671195075293,2.7133605391035416500 ] 
dist 86=[.1069658957273043982 ,3.0022350337754561329 ] 
dist 87=[.24691236046546012366,3.2131766847022424038 ] 
dist 88=[.27865509000643951976,3.3723296586849887933 ] 
dist 89=[.21509626232956476851,3.4933529727313939464 ] 
dist 90=[.15774037179258994379,3.5521998535401413263 ] 
dist 91=[.09408477071043491498,3.5767053640600141699 ] 
dist 92=[.00544335266531679821,3.5766738203602364549 ] 
dist 93=[-.08297831111233859457,1.8655940039547599493 ] 
dist 94=[-.14573319226437916221,1.9472321733645036066 ] 
dist 95=[-.20142107753656237841,2.0142799127017963274 ] 
dist 96=[-.32404831005231632802,2.0791109420472898070 ] 
dist 97=[-.51882661476153348225,2.1316772929213665815 ] 
dist 98=[-.71593280027464674757,2.1498017377032044680 ] 
dist 99=[-.95197550553968859946,2.1536437364649285993 ] 
dist 100=[-1.3020456585054869051 ,2.1491375486359273010 ] 
dist 101=[-1.6477303835670478112 ,2.0739197675275846769 ] 
dist 102=[-1.8662781928624097074 ,2.0501745056071180131 ] 
dist 103=[-2.0329667724329304661 ,2.0255021723585163195 ] 
dist 104=[-2.1718067392686135966 ,2.0104615211824637234 ] 
dist 105=[-2.2821184710284530807 ,1.7439503939768482956 ] 
dist 106=[-2.3350262335741820409 ,1.7356180292679498380 ] 
dist 107=[-2.3614802265504649012 ,1.7076971651971141265 ] 
dist 108=[-2.3662830367620365672 ,1.6933525050747061309 ] 
dist 109=[-2.2901392911175533726 ,1.4950106854442289286 ] 
dist 110=[-2.2674588660437420746 ,1.4613419626604664208 ] 
dist 111=[-2.2294223318566257093 ,1.3754488906662879156 ] 
dist 112=[-2.2143277890694339814 ,1.3535353965354443486 ] 
dist 113=[-2.1449901258829946053 ,1.2020881371165712912 ] 
dist 114=[-2.1236492167687891096 ,1.1694087204817954107 ] 
dist 115=[-2.0636784827763230548 ,1.1116202852104368020 ] 
dist 116=[-2.0393753410779500357 ,1.0962169367883774301 ] 
dist 117=[-1.7335255075131302793 ,.09159311273787703757] 
dist 118=[-1.8357932499294423442 ,.2000655035815246202 ] 
dist 119=[-1.9105579829331680227 ,.30178979161932288447] 
dist 120=[-1.9672289101141719188 ,.42056831910780237096] 
dist 121=[-2.0118071205123398309 ,.54094160973992256697] 
dist 122=[-2.0383243748488051993 ,.64905430744492685586] 
dist 123=[-2.0566821837368632597 ,.76874577646802855854] 
dist 124=[-2.0687000479976524980 ,.93534833213709811633] 
dist 125=[-2.0757283262258215983 ,1.1019562682540718842 ] 
dist 126=[-2.0741758354762092599 ,1.2778077197378146993 ] 
dist 127=[-2.0660537972558699207 ,1.4234179152955926393 ] 
dist 128=[-2.0581389926035148083 ,1.5655625086303688565 ] 
dist 129=[-.70883356256968654008,1.6943772636107071877 ] 
dist 130=[-.59487449068132346685,1.7868033606564372624 ] 
dist 131=[-.33310637025610698333,1.8701561228078798608 ] 
dist 132=[-.28585000664160679103,1.9627691182767196586 ] 
dist 133=[.04511799381089555731,2.0452283871853078350 ] 
dist 134=[.10300397049636697539,2.0880688773949606691 ] 
dist 135=[.20661751781914054266,2.1100336733108798725 ] 
dist 136=[.228667273594755141  ,2.1122768682686679761 ] 
dist 137=[.17036538248618047596,2.0981784074344629302 ] 
dist 138=[-.11438443475179628388,2.0878178823838939586 ] 
dist 139=[-.45964666179457875364,2.0580910831509327635 ] 
dist 140=[-.97687583341527219331,2.0429869505608599236 ] 
dist 141=[-1.4914445499869460716 ,1.7856793914875735916 ] 
dist 142=[-1.8260980414501981358 ,1.7425490799718661794 ] 
dist 143=[-2.0924227738497066862 ,1.6433214809959417997 ] 
dist 144=[-2.3344202681448119521 ,1.6254077749850963476 ] 
dist 145=[-2.5417237116707079304 ,1.4608044065720623690 ] 
dist 146=[-2.6696516217707607352 ,1.4278843717829537549 ] 
dist 147=[-2.7637189031556340159 ,1.3499526718881458847 ] 
dist 148=[-2.8359535084406739652 ,1.3240509102871439454 ] 
dist 149=[-2.8903306659904949887 ,1.0597440542764205912 ] 
dist 150=[-2.9131618312214112200 ,1.0170303355983872603 ] 
dist 151=[-2.9172475617727610091 ,.91477993417081471645] 
dist 152=[-2.9118899944682941651 ,.89091086237288666699] 
dist 153=[-2.8642047696963950601 ,.73767948125893911136] 
dist 154=[-2.8468318681277942898 ,.70687150056873660195] 
dist 155=[-2.7786791878106836415 ,.64946029234486136482] 
dist 156=[-2.7614453854863249524 ,.63442921627699882756] 
dist 157=[-1.3985665069864617404 ,.66886372117570209546] 
dist 158=[-1.3986080565699774783 ,.96605033290106868043] 
dist 159=[-1.3973957592331181323 ,1.2333300431074275187 ] 
dist 160=[-1.3941641808379397747 ,1.5611366668863768119 ] 
dist 161=[-1.0888191183973316762 ,1.8535623072261312209 ] 
dist 162=[-1.1326152783123318114 ,2.0549733348368292678 ] 
dist 163=[-1.1618396753902578120 ,2.2278806828872972496 ] 
dist 164=[-1.1758063054855755167 ,2.4066085375868967710 ] 
dist 165=[-1.1823701275071825779 ,2.5658664750145826191 ] 
dist 166=[-1.1820629735007263036 ,2.6611083759204403632 ] 
dist 167=[-1.1766619781720948324 ,2.7275129609810080707 ] 
dist 168=[-1.1726304021827759824 ,2.7717356275393000158 ] 
dist 169=[-1.0143275115880696181 ,2.7982147329486264454 ] 
dist 170=[-.98906126295165576759,2.8004060360224369990 ] 
dist 171=[-.93704620805305962901,2.7798470732307332505 ] 
dist 172=[-.92128789243460803813,2.7679721360647031158 ] 
dist 173=[-.85327830536428049353,1.4511088365884953306 ] 
dist 174=[-.8380028496138542055 ,1.3296088708424944778 ] 
dist 175=[-.79684100519567181218,1.1652615953145670415 ] 
dist 176=[-.81436496185778975113,1.1623838084556142196 ] 
dist 177=[-1.0355388207157033724 ,.57589379682774231594] 
dist 178=[-1.1985628549936791604 ,.66946956801932392997] 
dist 179=[-1.3498532751207038280 ,.8139060600464421855 ] 
dist 180=[-1.5242202845797154924 ,.95386682840800601281] 
dist 181=[-1.6840149756139673481 ,1.0799236629958773738 ] 
dist 182=[-1.7771782172372738322 ,1.1688912341493620175 ] 
dist 183=[-1.8391667932789115244 ,1.2475584263295608230 ] 
dist 184=[-1.8746125181589720289 ,1.3325203833234969860 ] 
dist 185=[-1.8962904826970873946 ,1.4073825338912675171 ] 
dist 186=[-1.9033606424050577916 ,1.4457596279597085420 ] 
dist 187=[-1.9010636227165811941 ,1.4660153481089212173 ] 
dist 188=[-1.8954043923921746888 ,1.4692585580795876217 ] 
dist 189=[-.65273328616474822181,1.4526044236502900254 ] 
dist 190=[-.66136935403133174214,1.4452166287620981356 ] 
dist 191=[-.6754034734573608089 ,1.4378478670361658151 ] 
dist 192=[-.70046994331511252781,1.4293909595366905506 ] 
dist 193=[-.73067289700713805771,1.0435652951703596111 ] 
dist 194=[-.76519412620644660491,.99706799882188982238] 
dist 195=[-.80943329935940692715,.99021104172079910222] 
dist 196=[-.88112961521031123568,1.1650663525018151072 ] 
dist 197=[-1.0186572156722955174 ,1.3304217685393107102 ] 
dist 198=[-1.1120586043686168512 ,1.4337427931123980069 ] 
dist 199=[-1.1908654867812854141 ,1.5112056975961580054 ] 
dist 200=[-1.2701770041969289733 ,1.5734150307918088955 ] 
dist 201=[-1.3398374014543813189 ,1.6209228443232727579 ] 
dist 202=[-1.3801432522243172792 ,1.6397436206751208671 ] 
dist 203=[-1.4066063861710136223 ,1.6458861330704336139 ] 
dist 204=[-1.4890026324895048692 ,1.6907764924742537160 ] 
dist 205=[-1.6057888864563492021 ,2.0225847168458713883 ] 
dist 206=[-1.6753707602599769329 ,2.2283959698713261826 ] 
dist 207=[-1.7235432497028959852 ,2.3809397731828831696 ] 
dist 208=[-1.7549287045931227420 ,2.5002566071774244895 ] 
dist 209=[-1.7734850346434193598 ,2.5921857585720495914 ] 
dist 210=[-1.7761452724834601344 ,2.6354751054978379557 ] 
dist 211=[-1.7618570127404725805 ,2.6537116357312162043 ] 
dist 212=[-1.7579799354267887573 ,2.6533960623356639635 ] 
dist 213=[-1.6333139604234386845 ,2.4793098842088063402 ] 
dist 214=[-1.6088925827779033794 ,2.4437891323139870668 ] 
dist 215=[-1.5417482876460248854 ,2.3795544055906647464 ] 
dist 216=[-1.5231849250152159864 ,2.3588789547809998918 ] 
dist 217=[-1.3849904667524898449 ,2.2688354853267650032 ] 
dist 218=[-1.3534514711331316840 ,2.2427939980750781373 ] 
dist 219=[-1.3270819133678663045 ,2.1785047100603240255 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 1, 2] 
dist 0=[59.152839874792407208  ,59.152839874792407208  ] 
dist 1=[57.808101609506190073  ,60.198532885934291065  ] 
dist 2=[56.106069115900508433  ,60.706579350389792151  ] 
dist 3=[53.813595972731210964  ,60.937768656127658855  ] 
dist 4=[50.111318232126467243  ,60.953223006774854746  ] 
dist 5=[46.308020927512949938  ,60.500358738848509350  ] 
dist 6=[43.612141128669118421  ,60.337517321022005618  ] 
dist 7=[41.206995586471395412  ,59.551719649199102764  ] 
dist 8=[38.564398524911667052  ,58.238134595510726760  ] 
dist 9=[35.965836387990074262  ,57.469625739026806036  ] 
dist 10=[33.736346689041497369  ,57.213983430516362039  ] 
dist 11=[31.345811653600380198  ,56.647042889195813530  ] 
dist 12=[28.103870480030738146  ,56.427148161968793185  ] 
dist 13=[24.875773007122022755  ,55.363843941612428989  ] 
dist 14=[22.540301636448684208  ,55.106073383446170646  ] 
dist 15=[20.405853464157906624  ,53.367765665084839488  ] 
dist 16=[17.980125291217556438  ,50.188014309728396068  ] 
dist 17=[15.544188156982350400  ,27.545747076665048111  ] 
dist 18=[13.368515303128811867  ,25.411450949108031437  ] 
dist 19=[10.959251687512574658  ,21.212844205181810099  ] 
dist 20=[7.5895259765635027658 ,20.958898877703891839  ] 
dist 21=[4.2726132657734247358 ,13.942930505427277816  ] 
dist 22=[2.0741790987214366073 ,12.954960164342230904  ] 
dist 23=[.26566514194429904084,11.169631943349679449  ] 
dist 24=[-1.4933928366514970193 ,10.795579214861066609  ] 
dist 25=[-3.0942706464910383876 ,6.4362303224049562698 ] 
dist 26=[-4.2708632660545885399 ,6.0595305723004923600 ] 
dist 27=[-5.3668267584731123523 ,5.4353484247716123422 ] 
dist 28=[-6.6457324054533283720 ,5.3067240651228307794 ] 
dist 29=[-7.8304126982537191756 ,-2.2176874443590388413 ] 
dist 30=[-8.6922703164422108696 ,-2.8506537738541865771 ] 
dist 31=[-9.8548785158628305557 ,-3.6679276423773550143 ] 
dist 32=[-11.259927915226461142  ,-3.1062903593092846776 ] 
dist 33=[-12.556480289982432115  ,-2.3833833818808949718 ] 
dist 34=[-13.285946716732727718  ,-1.5055317879826198322 ] 
dist 35=[-13.750373511503975843  ,-.35062134701461696552] 
dist 36=[-13.986937420376923213  ,1.4775794838893822165 ] 
dist 37=[-14.124187041970599991  ,3.3172465087879378871 ] 
dist 38=[-14.190908957711099510  ,4.5180909330497558049 ] 
dist 39=[-14.222496806334055086  ,5.4766199610822192123 ] 
dist 40=[-14.217735877101867591  ,6.3501687326016036627 ] 
dist 41=[-12.133251805620980468  ,7.0985416767962106692 ] 
dist 42=[-11.940717592712015634  ,7.5579444112937249402 ] 
dist 43=[-11.907482609535644218  ,7.8920042246542472459 ] 
dist 44=[-11.875503142763746170  ,8.1405137825678427343 ] 
dist 45=[-10.640683792396325168  ,8.3344921853288710961 ] 
dist 46=[-10.496665053945652694  ,8.4510723676334262133 ] 
dist 47=[-10.359814143615714662  ,8.5326210871212669586 ] 
dist 48=[-10.297567750165220052  ,8.5868710290158141696 ] 
dist 49=[-3.4052527482410070846 ,8.6186525965824808111 ] 
dist 50=[-3.2601029001459039644 ,8.6105406507631681899 ] 
dist 51=[-2.8993736407046343138 ,8.5711187903874294184 ] 
dist 52=[-2.8369230124168214445 ,8.8279312509710043869 ] 
dist 53=[1.0449971937752055838 ,9.0808677838682527570 ] 
dist 54=[1.4017979214931371206 ,9.2317891862056272804 ] 
dist 55=[2.1974536147007532037 ,9.3375139587430194863 ] 
dist 56=[2.3254730392713497303 ,9.4099316141348419009 ] 
dist 57=[3.2145108790217857420 ,9.4559765719462097572 ] 
dist 58=[3.3535134853578644671 ,9.4563781375846766263 ] 
dist 59=[3.6073486093429107614 ,9.4236955948829823013 ] 
dist 60=[3.5952147508807822923 ,9.3882099821880015418 ] 
dist 61=[1.9022508260061539178 ,9.6831881731716339428 ] 
dist 62=[.7376742454791360759 ,9.8368206724673183171 ] 
dist 63=[-.26050558277928386751,9.9031405849514147085 ] 
dist 64=[-1.2897456188994821834 ,9.9072467789749918483 ] 
dist 65=[-2.2577128625742014409 ,4.8223718871015239061 ] 
dist 66=[-3.0114952752471129242 ,4.8221485514669284697 ] 
dist 67=[-3.7513173390460736856 ,4.7783093116280785842 ] 
dist 68=[-4.6636239325292162524 ,4.7571110260247531637 ] 
dist 69=[-5.5248444356655264107 ,2.4649582817527266880 ] 
dist 70=[-6.0608821878284867407 ,2.2533125796435992533 ] 
dist 71=[-6.4604163628015441632 ,1.7493551398465921330 ] 
dist 72=[-6.7770925023197711151 ,1.6616832044455479718 ] 
dist 73=[-7.0189491451474039921 ,.95800165945528382709] 
dist 74=[-7.1200137376955146195 ,.8290529457641895937 ] 
dist 75=[-7.1598227050366053052 ,.62949332578641578202] 
dist 76=[-7.1573042821846584062 ,.57772335640646145787] 
dist 77=[-5.7477251262944625720 ,-.29385861313128363888] 
dist 78=[-5.7564737188149584611 ,.35961691929809551262] 
dist 79=[-5.7045328982815533514 ,.90703900010196579229] 
dist 80=[-5.6947719991699880395 ,1.4509987190776492920 ] 
dist 81=[-3.2312511199594712050 ,1.9495467983124868424 ] 
dist 82=[-3.1947847746546394842 ,2.3158510371211448577 ] 
dist 83=[-3.2041629923284296742 ,2.6546113478087525857 ] 
dist 84=[-3.1988122552362708278 ,3.0433154113675267085 ] 
dist 85=[-1.4871665540401274600 ,3.4005285683862819540 ] 
dist 86=[-1.3290432250932079794 ,3.6136836004210443057 ] 
dist 87=[-1.1145344369243312545 ,3.7616975660917825622 ] 
dist 88=[-1.0525892672118075345 ,3.8590697854108028280 ] 
dist 89=[-1.0956911184305882698 ,3.9239807608712415138 ] 
dist 90=[-1.1491405326673546641 ,3.9425135471610967904 ] 
dist 91=[-1.2203171716383195614 ,3.9371649723868377582 ] 
dist 92=[-1.3341270918576475784 ,3.9234604935043715814 ] 
dist 93=[-1.4544496734871561830 ,3.4081165893381587713 ] 
dist 94=[-1.5516010417691351639 ,3.4419838650145113896 ] 
dist 95=[-1.6501844479098904651 ,3.4494807148847010162 ] 
dist 96=[-1.7762125524836797995 ,3.4395832157495990252 ] 
dist 97=[-1.9098946770759689609 ,1.8724459393814982169 ] 
dist 98=[-2.0390042707412382474 ,1.8741101527300812476 ] 
dist 99=[-2.1891954477804581530 ,2.2421790741591014882 ] 
dist 100=[-2.4069619649682611821 ,2.7716672493767439715 ] 
dist 101=[-2.6189203047511583540 ,3.2888785071773404992 ] 
dist 102=[-2.7459408042527060945 ,3.6079750878226484394 ] 
dist 103=[-2.8347646816938486820 ,3.8424611557340374164 ] 
dist 104=[-2.8943612431708896728 ,4.0221496897217842250 ] 
dist 105=[-2.9318382497900904486 ,4.1592924297314715706 ] 
dist 106=[-2.9380436016133905831 ,4.2240555167766981298 ] 
dist 107=[-2.9216100666088353858 ,4.2496574709476614108 ] 
dist 108=[-2.9135547979000460456 ,4.2493942653089113482 ] 
dist 109=[-2.7008432247851185764 ,3.9249344233839507121 ] 
dist 110=[-2.6592079874726125154 ,3.8627110625025523204 ] 
dist 111=[-2.5507092371045276290 ,3.7506024878507977814 ] 
dist 112=[-2.5155183558126487896 ,3.7156940596625647244 ] 
dist 113=[-2.3054568463133441105 ,3.5688827428369366621 ] 
dist 114=[-2.2567464477276064116 ,3.5259519344084113308 ] 
dist 115=[-2.1639874955181837718 ,3.4269778349851624581 ] 
dist 116=[-2.1361867954496295315 ,3.3898572516413171895 ] 
dist 117=[-1.5072554520065457719 ,.29619581335457205875] 
dist 118=[-1.5193811483760270408 ,.32543740309428847924] 
dist 119=[-1.5243712312884714698 ,.34926049248687717992] 
dist 120=[-1.5209603423164738404 ,.37165440393902680657] 
dist 121=[-1.5124559994662103595 ,.39101215296225207432] 
dist 122=[-1.5057009493621192510 ,.41161748957418128824] 
dist 123=[-1.4810617677118107691 ,.48423894793745941762] 
dist 124=[-1.4696462734290185589 ,.55610551020513562971] 
dist 125=[-.61167244932670453601,.62185247618169439094] 
dist 126=[-.53345696597753461584,.67009284452734251031] 
dist 127=[-.35554097801581079119,.71475011051749858688] 
dist 128=[-.3482849900027721166 ,.76625171754682554859] 
dist 129=[-.09870730355183686265,.92922121949805234196] 
dist 130=[-.05940848019475685012,1.0589521685859721010 ] 
dist 131=[-.00968810939380346069,1.1683903661733893479 ] 
dist 132=[-.07894456582314435523,1.2785499768898518846 ] 
dist 133=[-.14996721217101543276,1.3805600021343873450 ] 
dist 134=[-.21476491764463881842,1.4574784429333818058 ] 
dist 135=[-.28719130800179731898,1.5306330738075003509 ] 
dist 136=[-.38865344481527585471,1.6176188846411764445 ] 
dist 137=[-.49026721586627568929,1.6981462187773878894 ] 
dist 138=[-.56330863662517295647,1.7455294592259994837 ] 
dist 139=[-.62921853008405272123,1.7776130758116877723 ] 
dist 140=[-.70240586312282723985,1.7970955159604286802 ] 
dist 141=[-.77448791058079342237,1.8068975074947710713 ] 
dist 142=[-.83600355579066771481,1.8055715896505035214 ] 
dist 143=[-.90146887521509786482,1.7887646805315128069 ] 
dist 144=[-1.1244502779223835758 ,1.7784639560286329018 ] 
dist 145=[-1.5716626647448231738 ,1.6889846136790391168 ] 
dist 146=[-1.8598946117216161174 ,1.6668521415658898618 ] 
dist 147=[-2.0862915143034135528 ,1.6134184852972723876 ] 
dist 148=[-2.2868491603267369730 ,1.5933618119981054992 ] 
dist 149=[-2.4549842601372978476 ,1.4901776769936533477 ] 
dist 150=[-2.5520528321967493056 ,1.4654397297840103834 ] 
dist 151=[-2.6154940566672407292 ,1.4062928461829159690 ] 
dist 152=[-2.6494998119948921026 ,1.3852409994336184331 ] 
dist 153=[-2.6677936056990504460 ,1.1329895138465849281 ] 
dist 154=[-2.6685590149425226487 ,1.0936579939547057130 ] 
dist 155=[-2.6566741675301990397 ,1.0264466297504143803 ] 
dist 156=[-2.6476395325862005516 ,1.0160176725737855844 ] 
dist 157=[-2.5826687362035196402 ,.99100909737083264353] 
dist 158=[-2.5633650187147525321 ,.98014368591184504389] 
dist 159=[-2.4889398699110896128 ,.97136871348712409756] 
dist 160=[-2.4749796017231046545 ,.96385110536728907932] 
dist 161=[-.92664975740910326539,.75518360107485189076] 
dist 162=[-.9251263006002985914 ,.77571514795372309526] 
dist 163=[-.9242121728465547519 ,.78647089897783104682] 
dist 164=[-.9238965763388173205 ,.78831508435899518357] 
dist 165=[-.72966673688719251954,.77975374722534061913] 
dist 166=[-.70251297114742554934,.77486471982854179793] 
dist 167=[-.65346561088583426431,.76593449204139438764] 
dist 168=[-.64088206933917386728,.76186227725953861865] 
dist 169=[-.59963007640759938851,.73900900190674855347] 
dist 170=[-.58721977700120210612,.73263479520831632464] 
dist 171=[-.57891032235990622998,.71024073089425829144] 
dist 172=[-.5769056334367727390 ,.70554546265131659085] 
dist 173=[.18432869729268993219,.6807523322849502390 ] 
dist 174=[.24431311755426247954,.6930764131956270162 ] 
dist 175=[.33420295421108492228,.6993682718218309062 ] 
dist 176=[.29141988495947019414,.6992553567211190432 ] 
dist 177=[.24845585506023577637,.5755581794117298204 ] 
dist 178=[.2105311989803636587 ,.63139601452675086903] 
dist 179=[.1691230989489063443 ,.6786635521729186145 ] 
dist 180=[.1122595451143914899 ,.72647419900516557298] 
dist 181=[.0557312768075476500 ,.76884172136498808671] 
dist 182=[.0156578344602450030 ,.7943941910650310863 ] 
dist 183=[-.01995862846315617233,.81247412950458930435] 
dist 184=[-.05871218053826475254,.82503128669116118712] 
dist 185=[-.09643800959831665587,.8330448139382330590 ] 
dist 186=[-.13476180075051650877,.8334859000454946590 ] 
dist 187=[-.17507346368276374634,.8296491881027726618 ] 
dist 188=[-.21714069533098926921,.8253287494644115240 ] 
dist 189=[-.26056821895446831783,.42029688642809437654] 
dist 190=[-.29779544600492860023,.38390801690953279224] 
dist 191=[-.3359803309803717706 ,.2954908670517479268 ] 
dist 192=[-.38538077609838041191,.28171073479236999773] 
dist 193=[-.4331261637331436077 ,.15327781280629777268] 
dist 194=[-.46470929592936057777,.12968943337581395666] 
dist 195=[-.49046177803469848428,.09869323758832000692] 
dist 196=[-.51494275060513952507,.09040851929980246326] 
dist 197=[-.53669187560655924596,-.09079303526632282748] 
dist 198=[-.55154386830291943841,-.05745749259211046944] 
dist 199=[-.56416521140758223534,-.01759318130390200501] 
dist 200=[-.57701295128660197606,.03630815498729996919] 
dist 201=[-.58779118446035927548,.09497589442222492382] 
dist 202=[-.59215495897478813308,.15385618670707568957] 
dist 203=[-.59264295434292342361,.2240576004614464759 ] 
dist 204=[-.59163709554290141281,.32788989054954237284] 
dist 205=[-.58094143220655923509,.43116500510449386936] 
dist 206=[-.57712968924262374377,.50287174721618025906] 
dist 207=[-.56397451389156447981,.56575438618156835081] 
dist 208=[-.55952760123243159971,.62614011569591527829] 
dist 209=[-.49742606619069471295,.68016704383697273277] 
dist 210=[-.48579509935853008761,.71768279556965218698] 
dist 211=[-.46181866103287685745,.78260011119880188639] 
dist 212=[-.45442220268796487101,.85795543988921870306] 
dist 213=[-.42188117892647720973,.92201683602782638798] 
dist 214=[-.41455605314944311771,.96066394367602053806] 
dist 215=[-.39108272561063050935,.98803354276885370345] 
dist 216=[-.35760576686711704838,1.0071095108430391687 ] 
dist 217=[-.04040560613587144025,1.0201105906768983817 ] 
dist 218=[-.00589615611810520541,1.0232460521231327737 ] 
dist 219=[-.08981462653660540122,1.0208746738366849236 ] 
dist 220=[-.29068150799183687932,1.0174868716946106294 ] 
dist 221=[-.49111878799534503808,.98958627308543950794] 
dist 222=[-.62261762649891980509,.98088209292509642959] 
dist 223=[-.72854704147137251322,.95729885217650167223] 
dist 224=[-.82698479190246627355,.9473234235212176967 ] 
dist 225=[-.91284195389936243612,.46909346642301607257] 
dist 226=[-.96858599553447499217,.45483874010848874532] 
dist 227=[-1.0128411075139261344 ,.42072976002546268717] 
dist 228=[-1.0528678943147996474 ,.41160621653300172916] 
dist 229=[-1.0858349673751679694 ,.31888392524374046776] 
dist 230=[-1.1019279755506788351 ,.30331503908451290572] 
dist 231=[-1.1087136944391752318 ,.27120915760755265462] 
dist 232=[-1.1084087192756931085 ,.26227705214927974705] 
dist 233=[-1.0953653050002981319 ,.22709960843081263724] 
dist 234=[-1.0891864584725978037 ,.2195546163774250221 ] 
dist 235=[-1.0687290775042116070 ,.20307300313146009026] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 0, 0, 2] 
dist 0=[47.702399395843354944  ,47.702399395843354944  ] 
dist 1=[46.160161914790809047  ,48.985623697822301028  ] 
dist 2=[44.394789215323886350  ,49.716766128363074654  ] 
dist 3=[42.125072047530262051  ,50.184310866293513971  ] 
dist 4=[38.569034977600892233  ,50.414959281990999680  ] 
dist 5=[34.953796082645229621  ,50.547420540116419266  ] 
dist 6=[32.447570459439645617  ,50.622860509049183455  ] 
dist 7=[30.269575720466074365  ,50.670551471164333508  ] 
dist 8=[27.964566971691325334  ,50.692110768942952803  ] 
dist 9=[25.748367289688486174  ,50.694082640513253992  ] 
dist 10=[23.924625250620441650  ,50.663420693820036196  ] 
dist 11=[22.034170098497485235  ,50.601731535144822910  ] 
dist 12=[19.550902618605767208  ,50.516641666390387865  ] 
dist 13=[17.109896080228282378  ,50.352522692260806830  ] 
dist 14=[15.387843479748166304  ,50.271957626571583279  ] 
dist 15=[13.856086564419434310  ,49.412925201381218858  ] 
dist 16=[12.174583518435610427  ,47.640835353003712541  ] 
dist 17=[10.515197971403388064  ,33.818858039334954495  ] 
dist 18=[9.0711150076843684162 ,32.482743021125524656  ] 
dist 19=[7.4991164799351893811 ,29.243562368243036069  ] 
dist 20=[5.3273989511538266132 ,28.773358069308397769  ] 
dist 21=[3.2007367819166680996 ,24.048485562264729973  ] 
dist 22=[1.8086248270064756899 ,23.173557625670592465  ] 
dist 23=[.67792241752813991237,22.159494539763916953  ] 
dist 24=[-.40342530695787411435,21.967187491566006137  ] 
dist 25=[-1.3800293402094068594 ,18.342980682979655287  ] 
dist 26=[-2.0919102158163351620 ,17.979155866415201503  ] 
dist 27=[-2.7517372201175447372 ,16.916370277324425006  ] 
dist 28=[-3.5202692047702959136 ,15.445183938031568814  ] 
dist 29=[-4.2360477993982778695 ,9.5651271574281821340 ] 
dist 30=[-4.6849565830788136950 ,9.2265343857270067951 ] 
dist 31=[-5.0281365728187106250 ,8.7431450254231914594 ] 
dist 32=[-5.3211465941859107803 ,8.6136406882163007360 ] 
dist 33=[-5.5630476820749072133 ,.33511986981675394092] 
dist 34=[-5.7019444186327032104 ,.95998851272591308398] 
dist 35=[-5.7940060671843413997 ,1.7496204925633573768 ] 
dist 36=[-6.1671473470492374947 ,2.9652298951745118795 ] 
dist 37=[-7.3811320922981842546 ,4.1785152009422522575 ] 
dist 38=[-8.2835711185541697163 ,4.9590678759765301405 ] 
dist 39=[-9.1343575366043921226 ,5.5689677249661565251 ] 
dist 40=[-10.141965671265555167  ,6.1019499553561052169 ] 
dist 41=[-11.082564567718560367  ,6.5422233065849347102 ] 
dist 42=[-11.665625303334097539  ,6.7824949476539211984 ] 
dist 43=[-12.100865288461202267  ,6.9213175496522851288 ] 
dist 44=[-12.450871207193236345  ,6.9570496951921000818 ] 
dist 45=[-12.721233113108728030  ,6.9524605956070230618 ] 
dist 46=[-12.838294121679705949  ,6.9304659001739337146 ] 
dist 47=[-12.875418568956466656  ,6.8912911268909406209 ] 
dist 48=[-12.863817786854591598  ,6.8564611591063428418 ] 
dist 49=[-3.2142052300272596424 ,6.7282541919670885154 ] 
dist 50=[-3.1074663674515813481 ,6.6763865312116263500 ] 
dist 51=[-2.9066746622036106358 ,6.5209138418140502408 ] 
dist 52=[-2.8530831722124401723 ,6.4494112172211695391 ] 
dist 53=[-.69232822844533179559,5.7238304960029838683 ] 
dist 54=[-.47134008580250200766,6.2751664649679797579 ] 
dist 55=[.02946673295381082496,6.7187957169732951523 ] 
dist 56=[.11578124344468631755,7.1317506507783070527 ] 
dist 57=[.71473949307351756814,7.4882339820220994718 ] 
dist 58=[.81463945117070104741,7.7065269324330031438 ] 
dist 59=[.99602325582361743391,7.8658573964802830117 ] 
dist 60=[1.0327569074131468188 ,7.9869180094790806987 ] 
dist 61=[1.4107746480242651347 ,8.0745493497758927992 ] 
dist 62=[1.4649591501756935409 ,8.1004133175935488760 ] 
dist 63=[1.4739536427418788543 ,8.0862033157129863543 ] 
dist 64=[1.4102096514548852493 ,8.0627265415274228839 ] 
dist 65=[1.3072457099476610827 ,3.2381074044493311773 ] 
dist 66=[1.1563992278289493792 ,2.8286671063447529118 ] 
dist 67=[.39142243147725259548,2.4301467970706900284 ] 
dist 68=[-.4245997460294824367 ,2.4312574173189540847 ] 
dist 69=[-1.1923508451387355379 ,2.0287851615295793539 ] 
dist 70=[-1.7903798710729270624 ,1.9776338978948245811 ] 
dist 71=[-2.3773484708213387118 ,1.8336771591395768458 ] 
dist 72=[-3.1010078980267219928 ,1.8123853964127555526 ] 
dist 73=[-3.7838080643841907706 ,1.5319184861308147517 ] 
dist 74=[-4.2077982362357975997 ,1.4742556820223771471 ] 
dist 75=[-4.5225592156317336785 ,1.4179710588637763100 ] 
dist 76=[-4.7696439087265942276 ,1.4055286406156532125 ] 
dist 77=[-4.9603140920991377666 ,.76036061556509309975] 
dist 78=[-5.0500414931410252726 ,.67994063446580331847] 
dist 79=[-5.0882091814503277874 ,.51441137503633602628] 
dist 80=[-5.0875103722625358313 ,.47147686421690824208] 
dist 81=[-1.3787404937949011920 ,.31728500691749384605] 
dist 82=[-1.3864725152484831307 ,.28543399287494012291] 
dist 83=[-1.3849171036326411632 ,.23980208813824990365] 
dist 84=[-1.3846544827689235781 ,.22715827400801813188] 
dist 85=[-.89594216338407791114,.49168040673940335288] 
dist 86=[-1.0798318181311281546 ,.74461259983230817709] 
dist 87=[-1.2409684004389971237 ,.98743721751432756892] 
dist 88=[-1.4129641703057862165 ,1.2790935593859095940 ] 
dist 89=[-1.5785408003660594847 ,1.5519083609233239425 ] 
dist 90=[-1.7140511844873328159 ,1.7195940548326906248 ] 
dist 91=[-1.8533086728105358950 ,1.8419962334484234658 ] 
dist 92=[-2.0338159228030098760 ,1.9341962650528595357 ] 
dist 93=[-2.2086322013751792675 ,2.0037838878942595905 ] 
dist 94=[-2.3251733961696888052 ,2.0360003431959105262 ] 
dist 95=[-2.4211321593506875797 ,2.1142930221786680100 ] 
dist 96=[-2.5138174178876624843 ,2.3033184506666251606 ] 
dist 97=[-2.5970275148922997546 ,2.4790363855762749568 ] 
dist 98=[-2.6551687789516989962 ,2.5746083957016114508 ] 
dist 99=[-2.7058820232135154887 ,2.6298984002214362736 ] 
dist 100=[-2.7594272719636237869 ,2.6448765705056937325 ] 
dist 101=[-2.8027428461466174649 ,2.6451776582423529049 ] 
dist 102=[-2.8126440381039968261 ,2.6418796405062066035 ] 
dist 103=[-2.8078525806140495388 ,2.8724879603828325651 ] 
dist 104=[-2.7958040389935413537 ,3.1082419930121689079 ] 
dist 105=[-2.6976538354341183431 ,3.2986075715275918227 ] 
dist 106=[-2.6670243422175244398 ,3.3970135189726415343 ] 
dist 107=[-2.6129464258057506486 ,3.4498833472279973978 ] 
dist 108=[-2.5941127655611048234 ,3.4590892964710226914 ] 
dist 109=[-2.0886523793494722282 ,3.3764783449857843131 ] 
dist 110=[-2.0135421011663378478 ,3.3479006870501387351 ] 
dist 111=[-1.8459674990502751321 ,3.3198969140045427456 ] 
dist 112=[-1.7949430782714306386 ,3.2987205259998699559 ] 
dist 113=[-1.5702461830471785517 ,3.2497745098365728544 ] 
dist 114=[-1.5238249944276701874 ,3.2239697660167561929 ] 
dist 115=[-1.4086708438977151678 ,3.1785327599214468035 ] 
dist 116=[-1.5779497467612693468 ,3.1600517435653878087 ] 
dist 117=[-1.8107540410579055767 ,-.10163485552742332642] 
dist 118=[-1.9664215703281206476 ,-.34299302676666365003] 
dist 119=[-2.0951683546635224690 ,-.89350799321451010788] 
dist 120=[-2.2205778640130137110 ,-.9792553684327433501 ] 
dist 121=[-2.3297588847602002082 ,-1.6395320283772003597 ] 
dist 122=[-2.3937624847364758796 ,-1.7472031057622314741 ] 
dist 123=[-2.4368534276352726241 ,-1.9238510990977356407 ] 
dist 124=[-2.4625990217551077854 ,-1.8513272760285792977 ] 
dist 125=[-2.6328349870816539170 ,-1.6837134129595608405 ] 
dist 126=[-2.7641487772722751598 ,-1.4800436152313202588 ] 
dist 127=[-2.8596493803371667797 ,-1.2113370002197732589 ] 
dist 128=[-2.9309821523110683987 ,-.78426813120947616504] 
dist 129=[-2.9811583722765681389 ,-.35074579626266460805] 
dist 130=[-2.9922611501308034343 ,-.05629223022890256059] 
dist 131=[-2.9875632695439529849 ,.19215104134249673256] 
dist 132=[-2.9747120388454748552 ,.44212715956450254228] 
dist 133=[-1.6634474405232107498 ,.6734093482527319777 ] 
dist 134=[-1.5441261931154002325 ,.84727839827178161426] 
dist 135=[-1.2478009116409031384 ,1.0120812750860625743 ] 
dist 136=[-1.2037448040345109077 ,1.2071975127690666780 ] 
dist 137=[-.75273192017522491269,1.3887217945634418492 ] 
dist 138=[-.66866443892008587059,1.4993030231747113529 ] 
dist 139=[-.56820286682814017337,1.5789038718328150960 ] 
dist 140=[-.54665594807966668903,1.6368386234015327411 ] 
dist 141=[.16171778549148229339,1.6794759295662394164 ] 
dist 142=[.24606217305820315368,1.6980498487432940778 ] 
dist 143=[.42993564686288719317,1.7032883308073296725 ] 
dist 144=[.46446064572833548445,1.7014568821412056185 ] 
dist 145=[.48997786549050139904,1.4668126110610052092 ] 
dist 146=[.37870089244471428056,1.5046809876351369589 ] 
dist 147=[.25268156271527550074,1.5250360518887105439 ] 
dist 148=[.12182096864914082534,1.5281030892399871511 ] 
dist 149=[-.00182371062945460860,1.1317601903379501228 ] 
dist 150=[-.09905954112067716249,1.1677163556675581234 ] 
dist 151=[-.19538632908068799376,1.2264775863421519634 ] 
dist 152=[-.31540708427182225558,1.2918031752687478966 ] 
dist 153=[-.42930877059447633665,1.3562494257447553418 ] 
dist 154=[-.50122681589377674933,1.4114977934547524989 ] 
dist 155=[-.55603362146043597999,1.4705115503112636481 ] 
dist 156=[-.66097975107919706931,1.5499746591737235996 ] 
dist 157=[-.82620052343002467541,1.6283349770021458358 ] 
dist 158=[-.98230649588540284014,1.6829456752391775680 ] 
dist 159=[-1.1613675495986027310 ,1.7305230920815066953 ] 
dist 160=[-1.4181671607619991188 ,1.7808190655037478156 ] 
dist 161=[-1.6686380605055096881 ,1.8288872410138561803 ] 
dist 162=[-1.8224524780975003713 ,1.8675721258276220326 ] 
dist 163=[-1.9346659950755866382 ,1.9067000527354980290 ] 
dist 164=[-2.0191757506670290327 ,1.9565268769252629904 ] 
dist 165=[-2.3655487373847008758 ,2.0020951673609446705 ] 
dist 166=[-2.6807785208983189887 ,2.0242334817855506899 ] 
dist 167=[-2.9226701748982177294 ,2.0333753003557759110 ] 
dist 168=[-3.1270919595474800629 ,2.0304133032197607177 ] 
dist 169=[-3.2913437914953555218 ,2.0113808006669923737 ] 
dist 170=[-3.3729891505261314926 ,2.0024887518998826082 ] 
dist 171=[-3.4149922019663220381 ,1.9565507752666025020 ] 
dist 172=[-3.4210960248668168250 ,1.9498884311325354684 ] 
dist 173=[-3.3617510504289008794 ,1.7831970576558129377 ] 
dist 174=[-3.3369366897673107427 ,1.7523195547830871053 ] 
dist 175=[-3.2918780565970616133 ,1.6612998268472942835 ] 
dist 176=[-3.2729595535647751186 ,1.6454163715946870174 ] 
dist 177=[-3.1718069836037268650 ,1.4496260762046263379 ] 
dist 178=[-3.1433079675312630706 ,1.4070858217273603852 ] 
dist 179=[-3.0487666005932868434 ,1.3628124585137758449 ] 
dist 180=[-3.0252846884140901873 ,1.3465037066380994712 ] 
dist 181=[.72536155613849036563,1.3379420869382083032 ] 
dist 182=[.97941237420763295983,1.5162145398357217085 ] 
dist 183=[1.0342405474982123068 ,1.7536980776957010278 ] 
dist 184=[.97616656855655744447,2.0365443188263845046 ] 
dist 185=[.90712494128219665035,2.3845539279824200857 ] 
dist 186=[.83955518310003496824,2.6215997615074182784 ] 
dist 187=[.76025036785566144566,2.8223126515903528318 ] 
dist 188=[.64439188090138233623,3.0253856234174205982 ] 
dist 189=[.51416375507174350697,3.2050696982653115611 ] 
dist 190=[.37753281794396922591,3.3124804101504864825 ] 
dist 191=[.21028857404332577916,3.3873216788524067051 ] 
dist 192=[-.04206690598618195473,3.4370793819772949901 ] 
dist 193=[-.29552925471830810667,3.4667972432999977630 ] 
dist 194=[-.46718955316185292707,3.4678631024001968374 ] 
dist 195=[-.61150016707406615803,3.4444349934891215278 ] 
dist 196=[-.7558559759220199885 ,3.4256487946442767651 ] 
dist 197=[-.88888075741726778629,1.7346096849710964659 ] 
dist 198=[-.98798833548227552224,1.5803990210544392425 ] 
dist 199=[-1.0810565911868864316 ,1.2116704506065372499 ] 
dist 200=[-1.1899886562227335586 ,1.1491989280561046792 ] 
dist 201=[-1.3692127917514778383 ,.63053858962301611302] 
dist 202=[-1.5750875615979718921 ,.53560287480952944977] 
dist 203=[-1.7693057096103616024 ,.39391130663141843694] 
dist 204=[-1.9978660811865970510 ,.35567298609142014452] 
dist 205=[-2.2081388860912653497 ,-.01429381650555444185] 
dist 206=[-2.3294055939588790404 ,.06206544997078595013] 
dist 207=[-2.4084581958050077756 ,.1618208692527892031 ] 
dist 208=[-2.4503338949529555752 ,.31933988265662078624] 
dist 209=[-2.4751426854572431547 ,.47714883764067208381] 
dist 210=[-2.4861138690406051232 ,.63239637723584940836] 
dist 211=[-2.4890274842667674458 ,.79183625472353963504] 
dist 212=[-2.4816952040238580113 ,.95030663157501442361] 
dist 213=[-.86101814528183032579,1.0956738057692038728 ] 
dist 214=[-.84778339083982301389,1.2028419081772730601 ] 
dist 215=[-.8586907065265441324 ,1.3023592505471604398 ] 
dist 216=[-.8826584431029184888 ,1.4172061152851241831 ] 
dist 217=[-.91314233495018293391,1.5217208044752048190 ] 
dist 218=[-.95004220314156354186,1.5800205857253776393 ] 
dist 219=[-.99864390956625943914,1.6481196154858871510 ] 
dist 220=[-1.0758070237230072784 ,1.8488314911266896110 ] 
dist 221=[-1.1571879836268736782 ,2.0344207439216578510 ] 
dist 222=[-1.2226142747081738599 ,2.1431453020965352853 ] 
dist 223=[-1.2887587915161122810 ,2.2161798970879457540 ] 
dist 224=[-1.3730029761118097913 ,2.2593971481833999788 ] 
dist 225=[-1.4622300784566685852 ,2.2861370591733950483 ] 
dist 226=[-1.5482507279466462403 ,2.2934404485830039964 ] 
dist 227=[-1.6482248311327619446 ,2.2879902480271670866 ] 
dist 228=[-1.7931118934171438489 ,2.2819603817669170014 ] 
dist 229=[-1.9342480058442719991 ,2.5262615265419930626 ] 
dist 230=[-2.0192586183126191433 ,2.7824307336915388967 ] 
dist 231=[-2.0792640379289294352 ,2.9727012338903181091 ] 
dist 232=[-2.1206519988789871941 ,3.1222788099815074985 ] 
dist 233=[-2.1467989625697578175 ,3.2377079441778004092 ] 
dist 234=[-2.1511968196266820585 ,3.2917522179228484310 ] 
dist 235=[-2.1374811162615563041 ,3.3147605372400426257 ] 
dist 236=[-2.1327852009722639730 ,3.3140151752623315282 ] 
dist 237=[-2.0098925230419314774 ,3.1092849331412444748 ] 
dist 238=[-1.9843236582778344203 ,3.0664984136382923934 ] 
dist 239=[-1.9075963464099717310 ,2.9885973794832574125 ] 
dist 240=[-1.9201058548380229935 ,2.9631567318379304755 ] 
dist 241=[-1.9414652612064644908 ,2.8504925491600269273 ] 
dist 242=[-1.9502321865036719623 ,2.8183523243859186831 ] 
dist 243=[-1.9514375228494775388 ,2.7361963253323816800 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 0, 2, 1, 0, 2] 
dist 0=[67.631854538955055427  ,67.631854538955055427  ] 
dist 1=[67.369346452448497944  ,67.693617494586031048  ] 
dist 2=[66.772461945812025457  ,67.677828838868059872  ] 
dist 3=[65.625445092033089171  ,67.519214915895581903  ] 
dist 4=[64.263043413802658985  ,67.381663945239644697  ] 
dist 5=[62.806156247993565301  ,66.858104696944035496  ] 
dist 6=[60.626502522171298717  ,66.616882585890090407  ] 
dist 7=[56.697602188998708731  ,64.650508491908004344  ] 
dist 8=[52.641251557880647196  ,62.687626413150686997  ] 
dist 9=[49.743898162706642001  ,61.804983809617321767  ] 
dist 10=[47.136344014362203547  ,61.466502807280829865  ] 
dist 11=[40.712403309162014019  ,61.072195507434350385  ] 
dist 12=[34.044771326251691681  ,60.770149630374050898  ] 
dist 13=[29.509046209609510059  ,60.495020534569883622  ] 
dist 14=[25.659587550123270438  ,58.165467080968068340  ] 
dist 15=[21.732292617041416458  ,39.248344818027538421  ] 
dist 16=[18.048927069616790076  ,29.056999848035984777  ] 
dist 17=[15.173556090133788923  ,27.790487107616301092  ] 
dist 18=[12.335569542189859674  ,25.242786100327775758  ] 
dist 19=[8.8016410409132369870 ,24.593839695824678403  ] 
dist 20=[5.4307476960273491595 ,22.327636743925968448  ] 
dist 21=[3.2437587783949784277 ,21.843587966161019774  ] 
dist 22=[1.5027847370060368666 ,21.241546807220889444  ] 
dist 23=[-.08733340695266998590,21.102928490418069961  ] 
dist 24=[-1.4980002863913516590 ,4.4430537195462726180 ] 
dist 25=[-2.7481692744199845470 ,3.0873041922384234453 ] 
dist 26=[-4.2386287752504885492 ,.13121190312776781548] 
dist 27=[-5.5185931987971531040 ,-.41014218467404952654] 
dist 28=[-6.3358491890154823431 ,-3.6153451117889925295 ] 
dist 29=[-7.1308560420750687070 ,-4.1361985507809771231 ] 
dist 30=[-8.5934395013173921135 ,-4.6978575462083219673 ] 
dist 31=[-10.338373264247081953  ,-5.3900853579541742349 ] 
dist 32=[-11.973479726256344051  ,-6.7062375055072938962 ] 
dist 33=[-12.997278708875553134  ,-6.7345896970458352957 ] 
dist 34=[-13.773398722954874760  ,-6.4452014934961786901 ] 
dist 35=[-14.418935117471955340  ,-5.8735189707783070812 ] 
dist 36=[-14.934305337703127310  ,-5.2343573379905963600 ] 
dist 37=[-15.190374328836772485  ,-4.6752951183622599755 ] 
dist 38=[-15.306689455711620223  ,-3.7915219523434087528 ] 
dist 39=[-15.320726008404534810  ,-1.9455465644664660872 ] 
dist 40=[-7.2752104671429453292 ,-.07247397567128485105] 
dist 41=[-7.1734837481590415052 ,1.1693805447640424740 ] 
dist 42=[-7.0823704774956725848 ,2.1842653019076973008 ] 
dist 43=[-7.0380928823006010537 ,3.1520931432621770953 ] 
dist 44=[-5.5035968001170229840 ,4.0360442145187764516 ] 
dist 45=[-5.3024363081963906572 ,4.6970327333002480792 ] 
dist 46=[-5.1501011579553304399 ,5.2778224139865451217 ] 
dist 47=[-4.7141811584378983836 ,5.9005004213273172177 ] 
dist 48=[-3.9742746115871539362 ,6.4631209430653922788 ] 
dist 49=[-3.8251742341231958941 ,6.8043295848892508029 ] 
dist 50=[-3.5757252619352862859 ,7.0488033365626116195 ] 
dist 51=[-3.5095957872078551501 ,7.2253901822450208892 ] 
dist 52=[-2.1893791364589183846 ,7.3451559992517322700 ] 
dist 53=[-2.0096109476621966226 ,7.3670677021640149934 ] 
dist 54=[-1.5893712622806339038 ,7.3441993734280556196 ] 
dist 55=[-1.5038845133999000026 ,7.3185243793093316821 ] 
dist 56=[-.92387465330312587803,7.2574647352390174937 ] 
dist 57=[-.8140089607985047689 ,7.2320952354998373036 ] 
dist 58=[-.61632374395826342214,7.1160136542489128790 ] 
dist 59=[-.56926497291720802032,7.0718677414794973664 ] 
dist 60=[-1.1195091882895524432 ,5.0888432738178671112 ] 
dist 61=[-1.6010489634108342454 ,5.0995000807658796421 ] 
dist 62=[-2.0611347503326348325 ,5.0964471809029170004 ] 
dist 63=[-2.6105894235715177735 ,1.2055702135358716129 ] 
dist 64=[-3.1347838061003465356 ,-.35646176954582837173] 
dist 65=[-3.4783203933030476999 ,-.54785904104482772729] 
dist 66=[-3.8301074049030972582 ,-.98449174957385058064] 
dist 67=[-4.2893268962686659275 ,-1.0492686057465260705 ] 
dist 68=[-4.7069428400830730197 ,-1.3487248441746913128 ] 
dist 69=[-4.9654718463470490716 ,-1.0569914421783026766 ] 
dist 70=[-5.1566260765481422097 ,-.6549057707334507615 ] 
dist 71=[-5.3054403873162413279 ,0                     ] 
dist 72=[-5.4154242206102318442 ,-1.1263184309403055479 ] 
dist 73=[-5.4516586987483613950 ,-.77316556531569279673] 
dist 74=[-5.4520768081434130026 ,-.46686575688050761535] 
dist 75=[-5.4342686442239229430 ,-.14617058114094003524] 
dist 76=[-3.2261804468440463618 ,.15775294544486443352] 
dist 77=[-3.1978066475067868301 ,.39722958956745180916] 
dist 78=[-3.1775104367982292116 ,.63455770976357017385] 
dist 79=[-2.0270228860002578688 ,.92998288745966046713] 
dist 80=[-1.3108484596160789339 ,1.2097613266615592129 ] 
dist 81=[-1.0565011651360579373 ,1.3847315185710495723 ] 
dist 82=[-.88446242416258952614,1.5160520087302637730 ] 
dist 83=[-.81191452684336226972,1.6218073185526890660 ] 
dist 84=[-.38916178244062461678,1.8306879140029397775 ] 
dist 85=[-.23068776457469952863,2.0784765955843260217 ] 
dist 86=[-.19299420562298484828,2.2682223529953560948 ] 
dist 87=[.10304553366304310996,2.4276849741206546542 ] 
dist 88=[-.09596304197108680943,2.5550487283047725536 ] 
dist 89=[-.26521726913347050538,2.6167869270546333901 ] 
dist 90=[-.4040571950768962462 ,2.6472970430434205236 ] 
dist 91=[-.53651135396967269972,2.6500732147369679561 ] 
dist 92=[-.65370855259757537659,2.6591163002429455377 ] 
dist 93=[-.73172848168062197286,2.6677027223283607133 ] 
dist 94=[-.79542830042678245572,2.6607654326431529582 ] 
dist 95=[-.85551759430476948991,1.8926973633498852323 ] 
dist 96=[-.90780676699813391046,1.9587682081576235508 ] 
dist 97=[-.94042819844005337392,2.0173060874132654957 ] 
dist 98=[-.96457811681094448721,2.0815394070895094412 ] 
dist 99=[-1.1802496074643556690 ,2.1703130037528919732 ] 
dist 100=[-1.3696493475484866427 ,2.2590133313463349425 ] 
dist 101=[-1.5538191089556762924 ,2.3229381714801198956 ] 
dist 102=[-1.7784581812948426172 ,2.3808710881556169281 ] 
dist 103=[-1.9892547222067638195 ,2.4456382189712857193 ] 
dist 104=[-2.1182269500477681836 ,2.5096527874390715326 ] 
dist 105=[-2.2117624115972449360 ,2.5645611647474115212 ] 
dist 106=[-2.2812276889540120733 ,2.6231327193519745653 ] 
dist 107=[-2.6766949257563714652 ,2.7017245772796497127 ] 
dist 108=[-3.3664634817576543914 ,2.7751034652614705241 ] 
dist 109=[-3.8027191033003604896 ,2.8128735404814025034 ] 
dist 110=[-4.1361204867583720475 ,2.8315930450983759140 ] 
dist 111=[-4.4155667671250776038 ,2.8289938489820890295 ] 
dist 112=[-4.6384423171703551395 ,2.8127537984850327220 ] 
dist 113=[-4.7461666801689302583 ,2.8021250316239425473 ] 
dist 114=[-4.8008026371716216983 ,2.7430891789914040685 ] 
dist 115=[-4.8118643953596447594 ,2.7337303355743752437 ] 
dist 116=[-4.7026846906031789174 ,2.5097573570828766797 ] 
dist 117=[-4.6644756238847279432 ,2.4680304363179286178 ] 
dist 118=[-4.5950135121127732758 ,2.3417714331338854130 ] 
dist 119=[-4.5672263137247817955 ,2.3733730420808757449 ] 
dist 120=[-4.4231481194513274885 ,2.3995711114090061506 ] 
dist 121=[-4.3824569764480783025 ,2.4151508334391239579 ] 
dist 122=[-4.2523546625588523614 ,2.4201515315559887331 ] 
dist 123=[-4.2168897968731351739 ,2.4179136520076111010 ] 
dist 124=[.98451355213377997989,2.4080885042580013900 ] 
dist 125=[1.1048614889093478990 ,2.3843692056936472166 ] 
dist 126=[.6275646711306649976 ,2.4065188286306995787 ] 
dist 127=[.14490363985385477069,2.8110931767380781854 ] 
dist 128=[-.18188366267648336023,3.2955776871187478617 ] 
dist 129=[-.45633367654188191394,3.6253675187183051387 ] 
dist 130=[-.73023758471011756948,3.9043952977111373172 ] 
dist 131=[-.98208218363231944507,4.1863838554292260991 ] 
dist 132=[-1.1685463840642074874 ,4.4359497877074943274 ] 
dist 133=[-1.3424241986108872983 ,4.5856372425073356825 ] 
dist 134=[-1.5440712028687326994 ,4.6905659858991695641 ] 
dist 135=[-1.7298453185602466806 ,4.7615765104855421073 ] 
dist 136=[-1.8404088436044588268 ,4.8052056948340924991 ] 
dist 137=[-1.9168244334713912840 ,4.8070709674862339309 ] 
dist 138=[-1.9663807800548727141 ,4.7786256209793987597 ] 
dist 139=[-1.9997409533647404241 ,4.7505871157749213733 ] 
dist 140=[-2.0115536053151258211 ,2.3857053381945232613 ] 
dist 141=[-2.0102432290461222302 ,2.1711139025812051110 ] 
dist 142=[-2.0057635146238094864 ,1.6577705750100176229 ] 
dist 143=[-1.5072011491221250220 ,1.5713886348556243403 ] 
dist 144=[-1.8814739433215332683 ,.84915390092453525744] 
dist 145=[-2.1617411560035058189 ,.71710165457192304336] 
dist 146=[-2.4262720504413495198 ,.52151655888914563048] 
dist 147=[-2.7377700106291630149 ,.49006523950022395465] 
dist 148=[-3.0244442669800988928 ,.61435071440775504516] 
dist 149=[-3.1899499970725680806 ,.73134062506111767137] 
dist 150=[-3.2980662642617492196 ,.86859542444104112159] 
dist 151=[-3.3558065914740160482 ,.9962096868710574866 ] 
dist 152=[-3.3900799042601111403 ,1.0747445569785618914 ] 
dist 153=[-3.4045845619118293215 ,1.1321877263890431075 ] 
dist 154=[-3.4073570849568445180 ,1.1756670687574542200 ] 
dist 155=[-3.3954630030851119895 ,1.2077174760481436128 ] 
dist 156=[-1.2253369036787491201 ,1.2195747327222726938 ] 
dist 157=[-1.2020647375788033788 ,1.2226398973322222757 ] 
dist 158=[-1.2156451464489805215 ,1.2196185723750655907 ] 
dist 159=[-1.2462693455080386206 ,1.5112300597070248850 ] 
dist 160=[-1.2854574493967666484 ,1.8358097329099578321 ] 
dist 161=[-1.3331978943069355436 ,2.0801560555363255591 ] 
dist 162=[-1.3962666710754559088 ,2.3120541038547285549 ] 
dist 163=[-1.4965995752009352652 ,2.5869782401800683282 ] 
dist 164=[-1.6025007074213133034 ,2.8409856372499239235 ] 
dist 165=[-1.6877799972421998606 ,2.9894450363244859902 ] 
dist 166=[-1.7741243392056662343 ,3.0887415417865368194 ] 
dist 167=[-1.8842704832356528140 ,3.1466323092647322642 ] 
dist 168=[-2.0010182368211954922 ,3.1818351378340674768 ] 
dist 169=[-2.1136945798413009155 ,3.1906243538913826911 ] 
dist 170=[-2.2447393485692865074 ,3.1821118185513196795 ] 
dist 171=[-2.4347568559905627197 ,3.1732476435850416611 ] 
dist 172=[-2.6198741174357486742 ,3.4452994106728524185 ] 
dist 173=[-2.7313702461112205389 ,3.7986928298777670983 ] 
dist 174=[-2.8100583710008608544 ,4.0617279431493441205 ] 
dist 175=[-2.8643018067922622953 ,4.2695345937443292930 ] 
dist 176=[-2.8985347688924457979 ,4.4302442525931782706 ] 
dist 177=[-2.9038825337508907199 ,4.5053966448622958293 ] 
dist 178=[-2.9556017051596978392 ,4.5378486659584722497 ] 
dist 179=[-3.1236147769116544195 ,4.5367101017172806509 ] 
dist 180=[-3.2072674094309311623 ,4.2700075986043728447 ] 
dist 181=[-3.2515836439312856961 ,4.2130492366348321503 ] 
dist 182=[-3.2626729099586011380 ,4.1090812538981591921 ] 
dist 183=[-3.1982238647874123102 ,4.0747553616195533937 ] 
dist 184=[-3.1730194344343645357 ,3.9210499147010568532 ] 
dist 185=[-3.1402571152398092477 ,3.8774284996020215690 ] 
dist 186=[-3.1216435008483821852 ,3.7636006686587485428 ] 
dist 187=[-3.0536717499390982690 ,3.7186573511365666373 ] 
dist 188=[-3.0282624937113311529 ,1.4099734536156170957 ] 
dist 189=[-2.9640859136868388318 ,1.3357012677739712556 ] 
dist 190=[-2.9368361164526103184 ,1.3147605408736993023 ] 
dist 191=[-.24926849022770686192,1.0600774625867792034 ] 
dist 192=[-.32575506673326559033,1.2238504915115671262 ] 
dist 193=[-.39161688800619241662,1.3513764585496431146 ] 
dist 194=[-.46219045368327137164,1.5792884073628775042 ] 
dist 195=[-.55747266373809483334,1.9099213009603130521 ] 
dist 196=[-.65151054601799344748,2.1401711270134255660 ] 
dist 197=[-.71711968024507332728,2.3405445241533905599 ] 
dist 198=[-.77434835265475156774,2.5519975671798933268 ] 
dist 199=[-.8349537103459680423 ,2.7422246262477960156 ] 
dist 200=[-.89295161692960227181,2.8579245567550058159 ] 
dist 201=[-.93977783618388681618,2.9409728088250113216 ] 
dist 202=[-.98729863462222550213,3.0009462163933674397 ] 
dist 203=[-1.0480661636311005606 ,3.0413628030080842469 ] 
dist 204=[-1.1039245122910720450 ,3.0470735927143987979 ] 
dist 205=[-1.1318613457474184378 ,3.0375559213201281500 ] 
dist 206=[-1.1463169584133079353 ,3.0226349809365329923 ] 
dist 207=[-1.1483975600946297218 ,1.6271888145797882581 ] 
dist 208=[-1.1305636274640249164 ,1.5003925964248918774 ] 
dist 209=[-1.1239971530882564896 ,1.1891475507784521901 ] 
dist 210=[-1.1183063719550142010 ,1.1413374830913670116 ] 
dist 211=[-1.2689073823056260034 ,1.0859624972600054350 ] 
dist 212=[-1.4144548748238840287 ,1.0535662127341922974 ] 
dist 213=[-1.5503491383687734869 ,1.0436647082286850581 ] 
dist 214=[-1.7082147606776353773 ,1.0318648624710308076 ] 
dist 215=[-1.8523564856402985249 ,1.0250420239373585958 ] 
dist 216=[-1.9335047289878027090 ,1.0053086158398875439 ] 
dist 217=[-1.9838807255836426936 ,.99676137926245381493] 
dist 218=[-2.0052698030386017561 ,.97957200549840021586] 
dist 219=[-2.0142428082762879762 ,.97262083925433026517] 
dist 220=[-2.0150913242509146667 ,.20198604207076358603] 
dist 221=[-2.0101464057405135235 ,.33287377984193855145] 
dist 222=[-2.0018573942018160241 ,.46948612623751884588] 
dist 223=[-1.0697314215592947001 ,.62207006013683659049] 
dist 224=[-1.1080106214367537562 ,.82923045350309327072] 
dist 225=[-1.1548125676807673448 ,1.0590039630654402047 ] 
dist 226=[-1.2101198134363476309 ,1.2896678195751308259 ] 
dist 227=[-1.2665446533657943038 ,1.5027029352783104802 ] 
dist 228=[-1.3178033492941936564 ,1.6621537125069757568 ] 
dist 229=[-1.3750027371881623539 ,1.8125820749874215135 ] 
dist 230=[-1.4551246050177489708 ,1.9896265792410500178 ] 
dist 231=[-1.5355080452457639054 ,2.1525311542408842324 ] 
dist 232=[-1.5937497422937465020 ,2.2465538948963154018 ] 
dist 233=[-1.6468156178776065595 ,2.3079480597207936726 ] 
dist 234=[-1.7065498476809476424 ,2.3406931938637556234 ] 
dist 235=[-1.7658533473172028364 ,2.3578057091140916070 ] 
dist 236=[-1.8171993535993973384 ,2.3568380441635047883 ] 
dist 237=[-1.8724442320692822606 ,2.3458722300844385192 ] 
dist 238=[-2.0279605317340016560 ,2.3356801583787706911 ] 
dist 239=[-2.1776849492562649984 ,2.4892212851180034268 ] 
dist 240=[-2.2979280731677222561 ,2.7983411854888119545 ] 
dist 241=[-2.3607067155618387212 ,3.0340981049961480201 ] 
dist 242=[-2.3935059580053910936 ,3.2307445769319931036 ] 
dist 243=[-2.4000030077137692733 ,3.3867619529200540343 ] 
dist 244=[-2.3058332705184294610 ,3.4604413719500218369 ] 
dist 245=[-2.2815445731385211318 ,3.4971720385565317478 ] 
dist 246=[-2.2560134885682535232 ,3.5057907390024540192 ] 
dist 247=[-2.2399280875440221543 ,3.4130729978482335683 ] 
dist 248=[-2.2058735631761332690 ,3.3833934940989257956 ] 
dist 249=[-2.1873405293558114958 ,3.3287780056416909794 ] 
dist 250=[-2.0510997096317697197 ,3.3074412194510322023 ] 
dist 251=[-1.7217595742197058326 ,3.1980858478802829811 ] 
dist 252=[-1.5095607796321885163 ,3.1676798513326406034 ] 
dist 253=[-1.4674451473150757097 ,3.0708401627506227433 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 0, 0, 1, 0, 2] 
dist 0=[44.499762022947001963  ,44.499762022947001963  ] 
dist 1=[43.372284600642140203  ,44.990752997995726087  ] 
dist 2=[41.618180284515015213  ,45.823421743362885316  ] 
dist 3=[38.830940475099712339  ,46.728156412068130395  ] 
dist 4=[35.984231851296934493  ,47.221689214805840816  ] 
dist 5=[33.992490121596305213  ,47.509031009487039576  ] 
dist 6=[32.242121454209188156  ,47.590926967408110156  ] 
dist 7=[30.358859463835030070  ,47.591829116707472589  ] 
dist 8=[28.529103279222896355  ,47.214055137958875276  ] 
dist 9=[26.992046958608389217  ,47.123661722731838553  ] 
dist 10=[25.370586812220822284  ,47.050778232978970580  ] 
dist 11=[23.203159264443070299  ,46.981836208343912962  ] 
dist 12=[21.054423174342962947  ,46.919383745526148768  ] 
dist 13=[19.507274714800596306  ,46.872219099111061248  ] 
dist 14=[18.098338021002348156  ,46.825820432701166170  ] 
dist 15=[16.501164017886654822  ,46.738725144510723852  ] 
dist 16=[14.895333215707419418  ,33.735906431676364234  ] 
dist 17=[13.451223856059484103  ,32.648614303816939300  ] 
dist 18=[11.840210757579731539  ,30.164751295657198000  ] 
dist 19=[9.5664423777916190643 ,29.693353449326483421  ] 
dist 20=[7.3229155838530000771 ,26.526517334423601714  ] 
dist 21=[5.8326411237174162392 ,25.956317921613539354  ] 
dist 22=[4.5988580519770740771 ,24.924185448737865384  ] 
dist 23=[3.3809433976568477574 ,24.689242980324675858  ] 
dist 24=[2.2567601171216048027 ,21.370620058170870000  ] 
dist 25=[1.3978001022277529859 ,20.912372424168968969  ] 
dist 26=[.56302892178839349876,19.768685235092615266  ] 
dist 27=[-.46436142902196771743,18.609046401216069941  ] 
dist 28=[-1.4470948102358933106 ,13.650638454505673052  ] 
dist 29=[-2.1032956984429328865 ,13.176472533053583019  ] 
dist 30=[-2.6500033956299180180 ,11.732939170724954647  ] 
dist 31=[-3.1949791093438094643 ,9.6124720333232924310 ] 
dist 32=[-3.7011833532709571037 ,1.7413537570483768826 ] 
dist 33=[-4.9720097141122110292 ,2.0527243402624915291 ] 
dist 34=[-6.2398021305723126680 ,2.4785585565882309744 ] 
dist 35=[-7.3893300085482451293 ,3.1659951040648499136 ] 
dist 36=[-8.2271536567069224715 ,3.8544651192453538330 ] 
dist 37=[-9.0006116493961436251 ,4.2846147842100797452 ] 
dist 38=[-9.8930702029134919771 ,4.6043068422538670526 ] 
dist 39=[-10.714529274607252307  ,4.8528010181453141431 ] 
dist 40=[-11.204372874167885713  ,5.0466951525239415372 ] 
dist 41=[-11.547498436809178686  ,5.1489069395725367721 ] 
dist 42=[-11.782828103132864536  ,5.2023674976704584958 ] 
dist 43=[-11.940283041023650350  ,5.2035750935735180234 ] 
dist 44=[-11.972285129829641436  ,4.6854055722815395510 ] 
dist 45=[-11.957069667608380799  ,4.5911973826192226120 ] 
dist 46=[-11.925758358978393944  ,4.4598958727748636707 ] 
dist 47=[-4.5306844968862994536 ,4.4083061694771415249 ] 
dist 48=[-4.2043731622241622607 ,4.2806058388898957387 ] 
dist 49=[-4.1299785706860940225 ,4.2247667822402364343 ] 
dist 50=[-3.9496577356305276802 ,4.3842230271036540549 ] 
dist 51=[-3.8906690908988015812 ,5.2234607596608074674 ] 
dist 52=[-.45844617015868730029,5.7820215701727961204 ] 
dist 53=[-.15522227194877571703,6.2418433438632011414 ] 
dist 54=[.5311587401122462941 ,6.6872404438966121907 ] 
dist 55=[.64450377427353059361,7.0771448697670890346 ] 
dist 56=[1.4566394722600446140 ,7.3155475675406933645 ] 
dist 57=[1.5898884105379702328 ,7.4889643010337154848 ] 
dist 58=[1.8262335518941440857 ,7.6194388546977569925 ] 
dist 59=[1.8711686885431479016 ,7.7126710401052719248 ] 
dist 60=[2.3419737064812776133 ,7.7374214848753097352 ] 
dist 61=[2.4032263650757817028 ,7.7187576773515796098 ] 
dist 62=[2.3935483028813017626 ,7.6971475886204143044 ] 
dist 63=[1.9667731210452319099 ,3.3430434769874163156 ] 
dist 64=[1.0957195623940161175 ,3.4046242495696855393 ] 
dist 65=[.34961473533584027067,3.4220461529798336927 ] 
dist 66=[-.41853609684883534456,3.4185618758107746052 ] 
dist 67=[-1.1398886982452729039 ,3.4054630463886089591 ] 
dist 68=[-1.6993506096116782211 ,2.3824274430143559385 ] 
dist 69=[-2.2461104879607942433 ,2.2759775284860234792 ] 
dist 70=[-2.9168212393016432274 ,2.0034597957293102386 ] 
dist 71=[-3.5478309896664581306 ,1.9603241354204628544 ] 
dist 72=[-3.9362367067479719011 ,1.5131803421848466736 ] 
dist 73=[-4.2204857906086978530 ,1.4262953779694529207 ] 
dist 74=[-4.4360279226012115257 ,1.3222737008706653238 ] 
dist 75=[-4.6008896063627300828 ,1.2929276986395307113 ] 
dist 76=[-4.6829862986544296174 ,.48634974733817782616] 
dist 77=[-4.7200391982817162458 ,.38620090245713821767] 
dist 78=[-4.7204184755981426703 ,.16945157609538718262] 
dist 79=[-1.7666519143974219545 ,.1210171121034272264 ] 
dist 80=[-1.8323384749946247260 ,-.10877443916272183666] 
dist 81=[-1.8671831748169815417 ,-.14891893985962175643] 
dist 82=[-1.8860968044485317060 ,.01610180290031910798] 
dist 83=[-1.8882837936600566345 ,.3359408561891121514 ] 
dist 84=[-1.0004613699095669048 ,.5839134412940050144 ] 
dist 85=[-1.1430734657096653813 ,.82605801182757283991] 
dist 86=[-1.2702641559034017882 ,1.1226870227508477423 ] 
dist 87=[-1.4095927287284041849 ,1.4014163895210336541 ] 
dist 88=[-1.5459427124830804853 ,1.5721881995442178829 ] 
dist 89=[-1.6612264324075901012 ,1.6962154387812821169 ] 
dist 90=[-1.7830328857644692358 ,1.7885283195380507651 ] 
dist 91=[-1.9453805326463470060 ,1.8591494758144479882 ] 
dist 92=[-2.1047389098670717278 ,1.8966474598551167262 ] 
dist 93=[-2.2146027616872228065 ,2.0873181960537542000 ] 
dist 94=[-2.3090484757740521946 ,2.3738994502478356785 ] 
dist 95=[-2.4068710978443725798 ,2.6473712459248784770 ] 
dist 96=[-2.4990669834422415776 ,2.8067933015547112535 ] 
dist 97=[-2.5710422201308123941 ,2.9131869791208108604 ] 
dist 98=[-2.6417375746514695456 ,2.9750761882678540225 ] 
dist 99=[-2.7287857758993468493 ,3.0146302268686400650 ] 
dist 100=[-2.8064514510936443868 ,3.0318890748508128188 ] 
dist 101=[-2.8397133310607625913 ,3.0361982092566903925 ] 
dist 102=[-2.8504202167306351893 ,3.0883226042935628732 ] 
dist 103=[-2.8462861180652485326 ,3.3140802811363210610 ] 
dist 104=[-2.7811327676651293170 ,3.4947406198528031338 ] 
dist 105=[-2.7568637216968853496 ,3.5875871411524210745 ] 
dist 106=[-2.7105335205749194938 ,3.6355551748235220231 ] 
dist 107=[-2.6921267553113192607 ,3.6436971436095621759 ] 
dist 108=[-2.2275012528885164456 ,3.5015470053737534246 ] 
dist 109=[-2.1565167446546741536 ,3.4645744368067837009 ] 
dist 110=[-1.9972466891220788456 ,3.4195321909994828700 ] 
dist 111=[-1.9478478546724986088 ,3.3952891008337001100 ] 
dist 112=[-1.7267629674379031798 ,3.3300762969252262314 ] 
dist 113=[-1.6802678960275633876 ,3.3008308593984586475 ] 
dist 114=[-1.6863398951978375807 ,3.2489965745740328252 ] 
dist 115=[-1.9638056831882942745 ,3.2290408012672343485 ] 
dist 116=[-2.1519882215996606195 ,-.19604420619496896278] 
dist 117=[-2.3105064090937737379 ,-.44929094967021089743] 
dist 118=[-2.4696355933925205810 ,-1.0253386893810520939 ] 
dist 119=[-2.6099098523535414101 ,-1.1154731535673546970 ] 
dist 120=[-2.6932088405678455820 ,-1.8006112885879391721 ] 
dist 121=[-2.7506077918875535177 ,-1.9118011932230497606 ] 
dist 122=[-2.7875520211157487598 ,-2.0970962843788371497 ] 
dist 123=[-2.8084687029677556620 ,-1.9330977006131885474 ] 
dist 124=[-2.8266589447170688557 ,-1.7117753078257564665 ] 
dist 125=[-2.9601142982873321310 ,-1.4170026357858624145 ] 
dist 126=[-3.0565675501595271803 ,-.94566081074841216262] 
dist 127=[-3.1274834213378713865 ,-.46659422820782430934] 
dist 128=[-3.1764003495013160122 ,-.1410039446262647603 ] 
dist 129=[-3.1850945019723801348 ,.133904093279680881  ] 
dist 130=[-3.1781011791006909542 ,.41079038103980390022] 
dist 131=[-3.1644409654630491250 ,.6671221917842453539 ] 
dist 132=[-1.7530726771132499855 ,.86003501046486257872] 
dist 133=[-1.6243352446490193724 ,1.0430776846697930177 ] 
dist 134=[-1.3064624987015860131 ,1.2600363054786779923 ] 
dist 135=[-1.2581251587014423883 ,1.4623156619220453879 ] 
dist 136=[-.77966500839272793695,1.5868004220413460194 ] 
dist 137=[-.69066371591099867751,1.6779115344000893787 ] 
dist 138=[-.58047574748244127399,1.7470577802601420851 ] 
dist 139=[-.55406925512883765804,1.7988407571295212236 ] 
dist 140=[.17816192236268974609,1.8206852592477076074 ] 
dist 141=[.26582943996440128008,1.8279511292837702951 ] 
dist 142=[.45957618025522353375,1.8249222071389855822 ] 
dist 143=[.4935043757060245771 ,1.5458085473814525379 ] 
dist 144=[.54228763958190600183,1.6207138139167513865 ] 
dist 145=[.41436863940993445212,1.6601820484039406088 ] 
dist 146=[.27967125427415271402,1.6811863819834085457 ] 
dist 147=[.15125267369467923681,1.6839288499569541270 ] 
dist 148=[.04837744697147162023,1.1438288769168369220 ] 
dist 149=[-.05529139623246074270,1.1726673865991032273 ] 
dist 150=[-.18688004352297564844,1.2286868830058973699 ] 
dist 151=[-.31295326679707110314,1.2925209372665521447 ] 
dist 152=[-.39462242195810139734,1.3563961263913316349 ] 
dist 153=[-.48250868309848398969,1.4125746580832151394 ] 
dist 154=[-.67915467326623050145,1.4737940889670975288 ] 
dist 155=[-.8861101793662771026 ,1.5577742990499504435 ] 
dist 156=[-1.0837686534376403326 ,1.6412879866553161652 ] 
dist 157=[-1.3121278365886449400 ,1.7006425502834819351 ] 
dist 158=[-1.6415618825116254132 ,1.7535627875668590950 ] 
dist 159=[-1.9638406326853436300 ,1.8114015478967359073 ] 
dist 160=[-2.1636561137362504613 ,1.8678309754381083044 ] 
dist 161=[-2.3116915661079996652 ,1.9151237076892245010 ] 
dist 162=[-2.4274027655840319474 ,1.9646718491881996360 ] 
dist 163=[-2.5167320011056122502 ,2.0300897672221290365 ] 
dist 164=[-2.5595199823335288144 ,2.0910526172663096503 ] 
dist 165=[-2.8058602912713216952 ,2.1228271504311873072 ] 
dist 166=[-3.0513684173286665453 ,2.1392138997427622244 ] 
dist 167=[-3.2572492133352306127 ,2.1387963130643738251 ] 
dist 168=[-3.4214614729937538785 ,2.1276293998594582733 ] 
dist 169=[-3.5007446904220270250 ,2.1200287709313529618 ] 
dist 170=[-3.5409565747925249760 ,2.0758029874430681992 ] 
dist 171=[-3.5492979575726788421 ,2.0692457962338640394 ] 
dist 172=[-3.4675192942605956730 ,1.8967158933548877797 ] 
dist 173=[-3.4390474168609104918 ,1.8649750709043192238 ] 
dist 174=[-3.3877929105859231884 ,1.7684698962446811255 ] 
dist 175=[-3.3673710522909186015 ,1.7535695899101638359 ] 
dist 176=[-3.2619747217595392297 ,1.5392822201176654221 ] 
dist 177=[-3.2318821270445502761 ,1.4928480490515224911 ] 
dist 178=[-3.1366287817346117833 ,1.4506565375749083063 ] 
dist 179=[-3.1095499886346287725 ,1.6619002400603874719 ] 
dist 180=[.73288188646192993853,1.8347267327630014652 ] 
dist 181=[.9950174128002622622 ,1.9820309251653579733 ] 
dist 182=[1.2830798113491598561 ,2.1326442797976239454 ] 
dist 183=[1.2110069807096942534 ,2.2666166333521066363 ] 
dist 184=[1.1347307699607539004 ,2.4457927252830231053 ] 
dist 185=[1.0409127607023608999 ,2.6909044553911899182 ] 
dist 186=[.89885966057687161093,2.8987026574585166257 ] 
dist 187=[.73699914421248167922,3.1093593603424568207 ] 
dist 188=[.56416343875797386642,3.2959265826867910740 ] 
dist 189=[.35050486037376217776,3.4076275604032881970 ] 
dist 190=[.02579052563668469275,3.4856742935775208466 ] 
dist 191=[-.30084912997422165563,3.5379873360803120455 ] 
dist 192=[-.52218859630918840002,3.5696417531278606521 ] 
dist 193=[-.70837939036937828514,3.5710411202173244818 ] 
dist 194=[-.89480192009467144912,3.5480822513518970545 ] 
dist 195=[-1.0666895574982519953 ,3.5285561452248886361 ] 
dist 196=[-1.1948968901391142791 ,1.7906456561635556481 ] 
dist 197=[-1.3154270818919520527 ,1.6323417087330501813 ] 
dist 198=[-1.4566885564290598885 ,1.2531681620194190107 ] 
dist 199=[-1.5863800273704306518 ,1.1894170056791570069 ] 
dist 200=[-1.6607544169274780523 ,.65412657338219428938] 
dist 201=[-1.7087156648635428409 ,.55609218993601402734] 
dist 202=[-1.8310836740437787152 ,.41156450494626760084] 
dist 203=[-2.0619596744033797297 ,.37198888846135946887] 
dist 204=[-2.2742932142619937540 ,.02326884023854035991] 
dist 205=[-2.3966333644418502941 ,.13476756647995110646] 
dist 206=[-2.4762413606029919633 ,.31322860883351995356] 
dist 207=[-2.5181106142323408333 ,.4928985591999360023 ] 
dist 208=[-2.5425856463495342275 ,.68508734557662905869] 
dist 209=[-2.5528062817393110903 ,.87766240162663639851] 
dist 210=[-2.5545219697918720371 ,1.0697456000750494889 ] 
dist 211=[-2.5454458963810466808 ,1.2463782631333379525 ] 
dist 212=[-.92073467318225784652,1.3773179343626973751 ] 
dist 213=[-.9232759225362658982 ,1.4996228691744160910 ] 
dist 214=[-.9796813605518651748 ,1.6418101930997817874 ] 
dist 215=[-1.0376811142087931544 ,1.7717499739390088513 ] 
dist 216=[-1.0820063101584626067 ,1.8451968480954961530 ] 
dist 217=[-1.1247216938639884538 ,1.8911949637552127042 ] 
dist 218=[-1.1762993418929134519 ,1.9116353339657978220 ] 
dist 219=[-1.2295083410920096376 ,1.9649868705696500958 ] 
dist 220=[-1.2787314106836711568 ,2.1557224407146502041 ] 
dist 221=[-1.3343699434979438637 ,2.2669914813099299274 ] 
dist 222=[-1.4131714510008770785 ,2.3411484119492502185 ] 
dist 223=[-1.4892160225920520228 ,2.3838383995615204428 ] 
dist 224=[-1.5455949611616248506 ,2.4095247554522930834 ] 
dist 225=[-1.6316989710420723892 ,2.4158508102417459269 ] 
dist 226=[-1.7314284545157108699 ,2.4450149240496638952 ] 
dist 227=[-1.8755615889861817685 ,2.5513689662088902907 ] 
dist 228=[-2.0158047419394653635 ,2.6269009751044914403 ] 
dist 229=[-2.1000160983450831033 ,2.8983146915507433688 ] 
dist 230=[-2.1591405824686019048 ,3.1004951284806119582 ] 
dist 231=[-2.1993094363326529028 ,3.2605146871860474701 ] 
dist 232=[-2.2241170377654973053 ,3.3843868320954114445 ] 
dist 233=[-2.2278458295518022544 ,3.4423665817941765627 ] 
dist 234=[-2.2122167749884392456 ,3.4675486574515340612 ] 
dist 235=[-2.2067367658672397793 ,3.4667288979730859790 ] 
dist 236=[-2.0790670093713013463 ,3.2656329350142614172 ] 
dist 237=[-2.0526138094642567752 ,3.2223914658959291224 ] 
dist 238=[-2.0224760486086526409 ,3.1435675570007071547 ] 
dist 239=[-2.0517420759719151130 ,3.1174801641609846401 ] 
dist 240=[-2.0752002857497465660 ,3.0004624415065494861 ] 
dist 241=[-2.0867396942492985894 ,2.9671860124508763179 ] 
dist 242=[-2.0917365669365216566 ,2.8801785718991256925 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 0, 1, 2] 
dist 0=[53.579761092420957715  ,53.579761092420957715  ] 
dist 1=[53.398825108266145194  ,53.661282237255100770  ] 
dist 2=[52.826472276701719146  ,53.836512890413424373  ] 
dist 3=[51.857128686473082649  ,54.113172006858964009  ] 
dist 4=[50.090948217195086202  ,54.599281661348364195  ] 
dist 5=[47.970236496375198635  ,55.092400597784401745  ] 
dist 6=[45.585245304534223113  ,55.397089206724376470  ] 
dist 7=[42.546019597614755826  ,55.621338399869909187  ] 
dist 8=[37.812990915562397827  ,55.793799012889066385  ] 
dist 9=[33.018750075346169582  ,55.919772322559438944  ] 
dist 10=[29.734980727378160044  ,55.958739060093530820  ] 
dist 11=[26.923332049698023812  ,55.942010886418705229  ] 
dist 12=[24.013856146293101828  ,55.851726122856679338  ] 
dist 13=[21.256945296765298220  ,39.599603600678962283  ] 
dist 14=[19.054106834823801312  ,38.229414607113885507  ] 
dist 15=[16.829604891054630683  ,34.867687909474728271  ] 
dist 16=[13.985467889791994656  ,34.381129669131587653  ] 
dist 17=[11.226649426975273555  ,29.331494005392192288  ] 
dist 18=[9.3424577723633616805 ,28.383530459641087104  ] 
dist 19=[7.7310742448134402642 ,27.317189483033039403  ] 
dist 20=[6.0612106166255016670 ,27.117053112970804527  ] 
dist 21=[4.4708908326027385229 ,20.731480309996123353  ] 
dist 22=[3.1764478398762289401 ,19.984306025928668658  ] 
dist 23=[1.8416653613982377272 ,18.275376483875807588  ] 
dist 24=[.08861727669319594388,18.013872683064784433  ] 
dist 25=[-1.6010878451714106161 ,15.904734853610527800  ] 
dist 26=[-2.6829538508448690248 ,15.545966453449598459  ] 
dist 27=[-3.5367253043225334403 ,15.021014562337348457  ] 
dist 28=[-4.3140326618331677600 ,14.897053115338690221  ] 
dist 29=[-4.9921475173156956901 ,-.26764737562720526771] 
dist 30=[-5.4492040869403902086 ,-1.2731685207153861839 ] 
dist 31=[-5.8370559256607165067 ,-3.4003742522982104813 ] 
dist 32=[-6.4233098049286392429 ,-3.6535624345306366743 ] 
dist 33=[-7.9684351068456737300 ,-3.1739575654537635947 ] 
dist 34=[-9.1264028685212934409 ,-2.7020187969615700336 ] 
dist 35=[-10.226745573905265496  ,-2.1499646696313644569 ] 
dist 36=[-11.541647350786425653  ,-1.3498288445620573185 ] 
dist 37=[-12.774015908185622982  ,-.4563988293766302132 ] 
dist 38=[-13.544644137131214689  ,.46823842325480641132] 
dist 39=[-14.127386954861775439  ,1.5896789200525444678 ] 
dist 40=[-14.609178310894938788  ,3.2684924963071565476 ] 
dist 41=[-14.991436777707086973  ,4.9371998091873642350 ] 
dist 42=[-15.176581779113760417  ,6.0185059738328082194 ] 
dist 43=[-15.253678480289303299  ,6.8741404102035036684 ] 
dist 44=[-15.253879716353383756  ,7.6428459191763018500 ] 
dist 45=[-5.0046368315372261470 ,8.2951077910511456502 ] 
dist 46=[-4.8985571675076468812 ,8.6863519507549454696 ] 
dist 47=[-4.6581311632024476504 ,8.9608449937194161584 ] 
dist 48=[-4.5791827320382410654 ,9.1475037660578078600 ] 
dist 49=[-3.6565589126250331410 ,9.2760729669453529175 ] 
dist 50=[-3.5136639181149081688 ,9.3188055228515495289 ] 
dist 51=[-3.1543884229214764506 ,9.3070046921546472429 ] 
dist 52=[-3.0869603264925062714 ,9.2832688072886199522 ] 
dist 53=[-2.5034156843504187561 ,9.0914684201885693593 ] 
dist 54=[-2.3872371346529469885 ,9.0282091138294592771 ] 
dist 55=[-2.2210256786623551241 ,8.7887063207445286122 ] 
dist 56=[-2.1691872331450491662 ,8.4325527314621076118 ] 
dist 57=[-1.1114676816941021114 ,8.5322412139451116445 ] 
dist 58=[-.97481551718147058837,8.5674957389497407308 ] 
dist 59=[-.66257595487177606078,8.5625259600515329938 ] 
dist 60=[-.60300718907922333164,8.5371204107158973275 ] 
dist 61=[-.2133289920936850166 ,3.3121474431092710950 ] 
dist 62=[-.14518117075643090739,2.8724141408516383890 ] 
dist 63=[-.01626976820580581235,1.8544405487015048473 ] 
dist 64=[-.34539007728771845771,1.6723234020321152683 ] 
dist 65=[-1.1615373638510473255 ,.90295699889997766346] 
dist 66=[-1.8000469698965120343 ,1.0775607929927459394 ] 
dist 67=[-2.4293330112818136142 ,1.2190512637254567019 ] 
dist 68=[-3.2087198226107848868 ,1.3520243152364831626 ] 
dist 69=[-3.9458056508248011547 ,1.4692086771788358676 ] 
dist 70=[-4.4063653797052090968 ,1.5477595868844113685 ] 
dist 71=[-4.7516286897282357952 ,1.6131308222807835647 ] 
dist 72=[-5.0288023021492289032 ,1.6778178799464992224 ] 
dist 73=[-5.2441533322818238575 ,1.7317294602951917866 ] 
dist 74=[-5.3428133230625365354 ,1.7541268121983033016 ] 
dist 75=[-5.3866617773917594722 ,1.7619256681426447473 ] 
dist 76=[-5.3833587870131475699 ,1.7586776229242520083 ] 
dist 77=[-1.0286076815621633049 ,1.7120660524093580096 ] 
dist 78=[-.88934455701767331503,1.6954345492304894934 ] 
dist 79=[-.67996128904510231435,1.6723189051887299368 ] 
dist 80=[-.76521062492360389126,1.6613027421822032073 ] 
dist 81=[-.84404992233055447656,1.3473634394776504826 ] 
dist 82=[-.8898366353457762753 ,1.3018919302335876986 ] 
dist 83=[-.92002824207743199211,1.2030304069162399008 ] 
dist 84=[-.93670082136828205605,1.3364710262224925834 ] 
dist 85=[-.94609764668534091435,1.6079628704740843272 ] 
dist 86=[-.94726613506489758722,1.7761256621082191044 ] 
dist 87=[-.9433107615560572073 ,1.9004051327856608479 ] 
dist 88=[-.93959482630191272331,1.9968722542368876050 ] 
dist 89=[-.83890441152601945207,2.0696158686840051693 ] 
dist 90=[-1.0880060282931957853 ,2.0992787942142911863 ] 
dist 91=[-1.3032033873644253028 ,2.1418570585733186675 ] 
dist 92=[-1.5279827117605570975 ,2.2773659432910041383 ] 
dist 93=[-1.7413248788111483099 ,2.3992740003652444122 ] 
dist 94=[-1.9108834773060676124 ,2.4596417672766523338 ] 
dist 95=[-2.0805831648685519079 ,2.4905599652389749344 ] 
dist 96=[-2.2944759438786225790 ,2.4948706629844277888 ] 
dist 97=[-2.4987348470274028687 ,2.4541765631560315778 ] 
dist 98=[-2.6299925943293467504 ,2.4391726935944612747 ] 
dist 99=[-2.7326745451656268112 ,2.4262275786849805743 ] 
dist 100=[-2.8229202260228945593 ,2.4128367760096468931 ] 
dist 101=[-2.8980137279932819326 ,1.9207217589231865098 ] 
dist 102=[-2.9402356416350018181 ,1.8506428173757767987 ] 
dist 103=[-2.9663187678191729082 ,1.7140179856123398893 ] 
dist 104=[-2.9770060099653495128 ,1.6768867335385538664 ] 
dist 105=[-2.9757465156279713747 ,2.0777355277015220973 ] 
dist 106=[-2.9674661655156277542 ,2.4746555031586485452 ] 
dist 107=[-2.9277592840961451474 ,2.7822651137175104458 ] 
dist 108=[-2.9072625897834709989 ,3.0475981404033469879 ] 
dist 109=[-2.7547456215636683411 ,3.2648749382400309962 ] 
dist 110=[-2.7135262455166165788 ,3.3807863682594623010 ] 
dist 111=[-2.6476825055606630466 ,3.4454892432002331382 ] 
dist 112=[-2.6244182674821631508 ,3.4600376915923602945 ] 
dist 113=[-2.0325668689649448491 ,3.4434730345344465180 ] 
dist 114=[-1.9471935583062896580 ,3.4319187517390862413 ] 
dist 115=[-2.0064718191926223502 ,3.4170362143835539612 ] 
dist 116=[-2.1131874059990863209 ,3.3985951997687450485 ] 
dist 117=[-2.2049656752524834069 ,3.3671343529989935336 ] 
dist 118=[-2.2579863358388334791 ,3.3441311120810419686 ] 
dist 119=[-2.2927185531686060630 ,3.3029787828015446144 ] 
dist 120=[-2.3115288718507032185 ,3.2849411149503044181 ] 
dist 121=[-2.3186615223066691736 ,.00714521356174305081] 
dist 122=[-2.3154133810983362374 ,-.23527081035316982344] 
dist 123=[-2.2899436834449153594 ,-.7898388313171380675 ] 
dist 124=[-2.2771202118194004345 ,-.68939605702266697077] 
dist 125=[-1.6252761897814282344 ,-.2738627677016185262 ] 
dist 126=[-1.8767313894221147909 ,.00818047133444126430] 
dist 127=[-2.1011313156960124627 ,.24595949203124388823] 
dist 128=[-2.3466463215375305016 ,.48491022280066613405] 
dist 129=[-2.5704048139300251723 ,.705818795897665224  ] 
dist 130=[-2.7080194168298817720 ,.87162306416155249405] 
dist 131=[-2.8086207458110844794 ,1.0285323962001366193 ] 
dist 132=[-2.8847277018172402495 ,1.2139582022478377287 ] 
dist 133=[-2.9390856058635103196 ,1.3861117728849632096 ] 
dist 134=[-2.9529265255603499332 ,1.4900742084075216496 ] 
dist 135=[-2.9501962436384095370 ,1.5638235899422138512 ] 
dist 136=[-2.9384546564038515561 ,1.6154465700211687884 ] 
dist 137=[-1.6764048941127437615 ,1.6527399159902274544 ] 
dist 138=[-1.5614825198387826187 ,1.6693223596738956707 ] 
dist 139=[-1.2736199687985008134 ,1.6738853547686219509 ] 
dist 140=[-1.2320702753629321037 ,1.6718813695641020678 ] 
dist 141=[-.78650303915164057954,.42308954250573736441] 
dist 142=[-.70312559838465484025,.40787345099030774221] 
dist 143=[-.60818801150157507254,.59070150665593582106] 
dist 144=[-.59102569398179191535,.81298642422691195562] 
dist 145=[-.12119680892432516567,1.0227646363196670054 ] 
dist 146=[-.22006907718682927443,1.1557044361690891522 ] 
dist 147=[-.31731201825704845812,1.2575337936555309123 ] 
dist 148=[-.43750553892146202552,1.3432088773321014447 ] 
dist 149=[-.55109922053380508754,1.4117012702494512169 ] 
dist 150=[-.62201524609089920067,1.4449851162712814844 ] 
dist 151=[-.67512249590561578867,1.4617101840125483830 ] 
dist 152=[-.7176746927780171792 ,1.4641628140630156722 ] 
dist 153=[-.80933165220659488462,1.1885586057573910860 ] 
dist 154=[-.94122407235986443113,1.2370686785415467691 ] 
dist 155=[-1.0914290181363984447 ,1.3050514613207316787 ] 
dist 156=[-1.3055668463496300073 ,1.3787809843605163375 ] 
dist 157=[-1.5137548058493608125 ,1.4504474507139656479 ] 
dist 158=[-1.6402241898003782655 ,1.5101950103136703253 ] 
dist 159=[-1.7308503229987199201 ,1.5725704254992056041 ] 
dist 160=[-1.7960450962342572632 ,1.6547157562016437836 ] 
dist 161=[-1.8444357133425257988 ,1.7348866740826134251 ] 
dist 162=[-1.8680220200870376786 ,1.7893817123142944043 ] 
dist 163=[-1.8779212366595881384 ,1.8354118859598421946 ] 
dist 164=[-1.8763360499675179761 ,1.8818070165593001304 ] 
dist 165=[-1.6848861637415017586 ,1.9247695683212477410 ] 
dist 166=[-1.6521589924635933025 ,1.9571007226639247416 ] 
dist 167=[-1.5951005049883448069 ,1.9877552105124658602 ] 
dist 168=[-1.8718130304207037126 ,2.0240199416391537228 ] 
dist 169=[-2.3924570591390586312 ,2.0558341525979970323 ] 
dist 170=[-2.7235554833445078581 ,2.0687330336041789910 ] 
dist 171=[-2.9786151541918466068 ,2.0701889051715377564 ] 
dist 172=[-3.1959240449120039556 ,2.0654280852407456070 ] 
dist 173=[-3.3718647586322456918 ,2.0338484928276456246 ] 
dist 174=[-3.4618987067799838970 ,2.0225993479954747625 ] 
dist 175=[-3.5089020227048918419 ,1.9712126004261743591 ] 
dist 176=[-3.5163747315967071524 ,1.9634853946153965947 ] 
dist 177=[-3.4741145422862450055 ,1.7863319327465224153 ] 
dist 178=[-3.4515662075340483583 ,1.7536473261758116728 ] 
dist 179=[-3.4104865546390216036 ,1.6602037985153659217 ] 
dist 180=[-3.3920816727686554071 ,1.6423963196730541170 ] 
dist 181=[-3.2898616918203871733 ,1.5741655647689054738 ] 
dist 182=[-3.2612453558359685906 ,1.6327823850307459324 ] 
dist 183=[-3.1621068539517588226 ,1.6748551134880077040 ] 
dist 184=[-3.1403516809788817998 ,1.7052427338375691340 ] 
dist 185=[.35535565634606030407,1.7257297184842209332 ] 
dist 186=[.24137580016323907106,1.7283053832354466905 ] 
dist 187=[.10359197734738431036,1.8067273199501460109 ] 
dist 188=[-.10238769782482778914,2.1056904941082229738 ] 
dist 189=[-.30885195888893594766,2.4647029685905810435 ] 
dist 190=[-.44856954331754052119,2.7091884175521136622 ] 
dist 191=[-.56591405141469578872,2.9161386014405343722 ] 
dist 192=[-.68312352069039479   ,3.1254189008777039497 ] 
dist 193=[-.79103217548893538692,3.3105325028008136349 ] 
dist 194=[-.87127220556632744062,3.4210780822876099110 ] 
dist 195=[-.94647572001453140962,3.4979669195641443202 ] 
dist 196=[-1.0342919096650581198 ,3.5488170401039744902 ] 
dist 197=[-1.1147679198517065720 ,3.5789269705593714955 ] 
dist 198=[-1.1606886040106299662 ,3.5798906125881859072 ] 
dist 199=[-1.1900138776213463483 ,3.5548864562424841247 ] 
dist 200=[-1.2042841916039907315 ,3.5357498030456721212 ] 
dist 201=[-1.2109529520044694602 ,1.7898990522376304091 ] 
dist 202=[-1.2099528930284196938 ,1.6305131459878724664 ] 
dist 203=[-1.2039064452883437581 ,1.2498053317842197209 ] 
dist 204=[-1.1992367787718509326 ,1.1849670922479657000 ] 
dist 205=[-1.3981359755953485323 ,.65058052094756823573] 
dist 206=[-1.6133159082786791953 ,.62427459746509993064] 
dist 207=[-1.8163511009377388906 ,.76512239573018739799] 
dist 208=[-2.0553388708242640666 ,.9045982101952714367 ] 
dist 209=[-2.2752243879076791687 ,1.0322132486776043469 ] 
dist 210=[-2.4020585544828687506 ,1.1257452992843779441 ] 
dist 211=[-2.4847683649863237412 ,1.2120579355886540299 ] 
dist 212=[-2.5286373039319569928 ,1.3108732468879796474 ] 
dist 213=[-2.5548115963741494243 ,1.4003847825285362722 ] 
dist 214=[-2.5669362371842218458 ,1.4495821443817249659 ] 
dist 215=[-2.5710662638396857564 ,1.4785856642613102966 ] 
dist 216=[-2.5653509639341811699 ,1.4875380468976617519 ] 
dist 217=[-.95178859886143970631,1.4882195701419787826 ] 
dist 218=[-.98009055788554233841,1.4842277660945747481 ] 
dist 219=[-1.0111093892051244956 ,1.4760568554060520687 ] 
dist 220=[-1.0538749458406100081 ,1.4696274688736590200 ] 
dist 221=[-1.0946780556654741311 ,1.4062015085869016976 ] 
dist 222=[-1.1178681621148787078 ,1.5775157447691159014 ] 
dist 223=[-1.1325591414515514682 ,1.7081613278153183851 ] 
dist 224=[-1.1394560587823470987 ,1.8560435201901201560 ] 
dist 225=[-1.2600597237337777703 ,2.0481144784146362984 ] 
dist 226=[-1.3459195235312225297 ,2.1611162073908409570 ] 
dist 227=[-1.4128577375319318766 ,2.2376227705781941385 ] 
dist 228=[-1.4712970664315678761 ,2.2841101760087204443 ] 
dist 229=[-1.5199260457683449106 ,2.3135665820736336531 ] 
dist 230=[-1.5755607819186846366 ,2.3221334782671977619 ] 
dist 231=[-1.6809578279895639565 ,2.3174705064057403579 ] 
dist 232=[-1.8339326630024981585 ,2.3114134212714670799 ] 
dist 233=[-1.9830335264523127446 ,2.5905983008102990805 ] 
dist 234=[-2.0729763203788125965 ,2.8500622670290659505 ] 
dist 235=[-2.1366255866531758947 ,3.0423860590273420677 ] 
dist 236=[-2.1808393810788039128 ,3.1928533129327755521 ] 
dist 237=[-2.2090617454950257220 ,3.3087135119375633949 ] 
dist 238=[-2.2140985637914937989 ,3.3629816786083613845 ] 
dist 239=[-2.2006257714609472179 ,3.3857545346121054280 ] 
dist 240=[-2.1963337961970683703 ,3.3850312679936892829 ] 
dist 241=[-2.0690654050434589491 ,3.1670186269223480572 ] 
dist 242=[-2.0425833302443700863 ,3.1222794361798597490 ] 
dist 243=[-1.9642073236222526494 ,3.0409027993712199632 ] 
dist 244=[-1.9450050710012891065 ,3.0145635927381030600 ] 
dist 245=[-1.9436302577318793311 ,2.8989491481142211177 ] 
dist 246=[-1.9505315135258108246 ,2.8658838510520726002 ] 
dist 247=[-1.9486513013624651464 ,2.7827208481325631420 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 1, 1, 2, 0, 2] 
dist 0=[56.689595415591260052  ,56.689595415591260052  ] 
dist 1=[56.256665200382599544  ,57.325286180968152447  ] 
dist 2=[55.163616299810801498  ,57.993044999381934171  ] 
dist 3=[53.397357593119226193  ,58.319126261677979274  ] 
dist 4=[50.474250130597364696  ,58.458064134804599221  ] 
dist 5=[47.443037435502498666  ,58.436797139376715759  ] 
dist 6=[45.245098400213824957  ,58.203993331099160088  ] 
dist 7=[43.232786604714461404  ,57.663230825278757161  ] 
dist 8=[40.942737205956600466  ,54.599346981656072354  ] 
dist 9=[38.644293980963649141  ,54.363650884074839959  ] 
dist 10=[36.598388932150647660  ,53.558307092841823733  ] 
dist 11=[34.341584423883859600  ,53.288284625989434458  ] 
dist 12=[31.200830204955158134  ,52.847645312184152899  ] 
dist 13=[28.037882620846216520  ,52.686014255167676491  ] 
dist 14=[25.692319045241404920  ,52.114163241049421724  ] 
dist 15=[23.491146138690364467  ,51.074389005407861608  ] 
dist 16=[20.904514272020296244  ,27.225281249185542621  ] 
dist 17=[18.260036255442720230  ,25.812772818414990775  ] 
dist 18=[15.827523746178478992  ,23.665932906202462111  ] 
dist 19=[13.077306456165116616  ,22.913810337780144905  ] 
dist 20=[9.1633880482702734406 ,22.728760228307966310  ] 
dist 21=[5.3034301023841317604 ,17.510483393356477900  ] 
dist 22=[2.7685801775978134580 ,12.527422214889885585  ] 
dist 23=[.71094802059160892624,12.137109241241810717  ] 
dist 24=[-1.2429209937699615762 ,8.9817555858858047986 ] 
dist 25=[-2.9888044378916636848 ,8.4794385716528124516 ] 
dist 26=[-4.2158634214642903205 ,8.0161776263488802525 ] 
dist 27=[-5.3088512873986175703 ,6.6960169572562622747 ] 
dist 28=[-7.1650745447369364935 ,4.2719969230401836623 ] 
dist 29=[-8.6464171430229204954 ,3.4286397807778166680 ] 
dist 30=[-10.146220612772532007  ,-1.7106419459130812919 ] 
dist 31=[-12.077884994224183795  ,-2.1620959452863828208 ] 
dist 32=[-13.901065551025846162  ,-3.0399248019917281855 ] 
dist 33=[-14.967792071674811052  ,-3.2392568266710937629 ] 
dist 34=[-15.694891105428121241  ,-3.8134066043982257086 ] 
dist 35=[-16.160504737343880084  ,-3.7330154864976501833 ] 
dist 36=[-16.487101583950374690  ,-2.1505868468052473197 ] 
dist 37=[-16.658093368276023255  ,-.53372983993278188833] 
dist 38=[-16.751465247163854687  ,.56473203743761827826] 
dist 39=[-16.766536601327260507  ,1.4890694372968816317 ] 
dist 40=[-14.695788392003976480  ,2.4119282920964437107 ] 
dist 41=[-14.386182359832292305  ,3.2587229383452641963 ] 
dist 42=[-13.849199690877154813  ,3.8798778453755360148 ] 
dist 43=[-13.702010691125961148  ,4.4523257500975115575 ] 
dist 44=[-13.233132676834378745  ,5.1049629440019353411 ] 
dist 45=[-13.077109061809863657  ,5.7045800707085740863 ] 
dist 46=[-12.970461742541390611  ,6.0656074321358486645 ] 
dist 47=[-12.922497052179676974  ,6.3195739812409816394 ] 
dist 48=[-2.1321602498614778994 ,6.4922253325705737739 ] 
dist 49=[-1.2540374579838734092 ,6.6064951005898411289 ] 
dist 50=[.04917570847030889066,6.6276739972916872466 ] 
dist 51=[.21366477537264898997,6.6113624046906952332 ] 
dist 52=[.25195527561686003346,6.5761434209623140829 ] 
dist 53=[.37014245970002429349,6.5731050223849517167 ] 
dist 54=[.39118271107333261772,6.8653684232485083732 ] 
dist 55=[.4190826729479744702 ,8.2272346182163497869 ] 
dist 56=[.41894910360469760178,9.5163624406855107954 ] 
dist 57=[.4088282711909264678 ,10.332577099771001990  ] 
dist 58=[.38545463351912380996,10.958919253145419702  ] 
dist 59=[.3483494325192448218 ,11.490181510522477713  ] 
dist 60=[.2834329719854382672 ,11.919889453007516940  ] 
dist 61=[.2134476292267626041 ,12.140882362001922119  ] 
dist 62=[.1560907880414791355 ,12.251418151127095212  ] 
dist 63=[.0973784257847554451 ,12.261243860073787391  ] 
dist 64=[-.6751294488739295919 ,1.2719430279570617382 ] 
dist 65=[-1.7868182201593729926 ,1.1138069205690208193 ] 
dist 66=[-2.7033794470949584007 ,.49686868997131255981] 
dist 67=[-3.5810394101389686082 ,.4925955996351125147 ] 
dist 68=[-4.3648756155264167955 ,.4906096317135087363 ] 
dist 69=[-4.9071721447572306296 ,.48219598001443205673] 
dist 70=[-5.3756687733114065553 ,.47915532901357630465] 
dist 71=[-5.8651418420859262973 ,.47704476582854047369] 
dist 72=[-6.3034087782424086619 ,.47561761855068282017] 
dist 73=[-6.5676311242312786607 ,.47465163892696112898] 
dist 74=[-6.7547805732194427440 ,.47436166278598524749] 
dist 75=[-6.8855420579930738872 ,.47440502954152431892] 
dist 76=[-6.9700964767708427887 ,.47473630387571119261] 
dist 77=[-6.9808460806415359293 ,.47482030656220167374] 
dist 78=[-6.9465462122367953140 ,.47386707554470064312] 
dist 79=[-6.9147171586642781726 ,.47180125644307396167] 
dist 80=[-3.6504691216665481827 ,.46994411221478951621] 
dist 81=[-3.3515025866625200699 ,.46170997141679769018] 
dist 82=[-2.6255500713503553519 ,.45877582905568986219] 
dist 83=[-2.5081269105273582649 ,.5981142476790932846 ] 
dist 84=[-1.4521017676237731828 ,1.2093080028334418975 ] 
dist 85=[-1.2571059067309220550 ,1.6719081609052395700 ] 
dist 86=[-.98977825906299695648,2.1132379747365160751 ] 
dist 87=[-.9095568446825097404 ,2.6396288580998841510 ] 
dist 88=[.30956822730634894762,3.1309432866451450337 ] 
dist 89=[.2647997294871302606 ,3.4323712482479135809 ] 
dist 90=[.19544102876665250032,3.6518554923718527112 ] 
dist 91=[.09653459082940850807,3.8163058339662131551 ] 
dist 92=[-.0426290609262031919 ,3.9395880589326298494 ] 
dist 93=[-.27253486641418564847,3.9948553045072034795 ] 
dist 94=[-.50732763768061243665,4.0137506169818137199 ] 
dist 95=[-.66598143720451441605,4.0102449326141346900 ] 
dist 96=[-.7987509862628857266 ,2.2243736430179550098 ] 
dist 97=[-.93031856710599728183,2.2271712423365935302 ] 
dist 98=[-1.0505331736078303472 ,2.1962415266954782166 ] 
dist 99=[-1.1380255514264598356 ,2.1806285232770239066 ] 
dist 100=[-1.2180153054330368377 ,2.1637451035893415777 ] 
dist 101=[-1.4838811554707983026 ,2.1514855761299622057 ] 
dist 102=[-1.7054678751029304413 ,1.7669737563768052421 ] 
dist 103=[-1.8763808285066759512 ,1.7103677347251515972 ] 
dist 104=[-2.0221146471843988359 ,1.6900413074962470826 ] 
dist 105=[-2.1399692693248019909 ,1.6553466098060262357 ] 
dist 106=[-2.1996833429639393522 ,1.6428039588435665328 ] 
dist 107=[-2.2309968247119161815 ,1.6089892061094570672 ] 
dist 108=[-2.2356046521570004720 ,1.5940837172848748451 ] 
dist 109=[-2.2014325374199066446 ,1.3761584508088363574 ] 
dist 110=[-2.1849194755853787618 ,1.3407804168066014645 ] 
dist 111=[-2.1587715730565746910 ,1.2507206069707295157 ] 
dist 112=[-2.1461075851592997936 ,1.2296897898625767746 ] 
dist 113=[-2.0851426557024261352 ,1.0742676554225966936 ] 
dist 114=[-2.0660883981756512600 ,1.0415015743283472552 ] 
dist 115=[-2.0072101839923442750 ,.98683541534081680626] 
dist 116=[-2.0050584650428640116 ,.97162353373672391671] 
dist 117=[-2.0752411943373208915 ,-.3083630249132021849 ] 
dist 118=[-2.1322198474415418985 ,-.19022831682100284657] 
dist 119=[-2.1662592173648126103 ,-.02146322419000191711] 
dist 120=[-2.1899894799699467037 ,.14897675260930067087] 
dist 121=[-2.2058331921341228415 ,.27381304491778196386] 
dist 122=[-2.2153901285294484104 ,.38883352145026737596] 
dist 123=[-2.2140358379644749882 ,.52015861548125506435] 
dist 124=[-2.2044424584071655226 ,.65160975188252584714] 
dist 125=[-2.1964874590227066530 ,.7671620245569225497 ] 
dist 126=[-.79827211922594398662,.89304574417936906519] 
dist 127=[-.67939320392023693124,1.0657540322564163636 ] 
dist 128=[-.40516492876959849998,1.2360655950671861994 ] 
dist 129=[-.35600314293103099012,1.4193226479365895732 ] 
dist 130=[-.00514357775861267920,1.5710232983233456785 ] 
dist 131=[.05654372878887361343,1.7190540123898165815 ] 
dist 132=[.16538226704582017513,1.8531714645897734010 ] 
dist 133=[.18835777382336019469,1.9493595746283356728 ] 
dist 134=[.35323323639908989898,2.0360654423869071707 ] 
dist 135=[.36486240650530816343,2.1323491408494583390 ] 
dist 136=[.35467736081618027718,2.2180528829521276920 ] 
dist 137=[.31211612397902743719,2.2625453487438203655 ] 
dist 138=[.25213134229599576917,2.2853112525275054621 ] 
dist 139=[.17243574209056920275,2.2871738575777128853 ] 
dist 140=[.06319992707267819434,2.2722921220385510373 ] 
dist 141=[-.18118273731311185655,2.2614603220151263100 ] 
dist 142=[-.56075364154343774449,2.2272908891566182230 ] 
dist 143=[-1.1282757420671481024 ,2.2097695781339917745 ] 
dist 144=[-1.6925621154827992134 ,1.9467786180907950445 ] 
dist 145=[-2.0592298032253719018 ,1.9013675055845077441 ] 
dist 146=[-2.3506749440464738821 ,1.7978094487402941042 ] 
dist 147=[-2.6148892346096702407 ,1.7641002753115097227 ] 
dist 148=[-2.8407965419177459919 ,1.6071052984331457714 ] 
dist 149=[-2.9794322371976098572 ,1.5726820586377077111 ] 
dist 150=[-3.0804574051738535530 ,1.4883689499686197534 ] 
dist 151=[-3.1563372012051928608 ,1.4624420164139868282 ] 
dist 152=[-3.2125231097573815744 ,1.1874836033031421936 ] 
dist 153=[-3.2349861451320158314 ,1.1423337847284441721 ] 
dist 154=[-3.2370428260876590922 ,1.0350295021462188976 ] 
dist 155=[-3.2306590401312501896 ,1.0085105759676171679 ] 
dist 156=[-3.1733865244888475167 ,.84875243635175617349] 
dist 157=[-3.1532319169705717470 ,.81630095224352813554] 
dist 158=[-3.0767197894001361720 ,.75337423407871350967] 
dist 159=[-3.0565686700871545170 ,.73613098608496822034] 
dist 160=[-1.3082494160256807284 ,.77659046560667029123] 
dist 161=[-1.3324227747369118820 ,1.1164761955039688432 ] 
dist 162=[-1.3471188515543330128 ,1.4115786360948632154 ] 
dist 163=[-1.3507661185723662984 ,1.7766552818602123790 ] 
dist 164=[-1.3471885171347143756 ,2.1019830168598515280 ] 
dist 165=[-1.3434616102985404727 ,2.3254594538168589148 ] 
dist 166=[-1.1805976542257684413 ,2.5166773625988246944 ] 
dist 167=[-1.1538177397122342679 ,2.7133291371520528384 ] 
dist 168=[-1.0992808771876998404 ,2.8882234261817356321 ] 
dist 169=[-1.0825815700627361680 ,2.9926505588969598181 ] 
dist 170=[-1.0100493397784088724 ,3.0652569684036165291 ] 
dist 171=[-.99332893102377453478,3.1132146144395062506 ] 
dist 172=[-.94820220587844414447,3.1415494041644047800 ] 
dist 173=[-.93627282347533862502,3.1434947684437621748 ] 
dist 174=[.52067158947200198633,3.1196502739604145174 ] 
dist 175=[.46776900811797471113,3.1058753887459915938 ] 
dist 176=[-.01937209213914576393,1.6150051257254126417 ] 
dist 177=[-.34896712590038389465,1.4775538172174254054 ] 
dist 178=[-.62557309377226211627,1.1966251559425036085 ] 
dist 179=[-.90134363828273745888,1.2997844040469804541 ] 
dist 180=[-1.1547442191719513241 ,1.3915653824161551834 ] 
dist 181=[-1.3421168490981491014 ,1.4915619471092681146 ] 
dist 182=[-1.5165985229643735975 ,1.5800552067584195796 ] 
dist 183=[-1.7185755823498539073 ,1.6259474664277835649 ] 
dist 184=[-1.9039272345133186804 ,1.6505684461435779573 ] 
dist 185=[-2.0120918946320452612 ,1.6549942915261990191 ] 
dist 186=[-2.0841923176866701353 ,1.6390590522345288081 ] 
dist 187=[-2.1256903511408978206 ,1.6318444525701218679 ] 
dist 188=[-2.1514473526160048679 ,1.6245400465492918002 ] 
dist 189=[-2.1607578995283268883 ,1.6152037811069470671 ] 
dist 190=[-2.1597789206081290123 ,1.1914731117591426254 ] 
dist 191=[-2.1533315684212206901 ,1.1400551682349467659 ] 
dist 192=[-.79975847502954952444,1.0145745431828066428 ] 
dist 193=[-.97288226114153977679,.98870345265217158911] 
dist 194=[-1.1263497842643071198 ,.7959165744337589339 ] 
dist 195=[-1.2304323749061208131 ,.7577391736437129112 ] 
dist 196=[-1.3180924994012711518 ,.78477583113944517956] 
dist 197=[-1.4060521774455781112 ,.9447647333692765332 ] 
dist 198=[-1.4833249268568810835 ,1.1019985613233264439 ] 
dist 199=[-1.5283521183293566835 ,1.2961388146211180799 ] 
dist 200=[-1.5583136661205307372 ,1.4794597637286719063 ] 
dist 201=[-1.5754800216475938553 ,1.5935371076292112869 ] 
dist 202=[-1.5830745795815802763 ,1.6785139310172958434 ] 
dist 203=[-1.5823486500747106300 ,1.7457547450784866226 ] 
dist 204=[-1.5634392873678082054 ,1.7963015317478382472 ] 
dist 205=[-1.5583427777091006410 ,1.8146880627353556754 ] 
dist 206=[-1.4912216691974549843 ,1.8200702409737353202 ] 
dist 207=[-1.6305770200053568252 ,1.8824827098605365500 ] 
dist 208=[-1.7661457658428560307 ,2.2425539350029248909 ] 
dist 209=[-1.8473526757655911400 ,2.4654163011381748725 ] 
dist 210=[-1.9041090377896008997 ,2.6300329573849970409 ] 
dist 211=[-1.9421457306548480181 ,2.7577535112503853081 ] 
dist 212=[-1.9655750683481652376 ,2.8557763258783440096 ] 
dist 213=[-1.9695201466723681035 ,2.9019231091135776891 ] 
dist 214=[-1.9557336782558066460 ,2.9208699818114145978 ] 
dist 215=[-1.9519654432936572998 ,2.9205202937806257331 ] 
dist 216=[-1.8178928859937733212 ,2.7169403692962700304 ] 
dist 217=[-1.7913196558726105373 ,2.6764684751610455095 ] 
dist 218=[-1.7187038186672166830 ,2.6032900631230955320 ] 
dist 219=[-1.6977514263239819982 ,2.5800350804471550453 ] 
dist 220=[-1.5486302794383060692 ,2.4800268403880850730 ] 
dist 221=[-1.5143691628590549389 ,2.4510544597730436094 ] 
dist 222=[-1.4562083986840248182 ,2.3811628806509769996 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 0, 0, 2, 0, 2] 
dist 0=[64.169820623434427754  ,64.169820623434427754  ] 
dist 1=[63.430713632455151388  ,64.445465091282551363  ] 
dist 2=[62.209221969348255461  ,64.547783473972925845  ] 
dist 3=[60.007354888480672138  ,64.594804381195791003  ] 
dist 4=[57.663875155035233528  ,64.610312398127470259  ] 
dist 5=[55.876870079256146394  ,64.586865057055567392  ] 
dist 6=[54.152090850849842132  ,64.549509110651124440  ] 
dist 7=[52.056975801655238789  ,64.384779904231025274  ] 
dist 8=[49.879196918878055470  ,62.676273519530767680  ] 
dist 9=[47.824206701052554473  ,58.641844803028090280  ] 
dist 10=[45.461218985115797890  ,57.792994385285590768  ] 
dist 11=[42.053312479145072269  ,56.372109499637273641  ] 
dist 12=[38.567915272702318874  ,55.982770257970807694  ] 
dist 13=[33.755378469228477282  ,54.880553644712220552  ] 
dist 14=[27.136638850609787453  ,54.543925219859871315  ] 
dist 15=[22.658026784562387400  ,54.173473868890579654  ] 
dist 16=[18.881377279486506575  ,52.079142734164523398  ] 
dist 17=[15.065836384829955902  ,32.162859519041993966  ] 
dist 18=[11.509390196011754959  ,31.631878557365591984  ] 
dist 19=[8.7674351493854003394 ,31.494532582451589239  ] 
dist 20=[6.0923920076796954479 ,17.455041200966397010  ] 
dist 21=[2.8032526343557226040 ,10.491451747342017884  ] 
dist 22=[-.3156296067296170135 ,9.2783401434861868428 ] 
dist 23=[-2.3107977864224147260 ,7.6354910798208830861 ] 
dist 24=[-3.8678656865180289148 ,7.2830920203074504797 ] 
dist 25=[-5.2374236619894870383 ,-.51658892324452806725] 
dist 26=[-6.6908479959995815490 ,-1.4327376316344560586 ] 
dist 27=[-9.0572368892509981960 ,-3.0586280213440295310 ] 
dist 28=[-11.283250785424162303  ,-3.7056960340095593162 ] 
dist 29=[-12.683995149936682836  ,-5.1441572300392346097 ] 
dist 30=[-13.752247604476822953  ,-5.3698614115016313750 ] 
dist 31=[-14.650263971846419295  ,-5.3589192680812078480 ] 
dist 32=[-15.373124277718766226  ,-5.2720949954822195166 ] 
dist 33=[-15.741807962562428503  ,-5.0679621801925542383 ] 
dist 34=[-15.922785686454869401  ,-4.8112442204488866503 ] 
dist 35=[-15.953058767906653307  ,-3.2895237676875018660 ] 
dist 36=[-5.8365641572510637634 ,-1.5932006663366528346 ] 
dist 37=[-5.3150627097693125423 ,-.36305910215270112518] 
dist 38=[-5.1998430598912715583 ,.67554026927472671497] 
dist 39=[-5.0747048538393073044 ,1.6989929916455887601 ] 
dist 40=[-5.0263929136944096165 ,2.6309749734580443765 ] 
dist 41=[-3.7741501014681111492 ,3.3049434322337995062 ] 
dist 42=[-3.4719384130712368878 ,3.9174838457410940671 ] 
dist 43=[-3.2254368354759298880 ,4.6046703778251493554 ] 
dist 44=[-3.1289684323814074627 ,5.2357059491802635944 ] 
dist 45=[-3.1097947889559883947 ,5.6243260767250470507 ] 
dist 46=[-2.5090965458938034894 ,5.9093326974878144682 ] 
dist 47=[-2.3504867607474247822 ,6.1270159686614646575 ] 
dist 48=[-2.3107887676209805301 ,6.2846129883828887620 ] 
dist 49=[-1.7927783243120351072 ,6.3299136705650305240 ] 
dist 50=[-1.4654851342639999623 ,6.3321655137930266743 ] 
dist 51=[-1.4021308317957568832 ,6.3179859231566222870 ] 
dist 52=[-1.2796708950050957130 ,3.7230971295887598011 ] 
dist 53=[-1.2471632385693702059 ,3.8163268859806362675 ] 
dist 54=[-.79251552984093337329,3.8839501615447956077 ] 
dist 55=[-.72789218991003012168,3.9119051588575288446 ] 
dist 56=[-.6901684848505962090 ,3.9170901361215594602 ] 
dist 57=[-1.0982925101083314411 ,3.9098789628125800137 ] 
dist 58=[-1.4908284792663628204 ,3.8547500203562360094 ] 
dist 59=[-1.9628924725204622417 ,3.8351696830576198483 ] 
dist 60=[-2.4056605466229788768 ,3.7483267925367717015 ] 
dist 61=[-2.6813920866065371396 ,3.7339540135020308530 ] 
dist 62=[-2.8867155407342901248 ,2.7918015704293881599 ] 
dist 63=[-3.0487330334982419363 ,2.7850754916807951993 ] 
dist 64=[-3.1725046943971734150 ,2.7745466132531418557 ] 
dist 65=[-3.2253097019846312181 ,-.2019366224950921251 ] 
dist 66=[-3.2460231148023534181 ,-.36191944218889463915] 
dist 67=[-3.2418205227463453247 ,-.72039607130552892455] 
dist 68=[-2.2589804898763656774 ,-.77678324005533173685] 
dist 69=[-2.4701263899326145383 ,-.7819828652942084312 ] 
dist 70=[-2.6590823568906326031 ,-.6967084478562040493 ] 
dist 71=[-2.7766312807592060821 ,-.5766879218173916106 ] 
dist 72=[-2.8643370968029164743 ,-.3460086736975194816 ] 
dist 73=[-2.9342028067507666664 ,-.1596213263016217499 ] 
dist 74=[-2.9872391330970242808 ,.0293651582737320375 ] 
dist 75=[-3.0077870740282502336 ,.2704525578176462966 ] 
dist 76=[-3.0084868893301066329 ,.5015269989157348224 ] 
dist 77=[-3.0023257090432455716 ,.6506096314348605855 ] 
dist 78=[-1.8972568662709471839 ,.7677920672130702669 ] 
dist 79=[-1.8849202643067338121 ,.8716876274763090177 ] 
dist 80=[-1.8745443574476234293 ,.9589171968580682306 ] 
dist 81=[-.93919365108103627582,1.0096710414100808278 ] 
dist 82=[-.85367769744982257021,1.0435007730000650252 ] 
dist 83=[-.65620470671743200151,1.0633021499916316358 ] 
dist 84=[-.6175721888944879338 ,1.0753415547011923001 ] 
dist 85=[-.36125054735455744242,1.0782231223784946612 ] 
dist 86=[-.31505101276803494893,1.1460153765802289376 ] 
dist 87=[-.22914244486218892503,1.2951795751130141874 ] 
dist 88=[-.2092277833559296652 ,1.4054928498679877293 ] 
dist 89=[-.15565085850351026746,1.4912305544572670145 ] 
dist 90=[-.1544192125509098262 ,1.5582391704822442309 ] 
dist 91=[-.15325370748246377492,1.5938532503758070746 ] 
dist 92=[-.11084304472937580831,1.6132143676513892408 ] 
dist 93=[-.17058535711539738262,1.6154082708280318971 ] 
dist 94=[-.27529731603073030253,1.2881406872894490376 ] 
dist 95=[-.40015454912208712346,1.2954190952215757139 ] 
dist 96=[-.5280777888834308535 ,1.2957071631510076492 ] 
dist 97=[-.64504592504913298812,.7632101593563691616 ] 
dist 98=[-.77619923642096979775,.7310970799042944702 ] 
dist 99=[-.96074480771932272757,.7210495924440078417 ] 
dist 100=[-1.1414509519490799605 ,.53673831906362295133] 
dist 101=[-1.3233045765239334562 ,.53828194129027012373] 
dist 102=[-1.4772231597994084486 ,.54321446716672830817] 
dist 103=[-1.6276336905296858692 ,.55243691029023772549] 
dist 104=[-1.7640155661879263448 ,.5665651315228839801 ] 
dist 105=[-1.8619654479620527835 ,.59104884574675651494] 
dist 106=[-1.9503850962249014354 ,.62022259057209489081] 
dist 107=[-2.0487456378859518336 ,.65304577419806508276] 
dist 108=[-2.1363786463898128752 ,.69470831761957113673] 
dist 109=[-2.1819989743594248691 ,.75912016611000031331] 
dist 110=[-2.2055198735887439668 ,.82313131729663625408] 
dist 111=[-2.2079681658699656876 ,.86319194813523962042] 
dist 112=[-2.1936561714407984585 ,.89321553151181105894] 
dist 113=[-2.1828447497919869834 ,.91720056323200053756] 
dist 114=[-2.1517112057967480444 ,.93531601625956951771] 
dist 115=[-2.1358378556673714696 ,1.0436358997278857014 ] 
dist 116=[-1.8656250366989361628 ,1.5853002514358363533 ] 
dist 117=[-1.8202418696661738887 ,1.9377392228698240778 ] 
dist 118=[-1.7166362316412814650 ,2.2183809255821176292 ] 
dist 119=[-1.6831066660545508945 ,2.4736409963591430744 ] 
dist 120=[-1.5276802459832098326 ,2.6924612954045047196 ] 
dist 121=[-1.4937809466073910592 ,2.8277435020515525722 ] 
dist 122=[-1.4130489414522182068 ,2.9274972430543892366 ] 
dist 123=[-1.3966591242426476291 ,3.0045958385119721029 ] 
dist 124=[-1.3498145100480539410 ,3.0627462295871880051 ] 
dist 125=[-1.3358018907562093764 ,3.0869137650449586585 ] 
dist 126=[-.97264644607291323232,3.0907959671450302770 ] 
dist 127=[-.94662685876086334685,3.0852690154108332301 ] 
dist 128=[-.79671407176258722517,3.0324311397087392512 ] 
dist 129=[-.7663572924512152398 ,3.0133358120085661162 ] 
dist 130=[-.70567104305364119565,2.9418058233248132981 ] 
dist 131=[-.68865435972048990024,2.9216188385186216471 ] 
dist 132=[-.75711851130555161529,1.3722269481418330386 ] 
dist 133=[-1.0902004143530696021 ,1.4537252439162236573 ] 
dist 134=[-1.3605785687371164715 ,1.5246125334638882086 ] 
dist 135=[-1.7001021588928996437 ,1.5678388297348694043 ] 
dist 136=[-2.0104332998054973606 ,1.5990126888610218341 ] 
dist 137=[-2.2235576876512055427 ,1.6218178289774288642 ] 
dist 138=[-2.4058583597972416378 ,1.6374581688724582568 ] 
dist 139=[-2.5932372794204326136 ,1.6400489558588893957 ] 
dist 140=[-2.7598345535021601217 ,1.6345113248902979838 ] 
dist 141=[-2.8592375508019430818 ,1.6291027076330589502 ] 
dist 142=[-2.9282613455283993477 ,.69642113118093897332] 
dist 143=[-2.9736733261959002003 ,.61588850539616858475] 
dist 144=[-3.0003272115790781927 ,.42602922998151011048] 
dist 145=[-3.0020727279821393739 ,.39378682694073341794] 
dist 146=[-2.9787673387193833816 ,.13705172055178337952] 
dist 147=[-2.9657219339420916860 ,.09102206172215151523] 
dist 148=[-1.5401909012057692314 ,.01909159890843171266] 
dist 149=[-1.4086663042264404761 ,.2956566929577197584 ] 
dist 150=[-1.0945092734872994920 ,.56485755208318020818] 
dist 151=[-1.0664814101587738730 ,.83415806330566877158] 
dist 152=[-1.1067581634578196664 ,1.0821987216312644803 ] 
dist 153=[-1.1317846330479258092 ,1.2665949073978296982 ] 
dist 154=[-1.1481315765253545966 ,1.4392814843476564396 ] 
dist 155=[-1.1537838463518327340 ,1.6406115416021705837 ] 
dist 156=[-1.1526756658360693856 ,1.8257535184604948528 ] 
dist 157=[-1.1499993158770060723 ,1.9338675830613350562 ] 
dist 158=[-.37330380085506509756,2.0060240661788636868 ] 
dist 159=[-.35729769247535050178,2.0477373562793548693 ] 
dist 160=[-.33212776868312499825,2.0741044887885933097 ] 
dist 161=[-.32502115815158110381,2.0850465617478448963 ] 
dist 162=[-.31098766587703430821,2.0867569587473415618 ] 
dist 163=[-.30967319233455484192,2.0803934389289668297 ] 
dist 164=[-.31342403461945424098,.82116069730630367175] 
dist 165=[-.32505585959642998087,.90740596195546953549] 
dist 166=[-.34785189254166532228,.98625503849147926362] 
dist 167=[-.55475924462852367676,1.0308643853466973980 ] 
dist 168=[-.74911496986269601803,1.0588524446869928538 ] 
dist 169=[-.90002003335643062898,1.0713972208368423450 ] 
dist 170=[-1.0476833419779579833 ,1.0771654651131036689 ] 
dist 171=[-1.2291100708622052820 ,1.0781204507448975493 ] 
dist 172=[-1.3999751283591464245 ,1.0757316110862063402 ] 
dist 173=[-1.5055093050970050204 ,1.0714672191787008562 ] 
dist 174=[-1.5831866832773454883 ,1.0718718529956348209 ] 
dist 175=[-1.6429326609581849762 ,1.1508030917513464187 ] 
dist 176=[-1.6868030597722984463 ,1.2344319234468963122 ] 
dist 177=[-1.7011512008384328314 ,1.3150774860017592826 ] 
dist 178=[-1.7043688395760220932 ,1.4088081320016462499 ] 
dist 179=[-1.7937699592596375023 ,1.5446291971298220141 ] 
dist 180=[-2.1323883336979387228 ,1.6768411909207563940 ] 
dist 181=[-2.3417100066057875340 ,1.7561742936878728925 ] 
dist 182=[-2.4960135230068562644 ,1.8117883941568595638 ] 
dist 183=[-2.6151566749737553182 ,1.8493866327895741854 ] 
dist 184=[-2.7063894408548351710 ,1.8729017172851091572 ] 
dist 185=[-2.7493532466256446459 ,1.8770178033361250829 ] 
dist 186=[-2.7667239012591448252 ,1.8649623399269174354 ] 
dist 187=[-2.7664137733966650480 ,1.8612974687383197501 ] 
dist 188=[-2.5668050316729582753 ,1.7335889809289163280 ] 
dist 189=[-2.5276835654064272944 ,1.7082327022548960345 ] 
dist 190=[-2.4569847240695744862 ,1.6395935096049982576 ] 
dist 191=[-2.4346844934937033322 ,1.6191380359694512587 ] 
dist 192=[-2.3395184797575276528 ,1.4795376695206011441 ] 
dist 193=[-2.3118968022800132779 ,1.4473499915024854910 ] 
dist 194=[-2.2462454389534902970 ,1.3906762676896386287 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 2, 0, 0, 2] 
dist 0=[66.671945560287095519  ,66.671945560287095519  ] 
dist 1=[66.308145040817387044  ,66.718537329393175989  ] 
dist 2=[65.623781410999865349  ,66.671945560287095519  ] 
dist 3=[64.321495784570034016  ,66.422000637993809598  ] 
dist 4=[62.807964728853949924  ,66.084288462271880878  ] 
dist 5=[61.280082258270004521  ,65.833725338937469692  ] 
dist 6=[59.446330359838919680  ,64.742666100963636121  ] 
dist 7=[56.711300024244000180  ,64.287335119411789696  ] 
dist 8=[53.599782288272229228  ,61.038668538809815487  ] 
dist 9=[50.262568568348176572  ,59.988197161910498795  ] 
dist 10=[46.114182911114024706  ,59.534994051094513024  ] 
dist 11=[39.763372149131625886  ,59.329981956183342774  ] 
dist 12=[33.360824156319798004  ,59.092070792270968908  ] 
dist 13=[29.005745205821662188  ,58.007114047047030204  ] 
dist 14=[25.307902804917765734  ,43.358045426822199240  ] 
dist 15=[21.529663965129323561  ,42.211094528083049826  ] 
dist 16=[17.979036371515969252  ,41.872033123043063513  ] 
dist 17=[15.189872382624930334  ,32.386050577144872177  ] 
dist 18=[12.417485622809483562  ,31.160794081081159144  ] 
dist 19=[8.9333686978459761894 ,28.648131205392563171  ] 
dist 20=[5.5849516665057101297 ,27.984425824628842379  ] 
dist 21=[3.3541956340341629904 ,25.521413709851773424  ] 
dist 22=[1.5079265773684251975 ,25.012722677619375091  ] 
dist 23=[-.30540710935747671146,24.062071444170934203  ] 
dist 24=[-1.9682113829440717328 ,23.827062611781732276  ] 
dist 25=[-3.3774987198936777686 ,6.7353735572051121376 ] 
dist 26=[-4.7666670097687461740 ,5.2550188610412862926 ] 
dist 27=[-5.8265160304057191357 ,2.0368669019018011358 ] 
dist 28=[-8.2656635569186470071 ,1.4030432864656720387 ] 
dist 29=[-10.768895881827603025  ,-2.0915361000888320505 ] 
dist 30=[-12.606419551901523182  ,-2.6704344800456026470 ] 
dist 31=[-14.313283630303822477  ,-3.8969516621331018576 ] 
dist 32=[-16.294938273571650730  ,-4.1134907372246428690 ] 
dist 33=[-18.120908778498063481  ,-5.6285336628033188356 ] 
dist 34=[-19.206130128277772888  ,-5.8421925560447670937 ] 
dist 35=[-19.960418734192288785  ,-5.7758975088987115324 ] 
dist 36=[-20.464833908872345069  ,-5.3155757007117801710 ] 
dist 37=[-20.806951558403338558  ,-4.6418253335810739263 ] 
dist 38=[-20.912959145358216364  ,-3.7234346138256402545 ] 
dist 39=[-20.901637549833214002  ,-2.4527932483303814123 ] 
dist 40=[-20.839826705047916087  ,0                     ] 
dist 41=[-8.5856411112524754046 ,1.7405914688242241448 ] 
dist 42=[-8.3508160869792223697 ,3.1476902110598475259 ] 
dist 43=[-8.2721342093142370642 ,4.3044502496546319856 ] 
dist 44=[-6.3558955305311191912 ,5.4196834075400243255 ] 
dist 45=[-6.3180165436918910701 ,6.4213691885922005949 ] 
dist 46=[-3.3293045577080345356 ,7.1252520069268777282 ] 
dist 47=[-3.1352651235602684954 ,7.7453809928577900630 ] 
dist 48=[-2.0743916076983551092 ,8.4131034354521254219 ] 
dist 49=[-1.8804670475458161741 ,9.0083272803426811291 ] 
dist 50=[-1.4716417433878861688 ,9.3391740712987476956 ] 
dist 51=[-1.3613467730316665132 ,9.5398343711274158578 ] 
dist 52=[-.41001427000973096025,9.6153693399970117808 ] 
dist 53=[-.25605244452433976443,9.6341138378718923311 ] 
dist 54=[-.01259543611009565013,9.6081757710219025059 ] 
dist 55=[.04781841333369755558,9.5448658530848361478 ] 
dist 56=[.12155792649371056632,9.2152492312785101741 ] 
dist 57=[.08117426449236972277,6.6088397620277051179 ] 
dist 58=[-.02736932036068574251,6.2910104677731153703 ] 
dist 59=[-.25733122263865223814,6.0267754698754529809 ] 
dist 60=[-.49897149338062790846,6.0676487952881817008 ] 
dist 61=[-.65414602441235298718,6.0713783749241020948 ] 
dist 62=[-.77578348794376467222,-.29727916433644707095] 
dist 63=[-.88359396908981034386,-.55673950673993053312] 
dist 64=[-1.3473123697506180665 ,-.95289728446165661091] 
dist 65=[-1.7921928875012296690 ,-.9789491129995551797 ] 
dist 66=[-2.1901714074337456466 ,-1.0224234231338117571 ] 
dist 67=[-2.4667986793508404163 ,-1.0281371383218618593 ] 
dist 68=[-2.7072038492934482437 ,-1.0215471802911691257 ] 
dist 69=[-2.9607077744879642216 ,-.99757977630622881175] 
dist 70=[-3.1878901019244888332 ,-.95652185853120721018] 
dist 71=[-3.3232889342352969655 ,-.88169896474891807786] 
dist 72=[-3.4173425594073567292 ,-.79118947159909421649] 
dist 73=[-3.4795565172397103795 ,-.68752218387776620116] 
dist 74=[-3.5166257902818440247 ,-.55456984295422164154] 
dist 75=[-3.5217747669227084199 ,-.34719757004961743081] 
dist 76=[-3.4927511233568140661 ,-.13739509494512486427] 
dist 77=[-3.4845378817071253700 ,.00526410172003425403] 
dist 78=[-1.9472379130784230685 ,.12585905494679082624] 
dist 79=[-1.8027365139548723358 ,.24763997469074058831] 
dist 80=[-1.4498276633853397445 ,.3606751512318004843 ] 
dist 81=[-1.3925200786418224576 ,.4463815782743822513 ] 
dist 82=[-.8710429937865326274 ,.74541103593548711014] 
dist 83=[-.77391137099430047587,.97420106801283291218] 
dist 84=[-.64236734869293596624,1.1897078593621550596 ] 
dist 85=[-.60192549739113554821,1.4428123037749578850 ] 
dist 86=[.15939500368364267511,1.6779836726283953864 ] 
dist 87=[.22615283836759172371,1.8219648915597542415 ] 
dist 88=[.21655807564584734501,1.9264614692197445257 ] 
dist 89=[.19399127599184827364,2.0041301733497966428 ] 
dist 90=[.15767860219641349805,2.0611692909376402300 ] 
dist 91=[.09324661448617414978,2.0833747376022273068 ] 
dist 92=[.02617952064757108717,2.0891214772662730528 ] 
dist 93=[-.02064838899796733553,2.0837311513631712005 ] 
dist 94=[-.06151000842229517982,.61774012321690227276] 
dist 95=[-.10478368989298187177,.53181320277566422854] 
dist 96=[-.14786226095821654334,.4303154861538389745 ] 
dist 97=[-.19766709214088037401,.41355211125389630706] 
dist 98=[-.24555074967299283655,.26764766648680993235] 
dist 99=[-.303168844636923554  ,.24094256760323083904] 
dist 100=[-.35719770910766763221,.20251050644601728329] 
dist 101=[-.42768872141349952383,.19170613152960313012] 
dist 102=[-.56169152050899278036,.00039080443304277860] 
dist 103=[-.64572233149909478208,-.02338756363715816124] 
dist 104=[-.70903883832931106886,-.03782216347724029702] 
dist 105=[-.76041921701773633067,-.00272372076186295903] 
dist 106=[-.80082979739515954379,.04234576031640004829] 
dist 107=[-.82039907395228385735,.11271490012081788665] 
dist 108=[-.82968234897809850035,.18346139009773313397] 
dist 109=[-.83016751442523734134,.23003423238031768717] 
dist 110=[-.68309838883256750918,.26773796890681272476] 
dist 111=[-.66635146285631692261,.30309710559925723551] 
dist 112=[-.62434662103538233347,.33415156511931879824] 
dist 113=[-.61310186104423905315,.35467778408623201665] 
dist 114=[-.54210720401213394268,.3713646549838454657 ] 
dist 115=[-.52700238159250134652,.38709433931846602102] 
dist 116=[-.49837066813557023075,.40038695727228091675] 
dist 117=[-.49040488949765575168,.40735215101591717839] 
dist 118=[-.35401752332521624697,.41097815113900978524] 
dist 119=[-.334960312407049861  ,.41102054852328932435] 
dist 120=[-.28881943827828433486,.40895596265013714379] 
dist 121=[-.28076498290712407837,.40732983714028179738] 
dist 122=[-.21393210556156724101,.40025052840030094549] 
dist 123=[-.20151953594526288635,.42478615305741387273] 
dist 124=[-.1827581813128125489 ,.47607566116596399772] 
dist 125=[-.17767454304148189106,.54359886023735035214] 
dist 126=[.1539775981389487229 ,.60837374122802491921] 
dist 127=[.16329626473582535087,.68676213845309670023] 
dist 128=[.21369902967722683356,.75636371438562072909] 
dist 129=[.22186609773683633847,.82473888366193603428] 
dist 130=[.23579274916860009378,.88700042612583253902] 
dist 131=[.23826852929401672626,.93220823576489591477] 
dist 132=[.23832122315528882111,.97353170308991684525] 
dist 133=[.23188038922275578716,1.0202940874363800702 ] 
dist 134=[.21993944732141545518,1.0624095401786255949 ] 
dist 135=[.19740827806560111037,1.0851911980050543391 ] 
dist 136=[.1698538202704556685 ,1.0981455449665410326 ] 
dist 137=[.13787287815896309175,1.1010490832249877305 ] 
dist 138=[.01662398882393831651,1.0981617638711069229 ] 
dist 139=[-.13694737311396950479,1.0946474769201725492 ] 
dist 140=[-.32206921406731364958,1.0770572365755522413 ] 
dist 141=[-.59818285328137194019,1.0709337579227369872 ] 
dist 142=[-.87242957766388077031,.97029948645192630405] 
dist 143=[-1.0501063667540579502 ,.951291962612981238  ] 
dist 144=[-1.1907446975045527270 ,.90789449498510064807] 
dist 145=[-1.3172393661215810299 ,.89334416472925685624] 
dist 146=[-1.4246882051258898648 ,.82402135470019136032] 
dist 147=[-1.4893507519571290656 ,.80848129610401854219] 
dist 148=[-1.5349496849557013083 ,.76937694620321596572] 
dist 149=[-1.5663536391297572078 ,.75737334206707408614] 
dist 150=[-1.5882323777077494820 ,.62573297544987840225] 
dist 151=[-1.5958334230058103342 ,.60405576431446356235] 
dist 152=[-1.5944361993811759365 ,.55093022722074860049] 
dist 153=[-1.5905008941610054569 ,.5387547894910641145 ] 
dist 154=[-1.5600851698418885598 ,.45461198074301021251] 
dist 155=[-1.5500049622853479803 ,.43739627386278797365] 
dist 156=[-1.5099228114160991923 ,.40687205048726186301] 
dist 157=[-1.5014713366242648868 ,.39913016302484623164] 
dist 158=[-.08767235053885299783,.41981264575325651765] 
dist 159=[-.10219246341685281279,.58292814392859223544] 
dist 160=[-.11729887006591980931,.71477697731228696466] 
dist 161=[-.13146801486649631734,.87630684531061954009] 
dist 162=[-.14763828883569975054,1.0372197144190865307 ] 
dist 163=[-.17072706599972030767,1.1476674131020375748 ] 
dist 164=[-.19408102381838491558,1.2420810003412243119 ] 
dist 165=[-.21130883408503774628,1.3390352148946702603 ] 
dist 166=[-.22731516243580729431,1.4252622383337253142 ] 
dist 167=[-.24579596384644607926,1.4768847902943555289 ] 
dist 168=[-.26440745813067608491,1.5129472363218796125 ] 
dist 169=[-.28093472972026615321,1.5371027968101677659 ] 
dist 170=[-.29906644338811297329,1.5517024886583747201 ] 
dist 171=[-.32407756379747741507,1.5527405285833743438 ] 
dist 172=[-.34791197080566642458,1.5420692814959278897 ] 
dist 173=[-.36134949665693665087,1.5346538256290330682 ] 
dist 174=[-.36971563245845785417,.79146097545124696266] 
dist 175=[-.37331993675693192757,.72326087669342268519] 
dist 176=[-.37465440630146251872,.5601270294141170991 ] 
dist 177=[-.43144372043286231158,.53220007335632582174] 
dist 178=[-.55789943678638330521,.44067830308803995862] 
dist 179=[-.65231460651485490808,.44162456850849885908] 
dist 180=[-.74113680889564725825,.40127984146166762252] 
dist 181=[-.84528171597353324935,.39425501704270684516] 
dist 182=[-.94106809945467942107,.38482345968497741994] 
dist 183=[-.9965488756231472578 ,.38099045879445084811] 
dist 184=[-1.0330093633959446219 ,.37288725543554709368] 
dist 185=[-1.0529264199086290902 ,.3696713072963417327 ] 
dist 186=[-1.0651928062878804012 ,.36749015154725761564] 
dist 187=[-1.0711353309479618210 ,.36615580052705390298] 
dist 188=[-1.0735687843632434176 ,-.00444281947941132858] 
dist 189=[-1.0718365400141576606 ,-.03346407355355205890] 
dist 190=[-.35817215254321335372,.00447105272431506921] 
dist 191=[-.36022691802384412144,.12280789182713539508] 
dist 192=[-.36560620830631308556,.22749843321882298882] 
dist 193=[-.37693399351278434587,.33460572616690528955] 
dist 194=[-.39120474138179841796,.43479608119905521083] 
dist 195=[-.40832218797548193837,.51189585140995547779] 
dist 196=[-.43077591065349548739,.58668792744680219928] 
dist 197=[-.46633212953903330107,.67767404502572684077] 
dist 198=[-.50379717810650000146,.76291423654215693582] 
dist 199=[-.53386419519585576345,.81478640947476349135] 
dist 200=[-.56421155676395364723,.85204679641925684286] 
dist 201=[-.60279280621699215108,.8790011775015481823 ] 
dist 202=[-.64361453818318812297,.89813798841700628735] 
dist 203=[-.68289769209737291105,.9042131443880077036 ] 
dist 204=[-.72849156380973533261,.90464758067625194398] 
dist 205=[-.79448444372899823871,.92040777635470843479] 
dist 206=[-.85868822455201256716,1.0983674272645598303 ] 
dist 207=[-.89714485013431570729,1.2086550631147647860 ] 
dist 208=[-.92401900707498441145,1.2902892577115793565 ] 
dist 209=[-.9420210653785624159 ,1.3539453930267279262 ] 
dist 210=[-.95299325977873366976,1.4029073866125369183 ] 
dist 211=[-.95485381209961347828,1.4259234199507586084 ] 
dist 212=[-.94753933985343064216,1.4355151490593327983 ] 
dist 213=[-.9460709267401475707 ,1.4353029030355292295 ] 
dist 214=[-.88287974618384715471,1.3394073793749607729 ] 
dist 215=[-.8702714033332275753 ,1.3200131418847036306 ] 
dist 216=[-.83506270504887627919,1.2848662656226718799 ] 
dist 217=[-.82544737693414728192,1.2735898265425105732 ] 
dist 218=[-.75129299641239150897,1.2245913463066349873 ] 
dist 219=[-.73591243339894948558,1.2104691245355237478 ] 
dist 220=[-.73033246262815025042,1.1756948780409592165 ] 
dist 221=[-.72575865204972874117,1.1622706151708014787 ] 
dist 222=[-.23240818874356909895,.20770847155876957305] 
dist 223=[-.26011723043857307955,.2153132228203507424 ] 
dist 224=[-.28522276109922310996,.22229946541393335567] 
dist 225=[-.30319640546940564235,.22745884418041600234] 
dist 226=[-.32265157858531754342,.23225523787366346726] 
dist 227=[-.35864050903216463188,.23779343168251566376] 
dist 228=[-.38891260238983629341,.24282725016975259936] 
dist 229=[-.41921686149588477625,.24561176712316974419] 
dist 230=[-.44619636651915176142,.2472742031834554416 ] 
dist 231=[-.46320557249970373363,.24783236725615054553] 
dist 232=[-.47613760581290897996,.24763465264647608919] 
dist 233=[-.48685226255506274082,.24669551982050132138] 
dist 234=[-.49529765826107988776,.24426297810850029113] 
dist 235=[-.49917704532216575571,.24284890404042821258] 
dist 236=[-.50044754916958953633,.23431350343175601496] 
dist 237=[-.4992674113157992273 ,.28018665441732906166] 
dist 238=[-.34221046629949110398,.32590294675238515403] 
dist 239=[-.37070854125501066222,.36797760966747936729] 
dist 240=[-.39476792704797340262,.40439384928541170579] 
dist 241=[-.4089683064662328296 ,.42753769184214862946] 
dist 242=[-.41863860814006626326,.4453476617726298483 ] 
dist 243=[-.42462628791020584388,.46048613759369646623] 
dist 244=[-.42816305887322322407,.47264981005304180547] 
dist 245=[-.42805625584945749675,.47859272983234744073] 
dist 246=[-.42616263150228957804,.48110558104058130953] 
dist 247=[-.42415996138340772377,.48061989363601847695] 
dist 248=[-.40971217940255386101,.47583754437544678467] 
dist 249=[-.40545015219061093383,.47356436167523752908] 
dist 250=[-.3955189894103572921 ,.46341195646388418431] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 1, 2, 0, 1] 
dist 0=[62.280784212705963945  ,62.280784212705963945  ] 
dist 1=[62.013240163994650386  ,62.423630189104444651  ] 
dist 2=[61.516167299271385391  ,62.422769183996807162  ] 
dist 3=[60.754858610096490749  ,62.316334471560490142  ] 
dist 4=[59.432059540962049503  ,62.214367702645707046  ] 
dist 5=[57.774589359942345342  ,61.725139843427852713  ] 
dist 6=[55.676918888427327463  ,61.487086351871568036  ] 
dist 7=[52.851066763559317714  ,61.245951723951544143  ] 
dist 8=[48.286062482509902886  ,61.075227071791187348  ] 
dist 9=[43.606563056241382765  ,60.648095434266211664  ] 
dist 10=[40.323526361657209709  ,60.437836634457213903  ] 
dist 11=[37.429159389590031772  ,60.039749377193338534  ] 
dist 12=[34.301501676369873333  ,59.876498402142032204  ] 
dist 13=[31.256364157606262576  ,38.998820292316757372  ] 
dist 14=[27.851040142773928668  ,37.201732832766052300  ] 
dist 15=[24.194467430208093800  ,32.858182927108777938  ] 
dist 16=[20.404370656482783489  ,32.235033681197860207  ] 
dist 17=[16.810565088677060538  ,25.993965941145137166  ] 
dist 18=[13.937381516775466058  ,24.854155139684014100  ] 
dist 19=[11.035727550310445345  ,23.518706397000490474  ] 
dist 20=[7.3275537108707573152 ,23.288549997343515823  ] 
dist 21=[3.7352626863134899610 ,15.202819285446627366  ] 
dist 22=[1.2959412388251556705 ,14.787717139237084723  ] 
dist 23=[-.7732445735289273066 ,13.947790774436288706  ] 
dist 24=[-2.8880501849423757149 ,13.756879115488663976  ] 
dist 25=[-4.8811530355288923888 ,8.4165532089480048958 ] 
dist 26=[-6.4650886443334320837 ,7.8753420553073118948 ] 
dist 27=[-8.0618415931609888289 ,6.9485364933832437004 ] 
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dist 34=[-15.195156406072468921  ,-6.5205070521439280069 ] 
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dist 38=[-13.398529569753721393  ,-5.5495415630281459693 ] 
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dist 40=[-12.845832788073556465  ,-1.7022680430461289030 ] 
dist 41=[-12.483808847346621961  ,.66359518859760141868] 
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dist 43=[-12.342426903414146531  ,3.5846251063767570334 ] 
dist 44=[-12.357152746146662514  ,4.8944771157227274856 ] 
dist 45=[-2.7663477299837623439 ,6.0890710910436873431 ] 
dist 46=[-2.4864681872823277041 ,6.9575270268046433746 ] 
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dist 50=[-.04830058379609075302,9.9377399793515687335 ] 
dist 51=[.33798774156215499764,10.241902844545459746  ] 
dist 52=[.42293145570704382546,10.398706207332661296  ] 
dist 53=[.56522518676341414258,10.483460669572158211  ] 
dist 54=[.51843112633697515842,10.500222047823671033  ] 
dist 55=[.37256087410902605073,10.470366690093465006  ] 
dist 56=[.05408603308258271104,10.383121429163649019  ] 
dist 57=[-.28487259203737416994,10.807678763112617558  ] 
dist 58=[-.51246954249495991688,11.037125218403960039  ] 
dist 59=[-.70140124990205893135,11.167623013589659121  ] 
dist 60=[-.8861722519347528656 ,11.197237736998065122  ] 
dist 61=[-1.0534800326266061553 ,2.7407620468713612306 ] 
dist 62=[-1.4670325959591197545 ,2.3001650756052849252 ] 
dist 63=[-2.2733856242122417337 ,1.2867887561089923348 ] 
dist 64=[-3.0429610129278102961 ,1.1067780520875381607 ] 
dist 65=[-3.7284861492812304554 ,-.17338338680992056493] 
dist 66=[-4.1995679843664642235 ,-.39611575276703549558] 
dist 67=[-4.6031244716110224867 ,-.79117906622532097496] 
dist 68=[-5.0193174661471979780 ,-.87346012698713438706] 
dist 69=[-5.3916966082378141373 ,-.88796960883345888563] 
dist 70=[-5.6204716818073726258 ,-.74364573885216996353] 
dist 71=[-5.7876956531805670018 ,-.55389763829845584079] 
dist 72=[-5.9144988071563448376 ,-.25299391560706136524] 
dist 73=[-6.0056148420420340266 ,.05137807490313427468] 
dist 74=[-6.0304621157889331962 ,.25495806089820870341] 
dist 75=[-6.0204663297363057679 ,.42331312388673018092] 
dist 76=[-6.0000369828547787806 ,.58716338364878805557] 
dist 77=[-2.8795587071503204434 ,.73519602234407766874] 
dist 78=[-2.6062285044695560336 ,.84044946607426968167] 
dist 79=[-1.9456472911706458923 ,.93431747150139200868] 
dist 80=[-1.8409090756597683207 ,1.0369278943017382708 ] 
dist 81=[-.89492190422661880645,1.1307442620150903098 ] 
dist 82=[-.72228263190569832417,1.1895282320801268075 ] 
dist 83=[-.48677856816506277255,1.4156251851804468840 ] 
dist 84=[-.41986388549292580298,1.8980068743648655389 ] 
dist 85=[.1442322818203766755 ,2.3510668757717889818 ] 
dist 86=[.16665536547594738502,2.6297481037580067151 ] 
dist 87=[.19974008767163348435,2.8335204549661440479 ] 
dist 88=[.20787962933362752658,2.9877794773378289121 ] 
dist 89=[.36244379726521064781,3.1066407761012019154 ] 
dist 90=[.37625318004175607971,3.1692156080874510055 ] 
dist 91=[.26144538408453588355,3.2024687745012917166 ] 
dist 92=[.00204049277431165517,3.2043678151307007612 ] 
dist 93=[-.26407569994227646259,2.2011298848060336704 ] 
dist 94=[-.44588565665344139788,2.2137258611763388240 ] 
dist 95=[-.60019768511441647237,2.2135363878776555024 ] 
dist 96=[-.75665497028758235131,2.2070849406451449733 ] 
dist 97=[-.9019247683337606752 ,2.1232702452091769182 ] 
dist 98=[-1.0116211172982868402 ,2.0978108255309544548 ] 
dist 99=[-1.1159226859824242392 ,2.0682879659535191802 ] 
dist 100=[-1.2396754219421376408 ,2.0525633249408369960 ] 
dist 101=[-1.3537911706582669342 ,1.6159686887944643259 ] 
dist 102=[-1.4196587061194194921 ,1.5538925199347661753 ] 
dist 103=[-1.4625783153397371561 ,1.4235981761588832048 ] 
dist 104=[-1.5288747461678184377 ,1.5152665748396292006 ] 
dist 105=[-1.8401887404977499250 ,1.6332945103028510877 ] 
dist 106=[-2.0336746555399728022 ,1.7028601785767357459 ] 
dist 107=[-2.1774343974202418670 ,1.7501837815413176913 ] 
dist 108=[-2.2903992451724734675 ,1.7794666667038863520 ] 
dist 109=[-2.3777581615774297478 ,1.7961507534621479741 ] 
dist 110=[-2.4193855348367991030 ,1.7976474303875784008 ] 
dist 111=[-2.4372312680036372129 ,1.7843551387138017817 ] 
dist 112=[-2.4374510532134331650 ,1.7774385819369282289 ] 
dist 113=[-2.2749130461270870645 ,1.6358632498843932624 ] 
dist 114=[-2.2416000507075903463 ,1.6090854834025340444 ] 
dist 115=[-2.1828530023681994060 ,1.5396486680817075523 ] 
dist 116=[-2.1640625545613937968 ,1.5182616466036045509 ] 
dist 117=[-2.1240125851506015865 ,1.3867224406957278772 ] 
dist 118=[-2.1478295155394756996 ,1.3567147627469882360 ] 
dist 119=[-2.1637450029678692143 ,1.3003336561009330933 ] 
dist 120=[-2.1730441038849202327 ,1.2837822835025062404 ] 
dist 121=[-2.1773926106420669864 ,.41776900974397816522] 
dist 122=[-2.1735528100231559895 ,.52040187871130578866] 
dist 123=[-2.1629976723698589935 ,.6359768996410876499 ] 
dist 124=[-2.1544237684272098755 ,.79924992945487938683] 
dist 125=[-.72788030986699987096,.96640926164480267559] 
dist 126=[-.60696174614274811346,1.1273565136127631051 ] 
dist 127=[-.33067914711006987799,1.2602614267107557257 ] 
dist 128=[-.27975456022042611343,1.3894034009650179179 ] 
dist 129=[.06498339805214855719,1.5060410107944647739 ] 
dist 130=[.12508930318297478695,1.5890555086158347929 ] 
dist 131=[.23538355524800365468,1.6632331940527317369 ] 
dist 132=[.25956377980734378996,1.7446130815847518014 ] 
dist 133=[.38318716853762068494,1.8165023600330383681 ] 
dist 134=[.39954673292631458932,1.8528136433193069284 ] 
dist 135=[.39305303497283826456,1.8699691262251676868 ] 
dist 136=[.35372664441235186625,1.8720916609904593379 ] 
dist 137=[.21052837258829422335,1.8524256530358219520 ] 
dist 138=[-.03784528294575655488,1.8413588427356891970 ] 
dist 139=[-.33971724842256204599,1.8164450263273885136 ] 
dist 140=[-.79274878508477743525,1.8047310732257965976 ] 
dist 141=[-1.2437772975031081496 ,1.5438513716636914995 ] 
dist 142=[-1.5376628263453154193 ,1.5025602646366036356 ] 
dist 143=[-1.7721689508517901672 ,1.4074575689876029812 ] 
dist 144=[-1.9863267311627269112 ,1.3769527344972125248 ] 
dist 145=[-2.1705404725622529563 ,1.2365402725828348703 ] 
dist 146=[-2.2855982563345523166 ,1.2061136266622744077 ] 
dist 147=[-2.3718388221279019113 ,1.1357575918887498207 ] 
dist 148=[-2.4411023894207055525 ,1.1128438551031028713 ] 
dist 149=[-2.4947098584515512276 ,.87456375001989665189] 
dist 150=[-2.5184958881146618707 ,.83646617305710057663] 
dist 151=[-2.5249782887382142369 ,.74654523227959969325] 
dist 152=[-2.5212001679174956378 ,.7250902957090829902 ] 
dist 153=[-2.4832635843700088536 ,.59469264934474984052] 
dist 154=[-2.4686361536350069008 ,.56868897352194384285] 
dist 155=[-2.4121402703402318461 ,.5183780244709111187 ] 
dist 156=[-2.3961894687121760177 ,.50484208407535981784] 
dist 157=[-1.0811582194990451101 ,.5428301814961801626 ] 
dist 158=[-1.1120112191142154519 ,.8025563560929752151 ] 
dist 159=[-1.1284821292173688338 ,1.0517553719397948026 ] 
dist 160=[-1.1319168124583540696 ,1.3339845143527373558 ] 
dist 161=[-1.1251826072583442207 ,1.5858523550812939715 ] 
dist 162=[-1.1196996814104014046 ,1.7594973841461386486 ] 
dist 163=[-1.1123828716194083087 ,1.9087454626793578852 ] 
dist 164=[-1.1067468813581091805 ,2.0632973524005480042 ] 
dist 165=[-.91921252817014744237,2.2010891109104378182 ] 
dist 166=[-.89096263899711964596,2.2834813220207410479 ] 
dist 167=[-.83362066238869253704,2.3409113461468457605 ] 
dist 168=[-.81699030359640793303,2.3791263451983549608 ] 
dist 169=[-.74878145914189169213,2.4019779807870643484 ] 
dist 170=[-.73328053849253216139,2.4039503770131088040 ] 
dist 171=[-.696224415639556525  ,2.3860601440934244808 ] 
dist 172=[-.68382424340807911392,2.3761784520830021618 ] 
dist 173=[-.03523578435310525318,1.2501110838368644616 ] 
dist 174=[-.28341704410657799749,1.1460709817815279930 ] 
dist 175=[-.49124013567132778018,.89665377387673723264] 
dist 176=[-.69768061782555697245,.89550898952640331554] 
dist 177=[-.88687904897410992003,1.0096810152279877619 ] 
dist 178=[-1.0259242128131248600 ,1.0891951630430728854 ] 
dist 179=[-1.1545506758784858234 ,1.1583995227351040512 ] 
dist 180=[-1.3021875780748895488 ,1.2314391002466354911 ] 
dist 181=[-1.4374198187488199875 ,1.2953656451919639775 ] 
dist 182=[-1.5165659273992718562 ,1.3282161338407334195 ] 
dist 183=[-1.5696066713866473832 ,1.3450612148002529904 ] 
dist 184=[-1.6007113751721598206 ,1.3479201943778219182 ] 
dist 185=[-1.6199056187937703458 ,1.3342673099698984988 ] 
dist 186=[-1.6254367254570880060 ,1.3259787077804669656 ] 
dist 187=[-1.6220013681482040737 ,1.3160560561520570732 ] 
dist 188=[-1.6175439433316441762 ,1.3089241107843504169 ] 
dist 189=[-.5567208304826875119 ,.90596667476620105607] 
dist 190=[-.56457383056548760955,.85993104881215346903] 
dist 191=[-.61446685035569810126,.74941783749558677338] 
dist 192=[-.75774145455237304594,.7267109087449988322 ] 
dist 193=[-.88555230756766798648,.57119507908215623306] 
dist 194=[-.97365594633776999334,.69464120527221383172] 
dist 195=[-1.0493983060822112171 ,.81686068862417901249] 
dist 196=[-1.1279015318124737699 ,.96901472039160599876] 
dist 197=[-1.1975317539373532725 ,1.1133050129017753366 ] 
dist 198=[-1.2378770476383833090 ,1.2041578457678412126 ] 
dist 199=[-1.2644383367162891762 ,1.2730866461754400952 ] 
dist 200=[-1.2790748338810010776 ,1.3299241567426136070 ] 
dist 201=[-1.2854451333100487112 ,1.3745160048831636515 ] 
dist 202=[-1.2848899088979372261 ,1.3945991950489777098 ] 
dist 203=[-1.2699358582811805945 ,1.4022881877156416932 ] 
dist 204=[-1.2819219252110565055 ,1.4507978805646305547 ] 
dist 205=[-1.3827105972183159327 ,1.7353687123945560665 ] 
dist 206=[-1.4427115444204457941 ,1.9118406744871496573 ] 
dist 207=[-1.4841892079432636951 ,2.0425912618476623310 ] 
dist 208=[-1.5110897562594176563 ,2.1447734351498630610 ] 
dist 209=[-1.5269591232841195307 ,2.2234752153713174665 ] 
dist 210=[-1.5291547120804485730 ,2.2605584006049539092 ] 
dist 211=[-1.5170146848430473010 ,2.2761467001716712193 ] 
dist 212=[-1.5133592110317836442 ,2.2759018074197020876 ] 
dist 213=[-1.4042079872382422830 ,2.1252583668184865432 ] 
dist 214=[-1.3829199354569804598 ,2.0946295159070756764 ] 
dist 215=[-1.3248615588620170186 ,2.0392824670727760808 ] 
dist 216=[-1.3085430634888823999 ,2.0215045632769146390 ] 
dist 217=[-1.1902891903009343434 ,1.9442604407982357625 ] 
dist 218=[-1.1632906890876147635 ,1.9218850452340719673 ] 
dist 219=[-1.1205790143275720903 ,1.8669091801496443071 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 0, 0, 2, 0, 1] 
dist 0=[54.077815092846493756  ,54.077815092846493756  ] 
dist 1=[52.972217794178657514  ,54.501984429543070039  ] 
dist 2=[51.209986260594870640  ,55.089863572270478744  ] 
dist 3=[48.280331446634134684  ,55.744769072797004391  ] 
dist 4=[45.249715129838300391  ,56.128518626814057610  ] 
dist 5=[43.084286520384696443  ,56.413684717484628172  ] 
dist 6=[41.134816418611929866  ,56.590559624520762512  ] 
dist 7=[38.966181420124726706  ,56.589085526853237462  ] 
dist 8=[36.817908734502369927  ,54.447701233924518559  ] 
dist 9=[34.949472513251808188  ,54.057939747456551053  ] 
dist 10=[32.924091711098820391  ,53.467022513876016443  ] 
dist 11=[30.148666481870901344  ,53.256317741616178944  ] 
dist 12=[27.370512851844022054  ,52.632396817190952705  ] 
dist 13=[25.333963514707491645  ,52.395075352928649176  ] 
dist 14=[23.444901543101067413  ,52.065524053516401101  ] 
dist 15=[21.255320005237551264  ,51.915018424494798188  ] 
dist 16=[19.030896792487100836  ,32.209459481049224234  ] 
dist 17=[17.002184116095400730  ,30.537481239903229787  ] 
dist 18=[14.720042514999794158  ,26.574200621077700736  ] 
dist 19=[11.482446382390982056  ,25.963160621443078540  ] 
dist 20=[8.2921144624047845826 ,20.501161440649496363  ] 
dist 21=[6.1986074016105227568 ,19.513090944642838974  ] 
dist 22=[4.4982139195637955962 ,18.202805727799367522  ] 
dist 23=[2.7368529965871664969 ,17.863932867090017188  ] 
dist 24=[.43131753578602967542,10.552174570033314437  ] 
dist 25=[-1.5605528085863981781 ,9.6573185909385168196 ] 
dist 26=[-3.6542761874064995156 ,8.3853884298522171793 ] 
dist 27=[-5.6633872358424838876 ,7.3303326722957916833 ] 
dist 28=[-7.3180229817596918906 ,5.2054387244076663321 ] 
dist 29=[-9.0385499759027713554 ,4.8569986156598638101 ] 
dist 30=[-11.312239885139403246  ,4.1260784624832670773 ] 
dist 31=[-13.487334774887231934  ,3.9995736528099695581 ] 
dist 32=[-14.814238586512750837  ,-1.0193676969813436139 ] 
dist 33=[-15.783244761075372371  ,-1.5009767104618489550 ] 
dist 34=[-16.527976928997385390  ,-2.4398353421197640700 ] 
dist 35=[-17.093248620870057358  ,-2.6582586673931136411 ] 
dist 36=[-17.344854307184956706  ,-2.5777519792996811377 ] 
dist 37=[-17.449611714740024503  ,-2.2583816845930064688 ] 
dist 38=[-17.434577062084607851  ,-1.9689349033448403540 ] 
dist 39=[-16.584262775756141186  ,-1.6485713203308355972 ] 
dist 40=[-16.401543722401309406  ,-1.3358819969181846612 ] 
dist 41=[-16.023683123364331026  ,-1.0767224671486258313 ] 
dist 42=[-15.892570970562943388  ,-.80861774330291933397] 
dist 43=[-15.260006359875772041  ,-.4599790619153661216 ] 
dist 44=[-15.109398625330109199  ,-.12292778731093509341] 
dist 45=[-14.638025516096024629  ,.09911436722235452057] 
dist 46=[-14.545646107933769379  ,.54802732782072829142] 
dist 47=[-12.377536405561271298  ,1.9009564714880725564 ] 
dist 48=[-5.2229385554517975829 ,4.6051100028701619738 ] 
dist 49=[-3.4485348561324955168 ,6.4120162446025451893 ] 
dist 50=[-3.0792845672053732757 ,7.9061170948197176210 ] 
dist 51=[-.98939449822638025884,9.3622079932275550524 ] 
dist 52=[-.62375847447375397286,10.681179710918167925  ] 
dist 53=[.1361087259874712207 ,11.628211663005039442  ] 
dist 54=[.32586684506260131636,12.579804271875003143  ] 
dist 55=[.98271320087592546285,13.703121874043269476  ] 
dist 56=[.99448665679977992359,14.337390761809322273  ] 
dist 57=[.97222084315492713194,14.744068323638706186  ] 
dist 58=[.9356528475661021307 ,14.995428119863844710  ] 
dist 59=[.87070702778141802173,15.051385048997217853  ] 
dist 60=[.80036541661104954311,14.984246904031713184  ] 
dist 61=[.7422189780598284701 ,14.899866240813014452  ] 
dist 62=[.25585398343132576603,14.082079234494738783  ] 
dist 63=[-.66464521266789454436,6.3598467235948250830 ] 
dist 64=[-1.2681400470441456278 ,1.7006606028328207305 ] 
dist 65=[-1.7541963344076653510 ,1.3174434004942253280 ] 
dist 66=[-2.2061966116906033196 ,.99425355597286024436] 
dist 67=[-2.6011418795910893173 ,.98821564384415685361] 
dist 68=[-2.8595996867794292904 ,.68553839510264065274] 
dist 69=[-3.0674325313121236442 ,.65260299347095167098] 
dist 70=[-3.2604560686923518010 ,.572897896359940781  ] 
dist 71=[-3.4277564244396897429 ,.55922448344888752279] 
dist 72=[-3.8282336314432768561 ,.44107604939867280762] 
dist 73=[-4.2165048775501238583 ,.41846450825307634698] 
dist 74=[-4.5135655114835064674 ,.38722824063632645481] 
dist 75=[-4.7633097986983494150 ,.37753003992158324124] 
dist 76=[-4.9631864341582348331 ,.18554354975987858178] 
dist 77=[-5.0612849903478239517 ,.16061024644580972458] 
dist 78=[-5.1065956026959529033 ,.1061532560143401953 ] 
dist 79=[-5.1104536514945044705 ,.09339555367952178188] 
dist 80=[-1.1697063599734258644 ,.03079524461187472339] 
dist 81=[-.88934057271025160614,.41142495605957192086] 
dist 82=[-.88546226037426131814,.7800712738211341155 ] 
dist 83=[-.88416335202530854594,1.1386251733660419733 ] 
dist 84=[-.57697721603435925662,1.4623064077525446047 ] 
dist 85=[-.54444991705679500821,1.6918593475090603982 ] 
dist 86=[-.48945378596242193646,1.8959495707239156335 ] 
dist 87=[-.47568706832925909804,2.1180750645554896017 ] 
dist 88=[-.44174274236961661702,2.3200347739403361461 ] 
dist 89=[-.43611997338615388173,2.4436900510168966830 ] 
dist 90=[-.43979951784605325143,2.5334491313267543841 ] 
dist 91=[-.456970458368157422  ,2.6002009389153528317 ] 
dist 92=[-.47920580051103605067,2.6469575728449135001 ] 
dist 93=[-.50309867348352187897,2.6569611025180028891 ] 
dist 94=[-.5326613714899688608 ,2.6526436807760903565 ] 
dist 95=[-.57754090533599349266,2.6422530891902916140 ] 
dist 96=[-.62868974867943980761,1.4633491969321136376 ] 
dist 97=[-.68327823837920958856,1.3554451097461925703 ] 
dist 98=[-.75074792724800959038,1.0867575839578433818 ] 
dist 99=[-.85330397219767827222,1.0468946908699770719 ] 
dist 100=[-.95547353561672931346,.63559018215577187216] 
dist 101=[-1.0214080924129036963 ,.5587752486742392413 ] 
dist 102=[-1.0733557750644527687 ,.46756917791208674394] 
dist 103=[-1.1197268191082705912 ,.44824144255902333822] 
dist 104=[-1.1589329727622151510 ,-.01641789915781703398] 
dist 105=[-1.1823000004925832480 ,-.02253445083996345346] 
dist 106=[-1.1985529126883909099 ,-.00838128912369103849] 
dist 107=[-1.2370977193421692444 ,.01690013603204524077] 
dist 108=[-1.2907081427198446349 ,.05630208617336554650] 
dist 109=[-1.3137299365933666032 ,.11344818937409179103] 
dist 110=[-1.3237336584701102831 ,.20948813553561307802] 
dist 111=[-1.3254143917443935586 ,.30805264241277818018] 
dist 112=[-1.2061182121182041540 ,.375266337490058972  ] 
dist 113=[-1.2369325986292976041 ,.43215666188930065601] 
dist 114=[-1.2517601136727842411 ,.4895555962275645849 ] 
dist 115=[-1.2586172927740669788 ,.54264429036819640961] 
dist 116=[-1.2576204604725000454 ,.58234622628511399052] 
dist 117=[-1.2513852914615629640 ,.61970303965605130856] 
dist 118=[-1.2466564433532324462 ,.66343788702257618577] 
dist 119=[-1.0888814376988953851 ,.70342323677356506997] 
dist 120=[-1.0634941254679697954 ,.72582724232668253746] 
dist 121=[-1.0090978116328378305 ,.73955325508242291301] 
dist 122=[-.99218192905676793407,.74493286579835773817] 
dist 123=[-.91638426823876835871,.74582784607214277357] 
dist 124=[-.90039116199635890157,.74383547998822080272] 
dist 125=[-.85272049373108058685,.73565069993143960812] 
dist 126=[-.84571820454468686652,.73049095897680469183] 
dist 127=[.21413082006752003751,.59439026799245179413] 
dist 128=[.26846160196999285182,.72809197305604200735] 
dist 129=[.27334103940214941511,.85452464899573231169] 
dist 130=[.27078852526941075546,.98506967873794839833] 
dist 131=[.25757511226759092498,1.0975073038302250625 ] 
dist 132=[.23867716737206996238,1.1680673379229238237 ] 
dist 133=[.2134390753683179592 ,1.2213642994405207325 ] 
dist 134=[.17884162931608392685,1.2649329445661084834 ] 
dist 135=[.12260229442750780273,1.3003579801023002627 ] 
dist 136=[.06291490086558725518,1.3211657719069233783 ] 
dist 137=[.01455523420032095639,1.3352312635866968714 ] 
dist 138=[-.03463942079850813761,1.3437551676268252754 ] 
dist 139=[-.09767393394999493657,1.3480608406979505850 ] 
dist 140=[-.16462482690372120459,1.3452963941700437812 ] 
dist 141=[-.22945338201669167523,1.3374417602357319013 ] 
dist 142=[-.30503820662517379884,1.3320520783431033703 ] 
dist 143=[-.41491322268449732889,.49663824277781615261] 
dist 144=[-.52760722440586755542,.42463004577181939548] 
dist 145=[-.62416389741259409092,.25932837066107657311] 
dist 146=[-.70374884021618966497,.22878140687338377025] 
dist 147=[-.78080944475705170274,.01943300369793088580] 
dist 148=[-.85020823637953062873,-.01739066759256846865] 
dist 149=[-.89922583727760717486,-.08193317466609764207] 
dist 150=[-.94262845331251594152,-.09652027574220850676] 
dist 151=[-.98962593021778056246,-.20501170046887867475] 
dist 152=[-1.0307822439839577423 ,-.22319032112599837654] 
dist 153=[-1.0508809267257892503 ,-.23302092601326049529] 
dist 154=[-1.0601441004034095333 ,-.22210257631687366214] 
dist 155=[-1.0608149833612128758 ,-.20064568400404047083] 
dist 156=[-1.0509388071183652898 ,-.16240250449829817382] 
dist 157=[-1.0523788897115505028 ,-.02427970096288823047] 
dist 158=[-1.0503773022680337056 ,.14430807375294235202] 
dist 159=[-1.0188424938495947414 ,.3981026725754936074 ] 
dist 160=[-.84399863333445867374,.65109688008929898496] 
dist 161=[-.81800043515945937894,.81649357840937382631] 
dist 162=[-.75833455560006833545,.94907644088855801183] 
dist 163=[-.73999224033867835968,1.0711746877973932904 ] 
dist 164=[-.65465647865035067248,1.1769055796045364536 ] 
dist 165=[-.63657552769481465447,1.2441989827159402903 ] 
dist 166=[-.59527427074369131499,1.2961019865638599889 ] 
dist 167=[-.5821264197039175372 ,1.3404419283348576328 ] 
dist 168=[-.44812986518417591454,1.3759347440508223582 ] 
dist 169=[-.4266620245849419346 ,1.3925458485517144248 ] 
dist 170=[-.37777692226328412131,1.3984879463337646558 ] 
dist 171=[-.36491422212349479172,1.3971855356306923885 ] 
dist 172=[-.29949979329819708782,1.3781421228413679027 ] 
dist 173=[-.28656292219416382475,1.3701248521874391644 ] 
dist 174=[-.25819992415112615095,1.3412086166639402118 ] 
dist 175=[-.3156307617514056789 ,1.3307491265749471130 ] 
dist 176=[-.36600456552927993956,.72355591842519241447] 
dist 177=[-.44131718506153204319,.73984486677195866996] 
dist 178=[-.58747102219565757843,.74570733062494030983] 
dist 179=[-.74308804813528897458,.74725632754325774422] 
dist 180=[-.88195976971876089787,.74633772270295356257] 
dist 181=[-.97768445261524327484,.74343725674391396135] 
dist 182=[-1.0599376840557907650 ,.7402383247133443901 ] 
dist 183=[-1.1450740122246815700 ,.62216572846748260548] 
dist 184=[-1.2209230002096902838 ,.60414318016358308806] 
dist 185=[-1.2661295011142603974 ,.56855017598264091167] 
dist 186=[-1.2974574513418338295 ,.55832316127935014308] 
dist 187=[-1.3179440643934382314 ,.51730310869873337192] 
dist 188=[-1.3298458635327041848 ,.50741528878710786251] 
dist 189=[-1.3307829039626200103 ,.48551430270249889952] 
dist 190=[-1.3197681475062757729 ,.47825543150443337121] 
dist 191=[-1.3147450583016773066 ,-.21286648182163848405] 
dist 192=[-.69423006490463906956,-.00337698942175672480] 
dist 193=[-.63663439192479487645,.13819129754977896322] 
dist 194=[-.55062757234897445864,.25680854761492020562] 
dist 195=[-.62531571295094676623,.37474857843643780444] 
dist 196=[-.67700496092143442323,.48290857558019499964] 
dist 197=[-.72164618629426828538,.56251383477215633553] 
dist 198=[-.76821649060641268573,.63626955427072258796] 
dist 199=[-.80904460280284513035,.72109517751497056412] 
dist 200=[-.83077930190038465977,.79893672823878665477] 
dist 201=[-.84264598392377149334,.84483412091657943625] 
dist 202=[-.84463113184964703321,.87601778278902665721] 
dist 203=[-.8412718275340451001 ,.89517017866775772895] 
dist 204=[-.83714579400754098599,.90742190935061052943] 
dist 205=[-.8285719644671166341 ,.91107964512887827143] 
dist 206=[-.82412426348335853885,.90935685961366560049] 
dist 207=[-.53590211367238092187,.906940545135734526  ] 
dist 208=[-.50479663337044153668,.29164004477580171169] 
dist 209=[-.43039540843720955286,.31575194852326937415] 
dist 210=[-.41569139721148720335,.40504507200218165484] 
dist 211=[-.3080287179185580861 ,.48537087213148116067] 
dist 212=[-.28743361520005418672,.54189860918808196833] 
dist 213=[-.35000229157375524238,.59171919717512964925] 
dist 214=[-.4176572012724492055 ,.6452911204365664641 ] 
dist 215=[-.50217618837417616434,.69346063097039471423] 
dist 216=[-.58246732629559816171,.72172975567453659439] 
dist 217=[-.63325836411187092253,.74078910338446964397] 
dist 218=[-.67206513183786159959,.75221622604882455821] 
dist 219=[-.70455242789135714805,.75843290690503554928] 
dist 220=[-.73041840187647377514,.75873917903925122917] 
dist 221=[-.74281406483065618932,.75260851577126297728] 
dist 222=[-.74798333066425141113,.74936029666117858586] 
dist 223=[-.80522135439818432734,.70726441964871397462] 
dist 224=[-.95889955570514184658,.76659728491806267757] 
dist 225=[-1.0539339530607659801 ,.80201868957149481026] 
dist 226=[-1.1240290617070713293 ,.82662790198056392581] 
dist 227=[-1.1782217692063561988 ,.84283176978189306278] 
dist 228=[-1.2197574338756270728 ,.8527319039191545917 ] 
dist 229=[-1.2393617122414251129 ,.85422135721065855569] 
dist 230=[-1.2473364265614003243 ,.84858789262701183001] 
dist 231=[-1.2472441556320640269 ,.8462324476504107111 ] 
dist 232=[-1.1574091075097449460 ,.78393803135405774168] 
dist 233=[-1.1397706465349556162 ,.77181874094515901422] 
dist 234=[-1.1079743398144088019 ,.73973574467716359893] 
dist 235=[-1.0979487544963922806 ,.72990688265176207394] 
dist 236=[-1.0552271904068100245 ,.66679450853220593133] 
dist 237=[-1.0427689999564422880 ,.65227436181366229149] 
dist 238=[-1.0132935782086972307 ,.62574810914925584756] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 2, 1, 1, 0, 2] 
dist 0=[62.570575200713416976  ,62.570575200713416976  ] 
dist 1=[61.946920958447162248  ,62.785766446194527359  ] 
dist 2=[60.846131796118482853  ,63.021119665924733192  ] 
dist 3=[58.923051827510998244  ,63.222428406218299014  ] 
dist 4=[56.615643643540660103  ,63.283505788054909273  ] 
dist 5=[53.980373395383366435  ,63.253338391040474372  ] 
dist 6=[50.596758136937579099  ,63.145223923001157286  ] 
dist 7=[45.301491828684846083  ,62.854095518339717411  ] 
dist 8=[39.928969438165826732  ,62.687626413150686992  ] 
dist 9=[36.236778795292093731  ,62.194876212262142061  ] 
dist 10=[33.063406101132284629  ,61.956777564627602101  ] 
dist 11=[29.761962763699175704  ,60.610583264686933299  ] 
dist 12=[26.624197181611023455  ,60.193033353373194882  ] 
dist 13=[24.103963045190378577  ,59.755480754402381160  ] 
dist 14=[21.548096086798886617  ,57.621283554430258104  ] 
dist 15=[18.267345329645124629  ,52.168846295892516496  ] 
dist 16=[15.081823397041498820  ,31.701024354312170531  ] 
dist 17=[12.905801167292079631  ,29.495445791698683458  ] 
dist 18=[11.045755473670041795  ,27.971800138755487497  ] 
dist 19=[9.1214322089545310395 ,23.557124696017855721  ] 
dist 20=[7.2926551072868276910 ,17.240245444896814051  ] 
dist 21=[5.8134041392146323580 ,15.809126050095449633  ] 
dist 22=[4.2978791900031569024 ,14.241586311890790912  ] 
dist 23=[2.3226122220698051925 ,13.607410212303375897  ] 
dist 24=[.42299231186806013987,11.665050239788265855  ] 
dist 25=[-.79053477392283915261,11.073070036438904662  ] 
dist 26=[-1.7437938618614417250 ,10.943271477039138041  ] 
dist 27=[-3.5299234379526868263 ,3.9945495863594654905 ] 
dist 28=[-5.3341700359670454852 ,1.0884650443305428678 ] 
dist 29=[-6.7076199129811260623 ,.66182607632590618543] 
dist 30=[-8.0374825718997141005 ,-.50734363120949483821] 
dist 31=[-9.6693655659802694463 ,-1.8787046016790507118 ] 
dist 32=[-11.197623296329748229  ,-4.1011484252713023488 ] 
dist 33=[-12.113757492728090683  ,-4.0921706705903299278 ] 
dist 34=[-12.766460234091525239  ,-3.9894409178757914429 ] 
dist 35=[-13.241295479359548058  ,-3.7365919134615280735 ] 
dist 36=[-13.588392635362073878  ,-3.4103857802727161448 ] 
dist 37=[-13.730109433414931120  ,-3.0145405646320886637 ] 
dist 38=[-13.774733557606697843  ,-2.4939406596483367860 ] 
dist 39=[-13.752299593898668661  ,-1.6696594376167218129 ] 
dist 40=[-13.079463827250726978  ,-.83626274470045127524] 
dist 41=[-13.130766714781865262  ,-.27910358747885020897] 
dist 42=[-13.129242716465954209  ,.18113257798190008849] 
dist 43=[-12.294001739362430500  ,1.5093980572785712479 ] 
dist 44=[-11.730101115620994386  ,2.7201962010157739435 ] 
dist 45=[-11.604892629947322618  ,3.6991044623281331793 ] 
dist 46=[-11.215392609574923495  ,4.6163192223215857397 ] 
dist 47=[-11.153542681619029892  ,5.4229934248396349976 ] 
dist 48=[-5.0386284135105847062 ,5.9608985195997047527 ] 
dist 49=[-4.4574204664916749154 ,6.4062266926232123761 ] 
dist 50=[-3.1395748170284877761 ,6.9240206240593923975 ] 
dist 51=[-2.8835205152605438104 ,7.3822378871574494924 ] 
dist 52=[-1.2441521138302078642 ,7.6516701039727650751 ] 
dist 53=[-.95233227008459712365,7.8348573881819417580 ] 
dist 54=[-.40278553402721491215,8.0704697444291180720 ] 
dist 55=[-.27430177670408650865,8.9168463877632575311 ] 
dist 56=[.74206378197694177671,9.6811459226778617878 ] 
dist 57=[.48725277529141204006,10.112104352160434900  ] 
dist 58=[.27010034084008786324,10.382262786883912029  ] 
dist 59=[.04899730228659967762,10.504647750325704532  ] 
dist 60=[-.15661327793766034779,10.563150382027696614  ] 
dist 61=[-.69182806925109635657,10.578278916790709656  ] 
dist 62=[-1.4745482797288104108 ,10.565054247852531026  ] 
dist 63=[-2.2009613756249288049 ,10.525615157424524297  ] 
dist 64=[-2.7498978706394531899 ,1.6882486190349180127 ] 
dist 65=[-3.2727910405947043565 ,1.3755935279950779279 ] 
dist 66=[-3.8954554427187744488 ,1.2880384974700755961 ] 
dist 67=[-4.4725242488166206928 ,-.29555977964470381801] 
dist 68=[-4.8136053280598187831 ,-.49343862306893829621] 
dist 69=[-5.0467876453748986713 ,-.4600078351926299539 ] 
dist 70=[-5.1935139248367738317 ,-.3464973597585185004 ] 
dist 71=[-5.6692858024079507708 ,-.15520600341900920336] 
dist 72=[-6.1644199464901284712 ,.04156517018306993196] 
dist 73=[-6.4722394868953474042 ,.17691750057827754464] 
dist 74=[-6.7014759222838174226 ,.29239960444574483583] 
dist 75=[-6.8830664484452145655 ,.40997438706474346187] 
dist 76=[-7.0199308955606782630 ,.51898812503906080111] 
dist 77=[-7.0707129476444235439 ,.60033738543947269623] 
dist 78=[-7.0727567039414115507 ,.67642897345568039826] 
dist 79=[-7.0570076284707877136 ,.76445432715654850611] 
dist 80=[-3.4941803492228586476 ,.84501141969073818539] 
dist 81=[-3.1857846130521747030 ,.95046181862523053975] 
dist 82=[-2.4376433259966243253 ,1.2579308748887760751 ] 
dist 83=[-2.3201208709662426464 ,1.5451937288258311707 ] 
dist 84=[-1.2410636794806823009 ,1.7241391980346717838 ] 
dist 85=[-1.0439051067021146909 ,1.8576113465509569084 ] 
dist 86=[-.77909098230111285478,1.9635008179114129914 ] 
dist 87=[-.70661008989851668814,2.0438547124723998139 ] 
dist 88=[-.57790365356732693469,2.3649677180183037894 ] 
dist 89=[-.60261871233948992017,2.6981385818415885110 ] 
dist 90=[-.62274340726940491899,2.9504346380762129614 ] 
dist 91=[-.64120913946407566929,3.1574717122455847659 ] 
dist 92=[-.65662362042272362432,3.3214624069422118599 ] 
dist 93=[-.74038391039063234819,3.4020572281927562070 ] 
dist 94=[-.84062241899488910772,3.4417760572588183290 ] 
dist 95=[-.97009708171643007435,3.4449539948947816360 ] 
dist 96=[-1.0952055772918253028 ,2.1195528219794455900 ] 
dist 97=[-1.1780480842736133287 ,2.1036126709257142382 ] 
dist 98=[-1.2456817762212641252 ,2.1293185643077538933 ] 
dist 99=[-1.3101507764543096803 ,2.1632082048182135319 ] 
dist 100=[-1.3676652104279678181 ,2.1999674373336059169 ] 
dist 101=[-1.4075845345105992722 ,2.2370917842661056141 ] 
dist 102=[-1.4423669971119709630 ,2.2816629020282550084 ] 
dist 103=[-1.4794426135604190735 ,2.3481050048027687834 ] 
dist 104=[-1.5112691090547936716 ,2.4167063425694238477 ] 
dist 105=[-1.5251116829841495782 ,2.4698700788079170176 ] 
dist 106=[-1.5286261208712661320 ,2.5218438366867758936 ] 
dist 107=[-1.5266103903872268723 ,2.5856599748252871824 ] 
dist 108=[-1.5036712903619223483 ,2.6519969419319863493 ] 
dist 109=[-1.8605550159407999259 ,2.7139980543688582282 ] 
dist 110=[-2.3994374887456223447 ,2.7844727204527028145 ] 
dist 111=[-3.1789163281681493526 ,2.8845657668017994288 ] 
dist 112=[-3.9444327890809929717 ,2.9804548814115372023 ] 
dist 113=[-4.4276237059840608087 ,3.0341518842154442565 ] 
dist 114=[-4.7958038441295237982 ,3.0669535147771710035 ] 
dist 115=[-5.1024951142602700799 ,3.0795117610768059238 ] 
dist 116=[-5.3456769487133997409 ,3.0778787531971810344 ] 
dist 117=[-5.4604970298896220103 ,3.0698609805573059224 ] 
dist 118=[-5.5173449603454565941 ,3.0261773216306219828 ] 
dist 119=[-5.5292187367041183387 ,3.0082421339821914601 ] 
dist 120=[-5.3870147908728725792 ,2.8293412137010124500 ] 
dist 121=[-5.3411544284070803258 ,2.7909654687009878085 ] 
dist 122=[-5.2532942574511559816 ,2.6756059381402400114 ] 
dist 123=[-5.2184638539839847132 ,2.6505252927086112996 ] 
dist 124=[-5.0364744432209297504 ,2.3882536585067620670 ] 
dist 125=[-4.9882145442670015574 ,2.3289490327655730130 ] 
dist 126=[-4.8271964293394741717 ,2.2571085580767386881 ] 
dist 127=[-4.7923574378756605377 ,2.2268672937040064284 ] 
dist 128=[-1.7053291633713242777 ,2.0059765585919810615 ] 
dist 129=[-1.7889735145319044182 ,2.5174717991302290797 ] 
dist 130=[-1.8444125883358820337 ,2.9244251226141977416 ] 
dist 131=[-1.8756959916524843019 ,3.3970408157329879569 ] 
dist 132=[-1.8937462799084759144 ,3.9521658918401268705 ] 
dist 133=[-1.8963978006835853501 ,4.3274392442608049888 ] 
dist 134=[-1.8896381692676853805 ,4.6421591770728111581 ] 
dist 135=[-1.8830161590100418681 ,4.9557283103429911977 ] 
dist 136=[-1.3357831013316199416 ,5.2316831295352615758 ] 
dist 137=[-1.2767532475775939564 ,5.3963512974012555676 ] 
dist 138=[-1.1256158250959519022 ,5.5107530365086620600 ] 
dist 139=[-1.1015373912269448815 ,5.5861791112196647465 ] 
dist 140=[-.85223410160635858565,5.6306319482973243273 ] 
dist 141=[-.80350489871724827687,5.6305033702047664337 ] 
dist 142=[-.74541107909300246012,5.5926073366044755517 ] 
dist 143=[-.72851562766707211496,5.5586805334593315179 ] 
dist 144=[-.26896472618666518367,2.7394147060326066308 ] 
dist 145=[-.71798167460761084507,2.4836207249313681969 ] 
dist 146=[-1.2119034586387839453 ,1.8755474786521497136 ] 
dist 147=[-1.7088501256059397991 ,1.7710112893805184542 ] 
dist 148=[-2.1685283331159377404 ,1.2497436003854220051 ] 
dist 149=[-2.5137811510281706324 ,1.2671255479355300611 ] 
dist 150=[-2.8406654057374700224 ,1.2756030840644104218 ] 
dist 151=[-3.2270685427573466394 ,1.2743135318040755211 ] 
dist 152=[-3.5834655265609905155 ,.66060909091813758022] 
dist 153=[-3.7906507692856238399 ,.70873567939063189107] 
dist 154=[-3.9278105928931995564 ,.79120448544968908529] 
dist 155=[-4.0048659233249237640 ,.88458982257502781089] 
dist 156=[-4.0529002557599514430 ,.97765010212402124302] 
dist 157=[-4.0742922297349634153 ,1.0588203262759424690 ] 
dist 158=[-4.0802239064640654529 ,1.1466842499740229096 ] 
dist 159=[-4.0670305546314872368 ,1.2664456269851955835 ] 
dist 160=[-1.2940588920196595613 ,1.3851634004329804792 ] 
dist 161=[-1.2422376602362471672 ,1.4688627376967139862 ] 
dist 162=[-1.2400046400452316530 ,1.5427866132697894341 ] 
dist 163=[-1.2589427720798294673 ,1.6282970984725777645 ] 
dist 164=[-1.2900225123251041481 ,2.0052684488475669143 ] 
dist 165=[-1.3362211513716062700 ,2.2890769190176772884 ] 
dist 166=[-1.4022673685049573625 ,2.5584484359431413780 ] 
dist 167=[-1.5290201331766923339 ,2.8778313629965626428 ] 
dist 168=[-1.9365586248918038754 ,3.1729334200762678436 ] 
dist 169=[-2.1928132907826440000 ,3.3454463263725739082 ] 
dist 170=[-2.3868546041461282664 ,3.4608750370542703447 ] 
dist 171=[-2.5462102706360450578 ,3.5282611348644830961 ] 
dist 172=[-2.6730235493818201132 ,3.5699620570845588049 ] 
dist 173=[-2.7372456803389758723 ,3.5829268101942511567 ] 
dist 174=[-2.7695526517290967641 ,3.5773009764119921259 ] 
dist 175=[-2.7741761373844952052 ,3.5674820321982405878 ] 
dist 176=[-2.9057351857691851461 ,3.8993929140638450937 ] 
dist 177=[-3.0521514322248845626 ,4.2733610475713556385 ] 
dist 178=[-3.1576928674560602546 ,4.5489682008165248433 ] 
dist 179=[-3.2347238400728213055 ,4.7616855322134912959 ] 
dist 180=[-3.2873303005260944002 ,4.9243661284578931068 ] 
dist 181=[-3.2979189098053832414 ,5.0003622816714722762 ] 
dist 182=[-3.2884369205732682666 ,5.0308236613597340694 ] 
dist 183=[-3.2807677224406034935 ,5.0295855304030701056 ] 
dist 184=[-3.1154658395472589048 ,4.6742159470937362818 ] 
dist 185=[-3.0791913645569975913 ,4.6041969257275979514 ] 
dist 186=[-2.9698976082995280684 ,4.4766117763931151656 ] 
dist 187=[-2.9419965298028756169 ,4.4360881007890007551 ] 
dist 188=[-2.9643918344739838616 ,4.2613199754732786069 ] 
dist 189=[-2.9766179392146170011 ,4.2114102686240079311 ] 
dist 190=[-2.9749422797103294957 ,4.0896532816341367806 ] 
dist 191=[-2.9662633163524102280 ,4.0430384335983038798 ] 
dist 192=[-.1559323309329193225 ,2.2305233914729337297 ] 
dist 193=[-.29337703985069222204,2.3298669355867702011 ] 
dist 194=[-.41063057930553522894,2.4018799487135872256 ] 
dist 195=[-.53068532819196702246,2.4552276453537627243 ] 
dist 196=[-.64308608908790244229,2.4923756121298447753 ] 
dist 197=[-.72980590443053443178,2.4997644562250479599 ] 
dist 198=[-.8141651828451863804 ,2.4946432683625922539 ] 
dist 199=[-.9171492832528313353 ,2.4831730097008366210 ] 
dist 200=[-1.0138498091723555146 ,1.3519581041217574565 ] 
dist 201=[-1.0731422644656311731 ,1.2498911019331507456 ] 
dist 202=[-1.1162811840234765775 ,.9968414873652787559 ] 
dist 203=[-1.1485408952408465541 ,.95973587511393704532] 
dist 204=[-1.1712691184696553919 ,.57637663196394478163] 
dist 205=[-1.1919121024498505844 ,.50516198404887706636] 
dist 206=[-1.2924932238317691040 ,.42116700454087432453] 
dist 207=[-1.4092510885280212420 ,.4044786736719924659 ] 
dist 208=[-1.5158266968497434575 ,.46620017470723566555] 
dist 209=[-1.5757891359491898346 ,.61242635381598989773] 
dist 210=[-1.6129690161860812802 ,.72819487025528617345] 
dist 211=[-1.6286619313795773846 ,.83235143878826489911] 
dist 212=[-1.6344435341933886939 ,.92083400255692638155] 
dist 213=[-1.6320866166349642127 ,.97407675566326832103] 
dist 214=[-1.6233193939367754390 ,1.0116045880865933552 ] 
dist 215=[-1.6171568893931358677 ,1.0373986251572903534 ] 
dist 216=[-.99433139801459856626,1.0568121386873157053 ] 
dist 217=[-1.0319183488388093719 ,1.0688867872409646080 ] 
dist 218=[-1.0806081949737606395 ,1.0778785935592020460 ] 
dist 219=[-1.1351297160965292010 ,1.2612453852631943318 ] 
dist 220=[-1.1891077840669788701 ,1.4399426486054111164 ] 
dist 221=[-1.2356289182486358690 ,1.5720972353057684709 ] 
dist 222=[-1.2855127295022775948 ,1.6952185100581792481 ] 
dist 223=[-1.3529044809872208606 ,1.8378810246581740249 ] 
dist 224=[-1.4194330086993299057 ,1.9679942894756244080 ] 
dist 225=[-1.4658726712148043774 ,2.0410546746609389049 ] 
dist 226=[-1.5064036288081075396 ,2.0861796945316806525 ] 
dist 227=[-1.5493601600647014143 ,2.1048539650735874865 ] 
dist 228=[-1.5904864919282626069 ,2.1109063994553813221 ] 
dist 229=[-1.6237156094621390994 ,2.1056797557360434426 ] 
dist 230=[-1.6574574252098036414 ,2.0926392695622668946 ] 
dist 231=[-1.7006276207949527615 ,2.0835514137226505467 ] 
dist 232=[-1.7403068089347098498 ,2.1284279275750478052 ] 
dist 233=[-1.7601221427371364012 ,2.4088285436072104427 ] 
dist 234=[-1.7691390913350445056 ,2.6242276828665882468 ] 
dist 235=[-1.7663669337631416848 ,2.8066618875104282420 ] 
dist 236=[-1.8949046024333597066 ,2.9535362016101679398 ] 
dist 237=[-2.0141297271544006482 ,3.0270791651001720284 ] 
dist 238=[-2.1050463918060499377 ,3.0649144561837284859 ] 
dist 239=[-2.1808491805618579027 ,3.0693417004411456219 ] 
dist 240=[-2.2425013027374067813 ,3.0218171719331304482 ] 
dist 241=[-2.2769680416166317698 ,3.0004075082577716557 ] 
dist 242=[-2.2980532952344241932 ,2.9606323479217629076 ] 
dist 243=[-2.3063248188199496709 ,2.9435521845596592724 ] 
dist 244=[-2.3057054244077842507 ,2.8504706462168702868 ] 
dist 245=[-2.2986527001051582613 ,2.8249279691522377565 ] 
dist 246=[-2.2720965066408029026 ,2.7371072142272301779 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 1, 0, 1, 0, 2] 
dist 0=[62.927323673209991310  ,62.927323673209991310  ] 
dist 1=[62.491929043974669594  ,63.218261040465949574  ] 
dist 2=[61.044365780882471333  ,63.592954363982182012  ] 
dist 3=[59.222462900836468510  ,63.665224120476000770  ] 
dist 4=[57.030259941911922565  ,63.078410459560644730  ] 
dist 5=[54.143391290419028423  ,62.906143039994181266  ] 
dist 6=[49.547851756361528372  ,62.324340831574537637  ] 
dist 7=[44.851996849416897872  ,62.148002927336450723  ] 
dist 8=[41.564549981086407093  ,61.515334088760916583  ] 
dist 9=[38.674233095929148480  ,61.279953895178716320  ] 
dist 10=[35.563892063929576754  ,60.702932671782385060  ] 
dist 11=[32.543848027039944177  ,60.460286903357089855  ] 
dist 12=[30.013899261654880787  ,59.206486753836306034  ] 
dist 13=[27.353618170133010429  ,58.866488599958561588  ] 
dist 14=[23.812821137902317882  ,57.021773239295737332  ] 
dist 15=[20.317804326319106238  ,53.610823514568034464  ] 
dist 16=[17.840092511665909812  ,29.401019875092777154  ] 
dist 17=[15.627299986858844194  ,27.124430612389792318  ] 
dist 18=[13.189750828122248002  ,24.120870919811581354  ] 
dist 19=[10.785584784280895783  ,23.830918226985905536  ] 
dist 20=[8.7055970632407477208 ,14.661655478294023357  ] 
dist 21=[6.4572073402807026918 ,13.748951183253411852  ] 
dist 22=[3.3794908909287994270 ,13.598033032218691051  ] 
dist 23=[.37079277880170763403,11.218723520496203399  ] 
dist 24=[-1.6020686842453697316 ,8.4129959786344953626 ] 
dist 25=[-3.2021943485653026853 ,8.0048867815245590028 ] 
dist 26=[-4.7216210181042516048 ,7.2808117781005992513 ] 
dist 27=[-6.0808764484590212705 ,7.1383751652093600370 ] 
dist 28=[-7.3785199195433751345 ,.26029886614676326828] 
dist 29=[-8.5765629389458662403 ,-.19680341940951165607] 
dist 30=[-9.6913139664976928980 ,-1.9675330021003888116 ] 
dist 31=[-10.999027849394816074  ,-3.7274002556111869678 ] 
dist 32=[-12.193711268110097329  ,-4.9152493140265204902 ] 
dist 33=[-12.857224701126181965  ,-5.0600553084908626454 ] 
dist 34=[-13.269352976262466082  ,-4.2328960898843025270 ] 
dist 35=[-13.458560540043250241  ,-3.2408574694289303170 ] 
dist 36=[-13.556974181844342220  ,-2.1197187704883427680 ] 
dist 37=[-13.605404984913685525  ,-.69353791031428461944] 
dist 38=[-13.630238877232662369  ,1.5155421773168210469 ] 
dist 39=[-13.632677735717539839  ,3.7321865290868020118 ] 
dist 40=[-12.676802809282617943  ,5.1887257978649261740 ] 
dist 41=[-12.696348179227960450  ,6.3634210477853854434 ] 
dist 42=[-12.625676521227253542  ,7.4561135215648381196 ] 
dist 43=[-12.608361447525179831  ,8.4091110280110312670 ] 
dist 44=[-10.011035948413284327  ,9.0267066809185487598 ] 
dist 45=[-9.8703194715436111961 ,9.5154460190311270216 ] 
dist 46=[-9.7589992778734372328 ,9.9545510811685427414 ] 
dist 47=[-9.7247881948260483860 ,10.321928867544223725  ] 
dist 48=[-3.9464913570956345211 ,10.524549379247743628  ] 
dist 49=[-3.3069570377448824402 ,10.644788583047315793  ] 
dist 50=[-3.2060488799453309602 ,10.683443323759374268  ] 
dist 51=[-2.2361464729854534825 ,10.666153401049838790  ] 
dist 52=[-2.0538146085590100890 ,10.635232336002795932  ] 
dist 53=[-1.8211040495289746241 ,10.450953797799721220  ] 
dist 54=[-1.7556056522239416586 ,10.270130692273620544  ] 
dist 55=[.12807016692045006554,7.5352237050194895890 ] 
dist 56=[.34147993694124574166,7.5602161200068431780 ] 
dist 57=[.82290510659321270791,7.9652888521923050227 ] 
dist 58=[.90111331386401310822,8.4323568678473738760 ] 
dist 59=[1.4629639165303511679 ,8.8290958896362616135 ] 
dist 60=[1.3493921254182962666 ,9.1506939068021159839 ] 
dist 61=[.39546624806926080953,9.3177817839394966215 ] 
dist 62=[-.4220242116368281174 ,9.4038272454299119773 ] 
dist 63=[-1.2646674540528289881 ,9.4104853076008985862 ] 
dist 64=[-2.0569074972143936425 ,2.5150021396751223407 ] 
dist 65=[-2.6733568866081342058 ,2.5981683008086452462 ] 
dist 66=[-3.2778846166538126175 ,2.6546413064125383192 ] 
dist 67=[-4.0225862596387993466 ,2.6906556935374213282 ] 
dist 68=[-4.7250913456061285785 ,2.6970869620848115736 ] 
dist 69=[-5.1612932498146051315 ,2.6831241468117219976 ] 
dist 70=[-5.4851243818236088417 ,2.6767558590544631208 ] 
dist 71=[-5.7393555371245237307 ,1.6925262124521468209 ] 
dist 72=[-5.9316602325258483763 ,1.5971030599843706845 ] 
dist 73=[-6.0084681077545009212 ,1.3556596561419673374 ] 
dist 74=[-6.0360918349587045021 ,1.3201199744930911562 ] 
dist 75=[-6.0321774885791312473 ,.93610588495150485515] 
dist 76=[-5.2380889153690498554 ,.86303879118203104151] 
dist 77=[-5.2396919748314531113 ,.81462856319107027354] 
dist 78=[-5.1882356744358776705 ,1.1793289581881176247 ] 
dist 79=[-5.1665924445388959873 ,1.6629963559322723894 ] 
dist 80=[-2.7084790609861701819 ,2.1064103790512434666 ] 
dist 81=[-2.4815836369011244682 ,2.4324062448902704800 ] 
dist 82=[-1.9363416052358992408 ,2.7341063696954635904 ] 
dist 83=[-1.8436148270250514462 ,3.0806474440607538037 ] 
dist 84=[-1.4688422727836727031 ,3.3966955236426667628 ] 
dist 85=[-1.4801747124056167438 ,3.5767710177095853077 ] 
dist 86=[-1.4799322004715863149 ,3.6913961196222533696 ] 
dist 87=[-1.0382369099571838034 ,3.7463552489764623707 ] 
dist 88=[-1.1072713186984084469 ,3.7750973615863250330 ] 
dist 89=[-1.1957576894729169854 ,3.7851503054894357686 ] 
dist 90=[-1.2926914161675471110 ,3.7834788860534484559 ] 
dist 91=[-1.3874685503262641469 ,3.7677960666490170392 ] 
dist 92=[-1.4673448661158458231 ,3.5546444969767063638 ] 
dist 93=[-1.5514783078711047009 ,3.5813218505984214511 ] 
dist 94=[-1.6632315740445177900 ,3.5903166309777759044 ] 
dist 95=[-1.7727093111765105858 ,3.5782597923756330153 ] 
dist 96=[-1.9420707363187728895 ,2.0088046015404514618 ] 
dist 97=[-2.1700373334913527889 ,1.9205366362876721119 ] 
dist 98=[-2.3663528759156913909 ,1.7897215197540339415 ] 
dist 99=[-2.5699759488191916067 ,1.7503060193934387706 ] 
dist 100=[-2.7520474798179363624 ,.94936654384321573697] 
dist 101=[-2.8624110412207947251 ,1.2813766683601830580 ] 
dist 102=[-2.9410389925407161849 ,1.8037221468916034368 ] 
dist 103=[-2.9965649912209183004 ,2.3189937301635056182 ] 
dist 104=[-3.0328185195170912302 ,2.6455389076239982124 ] 
dist 105=[-3.0362506224578318898 ,2.8957972841542356908 ] 
dist 106=[-3.0226100859670208900 ,3.1067413594208575242 ] 
dist 107=[-3.0053626992470530197 ,3.2758292971655655501 ] 
dist 108=[-2.2101701187965160220 ,3.3591141985404109345 ] 
dist 109=[-2.1632330184672013668 ,3.4026042302877434422 ] 
dist 110=[-2.1438151262792707956 ,3.4129322420906480951 ] 
dist 111=[-1.8901711851068536279 ,3.3412679916514767690 ] 
dist 112=[-1.8472214671976029519 ,3.3145591633974204979 ] 
dist 113=[-1.7315120128522720758 ,3.2745812714674508336 ] 
dist 114=[-1.7080074655195577196 ,3.2552610468321602965 ] 
dist 115=[-1.4891481387962413365 ,3.1731665335050274598 ] 
dist 116=[-1.4425528644766464453 ,3.1457761919768401205 ] 
dist 117=[-1.3803417722378150401 ,3.0698609805573059102 ] 
dist 118=[-1.3579775257165184007 ,3.0375201433653898918 ] 
dist 119=[-1.1217571730475023224 ,1.8562531097786578671 ] 
dist 120=[-1.3299088119177678208 ,1.9077556424048967486 ] 
dist 121=[-1.4937809466073910357 ,1.9325117867893384358 ] 
dist 122=[-1.7710972773148177595 ,1.9423842418021384780 ] 
dist 123=[-2.1162403225467126528 ,1.9401766188859621468 ] 
dist 124=[-2.3547985745646639499 ,1.5769874771970862206 ] 
dist 125=[-2.5605199297183040170 ,1.5333434740212095207 ] 
dist 126=[-2.7746728639183419248 ,1.4184492492539601120 ] 
dist 127=[-2.9663376792034162726 ,1.3960651896385311708 ] 
dist 128=[-3.0823501388351955660 ,1.1905996797741739171 ] 
dist 129=[-3.1649504025183293387 ,1.1481109736556673916 ] 
dist 130=[-3.2233265427380157006 ,1.0901374777592875119 ] 
dist 131=[-3.2615365079136203682 ,1.0703390361426088144 ] 
dist 132=[-3.2659065944768448575 ,.64270199691485906785] 
dist 133=[-3.2520468625502709128 ,.58662277292883392929] 
dist 134=[-3.2352225402838733869 ,.4609334068252815034 ] 
dist 135=[-1.7041239165058417366 ,.4327886927858012889 ] 
dist 136=[-1.5649519480674233544 ,.63756598964665499279] 
dist 137=[-1.2264567713230337968 ,.88091246097174078091] 
dist 138=[-1.1726682816315501165 ,1.1236195979160759139 ] 
dist 139=[-1.1422908716830726334 ,1.3467513096733077066 ] 
dist 140=[-1.1336779620415473636 ,1.5120088974409492004 ] 
dist 141=[-1.2745148651105862106 ,1.6661916025245057016 ] 
dist 142=[-1.4218409497161946927 ,1.8451433445187743634 ] 
dist 143=[-1.5751440552012350721 ,2.0084667602040255392 ] 
dist 144=[-1.7202591247949081354 ,2.1003060714590226642 ] 
dist 145=[-1.8349168926649105918 ,2.1571829977180033010 ] 
dist 146=[-1.9490370649683558415 ,2.1810378377519192662 ] 
dist 147=[-2.0920042467746578595 ,2.1913832799492975448 ] 
dist 148=[-2.2281090108571541200 ,2.1943710655985543105 ] 
dist 149=[-2.3148498803668453621 ,2.1925336676633783571 ] 
dist 150=[-2.3818922189411445870 ,2.1836346374801022366 ] 
dist 151=[-2.4394079070669518931 ,1.0382814359852195701 ] 
dist 152=[-2.4862622367297747406 ,1.0586965189735360683 ] 
dist 153=[-2.5107687867368931233 ,1.0951593938795018586 ] 
dist 154=[-2.5235369018778003972 ,1.1416878684077843901 ] 
dist 155=[-2.5235558072116746606 ,1.7102876129733437656 ] 
dist 156=[-2.5158027736565178170 ,2.3164603009854346634 ] 
dist 157=[-2.5048471868965712441 ,2.7043962494817947149 ] 
dist 158=[-2.4744277283661149771 ,3.0060320118248395134 ] 
dist 159=[-2.4580549283028288497 ,3.2679400722239755170 ] 
dist 160=[-2.3581062528460729206 ,3.4836742267034604053 ] 
dist 161=[-2.3405789738411207507 ,3.6011160383779679143 ] 
dist 162=[-2.3817561307605453880 ,3.6688392369778110979 ] 
dist 163=[-2.4059947700867984050 ,3.6862406676737022723 ] 
dist 164=[-2.4083477698490728381 ,3.6835100468045052135 ] 
dist 165=[-2.3996001412241897644 ,3.6709232746439797661 ] 
dist 166=[-2.3893446753717192355 ,3.6487477756332696943 ] 
dist 167=[-2.5625718793407377975 ,3.6319733682131109752 ] 
dist 168=[-2.8631037873097738668 ,3.5579421108731510134 ] 
dist 169=[-3.0907559875990964651 ,3.5316565618747932965 ] 
dist 170=[-3.2778620898700478355 ,3.4477733799544968370 ] 
dist 171=[-3.4252057241067230329 ,3.4166522506874647603 ] 
dist 172=[-3.4942362681075644308 ,2.1486296221661421009 ] 
dist 173=[-3.5274486106299363949 ,2.1187987107303126790 ] 
dist 174=[-3.5319052141719202187 ,2.1657871038495331443 ] 
dist 175=[-3.4051888667962897431 ,2.2257983225924764030 ] 
dist 176=[-3.3708000273705235198 ,2.2622787906290277315 ] 
dist 177=[-3.3077496765757878203 ,2.2884324211629935751 ] 
dist 178=[-3.2846328623402552607 ,2.3072498001656683824 ] 
dist 179=[-3.1715209486333311425 ,2.3198621568120467661 ] 
dist 180=[-3.2045700248504659681 ,2.3212637699069673265 ] 
dist 181=[-3.3338869147558618084 ,2.3147167672013963139 ] 
dist 182=[-3.4258187559787145670 ,2.3058942134365126142 ] 
dist 183=[-3.4905103220005058960 ,-.15922778299160857078] 
dist 184=[-3.5325945314428715668 ,-.17161478856719417628] 
dist 185=[-3.5378519843253085836 ,-.17281560140442993002] 
dist 186=[-3.5214224346621536994 ,-.1590480631466167387 ] 
dist 187=[-3.5049961270698658899 ,-.13673968327471998822] 
dist 188=[-1.8709878574814494884 ,.31192089324986337834] 
dist 189=[-1.7216622033348778879 ,.63249766810525379612] 
dist 190=[-1.3581331507882645675 ,.90164185642877995385] 
dist 191=[-1.3000949895544867307 ,1.1701780769035922568 ] 
dist 192=[-.76841285766163937268,1.4170911043786104762 ] 
dist 193=[-.67014658038751561561,1.5999792208999530438 ] 
dist 194=[-.68190623767500574073,1.7706112558387236890 ] 
dist 195=[-.74078890844666491785,1.9686328386186422811 ] 
dist 196=[-.79410317100284336353,2.1493155229144562756 ] 
dist 197=[-.85343498138370978807,2.2507818554833782778 ] 
dist 198=[-.93632140888670852507,2.3134349533245712689 ] 
dist 199=[-1.0157527585531212713 ,2.3392911210628436726 ] 
dist 200=[-1.0613025599470487060 ,2.3506062868095954532 ] 
dist 201=[-1.0906606676085948966 ,2.3552567554121200841 ] 
dist 202=[-1.1055044677092620814 ,2.3559025575287035043 ] 
dist 203=[-1.1130088915988487889 ,2.3512478465840621704 ] 
dist 204=[-1.1130901359884441913 ,1.3050768051170759954 ] 
dist 205=[-1.1080069155228972683 ,1.3176995372223713726 ] 
dist 206=[-1.1041033872412685575 ,1.3191802857210318295 ] 
dist 207=[-1.2258399148138304877 ,1.2287586319663705103 ] 
dist 208=[-1.4680025174071282672 ,1.2852619910377194316 ] 
dist 209=[-1.6515692518062493105 ,1.3396651924863120665 ] 
dist 210=[-1.8270060273453344917 ,1.4028530795481087646 ] 
dist 211=[-2.0367389997274539893 ,1.4943976444579281922 ] 
dist 212=[-2.2313976671125098746 ,1.5875647556843090465 ] 
dist 213=[-2.3467024368917456272 ,1.6572234397841466896 ] 
dist 214=[-2.4257385115220175975 ,1.7228683658221671729 ] 
dist 215=[-2.4757188047938718043 ,1.8000209627423359394 ] 
dist 216=[-2.5071072513080626681 ,1.8784739536738377488 ] 
dist 217=[-2.5119772276587482249 ,1.9493038421567189582 ] 
dist 218=[-2.5047601037349421053 ,2.0279658102209665742 ] 
dist 219=[-2.4935247843376612297 ,2.1376577956290850239 ] 
dist 220=[-2.7837396096536637363 ,2.2426789674051029368 ] 
dist 221=[-3.1096695332056682520 ,2.3027079196710299418 ] 
dist 222=[-3.3563213401028706531 ,2.3411430049855115385 ] 
dist 223=[-3.5586054255174397915 ,2.3600260541785235876 ] 
dist 224=[-3.7177844693089252612 ,2.3648360909741041376 ] 
dist 225=[-3.7924812816499702529 ,2.3619678465125223063 ] 
dist 226=[-3.8282618332944145356 ,2.3266707400335338007 ] 
dist 227=[-3.8321958697881993243 ,2.3204766636513748086 ] 
dist 228=[-3.6888186905024716795 ,2.2503017602830309271 ] 
dist 229=[-3.6506545076964436683 ,2.2862251951895151976 ] 
dist 230=[-3.5809242427007442322 ,2.3129759578312736405 ] 
dist 231=[-3.5556091104274803803 ,2.3341178268853615264 ] 
dist 232=[-3.4328079804948575807 ,2.3499783673523844839 ] 
dist 233=[-3.3982213850527063374 ,2.3556617694278370543 ] 
dist 234=[-3.2962059624251576441 ,2.3549629911781667402 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 2, 0, 2, 0, 0, 2] 
dist 0=[60.699992923502962919  ,60.699992923502962919  ] 
dist 1=[59.383652847132688702  ,61.327526314264322693  ] 
dist 2=[57.722418743064042431  ,61.650054258905767827  ] 
dist 3=[55.717733194195576345  ,61.748571351557515794  ] 
dist 4=[53.073993270292667100  ,61.707949751602062660  ] 
dist 5=[48.861032540027712198  ,61.136403837254537207  ] 
dist 6=[44.552419784638790125  ,60.972384986361430406  ] 
dist 7=[41.526697678348035472  ,60.267268692730386023  ] 
dist 8=[38.856198181472934026  ,59.927217494212429100  ] 
dist 9=[35.965836387990074260  ,59.368828721697572903  ] 
dist 10=[33.148902553440996463  ,58.775943670584848925  ] 
dist 11=[30.771438103725735747  ,58.525749383535911590  ] 
dist 12=[28.255655687647151325  ,57.215743123884947873  ] 
dist 13=[24.886082613004843746  ,56.862396070336632715  ] 
dist 14=[21.549486379928315826  ,56.474192480121556684  ] 
dist 15=[19.165173212842918850  ,54.262324446695463519  ] 
dist 16=[17.015921238870631482  ,48.864027023725610800  ] 
dist 17=[14.617639220830399030  ,28.710514207992224234  ] 
dist 18=[12.234005266443966577  ,26.540602429124264965  ] 
dist 19=[10.142789527634335408  ,24.322590242613321690  ] 
dist 20=[7.8576812933631223408 ,20.759203742985509628  ] 
dist 21=[4.6987628430498295505 ,15.281160380311687065  ] 
dist 22=[1.6030850504537261082 ,13.671400077325376590  ] 
dist 23=[-.42955354770273536151,11.862860819327115836  ] 
dist 24=[-2.0810389304016921145 ,11.489163067341882494  ] 
dist 25=[-3.6538497565475732470 ,8.9555355520821794109 ] 
dist 26=[-5.0638002061007039002 ,8.2649362539713212302 ] 
dist 27=[-6.0646748778278918264 ,8.1236688136576982992 ] 
dist 28=[-6.9622697546347627054 ,3.5986660868645909437 ] 
dist 29=[-7.9598182739044459703 ,1.2064531349638093333 ] 
dist 30=[-8.8594060462470449991 ,-3.2022055581445899847 ] 
dist 31=[-9.4585626603212313308 ,-3.5537963824458515550 ] 
dist 32=[-10.918714547057755044  ,-4.8215223608811342074 ] 
dist 33=[-12.269159761416124110  ,-4.4075613312580866943 ] 
dist 34=[-13.035581914472931999  ,-3.5876360529782802999 ] 
dist 35=[-13.531331577645746030  ,-2.6265068846577131291 ] 
dist 36=[-13.799367949921721075  ,-1.3819637830189194016 ] 
dist 37=[-13.965104116865829269  ,.5687066749635133267 ] 
dist 38=[-14.051266841145778356  ,2.5316466180810764252 ] 
dist 39=[-14.099277852782479322  ,3.8253220446773787499 ] 
dist 40=[-14.111002623067939494  ,4.8726629694548517646 ] 
dist 41=[-13.482667557911459008  ,5.8533338925582757836 ] 
dist 42=[-13.427314609821853853  ,6.7128496817062144391 ] 
dist 43=[-13.408944684541436072  ,7.2770610737843705641 ] 
dist 44=[-11.099207484829153812  ,7.7315817870654088446 ] 
dist 45=[-10.646849562467102391  ,8.1536650515713620444 ] 
dist 46=[-10.507526174731168267  ,8.5142312737988373977 ] 
dist 47=[-10.418013220192615031  ,8.7233710781527141026 ] 
dist 48=[-10.396591727692557510  ,8.8610806317539251871 ] 
dist 49=[-2.6241775765114209477 ,8.9366269751919609794 ] 
dist 50=[-1.7814176394177235974 ,8.9657762450062220409 ] 
dist 51=[-1.6257969535728574982 ,8.9906017814135929875 ] 
dist 52=[-1.3522169092895705304 ,9.3683214511790326494 ] 
dist 53=[-1.2902510265152093758 ,9.5958389576618170127 ] 
dist 54=[.88822484050720017228,9.7574263511925910829 ] 
dist 55=[1.1126033289671755666 ,9.8719079362057919215 ] 
dist 56=[1.6010968616812733026 ,9.9478642537014518805 ] 
dist 57=[1.6876172258099985205 ,9.9556438837672253894 ] 
dist 58=[2.1916080778623315893 ,9.9159121480738188006 ] 
dist 59=[2.2709407259773560273 ,9.8844786630127319293 ] 
dist 60=[2.1919479215086287922 ,9.0530438519412407091 ] 
dist 61=[1.0207718346816301241 ,9.4084431590660940849 ] 
dist 62=[.02002949848208723052,9.6011717128170968360 ] 
dist 63=[-1.0068908238237117457 ,9.7118022492532862619 ] 
dist 64=[-1.9695551380588068084 ,9.7394573619923766812 ] 
dist 65=[-2.7140017568518290043 ,3.2629965947114668977 ] 
dist 66=[-3.4397477922989415601 ,3.2632830556594534739 ] 
dist 67=[-4.3278427562476059127 ,3.2538718701058321611 ] 
dist 68=[-5.1627821793381704045 ,3.2157975939499756428 ] 
dist 69=[-5.6764895101162794315 ,3.1928533737387063240 ] 
dist 70=[-6.0523419397058958685 ,1.9368561994823681247 ] 
dist 71=[-6.3373484349078349385 ,1.8082598089095090829 ] 
dist 72=[-6.5541963126299056820 ,1.5045942264869588589 ] 
dist 73=[-6.6581528122332630049 ,1.4447951832979685511 ] 
dist 74=[-6.6991734137483018886 ,1.0216109282947504561 ] 
dist 75=[-6.6997885017741772898 ,.94222128778665428484] 
dist 76=[-5.0132854854681130232 ,.80211046408464190392] 
dist 77=[-5.0960110032356176065 ,.76988578688080899486] 
dist 78=[-5.1235336223765216909 ,.22176613592175932782] 
dist 79=[-5.1187565715609709338 ,.32849365476586284485] 
dist 80=[-5.1058148201911869372 ,.77852688344144432183] 
dist 81=[-2.6800655427109903646 ,1.1188548049194019222 ] 
dist 82=[-2.7137072401877984850 ,1.4432157484416132079 ] 
dist 83=[-2.7175780080457515839 ,1.8295891691807126376 ] 
dist 84=[-2.7081555505588652446 ,2.1908952827470352627 ] 
dist 85=[-2.6940513016014891079 ,2.4152773276430984628 ] 
dist 86=[-.51723449859382314941,2.5818727858953016938 ] 
dist 87=[-.39042356613406320743,2.7126790085874949619 ] 
dist 88=[-.56502232574068004032,2.8122568914684363267 ] 
dist 89=[-.76939105228980511873,2.9193994694796249624 ] 
dist 90=[-1.0341546075535175253 ,3.1524978510391554267 ] 
dist 91=[-1.4496211714348848356 ,3.4574153421741265617 ] 
dist 92=[-1.8665148527885129225 ,3.7436683931666177066 ] 
dist 93=[-2.1369642348175448933 ,3.9023139718865605427 ] 
dist 94=[-2.3511872168086538107 ,3.9979333659192610509 ] 
dist 95=[-2.5438203353423043841 ,4.0326951927040843512 ] 
dist 96=[-2.7071338906178715159 ,4.0442964602986864669 ] 
dist 97=[-2.8044090250684665559 ,4.0474744813679182587 ] 
dist 98=[-2.8716001879540074238 ,4.0451997018256259089 ] 
dist 99=[-2.9149055309824274825 ,4.0349707222648329606 ] 
dist 100=[-2.9415367525226243712 ,3.3306964938019954056 ] 
dist 101=[-2.9422178957362173000 ,3.2282150355006590466 ] 
dist 102=[-2.9301178075153645599 ,3.0388603392618730062 ] 
dist 103=[-2.9165974281785020176 ,2.9883357032530555641 ] 
dist 104=[-2.8174071042871667074 ,2.8101810383067786555 ] 
dist 105=[-2.7877837779989346882 ,2.8269901467906112163 ] 
dist 106=[-2.7199155822359185030 ,2.8986196946325053575 ] 
dist 107=[-2.6934390253855684893 ,2.9372632833237136091 ] 
dist 108=[-2.6505407720951734775 ,2.9590782947174854917 ] 
dist 109=[-2.6450457556979153233 ,2.9635691523722205640 ] 
dist 110=[-2.3524814498615168576 ,2.5682250713644285211 ] 
dist 111=[-2.3028555803299759999 ,2.5068322951470502826 ] 
dist 112=[-2.2044996103216026988 ,2.4101807448728779260 ] 
dist 113=[-2.1743197912911726149 ,2.3797627981037725042 ] 
dist 114=[-2.0443048526630631522 ,2.2987110810978520070 ] 
dist 115=[-2.0126775130323424558 ,2.2703052785857706797 ] 
dist 116=[-1.9306811436259894405 ,2.2527695993831327862 ] 
dist 117=[-1.9038062250628969507 ,2.2455228312396067137 ] 
dist 118=[-.80650291948021681095,-.00208476470296394148] 
dist 119=[-.79597893889014870383,.03414656370158586275] 
dist 120=[-.88819910527793116228,.0847532884354520811 ] 
dist 121=[-1.1859347998077308173 ,.1352183339226615332 ] 
dist 122=[-1.4505236281531268783 ,.1709062054493323102 ] 
dist 123=[-1.6310113422253204098 ,.2024834449571925009 ] 
dist 124=[-1.7840992575521972858 ,.2365923694617598294 ] 
dist 125=[-1.9393922258511764909 ,.2696845430315936694 ] 
dist 126=[-2.0786351224471806609 ,.2972366047751932451 ] 
dist 127=[-2.1676991213198850312 ,.32605737393795474599] 
dist 128=[-2.2368926202089880046 ,.36425945218168153057] 
dist 129=[-2.2968696371791259049 ,.50125329668008832033] 
dist 130=[-2.3461947138103449346 ,.6075800089986305475 ] 
dist 131=[-2.3728965127044017616 ,.71148928045791854957] 
dist 132=[-2.3880920342152528983 ,.81606857551437588642] 
dist 133=[-2.3915177630565040397 ,.91293345758898303114] 
dist 134=[-.97084777196532043999,.98605722158528483233] 
dist 135=[-.85603997355862410976,1.0557033906797101957 ] 
dist 136=[-.57893834328532232186,1.1386851093953451036 ] 
dist 137=[-.53761092152177490691,1.2156251308326055651 ] 
dist 138=[-.14553292508351790469,1.2611611067418073828 ] 
dist 139=[-.07515657252038823649,1.2923320588204519853 ] 
dist 140=[.01560571099811143455,1.3119520280129742098 ] 
dist 141=[.02636825377572550866,1.3226537729944240270 ] 
dist 142=[-.09105371154997477158,1.3238246942109379234 ] 
dist 143=[-.26391390590083343405,1.3105957236846005383 ] 
dist 144=[-.52264819181274452793,1.3083141976402180935 ] 
dist 145=[-.77974121907843912702,1.2191980831103849933 ] 
dist 146=[-.9549936138283770396 ,1.2014075477427516252 ] 
dist 147=[-1.1004368732674735254 ,1.1523169591077675555 ] 
dist 148=[-1.2299982982972591305 ,1.1385966787614150224 ] 
dist 149=[-1.3391806263529063283 ,1.0477932759798965702 ] 
dist 150=[-1.4033324568820111722 ,1.0126931508346477916 ] 
dist 151=[-1.4467052501062460789 ,.97458210876394554892] 
dist 152=[-1.4730056686268768625 ,.96273877261010713711] 
dist 153=[-1.4903354390929514132 ,.82772226852781607482] 
dist 154=[-1.4979218547215284502 ,.81178622568454203272] 
dist 155=[-1.4998554104216296263 ,.80400742099675055717] 
dist 156=[-1.4948630642534460161 ,.79678872038481906117] 
dist 157=[-1.4852324818191749768 ,.79140811742914205951] 
dist 158=[-1.4773207071021470001 ,.78181657692654878002] 
dist 159=[-1.4543517157384246913 ,.7781844943158646293 ] 
dist 160=[-1.4428993804908869398 ,.77636402199017169047] 
dist 161=[-.37044135160531794582,.77653913535909007237] 
dist 162=[-.5490071012216274199 ,.77796970504354127762] 
dist 163=[-.7177286090226339018 ,.78115468192771523042] 
dist 164=[-.91122706320497657934,.78621274431983591236] 
dist 165=[-1.1886341563090290344 ,.79511032806381577525] 
dist 166=[-1.4610860691391078616 ,.8806327115940781068 ] 
dist 167=[-1.6348185524379607087 ,.9952832011532688153 ] 
dist 168=[-1.7691816954910845347 ,1.1291551844139931422 ] 
dist 169=[-1.8845839261470742016 ,1.2519231324138806491 ] 
dist 170=[-1.9787080027862666964 ,1.3222804860961548428 ] 
dist 171=[-2.0281902844879584601 ,1.3675813870089279335 ] 
dist 172=[-2.0543636960895039255 ,1.3903966134261613113 ] 
dist 173=[-2.0584180024466663918 ,1.4035084195509793685 ] 
dist 174=[-2.0456816369503856116 ,1.4101034186299404578 ] 
dist 175=[-2.0356824446851829351 ,1.4131823130428165049 ] 
dist 176=[-2.0074579129685055270 ,1.4122739959936444332 ] 
dist 177=[-1.9929556471005761360 ,1.1373422989689401333 ] 
dist 178=[-1.9059774261521811942 ,1.1027649908649717128 ] 
dist 179=[-1.8827732493860614059 ,1.0099168924462738498 ] 
dist 180=[-1.8265703901245928703 ,.99492057677272479664] 
dist 181=[-1.8052525399845998419 ,.83937504682999836388] 
dist 182=[-.70474880424619973911,.84667303509139575336] 
dist 183=[-.77327365274971619577,1.1698214345611465537 ] 
dist 184=[-.84440638709063746937,1.4293827451672636824 ] 
dist 185=[-.90845928485245302644,1.6693013328813368388 ] 
dist 186=[-.94874321264001861611,1.8776556406007188316 ] 
dist 187=[-.97923857448060646892,2.0113027903794247184 ] 
dist 188=[-1.0042448630478086604 ,2.1155552615731537387 ] 
dist 189=[-1.0237320760477535615 ,2.2066496050243527030 ] 
dist 190=[-1.0322111503734877571 ,2.2827898253476765874 ] 
dist 191=[-1.0342209868426128504 ,2.3273888824169559932 ] 
dist 192=[-1.0322153383670150440 ,2.3573338635656723907 ] 
dist 193=[-.47333731559617102769,2.3750193993600232910 ] 
dist 194=[-.5576141465182030516 ,2.3834306870130553657 ] 
dist 195=[-.64420821100293621389,2.3783127223737583946 ] 
dist 196=[-.74135830102418021614,2.3612181746279028754 ] 
dist 197=[-.83764682351706704892,2.3488332280673215465 ] 
dist 198=[-.9208020037560103385 ,1.0126017119926613856 ] 
dist 199=[-1.0101106092507554592 ,.90184488743125200605] 
dist 200=[-1.1309443333352191182 ,.64629610932140029275] 
dist 201=[-1.2503071503070898460 ,.59731743615414592069] 
dist 202=[-1.3337465828737486153 ,.44911284906906063724] 
dist 203=[-1.4066920063831783993 ,.52547345007177597242] 
dist 204=[-1.4841899540842406880 ,.60619471264288374807] 
dist 205=[-1.5584939471182568114 ,.6833520333901740018 ] 
dist 206=[-1.6186960707071411151 ,.74549773437213044583] 
dist 207=[-1.6799726040638879391 ,.80843521607186131785] 
dist 208=[-1.7585589836297629663 ,.88875443778699949785] 
dist 209=[-1.8308477851000108461 ,.9646297589944812767 ] 
dist 210=[-1.8670018865879786318 ,1.0098403082621334438 ] 
dist 211=[-1.8835275153207869873 ,1.0411701902736280418 ] 
dist 212=[-1.8856123546238686210 ,1.0616714139508465218 ] 
dist 213=[-1.8574842012483476318 ,1.0742583075528900838 ] 
dist 214=[-.35346897468762704134,1.0760793954203931046 ] 
dist 215=[-.39416399298183592458,1.0697377593556928703 ] 
dist 216=[-.44877977437678393678,1.0662254261426331752 ] 
dist 217=[-.50249758747559063098,.98558020924766954965] 
dist 218=[-.53961002765044323647,.97005328025409043322] 
dist 219=[-.57158251935204220268,.92987545748071996691] 
dist 220=[-.60479681105718312912,.91697386666936466803] 
dist 221=[-.63617135688667297845,.84044957211254928817] 
dist 222=[-.66080435132237077007,.9550519510622411051 ] 
dist 223=[-.68515528016702491777,1.0308336068472015534 ] 
dist 224=[-.71540271396404086993,1.0845286290517442734 ] 
dist 225=[-.74274092542297243181,1.1219660736478159059 ] 
dist 226=[-.75548696498347531885,1.1491773732426637777 ] 
dist 227=[-.76097512269258233758,1.1620793945369040761 ] 
dist 228=[-.76072496358287621147,1.1669462932888730950 ] 
dist 229=[-.7455277944952912224 ,1.1953815830312475483 ] 
dist 230=[-.8784049817164780559 ,1.3147499247956190186 ] 
dist 231=[-.97409548840715552007,1.3828396936252977670 ] 
dist 232=[-1.0468075406561511760 ,1.4262902793807592889 ] 
dist 233=[-1.1069572752485142811 ,1.4473667758841400519 ] 
dist 234=[-1.1542783863070443598 ,1.4588844252097470923 ] 
dist 235=[-1.1758160462053607292 ,1.4642014017997387167 ] 
dist 236=[-1.1858688171321271037 ,1.4659888338643913526 ] 
dist 237=[-1.1873768072995169485 ,1.4634233492599274389 ] 
dist 238=[-1.1532994589396184746 ,1.2151209333968665426 ] 
dist 239=[-1.1430021806515000126 ,1.1784045832246717904 ] 
dist 240=[-1.1209831965201022857 ,1.1122148187564971656 ] 
dist 241=[-1.1121242728300622483 ,1.0946489897168934404 ] 
dist 242=[-1.0646801847741416642 ,1.0340578599569361756 ] 
dist 243=[-1.0529631818152086611 ,1.0158615348807641667 ] 
dist 244=[-1.0146987737784876868 ,.99587346409741564195] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 1, 1, 2, 1, 2] 
dist 0=[44.933325617589759212  ,44.933325617589759212  ] 
dist 1=[43.515694467812893947  ,46.131221970132763169  ] 
dist 2=[41.663701418217986932  ,47.106343807479893075  ] 
dist 3=[38.731221590385297686  ,47.634538353352154268  ] 
dist 4=[35.739993363504075119  ,47.937065393332311328  ] 
dist 5=[33.653239843999953738  ,48.011571839158766258  ] 
dist 6=[31.825767221842835629  ,48.001519358240875152  ] 
dist 7=[29.869490667428959629  ,47.966475244377887696  ] 
dist 8=[27.974778247272110981  ,47.906738391712851592  ] 
dist 9=[26.392792906531544861  ,47.686451280929132139  ] 
dist 10=[24.732379443055682175  ,47.616759875767599145  ] 
dist 11=[22.523851877720566779  ,47.563743936365076763  ] 
dist 12=[20.339467914641625357  ,47.518783697349538705  ] 
dist 13=[18.775134272090286607  ,47.481190870358632248  ] 
dist 14=[17.359191219762190807  ,47.457401663969414127  ] 
dist 15=[15.767011475287056209  ,47.357106767605463407  ] 
dist 16=[14.173471354470403891  ,46.420866161535868221  ] 
dist 17=[12.751486171919941360  ,33.902068690621884592  ] 
dist 18=[11.174032350826007507  ,32.786148718511771050  ] 
dist 19=[8.9582049150976694120 ,30.228188569474505216  ] 
dist 20=[6.7747425739629914880 ,29.751241589930141302  ] 
dist 21=[5.3265078227374838814 ,26.466055567448688825  ] 
dist 22=[4.1296319608920206179 ,25.874544647434757452  ] 
dist 23=[2.9513015522791189547 ,24.822621863958933750  ] 
dist 24=[1.8654392972543076448 ,24.588602992148987030  ] 
dist 25=[1.0383502445374106051 ,21.066203655910272626  ] 
dist 26=[.2368758579837247481 ,20.587371218729133525  ] 
dist 27=[-.74649088888843413105,19.176700660366161538  ] 
dist 28=[-1.6859121797432756141 ,13.578755405538695697  ] 
dist 29=[-2.3116516518805098467 ,12.948522160341959667  ] 
dist 30=[-2.8314050384542148414 ,12.602992921936337907  ] 
dist 31=[-3.4964415521244634344 ,10.996338243731309992  ] 
dist 32=[-4.8525880278565031528 ,7.7062675632948527929 ] 
dist 33=[-6.1682038238536655565 ,2.0231853140363453447 ] 
dist 34=[-7.3632731516526606571 ,2.4837976982452766625 ] 
dist 35=[-8.2378278104962525690 ,3.2189827802633313882 ] 
dist 36=[-9.0486571083286177715 ,3.9541784563541169403 ] 
dist 37=[-9.9892069064270213547 ,4.4150243351317696962 ] 
dist 38=[-10.857308118379357312  ,4.7596321028210387327 ] 
dist 39=[-11.378733144162923203  ,5.0317679407931277250 ] 
dist 40=[-11.748485203413338339  ,5.2451281421673215805 ] 
dist 41=[-12.010668219365779741  ,5.3555803927093475560 ] 
dist 42=[-12.190267687366785494  ,5.4106706069540606923 ] 
dist 43=[-12.230100228811040982  ,5.4144146720143143592 ] 
dist 44=[-12.220126292688073782  ,4.9397296776060618394 ] 
dist 45=[-12.200619592905306698  ,4.8493947305677040198 ] 
dist 46=[-4.5387039916077708200 ,4.7212797986956715764 ] 
dist 47=[-4.4579837704658218443 ,4.6706552023536011222 ] 
dist 48=[-4.1150572755426514940 ,4.5326929258309291219 ] 
dist 49=[-4.0398287142208218812 ,4.4758715912136895686 ] 
dist 50=[-3.8441872369578915651 ,5.2476661948002916454 ] 
dist 51=[-3.7949611367411524371 ,5.8121639568948981270 ] 
dist 52=[-.51099469459147397351,6.2770532623416961030 ] 
dist 53=[-.21689665418654240578,6.7276487479915967851 ] 
dist 54=[.44914722479825909242,7.1222524926987697893 ] 
dist 55=[.5596400068223701116 ,7.3637324896414755913 ] 
dist 56=[1.3494950234515467377 ,7.5396288643713595684 ] 
dist 57=[1.4794048867367877372 ,7.6724171201632688915 ] 
dist 58=[1.7102320702222288172 ,7.7676801688255154697 ] 
dist 59=[1.7544216262367043863 ,7.7937810838842070715 ] 
dist 60=[2.2199953233047902359 ,7.7756480346744709833 ] 
dist 61=[2.2823406420372850260 ,7.7544754476607937784 ] 
dist 62=[1.9949860206274586786 ,3.3359798435719198426 ] 
dist 63=[1.1182645837692212284 ,3.2202955665844323144 ] 
dist 64=[.3670708672344980919 ,3.2818759249522964024 ] 
dist 65=[-.40667777745679562889,3.3014652848792704647 ] 
dist 66=[-1.1334986554053454486 ,3.2996244450398824730 ] 
dist 67=[-1.6975338162402361430 ,3.2889548971363106386 ] 
dist 68=[-2.2490698064584351622 ,2.3529535804382255965 ] 
dist 69=[-2.9260585702897889387 ,2.2540582481830781666 ] 
dist 70=[-3.5631701195974886435 ,1.9985368375120993985 ] 
dist 71=[-3.9556496604384498852 ,1.9585584344211957449 ] 
dist 72=[-4.2432538631371521193 ,1.5315559368275957013 ] 
dist 73=[-4.4620322252231980377 ,1.4480765711088740435 ] 
dist 74=[-4.6295482333706110182 ,1.3509243171903539772 ] 
dist 75=[-4.7126796006623412803 ,1.3246438145758298405 ] 
dist 76=[-4.7497759760003659892 ,.52920561180654636655] 
dist 77=[-4.7505000016279735576 ,.43048136436515159861] 
dist 78=[-1.6258736831031664624 ,.21886337021638316921] 
dist 79=[-1.7028589622223984472 ,.16911645590955495379] 
dist 80=[-1.7659416136607361687 ,-.04861310049588045605] 
dist 81=[-1.7994533164656580624 ,.01682668449401084314] 
dist 82=[-1.8175465266364738721 ,.33751125789878340257] 
dist 83=[-1.8190981732478829963 ,.58596285696352925884] 
dist 84=[-.99643623002157477382,.82840544863194525606] 
dist 85=[-1.1470739399778218986 ,1.1251582835651546512 ] 
dist 86=[-1.2809312770881197829 ,1.4038779025402970465 ] 
dist 87=[-1.4267922026603050910 ,1.5744152627257241449 ] 
dist 88=[-1.5690696968665062445 ,1.6979973865792737407 ] 
dist 89=[-1.6886077754594603481 ,1.7894609102498263337 ] 
dist 90=[-1.8142483517700071370 ,1.8593353734834093915 ] 
dist 91=[-1.9808476355945851366 ,1.8967980161302503568 ] 
dist 92=[-2.1439820869003409506 ,2.0908169698291902698 ] 
dist 93=[-2.2557832867095880981 ,2.3734676315127708132 ] 
dist 94=[-2.3511872168086537952 ,2.6429702399274972378 ] 
dist 95=[-2.4488804385271506292 ,2.7997866775085746667 ] 
dist 96=[-2.5402601523500244933 ,2.9040825301060218996 ] 
dist 97=[-2.6104543515723471824 ,2.9640277689529162920 ] 
dist 98=[-2.6783265602949300681 ,3.0019376750313656541 ] 
dist 99=[-2.7604021650033420690 ,3.0182944164475021186 ] 
dist 100=[-2.8328728852129249885 ,3.0220750454451066948 ] 
dist 101=[-2.8624246607367139996 ,3.0130288091534889739 ] 
dist 102=[-2.8705588621095892282 ,3.0843785050254894989 ] 
dist 103=[-2.8650269280776322209 ,3.3141642502319349095 ] 
dist 104=[-2.7936054061184876255 ,3.4983312430222866184 ] 
dist 105=[-2.7680192970613337184 ,3.5930559364885213681 ] 
dist 106=[-2.7198764453110517193 ,3.6423341380399170077 ] 
dist 107=[-2.7011993617926636703 ,3.6507172604858815906 ] 
dist 108=[-2.2253193024512792092 ,3.5173135084724461610 ] 
dist 109=[-2.1529648510377976644 ,3.4813089161715355284 ] 
dist 110=[-1.9907376787455178838 ,3.4387172415154084205 ] 
dist 111=[-1.9405719563567985677 ,3.4147498214159560573 ] 
dist 112=[-1.7166341847195191638 ,3.3514554829526259799 ] 
dist 113=[-1.6863883993727346088 ,3.3224793605743201106 ] 
dist 114=[-1.9622558344521486368 ,3.2710255273596824340 ] 
dist 115=[-2.1492289859003444436 ,3.2510563730254263205 ] 
dist 116=[-2.3065942551707661104 ,-.18378444215282234371] 
dist 117=[-2.4643502326995763822 ,-.43772534203412612472] 
dist 118=[-2.6033322621029676462 ,-1.0155350853381326025 ] 
dist 119=[-2.6858012872210278957 ,-1.1059244510976137445 ] 
dist 120=[-2.7425519810341581221 ,-1.7938560786188123028 ] 
dist 121=[-2.7789287270859937554 ,-1.9055721335751669725 ] 
dist 122=[-2.7993749691210842905 ,-1.9247044582478243180 ] 
dist 123=[-2.7993365497229038742 ,-1.7034795425736278918 ] 
dist 124=[-2.8258771476720155091 ,-1.4090114941393777942 ] 
dist 125=[-2.9603828148211883709 ,-.93833484782156056017] 
dist 126=[-3.0576521630736289337 ,-.45998403014251792291] 
dist 127=[-3.1292746464682026304 ,-.13490011761964997454] 
dist 128=[-3.1787713887456668499 ,.13955991579192319546] 
dist 129=[-3.1877759324986922100 ,.41596314155441638552] 
dist 130=[-3.1809798571978958419 ,.67182859698828862419] 
dist 131=[-3.1674483252776960046 ,.86436001606710133317] 
dist 132=[-1.7590104351496774667 ,1.0470119378023163089 ] 
dist 133=[-1.6305153967528780959 ,1.2634669041852027638 ] 
dist 134=[-1.3129544113181656204 ,1.4652426591899517701 ] 
dist 135=[-1.2648046553169299118 ,1.5893368273595628590 ] 
dist 136=[-.78593435792539426906,1.6800666036444806141 ] 
dist 137=[-.69681585062435631681,1.7487460108701753358 ] 
dist 138=[-.58702873917581711138,1.8001181536920661987 ] 
dist 139=[-.56106983288730141119,1.8218046667531485587 ] 
dist 140=[.17497218389176024195,1.8289380575726277892 ] 
dist 141=[.26304321809562838084,1.8259505164943241964 ] 
dist 142=[.45729023605653244171,1.4457737279185548864 ] 
dist 143=[.49169335739829111511,1.5378819526343386619 ] 
dist 144=[.40486707659783402945,1.6132501355885951453 ] 
dist 145=[.27004031652251839423,1.6533105214282796945 ] 
dist 146=[.14168563634015897795,1.6751139063741344557 ] 
dist 147=[.03916657629471304948,1.6778481142342279284 ] 
dist 148=[-.06386476809373106936,1.1529951106386835715 ] 
dist 149=[-.19426725905134218538,1.1834132805196879050 ] 
dist 150=[-.3190232664396718432 ,1.2407015379998505674 ] 
dist 151=[-.39953209973696069774,1.3057354687679558742 ] 
dist 152=[-.48616809112571286302,1.3706722913981443944 ] 
dist 153=[-.68112708715747459902,1.4275680617227195738 ] 
dist 154=[-.88623668637879709475,1.4893888168890041970 ] 
dist 155=[-1.0820289982372056404 ,1.5739682284498031619 ] 
dist 156=[-1.3081535553079849633 ,1.6579775304535453099 ] 
dist 157=[-1.6342718325460674501 ,1.7175201512755661575 ] 
dist 158=[-1.9532559305313387360 ,1.7704389938470711799 ] 
dist 159=[-2.1509210069655526904 ,1.8280175235519877503 ] 
dist 160=[-2.2972366483017170153 ,1.8840408991338897661 ] 
dist 161=[-2.4113708568302772404 ,1.9307504697131039126 ] 
dist 162=[-2.4994057753231593436 ,1.9794750136926911712 ] 
dist 163=[-2.5416015539718674325 ,2.0435276508720852686 ] 
dist 164=[-2.5595322047456717287 ,2.1030878115792280927 ] 
dist 165=[-2.8178942346345146329 ,2.1338894996474370137 ] 
dist 166=[-3.0655561522109553397 ,2.1494335420838409545 ] 
dist 167=[-3.2734529117465909950 ,2.1481324438467562423 ] 
dist 168=[-3.4394334973066558853 ,2.1361447217164080190 ] 
dist 169=[-3.5198826896942057557 ,2.1282412581442115401 ] 
dist 170=[-3.5607724983548005718 ,2.0832934900196639222 ] 
dist 171=[-3.5689352846940075689 ,2.0765547556132810742 ] 
dist 172=[-3.4892377031777896377 ,1.9021993298625785408 ] 
dist 173=[-3.4609474344879597706 ,1.8701485872120331393 ] 
dist 174=[-3.4100206579544767847 ,1.7730406858830983178 ] 
dist 175=[-3.3896095213072512890 ,1.7578915067300708830 ] 
dist 176=[-3.2838594017333306006 ,1.5430981070687209661 ] 
dist 177=[-3.2536781655159568858 ,1.4965631748569096701 ] 
dist 178=[-3.1576928674560602546 ,1.6463717779292947187 ] 
dist 179=[-3.1307185588509961126 ,1.8178459999067240839 ] 
dist 180=[.73742676558608869463,1.9640292752326707292 ] 
dist 181=[1.0011464370925868322 ,2.1135476069254278498 ] 
dist 182=[1.1931867132612844508 ,2.2465671756810364862 ] 
dist 183=[1.1170760303191976034 ,2.3269323136138943804 ] 
dist 184=[1.0238033440334939703 ,2.4607056597657927885 ] 
dist 185=[.88295503400363669954,2.7073018628170285936 ] 
dist 186=[.72262780910672812548,2.9163581897560277098 ] 
dist 187=[.55164781408118322512,3.1282893428718530780 ] 
dist 188=[.34043260474249369691,3.3159819265449828195 ] 
dist 189=[.01959572012002934107,3.4283463282499883909 ] 
dist 190=[-.30310773906211219602,3.5068438220838197472 ] 
dist 191=[-.52176949760316027489,3.5594339072943675285 ] 
dist 192=[-.70569722897527028915,3.5912318469419999064 ] 
dist 193=[-.88983757093220474638,3.5926298411130198862 ] 
dist 194=[-1.0596112332028047033 ,3.5694510257364211489 ] 
dist 195=[-1.1862264997923743015 ,3.5498386340420372290 ] 
dist 196=[-1.3052453691921843516 ,1.8015133606565276100 ] 
dist 197=[-1.4447149553212943194 ,1.6422407992463399381 ] 
dist 198=[-1.5727513709201788996 ,1.2607830949932796587 ] 
dist 199=[-1.6461602625437063053 ,1.1966148683126066446 ] 
dist 200=[-1.6934782454384175026 ,.65819941696856317367] 
dist 201=[-1.7174310603903137325 ,.5595936891004874545 ] 
dist 202=[-1.8409711430705837170 ,.41411182855088720868] 
dist 203=[-2.0735391015601893113 ,.37430989537664955193] 
dist 204=[-2.2874293050837756785 ,.13861717288705884847] 
dist 205=[-2.4106660432643257936 ,.3165953222150732205 ] 
dist 206=[-2.4908567797884483725 ,.49570806857360537402] 
dist 207=[-2.5330308061245099530 ,.68616863265153130905] 
dist 208=[-2.5577003643905317281 ,.87737016145005294381] 
dist 209=[-2.5680639981309259321 ,1.0680393373430256760 ] 
dist 210=[-2.5699119995808486316 ,1.2433437920114394138 ] 
dist 211=[-2.5607684867797232834 ,1.3732522420578289454 ] 
dist 212=[-.92383009469566203767,1.4945481634885114100 ] 
dist 213=[-.97695324527687805801,1.6354958594369019888 ] 
dist 214=[-1.0344614094962818474 ,1.7642682842272631821 ] 
dist 215=[-1.0783480276825850206 ,1.8369944330609641297 ] 
dist 216=[-1.1205805477050093064 ,1.8824624419537618291 ] 
dist 217=[-1.1714899650553371524 ,1.9024958262954878290 ] 
dist 218=[-1.2239644297164984442 ,1.9108152828885534186 ] 
dist 219=[-1.2724401599742350280 ,1.9711966153400078345 ] 
dist 220=[-1.3271804184795854843 ,2.1631444072618321871 ] 
dist 221=[-1.4046453273114532683 ,2.2751756407727197711 ] 
dist 222=[-1.4793739714439680652 ,2.3499094835868373206 ] 
dist 223=[-1.5231985534239472492 ,2.3930726407102535058 ] 
dist 224=[-1.5526964087584643043 ,2.4191249582549938374 ] 
dist 225=[-1.6394901132901196618 ,2.4296728832556246393 ] 
dist 226=[-1.7400364139955886774 ,2.5357499917555937876 ] 
dist 227=[-1.8853709833840283014 ,2.5853039857560577335 ] 
dist 228=[-2.0267908312827546351 ,2.6411027149866651019 ] 
dist 229=[-2.1117203112414293801 ,2.9136824838916310588 ] 
dist 230=[-2.1713629046158755947 ,3.1166944583173409772 ] 
dist 231=[-2.2119106195142409561 ,3.2773041462169552365 ] 
dist 232=[-2.2369774718490628951 ,3.4016094512059328572 ] 
dist 233=[-2.2407748191867653260 ,3.4597945651894253460 ] 
dist 234=[-2.2251009515032247974 ,3.4850352723411823093 ] 
dist 235=[-2.2196479003413384222 ,3.4842155961279549494 ] 
dist 236=[-2.0911074520403776500 ,3.2812514606848268301 ] 
dist 237=[-2.0644771280660516219 ,3.2376922738997574002 ] 
dist 238=[-2.0285969908417953445 ,3.1582978604460107629 ] 
dist 239=[-2.0579496318049370586 ,3.1320451861492037021 ] 
dist 240=[-2.0813967143621727463 ,3.0143875659038497893 ] 
dist 241=[-2.0927741861824901845 ,2.9809205163636368175 ] 
dist 242=[-2.0974679530109124626 ,2.8935479976006459239 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 0, 2, 0, 1] 
dist 0=[67.518690916242007609  ,67.518690916242007609  ] 
dist 1=[67.068689100448275544  ,67.752557315157012633  ] 
dist 2=[66.205448125022446643  ,67.752960090777261117  ] 
dist 3=[65.048040552787898460  ,67.623147059889360084  ] 
dist 4=[63.423526510001428495  ,67.488985012311690741  ] 
dist 5=[61.143399623274130824  ,67.015859218316031510  ] 
dist 6=[57.368203514214126376  ,66.763091031617336684  ] 
dist 7=[53.461474195833437682  ,63.322497680320024431  ] 
dist 8=[50.656070583070474773  ,62.643454112200687700  ] 
dist 9=[48.115954601405287157  ,61.699938511479875129  ] 
dist 10=[45.268250643317719765  ,61.356998965429844217  ] 
dist 11=[42.434812768171895370  ,60.863715374248270804  ] 
dist 12=[39.805733312208706664  ,60.649481284217875688  ] 
dist 13=[33.032924561763621853  ,60.485042764028883458  ] 
dist 14=[28.433162771564174221  ,59.376325255597757613  ] 
dist 15=[24.537301484394963234  ,30.348745851963772904  ] 
dist 16=[20.575244821976871137  ,29.090450253815870349  ] 
dist 17=[16.866992965015220789  ,26.553611907507349925  ] 
dist 18=[13.984644565035687679  ,25.903504671396372509  ] 
dist 19=[11.151291029545347357  ,23.610415603027415194  ] 
dist 20=[7.6388125733283067516 ,23.122071631523427247  ] 
dist 21=[4.2956632140468305095 ,22.460179450870433468  ] 
dist 22=[2.1384360740775947740 ,22.258879987761600269  ] 
dist 23=[.4342605395170436484 ,5.4180481863991368320 ] 
dist 24=[-1.1000006909495156800 ,4.0290309238260451808 ] 
dist 25=[-2.7475925228181721700 ,.98875581161198815932] 
dist 26=[-4.2465061954794082848 ,.43363162132677585994] 
dist 27=[-5.8895149712187433114 ,-2.7403870865538426378 ] 
dist 28=[-7.4894245184620027510 ,-2.8480739990937701350 ] 
dist 29=[-9.0005151110849652847 ,-4.5372390129805025190 ] 
dist 30=[-10.793511523400288136  ,-4.7804317883382759710 ] 
dist 31=[-12.468428055415930578  ,-6.3276195505771101429 ] 
dist 32=[-13.507813890646217780  ,-6.5630835827042690391 ] 
dist 33=[-14.284849358872017701  ,-6.5456783610145715374 ] 
dist 34=[-14.911658798646116435  ,-6.1847608499003333744 ] 
dist 35=[-15.397305555920434761  ,-5.6359013336123628217 ] 
dist 36=[-15.610422955156052218  ,-4.8680563966677428087 ] 
dist 37=[-15.698231409195267745  ,-3.7958875716945569535 ] 
dist 38=[-15.683142070831077045  ,-2.0323774974845640530 ] 
dist 39=[-7.5108161106924455674 ,-.2160737412724275179 ] 
dist 40=[-7.4736864428888906308 ,1.2092529326506104827 ] 
dist 41=[-7.0076884549658316727 ,2.3889234662257334983 ] 
dist 42=[-6.8961900530124724757 ,3.5386763725010711262 ] 
dist 43=[-6.7775849828261382402 ,4.5789622072211978332 ] 
dist 44=[-6.7176412596806664255 ,5.3220591880510445597 ] 
dist 45=[-5.5213037730134049401 ,5.9888726905205859527 ] 
dist 46=[-5.4779382761894456742 ,6.7249942854406772459 ] 
dist 47=[-4.4893414189900298492 ,7.3926253226714796941 ] 
dist 48=[-4.3713792574491497037 ,7.7862266412487500775 ] 
dist 49=[-3.6931703280950458936 ,8.0543830746759882923 ] 
dist 50=[-3.5564097162216180300 ,8.2214804787845400258 ] 
dist 51=[-3.2867087646378416583 ,8.3231951607261465436 ] 
dist 52=[-3.2117571524899174173 ,8.3329264681262435866 ] 
dist 53=[-2.1472418707456187607 ,8.2989610424606044855 ] 
dist 54=[-1.9946095328759316808 ,8.3684478646331339690 ] 
dist 55=[-1.6162964186370742622 ,8.3897044872128407548 ] 
dist 56=[-1.5536168134536520588 ,8.3805335806039577079 ] 
dist 57=[-.9745059406981853028 ,8.2309766314963038102 ] 
dist 58=[-1.7546336028554566556 ,8.1749023985131595637 ] 
dist 59=[-2.4667480116209643595 ,7.9995984928060746566 ] 
dist 60=[-2.9845734743327258451 ,7.9228057869188191401 ] 
dist 61=[-3.4579186519386346269 ,6.0500524849849688355 ] 
dist 62=[-3.9926736119436604714 ,6.0490429663502579121 ] 
dist 63=[-4.4843285785421248978 ,.54009833839670480303] 
dist 64=[-4.7857872373902983046 ,.30484731931041581192] 
dist 65=[-5.0049876499167140124 ,-.22466020912175238562] 
dist 66=[-5.1685592384361172902 ,-.32052596286811839656] 
dist 67=[-5.2835063248626776371 ,-.94383659872644718302] 
dist 68=[-5.3108197604122031323 ,-1.0476814147210503147 ] 
dist 69=[-5.3042044817522358578 ,-1.0179727814366556742 ] 
dist 70=[-5.3001089457153407220 ,-.8648184445820967367 ] 
dist 71=[-4.0204265905192955024 ,-.69689627082793994788] 
dist 72=[-4.1566126843931085781 ,-.5747171016630372971 ] 
dist 73=[-4.2585568123888016740 ,-.3978611534398500091 ] 
dist 74=[-4.3404473264718530390 ,.0645023936321060366 ] 
dist 75=[-4.4031975291264810742 ,.4952374220627357353 ] 
dist 76=[-4.4287458409544460379 ,.8230035259159543754 ] 
dist 77=[-4.4319411434043883042 ,1.1371897878597851571 ] 
dist 78=[-4.4193041870766251454 ,1.5138106402055306116 ] 
dist 79=[-1.6828193937408997720 ,1.8672171211940975208 ] 
dist 80=[-1.4533240508836670108 ,2.0888281471977451787 ] 
dist 81=[-.92695213894653352322,2.2557837610856856715 ] 
dist 82=[-.82863099606061490334,2.3911932532389870022 ] 
dist 83=[-.2183695079499823993 ,2.4958336640665217854 ] 
dist 84=[-.2690516996267934241 ,2.5400814590677866247 ] 
dist 85=[-.3382421982673372956 ,2.5590100455330244738 ] 
dist 86=[-.4499218503317746118 ,2.5626478294280864875 ] 
dist 87=[-.56270990197183057932,2.1378447389804090582 ] 
dist 88=[-.63630809233043009498,2.3875451335886406960 ] 
dist 89=[-.69459406191566901083,2.5753228153996639314 ] 
dist 90=[-.74639134835889550246,2.7269480098131802160 ] 
dist 91=[-.78934595046870314913,2.8447297723399834354 ] 
dist 92=[-.81239438050920638269,2.8975345584346530279 ] 
dist 93=[-.82489107952616326066,2.9208309003919813340 ] 
dist 94=[-.82631637035973075382,2.9209121983683295628 ] 
dist 95=[-.82123098045459919324,.7283940094913605395 ] 
dist 96=[-.81603830040654867828,.69102452973498387477] 
dist 97=[-.84769050660686747628,.6510705218412663993 ] 
dist 98=[-1.0079669369893738859 ,.64322960286005075236] 
dist 99=[-1.1599226179581776482 ,.56717673189439189464] 
dist 100=[-1.2803065023450839863 ,.55126962412688256272] 
dist 101=[-1.4004630002650742477 ,.53005068853931943921] 
dist 102=[-1.5515640886832258056 ,.52253831131375477041] 
dist 103=[-1.6946692418801505378 ,.2631676478241106046 ] 
dist 104=[-1.8799419927368404551 ,.23243599925315550505] 
dist 105=[-2.0500315437035495907 ,.17130177747040066256] 
dist 106=[-2.2181301259783303812 ,.15563201231620685737] 
dist 107=[-2.3718437628535627425 ,.10082380406618442795] 
dist 108=[-2.4845374181470254132 ,.08860411926076293469] 
dist 109=[-2.5886334878287059088 ,.07303015484591127615] 
dist 110=[-2.7080417770287237435 ,.06790273112658729845] 
dist 111=[-2.8164423410659405228 ,.06686924940765630751] 
dist 112=[-2.8766169326710210532 ,.07244760038507204188] 
dist 113=[-2.9129119859420765206 ,.08384568144783343514] 
dist 114=[-2.9260323729185152662 ,.10604817550849861384] 
dist 115=[-2.9232183539238111563 ,.13822866459300650018] 
dist 116=[-2.9168366472287242577 ,.56195935079217242257] 
dist 117=[-2.8672217541733170276 ,1.0702425883330927700 ] 
dist 118=[-2.8587262228241057233 ,1.8255186767331946876 ] 
dist 119=[-2.6482484997413721582 ,2.5747776760808580479 ] 
dist 120=[-2.6040338160064859945 ,3.0590632295097874710 ] 
dist 121=[-2.5054202222494581081 ,3.4410974952157042031 ] 
dist 122=[-2.4716660252951402339 ,3.7824611382535283613 ] 
dist 123=[-2.3083958011380574567 ,4.0708057562490896791 ] 
dist 124=[-2.2712852777291919763 ,4.2413414241058209075 ] 
dist 125=[-2.1688148179096839029 ,4.3579525378482179171 ] 
dist 126=[-2.1429516144058525088 ,4.4311903283185316624 ] 
dist 127=[-1.8231132376031867885 ,4.4781087136055708017 ] 
dist 128=[-1.7683761803134380802 ,4.4897271440099796700 ] 
dist 129=[-1.6348822310991801642 ,4.4777335242476544063 ] 
dist 130=[-1.6010868287577547699 ,4.4650157774431912700 ] 
dist 131=[-1.3878859585690976576 ,4.3665059486873085400 ] 
dist 132=[-1.3432387524060704130 ,4.3357143636637253940 ] 
dist 133=[-1.2596742064748180485 ,4.2191605947339820404 ] 
dist 134=[-1.2368733931332615380 ,4.1935073527964956910 ] 
dist 135=[-1.2819436232409849846 ,.2921691812677199941 ] 
dist 136=[-1.7615135739876495343 ,.2837206974442192740 ] 
dist 137=[-2.1485993578537434275 ,.2675875435543932112 ] 
dist 138=[-2.5928115844591437580 ,.2632346768679950447 ] 
dist 139=[-3.0485577253261513846 ,.2473199621229914800 ] 
dist 140=[-3.3599224497152761532 ,.2432173986752691231 ] 
dist 141=[-3.6245393068038852897 ,.2363628957604913500 ] 
dist 142=[-3.8938103091641185262 ,.2343008464464933914 ] 
dist 143=[-4.1324211714424959625 ,.22750619270198258142] 
dist 144=[-4.2747333418580715903 ,.22551444794788150917] 
dist 145=[-4.3734886528765366616 ,.22458863509123514029] 
dist 146=[-4.4383450343616382216 ,.22479315844607472476] 
dist 147=[-4.4763036117194084711 ,.2256338986280542029 ] 
dist 148=[-4.4779108222712012710 ,.22725095917309579   ] 
dist 149=[-4.4442020331297535025 ,.22970073024324732114] 
dist 150=[-4.4222671028858601175 ,.23386578831387986086] 
dist 151=[-2.2550520124675576777 ,.2382845109469974488 ] 
dist 152=[-2.0561440359025586124 ,.43667323957784499991] 
dist 153=[-1.5822043094620886446 ,.84075694809068290475] 
dist 154=[-1.5000484867841054749 ,1.2465973107130210925 ] 
dist 155=[-.83779073187372465364,1.6214609378343527008 ] 
dist 156=[-.7165326992730357998 ,1.9019785533088972064 ] 
dist 157=[-.6305935938243362603 ,2.1665145503134891276 ] 
dist 158=[-.6238037691123449333 ,2.4776261610593396628 ] 
dist 159=[.25121188886823652534,2.7640496540365227465 ] 
dist 160=[.27192674606642293168,2.9301057512133856109 ] 
dist 161=[.26488639689213951605,3.0394389637318176640 ] 
dist 162=[.24888102881761534856,3.0995991771379646870 ] 
dist 163=[.22839595993281475507,3.1371265672723959087 ] 
dist 164=[.20348375245618056229,3.1561782196968073990 ] 
dist 165=[.17061589017969387212,3.1653002001681791739 ] 
dist 166=[.11839325979583588599,3.1632161138783918931 ] 
dist 167=[.00308221753847125965,1.0002015694994765492 ] 
dist 168=[-.34384386304672441562,1.0569569231911311001 ] 
dist 169=[-.64872044380414401661,1.1005034141552084868 ] 
dist 170=[-.95989233088041474478,1.1372955307119213347 ] 
dist 171=[-1.2505131772898761863 ,1.1668462178488015785 ] 
dist 172=[-1.4734130096914453819 ,1.1815033699807383664 ] 
dist 173=[-1.6889394882669784412 ,1.1880261900617399002 ] 
dist 174=[-1.9501502556524269188 ,1.2395182678091844856 ] 
dist 175=[-2.1943777330451031274 ,1.3461244259107033149 ] 
dist 176=[-2.3421586823173631735 ,1.4330907908572673851 ] 
dist 177=[-2.4472991972982865780 ,1.5221564508130628174 ] 
dist 178=[-2.5214341587091887308 ,1.6371317574004072820 ] 
dist 179=[-2.5736474547466303707 ,1.7596697353866069473 ] 
dist 180=[-2.5913398504138869189 ,1.8788995284536048678 ] 
dist 181=[-2.5924041837548918748 ,2.0182862658428599275 ] 
dist 182=[-2.6442825547072483766 ,2.2212253217637572937 ] 
dist 183=[-3.1334852106434418599 ,2.4191952749641451021 ] 
dist 184=[-3.4355286562614416986 ,2.5387588688245899406 ] 
dist 185=[-3.6577608461914878990 ,2.6235239763596701052 ] 
dist 186=[-3.8285823862033381215 ,2.6826836387429515750 ] 
dist 187=[-3.9590639009823152902 ,2.7208450697713712624 ] 
dist 188=[-4.0203708788818434874 ,2.7285395747674431258 ] 
dist 189=[-4.0447382588092222027 ,2.7125539010403060958 ] 
dist 190=[-4.0441390285887033719 ,2.7096357883178802814 ] 
dist 191=[-3.7455783919491111886 ,2.5391355873619154032 ] 
dist 192=[-3.6876654779300775564 ,2.5043434575572700713 ] 
dist 193=[-3.5827801998608979196 ,2.4081630457848429596 ] 
dist 194=[-3.5498343287878408180 ,2.3798494195159237380 ] 
dist 195=[-3.4096973148171137683 ,2.1778083109622328689 ] 
dist 196=[-3.3691692701885818870 ,2.1310014641325369329 ] 
dist 197=[-3.2732839486025247573 ,2.0518332806122255333 ] 
dist 198=[-3.2369784001992272830 ,2.0310111293752870168 ] 
dist 199=[.1397264961384473120 ,.8631314885402286106 ] 
dist 200=[.1067355413823440400 ,.9170791111118226112 ] 
dist 201=[.0736387162155107015 ,.9578359284860529176 ] 
dist 202=[.0318409845166891873 ,.9911317512673442812 ] 
dist 203=[-.0122317013894560261 ,1.0407552407636590775 ] 
dist 204=[-.05439962326029664266,1.1476020701185489790 ] 
dist 205=[-.10314329075820273264,1.2361787812495648626 ] 
dist 206=[-.17344026255932913291,1.3227425151498462920 ] 
dist 207=[-.24337416390902720205,1.3991531102152696727 ] 
dist 208=[-.29066876844323074132,1.4472275611518111821 ] 
dist 209=[-.33031448276194179341,1.4836629924293530826 ] 
dist 210=[-.369741039388875965  ,1.5136417546053151001 ] 
dist 211=[-.40588308038570428004,1.5371047662535514169 ] 
dist 212=[-.4324284293404526644 ,1.5475464329696439605 ] 
dist 213=[-.4569571765013004935 ,1.5504253205490975327 ] 
dist 214=[-.4850555360524562548 ,1.5463785078008604410 ] 
dist 215=[-.5104710022161886209 ,.62666107905385139736] 
dist 216=[-.5242989417757156210 ,.55006473004935932921] 
dist 217=[-.5322482813622458438 ,.36833955560707471516] 
dist 218=[-.5342171670134405252 ,.33888746738081522212] 
dist 219=[-.5331954101784666596 ,.11012538895142800497] 
dist 220=[-.5311784812908100429 ,.15657059139070428152] 
dist 221=[-.5242286697052118997 ,.21315105549002313838] 
dist 222=[-.52085310098407871087,.29820530461195254589] 
dist 223=[-.5829878533688428511 ,.40021091953598814313] 
dist 224=[-.66356219397019131345,.49069981815320376444] 
dist 225=[-.72447603652444021448,.56641151438707322423] 
dist 226=[-.77430032684311508198,.64152451461153603794] 
dist 227=[-.81406275012383972343,.71030913380335990526] 
dist 228=[-.83484025368962118486,.76077713761742797666] 
dist 229=[-.84564707437766298286,.80738558900657284105] 
dist 230=[-.84752658966890371712,.8607744146101193869 ] 
dist 231=[-.56271825729838537463,.9091164549548249791 ] 
dist 232=[-.55806793135909137697,.9355934517134729176 ] 
dist 233=[-.54568671897183207891,.9510674629931506246 ] 
dist 234=[-.54041434958899509341,.9555191405363200949 ] 
dist 235=[-.51132366812372195844,.9546492931087216711 ] 
dist 236=[-.50398882058717732693,.9512052307599272965 ] 
dist 237=[-.48764773659569637988,.9408721888615945181 ] 
dist 238=[-.48190563909359020852,.9348749182937492277 ] 
dist 239=[-.6111385469835854644 ,.8173255504804298055 ] 
dist 240=[-.75895270177947358731,.7979417502876574384 ] 
dist 241=[-.87687109756596018863,.86524666695675497738] 
dist 242=[-.9844903164076440017 ,.9450171952143511384 ] 
dist 243=[-1.0769953782785159655 ,1.0134688739162986138 ] 
dist 244=[-1.1346214027622518433 ,1.0559271322969471124 ] 
dist 245=[-1.1776202136376640153 ,1.0874002473866574391 ] 
dist 246=[-1.2117751957781987686 ,1.1120284675138281732 ] 
dist 247=[-1.2383171396700825548 ,1.1299148507763137100 ] 
dist 248=[-1.2509463209668926896 ,1.1344931109777859043 ] 
dist 249=[-1.2557753237974537293 ,1.1329212638046237398 ] 
dist 250=[-1.2537031069067427271 ,1.1285451256012146238 ] 
dist 251=[-1.2409378424246909483 ,1.0919365367366561149 ] 
dist 252=[-1.2351953581535493638 ,1.0804427593423882529 ] 
dist 253=[-1.2066513832983380516 ,1.0309508596201519568 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 2, 2, 1, 2] 
dist 0=[62.626004539083767534  ,62.626004539083767534  ] 
dist 1=[62.375809511439028664  ,62.956829627948748856  ] 
dist 2=[61.722515519615366938  ,63.255443931204469302  ] 
dist 3=[60.573147168043594655  ,63.377001332627445157  ] 
dist 4=[58.607175842562555838  ,63.391943436779385580  ] 
dist 5=[56.263150330666248827  ,63.299319833960725450  ] 
dist 6=[53.604238164631213591  ,63.055778395979307193  ] 
dist 7=[50.201237725449397257  ,62.903971561496765905  ] 
dist 8=[44.886141614494507046  ,62.417432634869391304  ] 
dist 9=[39.493246098622787100  ,62.176148191832011900  ] 
dist 10=[35.779497495642201070  ,60.786042731029131569  ] 
dist 11=[32.578682806530845639  ,60.366125880653261478  ] 
dist 12=[29.233571729096400562  ,60.056822298937512387  ] 
dist 13=[26.044250586031252095  ,59.108861401872854795  ] 
dist 14=[23.465186318652018570  ,53.120440379166017441  ] 
dist 15=[20.833523178783425477  ,49.216185240368308033  ] 
dist 16=[17.433588798455473197  ,32.354047935180614228  ] 
dist 17=[14.122019313200719645  ,30.181848304820064217  ] 
dist 18=[11.842876569419881917  ,25.168683367019111860  ] 
dist 19=[9.8767396697747367073 ,24.328799700913480665  ] 
dist 20=[7.8146347206219750749 ,17.891083310729027303  ] 
dist 21=[5.8386004175065471546 ,16.760212349261993217  ] 
dist 22=[4.2155408863314897857 ,14.956177634352289120  ] 
dist 23=[2.5316723861238601933 ,14.528935928994365584  ] 
dist 24=[.31140037850377224629,12.747261454208940906  ] 
dist 25=[-1.8249638388523219642 ,12.556027134914011863  ] 
dist 26=[-3.1738591403528150898 ,5.4469712317218350663 ] 
dist 27=[-4.7615439766095020779 ,5.0983183627758307341 ] 
dist 28=[-6.5445674643489936018 ,4.1109684708079071612 ] 
dist 29=[-8.2495528548540222109 ,1.6016268276474850375 ] 
dist 30=[-9.7827698809903238877 ,1.2823863403227234789 ] 
dist 31=[-11.393073467313796885  ,-.19667358360972726307] 
dist 32=[-13.364236245057678103  ,-4.2947783044538009171 ] 
dist 33=[-14.551461515805544272  ,-4.4244570726659656543 ] 
dist 34=[-15.399956728916888020  ,-4.7155622378051844203 ] 
dist 35=[-16.017483632535718689  ,-4.6453394442334427040 ] 
dist 36=[-16.475586218075603384  ,-4.4109596165456685444 ] 
dist 37=[-16.686792520693354112  ,-3.8956851328921820543 ] 
dist 38=[-16.761336313307463029  ,-3.2426788055447504125 ] 
dist 39=[-16.757563020666868784  ,-2.4581975633030479677 ] 
dist 40=[-15.455996603451182715  ,-1.4288033699438039239 ] 
dist 41=[-15.253878482950912391  ,.20197392905875965154] 
dist 42=[-14.779786096202654282  ,2.5870487045541673345 ] 
dist 43=[-14.643193999640972890  ,4.4367413409431518079 ] 
dist 44=[-14.065882781338645344  ,5.9872772540702767640 ] 
dist 45=[-13.911358935800525371  ,7.5326126816999659633 ] 
dist 46=[-13.547219981050503542  ,8.9546707107438315528 ] 
dist 47=[-13.414667680571551454  ,10.013437735622198292  ] 
dist 48=[-3.9682707493185569391 ,11.008220565540107933  ] 
dist 49=[-3.1257389901231710938 ,12.175136351650857519  ] 
dist 50=[-1.2745354058375681266 ,13.250231734751652989  ] 
dist 51=[-.88806994594084202819,13.878679706804402015  ] 
dist 52=[1.1950288922141256880 ,14.300375810298904785  ] 
dist 53=[1.4417928917879337690 ,14.550466394531562961  ] 
dist 54=[1.2783090361383360276 ,14.700696711907856184  ] 
dist 55=[1.0253581868660174970 ,14.723786664955533900  ] 
dist 56=[.58549128971032797905,14.679387192697522634  ] 
dist 57=[.13239914351576397708,14.625425604638378237  ] 
dist 58=[-.29591240480511086496,13.115203998669424410  ] 
dist 59=[-.67652489119468727405,12.874224452232709020  ] 
dist 60=[-1.0573805813514087584 ,12.224928103892684739  ] 
dist 61=[-1.4080524434226278887 ,12.078559895221908409  ] 
dist 62=[-1.6683051323141386121 ,10.832792870637613625  ] 
dist 63=[-1.9115527642297907723 ,10.099377623542717383  ] 
dist 64=[-2.1944336298148162024 ,-.80638149134570665293] 
dist 65=[-2.8120799167589001839 ,-.8823579239050325904 ] 
dist 66=[-3.4424328267370849247 ,-1.2004040523975155162 ] 
dist 67=[-3.8415680291905138714 ,-1.1731413929770575528 ] 
dist 68=[-4.1470250610878063358 ,-1.0874685247125162280 ] 
dist 69=[-4.4036789201718990961 ,-.97114009357397408085] 
dist 70=[-4.6087409155801313350 ,-.82161628858599455921] 
dist 71=[-4.7083858166573493887 ,-.6195831336094404589 ] 
dist 72=[-4.7556661918808491624 ,-.29383671964685542586] 
dist 73=[-4.7584129785981294010 ,.13438760240995071666] 
dist 74=[-2.0916496720591781267 ,.46182921863940135955] 
dist 75=[-1.8923533457465943065 ,.7309148390270609088 ] 
dist 76=[-1.8582656824449306995 ,.9896134571569099095 ] 
dist 77=[-1.5119851227637251863 ,1.2209247126445099043 ] 
dist 78=[-1.4423467279659226353 ,1.3807839787126819591 ] 
dist 79=[-1.3567101847984602124 ,1.5184488245353583664 ] 
dist 80=[-1.3262978922315854963 ,1.6612408007000136533 ] 
dist 81=[-.64004864761465903382,1.7894550598143124133 ] 
dist 82=[-.55211585237514546659,1.8689840587621815993 ] 
dist 83=[-.36079608001137182175,1.9278473625324213285 ] 
dist 84=[-.3154753441434390476 ,1.9736551725182553538 ] 
dist 85=[-.21834585628272359511,2.0211202070208698263 ] 
dist 86=[-.20356865630971006859,2.0757113982804620994 ] 
dist 87=[-.17429979027665026922,2.0962924295458847842 ] 
dist 88=[-.16670868485961192639,2.1006585659258544636 ] 
dist 89=[-.14082289194104926778,2.0947407325258382624 ] 
dist 90=[-.1380090950146836826 ,1.1746254602642360885 ] 
dist 91=[-.14220690877773655901,1.0923624423467383907 ] 
dist 92=[-.1566698771146447056 ,.88584897841167293023] 
dist 93=[-.2467992634831602534 ,.85576108418584270876] 
dist 94=[-.3798350926510095751 ,.5983363868967580337 ] 
dist 95=[-.5064470065099450629 ,.5548592701945630148 ] 
dist 96=[-.65693956766704134705,.4862802073022383052 ] 
dist 97=[-.7980229635981766251 ,.4685082327184437507 ] 
dist 98=[-.8871100766754110412 ,-.0705591510282104730 ] 
dist 99=[-.9549515821940991500 ,-.1292812986103936846 ] 
dist 100=[-1.0112945013867640932 ,-.2434364940160998069 ] 
dist 101=[-1.0557638331495005797 ,-.2695227790900824564 ] 
dist 102=[-1.0762458828882452305 ,-.47969094421004866712] 
dist 103=[-1.0853012191358787925 ,-.50166219708186915101] 
dist 104=[-1.0846193388366552982 ,-.54095417409759699925] 
dist 105=[-1.0404872398433027441 ,-.54780999176034348488] 
dist 106=[-.72973876525856619513,-.4802371131425824089 ] 
dist 107=[-.65499058107697114062,-.40390179724504869125] 
dist 108=[-.63824537999870748089,-.31575917616898617771] 
dist 109=[-.56202532002928432647,-.22711275303762525826] 
dist 110=[-.5024282005623359291 ,-.14875815418795199073] 
dist 111=[-.46144876389122513703,-.06316085192540634566] 
dist 112=[-.45111793546786933175,.05438358567638476405] 
dist 113=[-.4284994511752771851 ,.17113804364531095475] 
dist 114=[-.2553406850636407630 ,.25359180997390747446] 
dist 115=[-.2330817148293778432 ,.32651457399913232651] 
dist 116=[-.1841564882063549756 ,.40526560892969114257] 
dist 117=[-.1729803411150704696 ,.48154431939097458196] 
dist 118=[-.1173563712277148354 ,.54461615650371447159] 
dist 119=[-.1076779831861746306 ,.60999332231486026174] 
dist 120=[-.0851722705074381764 ,.6954851068366050652 ] 
dist 121=[-.0818063428581621560 ,.77779697534202017631] 
dist 122=[.1115978767003905547 ,.85521647140182717728] 
dist 123=[.1300734300943918104 ,.92465058903849957653] 
dist 124=[.1617289643296522103 ,.99230063986213262243] 
dist 125=[.16825087544066660598,1.0535157384810577912 ] 
dist 126=[.17743105572361881988,1.0972761003320842239 ] 
dist 127=[.17163356724101723009,1.1365735066574846078 ] 
dist 128=[.15716017736373551586,1.1799826603781326890 ] 
dist 129=[.1271782386225950029 ,1.2184930813185424296 ] 
dist 130=[.09298068639324319126,1.2382455909289734233 ] 
dist 131=[.06168475898596220228,1.2480145260151782486 ] 
dist 132=[.02661711435108928915,1.2477041684288672957 ] 
dist 133=[-.05772252386670267002,1.2393154298540907110 ] 
dist 134=[-.24373681403532444561,1.2339827455212627776 ] 
dist 135=[-.46645370614223397481,1.2105830732443277291 ] 
dist 136=[-.79691285400669329677,1.2033533133311095793 ] 
dist 137=[-1.1248164848058359977 ,1.0861464451706492187 ] 
dist 138=[-1.3373409002820228151 ,1.0637126636990933565 ] 
dist 139=[-1.5056437778079433700 ,1.0155213275639245557 ] 
dist 140=[-1.6571426931582222166 ,.99999946599906236068] 
dist 141=[-1.7859006127839499431 ,.92831714341229956701] 
dist 142=[-1.8634877658692891873 ,.91273562735304469027] 
dist 143=[-1.9183120552697265171 ,.86592555643211108598] 
dist 144=[-1.9562683548965134896 ,.85819156654693868626] 
dist 145=[-1.9823838481516129194 ,.74322366066125761456] 
dist 146=[-1.9899736327031426378 ,.72200737200391275879] 
dist 147=[-1.9861256140756907344 ,.67531036460961820677] 
dist 148=[-1.9807624905102074759 ,.66081166778792958333] 
dist 149=[-1.9338393446562012803 ,.59586618459881305262] 
dist 150=[-1.9188710662117777615 ,.58219505449531949069] 
dist 151=[-1.8708705369778172243 ,.54549855511774106658] 
dist 152=[-1.8542283626620313717 ,.53782632428742320738] 
dist 153=[-.9181023282831059883 ,.58126083252838431136] 
dist 154=[-.7587009312725578159 ,.82813275384463224973] 
dist 155=[-.73552953649386117551,1.0279372803844570642 ] 
dist 156=[-.68073619568682975621,1.2313369976722864310 ] 
dist 157=[-.66547075900220899531,1.4332668713156352467 ] 
dist 158=[-.58270072958629006592,1.5701614660961083001 ] 
dist 159=[-.56531220087696580415,1.6853600596520053021 ] 
dist 160=[-.52942476132400869123,1.8007453992740443552 ] 
dist 161=[-.51880960517584090887,1.9022903990749280042 ] 
dist 162=[-.37688620895873901015,1.9622794122014066866 ] 
dist 163=[-.35594037737022359361,2.0032006383896567333 ] 
dist 164=[-.30556463737901240991,2.0286820594517353800 ] 
dist 165=[-.29562217064922369226,2.0422313548552778584 ] 
dist 166=[-.22167880756814582143,2.0418092023587633558 ] 
dist 167=[-.20744437470601081291,2.0230053579116031653 ] 
dist 168=[-.18371613849544210586,2.0131333721118002658 ] 
dist 169=[-.17770958304054787342,1.0976304986507135395 ] 
dist 170=[-.22995575021700177694,.91698540572926510429] 
dist 171=[-.34040471588300705828,.6985481875996261777 ] 
dist 172=[-.53643632648174680212,.65941852379939214067] 
dist 173=[-.72006587768088234133,.35987679562276234024] 
dist 174=[-.85789046815187455533,.30522776511752529821] 
dist 175=[-.98826806459603486495,.21609967919130369371] 
dist 176=[-1.1421911615231500759 ,.19443868354732794053] 
dist 177=[-1.2843504376224127427 ,-.15662721299242172329] 
dist 178=[-1.3678024750538350594 ,-.19347230424774560506] 
dist 179=[-1.4240572360880787722 ,-.25413867132127911527] 
dist 180=[-1.4577279262279459789 ,-.26761454950794029385] 
dist 181=[-1.4800536435595932816 ,-.28216826521364845726] 
dist 182=[-1.4910535317571444225 ,-.26823880169589907382] 
dist 183=[-1.4958394935181505652 ,-.23602543175674794168] 
dist 184=[-1.4933771738508106678 ,-.1705316358973657994 ] 
dist 185=[-1.0146911037592319225 ,-.09815941057570778586] 
dist 186=[-.54609527820828601018,.06235232768147210611] 
dist 187=[-.50284363021996516901,.19924863579531156816] 
dist 188=[-.39813306693086785915,.33930947294498441977] 
dist 189=[-.38077055568009506289,.47033179534069930552] 
dist 190=[-.37593651606105805196,.57117394328264754705] 
dist 191=[-.40176217259363959523,.66901436772444217629] 
dist 192=[-.44612762748382226011,.78806355464045401415] 
dist 193=[-.49421208511691571   ,.89960608505587089412] 
dist 194=[-.5348720171037918095 ,.96750274622551647832] 
dist 195=[-.57780032393650766592,1.0162945608309602026 ] 
dist 196=[-.63493149454700856487,1.0516279736712497393 ] 
dist 197=[-.6966745884031026822 ,1.0772740998369887592 ] 
dist 198=[-.75799862820119535611,1.0874225332820004485 ] 
dist 199=[-.83063084738023998187,1.0896415210622065424 ] 
dist 200=[-.93748048142318720962,1.1816750741927244610 ] 
dist 201=[-1.0421790007924421976 ,1.3758201346028697191 ] 
dist 202=[-1.1062298848345917113 ,1.4942720678156123605 ] 
dist 203=[-1.1526346148927747442 ,1.5797416573080899386 ] 
dist 204=[-1.1869428271460325361 ,1.6423149863318122779 ] 
dist 205=[-1.2109496676703548699 ,1.6889653806351983089 ] 
dist 206=[-1.2166337629185438960 ,1.7109151453754947377 ] 
dist 207=[-1.2153161128020289234 ,1.7189361655552591221 ] 
dist 208=[-1.2143562522321602129 ,1.7179608496328726601 ] 
dist 209=[-1.1431884468810013074 ,1.5555373215441665839 ] 
dist 210=[-1.1281393314763617631 ,1.5268132598065321865 ] 
dist 211=[-1.0891724787679850248 ,1.4749702069816728438 ] 
dist 212=[-1.0745404900765801148 ,1.4595315530812662263 ] 
dist 213=[-.99734943109985928041,1.3976247003454529153 ] 
dist 214=[-.97880745820606417753,1.3794729978803280885 ] 
dist 215=[-.94105674081518522215,1.3415627589780390764 ] 
dist 216=[-.92896676342619172712,1.3281350421651027364 ] 
dist 217=[-.62839945790010643028,.58605490372174032087] 
dist 218=[-.76353254501006924453,.62187932005607220897] 
dist 219=[-.8479591673624948367 ,.64259969099371734409] 
dist 220=[-.91125039789789341805,.65617092167726974881] 
dist 221=[-.96207228860720140771,.66347931566956924755] 
dist 222=[-1.0016921703122060454 ,.66648778663260323849] 
dist 223=[-1.0202967816949497023 ,.66606009835475723504] 
dist 224=[-1.0287357681289054924 ,.65796873653109765816] 
dist 225=[-1.0285408512203229258 ,.65555785454997427209] 
dist 226=[-.97650582128447068594,.60159309771862544826] 
dist 227=[-.96449879681057730776,.59151408459481242311] 
dist 228=[-.94261326689874901008,.56350910425188468597] 
dist 229=[-.93515469042553310931,.55679659901805412034] 
dist 230=[-.75899933570598979395,.49954480994262306288] 
dist 231=[-.72445981005879263857,.48678769166016541951] 
dist 232=[-.53918065405525110049,.47729523749236069794] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 1, 2, 0, 1] 
dist 0=[60.963381437837934715  ,60.963381437837934715  ] 
dist 1=[60.217176529178426003  ,61.369198902594361339  ] 
dist 2=[58.731727392528602741  ,61.495495159643774804  ] 
dist 3=[56.888463189408462559  ,61.490477520236024142  ] 
dist 4=[54.713551007285053736  ,61.371820781638545512  ] 
dist 5=[51.875524047736180153  ,61.215385813432781442  ] 
dist 6=[47.384438976117420304  ,61.059545718643925198  ] 
dist 7=[42.803790363490781384  ,60.873745394847491216  ] 
dist 8=[39.608057430650951805  ,60.729418769488593925  ] 
dist 9=[36.809485242613874184  ,60.284606106605041612  ] 
dist 10=[33.814464161339230843  ,60.089472633824495692  ] 
dist 11=[30.915534157640582385  ,59.611039249141330146  ] 
dist 12=[28.500423454760504145  ,59.401058850415708101  ] 
dist 13=[25.971918156994945343  ,58.292718817827382952  ] 
dist 14=[22.619751906535472368  ,57.049012273699873829  ] 
dist 15=[19.315008778550364105  ,34.598141227608689843  ] 
dist 16=[16.975609711174149781  ,33.973395856999339845  ] 
dist 17=[14.888948160744430327  ,28.179276009547889654  ] 
dist 18=[12.593078411561214998  ,27.111428128926454766  ] 
dist 19=[10.328875644474052629  ,25.747441331011921625  ] 
dist 20=[8.3681462194589390708 ,25.395077778610945918  ] 
dist 21=[6.2460077674896590646 ,16.872368025423885479  ] 
dist 22=[3.3360709115952146315 ,15.816505226233068400  ] 
dist 23=[.50175025534261729407,13.562230520779347004  ] 
dist 24=[-1.3185348478007521359 ,13.051231039016485481  ] 
dist 25=[-2.7536146601497370608 ,10.717136075039142054  ] 
dist 26=[-4.2499375629128666080 ,10.305953341616536434  ] 
dist 27=[-6.2706741729734283509 ,9.4541765504482135830 ] 
dist 28=[-7.8783594828706905034 ,9.2643030498550507630 ] 
dist 29=[-9.4998297304449545925 ,1.3501701844398620905 ] 
dist 30=[-11.577051807369095411  ,-.03069148394090213757] 
dist 31=[-13.546501045469889704  ,-1.6318657348595934004 ] 
dist 32=[-14.737698598250625503  ,-1.9898715166579441504 ] 
dist 33=[-15.595879730753606030  ,-3.4376036015709410612 ] 
dist 34=[-16.234342259394863699  ,-3.6996178463045670704 ] 
dist 35=[-16.708544624994194769  ,-4.0861836310994667236 ] 
dist 36=[-16.910042073465768741  ,-4.1700685058408987473 ] 
dist 37=[-16.981173733752339312  ,-4.1529781408849837514 ] 
dist 38=[-16.958167784614290954  ,-3.7084334827406202781 ] 
dist 39=[-15.935164294181539912  ,-2.3982077806133370081 ] 
dist 40=[-15.733534912410332456  ,-1.4942103334403144771 ] 
dist 41=[-15.309465168024780002  ,-.71717156009159363974] 
dist 42=[-15.166160968468459290  ,.08686389407185111377] 
dist 43=[-15.071721230451046132  ,.84438768030217021337] 
dist 44=[-15.022513392798786155  ,1.4360048432926956555 ] 
dist 45=[-13.840212199476228549  ,3.6268592174358687348 ] 
dist 46=[-13.754591977969287414  ,5.5862022179553337359 ] 
dist 47=[-5.4737218255494352010 ,7.2115449777157064391 ] 
dist 48=[-4.6948203059315695356 ,8.8037797027633014931 ] 
dist 49=[-2.9774869296328531303 ,10.251275227923603778  ] 
dist 50=[-2.6087675893587645118 ,11.299187763149185128  ] 
dist 51=[-.63472212565676726312,12.254501816432519576  ] 
dist 52=[-.29131353851090414871,13.332658318856335679  ] 
dist 53=[.45451001478098592635,14.303942262621019786  ] 
dist 54=[.60790121912142497088,14.832854072893282274  ] 
dist 55=[.5646168880671310532 ,15.139176646060884157  ] 
dist 56=[.20929023309010761816,15.222262794416353019  ] 
dist 57=[-.12262796566243872056,15.225823993560847937  ] 
dist 58=[-.45741058900899556031,15.214677790990878540  ] 
dist 59=[-.76713346186441305606,15.190696846299475084  ] 
dist 60=[-.99914596610159036488,14.852274001769225074  ] 
dist 61=[-1.2179978433485288079 ,12.442659288847455158  ] 
dist 62=[-1.4752729427841602018 ,11.706028908429339435  ] 
dist 63=[-1.7143040045128432875 ,.68052014897219497215] 
dist 64=[-1.9864728859305018389 ,.51759344508354018211] 
dist 65=[-2.5322353995138269941 ,-.56341958875799166299] 
dist 66=[-3.0374228360924008940 ,-.62562637466907536032] 
dist 67=[-3.4772773230695167881 ,-.53700425454998100208] 
dist 68=[-3.7624054853069483573 ,-.4173746710180390607 ] 
dist 69=[-3.9886519705089547573 ,-.25251425801745307364] 
dist 70=[-4.1936343998860811505 ,.01647275697208111444] 
dist 71=[-4.3678686539191941888 ,.28981543313019088718] 
dist 72=[-4.4714345381484823464 ,.47204107654749165553] 
dist 73=[-4.6176126960205402226 ,.62181645138392270475] 
dist 74=[-4.7374642920705942907 ,.76574747041618991418] 
dist 75=[-4.8038616257537270237 ,.8942880078998654609 ] 
dist 76=[-4.8145228811664995072 ,.98268117764340760151] 
dist 77=[-4.5902609932043963388 ,1.0582496531816323067 ] 
dist 78=[-4.5699439152071557207 ,1.1356305662388808360 ] 
dist 79=[-1.9046022776821590080 ,1.2043864908563583013 ] 
dist 80=[-1.6718964881486779520 ,1.2455585699024516806 ] 
dist 81=[-1.1340090300873357718 ,1.2741969358634648630 ] 
dist 82=[-1.0352011460888446170 ,1.2929833999895229793 ] 
dist 83=[-.52381802439347174516,1.3038376024141846611 ] 
dist 84=[-.49920108440167025356,1.4696607967302539341 ] 
dist 85=[-.46063890038380241391,1.8050656746581370690 ] 
dist 86=[-.45010465024854708074,2.2121083319629760739 ] 
dist 87=[.4540544354504399785 ,2.5930736422956747480 ] 
dist 88=[.52728243449390746814,2.8244546022278233995 ] 
dist 89=[.69060986668061838282,2.9901496552584888376 ] 
dist 90=[.71449933858079725364,3.1090809565738430581 ] 
dist 91=[.76898312607419874836,3.1975196839453805750 ] 
dist 92=[.68705261266671960087,3.2415749591021467898 ] 
dist 93=[.57080021326480051559,3.2614875588967965506 ] 
dist 94=[.38026176790943914903,3.2584166025470954409 ] 
dist 95=[.21509537608306293025,1.0719189575930972093 ] 
dist 96=[.04201953851192288830,1.0486849679961834320 ] 
dist 97=[-.12231049809697118239,1.0577565692509338160 ] 
dist 98=[-.27671534714960418458,1.0647215477752371468 ] 
dist 99=[-.51154290231652146873,1.0698176860208690534 ] 
dist 100=[-.68995799633065571985,1.0714292814015252531 ] 
dist 101=[-.86083746585768883907,1.0708078129832152198 ] 
dist 102=[-1.0656176500454011753 ,1.0669908274125140060 ] 
dist 103=[-1.2568579879951371846 ,.31901699518265495284] 
dist 104=[-1.3737299594494005115 ,.25733882898618288838] 
dist 105=[-1.4582757757785651963 ,.22107272691469021889] 
dist 106=[-1.5205636685086228901 ,.30764027116634611902] 
dist 107=[-1.5672084879719919360 ,.41012958331268089173] 
dist 108=[-1.5893564197952424257 ,.52473599239337413248] 
dist 109=[-1.6474723407836426584 ,.66988896817347376939] 
dist 110=[-1.8196319422614854098 ,.89421237592134059978] 
dist 111=[-1.9823026358540227083 ,1.1181794407852614008 ] 
dist 112=[-2.0735818050027533248 ,1.2619079656563539297 ] 
dist 113=[-2.1300033199602636798 ,1.3740255102821693382 ] 
dist 114=[-2.1535964223075092954 ,1.4719036468716652195 ] 
dist 115=[-2.1640869519123030269 ,1.5528143594471443429 ] 
dist 116=[-2.1682224045726660491 ,1.5972500564050474657 ] 
dist 117=[-2.1685277849808654741 ,1.6233316341001382839 ] 
dist 118=[-2.1637119386719017401 ,1.6310240976661903583 ] 
dist 119=[-1.7901029932831714484 ,1.6299380481618330919 ] 
dist 120=[-1.7353970588438969294 ,1.6240130741289149955 ] 
dist 121=[-1.6352830196336398226 ,1.6078336903669343049 ] 
dist 122=[-1.6086264059743189488 ,1.5983361773096711486 ] 
dist 123=[-1.5154249866238759094 ,1.5385865919304890554 ] 
dist 124=[-1.4885134393709228532 ,1.5221290864534269540 ] 
dist 125=[-1.4561443032698647704 ,1.4573865315062614017 ] 
dist 126=[-1.4415414700295466721 ,1.3445177455526470730 ] 
dist 127=[.05514022518811722645,.28153452634201688442] 
dist 128=[.07905787867705568780,.30687430639169123159] 
dist 129=[.11847098374884373301,.37425301383334252314] 
dist 130=[.10649491837755099515,.43581946890517921115] 
dist 131=[.08950428596305525539,.49891496616482788504] 
dist 132=[.06681104169990103450,.58648777636459444337] 
dist 133=[.03564487238839943332,.66931701547719856862] 
dist 134=[-.01514493461104300105,.7214259402799804819 ] 
dist 135=[-.06692886077521446737,.76098038682031427833] 
dist 136=[-.10206109430751659589,.79371333594945869593] 
dist 137=[-.1316508052626569105 ,.8195430640835174492 ] 
dist 138=[-.16132646417112041974,.83155227427352978835] 
dist 139=[-.18871280682516592099,.83645060681596626768] 
dist 140=[-.20917104624856082267,.83621399327367275828] 
dist 141=[-.22843253794555231695,.40735858615622769611] 
dist 142=[-.25516211021841051437,.40455025056089400917] 
dist 143=[-.3130138630325232194 ,.32588709003168460714] 
dist 144=[-.36684298237668693414,.3143594322184248272 ] 
dist 145=[-.41385396914784697844,.28953157993788932687] 
dist 146=[-.44450482754208902519,.28218683478788751363] 
dist 147=[-.46898719637320984216,.25072032161372638913] 
dist 148=[-.50131009932602009709,.24437231018723878533] 
dist 149=[-.53185569279364641538,.22672416674151408838] 
dist 150=[-.54988314390264660704,.22406696495266738365] 
dist 151=[-.56322002948283852049,-.22077276535522685999] 
dist 152=[-.57190675288799576261,-.23816555760377605515] 
dist 153=[-.57693569616871570534,-.27484656296943551662] 
dist 154=[-.57738274797392181849,-.28091261401718330578] 
dist 155=[-.57269200332748444981,-.23494202776539568141] 
dist 156=[-.57078430266568120479,-.13882597364319653903] 
dist 157=[-.45276098657995479535,-.04144353780798412936] 
dist 158=[-.46082179210305894911,.02488288531267737872] 
dist 159=[-.46623655901154351017,.08100301820855372723] 
dist 160=[-.46936601490471475438,.13768136182533222453] 
dist 161=[-.47141510707047037577,.19022907550680560218] 
dist 162=[-.47251968925225168002,.22987771686865002493] 
dist 163=[-.47292926976696545018,.267595280789356414  ] 
dist 164=[-.47220555114720269532,.31244761355797754106] 
dist 165=[-.47051309638151771928,.35399255294141925837] 
dist 166=[-.46839008426230504842,.37852066844209760489] 
dist 167=[-.13001520286902991911,.39525782741557726772] 
dist 168=[-.10173451664680622031,.40572799577202967423] 
dist 169=[-.03811294000995557215,.41270954980821771809] 
dist 170=[-.02586419553260538557,.4155260565595872714 ] 
dist 171=[.02691155243684827072,.41583638294515435826] 
dist 172=[0                     ,.41480788519910774777] 
dist 173=[.05302422333227979851,.23304742961058360932] 
dist 174=[.05567918443565690651,.27104569818744723731] 
dist 175=[.07614839702258190488,.31721500059705102518] 
dist 176=[.07440243773009281254,.34612994629829295128] 
dist 177=[.04899277861775577311,.36789528756751629432] 
dist 178=[.02722756171175007285,.38554133279320090247] 
dist 179=[.00401435404052879139,.39915221185456222131] 
dist 180=[-.02717511457552127499,.40481920595757640795] 
dist 181=[-.05788013883658275359,.40717684027727159523] 
dist 182=[-.07916329208889734735,.407585627197961443  ] 
dist 183=[-.09758362602507772790,.01942222734209072386] 
dist 184=[-.11687214461051728643,.00106195417942654715] 
dist 185=[-.13521430841628969223,-.01140657869685150231] 
dist 186=[-.15542563919199061386,-.00974140357798594313] 
dist 187=[-.18519915771921589271,-.00556598899391840285] 
dist 188=[-.20692103478376609362,.00309248580878499399] 
dist 189=[-.22686616286756467745,.01250600852030935649] 
dist 190=[-.24955189080141604334,.01969288177623114907] 
dist 191=[-.2700691981771522032 ,.02659109469197512334] 
dist 192=[-.28136408621133393905,.03485668569463454578] 
dist 193=[-.28804741945764399696,.04332864750206117462] 
dist 194=[-.29016836658456274552,.05105163770046483964] 
dist 195=[-.29063653885365703512,.05967886131419327501] 
dist 196=[-.29072627830704208452,.07175888133448669184] 
dist 197=[-.29055659112754708861,.08385488555344400251] 
dist 198=[-.28998879163390906303,.09254707594895175560] 
dist 199=[-.22676072715280530663,.10038811081695666825] 
dist 200=[-.21887139519775848038,.10909133553323494991] 
dist 201=[-.19862180087147414743,.11766115656373881073] 
dist 202=[-.19490687263653865155,.13677231914100003562] 
dist 203=[-.17447873650447337003,.16154508541055702382] 
dist 204=[-.17031388954070517442,.17823379965164618229] 
dist 205=[-.16481627971693941554,.19216405666996874948] 
dist 206=[-.1626934304980194908 ,.20593357675223924333] 
dist 207=[-.1121051541241629811 ,.21808578530584057241] 
dist 208=[-.10517198664015230619,.22556464221929137227] 
dist 209=[-.09020341798234631724,.23103905539263632343] 
dist 210=[-.08595562386968807529,.23519546433872435652] 
dist 211=[-.06851101441389894519,.23817908778423415772] 
dist 212=[-.06512509542764434363,.23897533911403374144] 
dist 213=[-.05650848904828406393,.23842089659898591899] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 2, 2, 1, 2] 
dist 0=[54.785803989369906779  ,54.785803989369906779  ] 
dist 1=[53.518831895043362657  ,55.600439756464682840  ] 
dist 2=[51.300702757927748050  ,56.012621271493845042  ] 
dist 3=[48.964547066719900016  ,56.259243756071609489  ] 
dist 4=[47.226329048472209731  ,56.412811593021783636  ] 
dist 5=[45.590661839967602954  ,56.527870356439127463  ] 
dist 6=[43.663856057170470204  ,56.620517173797102308  ] 
dist 7=[41.693499986326141888  ,56.669920291379868005  ] 
dist 8=[39.883826229648832913  ,56.223491147763577152  ] 
dist 9=[37.841921641940545585  ,52.868277824426971307  ] 
dist 10=[34.944068529592480322  ,52.286905335848507210  ] 
dist 11=[32.001497642549019740  ,51.286029894403611076  ] 
dist 12=[29.780872695994004656  ,51.008292530617198985  ] 
dist 13=[27.659077573995516930  ,50.089066610652918139  ] 
dist 14=[25.110845027986523002  ,49.789119648971107119  ] 
dist 15=[22.475736641623378544  ,49.460062754336873820  ] 
dist 16=[20.006661698765603110  ,48.859367789775038440  ] 
dist 17=[17.179245537242737162  ,27.948921701350598489  ] 
dist 18=[13.112415993219466494  ,26.622106530233482973  ] 
dist 19=[9.0836360037458373064 ,21.976356331295679108  ] 
dist 20=[6.4080574612538065948 ,21.374010188426154142  ] 
dist 21=[4.2031689430550323174 ,15.635153936680675255  ] 
dist 22=[2.0544391977813171455 ,14.616427480525307673  ] 
dist 23=[.09781283650947195284,13.360718566303837582  ] 
dist 24=[-1.7766267622762399950 ,13.150482943993337907  ] 
dist 25=[-3.6152081969436928645 ,7.6297431905376071425 ] 
dist 26=[-5.4982634903697103561 ,6.0876890019210644283 ] 
dist 27=[-7.2766851677837465027 ,2.9868247574668924648 ] 
dist 28=[-8.6982697592419225806 ,2.6358943780725487893 ] 
dist 29=[-10.140243622540588809  ,.84372672490092045543] 
dist 30=[-12.001904733940556944  ,.54983133723800443314] 
dist 31=[-13.759217483942833013  ,.08794037485076333387] 
dist 32=[-14.784634526247826937  ,.01460139412236909883] 
dist 33=[-15.480793538054351429  ,-1.8470768529801196180 ] 
dist 34=[-15.921867763362685397  ,-.5064448141775712751 ] 
dist 35=[-16.227450487941877595  ,.86482537608998860007] 
dist 36=[-16.381539251196518026  ,1.7813193835092576309 ] 
dist 37=[-16.457894671338593259  ,2.5348022110360721969 ] 
dist 38=[-16.451459416437063014  ,3.2565883617731702850 ] 
dist 39=[-14.462867118295963736  ,3.8977601155441786065 ] 
dist 40=[-14.161453024380761343  ,4.3299803798099648407 ] 
dist 41=[-13.619669307454839744  ,4.6893314397276922954 ] 
dist 42=[-13.473946103229006560  ,5.0399893066807551637 ] 
dist 43=[-12.967625502797690330  ,5.3492676787976478396 ] 
dist 44=[-12.811658128713982018  ,5.5436843046918024989 ] 
dist 45=[-12.645386458605400734  ,5.6897436016845965156 ] 
dist 46=[-12.557374869373639822  ,5.8063515413551496747 ] 
dist 47=[-6.5641445593912230382 ,5.8938513106284901198 ] 
dist 48=[-6.5518435861719545526 ,5.9238907836838860661 ] 
dist 49=[-1.7839256468589194560 ,5.9170237002673955956 ] 
dist 50=[-1.7257022184212509194 ,5.8972209434450846058 ] 
dist 51=[.753207240793686649  ,5.0449790666152559516 ] 
dist 52=[.98512506414559578028,6.1426514929400799626 ] 
dist 53=[1.5020365031837297788 ,7.2071268670198940374 ] 
dist 54=[1.5815446815985102013 ,8.5050352281261005462 ] 
dist 55=[2.1568068488411173653 ,9.7277851355114001700 ] 
dist 56=[2.2459973194626794589 ,10.492297298658499964  ] 
dist 57=[2.4022539057384846537 ,11.067878911027440684  ] 
dist 58=[2.4291414944833591555 ,11.536520080566864357  ] 
dist 59=[2.6154784252234393466 ,11.900912554189850604  ] 
dist 60=[2.6088703515003665518 ,12.060395379446649577  ] 
dist 61=[2.1678554123346692407 ,12.123509778688729340  ] 
dist 62=[.68722824076340302688,12.109103320146708328  ] 
dist 63=[-.81160569746322545724,5.1302725754165229948 ] 
dist 64=[-1.9149228813348841069 ,5.1087206174448666772 ] 
dist 65=[-2.8772015283837966630 ,3.0070319137173638460 ] 
dist 66=[-3.8083631793492349134 ,2.9942199163770007352 ] 
dist 67=[-4.6464721068728485730 ,1.3613074820047309332 ] 
dist 68=[-5.2375649239430373197 ,1.2183516737419770451 ] 
dist 69=[-5.7600960927749084016 ,.88239988648556170053] 
dist 70=[-6.3247417727449823616 ,.82431064923154105263] 
dist 71=[-6.8327782350117875557 ,.37277806415375526386] 
dist 72=[-7.1294823514041103236 ,.29174933751231945299] 
dist 73=[-7.3279632623282330552 ,.16195345640470397876] 
dist 74=[-7.4441216129998476136 ,.1304493943291038254 ] 
dist 75=[-7.5071664896996625856 ,-.37962884651536758729] 
dist 76=[-7.5084887500570550560 ,-.4455351599188696393 ] 
dist 77=[-7.4539433704570880408 ,-.57344222004138941058] 
dist 78=[-7.4118147521783572925 ,-.60248055837325293085] 
dist 79=[-4.6230247748118107502 ,-.6460860729674363552 ] 
dist 80=[-4.3427212188416512840 ,.2194900085241125889 ] 
dist 81=[-3.6525540436219355446 ,.9424274455242906967 ] 
dist 82=[-3.5361714222808243180 ,1.6572636016173827183 ] 
dist 83=[-2.4894679835167870742 ,2.3101460107052929495 ] 
dist 84=[-2.2908220137605154184 ,2.7859920461580608832 ] 
dist 85=[-2.0180305987013707242 ,3.2222251148760998190 ] 
dist 86=[-1.9335975919062370670 ,3.7171337092084502752 ] 
dist 87=[-.46540852010753466944,4.1724073001021079119 ] 
dist 88=[-.46404243478439351067,4.4505558167531673700 ] 
dist 89=[-.47073751664046574636,4.6516844846644067122 ] 
dist 90=[-.49020617118036682946,4.7997415014591906104 ] 
dist 91=[-.51416257487869547591,4.9031617922384035996 ] 
dist 92=[-.53875142192812138274,4.9274302317701860137 ] 
dist 93=[-.56845687308633677107,4.9221197797702822016 ] 
dist 94=[-.61281176658050202901,4.9170546101392376600 ] 
dist 95=[-.66303186847386154472,1.9720468298181648463 ] 
dist 96=[-.71612377616437692985,1.9649039330174829340 ] 
dist 97=[-.78132369960430008659,1.3805836194836650538 ] 
dist 98=[-.87982505003159058504,1.3146394097700262484 ] 
dist 99=[-.97707581957613604249,1.3847990466597106376 ] 
dist 100=[-1.0372849815011446254 ,1.5045604460619661849 ] 
dist 101=[-1.0816920774371697020 ,1.5909547355867943484 ] 
dist 102=[-1.3617377216663326199 ,1.6542794213580949505 ] 
dist 103=[-1.6863211781827176171 ,1.7015902033664970427 ] 
dist 104=[-1.8896451621241106220 ,1.7240894476268201576 ] 
dist 105=[-2.0426144609136749336 ,1.7327153290703948434 ] 
dist 106=[-2.1663449094321491685 ,1.7318568373965721503 ] 
dist 107=[-2.2621927818349466975 ,1.5718643974619870747 ] 
dist 108=[-2.3039599762351988619 ,1.5436576416907557140 ] 
dist 109=[-2.3221535228578271823 ,1.4929625175859591385 ] 
dist 110=[-2.3239577515818725332 ,1.4779349762215744903 ] 
dist 111=[-1.7681162824564395257 ,1.4181603013339454814 ] 
dist 112=[-1.7105138427090002310 ,1.4004376346197972260 ] 
dist 113=[-1.5676956553932280862 ,1.3642536632133768772 ] 
dist 114=[-1.5348579932369868465 ,1.3515503875354533060 ] 
dist 115=[-1.3051205528810038589 ,-.30352593568142115322] 
dist 116=[-1.2582595881416711052 ,-.20020625490823758372] 
dist 117=[-1.1748373054437353052 ,-.02347927457386149447] 
dist 118=[-1.1537383728392392581 ,.21682944295609724709] 
dist 119=[-1.0775229444011683958 ,.45441931211293802225] 
dist 120=[-1.1860575001082013049 ,.62032224045276786468] 
dist 121=[-1.2766644140914935294 ,.76508329601817791844] 
dist 122=[-1.3662807215222850070 ,.91838021680704846643] 
dist 123=[-1.4454941480556018025 ,1.0650785217308119948 ] 
dist 124=[-1.4946002597998578085 ,1.1835480257335387000 ] 
dist 125=[-1.5309778024183818496 ,1.3038766430141035730 ] 
dist 126=[-1.5594117188849601976 ,1.4580382569242704882 ] 
dist 127=[-1.5805112108729820787 ,1.6048700148078406654 ] 
dist 128=[-1.5876289895377536396 ,1.7939981559514514226 ] 
dist 129=[-1.5858609054774174285 ,1.9610281759511196120 ] 
dist 130=[-1.5820548842630621232 ,2.1258834070393594519 ] 
dist 131=[-.70215760945985137719,2.2764757850851804052 ] 
dist 132=[-.62721059544225149768,2.3865974181028152090 ] 
dist 133=[-.44716075550697845649,2.4880260532386977755 ] 
dist 134=[-.41898631656843515373,2.6039322968488029405 ] 
dist 135=[-.16537049809882259496,2.7088998445628649065 ] 
dist 136=[-.11954205313228886433,2.7666830027260110373 ] 
dist 137=[-.05700790668153708877,2.8008885314881324821 ] 
dist 138=[-.04009338069141296703,2.8117822713830435324 ] 
dist 139=[-.08726684647870779120,2.8072839230587619194 ] 
dist 140=[-.49097308163690472011,2.8004703801346419183 ] 
dist 141=[-.97588171189621832373,2.7518072830648610553 ] 
dist 142=[-1.6971595211622545184 ,2.7429835931028427377 ] 
dist 143=[-2.4129463202377460293 ,2.5237236698189690572 ] 
dist 144=[-2.8759554312876183195 ,2.4792927153502225404 ] 
dist 145=[-3.2416109683323216985 ,2.3796483666843935041 ] 
dist 146=[-3.5690402366190143130 ,2.3458233755956388259 ] 
dist 147=[-3.8461178244188780608 ,2.1831946273097975256 ] 
dist 148=[-4.0109152080358348232 ,2.1464362646288316135 ] 
dist 149=[-4.1247480006983190461 ,2.0472324543283040775 ] 
dist 150=[-4.1985263992874771124 ,2.0210682606305848717 ] 
dist 151=[-4.2471995120386970290 ,1.7074639636162449267 ] 
dist 152=[-4.2608829693658162423 ,1.6542452732542800602 ] 
dist 153=[-4.2515712646874348733 ,1.5247788923332557508 ] 
dist 154=[-4.2400064020078539389 ,1.4923759769929269562 ] 
dist 155=[-4.1493806776650378435 ,1.2873666907495534738 ] 
dist 156=[-4.1206227603332647804 ,1.2446670162722670566 ] 
dist 157=[-4.0113273204873206649 ,1.1648154120307155356 ] 
dist 158=[-3.9868958504640883901 ,1.1431480111553041706 ] 
dist 159=[-1.2355474273984959140 ,1.1750308526212334154 ] 
dist 160=[-1.2319206711180263696 ,1.6257318076681666518 ] 
dist 161=[-1.2253692395572746057 ,1.9901217505527624409 ] 
dist 162=[-1.2196787573408770651 ,2.4393056188861655691 ] 
dist 163=[-1.1298814099657638152 ,2.8714930826935815620 ] 
dist 164=[-1.2549178197436832623 ,3.1671727759386617616 ] 
dist 165=[-1.3500449110721064662 ,3.4188981742343386209 ] 
dist 166=[-1.4289600990678642479 ,3.6757540575098776941 ] 
dist 167=[-1.4912301737748586409 ,3.9035636331228902625 ] 
dist 168=[-1.5199577370161066061 ,4.0394220823976518334 ] 
dist 169=[-1.5335141074122182673 ,4.1336838284301862689 ] 
dist 170=[-1.5352636684363884638 ,4.1955584580185419030 ] 
dist 171=[-1.4940520070877754780 ,4.2317412125539256582 ] 
dist 172=[-1.4811335500935127233 ,4.2334921448344206104 ] 
dist 173=[-1.4534272140199802762 ,4.2012062214182583013 ] 
dist 174=[-1.4421537631309970518 ,4.1812145604506148863 ] 
dist 175=[-1.3814076727891393195 ,2.1458462333876639918 ] 
dist 176=[-1.3663404740491332807 ,1.9587397412197323066 ] 
dist 177=[-1.3172567411403766993 ,1.5124129167098139486 ] 
dist 178=[-1.3073087601035627220 ,1.4352168448433098154 ] 
dist 179=[-1.5523209219765529738 ,.80980313586308029969] 
dist 180=[-1.8127493417320444734 ,.74920454528943944577] 
dist 181=[-2.0572546711244125155 ,.95035821436304338748] 
dist 182=[-2.3432342568334291544 ,1.1495253089256146942 ] 
dist 183=[-2.6061717773958533001 ,1.3316976411802163316 ] 
dist 184=[-2.7587633893481252648 ,1.4650546912347606570 ] 
dist 185=[-2.8594218031768988160 ,1.5879278008314655892 ] 
dist 186=[-2.9152025645843935886 ,1.7282747672082285867 ] 
dist 187=[-2.9497333282945095042 ,1.8551599520789308517 ] 
dist 188=[-2.9656262023081818147 ,1.9243306766342219411 ] 
dist 189=[-2.9708719530249169058 ,1.9643221474181601899 ] 
dist 190=[-2.9629286555503425041 ,1.9748063877545276952 ] 
dist 191=[-.92968415300144576057,1.9744828898228106713 ] 
dist 192=[-.92926961036770263053,1.9713641235194141981 ] 
dist 193=[-.93937069880882259043,1.9656036289857225909 ] 
dist 194=[-.96648163380739839929,1.9557799011947953977 ] 
dist 195=[-1.0024163789234294057 ,1.5983639380803649800 ] 
dist 196=[-1.0477129651723804910 ,1.5493112152043093674 ] 
dist 197=[-1.1084677627040472204 ,1.5785037455715945234 ] 
dist 198=[-1.2858615904281638633 ,1.8309020233001037617 ] 
dist 199=[-1.4608240691835663737 ,2.0676167637253398919 ] 
dist 200=[-1.5751945168305504245 ,2.2121256971567126856 ] 
dist 201=[-1.6668742310785213508 ,2.3164815348236098582 ] 
dist 202=[-1.7513239980417708904 ,2.3930260465140919133 ] 
dist 203=[-1.8234070495847501921 ,2.4478982567221668365 ] 
dist 204=[-1.8657536173928361778 ,2.4658005670875942444 ] 
dist 205=[-1.9485443901846552408 ,2.4679929629186499743 ] 
dist 206=[-2.1395030361767509512 ,2.5209206006800781201 ] 
dist 207=[-2.3256165621948198898 ,2.9928564812641630823 ] 
dist 208=[-2.4377317678300587503 ,3.2845156035525312194 ] 
dist 209=[-2.5168675729264823846 ,3.4994317685629005085 ] 
dist 210=[-2.5714270254955606558 ,3.6652272905012176372 ] 
dist 211=[-2.6061251518579728653 ,3.7921000840038347079 ] 
dist 212=[-2.6127957520670262122 ,3.8517454627429012190 ] 
dist 213=[-2.5963883878970575405 ,3.8757515851995017483 ] 
dist 214=[-2.5929698373169805970 ,3.8752061279691115108 ] 
dist 215=[-2.4254652382754600326 ,3.5953185227830337738 ] 
dist 216=[-2.3915988952427844407 ,3.5405240334572908678 ] 
dist 217=[-2.2981517003932820655 ,3.4413340486564683032 ] 
dist 218=[-2.2709593147506699591 ,3.4100370774967064479 ] 
dist 219=[-2.0756759713933578488 ,3.2763341066947037412 ] 
dist 220=[-2.0305737139074698248 ,3.2376527437442607139 ] 
dist 221=[-1.9555694976136285646 ,3.1454080585061649808 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 2, 2, 0, 1, 2] 
dist 0=[56.084365574653507422  ,56.084365574653507422  ] 
dist 1=[54.984902301095268418  ,56.521073523056474921  ] 
dist 2=[53.209728542456463112  ,57.164982166452192584  ] 
dist 3=[50.277009108491250023  ,57.840920806951022783  ] 
dist 4=[47.241863494865906094  ,58.170460446712583660  ] 
dist 5=[45.057763588748751946  ,58.309598607815361189  ] 
dist 6=[43.076590183473379128  ,58.288611718276606721  ] 
dist 7=[40.851670421278712351  ,57.983775360693392685  ] 
dist 8=[38.637820627229547430  ,55.185798564774672504  ] 
dist 9=[36.700888233740119308  ,54.423002999929248072  ] 
dist 10=[34.594045203115991325  ,54.183991509758863225  ] 
dist 11=[31.701917742489718649  ,53.367475577888761855  ] 
dist 12=[28.812659312080660819  ,53.093191802696536890  ] 
dist 13=[26.717260123343781904  ,52.638353761403622054  ] 
dist 14=[24.800217786075564657  ,52.473929620456071772  ] 
dist 15=[22.622927627680753936  ,51.679344918872279396  ] 
dist 16=[20.352263364258440921  ,29.945955983563093647  ] 
dist 17=[18.245851108929243528  ,25.731811406384212406  ] 
dist 18=[15.875192740778769822  ,25.126697541907136017  ] 
dist 19=[12.511129579179551644  ,22.800891493410217366  ] 
dist 20=[9.1825979243282870504 ,18.201389461678532758  ] 
dist 21=[6.9537651483662948863 ,16.925083541344669567  ] 
dist 22=[5.0942732000788309861 ,16.706667011706131124  ] 
dist 23=[3.2416272138629586638 ,10.963489808423352709  ] 
dist 24=[.13335947178909846565,7.7023219395718329783 ] 
dist 25=[-2.0311104193779458800 ,7.0332647757037067181 ] 
dist 26=[-3.8398883771752630195 ,5.6786822564704794309 ] 
dist 27=[-5.6457576594032192773 ,4.1067828950680142373 ] 
dist 28=[-7.3225024528265939193 ,3.0478560366562074788 ] 
dist 29=[-8.6165252276918049486 ,2.5461247722841328923 ] 
dist 30=[-9.8875635533494835713 ,2.4555148421611661155 ] 
dist 31=[-11.474424501430714659  ,-1.1946942185704434356 ] 
dist 32=[-12.957993539388687860  ,-1.0005594378675101145 ] 
dist 33=[-13.816680180135749319  ,-.6461383647459349289 ] 
dist 34=[-14.392548750399599551  ,-.11098039797241481343] 
dist 35=[-14.745206640906403921  ,.80412756473468219881] 
dist 36=[-14.979219651913567452  ,1.7407607350502731493 ] 
dist 37=[-15.080256279080079435  ,2.3620347915512511627 ] 
dist 38=[-15.106919934218589922  ,2.8672227240250126138 ] 
dist 39=[-15.076311283651780809  ,3.3415258382355491405 ] 
dist 40=[-13.384595956905713844  ,3.7563562285332433639 ] 
dist 41=[-13.120913346641704016  ,4.0246567024877696749 ] 
dist 42=[-12.609271489382973814  ,4.2356310754566809078 ] 
dist 43=[-12.462381048123150108  ,4.4220968578861463795 ] 
dist 44=[-11.883572345564228571  ,4.5732804102885224753 ] 
dist 45=[-11.735540542393815075  ,4.6436087007622992758 ] 
dist 46=[-11.436353214681224204  ,4.6678259240799456952 ] 
dist 47=[-11.340919203391451763  ,4.6643014192384210534 ] 
dist 48=[-5.4282507742538780564 ,4.5779071824738937960 ] 
dist 49=[-5.3057155946549373619 ,4.5417726884546836129 ] 
dist 50=[-5.0413941152903508143 ,4.8081569807777380633 ] 
dist 51=[-4.9595855487053953555 ,5.4520822151430252149 ] 
dist 52=[1.0685225667941290503 ,5.9777279663849668420 ] 
dist 53=[1.3573788223536779829 ,6.9433890399162809043 ] 
dist 54=[.99274148241349727768,7.8532816921058147016 ] 
dist 55=[.53746017659388315427,8.9256931476044703489 ] 
dist 56=[.1047886712327486551 ,9.9180751576112793264 ] 
dist 57=[-.2377352607610100723 ,10.508556222583769374  ] 
dist 58=[-.5785167602204513076 ,10.918242970903482693  ] 
dist 59=[-1.0043342575473157273 ,11.188960137478625425  ] 
dist 60=[-1.4080356807782671115 ,11.375345644455296117  ] 
dist 61=[-1.6606790398901510604 ,11.448388960251293423  ] 
dist 62=[-1.8503429212219877900 ,11.452642812736561456  ] 
dist 63=[-2.0029668935546211383 ,11.434541227507203488  ] 
dist 64=[-2.1241389349673179855 ,3.8946789035764108139 ] 
dist 65=[-2.4515550398635913417 ,3.2202590003615031944 ] 
dist 66=[-3.2025165274234463194 ,3.0875805940720640481 ] 
dist 67=[-3.8817173507438682939 ,2.1397241668058118378 ] 
dist 68=[-4.3656989077404446709 ,1.9608593281546604248 ] 
dist 69=[-4.7985056850012740938 ,1.6497328427179860478 ] 
dist 70=[-5.2736812637947004163 ,1.5764542722332508984 ] 
dist 71=[-5.6990427880338382548 ,.30261071432994907334] 
dist 72=[-5.9331600685209781053 ,.13199340943926152017] 
dist 73=[-6.0718373983579192618 ,-.03169658442930648374] 
dist 74=[-6.1164346051587178750 ,.13692495776882962456] 
dist 75=[-6.1225324024413591775 ,.36737002906359068508] 
dist 76=[-6.1076262891281059024 ,.59539111212282150449] 
dist 77=[-6.0747286210786915713 ,.75437506583610807716] 
dist 78=[-6.0451252482304676695 ,.89273459877133995076] 
dist 79=[-4.5406787985117036694 ,1.0385563334554181486 ] 
dist 80=[-1.3665187287627443402 ,1.1775952022441662863 ] 
dist 81=[-1.1064101730447770555 ,1.2889442959249495235 ] 
dist 82=[-.7046741268424253303 ,1.4011724151615846148 ] 
dist 83=[-.6889200861549471793 ,1.5437825561262878643 ] 
dist 84=[.2663959925315300096 ,1.7253198907615848194 ] 
dist 85=[.38134250079130316246,1.9644866698749722070 ] 
dist 86=[.62081216803513700129,2.2328812744649039101 ] 
dist 87=[.67304161060596080668,2.4772977436378420649 ] 
dist 88=[1.0426927804457988776 ,2.6208433076003649369 ] 
dist 89=[1.1004504598696169724 ,2.8519616066922203588 ] 
dist 90=[1.0965944511928919020 ,3.0743801009106508346 ] 
dist 91=[1.0078898577151318511 ,3.2621630116841255100 ] 
dist 92=[.87205955572205599888,3.4126201022309640514 ] 
dist 93=[.68026932417640595623,3.4861545292050654411 ] 
dist 94=[.41155204525264901554,3.5200804791600951488 ] 
dist 95=[-.05147769055919472774,3.5224338433454072368 ] 
dist 96=[-.48261343240841232164,3.4840722783393265635 ] 
dist 97=[-.78715628165828381435,3.4831427321075748217 ] 
dist 98=[-1.1452727751127840649 ,3.4519574373390838076 ] 
dist 99=[-2.0013674306409126752 ,3.4349610653033445800 ] 
dist 100=[-2.8511497748810681478 ,3.2575761502518180665 ] 
dist 101=[-3.3993347469456447099 ,3.2149123174995960836 ] 
dist 102=[-3.8305364031919558344 ,3.1127672404037966992 ] 
dist 103=[-4.2136593875115112352 ,3.0748366734343315961 ] 
dist 104=[-4.5356912271541770950 ,2.8810468127484145961 ] 
dist 105=[-4.7231953385840589397 ,2.8348904175528108868 ] 
dist 106=[-4.8477372354967584534 ,2.7228024312422141859 ] 
dist 107=[-4.9186111654719253276 ,2.6827066106218847110 ] 
dist 108=[-4.9606661175976504936 ,2.2221114734842486799 ] 
dist 109=[-4.9702451667898165358 ,2.1494380976829965465 ] 
dist 110=[-4.9578914296307285995 ,1.9565217430203992220 ] 
dist 111=[-4.9415534883584663127 ,1.9251502476683910356 ] 
dist 112=[-4.8493613398097293858 ,1.5806203438942166171 ] 
dist 113=[-4.8181028896469350935 ,1.5108127731191155318 ] 
dist 114=[-4.6932067511760194146 ,1.4318456523798890833 ] 
dist 115=[-4.6672081468908555528 ,1.4072746959624904674 ] 
dist 116=[-.8169295427410068516 ,1.3761637095205241385 ] 
dist 117=[-.7737046749825481992 ,1.7985612957626283782 ] 
dist 118=[-.6910955822739399777 ,2.1379759732098976497 ] 
dist 119=[-.6700339915336835125 ,2.6001131369414847885 ] 
dist 120=[.09221676926593931940,3.1057521932694294138 ] 
dist 121=[.17236323190256568928,3.4551121428280083732 ] 
dist 122=[.31671808758892030343,3.7562067731228516422 ] 
dist 123=[.34707410196220298349,4.0693184236617947437 ] 
dist 124=[.719633738824442465  ,4.3492204671158058425 ] 
dist 125=[.77916932325763722223,4.5178407572904559716 ] 
dist 126=[.73620998213735199542,4.6369140000847082807 ] 
dist 127=[.4555317263662742503 ,4.7191663585509413386 ] 
dist 128=[.16935281508804910233,4.7712683310134550859 ] 
dist 129=[-.02673636183257293314,4.7767959948209168082 ] 
dist 130=[-.19392176932382901639,4.7501758210974151084 ] 
dist 131=[-.36481752416794821127,4.7277160577745012511 ] 
dist 132=[-.5245358991463703159 ,2.4843331153415072857 ] 
dist 133=[-.66552757109020524878,2.2789251875028759794 ] 
dist 134=[-1.0562269998630905440 ,1.7830601416555051343 ] 
dist 135=[-1.4472640664156676846 ,1.7011120864849090109 ] 
dist 136=[-1.8075695401007948055 ,.98842129069634297904] 
dist 137=[-2.0756808494260466638 ,.85714121159165612868] 
dist 138=[-2.3270271635202033801 ,.67059225459684070808] 
dist 139=[-2.6204550227727801455 ,.61696966754363440683] 
dist 140=[-2.8890852182040538405 ,-.2148973053437397744 ] 
dist 141=[-3.0415151045678122739 ,-.27234771958998094232] 
dist 142=[-3.1376851025595947587 ,-.32814117945925678862] 
dist 143=[-3.1819009445477921251 ,-.1346938302916554948 ] 
dist 144=[-3.2051687236908309056 ,.06738165741804046047] 
dist 145=[-3.2177784751771102264 ,.20314145448371359473] 
dist 146=[-3.2249613850637593916 ,.31600443460095291996] 
dist 147=[-3.2265798116550703623 ,.42675141925692332608] 
dist 148=[-1.2932220153843532906 ,.52734340418192177034] 
dist 149=[-1.3255284835565948174 ,.67014080634304424645] 
dist 150=[-1.3629102821203985297 ,1.0043592217241020852 ] 
dist 151=[-1.4169436295492531165 ,1.3444542790661400727 ] 
dist 152=[-1.4774534702174519544 ,1.6614484348782155017 ] 
dist 153=[-1.5406664757387269856 ,1.9035185506515271710 ] 
dist 154=[-1.6178606613676126390 ,2.1365746261545458846 ] 
dist 155=[-1.7341392689758821504 ,2.4176141763589624134 ] 
dist 156=[-1.8543593483231210650 ,2.6796737918389378861 ] 
dist 157=[-1.9472732665667000185 ,2.8370195862236285266 ] 
dist 158=[-2.0378001862519432878 ,2.9474845948905113298 ] 
dist 159=[-2.1484924457805858469 ,3.0225363572829341476 ] 
dist 160=[-2.2633948475428005276 ,3.0730294606710220046 ] 
dist 161=[-2.3707119035107125148 ,3.0855264563819634852 ] 
dist 162=[-2.4927948208808506531 ,3.0812427807183856701 ] 
dist 163=[-2.6665921858174974415 ,3.0684029888063391544 ] 
dist 164=[-2.8344866302809526083 ,3.5652029001341236640 ] 
dist 165=[-2.9330211270361961253 ,3.9557894848677363622 ] 
dist 166=[-2.9993966300035722690 ,4.2486787877418783585 ] 
dist 167=[-3.0390099860538149501 ,4.4840317455462716614 ] 
dist 168=[-3.0582657221304076732 ,4.6675705946308381671 ] 
dist 169=[-3.0591265105440001070 ,4.7537622813662448562 ] 
dist 170=[-3.0224284180549138756 ,4.7929406464242146600 ] 
dist 171=[-3.0170607260243687462 ,4.7920456603486249498 ] 
dist 172=[-2.8053814553591880858 ,4.5538156842284634429 ] 
dist 173=[-2.7642148361451748890 ,4.4985459560027058165 ] 
dist 174=[-2.6427320590534910301 ,4.3979884415841642996 ] 
dist 175=[-2.6716563894091164065 ,4.3636670358791620900 ] 
dist 176=[-2.6937497766156630015 ,4.2055804305456181499 ] 
dist 177=[-2.7012366482141300031 ,4.1605796252144086490 ] 
dist 178=[-2.6994414624420804454 ,4.0379903197058333086 ] 
dist 179=[-2.6896505607067631853 ,3.9904140858963781572 ] 
dist 180=[-2.4094118541875861993 ,1.9208432580144314072 ] 
dist 181=[-2.4774304285492444968 ,1.9036617685287002322 ] 
dist 182=[-2.5135990831622253348 ,1.8678618155760099597 ] 
dist 183=[-2.5195713060489045869 ,1.8535726796345654873 ] 
dist 184=[-2.4524030334228793070 ,1.5488403568718175462 ] 
dist 185=[-2.4304707734921034888 ,1.5019270747454082359 ] 
dist 186=[-2.4076505973538899678 ,1.3925221838911024439 ] 
dist 187=[-2.3920905278779573222 ,1.3604233669419206103 ] 
dist 188=[-2.3531020036692739524 ,1.1991323623032105376 ] 
dist 189=[-2.3340143498849680268 ,1.1650938505953421483 ] 
dist 190=[-2.2988448641263629286 ,1.0911916133326208415 ] 
dist 191=[-2.2846528008904610204 ,1.0684731213214179606 ] 
dist 192=[-1.0733285156190392028 ,.75666045719492832672] 
dist 193=[-1.0820614742185886859 ,.81005784925995588696] 
dist 194=[-1.0837761242070528585 ,.84900757908962694949] 
dist 195=[-1.0821943235757595549 ,1.0265601531386055828 ] 
dist 196=[-1.0366658532355339963 ,1.2803332679489518540 ] 
dist 197=[-1.0264763642603782902 ,1.4597389641075093352 ] 
dist 198=[-.99122068588728554713,1.6186845865003104506 ] 
dist 199=[-.98485722608376383741,1.7908405901449970508 ] 
dist 200=[-.892373852943582477  ,1.9472344980039497261 ] 
dist 201=[-.87119814452758635514,2.0433028498696542530 ] 
dist 202=[-.85145103786404304335,2.1133986942335639447 ] 
dist 203=[-.84385145346070974003,2.1661834612332766803 ] 
dist 204=[-.56093719384161471306,2.2036809887434296469 ] 
dist 205=[-.52349469981117714504,2.2127932284976768230 ] 
dist 206=[-.44788819632264003982,2.2100302442593587478 ] 
dist 207=[-.42779570367352861715,2.2003081265563267926 ] 
dist 208=[-.48050690701344535739,1.2420766881980855542 ] 
dist 209=[-.62986313875180879605,1.1550743904123318799 ] 
dist 210=[-.75414247275016483392,.93834187036646651008] 
dist 211=[-.87633469123308409441,.92240999054695518924] 
dist 212=[-.98752769351035611472,.57414364187449823842] 
dist 213=[-1.0679296394299459330 ,.51202354876305596956] 
dist 214=[-1.1410069204755118072 ,.53982818770280778455] 
dist 215=[-1.2229797178634930359 ,.65425329288428264201] 
dist 216=[-1.2962758146637063275 ,.76729173992217895801] 
dist 217=[-1.3347406607429226915 ,.86431422313584843162] 
dist 218=[-1.3553360144929450920 ,.9680040793116882041 ] 
dist 219=[-1.3595035228185787544 ,1.1076382934647221937 ] 
dist 220=[-1.3494606408989047257 ,1.2452678957701292447 ] 
dist 221=[-1.3432669385604158618 ,1.3409599717505545062 ] 
dist 222=[-1.3358035813565932220 ,1.4240739625102358295 ] 
dist 223=[-1.3284756661874886327 ,1.5115258889808113010 ] 
dist 224=[-.97058615817534657977,1.5948609590233921888 ] 
dist 225=[-1.0231201000707418070 ,1.6615506789591301529 ] 
dist 226=[-1.0795535310415576531 ,1.7286832371932433758 ] 
dist 227=[-1.1678612927383159808 ,1.8137822043858545756 ] 
dist 228=[-1.5104188512144197181 ,1.8916164488572474945 ] 
dist 229=[-1.7251628578556397119 ,1.9297686837762035005 ] 
dist 230=[-1.8870105966328039118 ,1.9476418327881095201 ] 
dist 231=[-2.0185541033451005630 ,1.9490457048629848570 ] 
dist 232=[-2.1237557466958104920 ,1.9192439143682126401 ] 
dist 233=[-2.1805196152165714534 ,1.9049092659995405130 ] 
dist 234=[-2.2125690251368153453 ,1.8839339466830141092 ] 
dist 235=[-2.2191773351630459914 ,1.8569977749135465720 ] 
dist 236=[-2.0852979288414964327 ,1.2402805886058877444 ] 
dist 237=[-2.0578101510356810630 ,1.1635101233406823492 ] 
dist 238=[-2.0297842215374747449 ,1.1058386999161173720 ] 
dist 239=[-2.0129696997821187963 ,1.5443713787512553871 ] 
dist 240=[-1.9886228096340577734 ,1.9770153889985549876 ] 
dist 241=[-1.9770823711602450540 ,2.2526642208184711032 ] 
dist 242=[-1.9687773398503141067 ,2.4655872108255571801 ] 
dist 243=[-1.9627340991868596700 ,2.6480051432944674502 ] 
dist 244=[-1.6358200464991998794 ,2.7964415747121151788 ] 
dist 245=[-1.6262282233599525284 ,2.8738056636710789885 ] 
dist 246=[-1.5858893840277667642 ,2.9144455611531580117 ] 
dist 247=[-1.5778968943507603910 ,2.9223159895678303243 ] 
dist 248=[-1.4470042904330641244 ,2.8971111338337988919 ] 
dist 249=[-1.4216131991756748442 ,2.8802293524963020058 ] 
dist 250=[-1.3520214535849944797 ,2.8487204659155105239 ] 
dist 251=[-1.3354954130212695453 ,2.8337752621195420780 ] 
dist 252=[-1.1966435398442314898 ,2.7478183010740918348 ] 
dist 253=[-1.1659387307118949983 ,2.7243518316746668927 ] 
dist 254=[-1.1208300620476989234 ,2.6389334549603883952 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 0, 0, 2, 0, 1] 
dist 0=[53.373084888697419346  ,53.373084888697419346  ] 
dist 1=[52.326473128122481288  ,53.798775851608985146  ] 
dist 2=[50.644975613192980724  ,54.451609745973873108  ] 
dist 3=[47.889060964343377682  ,55.136822649632250155  ] 
dist 4=[45.044759791502667912  ,55.470716675105593565  ] 
dist 5=[43.010236689649235562  ,55.611447027370732328  ] 
dist 6=[41.176266510405619690  ,55.607228219581546638  ] 
dist 7=[39.132423985540679689  ,55.296852535747404045  ] 
dist 8=[37.105430872019531035  ,53.180745522605126393  ] 
dist 9=[35.338449678925127629  ,52.570668575796461430  ] 
dist 10=[33.419424686313660032  ,52.368834468864631491  ] 
dist 11=[30.784804323340160518  ,51.675315788286010200  ] 
dist 12=[28.144625007020965671  ,51.438892317970614285  ] 
dist 13=[26.203113783097066285  ,51.009161172339307586  ] 
dist 14=[24.395720341442774224  ,50.858859613923737813  ] 
dist 15=[22.290727582916451859  ,50.049250503541019851  ] 
dist 16=[20.146035767536686616  ,30.842664271032495106  ] 
dist 17=[18.179575886079045268  ,27.044354421274947808  ] 
dist 18=[15.958553835176870185  ,26.496161357079881158  ] 
dist 19=[12.796106459942131839  ,22.750070112144089452  ] 
dist 20=[9.6699319223980450925 ,20.144214795827422759  ] 
dist 21=[7.5936930371211638616 ,18.978569364669159486  ] 
dist 22=[5.8792963592079394299 ,18.769519692215823731  ] 
dist 23=[4.1990852101176817760 ,12.904074446805491523  ] 
dist 24=[2.1781298255561078179 ,10.077210025754742743  ] 
dist 25=[.00516578696990550829,9.3230788040623990546 ] 
dist 26=[-1.8558981585600315136 ,8.0388326687384886569 ] 
dist 27=[-3.7873386851864158049 ,6.5104277252737350887 ] 
dist 28=[-5.6267827641852831358 ,5.5579325153166901998 ] 
dist 29=[-7.1211866584269044194 ,5.0597009730216907115 ] 
dist 30=[-8.6581178928964094747 ,4.9469786437850475295 ] 
dist 31=[-10.668988840985914352  ,-1.8715531736801433969 ] 
dist 32=[-12.580738581487086000  ,-2.1480895553313124771 ] 
dist 33=[-13.721944701714547378  ,-2.1298575659665605363 ] 
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dist 35=[-15.095342111366216005  ,-1.6736063804338575606 ] 
dist 36=[-15.516144193362798383  ,-1.3197772242374567164 ] 
dist 37=[-15.731394524864750572  ,-1.0584624447790046074 ] 
dist 38=[-15.840742765799564210  ,-.8182301483064934358 ] 
dist 39=[-15.837288153948620246  ,-.5477520315469673031 ] 
dist 40=[-14.336280991316218914  ,-.2813771674788918996 ] 
dist 41=[-14.091669845715153270  ,-.05715836538599570772] 
dist 42=[-13.674148867453174431  ,.17782608123646331948] 
dist 43=[-13.551363783049131301  ,.48745991636396685447] 
dist 44=[-13.145047689159684267  ,.7890538417811319527 ] 
dist 45=[-13.008677026723707383  ,.99214702915450139381] 
dist 46=[-12.857251337418235232  ,1.1616936056519637212 ] 
dist 47=[-12.776335829541774607  ,1.7882581627094673344 ] 
dist 48=[-3.3802650499444590069 ,2.8877411309337942506 ] 
dist 49=[-3.2906658642941543473 ,3.7773639041910436844 ] 
dist 50=[-3.1385470102480727005 ,4.6129036424509701561 ] 
dist 51=[-3.0984217575211795769 ,5.3496967583846282343 ] 
dist 52=[1.9688534544842910162 ,5.8452946580769910585 ] 
dist 53=[2.0062836276029719522 ,6.2593128880795124422 ] 
dist 54=[2.0570721694371157184 ,6.6706288723567455624 ] 
dist 55=[2.0492891150064229401 ,7.5441111019131314531 ] 
dist 56=[2.0204236063070735152 ,8.7120966258655583932 ] 
dist 57=[1.9640545595602508693 ,9.4423144727858266991 ] 
dist 58=[1.8774472396215731648 ,9.9922343022855249965 ] 
dist 59=[1.7278529773232645471 ,10.440578025964948501  ] 
dist 60=[1.5662588529232785395 ,10.790031944976039910  ] 
dist 61=[1.4316954313911407452 ,10.945264277972346499  ] 
dist 62=[1.2915879080219493925 ,11.010237894027220366  ] 
dist 63=[.8610100150928586267 ,10.999283399619739000  ] 
dist 64=[-.0041506279350774731 ,3.7636349776057934997 ] 
dist 65=[-1.0054754644989526095 ,3.0140229430117223520 ] 
dist 66=[-1.8239151178418003094 ,2.8884145979426547608 ] 
dist 67=[-2.6038895628658944008 ,1.8042344217489288364 ] 
dist 68=[-3.2978392381610864650 ,1.6029244244087220171 ] 
dist 69=[-3.7731537816253597732 ,1.3159930798767821525 ] 
dist 70=[-4.1786765976864002318 ,1.2329826318279621203 ] 
dist 71=[-4.5942833821768639453 ,.02422000112456277050] 
dist 72=[-4.9679459226924368926 ,-.19098278647071405722] 
dist 73=[-5.2061456287750126015 ,-.22692049486666306743] 
dist 74=[-5.3905689900467960271 ,-.30562451950376354897] 
dist 75=[-5.5496404272264570668 ,-.31805050540681238817] 
dist 76=[-5.6801109171937894490 ,-.40942801042862480746] 
dist 77=[-5.7504027591421116707 ,-.42111439690025448449] 
dist 78=[-5.7900270560501739589 ,-.41431462625457264138] 
dist 79=[-5.7981179395542985205 ,-.38070499291437543478] 
dist 80=[-2.3729238660762058220 ,-.3325942329645827275 ] 
dist 81=[-2.0957143958010419859 ,-.2501000584084407601 ] 
dist 82=[-1.6007253940896728430 ,.1410546091184018696 ] 
dist 83=[-1.6000576768093039061 ,.5014359066841851298 ] 
dist 84=[-.40948002840615245633,.7691431486775378603 ] 
dist 85=[-.24513011838265347176,1.0195580002065939644 ] 
dist 86=[-.1268572510770499448 ,1.3110124383536012098 ] 
dist 87=[.04703298337265218430,1.5833473382999789414 ] 
dist 88=[.3248498744841786367 ,1.7575130768313437992 ] 
dist 89=[.3622592755100508625 ,1.8927551197863465718 ] 
dist 90=[.41185225783819258664,2.0710807351125718015 ] 
dist 91=[.40419559575113434072,2.2781803528355342706 ] 
dist 92=[.38794059322848920183,2.4482982655534455778 ] 
dist 93=[.36222016316307731586,2.5398146072929944942 ] 
dist 94=[.32467215042278328743,2.5910574063196163237 ] 
dist 95=[.2612154128342204403 ,2.6023314486000950537 ] 
dist 96=[.18602508318717279747,1.6258130222015893987 ] 
dist 97=[.10165253606608735952,1.5807444901724164250 ] 
dist 98=[-.00554498080322780191,1.4875105000396890726 ] 
dist 99=[-.17181900403199149827,1.4612511565389567271 ] 
dist 100=[-.33906210585636874749,1.3535436054668303206 ] 
dist 101=[-.45012492486464962548,1.3287394406307311320 ] 
dist 102=[-.54121506217721783712,1.2692531959754211261 ] 
dist 103=[-.62875115224639739224,1.2490185918969010464 ] 
dist 104=[-.70718897377289193553,1.1539765362040894436 ] 
dist 105=[-.76196563914886095206,1.1298577241629959506 ] 
dist 106=[-.80981756026317887713,1.1029443067617181330 ] 
dist 107=[-.86060834299654484522,1.0905290139912768116 ] 
dist 108=[-.94265912010521898851,1.0832302030883213305 ] 
dist 109=[-1.2033990794733864103 ,1.0864140140662818254 ] 
dist 110=[-1.4975799290629794700 ,1.0974572735297628342 ] 
dist 111=[-1.9137559733609892407 ,1.1219047657052251319 ] 
dist 112=[-2.3208003139527216725 ,1.1484479480816693904 ] 
dist 113=[-2.5785594972844216906 ,1.1678445421300976690 ] 
dist 114=[-2.7760072295494151944 ,1.1855220071776312894 ] 
dist 115=[-2.9424332143528845731 ,1.2052309578399452889 ] 
dist 116=[-3.0759810191888480609 ,1.2245118415010794224 ] 
dist 117=[-3.1422627775412905653 ,1.2404897141403970082 ] 
dist 118=[-3.1742296891492066150 ,1.2569656631296423934 ] 
dist 119=[-3.1776783512292580975 ,1.2782334500192748630 ] 
dist 120=[-3.1309254885623612993 ,1.2985401203581741571 ] 
dist 121=[-3.1109826792322537044 ,1.3111887799733727280 ] 
dist 122=[-3.0593989836741252353 ,1.3205416386743103817 ] 
dist 123=[-3.0356055807015437602 ,1.3277207462713436494 ] 
dist 124=[-2.8992274046840196676 ,1.3328662555987662791 ] 
dist 125=[-2.8639326739102061214 ,1.3341172054508508822 ] 
dist 126=[-2.7746466631374143847 ,1.3327251221729453851 ] 
dist 127=[-2.7405698863902960886 ,1.4674862863330489720 ] 
dist 128=[-1.2687351404277189560 ,1.7596621027679511340 ] 
dist 129=[-1.1835905413550160110 ,1.9924753367954563622 ] 
dist 130=[-1.1583955694660723791 ,2.2045768008487634034 ] 
dist 131=[-1.0513923676694602208 ,2.4909469205864285291 ] 
dist 132=[-1.0284793873967186540 ,2.8073454819217323581 ] 
dist 133=[-.9671945654625456210 ,3.0125723421862852345 ] 
dist 134=[-.9538904393402807179 ,3.1753054152055641001 ] 
dist 135=[-.8373675531869165378 ,3.3221905267927996777 ] 
dist 136=[-.8129745164249187025 ,3.4461581633584507154 ] 
dist 137=[-.7704133706948700033 ,3.5198054548786390461 ] 
dist 138=[-.7589431152785066605 ,3.5686884403035926027 ] 
dist 139=[-.72091099493776986732,3.5942036109638236518 ] 
dist 140=[-.70865798718417204098,3.6027106811738668104 ] 
dist 141=[-.69681529894273083088,3.5959049949837574505 ] 
dist 142=[-.68972136700708568706,3.5565191304166733107 ] 
dist 143=[-.76534221003785782898,3.5320949645999729137 ] 
dist 144=[-1.1640226801385477851 ,1.5962273695394966872 ] 
dist 145=[-1.4877989249618873427 ,1.4199976958246748879 ] 
dist 146=[-1.7930701830102470063 ,1.0127910682397983456 ] 
dist 147=[-2.0623343490408269795 ,.93557300123278427858] 
dist 148=[-2.2424790538045256610 ,.40698581393558782491] 
dist 149=[-2.3914864844518876454 ,.31219634039021618145] 
dist 150=[-2.5365463141021594485 ,.14002279604440054003] 
dist 151=[-2.6627014383950396218 ,.10142115319954916764] 
dist 152=[-2.7386346840092461617 ,-.43056992808976028924] 
dist 153=[-2.7902883897444167095 ,-.50469040223149835947] 
dist 154=[-2.8199305084988266419 ,-.6292041015594722425 ] 
dist 155=[-2.8330956368140736622 ,-.65591006688099614295] 
dist 156=[-2.8310389232347635700 ,-.68828642542394601194] 
dist 157=[-2.8316841385945495027 ,-.66150978950375223779] 
dist 158=[-2.8471540378160024404 ,-.59461153455436248978] 
dist 159=[-2.8493776334267236507 ,-.27313708367086553263] 
dist 160=[-1.2659685230739222987 ,.07586437083481351306] 
dist 161=[-.96302436569361421226,.37037927791553332523] 
dist 162=[-.90675852091988791233,.6666652714724367332 ] 
dist 163=[-.49852151783970928971,.94065350354970664778] 
dist 164=[-.42418675521219502734,1.1471413108569733702 ] 
dist 165=[-.2957144411480179333 ,1.3450927130669750551 ] 
dist 166=[-.26657282878198388176,1.5798653503603812160 ] 
dist 167=[-.20161015812506043932,1.7975443890754635712 ] 
dist 168=[-.26200059864951673263,1.9273102498448993060 ] 
dist 169=[-.32214341927128793186,2.0172581272622280792 ] 
dist 170=[-.39350755518932459103,2.0761058941382141112 ] 
dist 171=[-.49865853288351494954,2.1173348442595599067 ] 
dist 172=[-.61722054888395068892,2.1370014752440173052 ] 
dist 173=[-.74208088365211777643,2.1445976098659871143 ] 
dist 174=[-.89521487337274385651,2.1400740420868868431 ] 
dist 175=[-1.1265604882574541175 ,1.8588448692332375384 ] 
dist 176=[-1.3557971544385607581 ,2.0517432128770028019 ] 
dist 177=[-1.5005175987549265509 ,2.1626339256853555063 ] 
dist 178=[-1.6107485538264463433 ,2.2345087261754931968 ] 
dist 179=[-1.7024038585164210628 ,2.2717603180967015084 ] 
dist 180=[-1.7748704819858891819 ,2.2934939531784711338 ] 
dist 181=[-1.8085556085259291635 ,2.3034608545066708722 ] 
dist 182=[-1.8242792072935384188 ,2.3067077077893640531 ] 
dist 183=[-1.8250990485027792162 ,2.3016274018767577885 ] 
dist 184=[-1.7804225981384844050 ,1.9297345966640233429 ] 
dist 185=[-1.7657255142887044540 ,1.8739649899752237260 ] 
dist 186=[-1.7324475557498870884 ,1.7732087578096350734 ] 
dist 187=[-1.7185306417791180009 ,1.7462138528350814429 ] 
dist 188=[-1.6424300376488758410 ,1.6516612873403866526 ] 
dist 189=[-1.6233391129490552658 ,1.6234860523217361484 ] 
dist 190=[-1.5666402068072619677 ,1.5890291084579974159 ] 
dist 191=[-1.7863322852810111202 ,1.5734100007522142517 ] 
dist 192=[-1.9208620489259636664 ,1.4702746358955322072 ] 
dist 193=[-2.0149481571390435222 ,1.5448795835561415418 ] 
dist 194=[-2.0782056194200618322 ,1.6015390710144417941 ] 
dist 195=[-2.1234503792729065163 ,1.6430926326953752609 ] 
dist 196=[-2.1456776057913136348 ,1.6574408553839709981 ] 
dist 197=[-2.1552679783812056426 ,1.6607094176911678528 ] 
dist 198=[-2.1514185499794344862 ,1.6580683658236803564 ] 
dist 199=[-1.8849736014199285302 ,1.5585471454750726930 ] 
dist 200=[-1.8418684444288624661 ,1.5373983997868060592 ] 
dist 201=[-1.7662712171940390400 ,1.4890117806750246556 ] 
dist 202=[-1.7450984764104171845 ,1.4714408700716118659 ] 
dist 203=[-1.6613323891106627892 ,1.3829567257792276094 ] 
dist 204=[-1.5017406869078781619 ,1.3621526990506305970 ] 
dist 205=[-1.4653131471481537736 ,1.3061291779539031776 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 2, 2, 1, 0, 1] 
dist 0=[57.130334764941560320  ,57.130334764941560320  ] 
dist 1=[56.607199811229094383  ,57.942676832838468860  ] 
dist 2=[55.331127504382611606  ,58.801275254632860602  ] 
dist 3=[53.290517136131958444  ,59.229824894672240021  ] 
dist 4=[49.958975506214387869  ,59.425724706015470847  ] 
dist 5=[46.526873583199926889  ,59.429020358872299440  ] 
dist 6=[44.084785899134449985  ,59.160700274356809108  ] 
dist 7=[41.897781305498813555  ,58.671931452587942109  ] 
dist 8=[39.484115689791168923  ,56.083568514078578334  ] 
dist 9=[37.106711793051902836  ,55.855156798542808238  ] 
dist 10=[35.064509404788915752  ,55.128513620863336258  ] 
dist 11=[32.874787802740381091  ,54.865258007981097145  ] 
dist 12=[29.908479434528082195  ,54.435764988119475997  ] 
dist 13=[26.962588550971990790  ,54.271901394381319088  ] 
dist 14=[24.842326515358510844  ,53.664653316397501684  ] 
dist 15=[22.873319450326929067  ,52.578647017762226207  ] 
dist 16=[20.625111308660450869  ,27.582605676506673234  ] 
dist 17=[18.360251130068810961  ,26.322070187833760956  ] 
dist 18=[16.324158530873354481  ,21.237745197222147293  ] 
dist 19=[14.057360721373582718  ,20.772929859528130044  ] 
dist 20=[10.869971270915293071  ,20.691700394028029739  ] 
dist 21=[7.7251884442137885416 ,17.671287653660331248  ] 
dist 22=[5.6284594639563461982 ,11.962653713591441172  ] 
dist 23=[3.8631131481510884379 ,11.584580261064867275  ] 
dist 24=[.52267449378408857048,7.5985746578567746628 ] 
dist 25=[-1.7221382106986702188 ,7.0201383723366860247 ] 
dist 26=[-3.6012778559235024758 ,6.3360396644218725733 ] 
dist 27=[-5.4821773110032665623 ,5.0696007246792195298 ] 
dist 28=[-7.2310413679796796648 ,3.0175685330124433983 ] 
dist 29=[-8.5837829626948618065 ,2.9054316469738392216 ] 
dist 30=[-9.9147925679695000034 ,-1.5094586182087030917 ] 
dist 31=[-11.578723590924377260  ,-1.6041446331992628403 ] 
dist 32=[-13.133164176971019915  ,-1.4514516885509360437 ] 
dist 33=[-14.027089351369608271  ,-1.1779975442670768146 ] 
dist 34=[-14.618654590060143794  ,-.75911089375822615796] 
dist 35=[-14.964256530755713296  ,-.15787456922590383073] 
dist 36=[-15.191758993589611854  ,.84302798160926591537] 
dist 37=[-15.310682627190862445  ,1.8604211291606655340 ] 
dist 38=[-15.376454799260227148  ,2.5276848083428660563 ] 
dist 39=[-15.390046694431473322  ,3.0623938092936635072 ] 
dist 40=[-13.263766410200192318  ,3.5517052930057643645 ] 
dist 41=[-12.955833947504291571  ,3.9713027890958527627 ] 
dist 42=[-12.406455450200200179  ,4.2282471645751745005 ] 
dist 43=[-12.263282431147617098  ,4.4140488248460136554 ] 
dist 44=[-11.791080765716079068  ,4.5501522353097998508 ] 
dist 45=[-11.641496417317410504  ,4.6521602959511281085 ] 
dist 46=[-11.541927217092022682  ,4.7020394740644953621 ] 
dist 47=[-11.508468148710345050  ,4.7230655355952735226 ] 
dist 48=[-4.9387194697719796290 ,4.7099393072981081520 ] 
dist 49=[-4.4514066803881216124 ,5.0821387627539118488 ] 
dist 50=[-4.3358391979329243672 ,5.8041741804775769106 ] 
dist 51=[-4.1530065543229690372 ,6.2934840313646158769 ] 
dist 52=[-4.0992135758745173470 ,6.7062567925409579701 ] 
dist 53=[1.2158200395899414834 ,7.1229372094572954959 ] 
dist 54=[.6211022544246864988 ,7.4843335047438549478 ] 
dist 55=[.1139717388493018179 ,7.6764962152652108946 ] 
dist 56=[-.4032915791044469477 ,8.8188846079824268964 ] 
dist 57=[-.8850092111299575071 ,9.5549981029493852996 ] 
dist 58=[-1.2504663657617994700 ,10.118877812615006677  ] 
dist 59=[-1.5994136894356948705 ,10.595309711188930895  ] 
dist 60=[-2.0153665438363621786 ,10.979083163890166882  ] 
dist 61=[-2.4036310363053080348 ,11.173081214603148265  ] 
dist 62=[-2.6421863291965235801 ,11.265093179580242570  ] 
dist 63=[-2.8159889514855767514 ,11.274432796965159898  ] 
dist 64=[-2.9460300155673518979 ,3.8398995296254817768 ] 
dist 65=[-3.1336119139244251546 ,3.7070649767018298285 ] 
dist 66=[-3.8492346207661883099 ,2.6972254085481701696 ] 
dist 67=[-4.3559013601454398951 ,2.5054275315038920644 ] 
dist 68=[-4.8057377431427085694 ,2.1931565250124613634 ] 
dist 69=[-5.2947194782865684458 ,2.1132339249340287950 ] 
dist 70=[-5.7353235160006481083 ,.65972585515837807176] 
dist 71=[-5.9921809221469164518 ,.47045936325490284489] 
dist 72=[-6.1633890491889329835 ,.13661369468556277259] 
dist 73=[-6.2622829746557571538 ,.38493681956262066531] 
dist 74=[-6.3817660631112988844 ,.57513048554851184668] 
dist 75=[-6.4764037919169534321 ,.75845163485165122208] 
dist 76=[-6.5396088237323469216 ,.97938325645757293303] 
dist 77=[-6.5465127265025954932 ,1.1869696755421848327 ] 
dist 78=[-6.5210420932674734751 ,1.3170770578778616131 ] 
dist 79=[-6.4952540149930878994 ,1.4148544711035633888 ] 
dist 80=[-2.6780303401147961673 ,1.4935131361973831718 ] 
dist 81=[-2.3454317815052104592 ,1.5756989293996590484 ] 
dist 82=[-1.5803669395773270474 ,2.1249317590750480546 ] 
dist 83=[-1.4355845631009005806 ,2.5203782541777214850 ] 
dist 84=[-.45947925869131559731,2.8779659005692855694 ] 
dist 85=[-.28656316720584244747,3.2762304544815143458 ] 
dist 86=[.03217714228785516781,3.6409452464292083632 ] 
dist 87=[.1037678607242858673 ,3.8647219907359669521 ] 
dist 88=[.8894513330840082182 ,4.0276446040854707842 ] 
dist 89=[.7796673663140639958 ,4.1496181267519660488 ] 
dist 90=[.6783983385287436007 ,4.3266406873979133466 ] 
dist 91=[.5642939251670659332 ,4.5102941814671296661 ] 
dist 92=[.4033049289000887608 ,4.6472147106988272599 ] 
dist 93=[.2415612889570886937 ,4.7103531760631962583 ] 
dist 94=[.1244367175602445065 ,4.7314020520723418275 ] 
dist 95=[-.19101495090723503894,4.7289029670621277293 ] 
dist 96=[-.51277347279936074643,2.8331438408857822827 ] 
dist 97=[-.83528057571830682517,2.9136251505878883469 ] 
dist 98=[-1.1867726608446596666 ,2.9705428211488496485 ] 
dist 99=[-1.6812427084258471388 ,3.0209418716897820500 ] 
dist 100=[-2.4108324251561586726 ,3.0753987460984488462 ] 
dist 101=[-3.1313026747697817400 ,3.1203949101118350108 ] 
dist 102=[-3.5894019545668578609 ,3.1330518221280271864 ] 
dist 103=[-3.9420723991767589658 ,3.1276094189519493623 ] 
dist 104=[-4.2420021596628633856 ,3.1178119471014810422 ] 
dist 105=[-4.4843320037083728168 ,3.0332243672592158024 ] 
dist 106=[-4.6072466138661103934 ,3.0062900470843559485 ] 
dist 107=[-4.6714871496265612851 ,2.9340571863281372335 ] 
dist 108=[-4.6805364988414699846 ,2.9033758221321566199 ] 
dist 109=[-4.6139795159462591469 ,2.4885834578343602456 ] 
dist 110=[-4.5812495645920064665 ,2.4212204955465343407 ] 
dist 111=[-4.5241913016643181848 ,2.2460741142241609689 ] 
dist 112=[-4.4990395888617085982 ,2.2089550531622833806 ] 
dist 113=[-4.3651025500526737057 ,1.8978135115442527814 ] 
dist 114=[-4.3259282440668124244 ,1.8325480888325523459 ] 
dist 115=[-4.1975510637994063005 ,1.7362594564948285119 ] 
dist 116=[-4.1625205811431274358 ,1.7056773225654384450 ] 
dist 117=[-2.0629891656289188581 ,1.7183752663331527959 ] 
dist 118=[-2.1862408774338332624 ,1.7635898124113903108 ] 
dist 119=[-2.2732866835567304607 ,1.7854141299675554496 ] 
dist 120=[-2.3503143510697223820 ,1.9024097454504870121 ] 
dist 121=[-2.4335821677413031827 ,2.0115048800935895504 ] 
dist 122=[-2.5142309679468048370 ,2.1041895362341284285 ] 
dist 123=[-2.5807944727820264498 ,2.1599890446821712037 ] 
dist 124=[-2.6495786446252649363 ,2.1993972715716042325 ] 
dist 125=[-2.7390574696283772396 ,2.5222165184204087444 ] 
dist 126=[-2.8214604985455834823 ,3.1781082666854144756 ] 
dist 127=[-2.8620159940081488619 ,3.5924733994497539801 ] 
dist 128=[-2.8794951930204220663 ,3.9084942686988245397 ] 
dist 129=[-2.8779826031073418460 ,4.1720835947388314024 ] 
dist 130=[-2.8468117983728237460 ,4.3812839842684297977 ] 
dist 131=[-2.8316238185334085849 ,4.4803377696149226229 ] 
dist 132=[-2.7751004914707327574 ,4.5300271977083750558 ] 
dist 133=[-2.7536527807810244956 ,4.5423045527006316829 ] 
dist 134=[-2.4467120959978792411 ,4.4181276043904945283 ] 
dist 135=[-2.3937670431887757541 ,4.3787330549664800517 ] 
dist 136=[-2.2490492785988030493 ,4.3076476444037531005 ] 
dist 137=[-2.2195690182833909624 ,4.2801682264224832398 ] 
dist 138=[-1.9430262189396233315 ,4.1412260755438391466 ] 
dist 139=[-1.9347529453854562107 ,4.1015327160969899931 ] 
dist 140=[-1.9100963657506689706 ,3.9791038197644795168 ] 
dist 141=[-1.8966182706747967640 ,3.9421822264232194454 ] 
dist 142=[-.05305306725559596086,1.7127473990836558725 ] 
dist 143=[-.32480382478268386633,1.7078950572139590883 ] 
dist 144=[-.5479189512693961090 ,.94333792043806756574] 
dist 145=[-.7623409228840227257 ,.86996663082954386476] 
dist 146=[-.9542319840471147926 ,.69517476800021428383] 
dist 147=[-1.0874739572259545117 ,.6637981775885415104 ] 
dist 148=[-1.2030084965238020316 ,.41797519700617581003] 
dist 149=[-1.3242689139570046223 ,.3724721633029171688 ] 
dist 150=[-1.4339285630052780043 ,.30030565220689330908] 
dist 151=[-1.5031877252200126565 ,.28186360331680718195] 
dist 152=[-1.5559890970662873042 ,-.04003999631756345317] 
dist 153=[-1.5999945906590732380 ,-.08154780921571256179] 
dist 154=[-1.6348792127763932463 ,-.17062175903760794532] 
dist 155=[-1.6512951234113181693 ,-.18922586524144096941] 
dist 156=[-1.6572952836441225487 ,-.27853617839215902435] 
dist 157=[-1.6543701420632632907 ,-.29383817715443158296] 
dist 158=[-1.2735430691474527526 ,-.32057015792651761546] 
dist 159=[-1.2690512895254711384 ,-.3255402193144478834 ] 
dist 160=[-.51174066869447096548,-.32939521010264957014] 
dist 161=[-.48524584900060088848,-.1843392011479375376 ] 
dist 162=[-.35776757270403608462,-.04727226544249305447] 
dist 163=[-.38081828492659961586,.06045510385231420142] 
dist 164=[-.40805553922129620693,.1670795443956267843 ] 
dist 165=[-.43846607508515180761,.2997466758780882321 ] 
dist 166=[-.47696578252822268146,.4259070800565729393 ] 
dist 167=[-.53647057486157198143,.5065782034669641192 ] 
dist 168=[-.59859001170927170552,.5691992051971619326 ] 
dist 169=[-.64751924605861846271,.6233638527451861132 ] 
dist 170=[-.69605830663646271827,.6678124185385739691 ] 
dist 171=[-.75662063983138836437,.6916802303911661696 ] 
dist 172=[-.8201236514350858978 ,.7050043398534169574 ] 
dist 173=[-.88039266292979729208,.76416906009970878439] 
dist 174=[-.9497104309429624954 ,.91364815412012879574] 
dist 175=[-1.0493083906558143819 ,1.1297998105757130401 ] 
dist 176=[-1.1459555905956592098 ,1.3410217006757374909 ] 
dist 177=[-1.2035023925157053351 ,1.4708351798062875872 ] 
dist 178=[-1.2433081742164335851 ,1.5656399567259485798 ] 
dist 179=[-1.2691858471731423329 ,1.6372045281670871312 ] 
dist 180=[-1.2854860479729158703 ,1.6918138541444096395 ] 
dist 181=[-1.2876503754032076333 ,1.7189796507338468335 ] 
dist 182=[-1.2830103173053820086 ,1.7311964673527873637 ] 
dist 183=[-1.2766646932526095937 ,1.7311877645090541238 ] 
dist 184=[-1.1691583011797112366 ,1.5792820228144514271 ] 
dist 185=[-1.1489367012692495148 ,1.5518687375189101020 ] 
dist 186=[-1.1005388727160617698 ,1.5063735485728403807 ] 
dist 187=[-1.0835803892109656303 ,1.4917641771182574381 ] 
dist 188=[-1.0002087356930422954 ,1.4406614032359617076 ] 
dist 189=[-.98101415190262169653,1.4235438537274387025 ] 
dist 190=[-1.0731312747311302145 ,1.3932487193477852929 ] 
dist 191=[-1.2140980454292288956 ,1.3829695554258388419 ] 
dist 192=[-1.3232394124760215016 ,.7335700413490264217 ] 
dist 193=[-1.4172143293590057696 ,.7313147109315363111 ] 
dist 194=[-1.4940564339879747943 ,.7277487079382309057 ] 
dist 195=[-1.5348503089908642449 ,.7237790870107596588 ] 
dist 196=[-1.5569879675574373889 ,.7157340622397447679 ] 
dist 197=[-1.5609185611307039995 ,.7117774303847445323 ] 
dist 198=[-1.5535551058238678811 ,.6895160870292542822 ] 
dist 199=[-1.5460272130665242233 ,.6822572961994233786 ] 
dist 200=[-1.5285102846765620899 ,.6676752061132602083 ] 
dist 201=[-1.5194494824748702767 ,.6622248758792994147 ] 
dist 202=[-1.4649678285295307969 ,.6344422310431309284 ] 
dist 203=[-1.4328756095266855322 ,.6275759547694750781 ] 
dist 204=[-1.2926137949017888656 ,.60437290393825518453] 
dist 205=[-1.1910646003516601171 ,.60032993992376279349] 
dist 206=[-.4211303877199077954 ,.58484737003095922069] 
dist 207=[-.4150604321811327620 ,.79512607347968995344] 
dist 208=[-.01389159623289538101,.96459217503985663932] 
dist 209=[.02331557024609378786,1.1222038845707851040 ] 
dist 210=[.09644756678654828839,1.2597648303922493451 ] 
dist 211=[.11395650167599383823,1.3492456624095720648 ] 
dist 212=[.16798815740304816982,1.4204733680990903497 ] 
dist 213=[.17829993586943406259,1.4852203019740972964 ] 
dist 214=[.17698130317558734371,1.5397604215430376596 ] 
dist 215=[.15945164244149809256,1.5702715818790922202 ] 
dist 216=[.13503086915455740226,1.5889677850697926850 ] 
dist 217=[.1062220794828369611 ,1.5963757317546240001 ] 
dist 218=[.06874102945573030598,1.5959459285362026926 ] 
dist 219=[.00972412349730018564,1.5920442020459937584 ] 
dist 220=[-.05847579216183522034,1.5687819434108327147 ] 
dist 221=[-.1325899542557028194 ,1.5602785135779950635 ] 
dist 222=[-.22508731587987775316,.9424180978738990980 ] 
dist 223=[-.36662146908051172019,.9365295406728797485 ] 
dist 224=[-.50950508890025470979,.46427765917925252906] 
dist 225=[-.65023264946453810836,.42918756376013249441] 
dist 226=[-.76742047250398022125,.20017728667312512391] 
dist 227=[-.88280181255557685633,.15905249387687625682] 
dist 228=[-.98791922179325830537,.08179618447547129515] 
dist 229=[-1.0641627665683968135 ,.06370992201513556521] 
dist 230=[-1.1574908925324871152 ,-.15762564635738103912] 
dist 231=[-1.2313710989999290617 ,-.18949073629379556184] 
dist 232=[-1.2824671884278646094 ,-.23944436273427024665] 
dist 233=[-1.3198820963957225224 ,-.25116633841595860485] 
dist 234=[-1.3402641911784824981 ,-.25785591832406978835] 
dist 235=[-1.3442530233122170854 ,-.24221389365710416422] 
dist 236=[-1.3382349802852991985 ,-.20976244338379116701] 
dist 237=[-1.3068634711865848933 ,-.14596727528598444992] 
dist 238=[-.82539660237168876141,-.07735103619166051279] 
dist 239=[-.81711985894427488152,.02615948221208700758] 
dist 240=[-.39731438254257183177,.22479113775055478857] 
dist 241=[-.35493877593826475935,.35835686261666760298] 
dist 242=[-.26231851464593870851,.46958104188796444292] 
dist 243=[-.23979757859734774813,.57908932682310751855] 
dist 244=[-.13431038701810022783,.67885374980647433619] 
dist 245=[-.11548960867841552302,.75120837159011142421] 
dist 246=[-.07014178413343877786,.81720125455834339095] 
dist 247=[-.06360860382798446326,.8915878431878870745 ] 
dist 248=[.35259512033316298877,.95850187454528594964] 
dist 249=[.39209695214259771249,.9946857407395724694 ] 
dist 250=[.45650111701901163628,1.0152193567996020259 ] 
dist 251=[.48585156412981205142,1.0202330917920456381 ] 
dist 252=[.42911865423105633772,1.0187509888273860587 ] 
dist 253=[.32896799117804158061,1.0176225502735864774 ] 
dist 254=[.2004646863937831183 ,1.0161486985282073546 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 0, 0, 2] 
dist 0=[65.741482348638716428  ,65.741482348638716428  ] 
dist 1=[65.340944141988639888  ,65.918772095797672839  ] 
dist 2=[64.197890223967153787  ,66.170389405248237735  ] 
dist 3=[62.789493878041862341  ,66.367629939348078196  ] 
dist 4=[61.329456716166584402  ,66.327816311082512577  ] 
dist 5=[59.549386145918396042  ,66.169208039850393457  ] 
dist 6=[56.611043096542420058  ,66.020832484209007923  ] 
dist 7=[52.912235566108586268  ,65.577737328578233020  ] 
dist 8=[50.247179360162567203  ,65.270358139388688290  ] 
dist 9=[46.364181234075735109  ,61.713728985280650939  ] 
dist 10=[40.043473652423624885  ,61.025885813776711684  ] 
dist 11=[33.668713027051819314  ,60.074605905675090749  ] 
dist 12=[29.330692082368791267  ,59.731970702130048929  ] 
dist 13=[25.646976464970455583  ,59.127414050136005495  ] 
dist 14=[21.884975943647918524  ,57.910399934768041565  ] 
dist 15=[18.353753255221109881  ,51.675652577589636392  ] 
dist 16=[15.591617397985728369  ,47.501473380008692235  ] 
dist 17=[12.859863100121799466  ,29.244059385771241883  ] 
dist 18=[9.4500892771648288809 ,26.906345367557922320  ] 
dist 19=[6.1928172955187272778 ,23.815952934471790355  ] 
dist 20=[4.0700108695756645164 ,23.330654266278941107  ] 
dist 21=[2.3690390335842205021 ,22.711184739981159663  ] 
dist 22=[.7960446978741935182 ,22.538896487584214259  ] 
dist 23=[-.57646717855307559099,10.388790367769091253  ] 
dist 24=[-1.4769557582936687117 ,10.062617078867041753  ] 
dist 25=[-2.2050530550455840495 ,1.7183352542577107212 ] 
dist 26=[-3.9159124734949874581 ,.7495037412579043210 ] 
dist 27=[-6.1345750511925148001 ,-1.2505375689802070229 ] 
dist 28=[-7.7973334672101036671 ,-1.6199027009302885390 ] 
dist 29=[-9.3770702907663838125 ,-3.2126684980970522049 ] 
dist 30=[-11.264121111161519501  ,-3.8002926422821617230 ] 
dist 31=[-13.032059390597322702  ,-4.7154973933687233806 ] 
dist 32=[-14.135985486275013441  ,-5.0272980541484947289 ] 
dist 33=[-14.968788866401549340  ,-5.3333292700212396477 ] 
dist 34=[-15.653660678550886155  ,-4.9375806436893301000 ] 
dist 35=[-16.194144012990892710  ,-4.4847308400902444791 ] 
dist 36=[-16.450178945996446699  ,-4.0771481352804168507 ] 
dist 37=[-16.561673963692373516  ,-3.6276941315230745220 ] 
dist 38=[-16.562987051730798542  ,-2.0302305533697081724 ] 
dist 39=[-8.3889726983161399934 ,-.04463884010669575024] 
dist 40=[-8.3642751230409226164 ,1.4417173237875464209 ] 
dist 41=[-6.8428205666055746347 ,2.6672919796091938946 ] 
dist 42=[-6.6356465623620108989 ,3.8543173022096839867 ] 
dist 43=[-6.2250508716287353017 ,4.9234900977232778099 ] 
dist 44=[-6.1152359892498276491 ,5.6790276312358307066 ] 
dist 45=[-5.7153965001545757806 ,6.3486411184259459642 ] 
dist 46=[-5.6199762385871968236 ,7.0751824665574352745 ] 
dist 47=[-5.4813307228037103961 ,7.7319288851462295845 ] 
dist 48=[-5.4367942512191103787 ,8.1231217595194221507 ] 
dist 49=[-2.7744204456921356039 ,8.3946423897953124145 ] 
dist 50=[-2.7169815778759151645 ,8.5738773330000188398 ] 
dist 51=[-1.5411714655090734765 ,8.6841082782773951169 ] 
dist 52=[-1.3842227392221591125 ,8.7016411760762543886 ] 
dist 53=[-1.0349593998213376661 ,8.6429991607397479771 ] 
dist 54=[-.9518808724680005211 ,8.6195898812139470481 ] 
dist 55=[-.5234643565222316780 ,5.2514756345545638167 ] 
dist 56=[-.4437549885707997424 ,5.2376519191972915592 ] 
dist 57=[-.5217798708795600416 ,5.1767619176983930764 ] 
dist 58=[-1.3372895828675301374 ,5.1397336091557328328 ] 
dist 59=[-2.0874863910601541020 ,4.6247343446193466889 ] 
dist 60=[-2.6429695482547798210 ,4.7902076191478610661 ] 
dist 61=[-3.1608202753561807516 ,4.9139297912798890488 ] 
dist 62=[-3.7609745390651496965 ,4.9592502365724470605 ] 
dist 63=[-4.3167606224403540222 ,4.9737063061702527909 ] 
dist 64=[-4.6576646991711842894 ,4.9740565956412542238 ] 
dist 65=[-4.9057210721976083120 ,-.0799061886993051869 ] 
dist 66=[-5.0911777029579517006 ,-.3169074338697927942 ] 
dist 67=[-5.2251540657689065586 ,-.8558564676025675683 ] 
dist 68=[-5.2678698464005314654 ,-.93678062587493402041] 
dist 69=[-5.2742773140652549291 ,-1.4975503698558704778 ] 
dist 70=[-5.2634177318065999811 ,-1.2243834985160685555 ] 
dist 71=[-3.5065961086355758652 ,-.9346125466831977063 ] 
dist 72=[-3.5495628243508974682 ,-.7311996810407920785 ] 
dist 73=[-3.5641469232661551525 ,-.5532006766011826796 ] 
dist 74=[-3.5600609243139759100 ,-.1502935007786718647 ] 
dist 75=[-2.5566072289738285023 ,.2523697656216200813 ] 
dist 76=[-2.6155223004722676990 ,.5601420313571547893 ] 
dist 77=[-2.6591535059286440336 ,.8564602821648569680 ] 
dist 78=[-2.6739415462885691258 ,1.2134912061917424387 ] 
dist 79=[-2.6711998515134487070 ,1.5495566203120997242 ] 
dist 80=[-2.6646359031691781813 ,1.7622711355290636923 ] 
dist 81=[-1.1844419065778334605 ,1.9248315270494412378 ] 
dist 82=[-1.0568626271232011380 ,2.0608560326349966725 ] 
dist 83=[-.76305823416537006816,2.1689951778432473517 ] 
dist 84=[-.70697551949813964088,2.2203331098909307403 ] 
dist 85=[-.3312740657049356852 ,2.2447412989133479558 ] 
dist 86=[-.2646000093277344973 ,2.2454892422810066387 ] 
dist 87=[-.1409665278241129262 ,1.6556835985802758422 ] 
dist 88=[-.1129679752311390419 ,1.5981523656963969390 ] 
dist 89=[-.08728240858960935404,1.4587596433084549130 ] 
dist 90=[-.1463534053387178729 ,1.4640675739898075173 ] 
dist 91=[-.2004397081552079059 ,1.4957761123101082947 ] 
dist 92=[-.2392417555278468187 ,1.5724068549278825145 ] 
dist 93=[-.2738588573842795879 ,1.6305408757884264178 ] 
dist 94=[-.3112687649504719621 ,1.6585214587365345419 ] 
dist 95=[-.3446753513790724429 ,1.6697021304251705578 ] 
dist 96=[-.42810658454468117323,1.6694408237745628080 ] 
dist 97=[-.58794007249679349578,1.2497608800355343470 ] 
dist 98=[-.76365436282333339084,1.2665079378213353264 ] 
dist 99=[-.93571129847355352842,1.2827150598280897494 ] 
dist 100=[-1.0809920188501758159 ,1.2937124722475178335 ] 
dist 101=[-1.2342837367665345244 ,1.3030099221962406260 ] 
dist 102=[-1.4383523525090094872 ,1.3124091098190764804 ] 
dist 103=[-1.6356448735007816461 ,1.3210996986783844051 ] 
dist 104=[-1.8209332583476333797 ,1.3275508565137185035 ] 
dist 105=[-1.9771321391341411287 ,1.3335170333362218170 ] 
dist 106=[-2.1278996872336841330 ,1.3402417762483339940 ] 
dist 107=[-2.2634403691467461894 ,1.3454671014241546276 ] 
dist 108=[-2.3588843309597714610 ,1.3454467240151755643 ] 
dist 109=[-2.4431370706456705918 ,1.3414685892066460285 ] 
dist 110=[-2.5340254287111835967 ,1.3361654398191436326 ] 
dist 111=[-2.6134983291268367096 ,1.3168612402519670218 ] 
dist 112=[-2.6522027601569785676 ,1.3085083768904871668 ] 
dist 113=[-2.6684185477794123667 ,1.2814951446580513984 ] 
dist 114=[-2.6680367359814973357 ,1.2699116968789781065 ] 
dist 115=[-2.6361719029436565010 ,1.1929785052615149736 ] 
dist 116=[-2.6211507444605979208 ,1.1750197162807411479 ] 
dist 117=[-2.5862428576486032823 ,1.1297217756016038206 ] 
dist 118=[-2.5713644478874269211 ,1.5216292912388380694 ] 
dist 119=[-2.4837579643435910747 ,2.2068394519143234905 ] 
dist 120=[-2.4606859748802439517 ,2.6518273104802320134 ] 
dist 121=[-2.3820154591400520264 ,3.0052413073096486597 ] 
dist 122=[-2.3656972763440507946 ,3.3251510730741317783 ] 
dist 123=[-1.8705416359022146501 ,3.5983391208876814895 ] 
dist 124=[-1.8340717788088194943 ,3.7653761352237959572 ] 
dist 125=[-1.7326463010346967838 ,3.8863657519542100765 ] 
dist 126=[-1.7120130966953111902 ,3.9758711253339714091 ] 
dist 127=[-1.4474569731855310745 ,4.0408047807394011520 ] 
dist 128=[-1.4004165167800284369 ,4.0637736581850249020 ] 
dist 129=[-1.2966682515270418239 ,4.0609736227615222161 ] 
dist 130=[-1.2649321913693382804 ,4.0522474806396708282 ] 
dist 131=[-1.1245950917850273910 ,3.9647980372029834187 ] 
dist 132=[-1.0954543720114263349 ,3.9356458881468856569 ] 
dist 133=[-1.0190990481892561787 ,3.8413242403512837847 ] 
dist 134=[-1.0028580388340728732 ,3.8073836312679483382 ] 
dist 135=[-1.0949665800946931315 ,2.7650425097328762538 ] 
dist 136=[-1.5888752215538179529 ,2.7636386480413877674 ] 
dist 137=[-1.9894510612544373292 ,2.7475185533370229907 ] 
dist 138=[-2.4385263883995844503 ,2.7327155280788551823 ] 
dist 139=[-2.8482278948122176594 ,1.2498300211228038344 ] 
dist 140=[-3.1266665632923394711 ,1.1175646813938938852 ] 
dist 141=[-3.3617208599084690051 ,.80690954616283485109] 
dist 142=[-3.5983652850229538135 ,.75187716942476537452] 
dist 143=[-3.8070773546649695080 ,.33359114811036005445] 
dist 144=[-3.9307088772975380340 ,.25817273295060103712] 
dist 145=[-4.0154575834456675329 ,.13413679243726493562] 
dist 146=[-4.0690611541862504560 ,.10473835490844586547] 
dist 147=[-4.0984232977251058459 ,-.28285668369327686191] 
dist 148=[-4.0982559398304032434 ,-.3242532170248715662 ] 
dist 149=[-4.0622050833538210524 ,-.37200187242601222511] 
dist 150=[-4.0424550725172060334 ,-.37390709518616388122] 
dist 151=[-2.0359971908159743669 ,-.16231743934360128536] 
dist 152=[-1.9944693796037756138 ,.30007707483132022253] 
dist 153=[-2.0006501725363548899 ,.68979294971795282369] 
dist 154=[-1.9970916245510000545 ,1.0810515088708657906 ] 
dist 155=[-.73468058072605589247,1.4423436987363441265 ] 
dist 156=[-.62485215160553296958,1.7125242457748397168 ] 
dist 157=[-.44733878620083975774,1.9671314368421968446 ] 
dist 158=[-.42479791229499299445,2.2663004576309226094 ] 
dist 159=[-.41440317036721576594,2.5423412720348416980 ] 
dist 160=[-.42053924387731925189,2.7046914947429822038 ] 
dist 161=[-.43749508413785382081,2.8145069132106628997 ] 
dist 162=[-.47361165238230328636,2.8809917237911015638 ] 
dist 163=[-.51523737664505239512,2.9249609695528164172 ] 
dist 164=[-.55416870946022537321,2.9449626480791724500 ] 
dist 165=[-.59850276207166157441,2.9511922939556093499 ] 
dist 166=[-.66167893768031372317,2.9430037332537728425 ] 
dist 167=[-.73196852338774836762,1.5469326775488686662 ] 
dist 168=[-.80467721202244191555,1.5561445901396644048 ] 
dist 169=[-.89292926358670503744,1.5564853918508276471 ] 
dist 170=[-1.0252200775422172028 ,1.5528353039925307479 ] 
dist 171=[-1.1558592819153792776 ,1.7283962174615612145 ] 
dist 172=[-1.2375227239609765874 ,1.8660218122477927396 ] 
dist 173=[-1.3065060847762114275 ,1.9648078072812496362 ] 
dist 174=[-1.5493133927179560059 ,2.0361496978952467762 ] 
dist 175=[-1.7776510592661780292 ,2.0885187625617381421 ] 
dist 176=[-1.9181073294086240578 ,2.1116181334986101105 ] 
dist 177=[-2.0208067874784221294 ,2.1179770036979962930 ] 
dist 178=[-2.0985340907600954894 ,2.1160453114058645150 ] 
dist 179=[-2.1558937819746741501 ,1.9181855973436797677 ] 
dist 180=[-2.1773448499291716028 ,1.8829564922540367004 ] 
dist 181=[-2.1830826507767075489 ,1.8163509437544586826 ] 
dist 182=[-2.3613566432852439666 ,1.8956321273762234610 ] 
dist 183=[-2.7574353651574325018 ,2.0998451429277001132 ] 
dist 184=[-2.9995746841466273404 ,2.2244832220668962575 ] 
dist 185=[-3.1748737050056863339 ,2.3144286741995972584 ] 
dist 186=[-3.3043158891850776445 ,2.3802538376189071551 ] 
dist 187=[-3.4012506167819431705 ,2.4257931406074230593 ] 
dist 188=[-3.4468705782508828358 ,2.4362907912765121980 ] 
dist 189=[-3.4635585213909798544 ,2.4318274030329247462 ] 
dist 190=[-3.4621085433935918561 ,2.4294292382792175387 ] 
dist 191=[-3.1458147694034542628 ,2.2831662513013784455 ] 
dist 192=[-3.0892006540803999710 ,2.2525652924487648746 ] 
dist 193=[-2.9869970325856059979 ,2.1728962773813326324 ] 
dist 194=[-2.9563388132533283981 ,2.1438833689928064942 ] 
dist 195=[-2.8323775135661963791 ,1.9856984094832559562 ] 
dist 196=[-2.7960842968208046823 ,1.9479382136577942316 ] 
dist 197=[-2.7188650535253279893 ,1.8724716508004558294 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 1, 2, 1, 1, 2] 
dist 0=[59.667076657616610555  ,59.667076657616610555  ] 
dist 1=[58.174246419495836988  ,60.431684976127368818  ] 
dist 2=[56.325599113235354624  ,60.846131796118482857  ] 
dist 3=[54.140337544972101919  ,60.941094368300686561  ] 
dist 4=[51.287311853396021862  ,60.886038139256390328  ] 
dist 5=[46.772551324668021761  ,60.448038869694886154  ] 
dist 6=[42.173723541855688103  ,60.285009538586359094  ] 
dist 7=[38.984928451724495855  ,60.059070926220215966  ] 
dist 8=[36.214189851707297756  ,59.644147108141081338  ] 
dist 9=[33.284123847263767870  ,59.447096962479783295  ] 
dist 10=[30.470045143583975255  ,59.006774301735576323  ] 
dist 11=[28.162041616612425401  ,58.815897013006836142  ] 
dist 12=[25.777884115048518456  ,57.831670982788436478  ] 
dist 13=[22.659067513777291492  ,57.549211151007637596  ] 
dist 14=[19.603097885093854922  ,57.209469599764574378  ] 
dist 15=[17.469506404288322461  ,55.157176392270851319  ] 
dist 16=[15.596508506556673632  ,50.051131229419523296  ] 
dist 17=[13.580609715093047775  ,30.619224262820379413  ] 
dist 18=[11.616958172771829550  ,28.516856581501876165  ] 
dist 19=[9.9518963999696106605 ,24.013119164545356232  ] 
dist 20=[8.1777293366996136440 ,22.877668686289754277  ] 
dist 21=[5.7768559201403680640 ,16.813216402588021735  ] 
dist 22=[3.4400851273836400298 ,15.758967053704370404  ] 
dist 23=[1.9218137319187628249 ,14.001134886089882783  ] 
dist 24=[.70238550192864012293,13.611330090377276485  ] 
dist 25=[-.43973573088108281439,8.5879392215598130428 ] 
dist 26=[-1.4545431597546259561 ,8.0205872518381056678 ] 
dist 27=[-2.1651053225312510880 ,7.8985037244196824453 ] 
dist 28=[-3.7298410612101607942 ,4.8578126463222650368 ] 
dist 29=[-5.5900888723078389152 ,2.4247820366390473073 ] 
dist 30=[-7.0407274844321556331 ,-2.1165092340568266119 ] 
dist 31=[-8.4781808040182718262 ,-2.5708527707527567629 ] 
dist 32=[-10.287459183869200885  ,-3.3680608570373570128 ] 
dist 33=[-11.992934702686985057  ,-3.2728787765005371542 ] 
dist 34=[-13.015961530532949169  ,-3.0952927598686165012 ] 
dist 35=[-13.744683831120220634  ,-2.8174706811090253356 ] 
dist 36=[-14.273494413509660670  ,-2.4157276978549213323 ] 
dist 37=[-14.663076185103328173  ,-1.7435261399655833241 ] 
dist 38=[-14.834927358491916421  ,-1.0556994391780640386 ] 
dist 39=[-14.893748727600671143  ,-.5914015388207237188 ] 
dist 40=[-14.882643494835689628  ,-.2038787033287887861 ] 
dist 41=[-13.860930321270280134  ,.17807228565272448449] 
dist 42=[-13.674048429682280619  ,.52581408118356636936] 
dist 43=[-13.297355930040680002  ,.77707371980323717558] 
dist 44=[-13.176589827623657223  ,1.8271803491847972693 ] 
dist 45=[-12.636095277197106081  ,2.9650579081342447413 ] 
dist 46=[-12.504528261290818981  ,3.8822688442907023018 ] 
dist 47=[-12.146947634460761483  ,4.7374036987590863992 ] 
dist 48=[-12.041167274507969801  ,5.4868307272232252287 ] 
dist 49=[-4.7046539019394730401 ,5.9822859869509031828 ] 
dist 50=[-4.0335344808421954636 ,6.3866532545060702067 ] 
dist 51=[-2.5190866303798883047 ,6.8088847101120620847 ] 
dist 52=[-2.2285442762945421629 ,7.2161361580636639547 ] 
dist 53=[-.53139948584498359501,7.4529461188214578317 ] 
dist 54=[-.05845152213512915626,7.6107654158710940449 ] 
dist 55=[.55639659437237751072,7.9854880915506164293 ] 
dist 56=[.69892199773836555557,8.9812015442639971482 ] 
dist 57=[.65078635736973016764,9.8900450835262765059 ] 
dist 58=[.5031035321057659373 ,10.409797467052128901  ] 
dist 59=[.3816323113667033571 ,10.744958470854174033  ] 
dist 60=[.2566729107611534732 ,10.917050737479312383  ] 
dist 61=[-.1473577623146858262 ,11.017746459672308834  ] 
dist 62=[-.91050087109857026236,11.067827564923843278  ] 
dist 63=[-1.6790380017087108989 ,11.090839430360441158  ] 
dist 64=[-2.3900370128928872039 ,11.083150875552760000  ] 
dist 65=[-2.9237667545435830132 ,1.6306990559156311048 ] 
dist 66=[-3.4288088200961117578 ,1.3259914249631794694 ] 
dist 67=[-4.0255037098920859253 ,1.2422637437539067758 ] 
dist 68=[-4.5762555149745530996 ,.0357703378376786164 ] 
dist 69=[-4.8980910044809989056 ,.08888278242046440973] 
dist 70=[-5.1136071044717367125 ,.14567632844355656742] 
dist 71=[-5.2402990038154836483 ,.18527391333346019887] 
dist 72=[-5.7165577926201594937 ,.21921865722650112325] 
dist 73=[-6.2087618327830376946 ,.25353112200123937284] 
dist 74=[-6.5151580245903477998 ,.28470794881866244958] 
dist 75=[-6.7438186571361742315 ,.30616187754675012405] 
dist 76=[-6.9258567578272600059 ,.32411959634417263162] 
dist 77=[-7.0638023327025981991 ,.34133242044428530055] 
dist 78=[-7.1165341548610299930 ,.35606766906746056292] 
dist 79=[-7.1194203803323141670 ,.36417511485829369712] 
dist 80=[-7.1052883119436420077 ,.45333144705929345421] 
dist 81=[-3.4688281101794611934 ,.71978075532900053862] 
dist 82=[-3.1555388372979772818 ,.96990419274834800277] 
dist 83=[-2.3968607169918829021 ,1.2622620599840552001 ] 
dist 84=[-2.2774476652589995630 ,1.5350810619747310932 ] 
dist 85=[-1.1879472730219014258 ,1.7072914934101914077 ] 
dist 86=[-.98926675148666249378,1.8384205556938917552 ] 
dist 87=[-.72062786269448226973,1.9473796037505295324 ] 
dist 88=[-.64653691413645686901,2.0335028288597599016 ] 
dist 89=[-.54659228317194529102,2.3652707141368501644 ] 
dist 90=[-.5369534304934637847 ,2.7031257156337266340 ] 
dist 91=[-.53087306437971833458,2.9585387412590192523 ] 
dist 92=[-.56771791466973412626,3.1673637534644916637 ] 
dist 93=[-.66035770052715399241,3.3329070334505024308 ] 
dist 94=[-.75186816663196189323,3.4156795563924014063 ] 
dist 95=[-.81583955524282533687,3.4565503223580699264 ] 
dist 96=[-.87180797019336170629,3.4613476053612870301 ] 
dist 97=[-.93142197130282048491,2.1105218013164705422 ] 
dist 98=[-.98882844256355071381,2.0856723956722051581 ] 
dist 99=[-1.0360171122957868707 ,2.1022786167371434088 ] 
dist 100=[-1.0848371649784290393 ,2.1265415672311130379 ] 
dist 101=[-1.1488005139700608320 ,2.1540971313729022623 ] 
dist 102=[-1.2094454248709888893 ,2.1838088868569793763 ] 
dist 103=[-1.2450271918747043356 ,2.2208748415900694243 ] 
dist 104=[-1.2691992113532272107 ,2.2777435686310558057 ] 
dist 105=[-1.2842782718374440075 ,2.3371513985777418897 ] 
dist 106=[-1.2924847450093793924 ,2.3843250725958119200 ] 
dist 107=[-1.2922860581463474449 ,2.4315191382882963374 ] 
dist 108=[-1.2823529002896102250 ,2.4909698014170874116 ] 
dist 109=[-1.3967451259419997809 ,2.5535500673976774610 ] 
dist 110=[-1.8514528345575485175 ,2.6131996840176775164 ] 
dist 111=[-2.3775317895641783597 ,2.6819043864160800381 ] 
dist 112=[-3.1374295839701745673 ,2.7805599908712628527 ] 
dist 113=[-3.8834589457345085381 ,2.8755022472354848429 ] 
dist 114=[-4.3542211320664914143 ,2.9293862614164091819 ] 
dist 115=[-4.7127898239326205935 ,2.9632383824725862453 ] 
dist 116=[-5.0112319748358269714 ,2.9782947668733383889 ] 
dist 117=[-5.2476942786627712960 ,2.9798906184657677134 ] 
dist 118=[-5.3590044238152772124 ,2.9727583842305260665 ] 
dist 119=[-5.4138614721262144095 ,2.9349659262796543076 ] 
dist 120=[-5.4250746955565379435 ,2.9156546278035360384 ] 
dist 121=[-5.2842680851064832297 ,2.7577903285812256744 ] 
dist 122=[-5.2391677209238709054 ,2.7222630458583383165 ] 
dist 123=[-5.1517016761519132615 ,2.6160462092910495085 ] 
dist 124=[-5.1169695099119237505 ,2.5908809479711193712 ] 
dist 125=[-4.9347465502701297866 ,2.3483691946355530486 ] 
dist 126=[-4.8871209123496596089 ,2.2928910076120832146 ] 
dist 127=[-4.7261799708769268613 ,2.2207136598851404080 ] 
dist 128=[-4.6936713403576347203 ,2.1923278449895948383 ] 
dist 129=[-1.7343211492427867610 ,1.9817465558670676252 ] 
dist 130=[-1.7466043674284934806 ,2.4972951599785303303 ] 
dist 131=[-1.7463466828444284348 ,2.9077246443634192311 ] 
dist 132=[-1.7383554343208061515 ,3.3739984050644809123 ] 
dist 133=[-1.7315345223218816294 ,3.9184797920704977755 ] 
dist 134=[-1.2078869235121598669 ,4.2859318352725939819 ] 
dist 135=[-1.1515606535131865979 ,4.5934160054056321298 ] 
dist 136=[-1.0094074532999964863 ,4.8986771414339754899 ] 
dist 137=[-.98573926803880245051,5.1669316494730411770 ] 
dist 138=[-.75728426714123938952,5.3267881184446203707 ] 
dist 139=[-.71283609308541627148,5.4375823410511661324 ] 
dist 140=[-.65601789635061868611,5.5101116535489872636 ] 
dist 141=[-.63704117873579153589,5.5523534259789978693 ] 
dist 142=[-.23587012358176402013,5.5516763919604144779 ] 
dist 143=[-.18516781918534817023,5.5131868851813999858 ] 
dist 144=[-.07329395648701356165,5.4794575512620284049 ] 
dist 145=[-.09786767632852838741,2.6879487621205971661 ] 
dist 146=[-.68124063150375545978,2.4346653402648527967 ] 
dist 147=[-1.1736415711180946385 ,1.8334862307665095723 ] 
dist 148=[-1.6692828019229687678 ,1.7295875324525061962 ] 
dist 149=[-2.1278987190377495549 ,1.2285048380369534792 ] 
dist 150=[-2.4726006125838920782 ,.74714145476746269107] 
dist 151=[-2.7992052622189132829 ,.58315498588548661054] 
dist 152=[-3.1856285141190897222 ,.65194341641573276167] 
dist 153=[-3.5422282964492838514 ,.73154052516598555715] 
dist 154=[-3.7498626489313946901 ,.81182399268510662643] 
dist 155=[-3.8877382376133499023 ,.88334909322698154867] 
dist 156=[-3.9660599124020319182 ,.96202951937177351906] 
dist 157=[-4.0153896351288274476 ,1.0708559678935461849 ] 
dist 158=[-4.0376130727518824322 ,1.1794401683786599690 ] 
dist 159=[-4.0441942770582834021 ,1.2571531918708001278 ] 
dist 160=[-4.0313625132334374143 ,1.3269920863469167930 ] 
dist 161=[-1.2402506972746621950 ,1.4041628267617154546 ] 
dist 162=[-1.1834448158655505559 ,1.4799599981377540114 ] 
dist 163=[-1.1767842281028896594 ,1.5443179797341099443 ] 
dist 164=[-1.1912987466217304892 ,1.6124960702394341291 ] 
dist 165=[-1.3948222822800171902 ,1.9380268322776039477 ] 
dist 166=[-1.7478182210039284327 ,2.2171906997872404978 ] 
dist 167=[-1.9689011868129476318 ,2.4821885611071932018 ] 
dist 168=[-2.1352914229030160204 ,2.7964356559636242099 ] 
dist 169=[-2.2701052379479223571 ,3.0868179103507247730 ] 
dist 170=[-2.3768779980006629170 ,3.2566167316786202888 ] 
dist 171=[-2.4314055452630226567 ,3.3702858117263643159 ] 
dist 172=[-2.4581597728947066072 ,3.4367595314269135166 ] 
dist 173=[-2.4625631162677208220 ,3.4781236251566982739 ] 
dist 174=[-2.3304483763467331642 ,3.4916247604548001666 ] 
dist 175=[-2.3346100587457260076 ,3.4872766416060818026 ] 
dist 176=[-2.5821977985721081880 ,3.4776642674790897486 ] 
dist 177=[-2.8246858319230123498 ,3.8103963039320060791 ] 
dist 178=[-2.9729664359629450375 ,4.1691578349095779141 ] 
dist 179=[-3.0803307395335582763 ,4.4328013458836318056 ] 
dist 180=[-3.1595999466672119892 ,4.6348853860468695831 ] 
dist 181=[-3.2145352249476908447 ,4.7889134773010873214 ] 
dist 182=[-3.2260426287229887411 ,4.8608476947125373617 ] 
dist 183=[-3.2195480381411113298 ,4.8890018907659330997 ] 
dist 184=[-3.2123637247290847982 ,4.8878077967894908926 ] 
dist 185=[-3.0546810966248720695 ,4.5266991402157293861 ] 
dist 186=[-3.0196602989231625164 ,4.4568389452412867502 ] 
dist 187=[-2.9148636420397334790 ,4.3295998817806722978 ] 
dist 188=[-2.8869068394772222863 ,4.2895679537613826233 ] 
dist 189=[-2.8580880971351894780 ,4.1185827523283892052 ] 
dist 190=[-2.8686158547057796694 ,4.0696706260923413879 ] 
dist 191=[-2.8644201210088117598 ,3.9525240315114465795 ] 
dist 192=[-2.8565426645939208690 ,3.9080740319507171787 ] 
dist 193=[-.18581529053221650103,2.1422484779538493578 ] 
dist 194=[-.33418852499356414275,2.1762303408524659934 ] 
dist 195=[-.45950416460848906908,2.1839273648815891536 ] 
dist 196=[-.5857942425101141311 ,2.1802661120875951184 ] 
dist 197=[-.70276426600526040592,2.1708261690233270809 ] 
dist 198=[-.79090003533002368902,1.1877356177233273993 ] 
dist 199=[-.87463389435315436755,1.0993312596910163877 ] 
dist 200=[-.9740439680975750777 ,.87917428030294588011] 
dist 201=[-1.0659814926094983281 ,.84757169862957553797] 
dist 202=[-1.1199055592620091854 ,.51123574237857489118] 
dist 203=[-1.1562150474410976799 ,.44867816829389935068] 
dist 204=[-1.1778834701786118051 ,.37721872318547311106] 
dist 205=[-1.2338653045459696056 ,.36479405731874307088] 
dist 206=[-1.3224333744150753862 ,-.12489875852070556696] 
dist 207=[-1.3722295348118912638 ,-.09715572218807513586] 
dist 208=[-1.4030621502094743762 ,.12807379578369932943] 
dist 209=[-1.4159814842393639157 ,.35762826612278766499] 
dist 210=[-1.4203607231851328806 ,.50734755493608789334] 
dist 211=[-1.4171261256412158138 ,.62697571749207665467] 
dist 212=[-1.4085049745455777930 ,.73649124285694192391] 
dist 213=[-1.4025427413088783130 ,.83087193892228385684] 
dist 214=[-.91309998241995590261,.89012451839393256514] 
dist 215=[-.94838339650947508545,.93488063654318574642] 
dist 216=[-.99487534454597891832,1.0064033269733856871 ] 
dist 217=[-1.0460261548305920808 ,1.1783256095935639760 ] 
dist 218=[-1.0961436549617087668 ,1.3359200435583722877 ] 
dist 219=[-1.1385130405825815807 ,1.4518921532773801309 ] 
dist 220=[-1.1832438386203744580 ,1.5593687274133081645 ] 
dist 221=[-1.2427810868351506394 ,1.6830734577212400607 ] 
dist 222=[-1.3011517964445260040 ,1.7954624482531543955 ] 
dist 223=[-1.3412286737220844871 ,1.8577985736620744311 ] 
dist 224=[-1.3755055628029143359 ,1.8952942413431020764 ] 
dist 225=[-1.4107382821859414197 ,1.9085898784219377368 ] 
dist 226=[-1.4438067027597881729 ,1.9109246536897378662 ] 
dist 227=[-1.4694492528283264161 ,1.9046945124848146566 ] 
dist 228=[-1.4945129344145434366 ,1.8917869988146009918 ] 
dist 229=[-1.5252712828526254234 ,1.8835508696611908853 ] 
dist 230=[-1.5529342283684844496 ,1.8923900971064381741 ] 
dist 231=[-1.5656495913364130997 ,2.1475965154009770428 ] 
dist 232=[-1.5698237212686200752 ,2.3441750812195856454 ] 
dist 233=[-1.5914640840781864260 ,2.5116171331451009890 ] 
dist 234=[-1.7655003630918896091 ,2.6471408947832136882 ] 
dist 235=[-1.8757034436515063894 ,2.7163901689551187736 ] 
dist 236=[-1.9600447867927983349 ,2.7523843342324977837 ] 
dist 237=[-2.0309122494752605488 ,2.7580158120491090056 ] 
dist 238=[-2.0885896158143813825 ,2.7246073686335449151 ] 
dist 239=[-2.1203128394988206095 ,2.7070228773006244147 ] 
dist 240=[-2.1390373070221855646 ,2.6741917983070290436 ] 
dist 241=[-2.1448606590048814828 ,2.6594316624710468537 ] 
dist 242=[-2.1419310107081911413 ,2.5768287712021157785 ] 
dist 243=[-2.1351060877144521403 ,2.5542849520883298142 ] 
dist 244=[-2.1062511359357447067 ,2.4743684915292891233 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 1, 1, 0, 0, 1] 
dist 0=[55.581534260631044416  ,55.581534260631044416  ] 
dist 1=[54.237293541437248430  ,56.527950310519594439  ] 
dist 2=[52.342791406111597595  ,57.240283556125691543  ] 
dist 3=[49.199538648718166377  ,57.649983207195775418  ] 
dist 4=[45.951281890134371757  ,57.916631053216295151  ] 
dist 5=[43.637462621220581634  ,58.057840946647876933  ] 
dist 6=[41.562381655703285362  ,58.082180485301951550  ] 
dist 7=[39.266938487910119036  ,58.040632000305195664  ] 
dist 8=[37.001257601018771402  ,57.402193963586323732  ] 
dist 9=[35.044686005604489907  ,55.623824536464810007  ] 
dist 10=[32.935969689213271234  ,55.189131945091390200  ] 
dist 11=[30.062257761293169329  ,54.539808461673623748  ] 
dist 12=[27.193593547130165451  ,54.307669452901970707  ] 
dist 13=[25.104707521216563568  ,53.664243193152503194  ] 
dist 14=[23.181310595960055892  ,53.409217899035177768  ] 
dist 15=[20.972993511004784582  ,53.066035107216332388  ] 
dist 16=[18.741164580955625632  ,51.704861508427524251  ] 
dist 17=[16.723278587688946753  ,31.578203437482966317  ] 
dist 18=[14.318676495667486909  ,29.791382465662940019  ] 
dist 19=[11.282738665506766396  ,25.524912484821211777  ] 
dist 20=[8.1408813961267402817 ,24.911224826151557835  ] 
dist 21=[5.5589015745027130405 ,18.980346764909660730  ] 
dist 22=[2.2324560519837031048 ,17.916527060357758357  ] 
dist 23=[-.0309892243289369203 ,16.622978610219859978  ] 
dist 24=[-1.9561096088927125414 ,16.398840272853798251  ] 
dist 25=[-3.9321683657398463265 ,8.3115490774052421641 ] 
dist 26=[-5.8003347565820770234 ,7.3578981023763067663 ] 
dist 27=[-7.2954079499382816259 ,5.3434898691199367165 ] 
dist 28=[-8.8127258950477910461 ,4.9256874420888004479 ] 
dist 29=[-10.771453413389113802  ,3.0006150921544383557 ] 
dist 30=[-12.626125343020959834  ,2.6694136386216706205 ] 
dist 31=[-13.728041684001279160  ,2.1532363347572808741 ] 
dist 32=[-14.499643730164399991  ,2.0514898867283280389 ] 
dist 33=[-15.033906013741622649  ,-1.4741501172022439230 ] 
dist 34=[-15.423743764808351078  ,-1.0342188918117283675 ] 
dist 35=[-15.617682841990360356  ,-.2685421826222804381 ] 
dist 36=[-15.708840842363240377  ,.5185469970833919537 ] 
dist 37=[-15.695006695970101897  ,1.0441438879024284864 ] 
dist 38=[-14.151329264579400213  ,1.4751439278207041214 ] 
dist 39=[-13.900511368571568091  ,1.8855947854655617452 ] 
dist 40=[-13.450754378384252553  ,2.2484201986032802578 ] 
dist 41=[-13.324958682725147488  ,2.4897802132850796059 ] 
dist 42=[-12.864720076817961197  ,2.6871599058591473442 ] 
dist 43=[-12.723122473638306434  ,2.8748522911761026224 ] 
dist 44=[-12.517313089277381873  ,3.0353839051824895927 ] 
dist 45=[-12.436935577771028271  ,3.1245085262198275497 ] 
dist 46=[-8.8060253948294799705 ,3.1780676208081123689 ] 
dist 47=[-8.8099314810626373885 ,3.1966949265094548277 ] 
dist 48=[-8.7982249159944907082 ,3.1914494844355431447 ] 
dist 49=[-3.3182686985519179692 ,3.5984662024206946389 ] 
dist 50=[-3.1270715750586109551 ,4.9763980179181666854 ] 
dist 51=[-3.0726462858207230378 ,6.0261073419801143731 ] 
dist 52=[1.1214497896714119787 ,7.0366719145005175720 ] 
dist 53=[.7447407195927117461 ,8.2585109575036237193 ] 
dist 54=[.4159780187622340984 ,9.4047123029476810008 ] 
dist 55=[.0691377106101656105 ,10.113433589786331398  ] 
dist 56=[-.2607035777389619910 ,10.637918012997358104  ] 
dist 57=[-.5217798708795600539 ,11.048778011942259916  ] 
dist 58=[-.7813490039682838615 ,11.355886254413655449  ] 
dist 59=[-1.1052756161279379480 ,11.466293310060590416  ] 
dist 60=[-1.4119792505743635222 ,11.501298652293137208  ] 
dist 61=[-1.6029291112473540973 ,11.507255544460972776  ] 
dist 62=[-1.7450765213068140635 ,7.2688887189085819490 ] 
dist 63=[-1.8572550045916967788 ,7.1652665983329562262 ] 
dist 64=[-2.7843128101508974410 ,7.1116949335781977941 ] 
dist 65=[-3.6692849109603727367 ,4.1760632990556510834 ] 
dist 66=[-4.4559749987058023461 ,3.8802839753309879789 ] 
dist 67=[-4.9935192591903073251 ,3.1772335757499572417 ] 
dist 68=[-5.4506980845054407122 ,3.0465647098869310599 ] 
dist 69=[-5.9168657463500133987 ,2.0562906924643094428 ] 
dist 70=[-6.3321631370389646745 ,1.8712639341334503956 ] 
dist 71=[-6.5864140865772389384 ,1.5686488761353777864 ] 
dist 72=[-6.7711799266200286464 ,1.4931019051889272216 ] 
dist 73=[-6.9092283725815321205 ,.99742212329862879773] 
dist 74=[-7.0066055621495604561 ,1.0818261922341239779 ] 
dist 75=[-7.0290943160944922618 ,1.1657816238704232714 ] 
dist 76=[-7.0129072686241914624 ,1.2405679897253678647 ] 
dist 77=[-6.9864277887577024160 ,1.2884164528583731434 ] 
dist 78=[-5.6631957564741907680 ,1.3253597551260774493 ] 
dist 79=[-5.6431367507764149909 ,1.3566834172296207877 ] 
dist 80=[-5.6197265793630705919 ,1.3816658786160922268 ] 
dist 81=[-2.0531457704090346406 ,1.3933289356533490408 ] 
dist 82=[-.99708776447080687096,1.3972952772499864969 ] 
dist 83=[-.80609341094704051237,1.6009668956770637812 ] 
dist 84=[-.5052887247521480043 ,2.0838770133544781870 ] 
dist 85=[-.43008056858967670875,2.6719203135624049543 ] 
dist 86=[.12676198513220660397,3.2231777568398503441 ] 
dist 87=[-.04922938746323863473,3.5593703150865254023 ] 
dist 88=[-.22477307604423806266,3.8016287289353079275 ] 
dist 89=[-.37779014921456332161,3.9782313838641064945 ] 
dist 90=[-.54320635668678680354,4.1119626332710744548 ] 
dist 91=[-.76821795314517105017,4.1832163623072862517 ] 
dist 92=[-.99080633418827993909,4.2221894352659905601 ] 
dist 93=[-1.1465664328713672870 ,4.2271327879788336683 ] 
dist 94=[-1.2828409663486977544 ,3.6762293865241790538 ] 
dist 95=[-1.4277232373749822478 ,3.6703494846944682966 ] 
dist 96=[-1.5666859768172358234 ,3.6628225280998644342 ] 
dist 97=[-1.6793625652989866320 ,2.3865754405054245188 ] 
dist 98=[-1.7941659423015196139 ,2.4817692521154095804 ] 
dist 99=[-1.9416348004587503499 ,2.6024026032706411348 ] 
dist 100=[-2.1172095946029801416 ,2.7124250954491328818 ] 
dist 101=[-2.4187656136580303489 ,2.7652860705133469739 ] 
dist 102=[-2.6455590113842288076 ,2.7897608007335993883 ] 
dist 103=[-2.8289898404059338402 ,2.7904936058612114141 ] 
dist 104=[-2.9751240711723598555 ,2.7403051778838697259 ] 
dist 105=[-3.0531382612744659293 ,2.7177398150493292672 ] 
dist 106=[-3.0960567951884736939 ,2.6907489791638463999 ] 
dist 107=[-3.1021864100857250329 ,2.6742150118851111718 ] 
dist 108=[-2.9067942224449715513 ,2.1679150257693659484 ] 
dist 109=[-2.9647468156519914656 ,2.2059535588085311314 ] 
dist 110=[-3.4671826796858585106 ,2.4346979641219850946 ] 
dist 111=[-3.7747115339989438947 ,2.5755327885695428407 ] 
dist 112=[-3.9979631717024290799 ,2.6784831137779180035 ] 
dist 113=[-4.1641770968457187024 ,2.7561338079182733852 ] 
dist 114=[-4.2890024995967362720 ,2.8112050706305629564 ] 
dist 115=[-4.3471239123737026082 ,2.8240966721208971773 ] 
dist 116=[-4.3675943531703211731 ,2.8220783421118654649 ] 
dist 117=[-4.3664802635381388065 ,2.8177132830067300208 ] 
dist 118=[-3.9939213166933883543 ,2.6781850536275135542 ] 
dist 119=[-3.9260426020067400507 ,2.6467594527255662150 ] 
dist 120=[-3.8015265823877830185 ,2.5576393633584565961 ] 
dist 121=[-3.7634512341519784288 ,2.5290352198604094212 ] 
dist 122=[-3.6052200890302062394 ,2.3306203206242506695 ] 
dist 123=[-3.5603662592969810021 ,2.2833808577958518822 ] 
dist 124=[-3.4583631294651725085 ,2.2020659090310100691 ] 
dist 125=[-3.4208908639489891299 ,2.2949132922476321406 ] 
dist 126=[-2.0369149040110854716 ,2.3798448404901872155 ] 
dist 127=[-2.1072469023103208224 ,2.4484723588772930521 ] 
dist 128=[-2.2021265288754186192 ,2.5012027487289173373 ] 
dist 129=[-2.2910943857227730184 ,2.5750580541297315968 ] 
dist 130=[-2.3378412416667004813 ,2.8946118233807501012 ] 
dist 131=[-2.3624116741827673222 ,3.1365495115516225908 ] 
dist 132=[-2.3638912224120855123 ,3.3351763910321089798 ] 
dist 133=[-2.3513586296703981302 ,3.4918023518122477698 ] 
dist 134=[-2.3407950402442132982 ,3.5661909832206328571 ] 
dist 135=[-2.3019748511909190184 ,3.6022209862191145118 ] 
dist 136=[-2.2824526382120760691 ,3.6058277442119402550 ] 
dist 137=[-2.0216677570611722874 ,3.4684596762586713787 ] 
dist 138=[-1.9765846794337213447 ,3.4318777861378761689 ] 
dist 139=[-1.8597317550602201454 ,3.3662344772121357772 ] 
dist 140=[-1.8306053027177847687 ,3.3426087190928409080 ] 
dist 141=[-1.6183321297233715721 ,3.2295400838937796067 ] 
dist 142=[-1.5722281700867509165 ,3.1967729683704444923 ] 
dist 143=[-1.4950302257973423769 ,3.1033639938744733958 ] 
dist 144=[-1.4730365475067235036 ,3.0693797874699293003 ] 
dist 145=[-1.1014702027054490136 ,-.21829791048151865956] 
dist 146=[-1.1204040583106778395 ,-.3880871615594952136 ] 
dist 147=[-1.1245909802071080049 ,-.7683823908643466761 ] 
dist 148=[-1.1150899708650080307 ,-.8321509444014417613 ] 
dist 149=[-1.3625625037700508448 ,-.92881400278416254464] 
dist 150=[-1.5386786769438144305 ,-.87824980609487737063] 
dist 151=[-1.6959027106517513101 ,-.80299762225878687446] 
dist 152=[-1.8680176375229766211 ,-.7178674136206488562 ] 
dist 153=[-2.0237526095934467472 ,-.62789398429455476124] 
dist 154=[-2.1156367325108354435 ,-.51734334551737669777] 
dist 155=[-2.1781707011443277925 ,-.35012460011176724074] 
dist 156=[-2.2168239939885289111 ,-.17702799415418251679] 
dist 157=[-2.2393410026169741075 ,-.04302635776707550160] 
dist 158=[-2.2412286497248489953 ,.10393197809674557343] 
dist 159=[-2.2272687666945290367 ,.32637073289828149414] 
dist 160=[-2.2162617525224396087 ,.5631485286918518253 ] 
dist 161=[-1.4016239165979606155 ,.79316903477772485056] 
dist 162=[-1.3427173236389685790 ,1.0618528079368869494 ] 
dist 163=[-1.3577337742902749837 ,1.4528692767794653249 ] 
dist 164=[-1.3707319642967964121 ,1.8380896757366019012 ] 
dist 165=[-1.3755295157321853604 ,2.0836536129059671691 ] 
dist 166=[-1.3752001027106030550 ,2.2734875754179809714 ] 
dist 167=[-1.3705045155737044986 ,2.4363922311452372760 ] 
dist 168=[-1.3562828344383735885 ,2.5691593336819399588 ] 
dist 169=[-1.3485400482530090125 ,2.6387706406155535002 ] 
dist 170=[-1.3233658650865838496 ,2.6753334925095156024 ] 
dist 171=[-1.3111170031129914489 ,2.6823303290656885726 ] 
dist 172=[-1.2377211309646888730 ,2.6629798040147064269 ] 
dist 173=[-1.2199286414269680237 ,2.6485871845147018216 ] 
dist 174=[-1.1757044693084610175 ,2.6171569802430175990 ] 
dist 175=[-1.1593631149252317107 ,2.6015985014783121548 ] 
dist 176=[-1.0761473791982236685 ,2.5096591224692743514 ] 
dist 177=[-1.0564049127890210631 ,2.4853639523346153480 ] 
dist 178=[-1.0132822986317348417 ,2.4055493078874354302 ] 
dist 179=[-.9989016887879354561 ,2.3869158163434027153 ] 
dist 180=[-.93905673063445054889,.88893235067059551604] 
dist 181=[-1.2396079452002829895 ,.96418807025048216924] 
dist 182=[-1.5299494199022098821 ,1.0320204472529021384 ] 
dist 183=[-1.8393274079533603714 ,1.1072808432513046669 ] 
dist 184=[-2.1110434199324241564 ,1.2121655560503805558 ] 
dist 185=[-2.2907851501088682102 ,1.3171475995760167594 ] 
dist 186=[-2.4372223389263119195 ,1.3927945422022819268 ] 
dist 187=[-2.5760817090650797101 ,1.4612916251781791445 ] 
dist 188=[-2.6962683818414811187 ,1.5377492260993726048 ] 
dist 189=[-2.7682184362524325051 ,1.6132785873026466714 ] 
dist 190=[-2.8184709961424465441 ,1.6780704176258856954 ] 
dist 191=[-2.8521060614838818627 ,1.7472658612746128246 ] 
dist 192=[-2.8724100579317609883 ,1.8403575074730672453 ] 
dist 193=[-2.8701070875242524520 ,1.9280037495991404416 ] 
dist 194=[-2.8551470641741815093 ,1.9754764689365485963 ] 
dist 195=[-2.8410665591919072758 ,2.0025031859115665037 ] 
dist 196=[-.98656156615503690121,2.0085910861578246774 ] 
dist 197=[-.86863114985949677105,2.0038487819749722580 ] 
dist 198=[-.85705220797643350582,1.9965326765137563620 ] 
dist 199=[-.86240012121945144588,1.9685592454790722337 ] 
dist 200=[-.86304900400306456628,1.9529215544946775008 ] 
dist 201=[-.86073583323578821798,1.7358084651436438027 ] 
dist 202=[-.85724590278104965153,1.6982839185581655162 ] 
dist 203=[-.84625584091661075243,1.6033274843580523909 ] 
dist 204=[-.84023365001232560179,1.7937625305199960811 ] 
dist 205=[-.80324847375468483791,1.9056123234715362117 ] 
dist 206=[-.79324309729904434947,1.9801550214720902454 ] 
dist 207=[-.77063937306079948714,2.0230536733575714593 ] 
dist 208=[-.76230722436761334202,2.0507852143579809911 ] 
dist 209=[.31278011699666475426,2.0648251361080863667 ] 
dist 210=[.24184898340747949188,2.0714973486258750228 ] 
dist 211=[.11376432502233235713,2.0698386768569277804 ] 
dist 212=[-.02109326851812822285,1.1859476948745874298 ] 
dist 213=[-.25229929643615499683,1.2309896443743748702 ] 
dist 214=[-.44828986618676371995,1.2513345589283529915 ] 
dist 215=[-.64690653904649444572,1.2600500558073889542 ] 
dist 216=[-.8315219751237458574 ,1.2589225301425341382 ] 
dist 217=[-.9716611906176315711 ,1.1929806961099855941 ] 
dist 218=[-1.1057784348073128601 ,1.1779418454695535735 ] 
dist 219=[-1.2663724451922675014 ,1.1490257473312716002 ] 
dist 220=[-1.4155462127274382421 ,1.1390111215696936415 ] 
dist 221=[-1.5041076560973715689 ,1.0914548959342124857 ] 
dist 222=[-1.5650548243484840943 ,1.0790291144946970490 ] 
dist 223=[-1.6040737047676729558 ,1.0421748959880162837 ] 
dist 224=[-1.6302875626273688966 ,1.0318126484194006588 ] 
dist 225=[-1.6401542798742424077 ,.25077125534941044732] 
dist 226=[-1.6399168792277655936 ,.33550006879466719752] 
dist 227=[-1.6364322237565162248 ,.52661844859602967001] 
dist 228=[-1.4396549434058182723 ,.71658469140228038911] 
dist 229=[-1.4107900589812784546 ,.83750724916296849954] 
dist 230=[-1.3256376534882110553 ,.93076657198788488798] 
dist 231=[-1.3132300055527199244 ,1.0103826773327217260 ] 
dist 232=[-1.1711757508846922321 ,1.0749757240450423872 ] 
dist 233=[-1.1601061698409628997 ,1.1083073478721371804 ] 
dist 234=[-1.1515163837217764585 ,1.1265570874186133103 ] 
dist 235=[-1.1440933158027561079 ,1.1309881046674161349 ] 
dist 236=[-.88638125004751526411,1.1146339760822026481 ] 
dist 237=[-.84989657843359485567,1.1078346055756027964 ] 
dist 238=[-.77868330604416084633,1.1005472681986073336 ] 
dist 239=[-.75938938972414256096,1.0941002282681909407 ] 
dist 240=[-.68779761303917604992,1.0799900550259757758 ] 
dist 241=[-.67031426015337621065,1.0719603702816198417 ] 
dist 242=[-.6398489964947638566 ,1.0568919008996144248 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 0, 2, 0, 0, 2] 
dist 0=[66.340523011248146032  ,66.340523011248146032  ] 
dist 1=[65.712520313863783736  ,66.566018302267406771  ] 
dist 2=[64.705311433735174224  ,66.838246876538500974  ] 
dist 3=[63.226405403450770244  ,67.052611129391519011  ] 
dist 4=[61.116550660579375982  ,67.082173673742205796  ] 
dist 5=[57.590047971491884340  ,66.998957601863434304  ] 
dist 6=[53.930072503751380333  ,66.875139858900568179  ] 
dist 7=[51.287204969392623996  ,66.473756874080228425  ] 
dist 8=[48.879253021275731639  ,65.595823095663198107  ] 
dist 9=[46.157041846296754437  ,62.652001123133037921  ] 
dist 10=[43.435384914092243830  ,61.968771475745703470  ] 
dist 11=[38.334396206904959178  ,60.968576382261797551  ] 
dist 12=[31.552214961662058458  ,60.627191499965968814  ] 
dist 13=[26.955271862586898919  ,59.871495440010217622  ] 
dist 14=[23.071753946920451010  ,59.531229626986509776  ] 
dist 15=[19.138282244967334720  ,57.200709443234578112  ] 
dist 16=[15.466774903974249555  ,51.818495780705571918  ] 
dist 17=[12.629291067369004343  ,30.106986942813257963  ] 
dist 18=[9.8551725421486824058 ,27.756229557762683457  ] 
dist 19=[6.4367186017373607756 ,24.458693397013627593  ] 
dist 20=[3.1923419409410412659 ,23.823942832509462894  ] 
dist 21=[1.1132694411428845746 ,23.636233963150894506  ] 
dist 22=[-.5132418176864912787 ,12.623718337685729720  ] 
dist 23=[-1.9507041433814020670 ,10.948855935413289774  ] 
dist 24=[-3.1591718364705268188 ,10.647649667646227687  ] 
dist 25=[-3.8714186469385892045 ,1.6278329831658766688 ] 
dist 26=[-5.1832543991681234381 ,.5925596671639825337 ] 
dist 27=[-6.8372196497637471731 ,-1.6320625673704332326 ] 
dist 28=[-8.4037948530277628789 ,-1.9821575847379164170 ] 
dist 29=[-10.268661488699756487  ,-4.1137616516757069019 ] 
dist 30=[-12.013234801669267700  ,-4.4355465325915598055 ] 
dist 31=[-13.099271887536116515  ,-5.0929012683768954070 ] 
dist 32=[-13.914991238645572573  ,-5.3908278368916975701 ] 
dist 33=[-14.579664414675434305  ,-5.7396431096746043678 ] 
dist 34=[-15.099692443580895349  ,-5.4468549093144539782 ] 
dist 35=[-15.337596255868085329  ,-4.9314773286331879744 ] 
dist 36=[-15.441010533831864944  ,-3.9739646627438242969 ] 
dist 37=[-15.432905722337395388  ,-2.2688436110913672463 ] 
dist 38=[-9.5757418037966045713 ,-.5097931980908371117 ] 
dist 39=[-9.4957731063099180399 ,.85196266805160463598] 
dist 40=[-9.4679340836779075391 ,1.9804858812521194931 ] 
dist 41=[-8.8323987227944754497 ,3.0824782406371446891 ] 
dist 42=[-8.7170584683899297830 ,4.0806811723310318174 ] 
dist 43=[-8.3817380027528413124 ,4.7953068759664482767 ] 
dist 44=[-8.3178812796257991040 ,5.4380861105590474364 ] 
dist 45=[-7.6156522343313879566 ,6.1498434605407755651 ] 
dist 46=[-7.4641209896444325199 ,6.7969661507078647430 ] 
dist 47=[-7.2853598172570168049 ,7.1819270468105497354 ] 
dist 48=[-7.2109156941610951279 ,7.4484252861296020850 ] 
dist 49=[-4.7467047731198470837 ,7.6228847675377499788 ] 
dist 50=[-4.4535769750109618517 ,7.7335295916022530884 ] 
dist 51=[-3.7972447299933310250 ,7.7495635052200749895 ] 
dist 52=[-3.6404398972613662633 ,7.7200197412970441115 ] 
dist 53=[-2.8126409386485904639 ,7.7529586201143921230 ] 
dist 54=[-2.6549657629197300517 ,8.2676906737736069125 ] 
dist 55=[-2.3202834252251927313 ,8.6800307086505143151 ] 
dist 56=[-2.2259314145324847536 ,9.0615699315384298662 ] 
dist 57=[-1.3741933362383896214 ,9.3773064525635850870 ] 
dist 58=[-2.0340983194005804685 ,9.5270442634663088771 ] 
dist 59=[-2.5179936760799457001 ,9.5876011907388945372 ] 
dist 60=[-2.9643174938144130710 ,9.5887770380576289609 ] 
dist 61=[-3.4744195873453726180 ,9.4418728717406209921 ] 
dist 62=[-3.9452366565601179081 ,9.3776144270456703170 ] 
dist 63=[-4.2348947073768829741 ,9.2315310146970163014 ] 
dist 64=[-4.4466354341762000134 ,9.1669467476065679707 ] 
dist 65=[-4.6066957816865115686 ,-.42753528390318795911] 
dist 66=[-4.7209121661611034472 ,-1.0017355714523885588 ] 
dist 67=[-4.7498170476626903584 ,-1.0523858493444656631 ] 
dist 68=[-4.7499081222548102015 ,-1.0086518842913964676 ] 
dist 69=[-4.7491653937657983425 ,-.8871477291160400408 ] 
dist 70=[-3.5529403770542565586 ,-.7513079478165509665 ] 
dist 71=[-3.6249165125659744698 ,-.6503919712314686916 ] 
dist 72=[-3.6788652792763503875 ,-.4851441261810633785 ] 
dist 73=[-3.6983443396426642631 ,-.0800211077048181178 ] 
dist 74=[-3.6963023844543581879 ,.2988225673224081587 ] 
dist 75=[-3.6866369124159368905 ,.5894131332292380029 ] 
dist 76=[-1.4897409491691147538 ,.8701595807609587486 ] 
dist 77=[-1.3030790636546415083 ,1.2097871044296414003 ] 
dist 78=[-.87385282606224290084,1.5292917463169977122 ] 
dist 79=[-.79320487341116718543,1.7297942088961499567 ] 
dist 80=[-.24773709487798982913,1.8810068503921695341 ] 
dist 81=[-.2432558714943575118 ,2.0039195229772563335 ] 
dist 82=[-.2612889079294439328 ,2.0997420548105923149 ] 
dist 83=[-.2904639384940724272 ,2.1429219131450737056 ] 
dist 84=[-.3329719702143381084 ,2.1624596969712068636 ] 
dist 85=[-.4040702462797148513 ,2.1639718066584283746 ] 
dist 86=[-.47607505975902562831,2.1787380641545669107 ] 
dist 87=[-.52218574134356838186,2.2963116873891056700 ] 
dist 88=[-.55756592889221548867,2.3867000413885683243 ] 
dist 89=[-.58684699554901089024,2.4285581433901075092 ] 
dist 90=[-.60936445797159996944,2.4457557913935183538 ] 
dist 91=[-.61779635163364228524,2.4446304811856102533 ] 
dist 92=[-.6206031419620587197 ,1.1412523181365000790 ] 
dist 93=[-.62080990208149950935,1.1211944226554883882 ] 
dist 94=[-.5866524681980624122 ,.7474389945284040402 ] 
dist 95=[-.5776851737542543420 ,.6965028674310072077 ] 
dist 96=[-.7009319063308670946 ,.63002559286103935506] 
dist 97=[-.84994166745386653611,.61904158859915778971] 
dist 98=[-.9932627691672177387 ,.5674660341472170665 ] 
dist 99=[-1.1101560415333848605 ,.55628120464176244391] 
dist 100=[-1.2299182292841546580 ,.52984127313107248443] 
dist 101=[-1.3847320921558479089 ,.52134321254397419052] 
dist 102=[-1.5326347685112864677 ,.16956614545462013506] 
dist 103=[-1.7109199773604319950 ,.13355718003055624152] 
dist 104=[-1.8726079603681453044 ,.06088688868687115906] 
dist 105=[-2.0319498469425446078 ,.04244901787180181008] 
dist 106=[-2.1773542570894189726 ,-.02148358868650674773] 
dist 107=[-2.2834327648719033876 ,-.03507632990718432668] 
dist 108=[-2.3808926955040060671 ,-.05057334826392564216] 
dist 109=[-2.4919090982682969468 ,-.0470540663663141007 ] 
dist 110=[-2.5922739922350827937 ,.0435265207776058587 ] 
dist 111=[-2.6472345053566847953 ,.1345634977240374958 ] 
dist 112=[-2.6793911150833724140 ,.2185443569445125004 ] 
dist 113=[-2.6887687444325474478 ,.2809940397900946503 ] 
dist 114=[-2.6835648333767096448 ,.3394284237929844334 ] 
dist 115=[-2.6765061098043176358 ,.45247768333381250605] 
dist 116=[-2.6303832938160349500 ,.91538283857489123623] 
dist 117=[-2.6205657199769911170 ,1.6041651916479969868 ] 
dist 118=[-2.4030325319410236483 ,2.2878055130644617912 ] 
dist 119=[-2.3596105574536055120 ,2.7302033118912263912 ] 
dist 120=[-2.2622973527813682950 ,3.0797840545939598618 ] 
dist 121=[-2.2294513582588120195 ,3.3931646125154488484 ] 
dist 122=[-2.0721914317631837908 ,3.6585981127142867914 ] 
dist 123=[-2.0367870400561761837 ,3.8169134166314392190 ] 
dist 124=[-1.9414216754526021525 ,3.9268128748990493754 ] 
dist 125=[-1.9164407989887145884 ,3.9991145239285836224 ] 
dist 126=[-1.6175489880702708412 ,4.0474131101432473532 ] 
dist 127=[-1.5667759453225504411 ,4.0615604570431702987 ] 
dist 128=[-1.4439115358353019348 ,4.0534123498323355475 ] 
dist 129=[-1.4126727622277429740 ,4.0426431689290830874 ] 
dist 130=[-1.2199535557521961234 ,3.9567472387682114499 ] 
dist 131=[-1.1798056992520585486 ,3.9293212995540984960 ] 
dist 132=[-1.1035163115019598217 ,3.8258843340031744498 ] 
dist 133=[-1.0825210432198245356 ,3.8019884861564708107 ] 
dist 134=[-1.1356096059058814666 ,.1299619527387418751 ] 
dist 135=[-1.5715916587767580805 ,.1259730859696992085 ] 
dist 136=[-1.9237646515590719817 ,.1198601663564256876 ] 
dist 137=[-2.3284294275182387860 ,.1212369705238234223 ] 
dist 138=[-2.7399333904722268656 ,.1264647768496331129 ] 
dist 139=[-3.0212627756521610453 ,.1382269719707272828 ] 
dist 140=[-3.2605557884164955670 ,.15109287670926261382] 
dist 141=[-3.5043790994100363532 ,.16072128389515878809] 
dist 142=[-3.7205370108383385929 ,.16973880860225419442] 
dist 143=[-3.8494717774644625780 ,.18017878939322011625] 
dist 144=[-3.9389601564497227156 ,.19064229054468877032] 
dist 145=[-3.9977611624341690385 ,.19975820940206705825] 
dist 146=[-4.0322049608638426349 ,.20957703327376977099] 
dist 147=[-4.0337737314430414850 ,.2228469779709001631 ] 
dist 148=[-4.0033297773127512154 ,.23587662612369931175] 
dist 149=[-3.9838253039768369411 ,.2447406082754505447 ] 
dist 150=[-2.0355229840868183877 ,.2522124046496766759 ] 
dist 151=[-1.8565993539955593771 ,.38535259338675263933] 
dist 152=[-1.4301943616319894345 ,.74977083690093260313] 
dist 153=[-1.3562589194591074614 ,1.1157365843537433088 ] 
dist 154=[-.76010386138850813798,1.4537406756049443759 ] 
dist 155=[-.65091677842390109802,1.7066202234180817035 ] 
dist 156=[-.48257025705851308131,1.9450355303627934992 ] 
dist 157=[-.43874197137307477755,2.2253406116213909473 ] 
dist 158=[.24972606951108926158,2.4834344571805279498 ] 
dist 159=[.26345390594632725637,2.6332503102097380878 ] 
dist 160=[.2451292145426507933 ,2.7321214311304624697 ] 
dist 161=[.22294776280588646059,2.7870013398559943160 ] 
dist 162=[.19374576711771328472,2.8214070634053242165 ] 
dist 163=[.14741383082574332868,2.8386075931022432102 ] 
dist 164=[.09858208078280842235,2.8464585523115437629 ] 
dist 165=[.05940663309443859408,2.8435670058624206445 ] 
dist 166=[.01988103996401248405,1.0133103933620755589 ] 
dist 167=[-.29254817372735035754,1.0456112863977014676 ] 
dist 168=[-.5661031594885220709 ,1.0715432106198268382 ] 
dist 169=[-.84555164362205222755,1.0843820516095311608 ] 
dist 170=[-1.1066955644557885438 ,1.0900602833730501958 ] 
dist 171=[-1.3072350961190480400 ,1.0886256577959714031 ] 
dist 172=[-1.5013760705090558855 ,1.0803267067687407818 ] 
dist 173=[-1.7369983062653074492 ,1.1193309026260199279 ] 
dist 174=[-1.9574647071451013655 ,1.2159062417607635961 ] 
dist 175=[-2.0911499709761485872 ,1.2946029222011446408 ] 
dist 176=[-2.1866025794409918388 ,1.3751210882128553174 ] 
dist 177=[-2.2545594584200361676 ,1.4789577158404667229 ] 
dist 178=[-2.3026839340739502433 ,1.5895714307245919856 ] 
dist 179=[-2.3190228438802314621 ,1.6971202156518621601 ] 
dist 180=[-2.3203897277503601462 ,1.8227910149886389094 ] 
dist 181=[-2.3818418244830883428 ,2.0056886846608019848 ] 
dist 182=[-2.8229787452874714484 ,2.1840723554187276333 ] 
dist 183=[-3.0953459810373056142 ,2.2917355503119780340 ] 
dist 184=[-3.2957434379872681248 ,2.3679761717566910443 ] 
dist 185=[-3.4497805758846072624 ,2.4210162389426542302 ] 
dist 186=[-3.5674462444978118075 ,2.4551488239804958952 ] 
dist 187=[-3.6227500453339354828 ,2.4619385441688844911 ] 
dist 188=[-3.6447381100771051016 ,2.4474940894382077444 ] 
dist 189=[-3.6442183319944303162 ,2.4445567418207949357 ] 
dist 190=[-3.3749195171453719488 ,2.2888776499751069532 ] 
dist 191=[-3.3226967478934528706 ,2.2572267346601025203 ] 
dist 192=[-3.2281463101619541709 ,2.1700909116018947393 ] 
dist 193=[-3.1984558106974509462 ,2.1442915101572759580 ] 
dist 194=[-3.0722228591878050563 ,1.9622691122507311427 ] 
dist 195=[-3.0356926832807184582 ,1.9201078471432767393 ] 
dist 196=[-2.9493618975166657571 ,1.8480807290531438693 ] 
dist 197=[-2.9166850221832088160 ,1.8268830427672356597 ] 
dist 198=[.1605076264611284994 ,.9659532492512332985 ] 
dist 199=[.1163584542570162494 ,.9962006283897140620 ] 
dist 200=[.06840410741318407063,1.0193418440280492661 ] 
dist 201=[.02044682742558657277,1.0285884360770440351 ] 
dist 202=[-.03658349453130418174,1.0303384033609714789 ] 
dist 203=[-.1207250117927653201 ,1.0603615494110418462 ] 
dist 204=[-.20485294429512940414,1.1411483590521194826 ] 
dist 205=[-.26182844412353228624,1.2192190783205777577 ] 
dist 206=[-.30968774401686182884,1.2879980179501854084 ] 
dist 207=[-.35745448362752205801,1.3317186785918393339 ] 
dist 208=[-.40136356823472860598,1.3653755904548076768 ] 
dist 209=[-.4338359570187129889 ,1.3940069056551961292 ] 
dist 210=[-.4640696313708242846 ,1.4171485724085334161 ] 
dist 211=[-.4990489142863179403 ,1.4289051469314977529 ] 
dist 212=[-.5308861743796929086 ,1.4345471896266956837 ] 
dist 213=[-.5485873358764702852 ,1.4332950467346036561 ] 
dist 214=[-.5592786337729332441 ,.54749628403768383488] 
dist 215=[-.5631561145947202303 ,.47506432824341207941] 
dist 216=[-.5636879495888806669 ,.30359712068373436658] 
dist 217=[-.5619176433826590065 ,.27596161630927574874] 
dist 218=[-.5567153598853051177 ,.16860073472756095597] 
dist 219=[-.5534521359476426778 ,.24756010873877113262] 
dist 220=[-.51976292920318068027,.34133400812381734697] 
dist 221=[-.5526770349690397347 ,.43079293075960528325] 
dist 222=[-.58082393928809171044,.50579028436458658323] 
dist 223=[-.60974980073042790957,.58043667797177351762] 
dist 224=[-.64269784978667410566,.64895225779302795314] 
dist 225=[-.69313164023527694528,.69949396104319640617] 
dist 226=[-.73377812796991520695,.74644207075012076242] 
dist 227=[-.75420458299210433159,.80062278453105665688] 
dist 228=[-.76511548567588967659,.8498991027210991544 ] 
dist 229=[-.76780365105358959003,.8772837023068426339 ] 
dist 230=[-.42749953569855401979,.8938184740117112418 ] 
dist 231=[-.42199199417011145414,.8998152165184248179 ] 
dist 232=[-.39402004948124452321,.9005780532246457994 ] 
dist 233=[-.38740494612324093363,.8978460474574050724 ] 
dist 234=[-.37229773626904687095,.8893814059231622851 ] 
dist 235=[-.36711880382048494094,.8840986178026290635 ] 
dist 236=[-.53238673008190009421,.77406866921775113049] 
dist 237=[-.66811331895782758797,.75607771813374698494] 
dist 238=[-.7764267936599351405 ,.76445420551429580182] 
dist 239=[-.8753443622660823552 ,.83083141347346442157] 
dist 240=[-.96041477177541563301,.88768977085402226368] 
dist 241=[-1.0134901433838832494 ,.92277604799747341832] 
dist 242=[-1.0531881823717953010 ,.94857102196536637755] 
dist 243=[-1.0848945099622725731 ,.96836312917528661196] 
dist 244=[-1.1097457142055132059 ,.98234127337351520171] 
dist 245=[-1.1220975959629431256 ,.98494290644989653725] 
dist 246=[-1.1276323151304398269 ,.98272482532080733874] 
dist 247=[-1.1257835478338539499 ,.97820915766687125574] 
dist 248=[-1.1180610020413851417 ,.94265792400017762867] 
dist 249=[-1.1132385495346776754 ,.931761912995737195  ] 
dist 250=[-1.0905837768564371688 ,.9130879429061425811 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 1, 1, 0, 1] 
dist 0=[42.504034184999747864  ,42.504034184999747864  ] 
dist 1=[41.141978271371590957  ,43.515694467812893947  ] 
dist 2=[38.943208146933431198  ,44.315138152623743579  ] 
dist 3=[36.684507506833104537  ,44.949699935205317444  ] 
dist 4=[35.082970344878110653  ,45.303089179516173597  ] 
dist 5=[33.653239843999953741  ,45.518501102669065390  ] 
dist 6=[32.080224748149405621  ,45.602616825506002558  ] 
dist 7=[30.530904720390167004  ,45.616467863250729167  ] 
dist 8=[29.195466499839185319  ,45.551390683802874255  ] 
dist 9=[27.756871311416076255  ,44.872171174209826854  ] 
dist 10=[25.795022745726389992  ,44.706295609888638080  ] 
dist 11=[23.831837461844988552  ,44.533907706329526694  ] 
dist 12=[22.387595113694488893  ,44.430008232143477118  ] 
dist 13=[21.041001205196237864  ,44.244782434777284836  ] 
dist 14=[19.467424765527982440  ,44.138212186071766178  ] 
dist 15=[17.858727506668504350  ,44.033203856347088585  ] 
dist 16=[16.371313211222454088  ,43.723671243692460334  ] 
dist 17=[14.679206564590540515  ,32.319676934766498106  ] 
dist 18=[12.251733933530161061  ,31.330881579037588380  ] 
dist 19=[9.8449613574136674947 ,29.106527118250130586  ] 
dist 20=[8.2354918653698296862 ,28.656859405663709182  ] 
dist 21=[6.8920005210877191568 ,25.924138004753146068  ] 
dist 22=[5.5486620921931432311 ,25.434750137749547657  ] 
dist 23=[4.2984967068032137537 ,24.481489241119986886  ] 
dist 24=[3.3275692693635621036 ,24.246390900008101587  ] 
dist 25=[2.3695401516865833935 ,21.748843139538626085  ] 
dist 26=[1.1710550757966364445 ,20.909764920864104799  ] 
dist 27=[.01635953949211748488,14.018441172617483775  ] 
dist 28=[-.76658381723411079214,13.690573547636415831  ] 
dist 29=[-1.4314195657185261463 ,13.223424342616962635  ] 
dist 30=[-2.1139923970908928460 ,12.322174537173622430  ] 
dist 31=[-2.7602005663483939231 ,8.3175376708348510028 ] 
dist 32=[-3.9580824451517327951 ,5.9764372188731800171 ] 
dist 33=[-5.1405832057534202635 ,2.6575557674394356846 ] 
dist 34=[-6.2726211672056153649 ,3.0597863486011945323 ] 
dist 35=[-7.2912603891232268968 ,3.4682924646426519470 ] 
dist 36=[-8.0207457500360833527 ,3.7188716083998327062 ] 
dist 37=[-8.6814198415230213960 ,3.8977275586056057960 ] 
dist 38=[-9.4252735549761846420 ,4.0208297366565613850 ] 
dist 39=[-10.100929170143011587  ,4.1100846476755492480 ] 
dist 40=[-10.489195472287472150  ,4.1543757544371572197 ] 
dist 41=[-10.743598659717015840  ,4.1729612195045563788 ] 
dist 42=[-10.884480545647245769  ,4.1637267882664490924 ] 
dist 43=[-10.963877531503200359  ,3.5574871676787791040 ] 
dist 44=[-10.972578082839246569  ,3.4555603492941059237 ] 
dist 45=[-10.940538900729117626  ,3.2945782551641159853 ] 
dist 46=[-10.908685168721650231  ,3.2427643199964948408 ] 
dist 47=[-4.6270559981313433486 ,3.0883313094068229541 ] 
dist 48=[-4.5603902390746604039 ,3.0318053365196779342 ] 
dist 49=[-4.4726193923883846938 ,3.1830446416025864394 ] 
dist 50=[-4.4357983367658356316 ,4.0961556105051429914 ] 
dist 51=[-.27152450692136711837,4.9003275603374897139 ] 
dist 52=[.07038962314467627296,5.4383254660709650932 ] 
dist 53=[.84353897056106712114,5.8842398556957072583 ] 
dist 54=[.96900111806942287983,6.3211188237069621955 ] 
dist 55=[1.8782183747185436471 ,6.7049369386424757436 ] 
dist 56=[2.0262385646720458160 ,6.9391369787688221170 ] 
dist 57=[2.2858112661308382698 ,7.1088783688627773848 ] 
dist 58=[2.3346873045407286160 ,7.2353834327117613043 ] 
dist 59=[2.8368525293464804904 ,7.3247243772036977287 ] 
dist 60=[2.8960084974843769956 ,7.3461187934562674670 ] 
dist 61=[2.8755209947322982368 ,7.3274483921733387229 ] 
dist 62=[2.7414542467056140574 ,7.3041267034907829704 ] 
dist 63=[1.8274443632135948755 ,3.9063393722795716693 ] 
dist 64=[1.0023369974809606968 ,3.9179435482768394814 ] 
dist 65=[.29641977725503999608,3.9057329058290719933 ] 
dist 66=[-.42901095721726594635,3.8927233102489096689 ] 
dist 67=[-1.1093877640452161930 ,2.5043424689924005412 ] 
dist 68=[-1.6356184977496393733 ,2.3671098136970669462 ] 
dist 69=[-2.1485178317440343937 ,2.0251917939905170470 ] 
dist 70=[-2.7757402154503825062 ,1.9692297266865873770 ] 
dist 71=[-3.3648325775335347751 ,1.4394005902837434097 ] 
dist 72=[-3.7256442747187060787 ,1.3385142995645021040 ] 
dist 73=[-3.9875548569376376408 ,1.2065612034214802327 ] 
dist 74=[-4.1821454907804661219 ,1.1648963323852391286 ] 
dist 75=[-4.3301039598121848402 ,.31096020929606338398] 
dist 76=[-4.4060116829196385019 ,.20481392527046592196] 
dist 77=[-4.4435473862983644183 ,-.03316042523816692105] 
dist 78=[-4.4418955781263602381 ,-.07638133480739507159] 
dist 79=[-2.1461932184148565347 ,-.35289510404127814988] 
dist 80=[-2.1775406411918605312 ,-.39857538962988101567] 
dist 81=[-2.1885561910828147834 ,-.3579895586956060556 ] 
dist 82=[-2.1854053874577313676 ,-.03200997074420508106] 
dist 83=[-1.0202059745708259172 ,.27533268528897434031] 
dist 84=[-1.1302240259505945872 ,.51537979642298160142] 
dist 85=[-1.2302507893983149742 ,.75145194830520659525] 
dist 86=[-1.3428196613807182598 ,1.0429750397767781331 ] 
dist 87=[-1.4547965414333575633 ,1.3180755555730887115 ] 
dist 88=[-1.5524344615211417895 ,1.4886659453482837622 ] 
dist 89=[-1.6581838072375092816 ,1.6150037347684256873 ] 
dist 90=[-1.8024935869178618688 ,1.7136265503115951104 ] 
dist 91=[-1.9457055455503861537 ,1.7900766739151493871 ] 
dist 92=[-2.0470560621497401886 ,1.8279662760219513935 ] 
dist 93=[-2.1369642348175448931 ,2.0259674322282963255 ] 
dist 94=[-2.2344983285574465249 ,2.3450880304007408350 ] 
dist 95=[-2.3291503658666468049 ,2.6515238909636369699 ] 
dist 96=[-2.4075351524224432598 ,2.8329232031711986661 ] 
dist 97=[-2.4887405148150027327 ,2.9573955875502431437 ] 
dist 98=[-2.5945988746222157501 ,3.0367001755489442372 ] 
dist 99=[-2.6920037306755916301 ,3.0911290399735913462 ] 
dist 100=[-2.7394813387961670263 ,3.1163342454801238561 ] 
dist 101=[-2.7600968977698632944 ,3.1250155937440229959 ] 
dist 102=[-2.7614049604245925368 ,3.3060734974035512882 ] 
dist 103=[-2.7208921763752795339 ,3.4725356794197809576 ] 
dist 104=[-2.7018518320590907043 ,3.5577509543791019175 ] 
dist 105=[-2.6626942279903328071 ,3.6004409305962173237 ] 
dist 106=[-2.6453760376582543445 ,3.6075769829139294023 ] 
dist 107=[-2.2267961868002468197 ,3.4318532871676948497 ] 
dist 108=[-2.1614668241422481246 ,3.3912186695120821218 ] 
dist 109=[-2.0143537516181268714 ,3.3366199252824964960 ] 
dist 110=[-1.9681202702524421054 ,3.3113770254268816994 ] 
dist 111=[-1.7588685439479777663 ,3.2385461338464683492 ] 
dist 112=[-1.7143314650892448418 ,3.2083067451691924622 ] 
dist 113=[-1.6041792394799399163 ,3.1548700889057551242 ] 
dist 114=[-1.6837188520555748924 ,3.1348718953872569786 ] 
dist 115=[-1.9724532412469753431 ,-.24646432825974313225] 
dist 116=[-2.1692288647010170399 ,-.4964751876751679615 ] 
dist 117=[-2.3360031393178988946 ,-1.0643148909279139164 ] 
dist 118=[-2.5050577522154065103 ,-1.1533294927495984039 ] 
dist 119=[-2.6546765669871640596 ,-1.8255510847590010947 ] 
dist 120=[-2.7439150841222856638 ,-1.9343338856271751320 ] 
dist 121=[-2.8058825262590778274 ,-2.1170635080732658022 ] 
dist 122=[-2.8467027275784073012 ,-2.1528816467080918373 ] 
dist 123=[-2.8707421955240321492 ,-1.9867245265764374084 ] 
dist 124=[-2.9561980310597314006 ,-1.7644656311933039925 ] 
dist 125=[-3.0491659858528230505 ,-1.4672850622311117530 ] 
dist 126=[-3.1169521327888158413 ,-.99091375858613044242] 
dist 127=[-3.1632175632971631316 ,-.50648181471619270238] 
dist 128=[-3.1707362327189916498 ,-.1771441208650265364 ] 
dist 129=[-3.1623715191662037783 ,.10102754120134976202] 
dist 130=[-3.1484891052602662518 ,.38135055240354972102] 
dist 131=[-1.7305724689415802173 ,.64094896559268766223] 
dist 132=[-1.6012011328331364684 ,.83644718072034434145] 
dist 133=[-1.2828860668844208114 ,1.0220599264595604120 ] 
dist 134=[-1.2338791129914684710 ,1.2422239656666366890 ] 
dist 135=[-.75812394274551676514,1.4476849197683665996 ] 
dist 136=[-.66976402617107864139,1.5746452049123912218 ] 
dist 137=[-.5581153499798371098 ,1.6681793735866511712 ] 
dist 138=[-.5298453838864704005 ,1.7402993679709797453 ] 
dist 139=[.18601347756107249295,1.7946698956165355972 ] 
dist 140=[.27197494291659866072,1.8173974040128212159 ] 
dist 141=[.46354782785283471579,1.8254161084769566475 ] 
dist 142=[.49557048658731375893,1.8220004643039516972 ] 
dist 143=[.7036145219286972312 ,1.6537005697105404128 ] 
dist 144=[.59969425917274091874,1.6906101757398921323 ] 
dist 145=[.47404015200508705797,1.7082654073949097634 ] 
dist 146=[.33992903633157902735,1.7109867702298075232 ] 
dist 147=[.21097540774338201785,1.1037658055791641084 ] 
dist 148=[.10589184018426902023,1.1264937446451298966 ] 
dist 149=[-.00162728233604122385,1.1778163188767189681 ] 
dist 150=[-.14030086758557111067,1.2373143329713000581 ] 
dist 151=[-.2742145506995475452 ,1.2974246789348994779 ] 
dist 152=[-.36274800170969417007,1.3511850891548492576 ] 
dist 153=[-.45825413077385296153,1.4105128977852535691 ] 
dist 154=[-.66611188176161541191,1.4928286870386800776 ] 
dist 155=[-.88536846295702586507,1.5751002022749087431 ] 
dist 156=[-1.0955106375126364516 ,1.6342477332554770035 ] 
dist 157=[-1.3388533049641971601 ,1.6876792083348125853 ] 
dist 158=[-1.6905606488526239028 ,1.7471414667301945759 ] 
dist 159=[-2.0349664631470817098 ,1.8057811939270317897 ] 
dist 160=[-2.2491822104732097765 ,1.8559262675254004706 ] 
dist 161=[-2.4086880103875986042 ,1.9093384334378158579 ] 
dist 162=[-2.5348385629976690292 ,1.9810027995810823191 ] 
dist 163=[-2.6327319541412749534 ,2.0483253643855486442 ] 
dist 164=[-2.7588236408519642210 ,2.0844158387946826994 ] 
dist 165=[-2.9956614301956520624 ,2.1044409088374894843 ] 
dist 166=[-3.1933481995725730082 ,2.1076797465734091894 ] 
dist 167=[-3.3503190854184888210 ,2.0998756180727546225 ] 
dist 168=[-3.4247320380824505066 ,2.0934616111783815492 ] 
dist 169=[-3.4621103838563298253 ,2.0522669203800687959 ] 
dist 170=[-3.4713352562153280398 ,2.0462169659083533919 ] 
dist 171=[-3.3800576931030899112 ,1.8794017254077638381 ] 
dist 172=[-3.3506925728632485535 ,1.8487240825123095426 ] 
dist 173=[-3.2979490711739360001 ,1.7538599498761925330 ] 
dist 174=[-3.2774819046136042720 ,1.7401040542573991612 ] 
dist 175=[-3.1737905118821846115 ,1.5257755501305408469 ] 
dist 176=[-3.1440404345035508588 ,1.4793495498999753862 ] 
dist 177=[-3.0521514322248845526 ,1.4399848234515240682 ] 
dist 178=[-3.0243275141093381471 ,1.4929451197510332035 ] 
dist 179=[.70987662362304277824,1.7587385691119881731 ] 
dist 180=[.96554707586784121708,1.9406003101496820123 ] 
dist 181=[1.4414158523505103588 ,2.0954802401304909578 ] 
dist 182=[1.3869789750203980652 ,2.2536366852751228934 ] 
dist 183=[1.3161725828438095827 ,2.3942284612192277216 ] 
dist 184=[1.2385029415819237440 ,2.6200010922418444869 ] 
dist 185=[1.1410794653391891996 ,2.8228797008713929968 ] 
dist 186=[.99146902353265680561,3.0286757783867491294 ] 
dist 187=[.82010943813597745798,3.2109969388331540236 ] 
dist 188=[.63592276403178146876,3.3202297494110149160 ] 
dist 189=[.40740687432755149096,3.3966430035832358695 ] 
dist 190=[.05920678101737484902,3.4480395588701948539 ] 
dist 191=[-.29125322071596729969,3.4793106736385125657 ] 
dist 192=[-.52878465962984627528,3.4807861273907139481 ] 
dist 193=[-.72864644217011208914,3.4589275981467469261 ] 
dist 194=[-.92883319857986016513,3.4397745892006928775 ] 
dist 195=[-1.1134560885154194732 ,1.7466363105361507647 ] 
dist 196=[-1.2512298559976607014 ,1.5925066637006552347 ] 
dist 197=[-1.3808171341337965340 ,1.2230581413878887149 ] 
dist 198=[-1.5327820559247004348 ,1.1611585184582611005 ] 
dist 199=[-1.6723411302128525507 ,.63880543060186621252] 
dist 200=[-1.7524384433898407878 ,.54312193451843613677] 
dist 201=[-1.8041703945360200270 ,.40282986593602253383] 
dist 202=[-2.0130765084410750066 ,.36416747597222917527] 
dist 203=[-2.2182144512169068695 ,-.08169187907842793897] 
dist 204=[-2.3363743457861324137 ,.00232054588863657162] 
dist 205=[-2.4132196114806135620 ,.11542965864872143391] 
dist 206=[-2.4535475891334775600 ,.29753659843089602552] 
dist 207=[-2.4769857212819467120 ,.48126589900476049361] 
dist 208=[-2.4864554656855106758 ,.6843416866598580108 ] 
dist 209=[-2.4874876063906727318 ,.88588127206402049993] 
dist 210=[-2.4786831940120045231 ,1.0871715140973026411 ] 
dist 211=[-.91286605437067600489,1.2724389259301627715 ] 
dist 212=[-.90638848517270747064,1.4100602947905573988 ] 
dist 213=[-.94601253227802382722,1.5388820375295918303 ] 
dist 214=[-1.0053544276349378654 ,1.6890464248890172302 ] 
dist 215=[-1.0665676142119818377 ,1.8264838757576831479 ] 
dist 216=[-1.1136564464931692425 ,1.9045352932503066324 ] 
dist 217=[-1.1593297763034152519 ,1.9538911481124561176 ] 
dist 218=[-1.2148958335401328787 ,1.9768557322747436410 ] 
dist 219=[-1.2724401599742350284 ,2.1311803614166930225 ] 
dist 220=[-1.3260049443615058907 ,2.2392423929125937914 ] 
dist 221=[-1.3868121630557930265 ,2.3109407794789153235 ] 
dist 222=[-1.4732476535192276057 ,2.3515582739904762971 ] 
dist 223=[-1.5567845937604890094 ,2.3756003725184308201 ] 
dist 224=[-1.6060287406141517410 ,2.3811760982117508381 ] 
dist 225=[-1.7018230996514527410 ,2.4117408848261126755 ] 
dist 226=[-1.8401012722635789997 ,2.5507876804996283248 ] 
dist 227=[-1.9745820400607681445 ,2.6597979558050875011 ] 
dist 228=[-2.0552275821733151295 ,2.8395021756721034682 ] 
dist 229=[-2.1117203112414293772 ,3.0392667869840561990 ] 
dist 230=[-2.1498526527572375984 ,3.1978306744573782648 ] 
dist 231=[-2.1731679244231793848 ,3.3207367662325790310 ] 
dist 232=[-2.1764657972851509544 ,3.3782538388126490212 ] 
dist 233=[-2.1606745366795104084 ,3.4034425657973502852 ] 
dist 234=[-2.1550142761108781929 ,3.4026173407160980731 ] 
dist 235=[-2.0304374302543542810 ,3.2108898093993523015 ] 
dist 236=[-2.0046511018251796810 ,3.1691047448231182625 ] 
dist 237=[-2.0062612288940090705 ,3.0928886912120767300 ] 
dist 238=[-2.0351783701138534761 ,3.0675096168745259822 ] 
dist 239=[-2.0588021960022158791 ,2.9530076899291328610 ] 
dist 240=[-2.0712877956135363872 ,2.9204962293274630379 ] 
dist 241=[-2.0779819973628600296 ,2.8346285442325103479 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 2, 0, 2, 1, 2] 
dist 0=[61.583359462538625316  ,61.583359462538625316  ] 
dist 1=[60.151961259125076876  ,62.304072648834014429  ] 
dist 2=[58.360490385479814264  ,62.679822201608120922  ] 
dist 3=[56.202210962195892666  ,62.733963025546760398  ] 
dist 4=[53.359177681958020430  ,62.611946141304151469  ] 
dist 5=[48.833812076879219313  ,62.111664720039013260  ] 
dist 6=[44.214234280582507010  ,61.656379008795028361  ] 
dist 7=[40.994980501439792231  ,61.342557069033474922  ] 
dist 8=[38.180886924488573911  ,61.163237015138689843  ] 
dist 9=[35.178647858063341484  ,60.615984444505440600  ] 
dist 10=[32.279576379178073957  ,60.387795044891160977  ] 
dist 11=[29.877080611219592997  ,59.895397379244233668  ] 
dist 12=[27.373570288730210096  ,59.691851376672025282  ] 
dist 13=[24.070593467385997734  ,58.676315711057753969  ] 
dist 14=[20.822519667760009025  ,58.306725637645312608  ] 
dist 15=[18.537888260998442001  ,55.886061190710934322  ] 
dist 16=[16.515321632796198414  ,31.738839986625884805  ] 
dist 17=[14.313189564280679423  ,27.618810993878386663  ] 
dist 18=[12.154479463160506019  ,24.284809734938472492  ] 
dist 19=[10.304647093161505344  ,22.915208172201006456  ] 
dist 20=[8.3182575314851925110 ,22.666252170388408558  ] 
dist 21=[5.6128238248581740071 ,14.226226487323467423  ] 
dist 22=[2.9686063330302359242 ,12.388599118213136886  ] 
dist 23=[1.2265978580409457951 ,11.987775599067225225  ] 
dist 24=[-.19761985096785628799,9.5417752577257006460 ] 
dist 25=[-1.5716118266178927795 ,7.3839157937527253717 ] 
dist 26=[-3.4125731511013653071 ,6.9898486822183343698 ] 
dist 27=[-5.3084254201093169360 ,6.3849340479144039817 ] 
dist 28=[-7.0462695186119730320 ,6.2484653608269811392 ] 
dist 29=[-8.3490244882661733763 ,-.2852237119588274279 ] 
dist 30=[-9.5919104282856800050 ,-2.6453978647345214475 ] 
dist 31=[-11.092560575434142110  ,-3.2236989610612042090 ] 
dist 32=[-12.480925735650370746  ,-3.0250225980739971609 ] 
dist 33=[-13.275549915056791128  ,-2.5822475132957359423 ] 
dist 34=[-13.797572085124521447  ,-2.0219281338132040393 ] 
dist 35=[-14.095846592024295647  ,-1.3539125460346677268 ] 
dist 36=[-14.285842499167897212  ,-.4826724888017340380 ] 
dist 37=[-14.374455118221801313  ,.88858513493501134009] 
dist 38=[-14.409363893568991367  ,2.2645781058837724150 ] 
dist 39=[-14.383370051494953432  ,3.1549180684689064866 ] 
dist 40=[-12.508285520274746085  ,3.8570298583728767475 ] 
dist 41=[-12.227854986171232754  ,4.4825337124587899941 ] 
dist 42=[-11.705104160861422985  ,5.0085926813003078114 ] 
dist 43=[-11.562708474488015913  ,5.3141810771882025298 ] 
dist 44=[-11.240921201441399224  ,5.5159309840872027290 ] 
dist 45=[-10.903968069759400952  ,5.6306550791060183397 ] 
dist 46=[-10.705380366401907024  ,5.7067927537966970579 ] 
dist 47=[-10.628569565153193795  ,5.7547920288510856542 ] 
dist 48=[-3.7555272358703180962 ,5.7915816003280270055 ] 
dist 49=[-3.6106209484925911330 ,6.1393512623288569926 ] 
dist 50=[-3.0756299073430214024 ,6.7084643982532654522 ] 
dist 51=[-2.9551667718028112767 ,7.1917441693668834597 ] 
dist 52=[-2.7485362843911304439 ,7.6845398678532162408 ] 
dist 53=[-2.6952000070827907955 ,8.1154842232112564354 ] 
dist 54=[.7750084526760966310 ,8.3519612691920194990 ] 
dist 55=[-.0374710184610333330 ,8.4917256115990957228 ] 
dist 56=[-.7186660424088563225 ,8.6154632448367445906 ] 
dist 57=[-1.3957002813809567804 ,9.2447691197971703277 ] 
dist 58=[-2.0156847915697830398 ,9.7135592288379610850 ] 
dist 59=[-2.4694119792389717149 ,10.086680998329893972  ] 
dist 60=[-2.8869207636270662113 ,10.370568236730011985  ] 
dist 61=[-3.3625203456618973204 ,10.483198711476232962  ] 
dist 62=[-3.8007615055193267839 ,10.521407285816342474  ] 
dist 63=[-4.0692917764156511021 ,10.508047669522011858  ] 
dist 64=[-4.2642357171276627912 ,3.9085514574142975092 ] 
dist 65=[-4.4089817412553822919 ,2.7694821878502856482 ] 
dist 66=[-4.5106130504325620426 ,2.5542614745687150478 ] 
dist 67=[-4.8244160326977378590 ,2.2132226305841038966 ] 
dist 68=[-5.3805017511667537529 ,2.1237725591795405928 ] 
dist 69=[-5.8850100624117502183 ,.49459627000893229756] 
dist 70=[-6.1817369799632201746 ,.2845853803378955165 ] 
dist 71=[-6.3827370622155561842 ,-.19512055451582954116] 
dist 72=[-6.5053467808356490335 ,-.1349635381421328527 ] 
dist 73=[-6.5783172851787125501 ,.2711390704805712975 ] 
dist 74=[-6.7094150536937225234 ,.6476978841292120034 ] 
dist 75=[-6.8089313848385142851 ,.93104321716596602658] 
dist 76=[-6.8730988284507577756 ,1.1994117750108090196 ] 
dist 77=[-6.8747358388316937741 ,1.5162322628791351351 ] 
dist 78=[-6.8449650506747677886 ,1.8130862630687725429 ] 
dist 79=[-6.8127480139453512136 ,2.0018378337404358168 ] 
dist 80=[-2.9370345172869325949 ,2.1469084568631489285 ] 
dist 81=[-2.5950282050499592929 ,2.2696014325802007727 ] 
dist 82=[-1.8063005344314666205 ,2.4093758739926840462 ] 
dist 83=[-1.6567676751070455437 ,2.7804705760500356390 ] 
dist 84=[-.64203987589187075014,3.1978439664288795258 ] 
dist 85=[-.46136168519418648828,3.5812254410171642840 ] 
dist 86=[-.1300609289491474669 ,3.8167494521550068466 ] 
dist 87=[-.05566763930607117485,3.9885566599750512419 ] 
dist 88=[.91205919942215218834,4.1177830434903397014 ] 
dist 89=[.8226272378452983389 ,4.3448579294383388146 ] 
dist 90=[.6450727755452780857 ,4.5951844707325762890 ] 
dist 91=[.4928270338003715932 ,4.7723414925375203419 ] 
dist 92=[.3304002896240841156 ,4.9024238678829630048 ] 
dist 93=[.1122244397072545877 ,4.9649930699905295039 ] 
dist 94=[-.17121254510295819337,4.9899521014939859010 ] 
dist 95=[-.48446768876955009008,4.9839142687133464782 ] 
dist 96=[-.79785506802840204032,2.7429426937419866507 ] 
dist 97=[-1.0860737774919943347 ,2.8528994925508947252 ] 
dist 98=[-1.2989545288632484476 ,2.9593038025958633739 ] 
dist 99=[-1.6202593585493521948 ,3.0470317871467635603 ] 
dist 100=[-2.1435598066853497770 ,3.1376389942014932655 ] 
dist 101=[-2.9096974973387517583 ,3.2555001622859157319 ] 
dist 102=[-3.6639735854220360917 ,3.3642433905302222493 ] 
dist 103=[-4.1399646946711890083 ,3.4184748298240026278 ] 
dist 104=[-4.5023193176508068531 ,3.4429521846655694937 ] 
dist 105=[-4.8033022439901510995 ,3.4425990646799161265 ] 
dist 106=[-5.0418769574964637060 ,3.4068571737753986156 ] 
dist 107=[-5.1552815497355436868 ,3.3883489003421945272 ] 
dist 108=[-5.2117085579830846888 ,3.3254127100529942961 ] 
dist 109=[-5.2229960666236295178 ,3.2956596756058841160 ] 
dist 110=[-5.0615930316068435538 ,2.9068893394607734034 ] 
dist 111=[-5.0135160320315586424 ,2.8404080960840055051 ] 
dist 112=[-4.9277419111942170192 ,2.6659552162205505138 ] 
dist 113=[-4.8954726287580412480 ,2.6255742889249538400 ] 
dist 114=[-4.7359816970550899244 ,2.3052442832700173918 ] 
dist 115=[-4.6896271769412721498 ,2.2363456275540211777 ] 
dist 116=[-4.5518743188704083022 ,2.1295097065903662736 ] 
dist 117=[-4.5056560268707743704 ,2.1133623915618762962 ] 
dist 118=[-2.4595858460178161860 ,2.1490563219010149614 ] 
dist 119=[-2.4984439131039605997 ,2.1560939932295903935 ] 
dist 120=[-2.5813573572792419706 ,2.1377524844664310938 ] 
dist 121=[-2.6602527176757273949 ,2.1689192722998588678 ] 
dist 122=[-2.7230916297332468622 ,2.2344723193883150162 ] 
dist 123=[-2.7859946251773055924 ,2.2793897072873537675 ] 
dist 124=[-2.8651149513473089027 ,2.5517552333690360933 ] 
dist 125=[-2.9366206041818738590 ,3.2394347480893101401 ] 
dist 126=[-2.9691452165915500056 ,3.6746748049325575718 ] 
dist 127=[-2.9791624345218625542 ,4.0075262715640740339 ] 
dist 128=[-2.9760288105202552970 ,4.2867729648787127474 ] 
dist 129=[-2.9298280180749075668 ,4.5095880985223578413 ] 
dist 130=[-2.9113416375439721281 ,4.6173348937147079614 ] 
dist 131=[-2.8491207768779458881 ,4.6721059388081379622 ] 
dist 132=[-2.8241629337412086745 ,4.6835738200682310376 ] 
dist 133=[-2.4892020148443727273 ,4.5741587728744654636 ] 
dist 134=[-2.4322010228476088147 ,4.5359840192536049441 ] 
dist 135=[-2.2776829652623324487 ,4.4672858968290637906 ] 
dist 136=[-2.2465502082636764979 ,4.4399168820700935856 ] 
dist 137=[-1.9514126064974859166 ,4.2987875370097270436 ] 
dist 138=[-1.9120262280835359635 ,4.2584182499269328684 ] 
dist 139=[-1.8824735608366600747 ,4.1310476974986033518 ] 
dist 140=[-1.8671777697953799157 ,4.0944706144104494599 ] 
dist 141=[-.05248068234092411654,2.0931738695064476089 ] 
dist 142=[-.3541962677111957981 ,2.0718934749802887553 ] 
dist 143=[-.6026586902342292490 ,2.0642417234643803734 ] 
dist 144=[-.8426736969344910063 ,1.0888155566570873336 ] 
dist 145=[-1.0582883694156964066 ,.99800378296862674011] 
dist 146=[-1.2094212666705632173 ,.78096384325248050509] 
dist 147=[-1.3419623637710892868 ,.7434305616221193649 ] 
dist 148=[-1.4834195072392743376 ,.43744930728534167561] 
dist 149=[-1.6116571327232872348 ,.3811531903306880646 ] 
dist 150=[-1.6914658695510085799 ,.29551123668558007402] 
dist 151=[-1.7509348094534678136 ,.27274360537693683342] 
dist 152=[-1.7980327209386897402 ,-.12710075953004275563] 
dist 153=[-1.8334673361754622620 ,-.17781433696919775905] 
dist 154=[-1.8464089028146133789 ,-.28665181989287423008] 
dist 155=[-1.8469540298478842465 ,-.30849857542347760287] 
dist 156=[-1.8426278133687852395 ,-.41639025982090627659] 
dist 157=[-1.4121388565075386583 ,-.43456967938319314564] 
dist 158=[-1.4158110813563699844 ,-.42056033622476630075] 
dist 159=[-1.4124657982526268444 ,-.26184613841357675348] 
dist 160=[-.64185603320367239078,-.09885763543440838562] 
dist 161=[-.48069662907666385829,.05396944708811258739] 
dist 162=[-.49264502980430402373,.17215370809510856323] 
dist 163=[-.51376476665178306707,.28734344998711379936] 
dist 164=[-.53911887627835421449,.4282297053374295996 ] 
dist 165=[-.56795726550793855586,.5616451024783840750 ] 
dist 166=[-.60481622808248343802,.6470340465588525250 ] 
dist 167=[-.66216374739385755842,.7134171983276596690 ] 
dist 168=[-.72218214008400014473,.7710155324102551646 ] 
dist 169=[-.76969456918450024462,.8184013304042993977 ] 
dist 170=[-.81704924477791267377,.8440439997365699626 ] 
dist 171=[-.87643709570716428807,.8586019875545247912 ] 
dist 172=[-.93886252176065751244,.8617660758801356474 ] 
dist 173=[-.99833317520031298203,.86708122708070558109] 
dist 174=[-1.0669030779156338089 ,1.0465307869596909065 ] 
dist 175=[-1.1656239748580621365 ,1.3056871555455582437 ] 
dist 176=[-1.2614836083731042113 ,1.5591886811620753232 ] 
dist 177=[-1.3186394915934993335 ,1.7160803804382568310 ] 
dist 178=[-1.3582671689962102409 ,1.8319626494779249536 ] 
dist 179=[-1.3842069251086619112 ,1.9218692257849952975 ] 
dist 180=[-1.3999204492667897444 ,1.9910479776528553299 ] 
dist 181=[-1.4022077591843941939 ,2.0242418067378781468 ] 
dist 182=[-1.3926795274311762567 ,2.0381133861222108396 ] 
dist 183=[-1.3888036724699527294 ,2.0385696306130679741 ] 
dist 184=[-1.2868887142857538084 ,1.8933974518215960390 ] 
dist 185=[-1.2671004750574782918 ,1.8649099952225264816 ] 
dist 186=[-1.2145498670042820911 ,1.8147627557283789154 ] 
dist 187=[-1.1986616126181255527 ,1.7990208826873690991 ] 
dist 188=[-1.0949780448945017639 ,1.7337029843817469617 ] 
dist 189=[-1.3274558649977362382 ,1.7138321263324460927 ] 
dist 190=[-1.5035177467316787152 ,1.6692532628402468598 ] 
dist 191=[-1.6391924273617988598 ,1.6524989724076430481 ] 
dist 192=[-1.7548793242220096183 ,1.0309239650437238944 ] 
dist 193=[-1.8486222056347587482 ,1.0230898500427819496 ] 
dist 194=[-1.8967570056012486380 ,1.0180659131406765588 ] 
dist 195=[-1.9216317320749536947 ,.9993111990027981576 ] 
dist 196=[-1.9258008609716229074 ,.9916542696670436520 ] 
dist 197=[-1.9045472778671823560 ,.9312851459679135978 ] 
dist 198=[-1.8928029348418806386 ,.9177182646524154254 ] 
dist 199=[-1.8693076071967985547 ,.8816572107758580552 ] 
dist 200=[-1.8584487923176291405 ,.8702660580357292426 ] 
dist 201=[-1.7961382942258932395 ,.7982744430820705608 ] 
dist 202=[-1.7799850490843801856 ,.7815498331960084984 ] 
dist 203=[-1.7032794072632721718 ,.7507858287750265933 ] 
dist 204=[-1.5264139545745538792 ,.7417814645572675818 ] 
dist 205=[-.8127016853015085070 ,.69701162152906144647] 
dist 206=[-.7850726711951753828 ,.90588095162937846539] 
dist 207=[-.7767364027104802913 ,1.0732551745999692833 ] 
dist 208=[-.18176770598287842537,1.2272990562647279743 ] 
dist 209=[-.12683271359982018438,1.3606229658779743815 ] 
dist 210=[-.01256681315426486799,1.4453426467712903833 ] 
dist 211=[.01682951487828569636,1.5105218006503303061 ] 
dist 212=[.12194201958467287802,1.5658963700703082126 ] 
dist 213=[.14272416474229205952,1.6109702378855642899 ] 
dist 214=[.17169730013790542514,1.6350584619208293178 ] 
dist 215=[.17784209319431119761,1.6483432770074545698 ] 
dist 216=[.1753465802254600324 ,1.6503203139306014967 ] 
dist 217=[.15944447701268956789,1.6448758432220514936 ] 
dist 218=[.13071146553775710027,1.6391852657531272646 ] 
dist 219=[.07703053833884516019,1.6112681590735302211 ] 
dist 220=[.01155431410370617116,1.6019703761310606068 ] 
dist 221=[-.06423241315879189376,1.2295202225202140446 ] 
dist 222=[-.22723464580919848101,1.2245550737076495943 ] 
dist 223=[-.41574223435779555623,1.2192194596698772486 ] 
dist 224=[-.60519367598971494654,.39369869260206546604] 
dist 225=[-.78029915023612210062,.16065378133155122225] 
dist 226=[-.91157902630574537884,.11918796028367048043] 
dist 227=[-1.0356409745777091977 ,.03632664139744763924] 
dist 228=[-1.1819533026339692794 ,.01575004766185349055] 
dist 229=[-1.3167258361169302637 ,-.17706162680735053609] 
dist 230=[-1.3947541590680645019 ,-.20705135895540532432] 
dist 231=[-1.4460074261882883609 ,-.24165891845168728159] 
dist 232=[-1.4739710212333437159 ,-.24338134730796260657] 
dist 233=[-1.4913521192633862482 ,-.23159115670543575403] 
dist 234=[-1.5003905384098981519 ,-.2002260472721153476 ] 
dist 235=[-1.5050309711290470218 ,-.14857799887645370389] 
dist 236=[-1.4996902910480935557 ,-.05587701191520719586] 
dist 237=[-.82521717349647538977,.04115061058978151793] 
dist 238=[-.81344145143375055805,.1100581203543412794 ] 
dist 239=[-.80775931386781077503,.17142770565978827844] 
dist 240=[-.24503425361804280054,.23838590135116669764] 
dist 241=[-.19545451654400610794,.30364966558054154943] 
dist 242=[-.08669342373667232789,.3582600518412052356 ] 
dist 243=[-.06300408902647493049,.41541749993802050301] 
dist 244=[.05885683425175432192,.49084181183781472082] 
dist 245=[.07962286157458189420,.56447229262559752989] 
dist 246=[.1268410293382449258 ,.61447398625035167789] 
dist 247=[.1395913616497680547 ,.6601599706799245295 ] 
dist 248=[.44800348451910213068,.74160780472305957159] 
dist 249=[.44050815844233968882,.79086318473412000504] 
dist 250=[.41878532514231159328,.8258738312131117467 ] 
dist 251=[.37201928702831768499,.85049780472825572278] 
dist 252=[.31285073744889331208,.86780221183245993349] 
dist 253=[.2416529693100084535 ,.87361427090320710188] 
dist 254=[.14814925836065907041,.8738880832461739267 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 1, 1, 2] 
dist 0=[52.952366976117430215  ,52.952366976117430215  ] 
dist 1=[51.449759431051874443  ,54.007239947786773324  ] 
dist 2=[48.941869671174398204  ,54.727571786004294979  ] 
dist 3=[46.336830337975430629  ,55.247129210170553656  ] 
dist 4=[44.446334981048157439  ,55.500525316500914827  ] 
dist 5=[42.715671822312974907  ,55.607422856310488146  ] 
dist 6=[40.748682097630098505  ,55.570666116800015274  ] 
dist 7=[38.778291854341907522  ,55.403156814083062844  ] 
dist 8=[37.034021253114898688  ,54.875426253510705242  ] 
dist 9=[35.119690655645208625  ,51.524998642866693459  ] 
dist 10=[32.470326486558436170  ,51.288393084469084384  ] 
dist 11=[29.813559099450652114  ,50.507369302914326934  ] 
dist 12=[27.869611547085164562  ,50.242925728481064267  ] 
dist 13=[26.073494610039509263  ,49.868712059037874728  ] 
dist 14=[24.006774800168407331  ,49.710144998883602766  ] 
dist 15=[21.921164276386581493  ,49.283393848664064221  ] 
dist 16=[20.049494412127051989  ,48.334752759689464803  ] 
dist 17=[17.973372590832062855  ,25.914202449902788802  ] 
dist 18=[15.071264676003674083  ,24.586852034139224588  ] 
dist 19=[12.107811198551689158  ,19.981934331184245290  ] 
dist 20=[10.028114848327064470  ,19.205913109435649381  ] 
dist 21=[8.2942451623565230298 ,15.813581461871157123  ] 
dist 22=[6.5676053598103757878 ,15.565769451104269270  ] 
dist 23=[4.9524928617228901553 ,12.075756503354914114  ] 
dist 24=[3.5413851223378630858 ,11.707698017795777312  ] 
dist 25=[1.1086166289826921301 ,8.8413654046128797220 ] 
dist 26=[-1.0067755089683122088 ,7.7306196534052869340 ] 
dist 27=[-2.7994123713884086114 ,3.2313134881683460756 ] 
dist 28=[-4.6296078872255376462 ,2.9201758966640762730 ] 
dist 29=[-6.3545203279794096073 ,2.3448180628333416206 ] 
dist 30=[-7.7275383713361448623 ,2.2319255211890281944 ] 
dist 31=[-9.1150154346773141720 ,-.35398365302616912331] 
dist 32=[-10.899437910032907320  ,-.4537628183654142982 ] 
dist 33=[-12.583056100045578055  ,-.50911232083843860977] 
dist 34=[-13.568118003917218485  ,-.44897851927569582387] 
dist 35=[-14.240311437890451696  ,-.36265920452430532887] 
dist 36=[-14.673155277738491724  ,-.2941636272226998569 ] 
dist 37=[-14.978056618059458227  ,-.22975336221114704031] 
dist 38=[-15.138333733835876358  ,-.15866461193804921464] 
dist 39=[-15.226924710531814252  ,-.09193254686274233986] 
dist 40=[-15.243965399735656129  ,-.04436910936132101976] 
dist 41=[-13.390299399651074644  ,-.00289914638631833691] 
dist 42=[-13.114002212077595698  ,.04004668802510550905] 
dist 43=[-12.635239677177517166  ,.07647548061629845898] 
dist 44=[-12.503892259373385253  ,.09225691130461988582] 
dist 45=[-12.088071104115076995  ,.09647321711682719820] 
dist 46=[-11.949171885791949609  ,.88022710346421737936] 
dist 47=[-11.858777584063486848  ,2.1123918444545368330 ] 
dist 48=[-11.820597227106976100  ,3.1779104321912848268 ] 
dist 49=[-4.3458390481425184978 ,4.0490367186155521450 ] 
dist 50=[-4.3022903772408158111 ,4.8823957416299483959 ] 
dist 51=[.29952387919195536501,5.6276400464025362292 ] 
dist 52=[.63199070832323122138,6.1471495202606315071 ] 
dist 53=[2.5367049320128853882 ,6.6009105876590966432 ] 
dist 54=[2.8509798964596352754 ,7.0838245944611467007 ] 
dist 55=[3.5064387939559817979 ,7.5097057659990522893 ] 
dist 56=[3.6275929974217152327 ,7.7358816688682334867 ] 
dist 57=[4.4264708162642432736 ,8.2486530106039209703 ] 
dist 58=[4.3961836544142460713 ,8.9684448888153148426 ] 
dist 59=[3.7549311256972329963 ,9.5183777069108073623 ] 
dist 60=[3.0056413991395246684 ,9.9805116237670647537 ] 
dist 61=[2.0486481573395418021 ,10.350910706458020078  ] 
dist 62=[.56069998407939545347,10.534648322501977129  ] 
dist 63=[-.9361710355602137382 ,10.618923278373965445  ] 
dist 64=[-1.9288146427232446560 ,10.628316673144152405  ] 
dist 65=[-2.7403180026063675476 ,4.6510175049232341737 ] 
dist 66=[-3.5146466348496860270 ,4.5355392464370853773 ] 
dist 67=[-4.2041869544107701902 ,3.5635038664173311540 ] 
dist 68=[-4.6774951904209015838 ,3.3731621271983372620 ] 
dist 69=[-5.0823588876535191201 ,3.0948558340846817626 ] 
dist 70=[-5.4989245307464110509 ,3.0116348341687936219 ] 
dist 71=[-5.8689117073943105013 ,1.3561157300025840956 ] 
dist 72=[-6.0879697788620334093 ,1.1422543086060417319 ] 
dist 73=[-6.2382728592134064935 ,.65000954096238154734] 
dist 74=[-6.3339347137741532059 ,.55949857350008302251] 
dist 75=[-6.3871961039475917770 ,-.06931677680588459890] 
dist 76=[-6.3908096610443968796 ,-.18035418714592178944] 
dist 77=[-6.3307008092902150357 ,-.38019471752667045726] 
dist 78=[-6.3090512876740667857 ,-.3769747568718221849 ] 
dist 79=[-5.2756223139590914044 ,-.05533533940854958831] 
dist 80=[-5.2618721376358942304 ,.16065893544253871092] 
dist 81=[-2.0427951741953900704 ,.51517717172856742989] 
dist 82=[-1.7736197588234505858 ,1.1323039206293027819 ] 
dist 83=[-1.1482161977318987352 ,1.6965178497645933278 ] 
dist 84=[-1.0365961907109968130 ,2.1086092564329531923 ] 
dist 85=[-.22320356362067256959,2.4872441745961877481 ] 
dist 86=[-.07950170287431061022,2.9180514439926210943 ] 
dist 87=[.16967722441286889442,3.3160964742941748486 ] 
dist 88=[.22371592947143649549,3.5640590984235060544 ] 
dist 89=[.7429802873273518388 ,3.7490705376840599534 ] 
dist 90=[.6612131524467582064 ,3.8960002297438061327 ] 
dist 91=[.5574758361848597568 ,4.0068450235297379392 ] 
dist 92=[.4330253068205009079 ,4.0479112349221593990 ] 
dist 93=[.27026110179329442008,4.0582247843600880297 ] 
dist 94=[.01380455343439074684,4.0464133175374313618 ] 
dist 95=[-.24675016212267162002,3.2054002782223193665 ] 
dist 96=[-.42585612519819826697,3.2107629389441129181 ] 
dist 97=[-.57868895852533874938,1.9760240014175676091 ] 
dist 98=[-.73453687690614219396,1.9193653151822537473 ] 
dist 99=[-.87945422109272620471,1.3565005798047494189 ] 
dist 100=[-.98872626592849167722,1.2497390887878561075 ] 
dist 101=[-1.0922850330230367164 ,1.1165000130148600178 ] 
dist 102=[-1.2144369666812854259 ,1.0797485968783484623 ] 
dist 103=[-1.3264024367146747567 ,.1631725452073659958 ] 
dist 104=[-1.3893593627340288012 ,.07333158442282733188] 
dist 105=[-1.4837162200877984560 ,.08009321891465394792] 
dist 106=[-1.6255281657218286146 ,.10903622564229047313] 
dist 107=[-1.7433088746819067843 ,.14991213032307623648] 
dist 108=[-1.8093404843941838093 ,.2042412279929937295 ] 
dist 109=[-1.8500919705220300770 ,.27861810405278110143] 
dist 110=[-1.8670804738822459628 ,.39941351076423870946] 
dist 111=[-1.8725346797522605949 ,.52065510202292765918] 
dist 112=[-1.9993446356574561163 ,.59680957342206765637] 
dist 113=[-2.1325057080177974472 ,.65421920438729329478] 
dist 114=[-2.2683488498589853325 ,.70073210846432321692] 
dist 115=[-2.3953789996987157589 ,.73754968185219416928] 
dist 116=[-2.4933679664645602854 ,.75629901932964306849] 
dist 117=[-2.5887558004807844870 ,.76537909467236241776] 
dist 118=[-2.7053979393567278013 ,.76678458906495283176] 
dist 119=[-2.8151476923788099800 ,.71783049960840977055] 
dist 120=[-2.8830285108834433473 ,.70407294147447836089] 
dist 121=[-2.9331454067750461402 ,.61973695987007331656] 
dist 122=[-2.9720078506767960754 ,.61073378125304031369] 
dist 123=[-3.0005532495414261952 ,.60780300601274719353] 
dist 124=[-3.0094963809817340860 ,1.0671821815780163574 ] 
dist 125=[-3.0057235536460957537 ,1.6121097782570507111 ] 
dist 126=[-2.9963793182725040878 ,2.4149325428095894577 ] 
dist 127=[-2.9545184506205746555 ,3.2086449167986355199 ] 
dist 128=[-2.9336321291237474878 ,3.7172350764416539682 ] 
dist 129=[-2.8895739121735042971 ,4.1134650825550001196 ] 
dist 130=[-2.8702745678019069736 ,4.4589476401873766562 ] 
dist 131=[-2.7621936806397433812 ,4.7446495694473754244 ] 
dist 132=[-2.7345363263355502403 ,4.9024038415405209662 ] 
dist 133=[-2.6417361654857574756 ,4.9964032939570156740 ] 
dist 134=[-2.6229667861029538389 ,5.0277806332900770071 ] 
dist 135=[-2.3241001880319876578 ,5.0313778423014223272 ] 
dist 136=[-2.2709163614667980432 ,5.0145552017069521231 ] 
dist 137=[-2.1306852038486518862 ,4.9798767221955315309 ] 
dist 138=[-2.0993907630058601180 ,4.9591236271999675728 ] 
dist 139=[-1.8407717114627241668 ,4.8262319480514845710 ] 
dist 140=[-1.7853439195383681232 ,4.7890116932151402308 ] 
dist 141=[-1.7027541404636908396 ,4.6429136825689144566 ] 
dist 142=[-1.6762827437932116445 ,4.6208901544233461336 ] 
dist 143=[-1.6135598717974110881 ,1.2493126443346477232 ] 
dist 144=[-2.1121350783776068604 ,1.2434456359113022151 ] 
dist 145=[-2.5121370939361534565 ,.8426461384463988084 ] 
dist 146=[-2.9815221768287961215 ,.79845394411992312188] 
dist 147=[-3.4967956079797402015 ,.69222735472784116705] 
dist 148=[-3.8479990602001497785 ,.6711677397855697681 ] 
dist 149=[-4.1456041685283267399 ,.51524259153850344033] 
dist 150=[-4.4470720011990216371 ,.4851795573844450653 ] 
dist 151=[-4.7138806613754333178 ,.43490314740637504372] 
dist 152=[-4.8732264659953401857 ,.42219992634494971396] 
dist 153=[-4.9840759242590217384 ,.18781620578732109026] 
dist 154=[-5.0574231047544936909 ,.15696682415840304883] 
dist 155=[-5.1008928017074668064 ,.0850625580999912446 ] 
dist 156=[-5.1024653555424563073 ,.0729219775109858805 ] 
dist 157=[-5.0665631867175581783 ,-.0210583529445482741 ] 
dist 158=[-5.0396045785019912843 ,-.0375738435282452633 ] 
dist 159=[-2.5498517986969409157 ,.06263065129631108973] 
dist 160=[-2.3223406892372639386 ,.59590362987657332109] 
dist 161=[-1.7797346310489858383 ,1.0454698782307111443 ] 
dist 162=[-1.6865813286639866250 ,1.4970468790797864926 ] 
dist 163=[-.92735896574197929365,1.9142289949541150070 ] 
dist 164=[-.78847028753404930532,2.2265921536950151098 ] 
dist 165=[-.57689282986883267174,2.5213555227200695960 ] 
dist 166=[-.52113855703904807866,2.8683300049999879242 ] 
dist 167=[-.42967252208634149305,3.1875373450045597514 ] 
dist 168=[-.51196066485600756489,3.3715359592569096544 ] 
dist 169=[-.59617709392183635161,3.4913486872660007269 ] 
dist 170=[-.65988970727065769836,3.5545158323894366078 ] 
dist 171=[-.72066284481657585473,3.5925882798524817781 ] 
dist 172=[-.79315298066657785248,3.6122989016061632183 ] 
dist 173=[-.86745531337531554245,3.6222916934711310159 ] 
dist 174=[-.93545739574986028831,3.6216043324873464699 ] 
dist 175=[-1.0117365449622108026 ,1.1652981298123995692 ] 
dist 176=[-1.1190570724040694484 ,1.1561822029370436145 ] 
dist 177=[-1.2222989746213077439 ,1.1802166490761924247 ] 
dist 178=[-1.3025321172751117626 ,1.2996284039836963100 ] 
dist 179=[-1.6398311629847046793 ,1.3865492202220000645 ] 
dist 180=[-1.8963835063924336831 ,1.4516336959851278319 ] 
dist 181=[-2.1424102631881647265 ,1.5016070419249030404 ] 
dist 182=[-2.4377241973514566764 ,1.5282446284226071962 ] 
dist 183=[-2.7124167107900701769 ,1.5824954843036958228 ] 
dist 184=[-2.8761841438200051007 ,1.6784824742143244649 ] 
dist 185=[-2.9897422142303797519 ,1.7765874951402998389 ] 
dist 186=[-3.0641467332836906759 ,1.9029703132468515021 ] 
dist 187=[-3.1140446322951321448 ,2.0375421651584376105 ] 
dist 188=[-3.1298418814418032092 ,2.1683104605678348329 ] 
dist 189=[-3.1268340023482851096 ,2.3210645722586459210 ] 
dist 190=[-3.1180162629701867330 ,2.5433341516379403756 ] 
dist 191=[-3.6043441115434479736 ,2.7601487024471712660 ] 
dist 192=[-3.9583802659098455739 ,2.8911411382808252724 ] 
dist 193=[-4.2198829861535255331 ,2.9840742383514445385 ] 
dist 194=[-4.4227814188667451871 ,3.0490691763038640715 ] 
dist 195=[-4.5784193037898425581 ,3.0909522456659169985 ] 
dist 196=[-4.6513883573471897567 ,3.0990272775902115537 ] 
dist 197=[-4.6812439304472206134 ,3.0808046025893500142 ] 
dist 198=[-4.6803521510615736713 ,3.0763225678347527406 ] 
dist 199=[-4.3582729554740602873 ,2.8937131464707721514 ] 
dist 200=[-4.2940130315680544594 ,2.8558805594949319718 ] 
dist 201=[-4.1773044400813925136 ,2.7469639044339372520 ] 
dist 202=[-4.1400662350371921108 ,2.7179344383539308273 ] 
dist 203=[-3.9789721289803817904 ,2.5647692286358908137 ] 
dist 204=[-3.9327069531390389938 ,2.5673653992967028650 ] 
dist 205=[-3.8194889683473307748 ,2.5578046691313395346 ] 
dist 206=[-3.7759789224898607844 ,2.5480087434704378128 ] 
dist 207=[-1.2126974471065545386 ,.30321326268581613081] 
dist 208=[-1.2098475454708405906 ,.41070247695777731825] 
dist 209=[-.6996652592747941814 ,.57268812386285904449] 
dist 210=[-.65399092174384421644,.73055594392288845038] 
dist 211=[-.54289104704838121725,.8733244370005266356 ] 
dist 212=[-.52381366158987797867,.9750777809896354544 ] 
dist 213=[-.35968219021517609211,1.0660815357458235378 ] 
dist 214=[-.32878448159354995876,1.1659701190995470770 ] 
dist 215=[-.28447684530971339117,1.2559916581921145708 ] 
dist 216=[-.2715322711566066834 ,1.3076342072897195697 ] 
dist 217=[-.02796089214072464099,1.3409589109743066604 ] 
dist 218=[-.03074265424223462964,1.3579057539449948640 ] 
dist 219=[-.08248464875609844584,1.3660077920460527098 ] 
dist 220=[-.15177788350705667669,1.3642216492652965963 ] 
dist 221=[-.22688164565045236717,1.3567750327585125110 ] 
dist 222=[-.30180339856621196422,1.3502691285508225367 ] 
dist 223=[-.39079519216416006604,.9092103335588770494 ] 
dist 224=[-.52202726580658505665,.86266757545936101872] 
dist 225=[-.65207204823721762716,.74714131285343923237] 
dist 226=[-.74270651862571831906,.74478912459995423279] 
dist 227=[-.84922167415042354145,.79038777443417509712] 
dist 228=[-.95382474132467088799,.83664933259851291596] 
dist 229=[-1.0489666080616537529 ,.8796889392186417002 ] 
dist 230=[-1.1177387570290530882 ,.9124351151277771815 ] 
dist 231=[-1.1802453434410153079 ,.94385139445053337784] 
dist 232=[-1.2503929706884712345 ,.98158651165494018601] 
dist 233=[-1.3131868055801440987 ,1.0167092352898115162 ] 
dist 234=[-1.3463572678914746888 ,1.0377045333367482866 ] 
dist 235=[-1.3641262931320229448 ,1.0523351991720300674 ] 
dist 236=[-1.3669237629428489559 ,1.0620685139620688198 ] 
dist 237=[-1.3600233612742372033 ,1.0678920658751476486 ] 
dist 238=[-1.3532060452057638937 ,1.0669264019508941144 ] 
dist 239=[-1.3382239710528336674 ,1.0615006347427069725 ] 
dist 240=[-1.3305820535790511148 ,1.0573224067606617183 ] 
dist 241=[-1.2113871137212888078 ,1.0293403084649110968 ] 
dist 242=[-1.4021128253952828642 ,1.0476855616696963074 ] 
dist 243=[-1.5513838359662300027 ,1.2164763634022182174 ] 
dist 244=[-1.6827127530690036313 ,1.3710927998425351671 ] 
dist 245=[-1.7921609243276166928 ,1.5044160024288562512 ] 
dist 246=[-1.8541439010961297066 ,1.5882626389615278812 ] 
dist 247=[-1.8931115664232807845 ,1.6517683431574213992 ] 
dist 248=[-1.9107452735098677744 ,1.7039460656116524564 ] 
dist 249=[-1.9177656878379963260 ,1.7453038348099686455 ] 
dist 250=[-1.9143943975028690755 ,1.7656463543571681904 ] 
dist 251=[-1.9034469041099105767 ,1.7744518315645710251 ] 
dist 252=[-1.8959239491045469867 ,1.7720464414498941986 ] 
dist 253=[-1.8447640059692085958 ,1.7568332775031786025 ] 
dist 254=[-1.8301005582997822110 ,1.7492972386132623418 ] 
dist 255=[-1.7773469358617555474 ,1.7100774903246944217 ] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 2, 2, 2, 0, 2] 
dist 0=[49.586789768344367332  ,49.586789768344367332  ] 
dist 1=[48.360072964679528603  ,50.227530495273329551  ] 
dist 2=[47.034393739004054626  ,50.589697293640322962  ] 
dist 3=[45.998531613836699369  ,50.704145847478310716  ] 
dist 4=[44.975275818761707966  ,50.727146060951180215  ] 
dist 5=[43.699931329680528729  ,50.707542975328735324  ] 
dist 6=[42.358156101749203433  ,50.677069924197267700  ] 
dist 7=[41.069664015271561436  ,50.630321620090762779  ] 
dist 8=[39.571703157066492175  ,50.530145117270263467  ] 
dist 9=[37.393585717451688262  ,46.914155113670909620  ] 
dist 10=[35.161639972440436781  ,46.369997462394884602  ] 
dist 11=[33.448736506476552985  ,45.386820437575235536  ] 
dist 12=[31.785667404693450314  ,45.123948861167978288  ] 
dist 13=[29.752625296996656182  ,44.198282440911455780  ] 
dist 14=[27.565925887199545286  ,43.927010155840583242  ] 
dist 15=[25.426663559334103133  ,43.564367472846960540  ] 
dist 16=[22.924845123785972596  ,43.415262345385644583  ] 
dist 17=[19.261494375298188737  ,30.618610291489780537  ] 
dist 18=[15.609606704020851674  ,24.435018611223325616  ] 
dist 19=[13.153507068669245013  ,20.943089601695865516  ] 
dist 20=[11.093686357442264587  ,20.441397594452345337  ] 
dist 21=[9.0250685726257246521 ,15.628902846035146526  ] 
dist 22=[7.0995496395005122488 ,14.767817646094008529  ] 
dist 23=[4.3464528518218013150 ,13.719305004570995721  ] 
dist 24=[1.4617020085140482623 ,13.539133257188129688  ] 
dist 25=[-.53613607640598385882,10.135610140248728981  ] 
dist 26=[-2.2736340904471148718 ,6.2664058506955416009 ] 
dist 27=[-4.1192274823029211454 ,4.6512139136121631474 ] 
dist 28=[-5.9033632343542207321 ,4.3072813665022363780 ] 
dist 29=[-7.3961119248489824951 ,2.7828513115232447743 ] 
dist 30=[-8.9702240090889173111 ,2.5162226808278712523 ] 
dist 31=[-11.080804617525586538  ,2.1102269527587410795 ] 
dist 32=[-13.098870872351655707  ,2.0328482594143459548 ] 
dist 33=[-14.303651970076949429  ,-1.0842220465505268004 ] 
dist 34=[-15.153153003493225973  ,-1.2680323714517686601 ] 
dist 35=[-15.751258304057588775  ,-1.2846792284456914537 ] 
dist 36=[-16.195097803623804830  ,-1.2583371127488360694 ] 
dist 37=[-16.427676680425169655  ,-1.1716860620081829593 ] 
dist 38=[-16.553444788825644083  ,-1.0570064715524770256 ] 
dist 39=[-16.569311700056097288  ,-.91835731060322226497] 
dist 40=[-14.909942396563804266  ,-.737650480306907251  ] 
dist 41=[-14.646700069025955562  ,-.45480274305275915549] 
dist 42=[-14.212500081893166020  ,-.16019259833077467336] 
dist 43=[-14.080825044132120446  ,.06770341829397438072] 
dist 44=[-13.685730507936468785  ,.28952439624816797109] 
dist 45=[-13.544087508397748925  ,.56030374464739535814] 
dist 46=[-13.435755479745625958  ,.84175975108123771554] 
dist 47=[-13.364866054432691635  ,1.1064546445242470812 ] 
dist 48=[-7.4291485028965588379 ,1.4100879566539172136 ] 
dist 49=[-5.4592194413371450289 ,2.1093373665325197747 ] 
dist 50=[-.0786312091755967571 ,3.7019386119632910332 ] 
dist 51=[.2884854426926990620 ,4.7886755904136069526 ] 
dist 52=[2.4443728820378159704 ,5.7122465514387572435 ] 
dist 53=[2.7372024443512826679 ,6.6537562811982802397 ] 
dist 54=[2.9460358527697428751 ,7.5340136026250392213 ] 
dist 55=[2.9675332358427132020 ,8.2131617741367635991 ] 
dist 56=[2.9403280737191463520 ,9.3206036947660101534 ] 
dist 57=[2.8405906107864274719 ,10.119347735967285695  ] 
dist 58=[2.7149201826221426952 ,10.724023075436341424  ] 
dist 59=[2.5841695577620090512 ,11.222040640150373869  ] 
dist 60=[2.4252537099594994096 ,11.613394941644848586  ] 
dist 61=[2.1870434374910226057 ,11.792323679080622843  ] 
dist 62=[1.9166374151912869652 ,11.870691611511098513  ] 
dist 63=[1.2339833457043319379 ,11.863553983485533389  ] 
dist 64=[-.18458639963084771326,5.5441636180722216522 ] 
dist 65=[-1.1233570920783575648 ,2.9136623773433698117 ] 
dist 66=[-1.8887733280747429828 ,2.6683819112336208930 ] 
dist 67=[-2.6158429330895224115 ,2.0796061414993880178 ] 
dist 68=[-3.2612115279708540351 ,1.9814345013417384313 ] 
dist 69=[-3.7007414922560006588 ,1.1441121053810996400 ] 
dist 70=[-4.0731019676078948031 ,.99000944635144713065] 
dist 71=[-4.4505795312869250291 ,.76788452158686148926] 
dist 72=[-4.7884868933631090644 ,.70511670264317291918] 
dist 73=[-5.0029907903865065930 ,-.4269320556782383893 ] 
dist 74=[-5.1680704003572093666 ,-.5675815127645131983 ] 
dist 75=[-5.3087448582353471967 ,-.78392243892670614398] 
dist 76=[-5.4228864978797273162 ,-.79024316131064476436] 
dist 77=[-5.4820832240138602600 ,-.74962183169823753739] 
dist 78=[-5.5123455962361127722 ,-.68289521807688290982] 
dist 79=[-5.5110201022016470847 ,-.58395535295360344604] 
dist 80=[-3.5941633513824261833 ,-.44269277837983588458] 
dist 81=[-2.4050416823888507690 ,-.20708867815723953836] 
dist 82=[-1.3545802004889620256 ,.03404991267086907850] 
dist 83=[-1.2533457334272582889 ,.19740720622450226911] 
dist 84=[-.7289977982211232740 ,.33482930244870700874] 
dist 85=[-.4224794882288266876 ,.4725120118442868032 ] 
dist 86=[-.3673036930955048961 ,.68487974718581397958] 
dist 87=[-.2737511166604382916 ,1.1655086970565240751 ] 
dist 88=[-.2523864159748444085 ,1.6234893162178215847 ] 
dist 89=[.0840771292958809184 ,1.9151702126188201360 ] 
dist 90=[.1287743698218457444 ,2.1402025610618373061 ] 
dist 91=[.2121739081207158939 ,2.3323453289102245620 ] 
dist 92=[.2302918857946395623 ,2.4880893250351525991 ] 
dist 93=[.2740930422138148122 ,2.5679382504920075060 ] 
dist 94=[.27294195357240536656,2.6108997912242616910 ] 
dist 95=[.25421126623293200986,2.6195184246594559175 ] 
dist 96=[.20693815913501930607,1.5859674230780112755 ] 
dist 97=[.03399577007363701322,1.3924395669665461252 ] 
dist 98=[-.1722567528853900942 ,1.2977057702024299138 ] 
dist 99=[-.31069957616869215   ,1.2706454809815684236 ] 
dist 100=[-.4257837042857001642 ,1.1613122638325156534 ] 
dist 101=[-.53883282918076315651,1.1365531838946051224 ] 
dist 102=[-.64169020387907325561,1.0807801463410322760 ] 
dist 103=[-.7161036682955044431 ,1.0628623562141756875 ] 
dist 104=[-.78378139400447493606,.98379586300441263522] 
dist 105=[-.85974910619924536241,.96263906785456425379] 
dist 106=[-.92899773015112651797,.948990061020512807  ] 
dist 107=[-.9698679913610619717 ,.94795349369842238368] 
dist 108=[-.99766048271867099867,.95409872182329403939] 
dist 109=[-1.2067621950101309833 ,.97055166189459036799] 
dist 110=[-1.4702729117790521672 ,.99757860411095870122] 
dist 111=[-1.8414933955294155473 ,1.0458652947444076839 ] 
dist 112=[-2.2037960867124286137 ,1.0959752478387353781 ] 
dist 113=[-2.4317376510730518067 ,1.1302694135391233166 ] 
dist 114=[-2.6046406795730057842 ,1.1593305661264362134 ] 
dist 115=[-2.7473596373817454139 ,1.1885871969826374835 ] 
dist 116=[-2.8596000477819201236 ,1.2154961241056059974 ] 
dist 117=[-2.9109093432782821254 ,1.2351994002438301184 ] 
dist 118=[-2.9342813404834434712 ,1.2532568284140282461 ] 
dist 119=[-2.9350329283229680728 ,1.2736002430957163780 ] 
dist 120=[-2.8600326391898487759 ,1.2916270220373189060 ] 
dist 121=[-2.8364319437360862714 ,1.3004492471298978174 ] 
dist 122=[-2.7803747295091906927 ,1.3041237063379440946 ] 
dist 123=[-2.7569473553992108276 ,1.3016335367841907666 ] 
dist 124=[-2.6289413893275374800 ,1.2953125299235559041 ] 
dist 125=[-2.5969052719264877552 ,1.2888608398476961017 ] 
dist 126=[-2.5091920192173788050 ,1.2701640275213434462 ] 
dist 127=[-2.4803626932552289946 ,1.2604856158071703554 ] 
dist 128=[-1.1842798191208697087 ,1.1793983462520497282 ] 
dist 129=[-1.0317812562713786397 ,1.5939022363910472561 ] 
dist 130=[-1.0054826125291098166 ,1.9267041316379516231 ] 
dist 131=[-.9491093939899629273 ,2.2341647814974040955 ] 
dist 132=[-.93165654965636984538,2.5137708360101114084 ] 
dist 133=[-.85363328106885379114,2.7061325753942440768 ] 
dist 134=[-.83718968423878573136,2.8606868191523600537 ] 
dist 135=[-.78882837730948000326,3.0036812830242707029 ] 
dist 136=[-.78134918296581738527,3.1256142842280285649 ] 
dist 137=[-.67136206990192726728,3.1961486323712292476 ] 
dist 138=[-.65082717826188546809,3.2424334466351811308 ] 
dist 139=[-.60779012683230508341,3.2676243622086226845 ] 
dist 140=[-.59491215460830622082,3.2772934182195000437 ] 
dist 141=[-.53957941869091948988,3.2716604588375682603 ] 
dist 142=[-.52770574816819786174,3.2379477125169301367 ] 
dist 143=[-.49524624441947277625,3.2154221635310039179 ] 
dist 144=[-.48856136112433804117,1.8319404277996951932 ] 
dist 145=[-.54738490925175002394,1.3016942292617899238 ] 
dist 146=[-.80232211576986578059,.93225645495174258506] 
dist 147=[-1.0088661618270152102 ,.86309547529899125252] 
dist 148=[-1.2027704189105243270 ,.37999097590179985533] 
dist 149=[-1.4012725298963510984 ,.29324377094842210395] 
dist 150=[-1.6335142216308580115 ,.13793643544189376186] 
dist 151=[-1.9109959183169883968 ,.10370404251388894251] 
dist 152=[-2.1684823719585672981 ,-.39553393402391805671] 
dist 153=[-2.3209597824116766019 ,-.46415081400576829885] 
dist 154=[-2.4254299220728506474 ,-.58068804239604551767] 
dist 155=[-2.4914068304746624964 ,-.59950863399352414459] 
dist 156=[-2.5370968703791840991 ,-.5934750763244399632 ] 
dist 157=[-2.5606391110479076960 ,-.54953768566409817494] 
dist 158=[-2.5724235239617472373 ,-.4695184479633917586 ] 
dist 159=[-2.5712096251642343888 ,-.31955038560949840896] 
dist 160=[-1.9558134593822668834 ,-.16053575677789769947] 
dist 161=[-1.0004589179548194043 ,.08043960426466631212] 
dist 162=[-.91183218553186336318,.30368882708963001254] 
dist 163=[-.70234759578485912806,.5295356179818691797 ] 
dist 164=[-.66461381622054097088,.73922911726673093275] 
dist 165=[-.37662393366949693609,.89804182537199654373] 
dist 166=[-.32395615422091754216,1.0496911029664607731 ] 
dist 167=[-.26788256083069550162,1.2308101747268226326 ] 
dist 168=[-.32318499757646305879,1.3988353782530011957 ] 
dist 169=[-.3772414160544060809 ,1.4982521104567182956 ] 
dist 170=[-.44063454945522178001,1.5662637496596294694 ] 
dist 171=[-.53318014515097015051,1.6090103035164336325 ] 
dist 172=[-.63715545877282092534,1.6386353553939722590 ] 
dist 173=[-.74614153022506514263,1.6543025704622365943 ] 
dist 174=[-.8794517550423948421 ,1.6627167657222274548 ] 
dist 175=[-1.0804564806516176987 ,1.7175134112720659992 ] 
dist 176=[-1.2794837628713774147 ,1.9146251612598586415 ] 
dist 177=[-1.4049050876140055911 ,2.0298688845527747221 ] 
dist 178=[-1.5001740753620292487 ,2.1070232717439620404 ] 
dist 179=[-1.5789207294858725850 ,2.1521843389812401496 ] 
dist 180=[-1.6408205697075099249 ,2.1813766564447901599 ] 
dist 181=[-1.6688854041126358796 ,2.1948249566514972714 ] 
dist 182=[-1.6813270154708691512 ,2.1992991179636042398 ] 
dist 183=[-1.6809070947034756767 ,2.1928116424790961376 ] 
dist 184=[-1.6377510341114407558 ,1.8756751483261065735 ] 
dist 185=[-1.6240871400367371544 ,1.8264578720380887834 ] 
dist 186=[-1.5906415919487089706 ,1.7373888710008575881 ] 
dist 187=[-1.5765204880951056299 ,1.7130319624647833592 ] 
dist 188=[-1.4989216541274048329 ,1.6251254118845677626 ] 
dist 189=[-1.4793855875887675549 ,1.5991486422693610403 ] 
dist 190=[-1.4288700020716507560 ,1.5610830772977014971 ] 
dist 191=[-1.4097885374007609636 ,1.5466993393745875726 ] 
dist 192=[-1.1226221510861546088 ,.92798668802495853481] 
dist 193=[-1.3099874428494789090 ,1.0303323796315686014 ] 
dist 194=[-1.4241548722185911423 ,1.0926333737041900185 ] 
dist 195=[-1.5063710989878574723 ,1.1373922845261431292 ] 
dist 196=[-1.5662747398435219861 ,1.1697633925022703842 ] 
dist 197=[-1.6110248057467843518 ,1.1922224052624967927 ] 
dist 198=[-1.6327881420169265704 ,1.1974427051890170185 ] 
dist 199=[-1.6418472856123251233 ,1.1963803654629672385 ] 
dist 200=[-1.6407800791895706268 ,1.1937798837862425301 ] 
dist 201=[-1.4785428468829281712 ,1.1146889392630088302 ] 
dist 202=[-1.4504144332405827979 ,1.0986195528133462282 ] 
dist 203=[-1.4012483595387161538 ,1.0591336338884995303 ] 
dist 204=[-1.3867594103213842540 ,1.0446313912885800439 ] 
dist 205=[-1.0642876169918365453 ,.97106397482312717557] 
dist 206=[-1.0031077536110973444 ,.95366036690180261769] 
dist 207=[-.79752442974508040597,.91471086868409015698] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 1, 0, 0, 2] 
dist 0=[60.199731136350949314  ,60.199731136350949314  ] 
dist 1=[58.886386707832279656  ,60.933597429452576292  ] 
dist 2=[57.240283556125691533  ,61.384081601803126295  ] 
dist 3=[55.177925185878126084  ,61.566072976607796594  ] 
dist 4=[52.413365109502870627  ,61.610519719435233304  ] 
dist 5=[47.963799672447432835  ,61.527060139209646177  ] 
dist 6=[43.411050268159831161  ,61.322027261084030586  ] 
dist 7=[40.234428789472577848  ,61.186932436026249905  ] 
dist 8=[37.453824219226904398  ,60.360305507383233855  ] 
dist 9=[34.481795207802452271  ,60.057086123561732116  ] 
dist 10=[31.608825712658140519  ,59.764877811995429608  ] 
dist 11=[29.223367568324955192  ,59.567421450190787190  ] 
dist 12=[26.733623018509891080  ,59.230701805679130393  ] 
dist 13=[23.443630879202197086  ,59.031282197081015269  ] 
dist 14=[20.205847517292502809  ,58.761615724236487933  ] 
dist 15=[17.924190550094078496  ,57.296277905382952979  ] 
dist 16=[15.899716057676070215  ,35.813780555315316635  ] 
dist 17=[13.688333823987584625  ,33.906609409312722236  ] 
dist 18=[11.516050670823479054  ,29.332660422166171798  ] 
dist 19=[9.6470037020397370721 ,28.673672162579823076  ] 
dist 20=[7.6332376922285328025 ,22.241388802475133158  ] 
dist 21=[4.8175302472353019872 ,21.080611243738009492  ] 
dist 22=[2.1958621505370629177 ,19.680913897095324284  ] 
dist 23=[.3662649051462471720 ,19.434528726244532112  ] 
dist 24=[-1.7261983574723303296 ,10.415225068927843385  ] 
dist 25=[-3.7002783364374241406 ,9.3459328788825133481 ] 
dist 26=[-5.2724534305568634245 ,7.0947207334022444511 ] 
dist 27=[-6.8605779905703987970 ,6.6093333836981917755 ] 
dist 28=[-8.9000906535831716204 ,4.4732038112372655180 ] 
dist 29=[-10.836104275750546478  ,4.0973617183561179811 ] 
dist 30=[-12.011044510557903738  ,3.5164277969070743296 ] 
dist 31=[-12.863590907176425405  ,3.3946577160245004468 ] 
dist 32=[-13.510797720733748558  ,-3.3920390366597870333 ] 
dist 33=[-14.002545030194340249  ,-3.9097780684035699133 ] 
dist 34=[-14.233392983550240966  ,-3.4140128233349907819 ] 
dist 35=[-14.332103292128468567  ,-2.8057389223094473359 ] 
dist 36=[-14.333134845720873813  ,-2.0019578472466181810 ] 
dist 37=[-13.498285401933759480  ,-.7259917767111046395 ] 
dist 38=[-13.333858107347110871  ,.5616616645633053525 ] 
dist 39=[-13.014268409403139982  ,1.4122852035417824713 ] 
dist 40=[-12.910136254840954036  ,2.1029269071784926776 ] 
dist 41=[-12.444878154351738397  ,2.7527514502195105040 ] 
dist 42=[-12.322944414406630503  ,3.3244045973142813517 ] 
dist 43=[-12.005945232321001852  ,3.7033811881254664705 ] 
dist 44=[-11.887443621760708740  ,4.0129176819012770131 ] 
dist 45=[-10.553078172268145554  ,4.3077230127738296651 ] 
dist 46=[-10.558639417576603086  ,4.5634908880492265870 ] 
dist 47=[-10.546775142878935342  ,4.7173592734329143863 ] 
dist 48=[-1.9399568027161744088 ,4.8259594466275595790 ] 
dist 49=[-1.5924214894957736021 ,5.8663508640932679472 ] 
dist 50=[-1.0848981997712943465 ,6.8114995940372398999 ] 
dist 51=[-.9859037304683248917 ,7.6926088394891424296 ] 
dist 52=[-.7749091475211908269 ,8.7171347216333171777 ] 
dist 53=[-.7177362966602675093 ,9.6578903961629846706 ] 
dist 54=[.5195782645162899620 ,10.204737366415953730  ] 
dist 55=[-.1177669139845010758 ,10.568398611702642501  ] 
dist 56=[-.6536044560620508321 ,10.778060182633386672  ] 
dist 57=[-1.1883258977197707145 ,10.910751374361043228  ] 
dist 58=[-1.6792043166685516788 ,10.967128925109723902  ] 
dist 59=[-2.0402605007533417997 ,10.978766640901764364  ] 
dist 60=[-2.3742413686139739261 ,10.947983288200221805  ] 
dist 61=[-2.7572136547259580640 ,8.4780354649980199882 ] 
dist 62=[-3.1092137144603438155 ,8.3634292718330854887 ] 
dist 63=[-3.3196907118333318436 ,8.2998426931180839268 ] 
dist 64=[-3.6809911395339168363 ,4.9259347896129317350 ] 
dist 65=[-4.5282998781518313834 ,4.5848072319244514294 ] 
dist 66=[-5.1132974565046239467 ,3.7715055286289453195 ] 
dist 67=[-5.6171791243919431921 ,3.6211276511893262758 ] 
dist 68=[-6.1409823633025851955 ,2.4672909141982967553 ] 
dist 69=[-6.6104474573591125838 ,2.2512069425191337765 ] 
dist 70=[-6.8975762056575299285 ,1.9023056390165506010 ] 
dist 71=[-7.1057983506119253900 ,1.8136746442830482112 ] 
dist 72=[-7.2604460426844481602 ,.59546981836600282536] 
dist 73=[-7.3686599603738908077 ,.95250866058834003867] 
dist 74=[-7.3916256669333296359 ,1.2797307323527482436 ] 
dist 75=[-7.3747016321657670953 ,1.5193278578077332582 ] 
dist 76=[-7.3429785504040185184 ,1.7397269674851341364 ] 
dist 77=[-6.5464124808453447426 ,1.9903688741945795749 ] 
dist 78=[-6.5234716199316958427 ,2.2209273543358582042 ] 
dist 79=[-6.4948449564163059713 ,2.3612447306879546246 ] 
dist 80=[-2.3530249105268777204 ,2.4617665826603115167 ] 
dist 81=[-1.2498789610822117146 ,2.5336713979056051319 ] 
dist 82=[-1.0490023602913962630 ,2.5823551562854527889 ] 
dist 83=[-.74181587411863283872,2.5927032973241127808 ] 
dist 84=[-.66169435882480820279,2.7926570304000764342 ] 
dist 85=[.27506562843838035467,3.3582836897170496721 ] 
dist 86=[.48887252805733335351,3.7048521069974890712 ] 
dist 87=[.20066673414897133863,3.9564881206042045739 ] 
dist 88=[-.05424689697312604416,4.1434884509754089622 ] 
dist 89=[-.32938882115533073409,4.2852293269762576820 ] 
dist 90=[-.59557157582303933054,4.3563396952964570279 ] 
dist 91=[-.81476498616326452678,4.3891592886460790470 ] 
dist 92=[-1.0409538231523229304 ,4.3875964557748331438 ] 
dist 93=[-1.3350547308429453950 ,4.1994074377471320996 ] 
dist 94=[-1.6199099782838689442 ,4.1944670147266415967 ] 
dist 95=[-1.8092320279763655260 ,4.1870112970413591665 ] 
dist 96=[-1.9643994885513336793 ,2.4770551349126691010 ] 
dist 97=[-2.1130402610531605873 ,2.3168435453971596374 ] 
dist 98=[-2.2457562377906076240 ,1.9800929447640366313 ] 
dist 99=[-2.3374199013446846526 ,2.1142475830873032801 ] 
dist 100=[-2.4164383037597967075 ,2.2639087019996101232 ] 
dist 101=[-2.4987435758801739286 ,2.4733407092066483570 ] 
dist 102=[-2.5671584689634959225 ,2.6737374072210579459 ] 
dist 103=[-2.7810896141107695798 ,2.7873498027154265295 ] 
dist 104=[-2.9751240711723598504 ,2.8588114214188389584 ] 
dist 105=[-3.1197772284034316294 ,2.8910807922533848179 ] 
dist 106=[-3.2307506323158651845 ,2.9051922093079369084 ] 
dist 107=[-3.2904266092115436382 ,2.9042342669388445081 ] 
dist 108=[-3.3684256824062347038 ,2.8920120208154673316 ] 
dist 109=[-3.9962147777124060404 ,2.9886486459670785594 ] 
dist 110=[-4.3835852798939997720 ,3.1309823044990563874 ] 
dist 111=[-4.6684487038658824457 ,3.2316443177862981428 ] 
dist 112=[-4.8873017619078461403 ,3.3012422137133150335 ] 
dist 113=[-5.0543871397272468350 ,3.3454455721378658373 ] 
dist 114=[-5.1327205057582352429 ,3.3539355929920389656 ] 
dist 115=[-5.1638911029816238536 ,3.3320796811735858488 ] 
dist 116=[-5.1629745714155800985 ,3.3279247830921430888 ] 
dist 117=[-4.7856677019602425286 ,3.1122700161513027344 ] 
dist 118=[-4.7124595314830786008 ,3.0684437924917686598 ] 
dist 119=[-4.5787897576793512260 ,2.9476558068901454943 ] 
dist 120=[-4.5366268579151819373 ,2.9120951029173101611 ] 
dist 121=[-4.3560474164673310891 ,2.6591845277211279972 ] 
dist 122=[-4.3045428823057038000 ,2.6005742156423124216 ] 
dist 123=[-4.1806388059633463751 ,2.5013463042301333365 ] 
dist 124=[-4.1335639523504896516 ,2.4718361497544105789 ] 
dist 125=[-2.4586048397103585257 ,2.2258159090046930618 ] 
dist 126=[-2.5325223205812350408 ,2.4076833915996280447 ] 
dist 127=[-2.6301565303015337481 ,2.5204775203982547049 ] 
dist 128=[-2.7207183673932942896 ,3.0281321933159790190 ] 
dist 129=[-2.7664206172585579982 ,3.4158996946734663580 ] 
dist 130=[-2.7877999338504553905 ,3.7106228172339438428 ] 
dist 131=[-2.7877964082431989277 ,3.9546355491190992424 ] 
dist 132=[-2.7615463780829554363 ,4.1477495313697658292 ] 
dist 133=[-2.7470573364355676538 ,4.2394291009771557586 ] 
dist 134=[-2.6966841532627686553 ,4.2847160769188804306 ] 
dist 135=[-2.6730273748605603164 ,4.2927624386866181623 ] 
dist 136=[-2.3602275722158009766 ,4.1526987897334377342 ] 
dist 137=[-2.3065617296958306089 ,4.1123126908648391147 ] 
dist 138=[-2.1656793639013594313 ,4.0398193242240243622 ] 
dist 139=[-2.1328103027274890966 ,4.0128329101375535764 ] 
dist 140=[-1.8734919832562719847 ,3.8802727365518513258 ] 
dist 141=[-1.8175882859879753945 ,3.8420033937767733512 ] 
dist 142=[-1.7305296433420384281 ,3.7288295101189992570 ] 
dist 143=[-1.7038173308026762485 ,3.6908521152558701184 ] 
dist 144=[-1.1432994234427074200 ,-.19223338450936023959] 
dist 145=[-1.2257627893138354085 ,-.37645012859247729994] 
dist 146=[-1.2921740309394925170 ,-.75947974487723731799] 
dist 147=[-1.3254424450446098916 ,-.78726896431445582704] 
dist 148=[-1.4314035828188401572 ,-.83680598993467838435] 
dist 149=[-1.6214475811129729328 ,-.84520357611304952541] 
dist 150=[-1.7906665335335621764 ,-.95137510609429928781] 
dist 151=[-1.9752415985706777210 ,-.88135649218799024516] 
dist 152=[-2.1423873104846004870 ,-.80915526240809055178] 
dist 153=[-2.2420804580634950737 ,-.71534479685089801704] 
dist 154=[-2.3112665291484688234 ,-.61509367893677063838] 
dist 155=[-2.3567150083013435985 ,-.51719532140081064072] 
dist 156=[-2.3843648788608090428 ,-.40248436933382223732] 
dist 157=[-2.3885038098741892729 ,-.23516186437028429436] 
dist 158=[-2.3721817585214406499 ,-.06444967114055884720] 
dist 159=[-2.3656955733131399379 ,.06378657508701897374] 
dist 160=[-1.4461071665961443850 ,.20696290990586137503] 
dist 161=[-1.3568286662769220025 ,.43715665026478823089] 
dist 162=[-1.3582689327345679593 ,.68156145458625914009] 
dist 163=[-1.3863954354357851246 ,.9180802091624222047 ] 
dist 164=[-1.4165814341703457652 ,1.1936699739272025772 ] 
dist 165=[-1.4573572465119282100 ,1.5939399145089800975 ] 
dist 166=[-1.4957223940010496974 ,1.9877103862744601751 ] 
dist 167=[-1.5162910683790050582 ,2.2373741356268965814 ] 
dist 168=[-1.5276946616614532733 ,2.4288269741972637725 ] 
dist 169=[-1.5295038470917288279 ,2.5903843285899156366 ] 
dist 170=[-1.5249747992412807923 ,2.7200049939992709628 ] 
dist 171=[-1.5194916871277276742 ,2.7840578310326725719 ] 
dist 172=[-1.4957021898467433612 ,2.8162946790668059365 ] 
dist 173=[-1.4851339070059087814 ,2.8192429906549083738 ] 
dist 174=[-1.3985166022440977360 ,2.7710046708670823252 ] 
dist 175=[-1.3791037535613625301 ,2.7508371757518390289 ] 
dist 176=[-1.3247182396253626003 ,2.7099091076336351910 ] 
dist 177=[-1.3095696473749183503 ,2.6922688902419648636 ] 
dist 178=[-1.1940344218829867794 ,2.5943339899266177339 ] 
dist 179=[-1.1674503972854534061 ,2.5695191377502286264 ] 
dist 180=[-1.1249832617166908532 ,2.4801531747093410782 ] 
dist 181=[-1.1115880637370996372 ,2.4664126804759352816 ] 
dist 182=[-1.0031535374907817447 ,1.1717643453841563400 ] 
dist 183=[-1.2788927486368973800 ,1.2699585278529400530 ] 
dist 184=[-1.5520532073800882598 ,1.3680354136480475367 ] 
dist 185=[-1.8740377817432182036 ,1.4383800142045507168 ] 
dist 186=[-2.1568961945738013118 ,1.5017461775178447724 ] 
dist 187=[-2.3441402537307735537 ,1.5719813891840788926 ] 
dist 188=[-2.4968368023141936283 ,1.6410785333188814445 ] 
dist 189=[-2.6418791203609810228 ,1.6999017143485191130 ] 
dist 190=[-2.7677088342044667290 ,1.7623355014079475482 ] 
dist 191=[-2.8437642530186354050 ,1.8458305195825873319 ] 
dist 192=[-2.8977735273873558335 ,1.9241970912697648416 ] 
dist 193=[-2.9356612136892869232 ,1.9661722430462042832 ] 
dist 194=[-2.9602013435090629529 ,1.9894266098387207524 ] 
dist 195=[-2.9609676307253960843 ,1.9931170859105041364 ] 
dist 196=[-2.9484610600488152823 ,1.9863322383557867593 ] 
dist 197=[-2.9362709309345361115 ,1.9788482463123999139 ] 
dist 198=[-.89090702496212837805,1.9474316045153615128 ] 
dist 199=[-.77542573000994536744,1.9333114538040347490 ] 
dist 200=[-.79224713414156585231,1.7299904584581653122 ] 
dist 201=[-.80695443204326779728,1.6944508176197862177 ] 
dist 202=[-.81740401240515171627,1.6003280995759593232 ] 
dist 203=[-.82475683416859385073,1.5778696617704821820 ] 
dist 204=[-.82954815597820736607,1.4378801308132097216 ] 
dist 205=[-.82977850594767834952,1.6409217449068803983 ] 
dist 206=[-.82671564118833797711,1.8284236178057918188 ] 
dist 207=[-.82374800393444324264,1.9378160634522876057 ] 
dist 208=[.34851423022042991551,2.0107277228629795917 ] 
dist 209=[.3379413043361945935 ,2.0527041596561055333 ] 
dist 210=[.30793827611466730233,2.0794543936438696322 ] 
dist 211=[.25139895270409703719,2.0916271560356837415 ] 
dist 212=[.16471083771440669087,2.0954298609342470068 ] 
dist 213=[.01444211529038642272,2.0889246684062492662 ] 
dist 214=[-.14181003330753773018,1.4643151955827237981 ] 
dist 215=[-.38416193674809987925,1.4671680012838406863 ] 
dist 216=[-.58906616585102233574,1.4431704229522042742 ] 
dist 217=[-.7958589659893617536 ,1.4326103623627293495 ] 
dist 218=[-.9875339206084239848 ,1.4142906582305313066 ] 
dist 219=[-1.1321322931723519173 ,1.4063900883511804264 ] 
dist 220=[-1.2696506204181715756 ,1.3651629238360781882 ] 
dist 221=[-1.4330832174131066795 ,1.3530394140359735616 ] 
dist 222=[-1.5842661246353889833 ,1.3140601889784382192 ] 
dist 223=[-1.6729197154341118102 ,1.3028445817966699502 ] 
dist 224=[-1.7325729303744516675 ,.40039129411586931858] 
dist 225=[-1.7680712690665801899 ,.31664390211585210165] 
dist 226=[-1.7904215750758111945 ,.1386097444069552271 ] 
dist 227=[-1.7976259582492684490 ,.09465759358957063456] 
dist 228=[-1.7951015535735169482 ,.14511191079149548405] 
dist 229=[-1.7903535689865365182 ,.34615496444245266509] 
dist 230=[-1.5595814629757445904 ,.54655641680337882509] 
dist 231=[-1.5257980521769688937 ,.67524330347029957291] 
dist 232=[-1.4304847258555455311 ,.77578322650608328766] 
dist 233=[-1.4142464340006697422 ,.86390433892871620928] 
dist 234=[-1.2234646936124709081 ,.93707938087522660909] 
dist 235=[-1.1830456663421807365 ,.97799804691136280622] 
dist 236=[-1.1394386018248727740 ,1.0030388125634701715 ] 
dist 237=[-1.0739086077234250366 ,1.0128749469069342583 ] 
dist 238=[-.66250664955702987575,1.0170293163124111063 ] 
dist 239=[-.60585230031830715933,1.0194053211505942341 ] 
dist 240=[-.53873418547120102329,1.0209247438091524818 ] 
dist 241=[-.51955432976914950316,1.0216635826464924548 ] 
dist 242=[-.44046776966730871449,1.0218402720048447709 ] 
dist 243=[-.42472655295784661631,1.0211181308987173708 ] 
dist 244=[-.38469582855310175877,1.0196012083533400187 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 2, 1, 0, 1] 
dist 0=[66.797171915154925924  ,66.797171915154925924  ] 
dist 1=[66.182236341529109885  ,67.139586184846929898  ] 
dist 2=[65.033328444409144657  ,67.200300766024977990  ] 
dist 3=[63.672978294770499612  ,67.096278013317882179  ] 
dist 4=[62.213795549501146946  ,66.991103057259181338  ] 
dist 5=[60.400404760286367905  ,66.451115006549391570  ] 
dist 6=[57.625837235151035761  ,66.289139629757346342  ] 
dist 7=[54.440560062482918826  ,64.399400813649159773  ] 
dist 8=[50.987323248487001039  ,62.890023984867275419  ] 
dist 9=[46.671103461539782288  ,62.087547140973077632  ] 
dist 10=[40.040133010015254345  ,61.773764365665842156  ] 
dist 11=[33.354131326482297872  ,61.183067221428381482  ] 
dist 12=[28.818209399281940542  ,60.988624594266857003  ] 
dist 13=[24.982286905438404998  ,59.351868723993380271  ] 
dist 14=[21.091293829122625838  ,56.191967748505907733  ] 
dist 15=[17.456373281891482057  ,38.312750883250205140  ] 
dist 16=[14.642923209816858497  ,38.092498437017954690  ] 
dist 17=[11.888617255943480591  ,27.970809787129814861  ] 
dist 18=[8.4898812860238273651 ,26.715306428607203312  ] 
dist 19=[5.2625368540152380220 ,24.183348463750257623  ] 
dist 20=[3.1925254443560592891 ,23.538134765347978228  ] 
dist 21=[1.5711969484738541349 ,21.280200939335767079  ] 
dist 22=[.02888660912569419832,20.801727376487016111  ] 
dist 23=[-1.3662397975445615456 ,20.195176464776993717  ] 
dist 24=[-2.3295209073441478241 ,20.051900088566926545  ] 
dist 25=[-3.1696830659823342677 ,3.9500664604583528031 ] 
dist 26=[-4.0749252902728773408 ,2.6377179142129911241 ] 
dist 27=[-4.8873817612345884448 ,-.21602014405893431779] 
dist 28=[-5.7000673986872058877 ,-.74272419497555504962] 
dist 29=[-6.6422469175070022929 ,-3.0393860608258973473 ] 
dist 30=[-7.6806786828751567787 ,-3.3283500562933004680 ] 
dist 31=[-8.7696663359209174442 ,-5.3160145713840986589 ] 
dist 32=[-10.450441065306762255  ,-5.5053456893710448237 ] 
dist 33=[-12.024304730879730121  ,-5.6238900523698387084 ] 
dist 34=[-13.008302202300703020  ,-5.2698399878505007731 ] 
dist 35=[-13.752663622877495319  ,-4.8721567853550940753 ] 
dist 36=[-14.369070071738549657  ,-4.5265773084096098549 ] 
dist 37=[-14.859201906041788200  ,-4.1559321165890022835 ] 
dist 38=[-15.099050988799416192  ,-3.6573860123299269917 ] 
dist 39=[-15.205255916858513462  ,-3.1169056576323624482 ] 
dist 40=[-15.215101631074714694  ,-1.7869134086407269941 ] 
dist 41=[-9.0897955831808890195 ,.08926744942482147028] 
dist 42=[-9.0056520943093265181 ,1.3313175278236810598 ] 
dist 43=[-8.4394202113348511168 ,2.3444608939677302233 ] 
dist 44=[-8.3115133779495080701 ,3.3076328386773762060 ] 
dist 45=[-8.0804920740397346809 ,4.2137558378269483237 ] 
dist 46=[-8.0151402397934302121 ,4.8770448759676137815 ] 
dist 47=[-4.8794118705057596633 ,5.4586537289925372445 ] 
dist 48=[-4.5411793649378855671 ,6.0804239647682420246 ] 
dist 49=[-3.7653775849825478982 ,6.6414556562709934677 ] 
dist 50=[-3.6058528395174140439 ,6.9807589537085996074 ] 
dist 51=[-2.5869045393359210462 ,7.2227641452499380178 ] 
dist 52=[-2.3966700405707091210 ,7.3955057028476782671 ] 
dist 53=[-2.0423881853257458457 ,7.5108622061856386855 ] 
dist 54=[-1.9558555287029332933 ,7.7118833093047432486 ] 
dist 55=[-.72060048978556138249,8.1027747378458208882 ] 
dist 56=[-.54779541636009365046,8.3153994512206118197 ] 
dist 57=[-.17071637923138990261,8.4391262167506227714 ] 
dist 58=[-.08301735527469301117,8.4750185439827577280 ] 
dist 59=[-.09407517252357541818,8.4658891413395389911 ] 
dist 60=[-.54823388413322127558,8.4395170353079514001 ] 
dist 61=[-1.1959339599486790190 ,8.3392880771382508253 ] 
dist 62=[-1.6857054801817754880 ,8.2816481408849246875 ] 
dist 63=[-2.1523248969709647417 ,1.3576158998999958976 ] 
dist 64=[-2.7077408079251488775 ,1.2720171260346600996 ] 
dist 65=[-3.2257340828662808011 ,-.32735795636131661426] 
dist 66=[-3.5431165820013451727 ,-.52311033960126879336] 
dist 67=[-3.7736462227005207309 ,-.9721131875122731937 ] 
dist 68=[-4.0320824265550286816 ,-1.0370863695655477780 ] 
dist 69=[-4.4830000020365930458 ,-1.3504424286473415019 ] 
dist 70=[-4.9608781473664356554 ,-1.0588341003511918377 ] 
dist 71=[-5.3928071171368978227 ,-.65628891698291329742] 
dist 72=[-5.6604296649167580944 ,0                     ] 
dist 73=[-5.8586596395960936517 ,-.97915846630454532081] 
dist 74=[-6.0137175887056588016 ,-.53486049397612381339] 
dist 75=[-6.1289832058531530611 ,-.08281088232401225927] 
dist 76=[-6.1684458004211547007 ,.22595162885633874421] 
dist 77=[-6.1674031307611337825 ,.48788836127269368569] 
dist 78=[-6.1504289146762755530 ,.75319963481527639236] 
dist 79=[-3.0953151982241018615 ,.9992945892562232225 ] 
dist 80=[-2.8285073105986446317 ,1.1845911030458248639 ] 
dist 81=[-2.1810845056671939654 ,1.3601871429774164634 ] 
dist 82=[-2.0787237021787064398 ,1.5675777058839020349 ] 
dist 83=[-1.1433931211780847179 ,1.7586037996584630093 ] 
dist 84=[-.97216102805234621858,1.8689452024445287322 ] 
dist 85=[-.74093029395894999629,1.9409074274441942589 ] 
dist 86=[-.67601657526854380699,1.9789168467787663432 ] 
dist 87=[-.13362678941548114786,2.1570916771492820102 ] 
dist 88=[-.17697583331016262979,2.4446745347445889896 ] 
dist 89=[-.24508891190414541009,2.6621134966507939196 ] 
dist 90=[-.36404070393847058626,2.8399411745360744483 ] 
dist 91=[-.48558925408255047382,2.9801400440917785475 ] 
dist 92=[-.56405364973027624281,3.0474869770901881424 ] 
dist 93=[-.62536615170506617722,3.0799546906046315892 ] 
dist 94=[-.7934584487640024475 ,3.0810424620598598261 ] 
dist 95=[-.99879977178580640367,1.8225078381255304608 ] 
dist 96=[-1.1602703004582273898 ,1.8115102617916144254 ] 
dist 97=[-1.3201529548943753235 ,1.8400499401350224158 ] 
dist 98=[-1.5191925756675147211 ,1.8772319654251607441 ] 
dist 99=[-1.7079822131607691118 ,1.9172785500354650238 ] 
dist 100=[-1.8269974298664523937 ,1.9572208229858778670 ] 
dist 101=[-1.9175113740068608626 ,2.0047806358347623639 ] 
dist 102=[-1.9926352638216123196 ,2.0751948259918278126 ] 
dist 103=[-2.0521046974427379342 ,2.1476605225803148287 ] 
dist 104=[-2.0801984880234836864 ,2.2033862394366356325 ] 
dist 105=[-2.0908160901334362455 ,2.2574489461401681930 ] 
dist 106=[-2.0895552071545440949 ,2.3232478777790622243 ] 
dist 107=[-2.0612988020106465956 ,2.3913522133804130732 ] 
dist 108=[-2.0488370215658407208 ,2.4545870372547235842 ] 
dist 109=[-2.1500089207310338876 ,2.5261543739123186057 ] 
dist 110=[-2.8422461130758109870 ,2.6274588988395404862 ] 
dist 111=[-3.5220202618042374464 ,2.7244938557506096822 ] 
dist 112=[-3.9504826539915655205 ,2.7790227388664392302 ] 
dist 113=[-4.2762511489168267547 ,2.8126091273981846972 ] 
dist 114=[-4.5463377639144640591 ,2.8261215750090349530 ] 
dist 115=[-4.7597345034336859757 ,2.8255043015806337774 ] 
dist 116=[-4.8593381795821513101 ,2.8190421862319495423 ] 
dist 117=[-4.9083195236297415020 ,2.7768067636784867603 ] 
dist 118=[-4.9197551488140535742 ,2.7636540187944722811 ] 
dist 119=[-4.7757142330719615433 ,2.5831602931215599829 ] 
dist 120=[-4.7324627940970020464 ,2.5466839438919611339 ] 
dist 121=[-4.6515827680279573312 ,2.4335284579820450282 ] 
dist 122=[-4.6205287174255793727 ,2.4133919257988165547 ] 
dist 123=[-4.4626837140948556111 ,2.1513054601124147438 ] 
dist 124=[-4.4195880282114251536 ,2.0930422949376279119 ] 
dist 125=[-4.2826412633158659492 ,2.0347437659338832470 ] 
dist 126=[-4.2470198157707916984 ,2.0125132686128592842 ] 
dist 127=[-1.0493298015522838205 ,1.7800075609880699981 ] 
dist 128=[-1.2295216406740011305 ,2.2020156858469377793 ] 
dist 129=[-1.3961690967383147057 ,2.5368495430121498229 ] 
dist 130=[-1.5874202391635170306 ,2.9464463963620494295 ] 
dist 131=[-1.7630076073971423708 ,3.4391115078607297873 ] 
dist 132=[-1.8671738239607601645 ,3.7731470772498915230 ] 
dist 133=[-1.9387604578855699451 ,4.0543522659054697408 ] 
dist 134=[-1.9843850938789260625 ,4.3362693298688417112 ] 
dist 135=[-2.0142512850144623732 ,4.5850124073574142876 ] 
dist 136=[-2.0229797930236335996 ,4.7338791249450699787 ] 
dist 137=[-2.0197666100412690903 ,4.8378377930860201069 ] 
dist 138=[-2.0136827499576906520 ,4.9074284386055139614 ] 
dist 139=[-1.4576472709866535810 ,4.9494640441499803148 ] 
dist 140=[-1.3980562332688864149 ,4.9503095285710607825 ] 
dist 141=[-1.2411639783962232544 ,4.9195046022888190099 ] 
dist 142=[-1.2186254445321813934 ,4.8904470893383115463 ] 
dist 143=[-.94765520506317160632,2.4284120609919167751 ] 
dist 144=[-.89439020438276420212,2.2052804605057007773 ] 
dist 145=[-1.1166709865654083176 ,1.6731091873082595914 ] 
dist 146=[-1.5416226861043778296 ,1.5827554692329184462 ] 
dist 147=[-1.9344653768039850844 ,1.0157801886994636290 ] 
dist 148=[-2.2291204371415261842 ,1.0928281970424359852 ] 
dist 149=[-2.5077109016597701915 ,1.1501107964002142357 ] 
dist 150=[-2.8364691816540911845 ,1.1952058946116453768 ] 
dist 151=[-3.1394111183631344162 ,1.2288805588750746066 ] 
dist 152=[-3.3150161339822662584 ,1.2406054482766005578 ] 
dist 153=[-3.4306333067226942715 ,1.2437377305792851819 ] 
dist 154=[-3.4942745545523458014 ,1.2431452793714951433 ] 
dist 155=[-3.5330434442855330914 ,.84226112261532606849] 
dist 156=[-3.5494420935867790188 ,.9168014114891430985 ] 
dist 157=[-3.5525631138453410165 ,1.0181810337615111626 ] 
dist 158=[-3.5407896803376264240 ,1.1290594560125067362 ] 
dist 159=[-1.2136019436371737913 ,1.2373349738343131296 ] 
dist 160=[-1.1756395372613571576 ,1.3283282412116393559 ] 
dist 161=[-1.1817620839920819146 ,1.4239348135224311033 ] 
dist 162=[-1.2058183040715336581 ,1.5506116278593270328 ] 
dist 163=[-1.2395275784148041494 ,1.8669071655523915620 ] 
dist 164=[-1.2841550957933826320 ,2.1179433950929876273 ] 
dist 165=[-1.3452535258797075209 ,2.3558298930484924570 ] 
dist 166=[-1.4446657089280283675 ,2.6373385968612083075 ] 
dist 167=[-1.5504464142198018597 ,2.8971693454719602941 ] 
dist 168=[-1.6369479755192130600 ,3.0485803363934114209 ] 
dist 169=[-1.7257301893461345994 ,3.1492861895642885984 ] 
dist 170=[-1.8406053014365271642 ,3.2068474434512616429 ] 
dist 171=[-2.1207656970424970752 ,3.2415217736556334690 ] 
dist 172=[-2.4246338300455389133 ,3.2509263161923675817 ] 
dist 173=[-2.6571799207119097547 ,3.2436044953101750166 ] 
dist 174=[-2.8525707032427209718 ,3.2344280931572079172 ] 
dist 175=[-3.0092363172547577599 ,3.4933481733074254568 ] 
dist 176=[-3.0872995237516270885 ,3.8414203030017748306 ] 
dist 177=[-3.1281447907620627750 ,4.0994641597941344416 ] 
dist 178=[-3.1363395973309681476 ,4.3014418337120756480 ] 
dist 179=[-3.0587952874602062499 ,4.4569481941606294698 ] 
dist 180=[-3.0324813337011626634 ,4.5296047640047918673 ] 
dist 181=[-2.9970978455451537437 ,4.5600834126568483947 ] 
dist 182=[-2.9784884453115040791 ,4.5589122782279257304 ] 
dist 183=[-2.9115338631766230148 ,4.2688851387512090083 ] 
dist 184=[-2.8866133885045742399 ,4.2091251506525071390 ] 
dist 185=[-2.8260035584479287360 ,4.1000715346792780339 ] 
dist 186=[-2.8006629625230496040 ,4.0646518356231513780 ] 
dist 187=[-2.7570246210686861219 ,3.9084643334445286548 ] 
dist 188=[-2.7719942253202652653 ,3.8640637728870462116 ] 
dist 189=[-2.7771656349433802410 ,3.7512190582196377595 ] 
dist 190=[-2.7702981399913552307 ,3.7071960664119374729 ] 
dist 191=[-.06242993059602970045,1.8300640112802333952 ] 
dist 192=[-.1480336451156491801 ,2.0505438896621906508 ] 
dist 193=[-.22430145967083258041,2.2423807099712148824 ] 
dist 194=[-.30758146616735404778,2.4447735443505528292 ] 
dist 195=[-.3888140602754390488 ,2.6268543387193357668 ] 
dist 196=[-.45691347204696434674,2.7376633113970851107 ] 
dist 197=[-.52831256150645109331,2.8172783953583416340 ] 
dist 198=[-.62270766066376505792,2.8749207028521478138 ] 
dist 199=[-.7149651214748842081 ,2.9138986087567650874 ] 
dist 200=[-.77783605908334510894,2.9194068198600260703 ] 
dist 201=[-.83110617789475502336,2.9107988858542349614 ] 
dist 202=[-.88506260755369553224,2.8962490873785939604 ] 
dist 203=[-.93520658498811957594,1.5574237917872979683 ] 
dist 204=[-.97326708185506721129,1.4359143352423415333 ] 
dist 205=[-1.0096915533187475396 ,1.1374914661394822379 ] 
dist 206=[-1.0533076389155304077 ,1.0918196191972993032 ] 
dist 207=[-1.2210329646206593480 ,.67998187948024885054] 
dist 208=[-1.3599282431274157972 ,.79431146261004370025] 
dist 209=[-1.4898115308417437535 ,.88229375723035891481] 
dist 210=[-1.6409901407976534966 ,.95708175395423134897] 
dist 211=[-1.7791871121979988158 ,1.0177081466067063067 ] 
dist 212=[-1.8572851656773535073 ,1.0491974195331134703 ] 
dist 213=[-1.9061553561557061865 ,1.0663680783023662623 ] 
dist 214=[-1.9277598853576976167 ,1.0698754255861594299 ] 
dist 215=[-1.9372840058910171362 ,1.0505276789405301599 ] 
dist 216=[-1.9379653411480723408 ,1.0434080105186914681 ] 
dist 217=[-1.9322957527651638998 ,1.0362126719293605435 ] 
dist 218=[-1.9246805714526460517 ,1.0299246028855722900 ] 
dist 219=[-1.0373169958227345418 ,1.0173652339510596046 ] 
dist 220=[-1.0730583488682382287 ,1.0097537652045523990 ] 
dist 221=[-1.1184035560153568557 ,1.0495974562022205102 ] 
dist 222=[-1.1717600603419885666 ,1.2714703714079103288 ] 
dist 223=[-1.2260692927538883686 ,1.4761081789842775820 ] 
dist 224=[-1.2752137508577853986 ,1.6288090956191564771 ] 
dist 225=[-1.3298985595409942025 ,1.7724161418975699826 ] 
dist 226=[-1.4063079791572180052 ,1.9407780476246531053 ] 
dist 227=[-1.4828839407320840516 ,2.0953556271824147910 ] 
dist 228=[-1.5382320999771273140 ,2.1839753849961107516 ] 
dist 229=[-1.5885254895753547933 ,2.2410844836219759907 ] 
dist 230=[-1.6449353423933026744 ,2.2699617527438803670 ] 
dist 231=[-1.7008228981423390767 ,2.2840742280585884580 ] 
dist 232=[-1.7490313276432038474 ,2.2822833591728516961 ] 
dist 233=[-1.8007487460651214755 ,2.2709463524219417037 ] 
dist 234=[-1.8706318203149433666 ,2.2614264636532903801 ] 
dist 235=[-1.9365921187490760557 ,2.3914115046843490084 ] 
dist 236=[-1.9726606254641354063 ,2.6897044756608026197 ] 
dist 237=[-1.9936623198744534592 ,2.9173529991327408906 ] 
dist 238=[-1.9995201172385657690 ,3.1075038086222582060 ] 
dist 239=[-1.9951731103700418920 ,3.2585741604297060572 ] 
dist 240=[-2.0306016767095380467 ,3.3303227926561880776 ] 
dist 241=[-2.1242464371730269127 ,3.3662007968813512298 ] 
dist 242=[-2.2014008777448287092 ,3.3741734352031465448 ] 
dist 243=[-2.2642555260458025656 ,3.2882658112689087491 ] 
dist 244=[-2.3075748026214709561 ,3.2601595858712815699 ] 
dist 245=[-2.3388325235414356455 ,3.2083793184532654207 ] 
dist 246=[-2.3449170114057686790 ,3.1879961420051561809 ] 
dist 247=[-2.2433327094846149972 ,3.0829612918163121982 ] 
dist 248=[-2.2184995871766006628 ,3.0538063142267855029 ] 
dist 249=[-2.1062380494670355686 ,2.9602621288102463128 ] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 0, 0, 1] 
dist 0=[58.681021601970640995  ,58.681021601970640995  ] 
dist 1=[57.560798796873487385  ,59.536045182768927445  ] 
dist 2=[56.012621271493845040  ,60.025311801711613081  ] 
dist 3=[53.851753472624026883  ,60.341086236662482190  ] 
dist 4=[50.285298649284382533  ,60.503196406632270944  ] 
dist 5=[46.600935000362992491  ,60.533971192238769570  ] 
dist 6=[43.969278645261255521  ,60.490209617120063278  ] 
dist 7=[41.600812672481617143  ,60.086289557977639236  ] 
dist 8=[38.967186055269063774  ,59.069296433347666613  ] 
dist 9=[36.359370193328162380  ,58.199589845580612787  ] 
dist 10=[34.093817808216819553  ,57.771012415256320379  ] 
dist 11=[31.640862087143935279  ,57.147483658439453642  ] 
dist 12=[28.284478809608026386  ,56.912651354003126596  ] 
dist 13=[24.929855632859832755  ,56.274110384780617665  ] 
dist 14=[22.483730372085012248  ,56.013692804476499154  ] 
dist 15=[20.229240527426462915  ,54.829753238044995794  ] 
dist 16=[17.639490711091517468  ,52.486781044443709962  ] 
dist 17=[15.024006557012370623  ,33.240628871357810597  ] 
dist 18=[12.294229310363984928  ,31.371898539396312008  ] 
dist 19=[9.5215968757580785130 ,26.918587257542454515  ] 
dist 20=[5.9827853115072324576 ,26.267365259611438503  ] 
dist 21=[2.5566863506821978406 ,20.097683907391471462  ] 
dist 22=[.2336608712222548131 ,18.990229825239611085  ] 
dist 23=[-1.7333647766548231964 ,17.611988464499334567  ] 
dist 24=[-3.7385290105832804385 ,17.344548022577679173  ] 
dist 25=[-5.6257538447589011895 ,9.0219405299510714961 ] 
dist 26=[-7.1226484544815836819 ,8.0338565860864244955 ] 
dist 27=[-8.6298419424290322667 ,5.9269261062957384528 ] 
dist 28=[-10.559999726903667124  ,5.5045568368937352232 ] 
dist 29=[-12.382303018518639880  ,3.4127882626196398088 ] 
dist 30=[-13.458940337325590402  ,3.0624175131771007134 ] 
dist 31=[-14.206017325841532167  ,2.4345081110725243407 ] 
dist 32=[-14.710892399681816860  ,2.3175703688562174395 ] 
dist 33=[-15.075254687988190556  ,-2.9939130770737796213 ] 
dist 34=[-15.260225575088108197  ,-3.4509433749210439852 ] 
dist 35=[-15.352947554872841383  ,-2.4898623189471807921 ] 
dist 36=[-15.347355757022168170  ,-.4431215561551639306 ] 
dist 37=[-13.674475892871344290  ,1.6261524583948397600 ] 
dist 38=[-13.412456758995911189  ,3.0057532007630000353 ] 
dist 39=[-12.945707980022810875  ,4.1398241846767472603 ] 
dist 40=[-12.818447791339395629  ,5.2301279527635106190 ] 
dist 41=[-12.371002002388544875  ,6.2047782862403736386 ] 
dist 42=[-12.229921951938616107  ,6.8776946586619462521 ] 
dist 43=[-12.068440845988860933  ,7.4564616816552528314 ] 
dist 44=[-11.987596874395845496  ,8.0556711531204138077 ] 
dist 45=[-9.6924779633397310765 ,8.5880534150118387432 ] 
dist 46=[-9.6872008943734101044 ,8.9002832735566245390 ] 
dist 47=[-9.6194327260182949113 ,9.1100320369503090896 ] 
dist 48=[-9.5851997534098105022 ,9.2336125439350940180 ] 
dist 49=[-1.0517917549874321707 ,9.2914418027762742752 ] 
dist 50=[-.9070588107295148726 ,9.2924370942442051589 ] 
dist 51=[-.67949647779062137329,9.1671655138670647790 ] 
dist 52=[-.62275513029740948142,9.1489399141099103040 ] 
dist 53=[.3204633023348786304 ,9.1361292531003821760 ] 
dist 54=[.43885943489139078147,9.8514183341055453618 ] 
dist 55=[.70013522089813309381,10.387001032064526902  ] 
dist 56=[.74324663317942682591,10.817707079612669602  ] 
dist 57=[1.0275210278842237376 ,11.148356231908931580  ] 
dist 58=[1.0716606232787023177 ,11.284581853891754167  ] 
dist 59=[1.1550260344338796050 ,11.335628824383569671  ] 
dist 60=[.63175779181938098805,11.326251666973118839  ] 
dist 61=[-.73322714773813411432,6.2370755895406339685 ] 
dist 62=[-1.7546204109089643390 ,6.2494153278360452279 ] 
dist 63=[-2.6645741217759313967 ,6.2527566837076847936 ] 
dist 64=[-3.5486854665169173860 ,6.2449200309123886794 ] 
dist 65=[-4.3467535902416813045 ,1.7950497904599684832 ] 
dist 66=[-4.9134893048289299483 ,1.5689208210249207292 ] 
dist 67=[-5.4184807689880534979 ,1.5513769084252699632 ] 
dist 68=[-5.9702841186045116489 ,1.5467299568517904097 ] 
dist 69=[-6.4678713835639846159 ,.91737508011761075402] 
dist 70=[-6.7565858064510515562 ,.85666867708764392383] 
dist 71=[-6.9473266165299930092 ,.70925019300606036528] 
dist 72=[-7.0540386756819354928 ,.68451925338469128809] 
dist 73=[-7.1109807877949990514 ,.4684260326110527869 ] 
dist 74=[-7.1084736613340359872 ,.42803967226994785011] 
dist 75=[-7.0672406575918443340 ,.37116299045132701595] 
dist 76=[-7.0282660651604550004 ,.35435371462704306776] 
dist 77=[-4.5695209908267102975 ,.03966727394118761471] 
dist 78=[-4.5185277229692711396 ,.4519638615555834011 ] 
dist 79=[-4.5712714047846494694 ,1.1415757291566087751 ] 
dist 80=[-4.5786965051794534749 ,1.8193289328337394816 ] 
dist 81=[-2.6125821823385111452 ,2.4356292449588178628 ] 
dist 82=[-2.4273688655102260757 ,2.8801454272470940769 ] 
dist 83=[-2.1735331577889159808 ,3.2829445192188514871 ] 
dist 84=[-2.0939928861673247964 ,3.7328737565336166929 ] 
dist 85=[-.5350503657988671379 ,4.1448788774042397398 ] 
dist 86=[-.41124395042812725404,4.3964182650318899997 ] 
dist 87=[-.44009651766531964926,4.5780812809004226099 ] 
dist 88=[-.47492027059686920071,4.7113693671009814257 ] 
dist 89=[-.51088289060777328366,4.8031099741095562212 ] 
dist 90=[-.5442712306039754014 ,4.8238342282595446246 ] 
dist 91=[-.58212293856385303337,4.8106801781897314186 ] 
dist 92=[-.63588348866351034941,4.8053735905672114800 ] 
dist 93=[-.69014638876917176726,2.1050043481581472572 ] 
dist 94=[-.72999734833649845295,2.1106232339763642747 ] 
dist 95=[-.7668413895724716212 ,2.0990751681953827132 ] 
dist 96=[-.80910241968833580654,2.0922889742474905847 ] 
dist 97=[-.85148215659752025435,1.2296842168839525389 ] 
dist 98=[-.88879376793383032479,1.1449210031259485506 ] 
dist 99=[-1.1176692788818610967 ,.93918404023577903885] 
dist 100=[-1.4596544614733907659 ,.90218764804651354735] 
dist 101=[-1.7801544351650584578 ,1.0448090305109418984 ] 
dist 102=[-1.9806747197658941957 ,1.1729146918480680844 ] 
dist 103=[-2.1312486483756819407 ,1.2688061909341729512 ] 
dist 104=[-2.2525237746912219390 ,1.3456007286741046237 ] 
dist 105=[-2.3458541260908067100 ,1.4061382743968087171 ] 
dist 106=[-2.3849767063343922949 ,1.4371716051704454206 ] 
dist 107=[-2.4012407680310419352 ,1.4524953425274000781 ] 
dist 108=[-2.4033807038167702626 ,1.4547163758553514027 ] 
dist 109=[-1.7868387245443596084 ,1.3664743370643051267 ] 
dist 110=[-1.7240713137709045854 ,1.3481638216906476620 ] 
dist 111=[-1.5681487951355664282 ,1.3222270719849444256 ] 
dist 112=[-1.5342362802800824275 ,1.3114536130853862308 ] 
dist 113=[-1.2845204908095844384 ,1.2802209254213121459 ] 
dist 114=[-1.2341525816482131342 ,1.2676263920150986217 ] 
dist 115=[-1.1485890396742698842 ,1.2476783215325246063 ] 
dist 116=[-1.1262712127556807226 ,1.2394680250289772562 ] 
dist 117=[-.6901268896543587854 ,.51133066186595589454] 
dist 118=[-.6322671700595223108 ,.67639524374925954522] 
dist 119=[-.50740322919262523616,.81883694325318733357] 
dist 120=[-.6118856355889228515 ,.96719507483783014893] 
dist 121=[-.7509995539605028335 ,1.1076590911632842698 ] 
dist 122=[-.8473915762420566768 ,1.2186395627845639024 ] 
dist 123=[-.9307740491184059002 ,1.3291351504431791300 ] 
dist 124=[-1.0179902208792516569 ,1.4677092440234988645 ] 
dist 125=[-1.0966587861859948645 ,1.5987790787676880182 ] 
dist 126=[-1.1459429660421060888 ,1.7781051010714986925 ] 
dist 127=[-1.1830535486186645415 ,1.9402623801117707016 ] 
dist 128=[-1.2131587263250376403 ,2.1009405098258910368 ] 
dist 129=[-1.2363945559157885543 ,2.2481257768640784340 ] 
dist 130=[-1.2461019052269008311 ,2.3564469143588198935 ] 
dist 131=[-1.2477448027560011108 ,2.4569072235254920234 ] 
dist 132=[-1.2455573696458333227 ,2.5727265289549758040 ] 
dist 133=[-.60244151484567720278,2.6781562589667649849 ] 
dist 134=[-.54780268881826909276,2.7371621108520019043 ] 
dist 135=[-.41370923062691586338,2.7733782673983207215 ] 
dist 136=[-.39414858167960724161,2.7878783105074254759 ] 
dist 137=[-.19626924394672987043,2.7872681167790299193 ] 
dist 138=[-.54450872691118496713,2.7816346305365814121 ] 
dist 139=[-1.0283687827433158521 ,2.7369813289058236892 ] 
dist 140=[-1.7474290625390782928 ,2.7278510816711951656 ] 
dist 141=[-2.4607360686417278067 ,2.5354639677625823512 ] 
dist 142=[-2.9216501212323237113 ,2.4943335132953089917 ] 
dist 143=[-3.2850943058761578311 ,2.4023358477709541106 ] 
dist 144=[-3.6095796407437559584 ,2.3706051492633068668 ] 
dist 145=[-3.8834725938152260319 ,2.2162845895390855263 ] 
dist 146=[-4.0450981912069139273 ,2.1810378377519192740 ] 
dist 147=[-4.1551652209393812694 ,2.0840060432856397769 ] 
dist 148=[-4.2233890382313888309 ,2.0589578709578855106 ] 
dist 149=[-4.2665998670734988204 ,1.7510587785541947692 ] 
dist 150=[-4.2768857693076781447 ,1.6985645093440461952 ] 
dist 151=[-4.2650424798418046888 ,1.5696509683950332151 ] 
dist 152=[-4.2526967657735058539 ,1.5378492691487122797 ] 
dist 153=[-4.1590170819306983081 ,1.3297071336543688077 ] 
dist 154=[-4.1298429244517647046 ,1.2861980379260185555 ] 
dist 155=[-4.0180153505758918283 ,1.2065958932386075820 ] 
dist 156=[-3.9944724047704583776 ,1.1853498485143804141 ] 
dist 157=[-1.0224404933469951710 ,1.2106256865827097637 ] 
dist 158=[-1.0533295715141561420 ,1.6602535331905768974 ] 
dist 159=[-1.0707201693570360158 ,2.0233543352045851250 ] 
dist 160=[-1.0741838064055456829 ,2.4608562301691972570 ] 
dist 161=[-1.0719505267521307106 ,2.8955110646992544817 ] 
dist 162=[-1.0669076721102998666 ,3.1927619498705854272 ] 
dist 163=[-1.0579959808293058212 ,3.4457013100230761508 ] 
dist 164=[-1.0531928312730844149 ,3.7035991067446315126 ] 
dist 165=[-1.0032603452496524544 ,3.9322801505041375120 ] 
dist 166=[-1.1375823822406084399 ,4.0686724524444441669 ] 
dist 167=[-1.2417120721413125874 ,4.1633222889009319890 ] 
dist 168=[-1.3315724005527028279 ,4.2254868086186153036 ] 
dist 169=[-1.4051728541021051453 ,4.2618736547940306538 ] 
dist 170=[-1.4444403169826634211 ,4.2635808775972393827 ] 
dist 171=[-1.4660049332822211784 ,4.2312848868022691499 ] 
dist 172=[-1.4697777158682824268 ,4.2109175561215723451 ] 
dist 173=[-1.4640818642275979540 ,2.1580874084979052947 ] 
dist 174=[-1.4571337662699320910 ,1.9694864802084429097 ] 
dist 175=[-1.4409474805919292353 ,1.5195875312644677374 ] 
dist 176=[-1.4324450760105180023 ,1.4418439675364391326 ] 
dist 177=[-1.5654177318908817920 ,1.2873495878334183378 ] 
dist 178=[-1.8284050592481207851 ,1.2826045928373143278 ] 
dist 179=[-2.0756613518058724976 ,1.2575171944212846226 ] 
dist 180=[-2.3653690894516529964 ,1.2520200134137644852 ] 
dist 181=[-2.6317827598872760942 ,.46717805086472571455] 
dist 182=[-2.7861198530171569783 ,.70007521256251644907] 
dist 183=[-2.8875882923634342085 ,.8952873852691090438 ] 
dist 184=[-2.9431128761425814247 ,1.0895696479752271818 ] 
dist 185=[-2.9773258242956676460 ,1.2679168263900865998 ] 
dist 186=[-2.9937827194637551355 ,1.3995602896870822750 ] 
dist 187=[-3.0003457652199163605 ,1.5219397813284224303 ] 
dist 188=[-2.9950898709483140572 ,1.6633289500261304568 ] 
dist 189=[-.94075859572206530128,1.7920155816337819027 ] 
dist 190=[-.9402288535554326025 ,1.8637219364317836921 ] 
dist 191=[-.95027192886255450394,1.9072682328652475151 ] 
dist 192=[-.97738695482556247395,1.9236204228804584099 ] 
dist 193=[-1.0133646625271969593 ,1.9285814198236590222 ] 
dist 194=[-1.0587583975833614376 ,1.9266897464487306348 ] 
dist 195=[-1.1196681521336408336 ,1.9194171542812176927 ] 
dist 196=[-1.2175377244268688642 ,1.9111779869329596734 ] 
dist 197=[-1.3212054727108270629 ,2.1088943405286806903 ] 
dist 198=[-1.4052421093974406363 ,2.2525393705539661315 ] 
dist 199=[-1.4908288909032589943 ,2.3554971153291321690 ] 
dist 200=[-1.6006756853168675808 ,2.4295520821184656446 ] 
dist 201=[-1.7174310603903137391 ,2.4821107856987303000 ] 
dist 202=[-1.8305731513833815342 ,2.4993172645240831332 ] 
dist 203=[-1.9624966746915765981 ,2.5007037561291533752 ] 
dist 204=[-2.1541667670522631547 ,2.5407898818166081244 ] 
dist 205=[-2.3409838834910275755 ,3.0170360338703454901 ] 
dist 206=[-2.4535475891334775578 ,3.3114179417615242209 ] 
dist 207=[-2.5330308061245099412 ,3.5284111446246183519 ] 
dist 208=[-2.5878904505848382827 ,3.6959406570849824392 ] 
dist 209=[-2.6227675533143494072 ,3.8241837361314366242 ] 
dist 210=[-2.6295145868828768906 ,3.8844551397410412792 ] 
dist 211=[-2.6127691898771770856 ,3.9087696857703190598 ] 
dist 212=[-2.6095731124936233440 ,3.9081979671886083158 ] 
dist 213=[-2.4423459807514798870 ,3.6276693820378113246 ] 
dist 214=[-2.4084621802676629107 ,3.5726164031963117433 ] 
dist 215=[-2.3145436580283534079 ,3.4729231393165402680 ] 
dist 216=[-2.2874808549764517607 ,3.4414228705346852536 ] 
dist 217=[-2.0901400934075415083 ,3.3066385875298278186 ] 
dist 218=[-2.0445846354644215216 ,3.2676767442518897357 ] 
dist 219=[-1.9875096154603593180 ,3.1744607833847614330 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 1, 2, 1, 0, 1] 
dist 0=[58.643121348683048108  ,58.643121348683048108  ] 
dist 1=[57.234101697386500743  ,59.346172326361022248  ] 
dist 2=[55.483985549288959437  ,59.726745964730649280  ] 
dist 3=[53.419069282289036542  ,59.848212522764811255  ] 
dist 4=[50.725215978994675622  ,59.844131396022142164  ] 
dist 5=[46.463869235958852471  ,59.563377331680960500  ] 
dist 6=[42.121409125873567947  ,59.403956046387646387  ] 
dist 7=[39.103566863078076418  ,59.213555131970462956  ] 
dist 8=[36.473640514798105104  ,59.073879831600583587  ] 
dist 9=[33.679702248314584172  ,58.608265914942184592  ] 
dist 10=[30.988013917122271979  ,58.416288475115319676  ] 
dist 11=[28.766020336616254384  ,57.923383890991854895  ] 
dist 12=[26.457535414489835143  ,57.706888214306790058  ] 
dist 13=[23.419870691547102284  ,56.554714232125966341  ] 
dist 14=[20.434466376449401962  ,56.181141717165782862  ] 
dist 15=[18.334315461593463436  ,53.880777574657067425  ] 
dist 16=[16.473905763246896455  ,33.321302870481188285  ] 
dist 17=[14.445388261870888704  ,27.822426814793897509  ] 
dist 18=[12.453913956037883222  ,26.515689162117096136  ] 
dist 19=[10.740788501877394652  ,25.280152603926374193  ] 
dist 20=[8.8946178095962122235 ,25.050627814322835070  ] 
dist 21=[6.3704203090119217630 ,16.141853286615604805  ] 
dist 22=[3.9058730417017084676 ,15.061082149818381595  ] 
dist 23=[2.2978356917106588545 ,13.428962251941701068  ] 
dist 24=[.99945995159465595181,12.260683517889113449  ] 
dist 25=[-.2272833061208223266 ,10.239606133062709711  ] 
dist 26=[-1.5549312121790711159 ,9.8432078174390684954 ] 
dist 27=[-3.4977998633200082681 ,9.2676074173515773652 ] 
dist 28=[-5.3156703014397376459 ,9.1244442656692559402 ] 
dist 29=[-6.7399733130652219403 ,1.8928474659393366041 ] 
dist 30=[-8.1578543351227308857 ,-1.7271953783583542930 ] 
dist 31=[-9.9517352733371953651 ,-2.8490277750682545618 ] 
dist 32=[-11.643493031320963517  ,-3.4883152359184834730 ] 
dist 33=[-12.653648090269875017  ,-3.4107743408870199946 ] 
dist 34=[-13.367683594151401061  ,-3.2449192416504602429 ] 
dist 35=[-13.875536027164816518  ,-2.9683085688177786407 ] 
dist 36=[-14.249012972967984581  ,-2.5603660603362592426 ] 
dist 37=[-14.425537389966050630  ,-1.8703460646700815482 ] 
dist 38=[-14.495011784534623045  ,-1.1618598005945753203 ] 
dist 39=[-14.489144697037621419  ,-.6800286393580879308 ] 
dist 40=[-13.302695082254650937  ,-.2740135914728760018 ] 
dist 41=[-13.099787327169119505  ,.1324365238730901344 ] 
dist 42=[-13.111354497347814261  ,.50653149996015334488] 
dist 43=[-13.147514626809316257  ,.78368532101160917703] 
dist 44=[-13.137600867998198391  ,1.0423810643784493354 ] 
dist 45=[-12.019952909723080855  ,1.6747523631345825084 ] 
dist 46=[-11.755411432475819085  ,3.0218880918031181901 ] 
dist 47=[-11.665104626390725221  ,4.1174002945980143486 ] 
dist 48=[-3.7864942890913635346 ,5.1550164883620843329 ] 
dist 49=[-3.0983120755926109181 ,6.0754781246709528956 ] 
dist 50=[-1.5479787200062398898 ,6.7035580814813473192 ] 
dist 51=[-1.2589906764684659995 ,7.2377174685434355391 ] 
dist 52=[-.9239600048806022441 ,7.7835006404341343034 ] 
dist 53=[-.89746464398596237712,8.2650820755690137178 ] 
dist 54=[1.5375169085679619159 ,8.5430636122444088788 ] 
dist 55=[1.4162620886783369483 ,8.7255004185624316935 ] 
dist 56=[1.2978141344904966248 ,8.8257585932660392149 ] 
dist 57=[1.1587565876337084614 ,9.1946478963485162073 ] 
dist 58=[1.0182674261769713894 ,9.5949715016760839270 ] 
dist 59=[.8939960396961015104 ,9.8690872143046879541 ] 
dist 60=[.7584085493651444661 ,10.062909682672488216  ] 
dist 61=[.5726732274485731189 ,10.142665682744239812  ] 
dist 62=[-.0197940810017463144 ,10.155280150387242612  ] 
dist 63=[-.8768302161023066706 ,10.142112962991411576  ] 
dist 64=[-1.7277231766819696337 ,3.6167705320793138981 ] 
dist 65=[-2.5075299752709439562 ,2.3379522501812250004 ] 
dist 66=[-3.0810513029797529532 ,2.0992724294696192150 ] 
dist 67=[-3.6123107269142524197 ,1.7633472742321254259 ] 
dist 68=[-4.2236039177203448962 ,1.6641608005391772050 ] 
dist 69=[-4.7873942583109632759 ,.1701838729091192096 ] 
dist 70=[-5.1291716481976340900 ,.00567764198859997394] 
dist 71=[-5.3733435923638252157 ,-.01296163618462576147] 
dist 72=[-5.5477381360567657894 ,-.04753705364296547369] 
dist 73=[-5.6707497244287787574 ,-.05510561673925619548] 
dist 74=[-5.7099327627837405313 ,-.07483046393692376598] 
dist 75=[-5.7118752237795427536 ,-.07684386177825571350] 
dist 76=[-5.7158316741333743135 ,-.07333513027352761359] 
dist 77=[-5.7875473017753345614 ,-.06173538835716488217] 
dist 78=[-5.8262014354004116070 ,-.04765412021081818749] 
dist 79=[-5.8298014120262310708 ,-.03421315811867209744] 
dist 80=[-2.4622882831120121122 ,.1269178456773991316 ] 
dist 81=[-2.1882670687727938824 ,.5584169212267786421 ] 
dist 82=[-1.5301206422618992506 ,.8804035810846764960 ] 
dist 83=[-1.4279387823950665856 ,1.1830005345094526775 ] 
dist 84=[-.8055482603150168467 ,1.5372151802890907034 ] 
dist 85=[-.8024477540307751199 ,1.8685977523093407704 ] 
dist 86=[-.13869676244293981507,2.0801410402570871183 ] 
dist 87=[-.08997347953234142769,2.2439477367853372634 ] 
dist 88=[.0165796141872820884 ,2.3849173508067834524 ] 
dist 89=[.0395566934794238955 ,2.5000443256487837631 ] 
dist 90=[.1601386450248644516 ,2.5607686773134153595 ] 
dist 91=[.1811879540267766569 ,2.5931396254311914842 ] 
dist 92=[.1739661905907420059 ,2.5955710207717337479 ] 
dist 93=[.1299928220273614647 ,2.4793785835623900811 ] 
dist 94=[.0814999146273387182 ,2.5270111582476173051 ] 
dist 95=[.0392967232108523387 ,2.5365848736640689387 ] 
dist 96=[-.00631982220516852311,1.6968336815548159290 ] 
dist 97=[-.06845673274581520403,1.6623029600113124524 ] 
dist 98=[-.13642419456095990171,1.5962808025639177930 ] 
dist 99=[-.20532370800940190682,1.5766229305823580750 ] 
dist 100=[-.28810546089247390865,1.4964392308736152622 ] 
dist 101=[-.4114942090106755526 ,1.4751946824608769738 ] 
dist 102=[-.53407851902961089908,1.4290352514567978310 ] 
dist 103=[-.613651864237437526  ,1.4132075133207848348 ] 
dist 104=[-.73760802353223861967,1.3405183738776314973 ] 
dist 105=[-.90911705500721170004,1.3194206308391612580 ] 
dist 106=[-1.0499406260725183666 ,1.2998340162915043217 ] 
dist 107=[-1.1950968019509560652 ,1.2890969041081362931 ] 
dist 108=[-1.3839497747860525823 ,1.2829231116139942420 ] 
dist 109=[-1.5704806058676545127 ,1.2844832481096703537 ] 
dist 110=[-1.7046416440666448823 ,1.2918974439870977840 ] 
dist 111=[-1.9984276084683001036 ,1.3090314517478818706 ] 
dist 112=[-2.4512829538333226195 ,1.3275683213651626569 ] 
dist 113=[-2.7387404349811548181 ,1.3405719831237144553 ] 
dist 114=[-2.9597100874526166475 ,1.3518205641264292451 ] 
dist 115=[-3.1473102919713529235 ,1.3633811034954701375 ] 
dist 116=[-3.2988520427129270859 ,1.3740463559288806316 ] 
dist 117=[-3.3759702341220071336 ,1.3817322424817452907 ] 
dist 118=[-3.4141176057404647943 ,1.3885793149386506529 ] 
dist 119=[-3.4201580162488861310 ,1.3958991798933689115 ] 
dist 120=[-3.3813061640018492393 ,1.4020122384405433097 ] 
dist 121=[-3.3616101149000170830 ,1.4040524975116838395 ] 
dist 122=[-3.3110730296353924921 ,1.4034129118397334634 ] 
dist 123=[-3.2869741558448492581 ,1.3988564591221090149 ] 
dist 124=[-3.1468099557009292739 ,1.3920761957402111117 ] 
dist 125=[-3.1101816996167693523 ,1.9081991476356913900 ] 
dist 126=[-3.0142140084533498369 ,2.2860154539525240423 ] 
dist 127=[-2.9768169453442500610 ,2.5867831866740174624 ] 
dist 128=[-1.5517130162720126470 ,2.8602816708087928974 ] 
dist 129=[-1.4130821909244997176 ,3.0947539017615418129 ] 
dist 130=[-1.3836196290243170549 ,3.2398411776113989795 ] 
dist 131=[-1.3013970351328804312 ,3.3470164421373332839 ] 
dist 132=[-1.2859928245015885453 ,3.4302583568428008408 ] 
dist 133=[-1.1200276715019457445 ,3.4920564496997623033 ] 
dist 134=[-1.0867235509031574486 ,3.5136872066165441724 ] 
dist 135=[-1.0244123752513789554 ,3.5128942687508562753 ] 
dist 136=[-1.0071357761402631372 ,3.6479493958443834383 ] 
dist 137=[-.94236503411832033691,3.7302428907218692954 ] 
dist 138=[-.92479895766900388816,3.7847634305982605715 ] 
dist 139=[-.89322033814014451861,3.8155088444837248104 ] 
dist 140=[-.88370659843111386934,3.8285702999735920756 ] 
dist 141=[-.95804971748802737054,3.8220552241408463076 ] 
dist 142=[-1.4480045011788612919 ,3.7860301103103113938 ] 
dist 143=[-1.8678359319170850607 ,3.7610979874037692850 ] 
dist 144=[-2.2672429530127248069 ,1.6664804836190730272 ] 
dist 145=[-2.6202465403741743878 ,1.4776014655588872679 ] 
dist 146=[-2.8576610262093317746 ,1.0406246805828903656 ] 
dist 147=[-3.0554025064342289191 ,.95866321146946971492] 
dist 148=[-3.2501531556315667113 ,.39633492111233469447] 
dist 149=[-3.4203664511647573957 ,.30018406261140043849] 
dist 150=[-3.5202275924773582330 ,.12274218263469132118] 
dist 151=[-3.5874921122086916167 ,.08225118143247468052] 
dist 152=[-3.6276723719355370627 ,-.44111470171123651391] 
dist 153=[-3.6472828716995422439 ,-.51520432977151276645] 
dist 154=[-3.6448899459706748994 ,-.63313921915990532887] 
dist 155=[-3.6081048981560293451 ,-.66009952563707910641] 
dist 156=[-3.5894379705555942860 ,-.67786449850306348262] 
dist 157=[-2.9317407914074355012 ,-.27941993459542272189] 
dist 158=[-2.9466608692307719525 ,.15752047201334197939] 
dist 159=[-2.9491574013538934684 ,.52612474472028516534] 
dist 160=[-1.1200970335850131733 ,.89674972387650715052] 
dist 161=[-.59404715536170405013,1.2393560301514838978 ] 
dist 162=[-.50303340798506128283,1.4961941162754180977 ] 
dist 163=[-.34119982901460417058,1.7388514499453212143 ] 
dist 164=[-.30531442103804672598,2.0248899342536360701 ] 
dist 165=[-.16840057381848607963,2.2895716401908148662 ] 
dist 166=[-.1840666180894119348 ,2.4470379402533122584 ] 
dist 167=[-.2300118815838575289 ,2.5557924516606819816 ] 
dist 168=[-.2865820765802930603 ,2.6261670565546234525 ] 
dist 169=[-.3446310156350689419 ,2.6747278257272209678 ] 
dist 170=[-.4147654562065715623 ,2.6964671673680791846 ] 
dist 171=[-.5195442593702603101 ,2.7026750164009764144 ] 
dist 172=[-.6383114090619600855 ,2.6968203985542445163 ] 
dist 173=[-.7642453573964700118 ,1.8744132442913783794 ] 
dist 174=[-.9192911397683857237 ,1.8829308348405542926 ] 
dist 175=[-1.1541858085861862455 ,1.9756547342445065162 ] 
dist 176=[-1.3871984364890561559 ,2.1844096551342522004 ] 
dist 177=[-1.5347361530727103442 ,2.3052843629536313404 ] 
dist 178=[-1.6476161869072673017 ,2.3847191464734781197 ] 
dist 179=[-1.7423771201464299391 ,2.4281613102724218332 ] 
dist 180=[-1.8179995943061528561 ,2.4544413246822214879 ] 
dist 181=[-1.8545346499053706780 ,2.4654113702284678359 ] 
dist 182=[-1.8717206276448915009 ,2.4672522205866155064 ] 
dist 183=[-1.8724862586493802314 ,2.4590458170495514217 ] 
dist 184=[-1.8379182876700446868 ,2.0891415824057191809 ] 
dist 185=[-1.8247617766259392979 ,2.0321102218537645106 ] 
dist 186=[-1.7917841586020156068 ,1.9268026061707138926 ] 
dist 187=[-1.7770685984876641764 ,1.8977182294637707472 ] 
dist 188=[-2.0128842193572259885 ,1.7901720446258815021 ] 
dist 189=[-2.2997154836984208502 ,1.7599453926009905960 ] 
dist 190=[-2.4718758054383659699 ,1.8205919067230758490 ] 
dist 191=[-2.5926928873460034478 ,1.9146007648856049848 ] 
dist 192=[-2.6747075622988290643 ,1.9871926379388315438 ] 
dist 193=[-2.7333614058302482264 ,2.0406629653207739879 ] 
dist 194=[-2.7609867459625841432 ,2.0583968916917381796 ] 
dist 195=[-2.7711280448243642899 ,2.0626163036983030787 ] 
dist 196=[-2.7665590504377891513 ,2.0621792584965561083 ] 
dist 197=[-2.4393580044624604032 ,1.9540207802725368712 ] 
dist 198=[-2.3855235280904185784 ,1.9298925227374207687 ] 
dist 199=[-2.2885406146180427558 ,1.8716769819247986189 ] 
dist 200=[-2.2609900461497632325 ,1.8496477178176328390 ] 
dist 201=[-2.1567062330354599179 ,1.7357981484258924592 ] 
dist 202=[-2.1257614153120594909 ,1.7084591166968637533 ] 
dist 203=[-2.0697652472546066148 ,1.6419045543769485065 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 2, 2, 0, 2] 
dist 0=[61.447252291082713234  ,61.447252291082713234  ] 
dist 1=[61.135531549584348156  ,61.586966329374638511  ] 
dist 2=[60.477691315452971548  ,61.832878569946374368  ] 
dist 3=[58.940655537309170865  ,62.006496615770994495  ] 
dist 4=[56.991003704065608983  ,62.110704336726042277  ] 
dist 5=[54.627356544410649916  ,62.162068538536457827  ] 
dist 6=[51.504603258710910732  ,62.124716338537857707  ] 
dist 7=[46.524245886742291520  ,62.014888098562504807  ] 
dist 8=[41.441571342498275281  ,61.892438418124935746  ] 
dist 9=[37.910230636039834425  ,61.521131603865937491  ] 
dist 10=[34.823431310722102670  ,61.340688920352206023  ] 
dist 11=[30.730388891219578913  ,61.180478119082363975  ] 
dist 12=[27.220819905253457590  ,61.005670477877526187  ] 
dist 13=[23.583656845379206386  ,60.705505199781559477  ] 
dist 14=[20.136199649132115642  ,55.430770355978285213  ] 
dist 15=[17.383605356914577254  ,54.435470793756073003  ] 
dist 16=[14.607428203947239367  ,48.637101073169347593  ] 
dist 17=[11.065007102184342457  ,37.390437001587760510  ] 
dist 18=[7.6361253058304434465 ,35.476272988360258625  ] 
dist 19=[5.3128336376331832688 ,30.870512097015224272  ] 
dist 20=[3.3473960718252631573 ,30.210358734032461425  ] 
dist 21=[1.3468078708885637870 ,23.680247619779466351  ] 
dist 22=[-.53430255339886730592,22.497557478858451015  ] 
dist 23=[-2.0234986506953520674 ,21.091518282028581501  ] 
dist 24=[-3.5204473027983397605 ,20.852476950926391907  ] 
dist 25=[-5.4343721654920895931 ,11.496857775910285717  ] 
dist 26=[-7.2488715068130293936 ,10.386113281480563581  ] 
dist 27=[-8.3489202462839114528 ,8.0616020594036775494 ] 
dist 28=[-9.1469441365573471133 ,7.5406310907527265588 ] 
dist 29=[-9.7539134644692278431 ,5.3786042596116688917 ] 
dist 30=[-10.223726512196004658  ,4.9879440758993440690 ] 
dist 31=[-10.473011472739079115  ,4.4226380661053065722 ] 
dist 32=[-10.612288284000946404  ,4.3270121889788347741 ] 
dist 33=[-10.641182293560648174  ,-3.4043574970744687819 ] 
dist 34=[-10.569716996763610583  ,-4.0307873777581533146 ] 
dist 35=[-10.598476946217433551  ,-5.2743714744434558386 ] 
dist 36=[-10.482385516133295670  ,-4.7089473161639433738 ] 
dist 37=[-10.438938762405990061  ,-3.6981490256801876114 ] 
dist 38=[-10.401366714617833400  ,-2.4208534702056103225 ] 
dist 39=[-10.362740471005170268  ,-.45006480035409185826] 
dist 40=[-9.5278989723869204666 ,1.5263665743928623090 ] 
dist 41=[-10.125313254558889354  ,2.8263881681818805873 ] 
dist 42=[-10.494616040810759388  ,3.8776143913338671861 ] 
dist 43=[-10.771089218486557017  ,4.8616941473499459449 ] 
dist 44=[-10.997082572073109186  ,5.7256878267855051789 ] 
dist 45=[-11.176060063785217030  ,6.2979582353975582063 ] 
dist 46=[-11.264404692277956630  ,6.7656946351938356257 ] 
dist 47=[-11.304208909328430573  ,7.2128199821639747127 ] 
dist 48=[-11.294074336119823199  ,7.6002415836668565135 ] 
dist 49=[-2.3378478741665216734 ,7.8298038220488211799 ] 
dist 50=[-1.6829188162767896169 ,7.9879871492951724849 ] 
dist 51=[-1.5291289188639448129 ,8.0905189883979566683 ] 
dist 52=[-.76234968175514392119,8.1498731307737488968 ] 
dist 53=[-.6245079362168457126 ,8.1445522323718407019 ] 
dist 54=[-.30968113669695569137,8.0904543800504117982 ] 
dist 55=[-.24859940179760550343,8.0432805700736478219 ] 
dist 56=[1.1394580566414960820 ,7.8727398988717387082 ] 
dist 57=[.15407087259973714612,8.2244815923907265119 ] 
dist 58=[-.66961985781551217858,8.4126461017194410772 ] 
dist 59=[-1.4848679690880607205 ,8.5175705955348743075 ] 
dist 60=[-2.2297431059874484908 ,8.5371204107158973299 ] 
dist 61=[-2.7728058294472411853 ,8.5106924393349611651 ] 
dist 62=[-3.2707553342312122110 ,8.4801620432873477715 ] 
dist 63=[-3.8357661342299170686 ,8.3458428510820233836 ] 
dist 64=[-4.3572615063009429140 ,8.2890586683591197525 ] 
dist 65=[-4.6816574419726285368 ,4.5839810320861461446 ] 
dist 66=[-4.9231553069895029708 ,4.2150943826986725707 ] 
dist 67=[-5.1139657554057233685 ,3.3441028033762133082 ] 
dist 68=[-5.2571355192277264849 ,3.1798753088719875510 ] 
dist 69=[-5.3085900631780016647 ,1.9734001845703870842 ] 
dist 70=[-5.3202237096382899723 ,1.7493754477996626161 ] 
dist 71=[-5.3045707360828084594 ,1.3699221788368642133 ] 
dist 72=[-5.6057024548947611527 ,1.2796010000552827155 ] 
dist 73=[-6.1657308585394712754 ,-.25828831164151052378] 
dist 74=[-6.4789978383656100484 ,-.46210537898954556275] 
dist 75=[-6.6712131475135747024 ,-.27812261509018806571] 
dist 76=[-6.7483025612930030084 ,.05533504089034979483] 
dist 77=[-6.7793627457390787527 ,.40441697171020629853] 
dist 78=[-6.7879575416849780439 ,.73538570818464107906] 
dist 79=[-6.7819932342116862587 ,1.1272789872633343787 ] 
dist 80=[-6.7550130417460023780 ,1.5266818787921881806 ] 
dist 81=[-.70218097598871926292,1.7777919535739698231 ] 
dist 82=[-.42362354769666348014,1.9677028035869426218 ] 
dist 83=[.21444807678314776182,2.1229894980796182643 ] 
dist 84=[.31776680958265629552,2.2475522840658415022 ] 
dist 85=[.32870167866915532534,2.3255998113002339494 ] 
dist 86=[.2400700110377355748 ,2.4085859882687240589 ] 
dist 87=[.11590503330670207387,2.4420351612526599951 ] 
dist 88=[-.05737702578276318163,2.4535361739459448266 ] 
dist 89=[-.34181127588321163123,2.4637848509648712036 ] 
dist 90=[-.63201365207957944025,2.6484593494065272059 ] 
dist 91=[-.82829494692068716944,2.7807581152627787662 ] 
dist 92=[-.99239807449240152809,2.8757815010131004329 ] 
dist 93=[-1.1543381034613830880 ,2.9418066502161420223 ] 
dist 94=[-1.3015017073894393364 ,3.0101237461806607563 ] 
dist 95=[-1.4067012064502377048 ,3.1521903158942361736 ] 
dist 96=[-1.5007572878500018646 ,3.2875797511073912797 ] 
dist 97=[-1.6034898079511195078 ,3.3743699216002123095 ] 
dist 98=[-1.6932277488156947809 ,3.4420712569633591354 ] 
dist 99=[-1.7354796565072587320 ,3.5012766525158483205 ] 
dist 100=[-1.7554237557563228474 ,3.5503294196662865197 ] 
dist 101=[-1.7562662414804440379 ,3.5775049019108451790 ] 
dist 102=[-2.0325906323171038871 ,3.5937340111038170855 ] 
dist 103=[-2.9790148468245069941 ,3.5990808431416971925 ] 
dist 104=[-3.9138016498075090756 ,3.5961528707350441906 ] 
dist 105=[-4.5108817590024334384 ,3.5819284104765200104 ] 
dist 106=[-4.9739025409305536536 ,3.5519379209057867668 ] 
dist 107=[-5.3738920516395389454 ,3.5345328232751918368 ] 
dist 108=[-5.7019541451412352020 ,3.4254110207690033994 ] 
dist 109=[-5.8780415962958492009 ,3.3953680025599620213 ] 
dist 110=[-5.9762794547697948029 ,3.2926112013345497559 ] 
dist 111=[-5.9957486072518753778 ,3.2690782977065599276 ] 
dist 112=[-5.9789684610799266585 ,2.9017409082363100371 ] 
dist 113=[-5.9499806255067522474 ,2.8375713391072705636 ] 
dist 114=[-5.9000467248834680163 ,2.6602844089500716184 ] 
dist 115=[-5.8729682696493186595 ,2.6272367557528549877 ] 
dist 116=[-5.7148093148536964216 ,2.2803385543295383371 ] 
dist 117=[-5.6690607041242418512 ,2.2065021676496697257 ] 
dist 118=[-5.5031807998419624984 ,2.1183556802743129439 ] 
dist 119=[-5.4688672243762131898 ,2.0825678284067387208 ] 
dist 120=[-.37156219656774504417,1.9482655657396996818 ] 
dist 121=[-.08474045701891583015,2.4924288839936829176 ] 
dist 122=[-.01006203200791140669,2.9274972430543892304 ] 
dist 123=[-.27532405610523018418,3.4694802417827589225 ] 
dist 124=[-.49831970492302159932,4.0822223677796632982 ] 
dist 125=[-.7212641818446482431 ,4.5007277047691173563 ] 
dist 126=[-.9265379533339283229 ,4.8563064314997370998 ] 
dist 127=[-1.0790489673821631188 ,5.2180313541846227322 ] 
dist 128=[-1.2218029516176910636 ,5.5388239458539688611 ] 
dist 129=[-1.3881608220051928852 ,5.7311182034140566644 ] 
dist 130=[-1.5408831881381159541 ,5.8657615254699996876 ] 
dist 131=[-1.6292456174809659696 ,5.9565716184959743293 ] 
dist 132=[-1.6872092138038146191 ,6.0120634265271743109 ] 
dist 133=[-1.7186671309267442617 ,6.0150926009577314896 ] 
dist 134=[-1.7377351118619271079 ,5.9774640313410502876 ] 
dist 135=[-1.7462764726868220044 ,5.9447873780020047547 ] 
dist 136=[-1.7487328783558179742 ,3.0177404097555799590 ] 
dist 137=[-1.7435350708863552738 ,2.7510266672439341562 ] 
dist 138=[-1.3836087728200000946 ,2.1128160400274133829 ] 
dist 139=[-1.8175564664493929400 ,2.0048597724643558472 ] 
dist 140=[-2.2929713832208416612 ,1.1057287513605323832 ] 
dist 141=[-2.6486317784172958017 ,.94109336897637099671] 
dist 142=[-2.9839588920791408720 ,.69612558176990099757] 
dist 143=[-3.3782615504954331948 ,.78182891948390864355] 
dist 144=[-3.7407971739538324998 ,.87280618792994173613] 
dist 145=[-3.9494032242115590516 ,.97193456336616325356] 
dist 146=[-4.0847730458923624334 ,1.0623117510301004824 ] 
dist 147=[-4.1551652209393812883 ,1.1183804620413690060 ] 
dist 148=[-4.1966322435814784413 ,1.1599321319833210104 ] 
dist 149=[-4.2166201975439940366 ,1.1923998431983521919 ] 
dist 150=[-4.2246591279315702159 ,1.2164474987589949890 ] 
dist 151=[-4.2184673322984643194 ,1.2244101870366302137 ] 
dist 152=[-1.4811607554350129931 ,1.2246264205387485288 ] 
dist 153=[-1.4736895788353802477 ,1.2207558614568236433 ] 
dist 154=[-1.4931415725540042914 ,1.2697284770667787570 ] 
dist 155=[-1.5345470426551293308 ,1.7010129606782917270 ] 
dist 156=[-1.5868340355212484892 ,2.1016369532809847146 ] 
dist 157=[-1.6496896484890400894 ,2.4053323759914413762 ] 
dist 158=[-1.7322214102433195563 ,2.6955880663532493384 ] 
dist 159=[-1.8629955217060376908 ,3.0426027376807781989 ] 
dist 160=[-2.0008250190183267987 ,3.3646886790874620026 ] 
dist 161=[-2.1114984799071911489 ,3.5555028395665385933 ] 
dist 162=[-2.2232636286972789444 ,3.6863344961405495113 ] 
dist 163=[-2.3654423135416237073 ,3.7691460385247816404 ] 
dist 164=[-2.5159364392296869659 ,3.8229361391904799124 ] 
dist 165=[-2.6608684994264044006 ,3.8379959418010044942 ] 
dist 166=[-2.8291820115289372952 ,3.8313190712226180442 ] 
dist 167=[-3.0729403264176456249 ,3.8196028895891758176 ] 
dist 168=[-3.3102426494931759646 ,4.3064884513029231960 ] 
dist 169=[-3.4528012383140247400 ,4.7460772625922185416 ] 
dist 170=[-3.5529548813165376711 ,5.0727670688978325226 ] 
dist 171=[-3.6211024877100718786 ,5.3299352349989289107 ] 
dist 172=[-3.6632707061305556770 ,5.5285333898806872241 ] 
dist 173=[-3.6701272568770917109 ,5.6215727168839709030 ] 
dist 174=[-3.6438963482525251326 ,5.6613755041025276624 ] 
dist 175=[-3.6365502371141702862 ,5.6601578800156925310 ] 
dist 176=[-3.4190479323356310583 ,5.3141986814536904045 ] 
dist 177=[-3.3743338684131052508 ,5.2415463143104832148 ] 
dist 178=[-3.2414560925629199498 ,5.1092786070655568671 ] 
dist 179=[-3.2153273216671145674 ,5.0659899334284718833 ] 
dist 180=[-3.2475458683410364764 ,4.8739179985516508040 ] 
dist 181=[-3.2582161201629218073 ,4.8191194673146430458 ] 
dist 182=[-3.2551226505505261460 ,4.6786187302776423419 ] 
dist 183=[-3.2446713185263633809 ,4.6235006122349647710 ] 
dist 184=[-2.6302876662877093346 ,1.3431399167034645162 ] 
dist 185=[-2.6135579701157643480 ,1.3173872143604431648 ] 
dist 186=[-.42624826168789197158,.95046628443412197545] 
dist 187=[-.56917048164415678106,1.0186328216660731513 ] 
dist 188=[-.7026734294348723270 ,1.0680531832562849678 ] 
dist 189=[-.8051467209420015920 ,1.2479376387103032795 ] 
dist 190=[-.9043246281844295670 ,1.5422902051949359485 ] 
dist 191=[-1.0246827838705654861 ,1.7495046044793584637 ] 
dist 192=[-1.1373322386809430461 ,1.9321814174224649537 ] 
dist 193=[-1.2057590970987275949 ,2.1286502427825889686 ] 
dist 194=[-1.2547731019502164479 ,2.3067171015417215505 ] 
dist 195=[-1.2899811284401091040 ,2.4159852925137417069 ] 
dist 196=[-1.3142958984816552549 ,2.4955792354249370348 ] 
dist 197=[-1.3198538596098469421 ,2.5552694705210658961 ] 
dist 198=[-1.3185341905831708428 ,2.5974630917375003348 ] 
dist 199=[-1.3154124168967389717 ,2.6072595108983619193 ] 
dist 200=[-1.2258104254410338349 ,2.6033382430907798315 ] 
dist 201=[-1.2090497432960137924 ,2.5918857162683209174 ] 
dist 202=[-1.1577308775114321459 ,1.4402476051020655603 ] 
dist 203=[-1.1477444304083069647 ,1.3361756355597658276 ] 
dist 204=[-1.0300540236126432852 ,1.0767872870534986483 ] 
dist 205=[-1.0157011109991506231 ,1.0392452625078974940 ] 
dist 206=[-1.1542911687053206642 ,1.0391489101491415240 ] 
dist 207=[-1.2557418658695306726 ,1.0775758944817999943 ] 
dist 208=[-1.3492120879736323312 ,1.1089274612476857102 ] 
dist 209=[-1.4559657856135047283 ,1.1281793967923512873 ] 
dist 210=[-1.5524764424737999855 ,1.1422199128545940501 ] 
dist 211=[-1.6050856027644313038 ,1.1527806702359700016 ] 
dist 212=[-1.6355004173558936956 ,1.1602695590798413585 ] 
dist 213=[-1.6434754435028540454 ,1.1620546624429187534 ] 
dist 214=[-1.6424628231676835373 ,1.1599955526523175463 ] 
dist 215=[-1.6370261963241267913 ,1.1555812240193310798 ] 
dist 216=[-1.6273156057525913658 ,.37277309944739077348] 
dist 217=[-1.6198531874366761969 ,.46529004401173918435] 
dist 218=[-1.1105687213078376226 ,.71145728490013216062] 
dist 219=[-1.1624820704882304970 ,.95515604370253503973] 
dist 220=[-1.2230010778457214712 ,1.1598986738043924007 ] 
dist 221=[-1.2889765676998003687 ,1.3644539435932444783 ] 
dist 222=[-1.3532653721913829171 ,1.5527565437800279954 ] 
dist 223=[-1.4070550080691278136 ,1.6926653040221905564 ] 
dist 224=[-1.4633576282700256613 ,1.8236543040697330693 ] 
dist 225=[-1.5376704601714682567 ,1.9763756668764134385 ] 
dist 226=[-1.6102392140539666299 ,2.1161606333959870460 ] 
dist 227=[-1.6595837193639317222 ,2.1955446831610613917 ] 
dist 228=[-1.7012738026483594243 ,2.2457409501589969092 ] 
dist 229=[-1.7433064239889168049 ,2.2690912612643211873 ] 
dist 230=[-1.7822427588604561909 ,2.2783407015552928784 ] 
dist 231=[-1.8115802375578255548 ,2.2739950698758100207 ] 
dist 232=[-1.8394456436631910469 ,2.2583640072113851796 ] 
dist 233=[-2.0163790482858663438 ,2.2466446450401515256 ] 
dist 234=[-2.1976980844856869389 ,2.2898517885181511256 ] 
dist 235=[-2.3433415717703638693 ,2.6032231967682009806 ] 
dist 236=[-2.4593441889696889058 ,2.8448870442499848901 ] 
dist 237=[-2.5224190744379066804 ,3.0512285874439670963 ] 
dist 238=[-2.5586882638487777744 ,3.2186092451992432834 ] 
dist 239=[-2.5677570396939543608 ,3.3048499395767446617 ] 
dist 240=[-2.3877278153901792645 ,3.3498817058722179630 ] 
dist 241=[-2.3533172213268534753 ,3.3576376542529656747 ] 
dist 242=[-2.3166024664935659112 ,3.3217319235900844458 ] 
dist 243=[-2.2962288841856487404 ,3.3011337285475320178 ] 
dist 244=[-2.2673149460686523852 ,3.2627087068479767434 ] 
dist 245=[-2.1860439685031915976 ,3.2450708199074982834 ] 
dist 246=[-1.7432003661391897362 ,3.1453000962087917714 ] 
dist 247=[-1.4423183931252226368 ,3.1180477297792638658 ] 
dist 248=[-1.3092473012640063380 ,3.0204594110903723998 ]