8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 1, 2, 2, 0, 1] 
dist 0=[50.744546614757203100  ,50.744546614757203100  ] 
dist 1=[50.073235405764000564  ,51.119727154585252915  ] 
dist 2=[48.931562415150037485  ,51.946040493910700264  ] 
dist 3=[47.222024094479253188  ,52.739666134602282804  ] 
dist 4=[45.274459551487872967  ,53.152847064987253491  ] 
dist 5=[43.182061333758686421  ,53.366270327161538400  ] 
dist 6=[40.578347333466259153  ,53.389003567920066962  ] 
dist 7=[36.588649074566381817  ,53.261889857318567125  ] 
dist 8=[32.562132790967015900  ,53.164210030644566850  ] 
dist 9=[29.811239525616069191  ,52.886477802250426596  ] 
dist 10=[27.461671769833819806  ,52.743285438370507518  ] 
dist 11=[25.037604775585002910  ,50.308130566994554788  ] 
dist 12=[22.743419766912818946  ,49.855738657991248090  ] 
dist 13=[20.912269667546316651  ,49.159188288393523055  ] 
dist 14=[19.063896836227695396  ,47.636065090441730909  ] 
dist 15=[16.700383982469465077  ,43.560862104048044608  ] 
dist 16=[14.405693299683551513  ,36.935917835137589004  ] 
dist 17=[12.831895844154268758  ,36.143413571415476961  ] 
dist 18=[11.478226610949001360  ,35.920779971899412512  ] 
dist 19=[10.062373359326860600  ,28.676500590401127559  ] 
dist 20=[8.7054370626568885964 ,27.734827614655751487  ] 
dist 21=[7.5865427362489982930 ,25.849465918593041923  ] 
dist 22=[6.4198137778195862578 ,25.356768139709404472  ] 
dist 23=[4.8705720697545999668 ,23.572769133045752389  ] 
dist 24=[3.3747869428634091929 ,23.182211621180385980  ] 
dist 25=[2.4214772182769443080 ,22.528941973352215085  ] 
dist 26=[1.6743394368689338733 ,22.361350875228693546  ] 
dist 27=[1.0030027804390676019 ,9.8906648328495149741 ] 
dist 28=[.2015061203295910673 ,7.8314048823092287137 ] 
dist 29=[-2.2021489432487168255 ,7.4989392881458636061 ] 
dist 30=[-4.5502081942756547643 ,6.5956631365986032433 ] 
dist 31=[-6.6915384178248596286 ,5.4618017722641289928 ] 
dist 32=[-8.2694299640475663033 ,-.78999388437172761481] 
dist 33=[-9.7417632416115803800 ,-.87309078307551495673] 
dist 34=[-11.461498110666660215  ,-.96074498615901040938] 
dist 35=[-13.053119067493269444  ,-.93592337088945766029] 
dist 36=[-14.013758352597585082  ,-.86767375301003456762] 
dist 37=[-14.699417405072547429  ,-.74526510571081332625] 
dist 38=[-15.192739481410589182  ,-.56186563664923274134] 
dist 39=[-15.563500182119461942  ,-.25018661941796422791] 
dist 40=[-15.759546646005962395  ,.0726363987297771025 ] 
dist 41=[-15.866049928566394534  ,.3006133720015694754 ] 
dist 42=[-15.878895336883029112  ,.5010390046548325287 ] 
dist 43=[-8.6065228958811496676 ,.7141949274568626365 ] 
dist 44=[-8.5946012347609584388 ,.9173916285396552185 ] 
dist 45=[-8.5793018229503275924 ,1.0781484351846611423 ] 
dist 46=[-8.5593798234036929043 ,1.2374186553324298321 ] 
dist 47=[-8.5286505948684051790 ,1.4346320928732934748 ] 
dist 48=[-3.7220281796920988711 ,1.6190850534119443553 ] 
dist 49=[-3.3265621633569103554 ,1.7274346897882359049 ] 
dist 50=[-2.8328589716703371574 ,1.7995957574714547581 ] 
dist 51=[-2.2503377953087914649 ,1.8396936049792139584 ] 
dist 52=[-.98809579959808679386,1.8638632384571016536 ] 
dist 53=[-.76493246614867235509,1.8726649115046676662 ] 
dist 54=[-.46440826745288131236,1.8716340532164798113 ] 
dist 55=[-.39517402035069226916,2.2776182505701692936 ] 
dist 56=[-.4698097099431321981 ,2.6925894554361433194 ] 
dist 57=[-.69116146954073075416,3.1039285021172847966 ] 
dist 58=[-.86945305606562452861,3.6198105049905889370 ] 
dist 59=[-1.0352024568091810088 ,4.1120847132475712459 ] 
dist 60=[-1.1799172458388073781 ,4.4292060524374674753 ] 
dist 61=[-1.2742976098025239688 ,4.6802018319233220763 ] 
dist 62=[-1.3497681037640528844 ,4.9083050133461059070 ] 
dist 63=[-1.4190494140378634010 ,5.1057269205540235590 ] 
dist 64=[-1.4787472673065085817 ,5.2341724038422739525 ] 
dist 65=[-1.5159835131931183239 ,5.3375728841291774827 ] 
dist 66=[-1.5438762163941596308 ,5.4350042548915611293 ] 
dist 67=[-1.5662879378234525020 ,5.5140901222154001040 ] 
dist 68=[-1.5834452297469560547 ,5.5442074512318695691 ] 
dist 69=[-1.5903684146132230115 ,5.5475777752140516632 ] 
dist 70=[-1.5911125387786021043 ,5.5398902676130596332 ] 
dist 71=[-1.5865504356920803283 ,5.4532342980096439030 ] 
dist 72=[-.89190582615764894772,5.4236512283669015990 ] 
dist 73=[-1.5587111507951859849 ,5.3451131416204101897 ] 
dist 74=[-2.5491133743060632567 ,5.3111101521515577955 ] 
dist 75=[-3.5314263577957157035 ,1.7071031157933779377 ] 
dist 76=[-4.1659781523067452476 ,1.6111342745224673150 ] 
dist 77=[-4.6677165040746009836 ,1.5899788462217594208 ] 
dist 78=[-5.1198958323693612907 ,1.5487780190010617658 ] 
dist 79=[-5.5061001263341303074 ,1.5372771543344348068 ] 
dist 80=[-5.7445096994651868632 ,1.1436277227145242105 ] 
dist 81=[-5.9206596111918441184 ,1.1080972656291409242 ] 
dist 82=[-6.0583952862245850903 ,1.0348006628946276371 ] 
dist 83=[-6.1643882141911923920 ,1.0148057843879484326 ] 
dist 84=[-6.2451627783868642813 ,.9362554964241278554 ] 
dist 85=[-6.3330849561999560317 ,.9203838741694633238 ] 
dist 86=[-6.3958255693785032532 ,.8817164351872800014 ] 
dist 87=[-6.4377091581595841878 ,.8729178935146489824 ] 
dist 88=[-6.4423394141531359915 ,.80840887446094198703] 
dist 89=[-6.4225102554107733315 ,.79498311117713566711] 
dist 90=[-6.4054134142397824457 ,.76818841512950364639] 
dist 91=[-3.4177271397959433466 ,.75989278517803434307] 
dist 92=[-3.1714666411432696891 ,.72247855853525275521] 
dist 93=[-2.5921549782814514247 ,.9395759286261036892 ] 
dist 94=[-2.4885182318087862952 ,1.5689305387281334066 ] 
dist 95=[-2.0168975825044563988 ,2.1475707696612854599 ] 
dist 96=[-1.5537627318310782336 ,2.5786380121172502284 ] 
dist 97=[-1.3197677502536814319 ,2.9842350667737637467 ] 
dist 98=[-1.2621412247545793778 ,3.4612144963309357035 ] 
dist 99=[-.28294271396022797736,3.9057585319920654567 ] 
dist 100=[-.2362590080565486375 ,4.1818870448820806669 ] 
dist 101=[-.33295268321331039015,4.3875424751391213506 ] 
dist 102=[-.44978300731607486526,4.5507820610607271317 ] 
dist 103=[-.61851317741907601509,4.6759053351648096969 ] 
dist 104=[-.78441847893181038078,4.7294282203919947524 ] 
dist 105=[-.88997656040957626011,4.7513660402121576872 ] 
dist 106=[-.97156310629156970202,4.7504161644540379846 ] 
dist 107=[-1.0417919085965162347 ,2.8907848056441271113 ] 
dist 108=[-1.0993710247896510842 ,3.0606781926145671314 ] 
dist 109=[-1.1304705430696927761 ,3.1783683475534502451 ] 
dist 110=[-1.1481501440708042308 ,3.2558972945936817074 ] 
dist 111=[-1.1521702131523396182 ,3.3112350861280085838 ] 
dist 112=[-1.1510546791224778750 ,3.3403213533546406340 ] 
dist 113=[-1.1482359777820831159 ,3.3558399347122594890 ] 
dist 114=[-1.1436505628227602634 ,3.3569805025640997391 ] 
dist 115=[-1.1391268090804815826 ,3.0009926608053536156 ] 
dist 116=[-1.1256399851387397928 ,2.9455272986047316583 ] 
dist 117=[-1.1192805573520299969 ,2.8559071406171253588 ] 
dist 118=[-1.1029094663646345484 ,2.8286614563033791815 ] 
dist 119=[-1.0955137733798928219 ,2.7508074861636930757 ] 
dist 120=[-.22862667840696152704,2.7222754601464959899 ] 
dist 121=[-.16481522771903730407,2.7026420694550477982 ] 
dist 122=[-.02881727011999168140,2.6900316254733299458 ] 
dist 123=[.00303177833233813172,.50623733237257124089] 
dist 124=[-.00828963074735171921,.40236910594499819198] 
dist 125=[-.32410462818403325482,.50146016551557446372] 
dist 126=[-.64465896647192923879,.60120881589351212926] 
dist 127=[-.94386587156697757623,.7279383851203761253 ] 
dist 128=[-1.1744707306819009435 ,.84981985450270694882] 
dist 129=[-1.3990778991926257108 ,.93022012845388787991] 
dist 130=[-1.6743448504883618342 ,.99563822680607594054] 
dist 131=[-1.9343720314104599390 ,1.0577241358409890978 ] 
dist 132=[-2.0981477030877142482 ,1.1129307321173432264 ] 
dist 133=[-2.2228386195448942253 ,1.1508938145061522252 ] 
dist 134=[-2.3268534436067514802 ,1.2004593378923764134 ] 
dist 135=[-2.4096543529148519154 ,1.2809394242094439210 ] 
dist 136=[-2.4496665799057965568 ,1.3557277814934949684 ] 
dist 137=[-2.4688343981231316917 ,1.3962570649708481450 ] 
dist 138=[-2.4697648520051264422 ,1.4194897464915801206 ] 
dist 139=[-.66821272303415088054,1.4252348916492027386 ] 
dist 140=[-.7066179291844294029 ,1.4248309230209282545 ] 
dist 141=[-.77580181848889534803,1.4235161458827148987 ] 
dist 142=[-.8448688782172323717 ,1.4212952283275955052 ] 
dist 143=[-.93182132726548162632,1.4172685775275396512 ] 
dist 144=[-1.0150327602134503788 ,1.2044183245118260890 ] 
dist 145=[-1.0691688093551838649 ,1.1731747519832600551 ] 
dist 146=[-1.1123636149649701440 ,1.1157820197082217585 ] 
dist 147=[-1.1519073395946179612 ,1.1004523066943638360 ] 
dist 148=[-1.1860648183844623895 ,1.0462613183235447258 ] 
dist 149=[-1.2077621767134531257 ,1.0533487830811927732 ] 
dist 150=[-1.2244792996014798388 ,1.1857125374578995163 ] 
dist 151=[-1.2387590735856135988 ,1.3146707939928133033 ] 
dist 152=[-1.2485247868217682871 ,1.4252233462629117612 ] 
dist 153=[-1.2494570020520405991 ,1.5464795019642791574 ] 
dist 154=[-1.2424634678969131818 ,1.7080820190949277479 ] 
dist 155=[-1.2384090800500573996 ,1.8617254917128814431 ] 
dist 156=[-1.2024941120402063050 ,1.9512156838334786088 ] 
dist 157=[-1.1939014956255865201 ,2.0109794222091879593 ] 
dist 158=[-1.1879780360185552381 ,2.0459530449440485206 ] 
dist 159=[-1.1841488015350874772 ,2.0686608006914131357 ] 
dist 160=[-1.2738014992372963943 ,2.0794519253099298305 ] 
dist 161=[-1.3340930626640958546 ,2.0836255158471213874 ] 
dist 162=[-1.3772186864193292880 ,2.0798964482488386322 ] 
dist 163=[-1.4096742727238281992 ,1.8383127686108007264 ] 
dist 164=[-1.4646912446318304438 ,1.8009126735996195998 ] 
dist 165=[-1.5056994272063464713 ,1.7346578379062344644 ] 
dist 166=[-1.5382596349132587073 ,1.7167831897687385232 ] 
dist 167=[-1.5628555613975801921 ,1.6540882983453286718 ] 
dist 168=[-1.5720809976018125369 ,1.6345946176921035030 ] 
dist 169=[-1.5726674308839262539 ,1.6097774907443898302 ] 
dist 170=[-1.5699328087520539969 ,1.5986676904542713968 ] 
dist 171=[-1.3720674601797716514 ,.83186387447624286783] 
dist 172=[-1.2922717581305119155 ,.95025910044268140646] 
dist 173=[-1.2726678665052276138 ,1.0377566411344736764 ] 
dist 174=[-1.2542862810358770720 ,1.1193816223430862842 ] 
dist 175=[-1.2448693025740153340 ,1.2143350778609482224 ] 
dist 176=[-.95902684514480420387,1.3014251473465199125 ] 
dist 177=[-1.0929340535178226169 ,1.3516636768438705821 ] 
dist 178=[-1.2660115544851325189 ,1.3845194984689972044 ] 
dist 179=[-1.4287874206142214635 ,1.4022286943499680525 ] 
dist 180=[-1.5300665390921402296 ,1.4122902193191070728 ] 
dist 181=[-1.6057330518823762085 ,1.4146237486701354455 ] 
dist 182=[-1.6662759209432119860 ,1.4117383206709691831 ] 
dist 183=[-1.7125014783179378091 ,1.4082211309992309946 ] 
dist 184=[-1.7310214264875518133 ,-.44384454958008186812] 
dist 185=[-1.7497620002760769932 ,-.46310310669561000791] 
dist 186=[-1.7758284277746214018 ,-.2507376346004787097 ] 
dist 187=[-1.7941634881366752906 ,-.03277449166722430524] 
dist 188=[-1.7968848918416017282 ,.11980340207691606933] 
dist 189=[-1.7912328715235225540 ,.25369912890379313408] 
dist 190=[-1.7853878912565630177 ,.39710270693416222574] 
dist 191=[-1.7236987287642915776 ,.53564797974194195607] 
dist 192=[-1.7057977733012911999 ,.65015684003703861102] 
dist 193=[-1.6833854842460038162 ,.76900428814749937464] 
dist 194=[-1.6726439158880661610 ,.9248717004218090026 ] 
dist 195=[-1.4744637161931429183 ,1.0771635587933400778 ] 
dist 196=[-1.5193286519859135770 ,1.1817427029074754969 ] 
dist 197=[-1.5489388471915846356 ,1.2714258387183725009 ] 
dist 198=[-1.5730519769207099963 ,1.3642660291714618086 ] 
dist 199=[-1.5959774388621661796 ,1.4520761771037164730 ] 
dist 200=[-1.6135110446698529144 ,1.5216866893926700051 ] 
dist 201=[-1.6161035148492560504 ,1.5913403721644389262 ] 
dist 202=[-1.6127417882746489484 ,1.6793312651712427720 ] 
dist 203=[-1.6065074841689002557 ,1.7606437549460855858 ] 
dist 204=[-1.5569699864367999204 ,1.8036417041393173302 ] 
dist 205=[-1.5419227519999701375 ,1.8269642207547975694 ] 
dist 206=[-1.5192483078902757771 ,1.8321881210733412245 ] 
dist 207=[-1.5101330843474485632 ,1.8381204368933974250 ] 
dist 208=[-1.2635997626062554091 ,1.8403956442320345590 ] 
dist 209=[-1.2273434971105713569 ,1.8404421321699931595 ] 
dist 210=[-1.1498211073590132538 ,1.8374713158574047269 ] 
dist 211=[-1.1269075300882476556 ,1.9140088602370632056 ] 
dist 212=[-1.0287218848134222602 ,1.9634960355633806742 ] 
dist 213=[-1.0087797695449340698 ,1.9909240757799009804 ] 
dist 214=[-.95270771610990304898,1.9968859108237661158 ] 
dist 215=[-.9442776918039383313 ,1.9884468219078432200 ] 
dist 216=[-.19151741769089723495,1.9844009328788977726 ] 
dist 217=[-.11996481211796770879,1.9801301408976286423 ] 
dist 218=[.02647710197421458160,1.9744201793973387071 ] 
dist 219=[-.26516480402659631854,1.6521551252172760314 ] 
dist 220=[-.49109862260490466444,1.6158119454202777169 ] 
dist 221=[-.68009126594257677061,1.5173371458037652876 ] 
dist 222=[-.86816476421789841723,1.5011294464096974914 ] 
dist 223=[-1.0413188023953964232 ,1.3166825950929806388 ] 
dist 224=[-1.1707581790259027343 ,1.2783350849211847632 ] 
dist 225=[-1.2930021810082422509 ,1.2368895028744851295 ] 
dist 226=[-1.4374331760078300628 ,1.2233601751142040016 ] 
dist 227=[-1.5711410223097101833 ,.79727569262703659643] 
dist 228=[-1.6505819003812378348 ,.74167526013080478331] 
dist 229=[-1.7054953164238265525 ,.62824874714205321761] 
dist 230=[-1.7412995531059171334 ,.59818180841503057066] 
dist 231=[-1.7659384299981858275 ,.48680610839121226264] 
dist 232=[-1.7762872859794374992 ,.46317222349269960541] 
dist 233=[-1.7781510815228644120 ,.42020762216952700813] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 0, 0, 0, 0, 1] 
dist 0=[43.246304958843652540  ,43.246304958843652540  ] 
dist 1=[42.557040026872780728  ,43.602923361154870706  ] 
dist 2=[41.803357657109692407  ,43.790559770368985346  ] 
dist 3=[41.189436485172650103  ,43.825335299438655863  ] 
dist 4=[40.558751961947536445  ,43.730214850866392212  ] 
dist 5=[39.738197703654824137  ,43.637012462687607853  ] 
dist 6=[38.856045500547457202  ,43.557541057651830230  ] 
dist 7=[37.979408405287606915  ,43.484159314814488668  ] 
dist 8=[36.936933679252997299  ,43.239565169075846171  ] 
dist 9=[35.392551162742306596  ,40.657343776878824207  ] 
dist 10=[33.795870121443348710  ,39.951238822573836147  ] 
dist 11=[32.544559835391991442  ,39.754078778757151350  ] 
dist 12=[31.303981753714689810  ,38.999910066855231671  ] 
dist 13=[29.686616055975219939  ,38.802003827317205486  ] 
dist 14=[27.944746374303102555  ,38.413583200843289826  ] 
dist 15=[26.223291746462529204  ,38.289894165777457182  ] 
dist 16=[24.179168194888461273  ,37.671562164087220475  ] 
dist 17=[21.147760614086570252  ,30.570218782814605871  ] 
dist 18=[18.115075354831753665  ,23.034506610868783824  ] 
dist 19=[16.065809156956788116  ,22.654071623024536228  ] 
dist 20=[14.335219473227727439  ,19.211336512222164732  ] 
dist 21=[12.576008116193332547  ,18.578241783858726977  ] 
dist 22=[10.923339667622317061  ,17.759464308543376197  ] 
dist 23=[9.6184872504537663273 ,17.539572842233104216  ] 
dist 24=[8.0349947259521631818 ,14.676918995111985095  ] 
dist 25=[5.6568044672126997089 ,14.058752172634660303  ] 
dist 26=[3.9648619214085877855 ,10.578840490018362876  ] 
dist 27=[2.4447928809245879971 ,10.261382882441312708  ] 
dist 28=[.75273307987754968087,8.8920867940783115983 ] 
dist 29=[-.93058966408082286083,8.6443311382957963984 ] 
dist 30=[-2.4162794175520844746 ,8.1185008094655839521 ] 
dist 31=[-4.0504713299158072871 ,7.9996048289723358790 ] 
dist 32=[-6.3281215969922096272 ,2.2821060803891236430 ] 
dist 33=[-8.5391984937830710584 ,1.9704528079234754669 ] 
dist 34=[-9.9075880645420869191 ,.66210705336712243448] 
dist 35=[-10.930207557536520981  ,.42840753883020205543] 
dist 36=[-11.759341170906229896  ,-.67131019240637091661] 
dist 37=[-12.419815756921378493  ,-.85970892263490521651] 
dist 38=[-12.768094944249278244  ,-1.2344132310083867311 ] 
dist 39=[-12.957645708739949342  ,-1.3196283796809649433 ] 
dist 40=[-12.996331043842111188  ,-1.5823866207178066780 ] 
dist 41=[-12.591759244435042196  ,-1.5874749331143087911 ] 
dist 42=[-12.489437718585745777  ,-1.5041148837636332969 ] 
dist 43=[-12.380390079155578724  ,-1.2810380720900350902 ] 
dist 44=[-12.311799091674855802  ,-.9875716021972578371 ] 
dist 45=[-12.174763004258883354  ,-.62311540079262124548] 
dist 46=[-12.099693337651433921  ,-.13824768315834395802] 
dist 47=[-12.028872210928584610  ,.63582778119707768707] 
dist 48=[-11.972396748847825287  ,1.4267540906850925272 ] 
dist 49=[-6.4434048639654611370 ,1.9789783225956471348 ] 
dist 50=[-3.6854313809023807020 ,2.4611093694966121741 ] 
dist 51=[-2.4496970847829205841 ,2.9725600458799719239 ] 
dist 52=[-1.9868667442441892834 ,3.4630057536342277465 ] 
dist 53=[-1.0177653155134372485 ,3.8614419786772645452 ] 
dist 54=[-.73628590909260822196,4.2685788143569726596 ] 
dist 55=[-.677786634689449642  ,4.7938903804794906496 ] 
dist 56=[.71355863184476417766,5.3030782987271720897 ] 
dist 57=[.98055712055792336233,5.6697585483836685557 ] 
dist 58=[1.3603300619296203811 ,6.2509073752623340773 ] 
dist 59=[1.4171392753350712403 ,6.6790062116162530445 ] 
dist 60=[1.8189343454638706506 ,7.0098948148977912368 ] 
dist 61=[1.8792215972465295396 ,7.2679959361494459086 ] 
dist 62=[1.7394887197713120658 ,7.4056413092391169182 ] 
dist 63=[1.3678694071251727439 ,7.4814509785574132229 ] 
dist 64=[.88883016496305345928,7.4930278296034174960 ] 
dist 65=[.13833180148043536082,4.3751969449310532443 ] 
dist 66=[-.6198297394933486981 ,3.8290010426041737410 ] 
dist 67=[-1.1294687508583354673 ,3.7026449546983951434 ] 
dist 68=[-1.5544129611747129030 ,3.5378182821300140568 ] 
dist 69=[-1.9745946528327575066 ,3.4998730449831178168 ] 
dist 70=[-2.3593363908040510872 ,3.1960042247979373155 ] 
dist 71=[-2.6428561794368246648 ,3.1305512863414679248 ] 
dist 72=[-2.9064248691707504930 ,3.0302152862223825663 ] 
dist 73=[-3.2115540400925944885 ,2.9989085216857506205 ] 
dist 74=[-3.4910474932243447995 ,2.7806761700438202450 ] 
dist 75=[-3.6523027655458720858 ,2.7667207294929882196 ] 
dist 76=[-3.7577473017024574647 ,2.6918436929872466247 ] 
dist 77=[-3.8144846064142951455 ,2.6735004705081961714 ] 
dist 78=[-3.8490510301682296112 ,2.6190512870836716637 ] 
dist 79=[-3.8660205360965504449 ,2.6051314459741350349 ] 
dist 80=[-3.8733287753981593122 ,1.5116072856044564898 ] 
dist 81=[-3.8693796926671882968 ,1.4790826479822367450 ] 
dist 82=[-2.7155098703946332321 ,.24726640516150331374] 
dist 83=[-2.9915707413433922438 ,.12361115922386281176] 
dist 84=[-3.2344680465911773269 ,-.12813769066814202805] 
dist 85=[-3.3977050203750653518 ,-.1915552949036957397 ] 
dist 86=[-3.5341836780337486391 ,-.41075751969903686371] 
dist 87=[-3.6702761795420655022 ,-.45549443554522762345] 
dist 88=[-3.7859317737286422229 ,-.50521708137276548364] 
dist 89=[-3.8408129095010643288 ,-.50682273744923549689] 
dist 90=[-3.8663986647219995572 ,-.48934639623746073895] 
dist 91=[-3.8667375187934050330 ,-.37875736428576341926] 
dist 92=[-3.8609665475381850500 ,-.13439404126763046955] 
dist 93=[-3.8506359372433201159 ,.13711823140461837989] 
dist 94=[-3.8330355378716412959 ,.41844635117535869306] 
dist 95=[-3.8201276470716810744 ,.76089631874743043216] 
dist 96=[-3.2940983218135334412 ,1.2764145275603456251 ] 
dist 97=[-2.7891586623615671999 ,1.7897002622318656909 ] 
dist 98=[-2.5457284562021990620 ,2.1232543645407181122 ] 
dist 99=[-2.4999540106084789414 ,2.3891589443377121601 ] 
dist 100=[-2.1246517347759388998 ,2.6324280981929595119 ] 
dist 101=[-2.0509329427464444654 ,2.8426894410459443293 ] 
dist 102=[-1.9415112672039890792 ,2.9768514812854034028 ] 
dist 103=[-1.9092255446658537325 ,3.0810806784826576264 ] 
dist 104=[-1.2635874359507254666 ,3.1718829995832020054 ] 
dist 105=[-1.1785605994869902327 ,3.2453040990919555026 ] 
dist 106=[-.98635494538098566319,3.3218830273485192255 ] 
dist 107=[-.945410577576176203  ,3.4212243597231078704 ] 
dist 108=[-.70394433912600546366,3.4955297863928703996 ] 
dist 109=[-.65976088490213884677,3.5284014535864255262 ] 
dist 110=[-.57175649679374616771,3.5396013026101819715 ] 
dist 111=[-.54915094161128100837,3.5370229251959774957 ] 
dist 112=[.48801117425887068499,3.3128354633397634512 ] 
dist 113=[.03967358841944743061,1.9703157185975718326 ] 
dist 114=[-.36812810784408123842,1.8503116275852237441 ] 
dist 115=[-.70741680508056537935,1.5966963136273099717 ] 
dist 116=[-1.0419304097066432454 ,1.5199751754071045462 ] 
dist 117=[-1.3477846731455822716 ,1.5002828477802880190 ] 
dist 118=[-1.5726859879752664925 ,1.3699504707483472585 ] 
dist 119=[-1.7813700350200093764 ,1.3419410184910933972 ] 
dist 120=[-2.0224955773892452187 ,1.2914528115043200953 ] 
dist 121=[-2.2459054774184144996 ,1.2777777377781637518 ] 
dist 122=[-2.3838798324283399134 ,1.1837418267824325884 ] 
dist 123=[-2.4856876157720124755 ,1.2212993166304419253 ] 
dist 124=[-2.5647430266013148924 ,1.2532676370324171848 ] 
dist 125=[-2.6236379921970346246 ,1.2859484672546979189 ] 
dist 126=[-2.6449807033209765557 ,1.3165358900681855966 ] 
dist 127=[-2.6514633121813744819 ,1.3401360198687225596 ] 
dist 128=[-2.6510476548933230244 ,1.3630723474563752805 ] 
dist 129=[-1.6812447279130975160 ,1.3909874140183644947 ] 
dist 130=[-1.8298450096936122854 ,1.4157416380774830432 ] 
dist 131=[-1.9434565365527219840 ,1.4260589919042946294 ] 
dist 132=[-2.0391754738948890124 ,1.4282399193380630219 ] 
dist 133=[-2.1161911223089561446 ,1.4265797601052654628 ] 
dist 134=[-2.1551426278829328192 ,1.4035628524637863353 ] 
dist 135=[-2.1745561208757602598 ,1.3951178509268562832 ] 
dist 136=[-2.1774264645574170458 ,1.3732798646382792405 ] 
dist 137=[-2.1565033737052131729 ,1.3636442560581083823 ] 
dist 138=[-2.1462253709457628341 ,1.2117808897232788628 ] 
dist 139=[-2.1217831051032282881 ,1.1868571051261838579 ] 
dist 140=[-2.1103398662245061735 ,1.1264566429116847023 ] 
dist 141=[-2.0442686157138058371 ,1.1091434713687823659 ] 
dist 142=[-2.0269950093427052697 ,1.0105319709779573300 ] 
dist 143=[-1.9775515369911457583 ,.98900894138534182564] 
dist 144=[-1.9614818385123700506 ,.94669106466749388245] 
dist 145=[-1.8494773825112565359 ,1.0185650753591509030 ] 
dist 146=[-1.3774514125617665197 ,1.1810476213136053354 ] 
dist 147=[-1.4037097087799785817 ,1.3100793494404728158 ] 
dist 148=[-1.4201153045377238082 ,1.4272563132250463162 ] 
dist 149=[-1.4290017699220975428 ,1.5279000606145020753 ] 
dist 150=[-1.4299423909542799672 ,1.5909425989055046288 ] 
dist 151=[-1.4187785289157547426 ,1.6385534461960826899 ] 
dist 152=[-1.4168210089851919326 ,1.6776078297437798953 ] 
dist 153=[-1.3416956984548399065 ,1.7080885650293983509 ] 
dist 154=[-1.3267808258641009036 ,1.7759662253983021062 ] 
dist 155=[-1.2850203992174831728 ,1.8353660592159552364 ] 
dist 156=[-1.2738850789462459887 ,1.8846911353867812570 ] 
dist 157=[-1.1852722217326893000 ,1.9237965728903624822 ] 
dist 158=[-1.1648964359302748626 ,1.9424075224165880692 ] 
dist 159=[-1.1339118595731094458 ,1.9495933596818564863 ] 
dist 160=[-1.1235958283775130417 ,1.9481975244290999810 ] 
dist 161=[-.67728911173521498428,1.4808832465825882087 ] 
dist 162=[-.62754564787586928764,1.1788557508169195523 ] 
dist 163=[-.51488853439780362136,1.2978989006169746566 ] 
dist 164=[-.49006043426179828351,1.3921352594485743052 ] 
dist 165=[-.34658048271785707956,1.4772258494841874291 ] 
dist 166=[-.31990112882189444241,1.5499832082237222348 ] 
dist 167=[-.26616796320778828296,1.5949905739210039453 ] 
dist 168=[-.2520281487045728462 ,1.6283238219477058242 ] 
dist 169=[-.34600220389063918399,1.6544851381591436870 ] 
dist 170=[-.42325506510869399266,1.6727382956784760650 ] 
dist 171=[-.50028072145130414827,1.6759170671140322147 ] 
dist 172=[-.59718334894540190897,1.6706816447787091123 ] 
dist 173=[-.69951700895909378761,1.6666200093682502037 ] 
dist 174=[-.81230044578585409488,1.6050202441196095187 ] 
dist 175=[-.95095432081661098884,1.5875365098558208548 ] 
dist 176=[-1.1418086996120107480 ,1.5701827042086294048 ] 
dist 177=[-1.3275676240113865674 ,1.5596630277056394534 ] 
dist 178=[-1.4458840508269818478 ,1.3323134582037385126 ] 
dist 179=[-1.5375247184349496888 ,1.4148948928866759365 ] 
dist 180=[-1.6168021931346291565 ,1.4864495081549781458 ] 
dist 181=[-1.6821329356832084186 ,1.5454088156911306397 ] 
dist 182=[-1.7181040054023295502 ,1.5777168772266875772 ] 
dist 183=[-1.7394963072935918118 ,1.5966618408688974502 ] 
dist 184=[-1.7466374709787944060 ,1.6022799962724889984 ] 
dist 185=[-1.7462627539310916174 ,1.6011211219127583691 ] 
dist 186=[-1.7421226069609785361 ,1.5968582432512329077 ] 
dist 187=[-1.7262319776824383929 ,1.5822675589494715423 ] 
dist 188=[-1.7167673475045834171 ,1.5737435580254026211 ] 
dist 189=[-1.7286336585278390676 ,1.5201839671513655550 ] 
dist 190=[-1.7540501273519927138 ,1.5053933931821925997 ] 
dist 191=[-1.7656118943955567364 ,1.4733749057077620728 ] 
dist 192=[-1.7692368583034054066 ,1.4616551978533271743 ] 
dist 193=[-1.7664105545194013816 ,1.2017971000817274875 ] 
dist 194=[-1.0889317874003647121 ,1.3050358417868286877 ] 
dist 195=[-1.0332750596501999655 ,1.3852897082602252718 ] 
dist 196=[-.90286384851673961121,1.4551807365124364137 ] 
dist 197=[-.87596496852927990208,1.5130765994632394974 ] 
dist 198=[-.69492461354783862481,1.5454527648634012742 ] 
dist 199=[-.66041913689691978853,1.5653422286984000134 ] 
dist 200=[-.59808890004440131122,1.5733986900175915283 ] 
dist 201=[-.58307120518247664647,1.5745359908870184892 ] 
dist 202=[-.33590302972295037449,1.5715393180435080360 ] 
dist 203=[-.30218581511544523287,1.5565826929573428102 ] 
dist 204=[-.22548314415994397586,1.5800429415226089605 ] 
dist 205=[-.21035747263879556939,1.6148619605950080897 ] 
dist 206=[-.1138339439797040265 ,1.6409063864086456260 ] 
dist 207=[-.09650832598287124655,1.6502103065196412738 ] 
dist 208=[-.06377761761782566233,1.6510236003933692935 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 2, 0, 1, 2] 
dist 0=[47.974184854098727949  ,47.974184854098727949  ] 
dist 1=[47.594240296054527311  ,48.237343451843831235  ] 
dist 2=[46.954197174484680788  ,48.410719841437301430  ] 
dist 3=[46.140563525640124356  ,48.518921969367679916  ] 
dist 4=[45.067193015476439482  ,48.521648528703813678  ] 
dist 5=[43.594512124830540815  ,48.453165723101640569  ] 
dist 6=[41.185940630709717730  ,48.398016909123333082  ] 
dist 7=[38.700074638708093203  ,48.019752749528680159  ] 
dist 8=[36.918627450044634722  ,47.869225178740664935  ] 
dist 9=[35.306663032907437819  ,47.675043488532373363  ] 
dist 10=[33.497646633819296894  ,47.573184140304296492  ] 
dist 11=[31.693284970392788956  ,47.242202538593760117  ] 
dist 12=[30.099783811795674891  ,47.111558419723953686  ] 
dist 13=[28.349986511319111069  ,46.818828038970499885  ] 
dist 14=[25.921058934349034463  ,46.602071126881607606  ] 
dist 15=[23.471223132751580948  ,34.691333889731416244  ] 
dist 16=[21.637768539880040188  ,33.627116701091825675  ] 
dist 17=[19.897763615047865803  ,31.033722067213162602  ] 
dist 18=[17.821035497751166256  ,30.649478367730961705  ] 
dist 19=[15.676323212110067962  ,26.794714650286173326  ] 
dist 20=[13.173193771795093699  ,26.069994568516158366  ] 
dist 21=[10.378520546930843916  ,25.230627453597865157  ] 
dist 22=[8.0240071658513842728 ,25.048709916014997796  ] 
dist 23=[4.7226812807839318532 ,18.620529946926103124  ] 
dist 24=[2.5348977580966454743 ,17.816778841516530153  ] 
dist 25=[.73398516427171217721,16.819308503979905888  ] 
dist 26=[-1.0214207610951708159 ,16.378180419890316170  ] 
dist 27=[-2.6230401547909626632 ,14.274219134776201048  ] 
dist 28=[-4.4802499656580006484 ,13.963897494153579597  ] 
dist 29=[-7.3281834708731734492 ,13.488061790336007342  ] 
dist 30=[-9.1440742752636237654 ,13.363494974138225858  ] 
dist 31=[-10.561330409386087479  ,3.1667485008673101340 ] 
dist 32=[-11.816289587648969069  ,2.3144228429987878604 ] 
dist 33=[-12.880001204620230711  ,.41528190685728287349] 
dist 34=[-13.533170730957308776  ,.09015011642487902711] 
dist 35=[-14.015744899700302090  ,-2.1189587308638367360 ] 
dist 36=[-14.398194027291290281  ,-2.4898885605054052231 ] 
dist 37=[-14.695504749303695142  ,-3.1519978041294742178 ] 
dist 38=[-14.837857446830228317  ,-2.3585387081177613635 ] 
dist 39=[-14.897049084206136977  ,-1.0924632095570646632 ] 
dist 40=[-14.883551180617360334  ,-.20240451356776132879] 
dist 41=[-14.771676134369227341  ,.58126343386863407329] 
dist 42=[-14.720323554107423046  ,1.4230787697909718024 ] 
dist 43=[-14.466729861616608042  ,2.2367437222509694002 ] 
dist 44=[-14.424403067104186646  ,2.9082190568020790594 ] 
dist 45=[-10.596231783927015607  ,3.6036754920986093700 ] 
dist 46=[-10.596662145533631823  ,4.5131732893159786522 ] 
dist 47=[-6.9921367557729736213 ,5.3997993938759381240 ] 
dist 48=[-6.7415826222164767127 ,6.0040310625792183934 ] 
dist 49=[-6.2424876065807817026 ,6.5169746325720745846 ] 
dist 50=[-6.1089850588484121097 ,7.0393162252774380915 ] 
dist 51=[-5.6146728661611262332 ,7.5276851543192060954 ] 
dist 52=[-5.5018273444689752672 ,7.9050670613115445028 ] 
dist 53=[-5.2988156983399464333 ,8.2734616513750511400 ] 
dist 54=[-5.2455266003928883848 ,8.7259885066762334146 ] 
dist 55=[-.7496420800978596685 ,9.1485046165634485326 ] 
dist 56=[-.6724395502364582995 ,9.3971163601189745215 ] 
dist 57=[-.57535482602969256155,9.5659819607396381746 ] 
dist 58=[-.56310931002186166932,9.6727052066362602013 ] 
dist 59=[-.58292076323559338967,9.7252708086629903090 ] 
dist 60=[-.64833533668006271636,9.6955772163541649021 ] 
dist 61=[-.75863579563417933592,2.4821478810273093795 ] 
dist 62=[-.95736981944277324064,2.7138183097891266166 ] 
dist 63=[-1.1629921243085552918 ,2.8940899641634707875 ] 
dist 64=[-1.3007819215632256363 ,3.0524883842882983570 ] 
dist 65=[-1.4140321692455529270 ,3.1856224556633897121 ] 
dist 66=[-1.5219279986805435482 ,3.2649716288909110407 ] 
dist 67=[-1.6168496977396904705 ,3.3206005519087908387 ] 
dist 68=[-1.6783979428309964056 ,3.3590038556025884271 ] 
dist 69=[-1.7265337033057996458 ,3.3831778057895137539 ] 
dist 70=[-1.7679461308621885800 ,3.3857331780173311357 ] 
dist 71=[-1.7996603825745444570 ,3.3722236680121361258 ] 
dist 72=[-1.8091407199344237267 ,3.3622236347455158172 ] 
dist 73=[-1.8078333623429438833 ,3.2579274995127757469 ] 
dist 74=[-1.8011487795436373084 ,3.2284485229743707994 ] 
dist 75=[-1.7419216597254571530 ,3.1911134341227422976 ] 
dist 76=[-1.7225038066484525606 ,3.1736920027687576039 ] 
dist 77=[-1.6857231113105645507 ,2.9104693717345843569 ] 
dist 78=[-1.6718839780972292835 ,2.8907045288400303551 ] 
dist 79=[-1.0227480871500444363 ,2.0711092203732902909 ] 
dist 80=[-1.3571561158958063894 ,2.0296981705458542144 ] 
dist 81=[-1.6619876088486569303 ,1.7059452203801284952 ] 
dist 82=[-1.8852953201374945717 ,1.6429733640228002349 ] 
dist 83=[-2.0919804894844581556 ,1.5457060116279021483 ] 
dist 84=[-2.3304784683206281776 ,1.5185536432229744136 ] 
dist 85=[-2.5496326775363098990 ,.98846428609359564349] 
dist 86=[-2.6790882761405315984 ,.9182412528796486225 ] 
dist 87=[-2.7678616032108198168 ,.75797937687703663894] 
dist 88=[-2.8245613865870832465 ,.72491141058527536097] 
dist 89=[-2.8637709859121362646 ,.51790590590362111472] 
dist 90=[-2.8827152275908557792 ,.47970888193117050657] 
dist 91=[-2.8905285077827974593 ,.40706573690302495643] 
dist 92=[-2.8856048513808486399 ,.38908912148131071049] 
dist 93=[-2.6734562007267736391 ,-.25467227836768085334] 
dist 94=[-2.6653321058316987568 ,-.32013555945733868461] 
dist 95=[-2.3261466975858164977 ,-.46637523712435957559] 
dist 96=[-2.3033845574318865081 ,-.49254782282097231927] 
dist 97=[-2.0696021656777276736 ,-.43886404958924988844] 
dist 98=[-2.0209595619253997944 ,-.20976141237230614848] 
dist 99=[-1.9625913949057279446 ,.01165888279303604346] 
dist 100=[-1.9395161661312648953 ,.19471146910616119001] 
dist 101=[-1.4192803965281903527 ,.38472734237844549757] 
dist 102=[-1.3500199166771616585 ,.63396462646349601362] 
dist 103=[-1.2777316553030077625 ,.87753703905178346527] 
dist 104=[-1.2991699637903859472 ,1.0449558583315192850 ] 
dist 105=[-1.3143001373868681378 ,1.1887283096298426500 ] 
dist 106=[-1.3250377537527744854 ,1.3379355785470932257 ] 
dist 107=[-1.3323994567556174584 ,1.4793726384669860561 ] 
dist 108=[-1.3340595682530710695 ,1.5921486604732863904 ] 
dist 109=[-1.3320676846064268380 ,1.7056816158449341473 ] 
dist 110=[-1.3200335017322550553 ,1.8501751033871395982 ] 
dist 111=[.37601138092618721653,1.9854768987851687589 ] 
dist 112=[.42090024511465798471,2.0623216403903029508 ] 
dist 113=[.58471011899185086774,2.1112264897703939558 ] 
dist 114=[.61615532802605106186,2.1349724095212299194 ] 
dist 115=[.6527284106996109022 ,2.1478843165402672926 ] 
dist 116=[.65248037056401359174,2.1535275234626883097 ] 
dist 117=[.63817186997997694732,2.1549801457342240519 ] 
dist 118=[.60519011659747748293,2.1511468440530974557 ] 
dist 119=[.55226728051469674801,2.1388033046164324055 ] 
dist 120=[.45833594237070860127,2.1582718108327292101 ] 
dist 121=[.34521429557085276943,2.1680460453474484226 ] 
dist 122=[.21567527208404451734,2.1713646148756486743 ] 
dist 123=[.04923055782482166838,2.1706078307643642281 ] 
dist 124=[-.21122561360884762648,2.1413045244399766295 ] 
dist 125=[-.4736624186535181025 ,1.9646865675503447988 ] 
dist 126=[-.64801818136410295492,1.9526528248687654940 ] 
dist 127=[-.79135278156275980217,1.3150596188045166053 ] 
dist 128=[-.92995900378480592925,1.2495342955642056351 ] 
dist 129=[-1.0550313880256127250 ,1.0859481952041866340 ] 
dist 130=[-1.1443426541180510819 ,1.0612171798840414334 ] 
dist 131=[-1.2246327412819803396 ,.8053197281609056006 ] 
dist 132=[-1.3136978205173809536 ,.75634928858836458237] 
dist 133=[-1.3937648457869145797 ,.69975266677811169586] 
dist 134=[-1.4381362050562963741 ,.68625715195764435751] 
dist 135=[-1.4649014246467995465 ,.23636512999615154866] 
dist 136=[-1.4746839664510745675 ,.18043924817077460911] 
dist 137=[-1.5319797489758960556 ,.06385887791839789753] 
dist 138=[-1.5917394143819488756 ,.03346744261552916704] 
dist 139=[-1.6377364768957792234 ,-.07789492964740574498] 
dist 140=[-1.6570139911468889877 ,-.09974377525029842141] 
dist 141=[-1.6651637426276349854 ,-.1298325264689069526 ] 
dist 142=[-1.6667180129942384082 ,.03172794942372078455] 
dist 143=[-1.3717722058314992323 ,.1696614982923766999 ] 
dist 144=[-1.3525877708301883541 ,.3114631934034509614 ] 
dist 145=[-1.2952952367090165022 ,.44494928823705758642] 
dist 146=[-1.2866565367322915599 ,.54969421111081455689] 
dist 147=[-1.1625705753585399536 ,.65348748974137236355] 
dist 148=[-1.1358188546020962069 ,.78318011930777817162] 
dist 149=[-1.1119447296655172946 ,.90695703741073065175] 
dist 150=[-1.1060482836387055652 ,.98713977666158033993] 
dist 151=[-.77227682352631398007,1.0507881013231231868 ] 
dist 152=[-.72897631005678195621,1.1085688886657320972 ] 
dist 153=[-.64407725591189256049,1.1582121387694626805 ] 
dist 154=[-.62220021600973611838,1.1893821564350809973 ] 
dist 155=[-.54593911798204687407,1.2130325599229959508 ] 
dist 156=[-.52803059289983378892,1.2326682227661513160 ] 
dist 157=[-.50681001956973521039,1.2467362513912726196 ] 
dist 158=[-.4998278439240372102 ,1.2494321118252006288 ] 
dist 159=[.01882711242935748202,1.2455229804711666201 ] 
dist 160=[-.05520313485872893162,1.2433489504511955778 ] 
dist 161=[-.12233888756525430483,1.1956540771684445570 ] 
dist 162=[-.1976090417668632151 ,1.1823828107058868532 ] 
dist 163=[-.27233881161771118608,1.1716479879982478418 ] 
dist 164=[-.33731806857985558575,1.1646919690399576667 ] 
dist 165=[-.40759582583933631136,1.1254601414224075052 ] 
dist 166=[-.50347284478401801904,1.1210816317325641150 ] 
dist 167=[-.59883652709043143155,1.1223672691943990918 ] 
dist 168=[-.66706556350891388084,1.1790187483317534741 ] 
dist 169=[-.72847917489946462722,1.2221604466180645146 ] 
dist 170=[-.79664156985908724191,1.2581985691756490556 ] 
dist 171=[-.86391868490788077055,1.2869577100478146358 ] 
dist 172=[-.92179894010978033225,1.3010442415565790851 ] 
dist 173=[-.98387752750954815212,1.3071069024702337029 ] 
dist 174=[-1.0679104977438277264 ,1.3065978339524828099 ] 
dist 175=[-1.1476500085861711866 ,.9862760886234965767 ] 
dist 176=[-1.1925920138143368795 ,.97877223055747977264] 
dist 177=[-1.2206412632217762569 ,.88801932504072700661] 
dist 178=[-1.2329573812183769272 ,.86818318305066554313] 
dist 179=[-1.2390356799053291882 ,.84764716198499387821] 
dist 180=[-1.2421892767388034295 ,.83982407054117476564] 
dist 181=[-1.2437998043206094353 ,.59729435177486139793] 
dist 182=[-1.2437226215071982859 ,.56489699396895998595] 
dist 183=[-1.1598450444863849601 ,.49977066251879740024] 
dist 184=[-1.2052764224851861999 ,.48242047887031202237] 
dist 185=[-1.2341587514467038011 ,.41816962957967556419] 
dist 186=[-1.2480339611366810540 ,.40393473735318557749] 
dist 187=[-1.2554284141686383233 ,.3782218873906848367 ] 
dist 188=[-1.2584402092853572367 ,.37167524124782343133] 
dist 189=[-1.2588208226561788541 ,.01978643091717469653] 
dist 190=[-1.2557039308552342832 ,.14480259749086812621] 
dist 191=[-1.1977375674778102446 ,.25119641453644917874] 
dist 192=[-1.1867696447731241442 ,.36002603979129304097] 
dist 193=[-1.1508261488656576490 ,.46212202356198611467] 
dist 194=[-1.1445863600095371776 ,.54467377599537516481] 
dist 195=[-1.0556475608452101219 ,.65741034729860875482] 
dist 196=[-1.0355113992835689407 ,.74354258542378893628] 
dist 197=[-1.0169159883065759623 ,.82670134743392598427] 
dist 198=[-1.0101585591999778135 ,.92757200394599074202] 
dist 199=[-.74331305253924967631,1.0223177978498818327 ] 
dist 200=[-.7077155431295329579 ,1.0810308918674051530 ] 
dist 201=[-.63742761519632755616,1.1246113163914686577 ] 
dist 202=[-.61891640720371770771,1.1589574441385531794 ] 
dist 203=[-.55209889514955766269,1.1847611260965310711 ] 
dist 204=[-.53658947969732753829,1.1942467164527373543 ] 
dist 205=[-.51266559692298727551,1.1970408559685258311 ] 
dist 206=[-.50560184294286651311,1.1961288742426978781 ] 
dist 207=[-.20152814218937016644,1.0853101350377808647 ] 
dist 208=[-.29043073772824993647,1.0868647591397946646 ] 
dist 209=[-.37561040677992223679,1.0818981318153758577 ] 
dist 210=[-.44489360046021752894,1.0793278291129461671 ] 
dist 211=[-.51581706355258467093,1.0361774440153961846 ] 
dist 212=[-.60754371704133875453,1.0242472252406969405 ] 
dist 213=[-.69656588424117718687,1.0132155906317741210 ] 
dist 214=[-.75669449001181670083,1.0061142829989124357 ] 
dist 215=[-.80718460954091714263,.99308334048996400233] 
dist 216=[-.85773520450824337556,1.0186909693111840268 ] 
dist 217=[-.90446656578429311016,1.0380641998741749780 ] 
dist 218=[-.93971229127838374391,1.0454648889597080049 ] 
dist 219=[-.97330122828816933961,1.0471413991000896021 ] 
dist 220=[-1.0134193009335527544 ,1.0451596014593289344 ] 
dist 221=[-1.0492829898783771443 ,.61479656628494943021] 
dist 222=[-1.0658907414141293470 ,.60724271475050115391] 
dist 223=[-1.0739183914790263255 ,-.00781101956287523663] 
dist 224=[-1.0755354986587410524 ,-.06136478161440490562] 
dist 225=[-1.0531174617712386606 ,-.1745519868635469077 ] 
dist 226=[-1.0469404064925090756 ,-.20038015567651130206] 
dist 227=[-1.0429015152834954297 ,-.310095185833365989  ] 
dist 228=[-1.0407222194193084787 ,-.32991372259837458134] 
dist 229=[-1.0170329336278532403 ,-.36337827188472247716] 
dist 230=[-1.0601017004654590081 ,-.37018645161721060419] 
dist 231=[-1.0898843192340414866 ,-.3761582502293343886 ] 
dist 232=[-1.1093366745398765021 ,-.36462026265154679101] 
dist 233=[-1.1220160375949913704 ,-.34070707656623916137] 
dist 234=[-1.1247634623572038382 ,-.29364529511348736301] 
dist 235=[-1.1229588045930153649 ,-.19369945658870255951] 
dist 236=[-1.1174685895342861773 ,-.01709446504416847031] 
dist 237=[-1.0373065512929347749 ,.16152247772015913811] 
dist 238=[-1.0063580862808982848 ,.28258111694793839094] 
dist 239=[-.97226098391850663898,.38469457232575552314] 
dist 240=[-.96717678830653377677,.48769168066515587958] 
dist 241=[-.89379994943355184111,.58340932494176322476] 
dist 242=[-.8770674958429692281 ,.65646691344425199776] 
dist 243=[-.86174693502414513278,.72694071374741162937] 
dist 244=[-.85605580962179913958,.81234564314514307018] 
dist 245=[-.63168818949825624263,.89253266551145561813] 
dist 246=[-.60168563143077094982,.94217924291550545233] 
dist 247=[-.54253465254314517228,.97897753646554003988] 
dist 248=[-.52694728345456830757,1.0078803189131736367 ] 
dist 249=[-.47067026238061049085,1.0295076941660441840 ] 
dist 250=[-.45755382127030650779,1.0397560293203680866 ] 
dist 251=[-.43723584753681057311,1.0448149552911845879 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 1, 1, 0, 1, 2] 
dist 0=[57.321662796689051530  ,57.321662796689051530  ] 
dist 1=[56.949389428926656225  ,57.428875512562866000  ] 
dist 2=[56.270760885192842112  ,57.419380700598275765  ] 
dist 3=[54.939719976560025298  ,57.327143364592422379  ] 
dist 4=[53.487560527520652173  ,57.215816372702822604  ] 
dist 5=[52.325190447778694181  ,57.143276921132144864  ] 
dist 6=[51.148771785050537449  ,57.084137701336117987  ] 
dist 7=[49.640603204435217074  ,56.948727861378635329  ] 
dist 8=[48.028970220672311759  ,52.283489465452393853  ] 
dist 9=[46.439329455883798866  ,51.597250048342632324  ] 
dist 10=[44.556517833527071231  ,50.370726434535805806  ] 
dist 11=[41.773903853942389538  ,50.051515812074524636  ] 
dist 12=[38.896042807059019882  ,48.978525115416924502  ] 
dist 13=[35.874102673647841552  ,48.653134348138043729  ] 
dist 14=[30.417317446783014625  ,48.335374841390033454  ] 
dist 15=[24.940492147863273392  ,48.153661743816940599  ] 
dist 16=[21.241828633800680631  ,34.415561075267216162  ] 
dist 17=[18.128139683366799589  ,34.004685964208891653  ] 
dist 18=[14.987396367828708095  ,33.529058231990665056  ] 
dist 19=[12.059233924598691397  ,33.351035878885855103  ] 
dist 20=[9.7943282325901627842 ,14.799757071381419472  ] 
dist 21=[7.5745002710042962132 ,13.818593680717647685  ] 
dist 22=[4.8258984075238415166 ,12.521289651449333811  ] 
dist 23=[2.2009662282889767288 ,12.232327105648364242  ] 
dist 24=[.47481662045083537563,5.4584343926381054564 ] 
dist 25=[-1.3040895247833945832 ,4.6635599439832468450 ] 
dist 26=[-3.1226313574498194151 ,2.8938075078313598828 ] 
dist 27=[-5.2976247259785427686 ,2.6402563373676616900 ] 
dist 28=[-7.3344030173537651771 ,.67802911462321787738] 
dist 29=[-8.6008598077926099200 ,.37811843922266522449] 
dist 30=[-9.5491138618457253750 ,-.09861488906143561170] 
dist 31=[-10.314897542372361868  ,-.17089844122074103979] 
dist 32=[-10.923809146445294093  ,-5.7611851141634228176 ] 
dist 33=[-11.245544729373620550  ,-5.7834958648874285383 ] 
dist 34=[-11.419709506714346301  ,-5.6067919954309608040 ] 
dist 35=[-11.448411881448107152  ,-5.1185613641292407102 ] 
dist 36=[-9.0727370685170977163 ,-4.5645071943605414162 ] 
dist 37=[-9.2492687919856346055 ,-4.1248913501852112592 ] 
dist 38=[-9.3370021582704654827 ,-3.6887280814856336776 ] 
dist 39=[-9.3453328650097748804 ,-3.1475390010963874569 ] 
dist 40=[-9.0807290585546958110 ,-2.5834554082922312076 ] 
dist 41=[-9.0117606559925244975 ,-2.0554975062568536534 ] 
dist 42=[-8.8841321981759462166 ,-1.4543233929288466022 ] 
dist 43=[-8.8386017830074634230 ,-.59768448941721533129] 
dist 44=[-8.6230285420666246742 ,.26919588327055350498] 
dist 45=[-8.5615023649123620832 ,.91146891408273628244] 
dist 46=[-8.3921218294646938665 ,1.5119135670312380501 ] 
dist 47=[-8.3275652596466549870 ,2.4081235348667119168 ] 
dist 48=[-4.3479218972997905457 ,3.5094720997210385502 ] 
dist 49=[-3.8662256820940267379 ,4.3996969067831035999 ] 
dist 50=[-3.4921435683535069995 ,5.2351103078764000789 ] 
dist 51=[-2.5967421600276493098 ,5.9716948398666446091 ] 
dist 52=[-1.4110955295541877832 ,6.4673759079039702145 ] 
dist 53=[-1.1992629546722442987 ,6.9087519150856960606 ] 
dist 54=[-.86220201784299093327,7.3727665764369646204 ] 
dist 55=[-.78025019187727952358,7.7513904018144978452 ] 
dist 56=[.55382068765366394162,8.0477633705086933148 ] 
dist 57=[.72473508680015643956,8.1833072445878715638 ] 
dist 58=[1.0794365158433373956 ,8.2486711582970578369 ] 
dist 59=[1.1584621753596062333 ,8.2647869144215041916 ] 
dist 60=[1.4728471519787757907 ,8.0591454512621281179 ] 
dist 61=[1.5302548291853594157 ,7.9996868915682033072 ] 
dist 62=[1.4391156670291617482 ,7.6182125341794828602 ] 
dist 63=[1.1583125346703661096 ,5.5879191646594389411 ] 
dist 64=[.83395709651087544575,4.4839867379588253615 ] 
dist 65=[.48101652954677497092,4.4906324339168371659 ] 
dist 66=[.03962980663638755649,4.4692408024552090502 ] 
dist 67=[-.6378194240786885909 ,4.4628665953090250738 ] 
dist 68=[-1.3162682761832660910 ,2.5085072868270592175 ] 
dist 69=[-1.7616788706837448813 ,2.4049542172688512390 ] 
dist 70=[-2.1217686003119949267 ,2.2390152014152525022 ] 
dist 71=[-2.4596984718205797513 ,2.1951839545792540239 ] 
dist 72=[-2.7576945132105937176 ,1.8883264633513138443 ] 
dist 73=[-2.9584160931752788087 ,1.9660926909395665657 ] 
dist 74=[-3.1264897302346876272 ,2.0477669591653600237 ] 
dist 75=[-3.2942152019105729868 ,2.1560287438133873354 ] 
dist 76=[-3.4400457669290054146 ,2.2728687181906410368 ] 
dist 77=[-3.5207258056349294883 ,2.3887290498856488703 ] 
dist 78=[-3.5973435345011496098 ,2.5257838440141406996 ] 
dist 79=[-3.8313578440946249871 ,2.7271230031355517847 ] 
dist 80=[-3.9717488349012446799 ,2.9239489747836538600 ] 
dist 81=[-4.0711618031189565373 ,3.0429788669198630868 ] 
dist 82=[-4.1414970618500001279 ,3.1274137769090578306 ] 
dist 83=[-4.1884873853610994915 ,3.1862210463919856513 ] 
dist 84=[-4.1969337311782974834 ,3.2255127750736633135 ] 
dist 85=[-4.1865798800639365665 ,3.2328149182418149477 ] 
dist 86=[-4.1763857554477471982 ,3.2266985660874786237 ] 
dist 87=[-4.0269192236333581243 ,3.2181711767364471431 ] 
dist 88=[-3.9943452991116231210 ,3.0288204046225732715 ] 
dist 89=[-3.9567398783494415972 ,2.9908633238201008231 ] 
dist 90=[-3.9608861955414840805 ,2.9020409226750269603 ] 
dist 91=[-3.9540494977813385647 ,2.8701401835978127350 ] 
dist 92=[-3.8418478804285070034 ,2.7104065150290098121 ] 
dist 93=[-3.8064810647484592643 ,2.6726921028637817975 ] 
dist 94=[-3.7709436775507008476 ,3.0077078874310456069 ] 
dist 95=[-3.7485173651158372027 ,3.5997307275596208988 ] 
dist 96=[-2.6125148346138508898 ,3.9742898992878994421 ] 
dist 97=[-2.4886629534102699424 ,4.2615808545465373091 ] 
dist 98=[-2.2128285538847737133 ,4.5052430057217354853 ] 
dist 99=[-2.1416785945214241942 ,4.7025071094960616927 ] 
dist 100=[-1.7960855377459095325 ,4.8045906130283724929 ] 
dist 101=[-1.7294688069282765436 ,4.8582255274483677812 ] 
dist 102=[-1.5786031260951295907 ,4.8681773904782816992 ] 
dist 103=[-1.5388540501821496024 ,4.8319803236012923283 ] 
dist 104=[-1.1675127110110576848 ,4.8093296565742133567 ] 
dist 105=[-1.1057279189664702232 ,4.7677846606233869771 ] 
dist 106=[-.98800634496631719429,4.7484284335876204701 ] 
dist 107=[-.95817797239069080185,4.7987221396599984569 ] 
dist 108=[-.85837737704555147544,4.8269779257268592544 ] 
dist 109=[-.83302537346904639196,4.8425818831160269273 ] 
dist 110=[-.81223761119061455655,4.8450378821668092732 ] 
dist 111=[-.80993202343819737003,2.3725408826090072827 ] 
dist 112=[-.81642799156279427185,2.1470413511398320334 ] 
dist 113=[-1.1233443141383642952 ,1.7739363978812663877 ] 
dist 114=[-1.6157522256850229876 ,1.7296795571735911640 ] 
dist 115=[-2.0622975203891760693 ,1.7208684461035438214 ] 
dist 116=[-2.3846464546345442944 ,.86684076984570522888] 
dist 117=[-2.6778512900209357038 ,.84414878066582571318] 
dist 118=[-3.0080585765383605888 ,.78981158590650011278] 
dist 119=[-3.3132092567830592276 ,.77664250723090132808] 
dist 120=[-3.5063988814575573022 ,.69385681033615308593] 
dist 121=[-3.6546171019312253812 ,.67682792902093453   ] 
dist 122=[-3.7802686549624447719 ,.64508963947824085076] 
dist 123=[-3.8818408251307101120 ,.63656046155695201887] 
dist 124=[-3.9339493752166691412 ,.48951619936161196101] 
dist 125=[-3.9598287149608353339 ,.46893044203988110872] 
dist 126=[-3.9599706163532259219 ,.41811776494768858691] 
dist 127=[-1.4940516122904216645 ,.40948289524672965857] 
dist 128=[-1.5279810716023651889 ,.33090307545532708559] 
dist 129=[-1.5415377937561062791 ,.31570849975850173327] 
dist 130=[-1.5457089023736254475 ,.29542733815305236946] 
dist 131=[-1.5429274929737870960 ,.28880885336674311956] 
dist 132=[-.85302194711133754635,.09566900035871383072] 
dist 133=[-.80183391227137474016,.07338220690554011521] 
dist 134=[-.68299627268517540374,.02440867327494646032] 
dist 135=[-.65916467498339235068,.01354874507660850572] 
dist 136=[-.5021915618099468996 ,.01249943214411524027] 
dist 137=[-.48139546308333941684,.05303757809678883677] 
dist 138=[-.4456684545778387814 ,.09977562593274101558] 
dist 139=[-.43700891318160513646,.17580590958064888806] 
dist 140=[-.28095942016880341094,.25110616592110288649] 
dist 141=[-.3120366328291376165 ,.33613339648380168046] 
dist 142=[-.34734953742003146967,.45673578482941255019] 
dist 143=[-.38636226498921849883,.57506968360244007353] 
dist 144=[-.42473146495308424165,.65104444649552481707] 
dist 145=[-.45746486815805588879,.71059401859905396904] 
dist 146=[-.49228859559009777299,.76336202050262394294] 
dist 147=[-.59413011206892642925,.80778724666712286219] 
dist 148=[-.70052367002819793214,.9146882785618330518 ] 
dist 149=[-.76899135958775065806,.99788400851318889361] 
dist 150=[-.8227345323815755079 ,1.0621537255375625728 ] 
dist 151=[-.87036385944068997842,1.1174962432217287604 ] 
dist 152=[-.91034543713008380175,1.1629525943956506822 ] 
dist 153=[-.93356438490960703817,1.1877607160050763817 ] 
dist 154=[-.94889788213064652725,1.2022510110096847318 ] 
dist 155=[-.9574012361737300896 ,1.2065275542729385292 ] 
dist 156=[-.96169418407130395571,1.2055729723141513688 ] 
dist 157=[-.9607253811257655557 ,1.2024792009791068138 ] 
dist 158=[-.95596589901702318664,1.1910008106395147054 ] 
dist 159=[-.95198671821222550499,1.1843530738641706440 ] 
dist 160=[-.92451994641087813089,1.1427352714843382192 ] 
dist 161=[-.91652549387105664287,1.1312958705363335565 ] 
dist 162=[-.89799411819334235827,1.1081901229457481920 ] 
dist 163=[-.89077648979265817209,1.1001116159586399709 ] 
dist 164=[-.61524806392911977834,-.38421881207091440048] 
dist 165=[-.61829146840301335139,-.42654093621522345777] 
dist 166=[-.61769295290423167444,-.43474170909274719917] 
dist 167=[-.63083537737877639647,-.45821243344414083031] 
dist 168=[-.66683292449748253723,-.4170161272055684685 ] 
dist 169=[-.6921319971020167634 ,-.37048074826024570132] 
dist 170=[-.7094566203016102125 ,-.30449460190972241099] 
dist 171=[-.72169495496219670173,-.23106040372198043801] 
dist 172=[-.72669303319832632587,-.15479978045415633003] 
dist 173=[-.72739643490138339595,-.06186829354031920697] 
dist 174=[-.72650917436248187968,.07810000427167221580] 
dist 175=[-.59592688386473836986,.21798682143847678381] 
dist 176=[-.58177320531053174512,.31059238005460804948] 
dist 177=[-.57762122595271053843,.38628260986258701761] 
dist 178=[-.56442930207966934027,.45865747631229794472] 
dist 179=[-.56054128044892592699,.52333986596787518569] 
dist 180=[-.45165394139908396006,.56832726590570641054] 
dist 181=[-.43003345967454084598,.60748736882061932909] 
dist 182=[-.4241256931158705502 ,.64890953290672822067] 
dist 183=[-.30317090430203726514,.68602386112436666073] 
dist 184=[-.28675198875370923484,.70799116690712058139] 
dist 185=[-.24809697987805924693,.7230546507301762146 ] 
dist 186=[-.24047677198034532618,.73261865521910439311] 
dist 187=[-.18664915369534508832,.73798317026125572325] 
dist 188=[-.17648420611647527243,.73864049932901811036] 
dist 189=[-.15874192938302552946,.73296346806591334643] 
dist 190=[-.15457566258049334452,.73184066968387228395] 
dist 191=[-.1820145792604943449 ,.62951071293541807677] 
dist 192=[-.20787999796965770739,.65780535933205431081] 
dist 193=[-.22900224750707002993,.67621792353878549788] 
dist 194=[-.24915235736004732513,.68597789876449012709] 
dist 195=[-.26711290983536106222,.69185682453985723342] 
dist 196=[-.27949590874050988799,.69477704640969425698] 
dist 197=[-.29014813377917318657,.69609522042689817557] 
dist 198=[-.30119885588009054517,.69557681693114803504] 
dist 199=[-.31058631362399160275,.60310014887827223044] 
dist 200=[-.31459991586501694888,.58926841316228459785] 
dist 201=[-.31635944720531027813,.56522989325906866594] 
dist 202=[-.31675741413834357086,.55875336269766743067] 
dist 203=[-.30799070865421074839,.5376195721946429677 ] 
dist 204=[-.30573201345263260863,.53075586321111434528] 
dist 205=[-.30438817033767530885,.5246275029193763519 ] 
dist 206=[-.30394242385551757766,.52090717942059922522] 
dist 207=[-.23971960074380912475,.08333116544968140227] 
dist 208=[-.23156870300507706946,.12640855691545760705] 
dist 209=[-.23517387009284202754,.16166141016156526605] 
dist 210=[-.2643262410181512119 ,.19545546398273376796] 
dist 211=[-.30341151850544396139,.22572390817356489619] 
dist 212=[-.34107053234116558262,.24690381988291058099] 
dist 213=[-.38165240285083032863,.26547867893115052653] 
dist 214=[-.44233490547108684735,.28534756985128447337] 
dist 215=[-.49961591345691735325,.30324091182065989561] 
dist 216=[-.53557380602626436847,.31393137474978981137] 
dist 217=[-.56280038532716003638,.32138908159487101353] 
dist 218=[-.58523173292725649992,.32638334078623777186] 
dist 219=[-.60286368355475961448,.3294167598921848089 ] 
dist 220=[-.61093413148659109777,.32993302963769467423] 
dist 221=[-.61439741123662363026,.32783254779409543784] 
dist 222=[-.61408697977702180655,.32560075718160087284] 
dist 223=[-.38846306158831521136,.21604738548973973309] 
dist 224=[-.37058423472735630904,.205106362303482017  ] 
dist 225=[-.36608554408659283726,.17961628651369111507] 
dist 226=[-.35637530660468674441,.16642433373962982267] 
dist 227=[-.35302751395298002961,.17324255190006963597] 
dist 228=[.11751852422571973956,.21000120648812296613] 
dist 229=[.13834303300322362604,.24747725161552832002] 
dist 230=[.14313020647681062006,.29573197203572952983] 
dist 231=[.15554197328384079393,.3424497411855135878 ] 
dist 232=[.14974022533671345086,.37379204987089984751] 
dist 233=[.1380313519076483719 ,.3998763292577206645 ] 
dist 234=[.11519971109822482069,.42560881708656334395] 
dist 235=[.08696635182772830995,.44918434265408295468] 
dist 236=[.05369862455578846554,.47534036108748754428] 
dist 237=[.01037254155624147709,.49678195735774731794] 
dist 238=[-.05800483600355619646,.51155551925958345243] 
dist 239=[-.12734291872537571632,.5237464720009991853 ] 
dist 240=[-.1745032278933487646 ,.53227790534050594819] 
dist 241=[-.21444440104474536743,.53635460360463525741] 
dist 242=[-.25496994331805450678,.53663837943974574156] 
dist 243=[-.29276331252193213314,.5272974937726406805 ] 
dist 244=[-.32179992517882080043,.5239542362541117563 ] 
dist 245=[-.34997960075904136394,.52111457809825390962] 
dist 246=[-.38435255125611543368,.5182930399474068068 ] 
dist 247=[-.41671036636505265415,.42995772180743431379] 
dist 248=[-.43684728194559732997,.41714146115722295422] 
dist 249=[-.4518844795712991794 ,.392473311015516441  ] 
dist 250=[-.4638886561394138541 ,.38574825798089615758] 
dist 251=[-.4730194532494443337 ,.36067014085921108619] 
dist 252=[-.47658847132382116091,.35436509357753884962] 
dist 253=[-.47738152229476627118,.34297578940183275545] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 2, 2, 1, 1, 2] 
dist 0=[47.276878256860025740  ,47.276878256860025740  ] 
dist 1=[46.546155505562312408  ,47.741425029781956956  ] 
dist 2=[45.478231862499099496  ,48.072257957271925086  ] 
dist 3=[43.666932248190942805  ,48.268872174714931179  ] 
dist 4=[41.772689665416512092  ,48.405275343576031842  ] 
dist 5=[40.373471739014833140  ,48.495430707778257142  ] 
dist 6=[39.065010522611373843  ,48.529899251703939733  ] 
dist 7=[37.533160703835579387  ,48.497346022055668392  ] 
dist 8=[35.969359111917511167  ,47.985787370921190844  ] 
dist 9=[34.533174707977370904  ,46.609164223167252045  ] 
dist 10=[32.910796946138198383  ,46.288127086896115647  ] 
dist 11=[30.603103455367299959  ,45.775453677486991244  ] 
dist 12=[28.252285612270243443  ,45.611222284842752337  ] 
dist 13=[26.457539003071552610  ,45.108690095172720014  ] 
dist 14=[24.720254555655229936  ,44.927781078345212953  ] 
dist 15=[22.598784777472738394  ,44.670126054045314005  ] 
dist 16=[20.383079388204223000  ,43.773734323360970766  ] 
dist 17=[18.269130825175278030  ,30.173975049793537176  ] 
dist 18=[15.816403140610589003  ,28.953117692633338427  ] 
dist 19=[12.246907997986278059  ,26.020813699780353198  ] 
dist 20=[8.7037515529831170992 ,25.591049424544494447  ] 
dist 21=[6.3561622460840364502 ,21.409171184751454271  ] 
dist 22=[4.4252876616413239649 ,20.641927245294330070  ] 
dist 23=[2.5470219845502369189 ,19.724667102520818147  ] 
dist 24=[.8366447412834725627 ,19.540619406225460724  ] 
dist 25=[-.42356471329772919035,15.633338552380255193  ] 
dist 26=[-1.6012604126448451453 ,13.159878654481084155  ] 
dist 27=[-2.9822493597196303948 ,11.779851679835925981  ] 
dist 28=[-4.2669486438245533124 ,10.485023609537691803  ] 
dist 29=[-7.2081000254948766697 ,9.0290579236857934678 ] 
dist 30=[-10.114062503321983432  ,8.7433201521774965934 ] 
dist 31=[-11.939057015946753331  ,8.2886967946146375644 ] 
dist 32=[-13.331360667282784929  ,8.1824643809678095501 ] 
dist 33=[-14.508386040587955533  ,.5919243042552102746 ] 
dist 34=[-15.466020451124596884  ,-.0438291584190719706 ] 
dist 35=[-15.981884639962619983  ,-1.4085621502445849148 ] 
dist 36=[-16.277881402474638274  ,-1.6684725446181819865 ] 
dist 37=[-16.357556274434817903  ,-1.6852125441586373765 ] 
dist 38=[-16.357194090856403881  ,-1.1801666114857405249 ] 
dist 39=[-16.333338238729458984  ,-.5973886896735847243 ] 
dist 40=[-16.290714950025401595  ,-.0115760346193114174 ] 
dist 41=[-16.227191412684110747  ,.5057962408979449829 ] 
dist 42=[-16.125205178122873778  ,1.0708684097576402101 ] 
dist 43=[-16.044389632538227969  ,1.8471621567405202445 ] 
dist 44=[-15.909563650752478950  ,2.6195713482209062737 ] 
dist 45=[-15.846297222486560053  ,3.1692256644345844821 ] 
dist 46=[-9.4333914672411413542 ,3.6601273571438452454 ] 
dist 47=[-9.4459865751552425420 ,4.1982010977435975568 ] 
dist 48=[-9.4271733515056874801 ,4.7245684181805892438 ] 
dist 49=[-3.7634451852355138901 ,5.1687955454810667272 ] 
dist 50=[-3.0249571953975365782 ,5.6374105595257125081 ] 
dist 51=[-2.9921682298582114031 ,6.2611024737600968808 ] 
dist 52=[-.3368334399188183099 ,6.8676339463511382513 ] 
dist 53=[-.08695288330887134856,7.2677859218261935937 ] 
dist 54=[.9944762823488630735 ,7.5929609368044225544 ] 
dist 55=[1.2672808478675599250 ,7.9003407705757405310 ] 
dist 56=[1.3220620615962585210 ,8.1723723362005838966 ] 
dist 57=[2.3553207828390175586 ,8.3565049311228304322 ] 
dist 58=[2.4778102243996303873 ,8.5992214485650429882 ] 
dist 59=[2.5391836001278363650 ,8.7630686602461944841 ] 
dist 60=[2.4305499240730936840 ,8.8425233551046008370 ] 
dist 61=[2.2667643829974114501 ,8.8463049707704472701 ] 
dist 62=[2.0382366708623768982 ,4.4482891947087666340 ] 
dist 63=[1.7193263912541258003 ,4.4915955058455604279 ] 
dist 64=[1.1949692142369623932 ,4.5210255618416946747 ] 
dist 65=[.6591440148139277289 ,4.5258541039923791445 ] 
dist 66=[.2944615224076128890 ,4.5137036102377015870 ] 
dist 67=[-.0137438183352339901 ,4.5017783016346988501 ] 
dist 68=[-.3243230726401071699 ,3.5773285330454955653 ] 
dist 69=[-.6116795347699417986 ,3.5510845696346382931 ] 
dist 70=[-.8272591695742833362 ,2.6229558339824706208 ] 
dist 71=[-1.0309721945095244267 ,2.5015686180774824325 ] 
dist 72=[-1.2709824740396869875 ,2.2555499559257628520 ] 
dist 73=[-1.4959152409973930741 ,2.1904857164558548570 ] 
dist 74=[-1.6394910205498330058 ,1.9513430813185359427 ] 
dist 75=[-1.7505631750311883363 ,1.8995288780096157759 ] 
dist 76=[-1.8458710059953442581 ,1.8093085609167160913 ] 
dist 77=[-1.9234377135886032607 ,1.7873189734589688994 ] 
dist 78=[-1.9637557384084746541 ,.2659046500466932362 ] 
dist 79=[-1.9844037479307310384 ,.2084377829469007372 ] 
dist 80=[-1.9862013612785010659 ,.1950558731862238070 ] 
dist 81=[-2.0445761737060342505 ,-.3631646439752568869 ] 
dist 82=[-2.0965404715627935849 ,-.3614273019302238378 ] 
dist 83=[-2.2957264068064171934 ,-.3439498656207668195 ] 
dist 84=[-2.4986811481081138026 ,-.3006131499410474700 ] 
dist 85=[-2.7375371211692402778 ,-.2441809506648783455 ] 
dist 86=[-2.9587014576476883968 ,-.1744446812638543693 ] 
dist 87=[-3.0910101486984052247 ,-.0817765123143922498 ] 
dist 88=[-3.1837495943802661593 ,.0661545740972821376 ] 
dist 89=[-3.2469087007179178042 ,.2224795989050851100 ] 
dist 90=[-3.2901547800550348955 ,.3486435362434260033 ] 
dist 91=[-3.3033981926218401870 ,.47665815962869485469] 
dist 92=[-3.3020834863415114262 ,.64037816027926681923] 
dist 93=[-3.2940066782893544316 ,.81420569681114151566] 
dist 94=[-2.0265893165594391380 ,.98255084725784435955] 
dist 95=[-1.9917062002177374611 ,1.1788707344755451496 ] 
dist 96=[-1.9772593795046732735 ,1.4643106168684818846 ] 
dist 97=[-1.7254141113525354503 ,1.7444298767520193970 ] 
dist 98=[-1.6991862553315086205 ,1.9195176702866785271 ] 
dist 99=[-1.6867948010621711342 ,2.0509203683101892320 ] 
dist 100=[-1.3798996732085196917 ,2.1567346758224050260 ] 
dist 101=[-1.4365937164030545828 ,2.2400665370283422988 ] 
dist 102=[-1.4799531785672610995 ,2.2817719768242471735 ] 
dist 103=[-1.5219135699839719007 ,2.3016406390852686462 ] 
dist 104=[-1.5729961477531717570 ,2.3041026488933190316 ] 
dist 105=[-1.6210662254750568022 ,2.1897532806356960560 ] 
dist 106=[-1.6509846886855636316 ,2.1644672543725697507 ] 
dist 107=[-1.6733051421383010217 ,2.1459163946774653273 ] 
dist 108=[-1.6910228764401325226 ,2.2007124714857278110 ] 
dist 109=[-1.7042944978900492583 ,2.2517972868337237670 ] 
dist 110=[-1.7088446686053862701 ,2.2839455892723625578 ] 
dist 111=[-1.7077254082625631359 ,2.2987736145194016259 ] 
dist 112=[-1.7034620628823708815 ,2.3025787367673246250 ] 
dist 113=[-1.6838458337248653060 ,2.2997893119602047164 ] 
dist 114=[-1.6761355883539181881 ,2.2758821143028521701 ] 
dist 115=[-1.6429705016724193328 ,2.2677733673049513443 ] 
dist 116=[-1.6360433673706578585 ,1.8810426777522856303 ] 
dist 117=[-1.5284199799680941871 ,1.8743030811953499105 ] 
dist 118=[-1.5021112820939464413 ,1.4138549979384723020 ] 
dist 119=[-1.4790264379867708716 ,1.3532998182212046740 ] 
dist 120=[-1.4681472022666778544 ,1.2358489975239110297 ] 
dist 121=[-1.0797185846779019978 ,1.2055066836724923996 ] 
dist 122=[-1.0263640421598892321 ,1.1001142645306159717 ] 
dist 123=[-.9224440168343706070 ,1.0744519224186160387 ] 
dist 124=[-1.0246549390294806408 ,1.0447227659306365654 ] 
dist 125=[-1.1290867141788084891 ,1.0336593822340068426 ] 
dist 126=[-1.2076609240964321141 ,.22873592684601755355] 
dist 127=[-1.2715281219901111006 ,.31114796834889629294] 
dist 128=[-1.3220279531204847392 ,.43847373990415982256] 
dist 129=[-1.3472456568504137464 ,.56621889773481245192] 
dist 130=[-1.3597252408673958024 ,.65030171247142558688] 
dist 131=[-1.3612126167472519848 ,.71841868135940633023] 
dist 132=[-1.4791429081954456747 ,.78245235144431556131] 
dist 133=[-1.5729034775214144815 ,.83886374534509426674] 
dist 134=[-1.6436560967529093901 ,.87656201072771304801] 
dist 135=[-1.7016130439873245895 ,.90771064687995924591] 
dist 136=[-1.7470002948538423872 ,.9379795745339324086 ] 
dist 137=[-1.7675793052863013460 ,.96307906043784293102] 
dist 138=[-1.7756753715263210892 ,.97359920736155695761] 
dist 139=[-1.7747100630005979767 ,.97749927271640858929] 
dist 140=[-1.7446314768806579741 ,.97619371861970526035] 
dist 141=[-1.7348993623898917809 ,.95342839640661832534] 
dist 142=[-1.7034647605634134568 ,.94518931246998753298] 
dist 143=[-1.6917640364335318054 ,.9367610467898503052 ] 
dist 144=[-1.6070695231869058740 ,.93122510171866593684] 
dist 145=[-1.5857718091782158953 ,.88184096364627503559] 
dist 146=[-1.5508639224217255753 ,1.0262151162254572601 ] 
dist 147=[-1.5394253074666118659 ,1.2305087254804265806 ] 
dist 148=[-.08592290813434092773,1.4293829800924122755 ] 
dist 149=[.00476396227344274422,1.5521282330088853848 ] 
dist 150=[.02342585656055719036,1.6426583434199633671 ] 
dist 151=[.04565122324599689258,1.7129458254116349432 ] 
dist 152=[.0482858581095862128 ,1.7675887997990132194 ] 
dist 153=[.0431521024217732455 ,1.8118894352751004702 ] 
dist 154=[.0267880056538866675 ,1.8804397664173042734 ] 
dist 155=[-.0009248348939005469 ,1.9445196485330154364 ] 
dist 156=[-.0513526570357634488 ,1.9979425941924448120 ] 
dist 157=[-.1125003492755752475 ,2.0239569855160068667 ] 
dist 158=[-.1829964018080319391 ,2.0348768679347414681 ] 
dist 159=[-.2738228374840802731 ,2.0353748161275826946 ] 
dist 160=[-.4161084514638331500 ,2.0337456843483260247 ] 
dist 161=[-.5599083931700375899 ,2.0356398235155583441 ] 
dist 162=[-.6567790190738702730 ,2.0222941685343605238 ] 
dist 163=[-.7377967537371216378 ,2.0180776294099305892 ] 
dist 164=[-.8183299389051115573 ,1.4728763597292520193 ] 
dist 165=[-.8923615741740330849 ,1.4886374283856844113 ] 
dist 166=[-.9474327901845590078 ,1.4963456091388690516 ] 
dist 167=[-.9991501067407064794 ,1.4996469854141408955 ] 
dist 168=[-1.0788405285401905217 ,1.4978137860865253399 ] 
dist 169=[-1.2008124596892298864 ,1.3161069341948688700 ] 
dist 170=[-1.3090569962011204883 ,1.2882640901775063927 ] 
dist 171=[-1.4268764842424410601 ,1.2399120749683128535 ] 
dist 172=[-1.5341533457196103753 ,1.2266894643255329426 ] 
dist 173=[-1.6003191210548118626 ,1.1826244623917932798 ] 
dist 174=[-1.6490423411500986736 ,1.1683795739633049968 ] 
dist 175=[-1.6867045679762488842 ,1.1533118202416551188 ] 
dist 176=[-1.7143827560928053683 ,1.1450355113946382923 ] 
dist 177=[-1.7232597096847223930 ,.1609615665399919983 ] 
dist 178=[-1.7236446180738525113 ,.0790982425768849189 ] 
dist 179=[-1.7189065425193674492 ,0                     ] 
dist 180=[-1.0802623808929422504 ,-.1371306611391271309 ] 
dist 181=[-.9991635378969339871 ,-.3428413437671385654 ] 
dist 182=[-.980592048967567749  ,-.2799136206804151634 ] 
dist 183=[-.95864274838685112267,-.1723528976385399995 ] 
dist 184=[-.94905684154672050987,-.0647857380661766431 ] 
dist 185=[-1.0378216846596316732 ,.0299866742153295035 ] 
dist 186=[-1.0972709644222729172 ,.13354680773903428133] 
dist 187=[-1.1456529036140846440 ,.27619235875929107701] 
dist 188=[-1.1915917800318971708 ,.41873860298709521992] 
dist 189=[-1.2324512049726572501 ,.52190459660449042593] 
dist 190=[-1.2605584382914154978 ,.61600033891804358988] 
dist 191=[-1.2847097952043450245 ,.722347103795425182  ] 
dist 192=[-1.3097788191180809377 ,.82846531891746681454] 
dist 193=[-1.3318833740871137156 ,.92165185656646859909] 
dist 194=[-1.3401226825287301501 ,1.0232478987381063297 ] 
dist 195=[-1.3413048370216460241 ,1.1629372434818771154 ] 
dist 196=[-1.3382067815058902116 ,1.2975419757268190344 ] 
dist 197=[-1.3070320121034107901 ,1.3788437329887987820 ] 
dist 198=[-1.2965644251578629892 ,1.4367025909488369561 ] 
dist 199=[-1.2779234818404405156 ,1.4777331994643046332 ] 
dist 200=[-1.2711031621038163617 ,1.5078525308926035931 ] 
dist 201=[-1.0851322793352607957 ,1.5221575847115823808 ] 
dist 202=[-1.0570181816368920079 ,1.5276274657610361148 ] 
dist 203=[-.9954592353295072224 ,1.5264128020827794564 ] 
dist 204=[-.9767050585812493097 ,1.4472556260577425140 ] 
dist 205=[-.8940061495806559392 ,1.4388128667132907364 ] 
dist 206=[-.8767893386109767266 ,1.4363104613616110166 ] 
dist 207=[-.8312132153621559921 ,1.4345226620937883914 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 2, 2, 1, 0, 1] 
dist 0=[42.951899865943549626  ,42.951899865943549626  ] 
dist 1=[42.653817278002760744  ,43.389450269771733517  ] 
dist 2=[41.900902964246226736  ,43.883083084697112002  ] 
dist 3=[40.716163706183394925  ,44.182145018884367776  ] 
dist 4=[38.768570980356527273  ,44.396424859173881088  ] 
dist 5=[36.758769357008127991  ,44.551336818819832514  ] 
dist 6=[35.325504019597773817  ,44.652207031079311829  ] 
dist 7=[34.036315501033626686  ,44.650505247339102184  ] 
dist 8=[32.601735510379104003  ,44.139384710589295659  ] 
dist 9=[31.178152396382861532  ,43.998049307858867741  ] 
dist 10=[29.932681258559242152  ,43.800299089362620332  ] 
dist 11=[28.574775293046452280  ,43.708298545060000968  ] 
dist 12=[26.701738074062248317  ,43.385961951431036800  ] 
dist 13=[24.817150097655497676  ,43.267261282644331640  ] 
dist 14=[23.412907202629752571  ,42.991178840692507279  ] 
dist 15=[22.085778522686292979  ,42.807126512334288165  ] 
dist 16=[20.508966287824159203  ,32.358731051636786809  ] 
dist 17=[18.883192097542352669  ,31.416410322124751043  ] 
dist 18=[17.360112769518667870  ,29.143097426478124215  ] 
dist 19=[15.612520529582581698  ,28.781660182847442895  ] 
dist 20=[13.089073829676552812  ,25.452179559999509789  ] 
dist 21=[10.589871006139545335  ,24.823055241801174529  ] 
dist 22=[8.9390371844143861867 ,24.024091798872279313  ] 
dist 23=[7.5843641531336061457 ,23.786549537552887784  ] 
dist 24=[6.2687825075666461291 ,18.388975338062502514  ] 
dist 25=[5.0695177101131409038 ,17.694880545812964071  ] 
dist 26=[3.6731113521768348490 ,16.247422727993115287  ] 
dist 27=[1.9883283987742612804 ,15.862306809793362690  ] 
dist 28=[.10663909282405570454,14.402447005666937467  ] 
dist 29=[-2.5495573191030833628 ,14.116152300169999570  ] 
dist 30=[-5.1482591471174480296 ,13.520961070810236436  ] 
dist 31=[-6.8003611064042967404 ,13.360870123159045600  ] 
dist 32=[-8.0850253430041229824 ,4.8869658865214952019 ] 
dist 33=[-9.2152597939016295447 ,4.1307600964241923882 ] 
dist 34=[-10.168791560912819497  ,2.4298086833744322421 ] 
dist 35=[-10.747414238683783195  ,2.1342092377293251582 ] 
dist 36=[-11.167208062817127766  ,.07966317250725689217] 
dist 37=[-11.486426419189006301  ,-.27566086979896977354] 
dist 38=[-11.736375187458691751  ,-.89448671541465682635] 
dist 39=[-11.879295593713353822  ,-1.0239653807030467388 ] 
dist 40=[-11.974259758566092066  ,-1.2281210190702974044 ] 
dist 41=[-12.031991350622319884  ,-1.1997341803640709440 ] 
dist 42=[-12.063710190280482007  ,-1.1434829187496543275 ] 
dist 43=[-12.054444086299420150  ,-1.0574972988533382501 ] 
dist 44=[-12.014201232735474335  ,-.91026795777709120167] 
dist 45=[-11.979779750403619574  ,-.75275286751376217263] 
dist 46=[-11.348714531497699800  ,-.62557364443713808316] 
dist 47=[-11.345819180609911694  ,-.49701913156358642006] 
dist 48=[-6.1315478175552404507 ,-.3337592855977198383 ] 
dist 49=[-5.7750938932350056555 ,-.16109930155127535114] 
dist 50=[-4.9061870162037373467 ,.00511547832160585533] 
dist 51=[-4.7774187122162104423 ,.22067584160616468379] 
dist 52=[-3.5064957432784408280 ,.9462104796829350996 ] 
dist 53=[-3.2725843195459819812 ,1.8496876155296547206 ] 
dist 54=[-2.9885790604736743382 ,2.7115951116619887265 ] 
dist 55=[-2.9285081627590005165 ,3.2712672483856363964 ] 
dist 56=[-1.0240878335984233819 ,3.7176007193261320978 ] 
dist 57=[-.79458315843568162821,4.1271325302062551953 ] 
dist 58=[-.30585016400857191209,4.4829704173421900095 ] 
dist 59=[-.20031760064937903669,4.7150517490570813084 ] 
dist 60=[.28642959834280271705,4.9020035729363304713 ] 
dist 61=[.37111642752047043651,5.0778942438532154553 ] 
dist 62=[.5254633355442056974 ,5.2231811681092516007 ] 
dist 63=[.55632753804634687847,5.2879565104206192204 ] 
dist 64=[1.2437646509209356266 ,5.3160315031442374513 ] 
dist 65=[1.1435380585424209343 ,5.3144254352117512696 ] 
dist 66=[1.0260532849218829769 ,5.2204632954226309200 ] 
dist 67=[.87342263896161037476,5.1849380954770433730 ] 
dist 68=[.63290032918697380708,5.1537274683374974962 ] 
dist 69=[.38886089347704179372,5.1290861773773407553 ] 
dist 70=[.2221873638330120455 ,4.5590765278250679468 ] 
dist 71=[.08023625076130740876,4.5204737496240710088 ] 
dist 72=[-.06512532002691647954,4.4291645310802870699 ] 
dist 73=[-.20158295330927273199,4.3952299391450917976 ] 
dist 74=[-.3079928425473160148 ,4.3512618898175580585 ] 
dist 75=[-.41278541202365930782,4.3858244127217420833 ] 
dist 76=[-.54278277298726857914,4.4040801500246796890 ] 
dist 77=[-.6662878765448150717 ,4.4025744627125536558 ] 
dist 78=[-.74516341099870281714,4.3779714453016175603 ] 
dist 79=[-1.0442748614044618486 ,4.3607982721662858789 ] 
dist 80=[-1.8197584044446283636 ,1.8140810081748435624 ] 
dist 81=[-2.3673645109766960271 ,1.7483325752367624153 ] 
dist 82=[-2.8456284628641012250 ,1.1812956431409688715 ] 
dist 83=[-3.2980337834538253799 ,1.0756347531546538577 ] 
dist 84=[-3.6996277492594670432 ,.92900858212379821905] 
dist 85=[-3.9750735139834854197 ,.885113525917717535  ] 
dist 86=[-4.2111468140593249640 ,.05518043988587660446] 
dist 87=[-4.4555996284699624082 ,-.04982609481408491290] 
dist 88=[-4.6715614056063078678 ,-.28353184722104237149] 
dist 89=[-4.7938977948673074177 ,-.24428430010878522351] 
dist 90=[-4.8712679630760383656 ,-.18886622586266210831] 
dist 91=[-4.9076890507259637536 ,-.11969729456383111838] 
dist 92=[-4.9204081864853812153 ,-.01368466122889573047] 
dist 93=[-4.9141636871316317297 ,.09698894733684776518] 
dist 94=[-4.8760258574832856752 ,.18476143940479622605] 
dist 95=[-4.8499158877467101001 ,.27256464524551710395] 
dist 96=[-3.8441466316417420925 ,.38336172544063442504] 
dist 97=[-3.7450139406238908611 ,.84977551988467126888] 
dist 98=[-3.4915142376225180111 ,1.3239275624252810598 ] 
dist 99=[-3.4442982968391754913 ,1.7980876730905087082 ] 
dist 100=[-3.0156342080941432125 ,2.2361025467111413737 ] 
dist 101=[-2.9284859160179922884 ,2.5659907922471779452 ] 
dist 102=[-2.8112500974967571393 ,2.8799616788334477758 ] 
dist 103=[-2.7712623908795358670 ,3.2544555552645481685 ] 
dist 104=[-1.9135506369649896299 ,3.6030952267949695634 ] 
dist 105=[-1.7996594489024649186 ,3.8138741169184551984 ] 
dist 106=[-1.5527877447481586519 ,3.9641299520500567560 ] 
dist 107=[-1.4878523432760962055 ,4.0711938757236417987 ] 
dist 108=[-1.2532664341775521766 ,4.1491647312200822963 ] 
dist 109=[-1.2530376312998353895 ,4.1832821623611004325 ] 
dist 110=[-1.2509328482169604421 ,4.1920853799066746855 ] 
dist 111=[-1.2471157502098085646 ,4.1889501567924041385 ] 
dist 112=[-1.2423726981320062330 ,2.3853667547920233254 ] 
dist 113=[-1.2315424161244812550 ,2.3796130816263047092 ] 
dist 114=[-1.2251478765710509809 ,2.3731625913500657008 ] 
dist 115=[-1.2112477058787204042 ,2.3649982879291738644 ] 
dist 116=[-1.2050760407701589662 ,2.3551189054625442363 ] 
dist 117=[-.09004530327983068192,2.1465372652052669978 ] 
dist 118=[-.29640199173058570093,2.2434244372866501202 ] 
dist 119=[-.45336449438062718433,2.2977193957849457430 ] 
dist 120=[-.60417687869430787106,2.3313339973704647133 ] 
dist 121=[-.78600144736470364429,2.3456574865129636342 ] 
dist 122=[-.97384510918492625566,2.3492986287713803574 ] 
dist 123=[-1.1486903762927112449 ,2.3455138313608791306 ] 
dist 124=[-1.3475258925665436436 ,2.3269451678672546408 ] 
dist 125=[-1.6311332281023616911 ,2.3148605972675761272 ] 
dist 126=[-1.9081160360227692987 ,-.35940780326362487627] 
dist 127=[-2.0805131492527783215 ,-.36783520308403566645] 
dist 128=[-2.2093444369428059370 ,-.35125798120000620487] 
dist 129=[-2.3124377394634496969 ,-.32137994300142398104] 
dist 130=[-2.3933041982555590376 ,-.27438820787705236496] 
dist 131=[-2.4334191796094650398 ,-.20585854616769035357] 
dist 132=[-2.4524149533335521023 ,-.09001573882362626742] 
dist 133=[-2.4544915068189752265 ,.03041858438167996863] 
dist 134=[-2.3457745283002151009 ,.11727519153176012833] 
dist 135=[-2.4147945159229024778 ,.19617316147028030929] 
dist 136=[-2.4618543298304864829 ,.28484417526286221479] 
dist 137=[-2.4912821634744586798 ,.37302089654071010273] 
dist 138=[-2.5071291443404729970 ,.44994739731134345994] 
dist 139=[-2.5087538531727865955 ,.53337810098901896948] 
dist 140=[-2.4879865429476784524 ,.64751719167859900736] 
dist 141=[-2.4845520930135810549 ,.76123603333864199876] 
dist 142=[-1.9117762706469909543 ,.84299031722356952671] 
dist 143=[-1.8604490314148854002 ,.91700248545302168353] 
dist 144=[-1.7304075466622549226 ,.9998207997172063068 ] 
dist 145=[-1.7051547128418822772 ,1.0819856536085925439 ] 
dist 146=[-1.4881836883978847140 ,1.2821365211323721415 ] 
dist 147=[-1.4440118427360225524 ,1.4443359561912282750 ] 
dist 148=[-1.3812553414510246561 ,1.5950278136765666696 ] 
dist 149=[-1.3610729812461734895 ,1.7694633755935907274 ] 
dist 150=[-.93376519913190963665,1.9296397474878601964 ] 
dist 151=[-.87679888622428354764,2.0234164147150697727 ] 
dist 152=[-.75077102341644445639,2.0865299091978656739 ] 
dist 153=[-.71985920307534683457,2.1243084782207354953 ] 
dist 154=[-.56789134675900295971,2.1491911325242304462 ] 
dist 155=[-.53962986739979087904,2.1608339046392503284 ] 
dist 156=[-.47536148147620572218,2.1650158079381916171 ] 
dist 157=[-.46067999690566483401,2.1601618701788246141 ] 
dist 158=[1.1558050034947688699 ,1.4863929757916964122 ] 
dist 159=[1.0522585928710245954 ,1.5235323295803048041 ] 
dist 160=[.90812800182258293016,1.5446918619622881133 ] 
dist 161=[.74887606519010013789,1.5572861195116977542 ] 
dist 162=[.58497189897370593188,1.5602360755931274984 ] 
dist 163=[.38620565839392122894,1.5566998385895576719 ] 
dist 164=[.08779965067266234707,1.5533157667442268547 ] 
dist 165=[-.2110296115100679256 ,1.2250669094038798367 ] 
dist 166=[-.41148496640920169854,1.1883406337704329621 ] 
dist 167=[-.57832852814953656918,1.0957645898129141292 ] 
dist 168=[-.74299331042830727905,1.0783492847771579614 ] 
dist 169=[-.89370998275026920765,.92607700621024037131] 
dist 170=[-1.0048778976298718368 ,.89537326107328642426] 
dist 171=[-1.1083962637729745360 ,.85259842048142218702] 
dist 172=[-1.2285775511918493012 ,.83867701570854433845] 
dist 173=[-1.3390447523688882307 ,.5964257759387944194 ] 
dist 174=[-1.4037889209192781659 ,.50690753954329821895] 
dist 175=[-1.4474504226838668409 ,.42140141334242878709] 
dist 176=[-1.4737671262979618651 ,.40064270776891016268] 
dist 177=[-1.4912530132394513814 ,.29893194216766014146] 
dist 178=[-1.4996657732941769933 ,.28019589807639724788] 
dist 179=[-1.5030407470892845059 ,.23738458828421005766] 
dist 180=[-1.5004157599843738113 ,.22813871282830134797] 
dist 181=[-1.4101510377791520588 ,.08347633240153146634] 
dist 182=[-1.4969838130166625178 ,.17749471100518820658] 
dist 183=[-1.5461012844542751528 ,.26118556493757574272] 
dist 184=[-1.5770124794202579261 ,.35268582588692468307] 
dist 185=[-1.5911720348421251668 ,.44222214484639834349] 
dist 186=[-1.5974823751538371349 ,.51807306160082115625] 
dist 187=[-1.5970634688827934047 ,.59843870394232110285] 
dist 188=[-1.5916364245559323534 ,.70599348911341114034] 
dist 189=[-1.5870971313900514710 ,.81207097247384607924] 
dist 190=[-1.2389400169997490810 ,.88653929531143982963] 
dist 191=[-1.1849633745689296917 ,.95212033065624106263] 
dist 192=[-1.1693374747698531752 ,1.0227242883197935145 ] 
dist 193=[-1.1060437070320671230 ,1.0911546285640514229 ] 
dist 194=[-1.0906780224173327587 ,1.1480586701649548344 ] 
dist 195=[-1.0553581540186794844 ,1.2074163869591054313 ] 
dist 196=[-1.0432372489510042258 ,1.2856375340722802097 ] 
dist 197=[-.63101498626114469321,1.3590785155038574672 ] 
dist 198=[-.75922634820711197555,1.3993566903182680632 ] 
dist 199=[-.86514215196817305424,1.4230459438286786890 ] 
dist 200=[-.96836226609246173003,1.4302767352111194820 ] 
dist 201=[-1.0619797814756968940 ,1.4311221055852747983 ] 
dist 202=[-1.1295660632055430898 ,1.4155987137015764019 ] 
dist 203=[-1.1910437908770283531 ,1.4236197391681709400 ] 
dist 204=[-1.2602778834793656447 ,1.4276777154463902641 ] 
dist 205=[-1.3226040731860959318 ,1.4273888821034167878 ] 
dist 206=[-1.3565083395994431293 ,1.3253537548118146628 ] 
dist 207=[-1.3760877138201912356 ,1.3645830702213771416 ] 
dist 208=[-1.3812355504613359654 ,1.3867940228770571358 ] 
dist 209=[-1.3804366598834324363 ,1.4010202466794852921 ] 
dist 210=[-1.3762810248596009653 ,1.4083775643611152955 ] 
dist 211=[-1.3688691471597208731 ,1.4121150401616619646 ] 
dist 212=[-1.3640763237932436764 ,1.4118912489563209278 ] 
dist 213=[-1.1964580277090173055 ,.95105012779391031414] 
dist 214=[-1.1720690923576810739 ,.67881816053002200239] 
dist 215=[-1.1075168387743059427 ,.64210189744803707076] 
dist 216=[-1.0946969374581808746 ,.56291990236063769491] 
dist 217=[-.97617912792417793586,.54068388716821476287] 
dist 218=[-.95110338663705170051,.45014176429726798781] 
dist 219=[-.9139261454326319317 ,.43281743799291797506] 
dist 220=[-.83315726724327285453,.38880756307025383692] 
dist 221=[-.80993279336060855158,.38200452087652359945] 
dist 222=[-.88314594058238481496,-.20116443707211070223] 
dist 223=[-.94754001587746191767,-.15002985856763986105] 
dist 224=[-1.0167629426397681788 ,-.07048114544062960602] 
dist 225=[-1.0838185648976037257 ,.02127421589020156341] 
dist 226=[-1.1395617178028909318 ,.12113191311504363689] 
dist 227=[-1.1977133531103227100 ,.24608265370390125294] 
dist 228=[-1.2743825752042719442 ,.43799722445987524465] 
dist 229=[-1.3464815100312647472 ,.630810780017208575  ] 
dist 230=[-1.3863905460109709150 ,.75934994849682506939] 
dist 231=[-1.4103726617556816549 ,.86545553403104128962] 
dist 232=[-1.4188982737050548840 ,.96872550031312199385] 
dist 233=[-1.4209845526915473006 ,1.0622998623688638789 ] 
dist 234=[-1.3940702290341185389 ,1.1297055202844303888 ] 
dist 235=[-1.3835143439833726849 ,1.1908696936027471821 ] 
dist 236=[-1.3774656254373438345 ,1.2595313420950230969 ] 
dist 237=[-1.2067425002917681334 ,1.3212335824451360200 ] 
dist 238=[-1.1802697525371147271 ,1.3546193116755912445 ] 
dist 239=[-1.1275056324284958698 ,1.3736637404573634875 ] 
dist 240=[-1.1120771119840283739 ,1.3781226087843664297 ] 
dist 241=[-1.0484768395657040375 ,1.3767839423136124202 ] 
dist 242=[-1.0335019113496175019 ,1.3726872219969085925 ] 
dist 243=[-.99722874021268377486,1.3657837348897149215 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 2, 2, 1, 0, 1] 
dist 0=[55.533174925075660094  ,55.533174925075660094  ] 
dist 1=[55.310104276079044097  ,55.595551862853983564  ] 
dist 2=[54.936968360041080752  ,55.552056683652318776  ] 
dist 3=[54.275374853141250922  ,55.489547153325559408  ] 
dist 4=[53.274673221979985553  ,55.132840975972604801  ] 
dist 5=[51.547121762016988536  ,55.007384361520957726  ] 
dist 6=[49.659750862039714794  ,54.927237351892092117  ] 
dist 7=[48.020679380587689817  ,54.281380698211198826  ] 
dist 8=[46.245791395458152420  ,50.776999087985927267  ] 
dist 9=[43.815832012987147360  ,49.367650766974421220  ] 
dist 10=[41.143241520540356533  ,48.143595092312309616  ] 
dist 11=[38.399207469408514123  ,47.829331142155979432  ] 
dist 12=[35.069979609338880885  ,46.996778656121789227  ] 
dist 13=[30.060027269331859427  ,46.481043262920157622  ] 
dist 14=[25.033745342070505245  ,46.229945015598835175  ] 
dist 15=[21.639191290730281042  ,45.579521225465922250  ] 
dist 16=[18.780803366630417248  ,36.867932512309175965  ] 
dist 17=[15.895750487449511058  ,35.255103183038649017  ] 
dist 18=[13.204152614229482214  ,34.860101122776337497  ] 
dist 19=[11.118190019118051196  ,34.350142014390648358  ] 
dist 20=[9.0694625024121636429 ,34.161594760796146964  ] 
dist 21=[6.5261045623788223091 ,14.995883590859740460  ] 
dist 22=[4.0928188148971716645 ,13.407146365514601072  ] 
dist 23=[2.4834830718294026483 ,12.139361535651366926  ] 
dist 24=[1.1626502672826321010 ,9.1697337111530022248 ] 
dist 25=[-.11858226989820147312,5.2895101688563057560 ] 
dist 26=[-1.2852859367048619003 ,3.7041783287977542366 ] 
dist 27=[-3.0618106358217698812 ,3.4585344964088862042 ] 
dist 28=[-5.2153120078156132435 ,2.1801134311814534394 ] 
dist 29=[-7.2312716529861713437 ,1.5409848196595373323 ] 
dist 30=[-8.4945129035531148556 ,1.0820813136141506982 ] 
dist 31=[-9.4521034377702984232 ,1.0065098974324914285 ] 
dist 32=[-10.247373841641989411  ,-4.8165215819529708542 ] 
dist 33=[-10.883298863766120313  ,-5.7426662452701843113 ] 
dist 34=[-11.204360610129540069  ,-5.8819270479498664428 ] 
dist 35=[-11.374826793426729108  ,-5.7801676175095077795 ] 
dist 36=[-11.409273899283669980  ,-5.5428271011077387138 ] 
dist 37=[-9.2728627854278294210 ,-5.0625843689795438229 ] 
dist 38=[-9.1308808943762640681 ,-4.5201277613122039907 ] 
dist 39=[-8.7244174540746205090 ,-4.0341582794048885759 ] 
dist 40=[-8.6546696128494503516 ,-3.4982599965324916804 ] 
dist 41=[-7.8366250218544701966 ,-2.7559503820077004939 ] 
dist 42=[-7.6642537342247220968 ,-1.9387867611891285308 ] 
dist 43=[-7.4742685119183183762 ,-1.1038230876964638365 ] 
dist 44=[-7.4073722128454497143 ,-.09597766525368732045] 
dist 45=[-7.2308345023728663082 ,1.4115317551204444935 ] 
dist 46=[-7.1775220683472288092 ,2.9118375679685653027 ] 
dist 47=[-7.1443843015344667224 ,3.8910382276275909195 ] 
dist 48=[-5.4181730344280743510 ,4.6765931217785569352 ] 
dist 49=[-5.3691760905769734873 ,5.4039984297927867449 ] 
dist 50=[-4.4612009470615354684 ,6.0391347934068815656 ] 
dist 51=[-4.2975082706884698026 ,6.4564356380330380281 ] 
dist 52=[-3.6567706199439114699 ,6.7946780546149949402 ] 
dist 53=[-.17718609679546858565,7.1143333715440390218 ] 
dist 54=[.10723584502009375137,7.3909263667597767939 ] 
dist 55=[.18044086463588111332,7.5572349523487868211 ] 
dist 56=[1.1542868792225037292 ,7.6749904497762852148 ] 
dist 57=[1.5036773341087592502 ,7.7575556531138691690 ] 
dist 58=[1.7959564935494985645 ,7.8110344262897317001 ] 
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dist 60=[2.0719654391289436772 ,7.7870696357218193949 ] 
dist 61=[2.1064192805145523811 ,7.7598036610756369521 ] 
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dist 68=[-.04081078884191754988,6.3990827668868990352 ] 
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dist 73=[-2.5507097242512184318 ,1.3523833141768789807 ] 
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dist 80=[-4.4005027521425779743 ,.96205482037344932935] 
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dist 88=[-4.9167926152174325956 ,2.8143359361753718615 ] 
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dist 90=[-4.7000552797648986247 ,3.5470761035962443264 ] 
dist 91=[-4.6592237591804394684 ,3.8398485319414871843 ] 
dist 92=[-4.6298398265765059485 ,4.1825402113038949437 ] 
dist 93=[-3.8281567843632880630 ,4.4979137625349523857 ] 
dist 94=[-3.6687680899281073837 ,4.6816484731130463220 ] 
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dist 96=[-3.3709903772968740990 ,4.8748153157997014541 ] 
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dist 98=[-3.0748745023718551007 ,4.9311432217754816056 ] 
dist 99=[-2.9681021889037689774 ,4.9244196132092673908 ] 
dist 100=[-2.9376600771128812239 ,4.9136563605243541506 ] 
dist 101=[-.60696634689318675939,4.6440087953163680388 ] 
dist 102=[-.42370628600862113504,4.7563465352471515530 ] 
dist 103=[-.30708737348623808252,4.8087707954358778907 ] 
dist 104=[.00040775625318124573,4.8283150935516691815 ] 
dist 105=[.03816823646265622628,4.8275679537280140078 ] 
dist 106=[.12465092702789604856,4.7673618426253905589 ] 
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dist 110=[.00888935241637227206,3.6959606307806955492 ] 
dist 111=[-.58357463861456411703,3.5941145256588606265 ] 
dist 112=[-1.0803042400261661066 ,3.3286014255328648732 ] 
dist 113=[-1.5765871562633573537 ,3.2853284114228109892 ] 
dist 114=[-2.0348721156340792194 ,2.8250834353323209658 ] 
dist 115=[-2.3799194519458047240 ,2.7322814895660878176 ] 
dist 116=[-2.7082526311260032177 ,2.3314486575643387795 ] 
dist 117=[-3.0998106753721382997 ,1.6883593519371793231 ] 
dist 118=[-3.4642737587584697304 ,1.0177169136623259895 ] 
dist 119=[-3.6844462349703497369 ,1.0301366285913114351 ] 
dist 120=[-3.8411419411216271853 ,1.0386657156033877369 ] 
dist 121=[-3.9522169311402400725 ,1.0396176444186638734 ] 
dist 122=[-4.0348696237651616868 ,1.0357734357101882753 ] 
dist 123=[-4.0781179416021599416 ,1.0321641141557627797 ] 
dist 124=[-4.1007831248985117971 ,.99928021797216816783] 
dist 125=[-4.1012996191772500801 ,.98978153512835767444] 
dist 126=[-.93578181194600248955,.97659020425073851583] 
dist 127=[-1.0805753252280591794 ,.97094869506648415392] 
dist 128=[-1.2206058458262725520 ,-.48232652453372397877] 
dist 129=[-1.3059711479999027358 ,-.56059676263879456896] 
dist 130=[-1.3676958716837775839 ,-.73434500737888564271] 
dist 131=[-1.4133572657887031037 ,-.7621042124946857605 ] 
dist 132=[-1.4478668337248773357 ,-.95456343406511165461] 
dist 133=[-1.4650747139611125529 ,-.98461834986342225498] 
dist 134=[-1.4729192776152290861 ,-1.0041461580115300902 ] 
dist 135=[-1.4725801014910192009 ,-.971634446608977476  ] 
dist 136=[-1.4702310116807868228 ,-.92816123483323335356] 
dist 137=[-1.4692604400311109250 ,-.87881359267103751687] 
dist 138=[-1.4566655933470202553 ,-.81570949064084999891] 
dist 139=[-1.4509462994907737491 ,-.71732033640402007853] 
dist 140=[-1.4281400384336612486 ,-.6037424321164349786 ] 
dist 141=[-1.4211274230453383221 ,-.40647142258395328556] 
dist 142=[-1.3368174672405747621 ,-.15593666229116115327] 
dist 143=[-1.3312756063361689004 ,.01329717602264458672] 
dist 144=[-.8919557906580185627 ,.15545308717281487287] 
dist 145=[-.85736409382274439021,.31224061627816512263] 
dist 146=[-.77394064552126931111,.44468949816863559809] 
dist 147=[-.75742763670400432948,.57434347670010942031] 
dist 148=[-.6331181615689731397 ,.69234108380981841483] 
dist 149=[-.60884444933583581147,.77826320698144291868] 
dist 150=[-.56946237515869346106,.85718500120115284   ] 
dist 151=[-.55901473054951578835,.94724193307292498005] 
dist 152=[-.35832215622267068964,1.0299069673015340710 ] 
dist 153=[-.33180742010636692213,1.0793222043341521416 ] 
dist 154=[-.26909999784319525814,1.1138667444476540848 ] 
dist 155=[-.25832702179731691283,1.1371689553022685631 ] 
dist 156=[-.17171365181531666302,1.1532220556519460295 ] 
dist 157=[-.15584016461594928404,1.1588311718428354477 ] 
dist 158=[-.13170767125769588634,1.1587651798329159017 ] 
dist 159=[-.12531855630190087847,1.1565328570356845306 ] 
dist 160=[.46531466935035662499,.93528820555654920477] 
dist 161=[.47302767800418192883,.92841390156817445445] 
dist 162=[.48210258991473219886,.90697592482200389194] 
dist 163=[.47286096312013081762,.90080146263650413213] 
dist 164=[.45200980122898497445,.84757751799775686557] 
dist 165=[.40987223507466491946,.83482744126396286945] 
dist 166=[.36180038051759921741,.81670868061737967147] 
dist 167=[.31725775443770348164,.81000187644900515678] 
dist 168=[.26674989552346141133,.72886248451124343344] 
dist 169=[.19486058301461259401,.74318224393718768429] 
dist 170=[.11467064136606153116,.75501926555690711102] 
dist 171=[.02830326304599339844,.76153976402145098311] 
dist 172=[-.08910277527973302644,.76537951646760265445] 
dist 173=[-.25971384046248769312,.76650446520477630552] 
dist 174=[-.42891751092755090497,.76554962741349254253] 
dist 175=[-.54070712030928678953,.76362945615163014257] 
dist 176=[-.63192639355617089962,.7557352741880839308 ] 
dist 177=[-.71901634284016080583,.75125434948694913462] 
dist 178=[-.79686791782200934695,.72261933025330245716] 
dist 179=[-.85121004655687573767,.71470481634372070806] 
dist 180=[-.89878852386139776206,.70078024240112330542] 
dist 181=[-.94964379229214506611,.69629594841926957948] 
dist 182=[-.9945751621845779246 ,.58237983500755541183] 
dist 183=[-1.0185058094743899118 ,.56546513600047941522] 
dist 184=[-1.0316668496958226191 ,.52807891171278111178] 
dist 185=[-1.0345083011799914756 ,.516740204952645516  ] 
dist 186=[-1.0314809978807932192 ,.46692366834468894006] 
dist 187=[-1.0284423113623948480 ,.45657752752088049248] 
dist 188=[-1.0241585125324041285 ,.43062480087403232689] 
dist 189=[-1.0201951976599633728 ,.42434005838309905393] 
dist 190=[-1.0180842327703441060 ,.07732499284577416940] 
dist 191=[-1.0179651846782179655 ,.19137739037031380156] 
dist 192=[-.64052160964101533914,.30686058713172519843] 
dist 193=[-.63076589800113001659,.38542404121050326498] 
dist 194=[-.53282242333848373734,.45201849948075506918] 
dist 195=[-.51335389985354413547,.51972626484995144013] 
dist 196=[-.48980467914650254204,.58300007940177269065] 
dist 197=[-.48196036526052953504,.63189618394854103576] 
dist 198=[-.29192055356300390953,.71390017819443248358] 
dist 199=[-.26735110307939922878,.77005532843796958884] 
dist 200=[-.21555809209986682604,.81382002505998600294] 
dist 201=[-.20163939666917327998,.85214428026332224313] 
dist 202=[-.14831917087465461502,.88405942307861898921] 
dist 203=[-.13790824954080668934,.90224201690157204477] 
dist 204=[-.11611238981502307489,.91385900204361873776] 
dist 205=[-.11026079629658114444,.91956812455091986836] 
dist 206=[-.00913372733629281704,.92137308470659042593] 
dist 207=[-.1814315616019416599 ,.91740624014312610856] 
dist 208=[-.35448386528539027279,.90816226714152970566] 
dist 209=[-.46981201324526615094,.9052156073049891176 ] 
dist 210=[-.56497744560408056229,.89333013671670418692] 
dist 211=[-.65754891758623709656,.88833150572148690495] 
dist 212=[-.74140082658666124608,.84863153673506477724] 
dist 213=[-.80176145830169517094,.83825110756030419205] 
dist 214=[-.85649275632464049433,.8225324870215077664 ] 
dist 215=[-.91787457504742318176,.81676485987153269073] 
dist 216=[-.97307758946896654327,.76800445734512151446] 
dist 217=[-1.0031457277337380152 ,.77511944169761798935] 
dist 218=[-1.0205666365789708633 ,.77839629467671981392] 
dist 219=[-1.0252874776289006799 ,.77791298647818053634] 
dist 220=[-1.0256266325736106822 ,.77287981151357285849] 
dist 221=[-1.0255578307026912379 ,.7691124376840495572 ] 
dist 222=[-1.0251760564691573810 ,.48999802785797303841] 
dist 223=[-1.0242661214401037342 ,.48488819693827458528] 
dist 224=[-.50228521137899991143,.08583308596658709291] 
dist 225=[-.57055542351169776968,.04795073531361292186] 
dist 226=[-.63261596351621891441,-.03274621010462687175] 
dist 227=[-.67769653512704740198,-.05135198505755790356] 
dist 228=[-.71899826794074186406,-.1330599678292347047 ] 
dist 229=[-.76597560451738170256,-.14770693154961424537] 
dist 230=[-.80855347601193526775,-.17594633766745510892] 
dist 231=[-.83229399890313446635,-.18232613792200799308] 
dist 232=[-.84679791279689520958,-.19866267002711907578] 
dist 233=[-.85250562739613990702,-.19567067853153983564] 
dist 234=[-.85606127465623646374,-.18405619993131966093] 
dist 235=[-.8581031802713694668 ,-.15762690679825147904] 
dist 236=[-.85909710183747500532,-.12367582517119691943] 
dist 237=[-.85892060264903831143,-.02763539643359054558] 
dist 238=[-.7503562503140139558 ,.12910354590759777858] 
dist 239=[-.73628865167731772372,.23468271885866633038] 
dist 240=[-.69842491643222269842,.32304600981438980809] 
dist 241=[-.69122969416160668241,.41106565149107737672] 
dist 242=[-.61996788073774497475,.4921691484872384096 ] 
dist 243=[-.60486182128103907722,.55292593322077631269] 
dist 244=[-.58612738835365159346,.61044004203443600692] 
dist 245=[-.57885662222546630713,.67860039773129217311] 
dist 246=[-.41307119459096872984,.74183124595600412213] 
dist 247=[-.39077960813466686307,.77966868398746744983] 
dist 248=[-.34385319252822427607,.80616672491523656767] 
dist 249=[-.33092768355228327859,.82413477185884952179] 
dist 250=[-.27994640071839145891,.8367254745933979339 ] 
dist 251=[-.26974590873943059995,.84175848577699265216] 
dist 252=[-.24645406273241478917,.84229182705558055431] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 2, 1, 0, 0, 1] 
dist 0=[53.287992621430434649  ,53.287992621430434649  ] 
dist 1=[53.084830903012117764  ,53.535661374759983436  ] 
dist 2=[52.671480939308680860  ,53.863059362598628172  ] 
dist 3=[51.795392385195033686  ,54.384222144728898569  ] 
dist 4=[50.097871790753236595  ,54.894386418090327473  ] 
dist 5=[48.051500149674200107  ,55.177870012220392534  ] 
dist 6=[45.782409848939792045  ,55.349026692363714771  ] 
dist 7=[42.911451637858396529  ,55.411036309229485970  ] 
dist 8=[38.461538264747033611  ,55.397753295617805992  ] 
dist 9=[33.954782676464800227  ,55.324279070866743896  ] 
dist 10=[30.856700195271848364  ,55.089178952924598910  ] 
dist 11=[28.191180397891796619  ,54.950836484146375987  ] 
dist 12=[25.411471748921446899  ,54.110351538280833841  ] 
dist 13=[22.763534283402609338  ,53.227903084272273717  ] 
dist 14=[20.623932545947662899  ,36.930185523670879788  ] 
dist 15=[18.441257173379178568  ,36.483144302754108108  ] 
dist 16=[15.620773214757640074  ,31.808203889905497775  ] 
dist 17=[12.871018426990794607  ,30.919175537483489929  ] 
dist 18=[10.970506159502971451  ,29.925882721017525206  ] 
dist 19=[9.3214930777711940710 ,29.722340275175419568  ] 
dist 20=[7.5757558551380763272 ,21.981255995476203211  ] 
dist 21=[5.8917729528672289808 ,21.654350788517049464  ] 
dist 22=[4.4888300078742647330 ,18.406270412497898543  ] 
dist 23=[3.0149229368199798691 ,17.876564599573436196  ] 
dist 24=[1.0462603255928259744 ,16.008741950999303010  ] 
dist 25=[-.85227335310519878829,15.613171685758473307  ] 
dist 26=[-2.0461921250090845338 ,15.070370648556929606  ] 
dist 27=[-2.9613932850680403380 ,14.908332421247037100  ] 
dist 28=[-3.7457964175191601854 ,11.445525802573498256  ] 
dist 29=[-4.3946378366829867515 ,10.694804274471531428  ] 
dist 30=[-5.6896364538541038424 ,-2.0979452786106262194 ] 
dist 31=[-7.4144731549287827507 ,-2.5494734084710164676 ] 
dist 32=[-8.7586747140812854246 ,-4.7676265788579943876 ] 
dist 33=[-9.9459172478324446272 ,-4.7166794763895190664 ] 
dist 34=[-10.950389367595079373  ,-4.5659947339603004978 ] 
dist 35=[-11.564332821121540277  ,-4.3177152776692330627 ] 
dist 36=[-12.617266275664306774  ,-3.8766105802646794330 ] 
dist 37=[-13.465240601139680681  ,-3.3501606811279450524 ] 
dist 38=[-14.105380322182586735  ,-2.7611124213583885266 ] 
dist 39=[-14.633128669149762618  ,-2.0166783608945126927 ] 
dist 40=[-15.051451108640209157  ,-.87027541576568723853] 
dist 41=[-15.254590909465416922  ,.2892932425589608512 ] 
dist 42=[-15.340800626300281924  ,1.0864316613178816156 ] 
dist 43=[-15.344323750346076236  ,1.7678882138660593704 ] 
dist 44=[-12.905137728945900410  ,2.4664404245442116466 ] 
dist 45=[-12.866744075005560462  ,3.1201603028224601126 ] 
dist 46=[-6.7472597086592438548 ,3.6230059442448852573 ] 
dist 47=[-6.2225952501622344723 ,4.1106216003099728261 ] 
dist 48=[-4.9555195100778333322 ,4.7038311017142020062 ] 
dist 49=[-4.7690929340852755848 ,5.2606387181367381484 ] 
dist 50=[-2.9611279400233356273 ,5.6031503177241268665 ] 
dist 51=[-2.6331653488537060497 ,5.8541988325282737976 ] 
dist 52=[-2.2279322511134107751 ,6.0462308752153634753 ] 
dist 53=[-2.1458279114529652216 ,6.1863321261115306092 ] 
dist 54=[.39137852068064892567,6.2303299454431086178 ] 
dist 55=[.69098973916256100035,6.2330419269525854205 ] 
dist 56=[.38663717332616849976,6.2088796637868935332 ] 
dist 57=[-.31432293282199737683,4.8117021386138395184 ] 
dist 58=[-.78970632122281240214,5.2143215910680078061 ] 
dist 59=[-1.1908405876062758674 ,5.4826599341507365353 ] 
dist 60=[-1.5954846265192886449 ,5.7051563796858540192 ] 
dist 61=[-1.9714220359826640121 ,5.9249845446673063100 ] 
dist 62=[-2.2579999689160668089 ,6.1103914501641043934 ] 
dist 63=[-2.5340555267834357316 ,6.1954704592747043404 ] 
dist 64=[-2.8680209364397698216 ,6.2349891745251561921 ] 
dist 65=[-3.1813167081020895945 ,6.2381256371880387928 ] 
dist 66=[-3.3748834998305739770 ,6.1306716060848744092 ] 
dist 67=[-3.5179109722027475782 ,6.0942464984146502762 ] 
dist 68=[-3.6294927892656504662 ,6.0648490977857219696 ] 
dist 69=[-3.7124658178552339517 ,6.0376767105289315503 ] 
dist 70=[-3.7413149848350883495 ,5.4512546865377511608 ] 
dist 71=[-3.7497547472212396191 ,5.4181341188734130285 ] 
dist 72=[-3.7512175714994340407 ,5.3385748962345305586 ] 
dist 73=[-3.6144879638930661703 ,5.3060478551172703644 ] 
dist 74=[-3.5857754782455284332 ,5.1302794202370689862 ] 
dist 75=[-3.4876558761710930250 ,5.0864658640879578951 ] 
dist 76=[-3.4700327678939257829 ,4.9718662716977203745 ] 
dist 77=[-3.2155656760081570656 ,4.9304273878071618425 ] 
dist 78=[-3.1572547695596710695 ,2.9802318796379600844 ] 
dist 79=[-3.1032497557418518561 ,2.7858681200372746909 ] 
dist 80=[-3.0823453687265837980 ,2.3155919074615807612 ] 
dist 81=[-2.2986432797628633029 ,2.5055586704986917763 ] 
dist 82=[-2.1977937991112120111 ,2.7108076783577796489 ] 
dist 83=[-2.5611935135598333822 ,2.8772594648991948167 ] 
dist 84=[-2.9047906323189581295 ,3.0344082657208466829 ] 
dist 85=[-3.3119504529911839184 ,3.1737040206499926496 ] 
dist 86=[-3.6905334298292756390 ,3.2689128193384102396 ] 
dist 87=[-3.9200491515605791452 ,3.3502040711197565887 ] 
dist 88=[-4.0847651016179972625 ,3.4339816059848281405 ] 
dist 89=[-4.2046349733475201871 ,3.5036764895213712833 ] 
dist 90=[-4.2936354417950062274 ,3.5287572794793415442 ] 
dist 91=[-4.3350797782342097971 ,3.5350938050027573979 ] 
dist 92=[-4.3497444175817826257 ,3.5299159042222633396 ] 
dist 93=[-4.3481637851190480039 ,3.4365558484946413728 ] 
dist 94=[-3.3935332645479863357 ,3.4063743943382022242 ] 
dist 95=[-3.3147952566331206430 ,3.3767758228629661450 ] 
dist 96=[-3.1083647543134762560 ,3.3573874425948076831 ] 
dist 97=[-3.0721534278380102296 ,3.1180881460243971406 ] 
dist 98=[-2.7071890990973951168 ,3.2397790803402308457 ] 
dist 99=[-2.6323528983458564456 ,3.3197885490472866556 ] 
dist 100=[-2.5414597662627300872 ,3.3638646784054771495 ] 
dist 101=[-2.5066012201040583900 ,3.3906151438329536764 ] 
dist 102=[-1.7314831916943739692 ,3.4014654083587445339 ] 
dist 103=[-1.6290207278838976708 ,3.4027362235163440251 ] 
dist 104=[-1.4136934992177180717 ,3.3946573278288724852 ] 
dist 105=[-1.3551875635221292727 ,3.0217343257919091745 ] 
dist 106=[-1.1282480777446648292 ,2.9690940495720313447 ] 
dist 107=[-1.4754512687131322842 ,2.8276293259542779900 ] 
dist 108=[-1.8197729778366280801 ,2.7994795917676481627 ] 
dist 109=[-2.1351992714187159064 ,2.5312941221026584606 ] 
dist 110=[-2.3685040183135693564 ,2.4737857485568986790 ] 
dist 111=[-2.5864791358295306341 ,2.4002340700223673589 ] 
dist 112=[-2.8407151864558835374 ,2.3723397729817336863 ] 
dist 113=[-3.0745434183903218598 ,2.1676139723736565631 ] 
dist 114=[-3.2110547628238192479 ,2.1698727044685187060 ] 
dist 115=[-3.3025084316930213548 ,2.1668166175438383255 ] 
dist 116=[-3.3564734162301225722 ,2.1442754609941332628 ] 
dist 117=[-3.3911740010301122478 ,2.1363049039078504888 ] 
dist 118=[-3.4057255612951631466 ,1.9914784918455524583 ] 
dist 119=[-3.4083178022675978323 ,1.9652158797671174878 ] 
dist 120=[-3.4009669891459565712 ,1.8932346672736281648 ] 
dist 121=[-.95439272894461065177,1.8764229039066654105 ] 
dist 122=[-1.1405585477749672530 ,1.7327972239846651715 ] 
dist 123=[-1.3136897186842279815 ,1.7009580820784242016 ] 
dist 124=[-1.5105194223558419442 ,1.6553766504778723152 ] 
dist 125=[-1.7913004045483646516 ,1.6396445754660361438 ] 
dist 126=[-2.0653563698578587356 ,1.3374697908988146779 ] 
dist 127=[-2.2353477658142249635 ,1.4614013242059303222 ] 
dist 128=[-2.3617738195383488406 ,1.6044920212057063493 ] 
dist 129=[-2.4619298784849922585 ,1.7353076507424830075 ] 
dist 130=[-2.5397472723395489332 ,1.8102448562297001176 ] 
dist 131=[-2.5769992866681272634 ,1.8586493978519154762 ] 
dist 132=[-2.5938402342530597926 ,1.8835595137148581693 ] 
dist 133=[-2.5943405752329921548 ,1.8981654949006419601 ] 
dist 134=[-2.4796003094097453372 ,1.9054357427979761408 ] 
dist 135=[-2.5193123240015892803 ,1.9087368217850970358 ] 
dist 136=[-2.5577277717107570086 ,1.9074844573499247353 ] 
dist 137=[-2.5823334360912948098 ,1.6492191412789369565 ] 
dist 138=[-2.5962179776396062546 ,1.6151630742423697967 ] 
dist 139=[-2.5953254107319836428 ,1.5226545594500713577 ] 
dist 140=[-2.5806626670843328852 ,1.5069647359037460249 ] 
dist 141=[-2.5683679288030306331 ,1.3327630240208720271 ] 
dist 142=[-1.5084852000797521482 ,1.2964146525831199083 ] 
dist 143=[-1.4118027586761284420 ,1.2559336645807328055 ] 
dist 144=[-1.1786818351300293815 ,1.2416762040895982496 ] 
dist 145=[-1.1401185957588416771 ,.83993506074132761428] 
dist 146=[-1.2514573046897179405 ,1.0457348132744531099 ] 
dist 147=[-1.3425676782630957883 ,1.2240215945329609080 ] 
dist 148=[-1.4299409174028274890 ,1.3906113046241466373 ] 
dist 149=[-1.5082769040190914140 ,1.5848460714567301594 ] 
dist 150=[-1.5633197090084125037 ,1.7650579799071642849 ] 
dist 151=[-1.6118855687539880571 ,1.8756753755163169257 ] 
dist 152=[-1.6643776893596513287 ,1.9565158565944917396 ] 
dist 153=[-1.7094438615081809232 ,2.0178790595105662761 ] 
dist 154=[-1.7283689596881236459 ,2.0636954723831764606 ] 
dist 155=[-1.7359634264733673375 ,2.0824789444692344353 ] 
dist 156=[-1.7357899794045208317 ,2.0886244230262114185 ] 
dist 157=[-1.6941047803656195540 ,2.0853528730450193686 ] 
dist 158=[-1.6808143418368957598 ,1.7431793103355983656 ] 
dist 159=[-1.6705969700147383927 ,1.7873872913399831714 ] 
dist 160=[-1.6619135314405281007 ,1.8121827274771583999 ] 
dist 161=[-1.5764091361899025054 ,1.8174861762095811072 ] 
dist 162=[-1.6264120038196519573 ,1.8144783114804546406 ] 
dist 163=[-1.6583641543491025854 ,1.8096254950250381424 ] 
dist 164=[-1.6740403907652827895 ,1.8021850620446345456 ] 
dist 165=[-1.6814250503205646171 ,1.7953524595568817209 ] 
dist 166=[-1.6802824637974112497 ,1.5589441771044689831 ] 
dist 167=[-1.6737002929302601728 ,1.5230272189365020836 ] 
dist 168=[-1.6684846224761637422 ,1.4524211679275315451 ] 
dist 169=[-1.5023661161798793310 ,1.4322322440610012789 ] 
dist 170=[-1.4772150957774360746 ,1.3515804251943871663 ] 
dist 171=[-1.4065577504714012292 ,1.3321058990074032287 ] 
dist 172=[-1.3941718356613428586 ,1.2888109041673633880 ] 
dist 173=[-1.2520704070218399686 ,1.2743477376126535777 ] 
dist 174=[-1.2763040998157312923 ,1.0722577992703179540 ] 
dist 175=[-1.3490275353807072514 ,1.1860186089549423234 ] 
dist 176=[-1.3994552423486800396 ,1.3222731662933792357 ] 
dist 177=[-1.4326832403552922378 ,1.4494288063909623077 ] 
dist 178=[-1.4562272788681476052 ,1.5268722167613420488 ] 
dist 179=[-1.4679985524725313841 ,1.5827734659464636655 ] 
dist 180=[-1.4734100525721190587 ,1.6239428008929636296 ] 
dist 181=[-1.4715617164570898325 ,1.6535062409713621687 ] 
dist 182=[-1.5543416391160091103 ,1.6630785061926571414 ] 
dist 183=[-1.6277667649151348245 ,1.6644205191225269956 ] 
dist 184=[-1.6766888650721883882 ,1.6611315768401521712 ] 
dist 185=[-1.7049793120815338464 ,1.4627018032415387667 ] 
dist 186=[-1.7233222112824260576 ,1.4409272737948121666 ] 
dist 187=[-1.7325390941476653404 ,1.3787958603713188652 ] 
dist 188=[-1.7368405053149597296 ,1.3674737569682295031 ] 
dist 189=[-1.7355690276121792960 ,1.2391259199472290939 ] 
dist 190=[-.7191290678263397558 ,1.2112897546823502053 ] 
dist 191=[-.8189191531626198105 ,1.1805736915071248790 ] 
dist 192=[-.9396257972244314815 ,1.1680588582468409505 ] 
dist 193=[-1.0528154072847926838 ,1.0948168236248926777 ] 
dist 194=[-1.1226026378760662502 ,1.0148393498157548317 ] 
dist 195=[-1.1739741641498936538 ,.99634772020746927799] 
dist 196=[-1.2136600641666612619 ,.97273319338249255163] 
dist 197=[-1.2435248328654244731 ,.96317620179118331969] 
dist 198=[-1.2556954720285523105 ,.99686407726608107963] 
dist 199=[-1.2599817953991451786 ,1.0697934491761983049 ] 
dist 200=[-1.2583774379982311050 ,1.1307388074444419070 ] 
dist 201=[-1.1999835323324001177 ,1.1913010852369580439 ] 
dist 202=[-1.1884701273981139688 ,1.2470253477926463160 ] 
dist 203=[-1.1551659495552415688 ,1.3027304104778878891 ] 
dist 204=[-1.1457218776282847756 ,1.3646750019264710544 ] 
dist 205=[-1.0709310545755496384 ,1.4400745304396667358 ] 
dist 206=[-1.1443615393637177268 ,1.5092179691099519526 ] 
dist 207=[-1.2267103610650338851 ,1.5461916038932179270 ] 
dist 208=[-1.3236502048375755262 ,1.5667188013808043610 ] 
dist 209=[-1.4132496077770523514 ,1.5710017974919628597 ] 
dist 210=[-1.4662989586053486751 ,1.5673299935821288032 ] 
dist 211=[-1.5027605504458859867 ,1.5624103171362317465 ] 
dist 212=[-1.5261483467414691961 ,1.5550637915719676173 ] 
dist 213=[-1.5406154224303004134 ,1.5491288082543164893 ] 
dist 214=[-1.5424326326362462038 ,1.3464259906670428256 ] 
dist 215=[-1.5372594196074293449 ,1.3154872513170437895 ] 
dist 216=[-1.5315269507605307694 ,1.2538306983400801867 ] 
dist 217=[-1.4907059224117891785 ,1.3090508618964319517 ] 
dist 218=[-1.4949079541583749003 ,1.3548581520551529165 ] 
dist 219=[-1.4939195868791692963 ,1.3837383125349251991 ] 
dist 220=[-1.4889319061330623228 ,1.3970624656395853179 ] 
dist 221=[-1.4843042982757550617 ,1.4033350065431416992 ] 
dist 222=[-1.3496672475694451757 ,1.4040704378995508004 ] 
dist 223=[-1.3826671417422870881 ,1.4008862223776890208 ] 
dist 224=[-1.4011332659937084047 ,1.3966841810259875953 ] 
dist 225=[-1.4048341473324456956 ,1.3838510615234967489 ] 
dist 226=[-1.4022552164476429994 ,1.4294026892222699705 ] 
dist 227=[-1.3975230895657769904 ,1.4655368608482779647 ] 
dist 228=[-1.3901361083943453340 ,1.4831143733811900689 ] 
dist 229=[-1.3849315666581202350 ,1.4929645088416969118 ] 
dist 230=[-1.2076800668715320611 ,1.4982101210431950001 ] 
dist 231=[-1.1803042489321493284 ,1.5012212126687786887 ] 
dist 232=[-1.1249251413261990200 ,1.5019097805258221421 ] 
dist 233=[-1.1086231746344673671 ,1.3555743189228701897 ] 
dist 234=[-1.0405394169764394403 ,1.3351048006273294767 ] 
dist 235=[-1.0249743432681767141 ,1.2773222254014758381 ] 
dist 236=[-.98572953730453198157,1.2663378113396277191 ] 
dist 237=[-.97382770106462375919,1.1483605798219298130 ] 
dist 238=[-.97537728323056475309,1.1227289874030934358 ] 
dist 239=[-1.0731605579602272967 ,1.0930337240358523669 ] 
dist 240=[-1.1885162555699754191 ,1.0803500049912032136 ] 
dist 241=[-1.2952234518665293488 ,.78123398486177217261] 
dist 242=[-1.3584872021084404644 ,.7408517713325370756 ] 
dist 243=[-1.4020595088583769888 ,.65733578432792281507] 
dist 244=[-1.4301696631924630746 ,.63456703241295941769] 
dist 245=[-1.4492372297283592525 ,.54659901216309161128] 
dist 246=[-1.4567151297856235394 ,.52827634411201171141] 
dist 247=[-1.4571357951171956422 ,.48958570115175088928] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 2, 2, 2, 0, 1] 
dist 0=[40.050346209576308410  ,40.050346209576308410  ] 
dist 1=[39.623283604957288510  ,40.442685905698709003  ] 
dist 2=[38.310216154428187442  ,41.030185054856010468  ] 
dist 3=[36.941108513876789811  ,41.470662246750792664  ] 
dist 4=[35.951484234765848053  ,41.799432247813463409  ] 
dist 5=[35.047881494321988621  ,41.940884010578023758  ] 
dist 6=[34.022061493828478982  ,41.987356623619808064  ] 
dist 7=[32.992245904267947802  ,41.971491937567183990  ] 
dist 8=[32.072445617797908430  ,41.067998542946275211  ] 
dist 9=[31.053563008723981807  ,40.885831232635397104  ] 
dist 10=[29.627580719900954173  ,40.556358566062677430  ] 
dist 11=[28.182563793199642778  ,40.450500186320915387  ] 
dist 12=[27.087432240310806168  ,39.985120161028426941  ] 
dist 13=[26.033728344755262288  ,39.853568124375353830  ] 
dist 14=[24.753934319259674350  ,39.511872204082575017  ] 
dist 15=[23.418308363568123890  ,39.377191442512367775  ] 
dist 16=[22.141190724563173103  ,29.995189425281128994  ] 
dist 17=[20.654720988087823051  ,29.137447732061700774  ] 
dist 18=[18.481923609414897419  ,27.054039634720094996  ] 
dist 19=[16.314914854902229407  ,26.733528684177691826  ] 
dist 20=[14.851521440056147996  ,23.636783946707000852  ] 
dist 21=[13.614455721937588130  ,23.049765024518073296  ] 
dist 22=[12.352289267213007165  ,22.344116843120064941  ] 
dist 23=[11.161384251334383478  ,22.159639799434448359  ] 
dist 24=[9.2716928734801630405 ,16.936478163410217942  ] 
dist 25=[7.6894913570989381988 ,16.270408409116693517  ] 
dist 26=[6.2536343021719576799 ,14.910405355280258126  ] 
dist 27=[4.6328298659710642448 ,14.554971670714289949  ] 
dist 28=[3.0068631327739427245 ,13.252223415667247666  ] 
dist 29=[1.5499176613051353255 ,12.984380591055346257  ] 
dist 30=[-.07105149066148343906,12.497394925157312428  ] 
dist 31=[-2.3532920187665218041 ,12.381557790011707021  ] 
dist 32=[-4.5822742353067581251 ,5.0482758415191678345 ] 
dist 33=[-5.9905741627101687753 ,4.7750246311144477948 ] 
dist 34=[-7.0768931944061886315 ,4.7106726391790544445 ] 
dist 35=[-8.0188528912566458484 ,1.1847817395673963493 ] 
dist 36=[-8.8049043882950757438 ,.87333858517566307299] 
dist 37=[-9.2681842096310059742 ,.15666854674469282349] 
dist 38=[-9.5886853147557228799 ,.04714803413903844504] 
dist 39=[-9.8044868826155986064 ,-.8772616792371729325 ] 
dist 40=[-9.9624674762192502698 ,-1.0406935781463362739 ] 
dist 41=[-10.051793100303990850  ,-1.2631052447822558289 ] 
dist 42=[-10.110976401726080064  ,-1.3194948950051227633 ] 
dist 43=[-10.147847036700124172  ,-2.4343232338307711430 ] 
dist 44=[-10.296257370922448738  ,-2.5700130710512097224 ] 
dist 45=[-10.393332536075360698  ,-2.8667996615504751827 ] 
dist 46=[-10.435735636449449462  ,-2.9202017676815528193 ] 
dist 47=[-10.429578341942902446  ,-3.2470311594638443049 ] 
dist 48=[-4.9255340512137434696 ,-3.3005830681576834841 ] 
dist 49=[-4.5908115316742532480 ,-3.1914429652155847672 ] 
dist 50=[-4.2174557383226847282 ,-2.3857539079002713034 ] 
dist 51=[-3.6658210183259393632 ,-1.5641493367944955790 ] 
dist 52=[-2.5643674966775409098 ,-.79479004575971687665] 
dist 53=[-2.3644123629874926597 ,-.19751188236771451732] 
dist 54=[-2.0786394916290409444 ,.38864013335863935884] 
dist 55=[-1.9985142624289778510 ,1.1137625941437679914 ] 
dist 56=[-1.5073923365178738762 ,1.8034967311045566555 ] 
dist 57=[-1.3987943332262635202 ,2.2484581003869316188 ] 
dist 58=[-1.3648184489355959678 ,2.6001911335758656370 ] 
dist 59=[-.7070197959368138559 ,2.9178183492788649243 ] 
dist 60=[-.62403555645825600544,3.1905095955204471159 ] 
dist 61=[-.44207909669994130745,3.3629481478376715722 ] 
dist 62=[-.40412278637716191482,3.4960505738536649544 ] 
dist 63=[-.19920190376594092914,3.6119214141546844915 ] 
dist 64=[-.16416672201900348186,3.7039871368266944376 ] 
dist 65=[-.08850929969076063407,3.7420566807232501383 ] 
dist 66=[-.07390497973669680327,3.7570184023663580852 ] 
dist 67=[.51574208326065541864,3.9116789473825558950 ] 
dist 68=[.57335845381132276316,4.0651614750726500329 ] 
dist 69=[.67472216863054414857,4.1560913007144713356 ] 
dist 70=[.69502303549405037172,4.2192004296522333236 ] 
dist 71=[.66175663211218928406,4.2616210857462412206 ] 
dist 72=[.40641129532849231392,4.2853691349175493935 ] 
dist 73=[.19223451292938006058,4.2876458810581799628 ] 
dist 74=[-.03260671482974315628,4.2552313042283003793 ] 
dist 75=[-.3306199945490046647 ,4.2500024553601596899 ] 
dist 76=[-.65287094305153941356,4.0594868890165206442 ] 
dist 77=[-.97451934783518049665,4.0107620607350526858 ] 
dist 78=[-1.3574995806302369910 ,3.9818007032154612046 ] 
dist 79=[-1.9246409694846579445 ,3.9728573882617039778 ] 
dist 80=[-2.4871326277338954408 ,2.1999490297532003463 ] 
dist 81=[-2.8515776123204012114 ,2.1847153524459668168 ] 
dist 82=[-3.1410592587000668193 ,2.1759222743716189284 ] 
dist 83=[-3.4043220178021012299 ,.68262565483486647325] 
dist 84=[-3.6309691538652965193 ,.30307170756834995184] 
dist 85=[-3.7743057888417675608 ,.2362696742904411918 ] 
dist 86=[-3.8843436328705816712 ,.13860502088462199366] 
dist 87=[-3.9781102966290671996 ,.11299574027566591018] 
dist 88=[-4.0507660932832053253 ,-.30916505202459788509] 
dist 89=[-4.1203122793377668975 ,-.36106950488503124979] 
dist 90=[-4.2111432542582986814 ,-.46667230219481930978] 
dist 91=[-4.2813943061343970134 ,-.4345720039684788406 ] 
dist 92=[-4.3331304127070299959 ,-.3812521688025762807 ] 
dist 93=[-4.3500276730309991665 ,-.30194439635925913988] 
dist 94=[-4.3464392977587670166 ,-.18870834340445485158] 
dist 95=[-4.3378878076096647063 ,0                     ] 
dist 96=[-2.6973254869433377345 ,.67813974858827402719] 
dist 97=[-2.5681633591679686502 ,1.2300221746016824238 ] 
dist 98=[-2.2729973390231832909 ,1.6838055284279216856 ] 
dist 99=[-2.2058771711672980576 ,2.1224798509011472518 ] 
dist 100=[-1.8192738163131675433 ,2.5179706368113112100 ] 
dist 101=[-1.7461335288702462414 ,2.7993906577284522772 ] 
dist 102=[-1.5983227054905396517 ,3.0512100770203365893 ] 
dist 103=[-1.5587494474532894698 ,3.3285526988212890456 ] 
dist 104=[-1.0709788451253122072 ,3.5818359770515191190 ] 
dist 105=[-1.0087273594836731891 ,3.7376178870401362335 ] 
dist 106=[-.98877700532341921078,3.8518200593373663084 ] 
dist 107=[-.59076004303447454809,3.9391215849842412486 ] 
dist 108=[-.54011944609537790885,4.0023763672711053667 ] 
dist 109=[-.42515416679645946361,4.0205799035561704068 ] 
dist 110=[-.40178402670849926533,4.0207847357760010327 ] 
dist 111=[-.25728342405920408942,4.0122375689630415838 ] 
dist 112=[-.23120086468424296353,2.2997760580512771789 ] 
dist 113=[-.18076421665672509112,2.5034906649024954580 ] 
dist 114=[-.16841661115676281952,2.6558578327396294811 ] 
dist 115=[.24048060116698450078,2.7782423107062819253 ] 
dist 116=[.28284296413335619096,2.8742835530735254331 ] 
dist 117=[.35982341923111956053,2.9214809211874642599 ] 
dist 118=[.37619408154185510474,2.9440806387806693098 ] 
dist 119=[.41253617015379612252,2.9461007333284604018 ] 
dist 120=[.408637932235771897  ,2.8327215077510499590 ] 
dist 121=[.38721089709026189745,2.8065502128477652406 ] 
dist 122=[.33628335213552227877,2.7650743552100799583 ] 
dist 123=[.2759113917708097521 ,2.7492134570277912297 ] 
dist 124=[.21678528001285837481,2.6888934776533822987 ] 
dist 125=[.14724699224486595686,2.6685929958541239474 ] 
dist 126=[.04531054427196669108,2.6223740067350937346 ] 
dist 127=[-.06967427429453077075,2.6041302381930421683 ] 
dist 128=[-.1912972768944545978 ,1.6752750395530054465 ] 
dist 129=[-.34111028183886132296,1.6597839571354342013 ] 
dist 130=[-.5686175375053976909 ,1.6510986364933523147 ] 
dist 131=[-.79617118342727187456,1.4205760895518165893 ] 
dist 132=[-.95620707901940740784,1.4593674091636657006 ] 
dist 133=[-1.1528066841840259223 ,1.4831833896135279447 ] 
dist 134=[-1.3376072977338916846 ,1.4927948453488785140 ] 
dist 135=[-1.5547129520398608724 ,1.4955275789858922151 ] 
dist 136=[-1.7566743312842653163 ,1.4923505228490303386 ] 
dist 137=[-1.8810274243583290029 ,1.4842768232979397129 ] 
dist 138=[-1.9723934830554479535 ,1.4787269165685911859 ] 
dist 139=[-2.0426898981710842824 ,1.3294721643117906766 ] 
dist 140=[-2.0959807627470819748 ,1.3049330123682949290 ] 
dist 141=[-2.1194654638307720738 ,1.2520693747499000992 ] 
dist 142=[-2.1284158314762627970 ,1.2353670345131836086 ] 
dist 143=[-2.1264689972973784631 ,1.1593742555487933143 ] 
dist 144=[-1.5867560762384885285 ,1.1430213874052079611 ] 
dist 145=[-1.5859723365494244024 ,1.0955849636171883019 ] 
dist 146=[-1.5811487392797471951 ,1.0870884525807013216 ] 
dist 147=[-1.2174151750990443634 ,.39100159369039139304] 
dist 148=[-1.1790078458793636315 ,.32444539416950092281] 
dist 149=[-1.0844543024851382026 ,.17782527288789751531] 
dist 150=[-1.0652511422670461256 ,.14640245180631869263] 
dist 151=[-.91627977930683495179,.10839541667588430825] 
dist 152=[-.88637239365869360959,.26443167337868837444] 
dist 153=[-.83938742673336039679,.38338224622848687966] 
dist 154=[-.82606982491428141491,.49799015882848428829] 
dist 155=[-.76912552732535852595,.63670406122920608255] 
dist 156=[-.83663043446653732065,.78039516612060092318] 
dist 157=[-.89857340903585134191,.91487983106754303523] 
dist 158=[-.96914039772340137116,1.0720105709927056507 ] 
dist 159=[-1.0398635353961029191 ,1.2957033432466404280 ] 
dist 160=[-1.1024271698112670423 ,1.5133527584405111855 ] 
dist 161=[-1.1774172672200735927 ,1.6499925363070261258 ] 
dist 162=[-1.2657119734355675618 ,1.7535713536423092126 ] 
dist 163=[-1.3577183233494285368 ,1.8392464175560165277 ] 
dist 164=[-1.4130065432754681431 ,1.9069670887946661148 ] 
dist 165=[-1.4508788760733736142 ,1.9388775144469212480 ] 
dist 166=[-1.4748648227502017654 ,1.9545866059053555380 ] 
dist 167=[-1.4901339139892519582 ,1.9576169880837822766 ] 
dist 168=[-1.4932159944686065230 ,1.9185141918122947689 ] 
dist 169=[-1.4903511182154229433 ,1.9058046159642655086 ] 
dist 170=[-1.4856794979036141693 ,1.8810439582864422861 ] 
dist 171=[-1.4555180628421760934 ,1.8711363874579529105 ] 
dist 172=[-1.3949423897076866370 ,1.8187218754863744897 ] 
dist 173=[-1.3781070342969134150 ,1.8051434096024278265 ] 
dist 174=[-1.3639174795832474632 ,1.7582013631092261433 ] 
dist 175=[-1.3544800348983583591 ,1.7494998093115414387 ] 
dist 176=[-1.2060879571900627983 ,1.5187449816076476989 ] 
dist 177=[-1.1608013503813301657 ,1.5076010505273768593 ] 
dist 178=[-1.1522046174397371310 ,1.4992109729714504112 ] 
dist 179=[-.93718315473104652565,.37326231974380562207] 
dist 180=[-1.0631743065114445172 ,.12261882003998699416] 
dist 181=[-1.1660680028765761939 ,.07842983189008078504] 
dist 182=[-1.2643664665710853453 ,-.00658689652226697257] 
dist 183=[-1.3522066689641088845 ,-.02672693707862894289] 
dist 184=[-1.4505400489336089776 ,-.23838016165532779642] 
dist 185=[-1.5316642763999954503 ,-.26984221734496021645] 
dist 186=[-1.5896211191682718259 ,-.31254799655742907104] 
dist 187=[-1.6311436356529904413 ,-.32069870304519933315] 
dist 188=[-1.6610036600992456389 ,-.31589164304084997722] 
dist 189=[-1.6724093244265504173 ,-.2915682907391622678 ] 
dist 190=[-1.6745347877666220248 ,-.24831438704724496037] 
dist 191=[-1.6714744254626842984 ,-.16795322485061445781] 
dist 192=[-1.5721185158364488114 ,-.08195532987565280395] 
dist 193=[-1.6180225805997715265 ,-.01620199361634947677] 
dist 194=[-1.6654221678193378656 ,.22633944795365307441] 
dist 195=[-1.6981678149638195346 ,.5687493821347579217 ] 
dist 196=[-1.7201109548177585806 ,.79503049014295089533] 
dist 197=[-1.7243882126334968571 ,.97963019067468847158] 
dist 198=[-1.7220046281592319181 ,1.1556684306607181944 ] 
dist 199=[-1.7173578446476892756 ,1.3127713364423815336 ] 
dist 200=[-1.6179318165545402923 ,1.4217899278620467314 ] 
dist 201=[-1.5983880863925461490 ,1.5164837091221931364 ] 
dist 202=[-1.5516936477208583725 ,1.6164073653380174588 ] 
dist 203=[-1.5349634835680106842 ,1.7057962677516928515 ] 
dist 204=[-1.4513990669927520025 ,1.7584409968385367623 ] 
dist 205=[-1.4317839481378229433 ,1.7942553231078969238 ] 
dist 206=[-1.3861999098578177427 ,1.8164686850725647055 ] 
dist 207=[-1.3704131370012410952 ,1.8286921521057828778 ] 
dist 208=[-.45539441228777970598,1.8298750025831241268 ] 
dist 209=[-.42328217426747496041,1.8165794991954117338 ] 
dist 210=[-.41270299972791333434,1.8128698782750873130 ] 
dist 211=[-.12252181221298792504,1.7359733157599168086 ] 
dist 212=[-.08729038706942485305,1.7754768649468872000 ] 
dist 213=[-.02818053143141376894,1.7905576713034199398 ] 
dist 214=[-.01466280116275096795,1.7952874701460707941 ] 
dist 215=[.00817767249931427873,1.8337525080568690280 ] 
dist 216=[.00200644371689267185,1.8784819045921550258 ] 
dist 217=[-.01911819499871051260,1.8979608577963094829 ] 
dist 218=[-.06618414296374231713,1.9050301388294168750 ] 
dist 219=[-.12121528512476316135,1.9031301100948449322 ] 
dist 220=[-.17413252598964861131,1.8942107847403326165 ] 
dist 221=[-.23565164883406039588,1.8966034140501340248 ] 
dist 222=[-.32501649595936208959,1.8852162042115176076 ] 
dist 223=[-.42547157785214429578,1.8821154531169502108 ] 
dist 224=[-.53125669318794116107,1.2946967129480742829 ] 
dist 225=[-.66123670940883747122,1.2370247556112140694 ] 
dist 226=[-.85826442841104648297,1.0974528855881592199 ] 
dist 227=[-1.0551680482942735623 ,1.0711435722348312470 ] 
dist 228=[-1.1846525251224470802 ,.8628259576855652035 ] 
dist 229=[-1.2895740833819602248 ,.82247760789201665548] 
dist 230=[-1.3884355379947287377 ,.76032565481023609712] 
dist 231=[-1.4758557156517429457 ,.7430041858815306637 ] 
dist 232=[-1.5679406451426060214 ,.40829420676271243173] 
dist 233=[-1.6345335708717892087 ,.364669672472556252  ] 
dist 234=[-1.6822118724434135035 ,.26314203777925142139] 
dist 235=[-1.7165592597399805626 ,.24510836432120944146] 
dist 236=[-1.7397751326225448859 ,.11070383074025668516] 
dist 237=[-1.7450218644903050855 ,.08648512218632813780] 
dist 238=[-1.7402245042642329582 ,.04640606352102904690] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 1, 1, 0, 1, 2] 
dist 0=[46.743306687226531554  ,46.743306687226531554  ] 
dist 1=[46.009937312491745637  ,47.043762391496277106  ] 
dist 2=[44.827714035078599761  ,47.510239910488543656  ] 
dist 3=[42.889969391935447415  ,47.994642247810923875  ] 
dist 4=[40.882836802605460979  ,48.221647289630288000  ] 
dist 5=[39.423396916689305364  ,48.305893946151806285  ] 
dist 6=[38.081771233706717652  ,48.303779922673845562  ] 
dist 7=[36.545033385038982880  ,48.013019638507220502  ] 
dist 8=[34.994939656287269499  ,46.718856817524554916  ] 
dist 9=[33.599819903316033386  ,46.288595125895308083  ] 
dist 10=[32.046466001792932129  ,46.149979161973972149  ] 
dist 11=[29.864088314397905342  ,45.615149869015322140  ] 
dist 12=[27.652085106247171956  ,45.445318350584546957  ] 
dist 13=[25.980246475677001977  ,45.084456798328002984  ] 
dist 14=[24.377852182940350206  ,44.950139114258495106  ] 
dist 15=[22.443025662059996051  ,44.197034091722258932  ] 
dist 16=[20.433111770704210998  ,30.868897579975346764  ] 
dist 17=[18.530490185909923696  ,28.101984954898467621  ] 
dist 18=[16.333772633221903156  ,27.701646682488325848  ] 
dist 19=[13.148439768868439460  ,24.637233255278372292  ] 
dist 20=[9.9875135184679758485 ,22.885677312270741710  ] 
dist 21=[7.8882205776183758098 ,22.022452190627795241  ] 
dist 22=[6.1552356863615981058 ,21.861459723750861016  ] 
dist 23=[4.4579784918395303446 ,16.834979408729021842  ] 
dist 24=[2.9040260962810286738 ,14.971266307002890200  ] 
dist 25=[1.7435688565414932646 ,14.640158972538003285  ] 
dist 26=[.6432648283378890060 ,13.682444611112869339  ] 
dist 27=[-.6705633159195341109 ,12.380099940332172543  ] 
dist 28=[-1.9056615412173694509 ,10.681833074147876358  ] 
dist 29=[-2.6914943613429259920 ,10.278779811259659320  ] 
dist 30=[-4.2996811556301885891 ,10.177143355299975711  ] 
dist 31=[-6.9540266582170254347 ,.7561657612255136306 ] 
dist 32=[-9.5330679603191403783 ,-.06064970233616971482] 
dist 33=[-11.142113895511049826  ,-1.7474853410287161492 ] 
dist 34=[-12.358295451842612834  ,-2.0557415366454961818 ] 
dist 35=[-13.367367216158650263  ,-1.8690415587930289287 ] 
dist 36=[-14.179514619831235206  ,-1.4919078782532039035 ] 
dist 37=[-14.608542880247701799  ,-1.1934611092782277208 ] 
dist 38=[-14.845089313757974416  ,-.89815697207642838782] 
dist 39=[-14.898146801238215592  ,-.5330064620367051121 ] 
dist 40=[-14.688258216063914058  ,-.1533769371999018785 ] 
dist 41=[-14.618329673811989023  ,.1999347198327649626 ] 
dist 42=[-14.549686640848463172  ,.6002826179862571596 ] 
dist 43=[-14.480850443005158510  ,1.1677404451304674359 ] 
dist 44=[-14.386666209562663208  ,1.7393139058886728621 ] 
dist 45=[-14.318345312827659146  ,2.1561769965877557342 ] 
dist 46=[-14.247358807055978227  ,2.5386136878743998468 ] 
dist 47=[-14.185454383204680346  ,2.9729544408418358567 ] 
dist 48=[-5.3790315524228771490 ,3.4064690578707649366 ] 
dist 49=[-4.6469855600624300442 ,3.7856590191709715478 ] 
dist 50=[-3.4192906427438911641 ,4.1970857635014902604 ] 
dist 51=[-3.3978646898601342573 ,4.7592466772854920546 ] 
dist 52=[-.41370791803305706008,5.3114037977167361521 ] 
dist 53=[-.01835879671849569238,5.6829358414730469405 ] 
dist 54=[.5649639640221447639 ,5.9928211722110399265 ] 
dist 55=[.7159801330012435081 ,6.2990491301797325709 ] 
dist 56=[2.0361989156232360133 ,6.5790763045247136712 ] 
dist 57=[2.0306790811801166141 ,6.7844394413420440243 ] 
dist 58=[1.9103944577444611919 ,6.9742493345597147306 ] 
dist 59=[1.7264666233975138949 ,7.1922371411792660583 ] 
dist 60=[1.4669899829912185366 ,7.3904583115038006434 ] 
dist 61=[1.1032742773867855514 ,7.5014009757606263211 ] 
dist 62=[.50346215101507505655,7.5853122916261975888 ] 
dist 63=[-.11079458072720214084,7.5972223726026079341 ] 
dist 64=[-.53216599881872987552,4.1158122263730340061 ] 
dist 65=[-.89201952479600694235,4.0245866541184103442 ] 
dist 66=[-1.2609130328425249282 ,3.9294649474496251134 ] 
dist 67=[-1.6064564120903700089 ,3.7428983747406942734 ] 
dist 68=[-1.8731796799467145174 ,3.5832905556900118356 ] 
dist 69=[-2.1327189583452055468 ,3.5253800496974431331 ] 
dist 70=[-2.4496149287439792658 ,3.5042283765970282406 ] 
dist 71=[-2.7471556478812034541 ,3.1044533261094124896 ] 
dist 72=[-2.9294823931301641061 ,2.4986995840208272682 ] 
dist 73=[-3.0619676987088736618 ,2.2643747141922519126 ] 
dist 74=[-3.1606693697992728031 ,2.2025838349057603248 ] 
dist 75=[-3.2324630931946889724 ,1.9788569582518214202 ] 
dist 76=[-3.2575977390278674140 ,1.9278250379471879996 ] 
dist 77=[-3.2625545174214898373 ,1.8497794003609107506 ] 
dist 78=[-3.2538633067411864709 ,1.8269650826106140385 ] 
dist 79=[-1.4063492241395580348 ,1.4205612700647512628 ] 
dist 80=[-1.6705068836703316318 ,.33475534196354596349] 
dist 81=[-2.0564102405243390505 ,.22332269906856089257] 
dist 82=[-2.3681090508871093668 ,.00152570056568882716] 
dist 83=[-2.6607311262928801135 ,-.0529462862518898570 ] 
dist 84=[-2.9193055948377036813 ,-.2321855945925107120 ] 
dist 85=[-3.0950779012342528246 ,-.2706574338391671003 ] 
dist 86=[-3.2442296007643474280 ,-.2943425357646728733 ] 
dist 87=[-3.3965464523895029946 ,-.2772201969140984477 ] 
dist 88=[-3.5284333785317882053 ,-.2428991636231336408 ] 
dist 89=[-3.5960183898327284956 ,-.1910776345536401786 ] 
dist 90=[-3.6303230037028331396 ,-.1167551081025459845 ] 
dist 91=[-3.6363528692413556359 ,.0074348356693116282 ] 
dist 92=[-3.6097851944551732926 ,.1539871681397178462 ] 
dist 93=[-3.5923658327737121365 ,.3175953079315896306 ] 
dist 94=[-3.5696710362666918312 ,.5249710207858120995 ] 
dist 95=[-3.5554502912665908883 ,.8462424512462609523 ] 
dist 96=[-2.4943569658536755180 ,1.1688376930559712647 ] 
dist 97=[-2.4061225461875592663 ,1.3815140348629141966 ] 
dist 98=[-2.3918846380840247854 ,1.5544209686804468115 ] 
dist 99=[-2.1874750384826320346 ,1.7183049922999396710 ] 
dist 100=[-2.1423354402934436693 ,1.8639270736066890863 ] 
dist 101=[-2.1012352926410501760 ,1.9639617393914482366 ] 
dist 102=[-2.0885625527970506547 ,2.0498558847667217038 ] 
dist 103=[-1.5089997050642769918 ,2.1390679507010854688 ] 
dist 104=[-1.4329075559517169832 ,2.2155849680228238689 ] 
dist 105=[-1.2824901622125796938 ,2.2508202013450412180 ] 
dist 106=[-1.2432184638197848518 ,2.3238918668103554376 ] 
dist 107=[-1.1030820451153564947 ,2.3980891721094665540 ] 
dist 108=[-1.0707651483391716981 ,2.4313890098394248415 ] 
dist 109=[-1.0243605691728025518 ,2.4515450472549531009 ] 
dist 110=[-1.0097733112246205668 ,2.4639808418827215824 ] 
dist 111=[-.3652298168905085906 ,2.4638108773142773206 ] 
dist 112=[-.870019927546854215  ,2.3764897235368452299 ] 
dist 113=[-1.2021536941080275292 ,2.3230735520876845598 ] 
dist 114=[-1.4713342698154787794 ,2.3126702750256493383 ] 
dist 115=[-1.7248768005098952930 ,2.2237260235279003752 ] 
dist 116=[-1.9488654459055411721 ,2.2010449764661735911 ] 
dist 117=[-2.1000935159213674687 ,2.1737077672596998562 ] 
dist 118=[-2.2269259845086217691 ,2.1601002676510424208 ] 
dist 119=[-2.3535445978086977473 ,2.0863221104518084602 ] 
dist 120=[-2.4656031639439790379 ,2.1715406568008061622 ] 
dist 121=[-2.5343239452796444765 ,2.2292370469482724801 ] 
dist 122=[-2.5844015773606268464 ,2.2644546245557429081 ] 
dist 123=[-2.6220551054735203344 ,2.2869909300240565608 ] 
dist 124=[-2.6487615209599759864 ,2.2940727426835805326 ] 
dist 125=[-2.6551455505774259345 ,2.2911844792369422893 ] 
dist 126=[-2.6501158851258625373 ,2.2870497055105180015 ] 
dist 127=[-2.6430260026495877656 ,2.1841917374297809075 ] 
dist 128=[-1.6570049960552926946 ,2.1712314620680231368 ] 
dist 129=[-1.8404137263087091062 ,2.1235188260596137852 ] 
dist 130=[-1.9802599780172386834 ,2.1135134503376401303 ] 
dist 131=[-2.0973704350421991744 ,1.9773178210542393475 ] 
dist 132=[-2.1912144199110970796 ,1.9448728488740051571 ] 
dist 133=[-2.2381829646659878566 ,1.9133881579962198410 ] 
dist 134=[-2.2630295824819693396 ,1.8981617390079529236 ] 
dist 135=[-2.2685629542649628429 ,1.4446269594865155811 ] 
dist 136=[-2.2298661711640089030 ,1.3823314572831808738 ] 
dist 137=[-2.2603392420982479923 ,1.2587830961033118027 ] 
dist 138=[-2.2947831659086365428 ,1.2255929477900285414 ] 
dist 139=[-2.3214323585712911709 ,1.1021406752658088120 ] 
dist 140=[-2.3287709520902983577 ,1.0736631235186823995 ] 
dist 141=[-2.3260051634770877852 ,1.0216820155645255232 ] 
dist 142=[-2.3200863586472142457 ,1.0077211372677561905 ] 
dist 143=[-2.0898239741409763294 ,.4754440632615283480 ] 
dist 144=[-.85027517663297810138,.6429496179141063053 ] 
dist 145=[-.74107588014582698275,.7827681898310996775 ] 
dist 146=[-.48812867534600834957,.9213724942656856654 ] 
dist 147=[-.44423185356886430547,1.0486058765915225864 ] 
dist 148=[-.11573561240949377604,1.1430421920819999659 ] 
dist 149=[-.05749136308522849290,1.2315589852886139653 ] 
dist 150=[.03870153616767868319,1.3351699828007046516 ] 
dist 151=[.06088040753071329293,1.4305998430105265165 ] 
dist 152=[.40519340739240273165,1.4864648855955571002 ] 
dist 153=[.450213818037073629  ,1.5240693878516195270 ] 
dist 154=[.53512557711856548993,1.5466165656211706704 ] 
dist 155=[.55373201092162974123,1.5601325541779894478 ] 
dist 156=[.46156728937195715163,1.5991393994986032188 ] 
dist 157=[.28064528331903070909,1.6178868364480005476 ] 
dist 158=[-.00081638831426026786,1.6253143258664834383 ] 
dist 159=[-.28478759312517384349,1.6235035101199250865 ] 
dist 160=[-.47572586428733717147,1.3997493390468639795 ] 
dist 161=[-.63508387052993239258,1.3399157984773227856 ] 
dist 162=[-.79301053884256078684,1.3281519097583292015 ] 
dist 163=[-.93793018451964121242,1.2058148169419871963 ] 
dist 164=[-1.0453738846033981083 ,1.1791454527159607923 ] 
dist 165=[-1.1459447093426254675 ,1.1472132068827993382 ] 
dist 166=[-1.2634327209130012177 ,1.1340122679908447919 ] 
dist 167=[-1.3714607068048624148 ,.8238540878796850711 ] 
dist 168=[-1.4342740678445717095 ,.78190030382255371288] 
dist 169=[-1.4759927012996295733 ,.69428829490057138112] 
dist 170=[-1.4998262280712730624 ,.67019839107698278832] 
dist 171=[-1.5148820251194556565 ,.5766163171088818099 ] 
dist 172=[-1.5215663399348239643 ,.6266056473773872941 ] 
dist 173=[-1.5233945297036897152 ,.67928059703489016994] 
dist 174=[-1.5196222370767529731 ,.74397237092084922225] 
dist 175=[-1.3377411485578048353 ,.84191033921763674957] 
dist 176=[-1.3124343205300072657 ,.93942053262007642563] 
dist 177=[-1.3454040163993251737 ,1.0024034647287230180 ] 
dist 178=[-1.4358324005124189488 ,1.0520975289435081348 ] 
dist 179=[-1.5101374456985691176 ,1.0965776431212659234 ] 
dist 180=[-1.5690057497020617757 ,1.1342367860651997464 ] 
dist 181=[-1.5978135543135364150 ,1.1567097023428048717 ] 
dist 182=[-1.6122716935743209019 ,1.1723216839483317377 ] 
dist 183=[-1.6138573570720379742 ,1.1825970427903277857 ] 
dist 184=[-1.5699319913521017451 ,1.1877867150644464742 ] 
dist 185=[-1.5575775814094577579 ,1.1875206306507203183 ] 
dist 186=[-1.5384084903502996422 ,1.1763438444150928216 ] 
dist 187=[-1.5303226789142440188 ,1.1732648153781790657 ] 
dist 188=[-1.4977579312018161394 ,1.1145305448274354736 ] 
dist 189=[-1.4868844635070602818 ,1.0991897016661447894 ] 
dist 190=[-1.4937609273310334221 ,1.0865941858659688438 ] 
dist 191=[-1.5545742584363125795 ,1.0796691099080463499 ] 
dist 192=[-1.5853636007717678176 ,.8005319680078540153 ] 
dist 193=[-1.6011509320281333595 ,.9292117851206700209 ] 
dist 194=[-1.6034087040012899497 ,1.0549155805856730733 ] 
dist 195=[-1.5875980757580083857 ,1.1691119042155820373 ] 
dist 196=[-1.5799114526011321951 ,1.2518612651258119938 ] 
dist 197=[-1.5717376596892774005 ,1.3274405915025737487 ] 
dist 198=[-1.5644995839013239023 ,1.4130193603458494072 ] 
dist 199=[-1.3298651004972427661 ,1.4903204081688341878 ] 
dist 200=[-1.2949534329296089717 ,1.5328602981855544094 ] 
dist 201=[-1.2267483910040580151 ,1.5580936829869521803 ] 
dist 202=[-1.2076031572956206134 ,1.5663173985834705408 ] 
dist 203=[-1.1329596990249254216 ,1.5674791817653141637 ] 
dist 204=[-1.1147757643302184237 ,1.5645244739305584417 ] 
dist 205=[-1.0769611144519836380 ,1.5579881573622514897 ] 
dist 206=[-1.0649127685586763924 ,1.5526246368119656504 ] 
dist 207=[.07541552869255268800,1.3580823966381313296 ] 
dist 208=[-.01474631725561001914,1.4238994758920897868 ] 
dist 209=[-.08180468031940791870,1.4854661036323220331 ] 
dist 210=[-.14477321518581753477,1.5283222913094653725 ] 
dist 211=[-.21861549780404709287,1.5568794243897781374 ] 
dist 212=[-.2937945161066332464 ,1.5757003439378979054 ] 
dist 213=[-.36210073915444191321,1.5796928331014896821 ] 
dist 214=[-.43846078540559479298,1.5773033186169651242 ] 
dist 215=[-.54578788669326998893,1.5717798804382479936 ] 
dist 216=[-.6539926382908418848 ,1.4653083978730081769 ] 
dist 217=[-.73385729083796430092,1.4453171453638150019 ] 
dist 218=[-.80827113492990316539,1.4002520741375940001 ] 
dist 219=[-.89472207016334967569,1.3848289112533561363 ] 
dist 220=[-.98232050091333013299,1.3101976375945395901 ] 
dist 221=[-1.0613165535125690950 ,1.2931630561646303950 ] 
dist 222=[-1.1491670826400044949 ,1.2480517139946817906 ] 
dist 223=[-1.2721109276784535331 ,1.2351833013159943572 ] 
dist 224=[-1.3909660685757030061 ,-.02786145911822721931] 
dist 225=[-1.4624973663087115869 ,-.11118596812928391044] 
dist 226=[-1.5130856920014036462 ,-.13007413268737845654] 
dist 227=[-1.5483466500462797790 ,-.18049623657950179369] 
dist 228=[-1.5730813396020470970 ,-.18478022662415200217] 
dist 229=[-1.5816532114984220769 ,-.1731753537883779601 ] 
dist 230=[-1.6219116381714894763 ,-.13684973156703649085] 
dist 231=[-1.6825690448500170873 ,-.09150852705764225143] 
dist 232=[-1.7117117373037132251 ,-.04391869014662553610] 
dist 233=[-1.7261789714277618796 ,.01444286799702805951] 
dist 234=[-1.7282597263544836173 ,.10277867566557159953] 
dist 235=[-1.6997241580684251632 ,.20364486405740462469] 
dist 236=[-1.6762090414368537804 ,.31202039641282524252] 
dist 237=[-1.6623915028876231169 ,.44667852766048261111] 
dist 238=[-1.5591585534036940762 ,.65244934627961873692] 
dist 239=[-1.2589770348367715344 ,.8585445591650612950 ] 
dist 240=[-.48920040060849328127,.9944973989259286323 ] 
dist 241=[-.416803843299038164  ,1.1051265050082926043 ] 
dist 242=[-.25672145244991808609,1.2101440685203212659 ] 
dist 243=[-.22266689413037698776,1.3035334733616593059 ] 
dist 244=[-.03703468348047175622,1.3677495105940840243 ] 
dist 245=[-.00467290243695932028,1.4229017833901296648 ] 
dist 246=[.06464314032663775685,1.4801132935765272717 ] 
dist 247=[.07986168710248649810,1.5289430083099613754 ] 
dist 248=[.19865490151516035368,1.5506398384189485121 ] 
dist 249=[.21919980354350962072,1.5606815373670619321 ] 
dist 250=[.23003333272506083582,1.5629923132365782736 ] 
dist 251=[.21820182445003753729,1.5247758208419934486 ] 
dist 252=[.19468199708354825112,1.5148703281460039848 ] 
dist 253=[.15579328326601968528,1.5013245098002777477 ] 
dist 254=[.09819515801263196316,1.4147731665720035004 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 1, 0, 1, 2] 
dist 0=[50.933962330756973516  ,50.933962330756973516  ] 
dist 1=[50.448284064492450250  ,51.302218023922569737  ] 
dist 2=[49.673935067694266211  ,51.607352106140228714  ] 
dist 3=[48.694519861741242243  ,51.850374916136110996  ] 
dist 4=[47.389786457932430011  ,51.970433986833275233  ] 
dist 5=[45.593317619561647582  ,52.022822535185724690  ] 
dist 6=[42.650075070532024611  ,51.995425235373609380  ] 
dist 7=[39.622162093709746700  ,51.928597962956900076  ] 
dist 8=[37.487498187903214222  ,51.828179530321084571  ] 
dist 9=[35.592988343634602217  ,51.669628613975189970  ] 
dist 10=[33.524020631264670391  ,51.579953345310471982  ] 
dist 11=[31.494213208363891774  ,51.095757583397309261  ] 
dist 12=[29.755911692711310566  ,50.949797411423454500  ] 
dist 13=[27.892775861801217492  ,50.436718783060809078  ] 
dist 14=[24.950170434833962073  ,50.311901574094396438  ] 
dist 15=[22.224577927056255651  ,38.185273744196043491  ] 
dist 16=[19.387924989451962515  ,37.049422069354452223  ] 
dist 17=[16.688541593065046046  ,34.268886555365421246  ] 
dist 18=[14.510842923879078477  ,33.845575542160668069  ] 
dist 19=[12.291978094698143683  ,29.655451819404863426  ] 
dist 20=[9.4276367509623437255 ,28.860160823779300754  ] 
dist 21=[6.6354100640930535152 ,27.919521646328661788  ] 
dist 22=[4.7042477410658015827 ,27.685453891179098764  ] 
dist 23=[3.0268207772900735698 ,20.549902145248415853  ] 
dist 24=[1.2475896038860255643 ,19.648517350621115412  ] 
dist 25=[-.4712955467315991103 ,17.801124928010410297  ] 
dist 26=[-1.9082778653849476858 ,17.319897049278444883  ] 
dist 27=[-3.4226470544186307381 ,15.563384094200536986  ] 
dist 28=[-5.4519139053299244526 ,15.205734041005147351  ] 
dist 29=[-7.4009773118563643118 ,14.569447102808263617  ] 
dist 30=[-8.5951338498863638795 ,14.424725531589384008  ] 
dist 31=[-9.4742943935253482182 ,3.1588776308369052691 ] 
dist 32=[-10.164320898372139053  ,2.1953978651519547389 ] 
dist 33=[-10.706558188326897905  ,.0991777232439375027 ] 
dist 34=[-10.994693664975164668  ,-.3025057333981271718 ] 
dist 35=[-11.155117333573561164  ,-2.5803255744671363654 ] 
dist 36=[-11.185960079099009120  ,-2.9559150344568075284 ] 
dist 37=[-10.531490172637832606  ,-3.7322075574428632561 ] 
dist 38=[-11.568567774968110317  ,-3.5247755029790885008 ] 
dist 39=[-12.718254016724662640  ,-2.9357808362937910945 ] 
dist 40=[-13.397220005121005964  ,-2.5059983208211552145 ] 
dist 41=[-13.864050996800943269  ,-2.1125873141923862777 ] 
dist 42=[-14.166281315112741724  ,-1.6682414010777697958 ] 
dist 43=[-14.378569209200464989  ,-1.2268111859028680958 ] 
dist 44=[-14.486086969959279842  ,-.8447978786535682476 ] 
dist 45=[-14.538191916962276335  ,-.4338371198624139527 ] 
dist 46=[-14.529099572497294095  ,.1233287891358682592 ] 
dist 47=[-4.6055318573219126411 ,.6753873100765465047 ] 
dist 48=[-4.0514480656200910000 ,1.7746992483765711360 ] 
dist 49=[-2.8005816237598535280 ,2.8193150578018542033 ] 
dist 50=[-2.7451226645532724785 ,3.6240717277852782062 ] 
dist 51=[-2.3305363843011200930 ,4.4069981590931742109 ] 
dist 52=[-2.2533223981739286632 ,5.3644253128732429235 ] 
dist 53=[-2.1259456143258271917 ,6.2663845385825497327 ] 
dist 54=[-2.0945826606306988417 ,6.8278820080501932707 ] 
dist 55=[1.8987164763581770461 ,7.2470168376733922564 ] 
dist 56=[2.1271017835128602178 ,7.5807072418652900957 ] 
dist 57=[2.5872449271595545644 ,7.8384638855254401068 ] 
dist 58=[2.6840169168751845869 ,7.9546468519958161545 ] 
dist 59=[3.0131045025706455693 ,8.0041257191100432197 ] 
dist 60=[3.0597960466567015652 ,7.9975486846784023530 ] 
dist 61=[2.2497956795596359737 ,4.4628650690044125942 ] 
dist 62=[1.6809923191348772767 ,4.5297310797894649707 ] 
dist 63=[1.1925669814842629533 ,4.6631760096235455891 ] 
dist 64=[.6866684560708020618 ,4.7366248205677392820 ] 
dist 65=[.2086046868796416690 ,4.7804220702117466189 ] 
dist 66=[-.1687992127366734137 ,4.7954721539293703624 ] 
dist 67=[-.5446616210085471168 ,4.7911023847856377848 ] 
dist 68=[-1.0166505717193548823 ,4.7824439746060631301 ] 
dist 69=[-1.4680133856763603399 ,4.7215407081525452524 ] 
dist 70=[-1.7615948913046027778 ,4.7087473997161871021 ] 
dist 71=[-1.9959555270312009761 ,3.8329317899281267220 ] 
dist 72=[-2.2110038022868782038 ,3.7798431899123835886 ] 
dist 73=[-2.3975345363667671068 ,3.6416759388347461496 ] 
dist 74=[-2.5181245980424232098 ,3.6077539429567062568 ] 
dist 75=[-2.6138779883804972897 ,3.3574379502940626000 ] 
dist 76=[-2.7013775385179475601 ,3.3033231313727826577 ] 
dist 77=[-2.7741947152423819611 ,3.2134616412271668077 ] 
dist 78=[-3.0436777477370312693 ,3.1877265008041412575 ] 
dist 79=[-3.7627057832405535695 ,.2793872011832418346 ] 
dist 80=[-4.2161481117505462826 ,.1566743427185126454 ] 
dist 81=[-4.5623792669677306464 ,-.1124402363265983884 ] 
dist 82=[-4.8534218585909983420 ,-.1680022926692356932 ] 
dist 83=[-5.0877548371960459777 ,-.3435616611982906194 ] 
dist 84=[-5.2075805529985346663 ,-.0498370684292855294 ] 
dist 85=[-5.2722923136381670169 ,.2516701737247625330 ] 
dist 86=[-5.2865911797547315389 ,.4821854703041866905 ] 
dist 87=[-5.2109134440169719103 ,.7047368003392699798 ] 
dist 88=[-5.2122029097135469602 ,.9745148895776891642 ] 
dist 89=[-5.2558690651302776977 ,1.2540094264918305219 ] 
dist 90=[-5.2866480031803700174 ,1.5153792959277563742 ] 
dist 91=[-5.3069712788269695081 ,1.8136262830988659337 ] 
dist 92=[-5.3088936044315894404 ,2.2403611492962366450 ] 
dist 93=[-5.2978100120281335305 ,2.6570044254397827543 ] 
dist 94=[-5.2814959645432652901 ,2.9149837084206241681 ] 
dist 95=[-2.6323790689404761023 ,3.1063034469767335194 ] 
dist 96=[-2.5828897437391373861 ,3.2568679804293917284 ] 
dist 97=[-2.4547984700573184294 ,3.3752080127083599854 ] 
dist 98=[-2.4255018933751864238 ,3.4843172633309033470 ] 
dist 99=[-2.1957323618062898758 ,3.6424137049415100216 ] 
dist 100=[-2.1464537201943200737 ,3.7959645701905049626 ] 
dist 101=[-2.0701567486822732602 ,3.9275029754836217120 ] 
dist 102=[-2.0467042029904627227 ,3.9977343164194798514 ] 
dist 103=[-1.1086420435297016897 ,4.0365561300035618281 ] 
dist 104=[-1.0027051950192634194 ,4.0427126817338017766 ] 
dist 105=[-.78610272859474415544,4.0320808115195080474 ] 
dist 106=[-.7295737421793391119 ,4.0196376983050053829 ] 
dist 107=[-.5242343547311347878 ,3.9719869979037558755 ] 
dist 108=[-.4814283417387548625 ,3.9465443928956009366 ] 
dist 109=[-.4110968960171725128 ,3.6103665083117003432 ] 
dist 110=[-.3938026899289213486 ,3.6120492365232224045 ] 
dist 111=[-.3644150794890312874 ,2.7070741560100746528 ] 
dist 112=[-.56680623929871200236,2.7388746019116679002 ] 
dist 113=[-.88989468480759880688,2.7520801295477751296 ] 
dist 114=[-1.1387770894868250827 ,2.7524686865443625212 ] 
dist 115=[-1.3809808782080722438 ,2.6876323948869912892 ] 
dist 116=[-1.6774158715261659812 ,2.6673166869280259610 ] 
dist 117=[-1.9570829097659307943 ,2.6519897738384103616 ] 
dist 118=[-2.1323621553791560108 ,2.6395175011648176080 ] 
dist 119=[-2.2647512702627346497 ,2.1802393632005079658 ] 
dist 120=[-2.3732322788367505369 ,2.1150465198052094122 ] 
dist 121=[-2.4582768208206390699 ,1.9897684035599032553 ] 
dist 122=[-2.4971241641064939640 ,1.9560758509512089742 ] 
dist 123=[-2.5156107137426581772 ,1.8328225781110718235 ] 
dist 124=[-2.5193892047477498540 ,1.8017607245534987453 ] 
dist 125=[-.8267201608042561885 ,1.7504663203838303174 ] 
dist 126=[-1.0392061982879660850 ,1.7351533463981594942 ] 
dist 127=[-1.2465989293481404663 ,.4124805780954723142 ] 
dist 128=[-1.3774206612977353317 ,.4290656868653122408 ] 
dist 129=[-1.4773191052375671610 ,.4483373517629529255 ] 
dist 130=[-1.5612669753077110144 ,.47623321779087574749] 
dist 131=[-1.6286412365464809790 ,.50745168540430475132] 
dist 132=[-1.6623799820008584860 ,.53998242142256299456] 
dist 133=[-1.7569181897484447693 ,.57963800576827463071] 
dist 134=[-1.9656272539294085096 ,.6392839411287106028 ] 
dist 135=[-2.1602095159068681960 ,.7009223776849980647 ] 
dist 136=[-2.2783684568679788954 ,.8169875906117315473 ] 
dist 137=[-2.3632173819775362503 ,.9368313607242954348 ] 
dist 138=[-2.4248294359394524165 ,1.0384707718215529249 ] 
dist 139=[-2.4692968241354399706 ,1.1462983043666083369 ] 
dist 140=[-2.4857136433245566915 ,1.2908535839300771608 ] 
dist 141=[-2.4888321375725502977 ,1.4296203213422154674 ] 
dist 142=[-2.4836372850368814278 ,1.5143445644552401914 ] 
dist 143=[-.26351490298684484196,1.5757690094249292033 ] 
dist 144=[-.32710362040527737787,1.6215279414797892048 ] 
dist 145=[-.39232306298075889308,1.6551021124074418241 ] 
dist 146=[-.4522690258496330491 ,1.6678862390832878572 ] 
dist 147=[-.51981759833184172514,1.6712224352289722429 ] 
dist 148=[-.61538148074388519561,1.6677459614937468417 ] 
dist 149=[-.71194312696330935144,1.5779411584040335055 ] 
dist 150=[-.78347539122155388479,1.5596492419272519647 ] 
dist 151=[-.8503615689925140341 ,1.5374161670750117651 ] 
dist 152=[-.9283830221081622041 ,1.6179538250512534100 ] 
dist 153=[-1.0075844216161247719 ,1.6760789126813239441 ] 
dist 154=[-1.0791819235821225040 ,1.7188753066446456167 ] 
dist 155=[-1.1589230976334591831 ,1.7512679913295481602 ] 
dist 156=[-1.2706299147228125488 ,1.8102562350584764503 ] 
dist 157=[-1.3783953597936670653 ,1.8606780523001675321 ] 
dist 158=[-1.4424063883469919044 ,1.9127290904419869821 ] 
dist 159=[-1.4866260248873164771 ,1.9561585792931220960 ] 
dist 160=[-1.5153996194671634232 ,1.9721686610762278402 ] 
dist 161=[-1.5345479398328436028 ,1.9769920846930227352 ] 
dist 162=[-1.5403498230183392555 ,1.9757366388710704480 ] 
dist 163=[-1.5389169451831890276 ,1.9187606674630348890 ] 
dist 164=[-1.5352472508857153842 ,1.9010707056977271515 ] 
dist 165=[-1.4660599621897728462 ,1.8878260777079126589 ] 
dist 166=[-1.5325693069390838644 ,1.8772009123728411044 ] 
dist 167=[-1.5773789603917085802 ,1.5348308577447464679 ] 
dist 168=[-1.6101211252995821485 ,1.4862819506680553831 ] 
dist 169=[-1.6717100654016412821 ,1.3918916373556002783 ] 
dist 170=[-1.7184335205058147681 ,1.3663491387340884523 ] 
dist 171=[-1.7524896041924896312 ,1.2715366014259937226 ] 
dist 172=[-1.7635266383328253595 ,1.2483416693151263181 ] 
dist 173=[-1.7656579053950776359 ,1.2068516551128310228 ] 
dist 174=[-1.7641715342033416162 ,1.1953453347569222895 ] 
dist 175=[-1.3241715132867055148 ,.69854387096093015145] 
dist 176=[-1.3453178960880509479 ,.86602324535119776697] 
dist 177=[-1.3552497655435244708 ,1.0182273211837672749 ] 
dist 178=[-1.3556626269755077278 ,1.1285890395638824032 ] 
dist 179=[-1.3365762844423112118 ,1.2294443087444586079 ] 
dist 180=[-1.3278957801331012232 ,1.3437014292455989538 ] 
dist 181=[-1.3184070998379478830 ,1.4479681865944495735 ] 
dist 182=[-1.3120215183502321969 ,1.5089481794326385654 ] 
dist 183=[-1.1149262978186241069 ,1.5498936713373765205 ] 
dist 184=[-1.0855994224643569556 ,1.5741984086116541694 ] 
dist 185=[-1.0262034868577019071 ,1.5893748116036503413 ] 
dist 186=[-1.0091197889589150636 ,1.5938857488586188388 ] 
dist 187=[-.93954165667092472478,1.5914394185684736153 ] 
dist 188=[-.92380737652045032628,1.5881939958252655820 ] 
dist 189=[-.88630631106672831003,1.4416314336750788794 ] 
dist 190=[-.8738046980516481846 ,1.4867195067459701010 ] 
dist 191=[-.37960826953159661632,1.5135972768574374464 ] 
dist 192=[-.45936550581556629729,1.5226776909280091618 ] 
dist 193=[-.53537520285952919824,1.5248472948437897768 ] 
dist 194=[-.59649948657872121322,1.5241386980659673622 ] 
dist 195=[-.65842152947652708524,1.5211918764544588498 ] 
dist 196=[-.73761330488505116995,1.5156482579109679737 ] 
dist 197=[-.81399917417964429318,1.3093015245277052580 ] 
dist 198=[-.86472143605145575095,1.2781236130662445450 ] 
dist 199=[-.9063472347811646734 ,1.3038056866982428781 ] 
dist 200=[-.9464267280206996437 ,1.3574313691341247908 ] 
dist 201=[-.9824260620365325457 ,1.3919951024393089707 ] 
dist 202=[-1.0077658969804367400 ,1.4095757681465092982 ] 
dist 203=[-1.0301347881986774293 ,1.4195555633830565026 ] 
dist 204=[-1.0542734189236714217 ,1.4237832394498121941 ] 
dist 205=[-1.0744354271792651258 ,1.4246067810556528527 ] 
dist 206=[-1.0809330120405020116 ,1.4210068759456459854 ] 
dist 207=[-1.0819323648225969823 ,.65125052796438756615] 
dist 208=[-1.0801554722486799826 ,.74828897430854652706] 
dist 209=[-1.0466444689487240268 ,.83637532943080531514] 
dist 210=[-1.0362248876446902223 ,.90008153698377220792] 
dist 211=[-1.0265602196462500788 ,.9581368819948314184 ] 
dist 212=[-1.1287349556431926670 ,1.0236658826141093839 ] 
dist 213=[-1.2447277081773865890 ,1.0827175759405972044 ] 
dist 214=[-1.3149166239514596044 ,1.1149181756987618298 ] 
dist 215=[-1.3650089534532238344 ,1.1336096775486457632 ] 
dist 216=[-1.4007863491332307197 ,1.1387400483685659165 ] 
dist 217=[-1.4265935445226872156 ,1.1388847575028023319 ] 
dist 218=[-1.4368903517143473764 ,1.1376789570790386700 ] 
dist 219=[-1.4390129724265987935 ,1.1352515811635097088 ] 
dist 220=[-1.4368577539660534570 ,1.1307734260566922411 ] 
dist 221=[-1.1031001723964329433 ,.9656269539963143990 ] 
dist 222=[-1.1051247082414751744 ,.9434259062285997574 ] 
dist 223=[-1.1022662525572069465 ,.8820962963649280007 ] 
dist 224=[-1.0990399995337288131 ,.8731638441438093772 ] 
dist 225=[-1.0850410536756205702 ,.7558164169712193118 ] 
dist 226=[-1.0790219669461228874 ,.7315693706408380401 ] 
dist 227=[-1.0299218198227064044 ,.7087832057041627054 ] 
dist 228=[-1.0170260471546161991 ,.74975109839220254147] 
dist 229=[-.99781990053587319142,.85735598535636936269] 
dist 230=[-.9906230502596604926 ,.93078163716915481854] 
dist 231=[-.80733798622955538139,.99324844215537364244] 
dist 232=[-.78096468107156326535,1.0571126636769190791 ] 
dist 233=[-.72392970784811938549,1.1170081696978914046 ] 
dist 234=[-.70718277721023366033,1.1636349909843785883 ] 
dist 235=[-.63580306468908674503,1.2094885981874241052 ] 
dist 236=[-.62150889464738327426,1.2662996339909978134 ] 
dist 237=[-.58282543660273180309,1.3180831977580682191 ] 
dist 238=[-.59990302193322339387,1.3438700486619112047 ] 
dist 239=[-.70539117548716890634,1.3572668476493276513 ] 
dist 240=[-.81008183332358139332,1.3591635382907907686 ] 
dist 241=[-.90626352671186622992,1.3455986996023300127 ] 
dist 242=[-.97778886774529101903,1.3390874382752854945 ] 
dist 243=[-1.0449611186253640599 ,1.3322225928381051814 ] 
dist 244=[-1.1237674678552535574 ,1.3260643038713946835 ] 
dist 245=[-1.1964185357215778058 ,1.1265304701300427723 ] 
dist 246=[-1.2390224838398438858 ,1.0969016524287407255 ] 
dist 247=[-1.2677773384520224085 ,1.0390213160240579307 ] 
dist 248=[-1.2851512226439741639 ,1.0227981439484792247 ] 
dist 249=[-1.2952740172987307054 ,.95966904394323407124] 
dist 250=[-1.2958660924719147320 ,.94428809043873101436] 
dist 251=[-1.2907830325217264804 ,.91247169729466602026] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 1, 0, 0, 1, 2] 
dist 0=[59.244753957943383109  ,59.244753957943383109  ] 
dist 1=[58.848312401656782934  ,59.611961719291943822  ] 
dist 2=[57.632755755521841742  ,60.056313695800703275  ] 
dist 3=[56.187441595763965360  ,60.251141818479844456  ] 
dist 4=[54.760449224925167054  ,60.296931633279866531  ] 
dist 5=[53.071266313714089668  ,60.249580353025394727  ] 
dist 6=[50.578773452771068059  ,59.946639250062400076  ] 
dist 7=[47.754832572481240037  ,59.798164056962281458  ] 
dist 8=[44.741974340438343394  ,57.495957957029789934  ] 
dist 9=[41.007531381277785053  ,57.024804992748451569  ] 
dist 10=[35.301943550437501512  ,56.268126536065931473  ] 
dist 11=[29.553218555790939604  ,56.026057581924117730  ] 
dist 12=[25.646396254500572446  ,55.275225743500734257  ] 
dist 13=[22.332592743725617865  ,55.007088890904216101  ] 
dist 14=[18.951753846343474861  ,53.360581113184869758  ] 
dist 15=[15.777154055787947318  ,49.592747719019900369  ] 
dist 16=[13.286673102122138152  ,33.495948526835122274  ] 
dist 17=[10.813733464507970252  ,31.724921097974521862  ] 
dist 18=[7.7086469881353746856 ,27.547962450677496169  ] 
dist 19=[4.7242983969124185532 ,26.899855325032850630  ] 
dist 20=[2.7332369215523592732 ,24.141726970127028046  ] 
dist 21=[1.0814890863440328391 ,23.704507252658209736  ] 
dist 22=[-.54813222791648657108,23.190527193607726848  ] 
dist 23=[-2.0483682875941717840 ,23.058100212832221091  ] 
dist 24=[-3.1839583834057383634 ,11.299701037027622550  ] 
dist 25=[-4.2776118218203004662 ,10.438095415384131190  ] 
dist 26=[-5.6116692449219887504 ,8.4949358119034800824 ] 
dist 27=[-6.8556994537754061791 ,8.2111161622062785019 ] 
dist 28=[-7.5899191577317680902 ,5.9470215110622221902 ] 
dist 29=[-8.0993644026058099482 ,5.5834236233104103226 ] 
dist 30=[-8.4447287561301312063 ,5.0344914990789201483 ] 
dist 31=[-10.267584350870095015  ,4.9142921655382369561 ] 
dist 32=[-12.051536259566724628  ,-5.4888318837488220448 ] 
dist 33=[-13.164407504849814622  ,-5.6361848379483390924 ] 
dist 34=[-14.001609281845722970  ,-5.5172892657336375068 ] 
dist 35=[-14.684385618440059766  ,-5.0096597094048157632 ] 
dist 36=[-15.217188041602785652  ,-4.2964688153266151819 ] 
dist 37=[-15.455276870810056204  ,-3.3570975308291376567 ] 
dist 38=[-15.561818167759467906  ,-2.0761257323458626212 ] 
dist 39=[-15.569564008930842665  ,0                     ] 
dist 40=[-11.477335463297750080  ,-2.9797621636153705797 ] 
dist 41=[-11.529605568233818871  ,-1.7834906762310057097 ] 
dist 42=[-11.546294729216982268  ,-.74812596156632935727] 
dist 43=[-11.521567937480276814  ,.55124007675223046323] 
dist 44=[-11.474024720309782344  ,1.6837292129854846469 ] 
dist 45=[-11.431348372910080905  ,2.6403069771853973392 ] 
dist 46=[-11.314291822775856900  ,3.6065861441135741785 ] 
dist 47=[-11.256166021997857676  ,4.5047393420843537401 ] 
dist 48=[-5.9212510639696464510 ,5.1893652636401298051 ] 
dist 49=[-5.4514285535836721904 ,5.8482816410137545578 ] 
dist 50=[-4.3218657369732090821 ,6.6436935961941439322 ] 
dist 51=[-4.1527933305417703286 ,7.3870680230103430282 ] 
dist 52=[-2.5538294637849771294 ,7.8382200690156159225 ] 
dist 53=[-2.2636610287427925696 ,8.1608958450520072373 ] 
dist 54=[-1.8968158180930080686 ,8.3914149175909436552 ] 
dist 55=[-1.8154683031260148495 ,8.5577184691311912688 ] 
dist 56=[.4068235459353518712 ,8.6242671795375893681 ] 
dist 57=[.6727401355284068140 ,8.6365489588218621954 ] 
dist 58=[1.2497937009806773615 ,8.6227531973739637800 ] 
dist 59=[.9821342076748072898 ,5.0572424722200246465 ] 
dist 60=[.2061022722534922022 ,5.2973667216476216929 ] 
dist 61=[-.4470130510240357792 ,5.4246124624362129489 ] 
dist 62=[-1.1031087891386587120 ,5.4937721707250710442 ] 
dist 63=[-1.7109934555401569368 ,5.5073894600215010639 ] 
dist 64=[-2.1717344706686336102 ,5.3256762093115685635 ] 
dist 65=[-2.6131044848394787811 ,5.2927448494853374928 ] 
dist 66=[-3.1437454342123546475 ,5.1733238162986959685 ] 
dist 67=[-3.6401938355733407219 ,5.1506052783709470223 ] 
dist 68=[-3.9451185896798815506 ,4.8253104292901315902 ] 
dist 69=[-4.1684584529322348196 ,4.7501591615468507377 ] 
dist 70=[-4.3392872855741141008 ,4.6781604739052681871 ] 
dist 71=[-4.4700766790140688749 ,4.6482475468886909022 ] 
dist 72=[-4.5335565712183379132 ,4.2308541192479487614 ] 
dist 73=[-4.5600580740555142106 ,4.2284737054074798452 ] 
dist 74=[-4.5619128883857338074 ,4.1896379913123418138 ] 
dist 75=[-4.2725651903044284633 ,4.1833646476497063146 ] 
dist 76=[-4.2242856633233222669 ,3.9999733406224167483 ] 
dist 77=[-4.0910405696660898613 ,3.9538597008770903617 ] 
dist 78=[-4.0535083112658405269 ,3.9247906048624810636 ] 
dist 79=[-3.7784304365790899468 ,3.9152293606674461395 ] 
dist 80=[-3.7155289370053655014 ,3.1055907502275253212 ] 
dist 81=[-3.6110117492935002318 ,3.0053662359973362346 ] 
dist 82=[-3.5796122849529228874 ,2.7523344384692665740 ] 
dist 83=[-2.8676190669576225568 ,2.7089665744749309462 ] 
dist 84=[-2.7676836341321430408 ,2.2921901770579914720 ] 
dist 85=[-2.7884221012517377677 ,2.2761327018235127400 ] 
dist 86=[-3.0481360864307155486 ,2.5947310190599906840 ] 
dist 87=[-3.3455450952303273872 ,2.9076469336591887142 ] 
dist 88=[-3.6171880787262381364 ,3.1748464104107338530 ] 
dist 89=[-3.7740329638791766575 ,3.4599844319836016135 ] 
dist 90=[-3.8771341867985640086 ,3.8445709044936491261 ] 
dist 91=[-3.9341995013045497487 ,4.2122274950923559364 ] 
dist 92=[-3.9699033098881551559 ,4.4297971526064229610 ] 
dist 93=[-3.9877016954274392954 ,4.5793931086799532840 ] 
dist 94=[-3.9958742848229972030 ,4.6756853729449962884 ] 
dist 95=[-3.9931031317843224802 ,4.7422228514724556053 ] 
dist 96=[-3.4439833395336696733 ,4.7730196449812653960 ] 
dist 97=[-3.3719938087144820487 ,4.7836241533683524034 ] 
dist 98=[-3.1987789827425546001 ,4.7757867621162311744 ] 
dist 99=[-3.1515198002109497625 ,4.4261173885169118394 ] 
dist 100=[-2.8772989649132933323 ,4.5144612816472385899 ] 
dist 101=[-2.8186744790548096655 ,4.5700334712165442030 ] 
dist 102=[-2.7042786775921652619 ,4.5955164131136084849 ] 
dist 103=[-2.6712448935565981940 ,4.6005607528159974732 ] 
dist 104=[-2.1403333700842684847 ,4.5955515998964899781 ] 
dist 105=[-2.0644058329230057591 ,4.5446173002661309538 ] 
dist 106=[-1.8730759730721038852 ,4.5341121858138636604 ] 
dist 107=[-1.8414930030830818022 ,2.9669420820752667676 ] 
dist 108=[-1.5323951898124042591 ,2.8157874491521162815 ] 
dist 109=[-1.4716573230633021171 ,2.4457682731134385261 ] 
dist 110=[-1.4063492339203570412 ,2.3848992995220915805 ] 
dist 111=[-1.8386353268474690402 ,2.2762119684782097278 ] 
dist 112=[-2.1640639930803507420 ,2.1169498441616097908 ] 
dist 113=[-2.4737158047405516543 ,2.0911729918463052294 ] 
dist 114=[-2.8430193609520270847 ,2.0213366798241143522 ] 
dist 115=[-3.1868533000624949264 ,2.0017955665561652487 ] 
dist 116=[-3.3948325955230593353 ,1.8616652309169527772 ] 
dist 117=[-3.5432080204859896081 ,1.8297910336649092230 ] 
dist 118=[-3.6491112913960862524 ,1.7759893403199777412 ] 
dist 119=[-3.7281455628944061507 ,1.7601764459336959877 ] 
dist 120=[-3.7692704036353632132 ,1.4043101095592366682 ] 
dist 121=[-3.7905173084631710451 ,1.3542433004640544196 ] 
dist 122=[-3.7902219017447014021 ,1.2390708564379315285 ] 
dist 123=[-1.3413966881763764660 ,1.2107189283439165332 ] 
dist 124=[-1.4971381196854254014 ,1.0535651442389292416 ] 
dist 125=[-1.6296290227189728385 ,1.0225892043512385192 ] 
dist 126=[-1.7705587765286126360 ,.95902235491688194431] 
dist 127=[-1.9600084140404103919 ,.94114149786135543831] 
dist 128=[-2.1404812055356260366 ,.40538532058289268739] 
dist 129=[-2.2455833895736204744 ,.55693084390059782782] 
dist 130=[-2.3157145544564718439 ,.75094885958057044191] 
dist 131=[-2.3565864064002931527 ,.93834007608587364238] 
dist 132=[-2.3834333265114505264 ,1.0634397581679864065 ] 
dist 133=[-2.3975721554136835244 ,1.1669138437985146806 ] 
dist 134=[-2.4051433647593515254 ,1.2679932220760344054 ] 
dist 135=[-2.4057548495853562074 ,1.3598713262167315118 ] 
dist 136=[-2.2976911058463758960 ,1.4266252760397988377 ] 
dist 137=[-2.3437414412699648732 ,1.4878250243617201684 ] 
dist 138=[-2.3692945881505519219 ,1.5575467680182427647 ] 
dist 139=[-2.3735965665859918286 ,1.6203273490264668469 ] 
dist 140=[-2.3683280742293068353 ,1.6538224393727132761 ] 
dist 141=[-2.3603461026293229381 ,1.6723476891667256739 ] 
dist 142=[-2.3391935185438317217 ,1.6753658587603115748 ] 
dist 143=[-2.3277642642067377636 ,1.6715409928047426766 ] 
dist 144=[-1.6462851479509816009 ,1.6657145902665884332 ] 
dist 145=[-1.5752757629916178641 ,1.6510893783412574628 ] 
dist 146=[-1.3943687802756958919 ,1.6432502958962815373 ] 
dist 147=[-1.3680762055501960600 ,1.4713963920349187361 ] 
dist 148=[-1.0734868711940761130 ,1.4434450528200996929 ] 
dist 149=[-1.0164624455483723212 ,1.3801497965973760907 ] 
dist 150=[-1.0456621131168654565 ,1.3597635293386536953 ] 
dist 151=[-1.1549673350733635768 ,1.3349855625855587048 ] 
dist 152=[-1.2516320675709336474 ,1.5267194322315596924 ] 
dist 153=[-1.3575837986701476358 ,1.6475470590343849570 ] 
dist 154=[-1.5039636122058886225 ,1.7395929263419263787 ] 
dist 155=[-1.6446847824632135004 ,1.8164370442132681905 ] 
dist 156=[-1.7280516394022369556 ,1.8776099511175503083 ] 
dist 157=[-1.7854036267343303712 ,1.9070972417868680944 ] 
dist 158=[-1.8222856423806893650 ,1.9210669210730973068 ] 
dist 159=[-1.8475160101254634266 ,1.9216315662443955394 ] 
dist 160=[-1.8583582582681874567 ,1.7175264685035490043 ] 
dist 161=[-1.8607438947305391823 ,1.7086794459075339278 ] 
dist 162=[-1.8576493185945009460 ,1.6716682544231870440 ] 
dist 163=[-1.7587511906186252794 ,1.6660045713000522855 ] 
dist 164=[-1.8146170630925671394 ,1.5528149661456287388 ] 
dist 165=[-1.8505272487771341472 ,1.5262474714981640601 ] 
dist 166=[-1.8686162748084765653 ,1.5067299718186588152 ] 
dist 167=[-1.8772016734509924325 ,1.5014580257056010248 ] 
dist 168=[-1.8751922201898741227 ,1.1146557603674374488 ] 
dist 169=[-1.8673980912191041850 ,1.0635081188159576440 ] 
dist 170=[-1.8605517416423579013 ,.96553310755733171334] 
dist 171=[-1.3845574029240953546 ,.94035440960845313039] 
dist 172=[-1.3338735582763333980 ,.8541278715122287548 ] 
dist 173=[-1.2060663352911139569 ,.83243592656024939703] 
dist 174=[-1.1845421760457068407 ,.81025652367791350569] 
dist 175=[-1.2205871841471002441 ,.88832466263876783146] 
dist 176=[-1.2606022497975719347 ,1.0202935875775791080 ] 
dist 177=[-1.2798080692928520056 ,1.1450296612418563022 ] 
dist 178=[-1.2886477835281837003 ,1.2925451719758661826 ] 
dist 179=[-1.2889729757763718040 ,1.4291659810133807097 ] 
dist 180=[-1.2712694664838413384 ,1.5104141936545587281 ] 
dist 181=[-1.2632654645199756675 ,1.5666651241602600924 ] 
dist 182=[-1.2529018496500839139 ,1.6035076471206515872 ] 
dist 183=[-1.2681218855095365022 ,1.6296795018852884188 ] 
dist 184=[-1.3928522413091888677 ,1.6433411958960434800 ] 
dist 185=[-1.4717788030253094574 ,1.6504545328445361068 ] 
dist 186=[-1.5323114780432906219 ,1.6504983526127878894 ] 
dist 187=[-1.5836203047849376393 ,1.5134148230680338461 ] 
dist 188=[-1.6251172384324779885 ,1.5349888022015712231 ] 
dist 189=[-1.6464856746931694450 ,1.5448932446336906053 ] 
dist 190=[-1.6572282802281381162 ,1.5454801678364716213 ] 
dist 191=[-1.6570212238166049131 ,1.5155390401934236103 ] 
dist 192=[-.45750163910382874436,1.5054519761032767484 ] 
dist 193=[-.54029128435369624528,1.4972967547854384743 ] 
dist 194=[-.64895847788506913373,1.4896495287281359202 ] 
dist 195=[-.75515686825916920465,1.3674390388600398242 ] 
dist 196=[-.82809334309365402953,1.3623053192163004444 ] 
dist 197=[-.89064095146480461119,1.3598011243349996677 ] 
dist 198=[-.95537486817157129107,1.3571248177029965267 ] 
dist 199=[-1.0165715803879828518 ,1.3535064047854699744 ] 
dist 200=[-1.0650018745606569036 ,1.3644382062368288678 ] 
dist 201=[-1.1133666600370826695 ,1.4275149240686960932 ] 
dist 202=[-1.1743034565509777196 ,1.4708312050256412602 ] 
dist 203=[-1.2303126951821865822 ,1.4985343869383663270 ] 
dist 204=[-1.2590100644699830268 ,1.5168940616984434352 ] 
dist 205=[-1.2745439653977747795 ,1.5288724845523824621 ] 
dist 206=[-1.2780105885338461663 ,1.5335418659075998762 ] 
dist 207=[-1.2649179503276694799 ,1.5315783380449255890 ] 
dist 208=[-1.2610467573743213947 ,1.5002450425071805643 ] 
dist 209=[-1.2582912418357428177 ,1.4917046904637726491 ] 
dist 210=[-1.2563359015160939722 ,1.4578950087018157085 ] 
dist 211=[-1.3099780180216215387 ,1.4523055572636408254 ] 
dist 212=[-1.3793754654764632594 ,1.3524914298132046572 ] 
dist 213=[-1.4290586611640474142 ,1.3290949027564523020 ] 
dist 214=[-1.4648440609833286754 ,1.3105225326743401553 ] 
dist 215=[-1.4904346268742599488 ,1.3044897800665774107 ] 
dist 216=[-1.4994253970474507590 ,1.1942229398108916808 ] 
dist 217=[-1.5007027222137984524 ,1.1947825136506434789 ] 
dist 218=[-1.4971944006353474943 ,1.1918135511898998140 ] 
dist 219=[-1.4178522295998783639 ,1.1616697307024615426 ] 
dist 220=[-1.4511908237830495568 ,1.1538639888371734082 ] 
dist 221=[-1.4650497176471798375 ,1.1255482980744515142 ] 
dist 222=[-1.4697110884103663230 ,1.1201787508549360608 ] 
dist 223=[-1.4675677906906380940 ,1.0414623619113319696 ] 
dist 224=[-1.2799886603690585856 ,1.0230104634775203324 ] 
dist 225=[-1.2723697306175948843 ,1.0061076057133385931 ] 
dist 226=[-1.2434123334965392427 ,.99898577076103153032] 
dist 227=[-1.2379483629869816244 ,1.0137739247972697199 ] 
dist 228=[-1.1543008420411964629 ,1.0821912299904342136 ] 
dist 229=[-1.1345836039640865877 ,1.1375718671961186010 ] 
dist 230=[-1.1169604490284172897 ,1.1896677452211409340 ] 
dist 231=[-1.1096436748382016069 ,1.2356919445097870799 ] 
dist 232=[-.83254766687689295593,1.2731348968696761940 ] 
dist 233=[-.79516211510558787481,1.3111600505919088303 ] 
dist 234=[-.72151407737292883428,1.3527174903627132667 ] 
dist 235=[-.70200843671308735999,1.3884646456039599913 ] 
dist 236=[-.63114207358130987481,1.4032981082128152248 ] 
dist 237=[-.65081858599332026011,1.4090619683586247640 ] 
dist 238=[-.77033450165857675542,1.4086020405095245677 ] 
dist 239=[-.88073980198817529887,1.3742744906922909114 ] 
dist 240=[-.96387398149914270047,1.3630721314338511629 ] 
dist 241=[-1.0429677704454640447 ,1.3542649230030403461 ] 
dist 242=[-1.1372446940041861768 ,1.3464237209871828759 ] 
dist 243=[-1.2249345366151268821 ,1.1102046723136063084 ] 
dist 244=[-1.2777357525475352371 ,1.0762530644007553282 ] 
dist 245=[-1.3150943985816387826 ,1.0105358775905668282 ] 
dist 246=[-1.3411456748995204216 ,.99266596135426820204] 
dist 247=[-1.3586565268345995644 ,.92602396033242708225] 
dist 248=[-1.3620899961526683556 ,.90953609378309309868] 
dist 249=[-1.3600055514245380847 ,.87960275703517999551] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 0, 0, 1, 0, 2] 
dist 0=[52.897857500625048210  ,52.897857500625048210  ] 
dist 1=[52.650033973035055217  ,52.965121870270427235  ] 
dist 2=[52.175142691317574796  ,52.930527962369937246  ] 
dist 3=[51.200514590826678346  ,52.868883052388699145  ] 
dist 4=[50.122539260576438524  ,52.595975223291485292  ] 
dist 5=[49.234840611743755036  ,52.495785018026170093  ] 
dist 6=[48.312845272730612652  ,52.431657140754780693  ] 
dist 7=[47.098055567903560344  ,52.303737083072644477  ] 
dist 8=[45.782486239621890334  ,48.086125267491958243  ] 
dist 9=[44.457994905962281558  ,47.474393998319083594  ] 
dist 10=[42.483520727496721892  ,46.385761070843728389  ] 
dist 11=[40.057295988335430232  ,46.106778638548960026  ] 
dist 12=[37.555882324463304335  ,45.193839296744027810  ] 
dist 13=[34.512784868712758687  ,44.912695051351802585  ] 
dist 14=[29.922815576555111511  ,44.697121721553941819  ] 
dist 15=[25.309503354338354009  ,44.539173178598419865  ] 
dist 16=[22.173086869843052942  ,34.185790508979883192  ] 
dist 17=[19.508588683979706529  ,33.827355122400948521  ] 
dist 18=[16.780116314113393868  ,33.436094458534386762  ] 
dist 19=[14.208831966118698160  ,33.290468579202301610  ] 
dist 20=[12.172020111355571797  ,15.734234170315942427  ] 
dist 21=[10.129532150582284560  ,14.909450656064525934  ] 
dist 22=[7.5352139510629084431 ,13.718644318275486568  ] 
dist 23=[5.0241193536238519118 ,13.399368005276502808  ] 
dist 24=[3.3138730310482726355 ,8.0354690613470043474 ] 
dist 25=[1.7178832815660503236 ,7.3770583470414301789 ] 
dist 26=[.0396435735742860716 ,5.9523426637957933333 ] 
dist 27=[-1.9824817526920019309 ,5.7032831995872036911 ] 
dist 28=[-3.8880217355482066715 ,4.2385337138109194432 ] 
dist 29=[-5.1006833760237227703 ,4.0101286837033203288 ] 
dist 30=[-6.0435324647837060560 ,3.5811912963759948172 ] 
dist 31=[-6.8713950213758311482 ,3.5013453480810223506 ] 
dist 32=[-7.5681628582835285697 ,-5.7598568897844615183 ] 
dist 33=[-8.0433909066322127101 ,-5.9687052115930292072 ] 
dist 34=[-8.6358080201218023808 ,-6.3497266377458881736 ] 
dist 35=[-9.1195373503938664939 ,-6.4137078962732921198 ] 
dist 36=[-9.6201428842255347645 ,-7.6076923892102494055 ] 
dist 37=[-9.9196806972044171018 ,-7.7061744447075660328 ] 
dist 38=[-10.099092618394765141  ,-7.8157934981297366162 ] 
dist 39=[-10.165819426200406523  ,-7.7677579192751407131 ] 
dist 40=[-10.186268147184407924  ,-7.6582226393102094720 ] 
dist 41=[-10.180663796215806325  ,-7.4704609072267325598 ] 
dist 42=[-10.156831211319587768  ,-6.8045228475312246857 ] 
dist 43=[-10.125745472604585477  ,-6.0035088607279126905 ] 
dist 44=[-10.037748674907455662  ,-5.1372491639017425158 ] 
dist 45=[-9.9926181797576561806 ,-4.0569308071899473686 ] 
dist 46=[-9.8793028231874419608 ,-2.4011299547375144365 ] 
dist 47=[-9.8277939384724768664 ,-.7352844672988011203 ] 
dist 48=[-6.1781063330261656625 ,.38522986821760280393] 
dist 49=[-6.1075490553569503987 ,1.3219063257670602344 ] 
dist 50=[-5.9213024462864950925 ,2.2538988081334662132 ] 
dist 51=[-5.8776213248659800610 ,3.1127974178773871605 ] 
dist 52=[-3.0820385044767550929 ,3.7577058990997726558 ] 
dist 53=[-2.7566380075192628927 ,4.3702042427957636033 ] 
dist 54=[-2.6811494342065022351 ,5.0997665207811150337 ] 
dist 55=[-1.6472097217484245191 ,5.7797707569648613972 ] 
dist 56=[-1.2602561964728087865 ,6.1944256314287312625 ] 
dist 57=[-.8967192136149611590 ,6.4947574819252985068 ] 
dist 58=[-.8232447437963416334 ,6.7183188838794699178 ] 
dist 59=[-.41139347459511916561,6.8893546608607136623 ] 
dist 60=[-.34027624509940449189,6.9799404727174457013 ] 
dist 61=[-.19394265242110175436,7.0290528721183019360 ] 
dist 62=[-.15791281207448969554,7.0344057907544288564 ] 
dist 63=[1.4465558833476115535 ,6.5123543123540676284 ] 
dist 64=[1.8299051289028950711 ,5.1313159576118582512 ] 
dist 65=[1.8931393619417811314 ,5.1762458939502664961 ] 
dist 66=[2.0021344223921706834 ,5.1976015876975353478 ] 
dist 67=[2.0235560600318356127 ,5.1927037702114126677 ] 
dist 68=[1.9643058331228722117 ,3.1881718242337579071 ] 
dist 69=[1.5706139590493944326 ,3.2477552906568629222 ] 
dist 70=[1.2292967702684295139 ,3.2940961675155429705 ] 
dist 71=[.87029045017894989361,3.3348836445374342682 ] 
dist 72=[.5273765589309026952 ,3.3658437964862318514 ] 
dist 73=[.2502542387923388097 ,3.3729106445882896476 ] 
dist 74=[-.0318380491032626355 ,3.3681936229542225982 ] 
dist 75=[-.3946362701395060808 ,3.3597351199040330571 ] 
dist 76=[-.74603121258912182793,3.2908423781154596250 ] 
dist 77=[-.9826305676675432964 ,3.2692138315285100832 ] 
dist 78=[-1.1806498958284275747 ,3.2218826015245085897 ] 
dist 79=[-1.3780751709757308740 ,3.2033564690984885618 ] 
dist 80=[-1.5603537437004153692 ,2.8540518032269542052 ] 
dist 81=[-1.8010927514727742854 ,2.7992968898532452470 ] 
dist 82=[-2.1780312895992758441 ,2.6665746207002923766 ] 
dist 83=[-2.5343769373703264567 ,2.6304197961333918282 ] 
dist 84=[-2.8507272064849047397 ,2.4141836410973668432 ] 
dist 85=[-3.0680101426515696161 ,2.3671717068127486183 ] 
dist 86=[-3.2546612045037605526 ,2.2783059668823199268 ] 
dist 87=[-3.4487522985050075697 ,2.2528815131485513546 ] 
dist 88=[-3.6206266581979812614 ,1.7975637426330080941 ] 
dist 89=[-3.7185820209533373140 ,1.7317988035648379203 ] 
dist 90=[-3.7813739620412665582 ,1.5737071593146347626 ] 
dist 91=[-3.8128336181532400726 ,1.5396934139322257079 ] 
dist 92=[-3.8257505633414752843 ,1.3008652947725169144 ] 
dist 93=[-3.8222090704127757854 ,1.2530537731836324148 ] 
dist 94=[-3.7951963530558336956 ,1.1704094651969922570 ] 
dist 95=[-3.7758645206151078284 ,1.1494380768021044435 ] 
dist 96=[-2.9631499612386347813 ,.86529337098627852026] 
dist 97=[-2.9413299188891109526 ,1.0792875638600632560 ] 
dist 98=[-2.9240483885562146037 ,1.3285085135180850699 ] 
dist 99=[-2.9085766849539980553 ,1.6911531153720868694 ] 
dist 100=[-1.8343934311481702323 ,2.0480447603557853978 ] 
dist 101=[-1.7542328894653004174 ,2.2743099936082803215 ] 
dist 102=[-1.6427241747233647431 ,2.4483696287728620122 ] 
dist 103=[-1.6081056740677347643 ,2.5968710487574351053 ] 
dist 104=[-.92159289749360234229,2.7177291698458130396 ] 
dist 105=[-.8331698362065827304 ,2.7814479113108096358 ] 
dist 106=[-.6362386117414596209 ,2.8156019436446607549 ] 
dist 107=[-.5946660843307010726 ,2.8229026732982533901 ] 
dist 108=[-.3603299688769723973 ,2.8094605890690169321 ] 
dist 109=[-.3188840855420966544 ,2.7974004073073504225 ] 
dist 110=[-.2327613747944081520 ,2.7776472679797832675 ] 
dist 111=[-.2104756809378990593 ,2.8159836661172519648 ] 
dist 112=[.49609501438668768232,2.8547548898768981692 ] 
dist 113=[.56762623706536569727,2.8701143620976771037 ] 
dist 114=[.69476919110546965317,2.8712847598295564126 ] 
dist 115=[.58905456981720616072,2.8674412373161133463 ] 
dist 116=[.06028324616525044363,2.3747489017457860650 ] 
dist 117=[-.29289568395772031313,2.3180227774717031196 ] 
dist 118=[-.58518735112787573757,2.1773381215774785035 ] 
dist 119=[-.87092152512676463114,2.1461365740657627364 ] 
dist 120=[-1.1306581022030370158 ,1.9170698513156576993 ] 
dist 121=[-1.3191762465444368690 ,1.8697096566154264344 ] 
dist 122=[-1.4916713958053142172 ,1.7915138317219561784 ] 
dist 123=[-1.6874457417651937794 ,1.7473968612065373209 ] 
dist 124=[-1.8687500626991715790 ,.90220803445360809421] 
dist 125=[-1.9834884619275009497 ,.80278366999780346828] 
dist 126=[-2.0714554900999283822 ,.5331753819204872461 ] 
dist 127=[-2.1459094294545660189 ,.2144856690130728557 ] 
dist 128=[-2.2060034870065977536 ,-.45245505884218256494] 
dist 129=[-2.2366583984545041621 ,-.46324958411138157878] 
dist 130=[-2.2516409708246439861 ,-.45575533041137290952] 
dist 131=[-2.2521179176999619636 ,-.42142751751122467646] 
dist 132=[-2.1844722295418397588 ,-.37962518504773683517] 
dist 133=[-2.2894888043194259574 ,-.34229656965581226286] 
dist 134=[-2.3719747455466098523 ,-.30115121974127584928] 
dist 135=[-2.4454102581785275644 ,-.24410165707834363572] 
dist 136=[-2.5057707755206756364 ,-.18123860585888555494] 
dist 137=[-2.5360632786512031895 ,-.11688319885409072399] 
dist 138=[-2.5501932819255827089 ,-.03912322315300566061] 
dist 139=[-2.5495868830349073863 ,.07724773316147010048] 
dist 140=[-2.5324440607570210142 ,.1976218866535624662 ] 
dist 141=[-2.5230313261732981079 ,.2913644447687654420 ] 
dist 142=[-2.4855987401393549986 ,.3835612166974039439 ] 
dist 143=[-2.4722935410870872061 ,.4977730869415447122 ] 
dist 144=[-1.6135474877174017856 ,.6174325605641372654 ] 
dist 145=[-1.5960933564109574850 ,.7313785379535004135 ] 
dist 146=[-1.5409489552208808232 ,.86300737598257244485] 
dist 147=[-1.5323057909422246551 ,1.0532553272270360088 ] 
dist 148=[-.96117988153320270025,1.2398273760434589876 ] 
dist 149=[-1.0321475582112326954 ,1.3567858552110133137 ] 
dist 150=[-1.0890682067232376074 ,1.4451997222999005025 ] 
dist 151=[-1.1417012775560915902 ,1.5178345509060091647 ] 
dist 152=[-1.1875396947604276965 ,1.5752924113211874333 ] 
dist 153=[-1.2173373153413620040 ,1.6035913206441962266 ] 
dist 154=[-1.2410754776891842366 ,1.6840800263250992898 ] 
dist 155=[-1.2627225900595172656 ,1.7435838487296220876 ] 
dist 156=[-1.2793773452057547702 ,1.7888542924694692161 ] 
dist 157=[-1.2831870111218468617 ,1.8125316597314168292 ] 
dist 158=[-1.2817945753264230671 ,1.8249479939373454372 ] 
dist 159=[-1.2776973074656289595 ,1.8252857298605869326 ] 
dist 160=[-1.2396074317716172850 ,1.8060784320090914569 ] 
dist 161=[-1.2278279674588588178 ,1.8114488303918593611 ] 
dist 162=[-1.2119868671761799957 ,1.8094394189132652969 ] 
dist 163=[-1.2047216898575765964 ,1.8033568187583263234 ] 
dist 164=[-1.0023143054198379144 ,1.4133067841139471820 ] 
dist 165=[-.9738001282303679372 ,1.3868846010369504519 ] 
dist 166=[-.9047838185535803891 ,1.3417141705216567887 ] 
dist 167=[-.8884445305778367473 ,1.3289433178480700513 ] 
dist 168=[-.7807466673173825415 ,1.2263174293670666724 ] 
dist 169=[-.7585185458084286284 ,1.2719411319123263073 ] 
dist 170=[-.7183253615666504569 ,1.3096389703675773028 ] 
dist 171=[-.7077841625383943590 ,1.3463676832753767453 ] 
dist 172=[-.71536447068148738319,1.3796278671438514978 ] 
dist 173=[-.78930709760308181224,1.4034717214649114862 ] 
dist 174=[-.8568648539466764156 ,1.4249364189607494368 ] 
dist 175=[-.93341590799595684735,1.4486829245999727006 ] 
dist 176=[-1.0099443351631045878 ,1.4686102010293865136 ] 
dist 177=[-1.0890185936323833741 ,1.4748284781449697853 ] 
dist 178=[-1.2239438796213348453 ,1.4742212314621843574 ] 
dist 179=[-1.3726206160008923638 ,1.4705409183970720934 ] 
dist 180=[-1.5047675002512445201 ,1.4371530575373056313 ] 
dist 181=[-1.5956410330092484598 ,1.4262387189956766683 ] 
dist 182=[-1.6737510024818479526 ,1.4034887017402133898 ] 
dist 183=[-1.7549550475457613757 ,1.3945884410680626370 ] 
dist 184=[-1.8256109432779736259 ,1.3282966842800603402 ] 
dist 185=[-1.8616154753867088803 ,1.3885140288359466087 ] 
dist 186=[-1.8800320646464757948 ,1.4387324692536313935 ] 
dist 187=[-1.8829505519124204766 ,1.4884226145730413112 ] 
dist 188=[-1.8665356092096147035 ,1.5300783322238309208 ] 
dist 189=[-1.8574402789892078374 ,1.5482281601308637196 ] 
dist 190=[-1.8470276757119512741 ,1.5557539923734601808 ] 
dist 191=[-1.8389624548682748732 ,1.5550103055852200403 ] 
dist 192=[-1.3988988991178851819 ,1.5220359221302421677 ] 
dist 193=[-1.3831775871716243496 ,1.5102166072878686473 ] 
dist 194=[-1.3373267681028794878 ,1.5001521602417739878 ] 
dist 195=[-1.3270822534745897552 ,1.4918595100678550329 ] 
dist 196=[-.85696268458123167442,1.3424842809442569240 ] 
dist 197=[-.81863925760283669872,1.4191404566295665407 ] 
dist 198=[-.75846708373903304014,1.4758243765929268366 ] 
dist 199=[-.7420931804349679595 ,1.5200908494777404510 ] 
dist 200=[-.42892524390528202772,1.5529972446658851928 ] 
dist 201=[-.388068947087488684  ,1.5643375192118999818 ] 
dist 202=[-.29213416386129299456,1.5673576608131830215 ] 
dist 203=[-.27585248021369355719,1.5670543131981966731 ] 
dist 204=[-.14644274896912469442,1.5135252495857543290 ] 
dist 205=[-.12309579016881280576,1.5006264572156541160 ] 
dist 206=[-.08709777526173918990,1.4870941563846301768 ] 
dist 207=[-.07790713812130666739,1.4871169163251980657 ] 
dist 208=[.17612787338808443097,1.3842059775637543988 ] 
dist 209=[.20566304429295940788,1.3668664625785567260 ] 
dist 210=[.20754655188771678469,1.3290161552844465684 ] 
dist 211=[-.12772564255279299926,1.3679961818011257135 ] 
dist 212=[-.46252804459702924544,1.4530804264629455167 ] 
dist 213=[-.68366911687795772919,1.5095795174153886528 ] 
dist 214=[-.8639472725898383133 ,1.5559947094837291451 ] 
dist 215=[-1.0356474009359207967 ,1.6008300750629627112 ] 
dist 216=[-1.1887344456921316684 ,1.6372503438081650886 ] 
dist 217=[-1.2947195240241378925 ,1.6500751071935117587 ] 
dist 218=[-1.3865231933018078470 ,1.6539780650749563083 ] 
dist 219=[-1.4830061930279416931 ,1.6547811750032286980 ] 
dist 220=[-1.5695932025233325441 ,1.5996275873984275483 ] 
dist 221=[-1.6218972212219934237 ,1.5854898390567524357 ] 
dist 222=[-1.6591155128541475903 ,1.5771557146516852360 ] 
dist 223=[-1.6854873742763801210 ,1.5745707368638866491 ] 
dist 224=[-1.7028706535947352980 ,.02557372467903063381] 
dist 225=[-1.7054951563726134401 ,.04081509848252171416] 
dist 226=[-1.6998665688118858226 ,.06872795087694956590] 
dist 227=[-1.6945642820149212607 ,.12124707081211390274] 
dist 228=[-1.6704974005531109959 ,.17780107116154880474] 
dist 229=[-1.6909238429868575457 ,.22181912619200824741] 
dist 230=[-1.6997067061105975305 ,.26509904025901669419] 
dist 231=[-1.7013830222435202644 ,.31870630120274196047] 
dist 232=[-1.6679374121722111627 ,.37487022222192792384] 
dist 233=[-1.6838842290634263937 ,.4283548505641581542 ] 
dist 234=[-1.6894954111757162523 ,.49013815723013353736] 
dist 235=[-1.7176302945972657009 ,.5794261237579500703 ] 
dist 236=[-1.7368721419356444976 ,.67053428061584811284] 
dist 237=[-1.7400578679497798775 ,.73958272553419037276] 
dist 238=[-1.7357859177470754608 ,.80571508133000344892] 
dist 239=[-1.7304787371668873708 ,.88518334689666307178] 
dist 240=[-1.2080891411030775032 ,.96716894183749551175] 
dist 241=[-1.1605954339362667795 ,1.0433489766954819498 ] 
dist 242=[-1.0464524004819890589 ,1.1298890818642922380 ] 
dist 243=[-1.0232038213196885626 ,1.2532265021579414413 ] 
dist 244=[-.85376218732482617772,1.3733917671462843667 ] 
dist 245=[-.82055537747683025177,1.4472700621028374915 ] 
dist 246=[-.76485749833275655911,1.5014056493550180547 ] 
dist 247=[-.75056955282098345847,1.5427678417439353898 ] 
dist 248=[-.47820562922090237743,1.5728035663910443822 ] 
dist 249=[-.44205606993691309991,1.5817298905459196449 ] 
dist 250=[-.35514251353901893301,1.5884084686588826447 ] 
dist 251=[-.34125029980764195375,1.6194897718238093329 ] 
dist 252=[-.21711128851589999591,1.6402826248560692462 ] 
dist 253=[-.19426475456307586739,1.6445003712238598075 ] 
dist 254=[-.16330304471343824856,1.6408578531117298938 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 1, 2, 1, 0, 1] 
dist 0=[52.235132198827986642  ,52.235132198827986642  ] 
dist 1=[51.859880551205992791  ,52.640046979753560893  ] 
dist 2=[51.427050983419105181  ,53.191110436650100987  ] 
dist 3=[50.826592102257856060  ,53.695687547485070594  ] 
dist 4=[49.430590428352235841  ,53.915021232023322392  ] 
dist 5=[47.730064037437069039  ,53.975948882676684224  ] 
dist 6=[45.863186836983026814  ,53.953716655003115541  ] 
dist 7=[43.512594350213311309  ,53.561865016545187060  ] 
dist 8=[39.880100397706259023  ,53.413325205189000428  ] 
dist 9=[36.200490608201485434  ,53.035221056602030699  ] 
dist 10=[33.661603654263106754  ,52.866892779936061157  ] 
dist 11=[31.465927964710855295  ,50.181081442687789990  ] 
dist 12=[29.156771722299443304  ,49.681182498068150392  ] 
dist 13=[26.943653384000540609  ,47.957847578748964142  ] 
dist 14=[25.131283664520672031  ,45.178518758756620081  ] 
dist 15=[23.259594383485608908  ,36.437537115762745698  ] 
dist 16=[20.809083437069740127  ,35.696367243263985147  ] 
dist 17=[18.402755568616066934  ,34.832479225209431709  ] 
dist 18=[16.707279245012050756  ,34.576115404888666799  ] 
dist 19=[15.049683937359327929  ,27.328546259487536870  ] 
dist 20=[12.852967824804639198  ,26.386930060159540866  ] 
dist 21=[10.654340705464006877  ,24.473677171476303943  ] 
dist 22=[7.8687053783575819811 ,23.969279356646213788  ] 
dist 23=[5.1772519211153113571 ,22.107088889974492925  ] 
dist 24=[3.3544536965458346446 ,21.714357754583707994  ] 
dist 25=[1.8116260118353262264 ,20.989001528454118055  ] 
dist 26=[.23796788861385072965,20.807536251520802567  ] 
dist 27=[-1.2453037838094453739 ,7.8424215795872797465 ] 
dist 28=[-2.4277204088966580648 ,7.3792070737858752262 ] 
dist 29=[-3.8566793593058378215 ,5.4147531330718440191 ] 
dist 30=[-6.1561418468986822977 ,4.5323334969488422956 ] 
dist 31=[-8.2445087411959072905 ,-.19756162652784477485] 
dist 32=[-9.7686361445143733123 ,-.30157973935775333062] 
dist 33=[-11.176130570900084894  ,-1.7210743339487596191 ] 
dist 34=[-12.798653113525724661  ,-1.8942986291648459410 ] 
dist 35=[-14.293258290633465274  ,-2.1937058205214016962 ] 
dist 36=[-15.189849122254678420  ,-2.2488631748067928816 ] 
dist 37=[-15.823145046810165595  ,-2.3121496304209472274 ] 
dist 38=[-16.266155057626714559  ,-2.2451287656602773426 ] 
dist 39=[-16.589653773251175512  ,-2.0980925253434088526 ] 
dist 40=[-16.745515455532576424  ,-1.8066474515752147183 ] 
dist 41=[-16.809189159504815072  ,-1.4959918705275815389 ] 
dist 42=[-16.795037265868686618  ,-1.2721315702470440148 ] 
dist 43=[-7.9838793094378222700 ,-1.0707451914530394535 ] 
dist 44=[-7.9109474788843095832 ,-.7061098100242048850 ] 
dist 45=[-7.8461180597063365215 ,.0016305601766952427 ] 
dist 46=[-7.8007416282944990158 ,.7430987357314880680 ] 
dist 47=[-2.9644634839984257704 ,1.4482601587758664788 ] 
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dist 57=[.1298194098199578069 ,5.8916789223294440174 ] 
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dist 76=[-4.6014225963961308558 ,2.6540352442384828122 ] 
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dist 80=[-6.5563183027390586490 ,2.6650430896533555248 ] 
dist 81=[-6.7776322769450025572 ,2.5922129405431700526 ] 
dist 82=[-6.9537987101376604214 ,2.5744903243451293465 ] 
dist 83=[-7.0938092482829640444 ,2.5123760610813705784 ] 
dist 84=[-7.1707882541117029141 ,2.5013224636188414888 ] 
dist 85=[-7.2165682685255579002 ,2.3343445692207747178 ] 
dist 86=[-7.2319767078083177618 ,2.2955892374875723771 ] 
dist 87=[-7.2267971007667691844 ,2.2612926190715774969 ] 
dist 88=[-7.2077226704321997208 ,2.2478650599383021630 ] 
dist 89=[-7.1421321980466321515 ,1.6108880157708501514 ] 
dist 90=[-7.1038844985188019023 ,1.5262086701295072798 ] 
dist 91=[-3.8887955210337970084 ,1.3886021689129643590 ] 
dist 92=[-3.6109547260043305037 ,1.3527342807531309689 ] 
dist 93=[-2.9382814528359994386 ,1.2780363536649968121 ] 
dist 94=[-2.8343489417204991651 ,1.2721326768233476694 ] 
dist 95=[-1.8618397281577382767 ,1.3813488420539202748 ] 
dist 96=[-1.6828596965741435271 ,1.8738717034426532119 ] 
dist 97=[-1.4519835830268914012 ,2.3551470849144082313 ] 
dist 98=[-1.3921091113393395049 ,2.9471189779629399333 ] 
dist 99=[.3026194322230966022 ,3.5073444386778521498 ] 
dist 100=[.4996934101255485973 ,3.8619059160974978889 ] 
dist 101=[.8991308671037126009 ,4.1338324242903326741 ] 
dist 102=[1.0009363376993319821 ,4.3642182946055130686 ] 
dist 103=[1.5619934521324710055 ,4.5503715146999912025 ] 
dist 104=[1.6279223161439932113 ,4.6457437046539099324 ] 
dist 105=[1.5904531200232587636 ,4.6959444441518395018 ] 
dist 106=[1.4725287455824868910 ,4.7041577016923313620 ] 
dist 107=[1.3328972079419553373 ,2.5108297825253213644 ] 
dist 108=[1.1736558293929112393 ,2.6214639522456325854 ] 
dist 109=[.9706714705919658562 ,2.6936521607002627854 ] 
dist 110=[.6549798366381933815 ,2.7325294224224168977 ] 
dist 111=[.3364747933720087841 ,2.7561835394189011604 ] 
dist 112=[.1222551499066715796 ,2.7675818305005671800 ] 
dist 113=[-.0565700738068873162 ,2.7722693144545248972 ] 
dist 114=[-.2338210275644108612 ,2.7690989440721500981 ] 
dist 115=[-.3964881448683340630 ,2.4249852796200538280 ] 
dist 116=[-.5171140616461874592 ,2.3731401656411817940 ] 
dist 117=[-.63006184222485878205,2.2816960730315884651 ] 
dist 118=[-.76209474800113860268,2.2574139122944357742 ] 
dist 119=[-.88532011462247411076,2.1748910418758502139 ] 
dist 120=[-.96311677993285982906,2.1488136670979021293 ] 
dist 121=[-1.0225634812320763664 ,2.1217346668362247725 ] 
dist 122=[-1.0725443409119890165 ,2.1067884008418077338 ] 
dist 123=[-1.1126418265582623810 ,.34923156302258016191] 
dist 124=[-1.1326390538283950677 ,.20356487424373925463] 
dist 125=[-1.1420674754787975885 ,-.12128165672156683554] 
dist 126=[-1.1432252198955545410 ,-.18178938347001222869] 
dist 127=[-.95292731444832000797,-.50291853000205106432] 
dist 128=[-1.1424367882591481799 ,-.42843443551506742204] 
dist 129=[-1.3259053881381970340 ,-.3604069617636087370 ] 
dist 130=[-1.5492161642615503815 ,-.2835164228646316733 ] 
dist 131=[-1.7594289567571713946 ,-.2069022670540519999 ] 
dist 132=[-1.8906153843037891049 ,-.1399686781809660149 ] 
dist 133=[-1.9890966357189298717 ,-.0673495661882020673 ] 
dist 134=[-2.0687608529139262289 ,.0319640804699340723 ] 
dist 135=[-2.1302790811285697917 ,.1308056088513078089 ] 
dist 136=[-2.1563278608671386158 ,.2015467682059569696 ] 
dist 137=[-2.1673892333896855895 ,.2652385026362539761 ] 
dist 138=[-2.1690808817765840031 ,.3359557495558513648 ] 
dist 139=[-.41460268965213526453,.4057915747952838969 ] 
dist 140=[-.3277864936066696243 ,.4659738570536030743 ] 
dist 141=[-.14399539553178787431,.5306422539474501481 ] 
dist 142=[-.13890295050293629258,.6183967357317530523 ] 
dist 143=[-.10088031526166114833,.7031351907394918498 ] 
dist 144=[-.11971622712000127124,.7557679173071894494 ] 
dist 145=[-.13897131904976189133,.7950083674759331063 ] 
dist 146=[-.1637785507727591481 ,.84326558664574129862] 
dist 147=[-.1902031964162144398 ,.89490531738973045524] 
dist 148=[-.2159142849009523329 ,.9500933735497189379 ] 
dist 149=[-.2459902457393074269 ,1.0441852787880785083 ] 
dist 150=[-.2898331295247185524 ,1.1391275769098620989 ] 
dist 151=[-.3346164536031111683 ,1.2282674097025701715 ] 
dist 152=[-.3684464006569409483 ,1.3005751828265911968 ] 
dist 153=[-.4006939796957147836 ,1.3734281385704701121 ] 
dist 154=[-.4391660489463234473 ,1.4662332250097635054 ] 
dist 155=[-.49740878721034107284,1.5524780008575862823 ] 
dist 156=[-.62473854047701737609,1.5991470731170391804 ] 
dist 157=[-.73206155133040924599,1.6258763276016152547 ] 
dist 158=[-.84004295455602387216,1.6325132465244695280 ] 
dist 159=[-.94009702671605713165,1.6321251894838363193 ] 
dist 160=[-1.0157854693524820038 ,1.6308022016688793263 ] 
dist 161=[-1.0880717460330133882 ,1.6285821084465921896 ] 
dist 162=[-1.1745485432988335660 ,1.6245956866771859069 ] 
dist 163=[-1.2550266669153126316 ,1.3817937057147964903 ] 
dist 164=[-1.3033743934787666258 ,1.3463875738440615296 ] 
dist 165=[-1.3374084687940699367 ,1.2814485235228350219 ] 
dist 166=[-1.3607664433752141608 ,1.2641858853688440169 ] 
dist 167=[-1.3755269347809433272 ,1.2036903202046224632 ] 
dist 168=[-1.3783471173738577923 ,1.1864408240577657401 ] 
dist 169=[-1.3709247223276309363 ,1.1648621598729320562 ] 
dist 170=[-1.3695317712692163903 ,1.1555734903406992603 ] 
dist 171=[-1.0367848533388682312 ,.11406945102260571765] 
dist 172=[-1.0372086736325284350 ,.02733693141830684014] 
dist 173=[-1.0337831865324494077 ,-.16443234183972934984] 
dist 174=[-1.0299801109035341545 ,-.03850173284233357053] 
dist 175=[-.8479915619947472680 ,.12993025292656963417] 
dist 176=[-.92103379670284802058,.24205537869996619585] 
dist 177=[-1.0268742135687744688 ,.33437246292781629792] 
dist 178=[-1.1538419932020535986 ,.42375228088365266615] 
dist 179=[-1.2724285500246868139 ,.50436684474458724269] 
dist 180=[-1.3448166831782606128 ,.56170231338214339036] 
dist 181=[-1.3972648253076422514 ,.61294635128757461668] 
dist 182=[-1.4362610914660207185 ,.66924983289272494971] 
dist 183=[-1.4645912814402873379 ,.72044994366006166691] 
dist 184=[-1.4744624248653354502 ,.75132694903526368202] 
dist 185=[-1.4765008891192409950 ,.77321710626015837366] 
dist 186=[-1.4735656804222365808 ,.7897771571797776743 ] 
dist 187=[-1.3959569718151040587 ,.8059313068727298048 ] 
dist 188=[-1.3816194484206899200 ,.8118472144864014341 ] 
dist 189=[-1.3367377978389296124 ,.8131070131413267522 ] 
dist 190=[-1.3283361193557049902 ,.8111573152226647031 ] 
dist 191=[-1.2642483602314771904 ,.51169144894110577478] 
dist 192=[-1.2506318047877397823 ,.61350673818179580596] 
dist 193=[-1.2301807460723504500 ,.71576475242444276676] 
dist 194=[-1.2222473494698543579 ,.84538641034776256683] 
dist 195=[-1.0135909500354902385 ,.96994255190542758835] 
dist 196=[-.98320973044772099637,1.0519848317270688195 ] 
dist 197=[-.91784488610604990833,1.1186190724727382645 ] 
dist 198=[-.89856950798533261236,1.1816791637276565294 ] 
dist 199=[-.816071588992638233  ,1.2376526480059747375 ] 
dist 200=[-.8175676733288515132 ,1.2760051584453774173 ] 
dist 201=[-.8748971974958195453 ,1.3088287891856941753 ] 
dist 202=[-.9370524652544232086 ,1.3427418175020541173 ] 
dist 203=[-.9975580827690625093 ,1.3707171923542421549 ] 
dist 204=[-1.0483042728583551857 ,1.3798416127864253762 ] 
dist 205=[-1.1016273143152382931 ,1.3819613093327430623 ] 
dist 206=[-1.1724192357318662447 ,1.3819649598493856111 ] 
dist 207=[-1.2391808510782668410 ,1.3672738187373460981 ] 
dist 208=[-1.2764180311224925141 ,1.3663765876860305460 ] 
dist 209=[-1.2991639461148206617 ,1.3614798401491508212 ] 
dist 210=[-1.3080861450620098258 ,1.3581626061161881443 ] 
dist 211=[-1.3108591899079745736 ,1.4386489652024828894 ] 
dist 212=[-1.3090605113426813296 ,1.4830052501072144165 ] 
dist 213=[-1.3035653118910414770 ,1.5093916730527302881 ] 
dist 214=[-1.2994816896866011606 ,1.5181543864797770301 ] 
dist 215=[-1.1485626013659264606 ,1.5202063587789753005 ] 
dist 216=[-1.1247397625707862362 ,1.5198059251177304947 ] 
dist 217=[-1.0765327659471773760 ,1.5175232013618211799 ] 
dist 218=[-1.0621467251031878177 ,1.5120561977512088384 ] 
dist 219=[-1.0011810688215819379 ,1.3208873129821595377 ] 
dist 220=[-.98718197841688999045,1.3028771608181246665 ] 
dist 221=[-.95072742581905474174,1.2482414955407001203 ] 
dist 222=[-.9403346601955920739 ,1.2400862521275875090 ] 
dist 223=[-.7282287798485568881 ,1.1186928740244354560 ] 
dist 224=[-.82794864344892943992,1.0922798557507771012 ] 
dist 225=[-.92409582888221598788,1.0694980909185708043 ] 
dist 226=[-1.0405560343358608083 ,1.0640251635787008755 ] 
dist 227=[-1.1498852443522701214 ,.72691808410126674543] 
dist 228=[-1.2175691790708625430 ,.68309239853918309533] 
dist 229=[-1.2677359447816578930 ,.59770939709926565655] 
dist 230=[-1.3071444778219275599 ,.57576809103260434573] 
dist 231=[-1.3366451672105785047 ,.49985026494602682084] 
dist 232=[-1.3472648876130128380 ,.48170809515200829877] 
dist 233=[-1.3504193236441445856 ,.46146605140822980732] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 0, 0, 1, 0, 2] 
dist 0=[47.585144873841813251  ,47.585144873841813251  ] 
dist 1=[46.915388652662208405  ,47.811659392819260087  ] 
dist 2=[45.836525293616323754  ,48.046619368897911606  ] 
dist 3=[43.978623336986050523  ,48.418179089793274694  ] 
dist 4=[42.037387918550834581  ,48.866231623535649322  ] 
dist 5=[40.625676231656407365  ,49.057264381106263717  ] 
dist 6=[39.327961332216781219  ,49.115117483889470247  ] 
dist 7=[37.841823067161826498  ,49.091800425508868124  ] 
dist 8=[36.343116370573498763  ,47.721706079028055860  ] 
dist 9=[34.995026690265501769  ,47.455985127481229007  ] 
dist 10=[33.494730477345009146  ,46.963320468422117901  ] 
dist 11=[31.387788593401415802  ,46.806276400399637529  ] 
dist 12=[29.252605304082846137  ,46.116582281821894557  ] 
dist 13=[27.639332155671847302  ,45.928757943045545619  ] 
dist 14=[26.093485058408805352  ,45.437049159638584649  ] 
dist 15=[24.227382609942509178  ,45.245146278252577220  ] 
dist 16=[22.153867688878249031  ,32.599275779196784684  ] 
dist 17=[19.594709664696041313  ,31.448499158461157764  ] 
dist 18=[16.917581694879482400  ,28.668570577743617113  ] 
dist 19=[14.361544573309024153  ,28.246879000699673200  ] 
dist 20=[12.204122306622623955  ,24.199869381504994225  ] 
dist 21=[10.157950499057865239  ,23.445144427816964841  ] 
dist 22=[7.3943506990817620007 ,22.525489552779375265  ] 
dist 23=[4.6921611628751569945 ,22.301513351648975873  ] 
dist 24=[2.8093984125269500926 ,15.909611303646499328  ] 
dist 25=[1.1592563685169361773 ,15.110935656276123160  ] 
dist 26=[-.6142655556191807477 ,13.453360912126277355  ] 
dist 27=[-2.3417324726036689880 ,13.021137786910672444  ] 
dist 28=[-3.8085048001897815077 ,11.430614248195751204  ] 
dist 29=[-5.3739773164211854936 ,11.118941859800013989  ] 
dist 30=[-7.4969454789294549421 ,10.541202322737519885  ] 
dist 31=[-9.5396286564317329528 ,10.407849647374856932  ] 
dist 32=[-10.784544189559329260  ,1.8110358040073896835 ] 
dist 33=[-11.692815215739642077  ,1.0666365900272671891 ] 
dist 34=[-12.389948035740528362  ,-.5189574006817931851 ] 
dist 35=[-12.932515847176982002  ,-.8438866689012993940 ] 
dist 36=[-13.222740147887556472  ,-2.3469420904088097203 ] 
dist 37=[-13.386980502927662716  ,-2.3990705904084365211 ] 
dist 38=[-13.425224930137672267  ,-2.4041955934197642699 ] 
dist 39=[-12.462172531930345095  ,-2.3351162448305710351 ] 
dist 40=[-12.292646762506410198  ,-2.2290211244336815248 ] 
dist 41=[-12.062995589020471958  ,-2.0822810889649642083 ] 
dist 42=[-12.076524301213637404  ,-1.8791357732721674698 ] 
dist 43=[-12.266378561480347822  ,-1.5476963064942048881 ] 
dist 44=[-12.388589699457100337  ,-1.1958298807449387386 ] 
dist 45=[-12.449703563499977132  ,-.9109862473632495767 ] 
dist 46=[-12.478375401424785446  ,-.6213149732635909815 ] 
dist 47=[-12.470966832190898144  ,-.01205064811411099749] 
dist 48=[-4.3994615509373965508 ,1.2760643428360308309 ] 
dist 49=[-4.3522330445419174419 ,2.1604772181551821974 ] 
dist 50=[-4.2871064023724208908 ,2.9175104856582097797 ] 
dist 51=[-4.2622041262069566304 ,3.6975316744151943084 ] 
dist 52=[.2496874802899616951 ,4.4319356053696836354 ] 
dist 53=[.5182932706754923228 ,5.0070560240832081173 ] 
dist 54=[.9010590633959790171 ,5.5754802632792201364 ] 
dist 55=[.9912835116826445417 ,6.4954372519269544846 ] 
dist 56=[2.5609062706044145285 ,7.1623144204856101992 ] 
dist 57=[2.7502444898006082414 ,7.6728173439120238822 ] 
dist 58=[3.0998980003366271276 ,8.1029846498262647690 ] 
dist 59=[3.1703844775420620881 ,8.4479243330525409107 ] 
dist 60=[3.3073053130847837488 ,8.6181563827391247261 ] 
dist 61=[3.1783087004644395283 ,8.7019305668671130668 ] 
dist 62=[2.9836844723701663880 ,8.7090872100256572088 ] 
dist 63=[2.6556582847054825530 ,4.5457249724090264835 ] 
dist 64=[2.0998246194403031317 ,4.5904188407604450936 ] 
dist 65=[1.6224245603062101079 ,4.6056925325968640145 ] 
dist 66=[1.1278957880741879095 ,4.6024663608587454030 ] 
dist 67=[.61989466870865480467,4.5920926054086092160 ] 
dist 68=[-.16313332637636647785,3.5615522094484025698 ] 
dist 69=[-.68447035401104689431,3.5123736316714708217 ] 
dist 70=[-1.1139069351371338350 ,3.4001204158543905618 ] 
dist 71=[-1.5301613126989763475 ,3.3623688454667988514 ] 
dist 72=[-1.9060711712240244767 ,2.9027188875920582794 ] 
dist 73=[-2.1744952715581828856 ,2.8318190570203909131 ] 
dist 74=[-2.4156110745731593569 ,2.6544468943562439562 ] 
dist 75=[-2.6825405700019168406 ,2.6205402256035525448 ] 
dist 76=[-2.9276279861649581215 ,2.3361283129237300035 ] 
dist 77=[-3.0815641492659649060 ,2.2795663858473341421 ] 
dist 78=[-3.1982242145330484151 ,2.1963228025385207764 ] 
dist 79=[-3.2945127411078368424 ,2.1711932532679155073 ] 
dist 80=[-3.5292944743890745231 ,.13699742558280447031] 
dist 81=[-3.8847475699783790292 ,.10633821871453120647] 
dist 82=[-4.1502752385071554768 ,.04310162899029239039] 
dist 83=[-4.3630664791785086329 ,.02725084624207222962] 
dist 84=[-4.5314833396891710330 ,-1.2265852656792750231 ] 
dist 85=[-4.6198417452884587893 ,-1.0521655492794248830 ] 
dist 86=[-4.6666414553041563381 ,-.7806709838153033645 ] 
dist 87=[-4.6736504060067094805 ,-.4960543660754865573 ] 
dist 88=[-4.5568453687835795259 ,-.2692295165502231189 ] 
dist 89=[-4.6001093167102903511 ,-.0414441902944355116 ] 
dist 90=[-4.6260415573250074446 ,.2470710225462028884 ] 
dist 91=[-4.6352866795293273874 ,.5525144220945412097 ] 
dist 92=[-4.6332540025522173095 ,.8479057283355294455 ] 
dist 93=[-4.6202893368701139529 ,1.1925878342208442970 ] 
dist 94=[-4.5856191506559132950 ,1.6948201942182678155 ] 
dist 95=[-4.5653133858649346010 ,2.1890170885044378972 ] 
dist 96=[-2.4287863751632834521 ,2.5273458909748574094 ] 
dist 97=[-2.3824399419679766725 ,2.8438061011391501801 ] 
dist 98=[-2.3417821290988024221 ,3.1319280546200537500 ] 
dist 99=[-2.3275824215409588339 ,3.3798747088635778343 ] 
dist 100=[-1.6141402803252684942 ,3.5359808444259736443 ] 
dist 101=[-1.5251143133291622208 ,3.6547658571915622319 ] 
dist 102=[-1.3384760940690694029 ,3.7537535347692847065 ] 
dist 103=[-1.2872259565659006502 ,3.8327280016781196533 ] 
dist 104=[-1.0863108906141102279 ,3.8716313832364522658 ] 
dist 105=[-1.0457028955901291431 ,3.8886708845239618115 ] 
dist 106=[-.9551618701192852739 ,3.8850974805020701872 ] 
dist 107=[-.9297411121938305299 ,3.8571382173519170598 ] 
dist 108=[-.8179051641335706006 ,3.8432598194412682949 ] 
dist 109=[-.7915468239300056546 ,3.7746736316277558137 ] 
dist 110=[-.7835447362958048861 ,3.7391792881674680499 ] 
dist 111=[-.7984499228424587842 ,3.0807097218534118601 ] 
dist 112=[-.8268808558627809121 ,2.4255547682089944802 ] 
dist 113=[-.87285939156458468324,2.4176031594079864297 ] 
dist 114=[-.94044819032097883797,2.3754950593279393296 ] 
dist 115=[-1.0551202818462506340 ,2.3692047527536042952 ] 
dist 116=[-1.1735834320519530844 ,2.2217555893210782701 ] 
dist 117=[-1.2563035700462911734 ,2.1864365009375149663 ] 
dist 118=[-1.3286224276529110405 ,2.1623285274871179635 ] 
dist 119=[-1.5498382262527156806 ,2.1561700697508912288 ] 
dist 120=[-1.7134786623258305764 ,1.6235889920909615016 ] 
dist 121=[-1.8368735731056134801 ,1.5531642136251515600 ] 
dist 122=[-1.9375835338619393540 ,1.4189507662494234021 ] 
dist 123=[-2.0175570352482085090 ,1.3845732972187937194 ] 
dist 124=[-2.0581922228125478201 ,1.2678689384325417980 ] 
dist 125=[-2.0785898607631327452 ,1.2380418283880025411 ] 
dist 126=[-2.0817195425965851869 ,1.2101701828857361504 ] 
dist 127=[-1.1408443403015391383 ,1.2032076954842779168 ] 
dist 128=[-1.1410809512006390977 ,-.0410099004220909705 ] 
dist 129=[-1.2229931711777995533 ,-.0199059262386557558 ] 
dist 130=[-1.2849508794035722447 ,.00619262738872237564] 
dist 131=[-1.3359984687171732109 ,.04585260734055806272] 
dist 132=[-1.3762251573029217373 ,.09111635739399238383] 
dist 133=[-1.3949847715836401418 ,.13958060650476040729] 
dist 134=[-1.4586608918672097081 ,.19961508172836973062] 
dist 135=[-1.6412014549617715997 ,.29105220158777303423] 
dist 136=[-1.8141347220789193183 ,.38614087429438911383] 
dist 137=[-1.9240958583706839238 ,.46074939829818780019] 
dist 138=[-2.0097623289550659187 ,.53458181508784302127] 
dist 139=[-2.0838159721414347430 ,.62657847050431119957] 
dist 140=[-2.1445412751836739271 ,.7231301286252060639 ] 
dist 141=[-2.1773142408882462300 ,.8151422208753167429 ] 
dist 142=[-2.1958635248758629718 ,1.0263478180974325202 ] 
dist 143=[-2.1997994008880364902 ,1.2391870931143426413 ] 
dist 144=[-.17743139056370679481,1.3753991530138079843 ] 
dist 145=[-.17911357215608925379,1.4816393320546368009 ] 
dist 146=[-.19284215644104609632,1.5748395895532315340 ] 
dist 147=[-.21321777679181754278,1.6525935033275129624 ] 
dist 148=[-.24143198294231131247,1.6971773664749162516 ] 
dist 149=[-.28076431181503302601,1.7260383025309160115 ] 
dist 150=[-.3455148042886829972 ,1.7410338289015909049 ] 
dist 151=[-.4148412849619106057 ,1.7481736358609960508 ] 
dist 152=[-.4724390636413489422 ,1.7460008464496016475 ] 
dist 153=[-.5324544877689265131 ,1.7380062028529362198 ] 
dist 154=[-.6114352500842660958 ,1.7750416052726800871 ] 
dist 155=[-.6965438961543332687 ,1.7950331917036465438 ] 
dist 156=[-.7810193517866399412 ,1.8054211757664965515 ] 
dist 157=[-.8812037214898654631 ,1.8093671336702723598 ] 
dist 158=[-1.0290119391180910417 ,1.8096189120285885647 ] 
dist 159=[-1.1747040703728080014 ,1.8065927251663266351 ] 
dist 160=[-1.2664440964086811011 ,1.7639319450292763915 ] 
dist 161=[-1.3362267700760683144 ,1.7528794000447459066 ] 
dist 162=[-1.3942846422717808931 ,1.7107219975123407445 ] 
dist 163=[-1.4403607855457370214 ,1.7037133960612142100 ] 
dist 164=[-1.4623233974447555979 ,1.5832450400429124607 ] 
dist 165=[-1.4723442605674830368 ,1.5552203672526257583 ] 
dist 166=[-1.4725210924857629678 ,1.5323543906418594047 ] 
dist 167=[-1.4496200816237313243 ,1.5248683905560941073 ] 
dist 168=[-1.4434082596708754267 ,1.1294799039722175014 ] 
dist 169=[-1.4915667926887547714 ,1.0769108504670177685 ] 
dist 170=[-1.5489672565814337351 ,.97480465897939072444] 
dist 171=[-1.5957668238034434147 ,.94824142424587184795] 
dist 172=[-1.6305391552034877221 ,.85490937749412050628] 
dist 173=[-1.6425305946067493050 ,.83227436659614392188] 
dist 174=[-1.6455621354409558600 ,.80374983741973395311] 
dist 175=[-1.6445564148504690637 ,.79305497268063816262] 
dist 176=[-1.1609457721599344277 ,.58300382331080898693] 
dist 177=[-1.1548762552097195399 ,.75402277215555473402] 
dist 178=[-1.1364751292857538733 ,.91761147826234605364] 
dist 179=[-1.1278975577955219426 ,1.0639077681954479280 ] 
dist 180=[-1.0784746464014071257 ,1.1659052997527971786 ] 
dist 181=[-1.0655895656785155858 ,1.2549846488259453387 ] 
dist 182=[-1.0403303123977542533 ,1.3497168069044543228 ] 
dist 183=[-1.0319633906587472405 ,1.4352200011635773711 ] 
dist 184=[-.8676446633847884916 ,1.4874637064403562892 ] 
dist 185=[-.84317648344427583568,1.5253390644918776107 ] 
dist 186=[-.78512759125670701386,1.5534974339436179575 ] 
dist 187=[-.77049687002625179779,1.5732458055551588715 ] 
dist 188=[-.68360953248962713965,1.5775563478800562533 ] 
dist 189=[-.66574160591457439146,1.5754212348568960681 ] 
dist 190=[-.63107439674794812552,1.5697552807260317617 ] 
dist 191=[-.62143338963095971556,1.3034795277469480798 ] 
dist 192=[-.23049783304106030275,1.3863047725514847879 ] 
dist 193=[-.2602258163455966283 ,1.4464787091010300982 ] 
dist 194=[-.30447125669251877296,1.4915094875056439499 ] 
dist 195=[-.34954926993485819314,1.5250118498002850658 ] 
dist 196=[-.39053479874396460092,1.5391686098967569186 ] 
dist 197=[-.43636333338340666158,1.5436918426810526816 ] 
dist 198=[-.50076944575792338228,1.5417868126792048587 ] 
dist 199=[-.5656575256809508542 ,1.4515487032009558758 ] 
dist 200=[-.6134094601393118223 ,1.4338379855343720607 ] 
dist 201=[-.6577419800450873195 ,1.4590044323823299252 ] 
dist 202=[-.7089831170011062350 ,1.4753369298452798172 ] 
dist 203=[-.7607270359709082463 ,1.4782293930409631667 ] 
dist 204=[-.8070658897052201482 ,1.4723435596562559738 ] 
dist 205=[-.8583085772866893582 ,1.4662289391652187684 ] 
dist 206=[-.9296229552519980676 ,1.4549366453468906568 ] 
dist 207=[-.9982658389991230971 ,1.4492405418443100902 ] 
dist 208=[-1.0388465421806284236 ,.85302927189338850634] 
dist 209=[-1.0666286764007756775 ,.93813935138659537756] 
dist 210=[-1.0841930659135518825 ,1.0162687320296249646 ] 
dist 211=[-1.0951868753084625453 ,1.0839477411119359504 ] 
dist 212=[-1.0967453104481734297 ,1.1273439594316133233 ] 
dist 213=[-1.0941155155516619611 ,1.1612673602480667714 ] 
dist 214=[-1.1349479673187824631 ,1.1911334738540261846 ] 
dist 215=[-1.2384006084955584517 ,1.2148765753038005727 ] 
dist 216=[-1.3004068452308750280 ,1.2243608466518111101 ] 
dist 217=[-1.3439393099694932921 ,1.2267238584374895509 ] 
dist 218=[-1.3736554627215598335 ,1.2247492861262189310 ] 
dist 219=[-1.3942552030001397874 ,1.2004567377172913825 ] 
dist 220=[-1.4013996381956152177 ,1.1918728014278629721 ] 
dist 221=[-1.4014841978529627319 ,1.1751324643522055284 ] 
dist 222=[-1.3985543875777761794 ,1.1685601619243572112 ] 
dist 223=[-1.0923264296477116995 ,.7898748662797727150 ] 
dist 224=[-.9219728814288392255 ,.7494047988399633547 ] 
dist 225=[-.9015397783257532668 ,.6506439200040767235 ] 
dist 226=[-.8526441433543915243 ,.6335547548013718315 ] 
dist 227=[-.8388099687953354709 ,.4850152126683437957 ] 
dist 228=[-.7619901866218800508 ,.4565752887336874159 ] 
dist 229=[-.7455102566674807243 ,.4168297858020608606 ] 
dist 230=[-.7123529819964477109 ,.4449275855992358808 ] 
dist 231=[-.7025411108860303235 ,.5432782335191608065 ] 
dist 232=[-.55652390063083714647,.6158534704985424747 ] 
dist 233=[-.53553510129239145138,.6834642105137407813 ] 
dist 234=[-.48137496353665726261,.7620007340831378257 ] 
dist 235=[-.47349406187583259787,.8415778586468160560 ] 
dist 236=[-.38302041667570644968,.9133433847092842504 ] 
dist 237=[-.45784449622273028325,.9931571751345015251 ] 
dist 238=[-.61539029361878542864,1.1048609098110228292 ] 
dist 239=[-.77285717028212164548,1.2128645949559119308 ] 
dist 240=[-.87636364608204075042,1.2779100284878793660 ] 
dist 241=[-.96017564528737039306,1.3239659815650007555 ] 
dist 242=[-1.0390344625874570146 ,1.3561723499593609541 ] 
dist 243=[-1.1086800531518433000 ,1.3790326713425370111 ] 
dist 244=[-1.1557183493931379440 ,1.3877831391232332491 ] 
dist 245=[-1.1952067814399264777 ,1.3890023463276959628 ] 
dist 246=[-1.2347172836104791280 ,1.3866790212407670326 ] 
dist 247=[-1.2675738538695213261 ,1.2851422078897130792 ] 
dist 248=[-1.2805037550132152938 ,1.2496417093855143462 ] 
dist 249=[-1.2854577299749644473 ,1.2141381166846324427 ] 
dist 250=[-1.2864811953091041963 ,1.2022041747102006387 ] 
dist 251=[-1.2474815031449741306 ,1.1452110776188003132 ] 
dist 252=[-1.2373617651870632512 ,1.1323582240229346333 ] 
dist 253=[-1.2312792102133947403 ,1.0923823459786560442 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 1, 1, 2, 0, 1] 
dist 0=[42.072076003512602373  ,42.072076003512602373  ] 
dist 1=[41.141484066873376508  ,42.489810826086761181  ] 
dist 2=[39.684457799210189433  ,43.227134751970182219  ] 
dist 3=[37.386662604050645860  ,44.014710242594618743  ] 
dist 4=[35.042959013666927310  ,44.437329826897043266  ] 
dist 5=[33.402448925663742880  ,44.673128830196533619  ] 
dist 6=[31.959195912312286425  ,44.724616875239807004  ] 
dist 7=[30.402965579168785606  ,44.684015987787406331  ] 
dist 8=[28.888013838375737780  ,44.634746667848000599  ] 
dist 9=[27.609344868181667597  ,44.560676250150873772  ] 
dist 10=[26.254607180728300967  ,44.490673710725765945  ] 
dist 11=[24.435365660062714320  ,44.276942343890270004  ] 
dist 12=[22.626799997920788386  ,44.178730071465652260  ] 
dist 13=[21.314443203741381332  ,43.918416916520617614  ] 
dist 14=[20.108572759175008026  ,43.800446450964532033  ] 
dist 15=[18.725013567334819877  ,43.064787329678963352  ] 
dist 16=[17.324222455393827802  ,32.644869659284843501  ] 
dist 17=[16.049055429284833649  ,30.371522824501640573  ] 
dist 18=[14.613865339468591750  ,30.035606932437350455  ] 
dist 19=[12.572831929247664043  ,26.568288853985467984  ] 
dist 20=[10.559298189095043834  ,25.907638659641086804  ] 
dist 21=[9.2338576733444394968 ,25.165584949550718673  ] 
dist 22=[8.1496956801181882451 ,25.005900208931118498  ] 
dist 23=[7.1006886378047548317 ,19.727650155245510555  ] 
dist 24=[6.1452441068587307083 ,18.099773373990952416  ] 
dist 25=[5.4350027739411447147 ,16.859860260002059019  ] 
dist 26=[4.7625255339543852189 ,16.153826066956210208  ] 
dist 27=[3.9577466319246469476 ,14.752205572961571129  ] 
dist 28=[3.1951632276071869233 ,14.450576907152645818  ] 
dist 29=[2.6912789527900068043 ,14.024127876192547539  ] 
dist 30=[.94614559282295417957,13.898000806680664223  ] 
dist 31=[-1.6757692023626997558 ,5.6283610760126784306 ] 
dist 32=[-4.2429033038100816820 ,2.0823369397579737108 ] 
dist 33=[-5.8830972485492807455 ,1.8467229070645234796 ] 
dist 34=[-7.1679341795089009047 ,1.7069444589015139799 ] 
dist 35=[-8.3148211431737898238 ,1.6826002807285151965 ] 
dist 36=[-9.2942724214174266984 ,.68260312927112073995] 
dist 37=[-9.9100537662056860207 ,.5954620797815131975 ] 
dist 38=[-10.382317149137999364  ,.41683837902757517162] 
dist 39=[-10.788558666987017637  ,.3802383519877969987 ] 
dist 40=[-11.125869419674271693  ,.21131601512760636108] 
dist 41=[-11.322613093021675474  ,.18302152319909021485] 
dist 42=[-11.457098191309653936  ,.11999640386300756201] 
dist 43=[-11.545117632824382187  ,.11045401826108737857] 
dist 44=[-11.598834404674366866  ,.01692689439549575585] 
dist 45=[-11.596007001318633331  ,.00122676939691308111] 
dist 46=[-11.556538855701181514  ,-.04235818832099826245] 
dist 47=[-11.525471984417387703  ,-.04856309669511481559] 
dist 48=[-6.4697712569844125563 ,-.14096607412453036958] 
dist 49=[-6.0328640941385226992 ,-.16140812990136263436] 
dist 50=[-4.9824349933231010820 ,-.17746294132177640533] 
dist 51=[-4.8188379428914186290 ,-.1821271246418506415 ] 
dist 52=[-3.3265046069157602998 ,-.91215165939411606089] 
dist 53=[-3.0539264966884913306 ,-.20011940312002989849] 
dist 54=[-2.6928501552874183698 ,.51751646917686854259] 
dist 55=[-2.5956205890096547227 ,1.4314488965386793651 ] 
dist 56=[-2.0485096816439047806 ,2.3134264493751072683 ] 
dist 57=[-2.1275859523862023070 ,2.9035731830382016313 ] 
dist 58=[-2.2007243925628071197 ,3.3939010031397618165 ] 
dist 59=[-2.2846534818023929593 ,3.8774568982539415986 ] 
dist 60=[-2.3606294186024832188 ,4.3210345640579812904 ] 
dist 61=[-2.4020229898069842593 ,4.6518522803419811511 ] 
dist 62=[-2.4258329308145209719 ,4.9645651629309666041 ] 
dist 63=[-2.4316400759973985673 ,5.3360623278414376986 ] 
dist 64=[-2.4280974574687922379 ,5.6767262252503291922 ] 
dist 65=[-2.4217853930242684071 ,5.8663482601612078624 ] 
dist 66=[-2.3982538227352353547 ,5.9827847759633272431 ] 
dist 67=[-2.3849200782312615768 ,6.0310861315974460001 ] 
dist 68=[-2.1875545720565581212 ,6.0523070935084620477 ] 
dist 69=[-2.1538360132757220474 ,6.0605085177540795139 ] 
dist 70=[-2.0644100983851851609 ,6.0610868149965400057 ] 
dist 71=[-2.0428366323568690698 ,6.0516957725478024588 ] 
dist 72=[-1.8717785114607513700 ,5.3839937150935922319 ] 
dist 73=[-1.8338746539011548424 ,5.3451131416204101772 ] 
dist 74=[-1.7764910763698961769 ,5.2876943174067049180 ] 
dist 75=[-1.7578756178047189035 ,5.2628790427113445572 ] 
dist 76=[-1.3344629571616824467 ,5.1737469535592608714 ] 
dist 77=[-1.2754120548998490484 ,5.1418275636581518942 ] 
dist 78=[-1.4497339799391897162 ,5.0700629422060440408 ] 
dist 79=[-2.0200125526015269760 ,5.0413542565519225989 ] 
dist 80=[-2.3880328046829839094 ,2.8181758717432385649 ] 
dist 81=[-2.6787015621027453022 ,2.8207880096660312326 ] 
dist 82=[-2.9402061130377263592 ,2.8176483763915048037 ] 
dist 83=[-3.1633137216562286553 ,2.8090483745617296895 ] 
dist 84=[-3.3007169764012638393 ,2.3055483753248855006 ] 
dist 85=[-3.4018896371917816263 ,2.2450665111010547148 ] 
dist 86=[-3.4803967600370430196 ,2.0892139145179784484 ] 
dist 87=[-3.5407549285109714666 ,2.0609940987833203092 ] 
dist 88=[-3.5694736046180231579 ,1.7931027804702442489 ] 
dist 89=[-3.5806841142203054638 ,1.7384097629834647006 ] 
dist 90=[-3.6026729751881497379 ,1.6683123045506060256 ] 
dist 91=[-3.6417496069268724600 ,1.6429910491749634589 ] 
dist 92=[-3.7503178512311052631 ,1.4917764173210140812 ] 
dist 93=[-3.8086277345365248281 ,1.6401079693770923197 ] 
dist 94=[-3.8413690965448528344 ,1.7719951914039421512 ] 
dist 95=[-3.8479113450059980665 ,1.9159950617827900840 ] 
dist 96=[-2.9559757443001254307 ,2.0568295684293732139 ] 
dist 97=[-2.9426364919387146909 ,2.1760816968224338951 ] 
dist 98=[-2.8948922339530761165 ,2.3024136523993402753 ] 
dist 99=[-2.8792349073672145582 ,2.4715077545535263447 ] 
dist 100=[-2.7404821289020390505 ,2.6317151962463261307 ] 
dist 101=[-2.7059341004251354747 ,2.7225739594183826134 ] 
dist 102=[-2.6576946662412747142 ,2.7800595609725443637 ] 
dist 103=[-2.6389803123251148381 ,2.8070514213139624107 ] 
dist 104=[-2.1700971553291632184 ,2.8206078930374019760 ] 
dist 105=[-2.1839590848176776658 ,2.8244614949414034003 ] 
dist 106=[-2.3016956037695876977 ,2.8219289857687665378 ] 
dist 107=[-2.4350484892578640027 ,2.8138111152126507146 ] 
dist 108=[-2.5555407529236653799 ,2.5674035396275257306 ] 
dist 109=[-2.6219391776443801994 ,2.5815225086716360667 ] 
dist 110=[-2.6614370942009189232 ,2.5801688292599476840 ] 
dist 111=[-2.6745480795558468516 ,2.3107320801902116615 ] 
dist 112=[-2.6761701853603667658 ,2.2113897584592280422 ] 
dist 113=[-2.6698105702874903225 ,2.1840973269578744291 ] 
dist 114=[-2.6563739271832652007 ,2.1335707396243385064 ] 
dist 115=[-2.6480545460283836237 ,2.1176937015231110663 ] 
dist 116=[.22039855726523502253,1.7967487063589872584 ] 
dist 117=[.17620429060655208206,1.8004516462389017719 ] 
dist 118=[.11888362232808662119,1.7982640856432253548 ] 
dist 119=[.02877277508784614239,1.6806948077555781743 ] 
dist 120=[-.06606838543299934444,1.6589752318983199465 ] 
dist 121=[-.14227980425811149978,1.6162916244747417191 ] 
dist 122=[-.21940342322872548371,1.6026455477554638335 ] 
dist 123=[-.31790649670409760515,1.5415884494038623103 ] 
dist 124=[-.42262112074829561535,1.5264111406242272730 ] 
dist 125=[-.52455085194146539463,1.4841825410298482428 ] 
dist 126=[-.6440028153959799557 ,1.4717542252517440484 ] 
dist 127=[-.81867413968829219012,1.1782708322278632320 ] 
dist 128=[-.99078505406278306169,.62229081897149048015] 
dist 129=[-1.1000220864203971850 ,.58969861566689109344] 
dist 130=[-1.1841889360680127375 ,.57978480618407144661] 
dist 131=[-1.2562301587745158684 ,.53609248551354734122] 
dist 132=[-1.3150384333538582604 ,.52694297009104376721] 
dist 133=[-1.3463871914793054888 ,.50316828773273601019] 
dist 134=[-1.3636748327014935932 ,.49777269340059268005] 
dist 135=[-1.3669996023765929850 ,.43465135090887848627] 
dist 136=[-1.3943291338490381963 ,.4237970388756371558 ] 
dist 137=[-1.4441682585242399719 ,.39855118596361758101] 
dist 138=[-1.4799620943875137840 ,.39135362549070270253] 
dist 139=[-1.5054263691688718660 ,.35387089976873006316] 
dist 140=[-1.5140308635351093748 ,.34585028642492912835] 
dist 141=[-1.5150075527955128954 ,.32923991091758987633] 
dist 142=[-1.5111305668426966022 ,.32422551383192974601] 
dist 143=[-1.4376146525614203736 ,.2548509438965698974 ] 
dist 144=[-.7957601349402374398 ,.2442601162128115847 ] 
dist 145=[-.73966599060834331255,.24750231747128800591] 
dist 146=[-.60649660071343962989,.39471754359209815844] 
dist 147=[-.58288887037518015787,.53781096676063084368] 
dist 148=[-.39629829407250562079,.66731698212943503313] 
dist 149=[-.36167786088934784782,.76029715606743207558] 
dist 150=[-.30799333971956031584,.84433012451515369426] 
dist 151=[-.29387823587980158035,.93811973263705339363] 
dist 152=[-.0555685125993542332 ,1.0244188154778882082 ] 
dist 153=[-.0933338833534025330 ,1.0785549552625718062 ] 
dist 154=[-.1390763608087010591 ,1.1194925244135500702 ] 
dist 155=[-.1864109604617847322 ,1.1531179192532398867 ] 
dist 156=[-.2305219260698220345 ,1.1794741279194125891 ] 
dist 157=[-.2806752134178818049 ,1.1914022696266813374 ] 
dist 158=[-.40709208081811430429,1.1953940194861711353 ] 
dist 159=[-.53782395618429258382,1.1947904677313940230 ] 
dist 160=[-.62387183947103008902,1.0515739016312013840 ] 
dist 161=[-.69362689735317002082,1.0960795893620921300 ] 
dist 162=[-.75933317053306664966,1.1302458742251990122 ] 
dist 163=[-.81735367439981479346,1.1555712940930722100 ] 
dist 164=[-.85643228663366527875,1.1647806803520325987 ] 
dist 165=[-.88907899925303274195,1.1674987485994669486 ] 
dist 166=[-.92142322947478703084,1.1669074744936444152 ] 
dist 167=[-.94876766541973701258,1.1181321856391619086 ] 
dist 168=[-.9614605552147435347 ,1.1073502589328472837 ] 
dist 169=[-.96694195539808216006,1.0824945796596745667 ] 
dist 170=[-.96662667133290794987,1.0732785590485858031 ] 
dist 171=[-.95099476067803502232,1.0262273537386065246 ] 
dist 172=[-.94448752398993583485,1.0149891041262973812 ] 
dist 173=[-.93586737503161501608,.9850631827371955057 ] 
dist 174=[-.93123791758183441053,.97559461263182169797] 
dist 175=[-.53709314089484076694,.7460237591053282739 ] 
dist 176=[-.56684103191402020727,.19545910285509352714] 
dist 177=[-.58778072760934131065,.22639425925297826008] 
dist 178=[-.60220111926451900366,.25178401572363946111] 
dist 179=[-.61233921360985964717,.27622785229571650017] 
dist 180=[-.61618430567046871074,.29817263764023345549] 
dist 181=[-.61659298840063660659,.3135866713345474514 ] 
dist 182=[-.6155272444166899488 ,.32715119191892940855] 
dist 183=[-.66455096076159206669,.34171058865186263848] 
dist 184=[-.73862437004929790055,.35437084983658445104] 
dist 185=[-.78350487625128725223,.36035446420136149038] 
dist 186=[-.81560377308279859879,.36327708097182536969] 
dist 187=[-.83865840863745977735,.36372959143454031854] 
dist 188=[-.85552621177350913325,.3567075533589485738 ] 
dist 189=[-.86293147770208542396,.35457691596138569053] 
dist 190=[-.86492998499376300659,.35301783893102173532] 
dist 191=[-.8642821294658866904 ,.35183700111469929424] 
dist 192=[-.16508879014815571023,.2845371587650251911 ] 
dist 193=[-.12747114588349239098,.2757268764948741727 ] 
dist 194=[-.06211991498106379057,.32355124485232700673] 
dist 195=[-.02781946796923515921,.38476366960874655515] 
dist 196=[.01694680542961607378,.42949037487083558524] 
dist 197=[.04224066484693206675,.47070005545170647849] 
dist 198=[.04729241562434759816,.517871328209693125  ] 
dist 199=[.07404793037346515978,.5610613013205522669 ] 
dist 200=[.06951394218016598823,.58638114435841608991] 
dist 201=[.03944466347831726486,.6034506058771791018 ] 
dist 202=[.01070268289076264802,.6137166296370643871 ] 
dist 203=[-.02373117880492477034,.62029078928872050482] 
dist 204=[-.05916769918076090377,.62262439275433429954] 
dist 205=[-.09190760447231027147,.62229050791711926743] 
dist 206=[-.12891937623040952022,.62100888961734453434] 
dist 207=[-.18139842005270485477,.65494901186439998207] 
dist 208=[-.23334746432129987009,.68880292343943985695] 
dist 209=[-.27600049892031161644,.70704190840918970518] 
dist 210=[-.32901052612396223338,.71735809728814743714] 
dist 211=[-.38180548654223484813,.71958633484447525114] 
dist 212=[-.43040680999585127251,.71874926377948082575] 
dist 213=[-.46667886833191256589,.716827851023072861  ] 
dist 214=[-.50085579733560581673,.71375129295271872724] 
dist 215=[-.54109360825069006831,.71101216984536912362] 
dist 216=[-.57822637767441346214,.6159315644405805387 ] 
dist 217=[-.60001016950000456254,.60146123803530608006] 
dist 218=[-.61470887558977530176,.57281918178566296603] 
dist 219=[-.62356421301555577629,.56458332866776947508] 
dist 220=[-.62881926719453725416,.53138393037809163379] 
dist 221=[-.62915031616741109212,.52347167669021429869] 
dist 222=[-.62724537950526172142,.50542071623221863854] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 0, 1, 0, 1] 
dist 0=[54.589438498015615946  ,54.589438498015615946  ] 
dist 1=[54.055005825117674876  ,54.876207940467619201  ] 
dist 2=[52.957637797727617603  ,54.984732725347553691  ] 
dist 3=[51.697200969532101662  ,55.001275819288782806  ] 
dist 4=[50.511386306166135576  ,54.920883717062057293  ] 
dist 5=[49.150422035876906675  ,54.813325656899342081  ] 
dist 6=[47.190266906779332955  ,54.721155465895767041  ] 
dist 7=[44.988708463761956656  ,54.621990474806707349  ] 
dist 8=[42.663472492377984171  ,54.142937758157026518  ] 
dist 9=[39.795875486485248316  ,50.630778435049281134  ] 
dist 10=[35.427975135700786192  ,50.032896912294535305  ] 
dist 11=[31.023534248648916337  ,49.110437806218958891  ] 
dist 12=[28.009899030730444467  ,48.833290930289709522  ] 
dist 13=[25.429622225560025795  ,48.236270961625117290  ] 
dist 14=[22.755881172159557177  ,47.310854335358194635  ] 
dist 15=[20.216999851452728637  ,42.807126512334288165  ] 
dist 16=[18.175175407361137087  ,39.816735334731594000  ] 
dist 17=[16.099645454261866857  ,31.653934124931235661  ] 
dist 18=[13.425748933370856461  ,31.173177269489183701  ] 
dist 19=[10.820272859875999456  ,29.442554563311340541  ] 
dist 20=[9.0178220873225444213 ,29.049979180415221527  ] 
dist 21=[7.4513292902821110954 ,28.421081737780584746  ] 
dist 22=[5.7880912755699599009 ,28.246187135938895761  ] 
dist 23=[4.1803144512867805762 ,13.485430242889240602  ] 
dist 24=[2.8349485623487487848 ,13.160205227813075581  ] 
dist 25=[1.4164242645625737570 ,8.0584228144434590196 ] 
dist 26=[-.80104728338439078861,7.4181424716634501098 ] 
dist 27=[-3.1267615094245561464 ,6.1681518159479981410 ] 
dist 28=[-4.8433715099920342466 ,5.8856241721886385091 ] 
dist 29=[-6.4479573011159237204 ,5.1001866265946016745 ] 
dist 30=[-8.3262081677391328885 ,4.6451091446604983727 ] 
dist 31=[-10.074349337123690098  ,3.4362688351865532414 ] 
dist 32=[-11.159261632470733874  ,2.8670940939698647488 ] 
dist 33=[-11.969690633814134237  ,-4.6805351474487701301 ] 
dist 34=[-12.621536672482027749  ,-4.8799182210651379040 ] 
dist 35=[-13.131496718084879801  ,-5.3916872460881999346 ] 
dist 36=[-13.375113679791958314  ,-5.4110080636695350851 ] 
dist 37=[-13.492154011914621796  ,-5.2577453298753241752 ] 
dist 38=[-13.496516287987948098  ,-4.8338672454138077735 ] 
dist 39=[-9.0784048723027066703 ,-4.3520922520367397707 ] 
dist 40=[-9.0955878611221315619 ,-3.9675614855620330750 ] 
dist 41=[-9.0789160764419792540 ,-3.5835196715571630129 ] 
dist 42=[-9.0535803391344719631 ,-3.1029602510590041340 ] 
dist 43=[-8.9563363682420343218 ,-2.5994417326736040941 ] 
dist 44=[-8.9040253604385995386 ,-2.0200695301021653508 ] 
dist 45=[-8.5861958318710704461 ,-1.4187990820842488644 ] 
dist 46=[-8.5017284928874229961 ,-.79365021328843293027] 
dist 47=[-8.3384741978474462897 ,.00252267609849344177] 
dist 48=[-8.2848872077460458860 ,.59889457014164071358] 
dist 49=[-5.6659760510849443303 ,1.3135231258086206980 ] 
dist 50=[-5.3839590784992509153 ,2.4945888465196365744 ] 
dist 51=[-4.7956158214809925736 ,3.4547477043746796330 ] 
dist 52=[-4.6270999100164228472 ,4.3651531468249205164 ] 
dist 53=[-3.2922537529320744094 ,5.1746652487075071007 ] 
dist 54=[-2.6267622662992194517 ,5.7321607888324889269 ] 
dist 55=[1.2168985628415535258 ,6.2124266830984872102 ] 
dist 56=[1.3093095485860697224 ,6.7137710517162489494 ] 
dist 57=[1.4060920644530542017 ,7.1665057758543071572 ] 
dist 58=[1.4241029276641668737 ,7.4526986822337565354 ] 
dist 59=[2.3236890960611459878 ,7.7507000015317927065 ] 
dist 60=[2.3928918293710664480 ,7.9428657012195333219 ] 
dist 61=[2.5178044302417825362 ,8.0608081476479478998 ] 
dist 62=[2.5406976629304852922 ,8.1097948940622160814 ] 
dist 63=[2.4975611370168056542 ,8.1202493341155726086 ] 
dist 64=[2.3390552172818389631 ,8.0365547107682482363 ] 
dist 65=[2.1234563641743634470 ,6.0297777162753116271 ] 
dist 66=[1.7740104432149924995 ,6.1174499288038882003 ] 
dist 67=[1.3654305197969453591 ,6.1727178436110490213 ] 
dist 68=[.91370732013987290167,6.1810919488402115059 ] 
dist 69=[.34373071932330562007,6.1638209843571046788 ] 
dist 70=[-.53696815835182854383,6.1469949281098031855 ] 
dist 71=[-1.4238720060556599153 ,2.4731875032810673806 ] 
dist 72=[-2.0186518425014771939 ,2.4496266518354558526 ] 
dist 73=[-2.5137098370363888999 ,2.3950684370154599981 ] 
dist 74=[-3.0025703944818329976 ,2.3755719810437429245 ] 
dist 75=[-3.4504919201939449938 ,1.4850348650432988800 ] 
dist 76=[-3.7821523823987557973 ,1.3944346078270881856 ] 
dist 77=[-4.0925075974313376334 ,1.1751387509199384036 ] 
dist 78=[-4.4554250297021819393 ,1.1398071581748289051 ] 
dist 79=[-4.7901488114895991082 ,.81773485756096719148] 
dist 80=[-4.9879737966264930032 ,.75708663094218197993] 
dist 81=[-5.1237429225840496837 ,.67789102446555631396] 
dist 82=[-5.2107494289843616173 ,.65349207172651161256] 
dist 83=[-5.2662817058402101808 ,.14840754690327809678] 
dist 84=[-5.3071678158263335150 ,.08438294640029967234] 
dist 85=[-5.3269176869223535880 ,-.05394408020589355567] 
dist 86=[-5.3198699374069620079 ,-.08556939735304077033] 
dist 87=[-5.2040316990341500615 ,.79776955004368606653] 
dist 88=[-5.1740493689931710167 ,1.4326964479331918657 ] 
dist 89=[-5.0562596601846639547 ,1.9672185614029217786 ] 
dist 90=[-5.0384270577002066904 ,2.5046119394381730929 ] 
dist 91=[-4.6961866056303559237 ,3.0028404806551448924 ] 
dist 92=[-4.6168274096649011833 ,3.3810374321924915356 ] 
dist 93=[-4.5571877965121994307 ,3.7438127863597431869 ] 
dist 94=[-4.5415745873705003256 ,4.1804828836488168863 ] 
dist 95=[-3.9629086639412063525 ,4.5888518455422736525 ] 
dist 96=[-3.9500269549906731900 ,4.8386614001811040611 ] 
dist 97=[-2.9716054250823241640 ,5.0201808827355239073 ] 
dist 98=[-2.8979092708047456402 ,5.1559679851216784376 ] 
dist 99=[-2.6451790422964659246 ,5.2548456130344353643 ] 
dist 100=[-2.5821002056097280831 ,5.2890429049271649444 ] 
dist 101=[-2.5160237800745966796 ,5.2961767924892506665 ] 
dist 102=[-2.4948036529783683818 ,5.2870360465325953728 ] 
dist 103=[-.37456260131263345719,4.3445161730986349810 ] 
dist 104=[-.35331985103604301171,4.5301272287177236945 ] 
dist 105=[-.32562221887302202298,4.6897673073103770209 ] 
dist 106=[-.31763081453573674545,4.7720250934725154971 ] 
dist 107=[.12111883322853789085,4.8134641226588006614 ] 
dist 108=[.02903759246322957052,4.8196288201168827772 ] 
dist 109=[-.05509552033381993950,4.7891380493756232686 ] 
dist 110=[-.15030995291444847005,4.7682611274472002587 ] 
dist 111=[-.24530641959977410077,4.7237783779756838889 ] 
dist 112=[-.32857539513470370371,4.7022621509339090776 ] 
dist 113=[-.41917711283140525854,3.9888844714401482516 ] 
dist 114=[-.54344471673457131212,3.9115138135276161316 ] 
dist 115=[-.88117715632627217044,3.6943536754047179529 ] 
dist 116=[-1.3717719368813826658 ,3.6630447809488620400 ] 
dist 117=[-1.8290552978412167097 ,3.2352547895160634024 ] 
dist 118=[-2.1804993453176273804 ,2.9896689646211997089 ] 
dist 119=[-2.5218726586794445254 ,2.0316410498433684471 ] 
dist 120=[-2.9389454804477787944 ,1.9896334346703790066 ] 
dist 121=[-3.3322558209984567603 ,1.4149620841259646384 ] 
dist 122=[-3.5787697659278279137 ,1.4138796559863165855 ] 
dist 123=[-3.7650182797505629079 ,.64256761891744878201] 
dist 124=[-3.9177586607704389602 ,.57886326101476366421] 
dist 125=[-4.0372419322627134888 ,.29906703343326554458] 
dist 126=[-4.0907270295589447912 ,.24836401489504308555] 
dist 127=[-4.1150195837039923971 ,.13715999764577026023] 
dist 128=[-4.1180121166532196232 ,.1141623723574627361 ] 
dist 129=[-1.5488085012099079841 ,-.88804837828826716575] 
dist 130=[-1.5483008052417789346 ,-.88894700028830572873] 
dist 131=[-1.3899159923876463072 ,-.87682012262599200187] 
dist 132=[-1.5375973309477822257 ,-.84686171584290135692] 
dist 133=[-1.6663789360480922634 ,-.79811671728578452737] 
dist 134=[-1.7506827440955533463 ,-.71099860611632796678] 
dist 135=[-1.8186428632307428566 ,-.60587143766759674963] 
dist 136=[-1.8821869775618799740 ,-.48524153802910652396] 
dist 137=[-1.9354809908844561275 ,-.33012643639096830684] 
dist 138=[-1.9625227011269528136 ,-.08735101034625073074] 
dist 139=[-1.9755671219858072702 ,.15828475234930315547] 
dist 140=[-1.9762247467594587844 ,.3248183302032380536 ] 
dist 141=[-1.9631952606559910082 ,.46533354543545901605] 
dist 142=[-1.9554666214482462053 ,.60712070227029995922] 
dist 143=[-1.9307929323855474790 ,.7389134786993702008 ] 
dist 144=[-1.9183855490499232002 ,.83953838048338205305] 
dist 145=[-1.2770512219541142543 ,.93663379111604804577] 
dist 146=[-1.2121401706033073457 ,1.0543416221337554286 ] 
dist 147=[-1.0519292026324454248 ,1.1648845212181489818 ] 
dist 148=[-1.0266271764932840325 ,1.2333825189474650110 ] 
dist 149=[-.78212515008334438071,1.2842262494215961285 ] 
dist 150=[-.7356710223343617831 ,1.3243033255811645843 ] 
dist 151=[-.67771373776461659812,1.3544218001799407641 ] 
dist 152=[-.6612161342535048672 ,1.3655175788594773510 ] 
dist 153=[-.53184576806194729237,1.3689604607269444097 ] 
dist 154=[-.52397818253841712532,1.3685238735494029411 ] 
dist 155=[-.0981548413798716336 ,1.3424408816190216453 ] 
dist 156=[-.07297815616362022996,1.3925722536927183880 ] 
dist 157=[.04143062914074153674,1.4310232972147346833 ] 
dist 158=[.06176174808444799026,1.4500520419410322010 ] 
dist 159=[.1046872922455530148 ,1.4585098377297936299 ] 
dist 160=[.11400049872932894772,1.4589593034169830792 ] 
dist 161=[.53278874710638373475,1.3676516799794212643 ] 
dist 162=[.57082155491624306892,1.3528186690085057079 ] 
dist 163=[.63998806947164760129,1.3110663634314735517 ] 
dist 164=[.65419164315449141026,1.3001602214545713284 ] 
dist 165=[.6736588197688343171 ,1.2116084132015902288 ] 
dist 166=[.54041730071225601948,1.1913524177566540020 ] 
dist 167=[.39661959351015034162,1.1609884922477153931 ] 
dist 168=[.25343837261294704884,1.1507618746746725086 ] 
dist 169=[.08323017771595436769,1.0197759865136944698 ] 
dist 170=[-.16844902150536262032,1.0560200827958165022 ] 
dist 171=[-.41935734454302970364,1.0843460199350382617 ] 
dist 172=[-.58648900096599735081,1.1092650885896717348 ] 
dist 173=[-.72431582383507265122,1.1300578253186226573 ] 
dist 174=[-.85825180444016443488,1.1419057330216389542 ] 
dist 175=[-.97949126119207738695,1.1494291258202664578 ] 
dist 176=[-1.0666392403170908538 ,1.1529463146059563822 ] 
dist 177=[-1.1455378367126555098 ,1.1530741218345310259 ] 
dist 178=[-1.2338500180153975559 ,1.1507792301044706347 ] 
dist 179=[-1.3136010697189302051 ,1.1394949967055881828 ] 
dist 180=[-1.3583270628906680405 ,1.1333980635671835526 ] 
dist 181=[-1.3859780233414914851 ,1.0887669288731969756 ] 
dist 182=[-1.3975714266586224477 ,1.0765140683127303712 ] 
dist 183=[-1.4024604811475696843 ,1.0570398226229756686 ] 
dist 184=[-1.4033502976393316759 ,1.0500543412268498828 ] 
dist 185=[-1.4014828866022796933 ,.86977410367457463246] 
dist 186=[-1.4251729226403025954 ,.84332119018851590221] 
dist 187=[-1.4453017804388972768 ,.78612401951793222144] 
dist 188=[-1.4497043801187071313 ,.76912152706089049439] 
dist 189=[-1.4438364554866702825 ,.69578096576520824631] 
dist 190=[-1.4411107190063255543 ,.68086482420974019908] 
dist 191=[-1.4383100638489181996 ,.64031548695650689785] 
dist 192=[-1.4346916703013507944 ,.68351852267448111934] 
dist 193=[-1.0708281147013855259 ,.74886384464746274945] 
dist 194=[-1.0385170077759672259 ,.83303803410947118425] 
dist 195=[-.95626991681200416669,.91459365475988938725] 
dist 196=[-.9418107357655227392 ,.96948703041027724037] 
dist 197=[-.80496104787070006482,1.0153825921533550305 ] 
dist 198=[-.77752669104528223461,1.0610229265051829607 ] 
dist 199=[-.74224122513122919566,1.1030282377282176026 ] 
dist 200=[-.7297761019937906773 ,1.1379662098500413718 ] 
dist 201=[-.46377541136347722497,1.1671304967974557636 ] 
dist 202=[-.42889063600972340393,1.1990585545485410698 ] 
dist 203=[-.59512313245350411102,1.2301566942454392202 ] 
dist 204=[-.73682335218849136966,1.2441752933929794043 ] 
dist 205=[-.85298444867269245527,1.2496434558573306783 ] 
dist 206=[-.96470331531002079258,1.2488623073994166750 ] 
dist 207=[-1.0650478333108264125 ,1.2285117506385209842 ] 
dist 208=[-1.1358080637984143435 ,1.2204432345607317280 ] 
dist 209=[-1.1984661972610539285 ,1.2065868740663190692 ] 
dist 210=[-1.2664708989349900040 ,1.2009640897477289515 ] 
dist 211=[-1.3265692848829683021 ,1.0368215230384622681 ] 
dist 212=[-1.3576692459313420562 ,1.0117954538286125118 ] 
dist 213=[-1.3745219983504566858 ,.95809180551792670269] 
dist 214=[-1.3777529977562757736 ,.98369538147132369257] 
dist 215=[-1.3666952309465747484 ,1.0342011823754472979 ] 
dist 216=[-1.3625846293977389658 ,1.0911851916505750857 ] 
dist 217=[-1.3589899525722120406 ,1.1425909643509589256 ] 
dist 218=[-1.3551571881994255127 ,1.1708302596739738717 ] 
dist 219=[.19104253564633322108,1.1875293205424022093 ] 
dist 220=[.10800258079452041756,1.1928691722384946425 ] 
dist 221=[.00775132810385448218,1.1930382587076189899 ] 
dist 222=[-.10018934443993216234,1.1897562452163828454 ] 
dist 223=[-.2048591591255963496 ,1.1823188208078685675 ] 
dist 224=[-.37400358794822818065,1.1777959832540838529 ] 
dist 225=[-.55632481869694862056,-.17360422133663049377] 
dist 226=[-.67766351650281224744,-.18312237807486723744] 
dist 227=[-.77761972360333661739,-.22760314734433334396] 
dist 228=[-.87458974728781037628,-.23078473450366637783] 
dist 229=[-.96227029001141942403,-.22154343681366100334] 
dist 230=[-1.0251466346683800516 ,-.19292074344806042121] 
dist 231=[-1.0819266795004789088 ,-.15400598883288261005] 
dist 232=[-1.1452741836115438326 ,-.10368233523928873925] 
dist 233=[-1.2020180130715165041 ,-.03533411208968427368] 
dist 234=[-1.2324388453350912958 ,.07552886179195324982] 
dist 235=[-1.2494219183466643828 ,.18927429200238904886] 
dist 236=[-1.2606467110192277160 ,.2691280437225571673 ] 
dist 237=[-1.2686390727722086160 ,.33948331564220589754] 
dist 238=[-1.2712729742984323698 ,.4153130161168543516 ] 
dist 239=[-1.2704872291775561853 ,.48889672330809505268] 
dist 240=[-1.2536095485234083898 ,.55028608184649166627] 
dist 241=[-1.0689815579381397124 ,.61452609390955769015] 
dist 242=[-1.0454733307401160448 ,.69948768021979806588] 
dist 243=[-.98412889479854263543,.78285746947766950575] 
dist 244=[-.97218299940614985845,.84074306806517214965] 
dist 245=[-.86304057562662509861,.89106639314725080712] 
dist 246=[-.84026363179169166563,.94424963592097648408] 
dist 247=[-.8098101636519950522 ,.99521978258776013323] 
dist 248=[-.7990814336184381856 ,1.0367084499607829828 ] 
dist 249=[-.56205274863246198266,1.1027220005309496934 ] 
dist 250=[-.53022916184360289302,1.1542925697093085425 ] 
dist 251=[-.46158602770761528514,1.1886202580916079242 ] 
dist 252=[-.44255334626959786976,1.2126374523073959987 ] 
dist 253=[-.36433086522617214102,1.2275557022578889090 ] 
dist 254=[-.34946128682188040367,1.2305550387332667816 ] 
dist 255=[-.31188675380257818752,1.2266922202606364292 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 1, 1, 0, 1, 2] 
dist 0=[45.271976984959011862  ,45.271976984959011862  ] 
dist 1=[44.556058285311217567  ,45.528417168927803411  ] 
dist 2=[43.419055896078881759  ,45.836644313845052321  ] 
dist 3=[41.494607123598232408  ,46.255811736171159134  ] 
dist 4=[39.497566573538759733  ,46.808147328312491374  ] 
dist 5=[38.070591749394309514  ,47.049154527209591372  ] 
dist 6=[36.784445042773556952  ,47.152754785747599076  ] 
dist 7=[35.349590137739683502  ,47.156280807274807256  ] 
dist 8=[33.923855408806565583  ,46.459475381070236280  ] 
dist 9=[32.673900868548873305  ,46.284498562343237819  ] 
dist 10=[31.309038487029450115  ,45.952767766156237156  ] 
dist 11=[29.423945776207357064  ,45.832567559659029430  ] 
dist 12=[27.526270355709579588  ,45.238959084428839434  ] 
dist 13=[26.110930395852630434  ,45.082934612713242255  ] 
dist 14=[24.772017921655573889  ,44.586224829415806239  ] 
dist 15=[23.179346187970474728  ,44.466302533954355487  ] 
dist 16=[21.536181688750425062  ,33.655828468722107742  ] 
dist 17=[19.961625554937864589  ,32.642125088052021179  ] 
dist 18=[17.474601825206172456  ,30.189940614691649924  ] 
dist 19=[15.103650757006065312  ,29.798389152419397228  ] 
dist 20=[13.129252116985209794  ,26.182970287309877301  ] 
dist 21=[11.218878463457534619  ,25.497923833059133217  ] 
dist 22=[8.6725470496538393525 ,24.627144113195787063  ] 
dist 23=[6.1840789190775456850 ,24.364336792308188352  ] 
dist 24=[4.4506005798760033078 ,18.456731864747971670  ] 
dist 25=[2.9311916027948506466 ,17.697705629027790940  ] 
dist 26=[1.2973416640326234550 ,16.106881998433182326  ] 
dist 27=[-.29532398881228814386,15.682507600491664580  ] 
dist 28=[-1.6508045111403329039 ,14.065922778142017140  ] 
dist 29=[-3.1008382797915443642 ,13.752061026708124032  ] 
dist 30=[-5.0724502653018376155 ,13.088309935823131377  ] 
dist 31=[-6.9739514847551693163 ,12.907921602021721065  ] 
dist 32=[-8.1440389321131300247 ,4.0151120672852038643 ] 
dist 33=[-9.0117211306481690493 ,3.2149270965709701616 ] 
dist 34=[-9.7043411649771407797 ,1.4803564579331964857 ] 
dist 35=[-10.252811695979637748  ,1.1321061606027526926 ] 
dist 36=[-10.544024154169276326  ,-.7486525880620725322 ] 
dist 37=[-10.705835437534016884  ,-.9274139469440995073 ] 
dist 38=[-10.736349876674356005  ,-1.2177107194478309580 ] 
dist 39=[-11.736127236853475686  ,-1.2840043278897834884 ] 
dist 40=[-12.678045981695509357  ,-1.4765175134669832254 ] 
dist 41=[-13.235131753351284719  ,-1.5089034123107345944 ] 
dist 42=[-13.619366614145427480  ,-1.4982521439762032939 ] 
dist 43=[-13.870813404096396350  ,-1.4279469860708839270 ] 
dist 44=[-14.039638031420062929  ,-1.3352952204379242758 ] 
dist 45=[-14.093765223942604894  ,-1.2352830575397377098 ] 
dist 46=[-14.086393920898937690  ,-1.1113961530143020339 ] 
dist 47=[-14.057867681088831132  ,-.38730577683751120284] 
dist 48=[-5.5096440347155438245 ,.62219634271825132654] 
dist 49=[-4.9741537029517351894 ,1.3146979135041880931 ] 
dist 50=[-4.9084108069504921239 ,1.9065056204812599268 ] 
dist 51=[-4.8913706165398885439 ,2.5144369214048311028 ] 
dist 52=[-1.7629106730618694570 ,3.0854413067050783220 ] 
dist 53=[-1.4521585540602480932 ,3.5300276552520383728 ] 
dist 54=[-1.0485467286776358439 ,3.9669542742240148775 ] 
dist 55=[-.96356176378762749622,4.5075522186202559425 ] 
dist 56=[.64352680508629902932,5.0206950205399926782 ] 
dist 57=[.750474009488474324  ,5.3502219473730814862 ] 
dist 58=[.95944136459207432857,5.7052983204835315659 ] 
dist 59=[1.0072640303136700432 ,5.9945676238065462073 ] 
dist 60=[1.0875356700956252035 ,6.1458622581321127192 ] 
dist 61=[.936249653123230643  ,6.2242868303429836150 ] 
dist 62=[.75150113850071856925,6.2393394534275963317 ] 
dist 63=[.47302523810470318504,3.9897729346998910122 ] 
dist 64=[.15574921592824812505,4.1958060202433438432 ] 
dist 65=[-.18389852044777777824,4.3228554965806126588 ] 
dist 66=[-.60497992384257933411,4.4176144965882850114 ] 
dist 67=[-1.2473198978010518702 ,4.4945428090136676792 ] 
dist 68=[-1.8908101492671476889 ,4.5553582976669162389 ] 
dist 69=[-2.3164958845189436937 ,4.5857174236243924321 ] 
dist 70=[-2.6642147389526304046 ,4.6002858485169660897 ] 
dist 71=[-2.9965170735611503287 ,4.5980366028281345193 ] 
dist 72=[-3.2935460200721377706 ,4.5871953933968340848 ] 
dist 73=[-3.5004784238763623131 ,4.5720192595247845968 ] 
dist 74=[-3.6810905077913398933 ,4.5402594962077449994 ] 
dist 75=[-3.8730671674445527495 ,4.5241785475279880740 ] 
dist 76=[-4.0417276700081561486 ,4.4284765279109454019 ] 
dist 77=[-4.1292699890952457957 ,4.4031927670905132636 ] 
dist 78=[-4.1755754158527818840 ,4.3130568935852222051 ] 
dist 79=[-4.1842484000600865943 ,4.2967010057992091526 ] 
dist 80=[-4.1556548713819971565 ,2.9155048016928421144 ] 
dist 81=[-4.6035367939451887933 ,2.8657743529727695839 ] 
dist 82=[-5.1082492909021717384 ,2.7774887688777967924 ] 
dist 83=[-5.5590226487592501567 ,2.7530776290573193542 ] 
dist 84=[-5.9411636882960468344 ,1.6008272103715200001 ] 
dist 85=[-6.1719117144568877947 ,1.4716635350385768768 ] 
dist 86=[-6.3362666266927896675 ,1.2175481393729121884 ] 
dist 87=[-6.4534009626907165474 ,1.1527720200038736033 ] 
dist 88=[-6.5393076994474311337 ,.92926664516438853447] 
dist 89=[-6.5789967653921817701 ,.87798685317142287785] 
dist 90=[-6.5926170366364563270 ,.82021045515406998712] 
dist 91=[-6.5806395265368130793 ,.80554544666030090944] 
dist 92=[-6.5372048366797386282 ,.80916867248175346953] 
dist 93=[-6.5126301183805309584 ,.84127556019626041631] 
dist 94=[-6.4138783159109663991 ,.90035194608296882058] 
dist 95=[-6.3811831175347609325 ,1.0116653503360673110 ] 
dist 96=[-3.8222972437830465076 ,1.1481184221339225215 ] 
dist 97=[-3.5929534306405871827 ,1.3075693381327320466 ] 
dist 98=[-3.0251918768005261108 ,1.5145503572802506117 ] 
dist 99=[-2.4823332346325265804 ,1.8407657219850691864 ] 
dist 100=[-1.5137955717523369539 ,2.1724508115373487714 ] 
dist 101=[-1.3463354203128024411 ,2.4012734593276058546 ] 
dist 102=[-1.1185445691427647390 ,2.5987890689020197600 ] 
dist 103=[-1.0520227893406737882 ,3.1211233357734975610 ] 
dist 104=[.20156188966044876797,3.6272009218853815262 ] 
dist 105=[.35512822915420803995,3.9409555198001698877 ] 
dist 106=[.70178746139247721183,4.1740273976629094234 ] 
dist 107=[.75680900336020130924,4.3580376671368056095 ] 
dist 108=[1.0631041147404705842 ,4.5027168179036950785 ] 
dist 109=[.90210303674555780057,4.5787919866095152214 ] 
dist 110=[.64793089776874804586,4.6191926776446411562 ] 
dist 111=[.39013961395616301518,4.6235840785981485181 ] 
dist 112=[.21469021135469458153,1.8292418481685044539 ] 
dist 113=[.06597538886959295136,1.9125137928736490887 ] 
dist 114=[-.08511822185295540468,1.9671360834805264091 ] 
dist 115=[-.22616647140278296435,1.9971656999487149705 ] 
dist 116=[-.33479098062930608472,2.0159323183429546217 ] 
dist 117=[-.44046884418978798079,2.0255768249955135676 ] 
dist 118=[-.56975926761959953073,2.0304525832425436045 ] 
dist 119=[-.69170907645467151186,2.0301548566161383031 ] 
dist 120=[-.7680898282183458806 ,1.7757318414291809524 ] 
dist 121=[-.82572155230049722267,1.7378262246226564456 ] 
dist 122=[-.87283972590835922213,1.6728936102797667749 ] 
dist 123=[-.91060294196030687217,1.6550835816774792131 ] 
dist 124=[-.93089449607246202781,1.5992598343086780327 ] 
dist 125=[-.94226785487539222002,1.5805818974395117742 ] 
dist 126=[-.94442954208223931268,1.5666970928300779376 ] 
dist 127=[-.54335700182413413228,1.5592562514153355891 ] 
dist 128=[-.54793372244951935251,.24474814716827750484] 
dist 129=[-.54923161446412662956,.13730202530899907849] 
dist 130=[-.54833513149675190505,-.10350375921204067887] 
dist 131=[-.53397242511822853475,-.14714326014715887447] 
dist 132=[-.60967879541785370061,-.36855187465237214242] 
dist 133=[-.7471404224948746125 ,-.34271538330729840385] 
dist 134=[-.88098781587215318794,-.30079315016882885244] 
dist 135=[-1.0449965508763407221 ,-.25617957239130532712] 
dist 136=[-1.1999564344557998260 ,-.21959543084817249095] 
dist 137=[-1.2976837677147091280 ,-.18190930714911680048] 
dist 138=[-1.3722548883371427284 ,-.13288570979402586072] 
dist 139=[-1.4347810553988203368 ,-.08032553926882986132] 
dist 140=[-1.4848228252363561197 ,-.02851625779734497482] 
dist 141=[-1.5095598711358605073 ,.03268521718337604198] 
dist 142=[-1.5213088197572974365 ,.12274331902485214198] 
dist 143=[-1.5225082499288699054 ,.21200586944543570277] 
dist 144=[-.3205140895988250152 ,.27003422021660936719] 
dist 145=[-.26325422527089936389,.31632903320193562469] 
dist 146=[-.18906363157024006174,.35875503369630880062] 
dist 147=[-.16484088158447614555,.39548193202411925066] 
dist 148=[-.15988865257881251831,.41902831081502131376] 
dist 149=[-.14897356075824903971,.43745039497928964002] 
dist 150=[-.14572270810788127605,.45372444889868380292] 
dist 151=[-.13214688181348861006,.46734797568666658609] 
dist 152=[-.12871022945526004178,.52985477891569130611] 
dist 153=[-.12671452596049322661,.60877057422165121732] 
dist 154=[-.1270010667837833868 ,.67620509679973291841] 
dist 155=[-.12853461843938518318,.74565899516901668853] 
dist 156=[-.1317384057181908033 ,.8111719928422689487 ] 
dist 157=[-.136737744811759265  ,.86822377948548509042] 
dist 158=[-.14543262287566875768,.92867418322060865397] 
dist 159=[-.2270884420970616317 ,1.0077044658980687695 ] 
dist 160=[-.34335973915208743885,1.0820740093760142859 ] 
dist 161=[-.42257279332170231167,1.1239220767502918306 ] 
dist 162=[-.48974190134980287394,1.1500520261742336771 ] 
dist 163=[-.55795499073466652232,1.1616680395945314279 ] 
dist 164=[-.62154826012517323502,1.1674203339133838242 ] 
dist 165=[-.67028325002918703183,1.1701357540323655322 ] 
dist 166=[-.71742810404167426957,1.1711796069748779488 ] 
dist 167=[-.77467658598498947898,1.1702464170995384481 ] 
dist 168=[-.82837654051419656436,1.0069150787492406648 ] 
dist 169=[-.86136154855386615618,.9829849548143503715 ] 
dist 170=[-.88546210480041683299,.9405886215067353587 ] 
dist 171=[-.90370967079256364913,.92952159115095986021] 
dist 172=[-.91677838084242909938,.89259931308834516351] 
dist 173=[-.92021313589711248437,.88099512618266851125] 
dist 174=[-.91942027317320209669,.87090903253307555384] 
dist 175=[-.9163230047082844513 ,.86549448571455522855] 
dist 176=[-.36898042595853040494,.16051325356885980457] 
dist 177=[-.37226895782099089668,.18558597782458931064] 
dist 178=[-.37269578205750308362,.21032768692942962569] 
dist 179=[-.37953783445763671015,.23291440193904118238] 
dist 180=[-.48001717219379757053,.24938797978534731263] 
dist 181=[-.55654450398939699998,.26450773562679624916] 
dist 182=[-.63021600833203737533,.28169042990240232565] 
dist 183=[-.71929943946760008149,.29716985989241254286] 
dist 184=[-.8028705775008344303 ,.30549283841236344004] 
dist 185=[-.85454079507885649109,.31014109194292146548] 
dist 186=[-.89276897570051655009,.3111668672299024013 ] 
dist 187=[-.92268615654831948545,.31039547829469423557] 
dist 188=[-.94509722632515625454,.30953843122015586122] 
dist 189=[-.95336187038205819176,.3082943404071973551 ] 
dist 190=[-.95610074649791304034,.30693077873485164874] 
dist 191=[-.95645459771469613125,-.1960713207315602912 ] 
dist 192=[-.92037113288803080563,-.06342832841606119264] 
dist 193=[-.91279038593210557067,.02866004894100430381] 
dist 194=[-.88842576296070076067,.10866946815759825286] 
dist 195=[-.88290201494778057391,.19310674009673555209] 
dist 196=[-.82233055542210189553,.27392806489045538608] 
dist 197=[-.80825593632464429917,.33950821078320507849] 
dist 198=[-.79188545888907151902,.40649172588888872137] 
dist 199=[-.78452810884193949648,.49291834521331852494] 
dist 200=[-.60258794383988483638,.5767019659687952741 ] 
dist 201=[-.58124968532979535534,.63313858212496340051] 
dist 202=[-.58977728131305462095,.68036807557378828158] 
dist 203=[-.62037170534270839163,.72740550386424368174] 
dist 204=[-.64640365069765026992,.77075025575604456311] 
dist 205=[-.67407630134124952303,.80324401844716975793] 
dist 206=[-.7112190999572567266 ,.83404142275965328181] 
dist 207=[-.74640027504234264299,.87062173990975418944] 
dist 208=[-.76624393499584014017,.90347525377656352005] 
dist 209=[-.77864938038179226657,.91939782775683564814] 
dist 210=[-.78414387617998298225,.92733622476650359939] 
dist 211=[-.7858697401294686772 ,.93123743727130560678] 
dist 212=[-.78459048376590415253,.94769737345934939915] 
dist 213=[-.77886148769337025683,.95487968985060403026] 
dist 214=[-.77497351970642768889,.95958535607190622055] 
dist 215=[-.7076205961527207935 ,1.0030879598530881232 ] 
dist 216=[-.6959351744545897121 ,1.0408625229798015508 ] 
dist 217=[-.66844881347267033113,1.0611157245014474937 ] 
dist 218=[-.65917740010337307543,1.0724102745294917200 ] 
dist 219=[-.61478138574505801544,1.0744288319985127170 ] 
dist 220=[-.60473559853699959472,1.0721147338588512622 ] 
dist 221=[-.58206169366055078313,1.0686607690582834953 ] 
dist 222=[-.57455120294168567643,1.0585429480778238152 ] 
dist 223=[-.2618797148155764248 ,1.0530188763630994936 ] 
dist 224=[-.22962926447953102272,.82145754051738599665] 
dist 225=[-.22241332196555419499,.80403497238600255876] 
dist 226=[-.31471071693599561275,.7559532725202573331 ] 
dist 227=[-.40720271788865599573,.74855118224709416279] 
dist 228=[-.49278187403096645043,.65610065525224476327] 
dist 229=[-.55748436008345062118,.63683971165113033292] 
dist 230=[-.61930788278324842855,.61780113524771204388] 
dist 231=[-.6933931497069730895 ,.61276391351025386037] 
dist 232=[-.76252009032543845195,.39149970105935197096] 
dist 233=[-.80455077039351599379,.36296646267840194554] 
dist 234=[-.83478741882969425711,.30593521674876344443] 
dist 235=[-.85683601408532728247,.29111324122747985446] 
dist 236=[-.87279542606692616354,.23822671545663273466] 
dist 237=[-.87872855054049372482,.22645967501974994545] 
dist 238=[-.87992092166491412901,.20956770494212414656] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 1, 1, 1, 0, 1] 
dist 0=[57.023644773401340424  ,57.023644773401340424  ] 
dist 1=[56.581484490942190755  ,57.235346980860123642  ] 
dist 2=[55.616113039288223262  ,57.280052215098815504  ] 
dist 3=[54.529315242238344264  ,57.219907963984304485  ] 
dist 4=[53.602178945725353146  ,56.893529917501688748  ] 
dist 5=[52.611348502104310144  ,56.570069152789863995  ] 
dist 6=[51.270273880991009274  ,56.402262000704301982  ] 
dist 7=[49.801667911210617245  ,56.316188546110978883  ] 
dist 8=[48.301511779909242931  ,55.536486789515305270  ] 
dist 9=[46.486449203647618926  ,50.641550669462737080  ] 
dist 10=[43.760091438287341630  ,49.859525185407231151  ] 
dist 11=[40.922619899432295814  ,48.476951851637641431  ] 
dist 12=[38.663756942556132895  ,48.130966739875435959  ] 
dist 13=[35.410226336362163901  ,47.049031108242528116  ] 
dist 14=[30.125936078537341341  ,46.725797472124768711  ] 
dist 15=[24.824636882318564753  ,46.568496742138404720  ] 
dist 16=[21.243831444651914760  ,45.752740620542174433  ] 
dist 17=[18.227987282082141387  ,35.831560924492427355  ] 
dist 18=[15.182979540030665996  ,35.635038491102527145  ] 
dist 19=[12.341601973482058798  ,17.640962659497836165  ] 
dist 20=[9.7359317281607629669 ,17.015279900171283764  ] 
dist 21=[6.8118661384211962494 ,11.380535956381481035  ] 
dist 22=[3.9222003013712905480 ,10.395983174961930507  ] 
dist 23=[1.2660573796122800768 ,9.1030588666189422455 ] 
dist 24=[-.72523035660453605027,8.8489035952142289008 ] 
dist 25=[-2.6164389867634584265 ,2.6789394586220397075 ] 
dist 26=[-4.8728166447347391587 ,2.3694188406382250230 ] 
dist 27=[-6.9841810582057338062 ,-.07112189572982751629] 
dist 28=[-8.2962479054007732380 ,-.33355900135708156882] 
dist 29=[-9.2779040338606977091 ,-1.8771048170675335136 ] 
dist 30=[-10.069777706358629447  ,-2.0517264569587795778 ] 
dist 31=[-10.699707109277886106  ,-2.3927747858444181692 ] 
dist 32=[-11.034458594657847735  ,-2.5606014499469872290 ] 
dist 33=[-11.218144847940891166  ,-5.3199844305453334480 ] 
dist 34=[-11.248473072285976067  ,-4.9790076447608621633 ] 
dist 35=[-7.8912439324130119530 ,-4.5709072777909356606 ] 
dist 36=[-7.9832275296988262637 ,-4.2313480876132771441 ] 
dist 37=[-8.0213649929962487428 ,-3.8811391461766345073 ] 
dist 38=[-8.0174412684478269616 ,-3.4295519819658150190 ] 
dist 39=[-7.3754116008443154107 ,-2.9509126259570048566 ] 
dist 40=[-7.2679780454703905358 ,-2.4922901144451596936 ] 
dist 41=[-7.0668956270499098072 ,-1.9621395683014798019 ] 
dist 42=[-7.0079295941464108259 ,-1.1976754505012345112 ] 
dist 43=[-6.7743553873913068337 ,-.42077917264060743239] 
dist 44=[-6.7092577925774467749 ,.15922596641375444763] 
dist 45=[-6.5796657632260580617 ,.7056275450820539948 ] 
dist 46=[-6.5366103664430788694 ,1.3487659868823326516 ] 
dist 47=[-5.7971821874629753646 ,2.0052446266719471298 ] 
dist 48=[-5.7491205497989467283 ,2.6051363332728680054 ] 
dist 49=[-4.2492972008029873854 ,3.2792967943208269758 ] 
dist 50=[-3.8377787399138028026 ,4.2325716767103316611 ] 
dist 51=[-.18158314182319045268,5.1633685970969018533 ] 
dist 52=[-.00780096954606592425,5.7478768644240040098 ] 
dist 53=[.29565914483157118107,6.1919785772487117417 ] 
dist 54=[.35954212462080099337,6.5621961071539670556 ] 
dist 55=[1.2684530905619721686 ,6.8580655148967509032 ] 
dist 56=[1.3907860737100733192 ,7.0053702363194012527 ] 
dist 57=[1.5979030250202108120 ,7.0815002867819753467 ] 
dist 58=[1.6406077780920625522 ,7.0928992419516782488 ] 
dist 59=[1.6497588539499265011 ,6.9982703178331527473 ] 
dist 60=[1.5062106153304480298 ,6.9582278697671025335 ] 
dist 61=[1.3162792912020041898 ,6.8811141773458616622 ] 
dist 62=[1.0139931468999758587 ,6.7963548611230536383 ] 
dist 63=[.6630307694302622664 ,6.0135885763961323798 ] 
dist 64=[.27874816643199613558,5.4823048740560847607 ] 
dist 65=[-.20341403527872304286,5.2522108051809856554 ] 
dist 66=[-.94511062690578545717,5.2332663411722484604 ] 
dist 67=[-1.6882323981463546207 ,2.1300263022394422207 ] 
dist 68=[-2.1761166212749067788 ,2.0159264703032233010 ] 
dist 69=[-2.5705028219507450600 ,1.0576489366774239515 ] 
dist 70=[-2.9404782116780236467 ,.88734671241759028572] 
dist 71=[-3.2665712162496492962 ,.6787045231377259314 ] 
dist 72=[-3.4858336748156762602 ,.7120860848187614568 ] 
dist 73=[-3.6689724481318898726 ,.7634464785196723933 ] 
dist 74=[-3.8509247041546884903 ,.8526010472956012463 ] 
dist 75=[-4.0080336593149737669 ,.95894629388884928741] 
dist 76=[-4.0920131159265714262 ,1.0788734580476008216 ] 
dist 77=[-4.1386540454143295550 ,1.2314160912298386993 ] 
dist 78=[-4.1715430241336619189 ,1.4678497033323815613 ] 
dist 79=[-4.2236447265667013621 ,1.7042639708839627296 ] 
dist 80=[-4.2325738009652005531 ,1.8567229297654385071 ] 
dist 81=[-4.2226365637438291359 ,1.9764769662647269243 ] 
dist 82=[-4.2090446209355617837 ,2.0824264702609302438 ] 
dist 83=[-3.0796878091307877131 ,2.1709716815821740236 ] 
dist 84=[-3.1327310111946953638 ,2.2212871129279909033 ] 
dist 85=[-3.1682191886927782585 ,2.2529856216527480575 ] 
dist 86=[-3.1745039134158974939 ,2.2672349568733865812 ] 
dist 87=[-3.1675901266841329046 ,2.2712449318487800443 ] 
dist 88=[-3.1592990943249348980 ,2.2669011650785732858 ] 
dist 89=[-3.0524098916039502491 ,2.2479030161495576294 ] 
dist 90=[-3.0291621382921269857 ,2.4823403355882024859 ] 
dist 91=[-2.9495215324915259653 ,2.7724309598162866547 ] 
dist 92=[-2.9374682432045502486 ,2.9499266800542033999 ] 
dist 93=[-2.7344691572145657718 ,3.0788606158204236042 ] 
dist 94=[-2.6887933019566477740 ,3.1751393924137466136 ] 
dist 95=[-2.6518372532663949788 ,3.2465000333176571839 ] 
dist 96=[-2.6425420240574230434 ,3.2759890542392891638 ] 
dist 97=[-1.1429475417885262196 ,3.2848391770520106250 ] 
dist 98=[-1.0846543270387766766 ,3.2799919002410290620 ] 
dist 99=[-.8147306688739389148 ,2.9590913029637003526 ] 
dist 100=[-.76497833939646912524,3.1574555486332290768 ] 
dist 101=[-.64658103102649462569,3.3241326533264508064 ] 
dist 102=[-.62499036698365578239,3.4222325396729473341 ] 
dist 103=[-.41395362412764193365,3.4891023212291963706 ] 
dist 104=[-.37560489082306671423,3.5311304737688110749 ] 
dist 105=[-.33143256588404189168,3.5567875281671920633 ] 
dist 106=[-.3226221311829752902 ,3.5582974201451241047 ] 
dist 107=[-.3283873514340511337 ,3.5566354569480446313 ] 
dist 108=[-.3561616863919715487 ,3.6002055736271550280 ] 
dist 109=[-.40542695949843777749,3.6298477411976300381 ] 
dist 110=[-.49699396809348388772,3.6344136451351370984 ] 
dist 111=[-.59550704489546176949,3.6256440328218888841 ] 
dist 112=[-.672501927795114056  ,3.6150052480309892834 ] 
dist 113=[-.7485711805939364626 ,2.4662469584107590917 ] 
dist 114=[-.84338180201188426786,2.4504635473172446942 ] 
dist 115=[-1.1690958739354059424 ,1.6852561387556196178 ] 
dist 116=[-1.5406311294555830347 ,1.6265086049046530662 ] 
dist 117=[-1.8769771704842037673 ,1.5701374482759573242 ] 
dist 118=[-2.1188618567755271811 ,1.5688381045483818902 ] 
dist 119=[-2.3379926814916775510 ,1.5467970528065026678 ] 
dist 120=[-2.5835153041807030683 ,1.5384920161833549853 ] 
dist 121=[-2.8090999292420119139 ,1.5154395799964027824 ] 
dist 122=[-2.9486416428442659348 ,1.5050263375306156628 ] 
dist 123=[-3.0519363215297389304 ,1.3552714367078491195 ] 
dist 124=[-3.1328229242957120902 ,1.3303169186395827058 ] 
dist 125=[-3.1931178168109070319 ,1.2684258817040768931 ] 
dist 126=[-3.2142073348054326054 ,1.2516647917176387370 ] 
dist 127=[-3.2188585972141707516 ,1.1465913300458580038 ] 
dist 128=[-3.2135540889473928329 ,1.1237059271558319978 ] 
dist 129=[-2.2717286964556130621 ,1.0812672370992748744 ] 
dist 130=[-2.2705409866222266600 ,1.0693108293715687575 ] 
dist 131=[-1.5898604068061651405 ,.53120858268149376708] 
dist 132=[-1.5715983096692433218 ,.47401239096277355612] 
dist 133=[-1.5479500066464295858 ,.34554279630788156387] 
dist 134=[-1.5374355562541295307 ,.31821617989434022528] 
dist 135=[-1.4872197579155971313 ,.16013197175919364349] 
dist 136=[-1.5308046995108532636 ,.13151995683460633561] 
dist 137=[-1.5606101045666742189 ,.07912353108367153277] 
dist 138=[-1.5794037423924184771 ,.18557508597208485582] 
dist 139=[-1.5897546217033139626 ,.2966975551737952174 ] 
dist 140=[-1.5909477364984194856 ,.38488117586078864091] 
dist 141=[-1.5788395608490880701 ,.47318141309071830914] 
dist 142=[-1.5766884035699933526 ,.584781665180895519  ] 
dist 143=[-1.4929682363663410972 ,.70290514896204694233] 
dist 144=[-1.4764016068705093706 ,.84347675028969339066] 
dist 145=[-1.4292055401982369110 ,1.0076524436373548703 ] 
dist 146=[-1.4172391143697995567 ,1.2346044115661599933 ] 
dist 147=[-1.3761156878096663216 ,1.4559072217283544474 ] 
dist 148=[-1.4853578266379953342 ,1.5975364091469463216 ] 
dist 149=[-1.5694327173700398500 ,1.7080162483324746158 ] 
dist 150=[-1.6410871650273303319 ,1.8049802673854576371 ] 
dist 151=[-1.6992108058097802533 ,1.8859292672844465141 ] 
dist 152=[-1.7292792337999892717 ,1.9324842553120868696 ] 
dist 153=[-1.7445053066027734993 ,1.9628185246114475552 ] 
dist 154=[-1.7467180792030941531 ,1.9790260497149651744 ] 
dist 155=[-1.7351718868992665103 ,1.9863358321085452631 ] 
dist 156=[-1.7280516394022369232 ,1.9843949853435538055 ] 
dist 157=[-1.7075000647204802458 ,1.9713077407398144674 ] 
dist 158=[-1.6971384963510336808 ,1.9616179985010127997 ] 
dist 159=[-1.6353824135005290075 ,1.8966031481638041708 ] 
dist 160=[-1.6188558248047920879 ,1.8780278123728699493 ] 
dist 161=[-1.5813524683447943302 ,1.8430792672767070048 ] 
dist 162=[-1.5675043884347111127 ,1.8310996176054519021 ] 
dist 163=[-1.1665592234532445926 ,.99527387354310995383] 
dist 164=[-1.2693301579864718860 ,.96160088721652493603] 
dist 165=[-1.3481451376259317181 ,.9100990874499057191 ] 
dist 166=[-1.4148963753657632399 ,.89512390365640811636] 
dist 167=[-1.4688005877100224362 ,.59183360735964685874] 
dist 168=[-1.4963382145868733479 ,.55154541634405706484] 
dist 169=[-1.5099459614987107746 ,.45927691673623701937] 
dist 170=[-1.5122295607010971666 ,.44011179586885876602] 
dist 171=[-1.4993448422275292889 ,.32029167722565396436] 
dist 172=[-1.4924415396962030208 ,.29816561701309877529] 
dist 173=[-1.4747033940353361071 ,.2558907859875302824 ] 
dist 174=[-1.4661233760472886189 ,.24541978019109254309] 
dist 175=[-1.4158716311179673473 ,-.11887291024590445856] 
dist 176=[-1.4026033953550850184 ,-.1574813427247058537 ] 
dist 177=[-1.3681198084683746044 ,-.225723791215372606  ] 
dist 178=[-1.3546199830727233356 ,-.04837539606686531510] 
dist 179=[-1.3776074064321658445 ,.26278310857202267533] 
dist 180=[-1.4442485447932550425 ,.46903137094757803633] 
dist 181=[-1.5013358113792805335 ,.63794355749557738878] 
dist 182=[-1.5603560660605014365 ,.80008262728034504708] 
dist 183=[-1.6106727759880157962 ,.94547137021523386342] 
dist 184=[-1.6330197728845985549 ,1.0475280913403885513 ] 
dist 185=[-1.6432509722320924047 ,1.1373978513299809335 ] 
dist 186=[-1.6452007400434165474 ,1.2341450866750884495 ] 
dist 187=[-1.6063797773413661244 ,1.3219244837700789646 ] 
dist 188=[-1.5957662684983097347 ,1.3760008020909010202 ] 
dist 189=[-1.5889007382336637454 ,1.4157494481466788146 ] 
dist 190=[-1.5853540684862513284 ,1.4463421825189353462 ] 
dist 191=[.07146259552704670604,1.4687093113558767021 ] 
dist 192=[.07293958073645752388,1.4756267192233468962 ] 
dist 193=[.06466694738346077777,1.4754194802155065897 ] 
dist 194=[.04093148465758272624,1.4712927189044718633 ] 
dist 195=[.01285940891863419404,1.3830524454075167110 ] 
dist 196=[-.01272239747332138591,1.4085473702015518233 ] 
dist 197=[-.04137834904131281276,1.4501511229650513838 ] 
dist 198=[-.08172211418657127567,1.5038539916961879695 ] 
dist 199=[-.12649624433073895731,1.5491121662318005832 ] 
dist 200=[-.17283636114793850526,1.5689336841922533620 ] 
dist 201=[-.22920726646677266358,1.5870674972601284078 ] 
dist 202=[-.31401911713683665164,1.6157228799786821778 ] 
dist 203=[-.40196101137398829037,1.6352533957938393515 ] 
dist 204=[-.47082573825456830115,1.6387611111243213962 ] 
dist 205=[-.53891826461574627083,1.6352673273453683204 ] 
dist 206=[-.62377883436437811039,1.6307345771007046742 ] 
dist 207=[-.71294695816827570377,1.1706188668949814300 ] 
dist 208=[-.79823340262858240889,1.1287575520546883828 ] 
dist 209=[-.89703352360819281516,1.0270622613082452564 ] 
dist 210=[-1.0401415012113505177 ,1.0063391895191896105 ] 
dist 211=[-1.1805296765150138958 ,.85119994439525446198] 
dist 212=[-1.2684740289168295623 ,.82044812808110721065] 
dist 213=[-1.3348622990279719702 ,.77029654022963381033] 
dist 214=[-1.3892103111778650153 ,.75684970071882595704] 
dist 215=[-1.4316713360437950279 ,.49342929562232467007] 
dist 216=[-1.4506132796895385939 ,.45835931777778477202] 
dist 217=[-1.4880904735254766107 ,.37554223471818240071] 
dist 218=[-1.5158945916998779024 ,.36068982168014985011] 
dist 219=[-1.5341801670965500334 ,.24610936882751620033] 
dist 220=[-1.5375044077795347288 ,.22493452274010701883] 
dist 221=[-1.5339283136678681940 ,.19123723192882160012] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 1, 1, 0, 1, 2] 
dist 0=[54.812619418084550353  ,54.812619418084550353  ] 
dist 1=[54.375217630550236117  ,54.924385330838917560  ] 
dist 2=[53.609351455693911806  ,54.924789712485644165  ] 
dist 3=[52.185456979452191407  ,54.917377864166376639  ] 
dist 4=[50.653799426267517972  ,54.908027469087636632  ] 
dist 5=[49.457497314038516607  ,54.900718436513827105  ] 
dist 6=[48.273876315374356194  ,54.893641758070053946  ] 
dist 7=[46.792936011215723476  ,54.780771079434374879  ] 
dist 8=[45.228474872716542784  ,50.633808493122398623  ] 
dist 9=[43.711254034526890015  ,50.020828909964185513  ] 
dist 10=[41.933204412214845180  ,48.967301125913093960  ] 
dist 11=[39.326872566278742245  ,48.687442441651905916  ] 
dist 12=[36.639392019269257854  ,47.826431665950900473  ] 
dist 13=[34.537179350757067142  ,47.541774022405546202  ] 
dist 14=[31.639379183949683525  ,47.370819032770035453  ] 
dist 15=[26.683488082166111807  ,47.203110887062509016  ] 
dist 16=[23.306200515906726727  ,32.687118120338476484  ] 
dist 17=[20.428995552258649396  ,32.310012359262973853  ] 
dist 18=[17.470386243540196664  ,31.821114112498024093  ] 
dist 19=[14.675145829350891432  ,31.645639920553760479  ] 
dist 20=[12.066555418114225444  ,15.803760173393408682  ] 
dist 21=[9.0070557636411614983 ,14.907644435401143928  ] 
dist 22=[6.4723497739902386769 ,13.603297420115992720  ] 
dist 23=[3.9796141733719592783 ,13.256807532315071400  ] 
dist 24=[1.6949493295477318735 ,7.4634267919357914748 ] 
dist 25=[-.00858925575790724820,6.7498956987336483444 ] 
dist 26=[-1.6182806263948672295 ,5.2186787226879029238 ] 
dist 27=[-3.5280885761205336929 ,4.9406750765170480248 ] 
dist 28=[-5.3145696810438280881 ,3.4156364867828938390 ] 
dist 29=[-6.4316717890208546271 ,3.1721311641552654109 ] 
dist 30=[-7.2762267227955414466 ,2.7541444750784942138 ] 
dist 31=[-8.1921933097219763544 ,2.6817882101790202024 ] 
dist 32=[-9.2099677983614711174 ,-4.9517321240013750593 ] 
dist 33=[-9.9662799688525060951 ,-5.1279290935256053354 ] 
dist 34=[-10.571621726455347668  ,-5.4047800787361293744 ] 
dist 35=[-11.050680402465340191  ,-5.4468109167533119618 ] 
dist 36=[-11.370003957092876157  ,-5.4331919294571477960 ] 
dist 37=[-11.644460094147582407  ,-5.3748592071362946418 ] 
dist 38=[-11.799844078618092016  ,-5.2761462035997069786 ] 
dist 39=[-11.835474448285549722  ,-5.1005174434943809173 ] 
dist 40=[-11.378926159480026521  ,-4.8918789308864693142 ] 
dist 41=[-11.279494161163247199  ,-4.6610336638314811150 ] 
dist 42=[-11.184270295164884900  ,-4.3710747595268559337 ] 
dist 43=[-11.120757705209422176  ,-3.9261986017450925004 ] 
dist 44=[-11.035117636146603962  ,-3.4631519402392440784 ] 
dist 45=[-10.995253877724607008  ,-3.1004647427932530077 ] 
dist 46=[-10.969457782600748788  ,-2.7421492656155170793 ] 
dist 47=[-10.956822257387805305  ,-2.2380782490036669246 ] 
dist 48=[-3.8588300295994096020 ,-1.6705025057173183463 ] 
dist 49=[-3.6007388521012500973 ,-.69263721449938275421] 
dist 50=[-3.4878528784121445530 ,.30742629695310485515] 
dist 51=[-3.4600781806719834688 ,1.2348310122950655240 ] 
dist 52=[-2.2611226638192540948 ,1.9408031325017821158 ] 
dist 53=[-2.1325022836410684464 ,2.6206275165457366080 ] 
dist 54=[-1.8260459563485885068 ,3.4436920561009006058 ] 
dist 55=[-1.7748699258949887495 ,4.2193639096989998216 ] 
dist 56=[-1.3348371473974544685 ,4.7099751121456404180 ] 
dist 57=[-1.2514227407519905476 ,5.0863416385520650604 ] 
dist 58=[-1.1384153765199023272 ,5.4058458906206424921 ] 
dist 59=[-1.1029551362938496966 ,5.6647050943945192774 ] 
dist 60=[-.40180096109894669773,5.7989065255804709464 ] 
dist 61=[-.31005676656076647696,5.8728265355531548086 ] 
dist 62=[-.11491422609287111178,5.8910695561762129168 ] 
dist 63=[-.06329578438838506974,5.5627372128806050573 ] 
dist 64=[.14757078197620154392,4.3488987217605617301 ] 
dist 65=[.18726801004465063411,4.3505157826181277843 ] 
dist 66=[.2810022423587608637 ,4.3367451727380387179 ] 
dist 67=[0                     ,4.3234668574278911421 ] 
dist 68=[2.0636724085496443222 ,3.3551616898719737846 ] 
dist 69=[1.8169154013881075099 ,3.2858121329431212344 ] 
dist 70=[1.4514684654901443645 ,3.2125774246357884349 ] 
dist 71=[1.0751569347121429103 ,3.1852279062803855193 ] 
dist 72=[.78498711720959240417,2.3561990961231733393 ] 
dist 73=[.50230925985371593151,2.2464374359612299952 ] 
dist 74=[.15582639144949173846,2.0229493253416630822 ] 
dist 75=[-.20543492298496919014,1.9632621799793704844 ] 
dist 76=[-.54715878739927997643,1.7404367154053055621 ] 
dist 77=[-.94037121880955154201,1.6925493577246633309 ] 
dist 78=[-1.5072450633820798946 ,1.6035663174819668199 ] 
dist 79=[-2.0649859406875528901 ,1.5808291499792142097 ] 
dist 80=[-2.4217573132434337342 ,1.3380203133077702814 ] 
dist 81=[-2.7000944345538077165 ,1.2698464581007884401 ] 
dist 82=[-2.9447083149589642402 ,1.2526993998951051645 ] 
dist 83=[-3.1493901691129708137 ,1.1977763068417459621 ] 
dist 84=[-3.2683187700420702215 ,1.1808451499525734011 ] 
dist 85=[-3.3474809896954253575 ,1.1677388807022581022 ] 
dist 86=[-3.3934336989596644698 ,1.1777205325950747742 ] 
dist 87=[-3.4233318920930839259 ,1.2202540834914081739 ] 
dist 88=[-3.4383971319104014554 ,1.2596274515397224233 ] 
dist 89=[-3.4456697581685313672 ,1.2887213874342188662 ] 
dist 90=[-3.4444200275902710494 ,1.3156039701460258083 ] 
dist 91=[-3.4379398563483929205 ,1.3461721318001437141 ] 
dist 92=[-3.4253265787686200421 ,1.3733920364225211031 ] 
dist 93=[-3.4029343619231118602 ,1.3869360089860203806 ] 
dist 94=[-3.3911104191716375815 ,1.3929179921276028417 ] 
dist 95=[-3.2255597448451799153 ,1.3903905326271751075 ] 
dist 96=[-2.8072298340582340171 ,1.3815574695073455575 ] 
dist 97=[-2.7909116475078836196 ,1.3756582319391726896 ] 
dist 98=[-2.7775980428651804467 ,1.3288729817894841603 ] 
dist 99=[-2.7648348836533499182 ,1.4377019233038029252 ] 
dist 100=[-.65390619460554321796,1.6512229696391525465 ] 
dist 101=[-.48651637968335778177,1.8068388184312846810 ] 
dist 102=[-.10005104606024690089,1.9499051390421364212 ] 
dist 103=[-.03730557173369666587,2.1133538095601446009 ] 
dist 104=[.45442027668928179749,2.2619122336296701106 ] 
dist 105=[.53944318189453933549,2.3455530332264355835 ] 
dist 106=[.67270491102615507852,2.3977487460590628992 ] 
dist 107=[.70418216514870015835,2.4208014933764422392 ] 
dist 108=[1.1037564197698842691 ,2.4314275614812540581 ] 
dist 109=[.88826555811085960603,2.4458417871192256763 ] 
dist 110=[.61096002109047017075,2.4527603840500632205 ] 
dist 111=[.17685262140964553335,2.4513273200731353630 ] 
dist 112=[-.261921679821792191  ,2.1039367082873607154 ] 
dist 113=[-.55785439129403145413,2.0597192922430049829 ] 
dist 114=[-.80577131413540802536,1.9656879219719141826 ] 
dist 115=[-1.0529131101782621869 ,1.9248132545987615770 ] 
dist 116=[-1.2805820600383509307 ,1.7043055090108646469 ] 
dist 117=[-1.4507816249530337409 ,1.6592385764276694381 ] 
dist 118=[-1.6114470357139339515 ,1.6023751692540336073 ] 
dist 119=[-1.8010631221641353755 ,1.5810032521541461433 ] 
dist 120=[-1.9763479809362665371 ,1.1028424963628377978 ] 
dist 121=[-2.0798156960852665877 ,1.0391194253876232922 ] 
dist 122=[-2.1504588413502811330 ,.90335955974193745343] 
dist 123=[-2.1947377398301381104 ,.86589477984982917184] 
dist 124=[-2.2248845625381176707 ,.717178891748136917  ] 
dist 125=[-2.2391261210783969711 ,.68822775305251717302] 
dist 126=[-2.2444284881189131557 ,.62049616996539439506] 
dist 127=[-2.2399749856763185561 ,.60588406026921830242] 
dist 128=[-2.1406415484082354158 ,-.24119361993728774144] 
dist 129=[-2.2868538741982007161 ,-.31870585885280794489] 
dist 130=[-2.4068619338717424758 ,-.47671501996306501692] 
dist 131=[-2.5021375076700120560 ,-.51554572428530686948] 
dist 132=[-2.5496164417272503170 ,-.64448725286734088561] 
dist 133=[-2.5736695303684795794 ,-.67029671169983506273] 
dist 134=[-2.5763983742709051380 ,-.68480193443635768492] 
dist 135=[-2.5031379088567904162 ,-.66740806502861675087] 
dist 136=[-2.4831744341841309506 ,-.63661956038515087787] 
dist 137=[-2.4547218831218242456 ,-.59256675429127636115] 
dist 138=[-2.4416829547681202855 ,-.53038105815146911808] 
dist 139=[-2.3958915772190626308 ,-.4272098318646559838 ] 
dist 140=[-2.3790737449464005948 ,-.30558864305393089166] 
dist 141=[-2.3409745380300269377 ,-.1697583987661571501 ] 
dist 142=[-2.3255246192058700886 ,.00251363193516464119] 
dist 143=[-2.0039522356796573776 ,.26959138143097585176] 
dist 144=[-1.7168072836420047250 ,.538788426244572972  ] 
dist 145=[-1.7278582288421343760 ,.71952174112808062357] 
dist 146=[-1.7301423121404497160 ,.87009178637377909469] 
dist 147=[-1.7278006309583941581 ,1.0188992268469239597 ] 
dist 148=[-1.6777081594831822120 ,1.1552206432733971644 ] 
dist 149=[-1.6619924345117718776 ,1.2559570849305820427 ] 
dist 150=[-1.6480777840866071532 ,1.3499502167402619604 ] 
dist 151=[-1.6380696873637208936 ,1.5166982349670458525 ] 
dist 152=[-1.3483325583664846052 ,1.6277459146991305041 ] 
dist 153=[-1.3066681303431679650 ,1.7095189332011431508 ] 
dist 154=[-1.2246384169172719072 ,1.7727589934732528612 ] 
dist 155=[-1.2020437630691341885 ,1.8208944735329116428 ] 
dist 156=[-1.1156478513173555439 ,1.8423761955154603517 ] 
dist 157=[-1.0951146453322806137 ,1.8508199426325401661 ] 
dist 158=[-1.0545159876279300622 ,1.8493611663808144871 ] 
dist 159=[-1.0423683139995161494 ,1.7945581987465831646 ] 
dist 160=[-.05418007319177812988,1.5784663231567374214 ] 
dist 161=[.03179564849468048090,1.5495998903378627533 ] 
dist 162=[.2186202346175726862 ,1.4721038704048163100 ] 
dist 163=[.24071630228686223617,1.4566632944615969028 ] 
dist 164=[.16013528070966075913,1.3107618341197290057 ] 
dist 165=[.06547586402953120435,1.2796618925359161117 ] 
dist 166=[-.07315119112725360978,1.2392204739623580416 ] 
dist 167=[-.21534787086863096464,1.2242397152987433261 ] 
dist 168=[-.32426151779225541398,1.1549908286879958508 ] 
dist 169=[-.42968445858313943295,1.2293025730839295023 ] 
dist 170=[-.5579578145939566995 ,1.2925979931987076924 ] 
dist 171=[-.6911785954089677213 ,1.3598650899285573594 ] 
dist 172=[-.8163574667810656128 ,1.4261090527559965558 ] 
dist 173=[-.95970069350057095342,1.4718457435999049379 ] 
dist 174=[-1.1654391776099933587 ,1.5123490471022847181 ] 
dist 175=[-1.3667682671610602447 ,1.5701291440628226605 ] 
dist 176=[-1.4925133617189295223 ,1.6226037284664856579 ] 
dist 177=[-1.5870627973186841803 ,1.6480790587743148752 ] 
dist 178=[-1.6638655589639124847 ,1.6601121763872186297 ] 
dist 179=[-1.7243474936254517412 ,1.6608018614491375639 ] 
dist 180=[-1.7537454009029337283 ,1.6390993855344041275 ] 
dist 181=[-1.7680684828432557636 ,1.6289336994246132818 ] 
dist 182=[-1.7689627881765399189 ,1.6172490473147469541 ] 
dist 183=[-1.7249193547153985364 ,1.6096902266856464689 ] 
dist 184=[-1.7135463837583956977 ,1.3751773149366359316 ] 
dist 185=[-1.7292168706030453353 ,1.3399594336405833168 ] 
dist 186=[-1.7497976786262313570 ,1.3063365378273062542 ] 
dist 187=[-1.7543709545906827905 ,1.2530784103755912854 ] 
dist 188=[-1.7380308991875108199 ,1.2382029730647565352 ] 
dist 189=[-1.7346284658047628575 ,1.2238073348124490322 ] 
dist 190=[-1.7292928569639670606 ,1.2149238151506728479 ] 
dist 191=[-1.7242825086627092657 ,1.0835797852504289212 ] 
dist 192=[-.53686213672868390645,.74219190531192948378] 
dist 193=[-.34624462897309005353,.88259966769793610705] 
dist 194=[-.30820647317767858098,.99859705916400530274] 
dist 195=[-.07811462829093610177,1.1116351133592072062 ] 
dist 196=[-.03773502376187577835,1.2141417862372158586 ] 
dist 197=[.04205943000781883458,1.2881049613002222456 ] 
dist 198=[.06144361117893743404,1.3553401178439389727 ] 
dist 199=[.2412058541990854917 ,1.4309938019331410753 ] 
dist 200=[.26895814782926896689,1.4990732947646521383 ] 
dist 201=[.30046224748774753958,1.5360773003990334275 ] 
dist 202=[.30129396237771455346,1.5574142542724971626 ] 
dist 203=[.28946714637706360693,1.5629604664550169649 ] 
dist 204=[.25940785183639960686,1.5617482658886238039 ] 
dist 205=[.21025164763106669693,1.5680438285939909931 ] 
dist 206=[.12220593156687702248,1.5681425574743158771 ] 
dist 207=[-.14285010861993525741,1.5409081551145024040 ] 
dist 208=[-.45832835468920980796,1.5575889319591437138 ] 
dist 209=[-.66813004848689017345,1.6005880261532897758 ] 
dist 210=[-.84073569275086127768,1.6289246030133527321 ] 
dist 211=[-1.0077482057630255942 ,1.6472950376519018094 ] 
dist 212=[-1.1584125738934737783 ,1.6505112720924335860 ] 
dist 213=[-1.2657652221911610154 ,1.6474369215806434238 ] 
dist 214=[-1.3619662132287044526 ,1.6412824471747842806 ] 
dist 215=[-1.4681182982931073473 ,1.5316893007479503137 ] 
dist 216=[-1.5640464415390608918 ,1.5110318113074730850 ] 
dist 217=[-1.6194393944986705209 ,1.4636517717713557195 ] 
dist 218=[-1.6557500738578997452 ,1.4473019620991602334 ] 
dist 219=[-1.6755142138162828421 ,1.3677190879383069036 ] 
dist 220=[-1.6862885001613540427 ,1.3494565103148776522 ] 
dist 221=[-1.6867170267006006037 ,1.3032860709026273905 ] 
dist 222=[-1.6811309076126525578 ,1.2883443011609199791 ] 
dist 223=[-1.6758739689464936916 ,.45475771504431243038] 
dist 224=[-1.5451000103278046040 ,.00991879024217952122] 
dist 225=[-1.6029308644504469044 ,-.03620459692410806774] 
dist 226=[-1.6449021443115745196 ,-.12253616856701565328] 
dist 227=[-1.6751273141919284739 ,-.14219099395183981298] 
dist 228=[-1.6860714333077640679 ,-.19536072967551401738] 
dist 229=[-1.6880376953340957917 ,-.20044519192511377309] 
dist 230=[-1.6842640370722708043 ,-.18931263886770095115] 
dist 231=[-1.7081321367366683864 ,-.1531352378948796992 ] 
dist 232=[-1.7385840899728801398 ,-.10771730514666506808] 
dist 233=[-1.7655596014070810992 ,-.05970151541125034996] 
dist 234=[-1.7894789706352247156 ,-.00057492541500621161] 
dist 235=[-1.8034211194659895796 ,.08919154875539109211] 
dist 236=[-1.8041282029978699789 ,.19181125462117740716] 
dist 237=[-1.7976643457328183530 ,.30224101491455392379] 
dist 238=[-1.7902739516060120735 ,.43957182324203496911] 
dist 239=[-1.3493779455641663741 ,.64956578160388389425] 
dist 240=[-1.2656441279881863594 ,.86014420736440822169] 
dist 241=[-1.1434708595034352624 ,.99980793737694424401] 
dist 242=[-1.1207663923317741490 ,1.1142993237039204127 ] 
dist 243=[-.93004393861134490003,1.2244036787873579657 ] 
dist 244=[-.8924689869217361725 ,1.3232857541555314850 ] 
dist 245=[-.83801561930699030638,1.3929839664243380718 ] 
dist 246=[-.82146060602530902981,1.4546665880557564070 ] 
dist 247=[-.48698195605288767909,1.5215547422449716143 ] 
dist 248=[-.44316568473958250271,1.5803690577955186332 ] 
dist 249=[-.34442235996179381321,1.6098253173973923746 ] 
dist 250=[-.32337912251186323586,1.6279244800791852320 ] 
dist 251=[-.20093844974840419052,1.6478159987396311484 ] 
dist 252=[-.17872884196009174424,1.6520121994897372597 ] 
dist 253=[-.13389084690038903503,1.6495803176851635108 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 1, 1, 1, 0, 2] 
dist 0=[40.240104866126697850  ,40.240104866126697850  ] 
dist 1=[39.790480888491659503  ,40.650551531299119966  ] 
dist 2=[38.405434103026412351  ,41.268670797588495184  ] 
dist 3=[36.963794762493513669  ,41.731554130475868402  ] 
dist 4=[35.921844040404893316  ,42.079267667328642046  ] 
dist 5=[34.970619744771651293  ,42.237511030917264295  ] 
dist 6=[33.891059010714500465  ,42.293362935525943138  ] 
dist 7=[32.807604601264223224  ,42.286318600886057705  ] 
dist 8=[31.840594418313718018  ,41.303794671366800664  ] 
dist 9=[30.770122712180264156  ,41.111818646478722168  ] 
dist 10=[29.273025029480170288  ,40.783579126505035573  ] 
dist 11=[27.756845460904008972  ,40.678342463341735456  ] 
dist 12=[26.609939733688418578  ,40.255699611836420184  ] 
dist 13=[25.508718632130997133  ,40.124506527770713459  ] 
dist 14=[24.174761045256458277  ,39.828927611026634622  ] 
dist 15=[22.784823889751631907  ,39.716469058401218923  ] 
dist 16=[21.459604706738353734  ,29.716476907809647642  ] 
dist 17=[19.920364528159597128  ,28.822526995978646561  ] 
dist 18=[17.674627332795605648  ,26.655374999970103815  ] 
dist 19=[15.438223563045750659  ,26.325135795469024660  ] 
dist 20=[13.936210287500147004  ,23.126211175670371561  ] 
dist 21=[12.675685119002411995  ,22.523054780950496546  ] 
dist 22=[11.404633589355707706  ,21.800133942966664741  ] 
dist 23=[10.214916810349980912  ,21.619302830086468758  ] 
dist 24=[9.2795106614600741215 ,16.490395672853727996  ] 
dist 25=[8.1645412327841495815 ,16.241149710044873365  ] 
dist 26=[6.6653048365533798456 ,15.242506647957206360  ] 
dist 27=[4.9595572943640487614 ,13.911379430000429692  ] 
dist 28=[3.2412397531260398625 ,12.607529698285066089  ] 
dist 29=[1.6913499348143381332 ,12.340419437983057005  ] 
dist 30=[-.04083450456018915818,11.864074140923593063  ] 
dist 31=[-2.4883511759053664162 ,11.754470698105795735  ] 
dist 32=[-4.8828222299084026992 ,4.2175882270995201006 ] 
dist 33=[-6.4031847416919144248 ,3.9748892368669635630 ] 
dist 34=[-7.5839161435369227922 ,3.9229073894406950530 ] 
dist 35=[-8.6209120240446729975 ,.85649314863585990473] 
dist 36=[-9.4951443803709448319 ,.58820073561179626107] 
dist 37=[-10.025471704475202034  ,-.01783906939673425397] 
dist 38=[-10.410386240946508007  ,-.11720968501332018538] 
dist 39=[-10.703851158218578908  ,-.86676341529067365696] 
dist 40=[-10.932757921999447083  ,-.99846858785758126206] 
dist 41=[-11.059606153325939964  ,-1.2010982039808802242 ] 
dist 42=[-11.139023564108624550  ,-1.2511323702199728648 ] 
dist 43=[-11.177818805793189399  ,-2.0677463039790105405 ] 
dist 44=[-11.189840118684654847  ,-2.1699628362656468723 ] 
dist 45=[-11.164160634170347017  ,-2.4022508666746313079 ] 
dist 46=[-11.106761651469895102  ,-2.4376420174445901841 ] 
dist 47=[-11.069755059900851194  ,-2.7219005765954078769 ] 
dist 48=[-5.8584525442255061778 ,-2.7426730859516316330 ] 
dist 49=[-5.4103081572678731866 ,-2.6197982564141153076 ] 
dist 50=[-4.3259364037158338156 ,-1.9654257748979619834 ] 
dist 51=[-4.1692337641592482505 ,-1.0371829325289044896 ] 
dist 52=[-2.6175020581326684787 ,-.16907177283164701951] 
dist 53=[-2.3361285237291262126 ,.50298634767387436014] 
dist 54=[-1.9975553406243353301 ,1.1606981079576132501 ] 
dist 55=[-1.9371541495964672476 ,1.9717176244493988399 ] 
dist 56=[-1.5990840984013601538 ,2.7416648345187703639 ] 
dist 57=[-1.5038543379786059222 ,3.2354976609777792204 ] 
dist 58=[-1.4767897069322315430 ,3.6225082330542801168 ] 
dist 59=[-1.2313789104447228354 ,3.9660877532484509596 ] 
dist 60=[-1.1915581516512918140 ,4.2567449239523244473 ] 
dist 61=[-1.1101810201946367226 ,4.4325823833983586642 ] 
dist 62=[-1.0879816386078201249 ,4.5590523780861233501 ] 
dist 63=[-1.0016358305522644495 ,4.6528467619842159161 ] 
dist 64=[-.98350188039391192733,4.7179659242923654249 ] 
dist 65=[-.94203865749887397869,4.7325972470854155218 ] 
dist 66=[-.92957863701287520081,4.7247583430688262216 ] 
dist 67=[-.86882761871744326023,4.7207897067999343268 ] 
dist 68=[-.85370874948402471955,4.5466714030601667932 ] 
dist 69=[-.83584655206744387919,4.4990620448720278158 ] 
dist 70=[-.82804076388754978751,4.4679873803992969727 ] 
dist 71=[-.81784170104922000032,4.4523432315418826486 ] 
dist 72=[-.81457157523140463571,3.8476846428609274620 ] 
dist 73=[-.81371035089100809677,3.8163681904111341640 ] 
dist 74=[-.81565012759719197189,3.7541076327491891143 ] 
dist 75=[-.81862506538488616861,3.7324981000101227182 ] 
dist 76=[-.82191568457333429584,3.6286654412765869377 ] 
dist 77=[-.82595867156971089387,3.6028527416940669743 ] 
dist 78=[-1.1858967076142520565 ,3.5229873372855004776 ] 
dist 79=[-1.8004930835374869829 ,3.5047753333998304500 ] 
dist 80=[-2.4094649673895746027 ,2.5056292025042904669 ] 
dist 81=[-2.8023667140084221464 ,2.4921655482354261420 ] 
dist 82=[-3.1125420519407100961 ,2.4827490091677959122 ] 
dist 83=[-3.3912880739540902110 ,1.3314519964474747645 ] 
dist 84=[-3.6288284992193838980 ,.81312264424614893007] 
dist 85=[-3.7745274242376274675 ,.71728034461332754376] 
dist 86=[-3.8810630258265667147 ,.59629716173231005717] 
dist 87=[-3.9622942677924243995 ,.56539616896460882862] 
dist 88=[-4.0234058363789234294 ,-.20979213041680416862] 
dist 89=[-4.0496227073603336892 ,-.30504725501048264341] 
dist 90=[-4.0554424617524235612 ,-.32203432141041156421] 
dist 91=[-4.0497348135635614005 ,-.13039332417225471445] 
dist 92=[-4.0785065386356197648 ,.02532350873831937117] 
dist 93=[-4.0817002674328693156 ,.18455111694967558463] 
dist 94=[-4.0697864746786332515 ,.39021177186509016264] 
dist 95=[-4.0575397859048043996 ,.61000894053416822324] 
dist 96=[-2.2588072045972204833 ,.82566422979525091759] 
dist 97=[-2.1014391901766269764 ,1.0796273925586150479 ] 
dist 98=[-1.9401612996891813388 ,1.4523292556424243612 ] 
dist 99=[-1.9231840718990197225 ,1.8198918577199323402 ] 
dist 100=[-1.8443364566673022449 ,2.0533429183586488900 ] 
dist 101=[-1.8265167989448051548 ,2.2332926444141210916 ] 
dist 102=[-1.7718199549828093281 ,2.3873095989057932257 ] 
dist 103=[-1.7621913666953394247 ,2.5129754457551038764 ] 
dist 104=[-1.6343378961792077547 ,2.5989570813208043135 ] 
dist 105=[-1.6094600942467025402 ,2.7723638000676597129 ] 
dist 106=[-1.5075719369411942058 ,2.9012221190012563462 ] 
dist 107=[-1.1135397979805380013 ,3.0030021656330887228 ] 
dist 108=[-1.1032913096319500237 ,3.0801920406685770701 ] 
dist 109=[-1.0949151598193496802 ,3.1109004660951384301 ] 
dist 110=[-1.0882024497879171743 ,3.1224167596391667469 ] 
dist 111=[-1.0809574287148320124 ,3.1229992653009511993 ] 
dist 112=[-1.0772379655979658927 ,2.5733889156799582616 ] 
dist 113=[-1.0748649509981209551 ,2.5622411319058059824 ] 
dist 114=[-1.0738505302107889662 ,2.5516423614394338706 ] 
dist 115=[.69995199028938724857,2.3029099746098789431 ] 
dist 116=[.67495655536570559222,2.3708921566818147000 ] 
dist 117=[.63221621067486615865,2.4000437183718721822 ] 
dist 118=[.56834701185649248774,2.4127233685472986581 ] 
dist 119=[.4590095097219577892 ,2.4149269853749400127 ] 
dist 120=[.3403537014637090449 ,2.3517223734260162280 ] 
dist 121=[.2392832419672292633 ,2.3344397926897019451 ] 
dist 122=[.1317459918219970546 ,2.2957702131985171579 ] 
dist 123=[-.0127371602542436935 ,2.2804529850361579687 ] 
dist 124=[-.16995119438326742584,2.2585165775655911180 ] 
dist 125=[-.32831332493819863928,2.2625851305659680410 ] 
dist 126=[-.51790882315685687964,2.2603638488671774058 ] 
dist 127=[-.79980395348587298686,2.2311631667631163393 ] 
dist 128=[-1.0795297975986141799 ,2.2201003912951529626 ] 
dist 129=[-1.2604705922788615954 ,2.1830386437456517406 ] 
dist 130=[-1.4037821449639957454 ,2.1687706143947773301 ] 
dist 131=[-1.5333096100773581634 ,1.4023949510317248892 ] 
dist 132=[-1.6441527194175974690 ,1.4050890307164302313 ] 
dist 133=[-1.7128873264776876292 ,1.4038260707974578566 ] 
dist 134=[-1.7639991300031572484 ,1.3891750723496428947 ] 
dist 135=[-1.8045070524117539145 ,1.3856115143349317314 ] 
dist 136=[-1.9073497379919971338 ,1.3142782617037483874 ] 
dist 137=[-1.9942641457583960179 ,1.3001637675534574216 ] 
dist 138=[-2.0591810668533672066 ,1.2564105364052883005 ] 
dist 139=[-2.1110968214220331937 ,1.2485198738357477897 ] 
dist 140=[-2.1507239656464651622 ,1.1465401480312484287 ] 
dist 141=[-2.1665931021931096226 ,1.1236750401696768502 ] 
dist 142=[-2.1701318103668147723 ,1.1009553285278184582 ] 
dist 143=[-2.1669117440850324013 ,1.0918897557660996192 ] 
dist 144=[-1.7199275841624025023 ,.72928641784653540899] 
dist 145=[-1.7253679464186265555 ,.6854693818453738532 ] 
dist 146=[-1.7226175837564191637 ,.5861189894619317387 ] 
dist 147=[-1.3985764673508961912 ,.56302691622665669065] 
dist 148=[-1.3637806743684975245 ,.43431645659388855986] 
dist 149=[-1.2783676206563537044 ,.40982937953142293587] 
dist 150=[-1.2584694061390102795 ,.35949998509187066148] 
dist 151=[-1.1216837445248799913 ,.37646998268884194606] 
dist 152=[-1.0933570950862541754 ,.48171342098065805223] 
dist 153=[-1.0433360948435577664 ,.56267264582045634586] 
dist 154=[-1.0304954194045401980 ,.64138381260931480458] 
dist 155=[-.9674440152638269262 ,.73766296265576143373] 
dist 156=[-1.0177273869385886094 ,.83794755273368651478] 
dist 157=[-1.0629616979978749897 ,.95485430652096674742] 
dist 158=[-1.1131279742685589755 ,1.0976095591892655162 ] 
dist 159=[-1.1626032785869792842 ,1.2925593531900649670 ] 
dist 160=[-1.2293182117675172065 ,1.4817036880873672066 ] 
dist 161=[-1.3536328069122654462 ,1.6012875440252962234 ] 
dist 162=[-1.4512674135701148640 ,1.6929020573468143072 ] 
dist 163=[-1.5379902672317268855 ,1.7703992139878673830 ] 
dist 164=[-1.6110244128536922614 ,1.8329735288619254722 ] 
dist 165=[-1.6540212845992189100 ,1.8650214789263226808 ] 
dist 166=[-1.6832165076066295895 ,1.8808932248667550488 ] 
dist 167=[-1.7011581098861541831 ,1.8832739624724251322 ] 
dist 168=[-1.7114622393058752728 ,1.8692358388717481089 ] 
dist 169=[-1.7108974128613859455 ,1.8615049701345282676 ] 
dist 170=[-1.7036677679619372845 ,1.8384729775380293142 ] 
dist 171=[-1.6967022316953173016 ,1.8270371280025129513 ] 
dist 172=[-1.6473348395379321822 ,1.7593379646207959303 ] 
dist 173=[-1.6328048244797570026 ,1.7413350938902531534 ] 
dist 174=[-1.6022237204442481819 ,1.7334527144688797584 ] 
dist 175=[-1.5908117123301253737 ,1.7052803053718123789 ] 
dist 176=[-1.2383637089899420263 ,1.6948007071693898902 ] 
dist 177=[-1.3473482643275811676 ,1.6792432794344406506 ] 
dist 178=[-1.4314605943672214278 ,1.6710260447517202398 ] 
dist 179=[-1.5036568481117713352 ,1.1310898686091386644 ] 
dist 180=[-1.5626943527534723826 ,1.0748167635567940715 ] 
dist 181=[-1.5942839451283170955 ,.94151281615490937039] 
dist 182=[-1.6118298543476516804 ,.91515435057603286809] 
dist 183=[-1.6148131674694922462 ,.72584119789147685096] 
dist 184=[-1.6109286313854231152 ,.68969119697623596358] 
dist 185=[-1.6056414403309395605 ,.62790180084818364593] 
dist 186=[-1.5890410498880919868 ,.61284180444932483825] 
dist 187=[-1.5800161971691800362 ,.34049560058123452867] 
dist 188=[-1.5247057087077830480 ,.30445234845386955811] 
dist 189=[-1.5096780455407212948 ,.21947127047756291367] 
dist 190=[-1.4763038636204323282 ,.20562681005713279746] 
dist 191=[-1.4640394530422941257 ,.09033163250193080822] 
dist 192=[-1.4678972730456048406 ,.32662445927498883667] 
dist 193=[-1.4752771034375344173 ,.54880457373475541582] 
dist 194=[-1.4741397804183638602 ,.72991398880718172022] 
dist 195=[-1.1009207186604979582 ,.90237122839283232716] 
dist 196=[-1.2208236708743480516 ,1.0561023115820303864 ] 
dist 197=[-1.3161426977770927842 ,1.1624675450008914427 ] 
dist 198=[-1.4028892301391261376 ,1.2545258564977445745 ] 
dist 199=[-1.4775314142161368941 ,1.3511516863057055357 ] 
dist 200=[-1.5245353978191206367 ,1.4384177422323788604 ] 
dist 201=[-1.5603211463562051363 ,1.4931172653058047050 ] 
dist 202=[-1.5901865111476608139 ,1.5344452364886700582 ] 
dist 203=[-1.6122764844161142920 ,1.5683401393416208419 ] 
dist 204=[-1.6170256701513330244 ,1.5948689828880010333 ] 
dist 205=[-1.6153487024287113909 ,1.6067961780862868363 ] 
dist 206=[-1.6117847061327392387 ,1.6103135076326774161 ] 
dist 207=[-1.5573695717301843334 ,1.6083271615026024441 ] 
dist 208=[-1.5413487804762243513 ,.81424805405454958561] 
dist 209=[-1.5252501242014878203 ,.85817531420014738276] 
dist 210=[-1.5154271024310865609 ,1.0294174160798840341 ] 
dist 211=[-.08976441937180805339,1.1963336446227625832 ] 
dist 212=[-.12924714216479832091,1.3024452077278364921 ] 
dist 213=[-.17244670498239948823,1.3843634539879376028 ] 
dist 214=[-.22665248135924092814,1.4547128072659327485 ] 
dist 215=[-.31006706599174828123,1.5122631950739013808 ] 
dist 216=[-.3973243211012599735 ,1.5430950636970637523 ] 
dist 217=[-.46686866482169098371,1.5630941478478708677 ] 
dist 218=[-.53677450115226307193,1.5939957495513445833 ] 
dist 219=[-.62547571098622001244,1.6170558933415242514 ] 
dist 220=[-.71950166564526007219,1.6232938662734597133 ] 
dist 221=[-.81066194459654755828,1.6223901459572724731 ] 
dist 222=[-.91721265338701020163,1.6407503227153319492 ] 
dist 223=[-1.0726705868527648892 ,1.6643631477208061790 ] 
dist 224=[-1.2256684760773336563 ,1.6733914875457845689 ] 
dist 225=[-1.3224001377140867464 ,1.6736823008931731741 ] 
dist 226=[-1.3964667044685309239 ,1.6712661918954050402 ] 
dist 227=[-1.4589964388288098497 ,1.0678145150306537620 ] 
dist 228=[-1.5093441152164798842 ,1.0163481246061814065 ] 
dist 229=[-1.5347858883590922729 ,.89518199011493393277] 
dist 230=[-1.5468900692117032048 ,.8701661930762183382 ] 
dist 231=[-1.5487087473014055726 ,.69961787703143475223] 
dist 232=[-1.5345692637661839258 ,.6668907754945214374 ] 
dist 233=[-1.5276681921192217503 ,.60833957353416669548] 
dist 234=[-1.5076328009327903668 ,.59427671193782233712] 
dist 235=[-1.4978901842558896140 ,.35232461669057403556] 
dist 236=[-1.4872629163341511908 ,.31957426262773778799] 
dist 237=[-1.5293814117400195959 ,.24335956183934074169] 
dist 238=[-1.5617200614130743680 ,.22961971989991969494] 
dist 239=[-1.5853017734029804618 ,.12844600373227279289] 
dist 240=[-1.5924658973156764950 ,.11012084129122342559] 
dist 241=[-1.5921970811833865885 ,.07944162906851302749] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 2, 1, 0, 1] 
dist 0=[45.963716802080345253  ,45.963716802080345253  ] 
dist 1=[45.837261000453809003  ,46.030044411412556252  ] 
dist 2=[45.439629029928441594  ,46.187497655846088803  ] 
dist 3=[44.775612503198849064  ,46.391318188180767080  ] 
dist 4=[43.585398304167952497  ,46.642575339152485630  ] 
dist 5=[42.144895240364359329  ,46.976280424120117103  ] 
dist 6=[40.481264130880724811  ,47.508939340825310629  ] 
dist 7=[38.331721563470356673  ,48.030978507861500032  ] 
dist 8=[34.950607437172768438  ,48.322295300887611468  ] 
dist 9=[31.516133107879876882  ,48.499757984128633728  ] 
dist 10=[29.153377604694288373  ,48.567603883259009629  ] 
dist 11=[27.117591120843871698  ,48.559477117114103086  ] 
dist 12=[24.988635682175796776  ,48.516359097143981332  ] 
dist 13=[22.955549155904749873  ,48.170907784869983873  ] 
dist 14=[21.302351019320621717  ,47.335757195000863233  ] 
dist 15=[19.605360712247452905  ,38.863641622895048530  ] 
dist 16=[17.396833852166742969  ,37.989506456451889768  ] 
dist 17=[15.233451770402729323  ,35.807542439573938003  ] 
dist 18=[13.716483755403457034  ,35.475206887482370705  ] 
dist 19=[12.375962508717809421  ,32.015506910987473551  ] 
dist 20=[10.916990500522095991  ,31.341293840173303908  ] 
dist 21=[9.4837941289034454939 ,30.585956054231966462  ] 
dist 22=[8.2457005259223458625 ,30.395573544886772092  ] 
dist 23=[6.9051182377419766701 ,23.814453879947036700  ] 
dist 24=[5.0613478064983150927 ,22.969355452098946416  ] 
dist 25=[3.2634741241738928618 ,21.278166441954565291  ] 
dist 26=[2.1061254245295680643 ,20.839729267270522827  ] 
dist 27=[-.02886681807759753549,19.268731741290238025  ] 
dist 28=[-1.6143486621721828074 ,18.926619823273186309  ] 
dist 29=[-2.8739276640256368835 ,18.388229988925856584  ] 
dist 30=[-4.0291629478280249314 ,18.242635352458438654  ] 
dist 31=[-5.0380562976417693659 ,5.2198191528154652330 ] 
dist 32=[-5.7128155114639934398 ,4.1249222312634392500 ] 
dist 33=[-6.2771887908152285506 ,1.6567758537350750703 ] 
dist 34=[-6.8451874215417057374 ,1.2404783701821164701 ] 
dist 35=[-7.3495804497666237592 ,-1.4862724693352669495 ] 
dist 36=[-7.6596899927663905703 ,-1.3429882933983444542 ] 
dist 37=[-8.3696663977503550711 ,-1.1350074099869763477 ] 
dist 38=[-9.8076841958947382212 ,-.8567463687814615871 ] 
dist 39=[-11.140741054897280778  ,-.4759509562500362912 ] 
dist 40=[-11.950127157904922831  ,.14127321332450311554] 
dist 41=[-12.533886975006865577  ,.76861195049487901295] 
dist 42=[-12.965675767098291131  ,1.1898852320336564707 ] 
dist 43=[-13.295108347354356366  ,1.5390656028947398100 ] 
dist 44=[-13.469938344942575817  ,1.8789845176715541146 ] 
dist 45=[-13.565798251450531302  ,2.1850333515852678893 ] 
dist 46=[-13.579584088614002925  ,2.3991213846069665632 ] 
dist 47=[-7.3117856111384864902 ,2.5856295015363290895 ] 
dist 48=[-6.9447635748417767426 ,2.7815582617408364452 ] 
dist 49=[-6.0493473521073528293 ,2.9576949416583130916 ] 
dist 50=[-5.9111780899997593552 ,3.0653096363407643891 ] 
dist 51=[-4.5923658733352071867 ,3.1425002478392972884 ] 
dist 52=[-4.3473244642734437198 ,3.1975544534130328526 ] 
dist 53=[-4.0377867284144906549 ,3.2339075533024317699 ] 
dist 54=[-3.9577336826633871623 ,3.2366746375067644312 ] 
dist 55=[-1.9561862667662716739 ,3.2246203973126258957 ] 
dist 56=[-1.7099779583094963326 ,3.2086702600588018917 ] 
dist 57=[-1.1789328967909836639 ,3.0571412738655900222 ] 
dist 58=[-1.0655028997779589826 ,3.6521375860740909211 ] 
dist 59=[-.50456812662469203195,4.2274950397105374004 ] 
dist 60=[-.40902848476592801104,4.5878444988336974294 ] 
dist 61=[-.2083900806606511418 ,4.8608040968895799450 ] 
dist 62=[-.38738792463443850378,5.0871311720960652591 ] 
dist 63=[-.5961692042261020139 ,5.2671452704783645372 ] 
dist 64=[-.85676079347745511375,5.3551496027531720010 ] 
dist 65=[-1.1050658606288980600 ,5.3999296419619328271 ] 
dist 66=[-1.2648363732152008588 ,5.4072148289519412774 ] 
dist 67=[-1.3903791996549676809 ,5.3342921422287748935 ] 
dist 68=[-1.5021112497286945492 ,5.3064704806312552370 ] 
dist 69=[-1.5965701261802929688 ,5.2539660367602049279 ] 
dist 70=[-1.6532035953207794805 ,5.2322202238011097566 ] 
dist 71=[-1.6931600939536806797 ,5.1157354942592488485 ] 
dist 72=[-1.7211142800715532805 ,5.1502879414005181763 ] 
dist 73=[-1.7402124921755573015 ,5.1978092530938161447 ] 
dist 74=[-1.7448281171243596928 ,5.2060659774536904080 ] 
dist 75=[-1.7417223428226151515 ,5.1895123914440184215 ] 
dist 76=[-1.7369700888860294462 ,5.1722497945073159595 ] 
dist 77=[-1.6979247303355009706 ,5.1384915437595872942 ] 
dist 78=[-1.6859313789892455589 ,5.1214288379293480352 ] 
dist 79=[-1.9668570978597408772 ,2.2203848609378621695 ] 
dist 80=[-2.4764551703403404913 ,2.1152561155695391813 ] 
dist 81=[-2.8950194239305734862 ,1.9874671817014128411 ] 
dist 82=[-3.2993511861624390891 ,1.9513340711298543684 ] 
dist 83=[-3.6641324355279637649 ,1.0012046441972958663 ] 
dist 84=[-3.9248322995411355308 ,.88078036927658591862] 
dist 85=[-4.1596000008562826251 ,1.0146770467032922592 ] 
dist 86=[-4.4209049340875342649 ,1.1604306644396878125 ] 
dist 87=[-4.6552926664493229660 ,1.3237582802360336333 ] 
dist 88=[-4.7826210074372901726 ,1.5538845784826151445 ] 
dist 89=[-4.8562752446433145344 ,1.7773046783207406109 ] 
dist 90=[-4.8763931735164729655 ,1.9138705027675541585 ] 
dist 91=[-4.8979570149705052575 ,2.0130581556222782655 ] 
dist 92=[-4.9296181475484427119 ,2.0872770971563444129 ] 
dist 93=[-4.9372493439682945764 ,2.1440176761619578045 ] 
dist 94=[-4.9387493692319656123 ,2.1734326177141085473 ] 
dist 95=[-4.7559698598927729888 ,2.1884932480238754192 ] 
dist 96=[-4.7191157989085418765 ,2.1883938831610964869 ] 
dist 97=[-4.5907377225028527483 ,2.0857492564411219569 ] 
dist 98=[-4.5715319998203070871 ,2.4713351288484101972 ] 
dist 99=[-4.2372460371658731380 ,2.9539494383147664928 ] 
dist 100=[-4.1616139463860331971 ,3.3166108746943752940 ] 
dist 101=[-4.1018982835517722439 ,3.6609937777953148851 ] 
dist 102=[-4.0870385085387058054 ,4.0706382987924140986 ] 
dist 103=[-3.0491175555747452124 ,4.4513482826417482844 ] 
dist 104=[-2.9129755472592720838 ,4.6802293050956808630 ] 
dist 105=[-2.6507019048902793293 ,4.8417647046445391249 ] 
dist 106=[-2.5833900340145505123 ,4.9536472484152149135 ] 
dist 107=[-2.3523163542734708588 ,5.0333514002152792241 ] 
dist 108=[-2.2952873579135560012 ,5.0664441768376943267 ] 
dist 109=[-2.2348549121422467851 ,5.0720915551844800128 ] 
dist 110=[-2.2158904440998701078 ,5.0668562307887654646 ] 
dist 111=[-.95873910375526416972,.89702942351734955933] 
dist 112=[-1.1383998236894731899 ,.99988930148013511348] 
dist 113=[-1.3070914755393656862 ,1.0912250283979438610 ] 
dist 114=[-1.4114706439398493947 ,1.1908568317747428135 ] 
dist 115=[-1.4887350512762737049 ,1.2817217013547126045 ] 
dist 116=[-1.5491940935555402971 ,1.3380585214775128053 ] 
dist 117=[-1.5960950176890326685 ,1.3799622942093887375 ] 
dist 118=[-1.6192464296611460836 ,1.4132023730988307148 ] 
dist 119=[-1.6295105367420190177 ,1.4383799326399324575 ] 
dist 120=[-1.6305830360842125236 ,1.4480938333358635820 ] 
dist 121=[-1.4207528066875868629 ,1.4501195665721196109 ] 
dist 122=[-1.4232107925475520515 ,1.4476539752243825253 ] 
dist 123=[-1.4169239780334142799 ,.99203533667118811581] 
dist 124=[-1.4143373591050503405 ,.95040749188603199805] 
dist 125=[-1.3563496840429282117 ,.85074733043493715461] 
dist 126=[-1.3405334588983801370 ,.83115656081076491119] 
dist 127=[-1.3280100296268135906 ,.68560752994777706372] 
dist 128=[-1.3204305401525547854 ,.65747179807267483575] 
dist 129=[-1.0559980787935450274 ,.61116392300951545515] 
dist 130=[-1.0192078608650879330 ,.59921349559130937156] 
dist 131=[-.94751903081591920653,.62717207557972888702] 
dist 132=[-.92830900539078068921,.71110918559680642916] 
dist 133=[-.85781977157449571544,.7934441819771492374 ] 
dist 134=[-.84073897404053763141,.86354423713216186074] 
dist 135=[-.81174069545451179088,.93814385784646135664] 
dist 136=[-.80360304872142749096,1.0384459474987622009 ] 
dist 137=[-.47250147676676953852,1.1342003769245922703 ] 
dist 138=[-.63212857233432526   ,1.1906486633910789836 ] 
dist 139=[-.78883692650162180664,1.2291505973615322106 ] 
dist 140=[-.89091936915924372278,1.2532670109319810751 ] 
dist 141=[-.97261479565206518312,1.2695656070063937931 ] 
dist 142=[-1.0479390155547447890 ,1.2768603142179044242 ] 
dist 143=[-1.1134779521309512818 ,1.2789676194892761029 ] 
dist 144=[-1.1561118115589972420 ,1.2765752681595393723 ] 
dist 145=[-1.1901740202530754804 ,1.2086258107410543296 ] 
dist 146=[-1.2214978868971398912 ,1.2694198321769274114 ] 
dist 147=[-1.2466131129681284986 ,1.3129916012933592142 ] 
dist 148=[-1.2558907949067476434 ,1.3444715944617737367 ] 
dist 149=[-1.2584011756883109538 ,1.3667983678744630426 ] 
dist 150=[-1.2564967829123498466 ,1.3738348553024223820 ] 
dist 151=[-1.2245800094094352079 ,1.3743472465400733101 ] 
dist 152=[-1.2140615835917476508 ,1.3706304003668580757 ] 
dist 153=[-1.2034296157405368962 ,.9545643517621884511 ] 
dist 154=[-1.1966254587364441022 ,.94643481766270621605] 
dist 155=[-1.1288180007137113639 ,.20135186732414397658] 
dist 156=[-1.1285712766701915432 ,.36711872583948554209] 
dist 157=[-1.1075008111602919797 ,.50469970475419101644] 
dist 158=[-1.0995374376347049996 ,.63986250882205518437] 
dist 159=[-1.0924854446011295138 ,.76319021853603292707] 
dist 160=[-1.0865529912303212041 ,.85352996739650572522] 
dist 161=[-.99589832043566374257,.93704522247291516241] 
dist 162=[-1.0488147766132093366 ,1.0331325300924769497 ] 
dist 163=[-1.0886061228157117416 ,1.1211806824943713612 ] 
dist 164=[-1.1209200810565321901 ,1.1726066485097985712 ] 
dist 165=[-1.1459873849333918260 ,1.2070757387411847469 ] 
dist 166=[-1.1733307898420742118 ,1.2274380002781986511 ] 
dist 167=[-1.1980728716207950712 ,1.2406081294975776360 ] 
dist 168=[-1.2211430544768131980 ,1.2463684574117143926 ] 
dist 169=[-1.2389280702064692901 ,1.2478076032022347545 ] 
dist 170=[-1.2429077837443194916 ,1.2450415875110295189 ] 
dist 171=[-1.2414022360772150418 ,1.0440736985612448216 ] 
dist 172=[-1.2399444003168914802 ,1.0194254841566562796 ] 
dist 173=[-1.1934369237467042168 ,.95674936060782825542] 
dist 174=[-1.1802626647315130857 ,.94359440045325121369] 
dist 175=[-1.1710611385288466252 ,.91414838984919071617] 
dist 176=[-1.1653344201716776951 ,1.0062326945857308298 ] 
dist 177=[-.9333816775434422067 ,1.0914992368275179736 ] 
dist 178=[-.90113135667617399061,1.1421433926279024801 ] 
dist 179=[-.83902192704165345557,1.1771209115963610499 ] 
dist 180=[-.82249877217584083002,1.1998555517330686827 ] 
dist 181=[-.76282549159678488256,1.2151230445185735651 ] 
dist 182=[-.8177097460335757564 ,1.2202974126320530106 ] 
dist 183=[-.89173827505263767546,1.2195785759477456880 ] 
dist 184=[-.95174060327061034836,1.2172665589702118570 ] 
dist 185=[-1.0129890385308616631 ,1.1579268024297469234 ] 
dist 186=[-1.0919934501828984742 ,1.1902629311087831196 ] 
dist 187=[-1.1663012122422784857 ,1.2099210443455762968 ] 
dist 188=[-1.2088026974490048627 ,1.2174324160336876174 ] 
dist 189=[-1.2361660343505838980 ,1.2193577447202716791 ] 
dist 190=[-1.2500470261350362889 ,1.2167179274170012130 ] 
dist 191=[-1.2574664114421047216 ,1.2105969505991950914 ] 
dist 192=[-1.2590364958303029738 ,1.2066041988208331472 ] 
dist 193=[-1.2566253390400532069 ,1.0759199955096939745 ] 
dist 194=[-1.2532920344717572819 ,1.0549089827026194025 ] 
dist 195=[-1.2399980474253363333 ,1.0108561977259571242 ] 
dist 196=[-1.2629870334729151176 ,.99729759333737592266] 
dist 197=[-1.2747979208722984712 ,.93728055281193022868] 
dist 198=[-1.2776409416415074931 ,.92428453077449837519] 
dist 199=[-1.2556360931563536767 ,.88633347579775591989] 
dist 200=[-1.2499370361233842818 ,.87965634805819917488] 
dist 201=[-1.2465215124524549247 ,.28562274754678187759] 
dist 202=[-1.2453289675221018016 ,.22982811194099831877] 
dist 203=[-1.0154901149044789062 ,.21186304483680679887] 
dist 204=[-.9862707212341707049 ,.36460348756274095794] 
dist 205=[-.91197873939756291107,.49129683187332754803] 
dist 206=[-.8982202823507946172 ,.61563635888245964663] 
dist 207=[-.77388054121515999033,.72900350502180601834] 
dist 208=[-.74868984861375244719,.81189922794709874326] 
dist 209=[-.71475303980878010347,.88838364866305419979] 
dist 210=[-.70323635670844278985,.9761595082564691861 ] 
dist 211=[-.46539070795252689859,1.0565097681745422495 ] 
dist 212=[-.43698799544215636824,1.1033537691820032956 ] 
dist 213=[-.37361806739093592027,1.1346416514097320404 ] 
dist 214=[-.35841221799728444776,1.1528968705680347572 ] 
dist 215=[-.28015241113025630689,1.1665509528020049589 ] 
dist 216=[-.2655041226573815542 ,1.1737291282779489117 ] 
dist 217=[-.23340569018987881425,1.1775388293550636336 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 0, 0, 2] 
dist 0=[39.003294896451232552  ,39.003294896451232552  ] 
dist 1=[38.485698516547181523  ,39.549110130796014236  ] 
dist 2=[37.866576137505293596  ,40.281692647623298656  ] 
dist 3=[37.225753430818915116  ,40.966906655593091779  ] 
dist 4=[36.621892570736147389  ,41.323615379484263839  ] 
dist 5=[35.291759804422397323  ,41.511834640689547290  ] 
dist 6=[33.801886085183591351  ,41.539905632129094634  ] 
dist 7=[31.948619395966019288  ,41.461129271940277240  ] 
dist 8=[29.103760500263351426  ,41.389655713297669417  ] 
dist 9=[26.110884867419988242  ,41.216356330435577039  ] 
dist 10=[23.666304890554183634  ,41.128046618715588048  ] 
dist 11=[21.144830895437612958  ,39.208939577989735540  ] 
dist 12=[17.844822266069334106  ,38.899174895274226738  ] 
dist 13=[14.279952003440170154  ,38.195677672011805961  ] 
dist 14=[10.700222569760560480  ,37.969315524034481180  ] 
dist 15=[6.4087501179467666433 ,36.923632995894807131  ] 
dist 16=[0                     ,36.694053561160293538  ] 
dist 17=[23.194865708279334805  ,36.142844549613180559  ] 
dist 18=[18.970036730780142752  ,35.963741067339533588  ] 
dist 19=[14.728641115394878818  ,28.399635417579923341  ] 
dist 20=[11.876915690883428742  ,27.625525193093158595  ] 
dist 21=[9.4877221442756192566 ,26.037258821383393259  ] 
dist 22=[7.0938988291161070532 ,25.622299166015251066  ] 
dist 23=[4.8703589377661737996 ,24.103626040596226632  ] 
dist 24=[3.1612643052683455577 ,23.793063584587936138  ] 
dist 25=[1.4953215443972663333 ,22.934175820014620791  ] 
dist 26=[-.55612313003520628936,21.882066497046993148  ] 
dist 27=[-2.5115268569411281062 ,13.377072235595376701  ] 
dist 28=[-3.7939684857567789197 ,12.479162387695193539  ] 
dist 29=[-4.8347474608699591098 ,10.069484513284585212  ] 
dist 30=[-5.8249514511627212118 ,7.2134366100547439461 ] 
dist 31=[-7.0453395818503748921 ,-2.0203980482295192469 ] 
dist 32=[-9.3500658624002797782 ,-1.9765941912569197922 ] 
dist 33=[-11.162527235448618735  ,-1.7494331078333294530 ] 
dist 34=[-12.788228604150758461  ,-1.2187937552068380053 ] 
dist 35=[-14.178721462614416790  ,-.6315808318285198669 ] 
dist 36=[-15.051693674471357389  ,-.1784795122756291085 ] 
dist 37=[-15.718020685257985925  ,.2592175740538166495 ] 
dist 38=[-16.283448126359922250  ,.7857417591636602554 ] 
dist 39=[-16.744342238624986127  ,1.3253073468287850185 ] 
dist 40=[-16.993053125525788298  ,1.8153637752862112259 ] 
dist 41=[-17.137391866676070291  ,2.3609151124105806475 ] 
dist 42=[-17.180817019128183876  ,3.1221023954383901374 ] 
dist 43=[-17.158681191279809350  ,3.8829980193471048943 ] 
dist 44=[-17.118200323364251442  ,4.4275261296690254802 ] 
dist 45=[-16.908932853121696766  ,4.9163999562114543603 ] 
dist 46=[-16.829751540165540050  ,5.4554593945409040055 ] 
dist 47=[-9.4322714148827569564 ,5.9841444293312595402 ] 
dist 48=[-8.7535885992577695302 ,6.4317213398888837047 ] 
dist 49=[-7.3285053229859446901 ,6.9048309610259678913 ] 
dist 50=[-7.2582854634209944999 ,7.5354587307713921188 ] 
dist 51=[-4.5534682754681164683 ,8.1431613225809265661 ] 
dist 52=[-4.1302878343459011180 ,8.5248249437000803833 ] 
dist 53=[-3.5476663619867426675 ,8.8134517105407308297 ] 
dist 54=[-3.3753269696226097397 ,9.0499483023272033737 ] 
dist 55=[-.2228101259289392970 ,9.2343466727568408506 ] 
dist 56=[.16472637563583958321,9.3150902913322802447 ] 
dist 57=[1.0432893013128596994 ,9.3351205585723747092 ] 
dist 58=[1.1806217998723050355 ,9.3225978764542000214 ] 
dist 59=[2.2254973612094678983 ,9.1810447545794300287 ] 
dist 60=[2.3964047086931835240 ,9.1291725529356924833 ] 
dist 61=[2.6767621864451804349 ,8.9262381643119570108 ] 
dist 62=[2.7343306515258350985 ,8.5578905022174764080 ] 
dist 63=[3.9249674151230906140 ,6.1189612680863020446 ] 
dist 64=[4.0489137953249082229 ,6.1606105372074275019 ] 
dist 65=[4.2529554910032670605 ,6.1686826879141560587 ] 
dist 66=[3.5919692692952952482 ,6.1567880009656193287 ] 
dist 67=[2.9051045705230102850 ,4.5895983933517741856 ] 
dist 68=[2.4134571882647404437 ,4.6345466498901031947 ] 
dist 69=[1.9710541773546988732 ,4.6517166187259859426 ] 
dist 70=[1.4806113604144255014 ,4.6476518567386237164 ] 
dist 71=[.9970735565801320447 ,4.5509251077893209258 ] 
dist 72=[.5821618016358569871 ,4.5234935090176048416 ] 
dist 73=[.1380782695706133993 ,4.4463371199694343556 ] 
dist 74=[-.46196975753247038158,4.4135782368316439884 ] 
dist 75=[-1.0565533338580755853 ,4.2330859080558736866 ] 
dist 76=[-1.4788694873238429612 ,4.1875070992078310441 ] 
dist 77=[-1.8560715922742200206 ,4.0972130296356740519 ] 
dist 78=[-2.2706419353183089508 ,4.0677137605819389204 ] 
dist 79=[-2.6779534044258375378 ,2.6330080538390044532 ] 
dist 80=[-3.0262367525748307891 ,2.4814756113157047880 ] 
dist 81=[-3.3984398844008113707 ,2.1277911281355864838 ] 
dist 82=[-3.9013310685948116255 ,2.0590144320349333559 ] 
dist 83=[-4.3839546285346233190 ,1.5759406766489772463 ] 
dist 84=[-4.6752612429407571206 ,1.4852537298156440450 ] 
dist 85=[-4.8827136632711941316 ,1.3276920747901916744 ] 
dist 86=[-5.0305346386526633995 ,1.2907643431161950837 ] 
dist 87=[-5.1411516229449842324 ,.6461103252877465078 ] 
dist 88=[-5.2000518763063149257 ,.5603463754530611327 ] 
dist 89=[-5.2325115512509490601 ,.3605710660946675407 ] 
dist 90=[-5.2375345031756556432 ,.3264730480544280447 ] 
dist 91=[-4.7775337546134677028 ,.0609777517900562488 ] 
dist 92=[-4.7466644319742472969 ,.0130804971504614075 ] 
dist 93=[-4.7404522128098991222 ,-.0613238124960698083 ] 
dist 94=[-4.7255099334427446420 ,-.0801570523297951457 ] 
dist 95=[-4.6965208518104374502 ,-.3964946218168025227 ] 
dist 96=[-4.6758380918033991216 ,-.4398625236559966617 ] 
dist 97=[-4.6275468957600755992 ,-.5057841753620741008 ] 
dist 98=[-4.6048094159902137808 ,-.5222837243047756393 ] 
dist 99=[-2.1992103697648042665 ,-.5324649777161597965 ] 
dist 100=[-1.9894453993809340432 ,-.3906617016917915614 ] 
dist 101=[-1.4828840389236218709 ,.0775231771438091995 ] 
dist 102=[-1.4492931852159077200 ,.5521346926401092697 ] 
dist 103=[-1.3304224223660120931 ,.99494012723451034419] 
dist 104=[-1.4511773787391777154 ,1.3361714094323222482 ] 
dist 105=[-1.5646811994039491116 ,1.6686208449615864466 ] 
dist 106=[-1.6978718593005347322 ,2.0763906522754198474 ] 
dist 107=[-1.8333657290986261987 ,2.4621203084235585092 ] 
dist 108=[-1.9560355496958681650 ,2.7065954762757010679 ] 
dist 109=[-2.0926325201529625546 ,2.8946621680888242164 ] 
dist 110=[-2.2836608306500145952 ,3.0552174137600111971 ] 
dist 111=[-2.4670825764422914899 ,3.1860702153058955252 ] 
dist 112=[-2.5733141667598748465 ,3.2555769443782084672 ] 
dist 113=[-2.6431028106199572494 ,3.2936318095583761733 ] 
dist 114=[-2.6811070900609978679 ,3.3006892980689034247 ] 
dist 115=[-2.7045756094820144236 ,2.7331610634052417574 ] 
dist 116=[-2.7163744907787305410 ,2.7256986994168308498 ] 
dist 117=[-2.7217739017423672987 ,2.6967638294983899515 ] 
dist 118=[-2.7197424457719249579 ,2.6809984252780142249 ] 
dist 119=[-2.3705462401386791106 ,2.5829517667242260543 ] 
dist 120=[-2.3176011212961265814 ,2.5563215800388330388 ] 
dist 121=[-2.2281610567772231718 ,2.5081969217485345466 ] 
dist 122=[-2.2030410540706790431 ,2.4664400606076752222 ] 
dist 123=[-2.1248942921479768839 ,2.2573117177164887228 ] 
dist 124=[-2.0984198664492310340 ,2.2751668258944773861 ] 
dist 125=[-2.0754444992667588812 ,2.2837987886016694896 ] 
dist 126=[-2.0602502602646199623 ,2.2821764512024826871 ] 
dist 127=[-.9931491842557564049 ,-.07739949442314031273] 
dist 128=[-1.2810432347561210299 ,-.09888399022224443707] 
dist 129=[-1.5140041253534900220 ,-.14228609315188702437] 
dist 130=[-1.7330720281528843243 ,-.1526204467961033762 ] 
dist 131=[-1.9265916154073045230 ,-.22328405884885565649] 
dist 132=[-2.0575769057152895212 ,-.23162295283268592561] 
dist 133=[-2.1679368826013968117 ,-.22632179374644193399] 
dist 134=[-2.2791373315584790739 ,-.20112565680704122145] 
dist 135=[-2.3762556589842045578 ,-.16515194880903283295] 
dist 136=[-2.4304040872350614909 ,-.11682626822924483902] 
dist 137=[-2.4635151881152675183 ,-.05023606943705282080] 
dist 138=[-2.4766480927825627122 ,.0586423803217865858 ] 
dist 139=[-2.4782961030269226552 ,.1749835690247732080 ] 
dist 140=[-2.4737535954196163749 ,.2713654006478189650 ] 
dist 141=[-2.4492146615905883482 ,.3715747808044326607 ] 
dist 142=[-2.4364411779473440612 ,.5032038455158216398 ] 
dist 143=[-1.8395532573585701058 ,.6449743857664221070 ] 
dist 144=[-1.8183594477677240927 ,.78566897065779467931] 
dist 145=[-1.7938378285801231418 ,.95255757974525320715] 
dist 146=[-1.7815494592922097148 ,1.1988876038484390377 ] 
dist 147=[-1.0085463780809914452 ,1.4422981409677071177 ] 
dist 148=[-.94810487748486395042,1.5975364091469463332 ] 
dist 149=[-.88145775891887463529,1.7179599697338497672 ] 
dist 150=[-.86868822858120847521,1.8224098249595776282 ] 
dist 151=[-.3072533731699201804 ,1.9086422156111051827 ] 
dist 152=[-.23858688706822962461,1.9563530677606818252 ] 
dist 153=[-.09686531737995923396,1.9850106357275278965 ] 
dist 154=[-.06052945434254012114,1.9951964654843234883 ] 
dist 155=[.06879596969542971503,1.9966096030206647850 ] 
dist 156=[.09464754150178460529,1.9914228288545715910 ] 
dist 157=[.13071693260416949459,1.9788953748444670138 ] 
dist 158=[.13907815602738670112,1.9736285841239677197 ] 
dist 159=[.82708326480254821724,2.0031567412230653552 ] 
dist 160=[.8815283256138697489 ,2.0181575930220858377 ] 
dist 161=[.62336916814838612034,2.0254035172757274952 ] 
dist 162=[.22874008241005278977,2.0239782834892319958 ] 
dist 163=[-.16705575609776091672,1.6193128475324953702 ] 
dist 164=[-.42987153757092203344,1.6007542716938570714 ] 
dist 165=[-.64565933815836594331,1.5716224227518640143 ] 
dist 166=[-.85374331097079519841,1.5612150846529859177 ] 
dist 167=[-1.0409888349092209368 ,1.4697773935236020345 ] 
dist 168=[-1.1735990760423880228 ,1.5071472666099554266 ] 
dist 169=[-1.2916016462480067364 ,1.5323832204626495563 ] 
dist 170=[-1.4205377222292546164 ,1.5476495504725102727 ] 
dist 171=[-1.5386742150082807231 ,1.5553011928490906878 ] 
dist 172=[-1.6135711984913719723 ,1.5555930571442699547 ] 
dist 173=[-1.6711400399496592711 ,1.5423639571247740095 ] 
dist 174=[-1.7201170050174258249 ,1.5396480856940686712 ] 
dist 175=[-1.7598285758226342872 ,1.4621116702776618814 ] 
dist 176=[-1.7804182005157505447 ,1.4461773248087565297 ] 
dist 177=[-1.7909508574510176480 ,1.4022388838627362244 ] 
dist 178=[-1.7905249620001558055 ,1.3895455817611171969 ] 
dist 179=[-1.3735855859659332119 ,1.2969182565535137039 ] 
dist 180=[-1.4659704074835673389 ,1.2753050217863495560 ] 
dist 181=[-1.5345921121709246184 ,1.2401257520083689253 ] 
dist 182=[-1.6404232282264033972 ,1.2291348896226614359 ] 
dist 183=[-1.7351547498684228412 ,.9730606541788958209 ] 
dist 184=[-1.7867356745952034444 ,.9365755360801842970 ] 
dist 185=[-1.8166303049728983732 ,.8551957973400060852 ] 
dist 186=[-1.8247914697005574678 ,.8319586209393155463 ] 
dist 187=[-1.8250487740525919788 ,.7264659301312293223 ] 
dist 188=[-1.8233925076016351595 ,.7052028368242105430 ] 
dist 189=[-1.8200331534733614122 ,.6552892321629572141 ] 
dist 190=[-1.8134943035489858012 ,.6419354380869539644 ] 
dist 191=[-1.4733362623919107440 ,.5980939243183552861 ] 
dist 192=[-1.4591586357940261097 ,.6880498809577557272 ] 
dist 193=[-1.4155320180762743014 ,.7927553216124808199 ] 
dist 194=[-1.4060899807426918727 ,.9449993207430817191 ] 
dist 195=[-.9691847826019842249 ,1.0945928334926584998 ] 
dist 196=[-1.0507880137295063938 ,1.1887199889684714968 ] 
dist 197=[-1.1149138999565286929 ,1.2602642924747153408 ] 
dist 198=[-1.1719763191671574137 ,1.3197204096246075044 ] 
dist 199=[-1.2201410191506208178 ,1.3668753490058008761 ] 
dist 200=[-1.2487495838201626142 ,1.3893211428749665415 ] 
dist 201=[-1.2685095038778498371 ,1.4001835449995232866 ] 
dist 202=[-1.2813513834468186165 ,1.4011004623795062418 ] 
dist 203=[-1.2884358500343977145 ,1.3835848145899507834 ] 
dist 204=[-1.2885394462926169235 ,1.4449499389802111286 ] 
dist 205=[-1.2792127699629879442 ,1.4894905599243530500 ] 
dist 206=[-1.2751945255214263759 ,1.5227361807742465281 ] 
dist 207=[-1.2213274235816325676 ,1.5461916038932179254 ] 
dist 208=[-1.2067711245486657496 ,1.5516555987232057353 ] 
dist 209=[-1.1915226364947108746 ,1.5507488099786719359 ] 
dist 210=[-1.1830332374916396322 ,1.5487717503523282560 ] 
dist 211=[-.8450997889746317122 ,1.3714201284171111031 ] 
dist 212=[-.8054135503625939442 ,1.4332808716751685256 ] 
dist 213=[-.7117651393365087976 ,1.4859950776645057590 ] 
dist 214=[-.6921977665667469228 ,1.5400597849167760978 ] 
dist 215=[-.5590005735967576614 ,1.5859083905319830680 ] 
dist 216=[-.5332277158910665227 ,1.6058277307420184171 ] 
dist 217=[-.4871702405173653274 ,1.6144722563622489855 ] 
dist 218=[-.60136726013894109605,1.6153090386421381730 ] 
dist 219=[-.72227430637744513272,1.5772622386681022985 ] 
dist 220=[-.83075502493644575092,1.5658867272388240459 ] 
dist 221=[-.95092980177990456304,1.5576915189574705831 ] 
dist 222=[-1.1185127349497400516 ,1.5516913076134438995 ] 
dist 223=[-1.2815355486067788263 ,.39651805309533159191] 
dist 224=[-1.3835091094568461336 ,.48836706414022533882] 
dist 225=[-1.4603042261957215181 ,.59964427480257925604] 
dist 226=[-1.5228297107994212116 ,.76655890849347514515] 
dist 227=[-1.5714098554251466742 ,.93263564500068686134] 
dist 228=[-1.5925437041132650382 ,1.0405676622025185978 ] 
dist 229=[-1.6020988544201991343 ,1.1265897163565598016 ] 
dist 230=[-1.6044639214720277399 ,1.2052141738108413114 ] 
dist 231=[-1.5859510033253417143 ,1.2730699930549768211 ] 
dist 232=[-1.6059530509639387604 ,1.3161090871255142949 ] 
dist 233=[-1.6290276673268553350 ,1.3492094150492810041 ] 
dist 234=[-1.6559399386806922351 ,1.3773934896997700355 ] 
dist 235=[-1.6737938496484882826 ,1.3988027931206098260 ] 
dist 236=[-1.6767220575470175875 ,1.4048621684479809108 ] 
dist 237=[-1.6714432849284770528 ,1.4045943664993325130 ] 
dist 238=[-1.6667834973640907314 ,1.4007525140543657322 ] 
dist 239=[-1.3094630306186867347 ,1.3602492567135636058 ] 
dist 240=[-1.2954317799242386449 ,1.3475409399488048926 ] 
dist 241=[-1.2585645566697812321 ,1.3315403595965869513 ] 
dist 242=[-1.2459031780645485420 ,1.3236092766095272014 ] 
dist 243=[-.8666259522863168569 ,1.2086118593157972180 ] 
dist 244=[-.83517241010927994612,1.2738032698062339611 ] 
dist 245=[-.78406457380755206663,1.3218916322277162234 ] 
dist 246=[-.77033246603725844173,1.3592175503288292613 ] 
dist 247=[-.50166151813996798172,1.4076252384298698939 ] 
dist 248=[-.46593409874210448217,1.4679116930321450174 ] 
dist 249=[-.38167810627273981016,1.5101687453599488673 ] 
dist 250=[-.36653664666158638895,1.5388809367414131028 ] 
dist 251=[-.25034614746929223692,1.5579288475724241576 ] 
dist 252=[-.22889862448662198906,1.5616118124424560627 ] 
dist 253=[-.19457445035283234048,1.5592082535481177047 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 1, 1, 1, 0, 1] 
dist 0=[42.790984822797553174  ,42.790984822797553174  ] 
dist 1=[41.900210208529806632  ,43.266167582437159166  ] 
dist 2=[40.939378609556422236  ,43.538443756745673251  ] 
dist 3=[40.184351297305362749  ,43.618745844442549258  ] 
dist 4=[39.433277341982217558  ,43.651594330458275672  ] 
dist 5=[38.488100172140461703  ,43.662824492972137993  ] 
dist 6=[37.486654778375210031  ,43.657983090352156183  ] 
dist 7=[36.510704409794714567  ,43.640378950508090424  ] 
dist 8=[35.362977134224131079  ,43.574566704543964790  ] 
dist 9=[33.675166116528878238  ,41.121776091089211807  ] 
dist 10=[31.930791378670643660  ,40.749804012083344148  ] 
dist 11=[30.556999438543838877  ,40.097431117220889543  ] 
dist 12=[29.186243170158290942  ,39.925127056855756773  ] 
dist 13=[27.453833996203028432  ,39.344011953850919381  ] 
dist 14=[25.612722719584134607  ,39.160388235204086479  ] 
dist 15=[23.807503590923307915  ,38.968619951009564087  ] 
dist 16=[21.674868278896225855  ,38.863327939491674716  ] 
dist 17=[18.525296279709947139  ,29.429419815283611328  ] 
dist 18=[15.377903025628699920  ,24.923692758626101385  ] 
dist 19=[13.253926107709789033  ,22.334266630086196549  ] 
dist 20=[11.463619143405106708  ,21.963604532218437569  ] 
dist 21=[9.6495342628804655180 ,18.604776219226735846  ] 
dist 22=[7.9492870220412468814 ,17.735278236896217646  ] 
dist 23=[6.6138268638440570895 ,17.520304074500765222  ] 
dist 24=[5.2836941754731454010 ,16.837767385083079124  ] 
dist 25=[3.6046333104343011919 ,16.256795717088125429  ] 
dist 26=[1.9819552094442246749 ,10.415327030469201078  ] 
dist 27=[.87704921909840455599,9.0354075533585807107 ] 
dist 28=[-.06555560594947405346,8.6869681927853920551 ] 
dist 29=[-1.0398079638973920258 ,7.4728306243962516873 ] 
dist 30=[-2.9027481107218248768 ,7.2269484042164543058 ] 
dist 31=[-5.6953586263328389063 ,6.9143437082256482310 ] 
dist 32=[-8.4235979126626465005 ,6.8611392279947898099 ] 
dist 33=[-10.138968900202321156  ,1.3191925279002080615 ] 
dist 34=[-11.450498687000034725  ,1.2591510608427066786 ] 
dist 35=[-12.564943130679171542  ,1.2780397119020206539 ] 
dist 36=[-13.476408475403244220  ,1.3336677144257070091 ] 
dist 37=[-13.976996683408049555  ,1.4497033236221578729 ] 
dist 38=[-14.277356849376572133  ,1.5921636106068558150 ] 
dist 39=[-14.389234402767139297  ,1.7535356363875108728 ] 
dist 40=[-14.428483960633499434  ,1.9576681773789195300 ] 
dist 41=[-14.438570913710042124  ,2.2708969010149222038 ] 
dist 42=[-14.432194455013708806  ,2.5942697746244098974 ] 
dist 43=[-14.404975739430842837  ,2.8390107953320949597 ] 
dist 44=[-14.368782059892319228  ,3.0715827414856080007 ] 
dist 45=[-14.326214678054488013  ,3.3466465420203952409 ] 
dist 46=[-14.271732797328125025  ,3.6265028925631981218 ] 
dist 47=[-14.216056889432773709  ,3.8782852572905455840 ] 
dist 48=[-8.1195641874921258193 ,4.1568150246242592107 ] 
dist 49=[-6.6902832357893690458 ,4.5434123460177278239 ] 
dist 50=[-3.4838350797550863503 ,4.9244141938096131671 ] 
dist 51=[-3.2347585665611247682 ,5.1806665963496546012 ] 
dist 52=[-.98718236798704860597,5.3939069137484149555 ] 
dist 53=[-.81430230946159340051,5.6034181074641173043 ] 
dist 54=[-.05619169836651443271,5.7939363472614502565 ] 
dist 55=[.06560096917116871853,5.9314556852206809630 ] 
dist 56=[.65819264690793843231,6.0562602875343513020 ] 
dist 57=[.72330578902517886187,6.1961037224241230394 ] 
dist 58=[1.6703831018181576549 ,6.3213885412481879514 ] 
dist 59=[1.6957219564798476614 ,6.3881320410792364103 ] 
dist 60=[1.6264921852291349430 ,6.4247797561428632002 ] 
dist 61=[1.5085861472941491453 ,6.4300099894131346169 ] 
dist 62=[1.3303002380498884827 ,6.4148470536617214196 ] 
dist 63=[1.0742875416191854479 ,6.3701546560015612709 ] 
dist 64=[.64627008804276565371,5.0540548896890956807 ] 
dist 65=[.20608465022892291411,5.0489932037315191736 ] 
dist 66=[-.09850080869818293430,5.0076223191297556574 ] 
dist 67=[-.36136826240716887392,4.9866964643355374043 ] 
dist 68=[-.63518339159297747684,4.8009989708485309596 ] 
dist 69=[-.89436784006231644534,4.7512201476334168635 ] 
dist 70=[-1.0988946004200102383 ,4.6798144177978447321 ] 
dist 71=[-1.3021555682257780530 ,4.6515817443099516606 ] 
dist 72=[-1.5563117238645547504 ,3.9226102054161110671 ] 
dist 73=[-1.7980081570100309069 ,3.8178459038529406528 ] 
dist 74=[-1.9515704784131420523 ,3.5934423831786967710 ] 
dist 75=[-2.0697192656399762827 ,3.5280056023415880874 ] 
dist 76=[-2.1701405419425038556 ,3.2514108714406418992 ] 
dist 77=[-2.2512782279426568417 ,3.1959139747693711064 ] 
dist 78=[-2.2924972876183960125 ,3.0441161419660251057 ] 
dist 79=[-2.3123003485801202540 ,3.0205159015871817402 ] 
dist 80=[-2.3140548680600515543 ,2.2550905098252246534 ] 
dist 81=[-2.6188049166708321192 ,2.2309809767645494914 ] 
dist 82=[-3.0676526234229282068 ,.40241291328625831444] 
dist 83=[-3.3511574108641083264 ,.31302246425703153747] 
dist 84=[-3.5682295748078415064 ,-.14227090737267605616] 
dist 85=[-3.7518519287467501329 ,-.22018498039557267264] 
dist 86=[-3.9002879514849864875 ,-.39586447052916875697] 
dist 87=[-3.9768887721114356078 ,-.42377078598669948842] 
dist 88=[-4.0162368290249781690 ,-.65222662996916647911] 
dist 89=[-4.0846248212123717239 ,-.69069708248431835032] 
dist 90=[-4.1819872534154768114 ,-.69031165436619895171] 
dist 91=[-4.2405829217869678984 ,-.6370720010063849713 ] 
dist 92=[-4.2762351640900742634 ,-.55410852116295865233] 
dist 93=[-4.2819856257719220887 ,-.43505132220349450871] 
dist 94=[-4.2723336489718175645 ,-.26679460252479923653] 
dist 95=[-4.2598782948310989047 ,.01257629703543650079] 
dist 96=[-3.7791812954315294829 ,.3005396524801442598 ] 
dist 97=[-3.7628725503104781934 ,.50310947375523347527] 
dist 98=[-2.2954792770834248844 ,.68197387749262109993] 
dist 99=[-2.1617138739930907717 ,.8753377843380347868 ] 
dist 100=[-1.8414746701360199802 ,1.0633475212737373303 ] 
dist 101=[-1.7856767562711398732 ,1.4581754218229596899 ] 
dist 102=[-1.3268252893170364148 ,1.8286350240267830965 ] 
dist 103=[-1.2408180160003912204 ,2.0973596391760834811 ] 
dist 104=[-1.1136188657121798322 ,2.3432176107850704504 ] 
dist 105=[-1.0779019103915572650 ,2.6223970409325746991 ] 
dist 106=[-.52130469267910176003,2.8803078426731366694 ] 
dist 107=[-.41260651940674739831,3.0412613329541006538 ] 
dist 108=[-.38447063671411757256,3.1621244107085335999 ] 
dist 109=[-.53004605829327030414,3.2599906056507912457 ] 
dist 110=[-.85322468766838331257,3.3356458374031526989 ] 
dist 111=[-1.3452734771838655448 ,3.3678392147875607934 ] 
dist 112=[-1.8376262003277206748 ,3.3794522162151160384 ] 
dist 113=[-2.1620169476179148086 ,3.3753848511313147755 ] 
dist 114=[-2.4254971537178370811 ,3.3756496198694726825 ] 
dist 115=[-2.6747357930487586005 ,3.4255391692272746892 ] 
dist 116=[-2.8957242432496078329 ,3.4562610685406559537 ] 
dist 117=[-3.0464458537107994369 ,3.4617479968475745280 ] 
dist 118=[-3.1745361899499290154 ,3.4542561434307620706 ] 
dist 119=[-3.3051876999578320714 ,3.4441132041633334572 ] 
dist 120=[-3.4173923909655124398 ,3.1709147730179340313 ] 
dist 121=[-3.4718530180028588106 ,3.1233825818642082792 ] 
dist 122=[-3.4978455534822357581 ,3.0213886092781957683 ] 
dist 123=[-3.4993191204987575889 ,2.9883178393516684762 ] 
dist 124=[-3.4529363922113049175 ,2.8346791143418770736 ] 
dist 125=[-3.4314211955560455567 ,2.8009100927042573920 ] 
dist 126=[-3.4092146855385651275 ,2.6999952944356773519 ] 
dist 127=[-3.3930691639274928698 ,2.6821259308438884479 ] 
dist 128=[.08751593170428814870,1.4115088626953463046 ] 
dist 129=[-.14140224750293832808,1.0718727399908762394 ] 
dist 130=[-.2962461385520820121 ,1.0468100975780356505 ] 
dist 131=[-.42661064433767645359,.97936004011755514602] 
dist 132=[-.5578009230596206741 ,.96878088454461434748] 
dist 133=[-.67960222081227107957,.84423024457676658433] 
dist 134=[-.77248181351970509142,.81853743449143374157] 
dist 135=[-.86202837955106490686,.7919708585387643029 ] 
dist 136=[-.97051835103268317886,.78445049759896353966] 
dist 137=[-1.0724049720051075022 ,.49809700356692269545] 
dist 138=[-1.1355876952046558797 ,.461024735222828357  ] 
dist 139=[-1.1825408276084597387 ,.38652601299301867843] 
dist 140=[-1.2196351752984269007 ,.36705259612803192041] 
dist 141=[-1.2475365991067658752 ,.29672683958612502898] 
dist 142=[-1.2577867303236846662 ,.28131672767180072409] 
dist 143=[-1.2611605090414303909 ,.25692378294975499297] 
dist 144=[-1.2616305959956211956 ,.25032058695470758894] 
dist 145=[-.31139532459244895518,-.09955219879542694750] 
dist 146=[-.21911636891514198179,-.06348813251077634082] 
dist 147=[-.13708400837346360849,-.03909284184088731254] 
dist 148=[-.12515208736087318956,-.01858723160542481743] 
dist 149=[-.05901836054117977334,.00195774131496105410] 
dist 150=[-.04002536071198364276,.03623117699756656008] 
dist 151=[-.03657517236815269805,.07914415266430506990] 
dist 152=[-.02952578542360784339,.13206384048552302775] 
dist 153=[-.02777250440433059053,.1822339750824675767 ] 
dist 154=[-.02212958607341801427,.21417421725298486585] 
dist 155=[-.02183507136963121018,.23890103370826970158] 
dist 156=[-.02334739043066918569,.26028072309010787359] 
dist 157=[-.02769639400210191976,.27790886777793257792] 
dist 158=[-.03350597288022302801,.28766423214425220595] 
dist 159=[-.04084544827095247990,.29355170540039562116] 
dist 160=[-.05068423793929975300,.29574763000365256685] 
dist 161=[-.06646336511930745941,.29649887375783245594] 
dist 162=[-.08242325565800899025,.29662035175941917329] 
dist 163=[-.09298365105505185115,.29633920798581959935] 
dist 164=[-.10157979426817767487,.2954782504337191686 ] 
dist 165=[-.10970609443473288273,.29434967675521607986] 
dist 166=[-.1168782324904143544 ,.29299877875352184809] 
dist 167=[-.12166879073512813057,.29125121232224696741] 
dist 168=[-.12561631557970500548,.29010858835654401172] 
dist 169=[-.12942551012048213483,.28575041837795834665] 
dist 170=[-.1325129519470080778 ,.28378043867145994269] 
dist 171=[-.13358065569703165984,.28179022949765332438] 
dist 172=[-.13386225642452618541,.28042969358751423903] 
dist 173=[-.1338166308295452549 ,.27750608706923691222] 
dist 174=[-.12898151115743547549,.27590679035753028252] 
dist 175=[-.15884310908533799168,.27378357706610164925] 
dist 176=[-.24346444021898075498,.27263343664712258297] 
dist 177=[-.32707832161994806992,.17396903007468035858] 
dist 178=[-.38074336962378854212,.10583283085631868179] 
dist 179=[-.42277956945838717842,.0983646498787066185 ] 
dist 180=[-.45997407130958864955,.08566226685809647376] 
dist 181=[-.49124060542821274765,.08264163468414326045] 
dist 182=[-.50961440337743817613,.07583749608025550534] 
dist 183=[-.52208008082980677843,.07547369320871670726] 
dist 184=[-.52976447689550476455,.07762509051355009817] 
dist 185=[-.53502038959037087008,.08375658229748344261] 
dist 186=[-.53779142609318477679,.09127310040508801967] 
dist 187=[-.53928144393706018371,.09895447895786431742] 
dist 188=[-.53942005828213830346,.10822518699456853124] 
dist 189=[-.53867896401731333266,.12208871770685495697] 
dist 190=[-.53683208168146725051,.13785077099057541746] 
dist 191=[-.53339999601697550611,.1547017143737821796 ] 
dist 192=[-.53151148363140442562,.17558971816772242592] 
dist 193=[-.29841778655076993549,.2074692373544891811 ] 
dist 194=[-.22264851541895973188,.23947001460843331584] 
dist 195=[-.16421297069515242583,.26084283995620061598] 
dist 196=[-.15558633646603113056,.27854132011086775955] 
dist 197=[-.11722851773709062924,.29587483324828115544] 
dist 198=[-.11876781204170486973,.31166816893831250718] 
dist 199=[-.11924882832933383753,.32321903008830816071] 
dist 200=[-.11920945741972758264,.33388904756693536004] 
dist 201=[-.1189324139344823135 ,.34616761296158658763] 
dist 202=[-.11627593679911196154,.35739455999913532182] 
dist 203=[-.11558962179783217876,.36386700129794924393] 
dist 204=[-.11293296176663968012,.36810984270215254004] 
dist 205=[-.11253818796619464667,.37043610445164899229] 
dist 206=[-.104887721520253017  ,.37136788388702633425] 
dist 207=[-.10311967592017148107,.3709409093185776329 ] 
dist 208=[-.10179647991607801037,.36682602088865126402] 
dist 209=[-.1014467023851153166 ,.20110278984870150122] 
dist 210=[-.07418071268916300094,.20590361971711347616] 
dist 211=[-.07080114551388332120,.20870470710706588326] 
dist 212=[-.06259688121115262088,.20953167827156576059] 
dist 213=[-.06101426522634360048,.20944914510005519019] 
dist 214=[-.04852059110347680955,.20886223020554656335] 
dist 215=[-.04605764152881754771,.20735026818477764656] 
dist 216=[-.04228840621663855414,.2064638795423557914 ] 
dist 217=[-.05643636345256228399,.18580163818542461765] 
dist 218=[-.07539122440102931697,.1824496014713342217 ] 
dist 219=[-.08911839841833641600,.17488274608746742234] 
dist 220=[-.10164972755333582425,.17245235680162137258] 
dist 221=[-.11583418366147612507,.16124958844424618102] 
dist 222=[-.13001049012008644229,.15880857111161576852] 
dist 223=[-.14251171723326778764,.15272805296224947767] 
dist 224=[-.15619678153790304868,.15096251817542187484] 
dist 225=[-.17510274420704273057,.07350237705258498762] 
dist 226=[-.19335138841905541568,.08926161926891083727] 
dist 227=[-.20441333923342033464,.09970323128909752317] 
dist 228=[-.21235024207141849312,.10824532746068931739] 
dist 229=[-.2181225829485285165 ,.11642239145699270691] 
dist 230=[-.22232502559864932191,.12373042832949741633] 
dist 231=[-.22399317711222476346,.12880309216776671582] 
dist 232=[-.22440900528302238816,.13320152019901487678] 
dist 233=[-.22405369732029766447,.13781650207644489478] 
dist 234=[-.21065563845762497384,.14175954238084184382] 
dist 235=[-.20811336513540684919,.14347541295601077907] 
dist 236=[-.20291057657165016222,.14423378372660528245] 
dist 237=[-.20119349943579450827,.14435963740206261103] 
dist 238=[-.17284511723638208886,.14092262686427904119] 
dist 239=[-.16721191353586267979,.13997771145040069135] 
dist 240=[-.13764552926724159452,.13936061924360035277] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 2, 2, 0, 0, 2] 
dist 0=[42.806392829691976487  ,42.806392829691976487  ] 
dist 1=[41.914117276071283617  ,43.534401362060491181  ] 
dist 2=[40.728569396210540305  ,44.107347380177627215  ] 
dist 3=[38.829111340143777514  ,44.380368035731021846  ] 
dist 4=[36.877957457881794660  ,44.513564512185951688  ] 
dist 5=[35.485826073831618545  ,44.528027683493548512  ] 
dist 6=[34.232877332958823813  ,44.219299045116242317  ] 
dist 7=[32.837407615657491322  ,44.130516665765081335  ] 
dist 8=[31.451864887161694601  ,43.688575909047752917  ] 
dist 9=[30.238364898318181012  ,43.599219984034383649  ] 
dist 10=[28.914169124250000070  ,43.230359133396405550  ] 
dist 11=[27.086121578667639908  ,43.109270692271760998  ] 
dist 12=[25.246004365834159338  ,42.788667200447523706  ] 
dist 13=[23.873402661599301776  ,42.654668249880518944  ] 
dist 14=[22.574652541556497258  ,41.954712126396932747  ] 
dist 15=[21.029287083818517964  ,41.738317134791949441  ] 
dist 16=[19.434637232131657600  ,40.446362462546632068  ] 
dist 17=[17.938654408708866112  ,29.107648652326300228  ] 
dist 18=[16.220492418788025400  ,26.050189323946228918  ] 
dist 19=[13.737501279087905319  ,25.221150015023427756  ] 
dist 20=[11.276676289706703502  ,24.440444551068135209  ] 
dist 21=[9.6469771250119928206 ,24.208787425354033090  ] 
dist 22=[8.3049482730688806885 ,19.629104326764642339  ] 
dist 23=[6.9938316943460773241 ,18.577529539929173618  ] 
dist 24=[5.7935007062859340459 ,18.332987359523947266  ] 
dist 25=[4.8941430476529050509 ,16.457748951135513346  ] 
dist 26=[4.0371191948454452106 ,16.140772367258633917  ] 
dist 27=[3.0056987035318731423 ,14.988995285296274120  ] 
dist 28=[2.0288269857453021413 ,14.006638637494987027  ] 
dist 29=[1.3897079859995901538 ,13.850255222671795213  ] 
dist 30=[.38076978423722864881,6.9063615661188807896 ] 
dist 31=[-1.5436203455740369522 ,5.4769583140856717281 ] 
dist 32=[-3.2635965183389125344 ,2.6333103541261438683 ] 
dist 33=[-5.7924727179279122923 ,2.3345896201453559179 ] 
dist 34=[-7.3954908538128945828 ,.21126399755506689472] 
dist 35=[-8.6367778928803809140 ,.02793306356275003358] 
dist 36=[-9.7199700906069905516 ,-.78091544267911090676] 
dist 37=[-10.627589186400928269  ,-.91581113654378399055] 
dist 38=[-11.167341640743037714  ,-1.1315580996694654432 ] 
dist 39=[-11.545890697383497297  ,-1.1576588811806752393 ] 
dist 40=[-11.809707794954822206  ,-1.1971150275407480508 ] 
dist 41=[-12.006160988674513746  ,-1.1752994281093036241 ] 
dist 42=[-12.115445924149774600  ,-1.1215686043055410290 ] 
dist 43=[-12.184799113948489230  ,-1.0121370431757728250 ] 
dist 44=[-12.221083705814335124  ,-.88957092477304237106] 
dist 45=[-12.235610011770262377  ,-.78327327995370929913] 
dist 46=[-12.217724317327503792  ,-.66934469739495287452] 
dist 47=[-12.173468547727895115  ,-.51605718018807357911] 
dist 48=[-12.136233850354532417  ,-.34966557210414287423] 
dist 49=[-5.9690045286051288623 ,-.18329015427973945149] 
dist 50=[-5.4500302047103241816 ,.01491834539261227703] 
dist 51=[-4.1990863309578897474 ,.30853299380496314181] 
dist 52=[-4.0193626697459761354 ,.59956585831259935211] 
dist 53=[-3.0688015483153116080 ,.78751464205487335295] 
dist 54=[-1.9310586146940128311 ,.93622151360557551167] 
dist 55=[-1.5451009544287257829 ,1.0804232152906931293 ] 
dist 56=[-1.4786478258365687087 ,1.9859468766129550990 ] 
dist 57=[-.3674930058277494665 ,2.8476489665498286612 ] 
dist 58=[.10763150288296480092,3.4037067682680640883 ] 
dist 59=[.19192050402489905555,3.8432815219315629306 ] 
dist 60=[.34272491824940333047,4.2400454026284039963 ] 
dist 61=[.37241202863276226619,4.5802616391309000426 ] 
dist 62=[1.2647440769315989582 ,4.7941878761068098812 ] 
dist 63=[1.1918781245524655367 ,4.9576602305707578717 ] 
dist 64=[1.1000819528926543843 ,5.0966716743708615363 ] 
dist 65=[.98988642191079994738,5.2049920204935665989 ] 
dist 66=[.84512546671253039441,5.2459366451510447659 ] 
dist 67=[.61535534671657352906,5.2582255073353137005 ] 
dist 68=[.38169879054966325005,5.2517617087688394082 ] 
dist 69=[.22142113907176768675,5.1286279098600422068 ] 
dist 70=[.08419463885562072822,5.0883173685366228757 ] 
dist 71=[-.05745894600284593450,5.0472980653615976713 ] 
dist 72=[-.19112158496831743249,5.0213087240449449150 ] 
dist 73=[-.29645266012516510498,4.4372890902874609080 ] 
dist 74=[-.40120332415515419016,4.3995774082019723516 ] 
dist 75=[-.53254517718524710421,4.3999497163636609306 ] 
dist 76=[-.65799162259865869362,4.3819882700638464218 ] 
dist 77=[-.94805090850317101682,4.3650454559850449776 ] 
dist 78=[-1.7156455895417627159 ,4.0349587075615899331 ] 
dist 79=[-2.2876008171672466209 ,3.9338324623362135369 ] 
dist 80=[-2.7591305211481427337 ,3.8984477304855833942 ] 
dist 81=[-3.2058210539056874703 ,2.3343814776303667159 ] 
dist 82=[-3.6027711034579696985 ,2.1759222743716189147 ] 
dist 83=[-3.8757588232402217783 ,1.7980239984605366474 ] 
dist 84=[-4.1104932530726506276 ,1.7341179082131409680 ] 
dist 85=[-4.3547705348002131845 ,1.1968167993993760689 ] 
dist 86=[-4.5709306213398384383 ,1.0964363745881290420 ] 
dist 87=[-4.6934214062751750604 ,.95337567714545455386] 
dist 88=[-4.7709378195232421526 ,.91167194494601629655] 
dist 89=[-4.8075266716566770722 ,.12652697383012505317] 
dist 90=[-4.8207477857129507015 ,.02660553545022679615] 
dist 91=[-4.8145648587127757873 ,-.09046145320760116241] 
dist 92=[-4.7789569242543160940 ,.01225497849797844934] 
dist 93=[-4.7542456173666547008 ,.09560909175292293399] 
dist 94=[-3.8038664682372033448 ,.28073348481124487406] 
dist 95=[-3.7796735382595841523 ,.83236303101324804601] 
dist 96=[-3.7789641520508516140 ,1.2954490737814837565 ] 
dist 97=[-3.4215153070439940171 ,1.7588940101459441604 ] 
dist 98=[-3.0054468990612655507 ,2.1872220114209847526 ] 
dist 99=[-2.9204911759272748385 ,2.5101495719654454961 ] 
dist 100=[-2.8079254743071111097 ,2.8178134571599896655 ] 
dist 101=[-2.7687153077229091394 ,3.1852299241879344744 ] 
dist 102=[-1.9204735162559898602 ,3.5274946643822693950 ] 
dist 103=[-1.8077447276920927379 ,3.7347711379873984102 ] 
dist 104=[-1.5647448918340366491 ,3.8829517091909006455 ] 
dist 105=[-1.4992374985514191893 ,3.9893387957028172834 ] 
dist 106=[-1.2255796336315641580 ,4.0669602575682491023 ] 
dist 107=[-1.1741132616308994397 ,4.1003102953279172800 ] 
dist 108=[-1.1427194473505478814 ,4.1090076310168711759 ] 
dist 109=[-1.1390357213622211389 ,4.1051944844295757591 ] 
dist 110=[-1.1352458826428331507 ,2.3344604297452748330 ] 
dist 111=[-1.1304099000605462478 ,2.3335196070226350907 ] 
dist 112=[-1.1253730088702432562 ,2.3319859173890584383 ] 
dist 113=[-1.1207861650420753311 ,2.3297120657098901340 ] 
dist 114=[-1.1157357556088069827 ,2.3264927849151185262 ] 
dist 115=[-1.1109219276774315263 ,2.3212123089447604333 ] 
dist 116=[.48050984956410513727,1.7510918611528535349 ] 
dist 117=[.32365495765286668932,1.8862228402668243041 ] 
dist 118=[.18601827964941170555,1.9826226502136106794 ] 
dist 119=[.03858689273012529993,2.0692670472009102738 ] 
dist 120=[-.1038975709289922645 ,2.1654626392608337493 ] 
dist 121=[-.23901534612799444748,2.2516082842893799798 ] 
dist 122=[-.400580643953293171  ,2.2981332757348677051 ] 
dist 123=[-.55605561178152631715,2.3246651093346389756 ] 
dist 124=[-.74384849460808525464,2.3309897979774788081 ] 
dist 125=[-.93804941848723480031,2.3277790950799448217 ] 
dist 126=[-1.1191101341233243397 ,2.3209937472058631020 ] 
dist 127=[-1.3252535436850240381 ,2.3009537357277904266 ] 
dist 128=[-1.6195795055780051801 ,2.2896988857670068754 ] 
dist 129=[-1.9072981993005103211 ,-.22218524759289867152] 
dist 130=[-2.0870720478427515510 ,-.16459169829947068154] 
dist 131=[-2.2222384280071631181 ,-.06562645529995084989] 
dist 132=[-2.3319088842433740237 ,.03782393277071827005] 
dist 133=[-2.4184286742358169078 ,.11331970840473987262] 
dist 134=[-2.4611907410414443339 ,.18279805158791497435] 
dist 135=[-2.4820816708769735755 ,.26223308943668572322] 
dist 136=[-2.4841274932934426541 ,.34199604221654758426] 
dist 137=[-2.3932737035156892048 ,.41278451613244193064] 
dist 138=[-2.4303228948581486530 ,.49056652422281826364] 
dist 139=[-2.4771792486035642654 ,.59824465666191814612] 
dist 140=[-2.5078196826759783446 ,.70608959612673809134] 
dist 141=[-2.5256979774378464234 ,.78453825575834785584] 
dist 142=[-2.5272560351639507230 ,.85649091711157424865] 
dist 143=[-2.5112588811794187286 ,.93840907903105928162] 
dist 144=[-2.5041666209362402476 ,1.0204852626553836058 ] 
dist 145=[-1.8701190772483705493 ,1.0930697531605915502 ] 
dist 146=[-1.8148363599625800716 ,1.1726230116465329219 ] 
dist 147=[-1.6767544589524410327 ,1.2825162433808470502 ] 
dist 148=[-1.6497378035506070815 ,1.3880734204775526142 ] 
dist 149=[-1.4263311195699921494 ,1.4503198611070167636 ] 
dist 150=[-1.3813279737831776733 ,1.4927760515717114969 ] 
dist 151=[-1.3149283865320323590 ,1.6101998111388835511 ] 
dist 152=[-1.2946708172621105137 ,1.7830121789107978672 ] 
dist 153=[-.87568650884140418032,1.9415886653796840084 ] 
dist 154=[-.81994196344903092593,2.0350430340987081574 ] 
dist 155=[-.69455503740276552449,2.0987096398679980231 ] 
dist 156=[-.6661205216329480901 ,2.1383821668864725064 ] 
dist 157=[-.50932690310027699545,2.1648100307920404908 ] 
dist 158=[-.48028655898597715128,2.1756136987768655363 ] 
dist 159=[-.41957418473280943069,2.1770487118783329458 ] 
dist 160=[-.40309270056363411208,2.1729343455996340284 ] 
dist 161=[.5716062896150367925 ,1.5314959902498666115 ] 
dist 162=[.37456458241397827694,1.5281461030767283227 ] 
dist 163=[.07838636859921686705,1.5238634691800558231 ] 
dist 164=[-.21818900105893097037,1.3574596792227539118 ] 
dist 165=[-.4168156134450238644 ,1.2415359902554316036 ] 
dist 166=[-.58178842336272896721,1.2160043654114522191 ] 
dist 167=[-.74403215551354656828,1.1827526224481613813 ] 
dist 168=[-.89215588561312772893,1.1700945384958117494 ] 
dist 169=[-1.0007671732111821895 ,.8749385525593605026 ] 
dist 170=[-1.1012636933696391559 ,.83462489545454425835] 
dist 171=[-1.2169952814129185451 ,.78860568164382307519] 
dist 172=[-1.3232375482742866567 ,.72461809412397184035] 
dist 173=[-1.3858571152550466035 ,.62685940481983879166] 
dist 174=[-1.4285244648189170386 ,.60756360982624492389] 
dist 175=[-1.4551285393898976976 ,.55978608420988942278] 
dist 176=[-1.4728828041276359202 ,.55043095110381630119] 
dist 177=[-1.4802257727086891925 ,.2496341821086091464 ] 
dist 178=[-1.4813451887524936968 ,.21007436615036827291] 
dist 179=[-1.4786090903730843620 ,.19939756614636698613] 
dist 180=[-1.3439971822369728521 ,.07818866673107201263] 
dist 181=[-1.3903340452825379863 ,.16365096971295998979] 
dist 182=[-1.4198955531092828962 ,.24041481972366801229] 
dist 183=[-1.4343131713782770264 ,.32539876832314007256] 
dist 184=[-1.4414789963224215283 ,.40918036726245863154] 
dist 185=[-1.5066600456413906703 ,.48114405929826464969] 
dist 186=[-1.5507837764384218926 ,.55824528849728071975] 
dist 187=[-1.5769810120316536537 ,.66253118257381308111] 
dist 188=[-1.5855749467637387434 ,.76588704486887795155] 
dist 189=[-1.5870971313900514702 ,.83927530073392906563] 
dist 190=[-1.5850674188526939632 ,.9047716387200758743 ] 
dist 191=[-1.5800487051910379184 ,.97662687314354499969] 
dist 192=[-1.5744992776362889532 ,1.0470715808205317123 ] 
dist 193=[-1.1120612396351783552 ,1.1069366864333225634 ] 
dist 194=[-1.0756384178291849657 ,1.1705164199915134449 ] 
dist 195=[-1.0628483803047501851 ,1.2557848064798814570 ] 
dist 196=[-.67752238380769636962,1.3365214964272780344 ] 
dist 197=[-.80256150755416971174,1.3820134270774621399 ] 
dist 198=[-.90536669284465344403,1.4103902219979102450 ] 
dist 199=[-1.0047470444376137970 ,1.4228164824216167972 ] 
dist 200=[-1.0943496952307206153 ,1.4282016399820344035 ] 
dist 201=[-1.1581263745827846695 ,1.4284762357568891055 ] 
dist 202=[-1.2152146840784908324 ,1.4250531722251121823 ] 
dist 203=[-1.2781195580919984176 ,1.4205871328617972094 ] 
dist 204=[-1.3339949473700388598 ,1.3977553870082372319 ] 
dist 205=[-1.3630244577737301096 ,1.4130463495377950258 ] 
dist 206=[-1.3782808206440875705 ,1.4203893219018782820 ] 
dist 207=[-1.3811862010591911688 ,1.4233229150612452808 ] 
dist 208=[-1.3719249065517188246 ,1.4210151800275461210 ] 
dist 209=[-1.3661973338300745285 ,1.3911937674483572768 ] 
dist 210=[-1.3592775272122518742 ,1.3938335109703608986 ] 
dist 211=[-1.3534484856123739797 ,1.3916163578577550284 ] 
dist 212=[-1.1587694107216135380 ,1.0942665212849390246 ] 
dist 213=[-1.1315794618816871123 ,.97071446770208805609] 
dist 214=[-1.0614043373102507818 ,.94490817496513130474] 
dist 215=[-1.0473436218888952725 ,.90860029870029270921] 
dist 216=[-.92464837899635498251,.89649629788951508185] 
dist 217=[-.89908130391904556999,.63232050303513379094] 
dist 218=[-.86337629704914366796,.59675897530207182944] 
dist 219=[-.8514025244103816953 ,.51859894115851020146] 
dist 220=[-.75063484969153019723,.49827858774946729641] 
dist 221=[-.82310456490896094352,.40473336845849494669] 
dist 222=[-.88782342892754039305,.38707711791378465728] 
dist 223=[-.95891411755352046915,.34510026488432303675] 
dist 224=[-1.0286873407744394913 ,.33657425475383916068] 
dist 225=[-1.0881474130376176426 ,.18185866307151348009] 
dist 226=[-1.1514611967878941015 ,.30298980174323491373] 
dist 227=[-1.2366166459919453310 ,.48838475406396185002] 
dist 228=[-1.3174592745839206370 ,.6743920271142857198 ] 
dist 229=[-1.3635581323039417315 ,.79796738117093251522] 
dist 230=[-1.3930462927188453054 ,.89950664785706899994] 
dist 231=[-1.4075862935230419293 ,.99755699388257461583] 
dist 232=[-1.4149410583452679133 ,1.0858894157685564976 ] 
dist 233=[-1.4157491292658420526 ,1.1486396997009488882 ] 
dist 234=[-1.4119159468011547874 ,1.2046851641105482053 ] 
dist 235=[-1.4081033669876201348 ,1.2662555153574374431 ] 
dist 236=[-1.2182021241480097831 ,1.3208519344318932296 ] 
dist 237=[-1.1940879853605754692 ,1.3490610093721939888 ] 
dist 238=[-1.1454663688129434281 ,1.3638540867086571017 ] 
dist 239=[-1.1308819911600391989 ,1.3665224743172409981 ] 
dist 240=[-1.0688361410364553556 ,1.3564058750387879084 ] 
dist 241=[-1.0544587824422944095 ,1.3507101544378505982 ] 
dist 242=[-1.0168811656938360609 ,1.3441263713603875680 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 1, 2] 
dist 0=[52.136982926796837638  ,52.136982926796837638  ] 
dist 1=[51.352916807277244446  ,52.791587679909133238  ] 
dist 2=[50.523132126447422438  ,53.104343148859281704  ] 
dist 3=[49.499287744435979952  ,53.233744351273328748  ] 
dist 4=[47.939957174920990093  ,53.237265227789926757  ] 
dist 5=[46.150933632100178304  ,52.935623302532158913  ] 
dist 6=[44.209586112415776916  ,52.800701881251071582  ] 
dist 7=[41.779555081440396103  ,52.509896072470316935  ] 
dist 8=[38.038589108084722599  ,52.380471595941802576  ] 
dist 9=[34.250944954458226352  ,49.549871837648428140  ] 
dist 10=[31.634386473437851455  ,49.051995481755370267  ] 
dist 11=[29.367402201129616446  ,48.401152142458440653  ] 
dist 12=[26.975813504043071541  ,48.159357092606520926  ] 
dist 13=[24.678481586559357444  ,42.822358290281046349  ] 
dist 14=[22.787783805519843489  ,42.287528363463779988  ] 
dist 15=[20.826583936353513717  ,38.287744432620984930  ] 
dist 16=[18.247287718932250550  ,36.341030703215544477  ] 
dist 17=[15.709073133421347308  ,29.506393522624907377  ] 
dist 18=[13.911764876565209630  ,28.614418059609313990  ] 
dist 19=[12.306032072073674413  ,26.816664618800556262  ] 
dist 20=[10.532785703261083277  ,26.343759040532806773  ] 
dist 21=[8.7777457222003081842 ,24.609720260535932498  ] 
dist 22=[7.2443498798973455180 ,24.236055062110695880  ] 
dist 23=[5.5715585260000743411 ,23.564958734000029852  ] 
dist 24=[3.2588229078600477780 ,23.399297921126227657  ] 
dist 25=[.9989482591715102388 ,10.206417914809144508  ] 
dist 26=[-.46275135426343122843,9.6452806633267474798 ] 
dist 27=[-1.6282309579306729654 ,8.6580149866781413638 ] 
dist 28=[-3.0219854323111715324 ,8.4644084392519706579 ] 
dist 29=[-5.0788368317769236131 ,6.1605412233479151500 ] 
dist 30=[-6.5816239792370701354 ,5.8826704363791206928 ] 
dist 31=[-7.9714109454192340454 ,4.7782830689648062937 ] 
dist 32=[-9.5769057766631087542 ,3.3524694971430943076 ] 
dist 33=[-11.063741788495957499  ,-3.1578761675219226616 ] 
dist 34=[-11.979570420773046486  ,-3.5395552922515243112 ] 
dist 35=[-12.655803242835048534  ,-4.2025072139879632098 ] 
dist 36=[-13.185621456175819288  ,-4.3339091040159028419 ] 
dist 37=[-13.591655597711372193  ,-4.5398126204042119966 ] 
dist 38=[-13.773364691990074752  ,-4.4367455005313071352 ] 
dist 39=[-13.850834315648326942  ,-4.1653060351924894159 ] 
dist 40=[-13.840450838557766119  ,-3.5972376912081155258 ] 
dist 41=[-10.344137391979101259  ,-2.9804454393259066939 ] 
dist 42=[-10.302622766170578230  ,-2.4118518097211688365 ] 
dist 43=[-10.206836535842538206  ,-1.9144491758566467959 ] 
dist 44=[-10.160344872760951437  ,-1.3851804550309199842 ] 
dist 45=[-9.8893234487372056721 ,-.87654486354973095828] 
dist 46=[-9.8195390537588420574 ,-.4613400772093293503 ] 
dist 47=[-9.5890552636877876658 ,-.02141357844081757318] 
dist 48=[-9.5394831348867323846 ,.72003886556699664943] 
dist 49=[-5.4870538962874276435 ,1.4652979014226924295 ] 
dist 50=[-5.0956875089872046637 ,2.0111939656639350904 ] 
dist 51=[-4.2483409570290196106 ,2.5158012293914805968 ] 
dist 52=[-4.0479620643117990915 ,3.4242142049061923297 ] 
dist 53=[-2.4183941460429218914 ,4.3455756602635080761 ] 
dist 54=[-2.1244584856086175242 ,5.0018339700582357958 ] 
dist 55=[-1.2336885191866819616 ,5.5895126425461281188 ] 
dist 56=[-.6879819453806609607 ,6.2370372426437712258 ] 
dist 57=[1.8986134530383209416 ,6.8312141744487284611 ] 
dist 58=[2.1173674045592745765 ,7.2059883150863672911 ] 
dist 59=[2.5407755192020966801 ,7.4917261371270086665 ] 
dist 60=[2.6366188233829276157 ,7.7307162629848887966 ] 
dist 61=[2.9036809792369010648 ,7.9217562658764518586 ] 
dist 62=[2.9310015884404714565 ,8.0162515830202049136 ] 
dist 63=[2.8824772128213947761 ,8.0587177626552439507 ] 
dist 64=[2.7187293534852077323 ,8.0423316385057876573 ] 
dist 65=[2.5133496550630629353 ,5.2272310871214155893 ] 
dist 66=[2.2985766675792901275 ,5.3829681024201621678 ] 
dist 67=[2.0361451769121995675 ,5.4932084378576523123 ] 
dist 68=[1.6403795479569033234 ,5.5709058882430767852 ] 
dist 69=[1.1892278157424715474 ,5.6222185864426327651 ] 
dist 70=[.70562698727753929864,5.6308759483503436011 ] 
dist 71=[.10539937539645569618,5.6159441401592992762 ] 
dist 72=[-.81139409771968968463,5.6035386328964157054 ] 
dist 73=[-1.7314404149908551308 ,1.7304593300300104156 ] 
dist 74=[-2.3446856943910335605 ,1.5973804785081370400 ] 
dist 75=[-2.8510938878039316361 ,1.2724621393319500593 ] 
dist 76=[-3.3446746825570118834 ,1.2255823568802395831 ] 
dist 77=[-3.7927765292917602263 ,.74708657647158522924] 
dist 78=[-4.1176557487494858101 ,.65875259376344051958] 
dist 79=[-4.4148661687333452238 ,.55627266041455971015] 
dist 80=[-4.7525548148312896275 ,.53771108037631565038] 
dist 81=[-5.0589377022569874123 ,-.2049538934952320556 ] 
dist 82=[-5.2311892694170858892 ,-.2938551750413903169 ] 
dist 83=[-5.3385111337453366242 ,-.4804534159434918887 ] 
dist 84=[-5.3856950967709796437 ,-.5233474103955966982 ] 
dist 85=[-5.4066170834364836769 ,-.6991142785867984659 ] 
dist 86=[-5.4090635122227385810 ,-.7312431475143994328 ] 
dist 87=[-5.4051925787554620075 ,-.7802162699868643459 ] 
dist 88=[-5.3902301797438060059 ,-.55153928208827183039] 
dist 89=[-5.0462362541171115349 ,.39907431147539282242] 
dist 90=[-4.9880176541841788936 ,1.0445610244715212172 ] 
dist 91=[-4.8092526245613598697 ,1.5903451244428073052 ] 
dist 92=[-4.7805119901961966291 ,2.1429923493752234941 ] 
dist 93=[-4.3759796120476985796 ,2.6579553230901993769 ] 
dist 94=[-4.2871209503272728653 ,3.0533204713987585507 ] 
dist 95=[-4.2055531385591080869 ,3.4369231177418371148 ] 
dist 96=[-4.1807943032878232107 ,3.9049330439968532955 ] 
dist 97=[-3.0492011969197339301 ,4.3459071521292009403 ] 
dist 98=[-2.9001815264575893335 ,4.6215919233231594502 ] 
dist 99=[-2.6073255897930345891 ,4.8290568910692684344 ] 
dist 100=[-2.5310421908062605890 ,4.9977218428639223577 ] 
dist 101=[-2.2604720335292052156 ,5.1285435383058048028 ] 
dist 102=[-2.1971682578230501368 ,5.1849481123962633222 ] 
dist 103=[-2.1106450760561573527 ,5.2074132243056669199 ] 
dist 104=[-2.0816901724001163823 ,5.2027776216401399632 ] 
dist 105=[-.21365669542267894281,4.4182979910604030479 ] 
dist 106=[-.29601945119984198221,4.5179139939305372266 ] 
dist 107=[-.37011010273347392874,4.5739378927777470801 ] 
dist 108=[-.45221403383879784158,4.5852234938627586953 ] 
dist 109=[-.53312461443227923607,4.5778246599655759180 ] 
dist 110=[-.60245571861926476988,4.5617000463092909993 ] 
dist 111=[-.6765479906241184257 ,4.5305135138724619510 ] 
dist 112=[-.77646201626243097253,4.5136051057459109935 ] 
dist 113=[-.87525582182273132954,3.9722968424434574877 ] 
dist 114=[-.94487919004492395934,3.9119410617311127860 ] 
dist 115=[-1.1546860451803629087 ,3.7389864836124653898 ] 
dist 116=[-1.5816541426831216775 ,3.7101743607089471581 ] 
dist 117=[-1.9800148092024337534 ,3.3182859932045299059 ] 
dist 118=[-2.2867445396979168040 ,3.2351318229281949539 ] 
dist 119=[-2.5852337608444714906 ,2.9450416780332182620 ] 
dist 120=[-2.9507183419044006070 ,2.4694838302429037854 ] 
dist 121=[-3.2959100174044326234 ,1.1027053429753226612 ] 
dist 122=[-3.5134053552020045246 ,.97932054418098689777] 
dist 123=[-3.6791496502105908753 ,.72315948235266386601] 
dist 124=[-3.8177767826665779992 ,.65608530950388807341] 
dist 125=[-3.9285303335730992636 ,.40942276263391356665] 
dist 126=[-3.9830234427101227270 ,.36018688423209218932] 
dist 127=[-4.0068604671337838897 ,.272246938789033414  ] 
dist 128=[-4.0090912793803904761 ,.25276880923737625736] 
dist 129=[-1.3376334802416710637 ,-.73226518517624676937] 
dist 130=[-1.3978111291437290433 ,-.72135785770853129099] 
dist 131=[-1.5453017597725850126 ,-.6898662216228526461 ] 
dist 132=[-1.7147781817608044040 ,-.62207499436677241554] 
dist 133=[-1.8629693628694373933 ,-.53615025968940586915] 
dist 134=[-1.9606747742552839301 ,-.43227935342450838841] 
dist 135=[-2.0402076051794607576 ,-.29536471987871700493] 
dist 136=[-2.1158621149976361865 ,-.04268196235125881868] 
dist 137=[-2.1797874648353493661 ,.23068741259183367552] 
dist 138=[-2.2124982890851059010 ,.41529604634882856204] 
dist 139=[-2.2286666216193354115 ,.57026381330367101835] 
dist 140=[-2.2299062768485823823 ,.72532452732661212172] 
dist 141=[-2.2161846796694655220 ,.86859744163402875033] 
dist 142=[-2.2074372160126489271 ,.97651474781084979228] 
dist 143=[-2.1810203641602364322 ,1.0792123558627778776 ] 
dist 144=[-2.1677099895592171261 ,1.2016496118644935493 ] 
dist 145=[-1.4609643360966018525 ,1.3155295240475966280 ] 
dist 146=[-1.3888958457186321714 ,1.3840706512022670376 ] 
dist 147=[-1.2106161000770918177 ,1.4325232994062968110 ] 
dist 148=[-1.1823884475528855036 ,1.4662217623974936605 ] 
dist 149=[-.90874232405706222458,1.4900115884849908686 ] 
dist 150=[-.85696829850558920265,1.4989164240132475649 ] 
dist 151=[-.83340552020751228548,1.4998855721196293183 ] 
dist 152=[-.8242130041942407502 ,1.4972321527282556607 ] 
dist 153=[-.31582847042622496519,1.4094113045231206414 ] 
dist 154=[-.2584708121528103344 ,1.4567552239570491913 ] 
dist 155=[-.1354689044069783159 ,1.5303043190537870834 ] 
dist 156=[-.10659874511956804767,1.5859820786339369124 ] 
dist 157=[.02276092241195944585,1.6285243951702206207 ] 
dist 158=[.04590468139355550606,1.6496349627982873743 ] 
dist 159=[.09470067539782690521,1.6591015131055652049 ] 
dist 160=[.10555208582231981644,1.6593616969961678601 ] 
dist 161=[.59336119661945143071,1.5493228543148314319 ] 
dist 162=[.63764670332615065818,1.5317558045741295345 ] 
dist 163=[.71826001768769228411,1.4826120040334095878 ] 
dist 164=[.69112629688064588236,1.4699851286231834278 ] 
dist 165=[.52711451013564551442,1.3670230761589770822 ] 
dist 166=[.3616468209830820957 ,1.3435946504270873344 ] 
dist 167=[.16336485703186408033,1.3086037871388722636 ] 
dist 168=[-.13162710922641902129,1.2968218666492587973 ] 
dist 169=[-.42603964085087795665,1.1683168927414640522 ] 
dist 170=[-.6220092245677350811 ,1.2121425935817572025 ] 
dist 171=[-.78345297211007221855,1.2467776496920035720 ] 
dist 172=[-.94005490916774617618,1.2779193697861963108 ] 
dist 173=[-1.0816133618172980377 ,1.3044016432333986794 ] 
dist 174=[-1.1830109484037444778 ,1.3204301570564159191 ] 
dist 175=[-1.2744417192137616548 ,1.3318269993196343652 ] 
dist 176=[-1.3762180872465866342 ,1.3398066113687810676 ] 
dist 177=[-1.4683074601216255601 ,1.3438151679843397095 ] 
dist 178=[-1.5210721291511956568 ,1.3424144922674314133 ] 
dist 179=[-1.5551513323325319464 ,1.3322107803314959443 ] 
dist 180=[-1.5726558536619027480 ,1.3254920860259553868 ] 
dist 181=[-1.5819460243309025322 ,1.2771640654846745469 ] 
dist 182=[-1.5832372531507556368 ,1.2634944902232467922 ] 
dist 183=[-1.5789174521174308364 ,1.2415367431323061822 ] 
dist 184=[-1.5748635203994456956 ,1.2336143581789997662 ] 
dist 185=[-1.5886978137793033304 ,1.0268392134291583113 ] 
dist 186=[-1.6295624695826954123 ,.99636257540522774041] 
dist 187=[-1.6522111696089094354 ,.93045799130081968283] 
dist 188=[-1.6570983414658378992 ,.91081348177537871881] 
dist 189=[-1.6482147397489274965 ,.82586365397422134497] 
dist 190=[-1.6449180104562086955 ,.80853958296541555428] 
dist 191=[-1.6420503368471275974 ,.76132372426205159299] 
dist 192=[-1.6390372069302409075 ,.81913150609290072835] 
dist 193=[-1.2306738034983843409 ,.91228004178637568578] 
dist 194=[-1.1921513058311116461 ,.97702190829540209741] 
dist 195=[-1.0950669845165918371 ,1.0333755815380330412 ] 
dist 196=[-1.0774671054661317811 ,1.0930425256738388590 ] 
dist 197=[-.91879696497387741097,1.1502986121457982933 ] 
dist 198=[-.88707233326266893537,1.1981846425039716706 ] 
dist 199=[-.84422826271780828081,1.2450198773983384906 ] 
dist 200=[-.82992288146154536263,1.3073031979686439952 ] 
dist 201=[-.75614144029706443832,1.3654421364474658148 ] 
dist 202=[-.90540169142595856307,1.3968898443496781334 ] 
dist 203=[-1.0270069137921354317 ,1.4148197374994880642 ] 
dist 204=[-1.1427026420302660928 ,1.4190006591468082738 ] 
dist 205=[-1.2457732026396544237 ,1.4172220847533763909 ] 
dist 206=[-1.3169852402693189839 ,1.4124947572544382609 ] 
dist 207=[-1.3785133196286823315 ,1.4023919818432269947 ] 
dist 208=[-1.4429302669374647440 ,1.3967508400228327432 ] 
dist 209=[-1.4988358048637608915 ,1.2419004189328806570 ] 
dist 210=[-1.5263907198307007234 ,1.2170503619133048183 ] 
dist 211=[-1.5402816963483731834 ,1.1633658619243097922 ] 
dist 212=[-1.5416484908731656590 ,1.1465918246291812594 ] 
dist 213=[-1.5216298577566509202 ,1.1279401934296844572 ] 
dist 214=[-1.5137612955498115382 ,1.1909464454238838363 ] 
dist 215=[-1.5066112541679197918 ,1.2474166151368021413 ] 
dist 216=[-1.4991173811002665266 ,1.3097803999481969505 ] 
dist 217=[.27508289746091604797,1.3653052186694977960 ] 
dist 218=[.20826384724599428101,1.3944767486265055602 ] 
dist 219=[.09288869978130498474,1.4099531071542071420 ] 
dist 220=[-.03227643555610251073,1.4129971214643930229 ] 
dist 221=[-.154205796692401433  ,1.4062792605014186426 ] 
dist 222=[-.25666491908097620375,1.4002433785907471644 ] 
dist 223=[-.36452115900969781679,1.3919505154380454094 ] 
dist 224=[-.50799321735095625102,1.3865806296595142747 ] 
dist 225=[-.69445570520732517659,-.20242658628857150575] 
dist 226=[-.83252958551988347669,-.21189154522203473485] 
dist 227=[-.94579946618247599424,-.20731418667823436147] 
dist 228=[-1.0548985628522148006 ,-.18236579353770407452] 
dist 229=[-1.1530213553009716648 ,-.14620867938223597656] 
dist 230=[-1.2224785801544388373 ,-.09689028743590967771] 
dist 231=[-1.2842729182727126012 ,-.02845651798954147155] 
dist 232=[-1.3518098568184124359 ,.08400253138014554176] 
dist 233=[-1.4115343087514195815 ,.19992083854528800651] 
dist 234=[-1.4421445751932708179 ,.28216236463510596639] 
dist 235=[-1.4583883225483395860 ,.35552016130169105645] 
dist 236=[-1.4749032382051801124 ,.43597653676868472216] 
dist 237=[-1.4860085969230433037 ,.51487750175884046368] 
dist 238=[-1.4883044924688771160 ,.58202580566659626364] 
dist 239=[-1.4622918666107263832 ,.65345225857515758416] 
dist 240=[-1.4313326549056202074 ,.74942880808420631759] 
dist 241=[-1.2075306522231352076 ,.84430190475073411296] 
dist 242=[-1.1773144572516279849 ,.91132313995624785595] 
dist 243=[-1.1001879005304557488 ,.97079876917925846173] 
dist 244=[-1.0849587422847377609 ,1.0355519009726836661 ] 
dist 245=[-.95361570344442087823,1.0987629278883148045 ] 
dist 246=[-.92657405557226338539,1.1520821152212907736 ] 
dist 247=[-.88836329294343501653,1.2083803892069354920 ] 
dist 248=[-.87586142126731245894,1.2834807732462559743 ] 
dist 249=[-.607294890528222136  ,1.3543988835100861769 ] 
dist 250=[-.57130176896156940133,1.3940029788048369859 ] 
dist 251=[-.49204020812881576886,1.4182554569090636542 ] 
dist 252=[-.47189750039881931877,1.4278973832252043630 ] 
dist 253=[-.37690043729558144056,1.4309132802738594521 ] 
dist 254=[-.35908048570301611242,1.4287186435172958906 ] 
dist 255=[-.31741021373023663558,1.3975115953276604679 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 2, 2, 0, 1] 
dist 0=[42.813482764668673845  ,42.813482764668673845  ] 
dist 1=[42.596820704237154558  ,42.984270043366929854  ] 
dist 2=[41.878511015706558126  ,43.519212240536269229  ] 
dist 3=[40.745859630003877606  ,44.078844777702887310  ] 
dist 4=[38.874327351108126064  ,44.348280999246627718  ] 
dist 5=[36.940416171377089482  ,44.478269102859667690  ] 
dist 6=[35.558560150902111655  ,44.483801095955422461  ] 
dist 7=[34.312793975083725354  ,43.925443483810461362  ] 
dist 8=[32.922211395885839483  ,43.778870423691302628  ] 
dist 9=[31.539738412782997504  ,43.558186971207894791  ] 
dist 10=[30.326161343715341899  ,43.465167831204741651  ] 
dist 11=[28.999578672762082458  ,43.111047830424196358  ] 
dist 12=[27.165375429078183054  ,42.989340377762882810  ] 
dist 13=[25.317828478840231650  ,42.692374224461886865  ] 
dist 14=[23.937750699250352618  ,42.570655851645350887  ] 
dist 15=[22.630047050315101801  ,32.247199602062074004  ] 
dist 16=[21.071348924429164851  ,31.316548654804068374  ] 
dist 17=[19.461534771209125457  ,29.070408357632207555  ] 
dist 18=[17.949281755705660344  ,28.713437738817410879  ] 
dist 19=[16.210881413715078247  ,25.419789242454505371  ] 
dist 20=[13.696875734965542895  ,24.797048243447657446  ] 
dist 21=[11.205279567115153759  ,24.007701971829703865  ] 
dist 22=[9.5563127366952154045 ,23.773339000002609154  ] 
dist 23=[8.1997007038001135314 ,18.416504560679087124  ] 
dist 24=[6.8765203297783638134 ,17.727437072846082244  ] 
dist 25=[5.6666190480922891059 ,16.342354141555705463  ] 
dist 26=[4.7626346446425533578 ,15.910218642470984559  ] 
dist 27=[3.1960664932756551249 ,14.464610185895176599  ] 
dist 28=[1.5268987351888824869 ,14.180375404343157419  ] 
dist 29=[-.33529217389271122345,13.591964790595137465  ] 
dist 30=[-2.9615613182364753714 ,13.434082378020493792  ] 
dist 31=[-5.5297068483312871198 ,4.9490776466690849938 ] 
dist 32=[-7.1597977124361975603 ,4.1931217605052282266 ] 
dist 33=[-8.4244640600267996747 ,2.4899215327124092570 ] 
dist 34=[-9.5321777833250538742 ,2.1959699716812663493 ] 
dist 35=[-10.463243639009093521  ,.12990780831203365386] 
dist 36=[-11.022085018817440652  ,-.13426801791390550632] 
dist 37=[-11.420235449742937989  ,-.84263343838689088646] 
dist 38=[-11.709548907333915425  ,-.97344044419748113747] 
dist 39=[-11.930431274714784899  ,-1.2408036719454155644 ] 
dist 40=[-12.055056005346475297  ,-1.2632651619140736567 ] 
dist 41=[-12.136070761462945785  ,-1.2856603431094767520 ] 
dist 42=[-12.182093043740770307  ,-1.2558820229094689478 ] 
dist 43=[-12.204407834201748909  ,-1.1936771379791451952 ] 
dist 44=[-12.190398401846817882  ,-1.0728569056317552363 ] 
dist 45=[-12.147907027079192658  ,-.93903367716540693464] 
dist 46=[-12.111781137719319805  ,-.82478644584185533255] 
dist 47=[-6.0974444874968297060 ,-.70380546620248458692] 
dist 48=[-5.7495317841468069366 ,-.54284119721498710409] 
dist 49=[-4.9003787997496488036 ,-.3689524877261876118 ] 
dist 50=[-4.7744656192024532467 ,-.19624105894546013291] 
dist 51=[-3.5284992113975090524 ,.00867274755267822047] 
dist 52=[-3.2988090750078135810 ,.31125983113236359715] 
dist 53=[-3.0205498341767426452 ,1.0219410428195724548 ] 
dist 54=[-2.9614707794829678286 ,1.9300218548061600897 ] 
dist 55=[-1.0812080759218492852 ,2.7951419910393533460 ] 
dist 56=[-.85431306198560546546,3.3549986241062527375 ] 
dist 57=[-.37164729009087868961,3.7993617575895203327 ] 
dist 58=[-.26635154374737622446,4.2034987489991028696 ] 
dist 59=[.21322772508351541653,4.5521757624242383416 ] 
dist 60=[.29716176257804988149,4.7752346127505882154 ] 
dist 61=[.44976955087717973192,4.9500809106739004340 ] 
dist 62=[.4803269105139025929 ,5.1065024696424269149 ] 
dist 63=[1.3112466032247188123 ,5.2321609700902431931 ] 
dist 64=[1.2390074962283659265 ,5.2841933884946221404 ] 
dist 65=[1.1474570511939032572 ,5.3037719741187414681 ] 
dist 66=[1.0368900324197152400 ,5.2994853847347199096 ] 
dist 67=[.89123584450814394202,5.1894303346246405575 ] 
dist 68=[.65962880484158807929,5.1511037833356683793 ] 
dist 69=[.42394996197197597594,5.1144613745572830900 ] 
dist 70=[.262039004010187222  ,5.0890128792556535589 ] 
dist 71=[.12315180252086900978,4.5097210918117594935 ] 
dist 72=[-.02063385045021507330,4.4696526471792980956 ] 
dist 73=[-.15656899224488416293,4.3737337412348916506 ] 
dist 74=[-.26412158844694438379,4.3593706595845053006 ] 
dist 75=[-.37148309368281634782,4.3790359779219836490 ] 
dist 76=[-.506651801962355834  ,4.3780412813843004218 ] 
dist 77=[-.63602845899796241476,4.3544814870595357842 ] 
dist 78=[-1.0095092171041263335 ,4.3376401079513883347 ] 
dist 79=[-1.7760223963738425593 ,2.3616123015274182824 ] 
dist 80=[-2.3219886228827087130 ,2.1989822544089836514 ] 
dist 81=[-2.7953785872069748852 ,1.8106748118030797617 ] 
dist 82=[-3.2432704354261342199 ,1.7456425353647603579 ] 
dist 83=[-3.6409143608789934159 ,1.1927657570222788035 ] 
dist 84=[-3.9137359376242659667 ,1.0896081752013422032 ] 
dist 85=[-4.1476458689381264661 ,.94428271970620073946] 
dist 86=[-4.3899883815190174987 ,.90143389169830313937] 
dist 87=[-4.6041769585104689880 ,.09343423128255307609] 
dist 88=[-4.7256961653834710790 ,-.00911694659076339590] 
dist 89=[-4.8027885487116380240 ,-.2385902297327936553 ] 
dist 90=[-4.8395909709039196996 ,-.28277119617350045608] 
dist 91=[-4.8528688676380877369 ,-.22005567351112529692] 
dist 92=[-4.8470380895748393732 ,-.1202752316050665396 ] 
dist 93=[-4.8094432593418597023 ,-.01487226579935179061] 
dist 94=[-4.7836104646183667029 ,.07063084578002013269] 
dist 95=[-3.7956598462988444930 ,.28386908848025756274] 
dist 96=[-3.6984643263390279660 ,.84051985672398820483] 
dist 97=[-3.4496335783604864455 ,1.3075625290559220156 ] 
dist 98=[-3.4032816334149954215 ,1.7745548907396528727 ] 
dist 99=[-2.9814954939951267301 ,2.2059035268185650392 ] 
dist 100=[-2.8956692116206916111 ,2.5306846047379629324 ] 
dist 101=[-2.7804518474695559586 ,2.8397064474289594528 ] 
dist 102=[-2.7410273758789245935 ,3.2081653624912577803 ] 
dist 103=[-1.8941329329081375757 ,3.5511117351090631662 ] 
dist 104=[-1.7816544531508807980 ,3.7583056601543617325 ] 
dist 105=[-1.5380281393688651426 ,3.9058305572517770220 ] 
dist 106=[-1.4737090687900340749 ,4.0106108879287891910 ] 
dist 107=[-1.1955283615864043944 ,4.0868022102456340994 ] 
dist 108=[-1.1732630781616610438 ,4.1202011556349511840 ] 
dist 109=[-1.1627791081886936358 ,4.1286690621981043991 ] 
dist 110=[-1.1563449909066376530 ,4.1256727016315635214 ] 
dist 111=[-1.1498016814839855984 ,2.3655034401629508312 ] 
dist 112=[-1.1443354942494317408 ,2.3649379905662396615 ] 
dist 113=[-1.1327664963139335604 ,2.3632626374931238366 ] 
dist 114=[-1.1260902041978875199 ,2.3600609811404271796 ] 
dist 115=[-1.1154086979926003154 ,2.3551601502616356996 ] 
dist 116=[-1.1105212835085589958 ,2.3467292756882205645 ] 
dist 117=[.15748237360570854529,2.0659999219545731606 ] 
dist 118=[-.04795399898034375857,2.1669638548810274092 ] 
dist 119=[-.25827606595331249458,2.2578230745135433774 ] 
dist 120=[-.41846763520402125353,2.3076775280482616564 ] 
dist 121=[-.57258988036254590933,2.3371636364143302375 ] 
dist 122=[-.75870253401276352189,2.3467043775320454769 ] 
dist 123=[-.95113836768151868457,2.3462110020692625161 ] 
dist 124=[-1.1305074972778009014 ,2.3405853946331802403 ] 
dist 125=[-1.3346866315252198386 ,2.3210733755063169852 ] 
dist 126=[-1.6261586851260209638 ,2.3094561120753154216 ] 
dist 127=[-1.9110122305823660444 ,-.30888659675370436731] 
dist 128=[-2.0887769806676885741 ,-.29765533574761079824] 
dist 129=[-2.2221739138733807578 ,-.2739274212396256289 ] 
dist 130=[-2.3299362909945382908 ,-.23360517774014555815] 
dist 131=[-2.4147992871183833771 ,-.17340443999685424407] 
dist 132=[-2.4567951938062963726 ,-.07033557906594372844] 
dist 133=[-2.4771146814268446909 ,.03727271502663530418] 
dist 134=[-2.4791801173524369689 ,.11559237935639720646] 
dist 135=[-2.3820582828734338409 ,.18745814887242631451] 
dist 136=[-2.4327540343360607600 ,.26930912451387424128] 
dist 137=[-2.4798833464696530143 ,.35132147405608504335] 
dist 138=[-2.5102140259847782129 ,.42383270854713185684] 
dist 139=[-2.5274311953903551984 ,.50328179487887724666] 
dist 140=[-2.5290271906388111310 ,.61298714161467537654] 
dist 141=[-2.5112307660924041869 ,.72273835892949009235] 
dist 142=[-2.5054642365915923818 ,.80237143648529379247] 
dist 143=[-1.8927116813417866227 ,.87520680640284071324] 
dist 144=[-1.8387768082596534126 ,.95782706984985711491] 
dist 145=[-1.7033458395532758519 ,1.0404359332429108949 ] 
dist 146=[-1.6769205541116284200 ,1.1132269633603494825 ] 
dist 147=[-1.4552452794089057545 ,1.2958097741350420171 ] 
dist 148=[-1.4104097928512105682 ,1.4587798742080824324 ] 
dist 149=[-1.3451933881621833394 ,1.6096992069195163269 ] 
dist 150=[-1.3248950374807265990 ,1.7836816823501243827 ] 
dist 151=[-.90123157047971393952,1.9433722541480496682 ] 
dist 152=[-.84481998829228446141,2.0372457363589215134 ] 
dist 153=[-.71874810669772634658,2.1009020648960924686 ] 
dist 154=[-.68925522843530265752,2.1399749172506587859 ] 
dist 155=[-.53378280647583041031,2.1658921466419266706 ] 
dist 156=[-.50494269443910548571,2.1770410492557402242 ] 
dist 157=[-.44264135403233483053,2.1795145690332718330 ] 
dist 158=[-.4256978907407565135 ,2.1751038705808223861 ] 
dist 159=[1.0434808575203034989 ,1.5098323912260163842 ] 
dist 160=[.90007695495060049696,1.5322471887425336453 ] 
dist 161=[.74137263425917940858,1.5459453764940525850 ] 
dist 162=[.57767555345275864668,1.5487928665348470896 ] 
dist 163=[.37890847098240483357,1.5453924216501254458 ] 
dist 164=[.08022068229794783580,1.5413058100070184072 ] 
dist 165=[-.2188712124962183757 ,1.2039435330491875225 ] 
dist 166=[-.41925094417424116643,1.1912897464565785147 ] 
dist 167=[-.5857541509947397842 ,1.0646070156247495070 ] 
dist 168=[-.7496253321802566522 ,1.0466237863518914245 ] 
dist 169=[-.89931506865692670342,.89452153232178970677] 
dist 170=[-1.0092114601681603516 ,.86400814992349871982] 
dist 171=[-1.1110338632047250891 ,.82006136326977069941] 
dist 172=[-1.2284941747019516367 ,.80634795071851296379] 
dist 173=[-1.3363494101162456874 ,.57849899984181890001] 
dist 174=[-1.3998328200239340215 ,.56842199199694350982] 
dist 175=[-1.4429808588411168874 ,.4005082031528823522 ] 
dist 176=[-1.4696685837310184159 ,.38124552931661153112] 
dist 177=[-1.4874517166475554698 ,.27805049885308919168] 
dist 178=[-1.4950566877567122074 ,.25905336219526936955] 
dist 179=[-1.4966591192259220806 ,.21844711007543310598] 
dist 180=[-1.4937843347101203319 ,.20729823409388993039] 
dist 181=[-1.3614906296887301124 ,.08133875836868543269] 
dist 182=[-1.4287040123264846707 ,.16929919707875380018] 
dist 183=[-1.5110554284888228535 ,.24809916019643658435] 
dist 184=[-1.5567208511678667435 ,.33502116610822960571] 
dist 185=[-1.5842722277109820061 ,.42052950423360861485] 
dist 186=[-1.5943184895736820203 ,.49368586689582258964] 
dist 187=[-1.5970634688827934154 ,.57181696927004870044] 
dist 188=[-1.5954717761659667145 ,.67717981064801442747] 
dist 189=[-1.5904000616956656412 ,.78145967756003782252] 
dist 190=[-1.5850674188526939754 ,.85526735997345053152] 
dist 191=[-1.2061298897891959248 ,.92089370302134704605] 
dist 192=[-1.1911124119231848710 ,.99251777342873401276] 
dist 193=[-1.1289529166671343906 ,1.0625165677348834681 ] 
dist 194=[-1.1139823010826259646 ,1.1216545402581495111 ] 
dist 195=[-1.0776898623476423969 ,1.1841615944250449706 ] 
dist 196=[-1.0648388893449813794 ,1.2676048626495547601 ] 
dist 197=[-.66786865627006932393,1.3464388107430177854 ] 
dist 198=[-.79429861248520039146,1.3905482486450945846 ] 
dist 199=[-.89836985406305084222,1.4176586254033749629 ] 
dist 200=[-.99917703797385141138,1.4286454752501538297 ] 
dist 201=[-1.0902007390169578853 ,1.4327568030686040762 ] 
dist 202=[-1.1552204056228416589 ,1.4324258832728475111 ] 
dist 203=[-1.2136594279392480558 ,1.4161189393476662996 ] 
dist 204=[-1.2784153255542126332 ,1.4237832394498121912 ] 
dist 205=[-1.3361360195237456839 ,1.4274325203089732509 ] 
dist 206=[-1.3664934227072232442 ,1.4265660571518125509 ] 
dist 207=[-1.3826213387452703484 ,1.3599650859334768377 ] 
dist 208=[-1.3860206111422602969 ,1.3817818123661657892 ] 
dist 209=[-1.3790871188794524032 ,1.3956722920952381795 ] 
dist 210=[-1.3737406403955611801 ,1.4026511363459259336 ] 
dist 211=[-1.3667175019721440333 ,1.4059064943843394952 ] 
dist 212=[-1.3611098458501468785 ,1.4049346120399048245 ] 
dist 213=[-1.1719056365566976683 ,.92760669248624352299] 
dist 214=[-1.1452639385287905386 ,.91548151172259795256] 
dist 215=[-1.0760849939918583408 ,.64885685567886755727] 
dist 216=[-1.0622897186834376626 ,.61292922091359640141] 
dist 217=[-.93990984528920215818,.53432481657275339073] 
dist 218=[-.91432320952186977326,.51345029436702758845] 
dist 219=[-.87914819997044206164,.42031630816041568219] 
dist 220=[-.84409556051154021225,.40270150127457908055] 
dist 221=[-.76993184764411382243,.3598463568171654274 ] 
dist 222=[-.8430138262777078486 ,.35189597923723333828] 
dist 223=[-.90801500637831128868,-.10218882472559568184] 
dist 224=[-.97901156689107780159,-.02286956875031470231] 
dist 225=[-1.0484557549542095273 ,.06814394694591488993] 
dist 226=[-1.1072605276905093235 ,.16655048434254417891] 
dist 227=[-1.1695542837478170529 ,.28925168010543184104] 
dist 228=[-1.2529249092981677178 ,.47723758123893642256] 
dist 229=[-1.3318894377111296801 ,.66591748478855376708] 
dist 230=[-1.3765959622950329025 ,.79138892202917939259] 
dist 231=[-1.4047806845918951375 ,.89461891500537774409] 
dist 232=[-1.4177974088410481209 ,.99452222350550553472] 
dist 233=[-1.4237898281356253904 ,1.0846705045332842235 ] 
dist 234=[-1.4239368061640687746 ,1.1489634179099552201 ] 
dist 235=[-1.3976772723547135974 ,1.2066471383877653010 ] 
dist 236=[-1.3785487085813694543 ,1.2704150317052513393 ] 
dist 237=[-1.2216279670604981104 ,1.3271813987886859541 ] 
dist 238=[-1.1967638869190428051 ,1.3569185882670104594 ] 
dist 239=[-1.1467933986992766830 ,1.3726853974849525058 ] 
dist 240=[-1.1319096449204010034 ,1.3759174328587898528 ] 
dist 241=[-1.0691289286806501617 ,1.3683011556705029176 ] 
dist 242=[-1.0545176988926891477 ,1.3630055225157786282 ] 
dist 243=[-1.0170881828077660223 ,1.3562946555613956180 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 2, 2, 1, 2] 
dist 0=[3.4137595599194024791 ,3.4137595599194024791 ] 
dist 1=[2.0532530846818479789 ,4.5322262928916408322 ] 
dist 2=[0                     ,5.6185293268697458823 ] 
dist 3=[4.3139792072758168338 ,6.6058297501525381680 ] 
dist 4=[5.6094356676496018622 ,7.3288090424965716201 ] 
dist 5=[6.5376843487452850164 ,7.9994317104932380330 ] 
dist 6=[6.8775699602580555217 ,8.7776480241151230270 ] 
dist 7=[7.3311260125944187896 ,9.5020575277499856848 ] 
dist 8=[7.6686801851668954312 ,9.9577219327124403081 ] 
dist 9=[9.4374266307144150714 ,10.305665633581762406  ] 
dist 10=[9.6698886800264752754 ,10.599647961627860988  ] 
dist 11=[10.123570875403501738  ,10.837883531840498682  ] 
dist 12=[10.219185813025364520  ,10.963079943208730979  ] 
dist 13=[10.475002549529912013  ,11.029954012916499428  ] 
dist 14=[10.324356309393892569  ,11.042329389806842513  ] 
dist 15=[10.075950797506165090  ,11.014105474578344363  ] 
dist 16=[9.8542739508738668639 ,10.976135204733101691  ] 
dist 17=[9.6101265632311206798 ,9.8762939157471247366 ] 
dist 18=[9.2717742605721923533 ,9.7719745170507638803 ] 
dist 19=[8.8985962651234393588 ,9.5558815518657261701 ] 
dist 20=[8.5152695304886246029 ,9.4922056531670870251 ] 
dist 21=[8.0505527264957466248 ,9.2709875075270236048 ] 
dist 22=[7.3522460929750959502 ,9.2368861975617101151 ] 
dist 23=[6.6264256746775755611 ,9.0165999313623101953 ] 
dist 24=[6.0517567143470472342 ,8.9765497715715187938 ] 
dist 25=[5.4764508263134600068 ,8.7580505768438054250 ] 
dist 26=[4.7479572269559463139 ,8.7271683796452698425 ] 
dist 27=[3.9743058749008756243 ,8.6171154368281075129 ] 
dist 28=[3.2185406965026584077 ,8.5840288288805134473 ] 
dist 29=[2.3287968646742940817 ,8.5381288559839979710 ] 
dist 30=[1.0198669107175790290 ,8.5196268770344179390 ] 
dist 31=[-.279697320645153782  ,8.4775859525098009949 ] 
dist 32=[-1.1320749908567020719 ,8.3799962256322844744 ] 
dist 33=[-1.8228596963604064616 ,-.57247706289453554123] 
dist 34=[-2.4769743366816098969 ,-.99975474001301456826] 
dist 35=[-3.0602287182154419931 ,-1.9371354338932524138 ] 
dist 36=[-3.4680147970180172430 ,-2.0917761274405160542 ] 
dist 37=[-3.8270219716941670993 ,-3.1054310673922809269 ] 
dist 38=[-4.2155500441158104133 ,-3.2642716105168137954 ] 
dist 39=[-4.5648291136217216130 ,-3.5605226741527775272 ] 
dist 40=[-4.7670659535089433835 ,-3.6181313861470321956 ] 
dist 41=[-4.9014615318584885013 ,-3.6882291113858155721 ] 
dist 42=[-4.9796555832572889889 ,-3.4861265666607313371 ] 
dist 43=[-5.0700312987603921070 ,-3.2144779839239019242 ] 
dist 44=[-5.1402649863733433619 ,-2.8686532676962431809 ] 
dist 45=[-5.1794869705207120067 ,-2.4028707583869272722 ] 
dist 46=[-5.1802777759288641954 ,-1.6524212492796827997 ] 
dist 47=[-5.1621101169000157817 ,-.88710866155517280562] 
dist 48=[-5.1424853519754912000 ,-.36195972102588237557] 
dist 49=[-3.7931528624607895193 ,.08739183561053462826] 
dist 50=[-3.6524958272389553816 ,.55029042754729193656] 
dist 51=[-3.2943570611034105649 ,.98610278022897331382] 
dist 52=[-3.2394762085112155613 ,1.3273938627532465799 ] 
dist 53=[-2.6579233984719788075 ,1.6646436974228513621 ] 
dist 54=[-2.5452429072436093237 ,2.0843573429943956069 ] 
dist 55=[-2.4156019938285803953 ,2.4835314971561700039 ] 
dist 56=[-2.3829821498620744635 ,2.7388211896863339898 ] 
dist 57=[-1.3193767403642943880 ,2.9375211829974755948 ] 
dist 58=[-1.1865716987736318075 ,3.1108557869873960361 ] 
dist 59=[-.90881718906965240952,3.2545561553912099669 ] 
dist 60=[-.83605779118956511346,3.3349888012579747783 ] 
dist 61=[-.56766020610491365943,3.3844542744696308353 ] 
dist 62=[-.54010281517677845701,3.4045648085642735598 ] 
dist 63=[-.42054645136878804672,3.4087385338890560711 ] 
dist 64=[-.39999933810985201182,3.3945948167930617806 ] 
dist 65=[.98054103698447875796,1.3584910063984996407 ] 
dist 66=[1.0959485959882646276 ,1.5359047020362312382 ] 
dist 67=[1.3443504471999378693 ,1.6911559627185534711 ] 
dist 68=[1.3869711024821994995 ,1.7940944371640418514 ] 
dist 69=[1.6335610243411241370 ,1.8786706119928590173 ] 
dist 70=[1.6719558074070034174 ,1.9606207080562678351 ] 
dist 71=[1.7342891495256633425 ,2.0310865107573744601 ] 
dist 72=[1.7276386125443253516 ,2.0698074690718456633 ] 
dist 73=[1.6713841067248117456 ,2.0928470614872105453 ] 
dist 74=[1.5636353890885415473 ,2.1006823911733713996 ] 
dist 75=[1.4311023141113278679 ,2.0995794486670705652 ] 
dist 76=[1.2759023586122136946 ,2.0954971029716979200 ] 
dist 77=[1.0743645750997193763 ,2.0723976968038083068 ] 
dist 78=[.75685595334346524716,2.0640588375246989125 ] 
dist 79=[.43473575132436834108,2.0398713435070587433 ] 
dist 80=[.21478096614453724129,2.0302175137762716133 ] 
dist 81=[.02747568764534494053,1.3532725476119962479 ] 
dist 82=[-.16433518101137749707,1.2867495737509509728 ] 
dist 83=[-.34446876161165410658,1.1200622780793311886 ] 
dist 84=[-.4851733135679709441 ,1.0960820039985334721 ] 
dist 85=[-.62403669151173088066,.83526662216552063119] 
dist 86=[-.79683744293619292893,.78575070762693804786] 
dist 87=[-.96152922766603274941,.73147295087151918529] 
dist 88=[-1.0680311031378842481 ,.72171024111276599824] 
dist 89=[-1.1524184286361686563 ,.26438670370821157781] 
dist 90=[-1.2288400177369518326 ,.20850543788589042128] 
dist 91=[-1.2944517933324242917 ,.09403137783518348930] 
dist 92=[-1.3356985575938370140 ,.06485000491872851020] 
dist 93=[-1.3671230374304799849 ,-.03785082503950583047] 
dist 94=[-1.3935494676028295585 ,-.0587198878520507911 ] 
dist 95=[-1.4130125293458382146 ,-.08527267460405615935] 
dist 96=[-1.4175502963495954408 ,-.08962238840126970441] 
dist 97=[-1.4152428181310151707 ,-.68134981478610709623] 
dist 98=[-1.4146087097280618410 ,-.72851923938938657906] 
dist 99=[-1.3756901342748711973 ,-.82401317640910582707] 
dist 100=[-1.3738192221911656504 ,-.84478029061246675278] 
dist 101=[-1.3380196940036660487 ,-.91584829601238272143] 
dist 102=[-1.3350909934919297144 ,-.92750097844860758881] 
dist 103=[-1.2830744343503511966 ,-.92239667124620645474] 
dist 104=[-1.2798689920488834552 ,-.88141435593003015389] 
dist 105=[-1.2132600623882135327 ,-.82820315020977822899] 
dist 106=[-1.2133107508146125843 ,-.7443332015213377445 ] 
dist 107=[-1.1927925648573770137 ,-.6470678440358502626 ] 
dist 108=[-1.1855100455716087117 ,-.52698332313026061701] 
dist 109=[-1.1793414249506910188 ,-.38322760500152681147] 
dist 110=[-1.1737539726750110826 ,-.17077215243842384141] 
dist 111=[-1.1356047874103187723 ,.04173599708156600325] 
dist 112=[-1.1341605837104608741 ,.18570510347227371993] 
dist 113=[-.93283768634183738226,.30717448295526920683] 
dist 114=[-.90783575453117627924,.42986097484652212441] 
dist 115=[-.84103424167451495104,.54408812891102306356] 
dist 116=[-.83144041984515428114,.63178786179008494113] 
dist 117=[-.7107525366174271372 ,.7169472977529704393 ] 
dist 118=[-.68627064357931250498,.82103646312505326047] 
dist 119=[-.66285181114091412774,.91936131736385586399] 
dist 120=[-.65838147637187950877,.9815094163950685079 ] 
dist 121=[-.38642918441316968997,1.0291340559705496684 ] 
dist 122=[-.35191269905082415305,1.0694777941332055302 ] 
dist 123=[-.2839954082664700308 ,1.1021248254705773942 ] 
dist 124=[-.26670499984341938028,1.1190237154837781271 ] 
dist 125=[-.20725800516427963695,1.1276608537223627417 ] 
dist 126=[-.19358403410130928265,1.1284253467223801849 ] 
dist 127=[-.17907447252296240738,1.1126071246850731789 ] 
dist 128=[-.17626711153615526248,1.1132269238710754441 ] 
dist 129=[-.10058641118872872385,.04697928007715610880] 
dist 130=[-.18486719938616389467,-.00260517596752337979] 
dist 131=[-.26336650278166876039,-.11360375020348201373] 
dist 132=[-.32357978346750891007,-.13320193312136269213] 
dist 133=[-.38195571419736978795,-.26233601147697610531] 
dist 134=[-.45312518419888604187,-.28377773624775321612] 
dist 135=[-.52018990409694268107,-.32389823605331777697] 
dist 136=[-.56218336182008066365,-.3323873198953221694 ] 
dist 137=[-.59388223535869565345,-.38918689846772041047] 
dist 138=[-.61985703276644176697,-.37694144963381224556] 
dist 139=[-.64020265169736474932,-.35647943866235782203] 
dist 140=[-.64943486353783782797,-.32571415099075357214] 
dist 141=[-.66291726562947857577,-.28152390622232682904] 
dist 142=[-.67046311551636096462,-.20748140624541402827] 
dist 143=[-.67341155034288093085,-.1308153403129870215 ] 
dist 144=[-.67258947373329996791,-.07615277861442297502] 
dist 145=[-.64187921526698508433,-.02715402853057193792] 
dist 146=[-.63586139643794943409,.02691119852560879300] 
dist 147=[-.61839570224620565444,.0800873362871056457 ] 
dist 148=[-.61344906216946727976,.12554029516018293899] 
dist 149=[-.57423161905901957932,.17404251271634213076] 
dist 150=[-.56505676233315112874,.2393924022731580675 ] 
dist 151=[-.55097180196947990412,.30404903116834935735] 
dist 152=[-.54626739806783334497,.34978616463469291935] 
dist 153=[-.4353272609290643835 ,.3904339654433412947 ] 
dist 154=[-.41970953640243231601,.43477999930721503176] 
dist 155=[-.38514517124120979714,.47813176977674404081] 
dist 156=[-.37523571230132477075,.5148137330429275161 ] 
dist 157=[-.33166241803951138374,.5536582007303930611 ] 
dist 158=[-.3250600166651249027 ,.60564631143960037535] 
dist 159=[-.30200553938805212608,.65502982237238314969] 
dist 160=[-.29710109205399377218,.68347862115211914065] 
dist 161=[.28953857045295343856,.70206456990836949881] 
dist 162=[.32810342398896337895,.71207756417485027248] 
dist 163=[.4108242522204759793 ,.7181570403677607373 ] 
dist 164=[.42612614452691993624,.72103988458864379539] 
dist 165=[.50751402135794014993,.72213962274759226214] 
dist 166=[.52068632819708149737,.72109749309047672743] 
dist 167=[.54116319010979313894,.71568016924786497208] 
dist 168=[.54336915929656780896,.71517421703892217253] 
dist 169=[.52290260214188849473,.70931574590238816763] 
dist 170=[.47325176031409335381,.71235210036484233339] 
dist 171=[.4083804078155077324 ,.71231087911520390166] 
dist 172=[.34099972443255057997,.71024630572026952954] 
dist 173=[.25884395795263090565,.70588595075957768225] 
dist 174=[.13499446649846968115,.70326780468451123446] 
dist 175=[.01060324579261944716,.69800785470208241981] 
dist 176=[-.07371493186293948244,.69558111668568683186] 
dist 177=[-.14486072222864306586,.52673336491934687449] 
dist 178=[-.21667125544667854471,.50811492567929612151] 
dist 179=[-.28344538787375811379,.45992627296777605448] 
dist 180=[-.33448675307599632001,.45277150560650733617] 
dist 181=[-.38379685824382795878,.37133081768367447141] 
dist 182=[-.44365895080727468189,.3552630042820176749 ] 
dist 183=[-.49991144230537355703,.33821880666113946083] 
dist 184=[-.5348126017994097484 ,.33443441051311444468] 
dist 185=[-.56076327189251811403,.17136761030037565219] 
dist 186=[-.58128798732118256821,.150928127476657588  ] 
dist 187=[-.59697793721583301552,.10930472690746993944] 
dist 188=[-.60363143401116601984,.09855354019293891315] 
dist 189=[-.60630761532591253062,.06014161567716022115] 
dist 190=[-.60612129838496464798,.05209367736960648176] 
dist 191=[-.60361362471498791703,.04039864261399861173] 
dist 192=[-.60359512965263822271,.0371413849005341461 ] 
dist 193=[-.55290454562787584584,.04783867021157977265] 
dist 194=[-.55148730087920905285,.09022384562410456010] 
dist 195=[-.54287207541811018865,.13079050443485479875] 
dist 196=[-.54154580911762621278,.16370469667293565179] 
dist 197=[-.5092056787122203976 ,.19732089852290016208] 
dist 198=[-.50653230939152468621,.24069039239562592473] 
dist 199=[-.49607330151584214958,.28272655230798066184] 
dist 200=[-.49459847755297963887,.31102146264916740714] 
dist 201=[-.37340931503496070444,.33467447480971538322] 
dist 202=[-.35729181873011206044,.35818383759776349456] 
dist 203=[-.32665598001821955493,.37980958258465715673] 
dist 204=[-.31879209564103243945,.39594509856171051489] 
dist 205=[-.29828643789722960673,.41115638203661052412] 
dist 206=[-.29493327282303345774,.42909456591757497499] 
dist 207=[-.27843249181874414622,.4451714953154316968 ] 
dist 208=[-.27639063323738386058,.45295376786733998025] 
dist 209=[-.14454776965964880343,.45680783527553156102] 
dist 210=[-.17827524811413322786,.45720372785219577918] 
dist 211=[-.21041884028766944841,.45248899796225598111] 
dist 212=[-.23628005782896487204,.4523387232055456078 ] 
dist 213=[-.26249479437077550308,.4456803020854259413 ] 
dist 214=[-.29604856677823304698,.44346194642387532361] 
dist 215=[-.32843675374576468434,.45877376998856271001] 
dist 216=[-.3499988110402025454 ,.48451161789986738594] 
dist 217=[-.36775882523369494462,.50384522290207086296] 
dist 218=[-.38497132206104906793,.51950137536165826312] 
dist 219=[-.40051010808310114547,.53159769770772412782] 
dist 220=[-.41158915108264486148,.53672121950720194694] 
dist 221=[-.42151834962190306355,.53847878544258791649] 
dist 222=[-.43246631617342323055,.53779953134513712687] 
dist 223=[-.44167999641264476917,.53666660995338292429] 
dist 224=[-.444687021598956058  ,.53669791922960345747] 
dist 225=[-.44799735514135680483,-.06196963724667533357] 
dist 226=[-.45360788554679312242,-.08987716332693647973] 
dist 227=[-.45604517610003714686,-.1491705674109570228 ] 
dist 228=[-.45658214860124221715,-.16183286870065523308] 
dist 229=[-.44418311599445147124,-.21961903228528435903] 
dist 230=[-.44096139076276514408,-.22898718738851336415] 
dist 231=[-.43901984516000365889,-.23326895091402780383] 
dist 232=[-.43977817234783354953,-.22765730616533533575] 
dist 233=[-.45673725449820346614,-.21560687350920771785] 
dist 234=[-.47034386295334344066,-.19161945043248790557] 
dist 235=[-.4807630383652297045 ,-.16179139257383608021] 
dist 236=[-.48907085711719230327,-.12642844091494910341] 
dist 237=[-.49553965514200459798,-.08023204571248505695] 
dist 238=[-.4997215853141006995 ,-.00716337188196698842] 
dist 239=[-.5021978753752415272 ,.07054303565318165582] 
dist 240=[-.50276057971954077348,.1248127351376404146 ] 
dist 241=[-.50116312174368580826,.17083905776825769262] 
dist 242=[-.49992045160959137613,.21766325475029261532] 
dist 243=[-.49208876086750812638,.26142778339356487809] 
dist 244=[-.49096312601509162255,.29524119843352059533] 
dist 245=[-.46121293863678388677,.3282475974009025579 ] 
dist 246=[-.4582978650129086861 ,.36879033435980150006] 
dist 247=[-.44939111709540409624,.40711777930043763333] 
dist 248=[-.44830210156589238118,.43128165238915617933] 
dist 249=[-.33601259780966259328,.44969971977463326074] 
dist 250=[-.32114382844076844596,.46509281373017267978] 
dist 251=[-.29304476775749144934,.4773610671839436523 ] 
dist 252=[-.28587978188638279953,.48330605541047279746] 
dist 253=[-.26752319773414595168,.4857535212851888764 ] 
dist 254=[-.26474882056980618395,.48583753596160240341] 
dist 255=[-.25019746618584211205,.48662548594021294257] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 2, 1, 2, 0, 2] 
dist 0=[55.621963535581518513  ,55.621963535581518513  ] 
dist 1=[54.472779439222086903  ,56.166427549177372904  ] 
dist 2=[53.036225496222237241  ,56.456140892423715990  ] 
dist 3=[51.344238950863732394  ,56.587960010365918653  ] 
dist 4=[49.137688211289061749  ,56.630308463456671104  ] 
dist 5=[45.646151208645685439  ,56.446901420160145855  ] 
dist 6=[42.080608280960797709  ,56.314317177739111860  ] 
dist 7=[39.578408258687187791  ,56.099891518178897700  ] 
dist 8=[37.370624256922656102  ,55.988209746383814414  ] 
dist 9=[34.980582534798028750  ,55.394033624066850555  ] 
dist 10=[32.649295486567328669  ,55.215759591502382743  ] 
dist 11=[30.675917786877260418  ,54.602266222450263656  ] 
dist 12=[28.581330819872186829  ,54.446243517862866399  ] 
dist 13=[25.765555858710453354  ,52.796403523580129536  ] 
dist 14=[22.968799733525026169  ,52.377725198340296310  ] 
dist 15=[20.949931598351598819  ,50.082242880662586114  ] 
dist 16=[19.107549615084411690  ,34.732261695181940055  ] 
dist 17=[17.015334067930619930  ,29.817056165101119927  ] 
dist 18=[14.912595442098137864  ,28.891594381586083871  ] 
dist 19=[13.027736762971201149  ,27.777507353656834621  ] 
dist 20=[10.932904352350583046  ,27.501066844799809148  ] 
dist 21=[7.9905394698344023504 ,19.433800814250643534  ] 
dist 22=[5.0984103621592025082 ,18.422049950238006831  ] 
dist 23=[3.2041409435670491127 ,16.325391930232215308  ] 
dist 24=[1.6686547839604539431 ,15.777967464342124661  ] 
dist 25=[.21026339933332876841,13.764424310140118194  ] 
dist 26=[-1.5741638369231057792 ,13.366285167353580504  ] 
dist 27=[-3.5151791408524068896 ,12.636981078623624030  ] 
dist 28=[-5.3598769303628482296 ,12.470377181612563658  ] 
dist 29=[-6.8518824371210045397 ,3.3854928478964450530 ] 
dist 30=[-8.3799337780353220181 ,.19040183432031894629] 
dist 31=[-10.369954862125414314  ,-1.8695833379327006441 ] 
dist 32=[-12.262351322655160901  ,-2.3077717884548853851 ] 
dist 33=[-13.400611154951297601  ,-4.3042141161091863152 ] 
dist 34=[-14.213481163181224006  ,-4.6500596642247080109 ] 
dist 35=[-14.805274125941327766  ,-4.5989329915145242782 ] 
dist 36=[-15.247730340446684694  ,-4.2646783038269050865 ] 
dist 37=[-15.463456569023487116  ,-3.6496604850691540707 ] 
dist 38=[-15.718568837680034804  ,-3.0013734828829486974 ] 
dist 39=[-16.195153835738440363  ,-2.5341734486415124635 ] 
dist 40=[-16.507600574229980118  ,-2.1122149530024398005 ] 
dist 41=[-16.710881141329383188  ,-1.6439780982349541971 ] 
dist 42=[-16.751352745981863568  ,-1.1834953841465551160 ] 
dist 43=[-16.722623018135749487  ,-.7922465347529484119 ] 
dist 44=[-16.660591899131299462  ,.53176792875024404157] 
dist 45=[-13.014288377747921958  ,2.5414863742500103017 ] 
dist 46=[-12.758548787664559090  ,3.8983003622312616109 ] 
dist 47=[-12.673049376153351992  ,5.0357147947380083095 ] 
dist 48=[-3.6061775587949539574 ,6.1701006335052946135 ] 
dist 49=[-2.8245727659759213066 ,7.2152060205227139706 ] 
dist 50=[-1.2483743564550513185 ,7.9964635528305085017 ] 
dist 51=[-1.1770348098450985724 ,8.7340955099447669843 ] 
dist 52=[-1.0615170923030981506 ,9.6052862213013189748 ] 
dist 53=[-1.0344696762376732965 ,10.412204804788646873  ] 
dist 54=[2.3173980783226862384 ,10.893407272226025524  ] 
dist 55=[2.5206179787479072904 ,11.228708353789162683  ] 
dist 56=[2.9501150467725408777 ,11.453382447910635986  ] 
dist 57=[3.0260386175083911182 ,11.595357144318262284  ] 
dist 58=[3.4173119637225976509 ,11.620254316333807643  ] 
dist 59=[3.4801615658229268981 ,11.563487565230495331  ] 
dist 60=[3.5382259837739112344 ,11.537500917881274718  ] 
dist 61=[3.5038416918692987463 ,10.798408462234612345  ] 
dist 62=[3.4349440745880611657 ,10.653321644984329036  ] 
dist 63=[2.6045783292163331309 ,10.210108147412344910  ] 
dist 64=[1.6785507846843684625 ,4.0613613663113702543 ] 
dist 65=[1.0479201037004964892 ,4.0586013085218507392 ] 
dist 66=[.5132111051736398725 ,4.0221730307745387743 ] 
dist 67=[-.0300875004000805988 ,4.0062188581941977532 ] 
dist 68=[-.53719042049247081913,3.9439266335386381310 ] 
dist 69=[-.92750069039734775323,3.9244437793640281449 ] 
dist 70=[-1.3070620222987127392 ,2.4592175370433508376 ] 
dist 71=[-1.7713453170190555602 ,2.3165389753038531724 ] 
dist 72=[-2.2096339381799007928 ,1.9622514983695632459 ] 
dist 73=[-2.4854817721355558993 ,1.9108250282126946336 ] 
dist 74=[-2.6954180536081021854 ,1.3669498477931221378 ] 
dist 75=[-2.8706676912325934454 ,1.2644382776560714399 ] 
dist 76=[-3.0106855678060526885 ,1.1490871133496646787 ] 
dist 77=[-3.0800457125388378974 ,1.1271317124589090944 ] 
dist 78=[-3.1161115631928663360 ,.20697676477648830243] 
dist 79=[-3.1230670497877485035 ,.09496583641435040742] 
dist 80=[-3.0717430464912213438 ,-.1371006024032578563 ] 
dist 81=[-3.0545589050689680604 ,-.1965651968035465978 ] 
dist 82=[-3.0050285589013151590 ,-.4087072381536892828 ] 
dist 83=[-2.9825996623024415377 ,-.4504646370759014806 ] 
dist 84=[-2.8553664075190056398 ,-.41946806005607625222] 
dist 85=[-2.8229524966714315272 ,-.20757804025941342548] 
dist 86=[-2.7529594492279388010 ,.02926774711186840734] 
dist 87=[-2.7287109188833996855 ,.36185599844168362366] 
dist 88=[-2.5924924636589026964 ,.69668518821903505818] 
dist 89=[-2.5689565796010989159 ,.9425078287834159169 ] 
dist 90=[-2.4463750946144207867 ,1.1701626064938655801 ] 
dist 91=[-2.4166295303930078322 ,1.4325362460163765921 ] 
dist 92=[-2.3474465052560441936 ,1.6972460945330508612 ] 
dist 93=[-2.3229733277326038371 ,1.9342676050819266365 ] 
dist 94=[-2.0067966966548213897 ,2.1965745300275088269 ] 
dist 95=[-1.9577862254428501268 ,2.5622730343797911134 ] 
dist 96=[-1.8282748408819490161 ,2.9163828469074983749 ] 
dist 97=[-1.8064814473227536493 ,3.1324444837560630272 ] 
dist 98=[-1.5747933630466714498 ,3.2890010212508755323 ] 
dist 99=[-1.5272964266419034630 ,3.4055668571436964038 ] 
dist 100=[-1.4726803854369345502 ,3.4940822771175720278 ] 
dist 101=[-1.4537635856356327874 ,3.5386520271000835645 ] 
dist 102=[-.82690464370327582119,3.5596484571281601816 ] 
dist 103=[-.74998253857796435237,3.5592889399233390953 ] 
dist 104=[-.60272267498419881136,3.6005510857478525896 ] 
dist 105=[-.56664262481257205795,3.6637926771311064664 ] 
dist 106=[-.45217998666201531921,3.7015770573001863392 ] 
dist 107=[-.42436385837425317659,3.7145791879404354440 ] 
dist 108=[-.41702175359270074199,3.7115225314242188822 ] 
dist 109=[-.4356852048447907842 ,3.7048110824235016336 ] 
dist 110=[-.4671085700557316704 ,3.6571054425084119548 ] 
dist 111=[-.5106983973520898925 ,3.6469875431535068667 ] 
dist 112=[-.5715562260492017028 ,2.3006937318707293043 ] 
dist 113=[-.6719066381808962725 ,2.1715760645623793660 ] 
dist 114=[-.7899954341768713319 ,1.8522111976830018233 ] 
dist 115=[-.9216567510220667794 ,1.8038127892961360305 ] 
dist 116=[-1.1600532131417233713 ,1.2924995229533337257 ] 
dist 117=[-1.4056415388874766227 ,1.0458482653093425891 ] 
dist 118=[-1.6407037697534382183 ,-.51083215375645245873] 
dist 119=[-1.9229667064003870829 ,-.59861670223522873296] 
dist 120=[-2.1866629822542244386 ,-.79123703750135937232] 
dist 121=[-2.3476132280429792011 ,-.82396721984341516359] 
dist 122=[-2.4641616137218731538 ,-1.0302959457198450448 ] 
dist 123=[-2.5506213909381466679 ,-1.0621709599772842852 ] 
dist 124=[-2.6164090590697201288 ,-1.1247227412439869407 ] 
dist 125=[-2.6504460094553447696 ,-1.0608675244104254786 ] 
dist 126=[-2.6677520024140239306 ,-.95308422994062988067] 
dist 127=[-2.6671588880611180733 ,-.76062318105458922078] 
dist 128=[-1.4384659990957007336 ,-.56001734798251972535] 
dist 129=[-1.4504571502835381663 ,-.41972244997767359459] 
dist 130=[-1.4551989798891988006 ,-.29677010796818784182] 
dist 131=[-1.4537391065284718290 ,-.1653714508945136343 ] 
dist 132=[-1.4425153391109440347 ,-.03861632458494343569] 
dist 133=[-1.4351525367768351926 ,.06580920015272244042] 
dist 134=[-.9918095966545796141 ,.1738827458289264012 ] 
dist 135=[-.94701502027405435975,.3152064714195238718 ] 
dist 136=[-.83515730928643722492,.45309138157072380664] 
dist 137=[-.81726409425247461527,.54744430577419056458] 
dist 138=[-.64144079977731907505,.62800562223971605034] 
dist 139=[-.60753346051370747305,.71084980054050749211] 
dist 140=[-.56577076561377521201,.7888768462236108592 ] 
dist 141=[-.55329969275311135932,.89109034027934133464] 
dist 142=[-.2462526344064520646 ,.99822339860007660628] 
dist 143=[-.2075037240551600939 ,1.0628280655138108136 ] 
dist 144=[-.1245522480397750719 ,1.1086488279950705125 ] 
dist 145=[-.1045107597703983700 ,1.1408056102078478121 ] 
dist 146=[-.0173573430425046632 ,1.1645685030869178023 ] 
dist 147=[-.03408954798143015882,1.1768884563222367313 ] 
dist 148=[-.09068577608315377004,1.1831837245191658909 ] 
dist 149=[-.14437745377119855024,1.1829094761436648761 ] 
dist 150=[-.20620838045201167303,1.1641212420847916028 ] 
dist 151=[-.29529324365654420341,1.1609738862657726726 ] 
dist 152=[-.38601081487819441255,1.0928241724932736178 ] 
dist 153=[-.45436098301690609824,1.0795741157141209945 ] 
dist 154=[-.51941214779355431031,1.0468500552566157934 ] 
dist 155=[-.5969676673665409634 ,1.0350136848263990526 ] 
dist 156=[-.67663404651241729535,1.0208906470576230945 ] 
dist 157=[-.75011386250506943891,1.0175941518301312222 ] 
dist 158=[-.83315141835776108048,.93156697503034077378] 
dist 159=[-.95097089922978975451,.92174993560129263066] 
dist 160=[-1.0654652643411862689 ,.73269936042348668353] 
dist 161=[-1.1352323195212877167 ,.71883822993829196581] 
dist 162=[-1.1856158297818941905 ,.6705845440489029128 ] 
dist 163=[-1.2227424143217415116 ,.6578620412547479687 ] 
dist 164=[-1.2503794942122558217 ,.64265729435653837048] 
dist 165=[-1.2628850694985614108 ,.63620283794227765686] 
dist 166=[-1.2669852702401115861 ,.15500229345618982769] 
dist 167=[-1.2663418063532861825 ,.2145997699404697291 ] 
dist 168=[-1.2145690208923031540 ,.26609813442835021899] 
dist 169=[-1.2534524383742728635 ,.32001918507240076067] 
dist 170=[-1.2793673114389870617 ,.37137688238155809207] 
dist 171=[-1.2943772323391139748 ,.41264232030005796452] 
dist 172=[-1.3023621116598000815 ,.45441907954103253727] 
dist 173=[-1.3024132664591676130 ,.50781503505927694873] 
dist 174=[-1.2947109025812580679 ,.55930752596260679323] 
dist 175=[-1.2891299191114665288 ,.59348570321459714267] 
dist 176=[-.96505376290129235488,.62151842449504378094] 
dist 177=[-.99582296439141875109,.64848133321551858337] 
dist 178=[-1.0193807617446954165 ,.67267542844360252182] 
dist 179=[-1.0289206888127419024 ,.68965518934128765329] 
dist 180=[-1.0321651188606765870 ,.70458525344439145252] 
dist 181=[-1.0305979387224259112 ,.72059430090114899319] 
dist 182=[-.53889955011709454431,.78528827483835938156] 
dist 183=[-.52625025959491125993,.88336705765957977737] 
dist 184=[-.27030993340586099313,.97399537744376316202] 
dist 185=[-.23739405975222698988,1.0282352395504135893 ] 
dist 186=[-.16488218151236887756,1.0662092690330252384 ] 
dist 187=[-.14881082961923691213,1.0919164354413632101 ] 
dist 188=[-.06501779135726069529,1.1102082993678199474 ] 
dist 189=[-.05025702009797945392,1.1185843859370783392 ] 
dist 190=[-.01764217276781815940,1.1212961950789364823 ] 
dist 191=[-.01101279062662043014,1.1198741666294408758 ] 
dist 192=[.02395534454759975151,1.0025048151191239647 ] 
dist 193=[-.03591969258154123520,1.0234064685888664234 ] 
dist 194=[-.08891276925948124794,1.0343416791325342682 ] 
dist 195=[-.14636263083327265838,1.0359514936650903063 ] 
dist 196=[-.20227603733062191743,1.0258114705078691420 ] 
dist 197=[-.24913764095188366924,1.0214983765045146120 ] 
dist 198=[-.29834344201604454313,1.0173362728413165373 ] 
dist 199=[-.36361402711644554707,1.0125545203897929006 ] 
dist 200=[-.42771157193212843226,.92420611561586531942] 
dist 201=[-.47223610421808069887,.9229625439938484464 ] 
dist 202=[-.51095167884369867421,.88205388501304714233] 
dist 203=[-.55186517637416793948,.87108449096675359833] 
dist 204=[-.60137866144826015937,.86400280319802903971] 
dist 205=[-.67416174304257602926,.8606499140964410313 ] 
dist 206=[-.74290071772220475503,.69963306458595980606] 
dist 207=[-.78610005965280212854,.69369833510060354895] 
dist 208=[-.81886190462581475831,.60011545497438037363] 
dist 209=[-.8459404828219851526 ,.58741086348183490751] 
dist 210=[-.86728341820485676744,.54285239279515212408] 
dist 211=[-.87715123041140692912,.53147223746609743567] 
dist 212=[-.8808907492011388743 ,.51710849974221558602] 
dist 213=[-.88061748835767516894,.53115717883055550668] 
dist 214=[-.77574156400589765742,.56799060448139187135] 
dist 215=[-.78920655478908726219,.61229289625705220563] 
dist 216=[-.86643696231271611507,.65368972427171937724] 
dist 217=[-.913118960495318906  ,.67892515418176921466] 
dist 218=[-.94637304828763324149,.69714831144654074195] 
dist 219=[-.97000477430657680316,.71055539153835357457] 
dist 220=[-.98689318882692945788,.71982347144178685086] 
dist 221=[-.9932319541137051628 ,.72163556204273651122] 
dist 222=[-.99422921288579625655,.72047463606925618154] 
dist 223=[-.99236978302107250253,.71876844977989955269] 
dist 224=[-.45527216341625941887,.6920413325403218787 ] 
dist 225=[-.44354254499209540266,.68615058676069869461] 
dist 226=[-.39986352091215258268,.66620890757939582441] 
dist 227=[-.38984028269004918252,.66269422833923218645] 
dist 228=[-.37151101449603810513,.61126081907438977085] 
dist 229=[-.36659854064738032423,.59946382510380989183] 
dist 230=[.06705602248678808812,.58878908484851436658] 
dist 231=[.10444405618760933099,.58478339168341196435] 
dist 232=[.18119195498316570323,.63733955904162316226] 
dist 233=[.20018045050514669816,.68180110706048823667] 
dist 234=[.26507209991214507414,.71796852524437576011] 
dist 235=[.21905537181791677122,.75229058084137629393] 
dist 236=[.15545396899714874643,.78281879798491893796] 
dist 237=[.08793483633163844666,.81028571306932654371] 
dist 238=[.00783908537085392299,.8377703141047101166 ] 
dist 239=[-.12501967448110548651,.86888453451026882562] 
dist 240=[-.25918160392250745887,.89623920918224044436] 
dist 241=[-.34968868620089374914,.90871779484629934862] 
dist 242=[-.4255645341231911759 ,.91434391130477824781] 
dist 243=[-.5013266129854928485 ,.91434236511295913212] 
dist 244=[-.57122817906588845467,.89704612249242896092] 
dist 245=[-.62371171798699811841,.89079602364124360579] 
dist 246=[-.67349324165553896224,.88544726419417212675] 
dist 247=[-.73260878035965777703,.88069106283211434864] 
dist 248=[-.78747108347573569829,.73454782925735099379] 
dist 249=[-.82027575793365661412,.71331658557407884568] 
dist 250=[-.84320290054342059874,.67203179576499086539] 
dist 251=[-.85863979442866946937,.66067822386539036474] 
dist 252=[-.86876959053522864615,.6176239384164386691 ] 
dist 253=[-.87051490780052816353,.60706441778722526824] 
dist 254=[-.86896980568178373495,.58683124389142477829] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 1, 0, 1] 
dist 0=[55.344044276429679850  ,55.344044276429679850  ] 
dist 1=[55.106238882320855898  ,55.452083832046315469  ] 
dist 2=[54.525416930509266334  ,55.514485760748139415  ] 
dist 3=[53.579520733727500895  ,55.555876820743739559  ] 
dist 4=[51.883382546441359509  ,55.579817475958602385  ] 
dist 5=[50.080803787693136770  ,55.586109975185395533  ] 
dist 6=[48.709756127605303812  ,55.556912081433705832  ] 
dist 7=[47.387511318789726718  ,54.777777933287299996  ] 
dist 8=[45.779993310383245036  ,53.057174511295264401  ] 
dist 9=[43.629973432585892643  ,51.696884766911424914  ] 
dist 10=[40.996930180822710310  ,51.125243096566063511  ] 
dist 11=[37.763400382304246153  ,50.160110262207886507  ] 
dist 12=[32.853202396222531570  ,49.893948042230411026  ] 
dist 13=[27.908043222540320196  ,49.092944177779187371  ] 
dist 14=[24.534798709423337748  ,48.819300640483008273  ] 
dist 15=[21.657806620135644706  ,47.677713592859907296  ] 
dist 16=[18.694561426886272584  ,45.523697929050281216  ] 
dist 17=[15.892138702156161730  ,30.724002180377373945  ] 
dist 18=[13.657306905055885583  ,30.336709581814089860  ] 
dist 19=[11.403049698554138005  ,29.929134013492029451  ] 
dist 20=[8.5226698464415940492 ,29.815844410383981828  ] 
dist 21=[5.7279176332276090145 ,17.422295315533008042  ] 
dist 22=[3.8154753488738107629 ,16.529920953695162761  ] 
dist 23=[2.1758680180889406987 ,15.222563201236246486  ] 
dist 24=[.4706481492844050902 ,14.876652428620815553  ] 
dist 25=[-1.1557585943746673057 ,9.0775453903369274507 ] 
dist 26=[-2.4809518577490104519 ,8.3610559234265484927 ] 
dist 27=[-3.8467268129391572608 ,6.8175795898137487352 ] 
dist 28=[-5.6361379348202409484 ,6.5382189776877612984 ] 
dist 29=[-7.3491203772193092147 ,4.9743949568960534467 ] 
dist 30=[-8.4096800203027754734 ,4.7259022352184853580 ] 
dist 31=[-9.2028656821990512699 ,4.2118051377910610207 ] 
dist 32=[-9.8471564282489854129 ,3.9101483478053548819 ] 
dist 33=[-10.360020835002856660  ,-6.7368165593042262906 ] 
dist 34=[-10.627717095522329073  ,-6.8507517753922686747 ] 
dist 35=[-10.769880549844867007  ,-6.7998801697397839051 ] 
dist 36=[-10.800116128411197170  ,-6.5158711522610752207 ] 
dist 37=[-11.043349744763634091  ,-6.1739413166602999936 ] 
dist 38=[-11.359636634015840109  ,-5.8916977998828091630 ] 
dist 39=[-11.535310629208728861  ,-5.6020537300706821099 ] 
dist 40=[-11.575556720960936364  ,-5.2298538136097191732 ] 
dist 41=[-11.394963976257134096  ,-4.8354392046726783791 ] 
dist 42=[-11.342608733626589738  ,-4.4567884054341263450 ] 
dist 43=[-11.294538224460032265  ,-4.0181562113073806180 ] 
dist 44=[-11.242319206416472698  ,-3.3840496300288094083 ] 
dist 45=[-11.192113859915110439  ,-2.4554816227482125545 ] 
dist 46=[-11.154740506999052965  ,-1.2973328342425735695 ] 
dist 47=[-11.120028925897685461  ,-.32648102797314567422] 
dist 48=[-11.080606713403942609  ,.64350126777530634763] 
dist 49=[-4.3315301078875902048 ,1.5395085896231290238 ] 
dist 50=[-3.7764236202006614719 ,2.2150640254780186879 ] 
dist 51=[-2.7915375565595406174 ,2.8590054288603152873 ] 
dist 52=[-2.7731272525861682380 ,3.6288019775288237786 ] 
dist 53=[-1.9022126807802797847 ,4.3524678650743260971 ] 
dist 54=[-1.7947231671145352593 ,4.8122660766073797853 ] 
dist 55=[-1.5616580188062494405 ,5.1671810346185208553 ] 
dist 56=[-1.5028126311812136035 ,5.4721940971358471847 ] 
dist 57=[-1.2290834844782861544 ,5.7221996613495783511 ] 
dist 58=[-1.1767968961808154788 ,5.8575558229321752124 ] 
dist 59=[-1.0573477121101972624 ,5.9351251710344220000 ] 
dist 60=[-1.0276237793879143583 ,5.9544991297765383984 ] 
dist 61=[-.7385804897368491978 ,5.1782337111857095456 ] 
dist 62=[-.6908109544942080302 ,5.0953806084759854982 ] 
dist 63=[-.5855358467684395810 ,4.9579698010923713383 ] 
dist 64=[-.5543594405508771427 ,4.8633078925478509071 ] 
dist 65=[-.4173421073877454041 ,4.6625005990623100775 ] 
dist 66=[-.3888380188970250920 ,4.6524813173356541108 ] 
dist 67=[-.3221750222136126731 ,4.5881751770655811153 ] 
dist 68=[-.3024516411894033138 ,4.5771205124476908808 ] 
dist 69=[.5802665254190314281 ,3.7698479108065312807 ] 
dist 70=[.3747166237950979896 ,3.7036356335467630427 ] 
dist 71=[.0788309826887750666 ,3.6474957688325825340 ] 
dist 72=[-.33549239525680692298,3.6305673102560046221 ] 
dist 73=[-.71895801326993988989,2.7348382191389834012 ] 
dist 74=[-1.0089417487656177390 ,2.6170659677364535886 ] 
dist 75=[-1.2860955033093381267 ,2.3861395964984164409 ] 
dist 76=[-1.6183881665051315194 ,2.3261073042843774974 ] 
dist 77=[-1.9293319433431135757 ,2.1143722015518976418 ] 
dist 78=[-2.1212785247747706941 ,2.0643566312548727501 ] 
dist 79=[-2.2629487056152266044 ,1.9994059944966442852 ] 
dist 80=[-2.3731971205642760252 ,1.9763465545875575253 ] 
dist 81=[-2.4591397438907962629 ,.08687867216824434839] 
dist 82=[-2.5037929547425416679 ,.1025298259929675787 ] 
dist 83=[-2.5268345044444760066 ,.13569713811301881076] 
dist 84=[-2.5287908338789324575 ,.20114592969160750691] 
dist 85=[-2.5498374651171991133 ,.27483109942387624062] 
dist 86=[-2.6160847128200818700 ,.340877970783702952  ] 
dist 87=[-2.6579872810898790483 ,.41378852860764377825] 
dist 88=[-2.6779939322287956601 ,.51489604665734789859] 
dist 89=[-2.8729111547250641300 ,.6261795723245144863 ] 
dist 90=[-3.0295380434431553111 ,.7397128080202696668 ] 
dist 91=[-3.1459326615441339955 ,.8765042098926856887 ] 
dist 92=[-3.2380307172752314716 ,1.0806116998744266056 ] 
dist 93=[-3.3075495103249755559 ,1.2815093654823585734 ] 
dist 94=[-3.3337896033655989086 ,1.4054975218203449324 ] 
dist 95=[-3.3417340906024887296 ,1.4967779145608379112 ] 
dist 96=[-3.3382308239423877474 ,1.5671594653675285697 ] 
dist 97=[-2.1448158793820371143 ,1.6218674939777313239 ] 
dist 98=[-2.1075179313691329390 ,1.6506068554952258925 ] 
dist 99=[-2.0437553615276749129 ,1.7164907185631142791 ] 
dist 100=[-2.0255781766981648727 ,2.0084188257153936736 ] 
dist 101=[.9071178935748666536 ,2.3255654641223203674 ] 
dist 102=[.9679121161119126312 ,2.5332889393168858583 ] 
dist 103=[1.0932691878634360819 ,2.6865240804052814890 ] 
dist 104=[1.1126938606226819374 ,2.8056523096617355390 ] 
dist 105=[1.0310478679067847622 ,2.8986919474572777258 ] 
dist 106=[.8804576213453416778 ,2.9845892475316371294 ] 
dist 107=[.67640266605151567204,3.0828653862144274146 ] 
dist 108=[.36475677358619657124,3.1674842094076401837 ] 
dist 109=[.05044330709787750425,3.2356703251020527137 ] 
dist 110=[-.16425758169013713402,3.2683528330360302374 ] 
dist 111=[-.34696541720248186172,3.2813139453636340768 ] 
dist 112=[-.53361574067722810033,3.2793701130177712982 ] 
dist 113=[-.7083789295746483810 ,3.2487141337115964023 ] 
dist 114=[-.8436549400560573593 ,3.2349189139205924685 ] 
dist 115=[-.9758450511197446740 ,3.1835099208207731903 ] 
dist 116=[-1.1383001457116917347 ,3.1651820508214655140 ] 
dist 117=[-1.2917687780899429944 ,2.2534330449336594684 ] 
dist 118=[-1.3881000746864128172 ,2.2185205285590424218 ] 
dist 119=[-1.4609922343840363523 ,2.1946437648577746356 ] 
dist 120=[-1.5617912079640399652 ,2.1878255869775758123 ] 
dist 121=[-1.7446815395283414048 ,1.6551289315075693310 ] 
dist 122=[-1.8612478640529933223 ,1.5845321975919367295 ] 
dist 123=[-1.9515588400402135286 ,1.4493754207336061660 ] 
dist 124=[-2.1402331418158147956 ,1.4145890338028277564 ] 
dist 125=[-2.3167238941021776096 ,1.2952844799575140439 ] 
dist 126=[-2.4248562363324824590 ,1.2651701922215640240 ] 
dist 127=[-2.5036324985557729350 ,1.2337990718595856562 ] 
dist 128=[-2.5629606710540386889 ,1.2233013729417671418 ] 
dist 129=[-2.6052734555482618519 ,-.0975652961650646703 ] 
dist 130=[-2.6161417755824762585 ,-.1346669951901563889 ] 
dist 131=[-2.6156350142290751114 ,-.10530142297074812539] 
dist 132=[-2.6125303744608777330 ,0                     ] 
dist 133=[-1.1364980606536818280 ,-.81692317031809804853] 
dist 134=[-1.1075369226306625348 ,-.68086488676829412216] 
dist 135=[-1.0457951164214306623 ,-.55740573621146135432] 
dist 136=[-1.0273376639339510835 ,-.4188895634769105608 ] 
dist 137=[-.9474963623379982954 ,-.2813068894679959613 ] 
dist 138=[-.93102402594210400438,-.1615670074124613753 ] 
dist 139=[-.88420339816867960188,-.0319550399090692190 ] 
dist 140=[-.87688892050391819643,.18894558688845559684] 
dist 141=[-.2225604231953232691 ,.46059916672841898709] 
dist 142=[-.16069373548228160453,.6417667556593471432 ] 
dist 143=[-.0531787260051324285 ,.79138330725605618392] 
dist 144=[-.0432084174539658123 ,.93710165766387313985] 
dist 145=[-.0365988936643287844 ,1.0691932329562986119 ] 
dist 146=[-.04705307316537224500,1.1644183749808948422 ] 
dist 147=[-.06995285119993719545,1.2508917057087983104 ] 
dist 148=[-.11578732465530938043,1.3480493081409885642 ] 
dist 149=[-.16582255376999026712,1.4357300821703151168 ] 
dist 150=[-.2054879580658151671 ,1.4843780145133026779 ] 
dist 151=[-.24512337955567457941,1.5295868076366949549 ] 
dist 152=[-.29504443485748590432,1.5868058281730664317 ] 
dist 153=[-.34772615405873977961,1.6304993889649519705 ] 
dist 154=[-.39838221517421412238,1.6485536565784583640 ] 
dist 155=[-.45724034194647803646,1.6558125133908946691 ] 
dist 156=[-.5426593722242756804 ,1.6564104276698674294 ] 
dist 157=[-.62989739354226776297,1.5984707071721928441 ] 
dist 158=[-.6960170703213356216 ,1.5844431547172472157 ] 
dist 159=[-.7593196949787772942 ,1.5543635718159774316 ] 
dist 160=[-.8353177719893954805 ,1.5431205649832723444 ] 
dist 161=[-.9136551315932116080 ,1.4854230008693061516 ] 
dist 162=[-.9862964148507031131 ,1.4715853038975205300 ] 
dist 163=[-1.0686803810703891360 ,1.4277695865145861333 ] 
dist 164=[-1.1859055015920845547 ,1.4189873893910240458 ] 
dist 165=[-1.2997863570833683325 ,-.2120391057162201689 ] 
dist 166=[-1.3688234187811263512 ,-.32093331716583976139] 
dist 167=[-1.4182355094866276914 ,-.5459641011057242543 ] 
dist 168=[-1.4537885664752349617 ,-.4562881197390769720 ] 
dist 169=[-1.4790459558832864300 ,-.3522879380549474632 ] 
dist 170=[-1.4873643384174591166 ,-.23837657052997371858] 
dist 171=[-1.4881575427562725207 ,-.09537588901090984892] 
dist 172=[-1.4840663505112982799 ,.12472507003526565646] 
dist 173=[-1.3972263414453301183 ,.34587373200601235764] 
dist 174=[-1.4624982261117621201 ,.49305489201921372047] 
dist 175=[-1.5078404951224272698 ,.61423828031007962774] 
dist 176=[-1.5378621522181474757 ,.73162183104741174006] 
dist 177=[-1.5580373471126854500 ,.83756893631101844342] 
dist 178=[-1.5640774518769737626 ,.91310502479476505289] 
dist 179=[-1.5628418101134908819 ,.98082111106138256711] 
dist 180=[-1.5589012423578063212 ,1.0555534455755820009 ] 
dist 181=[-1.2162364218475932860 ,1.1230027198123656980 ] 
dist 182=[-1.1789409604890609068 ,1.1616504635565474531 ] 
dist 183=[-1.0871082634450337950 ,1.1865879617348631596 ] 
dist 184=[-1.0679628495169737053 ,1.1993199168135117797 ] 
dist 185=[-.92262675601285925442,1.2057630341254868787 ] 
dist 186=[-.89327465065247563445,1.2056006332083649331 ] 
dist 187=[-.84612157176009499677,1.2372877800427117452 ] 
dist 188=[-.83300527442694781313,1.3419817449122925374 ] 
dist 189=[-.56811242219231879162,1.4370877927146908530 ] 
dist 190=[-.5325734420706137837 ,1.4934145947738736442 ] 
dist 191=[-.44973235114354174832,1.5321172375485339969 ] 
dist 192=[-.4333414625479066335 ,1.5568818826206541434 ] 
dist 193=[-.32100569832481636063,1.5724262799418618885 ] 
dist 194=[-.30003265592200093471,1.5743274294687493014 ] 
dist 195=[-.26250808817446741943,1.5705599272380473815 ] 
dist 196=[-.25378225346511276169,1.5644158590898257266 ] 
dist 197=[.96137642682699599032,1.3751020784642002511 ] 
dist 198=[.9172944670233069873 ,1.4358466962648808925 ] 
dist 199=[.85629892527026522316,1.4766778421281830088 ] 
dist 200=[.75625568627044490014,1.5010375521914713709 ] 
dist 201=[.63873842282248744531,1.5165656210762828374 ] 
dist 202=[.50799630310773474351,1.5221437200652337094 ] 
dist 203=[.34249201349799297394,1.5215073460967920284 ] 
dist 204=[.08622373570967543288,1.5183552018729420229 ] 
dist 205=[-.17200029013052090314,1.3639979866696175624 ] 
dist 206=[-.34531089639036084634,1.3388919411580406943 ] 
dist 207=[-.48964334092293168469,1.2911180522906160266 ] 
dist 208=[-.63220306621466981342,1.2771377417167624938 ] 
dist 209=[-.76274336423801314784,1.2206138963931429628 ] 
dist 210=[-.85910110185934871686,1.2058874572351030654 ] 
dist 211=[-.94889284819795115371,1.1729778095779840981 ] 
dist 212=[-1.0532254386800985891 ,1.1614667090200184785 ] 
dist 213=[-1.1490700817199499466 ,.50491259485185406582] 
dist 214=[-1.2049828812322654839 ,.4679415066800460327 ] 
dist 215=[-1.2423614199986443398 ,.38897291494958789884] 
dist 216=[-1.2642281745582923075 ,.36731654571270163088] 
dist 217=[-1.2785230946444169836 ,.28158065912420271954] 
dist 218=[-1.2856790301827270071 ,.26510623871348699459] 
dist 219=[-1.2889768435233202081 ,.22678677030721742973] 
dist 220=[-1.2878715647630623467 ,.21885329196529055683] 
dist 221=[-1.2362759508004127659 ,-.23415967349583166283] 
dist 222=[-1.3001258056142253930 ,-.2763774559690071622 ] 
dist 223=[-1.3431931442009680361 ,-.35433290501152610581] 
dist 224=[-1.3691723406127014890 ,-.37128929082626265111] 
dist 225=[-1.3866921902004023455 ,-.55583868847298185002] 
dist 226=[-1.3959942107423964696 ,-.58079489663307266409] 
dist 227=[-1.4010604407248666412 ,-.6718053282460412194 ] 
dist 228=[-1.4016733120253066469 ,-.4896615637539002882 ] 
dist 229=[-.59063879083440142626,-.30264742299893673166] 
dist 230=[-.55860121610991687599,-.17163667626397761921] 
dist 231=[-.48768946464010633955,-.05653659403685832761] 
dist 232=[-.46941108046115404232,.06697217665312726295] 
dist 233=[-.38262099457873727687,.18646179673790298431] 
dist 234=[-.36610646897178406562,.28552031179103317598] 
dist 235=[-.3278513453050129714 ,.38860691094578527639] 
dist 236=[-.31896620110315632693,.52417516373388586427] 
dist 237=[.08035381121643012516,.65681216868902044274] 
dist 238=[.1198547535990736418 ,.77597764383856044624] 
dist 239=[.19425144954199235742,.87967937268253742175] 
dist 240=[.2111190576248110949 ,.97970365008805911448] 
dist 241=[.38926986319724563733,1.0697278155009189218 ] 
dist 242=[.41439072547459980689,1.1335144413582076291 ] 
dist 243=[.50879082172178613953,1.1903077422369469944 ] 
dist 244=[.63897703078207364368,1.2524178617561001880 ] 
dist 245=[.91070118424302301973,1.3073190465969909587 ] 
dist 246=[.85977282689169787631,1.3353381087142970584 ] 
dist 247=[.79305698942716554483,1.3501028942515210184 ] 
dist 248=[.68732757797165725719,1.3523892627825558801 ] 
dist 249=[.56457433743557051814,1.3235385935488073504 ] 
dist 250=[.42990881377030311334,1.3186103197308676607 ] 
dist 251=[.26068618915853305995,1.2567549707931358805 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 0, 1, 2, 0, 1] 
dist 0=[55.321146188310758416  ,55.321146188310758416  ] 
dist 1=[54.994529344027884124  ,55.387119747899555606  ] 
dist 2=[54.389606152443175431  ,55.323986934724759560  ] 
dist 3=[53.233744351273328737  ,55.234753255662362155  ] 
dist 4=[51.921796027684197225  ,55.151859479885031276  ] 
dist 5=[50.693492309652811007  ,55.057136100818092868  ] 
dist 6=[49.288411564444035062  ,54.943183457781349277  ] 
dist 7=[47.270243608558893262  ,54.650609645730688905  ] 
dist 8=[45.006005999119914469  ,50.488180896178484481  ] 
dist 9=[42.618015964375793478  ,49.553996731423109139  ] 
dist 10=[39.675431971722318166  ,49.277705914580330911  ] 
dist 11=[35.195994846575458051  ,48.781376784368992804  ] 
dist 12=[30.680216535493603020  ,48.489558212275218509  ] 
dist 13=[27.592389242043167083  ,48.277136780509649818  ] 
dist 14=[24.950738905929296086  ,46.628012560650029108  ] 
dist 15=[22.216853154204615738  ,41.871435956065642715  ] 
dist 16=[19.623029892542146220  ,34.748780193618365121  ] 
dist 17=[17.540608219190209420  ,33.810700139416899733  ] 
dist 18=[15.427097358758743115  ,31.955309195553542158  ] 
dist 19=[12.708702619136222045  ,31.470139788697845092  ] 
dist 20=[10.062004382508278840  ,29.723590718943668534  ] 
dist 21=[8.2346541944336412821 ,29.327029658671475724  ] 
dist 22=[6.6503603293125095579 ,28.691799360371268106  ] 
dist 23=[4.9742476913255114751 ,28.514953423621414990  ] 
dist 24=[3.3576580424579686972 ,11.672966750502393201  ] 
dist 25=[2.0107086711494866333 ,10.252786981614023518  ] 
dist 26=[.59554010073667908107,7.0122462074415442622 ] 
dist 27=[-1.2945017276038834020 ,6.4824797874669993916 ] 
dist 28=[-3.2387804056247245353 ,5.1578815834605066032 ] 
dist 29=[-4.9765973511765193297 ,4.9912344725411679015 ] 
dist 30=[-6.6011417277584567126 ,4.3901182449090608220 ] 
dist 31=[-8.5029438372721092648 ,.39735222027343402972] 
dist 32=[-10.273045247756715008  ,-3.4433395233506443298 ] 
dist 33=[-11.371561990239132531  ,-3.9316804275867914448 ] 
dist 34=[-12.192120073809933091  ,-4.8599959443399102028 ] 
dist 35=[-12.852043274412186604  ,-5.0641730406061071103 ] 
dist 36=[-13.368351984119511688  ,-5.5946416649410469938 ] 
dist 37=[-13.615195011030362347  ,-5.6201698611230927331 ] 
dist 38=[-13.733797981479463817  ,-5.4716566134926167900 ] 
dist 39=[-13.737862791166571438  ,-5.0517679391884487209 ] 
dist 40=[-9.2478349900867078454 ,-4.5733887622650906972 ] 
dist 41=[-8.9546703367088886711 ,-4.1912358864081842161 ] 
dist 42=[-8.5484875611276954098 ,-3.8092629601797507788 ] 
dist 43=[-8.2484759344823723968 ,-3.3308679747720727121 ] 
dist 44=[-8.1670583513642189245 ,-2.8231216481354758397 ] 
dist 45=[-8.0209224860736562664 ,-2.0578741458421727685 ] 
dist 46=[-7.9747479507568511410 ,-.3352641631125904843 ] 
dist 47=[-6.2577921417428083355 ,1.3970878889369613021 ] 
dist 48=[-5.3388724375943234631 ,2.5387308532253579562 ] 
dist 49=[-4.7997976859540117478 ,3.4667048015199549176 ] 
dist 50=[-4.6575735057367258684 ,4.3462789600950704835 ] 
dist 51=[-4.1170772794698477051 ,5.1280953723202461786 ] 
dist 52=[-3.1544274945508222940 ,5.6659266388768599439 ] 
dist 53=[-2.9816573711035363346 ,6.1285886464322093940 ] 
dist 54=[-2.0925901301022686276 ,6.6104620383275651658 ] 
dist 55=[-1.9528910572184966094 ,7.0450541134264506505 ] 
dist 56=[1.2431000154732462352 ,7.3189483111925475204 ] 
dist 57=[1.5171053512061839392 ,7.5279529274374479634 ] 
dist 58=[1.6782500845780755833 ,7.7033141606519550710 ] 
dist 59=[1.6977978519260131147 ,7.8434604438418938708 ] 
dist 60=[2.4635182143706176722 ,7.9117352977914499816 ] 
dist 61=[2.5252690418541658108 ,7.9399054243142639344 ] 
dist 62=[2.6290601892761084234 ,7.9303068625357609429 ] 
dist 63=[2.6473415358045468664 ,5.4701951890095529628 ] 
dist 64=[2.5551413356866993856 ,5.8060905524269733718 ] 
dist 65=[2.3936536719915037896 ,6.0051901777352699256 ] 
dist 66=[2.1737715683912651669 ,6.1429076433560472498 ] 
dist 67=[1.8171538522495299485 ,6.2336227118338711017 ] 
dist 68=[1.4000982346049995277 ,6.2911238514122589448 ] 
dist 69=[.93888632459841329174,6.3001912369144294708 ] 
dist 70=[.35686142478864823823,6.2827776887368260186 ] 
dist 71=[-.54253059369121598598,6.2665266659761377913 ] 
dist 72=[-1.4482364197711348888 ,2.4986141518410931097 ] 
dist 73=[-2.0554994612772550692 ,2.4722029430592014183 ] 
dist 74=[-2.5608053649878805086 ,2.4165300044589896328 ] 
dist 75=[-3.0595462983002966178 ,2.3979424550840614452 ] 
dist 76=[-3.5163597422354395399 ,1.5289015924176258468 ] 
dist 77=[-3.8543231152548229943 ,1.4389331654513644807 ] 
dist 78=[-4.1702952490042751243 ,1.2218994787000506306 ] 
dist 79=[-4.5393671667515257516 ,1.1859277212223190127 ] 
dist 80=[-4.8795458287837442540 ,.86835440814267497252] 
dist 81=[-5.0801955517584197008 ,.80833505819524526884] 
dist 82=[-5.2174077382050516253 ,.72729728291215762975] 
dist 83=[-5.3043543304725610345 ,.70186219077108882561] 
dist 84=[-5.3594791758428804966 ,.20488284196593038891] 
dist 85=[-5.4003422711593473254 ,.14127835475776124318] 
dist 86=[-5.4202102471325366436 ,.00240376214205409035] 
dist 87=[-5.4128111028715798331 ,-.02863826789622661353] 
dist 88=[-5.2935571556806343778 ,.78704448335907778494] 
dist 89=[-5.2628231913517237262 ,1.4326545036071618361 ] 
dist 90=[-5.1423476375624387875 ,1.9763321255851000573 ] 
dist 91=[-5.1241821761472676968 ,2.5231890162570008928 ] 
dist 92=[-4.7748720424420877583 ,3.0303535613786274626 ] 
dist 93=[-4.6939315905935136904 ,3.4156005186515251779 ] 
dist 94=[-4.6332254722292650404 ,3.7853935890040317006 ] 
dist 95=[-4.6175218639182529415 ,4.2308705479781417101 ] 
dist 96=[-3.4618378837309398458 ,4.6476528051558083192 ] 
dist 97=[-3.3095984976462372345 ,4.9029091421493918588 ] 
dist 98=[-3.0173706262908963464 ,5.0887436287099648544 ] 
dist 99=[-2.9423364366670357510 ,5.2284267547435729290 ] 
dist 100=[-2.6852443410603297566 ,5.3304102773118664393 ] 
dist 101=[-2.6210382154041694322 ,5.3657692586345460752 ] 
dist 102=[-2.5543400635533616670 ,5.3735316036679373212 ] 
dist 103=[-2.5333503028052469991 ,5.3653685784306477142 ] 
dist 104=[-.31931543250720193435,4.7087811199611000102 ] 
dist 105=[-.29720870433942317812,4.7486287156100698830 ] 
dist 106=[-.26303448407111386299,4.7548704774224922418 ] 
dist 107=[-.2541722779711320312 ,4.7212013525256128924 ] 
dist 108=[.20327623536445814349,4.6996248401153907462 ] 
dist 109=[.10718302743165506164,4.6568944961231747884 ] 
dist 110=[.01883134250508869845,4.6367518353193945576 ] 
dist 111=[-.08198134898917454832,3.9796893706285460216 ] 
dist 112=[-.44708760751393639836,3.9070560086640713752 ] 
dist 113=[-.92708635665501157128,3.7009708804963382759 ] 
dist 114=[-1.4126385601100554334 ,3.6712719684172397437 ] 
dist 115=[-1.8648701624908885918 ,3.2596895809733332775 ] 
dist 116=[-2.2118554452142431801 ,3.1735092120671513926 ] 
dist 117=[-2.5483520828364971322 ,3.0688699175661628802 ] 
dist 118=[-2.9587046766468048396 ,2.7581261557089738441 ] 
dist 119=[-3.3453013868779238260 ,2.0410168677158510258 ] 
dist 120=[-3.5869646338639746749 ,1.4569709438815889112 ] 
dist 121=[-3.7687980958484856083 ,1.4644818078147718475 ] 
dist 122=[-3.9165630480189210759 ,1.4649295175389267442 ] 
dist 123=[-4.0310897251857881622 ,1.4621358513449944720 ] 
dist 124=[-4.0802344825527793249 ,.29272249055989297466] 
dist 125=[-4.1018857449821231184 ,.18056750523101558061] 
dist 126=[-4.1067038719135190946 ,.15883417630292000829] 
dist 127=[-1.6135541826696599950 ,-.7592790368411592498 ] 
dist 128=[-1.6317910598446692341 ,-.91915479736310113087] 
dist 129=[-1.6416781297084356968 ,-.94703805623451363116] 
dist 130=[-1.6473479720719724210 ,-.97930807611339705193] 
dist 131=[-1.6487483999294654030 ,-.97498275257331321746] 
dist 132=[-1.7001256524105234299 ,-.95688429051328921984] 
dist 133=[-1.7708807200279241766 ,-.921380657753713833  ] 
dist 134=[-1.8390025764410833267 ,-.86634022614311352582] 
dist 135=[-1.8968703906625180290 ,-.77025556368835439475] 
dist 136=[-1.9266914231005746002 ,-.65512800972014992472] 
dist 137=[-1.9417324414531487069 ,-.52407579808705010009] 
dist 138=[-1.9431489914422311567 ,-.35622931020111667213] 
dist 139=[-1.9322317077308969051 ,-.09423637171602438860] 
dist 140=[-1.9247304176879869148 ,.1705808571036106663 ] 
dist 141=[-1.9029071221015723555 ,.3497020591507033423 ] 
dist 142=[-1.8918611619389435121 ,.50038979687706585002] 
dist 143=[-1.2925929600243857142 ,.65171843006121446429] 
dist 144=[-1.2311797328247581137 ,.79192115389058929302] 
dist 145=[-1.1372753269845731664 ,.89820207763486270396] 
dist 146=[-1.1081050677098186954 ,1.0000220202730074230 ] 
dist 147=[-1.0962404911783639736 ,1.1224218627296146157 ] 
dist 148=[-.79143656868685770479,1.2368504414880935651 ] 
dist 149=[-.75059048715410241409,1.3068544824472228249 ] 
dist 150=[-.7026561569194983381 ,1.3577508846294622963 ] 
dist 151=[-.64432284904295376998,1.3959123578515879471 ] 
dist 152=[-.55854213233658943966,1.4238013462209423436 ] 
dist 153=[-.54034836146552625771,1.4336920035233905617 ] 
dist 154=[-.50418271001280114488,1.4359868127381634859 ] 
dist 155=[-.49429321857643562101,1.4335577612310324737 ] 
dist 156=[.01643960038126325305,1.4438436626579628553 ] 
dist 157=[.05696996445559640008,1.4520329982743920374 ] 
dist 158=[.06683562036540404597,1.4519359063128527648 ] 
dist 159=[.52982144753017976105,1.3820687835453309595 ] 
dist 160=[.57091778613743066066,1.3693920895348419783 ] 
dist 161=[.6475073339156692837 ,1.3320600008645109113 ] 
dist 162=[.66385493086611181342,1.3221627150354702662 ] 
dist 163=[.70162541111988305279,1.2373521408792908354 ] 
dist 164=[.69825762501280932586,1.2176186616870534663 ] 
dist 165=[.67765717484129403196,1.1893972240469211187 ] 
dist 166=[.62816801198639305954,1.1792513962878261974 ] 
dist 167=[.53813918381762300883,1.0453353693781800007 ] 
dist 168=[.39466204746220886938,1.0822618269039319642 ] 
dist 169=[.25235319239661930876,1.1105647299160804435 ] 
dist 170=[.08358801903767257048,1.1344929995825769322 ] 
dist 171=[-.16549318584275865547,1.1537496344511353788 ] 
dist 172=[-.4138052759882369731 ,1.1633981302516617254 ] 
dist 173=[-.57950098636665627918,1.1678157237865937783 ] 
dist 174=[-.71646795113697515045,1.1663766244422636430 ] 
dist 175=[-.85010693740397818203,1.1609884902504963851 ] 
dist 176=[-.97143557296026472871,1.1569729341763396954 ] 
dist 177=[-1.0592650320298771790 ,1.1411485544738962231 ] 
dist 178=[-1.1394107963442071272 ,1.1347979803850688552 ] 
dist 179=[-1.2300701033702068049 ,1.0827637769157735482 ] 
dist 180=[-1.3120846373205663369 ,1.0691939512027022657 ] 
dist 181=[-1.3577238791533461064 ,1.0493417285717813059 ] 
dist 182=[-1.3854747380553981573 ,1.0417910077788846041 ] 
dist 183=[-1.3960849665084151472 ,.84895361563740513809] 
dist 184=[-1.4088557562363811924 ,.82108261270048554863] 
dist 185=[-1.4307926288878046712 ,.76162865624706882346] 
dist 186=[-1.4361208385473311440 ,.744266588105241352  ] 
dist 187=[-1.4319236636271456512 ,.67077979929072234806] 
dist 188=[-1.4306364979541332614 ,.65593582479219150649] 
dist 189=[-1.4296935366205758418 ,.61516735909433532449] 
dist 190=[-1.4289910518857426633 ,.6087035196361583573 ] 
dist 191=[-1.0920507447853181601 ,.56787158844618280765] 
dist 192=[-1.0623512059871531484 ,.65191951034797484833] 
dist 193=[-.98554260204822919403,.71918541803247361142] 
dist 194=[-.97222079165262044372,.78706564542272973704] 
dist 195=[-.84023660518071256015,.87356644932980152689] 
dist 196=[-.81349154920527462257,.95693064653592290853] 
dist 197=[-.7805727001971416389 ,1.0122912204333117603 ] 
dist 198=[-.76825338851846840906,1.0577612930532223501 ] 
dist 199=[-.49901558587780520507,1.1016470637194079027 ] 
dist 200=[-.46361513651468221103,1.1416083823462430716 ] 
dist 201=[-.38877002660940779852,1.1730434189488320424 ] 
dist 202=[-.36842916715947080853,1.1973891235446301422 ] 
dist 203=[-.33210373143230678404,1.2219610077239778494 ] 
dist 204=[-.54929859461749032393,1.2454440708813367076 ] 
dist 205=[-.69376203583751166261,1.2541115326594259728 ] 
dist 206=[-.81264929935728585144,1.2560082028087850540 ] 
dist 207=[-.92775683482649434532,1.2532623163649111052 ] 
dist 208=[-1.0316571475364855183 ,1.2242223223495818788 ] 
dist 209=[-1.1058106899783786500 ,1.2143395032177017059 ] 
dist 210=[-1.1723937855627228501 ,1.1995537653650887672 ] 
dist 211=[-1.2460764140691142171 ,1.1931609633888383170 ] 
dist 212=[-1.3117113133928004225 ,1.0125136119552552370 ] 
dist 213=[-1.3461718010418690817 ,1.0079351703079213105 ] 
dist 214=[-1.3653892105467078119 ,1.0696894311433480229 ] 
dist 215=[-1.3701817843276396691 ,1.1259675535120523857 ] 
dist 216=[-1.3609339152981153010 ,1.1579062489531909285 ] 
dist 217=[-1.3585743516831774201 ,1.1781547496509778049 ] 
dist 218=[-1.3571918983830142722 ,1.1877683758781752037 ] 
dist 219=[-1.3567801473739707823 ,1.1916539721162042565 ] 
dist 220=[-.02630354486086624779,1.1900788555574609842 ] 
dist 221=[-.14622300282829077452,1.1833769537279903982 ] 
dist 222=[-.32986990916166529747,1.1783662211886927005 ] 
dist 223=[-.51431608649181609292,-.03152722165334680805] 
dist 224=[-.63742663409741612795,-.15788150773409315657] 
dist 225=[-.73923573153597118496,-.18013540004359834449] 
dist 226=[-.83865418546499616642,-.22588719695695892924] 
dist 227=[-.92897925131044042533,-.23627373711900379981] 
dist 228=[-.9944911871052041863 ,-.27196407115693011017] 
dist 229=[-1.0544057218283868359 ,-.27191512103086978384] 
dist 230=[-1.1223890813485016283 ,-.25911483984589050073] 
dist 231=[-1.1839076009958839023 ,-.22555331871477125124] 
dist 232=[-1.2180170785495867107 ,-.18118913951340690736] 
dist 233=[-1.2386004939343595159 ,-.12526843060174433432] 
dist 234=[-1.2466980152205700860 ,-.05014134875806987929] 
dist 235=[-1.2538555709011843706 ,.07088823763921098622] 
dist 236=[-1.2572793206108492810 ,.19475178864325487183] 
dist 237=[-1.2586253645611998795 ,.28119086158672054532] 
dist 238=[-1.2574903642788783266 ,.35680631948178267164] 
dist 239=[-1.0908632060405359761 ,.43746489465545874281] 
dist 240=[-1.0697457795627906779 ,.51523202654829613454] 
dist 241=[-1.0132979772568489097 ,.57930528096770072871] 
dist 242=[-1.0024326583262164687 ,.64564547667091815172] 
dist 243=[-.89737782339482123049,.73543854315264071184] 
dist 244=[-.87515481409500462219,.82359982967287656425] 
dist 245=[-.84696002673788850251,.90649456648995332543] 
dist 246=[-.83630599955865724184,1.0039174304688300501 ] 
dist 247=[-.59501359099044628501,1.0938626586725466664 ] 
dist 248=[-.56255725710194824826,1.1469100520330618178 ] 
dist 249=[-.49374915944513049779,1.1831065529445054468 ] 
dist 250=[-.47469452478823956317,1.2057901617112041162 ] 
dist 251=[-.39884265895287137981,1.2210747837872926949 ] 
dist 252=[-.38387446978531839693,1.2277368355991935740 ] 
dist 253=[-.34859525648522259877,1.2293597975373916292 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 1, 1, 1, 1, 2] 
dist 0=[40.710981389805373936  ,40.710981389805373936  ] 
dist 1=[39.646660317193232904  ,41.311480954539257316  ] 
dist 2=[38.522240524775449452  ,41.688290975210509785  ] 
dist 3=[37.681653053864922819  ,41.859288020732663461  ] 
dist 4=[36.885991889641607249  ,42.001545656802807049  ] 
dist 5=[35.940754391499066154  ,42.157763124683073918  ] 
dist 6=[34.968177419678820801  ,42.222863666351887368  ] 
dist 7=[34.063112735828983807  ,42.233584811119311630  ] 
dist 8=[33.030875858818203571  ,42.198457270494543484  ] 
dist 9=[31.549999463050832468  ,40.480974097962694008  ] 
dist 10=[30.034313262153766010  ,40.200999833874631198  ] 
dist 11=[28.862844331179191975  ,39.713243299798365576  ] 
dist 12=[27.714154327730719526  ,39.576237519028967035  ] 
dist 13=[26.289217570247764745  ,39.081696241031338633  ] 
dist 14=[24.787379518771856481  ,38.926910863575198694  ] 
dist 15=[23.331159311920216696  ,38.674293457997027071  ] 
dist 16=[21.621831386806416170  ,38.585144453735846106  ] 
dist 17=[19.108154786126353966  ,27.388264109742623070  ] 
dist 18=[16.598167478184120841  ,26.421021727681364792  ] 
dist 19=[14.903525314108474571  ,24.108944646822632534  ] 
dist 20=[13.472702298614346544  ,23.750762445889955634  ] 
dist 21=[12.017188035093574454  ,20.459240654491276779  ] 
dist 22=[10.647875699346061809  ,19.848768805351468927  ] 
dist 23=[9.5615860944158949530 ,19.073865311577875755  ] 
dist 24=[8.4687130822908936895 ,18.866356901641563271  ] 
dist 25=[7.0730550590434314482 ,16.029481462615035969  ] 
dist 26=[5.7148075732282720063 ,13.239569931988383546  ] 
dist 27=[4.1163827360944663458 ,11.920215255077351060  ] 
dist 28=[2.3297729332758477080 ,11.577031293419878200  ] 
dist 29=[.7117588936972580102 ,10.267245892624843037  ] 
dist 30=[-1.1015233697490221908 ,10.016078596277617227  ] 
dist 31=[-3.6691384319733087164 ,9.5095284774051956039 ] 
dist 32=[-6.1798751689015769631 ,9.3808031546210757484 ] 
dist 33=[-7.7660399695884915217 ,3.8046192292772830835 ] 
dist 34=[-8.9882781061317333894 ,2.0058934135079004117 ] 
dist 35=[-10.044550073417342980  ,1.1847817395673963326 ] 
dist 36=[-10.922336016926859030  ,.65065829084655211134] 
dist 37=[-11.431406367413922136  ,.57032906018756415806] 
dist 38=[-11.772822425024739874  ,-.1302069681560044191 ] 
dist 39=[-11.981056111187099711  ,-.2563314242320829047 ] 
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dist 41=[-12.200478353300908106  ,-.4553018835505268787 ] 
dist 42=[-12.248042448034263974  ,-1.4130022585853322892 ] 
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dist 44=[-12.278267798525625377  ,-1.7792509927071502130 ] 
dist 45=[-12.264123495721392002  ,-1.8430415801874573651 ] 
dist 46=[-12.232279086347142294  ,-2.0759861990410552736 ] 
dist 47=[-12.191201048983056173  ,-2.1221394215846602865 ] 
dist 48=[-9.5524532997881617013 ,-2.2073104273689612974 ] 
dist 49=[-5.0549661901425349266 ,-2.2271087276530304004 ] 
dist 50=[-3.7450544908963288632 ,-2.2283509224751967912 ] 
dist 51=[-3.5545288707661071739 ,-1.3880264825620276185 ] 
dist 52=[-2.1357913510628779978 ,-.4299295677987599473 ] 
dist 53=[-1.5679910995229926666 ,.3097599044621516899 ] 
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dist 55=[-.92395398047239951316,1.9193629970424452632 ] 
dist 56=[-.7575041401392652758 ,2.7606723613653788010 ] 
dist 57=[-.7181828499845650022 ,3.2978905296769716548 ] 
dist 58=[-.0540461679944589340 ,3.7161540815981999257 ] 
dist 59=[.0293451168737655085 ,4.0826622847362693165 ] 
dist 60=[.2096703895715904446 ,4.3891918336127889515 ] 
dist 61=[.24350294364160976721,4.5681142106343449292 ] 
dist 62=[.43146097788646916458,4.6889178783458527974 ] 
dist 63=[.46159398519366606478,4.7636527783847864842 ] 
dist 64=[.52285466114297378947,4.8089011003403792424 ] 
dist 65=[.5328689995200763085 ,4.8150899790476982482 ] 
dist 66=[.57664838291452060615,4.7999066549393893178 ] 
dist 67=[.57458469270706417763,4.7842226301525491002 ] 
dist 68=[.55698344272353662893,4.6355426396017904926 ] 
dist 69=[.5140382168994863863 ,4.5930332780225517778 ] 
dist 70=[.4584507854789382721 ,4.5336324078279224701 ] 
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dist 72=[.3002251834269961609 ,3.9664291089511565944 ] 
dist 73=[.1566840768097026574 ,3.9168136591795227133 ] 
dist 74=[.0049154092990931760 ,3.7945650233460939734 ] 
dist 75=[-.1180742456902132212 ,3.7557611428235962259 ] 
dist 76=[-.2434768258978535718 ,3.5450340668491273368 ] 
dist 77=[-.4049183194876178427 ,3.4974885895142761721 ] 
dist 78=[-.79679875529941080185,3.4013624419731865872 ] 
dist 79=[-1.2576267019476234347 ,3.3716803388893514492 ] 
dist 80=[-1.9321291869413164456 ,2.4948502477997971875 ] 
dist 81=[-2.5974516078486038153 ,2.0596477422753216475 ] 
dist 82=[-3.0216517306068702068 ,1.5750907563187859854 ] 
dist 83=[-3.3507114700343432796 ,1.5152223031562089506 ] 
dist 84=[-3.6362601667166353066 ,1.0682489803013009316 ] 
dist 85=[-3.8722250161550756319 ,.9847197527342186741 ] 
dist 86=[-4.0033639111971567771 ,.8496720495312727240 ] 
dist 87=[-4.0829609966234217946 ,.8155043717370066543 ] 
dist 88=[-4.1131975884615157133 ,.2018105933066691928 ] 
dist 89=[-4.1247791992036447754 ,.1223606071712620247 ] 
dist 90=[-4.1299102923007369359 ,-.0666431890709022461 ] 
dist 91=[-4.1313866707395713736 ,-.0947072359576922929 ] 
dist 92=[-4.1283660417911142541 ,-.3559981248107983951 ] 
dist 93=[-4.1227754796908860515 ,-.4028386406206703218 ] 
dist 94=[-4.1139886429862811937 ,-.4627428554143516937 ] 
dist 95=[-4.1012292052747552992 ,-.4755823937709821842 ] 
dist 96=[-4.0844817429919004315 ,-.62459540561650856917] 
dist 97=[-2.6541318561147251367 ,-.18075656610867766748] 
dist 98=[-1.6370262652266917036 ,.26416217208332239162] 
dist 99=[-1.5420084764043284740 ,.55912297973567371189] 
dist 100=[-1.3116111546944076568 ,.80070971479262596999] 
dist 101=[-1.2724636974985754347 ,1.0326013501583585930 ] 
dist 102=[-.93286831176871269187,1.2404908050287109278 ] 
dist 103=[-.86871026495310968175,1.3862785954453474476 ] 
dist 104=[-.7787837367147137760 ,1.5144809984098193588 ] 
dist 105=[-.7517190427135739780 ,1.6521800369326900415 ] 
dist 106=[-.2326619698326740656 ,1.7880187091483879736 ] 
dist 107=[-.1669948958012541337 ,1.9380176387059470357 ] 
dist 108=[-.0788501678548949154 ,2.0627914656190557382 ] 
dist 109=[-.06004069985605537470,2.1633637555744749461 ] 
dist 110=[-.00117216973031425395,2.2167664107014444547 ] 
dist 111=[.01174274425381327530,2.2458671033822975790 ] 
dist 112=[.01332837147274829465,2.2518660813183154764 ] 
dist 113=[0                     ,2.0224776557849454409 ] 
dist 114=[.51406667377642040658,1.8775913897064694625 ] 
dist 115=[.50170827603771259859,1.9814437035654707985 ] 
dist 116=[.47449310990750132548,2.0702912807801298739 ] 
dist 117=[.42772307842697878293,2.1255732825513756072 ] 
dist 118=[.35777252144832962558,2.1669954746416675146 ] 
dist 119=[.23802179881200897096,2.2005250412564571275 ] 
dist 120=[.10813491863560659354,2.2238655883191388734 ] 
dist 121=[-.00228618588073437023,2.2283218411685902237 ] 
dist 122=[-.11956535009634004317,2.2188233330617249866 ] 
dist 123=[-.28832492514454382963,2.2160253854700706793 ] 
dist 124=[-.48884322407159795153,2.1231621187331972090 ] 
dist 125=[-.67921124989301214663,2.0981364560389278978 ] 
dist 126=[-.8986674549252994547 ,2.0817062960161947473 ] 
dist 127=[-1.2153082627776854756 ,2.0736032091327384879 ] 
dist 128=[-1.5490767082342333948 ,.8417590185802245620 ] 
dist 129=[-1.7780449339049787440 ,.21223967066624966072] 
dist 130=[-1.9583573211210268129 ,.14910775733453385102] 
dist 131=[-2.1194733394375455712 ,.02184904476541466595] 
dist 132=[-2.2559641901343253800 ,-.00990662249312745801] 
dist 133=[-2.3379864103502119849 ,-.11719948021994192845] 
dist 134=[-2.3958397041758534038 ,-.13981843133939692532] 
dist 135=[-2.4358620526196519903 ,-.1582781237049087831 ] 
dist 136=[-2.4640327546536703049 ,-.1524538697469188530 ] 
dist 137=[-2.4745810782509305048 ,-.1364587382554368664 ] 
dist 138=[-2.4742506025755162126 ,-.1084338604610816120 ] 
dist 139=[-2.4693996469305378272 ,-.0662681614019458708 ] 
dist 140=[-2.4933933007271504429 ,.0061732483217121727 ] 
dist 141=[-2.5061270202717469484 ,.0924939519434258743 ] 
dist 142=[-2.5096789499390578971 ,.1900576811363269086 ] 
dist 143=[-2.5042037966374110310 ,.3145237569514468943 ] 
dist 144=[-1.8881872448714081315 ,.5082184763860282732 ] 
dist 145=[-1.3573704912886988688 ,.7030846265838426790 ] 
dist 146=[-1.1775951570862457300 ,.83466413960576454046] 
dist 147=[-1.1410705991002993969 ,1.0708974247251312484 ] 
dist 148=[-.89365192181698964375,1.2831461680995949914 ] 
dist 149=[-.84687817595282956958,1.4328928844505081741 ] 
dist 150=[-.76259715451081379903,1.5655632583480747468 ] 
dist 151=[-.74254751933778443054,1.7096585338794573154 ] 
dist 152=[-.41550106080231694459,1.8409982660409542401 ] 
dist 153=[-.37092240885698825732,1.9227552666974247430 ] 
dist 154=[-.27129714426627864605,1.9838650600445299356 ] 
dist 155=[-.25061142419472406806,2.0327858652231235081 ] 
dist 156=[-.13100749086868912831,2.0701170399345530020 ] 
dist 157=[-.10978423341272237935,2.0849618471923384392 ] 
dist 158=[-.06668186845781927169,2.0879073069145895003 ] 
dist 159=[-.05577516478531050359,2.0847075486422602811 ] 
dist 160=[-.11341703902110879136,1.4198757520867497921 ] 
dist 161=[-.405054001052268535  ,1.1388821655775514296 ] 
dist 162=[-.59833774485204471015,1.1078813421868110916 ] 
dist 163=[-.7565833434032625461 ,1.0330477182389348091 ] 
dist 164=[-.90837410480012330565,1.0148464152574417854 ] 
dist 165=[-1.0443813925288093697 ,.89886309833822592863] 
dist 166=[-1.1396301026850893783 ,.87493928598694619616] 
dist 167=[-1.2232503819210656436 ,.83053768335291079329] 
dist 168=[-1.3128426619246803880 ,.81863298890523407876] 
dist 169=[-1.3935249428790186926 ,.61079743202881642709] 
dist 170=[-1.4415833584076541073 ,.58203426111213454148] 
dist 171=[-1.4749301875790282361 ,.5101439987655050029 ] 
dist 172=[-1.4968983976633698751 ,.49915778620332904414] 
dist 173=[-1.5100674986311774283 ,.3867315277820664028 ] 
dist 174=[-1.5121374394868851027 ,.3652538991309545354 ] 
dist 175=[-1.5026700655660775518 ,.3399398546350687888 ] 
dist 176=[-1.5004591725168246509 ,.33363510665077145298] 
dist 177=[-1.3298355860060066752 ,.30061637022936339558] 
dist 178=[-1.4238723913657849024 ,.31599722790720735801] 
dist 179=[-1.5040773075362436498 ,.3405048733472051661 ] 
dist 180=[-1.5692933128011448958 ,.3689899418241537316 ] 
dist 181=[-1.6034999005954352455 ,.4002452094033375360 ] 
dist 182=[-1.6215590127255394592 ,.4395058255193340261 ] 
dist 183=[-1.6251762633553412777 ,.4999403735562148859 ] 
dist 184=[-1.6163404129144521293 ,.56311187947328364079] 
dist 185=[-1.6094064572429814639 ,.61329602047178826296] 
dist 186=[-1.5956794826164045197 ,.66356436709684886237] 
dist 187=[-1.5889121973699919504 ,.72707275690015676261] 
dist 188=[-1.5649894502372904164 ,.79421332416093312217] 
dist 189=[-1.5383705899505310012 ,.85897803007864675145] 
dist 190=[-1.5253471552597522993 ,.93439359535913849394] 
dist 191=[-1.5058607468584054966 ,1.0440419110999446707 ] 
dist 192=[-1.4982952341138082160 ,1.1513357029533501537 ] 
dist 193=[-1.2796148862613031333 ,1.2173542526091788675 ] 
dist 194=[-1.3571106848054788640 ,1.2657635827756676421 ] 
dist 195=[-1.4132809939776820117 ,1.3027784866439039434 ] 
dist 196=[-1.4550660340234015281 ,1.3298544753144822450 ] 
dist 197=[-1.4858815101038638159 ,1.3385965828544668169 ] 
dist 198=[-1.4982660532564723735 ,1.3404499653873660474 ] 
dist 199=[-1.5017850236122404445 ,1.3400343758609823382 ] 
dist 200=[-1.4993176263164864625 ,1.2823020983519857658 ] 
dist 201=[-1.4128397562099965695 ,1.2629545634042508138 ] 
dist 202=[-1.3956976578092634471 ,1.3109766827161856871 ] 
dist 203=[-1.3611674536496041440 ,1.3463205731127615809 ] 
dist 204=[-1.3496314172085945678 ,1.3718221407908726639 ] 
dist 205=[-1.2954706400080835043 ,1.3839953034030786664 ] 
dist 206=[-1.2824842049676897891 ,1.3896546127254981205 ] 
dist 207=[-1.2425797767581074958 ,1.3893357435105630536 ] 
dist 208=[-1.2341459758173966787 ,1.3880241936691313507 ] 
dist 209=[-.4900210158401651502 ,1.0423525286109101412 ] 
dist 210=[-.4207169051371711789 ,.9898255570444436538 ] 
dist 211=[-.2644203324777114379 ,.94691230626723724784] 
dist 212=[-.2335795641629542832 ,.88351932872775994051] 
dist 213=[-.0425055385924541062 ,.80693618011537370676] 
dist 214=[-.0763985130696547126 ,.7629482064431576781 ] 
dist 215=[-.2272102012113806483 ,.7512840794808641476 ] 
dist 216=[-.37761097157825284426,.66855008760829474555] 
dist 217=[-.4859686858154226694 ,.70686425613147085273] 
dist 218=[-.58430034583129257283,.76713003916616105351] 
dist 219=[-.69468493321904129584,.82324792094379913504] 
dist 220=[-.80439958440432840929,.88839022653969188102] 
dist 221=[-.90005883822103473188,.95435863296106935882] 
dist 222=[-1.0037709544868121353 ,1.0137726051298579443 ] 
dist 223=[-1.1456306570658258828 ,1.0797712984101403494 ] 
dist 224=[-1.2826061019219184607 ,1.1720198905048668330 ] 
dist 225=[-1.3668230978541444629 ,1.2610755628837449683 ] 
dist 226=[-1.4285436520108189587 ,1.3143296640418250949 ] 
dist 227=[-1.4757236681680717794 ,1.3515554891556732862 ] 
dist 228=[-1.5111807637245680335 ,1.3766368708400650273 ] 
dist 229=[-1.5261091717181251785 ,1.3931410247988109569 ] 
dist 230=[-1.5313364415384838295 ,1.3961325028989811990 ] 
dist 231=[-1.5292550831001924910 ,1.3937547112960222862 ] 
dist 232=[-1.4516345729004224094 ,1.3888291387926058504 ] 
dist 233=[-1.4009027434373582459 ,1.3006388076724021044 ] 
dist 234=[-1.4131156583546564185 ,1.2836336851794295043 ] 
dist 235=[-1.4170168614087556155 ,1.2441565920931885814 ] 
dist 236=[-1.4155252880137731613 ,1.2303255735278634544 ] 
dist 237=[-1.3783617620203855419 ,1.1622759516934230856 ] 
dist 238=[-1.3660381900265814083 ,1.1465053088430677394 ] 
dist 239=[-1.3553457617583539623 ,1.1075954169188189532 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 0, 1, 2] 
dist 0=[57.736484971681920518  ,57.736484971681920518  ] 
dist 1=[57.561540782898464915  ,57.828103136737992877  ] 
dist 2=[57.157036593130216401  ,57.899955229620238768  ] 
dist 3=[56.441253562878521164  ,57.936956930279057681  ] 
dist 4=[55.023483478471111829  ,57.889218242342994858  ] 
dist 5=[53.411087849211352483  ,57.769686727670850825  ] 
dist 6=[51.917965678714370275  ,57.674686176455416971  ] 
dist 7=[50.223318510361183842  ,54.226252830036980176  ] 
dist 8=[47.805939659303382252  ,53.664708620226657067  ] 
dist 9=[45.102393221983323455  ,52.704447526988115887  ] 
dist 10=[42.264796699167122630  ,52.437924904884053176  ] 
dist 11=[38.778815693646963671  ,51.578496978377676149  ] 
dist 12=[33.485719237122144627  ,51.294291460914618789  ] 
dist 13=[28.160782860553731972  ,51.012827087016594125  ] 
dist 14=[24.547531680220347518  ,50.420664591489224545  ] 
dist 15=[21.487592312488134722  ,34.884038015017183265  ] 
dist 16=[18.372181610030631291  ,33.862355111095592349  ] 
dist 17=[15.449643295601185205  ,31.855874449974715114  ] 
dist 18=[13.159730179456781306  ,31.338124023683255940  ] 
dist 19=[10.887816353841726232  ,29.517112560872970031  ] 
dist 20=[8.0366590103288556454 ,29.096977287957877433  ] 
dist 21=[5.2954619230839717709 ,28.528705121559548860  ] 
dist 22=[3.4624423828325190237 ,28.339228555219980532  ] 
dist 23=[1.9365775986886250547 ,10.312077613349568344  ] 
dist 24=[.4218103395756859554 ,8.8599967693985598557 ] 
dist 25=[-.97940824234129407391,7.1183358012349775796 ] 
dist 26=[-2.0522823307322996553 ,6.8534520729532837721 ] 
dist 27=[-3.2033000115997580969 ,4.9128025174768007382 ] 
dist 28=[-4.9977872454373392148 ,4.6106692939095832289 ] 
dist 29=[-6.6934850785613126228 ,4.0944943994250700404 ] 
dist 30=[-8.7049276587936505178 ,4.0021852038860727379 ] 
dist 31=[-10.580658770130015194  ,-4.9171487211002462465 ] 
dist 32=[-11.734268073701989320  ,-5.3781576833588071302 ] 
dist 33=[-12.583314453980736859  ,-6.1513402224133895524 ] 
dist 34=[-13.242505366616141784  ,-6.3076711492745529193 ] 
dist 35=[-13.756254335127463936  ,-6.4624947118586941806 ] 
dist 36=[-14.024391526262564268  ,-6.2724524956380184373 ] 
dist 37=[-14.165053144106501193  ,-5.8578012215291969912 ] 
dist 38=[-14.177746166147846963  ,-5.0330691243428999749 ] 
dist 39=[-10.036504582209020935  ,-4.1502375111224550563 ] 
dist 40=[-10.053117659941405805  ,-3.5035053557441832702 ] 
dist 41=[-10.039579662393146942  ,-2.9086677902508033770 ] 
dist 42=[-10.013601004909079464  ,-2.2322441911629743092 ] 
dist 43=[-9.9071361991469115509 ,-1.5573683858923095478 ] 
dist 44=[-9.8621900582239144240 ,-.15248280246344685882] 
dist 45=[-9.7153215976355330685 ,1.4497635754327868799 ] 
dist 46=[-9.6549245830574857797 ,2.5140066088429234980 ] 
dist 47=[-5.1963847695572976125 ,3.3879135661640024878 ] 
dist 48=[-4.7921970796809650185 ,4.2304549140648126997 ] 
dist 49=[-3.8307896692941311589 ,4.9881499086840314119 ] 
dist 50=[-3.6771356885868949150 ,5.5233629075123789088 ] 
dist 51=[-2.3433767919872134200 ,5.9978258144588933254 ] 
dist 52=[-2.1013053047707583307 ,6.5129336517928489924 ] 
dist 53=[-1.7643492137014229979 ,6.9793117484460883778 ] 
dist 54=[-1.6670698386406646611 ,7.2593115205360583572 ] 
dist 55=[.0779476537791097006 ,7.4561477778315038440 ] 
dist 56=[.2919376055797041175 ,7.5908084951633128189 ] 
dist 57=[.77739700882247411466,7.6754165845101684667 ] 
dist 58=[.85128021567573772357,7.6915288396394428876 ] 
dist 59=[1.4298617566555491905 ,7.6467991501221607950 ] 
dist 60=[1.5243707529670960617 ,7.6391763137043325870 ] 
dist 61=[1.6732815721114709504 ,5.3958058701212684626 ] 
dist 62=[1.7052531433526165705 ,5.4036087639653845173 ] 
dist 63=[1.4852287912763027576 ,4.6418739065329793277 ] 
dist 64=[.87858693689998281995,4.7109764418384210351 ] 
dist 65=[.3021153161292820255 ,4.7471430588016991357 ] 
dist 66=[-.1586634980075289261 ,4.7502987081783926302 ] 
dist 67=[-.6230043626189898072 ,4.7332335130201610193 ] 
dist 68=[-1.2137831563527789482 ,4.7187578358452894361 ] 
dist 69=[-1.7828170877295913092 ,4.6689269964349377075 ] 
dist 70=[-2.1604110305289710827 ,4.6428470532697014598 ] 
dist 71=[-2.4703687540965102439 ,3.0975352140021784650 ] 
dist 72=[-2.8912531444170783032 ,3.1502669870447967622 ] 
dist 73=[-3.2993781635801708792 ,3.1898830337656678811 ] 
dist 74=[-3.6713408916794417257 ,3.2218464378606724511 ] 
dist 75=[-3.9919288649034807419 ,3.2461526458686835679 ] 
dist 76=[-4.1950053122459055262 ,3.2551353628877602163 ] 
dist 77=[-4.3511426535494164160 ,3.2542400071339574823 ] 
dist 78=[-4.4844079825436166338 ,3.2476954252097400745 ] 
dist 79=[-4.5924975109228332630 ,3.2159590588050199403 ] 
dist 80=[-4.6481374530006463719 ,3.2021725559545770350 ] 
dist 81=[-4.6762165191268190393 ,3.1531171868885553740 ] 
dist 82=[-4.7072524043603538532 ,3.1348784377950669683 ] 
dist 83=[-4.7475978903618357271 ,2.9856410695257046949 ] 
dist 84=[-4.7552687781662019108 ,2.9470204266359934700 ] 
dist 85=[-4.7433219254728708210 ,2.8915987021201847655 ] 
dist 86=[-4.7304803474080827159 ,2.8701792506482740169 ] 
dist 87=[-3.7721005408991637190 ,2.3213002508490456779 ] 
dist 88=[-3.8735014390492625306 ,2.2415816105484393429 ] 
dist 89=[-3.9361518337111076230 ,2.0739931109313391802 ] 
dist 90=[-3.9562688710424700756 ,2.2318926488708143985 ] 
dist 91=[-3.9587163161911034423 ,2.5742152571687032658 ] 
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dist 94=[-3.9206674142133951027 ,3.8369275110077642655 ] 
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dist 100=[-2.2857300940427774608 ,4.4728948303904000393 ] 
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dist 119=[-3.5230746129511670974 ,.98650552895832385043] 
dist 120=[-3.6260148661588611235 ,.97184399333786961603] 
dist 121=[-3.7016793338783632929 ,.94096247368098773388] 
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dist 125=[-1.5182770611344377779 ,.844944853581151622  ] 
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dist 131=[-2.1075490608187144664 ,.65339580877372467689] 
dist 132=[-2.1192984983009965411 ,.64128601593418352685] 
dist 133=[-2.1205001144738761635 ,.61682729695691509315] 
dist 134=[-2.1146244550794458074 ,.6093592905570816634 ] 
dist 135=[-.8983484991638020733 ,.57036528027999436779] 
dist 136=[-.8175998919727793291 ,.64807880231601252256] 
dist 137=[-.6345131687312543759 ,.72297580543479316372] 
dist 138=[-.5974760235259359273 ,.78464087350682721109] 
dist 139=[-.3688684884971928742 ,.84846555387070747399] 
dist 140=[-.3278332610670837511 ,.93199354139898736506] 
dist 141=[-.2482469820227942469 ,1.0112543923717996228 ] 
dist 142=[-.2293598159753731925 ,1.0580485480021921215 ] 
dist 143=[-.23983650262655060266,1.0900714516680177695 ] 
dist 144=[-.29438300336321685318,1.1103671397419131365 ] 
dist 145=[-.34840722444052761568,1.1237356128387408902 ] 
dist 146=[-.395136953495668806  ,1.1281040657850578940 ] 
dist 147=[-.4454535856831995056 ,1.1270762420160873324 ] 
dist 148=[-.51379402754070748141,1.1248887406720418113 ] 
dist 149=[-.58159787301630777307,1.1328349360767454606 ] 
dist 150=[-.62977403964505081678,1.2809178312963357633 ] 
dist 151=[-.8094929056451486972 ,1.4230492230017488981 ] 
dist 152=[-.93319480756719341793,1.5104666260347455987 ] 
dist 153=[-1.0333012600391926520 ,1.5746439456499237216 ] 
dist 154=[-1.1273172498466805185 ,1.6240028887372290243 ] 
dist 155=[-1.2101548330666408891 ,1.6606324113788837013 ] 
dist 156=[-1.2656441563405936265 ,1.6739900054628227127 ] 
dist 157=[-1.3116753643798877054 ,1.6779839839522086552 ] 
dist 158=[-1.3567562880090587448 ,1.6772301475632083937 ] 
dist 159=[-1.3945768696138232407 ,1.6076838552890938765 ] 
dist 160=[-1.4116320141619913434 ,1.5922397008325046021 ] 
dist 161=[-1.4186495689496698425 ,1.5566817460665141716 ] 
dist 162=[-1.4176526555487800598 ,1.5434781577296395333 ] 
dist 163=[-1.3924790392880627150 ,1.4760044172831974028 ] 
dist 164=[-1.3824946568125562098 ,1.4598742302490612419 ] 
dist 165=[-1.3696493090631061381 ,1.4167630340975527346 ] 
dist 166=[-1.3626890991760420081 ,1.4032129986715188327 ] 
dist 167=[-1.0791995811977675978 ,-.62691823564453359499] 
dist 168=[-1.1002454798370897517 ,-.52757085182227045538] 
dist 169=[-1.1143340421817087033 ,-.41875298622990786967] 
dist 170=[-1.1203194327436012664 ,-.30813967068391244248] 
dist 171=[-1.1215194294703436514 ,-.17500888759913657914] 
dist 172=[-1.1193683313827237921 ,.02368299886815633089] 
dist 173=[-1.0526002234039580113 ,.22246733257490855876] 
dist 174=[-1.0522465652111492745 ,.35596652261218819018] 
dist 175=[-.95317354815869176892,.46721869306451224169] 
dist 176=[-.93689109312160587997,.57720673283505215133] 
dist 177=[-.91092873971124987549,.67796756857412175904] 
dist 178=[-.90267277535691864386,.75238972970934492833] 
dist 179=[-.87846206999774923073,.82177066156941058856] 
dist 180=[-.86954190906243581476,.90240786787060578438] 
dist 181=[-.86092531817217125059,.97631987618785615439] 
dist 182=[-.85538791061596625058,1.0188574023424931531 ] 
dist 183=[-.45910759156410905395,1.0465470070668039248 ] 
dist 184=[-.44169501712574586329,1.0611957652953393059 ] 
dist 185=[-.37417380433098296799,1.0699586054408753964 ] 
dist 186=[-.36033863013658942183,1.0741580076273779682 ] 
dist 187=[-.33065862923026226434,1.0758144425045029496 ] 
dist 188=[-.32210872498826368323,1.0744349742036917864 ] 
dist 189=[-.21577241649924005746,1.0172587482063801144 ] 
dist 190=[-.29482259669383139992,1.0285611568996815063 ] 
dist 191=[-.36049465886258855273,1.0331055415036651704 ] 
dist 192=[-.42507089693175448175,1.0337143189756184019 ] 
dist 193=[-.48398862657176737531,1.0050729698826173288 ] 
dist 194=[-.5270753072477799057 ,.99713989698128444563] 
dist 195=[-.56680742331128054847,.99192251060368737826] 
dist 196=[-.61233405308691353785,.98905136970029858532] 
dist 197=[-.6536981067566389899 ,.84999552695357134757] 
dist 198=[-.6768157151394314563 ,.85040777181431727878] 
dist 199=[-.69097883567084231399,.7195930197532944702 ] 
dist 200=[-.69660363292192833667,.70651427145129644928] 
dist 201=[-.69884436727810162942,.66126501854516107559] 
dist 202=[-.69950345489867027169,.64904704651200282981] 
dist 203=[-.69912563139334350175,.63510159627182242495] 
dist 204=[-.69723516691689416527,.6287925039461458212 ] 
dist 205=[-.5963182473992094785 ,.01337095080347335424] 
dist 206=[-.5828333777445178547 ,.09368300425028042774] 
dist 207=[-.5458178166414209152 ,.16173786406600015973] 
dist 208=[-.5400399630614276514 ,.23086930265358735697] 
dist 209=[-.54258078398938894733,.295408480273652477  ] 
dist 210=[-.61592416408529501355,.34513298885636724887] 
dist 211=[-.68713645189611360031,.39353104520505814828] 
dist 212=[-.77408080203821111143,.4527741688472483294 ] 
dist 213=[-.85602277924471845753,.5086598404243811112 ] 
dist 214=[-.90726856851426380447,.5436563936457445889 ] 
dist 215=[-.94585292855522302265,.5700483298681913792 ] 
dist 216=[-.97725771229528103171,.5915895023928411153 ] 
dist 217=[-1.0016513759823306588 ,.6083510670679509357 ] 
dist 218=[-1.0122514669255790361 ,.6156648873497794404 ] 
dist 219=[-1.0161126748977736409 ,.6186239253243119633 ] 
dist 220=[-1.0150518691919941401 ,.6180097727003104303 ] 
dist 221=[-.80917276645733759673,.6042166346470794599 ] 
dist 222=[-.80701769964669531091,.6001818937066767538 ] 
dist 223=[-.71077110241488488085,.5879861460791998955 ] 
dist 224=[-.69576398301302650681,.5832573686862616819 ] 
dist 225=[-.6680881209330681823 ,.5523908360573933183 ] 
dist 226=[-.66038018357947605768,.5408764775992003107 ] 
dist 227=[-.63148050539313516788,.58577623138905925158] 
dist 228=[-.6233939579582325856 ,.66130805582288179251] 
dist 229=[-.60878987588012840623,.73302791070813899936] 
dist 230=[-.6042553943661816009 ,.77879864681530137178] 
dist 231=[.05699242136123386192,.81468534939997825533] 
dist 232=[.10702555464570064416,.845288576099309495  ] 
dist 233=[.21436970928256197375,.87072298175070180662] 
dist 234=[.20709894431488747185,.88489396506682846938] 
dist 235=[.1177469947819904068 ,.89347326422501371366] 
dist 236=[-.02256671759180175702,.89667336980784890409] 
dist 237=[-.16466093456240570917,.89601544416084010489] 
dist 238=[-.2611195346799271769 ,.8944787705686938242 ] 
dist 239=[-.34262887054253047407,.88205787693888579305] 
dist 240=[-.42505611708669740102,.88012729585728760347] 
dist 241=[-.50177196984149619848,.82867748709042833754] 
dist 242=[-.56048547728895168016,.81596316147191676815] 
dist 243=[-.61726236860349092335,.80777742152274942298] 
dist 244=[-.68624875056252882366,.80542054883846373218] 
dist 245=[-.75108450618437966   ,.6052326929185010587 ] 
dist 246=[-.79129502374508709543,.57854043963938926345] 
dist 247=[-.82117062230017994192,.52793303205633870234] 
dist 248=[-.84475653516727836534,.51494325370794723345] 
dist 249=[-.86249585688110612289,.4708168478356044348 ] 
dist 250=[-.86903596788922128843,.45937511487003045533] 
dist 251=[-.87070305003936955954,.44843990900207406948] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 0, 0, 2, 0, 1] 
dist 0=[43.883495363076618448  ,43.883495363076618448  ] 
dist 1=[43.048366088976640719  ,44.247828807991542457  ] 
dist 2=[41.725382162026968410  ,44.867447761824559797  ] 
dist 3=[39.610582545378895470  ,45.515736660139889828  ] 
dist 4=[37.441981498850101215  ,45.828019232837164315  ] 
dist 5=[35.904007750274738031  ,45.983404411090647301  ] 
dist 6=[34.529832554528335284  ,46.005076473741796982  ] 
dist 7=[33.015145173329160876  ,45.668288485346768173  ] 
dist 8=[31.520893193463050499  ,45.372475902820852669  ] 
dist 9=[30.228101155109068952  ,45.159807305775042246  ] 
dist 10=[28.831027324798257734  ,45.064093019814055913  ] 
dist 11=[26.919867342480254892  ,44.688135584431955827  ] 
dist 12=[25.004487355086614097  ,44.559334795376760090  ] 
dist 13=[23.590333776163568654  ,44.226429985172510187  ] 
dist 14=[22.266805082421069420  ,44.086888289206512230  ] 
dist 15=[20.713115022795355102  ,43.249062870409267905  ] 
dist 16=[19.121388712476855771  ,32.082864206352631930  ] 
dist 17=[17.645517650479053672  ,29.672928029911381836  ] 
dist 18=[15.963928263734074021  ,29.292196310389449188  ] 
dist 19=[13.549556854488753224  ,25.753778884048199681  ] 
dist 20=[11.158668335538993219  ,25.085625816706790812  ] 
dist 21=[9.5708138233451865090 ,24.243597658049185514  ] 
dist 22=[8.2581443008096086951 ,23.999385695548494006  ] 
dist 23=[6.9671846061941169961 ,18.256616296760128231  ] 
dist 24=[5.7798353804253919548 ,17.521358231236574926  ] 
dist 25=[4.8812504118352039932 ,15.988299194753432746  ] 
dist 26=[4.0165271406843167286 ,15.581491932746305147  ] 
dist 27=[2.9643733006828979293 ,14.045499469056287822  ] 
dist 28=[1.9633926002439082593 ,13.744475052886372082  ] 
dist 29=[.4360030478984571304 ,13.128578989960758671  ] 
dist 30=[-1.3624249471001520151 ,12.966211539411489346  ] 
dist 31=[-3.8749768892740518526 ,4.1767479072681146826 ] 
dist 32=[-6.3237396391574840759 ,3.3952384987732962187 ] 
dist 33=[-7.8674522596601652964 ,1.6584526526373000422 ] 
dist 34=[-9.0533391295070345763 ,1.3436116480954845313 ] 
dist 35=[-10.071999165348774327  ,.683866047675994614  ] 
dist 36=[-10.914169786388912646  ,.20511991143401361976] 
dist 37=[-11.394861914143699281  ,.14418264704257087428] 
dist 38=[-11.707721803282913856  ,.01893861175759107026] 
dist 39=[-11.879630308249828854  ,-.01154051813974352726] 
dist 40=[-11.987442394165262572  ,-.15003250721936098226] 
dist 41=[-12.044078930366727700  ,-.17825981164763275865] 
dist 42=[-12.077069415260953636  ,-.23646370097382066894] 
dist 43=[-12.136987470433508633  ,-.25422133266608896275] 
dist 44=[-12.201467913336910830  ,-.48544653083524917202] 
dist 45=[-12.206391349547630298  ,-.5226991441680991603 ] 
dist 46=[-12.187538117988335936  ,-.60924704521051871195] 
dist 47=[-12.006441841322600074  ,-.63528234795537281072] 
dist 48=[-5.3336327388566756755 ,-.77072413614168218453] 
dist 49=[-4.7823079080041615485 ,-.80112533599021743627] 
dist 50=[-3.4674153093646660752 ,-.8622629084412555803 ] 
dist 51=[-3.2742715308911874537 ,-.88094362325908109392] 
dist 52=[-1.4628842323277464446 ,-.40174116385679495188] 
dist 53=[-1.1386876379503054813 ,.32355313006763913706] 
dist 54=[-1.0688603781590454391 ,1.0286189281672350081 ] 
dist 55=[-.64615342141228896759,1.8914341683655169293 ] 
dist 56=[-.15311933472634019483,2.7072908247189626372 ] 
dist 57=[-.10086863204949035989,3.2249795729010946159 ] 
dist 58=[-.00205020826375644905,3.6243039489639532112 ] 
dist 59=[.02048607443723903680,3.9677139455097181396 ] 
dist 60=[.25865481015345519521,4.2502223443567226492 ] 
dist 61=[.29354079862559743413,4.4065201891031833036 ] 
dist 62=[.33880985544786351923,4.5013722875898261707 ] 
dist 63=[.34510983321374122283,4.5388033727610095892 ] 
dist 64=[.3366058876629314602 ,4.5477910992886471953 ] 
dist 65=[.30644116289015168198,4.5420463756479171285 ] 
dist 66=[.2547815774209306553 ,4.5031485999876564599 ] 
dist 67=[.16049589940429849803,4.4828494495078856748 ] 
dist 68=[.06056614604531242348,4.3184192805186459423 ] 
dist 69=[-.01362752551446929653,4.2745268846146467250 ] 
dist 70=[-.08304778747599698771,4.2064388127487684357 ] 
dist 71=[-.16395647168689859266,4.1817856266451107576 ] 
dist 72=[-.24594709496746806878,3.6618248573124679609 ] 
dist 73=[-.31969945880785293686,3.6094902170974949622 ] 
dist 74=[-.40149269861732006647,3.5855162384629125304 ] 
dist 75=[-.51558689934789754584,3.5802666843379858463 ] 
dist 76=[-.71372211386038086558,3.5706075778848004347 ] 
dist 77=[-1.3138216617529645934 ,3.5559753845590612178 ] 
dist 78=[-2.1983036728430224801 ,3.5448877666996065542 ] 
dist 79=[-3.0727962479682593600 ,3.0548637928086269951 ] 
dist 80=[-3.6330449548232124997 ,1.8715270734913031637 ] 
dist 81=[-4.0707545574354350585 ,1.7457829442914805630 ] 
dist 82=[-4.4561092819276336272 ,1.4540510192378695566 ] 
dist 83=[-4.7786971281381373962 ,1.3977071751226560159 ] 
dist 84=[-4.9658696111859238335 ,1.0042511536991395509 ] 
dist 85=[-5.0899281628937360242 ,.93061042353610101377] 
dist 86=[-5.1606110907454782030 ,.80290698183932745011] 
dist 87=[-5.2066372596830299729 ,.77302324286596913037] 
dist 88=[-5.2322664888009142579 ,.25180141340321087102] 
dist 89=[-5.2480263974865955534 ,.18259971437734802871] 
dist 90=[-5.2546099268929763397 ,.01926165513247728770] 
dist 91=[-5.2548867916768991055 ,-.00710603520244885183] 
dist 92=[-5.2454446320249913961 ,-.23116613569011428329] 
dist 93=[-5.2270747898727132782 ,-.27184546336261001487] 
dist 94=[-5.2078599673673199324 ,-.32925072533693740724] 
dist 95=[-3.4844807965669991223 ,-.34557823451467312207] 
dist 96=[-2.0992220487152103939 ,-.71422191992318437118] 
dist 97=[-2.1027996297845686561 ,-.49267698199830736937] 
dist 98=[-2.1009335837560653388 ,.00267613853435407558] 
dist 99=[-2.0945878285369831966 ,.46598102528333983677] 
dist 100=[-1.8290150088439982288 ,.82447848337109206653] 
dist 101=[-1.7924970675655425634 ,1.1749437431399188275 ] 
dist 102=[-1.6894445309103881145 ,1.6061906087461275269 ] 
dist 103=[-1.6744449043253873252 ,2.0143191496156698225 ] 
dist 104=[-1.4703561902513191867 ,2.2725085634142551424 ] 
dist 105=[-1.4277373814449312502 ,2.4703608136034505872 ] 
dist 106=[-1.3885627405530128148 ,2.6376540373882943321 ] 
dist 107=[-1.3803376294561389405 ,2.7736490379932726098 ] 
dist 108=[-.87863334098263120482,2.8465738021727537258 ] 
dist 109=[-.81464500312502217956,2.8872658913020343230 ] 
dist 110=[-.68816431298331404849,2.8965307097544045898 ] 
dist 111=[-.65575066198200665721,2.1055359718203249145 ] 
dist 112=[-.54317009706791169512,2.1241159479342988312 ] 
dist 113=[-.51741269409519411738,2.1299375476324763302 ] 
dist 114=[-.4879063654189196784 ,2.1259577997451195504 ] 
dist 115=[-.48022091634048038762,2.0777759871360569116 ] 
dist 116=[.31211272442153931465,2.1011034597109729830 ] 
dist 117=[.24972884836433054145,2.1378603847903809958 ] 
dist 118=[.16670884607997962857,2.1594109417979801799 ] 
dist 119=[.03393547524730521334,2.1660240819900373169 ] 
dist 120=[-.10675995246733857358,2.1633061465487422157 ] 
dist 121=[-.22141268843501234141,2.1589557136868293275 ] 
dist 122=[-.34475209039470978795,2.1309348490731548046 ] 
dist 123=[-.52379853476186393763,2.1243302802233478580 ] 
dist 124=[-.70928013894291125966,2.0139772276709635552 ] 
dist 125=[-.88274244585736030358,1.9863027984529859866 ] 
dist 126=[-1.0806815420991302836 ,1.9620396090770037700 ] 
dist 127=[-1.3638793990896994487 ,1.9497113267745493429 ] 
dist 128=[-1.6408899089676925557 ,.17587651634934526994] 
dist 129=[-1.8141372259424859813 ,-.02849372331382873600] 
dist 130=[-1.9446332323337459843 ,-.07588527574794345458] 
dist 131=[-2.0509996074573742814 ,-.28097659686744141486] 
dist 132=[-2.1564376616549479891 ,-.31793939314609788142] 
dist 133=[-2.2541994900423897923 ,-.38810363331718219307] 
dist 134=[-2.3299107355030853842 ,-.40367529879234929645] 
dist 135=[-2.3953594594059648163 ,-.44166129373261573819] 
dist 136=[-2.4481261567677320979 ,-.43327291123814284683] 
dist 137=[-2.4732178269300086773 ,-.40357121901346632628] 
dist 138=[-2.4828557335941583962 ,-.33708626033582764579] 
dist 139=[-2.4898409200741787669 ,-.25210359565166544606] 
dist 140=[-2.5117099151848486174 ,-.14857039269741842253] 
dist 141=[-2.5143163570419167721 ,-.01165258833726124072] 
dist 142=[-2.5076000292173932597 ,.20657515422888910397] 
dist 143=[-2.4989079974077772168 ,.42797501740900730356] 
dist 144=[-1.4633141369564976997 ,.57755685339207666387] 
dist 145=[-1.3714816237203750060 ,.70314837984196293109] 
dist 146=[-1.1486315053252767873 ,.82880789975615521984] 
dist 147=[-1.1119934680419180610 ,1.0515708833922969902 ] 
dist 148=[-.78453291687414875697,1.2578487072824527050 ] 
dist 149=[-.72311583439879393969,1.4018241246018436448 ] 
dist 150=[-.63973686275940728692,1.5277354548411646249 ] 
dist 151=[-.61395824791701478631,1.6619087813618969365 ] 
dist 152=[-.22345972842417454957,1.7839012855482975168 ] 
dist 153=[-.18319102876030887385,1.8611963354418815187 ] 
dist 154=[-.10324613337003427488,1.9205471179763816701 ] 
dist 155=[-.08345652737776558152,1.9709270748406238489 ] 
dist 156=[-.01796725252928255169,2.0116976877309101172 ] 
dist 157=[-.00353208311496434617,2.0327009672075861082 ] 
dist 158=[-.18129651911314322542,2.0432690184377545722 ] 
dist 159=[-.46234233591827467441,2.0423996828964067827 ] 
dist 160=[-.64968109622057500214,1.3617839697608593364 ] 
dist 161=[-.80422413009569900818,1.3208458708497211649 ] 
dist 162=[-.95437801809054766216,1.3087012229150251871 ] 
dist 163=[-1.0901796359363655375 ,1.2220883468323904630 ] 
dist 164=[-1.1874398511921814034 ,1.2019204970293563583 ] 
dist 165=[-1.2750691851521398358 ,1.1679523803516214717 ] 
dist 166=[-1.3724295607183880030 ,1.1577523190275054769 ] 
dist 167=[-1.4602709079711778085 ,.92340007117707685782] 
dist 168=[-1.5099084119978698815 ,.89016923263675385958] 
dist 169=[-1.5410403862125827126 ,.81438058373800844373] 
dist 170=[-1.5550264739368945215 ,.79465460004626380028] 
dist 171=[-1.5611788218350699952 ,.69241132093944403073] 
dist 172=[-1.5610468255579387576 ,.6720611112560675571 ] 
dist 173=[-1.5562734451008598748 ,.62838183553390929199] 
dist 174=[-1.5515401501276238486 ,.61555649724524959324] 
dist 175=[-1.2250580808120523635 ,.33308355661510799281] 
dist 176=[-1.3936698570524741014 ,.40700748741201129573] 
dist 177=[-1.4976053856807398309 ,.46072233982198589572] 
dist 178=[-1.5741136760278751309 ,.5099209671964460853 ] 
dist 179=[-1.6332453833065698818 ,.56581759929030796248] 
dist 180=[-1.6785316110910301562 ,.6217359854142334107 ] 
dist 181=[-1.6997737106229542555 ,.67101973172588234944] 
dist 182=[-1.7085168223788827183 ,.72487550775067372309] 
dist 183=[-1.7083125297630081965 ,.79903886192333452429] 
dist 184=[-1.6367599768827653861 ,.87309462610166708362] 
dist 185=[-1.6555685325684274840 ,.92651973491329564242] 
dist 186=[-1.6585648750627822194 ,.97504851945244208966] 
dist 187=[-1.6431807226457444466 ,1.0295612734880493957 ] 
dist 188=[-1.6370070161449973539 ,1.0837221690675130587 ] 
dist 189=[-1.6313258163311173058 ,1.1308447804418787335 ] 
dist 190=[-1.6248358698104150309 ,1.1818144462917650520 ] 
dist 191=[-1.4708600451561663352 ,1.2513250660525440628 ] 
dist 192=[-1.5289503561635543330 ,1.3172591817282830476 ] 
dist 193=[-1.5665811022505383543 ,1.3539544013454787686 ] 
dist 194=[-1.5861579429222334918 ,1.3762306268469868915 ] 
dist 195=[-1.5972109247841444732 ,1.3846205829301660091 ] 
dist 196=[-1.6008176185335565101 ,1.3864878721816036979 ] 
dist 197=[-1.5996686173783832626 ,1.3830370220329977265 ] 
dist 198=[-1.5953253672618458806 ,1.3751527859422611351 ] 
dist 199=[-1.4087718851834727899 ,1.3699253129589694345 ] 
dist 200=[-1.3795108250753929206 ,1.3431865888624226709 ] 
dist 201=[-1.3247896678711154385 ,1.3897704390226727087 ] 
dist 202=[-1.3093351757792046925 ,1.4184611245338990461 ] 
dist 203=[-1.2499108817337554226 ,1.4381152131896045055 ] 
dist 204=[-1.2338464674477248449 ,1.4486307442853990744 ] 
dist 205=[-1.2025343403190722363 ,1.4562884210390811428 ] 
dist 206=[-1.1924203635535507226 ,1.4616560857116470354 ] 
dist 207=[-.23425874213034684554,1.4604948906524182954 ] 
dist 208=[-.15121877852505642827,1.3367442168664041647 ] 
dist 209=[.03274612048214678419,1.3178229659425309241 ] 
dist 210=[.06903268283894106259,1.2674121528213972220 ] 
dist 211=[-.03529311030947903922,1.2543702700451480292 ] 
dist 212=[-.1604652833394862486 ,1.1569203186673809810 ] 
dist 213=[-.26688801989133005758,1.1351539325994225931 ] 
dist 214=[-.37997362425544465172,1.0999517960118003998 ] 
dist 215=[-.53174128733888546537,1.0892656546334062451 ] 
dist 216=[-.68162772529034978915,1.0826351452681556209 ] 
dist 217=[-.78720562011609870404,1.1390211067013636559 ] 
dist 218=[-.88056277052782837943,1.1974664577774742823 ] 
dist 219=[-.98167300562974869001,1.2527664140843534794 ] 
dist 220=[-1.0800531485345575712 ,1.2965957560277470984 ] 
dist 221=[-1.1625147360865088173 ,1.3404147263717024714 ] 
dist 222=[-1.2491305969430331686 ,1.3956696150185031126 ] 
dist 223=[-1.3640943572528599140 ,1.4463956073051925329 ] 
dist 224=[-1.4732647587262511964 ,1.4721373797922285256 ] 
dist 225=[-1.5367568245867971978 ,1.4847040473827567498 ] 
dist 226=[-1.5789623178425255936 ,1.4866408314289244691 ] 
dist 227=[-1.6031667066842685547 ,1.4737591659230806218 ] 
dist 228=[-1.6181963609531019680 ,1.4662046247482583600 ] 
dist 229=[-1.6237810907356213062 ,1.4534084522991601820 ] 
dist 230=[-1.6235183985402381512 ,1.4474014723657091223 ] 
dist 231=[-1.6197576780675005895 ,1.2595439384949084754 ] 
dist 232=[-1.4654683335692661254 ,1.2304847530149029632 ] 
dist 233=[-1.4839489156909329622 ,1.1691189933789430358 ] 
dist 234=[-1.4878206568771917406 ,1.1505639862604669201 ] 
dist 235=[-1.4801219096118005844 ,1.0696024726018729823 ] 
dist 236=[-1.4752735706959033203 ,1.0524880751579882533 ] 
dist 237=[-1.4693708785653171999 ,1.0033794557416191734 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 2, 0, 2, 1, 2] 
dist 0=[53.136992340306606201  ,53.136992340306606201  ] 
dist 1=[52.968876694976031600  ,53.212314765649822413  ] 
dist 2=[52.670949312626012106  ,53.234790353267759459  ] 
dist 3=[52.076956740466573342  ,53.191627720905676048  ] 
dist 4=[51.149256216920177179  ,53.126323255868310546  ] 
dist 5=[49.518100463156102478  ,53.060198396988389048  ] 
dist 6=[47.790882346253060292  ,52.980329474932021147  ] 
dist 7=[46.479462212354088493  ,52.549110590509916471  ] 
dist 8=[45.216209001525668617  ,49.364217683228019559  ] 
dist 9=[43.418220047577939184  ,48.821194155776609286  ] 
dist 10=[41.168257052810150580  ,47.961458200144348300  ] 
dist 11=[38.394202754082373794  ,47.709091337704074134  ] 
dist 12=[34.168528951931124874  ,47.101868631790386465  ] 
dist 13=[29.904176387529825258  ,46.941509151365772581  ] 
dist 14=[26.975554787063340321  ,46.733864099298368719  ] 
dist 15=[24.455726085327186378  ,45.255274848712515091  ] 
dist 16=[21.824117743076019684  ,31.679166673411873844  ] 
dist 17=[19.311861448320899288  ,31.237187669361448229  ] 
dist 18=[17.268624955155772633  ,29.697331448151975899  ] 
dist 19=[15.170576811978756707  ,29.332094712010232049  ] 
dist 20=[12.439078381937530434  ,28.869336800796595560  ] 
dist 21=[9.7636670687828911948 ,28.700279905506637292  ] 
dist 22=[7.8894952344084023966 ,15.126607127790800284  ] 
dist 23=[6.2360386180079908964 ,14.821653451567039521  ] 
dist 24=[4.4420822725157363446 ,10.111440656528644747  ] 
dist 25=[2.5237780863769505376 ,9.3948487127075970466 ] 
dist 26=[.3586659975424587629 ,8.1744761318984896320 ] 
dist 27=[-1.2560717631692641392 ,7.8723915289563881617 ] 
dist 28=[-2.7824129866682230279 ,7.6023685629208675899 ] 
dist 29=[-4.7822680042137232043 ,6.8107287509788570520 ] 
dist 30=[-6.2902936674041379938 ,6.6806841569191554781 ] 
dist 31=[-7.3527193858623031055 ,6.1323582139370578392 ] 
dist 32=[-8.1746147040487188836 ,-5.1000443032796522040 ] 
dist 33=[-8.9883678358891838895 ,-5.2916458275534702720 ] 
dist 34=[-9.4978754028179683235 ,-6.3901459159273887893 ] 
dist 35=[-9.8861702729479852710 ,-6.5599777522239959673 ] 
dist 36=[-10.516445725625923371  ,-6.8356639212609013448 ] 
dist 37=[-10.901997364831062955  ,-6.8800952475000437074 ] 
dist 38=[-11.166732243512213229  ,-6.8681127592517232920 ] 
dist 39=[-11.341093345888831245  ,-6.8050353621150469370 ] 
dist 40=[-11.457275739646070659  ,-6.6951650384429104013 ] 
dist 41=[-11.489451366857236376  ,-6.4957238715867417749 ] 
dist 42=[-11.473704207113208057  ,-6.2561045789120073892 ] 
dist 43=[-11.450202120788813184  ,-5.8579801173730998962 ] 
dist 44=[-11.248598247812188270  ,-4.2271739124848104742 ] 
dist 45=[-11.185770987685309178  ,-2.5717583990479065042 ] 
dist 46=[-10.993135876162161742  ,-1.4357972920148145542 ] 
dist 47=[-10.921807751379215274  ,-.46204527951880843842] 
dist 48=[-7.0454676190276970330 ,.5459022847336929780 ] 
dist 49=[-6.6607118441141822457 ,1.4996697991501222487 ] 
dist 50=[-5.7578672384974287487 ,2.2571659357632679201 ] 
dist 51=[-5.5914246288193145424 ,3.0166498725690114362 ] 
dist 52=[-4.5470197128795139251 ,3.9783793330936726087 ] 
dist 53=[-4.5024578389113225433 ,4.9032538681909323571 ] 
dist 54=[-3.7534624986662549289 ,5.5156030283893884323 ] 
dist 55=[-3.6617359785715358127 ,6.0796531783770955958 ] 
dist 56=[-2.0749122496845847072 ,6.8759601338317835910 ] 
dist 57=[-1.9604131651897699946 ,7.3584845893597267209 ] 
dist 58=[-1.3948174754283114457 ,7.7041174372699330337 ] 
dist 59=[-1.3136342924407997046 ,7.9538399520749227646 ] 
dist 60=[-1.0658831719675829167 ,8.1421921832713157373 ] 
dist 61=[-1.0190504479052993501 ,8.2428228820882547605 ] 
dist 62=[-.43722573626002225607,8.2986260813754297241 ] 
dist 63=[-.39705671197839455088,8.3081073863121681518 ] 
dist 64=[.2126280770025807390 ,4.9481442881403025450 ] 
dist 65=[.2619235261115193599 ,5.0150001940973066741 ] 
dist 66=[.5737472337065316923 ,5.0556123822433933521 ] 
dist 67=[.6294458871664593023 ,5.0725054373139413528 ] 
dist 68=[.7345624491783697811 ,5.0755120309189239338 ] 
dist 69=[.7594195628884531271 ,5.0636723165741139070 ] 
dist 70=[1.2772230708427427542 ,4.0653927232405124644 ] 
dist 71=[.8201984334662141278 ,4.0842821335587576277 ] 
dist 72=[.4317860995476784142 ,4.0813901628291853688 ] 
dist 73=[.0353693959563087122 ,4.0136502978653414007 ] 
dist 74=[-.3359973394927716211 ,3.9871111407141209327 ] 
dist 75=[-.62445131165219839908,3.9612902932420722119 ] 
dist 76=[-.90757308818622682983,3.9428908781624031989 ] 
dist 77=[-1.2576981477669939590 ,3.3814962650536438124 ] 
dist 78=[-1.5902857535466065188 ,3.3038953056672238127 ] 
dist 79=[-1.8034240478057374895 ,3.1080016597457836688 ] 
dist 80=[-2.1274690445958473883 ,3.0673754442990093783 ] 
dist 81=[-2.5032785201042066063 ,2.7372062960050557660 ] 
dist 82=[-2.7756708473786653983 ,2.6685932790904572577 ] 
dist 83=[-3.0247948335830569186 ,2.5669848547674016874 ] 
dist 84=[-3.3077467569343846159 ,2.5351340681280622082 ] 
dist 85=[-3.5654080275647940978 ,1.8498306132922375299 ] 
dist 86=[-3.7135680537961709479 ,1.7563036404934534838 ] 
dist 87=[-3.8101162020358158511 ,1.5503395145868109388 ] 
dist 88=[-3.8617025354291898712 ,1.4955583764269030852 ] 
dist 89=[-3.8924066341115782426 ,1.2441114210300608153 ] 
dist 90=[-3.9055877691757978283 ,1.1957218044784711851 ] 
dist 91=[-3.9085424995211933347 ,1.0814328194239878308 ] 
dist 92=[-3.8984481558249569112 ,1.0557538469065342471 ] 
dist 93=[-3.2856241942657053075 ,.2283265591012182361 ] 
dist 94=[-3.2102165314797803043 ,.48754028130907717822] 
dist 95=[-3.0143936106694996110 ,.6813264782122629437 ] 
dist 96=[-2.9782268328216376621 ,.86430710567796271898] 
dist 97=[-2.7584130046919550163 ,1.0804240422352610057 ] 
dist 98=[-2.7644593541149816836 ,1.3014084745990454325 ] 
dist 99=[-2.7612816084901669296 ,1.5038419810262892807 ] 
dist 100=[-2.7404821289020390578 ,1.7315979751818973853 ] 
dist 101=[-2.7277872937246401737 ,2.0536953163098469161 ] 
dist 102=[-1.6359535483928308821 ,2.3673478854722816815 ] 
dist 103=[-1.4331042740595359428 ,2.5614025927309486262 ] 
dist 104=[-1.3769915868323053212 ,2.7051888035769246422 ] 
dist 105=[-1.1528909612015308748 ,2.8181743501502473339 ] 
dist 106=[-1.1098718224379036225 ,2.9058821138469752743 ] 
dist 107=[-1.0063485854595094834 ,2.9487549043236500931 ] 
dist 108=[-.98700794063284230781,2.9680601760531203969 ] 
dist 109=[.23359676429153754381,2.9696363980996091647 ] 
dist 110=[.34741652270277550068,2.9521319010865648637 ] 
dist 111=[.57484337066252451877,3.0617071873113601832 ] 
dist 112=[.63002250367046072191,3.1306447540921662970 ] 
dist 113=[.80766575112629687429,3.1622343323354188170 ] 
dist 114=[.84528771889494184371,3.1787479146060498725 ] 
dist 115=[.85515897405003935348,3.1874964953466627948 ] 
dist 116=[.82076598342263817296,3.1922289261755036212 ] 
dist 117=[.68613606378423708185,3.1926880583189173685 ] 
dist 118=[.15720483709064970491,2.7574526142105266892 ] 
dist 119=[-.198493083613058019  ,2.7010548071833574846 ] 
dist 120=[-.49555594964320087024,2.5502877657581112276 ] 
dist 121=[-.79043238009050929251,2.5238551206614430017 ] 
dist 122=[-1.0614657995285823825 ,2.2033951155028805566 ] 
dist 123=[-1.2633521521373113491 ,2.1374698580095347302 ] 
dist 124=[-1.4533205936522611070 ,1.8306855377193978229 ] 
dist 125=[-1.6767756217417694817 ,.56665180098745562836] 
dist 126=[-1.8847188872326582508 ,-.0015937047497937546 ] 
dist 127=[-2.0127708708702988202 ,-.0721831302403288250 ] 
dist 128=[-2.1068573509394830124 ,-.2317442979398570309 ] 
dist 129=[-2.1792316884285686447 ,-.2585620857422293757 ] 
dist 130=[-2.2341275006438627105 ,-.4488800648662037210 ] 
dist 131=[-2.2584441313587896363 ,-.4806540896868686973 ] 
dist 132=[-2.2677347366188806781 ,-.5367913626718367793 ] 
dist 133=[-2.3044523119538971401 ,-.52293755661908383648] 
dist 134=[-2.3554908753877165724 ,-.39584512177076536267] 
dist 135=[-2.3846470686092419500 ,-.30215782610621535486] 
dist 136=[-2.3916280485966481812 ,-.21504125683016602941] 
dist 137=[-2.3885350634716796293 ,-.11416188191377076406] 
dist 138=[-2.3810178138279630789 ,-.0121862667912258384 ] 
dist 139=[-2.3618242400230237662 ,.0793123625055042677 ] 
dist 140=[-2.3510485969659022939 ,.1806559039852058910 ] 
dist 141=[-1.8800636100683195472 ,.3219324665066291381 ] 
dist 142=[-1.6198836055678654198 ,.4638434675204753323 ] 
dist 143=[-1.5808281164927082799 ,.56772379790643222748] 
dist 144=[-1.5031478488926555565 ,.66365767641559725112] 
dist 145=[-1.4809406880585570810 ,.77385852736460023566] 
dist 146=[-1.3917835134396333423 ,.88484143706583855707] 
dist 147=[-1.3708294060379866190 ,1.0380668324480388607 ] 
dist 148=[-1.3232355113754177540 ,1.2353039591164570447 ] 
dist 149=[-1.3073400285050920566 ,1.4214249219837373057 ] 
dist 150=[-.65080097143828840419,1.5383516468814425158 ] 
dist 151=[-.73747922414538257013,1.6270457490272573920 ] 
dist 152=[-.81080330281610115338,1.7004792276268489196 ] 
dist 153=[-.88507142323773651637,1.7585627371089139074 ] 
dist 154=[-.95425263392912132174,1.7859925552964101577 ] 
dist 155=[-1.0072708645879919568 ,1.7990196795245328692 ] 
dist 156=[-1.0585911473640792012 ,1.7995907523860396374 ] 
dist 157=[-1.1209905653147994438 ,1.7674642369619653358 ] 
dist 158=[-1.1795996758319567204 ,1.7579493250925025607 ] 
dist 159=[-1.2157899234089778914 ,1.7319034916290677888 ] 
dist 160=[-1.2424629099504280792 ,1.7812278185256621733 ] 
dist 161=[-1.2630852668474636912 ,1.8084519738697470192 ] 
dist 162=[-1.2781957174779531878 ,1.8255346116480081837 ] 
dist 163=[-1.2828664543774978821 ,1.8343787640879218769 ] 
dist 164=[-1.2815928789053287700 ,1.8388877079364635951 ] 
dist 165=[-1.2787672824976018205 ,1.8386720967288712220 ] 
dist 166=[-1.2527552074307227199 ,1.4916467252847099683 ] 
dist 167=[-1.2449076049236893392 ,1.5280042758854273912 ] 
dist 168=[-1.2187704652380378320 ,1.5561737800923817193 ] 
dist 169=[-1.2108667106753495993 ,1.5768925669904947038 ] 
dist 170=[-1.1401359617278065824 ,1.5835021712523384568 ] 
dist 171=[-1.1228038742429551183 ,1.5828778772513696456 ] 
dist 172=[-1.0990254926359688170 ,1.5792402447932915320 ] 
dist 173=[-1.0897274383620636592 ,1.5446469915667945994 ] 
dist 174=[-1.0712095885965305804 ,1.5347291832990036391 ] 
dist 175=[-1.1455937712357668928 ,1.5025819267715857676 ] 
dist 176=[-1.2072371361774964143 ,1.4927994637622033068 ] 
dist 177=[-1.3046950837183609614 ,1.4080505699599194551 ] 
dist 178=[-1.4134041795435856641 ,1.3873116286040331337 ] 
dist 179=[-1.5124426424899290034 ,1.3582158268756458621 ] 
dist 180=[-1.6242692440406437390 ,1.3471230197586327880 ] 
dist 181=[-1.7252053194153824018 ,1.0717831339608862443 ] 
dist 182=[-1.7807738891765430681 ,1.0326499786047611512 ] 
dist 183=[-1.8138017921784391455 ,.94931188275166407422] 
dist 184=[-1.8247625783755271029 ,.92526504583183899634] 
dist 185=[-1.8275289429990478484 ,1.0251401835930722216 ] 
dist 186=[-1.8278426593112088946 ,1.1453430786859815812 ] 
dist 187=[-1.8264307876330399749 ,1.2330909908118940056 ] 
dist 188=[-1.8222954847120221261 ,1.3138753352370006789 ] 
dist 189=[-1.6289182129475161508 ,1.4062805337852143741 ] 
dist 190=[-1.4145433206839951749 ,1.4902047465139988932 ] 
dist 191=[-1.3818958336888819079 ,1.5371367006499175107 ] 
dist 192=[-1.3167567308529741695 ,1.5659464274847556354 ] 
dist 193=[-1.2979167377494750118 ,1.5775368083474143944 ] 
dist 194=[-1.2211670671001264876 ,1.5817166749617815776 ] 
dist 195=[-1.2031899840406995687 ,1.5809506514325487120 ] 
dist 196=[-1.1607794468639257498 ,1.5764062559876632332 ] 
dist 197=[-1.1462473399018227609 ,1.5713440608348153491 ] 
dist 198=[-.61480819812427380107,1.4581306957353791403 ] 
dist 199=[-.51745044056255211051,1.5070467565971726259 ] 
dist 200=[-.49237872083498171417,1.5388919879353284202 ] 
dist 201=[-.38069230659942295557,1.5557808681635663675 ] 
dist 202=[-.36011786345479610002,1.5645083762702094732 ] 
dist 203=[-.30953765277323342481,1.5637772041761919311 ] 
dist 204=[-.30167638709553764535,1.5579233922450361567 ] 
dist 205=[.21485941919430463073,1.5524567365230989327 ] 
dist 206=[.26427589260901924524,1.4101353754209134000 ] 
dist 207=[.17678522055289884859,1.3860214814482204786 ] 
dist 208=[.05071748930939181347,1.3339172854397978530 ] 
dist 209=[-.07354821440682885922,1.3171823145394111589 ] 
dist 210=[-.18025716505481165063,1.3544426028342166401 ] 
dist 211=[-.29456391522843966474,1.4223144462820797254 ] 
dist 212=[-.44915593818656195969,1.4977711494157814687 ] 
dist 213=[-.60238218623624918224,1.5652237395910212898 ] 
dist 214=[-.71123777141792570631,1.6011465804896477140 ] 
dist 215=[-.8084578010461530117 ,1.6208783208678269564 ] 
dist 216=[-.91524198802666260542,1.6247620927111834678 ] 
dist 217=[-1.0200261176604449593 ,1.6200447156631363732 ] 
dist 218=[-1.1311210795322860309 ,1.6139091316241470398 ] 
dist 219=[-1.2400612516147530277 ,1.6047846656002491705 ] 
dist 220=[-1.3380751147944541653 ,1.5988019450940802451 ] 
dist 221=[-1.4539215805956031953 ,-.09384845704455695102] 
dist 222=[-1.5453293645615310144 ,-.17954243513605776041] 
dist 223=[-1.6023284028844551755 ,-.19354251248077693413] 
dist 224=[-1.6398636889742656574 ,-.19213196643418679922] 
dist 225=[-1.6606625278902567828 ,-.16931872669475540589] 
dist 226=[-1.6724134465254745160 ,-.13447982537636680631] 
dist 227=[-1.6738343597202218848 ,-.08506847131704722109] 
dist 228=[-1.6689073649226581228 ,-.01549908569534037712] 
dist 229=[-1.6642520377983687055 ,.09980127059604866883] 
dist 230=[-1.6150220348193554360 ,.2189385838388267628 ] 
dist 231=[-1.6384232348378854769 ,.3038232880076498272 ] 
dist 232=[-1.6610595776905910870 ,.37989856023001588224] 
dist 233=[-1.6744621059413389826 ,.46387266213407366148] 
dist 234=[-1.6767160249605249050 ,.54652747025148168492] 
dist 235=[-1.6724509638146202596 ,.61733668468194739019] 
dist 236=[-1.6678531288808062299 ,.69305294239018542443] 
dist 237=[-1.3568893666848770638 ,.79529428962359741329] 
dist 238=[-1.3231908638368409545 ,.89657919554672108643] 
dist 239=[-1.2370626313839981113 ,.96847773162699568345] 
dist 240=[-1.2200206857194170813 ,1.0326400506419085827 ] 
dist 241=[-1.0729205895176387365 ,1.1030455141004469092 ] 
dist 242=[-1.0425979969785039688 ,1.1721000058151616179 ] 
dist 243=[-.99976866677129797317,1.2308697704911717699 ] 
dist 244=[-.98573262036584285964,1.3327027447708793412 ] 
dist 245=[-.68380634139981203187,1.4436872107529106007 ] 
dist 246=[-.64333080071852647013,1.5082073603699851552 ] 
dist 247=[-.55420306330994579275,1.5510632594197676495 ] 
dist 248=[-.53152320507812903072,1.5755726183117664855 ] 
dist 249=[-.4247037652298974693 ,1.5910389540569349812 ] 
dist 250=[-.40466159110670917625,1.5977999621453386256 ] 
dist 251=[-.35774309366177169419,1.5994815015526183043 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 1, 0, 1, 1, 2] 
dist 0=[48.332214232708658148  ,48.332214232708658148  ] 
dist 1=[47.534215637001540811  ,48.808206481140364233  ] 
dist 2=[46.535506260890291510  ,49.140358070956748096  ] 
dist 3=[45.257882398007380664  ,49.363733494982408414  ] 
dist 4=[43.528016283498744095  ,49.521313019041757926  ] 
dist 5=[40.723192492208181278  ,49.590555832744211603  ] 
dist 6=[37.843464967007326275  ,49.607623906060724289  ] 
dist 7=[35.814390277553139909  ,49.556580401895597164  ] 
dist 8=[34.014875802391451155  ,49.478840321996773426  ] 
dist 9=[32.051740447995086681  ,49.389346632631463892  ] 
dist 10=[30.127020675719027299  ,49.273059115345370841  ] 
dist 11=[28.480714765625969345  ,49.183766560707954579  ] 
dist 12=[26.717829935041021433  ,48.874225354789284813  ] 
dist 13=[24.327098675811470346  ,48.748175825679706639  ] 
dist 14=[21.941276450423818766  ,48.406922889245345248  ] 
dist 15=[20.197779669871496305  ,47.861826555574026771  ] 
dist 16=[18.584350522713289849  ,36.018226708018387184  ] 
dist 17=[16.717760555354348684  ,34.907135769390432552  ] 
dist 18=[14.821340967817403605  ,32.237714734922378982  ] 
dist 19=[13.088353356131256590  ,31.798999250803064131  ] 
dist 20=[11.134611714630125589  ,27.922780430573595639  ] 
dist 21=[8.3555062298034378294 ,27.190976637590459402  ] 
dist 22=[5.6177544926692846961 ,26.213152224119310541  ] 
dist 23=[3.8291162143173264272 ,25.903052270325978730  ] 
dist 24=[2.3837372783947970182 ,19.808949455229396341  ] 
dist 25=[1.0177688285507918687 ,19.021133897186400220  ] 
dist 26=[-.20203337722459619115,17.336168840081779548  ] 
dist 27=[-1.0633875178103311764 ,16.914068149359666217  ] 
dist 28=[-3.4191306774897447312 ,15.086734792021705154  ] 
dist 29=[-5.7844429979605071743 ,14.752915687983755961  ] 
dist 30=[-7.2691416155135079077 ,13.965945901831515871  ] 
dist 31=[-8.4024963917143972560 ,13.832023308424431077  ] 
dist 32=[-9.3635997597747685307 ,5.3811884036169478401 ] 
dist 33=[-10.149278947440494596  ,4.5943220950988488320 ] 
dist 34=[-10.581702266773535710  ,2.8908540813260202104 ] 
dist 35=[-10.843018783537518391  ,2.5402339792500561484 ] 
dist 36=[-10.945378039746468591  ,.68576866677854424046] 
dist 37=[-10.989511913553490386  ,.37169825554308170992] 
dist 38=[-11.914449448555963120  ,-.30787007419732659456] 
dist 39=[-12.906114020087010134  ,-.43190567628775247702] 
dist 40=[-13.799343140938779123  ,-1.3946674460195256671 ] 
dist 41=[-14.331076402125652269  ,-1.5665848631592866777 ] 
dist 42=[-14.702471879185529947  ,-1.6333505144855749934 ] 
dist 43=[-14.955111094766729693  ,-1.5176082736876138199 ] 
dist 44=[-15.119232113579205732  ,-1.2930203926326503529 ] 
dist 45=[-15.150561877967972144  ,-.8515273780177725259 ] 
dist 46=[-15.107067283380235016  ,-.41317392567670773709] 
dist 47=[-15.080885533452443771  ,.30628563197551795542] 
dist 48=[-6.3440798311809909217 ,1.1318471904792021826 ] 
dist 49=[-5.7589527733678215780 ,1.6974738520584264341 ] 
dist 50=[-4.3600555774737687535 ,2.1797400430867909933 ] 
dist 51=[-4.1550381591748967097 ,2.6729589845720824779 ] 
dist 52=[-2.2150460798255468064 ,3.1345828123588369016 ] 
dist 53=[-1.8688184537564364079 ,3.7110227310720378772 ] 
dist 54=[-1.4305547678357124305 ,4.2371596511855468469 ] 
dist 55=[-1.3450157183838524708 ,4.6413446719285791415 ] 
dist 56=[1.1730246104922311916 ,4.9854493075836216730 ] 
dist 57=[1.4660915585790829133 ,5.2655520817980098841 ] 
dist 58=[2.1091617026434999052 ,5.4144050671340613241 ] 
dist 59=[2.2104881576101509863 ,5.4965755277538345932 ] 
dist 60=[2.6051948110348694396 ,5.5107713244074370745 ] 
dist 61=[2.5599161999304932707 ,3.8853675859765827949 ] 
dist 62=[2.4926909832497241993 ,3.8909425084712128941 ] 
dist 63=[2.4094814326249978208 ,4.1555565398692997169 ] 
dist 64=[2.2982123207173774736 ,4.3955330050666161438 ] 
dist 65=[2.1213716383411960497 ,4.5465182585256930044 ] 
dist 66=[1.9170851704128815611 ,4.6625999905933444877 ] 
dist 67=[1.6918346721200308242 ,4.7630221477597384413 ] 
dist 68=[1.4088269810405495191 ,4.8470755342340472939 ] 
dist 69=[.97298588835474639013,4.8977292964626527573 ] 
dist 70=[.53403964268929135975,4.9344161174511900530 ] 
dist 71=[.23861937991014516305,4.9626847184106480836 ] 
dist 72=[-.00831886950465857472,4.9825552213305297731 ] 
dist 73=[-.25376820550816132003,4.9856617842286191653 ] 
dist 74=[-.47961033709665618179,4.9776019691320425260 ] 
dist 75=[-.64830013440294214144,4.9650218149574109286 ] 
dist 76=[-.80755061787532443187,4.9194087515526841502 ] 
dist 77=[-1.3670577333989115120 ,4.8991244481467227880 ] 
dist 78=[-1.8869910406942931522 ,4.8361408931424372293 ] 
dist 79=[-3.0342194551514242230 ,4.8066167731705815019 ] 
dist 80=[-4.1697893587650526723 ,.46202228514907632485] 
dist 81=[-4.9014986735247051791 ,.21457924394976581565] 
dist 82=[-5.4780611911238675884 ,.16999523701306978588] 
dist 83=[-5.9943101416151719715 ,.06753737629327070558] 
dist 84=[-6.4328546178923164824 ,.04950648735092855435] 
dist 85=[-6.6992440878232065158 ,-.08014354974475664970] 
dist 86=[-6.8908859630454295797 ,-.10600113924545426143] 
dist 87=[-7.0310823381375552004 ,-.11119681653339783245] 
dist 88=[-7.1365097749238874749 ,-.08971765877298299122] 
dist 89=[-7.1893505684892670266 ,-.05277666545466434100] 
dist 90=[-7.2140033868996465115 ,.00378811380436015355] 
dist 91=[-7.2068501122251893780 ,.08564238586076556694] 
dist 92=[-7.1798980625422991601 ,.22358809233690736449] 
dist 93=[-7.1554264720022806792 ,.3680312730472813996 ] 
dist 94=[-7.0664644402172136058 ,.4758365815653408125 ] 
dist 95=[-7.0211447085736427500 ,.57765071489391859472] 
dist 96=[-3.9393894508384329979 ,.69816685709235027073] 
dist 97=[-3.6652649386110812492 ,.82174798532457245143] 
dist 98=[-2.9926068107890329008 ,.93579727606657032909] 
dist 99=[-2.8953365737519301938 ,1.0649090124214831612 ] 
dist 100=[-1.8963088284741495585 ,1.5211841840492798798 ] 
dist 101=[-1.7116302321049306597 ,2.0234590150676693264 ] 
dist 102=[-1.4969005859769582643 ,2.5109218383420540843 ] 
dist 103=[-1.4576709196028435558 ,3.1058788223839839426 ] 
dist 104=[-.57106413022678577493,3.6666626676665156302 ] 
dist 105=[-.8192512546970729504 ,4.0177169683407025515 ] 
dist 106=[-1.0721100282720052609 ,4.2824817040084975740 ] 
dist 107=[-1.3769062718110665686 ,4.4988247096363103748 ] 
dist 108=[-1.8324161527214364115 ,4.6708986779100025301 ] 
dist 109=[-2.2852785731943076080 ,4.7589573897940304951 ] 
dist 110=[-2.5795113717159430282 ,4.8035505205669043789 ] 
dist 111=[-2.8139960376825382916 ,4.8109961720887763280 ] 
dist 112=[-3.0283709194685853907 ,3.2400937224028933145 ] 
dist 113=[-3.2135111807118820543 ,3.3162199613432471086 ] 
dist 114=[-3.3313052888575804544 ,3.3513942698069266616 ] 
dist 115=[-3.4223812139677317302 ,3.3648623322707413754 ] 
dist 116=[-3.5008771631310357524 ,3.3638902682173604228 ] 
dist 117=[-3.5621380940098980257 ,3.3175542909564116369 ] 
dist 118=[-3.5844146971540741638 ,3.3016598847020585670 ] 
dist 119=[-3.5881992179226281085 ,3.2314484940650764897 ] 
dist 120=[-3.5806492159906598979 ,2.7616417198247620014 ] 
dist 121=[-3.5023941567852903164 ,2.6303615228835045883 ] 
dist 122=[-3.4758587598234654473 ,2.5999749743891802040 ] 
dist 123=[-3.4284853215432481544 ,2.5186413178650450986 ] 
dist 124=[-3.4110441028987080629 ,2.4951582553117409251 ] 
dist 125=[-.94338972596710051256,1.8572118618417942530 ] 
dist 126=[-1.0033973447951731359 ,1.8318942854110631952 ] 
dist 127=[-1.0385715143333593104 ,1.8187397514387058207 ] 
dist 128=[-1.0622938521885558292 ,.28882256964591266084] 
dist 129=[-1.0765946323198656326 ,.16186014924588911352] 
dist 130=[-1.0845871187173677554 ,-.12071035407800320993] 
dist 131=[-1.0850583159090476738 ,-.17369276944306666783] 
dist 132=[-1.0786043719985671801 ,-.23629614143495685788] 
dist 133=[-1.0743350189906450092 ,-.06238224129625171708] 
dist 134=[-1.1849137757181689815 ,.11210028778269521104] 
dist 135=[-1.3791642449797105922 ,.22809377156423613509] 
dist 136=[-1.5619186206791880038 ,.3234175071750512788 ] 
dist 137=[-1.6758111623314271691 ,.41540893025505774926] 
dist 138=[-1.7611287071706224895 ,.49817590320248724827] 
dist 139=[-1.8298197154516181255 ,.55668517005925491253] 
dist 140=[-1.8826093877993108701 ,.60860674908020096861] 
dist 141=[-1.9044537116107142168 ,.66508136345573269838] 
dist 142=[-1.9135028521287632237 ,.71645998725831242985] 
dist 143=[-1.9152162945189449296 ,.74804437618256166776] 
dist 144=[-.34989553799993093492,.77116191732776893548] 
dist 145=[-.2722454964146764736 ,.78875295328918104784] 
dist 146=[-.18869544874721226163,.80143706454994271111] 
dist 147=[-.17682779036486800612,.80497338413927535876] 
dist 148=[-.16111584580716851681,.80463715130023534657] 
dist 149=[-.15612625353614716206,.80186498944738427413] 
dist 150=[-.06149000709057095679,.49129607578595765053] 
dist 151=[-.12841220351112612498,.63006787999996052019] 
dist 152=[-.18881647434270758052,.76542267348167996933] 
dist 153=[-.2561019397729797503 ,.85804095719446829267] 
dist 154=[-.32264858197650181639,.93782790944997790133] 
dist 155=[-.38010567995757939579,1.0195164715071473750 ] 
dist 156=[-.44190474728975668206,1.0952724346525929295 ] 
dist 157=[-.52578266345864068208,1.1557834734732018752 ] 
dist 158=[-.60902388779001346035,1.2160867900549838015 ] 
dist 159=[-.66828289436377020461,1.2920153488727290720 ] 
dist 160=[-.72132331960640758332,1.3621929040834431806 ] 
dist 161=[-.77974659540416425974,1.3995424090052719562 ] 
dist 162=[-.8371642079813962831 ,1.4203395687439355538 ] 
dist 163=[-.88619226549970412649,1.4250768634018141156 ] 
dist 164=[-.93847323645457061916,1.4205698424718674440 ] 
dist 165=[-1.0088764623886821785 ,1.4180520538568981737 ] 
dist 166=[-1.0757349144516970880 ,1.4151870198047516049 ] 
dist 167=[-1.1138681393893315535 ,1.4111327239128034490 ] 
dist 168=[-1.1382706000239620152 ,1.1957628149146909750 ] 
dist 169=[-1.1517558827054998287 ,1.1644446461176002480 ] 
dist 170=[-1.1822143909613109243 ,1.1065008000506397644 ] 
dist 171=[-1.2030200453701404428 ,1.0910437875734007307 ] 
dist 172=[-1.2162203527829387795 ,1.0363251882529078871 ] 
dist 173=[-1.2186686436501552020 ,1.0830081135650982150 ] 
dist 174=[-1.2126926647114906157 ,1.1303069084660482573 ] 
dist 175=[-1.2109634361105477581 ,1.1550567000088592798 ] 
dist 176=[-.96310656654283117819,1.1681555743660502860 ] 
dist 177=[-.95115366867733450088,1.1707961474950057324 ] 
dist 178=[-.90115669511941414082,1.1640572874707525658 ] 
dist 179=[-.88921542105494923134,1.1595256559657414037 ] 
dist 180=[-.85946095691420413706,1.1538524250965315954 ] 
dist 181=[-.84924449938681649493,1.1490513695699784243 ] 
dist 182=[-.90971469078770899961,.98676351314559420767] 
dist 183=[-1.0193897679394254358 ,.96442865226219746029] 
dist 184=[-1.1216606628274724718 ,.90299174335508664277] 
dist 185=[-1.1838035747521097552 ,.89376262056745516972] 
dist 186=[-1.2284860367937466050 ,.77654442159662275183] 
dist 187=[-1.2610635132523231203 ,.75224606086116348417] 
dist 188=[-1.2845061158306225570 ,.7286921883578822225 ] 
dist 189=[-1.2927238282311718270 ,.72303417404290874835] 
dist 190=[-1.2941237437871752714 ,.64213422561501899826] 
dist 191=[-1.2908942519164352989 ,.72700498383221581809] 
dist 192=[-1.2151933846797559302 ,.80081687281075410108] 
dist 193=[-1.2017553229361155167 ,.87888344648517654035] 
dist 194=[-1.1604037661754699080 ,.95376583339736622355] 
dist 195=[-1.1528126103777597475 ,1.0148718035275170145 ] 
dist 196=[-1.1062535552958033004 ,1.0776379297054249642 ] 
dist 197=[-1.0943950921700787022 ,1.1591546907702901013 ] 
dist 198=[-1.0771878571094543201 ,1.2356089964357831374 ] 
dist 199=[-1.0702368975371086322 ,1.2781683659750953290 ] 
dist 200=[-.8860150740267599615 ,1.3040951724307486416 ] 
dist 201=[-.85924663801736440431,1.3141528456138006898 ] 
dist 202=[-.80207354593921216284,1.3180743788646920242 ] 
dist 203=[-.78531170714647083726,1.3195041804144248041 ] 
dist 204=[-.76371977830974435748,1.3193955357591923865 ] 
dist 205=[-.84383770916264139228,1.3171705135145908278 ] 
dist 206=[-.92098565063634834703,1.1421090918762776044 ] 
dist 207=[-.9720288140790694465 ,1.1704319219533230564 ] 
dist 208=[-1.0137238190816515582 ,1.1935501014315874027 ] 
dist 209=[-1.0535603607007078210 ,1.2006350400986732796 ] 
dist 210=[-1.0891489101076830614 ,1.2019147880834606064 ] 
dist 211=[-1.1138884829426923037 ,1.2018505723530883294 ] 
dist 212=[-1.1354146067983176233 ,1.1588757265160869708 ] 
dist 213=[-1.1581761681895570218 ,1.1475174308051909790 ] 
dist 214=[-1.1767511603892650038 ,1.1405093642566703505 ] 
dist 215=[-1.1815673577816544854 ,1.1376107789275375432 ] 
dist 216=[-1.1812531264960670288 ,1.1450162635687300490 ] 
dist 217=[-1.1793527786513695693 ,1.1900975714100232039 ] 
dist 218=[-1.1391526469463426040 ,1.2209695808909351392 ] 
dist 219=[-1.1272625848508798937 ,1.2405204074467290357 ] 
dist 220=[-1.1170992163948888502 ,1.2528426980503152158 ] 
dist 221=[-1.1097304196859972063 ,1.2548637124522015708 ] 
dist 222=[-.89952411351200468779,1.2521642427026212234 ] 
dist 223=[-.86959888498374314147,1.2478773150614635828 ] 
dist 224=[-.81078352953246876844,1.1534699660033348141 ] 
dist 225=[-.79472164144686047093,1.1379980475392953624 ] 
dist 226=[-.73401305010226411051,1.0910120184262044889 ] 
dist 227=[-.71955960965200757463,1.0838752307699760359 ] 
dist 228=[-.69193943728135846262,.97915104517859375754] 
dist 229=[-.69851105118853022946,.9563085020990653164 ] 
dist 230=[-.7796811558447924021 ,.93632773037432400503] 
dist 231=[-.87899662218747274435,.93120899130828853722] 
dist 232=[-.97270939957076522632,.63964212974477504204] 
dist 233=[-1.0315147139687717960 ,.60162804314457552068] 
dist 234=[-1.0760201500758734778 ,.52738568672503371004] 
dist 235=[-1.1126525966973804573 ,.50824172025591351341] 
dist 236=[-1.1414145857885574899 ,.44157250183646250381] 
dist 237=[-1.1545027264362016382 ,.42573759635815703419] 
dist 238=[-1.1595787519956464853 ,.40703575582271758733] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 2, 1, 1, 1, 2] 
dist 0=[52.608433578841731513  ,52.608433578841731513  ] 
dist 1=[52.031804896849751556  ,53.017867704691784338  ] 
dist 2=[51.221194805633787052  ,53.311298654215177037  ] 
dist 3=[49.877083599372962184  ,53.424646179297384119  ] 
dist 4=[48.288757921286271004  ,53.427618683472810495  ] 
dist 5=[46.502671907480927279  ,53.382851969002098590  ] 
dist 6=[44.224824756557902849  ,53.053923891352311456  ] 
dist 7=[40.672307156685786143  ,52.939413816256022659  ] 
dist 8=[37.057992194516522213  ,52.458792225964101623  ] 
dist 9=[34.533249105883347538  ,52.365336388130072715  ] 
dist 10=[32.316340700059451501  ,50.623576564368935845  ] 
dist 11=[29.931382766882755194  ,50.234416058666148382  ] 
dist 12=[27.612527401732939422  ,49.854307789245720469  ] 
dist 13=[25.659480137986559808  ,49.647743883250278109  ] 
dist 14=[23.594163773478824235  ,44.574810702388978495  ] 
dist 15=[20.826583936353513692  ,43.649871535936908132  ] 
dist 16=[18.080254854041308836  ,38.666463935619038597  ] 
dist 17=[16.099645454261866820  ,31.821195429103315824  ] 
dist 18=[14.293579171920199736  ,27.766719595257637221  ] 
dist 19=[12.244192576426036758  ,24.172445718419652065  ] 
dist 20=[10.185114934256194318  ,23.512394585709803264  ] 
dist 21=[8.3399956765030436261 ,20.897663213045160878  ] 
dist 22=[6.2898184520297433772 ,19.259082065565668886  ] 
dist 23=[3.4108837170836593722 ,18.893287305990816100  ] 
dist 24=[.58699721660109644041,18.489539172620073474  ] 
dist 25=[-1.2433713622448553443 ,18.413886456741741715  ] 
dist 26=[-2.7054561312075846774 ,12.169180436102438111  ] 
dist 27=[-4.0577220562774927125 ,11.284341611185242811  ] 
dist 28=[-5.2446816883045325061 ,11.088362314807781186  ] 
dist 29=[-6.0463408851568105920 ,8.4431804446330637861 ] 
dist 30=[-6.7243578875479998279 ,8.0281542154266286880 ] 
dist 31=[-7.4176072865338167622 ,6.2613515231853743811 ] 
dist 32=[-8.0346832524406723621 ,3.3640700574928761622 ] 
dist 33=[-9.5724633653002311109 ,-4.4525055947475966676 ] 
dist 34=[-11.064531154832306050  ,-6.5844742539406405332 ] 
dist 35=[-12.190713593952019873  ,-6.8729461462033108476 ] 
dist 36=[-13.122454108611988406  ,-7.0499015869473471317 ] 
dist 37=[-13.870201602188302280  ,-6.5376377477463838584 ] 
dist 38=[-14.260900079417342512  ,-5.8168216242800081311 ] 
dist 39=[-14.474359705833565666  ,-4.6247509174813553879 ] 
dist 40=[-14.518396392941722010  ,-3.3978583355895774356 ] 
dist 41=[-14.303211557916157382  ,-2.5379246055505921557 ] 
dist 42=[-14.225798991116298390  ,-1.7829258601772549846 ] 
dist 43=[-14.147677440432355080  ,-.9746156399434778846 ] 
dist 44=[-14.082022734719292899  ,-.1944817348865492372 ] 
dist 45=[-13.952096320055318248  ,.4481599570881103010 ] 
dist 46=[-13.873151352222096632  ,1.1129464448243860101 ] 
dist 47=[-13.766920535355382381  ,1.9815351913056407937 ] 
dist 48=[-13.708614463257938309  ,2.8281961891222635544 ] 
dist 49=[-5.5524624571416761119 ,3.4054880708104347268 ] 
dist 50=[-4.8650374191479412892 ,3.8959325026888731423 ] 
dist 51=[-3.2599037723960910372 ,4.3959704605951800068 ] 
dist 52=[-3.0008433596662373412 ,4.8637707437879741224 ] 
dist 53=[-.8897189440104569078 ,5.2255318795247204474 ] 
dist 54=[-.5177195409239999946 ,5.5787628651878900284 ] 
dist 55=[.0393370987531602608 ,6.0124700586580625047 ] 
dist 56=[.01529894055383948295,6.4257301428963834307 ] 
dist 57=[-.26651751299963864303,6.6973444375141028974 ] 
dist 58=[-.56354097711916904746,6.9170051427259632220 ] 
dist 59=[-.77441242033100118067,7.1229328975165709536 ] 
dist 60=[-.96121845708854748205,7.3040164812205375053 ] 
dist 61=[-1.1624268219724171056 ,7.4796541145047051281 ] 
dist 62=[-1.3561191708197344361 ,7.6291799163877514934 ] 
dist 63=[-1.5130173013969849042 ,7.7049970662651167664 ] 
dist 64=[-1.6722114988227780125 ,7.7192680191427941336 ] 
dist 65=[-1.8750996769147333862 ,4.3774294482302807057 ] 
dist 66=[-2.0689505697274926611 ,3.8116124717891803330 ] 
dist 67=[-2.1921325227078913920 ,3.7278812272045034232 ] 
dist 68=[-2.2865894359640751727 ,3.5722631271411609394 ] 
dist 69=[-2.3659313115966965261 ,3.5301758749708685887 ] 
dist 70=[-2.4290519075053498432 ,3.3787789473242508895 ] 
dist 71=[-2.4588386884993681487 ,3.3365964648243116690 ] 
dist 72=[-2.4697592674146284289 ,3.2764688282506754496 ] 
dist 73=[-2.4671332458110026553 ,3.2540602942450592042 ] 
dist 74=[-.44120940898865605664,1.9749704972834161774 ] 
dist 75=[-.79017989532724783889,1.7766531529673568289 ] 
dist 76=[-1.1109502451676664573 ,1.7383724985572991938 ] 
dist 77=[-1.3498470534334954604 ,1.4617268698244016525 ] 
dist 78=[-1.6163490731711222363 ,1.4097198690369675591 ] 
dist 79=[-1.8871931033732438379 ,1.3207964290579582811 ] 
dist 80=[-2.1432152954575475767 ,1.2995311643736534903 ] 
dist 81=[-2.4462636994188423037 ,.5262971185213744288 ] 
dist 82=[-2.7275295759808283485 ,.4412115503916662434 ] 
dist 83=[-2.8966126722569046220 ,.27608331278929977429] 
dist 84=[-3.0161234938709201836 ,.23619203571203474626] 
dist 85=[-3.0995132979445649602 ,.1104389021956390165 ] 
dist 86=[-3.1597061636767045013 ,.08136028645471017725] 
dist 87=[-3.1865982794607831251 ,.07506240303508220898] 
dist 88=[-3.1943158992182105664 ,.09777566545203593448] 
dist 89=[-3.1913496050703442706 ,.13373943023886769362] 
dist 90=[-3.2398506854974073837 ,.18034324064115831173] 
dist 91=[-3.2641462435995614104 ,.2434169382629005303 ] 
dist 92=[-3.2667062853649433452 ,.3451647706066084733 ] 
dist 93=[-3.2444766013458790131 ,.4637465905342241286 ] 
dist 94=[-3.2308975135490080972 ,.64907333205222954589] 
dist 95=[-3.1952181140563288639 ,.86636776954082954634] 
dist 96=[-3.1777085765406559048 ,1.0884043048215931206 ] 
dist 97=[-2.3530215166953456485 ,1.3749541190855763349 ] 
dist 98=[-1.7390689553196031660 ,1.6527096291267673924 ] 
dist 99=[-1.6586296980962129649 ,1.8396608759079111504 ] 
dist 100=[-1.4976295485540867404 ,1.9959458499568775525 ] 
dist 101=[-1.4543372814549469654 ,2.1513239691419811352 ] 
dist 102=[-1.2550570664040306994 ,2.2943559426707599536 ] 
dist 103=[-1.2164353319726673069 ,2.4013835194823480766 ] 
dist 104=[-1.1254322018763327592 ,2.5026736193470143186 ] 
dist 105=[-1.1042492799305181118 ,2.6228433544675466203 ] 
dist 106=[-.7360764524176547636 ,2.7311244535580604313 ] 
dist 107=[-.80301229249738592329,2.7849654247126969308 ] 
dist 108=[-.86220279120170601835,2.8459485340767163162 ] 
dist 109=[-.90199459294839312052,2.8732377929557822363 ] 
dist 110=[-.93505935887778738682,2.8862819740072577710 ] 
dist 111=[-.96739210466441467019,2.8906214648125558730 ] 
dist 112=[-.99454740436197345328,2.8894713821415669454 ] 
dist 113=[-1.0069560623017260270 ,2.8805747112999269733 ] 
dist 114=[-1.0118736346720683431 ,2.9503834457562736675 ] 
dist 115=[-1.0799965761335435445 ,3.0171888155794485724 ] 
dist 116=[-1.3029413679791553625 ,3.0536011718772576698 ] 
dist 117=[-1.5025690902248703841 ,3.0610821538664088048 ] 
dist 118=[-1.6419383846888751414 ,3.0507733645537945621 ] 
dist 119=[-1.7637496237350346545 ,3.0400617443518362844 ] 
dist 120=[-1.8932889638691078718 ,3.0247967467572375132 ] 
dist 121=[-2.0100591650560648515 ,3.0133773150194419152 ] 
dist 122=[-2.0809115093860560685 ,2.4284970363386813683 ] 
dist 123=[-2.1316017321340323662 ,2.3700927093115741672 ] 
dist 124=[-2.1679272725222144654 ,2.2121686632706555666 ] 
dist 125=[-2.1921721215148621100 ,2.1880425584232141301 ] 
dist 126=[-2.1960100136701821666 ,1.8954925161254475984 ] 
dist 127=[-2.1893113649863290435 ,1.8353746413808782915 ] 
dist 128=[-2.1822751274078271576 ,1.7747090013528188787 ] 
dist 129=[-2.0503993788075246012 ,1.7591763272232160798 ] 
dist 130=[-2.2583650431212182839 ,1.0888193458214818386 ] 
dist 131=[-2.3847678917092732214 ,1.0027926873809670137 ] 
dist 132=[-2.4756492955527425711 ,.83027044194747840316] 
dist 133=[-2.5418208119871955248 ,.78547830283274985559] 
dist 134=[-2.5898551254983832089 ,.62555189171184427141] 
dist 135=[-2.6083465115933649436 ,.59036199965574906963] 
dist 136=[-2.6123877418119888401 ,.53947986002477867681] 
dist 137=[-2.6076194449176706020 ,.52437793324523523252] 
dist 138=[-1.8199132231548429511 ,-.08751760834737669525] 
dist 139=[-1.7742466352900701457 ,.09056202012294987993] 
dist 140=[-1.7586211290396478970 ,.24381950459602988235] 
dist 141=[-1.7184168561220422160 ,.40327089006128321031] 
dist 142=[-1.7028775781804599622 ,.55450942388685794696] 
dist 143=[-1.6917878247937982970 ,.67499173616801699624] 
dist 144=[-1.6838860269615595712 ,.79603810974682289018] 
dist 145=[-.32953121226473052141,.94953474939913066648] 
dist 146=[-.21853732592226490497,1.0970715811732047049 ] 
dist 147=[.0320642681818458522 ,1.1943337887658569259 ] 
dist 148=[.0768495817122123716 ,1.2734273357201002599 ] 
dist 149=[.37788786627917867588,1.3484503487357054025 ] 
dist 150=[.40264768245060182202,1.4151683731941394964 ] 
dist 151=[.30619160345440199982,1.4611184807514697608 ] 
dist 152=[.17824331471724144081,1.5007041595816052029 ] 
dist 153=[-.02612227305734120152,1.5420297068663557972 ] 
dist 154=[-.23427834053914509497,1.5764887317896467458 ] 
dist 155=[-.37735527261461045117,1.5886677944859603107 ] 
dist 156=[-.50014534650736486013,1.5921248512255427193 ] 
dist 157=[-.62733496811730286505,1.5917525008502109827 ] 
dist 158=[-.74760221032642502862,1.5413837397833490936 ] 
dist 159=[-.84276475566391030586,1.5316005612130705014 ] 
dist 160=[-.93775641106645466434,1.5324145206956460640 ] 
dist 161=[-1.0573423030089632657 ,1.5110981623807814002 ] 
dist 162=[-1.1717997460724503659 ,1.2159905777955545238 ] 
dist 163=[-1.2463233959944933609 ,1.1748852286361517301 ] 
dist 164=[-1.3058611306912829876 ,1.0966702682373133841 ] 
dist 165=[-1.3605080336234329477 ,1.0759903867802860816 ] 
dist 166=[-1.4078244955583918510 ,1.0024733422902113050 ] 
dist 167=[-1.4381057387158282608 ,.9835180728195015821 ] 
dist 168=[-1.4617073554720098706 ,.95727862198634701174] 
dist 169=[-1.4823651091305194799 ,.94780130650814083018] 
dist 170=[-1.4969772040710082986 ,-.0071380905556524050 ] 
dist 171=[-1.4994617691558313048 ,.0112805914804825121 ] 
dist 172=[-1.4916432946814258517 ,.0501665049083189353 ] 
dist 173=[-1.4891775948109912952 ,.0992007701749275183 ] 
dist 174=[-1.4229490898309603870 ,.1581188813715509514 ] 
dist 175=[-1.4050909101379163797 ,.2355284242616769027 ] 
dist 176=[-1.3924295233154663281 ,.35835615512079585285] 
dist 177=[-1.3856465150146292266 ,.48298627846083497931] 
dist 178=[-1.3577386835463280048 ,.56758903677330013816] 
dist 179=[-1.4370511356089273979 ,.63902591564882849513] 
dist 180=[-1.4969742977997001100 ,.71111645420410609668] 
dist 181=[-1.5461313001586264390 ,.77806136228637215384] 
dist 182=[-1.5846249641778994157 ,.82896427757842163688] 
dist 183=[-1.6019855950478036856 ,.87783851840501630639] 
dist 184=[-1.6083972824083557092 ,.93668820466437871857] 
dist 185=[-1.6074392453339038260 ,.9916686214324283009 ] 
dist 186=[-1.5803560495341827236 ,1.0251021472275488333 ] 
dist 187=[-1.5723459370770081583 ,1.0491380150748869385 ] 
dist 188=[-1.5388533275698730307 ,1.0666157228983645014 ] 
dist 189=[-1.5332865320734104468 ,1.0785301990418620834 ] 
dist 190=[-1.4300470159282659129 ,1.0803652989237073747 ] 
dist 191=[-1.4056252198125202951 ,1.0779784480618763704 ] 
dist 192=[-1.3866482019758339483 ,1.1391048101643536940 ] 
dist 193=[-1.3803956808872236956 ,1.2621757721332930212 ] 
dist 194=[-1.0253309521975048546 ,1.3775322579104548989 ] 
dist 195=[-.97801161525211162797,1.4485117320911387277 ] 
dist 196=[-.88662832228782273587,1.5005710193497417762 ] 
dist 197=[-.86290008127354929527,1.5404080518045633302 ] 
dist 198=[-.77997909770890709337,1.5693147122823552890 ] 
dist 199=[-.7595651457610878733 ,1.5777440815088761628 ] 
dist 200=[-.73461360437696873221,1.5787915293422727009 ] 
dist 201=[-.72484099932017191419,1.5782448188964354072 ] 
dist 202=[.57613565757823410472,1.5325655114237271496 ] 
dist 203=[.55808157473474576224,1.5297717420408745127 ] 
dist 204=[.50974633192796285827,1.5109555472896555944 ] 
dist 205=[.4456399373850112051 ,1.5057045755714446341 ] 
dist 206=[.36463740164482353507,1.4290403431516916654 ] 
dist 207=[.25573279378890727091,1.4094888615925174128 ] 
dist 208=[.08025965817851599039,1.4204367981834711770 ] 
dist 209=[-.09914429259128481440,1.4481035594147284690 ] 
dist 210=[-.2237385689705773098 ,1.4575205150597606426 ] 
dist 211=[-.33205554452899078729,1.4593518440112614454 ] 
dist 212=[-.44649249257172682252,1.4567385872332604465 ] 
dist 213=[-.55611949879966358767,1.4153353590442241312 ] 
dist 214=[-.64523917163219357296,1.4021249588543723077 ] 
dist 215=[-.7364182683409814412 ,1.3886105962105311866 ] 
dist 216=[-.8542662955727267202 ,1.3801939881848369650 ] 
dist 217=[-.9685937022235310989 ,1.1384543035280192106 ] 
dist 218=[-1.0457213316579412890 ,1.1035021886438128403 ] 
dist 219=[-1.1103824780225577654 ,1.0332894365855519802 ] 
dist 220=[-1.1749523109475771791 ,1.0135920678904058698 ] 
dist 221=[-1.2345374431512347035 ,.93587290664961897569] 
dist 222=[-1.2793036213617225899 ,.91816272355555705122] 
dist 223=[-1.3218009693878010187 ,.87937039956108537443] 
dist 224=[-1.3723320061304059214 ,.86702649676078839036] 
dist 225=[-1.4173555609857190606 ,-.38532413485847299241] 
dist 226=[-1.4553199236912791991 ,-.47599731285928149995] 
dist 227=[-1.5190508676654738587 ,-.50051392856832556405] 
dist 228=[-1.5634091172368703231 ,-.45749814306268519493] 
dist 229=[-1.5929393219316135893 ,-.37957706202308830467] 
dist 230=[-1.6125104614215854274 ,-.28516201887446117596] 
dist 231=[-1.6171175339445718414 ,-.17631156640602280795] 
dist 232=[-1.6149716812072532383 ,-.03601367931454747580] 
dist 233=[-1.6097357897854696122 ,.18392142176278049379] 
dist 234=[-1.1135316328917387463 ,.40638580497404758202] 
dist 235=[-1.0464958799695459806 ,.55677931478657907983] 
dist 236=[-1.0284930244732499130 ,.68320588986762543912] 
dist 237=[-.96308525737483365922,.81000860854114519569] 
dist 238=[-.94617178653909385348,.92737302757678979228] 
dist 239=[-.91931462891110150708,1.0161275859273039316 ] 
dist 240=[-.91080377790958694204,1.1009393920183459956 ] 
dist 241=[-.00631956697938384728,1.2025667931577940148 ] 
dist 242=[.07037249782501293611,1.2973775048793568193 ] 
dist 243=[.23470735366427875581,1.3549811487590997332 ] 
dist 244=[.27020551841488959645,1.3963699510564767758 ] 
dist 245=[.43773924047973007406,1.4264605815497931587 ] 
dist 246=[.46674165764759656316,1.4470411449614377405 ] 
dist 247=[.52210546590446616198,1.4517996708537927372 ] 
dist 248=[.53404705318468623572,1.4485777728384612732 ] 
dist 249=[.56116926607650879698,1.4479094983580615308 ] 
dist 250=[.55211722837586499878,1.3805490888569154044 ] 
dist 251=[.52536026177530457877,1.3671563230951680572 ] 
dist 252=[.46743727247195527934,1.3244409461222191965 ] 
dist 253=[.39389571109521453245,1.3163819405892931423 ] 
dist 254=[.30479865046956691721,1.2129977179789971897 ] 
dist 255=[.1872206225465801437 ,1.1895216027037827034 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 1, 2, 2, 0, 0, 1] 
dist 0=[45.936521495765364618  ,45.936521495765364618  ] 
dist 1=[45.635291583423247596  ,46.351309627597231089  ] 
dist 2=[44.847053192489324329  ,46.822724840822698578  ] 
dist 3=[43.597480989736096695  ,47.113814939702597634  ] 
dist 4=[41.518819571990303424  ,47.329010967520872502  ] 
dist 5=[39.366289931554132002  ,47.497165719048781445  ] 
dist 6=[37.821648375052622493  ,47.600811004348069801  ] 
dist 7=[36.422675860881407706  ,47.558231130417441632  ] 
dist 8=[34.851703765543157227  ,46.646500927181918325  ] 
dist 9=[33.284936523365410828  ,46.439149263526368827  ] 
dist 10=[31.902553545242305193  ,46.112045329214388229  ] 
dist 11=[30.385968549870480640  ,45.990454852248769090  ] 
dist 12=[28.282831462899360467  ,45.540016957611421209  ] 
dist 13=[26.162784783255341751  ,45.387598238069758636  ] 
dist 14=[24.578461005470001584  ,45.050552243499700076  ] 
dist 15=[23.077109430495394232  ,44.823572951581869236  ] 
dist 16=[21.288217206038823298  ,32.491071448430641036  ] 
dist 17=[19.441911646721502927  ,31.384685002273992513  ] 
dist 18=[17.710860699845465427  ,28.749282322202712461  ] 
dist 19=[15.724368411936405775  ,28.316063569364181033  ] 
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dist 80=[-4.0406828882281972278 ,.41594548057203383976] 
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dist 120=[-3.7571515097197852889 ,2.9417974308493470579 ] 
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dist 128=[-.55276594698727262925,.24539289408074219943] 
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dist 132=[-.69087379881427491115,.0065487621968585109 ] 
dist 133=[-.83212514783571441141,.07297178188709017011] 
dist 134=[-.96911447004623779439,.11803417582640142582] 
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dist 143=[-1.6072194480011141048 ,.36663522367568860499] 
dist 144=[-.31074198620818037773,.37329100960353020473] 
dist 145=[-.2474829119056773088 ,.37752865207450006245] 
dist 146=[-.19381106283850946007,.37891318676260587703] 
dist 147=[-.18711172619738139199,.3784641969015030154 ] 
dist 148=[-.18498869664477534569,.37761602037785622809] 
dist 149=[-.1455987033532869023 ,.26820480905288018495] 
dist 150=[-.18448016267838704325,.35915776565130007707] 
dist 151=[-.22008236220792812126,.48235114832935017323] 
dist 152=[-.26050274007237906579,.60315774053668296364] 
dist 153=[-.30091375868012655938,.68501653176489699494] 
dist 154=[-.33647934166708507036,.7540609149864563191 ] 
dist 155=[-.37530019333841124634,.82372812232951304564] 
dist 156=[-.42870386476043270944,.88854175736867459967] 
dist 157=[-.48201108674366536041,.94324021454494947664] 
dist 158=[-.52044749822265742297,.99969807024784837159] 
dist 159=[-.55534606275823335278,1.0721887376200514880 ] 
dist 160=[-.59453430301199220144,1.1398394978802766710 ] 
dist 161=[-.63347596273519241445,1.1769798623116025557 ] 
dist 162=[-.66739101990233165515,1.1989748139704283571 ] 
dist 163=[-.70411822401954581846,1.2061575355513710716 ] 
dist 164=[-.75428434926695601465,1.2078735029697238743 ] 
dist 165=[-.8022041873950932178 ,1.2080381105189278984 ] 
dist 166=[-.82996634035632747797,1.2071310012187748045 ] 
dist 167=[-.84827779214561579063,1.2045553585470701944 ] 
dist 168=[-.90424375995669681022,1.0303289367142305130 ] 
dist 169=[-.93955744882146345487,1.0048076678284061410 ] 
dist 170=[-.96470292096650338201,.95833484908480875051] 
dist 171=[-.98251577880719647573,.94600095191836955148] 
dist 172=[-.99423035487637328295,.92837336705782731748] 
dist 173=[-.99648155451837087562,.95787728488564400561] 
dist 174=[-.99251277757499830263,.9715581632902335754 ] 
dist 175=[-.99090999170504254459,.97787379361004104604] 
dist 176=[-.73290711435619170061,.97798081005911952257] 
dist 177=[-.68949203985404234017,.96086732510117287591] 
dist 178=[-.67987251484575899826,.95458131421927187349] 
dist 179=[-.65362280213375813437,.94912338583069342727] 
dist 180=[-.64729361007912586698,.94419810451476205066] 
dist 181=[-.63378598480710185668,.72613831160858901273] 
dist 182=[-.70941618626684612798,.7005168366953833987 ] 
dist 183=[-.80007797183633718301,.63391271402394681607] 
dist 184=[-.88472973777267473688,.62408892912848253155] 
dist 185=[-.93637192991252569236,.5104078693112945126 ] 
dist 186=[-.97375462219327136411,.48788250486618977514] 
dist 187=[-1.0014894326076892047 ,.46441862205133125907] 
dist 188=[-1.0217215902790035480 ,.45936768558996480467] 
dist 189=[-1.0291545348413940400 ,.39120908763786708403] 
dist 190=[-1.0308917035680437559 ,.46265752360767365769] 
dist 191=[-1.0284882621627072605 ,.52708827091729909957] 
dist 192=[-.97198938995345615154,.59883041910158683427] 
dist 193=[-.9616990420818102786 ,.66983308554100395061] 
dist 194=[-.93016686493322677388,.73131571269274083378] 
dist 195=[-.92392356653329552549,.79764650363591372998] 
dist 196=[-.85115303325321904108,.88800788515421321956] 
dist 197=[-.83476268729383564554,.97447945135501175458] 
dist 198=[-.81682960500873736654,1.0252840479506614758 ] 
dist 199=[-.8085726679801186198 ,1.0597360888486615419 ] 
dist 200=[-.65989405395803353482,1.0809291726586885192 ] 
dist 201=[-.64098779990287019639,1.0954372921293739751 ] 
dist 202=[-.60754895501643472257,1.1032021512002535659 ] 
dist 203=[-.6495143674576999487 ,1.1075276399164424926 ] 
dist 204=[-.70252657497993063411,1.1083025138959329965 ] 
dist 205=[-.75335194121959440316,.97803431634120429906] 
dist 206=[-.78658863089259580275,.95831013377780114991] 
dist 207=[-.81330132330698527984,.9282220910319708431 ] 
dist 208=[-.83808743485141296509,.95492663734409016366] 
dist 209=[-.85972844786222588872,.96624159558368584362] 
dist 210=[-.87388753770885429159,.97099587641142087536] 
dist 211=[-.88526905864514915089,.97150299353950866836] 
dist 212=[-.89582229631591394648,.94708902975443921658] 
dist 213=[-.90339663335150990603,.94001047620329860557] 
dist 214=[-.90429208945019513655,.9350885289626328688 ] 
dist 215=[-.89979936055456188335,.93182770766976939106] 
dist 216=[-.89707487659397224321,.9289444914712947355 ] 
dist 217=[-.86215264785084149997,.96182988664994415368] 
dist 218=[-.8523912441252297783 ,.98301135325113030581] 
dist 219=[-.84176394356341121702,.99375494681650324832] 
dist 220=[-.83597227414654798688,.99941288660453450921] 
dist 221=[-.67745292215352206278,1.0002965203344746457 ] 
dist 222=[-.65482778638931534393,.99785063886083608273] 
dist 223=[-.60896435468036668935,.99524450256112318113] 
dist 224=[-.59613076973267758136,.8860158386879410637 ] 
dist 225=[-.54542118161733667881,.87034133234709639124] 
dist 226=[-.53413960015965593118,.82521832253471717805] 
dist 227=[-.50909487937872353561,.81863364445784849008] 
dist 228=[-.5036812526116382505 ,.72604071638622992431] 
dist 229=[-.57113701667931467944,.70642622483674301645] 
dist 230=[-.6361577544063583655 ,.68892033888417295047] 
dist 231=[-.71488335740870788578,.68515514466456890044] 
dist 232=[-.78875354731864321257,.44677629176265247607] 
dist 233=[-.83439219437579206859,.41613396962588469988] 
dist 234=[-.86809711580280715765,.35609482096428587014] 
dist 235=[-.8943313311597239441 ,.3407206385260619114 ] 
dist 236=[-.91374906895551732593,.28762421164069794471] 
dist 237=[-.92024749571513205123,.27023131139584982946] 
dist 238=[-.92198788317793643178,.25511346323426968392] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 0, 0, 1, 0, 2] 
dist 0=[54.964280626923929949  ,54.964280626923929949  ] 
dist 1=[54.768053947912842929  ,55.080171732837634414  ] 
dist 2=[54.368780807843188424  ,55.117590372482345946  ] 
dist 3=[53.441221323929721703  ,55.073020764111947960  ] 
dist 4=[52.392127725627458500  ,54.835753463490964543  ] 
dist 5=[51.507473397439083585  ,54.685565162844407716  ] 
dist 6=[49.993163607965923132  ,54.514080951682006103  ] 
dist 7=[47.806461502942487710  ,54.397795508934044228  ] 
dist 8=[45.935059229891477422  ,50.717431970583762987  ] 
dist 9=[43.932442974114733682  ,50.157541511704314980  ] 
dist 10=[41.221484248197252924  ,49.043499897675556059  ] 
dist 11=[38.255069093832383722  ,48.721744674289920508  ] 
dist 12=[35.232088182867103803  ,47.410365799438467547  ] 
dist 13=[31.581247816885204910  ,47.103683162924444067  ] 
dist 14=[26.107131546155662900  ,46.371517941102637888  ] 
dist 15=[20.625708222023461918  ,46.118447819811398950  ] 
dist 16=[16.945540649708689552  ,35.124153561059682669  ] 
dist 17=[13.870817528647878402  ,34.729836574359825101  ] 
dist 18=[10.807143918612551654  ,34.373865225913330777  ] 
dist 19=[7.9745642671988702661 ,34.286253088432834019  ] 
dist 20=[5.8224866660079504687 ,20.667619820552878680  ] 
dist 21=[3.7496074907748877799 ,19.816310457957669436  ] 
dist 22=[1.2327214712850382654 ,18.783838460652791163  ] 
dist 23=[-1.1481681387161389311 ,18.581660064270704271  ] 
dist 24=[-2.6781953541489227214 ,11.797948984144121798  ] 
dist 25=[-3.8850916398848420155 ,10.969237359622279561  ] 
dist 26=[-4.9757159664344324458 ,9.2648775828022204203 ] 
dist 27=[-5.9175320635566285660 ,8.8300292444841972478 ] 
dist 28=[-6.5306550753268099619 ,7.2854493171951153899 ] 
dist 29=[-7.4076591249144315029 ,6.9803149024508839284 ] 
dist 30=[-8.4429048318733819541 ,6.5445939003648293969 ] 
dist 31=[-9.3272203609312742848 ,6.4467061314496326159 ] 
dist 32=[-10.049932100877274567  ,-6.9108591824769514588 ] 
dist 33=[-10.439759073911461639  ,-6.9340766137879743336 ] 
dist 34=[-10.661731479977106445  ,-6.7460119798350175348 ] 
dist 35=[-10.714108497027833454  ,-6.2267093980095248404 ] 
dist 36=[-8.2137995421658916961 ,-5.6361494978996695825 ] 
dist 37=[-8.1062784337035972727 ,-5.1634945720498717532 ] 
dist 38=[-8.0518851983977422505 ,-4.6905417751197433618 ] 
dist 39=[-7.3365506115332045058 ,-4.0978706483794951470 ] 
dist 40=[-7.2197730384273719827 ,-3.4768364503842730828 ] 
dist 41=[-6.8883162451700664461 ,-2.8902596719019192680 ] 
dist 42=[-6.8405298302659348542 ,-2.2180355322738492050 ] 
dist 43=[-6.1929562918686241316 ,-1.2548288400180051322 ] 
dist 44=[-6.0606268728052026274 ,-.2776483266586981093 ] 
dist 45=[-5.9347483871314211872 ,.46616186381431148202] 
dist 46=[-5.9108308162709397504 ,2.1656151413237672776 ] 
dist 47=[-4.4356392339909873462 ,3.8486329524630485870 ] 
dist 48=[-4.2456703644502338677 ,4.9425460931272134646 ] 
dist 49=[-3.9069950576644864691 ,5.8153474664411703118 ] 
dist 50=[-3.5453845333574085132 ,6.6156489386151176769 ] 
dist 51=[-2.7437128218972212522 ,7.3088733628702650471 ] 
dist 52=[-.76478185766927971969,7.7541849260830982062 ] 
dist 53=[-.57076862836280412264,8.1034639879176131982 ] 
dist 54=[-.1683493825878153667 ,8.4132576863955542002 ] 
dist 55=[-.0691243679928465678 ,8.6740820937364338349 ] 
dist 56=[.3036308238159996972 ,8.8278996484770606069 ] 
dist 57=[.3746005694691973006 ,8.9329171484811206690 ] 
dist 58=[.4921966783012577481 ,9.0224213548004982384 ] 
dist 59=[.5178306003827118342 ,9.0357029663755696627 ] 
dist 60=[.5501778541919962918 ,8.7316328862897196978 ] 
dist 61=[.5228410864440382045 ,8.6565899306047182301 ] 
dist 62=[.4589357500620739578 ,8.1803280125510970410 ] 
dist 63=[.3290578121049905141 ,5.1274394369876632095 ] 
dist 64=[.1671669629625752108 ,5.1232996060564698260 ] 
dist 65=[-.0245818679527927621 ,5.1072713231710486251 ] 
dist 66=[-.2747611330971387781 ,5.0796350846836573817 ] 
dist 67=[-.6699322829971071759 ,5.0629987889135719953 ] 
dist 68=[-1.0692127546789587239 ,.63064105767397260039] 
dist 69=[-1.3358298082597045186 ,.36130144005948559019] 
dist 70=[-1.5873017368400633771 ,-.2647208402808171407 ] 
dist 71=[-2.1712645484671267264 ,-.35627499744110323908] 
dist 72=[-2.5409280902644308834 ,-1.1547109598669907418 ] 
dist 73=[-2.8246737414879828353 ,-1.2899500752203355671 ] 
dist 74=[-3.0656606039568583116 ,-1.4775659810397219972 ] 
dist 75=[-3.2609503800528520093 ,-1.5127472862356532586 ] 
dist 76=[-3.3622783484434141918 ,-1.4233239814298645764 ] 
dist 77=[-3.4179261314203985286 ,-1.2799149440148282493 ] 
dist 78=[-3.4308800941192779288 ,-1.1040299536771552654 ] 
dist 79=[-3.1799324587628124982 ,-.83801206314475000271] 
dist 80=[-3.1462209539631598726 ,-.5346058380467322014 ] 
dist 81=[-3.0797607286218538173 ,-.20950530762134021992] 
dist 82=[-3.0570371642937736803 ,.19359818787551580028] 
dist 83=[-2.9510838993574226084 ,.80830148427373854968] 
dist 84=[-2.9236169295093040365 ,1.4228668596742367325 ] 
dist 85=[-2.8475315192048740947 ,1.8254211125295525597 ] 
dist 86=[-2.8230676733368600467 ,2.1495707783835604118 ] 
dist 87=[-2.6631629783399177466 ,2.4512395915008013851 ] 
dist 88=[-2.6259208571520255041 ,2.7151653813311360502 ] 
dist 89=[-2.5588479942954172523 ,2.8886864672027598031 ] 
dist 90=[-2.5397508561018802771 ,3.0290975610468716046 ] 
dist 91=[-2.4678624310174064486 ,3.1608767884318636353 ] 
dist 92=[-2.4461811383145322148 ,3.2744612683857097027 ] 
dist 93=[-2.4093184375633538562 ,3.3422568862637303387 ] 
dist 94=[-2.3971089691547334279 ,3.3893943919019475150 ] 
dist 95=[-1.7205441134342409219 ,3.4205364167711256837 ] 
dist 96=[-1.6087319444461464911 ,3.6565695899300824622 ] 
dist 97=[-1.5847177525887125662 ,4.0427309961715442921 ] 
dist 98=[-1.5237816110711406888 ,4.3771582697607228029 ] 
dist 99=[-1.5076053385849079784 ,4.6531257379510794799 ] 
dist 100=[-1.3293363230549154107 ,4.8059307992831198004 ] 
dist 101=[-1.2942133077373989750 ,4.8980003458207529364 ] 
dist 102=[-1.2591048088430095343 ,4.9315418592119821281 ] 
dist 103=[-1.2484442085825377386 ,4.9437268849351929690 ] 
dist 104=[-1.2485908843368461264 ,4.9505360551144332348 ] 
dist 105=[-1.2651439378449176296 ,4.9548379091250859463 ] 
dist 106=[-1.2967547741461851505 ,4.9569681000430377154 ] 
dist 107=[-1.3570199637158894663 ,4.9575908947477247752 ] 
dist 108=[-1.4244628092991347115 ,4.9558462896512357358 ] 
dist 109=[-1.4847393563059645216 ,4.9520028468709769127 ] 
dist 110=[-1.5512667474587969950 ,4.9442072629053073118 ] 
dist 111=[-1.6436919746430882531 ,2.7795443897842316920 ] 
dist 112=[-1.7457268243533399955 ,2.7489025791316818187 ] 
dist 113=[-1.8506328768070413862 ,2.7332384539493959354 ] 
dist 114=[-1.9778181074747757341 ,2.6995222366853327990 ] 
dist 115=[-2.1688126719533501694 ,2.6848794916871873728 ] 
dist 116=[-2.3594455178452857948 ,1.0999250012918878699 ] 
dist 117=[-2.4851948085435945890 ,.96233360007971692282] 
dist 118=[-2.5876342761756270062 ,.6413066423140760419 ] 
dist 119=[-2.6852168280533855441 ,.5875878000488470957 ] 
dist 120=[-2.7723731509297635472 ,.1640759614327785391 ] 
dist 121=[-2.8331963674841106190 ,.0888611648581690573 ] 
dist 122=[-2.8864933104343706639 ,-.0282933438981550948 ] 
dist 123=[-2.9436178698039553535 ,-.0572414053140159319 ] 
dist 124=[-2.9975913978554746129 ,-.52412674144498312359] 
dist 125=[-3.0267684035168773496 ,-.5834969372076521318 ] 
dist 126=[-3.0310615941652478638 ,-.70102957786768210557] 
dist 127=[-2.1260887909074670218 ,-.72831253666976808368] 
dist 128=[-2.1236897279193863466 ,-.80885221216578231585] 
dist 129=[-2.1024509478017789952 ,-.82016852796094024902] 
dist 130=[-2.0946578316395003894 ,-.81129895529790960778] 
dist 131=[-1.9994164589390997021 ,-.77270880938393383685] 
dist 132=[-1.9744892256850737281 ,-.72543543914427950597] 
dist 133=[-1.9466257841466993412 ,-.6819058997101225917 ] 
dist 134=[-1.9324290138940276675 ,-.6328766215145347446 ] 
dist 135=[-1.5561289299186958737 ,-.5636275069132826561 ] 
dist 136=[-1.5030736654200249727 ,-.4867511293828767416 ] 
dist 137=[-1.3945397798235477794 ,-.4072662868811355257 ] 
dist 138=[-1.3642473058309684837 ,-.3106664740178816545 ] 
dist 139=[-1.2445408764935532022 ,-.1654656818778972801 ] 
dist 140=[-1.2184826021686022700 ,-.0149888882757569041 ] 
dist 141=[-1.1604758760455975746 ,.1026780153399166290 ] 
dist 142=[-1.1423551825744351998 ,.2188736235849572371 ] 
dist 143=[-.7773627624354913789 ,.57546391726499651253] 
dist 144=[-.8161363654517590982 ,.82175494760343832517] 
dist 145=[-.8573830343625165239 ,1.0265374320500195161 ] 
dist 146=[-.90828051093278190694,1.2283412222506185171 ] 
dist 147=[-.9855519483178416416 ,1.4128940729909674355 ] 
dist 148=[-1.0623849018146383935 ,1.5488169555370858385 ] 
dist 149=[-1.1115296930460601191 ,1.6752151493651831062 ] 
dist 150=[-1.1497144854040425356 ,1.8217497906114503155 ] 
dist 151=[-1.1828166369814334601 ,1.9560213854275962944 ] 
dist 152=[-1.2100180939526318544 ,2.0334695173528605951 ] 
dist 153=[-1.2246559531351497261 ,2.0841629731826317687 ] 
dist 154=[-1.2328304292204218257 ,2.1116374735750151656 ] 
dist 155=[-1.2342340788646117872 ,2.1275425491894675762 ] 
dist 156=[-1.2311186589666555209 ,2.1320549705465601505 ] 
dist 157=[-1.2277276334178875365 ,2.1290963178811165092 ] 
dist 158=[-1.2107711048227861458 ,2.1237960393660135246 ] 
dist 159=[-1.2051644099693024642 ,1.8248901985861661900 ] 
dist 160=[-1.1426241475966381261 ,1.7882799563921183826 ] 
dist 161=[-1.1265436323614075340 ,1.7775502010015169607 ] 
dist 162=[-1.1078587645301407827 ,1.7375639334164597029 ] 
dist 163=[-1.1063237283347208361 ,1.7296929732138017327 ] 
dist 164=[-1.2040776373619861369 ,.70652523181776853503] 
dist 165=[-1.2955987795865091953 ,.61873794341585157121] 
dist 166=[-1.4025717474937102774 ,.42032192593438040802] 
dist 167=[-1.5010225823616316221 ,.3814084329656987082 ] 
dist 168=[-1.5585327296950544678 ,.1376176747543161674 ] 
dist 169=[-1.5970962322615083379 ,.0945788863674235375 ] 
dist 170=[-1.6199282764971908187 ,.0117951309996393348 ] 
dist 171=[-1.6333197134287259137 ,-.0078376810942600772 ] 
dist 172=[-1.6361668869574176003 ,-.21544399946202222437] 
dist 173=[-1.6410876584265028963 ,-.24627172658603336149] 
dist 174=[-1.6392186912901800540 ,.05665411645761546681] 
dist 175=[-1.4879587043822576204 ,.36296655008853543711] 
dist 176=[-1.5098767550196430782 ,.56829358915806336719] 
dist 177=[-1.5249995601960992434 ,.73895804115265736143] 
dist 178=[-1.5326461591026355856 ,.906924731141678409  ] 
dist 179=[-1.5321001961228386849 ,1.0602853742675799455 ] 
dist 180=[-1.5026285076939403341 ,1.1726533354187649177 ] 
dist 181=[-1.5691231965728387829 ,1.2765031127271929753 ] 
dist 182=[-1.6160950694332445339 ,1.3958639484596978450 ] 
dist 183=[-1.6487588921394254349 ,1.5047485188119974913 ] 
dist 184=[-1.6707824426931681926 ,1.5667848698369155487 ] 
dist 185=[-1.6752796071198352046 ,1.6063679861700292695 ] 
dist 186=[-1.6731781310592420076 ,1.6256376095185229120 ] 
dist 187=[-1.6688598089362552826 ,1.6362715416104038607 ] 
dist 188=[-1.5732035431522650849 ,1.6413889255361731919 ] 
dist 189=[-1.5543172983104125850 ,1.6434369499339765058 ] 
dist 190=[-1.5091153546719012188 ,1.6418231383122690284 ] 
dist 191=[-1.4928760404098084814 ,.8694402122865609438 ] 
dist 192=[-1.4116200732516900055 ,.9874225559465931405 ] 
dist 193=[-1.3925219163541324458 ,1.0897836117515776005 ] 
dist 194=[-1.3481947865240345699 ,1.2003421963403690239 ] 
dist 195=[-1.3328443579619976790 ,1.3510492280736757104 ] 
dist 196=[.36600550275097749346,1.4958935736651091247 ] 
dist 197=[.36893098219825601052,1.5830521340307535173 ] 
dist 198=[.3494869157035178034 ,1.6446782711815222390 ] 
dist 199=[.31984464587076504762,1.6876083271406806008 ] 
dist 200=[.28176118036758788148,1.7185857357257641380 ] 
dist 201=[.23020583352192375079,1.7325015868450987501 ] 
dist 202=[.14678978571486901908,1.7365925966370793703 ] 
dist 203=[.04927142525447717690,1.7493368766988020970 ] 
dist 204=[-.05857247513920092768,1.8058024851097050140 ] 
dist 205=[-.19464897674076816051,1.8327585737721269944 ] 
dist 206=[-.4048545390551063715 ,1.8451331539221453162 ] 
dist 207=[-.61641066821490406689,1.8453953487534569756 ] 
dist 208=[-.7578787163803897364 ,1.8586483272369461153 ] 
dist 209=[-.87511234396558058939,1.8598134114993401724 ] 
dist 210=[-.98994225157896982418,1.8504411101278711170 ] 
dist 211=[-1.0944560455253383586 ,1.8436557592715979049 ] 
dist 212=[-1.1705158380299012389 ,1.5515115033792420405 ] 
dist 213=[-1.2403140144973445090 ,1.5456281942086500430 ] 
dist 214=[-1.3198377814415950370 ,1.5395128822302886802 ] 
dist 215=[-1.3919391780980925394 ,1.3277359899474930426 ] 
dist 216=[-1.4321130040022246878 ,1.2957466438396587487 ] 
dist 217=[-1.4566064182485115712 ,1.2338967770541331181 ] 
dist 218=[-1.4702874437322927894 ,1.2164794214143514270 ] 
dist 219=[-1.4896996758906000387 ,1.1486451636926948746 ] 
dist 220=[-1.5068828840958652501 ,1.1316933531243714244 ] 
dist 221=[-1.5719170378694081285 ,1.0967969437889066092 ] 
dist 222=[-1.6179419186564872486 ,1.0855882082747788801 ] 
dist 223=[-1.6500702811229883276 ,.2691254540615984576 ] 
dist 224=[-1.6716183580661570647 ,.1453390589677896639 ] 
dist 225=[-1.6758927537129448216 ,.1239015848849697359 ] 
dist 226=[-1.6728969503780297183 ,.0764390681417221409 ] 
dist 227=[-1.6692673002295903851 ,.0662868640829656544 ] 
dist 228=[-1.0716099812559400330 ,-.33354839173445552559] 
dist 229=[-1.0367203959685672203 ,-.2725353620989074081 ] 
dist 230=[-1.0241388180353912204 ,-.15403737139911583029] 
dist 231=[-1.0093126095607801332 ,-.0241070594140620503 ] 
dist 232=[-1.0776635194556478157 ,.1032550648666195283 ] 
dist 233=[-1.1361783590478081902 ,.2115041553313725368 ] 
dist 234=[-1.1965854478908727229 ,.3265099418941814564 ] 
dist 235=[-1.2535947196972741099 ,.4808433914389698540 ] 
dist 236=[-1.2985450515169616347 ,.6332856947447818414 ] 
dist 237=[-1.3432715956914221163 ,.7407443760277176581 ] 
dist 238=[-1.3993837637916962066 ,.8358601606365870120 ] 
dist 239=[-1.4507694243749962023 ,.9390379756640794306 ] 
dist 240=[-1.4766296439897795516 ,1.0395427389688525085 ] 
dist 241=[-1.4893702651050905256 ,1.1239909427583246331 ] 
dist 242=[-1.4910899485721112364 ,1.2128857932831487375 ] 
dist 243=[-1.4765054848230999242 ,1.3311427997295854706 ] 
dist 244=[-1.4684261358839371420 ,1.4437041410051189740 ] 
dist 245=[-1.4578466281944229547 ,1.5098647265451862705 ] 
dist 246=[-1.4515194331649139847 ,1.5547332376978212257 ] 
dist 247=[-1.2519208838626531309 ,1.5823037626310122641 ] 
dist 248=[-1.2215624574393818974 ,1.6003733623671354082 ] 
dist 249=[-1.1593849947546142769 ,1.6073176088874770630 ] 
dist 250=[-1.1411126060877601811 ,1.6074476716693179652 ] 
dist 251=[-1.0645290550315080023 ,1.5808670177646643334 ] 
dist 252=[-1.0475104085644808486 ,1.5555321923933787324 ] 
dist 253=[-1.0036975711149825325 ,1.5516228916270180591 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 2, 0, 1] 
dist 0=[48.969568271872402730  ,48.969568271872402730  ] 
dist 1=[48.606879362843045443  ,49.285148450687791295  ] 
dist 2=[48.090718590799040504  ,49.613022098166411523  ] 
dist 3=[47.362422192179146369  ,50.012443282651642680  ] 
dist 4=[46.152475295219117882  ,50.613368085082177973  ] 
dist 5=[44.687951860736640092  ,51.188601530379326200  ] 
dist 6=[42.942956705422760419  ,51.485456934372040925  ] 
dist 7=[40.654393431084071952  ,51.634687677084021085  ] 
dist 8=[37.019079761732693515  ,51.629206848117317745  ] 
dist 9=[33.321256292103492945  ,51.515283924257238253  ] 
dist 10=[30.782954424271705638  ,51.438242131047077781  ] 
dist 11=[28.602192515505601918  ,51.082108719629241932  ] 
dist 12=[26.331939489526277361  ,50.981805697551416496  ] 
dist 13=[24.170645522695849621  ,41.684200399837660709  ] 
dist 14=[22.424737543374085430  ,40.766172285154325542  ] 
dist 15=[20.643262614278362026  ,38.472397833348583467  ] 
dist 16=[18.339380103655982343  ,38.112342984065653909  ] 
dist 17=[16.090122433667298357  ,34.457210061120421146  ] 
dist 18=[14.526521509241488107  ,33.740994222406574576  ] 
dist 19=[13.159240172472896266  ,32.913258947482522361  ] 
dist 20=[11.693730014317486701  ,32.677858855739123451  ] 
dist 21=[10.267648167460588567  ,25.702221487326919472  ] 
dist 22=[8.9238670518584004247 ,24.798698813974661839  ] 
dist 23=[7.3345392315153590740 ,22.970935052624644307  ] 
dist 24=[5.6170925568875548768 ,22.491305306898704348  ] 
dist 25=[3.9382128301430227771 ,20.734826317202452831  ] 
dist 26=[2.5024193215351691598 ,20.361100992096839145  ] 
dist 27=[.96096809629661793061,19.691854609169913944  ] 
dist 28=[-1.1411136851461311503 ,19.529765260843511478  ] 
dist 29=[-3.1800413238188681226 ,5.8729829060323332916 ] 
dist 30=[-4.4693052178539984120 ,4.7042137146599473166 ] 
dist 31=[-5.4655923222759771250 ,2.0885499454427121522 ] 
dist 32=[-6.3333151328412455528 ,1.6280123057041008196 ] 
dist 33=[-7.6282244263186482472 ,-.67807814978153298111] 
dist 34=[-9.0680008505093757876 ,-.7910642187540660785 ] 
dist 35=[-10.402005287541279721  ,-.97344743712028099497] 
dist 36=[-11.946652115139470248  ,-1.0078882873874846788 ] 
dist 37=[-13.371579507029554335  ,-1.0172757662355956915 ] 
dist 38=[-14.227403473703759139  ,-.9613397643652561655 ] 
dist 39=[-14.833322897799749192  ,-.8564190694748810211 ] 
dist 40=[-15.260054137469298395  ,-.6622693251006214225 ] 
dist 41=[-15.575076084373676692  ,-.4553018835505268627 ] 
dist 42=[-15.734722799540323838  ,-.2990684313989057277 ] 
dist 43=[-15.811965076258939978  ,-.15166614265869712561] 
dist 44=[-15.799856157832534830  ,.04068227946812493354] 
dist 45=[-6.9809187666190420351 ,.2301167182681004645 ] 
dist 46=[-6.4600107147408513690 ,.38935824019359949762] 
dist 47=[-5.2099294142582272048 ,.55567414609958215175] 
dist 48=[-5.0200504627515994597 ,.77331091307769373789] 
dist 49=[-3.2619556650852968001 ,.98274704239830692495] 
dist 50=[-2.9441468418016590127 ,1.1163554394648417145 ] 
dist 51=[-2.5300773143629142198 ,1.2187625456854657007 ] 
dist 52=[-2.4311732685673013422 ,1.3037728281164313009 ] 
dist 53=[-.07307491208484594995,1.3694651164091170746 ] 
dist 54=[.02701787443932436174,1.5906785242474259802 ] 
dist 55=[-.1135554303786340960 ,1.8610408050668007317 ] 
dist 56=[-.3407627893151069687 ,2.0983675966401978700 ] 
dist 57=[-.57027363146357506951,2.5854409052273228464 ] 
dist 58=[-.72002409556172754529,2.9718041591266832899 ] 
dist 59=[-.83965853932195377907,3.3471391958808823384 ] 
dist 60=[-.94905301597333769323,3.8074924208840060822 ] 
dist 61=[-1.0431712048510277192 ,4.2438871706912174969 ] 
dist 62=[-1.1018741218244207910 ,4.5235989716591037992 ] 
dist 63=[-1.1457304426187398962 ,4.7435152347089691266 ] 
dist 64=[-1.1806260466360950669 ,4.9410073989448864428 ] 
dist 65=[-1.2086063090245736844 ,5.1104202717302865525 ] 
dist 66=[-1.2248780108068652182 ,5.2181728671940035282 ] 
dist 67=[-1.2356332580833557024 ,5.3022499920168567142 ] 
dist 68=[-1.2416103344994310110 ,5.3771387862335159494 ] 
dist 69=[-1.2440135216222036554 ,5.4354588131619993585 ] 
dist 70=[-1.2405739385548547526 ,5.4533464833936390813 ] 
dist 71=[-1.2329079975660383752 ,5.4487993257289355964 ] 
dist 72=[-1.2276729896172295242 ,5.4383976543780439715 ] 
dist 73=[-.48646857583457872336,5.3447847896774372413 ] 
dist 74=[-.94054699067491926013,5.3148866994546932714 ] 
dist 75=[-1.6153093314000626794 ,5.2314527540284724154 ] 
dist 76=[-2.6152509343320150882 ,5.1955033814649675429 ] 
dist 77=[-3.6067584355569078519 ,1.5833764246366683398 ] 
dist 78=[-4.2478892284069687470 ,1.5331665515262172846 ] 
dist 79=[-4.7556153432802397334 ,1.4225695707435968062 ] 
dist 80=[-5.2146153104962180718 ,1.3932267767755026118 ] 
dist 81=[-5.6077115781542109578 ,1.2560453987630640980 ] 
dist 82=[-5.8523871078136880361 ,1.2290194565395492572 ] 
dist 83=[-6.0355725903763188782 ,1.1675291564715116195 ] 
dist 84=[-6.1832667115652477083 ,1.1504031886993992746 ] 
dist 85=[-6.3033411492478974251 ,.98344256013644622165] 
dist 86=[-6.4239553221155509279 ,.95638648758421760062] 
dist 87=[-6.5083918469967642468 ,.9110976297405430656 ] 
dist 88=[-6.5657802427761725212 ,.91133773804526018434] 
dist 89=[-6.6015157750165744203 ,.78127280721643030022] 
dist 90=[-6.5994822462169871958 ,.76117286523983937935] 
dist 91=[-6.5752667497849066524 ,.72477877723143537925] 
dist 92=[-6.5539413708940169309 ,.7150462725591636105 ] 
dist 93=[-3.6279415052054284787 ,.5334509003907193584 ] 
dist 94=[-3.3855781435594391985 ,.50831271174996829162] 
dist 95=[-2.8135757168880783388 ,1.0424683673586845957 ] 
dist 96=[-2.7109680273202971406 ,1.6864662859295468047 ] 
dist 97=[-1.9228384502697263627 ,2.2787558496970981314 ] 
dist 98=[-1.7776882898380766118 ,2.7203798714538065242 ] 
dist 99=[-1.5449968028013274177 ,3.1363236733636019231 ] 
dist 100=[-1.4866245770101358645 ,3.6261150999093640384 ] 
dist 101=[-.46683263569983280795,4.0822617597179403508 ] 
dist 102=[-.53266771460070069379,4.3639076533620920102 ] 
dist 103=[-.6133475278134310737 ,4.5717029518327794880 ] 
dist 104=[-.7257951006870112742 ,4.7330564423237312944 ] 
dist 105=[-.8350271499063700208 ,4.8560082662192308772 ] 
dist 106=[-.9028745756888372994 ,4.9105299013211120039 ] 
dist 107=[-.95340791777057601353,4.9319670624741206261 ] 
dist 108=[-.99353593246790111026,4.9278337767387142225 ] 
dist 109=[-1.0245381512414554100 ,2.8904744335528625161 ] 
dist 110=[-1.0386473062743528657 ,3.0701499786068180613 ] 
dist 111=[-1.0447926753258800338 ,3.1964255941160026134 ] 
dist 112=[-1.0441611072311468926 ,3.2831559262468748382 ] 
dist 113=[-1.0008877154370601454 ,3.3464014193557313558 ] 
dist 114=[-.99088329514700544006,3.3789091566990857389 ] 
dist 115=[-.97198864548983632858,3.3952184807400212073 ] 
dist 116=[-.96544612485537769664,3.3937661519773206391 ] 
dist 117=[-.93447781580412543467,3.0716659049906301534 ] 
dist 118=[-.92620098860416434588,3.0195236088675648848 ] 
dist 119=[-.90180870882334013667,2.9347676780863041648 ] 
dist 120=[-.89453471763387585695,2.9086687865936919775 ] 
dist 121=[-.16429374117888382796,2.8300121765279732256 ] 
dist 122=[-.1090003043307839831 ,2.8018196443719848541 ] 
dist 123=[.00559920341049814241,2.7742781594687651702 ] 
dist 124=[.03494709450656368779,2.7570037266334714614 ] 
dist 125=[.13937322111019858092,.6210110087310015479 ] 
dist 126=[-.03951876972807908998,.66397903387281646379] 
dist 127=[-.36129912320941390083,.75151905376182068294] 
dist 128=[-.68645644794052617048,.8600071438694532009 ] 
dist 129=[-.98904454680879992813,.96303084694705511272] 
dist 130=[-1.2207375793562507636 ,1.0287618313201120318 ] 
dist 131=[-1.4449645444604549485 ,1.0797673269797911538 ] 
dist 132=[-1.7177514595004725766 ,1.1240186415178943594 ] 
dist 133=[-1.9744354805159700128 ,1.1605485770089161929 ] 
dist 134=[-2.1343855289059015400 ,1.1807369502841302070 ] 
dist 135=[-2.2541651433845613791 ,1.1928280371349878439 ] 
dist 136=[-2.3505027491419446872 ,1.2574024397180343461 ] 
dist 137=[-2.4252540706764343255 ,1.3402185022103883702 ] 
dist 138=[-2.4588718464208691563 ,1.3859139309290683881 ] 
dist 139=[-2.4739394647515561457 ,1.4132030304574570808 ] 
dist 140=[-2.4746421373329879622 ,1.4225470813675694389 ] 
dist 141=[-.84053101959149269221,1.4253375910319338167 ] 
dist 142=[-.90553038725474875139,1.4264652731422221998 ] 
dist 143=[-.96816443502603440746,1.4266019788653364598 ] 
dist 144=[-1.0439380160039514410 ,1.4254314254682717347 ] 
dist 145=[-1.1149572750180088360 ,1.2090896950899294802 ] 
dist 146=[-1.1586154881399765443 ,1.1778015114185108833 ] 
dist 147=[-1.1905829584219631110 ,1.1221918043916709538 ] 
dist 148=[-1.2149421170710113290 ,1.1077638017564472445 ] 
dist 149=[-1.2325325426546275584 ,1.0599236514392071118 ] 
dist 150=[-1.2374840787543679037 ,1.0450271340087499498 ] 
dist 151=[-1.2367951076113933687 ,1.0326671271749779434 ] 
dist 152=[-1.2329912635015408775 ,1.1188973103402622218 ] 
dist 153=[-1.1986299631274601006 ,1.2544000178657252080 ] 
dist 154=[-1.1896155461281825210 ,1.3723256610288974353 ] 
dist 155=[-1.1610197534039403755 ,1.5054189354002101987 ] 
dist 156=[-1.1550354532776279559 ,1.6846044997711115064 ] 
dist 157=[-1.0974562486976428416 ,1.8559342926863732305 ] 
dist 158=[-1.0824781965770182724 ,1.9576737839942560283 ] 
dist 159=[-1.0729762289204952397 ,2.0280532010803778256 ] 
dist 160=[-1.0702025910745359593 ,2.0741925456564176848 ] 
dist 161=[-1.1665859907547683416 ,2.1064903585657981281 ] 
dist 162=[-1.2394220052592683050 ,2.1216078581779632474 ] 
dist 163=[-1.3088994303911444187 ,2.1270811115094711139 ] 
dist 164=[-1.3918780648438570480 ,2.1238152363546211167 ] 
dist 165=[-1.4690000082540231122 ,1.9165520340868064635 ] 
dist 166=[-1.5151052833459897113 ,1.8828230900726279061 ] 
dist 167=[-1.5472716420779305811 ,1.8226048187907812269 ] 
dist 168=[-1.5687696584786039352 ,1.8057148843450406325 ] 
dist 169=[-1.5817180132760186287 ,1.7429396071558184435 ] 
dist 170=[-1.5832157236607396594 ,1.7239770588439867539 ] 
dist 171=[-1.5735102724071949228 ,1.6912975847334642264 ] 
dist 172=[-1.5692985563938720091 ,1.6805986672313504590 ] 
dist 173=[-1.3351274504247982040 ,1.0396636055124580802 ] 
dist 174=[-1.3212538940856222246 ,1.1183593860036360412 ] 
dist 175=[-1.3071610047944667989 ,1.1901597018373776607 ] 
dist 176=[-1.2986503868700977857 ,1.2713247356592457298 ] 
dist 177=[-1.0596954448761805926 ,1.3445261098263695816 ] 
dist 178=[-1.0254721011841448354 ,1.3845394192781758010 ] 
dist 179=[-1.1392446457895691957 ,1.4078948021075734998 ] 
dist 180=[-1.3106533591173937471 ,1.4146075523183039199 ] 
dist 181=[-1.4708597874973322333 ,1.4151176208381899164 ] 
dist 182=[-1.5688050379418328279 ,1.4137180713956872805 ] 
dist 183=[-1.6399380314451230480 ,1.4106468762079150882 ] 
dist 184=[-1.6931229703138743732 ,1.4052040135425387616 ] 
dist 185=[-1.7329348451702571956 ,-.5732412243917577104 ] 
dist 186=[-1.7506871927110244844 ,-.55327581783169903228] 
dist 187=[-1.7567875356989998834 ,-.43803536664142103444] 
dist 188=[-1.7555690903697278296 ,-.2479618134437765739 ] 
dist 189=[-1.7878449934709167985 ,-.05210858847676923900] 
dist 190=[-1.8024413003862873068 ,.08620214214049888855] 
dist 191=[-1.8065649059262898262 ,.20883961031468643053] 
dist 192=[-1.8031996018098073183 ,.34214341612592184668] 
dist 193=[-1.7634938337887091952 ,.47210362605895986521] 
dist 194=[-1.7496254597022385793 ,.58140024695196055112] 
dist 195=[-1.7293692739645745606 ,.69650669709979448697] 
dist 196=[-1.7202738871429509295 ,.8496615716837647971 ] 
dist 197=[-1.5550999288364981122 ,1.0003271654023203678 ] 
dist 198=[-1.5717522394962531252 ,1.1055012102462550908 ] 
dist 199=[-1.5806453214797333504 ,1.1975209350060135289 ] 
dist 200=[-1.5812776124156670684 ,1.2956868623836498532 ] 
dist 201=[-1.5768344073514885292 ,1.3903393489451666964 ] 
dist 202=[-1.5719756121980212246 ,1.4683400208319229713 ] 
dist 203=[-1.5528399448289116964 ,1.5491279079173322461 ] 
dist 204=[-1.5433473720110565662 ,1.6549141036373556697 ] 
dist 205=[-1.4785674237222792494 ,1.7543764275362187504 ] 
dist 206=[-1.4612140555398102226 ,1.8099236990938654369 ] 
dist 207=[-1.4316625377677636558 ,1.8439860241809062980 ] 
dist 208=[-1.4219836003687419905 ,1.8626437039248483765 ] 
dist 209=[-1.1791176832120487456 ,1.8756716031261497489 ] 
dist 210=[-1.1435833316702049219 ,1.8826237657616643796 ] 
dist 211=[-1.0645552277578742287 ,1.8864719073597199942 ] 
dist 212=[-1.0407135091560213047 ,1.8871038162966451711 ] 
dist 213=[-.93649739150891698171,1.9690476588438241622 ] 
dist 214=[-.91500540469271470478,2.0118349257871034194 ] 
dist 215=[-.8625781573571124484 ,2.0344780179369822568 ] 
dist 216=[-.84924093512404531059,2.0386157061219176880 ] 
dist 217=[-.20340073293933686792,2.0239210349757439234 ] 
dist 218=[-.13929549655133354888,2.0160947827923072088 ] 
dist 219=[-.01094538010550441612,2.0073034310998813507 ] 
dist 220=[.02088426038483089977,1.9985404769977646257 ] 
dist 221=[-.28033627580283556331,1.6091776184854007490 ] 
dist 222=[-.51511664323459361444,1.5668406802084195140 ] 
dist 223=[-.71074436177604674266,1.4560386598026646952 ] 
dist 224=[-.90417254109219135176,1.4370585610206903385 ] 
dist 225=[-1.0814501197306981120 ,1.2420116361362903171 ] 
dist 226=[-1.2126104099202611622 ,1.2021671107851854490 ] 
dist 227=[-1.3351452929238832600 ,1.1548520102757422714 ] 
dist 228=[-1.4779917913856323098 ,1.1376706472777369112 ] 
dist 229=[-1.6092335947354660360 ,.7239915999620090548 ] 
dist 230=[-1.6854466150269848078 ,.66972334426712653169] 
dist 231=[-1.7359547379845752179 ,.5561405776568586599 ] 
dist 232=[-1.7645931240505538186 ,.52548457203273207163] 
dist 233=[-1.7830071261347849012 ,.40783500436618812122] 
dist 234=[-1.7927066126932844695 ,.38429700566037882221] 
dist 235=[-1.7978815713483095499 ,.33507813715210240868] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 2, 0, 1, 2, 0, 2] 
dist 0=[48.761690521170645581  ,48.761690521170645581  ] 
dist 1=[48.383666753729617876  ,49.105122927715170671  ] 
dist 2=[47.907190877248520414  ,49.403238763846763972  ] 
dist 3=[47.170254656886592510  ,49.600111116437769367  ] 
dist 4=[46.244667681031361538  ,49.760059681759004926  ] 
dist 5=[45.014644808541982625  ,49.910517754999744606  ] 
dist 6=[43.322395380258458243  ,50.019908609560658884  ] 
dist 7=[40.550733038032305763  ,50.015929755367011432  ] 
dist 8=[37.702285442045106140  ,49.934571781670358489  ] 
dist 9=[35.703313858502671952  ,49.871205781734858477  ] 
dist 10=[33.938304632953640145  ,49.413548107560457335  ] 
dist 11=[32.024118533335861201  ,49.277541160705356094  ] 
dist 12=[30.153406737440916829  ,48.813527241434768546  ] 
dist 13=[27.103417192439689007  ,48.688999739240413730  ] 
dist 14=[24.146692079320739211  ,39.029521122810989953  ] 
dist 15=[21.614364687839662848  ,38.079893098195856392  ] 
dist 16=[18.990560596496696763  ,35.727282277563399971  ] 
dist 17=[16.500328167775755928  ,35.364875383164236777  ] 
dist 18=[14.501142881824212809  ,31.700249142078484126  ] 
dist 19=[12.472560564817638030  ,30.991401211134543676  ] 
dist 20=[9.8643535616398118462 ,30.171590732937617765  ] 
dist 21=[7.3254542625790596697 ,29.955360747610000240  ] 
dist 22=[5.5733753450401099046 ,23.242122492057776117  ] 
dist 23=[4.0549850662243345335 ,22.381504035219619195  ] 
dist 24=[2.4490723819924060284 ,20.638497277020150086  ] 
dist 25=[.89949272338051966331,20.183663463726012714  ] 
dist 26=[-.39446487500048139224,18.529084766857257332  ] 
dist 27=[-1.7576018455623553100 ,18.179790632819140848  ] 
dist 28=[-3.5847928738544714549 ,17.570454951700670956  ] 
dist 29=[-5.3434566156582378433 ,17.426650149908377525  ] 
dist 30=[-6.4329864675917143093 ,5.0667782175696161248 ] 
dist 31=[-7.2502616278544163003 ,4.0143095904210049002 ] 
dist 32=[-7.9205008466116110702 ,1.6736158486166564461 ] 
dist 33=[-8.4539342736409261442 ,1.2554989696252255833 ] 
dist 34=[-8.7245037848262646105 ,-1.4604792053528452664 ] 
dist 35=[-8.8705013083422105418 ,-1.9191385026216492997 ] 
dist 36=[-9.3411627974734136880 ,-2.7691151643761787172 ] 
dist 37=[-10.726114695600850444  ,-2.9523956209117083859 ] 
dist 38=[-12.004705631095912644  ,-3.9139878207988592530 ] 
dist 39=[-12.775567610010649311  ,-3.8080147865888674366 ] 
dist 40=[-13.324992927305921335  ,-3.6685825157245810141 ] 
dist 41=[-13.719085577642600507  ,-3.5357068380859544346 ] 
dist 42=[-14.012506356615248220  ,-3.3842315374875422019 ] 
dist 43=[-14.159720817665247070  ,-3.1700387077365837742 ] 
dist 44=[-14.228736773836014369  ,-2.0465165482001903668 ] 
dist 45=[-14.221444418107574238  ,-.38354928653857820251] 
dist 46=[-6.9317973136591749840 ,.73435478802997327222] 
dist 47=[-6.4995108408525937973 ,1.6667510784539986240 ] 
dist 48=[-5.4482947160539695282 ,2.5893682657524804022 ] 
dist 49=[-5.2951790774615042305 ,3.4347071756707561041 ] 
dist 50=[-3.7712018139761665664 ,4.0586581595338678149 ] 
dist 51=[-3.4928237956391370618 ,4.6396167392581653863 ] 
dist 52=[-3.1583576045222522150 ,5.3132865526355551548 ] 
dist 53=[-3.0947695347367908902 ,5.9361274894834585058 ] 
dist 54=[-2.7343514492866081158 ,6.3142554503424119300 ] 
dist 55=[-2.7216261743645668996 ,6.5853099282512129738 ] 
dist 56=[-.03055177868720276926,6.7809926332642436697 ] 
dist 57=[.08846265831678164838,6.9217812677892009164 ] 
dist 58=[.64091798557913341964,6.9736987848532759401 ] 
dist 59=[.73628855842341962131,6.9831729204020941251 ] 
dist 60=[.89792754701236987801,6.9663703651285892963 ] 
dist 61=[.92912134184490820386,4.3114228076600304043 ] 
dist 62=[2.3428241247612550068 ,4.4755538954922788691 ] 
dist 63=[1.8875534368979549820 ,4.6267965774416616554 ] 
dist 64=[1.4075274161018663802 ,4.7534239962351094384 ] 
dist 65=[.94866029628140820072,4.8192639996558541478 ] 
dist 66=[.57775728624992367892,4.8534612239034744594 ] 
dist 67=[.20030996790992556501,4.8546727963910493954 ] 
dist 68=[-.28476886712270279096,4.8361497891124893790 ] 
dist 69=[-.75418032583901237559,4.8213205855518831428 ] 
dist 70=[-1.0691447289192375926 ,4.7607959214880297781 ] 
dist 71=[-1.3314937491784491335 ,4.7364259084199809698 ] 
dist 72=[-1.5909595035206088850 ,4.5903848034329171550 ] 
dist 73=[-1.8291900804219540547 ,4.6289523662914230179 ] 
dist 74=[-2.0068433484793393983 ,4.6528200722978258150 ] 
dist 75=[-2.1746287925720615070 ,4.6520121552856108959 ] 
dist 76=[-2.3735948302080253805 ,4.6385512544180028262 ] 
dist 77=[-2.5778445081844449587 ,4.6245387112452202330 ] 
dist 78=[-2.8814774298865600691 ,2.8229472611907273777 ] 
dist 79=[-3.2439420534444650483 ,2.7854869846871976159 ] 
dist 80=[-3.5819211038830338443 ,1.9718481790217310864 ] 
dist 81=[-3.7878161561744032916 ,1.8629465395268166666 ] 
dist 82=[-4.0239397086097065024 ,1.6295116874262316468 ] 
dist 83=[-4.3075447678397041819 ,1.5645663385410752085 ] 
dist 84=[-4.5572273841851185522 ,1.3031352532979347700 ] 
dist 85=[-4.8264731732917986989 ,1.2529573776069906583 ] 
dist 86=[-5.0646664955952506388 ,1.1291665620023849527 ] 
dist 87=[-5.1903780709466913895 ,1.1077206585534309324 ] 
dist 88=[-5.2594040239022007957 ,.63612421833901437149] 
dist 89=[-5.2742355481356418945 ,.91630993323073323271] 
dist 90=[-5.2508200730370016470 ,1.1873241440416825478 ] 
dist 91=[-5.2383631077915542136 ,1.5036332744795433440 ] 
dist 92=[-5.2244954312000352830 ,1.9646624231974425346 ] 
dist 93=[-5.2052541337274617167 ,2.4184201770928189542 ] 
dist 94=[-4.5807009535014428105 ,2.7057190054012896802 ] 
dist 95=[-4.4967054186291850510 ,2.9262843721796136435 ] 
dist 96=[-4.2675091476956625734 ,3.1136666468657662840 ] 
dist 97=[-4.2280567158736149235 ,3.2655731552409859128 ] 
dist 98=[-3.7923877165209064706 ,3.3445373923465786121 ] 
dist 99=[-3.7009639557720004193 ,3.3872130661002466942 ] 
dist 100=[-3.5986899220298493508 ,3.3952693493316524362 ] 
dist 101=[-3.5614692215802390458 ,3.5135872025258149772 ] 
dist 102=[-2.5413597541543058123 ,3.9575239712986329861 ] 
dist 103=[-2.4063711382627771071 ,4.2382356047424758497 ] 
dist 104=[-2.1302372514075885865 ,4.4532411498966424685 ] 
dist 105=[-2.0563355953814270490 ,4.6348913036249479508 ] 
dist 106=[-1.7786200552864318092 ,4.7812336444144760657 ] 
dist 107=[-1.7198633332899900367 ,4.8552927750196569914 ] 
dist 108=[-1.6070738270005111933 ,4.8905565052599198292 ] 
dist 109=[-1.5775453404431330982 ,4.8952952226080355678 ] 
dist 110=[-.73046958941103939687,1.5430393159712643989 ] 
dist 111=[-.70831689528505491962,1.4076026623398486724 ] 
dist 112=[-.83857315864501835273,1.5632164984923084314 ] 
dist 113=[-1.1527909736083699113 ,1.6577775367341150590 ] 
dist 114=[-1.3849090571903546089 ,1.7257919898457987546 ] 
dist 115=[-1.6013713089332251529 ,1.7754294400331885644 ] 
dist 116=[-1.8530912487337518910 ,1.8119926805248848875 ] 
dist 117=[-2.0874542427832541341 ,1.8278181426740702376 ] 
dist 118=[-2.2346383551574744079 ,1.8324253457817363706 ] 
dist 119=[-2.3461544066059806723 ,1.8307816314800149278 ] 
dist 120=[-2.4381622779028857505 ,1.5290717559251367284 ] 
dist 121=[-2.5106078223161403012 ,1.4949109445927082390 ] 
dist 122=[-2.5440500504765563110 ,1.4084057454262811374 ] 
dist 123=[-2.5585622124222832258 ,1.3896762483540976521 ] 
dist 124=[-2.5576318427672340255 ,1.2429249686787169420 ] 
dist 125=[-1.9921254101922126520 ,1.2123161889823740328 ] 
dist 126=[-2.0577127575699467374 ,1.1647751466694767439 ] 
dist 127=[-2.0988133664753626327 ,1.1505911308727354945 ] 
dist 128=[-2.1173787777349481024 ,1.0425100751791550372 ] 
dist 129=[-2.1255772070854719675 ,1.0974431429917606914 ] 
dist 130=[-2.1252846834807564748 ,1.1455130047235391962 ] 
dist 131=[-2.1187514098246406941 ,1.1967732447887741275 ] 
dist 132=[-2.1126885359799814090 ,1.2461300519047682347 ] 
dist 133=[-1.8769222027319027094 ,1.2865948701385755666 ] 
dist 134=[-1.8397099559345577027 ,1.3282560176097200415 ] 
dist 135=[-1.7656082503096387069 ,1.3823732564611746685 ] 
dist 136=[-1.7437169036284367157 ,1.4325929609412189248 ] 
dist 137=[-1.6525755565161976342 ,1.4586957160624610100 ] 
dist 138=[-1.6309662125722735425 ,1.4720680043793718958 ] 
dist 139=[-1.5776665509303358572 ,1.4741142010357356553 ] 
dist 140=[-1.5592629601830785497 ,1.4653682233855524434 ] 
dist 141=[-1.4811966928641135362 ,1.4589321561021837359 ] 
dist 142=[-1.5508884387477662957 ,1.4532924868309748386 ] 
dist 143=[-1.6242696781166094141 ,1.5418802375737681161 ] 
dist 144=[-1.6880118001479915291 ,1.6113085676254190990 ] 
dist 145=[-1.7192261868688756556 ,1.6656955286846252678 ] 
dist 146=[-1.7351399984827941815 ,1.6942409533009119931 ] 
dist 147=[-1.7377983809760651321 ,1.7093414057686319497 ] 
dist 148=[-1.7124879399221575865 ,1.7108023157378431606 ] 
dist 149=[-1.7043273911903882994 ,1.7843704089951400795 ] 
dist 150=[-1.6979907470349235250 ,1.8674036780776466957 ] 
dist 151=[-1.6925011810810593843 ,1.9231373092558746985 ] 
dist 152=[-1.2689772851363552475 ,1.9562262344592081382 ] 
dist 153=[-1.2285638652059649148 ,1.9777702282005646822 ] 
dist 154=[-1.2273567316192879200 ,1.9874184861947935807 ] 
dist 155=[-1.2187555801277539444 ,1.9902025858070013929 ] 
dist 156=[-1.2124341823767180412 ,1.9858243999606312640 ] 
dist 157=[-1.1686379384389700371 ,1.0144523491940600691 ] 
dist 158=[-1.1577869165723129962 ,1.1214019895061373436 ] 
dist 159=[-1.1265222721656234826 ,1.2436514588726133792 ] 
dist 160=[-1.1169239277993101854 ,1.3559228965269015433 ] 
dist 161=[-1.0456895013680746647 ,1.4230452253830517276 ] 
dist 162=[-1.0286645574941597659 ,1.4699691768326851875 ] 
dist 163=[-1.0013747346879108344 ,1.5016177724694834584 ] 
dist 164=[-.99254056094891075221,1.5234306333094752193 ] 
dist 165=[-1.0042473492752247722 ,1.5310949355476416288 ] 
dist 166=[-1.0817937710965214188 ,1.5310464292559888470 ] 
dist 167=[-1.1476059375309074818 ,1.5280585277370794073 ] 
dist 168=[-1.2146596094004058300 ,1.2194764998722477834 ] 
dist 169=[-1.2774409004909334650 ,1.1851243580977020290 ] 
dist 170=[-1.3501997453444883247 ,1.1081013485384182852 ] 
dist 171=[-1.4304739200209265589 ,1.2096525650118476515 ] 
dist 172=[-1.5314140913903609835 ,1.3002118413506299418 ] 
dist 173=[-1.6256171830433041980 ,1.3629815174337971754 ] 
dist 174=[-1.6790008028828476060 ,1.4174484180059895134 ] 
dist 175=[-1.7127657172357223370 ,1.4748675347903855210 ] 
dist 176=[-1.7286534876473547020 ,1.5244697931765083285 ] 
dist 177=[-1.7359322002244735112 ,1.5477350279393781902 ] 
dist 178=[-1.7353275234790749234 ,1.5587593905076879606 ] 
dist 179=[-1.7288470702531832980 ,1.5594964301708723655 ] 
dist 180=[-1.7241522479692545987 ,1.5325823567837909757 ] 
dist 181=[-1.5408598981706681106 ,1.5548948027999789888 ] 
dist 182=[-1.5114162448629993480 ,1.5941515177721095098 ] 
dist 183=[-1.4513253255494649364 ,1.6157844635841942889 ] 
dist 184=[-1.4331197020176047277 ,1.6202781387443007500 ] 
dist 185=[-1.4849831019988097304 ,1.6118227794474264181 ] 
dist 186=[-1.5363346724546482017 ,1.6080662388759253205 ] 
dist 187=[-1.5720225494326884264 ,1.6043024906456242064 ] 
dist 188=[-1.5971103361263112073 ,1.5995407932422188435 ] 
dist 189=[-1.6061508620662247094 ,1.4360782748424544890 ] 
dist 190=[-1.6069039209862636484 ,1.5019768890465329615 ] 
dist 191=[-1.6037195994795982004 ,1.5480660026583922304 ] 
dist 192=[-1.6219091674702565136 ,1.5791946996131446798 ] 
dist 193=[-1.6429193433247231511 ,1.6002291954554693522 ] 
dist 194=[-1.6521332815121610242 ,1.6060264736428822841 ] 
dist 195=[-1.6526800728280807194 ,1.6046981769508581546 ] 
dist 196=[-1.6345855843573510949 ,1.6000243073335864568 ] 
dist 197=[-1.6360842829524726086 ,1.4879657092091360673 ] 
dist 198=[-1.6318224750647526992 ,1.4672504047290056113 ] 
dist 199=[-1.6257930265031484562 ,1.4224861644423225121 ] 
dist 200=[-1.2588353048678961826 ,1.4075251364031728002 ] 
dist 201=[-1.2210549184547163292 ,1.3363774302097419827 ] 
dist 202=[-1.1272378940408082366 ,1.3203937921961829550 ] 
dist 203=[-1.1084002416900456784 ,1.2729798133346777046 ] 
dist 204=[-.95775050457370770991,1.2636219611645699965 ] 
dist 205=[-.92732939190008651307,1.1041550001541287362 ] 
dist 206=[-.88101376382908765059,1.2057883481287244448 ] 
dist 207=[-.86733439158225828224,1.3209691767561221586 ] 
dist 208=[-.58612481452321265255,1.4262077482628329995 ] 
dist 209=[-.54854456791060811492,1.4881558559280111061 ] 
dist 210=[-.46304090249935929167,1.5302739829504550330 ] 
dist 211=[-.44434926912598213484,1.5563587495792995544 ] 
dist 212=[-.33430373679954228778,1.5732096843091652752 ] 
dist 213=[-.31380746726677318173,1.5784707144401632394 ] 
dist 214=[-.27302210230857330666,1.5765133310696588600 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 2, 0, 2, 0, 1] 
dist 0=[48.569230261880454181  ,48.569230261880454181  ] 
dist 1=[48.107688226636950994  ,49.054562862833483264  ] 
dist 2=[46.750204689711313592  ,49.736117173644929552  ] 
dist 3=[45.107576298058015048  ,50.309644424842791066  ] 
dist 4=[43.297720591961351056  ,50.770631010412113394  ] 
dist 5=[41.014909371074847757  ,51.002786149705678171  ] 
dist 6=[37.483351706810942101  ,51.111198675512708816  ] 
dist 7=[33.906125425065966313  ,51.090708790780250160  ] 
dist 8=[31.440798722763219758  ,50.957393111102544965  ] 
dist 9=[29.312215728478740850  ,50.883786634841504371  ] 
dist 10=[27.079543979909212729  ,50.484778983826034285  ] 
dist 11=[24.943705887812881951  ,50.425813572666390936  ] 
dist 12=[23.201579993319952930  ,48.969759911694035800  ] 
dist 13=[21.408830227028285366  ,48.636447348800985149  ] 
dist 14=[19.070316808234287094  ,47.387370093920784261  ] 
dist 15=[16.778214664835119313  ,45.219648517885567365  ] 
dist 16=[15.170557959657006107  ,33.149467882108902193  ] 
dist 17=[13.750003039539698139  ,32.426116522803975611  ] 
dist 18=[12.204853170243926457  ,31.604504212637658107  ] 
dist 19=[10.688430828660920129  ,31.394920984178855333  ] 
dist 20=[9.3821137232010518685 ,24.439051388786478470  ] 
dist 21=[7.9715215306031116818 ,23.548161771412925702  ] 
dist 22=[6.0374647551926875068 ,21.753550412904579306  ] 
dist 23=[4.1528389595059707351 ,21.287127557108454194  ] 
dist 24=[2.9395819441154667537 ,19.604949031758355191  ] 
dist 25=[1.9769521779141138832 ,19.244816232847235801  ] 
dist 26=[1.0942178737433283926 ,18.654071769476354196  ] 
dist 27=[.32141815813786031507,18.503628570076639678  ] 
dist 28=[-.20189455923116623666,10.784791339433028583  ] 
dist 29=[-.64813463501336699964,10.424732902164196999  ] 
dist 30=[-2.3853078449395307839 ,9.0009092814249066413 ] 
dist 31=[-4.3789907896751754700 ,6.7415224033735148891 ] 
dist 32=[-6.1949747828941455310 ,-1.3614583935286156307 ] 
dist 33=[-7.5307456454585613264 ,-1.4715262167358645875 ] 
dist 34=[-8.7753080752712692638 ,-1.4274946040256729184 ] 
dist 35=[-10.226990892273993266  ,-1.3208816687076499858 ] 
dist 36=[-11.569476793479702610  ,-1.1356031379265165161 ] 
dist 37=[-12.377852080806396590  ,-.85970892263490521341] 
dist 38=[-12.952843859033290441  ,-.3914939873792198136 ] 
dist 39=[-13.363045766202660835  ,.0916674280175380942 ] 
dist 40=[-13.669949274183609038  ,.4273208574698023196 ] 
dist 41=[-13.832258213497766927  ,.7170646904886321216 ] 
dist 42=[-13.920606381043679049  ,1.0173692353654065637 ] 
dist 43=[-13.931934688140456354  ,1.2992696077520975844 ] 
dist 44=[-11.440285914917604736  ,1.5156739362692139881 ] 
dist 45=[-11.410694774884897076  ,1.7241595620212568936 ] 
dist 46=[-11.311585020961734188  ,1.9744266288382090023 ] 
dist 47=[-11.255389573595368603  ,2.2066419963226330389 ] 
dist 48=[-6.2399831696710401026 ,2.3431910372822385510 ] 
dist 49=[-5.7955380052915792465 ,2.4348524419880638203 ] 
dist 50=[-4.7190494899154258839 ,2.4882748960073290636 ] 
dist 51=[-4.5602684208887393550 ,2.5218824173544316363 ] 
dist 52=[-3.0107942745413569320 ,2.5345166580423001666 ] 
dist 53=[-2.7279576541044879250 ,2.5337549573433638737 ] 
dist 54=[-2.3817096365718616067 ,2.5256548970222248879 ] 
dist 55=[-2.3109450026344613210 ,2.7197311900790754545 ] 
dist 56=[-.11167823405252158125,3.4991925844338699333 ] 
dist 57=[-.34878582285509642188,3.9920117687433267525 ] 
dist 58=[-.59752725496889917005,4.3700765764062699237 ] 
dist 59=[-.83447523526206120094,4.6915003944875550896 ] 
dist 60=[-1.0245401803951836143 ,4.9531317015619608245 ] 
dist 61=[-1.2165574631879641348 ,5.0925920724224223874 ] 
dist 62=[-1.4613200419407867497 ,5.1702528479600925422 ] 
dist 63=[-1.6969536186233771287 ,5.1875141300090575882 ] 
dist 64=[-1.8525506800485922335 ,5.1695471087983737579 ] 
dist 65=[-1.9792863526933912508 ,5.1568197244054918564 ] 
dist 66=[-2.0997515981849871193 ,5.0786687949010386133 ] 
dist 67=[-2.2069886617074010929 ,5.0664752738521664713 ] 
dist 68=[-2.2809435678923865722 ,4.7774876929946080677 ] 
dist 69=[-2.3447338455578510468 ,4.7079879392249720016 ] 
dist 70=[-2.4114246739407132846 ,4.6592122910137486481 ] 
dist 71=[-2.4671683208911025557 ,4.6456973845716156311 ] 
dist 72=[-2.4872695952365821758 ,4.3745704259621144578 ] 
dist 73=[-2.4932190328641094995 ,4.3411898158053661021 ] 
dist 74=[-2.4924482567717859494 ,4.2733117168836461462 ] 
dist 75=[-2.4144411628112521057 ,4.2487301542720447601 ] 
dist 76=[-3.0610347946515909951 ,4.0087272297018338469 ] 
dist 77=[-3.5660882936857791956 ,3.9726575019095563327 ] 
dist 78=[-3.9633332782329463246 ,3.9177739389037323965 ] 
dist 79=[-4.3177891374511440781 ,3.8970423266475284392 ] 
dist 80=[-4.6180439918691653744 ,2.8339565035867365623 ] 
dist 81=[-4.7989433322040900034 ,2.7167876222340760773 ] 
dist 82=[-4.9273363129337593296 ,2.4195934140128344226 ] 
dist 83=[-5.0180312567681238301 ,2.3758655621571879740 ] 
dist 84=[-5.0835697749772519558 ,2.1945902605835991500 ] 
dist 85=[-5.1115366630755502748 ,2.2259265576796144943 ] 
dist 86=[-5.1175371608781084192 ,2.2504285871599428607 ] 
dist 87=[-5.1204662047039039348 ,2.2662200286298282438 ] 
dist 88=[-5.1589065487300986064 ,2.2672799304759629334 ] 
dist 89=[-5.1686177252521978454 ,2.2535020168069853051 ] 
dist 90=[-5.1591511083170854986 ,2.2458922116134268970 ] 
dist 91=[-5.1466604897005571260 ,2.1560119492439559751 ] 
dist 92=[-3.7089306126408469499 ,2.1311871423142276480 ] 
dist 93=[-3.7625244707148285454 ,2.1026294588932573219 ] 
dist 94=[-3.7871710516384668766 ,2.0880530141080011748 ] 
dist 95=[-3.7901007450799868398 ,2.2528682984761123054 ] 
dist 96=[-2.8834246430610162415 ,2.3771559312266568989 ] 
dist 97=[-2.8336690371608163176 ,2.4701244035773354556 ] 
dist 98=[-2.6928712574698097567 ,2.5447029093907732442 ] 
dist 99=[-2.6712217780694999233 ,2.7182902688388766781 ] 
dist 100=[-2.3901130610399805179 ,3.0734906195560464145 ] 
dist 101=[-2.3309535458815118397 ,3.2955214200287329571 ] 
dist 102=[-2.2738338264182835271 ,3.4625572010051082984 ] 
dist 103=[-2.2588127555896975336 ,3.5982378932921954240 ] 
dist 104=[-1.5632105987713234315 ,3.7033612381493688455 ] 
dist 105=[-1.4732877490003923612 ,3.7484195695166114317 ] 
dist 106=[-1.4266117884357983424 ,3.7676535820596706797 ] 
dist 107=[-1.6340664970451410287 ,3.7697200609220597145 ] 
dist 108=[-1.7868630930812428991 ,2.4539482782375944255 ] 
dist 109=[-1.9289311089285002719 ,2.5946943917421766742 ] 
dist 110=[-2.0935682604405585314 ,2.6957162944503800753 ] 
dist 111=[-2.2443602063123440812 ,2.7691951708078467796 ] 
dist 112=[-2.3311676366341241576 ,2.8226358920306090303 ] 
dist 113=[-2.3877681876165389512 ,2.8436518794660544635 ] 
dist 114=[-2.4179914332846254369 ,2.8487139558399717499 ] 
dist 115=[-2.4350638445459543196 ,2.8439639567858520329 ] 
dist 116=[-2.4391682562935229078 ,2.6710298992005397053 ] 
dist 117=[-2.4345621656756021200 ,2.6380248342137321817 ] 
dist 118=[-2.4284391957384192655 ,2.5708081736602111319 ] 
dist 119=[.0234929426217359705 ,2.5486183527278294372 ] 
dist 120=[-.1520031569609528844 ,2.4452052919397724818 ] 
dist 121=[-.3261208602632993348 ,2.4208767861194753791 ] 
dist 122=[-.5326499817404195176 ,2.3463507337998972070 ] 
dist 123=[-.8375355247338822448 ,2.3313085240304553365 ] 
dist 124=[-1.1392545627511889895 ,1.2783653381163673569 ] 
dist 125=[-1.3331503579095732035 ,1.3725090490425146192 ] 
dist 126=[-1.4852983637064977440 ,1.4794174409690759570 ] 
dist 127=[-1.6203789364929528840 ,1.5761945221827225407 ] 
dist 128=[-1.7342661047532570967 ,1.6299000177053606877 ] 
dist 129=[-1.8018228607871034397 ,1.6623695785642304897 ] 
dist 130=[-1.8539432797653482679 ,1.6743831819814224786 ] 
dist 131=[-2.0480805223221847654 ,1.6785446517357267363 ] 
dist 132=[-2.2261075731475135405 ,1.6796693548512786213 ] 
dist 133=[-2.3339529174989086319 ,1.6787914604481511541 ] 
dist 134=[-2.4110884431940471636 ,1.6749507354855168525 ] 
dist 135=[-2.4665395379948775122 ,1.4325542271255707254 ] 
dist 136=[-2.5052960220954881763 ,1.4005660448729437960 ] 
dist 137=[-2.5157893624899839704 ,1.3129911923139273440 ] 
dist 138=[-2.5151919085619507123 ,1.2996687356325078816 ] 
dist 139=[-2.5096808770888009330 ,1.1343190686548315685 ] 
dist 140=[-1.0506316974980112472 ,1.1001915407750985052 ] 
dist 141=[-.9520627962875021416 ,1.0662390054716383072 ] 
dist 142=[-1.0797466999157103255 ,1.0577199381808897259 ] 
dist 143=[-1.2125099976050558647 ,.7367331072746092984 ] 
dist 144=[-1.2955504481635538455 ,.6413558521126206990 ] 
dist 145=[-1.3580942620818300061 ,.6216601319520187788 ] 
dist 146=[-1.4090484667375026748 ,.5829995594967295157 ] 
dist 147=[-1.4486815232866210729 ,.68892911785244965659] 
dist 148=[-1.4660400005400385255 ,.81374441921363309002] 
dist 149=[-1.4731907685788069415 ,.90358682399490870838] 
dist 150=[-1.4720719371288426219 ,.98505720549912360061] 
dist 151=[-1.4396804291565846268 ,1.0764683163891332247 ] 
dist 152=[-1.4309816655135011081 ,1.1673682958258935751 ] 
dist 153=[-1.3996462918785531876 ,1.2868783323938943636 ] 
dist 154=[-1.3924836587105086717 ,1.4221473662920907756 ] 
dist 155=[-1.3046101705975133259 ,1.6023054312288470669 ] 
dist 156=[-1.2836690493554197667 ,1.7751904527690518863 ] 
dist 157=[-1.2613340998873085898 ,1.8814307425907675177 ] 
dist 158=[-1.3684969575831567769 ,1.9593018536804467111 ] 
dist 159=[-1.4882226986716786073 ,2.0189406595080491136 ] 
dist 160=[-1.5933284758808974997 ,2.0630484138814226536 ] 
dist 161=[-1.6631075382943366708 ,2.0789167691751290887 ] 
dist 162=[-1.7203293856991075739 ,2.0834123592993190863 ] 
dist 163=[-1.7753083005922609930 ,2.0821170444761491348 ] 
dist 164=[-1.8209234182942513471 ,1.9937009227219445330 ] 
dist 165=[-1.8407727822546217881 ,1.9742450215091448232 ] 
dist 166=[-1.8483455609903430122 ,1.9296128270795599878 ] 
dist 167=[-1.8463452061223751507 ,1.9131207084555731076 ] 
dist 168=[-1.8109508455343577900 ,1.8290934875541278440 ] 
dist 169=[-1.7975249493233548192 ,1.8090485702616904214 ] 
dist 170=[-1.7798256400856433293 ,1.7552657976291374160 ] 
dist 171=[-1.7706522340603212876 ,1.7386015353832333714 ] 
dist 172=[-1.3209822734571841079 ,1.1338719628735605963 ] 
dist 173=[-1.4022834127519205160 ,1.2186162697629260990 ] 
dist 174=[-1.4684093705684674834 ,1.3158256221480612381 ] 
dist 175=[-1.5187237680187103182 ,1.4043417824318187392 ] 
dist 176=[-1.5566794230687399604 ,1.4543875393883657038 ] 
dist 177=[-1.5734740272301286044 ,1.4858608361118780282 ] 
dist 178=[-1.5796227602092582196 ,1.5002442956702447370 ] 
dist 179=[-1.5783162615955242572 ,1.5071031208851979553 ] 
dist 180=[-1.4898222982140190266 ,1.5085397688874871809 ] 
dist 181=[-1.4721395879440516793 ,1.5062839091843918677 ] 
dist 182=[-1.4385625342825335501 ,1.5016656640930143092 ] 
dist 183=[-1.4275966851054629648 ,1.3147338484773992525 ] 
dist 184=[-1.3781239520698277177 ,1.2883700413937328584 ] 
dist 185=[-1.3650646248176698779 ,1.2189983754998034642 ] 
dist 186=[-1.3291193294968083112 ,1.2048776045220609602 ] 
dist 187=[-1.3169674868080589758 ,1.0786541524155626146 ] 
dist 188=[-.89438063885229986726,1.0519516802578145489 ] 
dist 189=[-.97762485518506013493,1.0154187522745293147 ] 
dist 190=[-1.0708875350207621061 ,1.0027073158170504046 ] 
dist 191=[-1.1560429522309518248 ,.71965850629804437773] 
dist 192=[-1.2069283180336029341 ,.78954085946921094221] 
dist 193=[-1.2424568179955948977 ,.89972129411922175205] 
dist 194=[-1.2663191460164826986 ,1.0017684754897657854 ] 
dist 195=[-1.2821528329222702754 ,1.1194205049637373402 ] 
dist 196=[-1.2856359370426007531 ,1.2277385441907295288 ] 
dist 197=[-1.2838239679106977789 ,1.2925305234980969145 ] 
dist 198=[-1.2793103013735138970 ,1.3378568828806595110 ] 
dist 199=[-.96172519202585573602,1.3684804898940759247 ] 
dist 200=[-.92825860859858360466,1.3898560773396927568 ] 
dist 201=[-.94538397936366426443,1.3982697855334479017 ] 
dist 202=[-1.0617862758487622094 ,1.3989927322600085534 ] 
dist 203=[-1.1670394711228775277 ,1.3970786506251178394 ] 
dist 204=[-1.2424925051880028960 ,.46340763744585685166] 
dist 205=[-1.3105932699646650766 ,.40448689109155060711] 
dist 206=[-1.3865005723035511706 ,.34302176358905803556] 
dist 207=[-1.4544337454106178492 ,.47147842229253544747] 
dist 208=[-1.4907057636985730842 ,.56122750405993919865] 
dist 209=[-1.5107459405003086047 ,.63982186520024175431] 
dist 210=[-1.5150904525853285455 ,.72375593269849541237] 
dist 211=[-1.5109133691146595731 ,.80471128018396057157] 
dist 212=[-1.5065296079604930888 ,.87141641049939428534] 
dist 213=[-1.5002754242218716802 ,.94046812664064851951] 
dist 214=[-1.4943253875316260532 ,1.0307893712355589243 ] 
dist 215=[-.7432511925401643663 ,1.1167715006603907901 ] 
dist 216=[-.82514063295922610976,1.1685045359349203196 ] 
dist 217=[-.89903666274080196267,1.2050622103740437078 ] 
dist 218=[-.98125795663937267254,1.2304750421092492375 ] 
dist 219=[-1.0963803959009093957 ,1.2477634967971905440 ] 
dist 220=[-1.2077211845873270231 ,1.2518934974041625524 ] 
dist 221=[-1.2748485586164393012 ,1.2551845884739623152 ] 
dist 222=[-1.3224688468168357123 ,1.3253275602272959009 ] 
dist 223=[-1.3559459888322304926 ,1.3878105449483816088 ] 
dist 224=[-1.3798947219796711100 ,1.4206306889711986369 ] 
dist 225=[-1.3894815220513768206 ,1.4382957093378636886 ] 
dist 226=[-1.3912021131051613243 ,1.4518508360776387716 ] 
dist 227=[-1.3892419327520630963 ,1.4662372525753663748 ] 
dist 228=[-1.2858769644695471998 ,1.4705537427042521371 ] 
dist 229=[-1.2672859892746141306 ,1.4683202033271096092 ] 
dist 230=[-1.2310205354689115458 ,1.4654145198705261839 ] 
dist 231=[-1.2196203473935529604 ,1.2097660433392431933 ] 
dist 232=[-1.1694810040312344746 ,1.1810992568484943013 ] 
dist 233=[-1.1569252506595389822 ,1.1073355501867056049 ] 
dist 234=[-1.1230787363075970036 ,1.0925947101175392069 ] 
dist 235=[-1.1122352964933129033 ,.96460305761791712891] 
dist 236=[-1.0041778903126191713 ,.93803002685318184244] 
dist 237=[-1.0960308357377670125 ,.90069687135005859632] 
dist 238=[-1.2008320248229387013 ,.88830351801796023506] 
dist 239=[-1.2965397897569457663 ,.61930801593043525222] 
dist 240=[-1.3520966919257921716 ,.58316100245688964169] 
dist 241=[-1.3888910923597613167 ,.50377202528141420853] 
dist 242=[-1.4097086909508460207 ,.48319845866871955761] 
dist 243=[-1.4225153047237435181 ,.38846444380757034332] 
dist 244=[-1.4273344120271208288 ,.37062714913316866863] 
dist 245=[-1.4272257098838481985 ,.32819395022322253064] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 1, 1, 0, 0, 1] 
dist 0=[48.177979682447162463  ,48.177979682447162463  ] 
dist 1=[47.147799824596766990  ,49.004337248040707686  ] 
dist 2=[45.768884671677243863  ,49.641051852827286441  ] 
dist 3=[43.549677286523158845  ,49.913947547324301540  ] 
dist 4=[41.266399447313191483  ,50.031611689723620160  ] 
dist 5=[39.631589263930413446  ,50.048333603205686477  ] 
dist 6=[38.155234187806255032  ,49.458292575620488086  ] 
dist 7=[36.504832022579221491  ,49.293278625327504163  ] 
dist 8=[34.864794290127416351  ,48.760123272440948934  ] 
dist 9=[33.429893591525585900  ,48.620455355959251223  ] 
dist 10=[31.867614007129195672  ,47.907012641597746009  ] 
dist 11=[29.718993885035311088  ,47.729274221845206132  ] 
dist 12=[27.567145577381463909  ,47.122110374632068674  ] 
dist 13=[25.992008555095489212  ,47.016699160001592822  ] 
dist 14=[24.534841802686446918  ,45.456719073899285595  ] 
dist 15=[22.854104434414426109  ,45.085142215287175686  ] 
dist 16=[21.114386144445736675  ,43.107497240004160564  ] 
dist 17=[19.440198855657024039  ,31.068608467165692224  ] 
dist 18=[17.529479995371734064  ,27.015324070609225983  ] 
dist 19=[14.783756438985594377  ,26.249127141304328321  ] 
dist 20=[12.060573522814073762  ,25.346211300978906857  ] 
dist 21=[10.239831737306236601  ,25.130099324350843689  ] 
dist 22=[8.7223173374342268720 ,18.309899257666561461  ] 
dist 23=[7.2110091072892102288 ,17.452719321934553596  ] 
dist 24=[5.8100071063386197856 ,15.695980062209465780  ] 
dist 25=[3.4870728281086140488 ,15.239813573346597278  ] 
dist 26=[1.6696977398723069563 ,13.581969609450362672  ] 
dist 27=[.11140873149826905249,13.245208738070254336  ] 
dist 28=[-1.5100111744770481088 ,12.658221476987793879  ] 
dist 29=[-3.0581149477790718265 ,12.526302205767421830  ] 
dist 30=[-4.3242082016508587925 ,2.1108630738080352237 ] 
dist 31=[-5.6347742356158595512 ,1.2235509368929370994 ] 
dist 32=[-7.3619037670608733334 ,-.10847303289449071083] 
dist 33=[-9.0084220829081469771 ,-.24370660688405702135] 
dist 34=[-9.9971376734131582840 ,-.4558525461349483588 ] 
dist 35=[-10.702514606191326233  ,-.50004472437951055507] 
dist 36=[-11.216305314563920950  ,-1.0133232080924834810 ] 
dist 37=[-11.603038513004313124  ,-1.0785911662743437277 ] 
dist 38=[-12.396347128002030261  ,-1.1480991948070482093 ] 
dist 39=[-13.032226692184984380  ,-1.1405169911391515761 ] 
dist 40=[-13.472035593728490707  ,-1.1037463519761833383 ] 
dist 41=[-13.761617277156344039  ,-1.0301959209345718836 ] 
dist 42=[-13.964473173372944376  ,-.9170883519152262359 ] 
dist 43=[-14.057865026511088109  ,-.7222320022548194007 ] 
dist 44=[-14.089577227970057942  ,-.5124556386980817431 ] 
dist 45=[-14.070263470345365038  ,-.3396363975623531769 ] 
dist 46=[-9.8791755802323587211 ,1.2012136489489561477 ] 
dist 47=[-9.7420626747094715424 ,2.2510028725636301075 ] 
dist 48=[-9.6814901900684386219 ,3.1398760836461678067 ] 
dist 49=[-4.6304293684303824364 ,4.0403259521667991048 ] 
dist 50=[-4.5534906080405118680 ,4.8784251286743764282 ] 
dist 51=[-4.5287109240967096767 ,5.5185703732823610806 ] 
dist 52=[-.17760665466229704766,6.1359479326261339519 ] 
dist 53=[.24869152019612634266,6.8832783455037082252 ] 
dist 54=[.89144323796144543234,7.5837665396592459756 ] 
dist 55=[.98421250382615585566,8.0142473065053463590 ] 
dist 56=[1.7778270968830348621 ,8.3293256032958121588 ] 
dist 57=[1.9095841703916081496 ,8.5692986617972525202 ] 
dist 58=[2.0946488022673326229 ,8.7427807860363856797 ] 
dist 59=[2.0850127378928889888 ,8.7925399220338721770 ] 
dist 60=[1.9066838055011338808 ,8.7922189577788945112 ] 
dist 61=[1.7303018071384287358 ,8.7657177816951025197 ] 
dist 62=[1.5218375529047875027 ,8.4246078767958591353 ] 
dist 63=[1.0759393889360054312 ,8.3417356770707403678 ] 
dist 64=[0                     ,8.0211865111668885811 ] 
dist 65=[.50434869810426296349,3.7087120859743502990 ] 
dist 66=[.05481460557805669053,3.5020772800162505583 ] 
dist 67=[-.62705888359839178347,3.4572174024999230785 ] 
dist 68=[-1.3080769510396549039 ,3.3264823199704345278 ] 
dist 69=[-1.7542097758895085598 ,3.3028237488027635171 ] 
dist 70=[-2.1136628987457790131 ,2.9779128224797064572 ] 
dist 71=[-2.4487407751765670432 ,2.9183571713221079080 ] 
dist 72=[-2.7424611026538452908 ,2.7961004639213353984 ] 
dist 73=[-2.9368545616555388421 ,2.7607370798903199185 ] 
dist 74=[-3.0957045564526452594 ,2.6160938486626444279 ] 
dist 75=[-3.2475681364225082440 ,2.5837441260982777227 ] 
dist 76=[-3.3800698123350547769 ,2.5076122848468144652 ] 
dist 77=[-3.4616388111344656034 ,2.4824276414455114453 ] 
dist 78=[-3.5243126377519774290 ,1.5006647321208135215 ] 
dist 79=[-4.0088619018420398905 ,1.4830290507698887675 ] 
dist 80=[-4.4263605777457036629 ,1.4220546534434937470 ] 
dist 81=[-4.7956647943669443724 ,1.4046484780159839014 ] 
dist 82=[-5.1003444519350186774 ,1.3818679639142783574 ] 
dist 83=[-5.2689694749193624748 ,1.3724729424863660392 ] 
dist 84=[-5.3704540466125812077 ,1.3552557273150279620 ] 
dist 85=[-5.4071147174805867006 ,1.3583663662845423638 ] 
dist 86=[-5.4202480328528452574 ,1.3718517251677984996 ] 
dist 87=[-5.4278096667744279996 ,1.4026240869311911213 ] 
dist 88=[-5.4328606712624420288 ,1.4418447566708712532 ] 
dist 89=[-5.4359609374856800833 ,1.4890849413508844846 ] 
dist 90=[-5.4377228515163231540 ,1.5511033227808888160 ] 
dist 91=[-5.4374313054245064804 ,1.6493376810607536593 ] 
dist 92=[-5.4356895199207011070 ,1.7529928536789272358 ] 
dist 93=[-5.4316730675007948725 ,1.8366714060473090937 ] 
dist 94=[-2.6708830703038175924 ,1.9217187642709546578 ] 
dist 95=[-2.6561321476195392725 ,2.0308789595592827104 ] 
dist 96=[-2.6083224664286909020 ,2.1472758965347288964 ] 
dist 97=[-2.5899266184859475506 ,2.2612392110438512420 ] 
dist 98=[-2.5521467735667689014 ,2.3953888861337743144 ] 
dist 99=[-2.5372732773050216020 ,2.5924084054849934366 ] 
dist 100=[-.95996733281837936686,2.7875991209269089630 ] 
dist 101=[-.82330068834823083831,2.9144580518758180511 ] 
dist 102=[-.5076163060500185684 ,3.0157662908735221667 ] 
dist 103=[-.4532353987531235333 ,3.1089491301669675392 ] 
dist 104=[-.0471094188145951127 ,3.1900123180962142580 ] 
dist 105=[.0244297926020525562 ,3.2429395333627155524 ] 
dist 106=[.1428117851748187199 ,3.2855456401847856319 ] 
dist 107=[.1697973323960615215 ,3.3335819699126600639 ] 
dist 108=[.58077261517088718664,3.3628205947907282336 ] 
dist 109=[.63455364330003838941,3.3676679454511579738 ] 
dist 110=[.73312450981604558078,2.3901470811904059625 ] 
dist 111=[.75373691985398933071,2.3861204704739646978 ] 
dist 112=[.79782568335900170007,2.3583840847260604492 ] 
dist 113=[.79046951177933556053,2.3498275514988611912 ] 
dist 114=[.75992462002088790351,2.2359208025738085965 ] 
dist 115=[.68987238520055997855,2.2067597508366518404 ] 
dist 116=[.61162494978098828749,2.1762261533882670848 ] 
dist 117=[.5483669718965599821 ,2.1597808474553268472 ] 
dist 118=[.4840501396448592789 ,1.7249710994277198168 ] 
dist 119=[.4015545362367208470 ,1.6641371954142466843 ] 
dist 120=[.3137379144312600452 ,1.5409544375182600410 ] 
dist 121=[.2281713972121118434 ,1.5070146567401356027 ] 
dist 122=[.1278724175233235173 ,1.3755672924226928666 ] 
dist 123=[-.0187591604859208529 ,1.3464054263842675670 ] 
dist 124=[-.1690608367415593715 ,1.2855666047823032670 ] 
dist 125=[-.2840165029837951781 ,1.2673914078499815516 ] 
dist 126=[-.58429039968004989835,.5643556759818173999 ] 
dist 127=[-.8536888901677007514 ,.6077948103645343413 ] 
dist 128=[-1.0781116819479832621 ,.6580418363956187801 ] 
dist 129=[-1.2999935194108365883 ,.7128051906309177030 ] 
dist 130=[-1.5033998738463767266 ,.78130941444016228001] 
dist 131=[-1.6540741129318441487 ,.88638094733363928494] 
dist 132=[-1.7950632370327742126 ,.99145127113000366174] 
dist 133=[-1.9598109687738391591 ,1.0599485688455441592 ] 
dist 134=[-2.1114810721336753531 ,1.1146909547126381921 ] 
dist 135=[-2.2002678048920912358 ,1.1648745007485009488 ] 
dist 136=[-2.2600464920365677214 ,1.2081952875119917422 ] 
dist 137=[-2.2959225176229605013 ,1.2355507116542975651 ] 
dist 138=[-2.3184172153276766663 ,1.2563925537453121658 ] 
dist 139=[-2.3247812073727665445 ,1.2737154096652599733 ] 
dist 140=[-2.3208597719834534610 ,1.2858381505629997506 ] 
dist 141=[-2.3160561643483643544 ,1.2873936937551250174 ] 
dist 142=[-1.7476304221745816727 ,1.2818824191170006234 ] 
dist 143=[-1.7392157638217890663 ,1.2775186118420477619 ] 
dist 144=[-1.6948280257416538301 ,1.2288207872956624735 ] 
dist 145=[-1.6826611596342353956 ,1.2148824553270454059 ] 
dist 146=[-1.6420474180693677203 ,1.1983035149423475299 ] 
dist 147=[-1.6326158639620800664 ,1.2829992044408783110 ] 
dist 148=[-.62532508911227754522,1.3860174236142218884 ] 
dist 149=[-.53786215424122921518,1.5068309202008881945 ] 
dist 150=[-.34114062186208322244,1.6182397315306173607 ] 
dist 151=[-.30234137689925783838,1.6837249662828462285 ] 
dist 152=[-.0642518830680201528 ,1.7281488610343702715 ] 
dist 153=[-.0225294167809060838 ,1.7554986522250916303 ] 
dist 154=[.0590635537848479215 ,1.7722616536912520482 ] 
dist 155=[.0786213759742017714 ,1.7763667322135586500 ] 
dist 156=[.26648311222069351056,1.7809988597865529683 ] 
dist 157=[-.03151032450301708153,1.7790164605772343749 ] 
dist 158=[-.35829199871096895178,1.6211395055199591813 ] 
dist 159=[-.57776746653033815328,1.5975534935173772866 ] 
dist 160=[-.76065283328357659784,1.5328007104473781648 ] 
dist 161=[-.94139700213004008234,1.5465499405509926870 ] 
dist 162=[-1.1069082625836769521 ,1.5536587703698236750 ] 
dist 163=[-1.2289957783852854477 ,1.5535751773335955905 ] 
dist 164=[-1.3426424125974457071 ,1.5035635665922064105 ] 
dist 165=[-1.4744627529707630598 ,1.5629376321158163746 ] 
dist 166=[-1.5951373713082327401 ,1.6037660494594841234 ] 
dist 167=[-1.6642987827564510881 ,1.6300069420039362488 ] 
dist 168=[-1.7089513841361259545 ,1.6465415190650937193 ] 
dist 169=[-1.7318068972299068241 ,1.6486268223053541085 ] 
dist 170=[-1.7451574133664354909 ,1.6447836347493895105 ] 
dist 171=[-1.7518751680873139042 ,1.6383321108473131802 ] 
dist 172=[-1.7550116915276139336 ,1.5260253790327440374 ] 
dist 173=[-1.7540727960426609244 ,1.5050587654944791183 ] 
dist 174=[-.8155014086203262983 ,1.4565840548424441451 ] 
dist 175=[-.9287306032809823021 ,1.4398670432173635219 ] 
dist 176=[-1.0609755311607701672 ,1.3585342523810272942 ] 
dist 177=[-1.2034840506335862550 ,1.3398784167105538692 ] 
dist 178=[-1.3317568096868531777 ,1.2939051975857776989 ] 
dist 179=[-1.4227197331272918508 ,1.2781485533260476106 ] 
dist 180=[-1.5038126243418314918 ,-.45029617672697142325] 
dist 181=[-1.5926907687773408746 ,-.43468109016411920472] 
dist 182=[-1.6714224454706157512 ,-.40798025986174899533] 
dist 183=[-1.7120156991947030669 ,-.37059195831944644415] 
dist 184=[-1.7342517493908159207 ,-.3182218708525860242 ] 
dist 185=[-1.7397043837450923620 ,-.2317198791245900623 ] 
dist 186=[-1.7229366731559110568 ,-.12989243826402029132] 
dist 187=[-1.7185441157547089808 ,-.01635134823306282914] 
dist 188=[-1.7533903929158459469 ,.12753144590318894401] 
dist 189=[-1.7822255432532300127 ,.35046485644373444524] 
dist 190=[-1.7961536584583990811 ,.57509597948078994757] 
dist 191=[-1.8058555794217481390 ,.72575614505283727627] 
dist 192=[-1.8192339590241677821 ,.85110045713246630786] 
dist 193=[-1.8198036188586151591 ,.97468910584096639848] 
dist 194=[-1.8123632359811967536 ,1.0877116471717493589 ] 
dist 195=[-1.8045251593903712495 ,1.1708845103174521691 ] 
dist 196=[-1.5748498666188237853 ,1.2481389925016537350 ] 
dist 197=[-1.5674991568080546745 ,1.3375419431692318633 ] 
dist 198=[-1.3286539209999988636 ,1.4193482560297580084 ] 
dist 199=[-1.2933582132658086026 ,1.4662829510292166917 ] 
dist 200=[-1.2253294222866112353 ,1.5005694605451340489 ] 
dist 201=[-1.2065095535151995769 ,1.5330928909205854989 ] 
dist 202=[-1.1349098929939611995 ,1.5556601089803640948 ] 
dist 203=[-1.1169439751853252255 ,1.5666894323521828570 ] 
dist 204=[-1.0823712693048706255 ,1.5713819882174800046 ] 
dist 205=[-1.0718645490344356459 ,1.5686488456152595733 ] 
dist 206=[-.3451741769008316410 ,1.5990897443193787005 ] 
dist 207=[-.3212486337902342063 ,1.6296848437577976273 ] 
dist 208=[-.2055176338368990641 ,1.6500289080032932229 ] 
dist 209=[-.1846820971069013737 ,1.6543529566106924407 ] 
dist 210=[-.1362343076594185212 ,1.6520319189690408704 ] 
dist 211=[-.1274736951285016435 ,1.6460632942627941832 ] 
dist 212=[.35233567797915701198,1.1124040757353996628 ] 
dist 213=[.21401889063497588892,1.0993148461766994578 ] 
dist 214=[.09114982633146503938,1.0735339054556642481 ] 
dist 215=[-.04278896787843967555,1.1437177690763844819 ] 
dist 216=[-.1736223910627198570 ,1.2031922683062250829 ] 
dist 217=[-.2840983183254279523 ,1.2636180605985255695 ] 
dist 218=[-.4008473339409773324 ,1.3200378544128736469 ] 
dist 219=[-.5567217675221264711 ,1.3635197507859999968 ] 
dist 220=[-.7103240712592621429 ,1.4058497279294463944 ] 
dist 221=[-.8180052314316459245 ,1.4576668537948998732 ] 
dist 222=[-.9127000467063344737 ,1.5044816262299540027 ] 
dist 223=[-1.0144693739554888416 ,1.5268440849376174278 ] 
dist 224=[-1.1130386974469605732 ,1.5371284281412791668 ] 
dist 225=[-1.1949625256244646510 ,1.5373435499603278424 ] 
dist 226=[-1.3005493833591807975 ,1.5154704393903695549 ] 
dist 227=[-1.3930851101787753046 ,1.5057214002157817357 ] 
dist 228=[-1.4998041643495033959 ,1.4941678215553384278 ] 
dist 229=[-1.5615156702104770771 ,1.4870467225571009492 ] 
dist 230=[-1.6021022076539185961 ,1.2684499608909073787 ] 
dist 231=[-1.6244971679081268490 ,1.2356919445097870762 ] 
dist 232=[-1.6398228884210130130 ,1.1691725957207105156 ] 
dist 233=[-1.6427245094328494511 ,1.1499130747244597635 ] 
dist 234=[-1.6243990702433918096 ,1.0707426652997481752 ] 
dist 235=[-1.6055733840622055987 ,1.0529323538729920669 ] 
dist 236=[-1.6011867468822643227 ,1.0093178834308926063 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 1, 1, 2, 0, 1] 
dist 0=[42.528257262159077156  ,42.528257262159077156  ] 
dist 1=[41.829683926848077669  ,42.828043246083787494  ] 
dist 2=[40.716723105498854457  ,43.326571025856607162  ] 
dist 3=[38.924491688307851322  ,43.846240444133511010  ] 
dist 4=[37.080060656171759518  ,44.093241438926673560  ] 
dist 5=[35.758504241633219803  ,44.208117439244760948  ] 
dist 6=[34.563336829443505366  ,44.209652302957319342  ] 
dist 7=[33.223495685851315097  ,43.925169152854114234  ] 
dist 8=[31.888107290791753074  ,43.421928712492753276  ] 
dist 9=[30.710526964590908826  ,43.176195849576614161  ] 
dist 10=[29.418798006431264650  ,43.081085440618477157  ] 
dist 11=[27.627117797310057733  ,42.701650620169019349  ] 
dist 12=[25.819797736788169372  ,42.577082994284290125  ] 
dist 13=[24.465405730284384162  ,42.268908064846445032  ] 
dist 14=[23.177725530391917848  ,42.143676648462329242  ] 
dist 15=[21.636643761257779705  ,41.404285752805416737  ] 
dist 16=[20.041626839054678610  ,31.030871795015980840  ] 
dist 17=[18.538142395118247058  ,28.808113982365660451  ] 
dist 18=[16.805823542942167591  ,28.455096419986480366  ] 
dist 19=[14.295892102954543156  ,25.197071378356168930  ] 
dist 20=[11.806388987765821056  ,24.581195118684024195  ] 
dist 21=[10.155612110836763432  ,23.800998818107196221  ] 
dist 22=[8.7940992137723972508 ,23.569900109598128303  ] 
dist 23=[7.4607210073761069651 ,18.402399221936973407  ] 
dist 24=[6.2383162538998536387 ,17.591552329663269825  ] 
dist 25=[5.3202769982288876918 ,16.347920643841464968  ] 
dist 26=[4.4437956937252871280 ,15.795771199646367111  ] 
dist 27=[3.3832610866856289539 ,14.368475129807407677  ] 
dist 28=[2.3770002948786938582 ,14.087598181896899313  ] 
dist 29=[1.2425765980154322895 ,13.507405661825191885  ] 
dist 30=[-.60445760185434996827,13.351994185605601129  ] 
dist 31=[-3.2088736614566756946 ,4.9441566550924299436 ] 
dist 32=[-5.7550487194188018551 ,4.1956532225445233506 ] 
dist 33=[-7.3695137319065714656 ,2.5072094232739362263 ] 
dist 34=[-8.6201855058041914950 ,2.2173390333834761283 ] 
dist 35=[-9.7124408556458891126 ,.26066082324095540098] 
dist 36=[-10.628257347613032751  ,-.1933461666334645412 ] 
dist 37=[-11.173937481651989525  ,-.7992201505597781727 ] 
dist 38=[-11.557908890174837720  ,-.9297818033043632314 ] 
dist 39=[-11.827906893416825746  ,-1.3013698743923790843 ] 
dist 40=[-12.030090505928715973  ,-1.3903036097960834733 ] 
dist 41=[-12.142998478869752850  ,-1.3856235891778298759 ] 
dist 42=[-12.215141720978214310  ,-1.3457332498397114945 ] 
dist 43=[-12.253827780569939573  ,-1.2493484970091446422 ] 
dist 44=[-12.270335143628376650  ,-1.1372667730900729588 ] 
dist 45=[-12.253559347955703807  ,-1.0345781683313910508 ] 
dist 46=[-12.209992669820812759  ,-.9199574046102051805 ] 
dist 47=[-12.172830993947737466  ,-.75997708388911471186] 
dist 48=[-5.9943241719697454223 ,-.58358568884605872407] 
dist 49=[-5.4744185639747298508 ,-.40331465431771369518] 
dist 50=[-4.7251788283151592440 ,-.18571312414153634622] 
dist 51=[-4.0410285464475768952 ,.13984603674159623253] 
dist 52=[-3.2817394629045092543 ,.46359456506401281186] 
dist 53=[-3.0093811619907332625 ,.67401668653109710836] 
dist 54=[-2.9511600069855575704 ,1.0656150120979675825 ] 
dist 55=[-1.4945431712954532240 ,1.9746320108553903122 ] 
dist 56=[-.88246375991556340274,2.8398662633398634169 ] 
dist 57=[-.40824644537789779552,3.3985349650202940141 ] 
dist 58=[-.30434113078147510204,3.8405442636350252431 ] 
dist 59=[.16699166071761580042,4.2401378510908324552 ] 
dist 60=[.24966154124184762272,4.5832231409537221241 ] 
dist 61=[.40032413113740303437,4.7997419776370481672 ] 
dist 62=[.4306883136373507435 ,4.9661046575091455402 ] 
dist 63=[1.2421333552868879840 ,5.1091750440521114496 ] 
dist 64=[1.1599173158627459227 ,5.2214581754676433314 ] 
dist 65=[1.0568121366872492194 ,5.2649095311092793796 ] 
dist 66=[.91870001469935262727,5.2788084138204346834 ] 
dist 67=[.69675254609336505321,5.2727264598671467352 ] 
dist 68=[.47013738964096411054,5.1525060115545943571 ] 
dist 69=[.31339009984474392671,5.1126078129501927339 ] 
dist 70=[.1778243495853883804 ,5.0722572498198892008 ] 
dist 71=[.03574447411457727435,5.0463702712113634367 ] 
dist 72=[-.09962982609219997168,4.4630320409341424064 ] 
dist 73=[-.20843298265131040051,4.4220045175861085159 ] 
dist 74=[-.31859902663793777776,4.3230621727404492575 ] 
dist 75=[-.45941080877970225379,4.3260647630972546706 ] 
dist 76=[-.59519652180428239605,4.3251939833399011541 ] 
dist 77=[-.68530038976187891022,4.3011254846382632517 ] 
dist 78=[-.9869756034351743564 ,4.2851829639641475370 ] 
dist 79=[-1.7401524552580028414 ,3.9220531273486736262 ] 
dist 80=[-2.2735304797539640210 ,2.3426899720132489378 ] 
dist 81=[-2.7401406755704016501 ,2.1828754267682470540 ] 
dist 82=[-3.1815561215345878016 ,1.8017811634895494915 ] 
dist 83=[-3.5734004949426433376 ,1.7373860874162341878 ] 
dist 84=[-3.8421445897941529394 ,1.1957874839673186534 ] 
dist 85=[-4.0724492550162510117 ,1.0946472761588578181 ] 
dist 86=[-4.3108771643103789731 ,.95054342711219868888] 
dist 87=[-4.5216257832284889618 ,.90854429724867329674] 
dist 88=[-4.6414348796143920178 ,.1183703750381312741 ] 
dist 89=[-4.7177517696729924671 ,.0178573614148016180 ] 
dist 90=[-4.7548464593304461018 ,-.2079940116559608059 ] 
dist 91=[-4.7686670700930555233 ,-.2355379209566607176 ] 
dist 92=[-4.7634018725398867266 ,-.1351423733084450257 ] 
dist 93=[-4.7259724601821969991 ,-.0517035512614775086 ] 
dist 94=[-4.7018073193047142600 ,.0352808977298188681 ] 
dist 95=[-3.7916812559582655898 ,.28247033379092306095] 
dist 96=[-3.6286239734153615389 ,.82917115665962177529] 
dist 97=[-3.3840287746355555081 ,1.2877567769395102713 ] 
dist 98=[-3.3384161948510154547 ,1.7461091131236833278 ] 
dist 99=[-2.9240774157578125958 ,2.1693531123059449030 ] 
dist 100=[-2.8397762422582439306 ,2.4878143989399427204 ] 
dist 101=[-2.7264046210765063120 ,2.7906082877817991193 ] 
dist 102=[-2.6876920781053666196 ,3.1513291489112712523 ] 
dist 103=[-1.8565893932498927386 ,3.4869074290130304134 ] 
dist 104=[-1.7462055813309141054 ,3.6893503265236081048 ] 
dist 105=[-1.5069502097868612109 ,3.8331276683294501809 ] 
dist 106=[-1.4439513826496223723 ,3.9345459149869266669 ] 
dist 107=[-1.1702830105043854049 ,4.0080908519423792976 ] 
dist 108=[-1.1195617816302172691 ,4.0405994240031095577 ] 
dist 109=[-1.0626096506135659717 ,4.0492742053233758282 ] 
dist 110=[-1.0508393723460371697 ,4.0460218723012949058 ] 
dist 111=[-1.0445776475182856366 ,2.3415100875019858842 ] 
dist 112=[-1.0301850295914976259 ,2.3438787538708816014 ] 
dist 113=[-1.0230056638082813268 ,2.3436582222981391920 ] 
dist 114=[-1.0148470861746490257 ,2.3415306881908679667 ] 
dist 115=[-1.0098332816465631891 ,2.3363136805490463752 ] 
dist 116=[.4575447092457002869 ,1.8964336730968087781 ] 
dist 117=[.33666925635645190139,1.9929803687296332977 ] 
dist 118=[.19486220861637382636,2.0796684345531804429 ] 
dist 119=[-.01251141253511477813,2.1757788879723476949 ] 
dist 120=[-.22494427592372622507,2.2617759621019716809 ] 
dist 121=[-.38695173577654640546,2.3080914339528222557 ] 
dist 122=[-.54302279608032163163,2.3343293664953315963 ] 
dist 123=[-.73177693214196740219,2.3401686313897417032 ] 
dist 124=[-.92709965584108835447,2.3365021196366709467 ] 
dist 125=[-1.1093972901210795470 ,2.3294750415360654917 ] 
dist 126=[-1.3170985381716764165 ,2.3093201743697058491 ] 
dist 127=[-1.6138271849816392049 ,2.2981104319850349139 ] 
dist 128=[-1.9039793335337894951 ,-.2292306713527898199 ] 
dist 129=[-2.0854338704566994625 ,-.19515064226353348147] 
dist 130=[-2.2220511817703495356 ,-.14276887765381500601] 
dist 131=[-2.3332381772549290135 ,-.05171788853077394743] 
dist 132=[-2.4210674159399072629 ,.04381261242802441358] 
dist 133=[-2.4644539026629324187 ,.11407400024363096336] 
dist 134=[-2.4857941784187942944 ,.17928039541663975316] 
dist 135=[-2.4878451790128161836 ,.2546371454801723776 ] 
dist 136=[-2.4012557549029208517 ,.33075573444259020273] 
dist 137=[-2.4376301030852860328 ,.3990042118582083787 ] 
dist 138=[-2.4846615984830793462 ,.47456686567514627734] 
dist 139=[-2.5156227488299163822 ,.57988028944779837091] 
dist 140=[-2.5338908362437758147 ,.6856659711196254295 ] 
dist 141=[-2.5354638447420184493 ,.7631144496533841228 ] 
dist 142=[-2.5201259663165635583 ,.83464951111667634841] 
dist 143=[-2.5125155911917712761 ,.91683387471526711827] 
dist 144=[-1.8706882176920408642 ,.99959360099374929848] 
dist 145=[-1.8149237633297124111 ,1.0734262634009103475 ] 
dist 146=[-1.6758013084145763632 ,1.1548792055656799165 ] 
dist 147=[-1.6485605823944173975 ,1.2680562688441809284 ] 
dist 148=[-1.4240514880671852040 ,1.3770339388983893398 ] 
dist 149=[-1.3788670595036758784 ,1.4644513404782692854 ] 
dist 150=[-1.3119754122075891506 ,1.6149548900250263729 ] 
dist 151=[-1.2916628958885709656 ,1.7878908993569574407 ] 
dist 152=[-.87243606882195700722,1.9465648045798190949 ] 
dist 153=[-.81666941885139292637,2.0401413971974659420 ] 
dist 154=[-.69103539837927170053,2.1039716056457189605 ] 
dist 155=[-.66276175358230080923,2.1439067599645120729 ] 
dist 156=[-.50513255297685507011,2.1705327181173798824 ] 
dist 157=[-.47594825165861583683,2.1812424581306775075 ] 
dist 158=[-.41541707676948890728,2.1823515675904606152 ] 
dist 159=[-.39910686321259767294,2.1783067718662630376 ] 
dist 160=[.7321286564948205218 ,1.5315920824740460776 ] 
dist 161=[.56906806377522588173,1.5343542087799506071 ] 
dist 162=[.37084630113919671004,1.5310932482727817283 ] 
dist 163=[.07272520882270362224,1.5263927608676550121 ] 
dist 164=[-.22578063233554553433,1.2319953581089139712 ] 
dist 165=[-.42553774754582373108,1.2064782075948508756 ] 
dist 166=[-.59126975915972651477,1.1724197603989170934 ] 
dist 167=[-.75396226757902653668,1.1598249644127013408 ] 
dist 168=[-.90229882001337862024,.86822957408826299772] 
dist 169=[-1.0107276365446179014 ,.83375691295111275069] 
dist 170=[-1.1107158205301486307 ,.78887613882545335341] 
dist 171=[-1.2253595938304443600 ,.7753877572536307912 ] 
dist 172=[-1.3305230654376984341 ,.61994800737305959466] 
dist 173=[-1.3926703848161232623 ,.60070331376220686888] 
dist 174=[-1.4352184626161292940 ,.5516455189933823304 ] 
dist 175=[-1.4621528497491474247 ,.54336586278867837397] 
dist 176=[-1.4801408366297193347 ,.2587976745427186898 ] 
dist 177=[-1.4869791120737163320 ,.2396135191907387300 ] 
dist 178=[-1.4869557804593383112 ,.2010951649364899106 ] 
dist 179=[-1.4844289639299008926 ,.19109961811500501883] 
dist 180=[-1.3410663821696225418 ,.07986930069423037830] 
dist 181=[-1.3904642323377206930 ,.16209831882001404568] 
dist 182=[-1.4226375223952180560 ,.23623221719284888413] 
dist 183=[-1.4399028854170134083 ,.31872070380009187521] 
dist 184=[-1.5180436023053038450 ,.40028313617910195101] 
dist 185=[-1.5605131603984960455 ,.47071967748020532105] 
dist 186=[-1.5849992984906197114 ,.54650742533267323403] 
dist 187=[-1.5913562180147615138 ,.64942693533798468995] 
dist 188=[-1.5909250398693089421 ,.75161275703267458151] 
dist 189=[-1.5883164661282241683 ,.82447121474006112772] 
dist 190=[-1.5836149259543843341 ,.88980467662290872891] 
dist 191=[-1.5775900460691543443 ,.96195445403197393825] 
dist 192=[-1.1462667809173195181 ,1.0329646061488691241 ] 
dist 193=[-1.1316914384662449055 ,1.0937481090712218779 ] 
dist 194=[-1.0946754195755611146 ,1.1586803802330975213 ] 
dist 195=[-1.0824198536668583266 ,1.2462469796226491444 ] 
dist 196=[-.69770770138712910399,1.3293757865874946418 ] 
dist 197=[-.82210391895830528102,1.3765950948835450526 ] 
dist 198=[-.92416263346601857352,1.4065429637859684112 ] 
dist 199=[-1.0224599305311527001 ,1.4207376219448060933 ] 
dist 200=[-1.1108457735910252836 ,1.4276620020369587855 ] 
dist 201=[-1.1733420705249631080 ,1.4285929963925677449 ] 
dist 202=[-1.2288577994713759152 ,1.4253052187401232244 ] 
dist 203=[-1.2893795132593265894 ,1.4153927911516964498 ] 
dist 204=[-1.3427762369165199459 ,1.4136895120598638878 ] 
dist 205=[-1.3698519329636860355 ,1.4209465477853369755 ] 
dist 206=[-1.3838298670701477186 ,1.4232458786025409010 ] 
dist 207=[-1.3858568657922080002 ,1.4200220863386572918 ] 
dist 208=[-1.3722509804767607846 ,1.3898971924525393661 ] 
dist 209=[-1.3658702324185904110 ,1.3964420438492575094 ] 
dist 210=[-1.3592444106937818276 ,1.3983645770023958628 ] 
dist 211=[-1.3529258323755362397 ,1.3951534593346136201 ] 
dist 212=[-1.1449827287953306578 ,.95616965085521264545] 
dist 213=[-1.1164174238641628590 ,.93033019890608659097] 
dist 214=[-1.0433251642562542558 ,.89309232205139523767] 
dist 215=[-1.0287205467988023294 ,.88104607159911009348] 
dist 216=[-.90326446055701592063,.62076640537887296598] 
dist 217=[-.87730360495456610594,.58571401098576731225] 
dist 218=[-.84050100575493078256,.50799311325049729078] 
dist 219=[-.82844317500258032468,.48847100710866788772] 
dist 220=[-.731973393281272075  ,.39348357699112135152] 
dist 221=[-.80471647479462911255,.37556596610273752014] 
dist 222=[-.87005307741588462419,.33469648320508839844] 
dist 223=[-.94239312206404332004,.32495555225145459683] 
dist 224=[-1.0137265818480448610 ,.1091827005532203492 ] 
dist 225=[-1.0750453080201587409 ,.20595309852938469041] 
dist 226=[-1.1407930025224720719 ,.32623058043159923871] 
dist 227=[-1.2298048751369699556 ,.5100827414517144863 ] 
dist 228=[-1.3145686635181842434 ,.69444715345159140693] 
dist 229=[-1.3633598425264228915 ,.81676941381431568177] 
dist 230=[-1.3951566060410406234 ,.91710025060970747643] 
dist 231=[-1.4120861514980091863 ,1.0136861026456777257 ] 
dist 232=[-1.4214993506962858175 ,1.1005004815537856127 ] 
dist 233=[-1.4232943874396564010 ,1.1618286318961142316 ] 
dist 234=[-1.4198525536175156563 ,1.2162491087209877649 ] 
dist 235=[-1.4083631378428950316 ,1.2754917434828674298 ] 
dist 236=[-1.2307630392905353021 ,1.3277212477227254458 ] 
dist 237=[-1.2073993267317343240 ,1.3541489024398966267 ] 
dist 238=[-1.1600573291748144829 ,1.3677654919276352176 ] 
dist 239=[-1.1457030774109035273 ,1.3696898803850522143 ] 
dist 240=[-1.0838524773644376680 ,1.3560257896424366576 ] 
dist 241=[-1.0696098166198358057 ,1.3496938406919144063 ] 
dist 242=[-1.0312840946103822493 ,1.3431709257285775206 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 2, 1, 1, 2] 
dist 0=[50.967280102595548963  ,50.967280102595548963  ] 
dist 1=[50.805841615909313641  ,51.090090339329755017  ] 
dist 2=[50.575168554391685002  ,51.178518898945038463  ] 
dist 3=[50.032598667645443348  ,51.202565864990313588  ] 
dist 4=[49.078106055003256440  ,51.183556595221756862  ] 
dist 5=[47.893769756313605509  ,51.109924529250810661  ] 
dist 6=[46.433189039274828722  ,50.999026803329127067  ] 
dist 7=[44.486534286586084522  ,50.911604290557260978  ] 
dist 8=[41.360858815411562720  ,50.816520335972248132  ] 
dist 9=[38.154523652933579800  ,50.715734909955933331  ] 
dist 10=[35.885674496056541276  ,50.540619635234146561  ] 
dist 11=[33.863139208568863175  ,50.418084843546641925  ] 
dist 12=[31.640421169306816899  ,50.210692889249227264  ] 
dist 13=[29.451505612039060409  ,49.922732834411634591  ] 
dist 14=[27.167165070445192270  ,36.161710714740837927  ] 
dist 15=[24.515330166588478175  ,34.954123265500975962  ] 
dist 16=[21.937859982482781783  ,32.022057680454928932  ] 
dist 17=[19.769091127072237849  ,31.585389159397794964  ] 
dist 18=[17.477776493240443249  ,27.273544340747441526  ] 
dist 19=[14.410507196402864529  ,26.467844839583774954  ] 
dist 20=[11.368882987285245018  ,25.515708932752319758  ] 
dist 21=[9.1797963816257501385 ,25.304496072251899625  ] 
dist 22=[7.1884316574947203581 ,19.554626925849742862  ] 
dist 23=[4.9362662573764494421 ,19.107436973101431366  ] 
dist 24=[2.6779367829858838756 ,18.999971092308533374  ] 
dist 25=[.66155542060532540188,16.791960204526995754  ] 
dist 26=[-1.5728389426668433954 ,16.487059116329130876  ] 
dist 27=[-4.7028586987721694393 ,15.357563573466778238  ] 
dist 28=[-7.7587295980385659815 ,12.699378302935375994  ] 
dist 29=[-9.6970506996299858902 ,12.570198522866938347  ] 
dist 30=[-11.197519458456256812  ,2.5489874349476780117 ] 
dist 31=[-12.503891232083167833  ,1.7031662428192499279 ] 
dist 32=[-13.594598762692243047  ,-.1512220083014389836 ] 
dist 33=[-14.233527466296996981  ,-.48797486998394382506] 
dist 34=[-14.668893002595334146  ,-2.5470837251596093587 ] 
dist 35=[-14.946751595855805377  ,-2.8875912920027690571 ] 
dist 36=[-15.141161235474891231  ,-3.5476710994489415874 ] 
dist 37=[-15.243054707913798463  ,-3.6950971309181948107 ] 
dist 38=[-15.299781315018040719  ,-4.7897404851126059244 ] 
dist 39=[-15.313081400760181310  ,-4.9623515081160222900 ] 
dist 40=[-15.299735013303909250  ,-4.2772172250268313796 ] 
dist 41=[-15.249682334442655348  ,-2.7027710259688108081 ] 
dist 42=[-15.163892058470778440  ,-1.6140812907046250808 ] 
dist 43=[-15.112733877672069300  ,-.6739361125276711877 ] 
dist 44=[-11.603106552006810234  ,.30794774817396196823] 
dist 45=[-11.595671528088912879  ,1.2405400904370554121 ] 
dist 46=[-4.6159534265288641197 ,1.9840820450357530916 ] 
dist 47=[-4.3641601868961080788 ,2.7311040204315044058 ] 
dist 48=[-3.8826241471397156714 ,3.6776679772515258056 ] 
dist 49=[-1.8320131581254113352 ,4.5861297155741238621 ] 
dist 50=[-1.4363779613941964424 ,5.1811172134212225418 ] 
dist 51=[-1.0013078061040164125 ,5.6601872496270841628 ] 
dist 52=[-.74102569642965300025,6.1060369812613646792 ] 
dist 53=[-.19055094456897923661,6.4961486570913549153 ] 
dist 54=[-.08953033465613075750,6.7527582101231996045 ] 
dist 55=[.08953641783239935392,6.9605261752531008916 ] 
dist 56=[.12522286985999118576,7.2884368618870019184 ] 
dist 57=[1.0983728411193468038 ,7.4684283292284108934 ] 
dist 58=[.93131734140163769153,7.5645679248877227445 ] 
dist 59=[.70206285577655519958,7.5805945502219497904 ] 
dist 60=[.38434844077462452978,4.6789888674892941156 ] 
dist 61=[-.13555080570999497166,4.7214080391513824246 ] 
dist 62=[-.66475753185311505836,4.7359869945952812816 ] 
dist 63=[-1.0196173629954489201 ,4.7371088922382363854 ] 
dist 64=[-1.3135177823537486253 ,4.5983535022141943249 ] 
dist 65=[-1.5996322758533370152 ,4.5597195131247230082 ] 
dist 66=[-1.8576022840875975999 ,4.5343105875072726522 ] 
dist 67=[-2.0392501324878487928 ,4.5205692401783630541 ] 
dist 68=[-2.1990474176355219521 ,3.6900242925921166533 ] 
dist 69=[-2.3698290507934020617 ,3.5756260047947191068 ] 
dist 70=[-2.5235006780780693789 ,3.5388968501192107878 ] 
dist 71=[-2.6150581355220910248 ,3.4719462736397551824 ] 
dist 72=[-2.6781350823147443223 ,3.4532593861610228497 ] 
dist 73=[-2.7182612186042497061 ,3.0496819381179408425 ] 
dist 74=[-2.7401458434865472200 ,2.9854979968368006855 ] 
dist 75=[-2.7424808716366452983 ,2.9594606640912405052 ] 
dist 76=[-2.7141697284465625013 ,1.6297396644610830744 ] 
dist 77=[-2.7095916047684483335 ,1.6184235919597234952 ] 
dist 78=[-1.5983799814597161070 ,1.0676463882742781529 ] 
dist 79=[-1.9501293664754802964 ,.93538406862894171765] 
dist 80=[-2.2261616103959995870 ,.90456391402836304187] 
dist 81=[-2.4713886116406416614 ,.67821988969399565978] 
dist 82=[-2.6783763354952044403 ,.47053325523838421937] 
dist 83=[-2.8017769680101022819 ,.43324304343287676632] 
dist 84=[-3.0498421377835912230 ,.3749156554830786537 ] 
dist 85=[-3.2464357693750974288 ,.36035840709648445743] 
dist 86=[-3.3931298133372690846 ,.11589149148317703531] 
dist 87=[-3.5103133330151449434 ,.08494679735196069266] 
dist 88=[-3.5997206564506911864 ,.01463064740780752794] 
dist 89=[-3.6355251512878642558 ,.00338934515360020520] 
dist 90=[-3.6488767017650382648 ,-.08350693451704875200] 
dist 91=[-3.6486415019017357106 ,-.09861119209629880314] 
dist 92=[-3.0251661237415680338 ,-.10641602704444152054] 
dist 93=[-3.0145396422243601996 ,.18467804926594284906] 
dist 94=[-1.5397909334004094022 ,.43298031956857372351] 
dist 95=[-1.4789244827749636727 ,.68775668316582897685] 
dist 96=[-1.4574421860754581983 ,.92719399760245014236] 
dist 97=[-.97884222866382743183,1.1142930685643204612 ] 
dist 98=[-.91643918021599729004,1.2989303401479723093 ] 
dist 99=[-.91632982508805982611,1.5285685733062249387 ] 
dist 100=[-.92765704663456156767,1.7472232216798605462 ] 
dist 101=[-.93296864585425395183,1.8880344128921726011 ] 
dist 102=[-.93446837781324887465,1.9988969276911729267 ] 
dist 103=[-.93361583536386646382,2.0980284632524375849 ] 
dist 104=[-.9256582677027254994 ,2.1822243959251091478 ] 
dist 105=[-.92310739737237613925,2.2334911697554042712 ] 
dist 106=[-.88771816548249412753,2.2706317889776199778 ] 
dist 107=[-.87849864867465948755,2.2984846581356210604 ] 
dist 108=[-.86935030646414449244,2.3159668784983699930 ] 
dist 109=[-.86407763825064631571,2.3180105467578152808 ] 
dist 110=[-.88543360006525044004,2.3019362424120666208 ] 
dist 111=[-1.0894463633303192338 ,2.2972901097092965306 ] 
dist 112=[-1.2789696692398819400 ,2.1915716787449272910 ] 
dist 113=[-1.4231710377347439325 ,2.1637022059591465493 ] 
dist 114=[-1.5617018001585776746 ,2.1421392870271517001 ] 
dist 115=[-1.7285951718674938334 ,2.1307279024287369846 ] 
dist 116=[-1.8845229772751192219 ,1.7456328222874709583 ] 
dist 117=[-1.9792936768052131944 ,1.7524210454117725176 ] 
dist 118=[-2.0473483603231709519 ,1.7506241467231436924 ] 
dist 119=[-2.0966615532292237254 ,1.7430104346109162736 ] 
dist 120=[-2.1310654834701976636 ,1.7367432223248397724 ] 
dist 121=[-2.1396210974988805760 ,1.3167637289729939413 ] 
dist 122=[-2.1385794160258107083 ,1.2724386091042128235 ] 
dist 123=[-2.1346880383885709476 ,1.2589882029196123499 ] 
dist 124=[-.49226586174295781779,.95610651281889591606] 
dist 125=[-.75082978433422212498,.95224103282435882911] 
dist 126=[-1.0204675597792718905 ,.93474122465117491702] 
dist 127=[-1.1924192831526874276 ,.92787856126240353315] 
dist 128=[-1.3586998782182111513 ,.91672319376289958357] 
dist 129=[-1.5001238278258486310 ,.91216921451736637443] 
dist 130=[-1.6320852740600719342 ,.89122582627742895294] 
dist 131=[-1.7857383606380908652 ,.88479082042972807254] 
dist 132=[-1.9269174324941163441 ,.86538181883859715826] 
dist 133=[-2.0090892899122652684 ,.85852698509729631387] 
dist 134=[-2.0638330565841234370 ,.8088540188532667125 ] 
dist 135=[-2.0955297157570727065 ,.79772647913549081674] 
dist 136=[-2.1151172036199661036 ,.77008085753071665119] 
dist 137=[-2.1215210115152163838 ,.76006177836679239959] 
dist 138=[-2.1195082579232319292 ,.70924690952310130739] 
dist 139=[-2.1148358216500073916 ,.69717698708329456726] 
dist 140=[-1.9047461953834885805 ,.67219240945567050088] 
dist 141=[-1.9021123202353426752 ,.66412708851966975997] 
dist 142=[-1.8796868563938513616 ,.47277285282603663889] 
dist 143=[-1.8743166965746437326 ,.64605259800680430176] 
dist 144=[-1.7777537767860152556 ,.83617090054928288417] 
dist 145=[-1.7532596441376014325 ,.98391703884726623006] 
dist 146=[-1.7326272998865124456 ,1.1289500979140624996 ] 
dist 147=[-1.7220945271841743501 ,1.3082457817675387123 ] 
dist 148=[-1.3439916818053979658 ,1.4783576720034600535 ] 
dist 149=[-1.2920716253793883606 ,1.5867377998215184280 ] 
dist 150=[-1.1903781316497177862 ,1.6706901121123481800 ] 
dist 151=[-1.1632519864554589021 ,1.7433041280255934576 ] 
dist 152=[-1.0640324415350121113 ,1.8031250300487533414 ] 
dist 153=[-1.0403658874702070994 ,1.8360192160946401391 ] 
dist 154=[-1.0006781417268585268 ,1.8555325094279947751 ] 
dist 155=[-.98957406236718803095,1.8619543839325839206 ] 
dist 156=[.2119663313413138119 ,1.8599544697501462264 ] 
dist 157=[.11855763341695006106,1.8564936027638140743 ] 
dist 158=[.02009334453681781143,1.8311145493093484076 ] 
dist 159=[-.05277799026546867191,1.8265609808620130115 ] 
dist 160=[-.12082054719663269201,1.7430599289753857727 ] 
dist 161=[-.208342111192379397  ,1.7264540853435150453 ] 
dist 162=[-.32277919599069910221,1.7069274832759372997 ] 
dist 163=[-.41944419161170513479,1.6966396376790481061 ] 
dist 164=[-.52159617833091127062,1.6944389216706213426 ] 
dist 165=[-.65793528897485656583,1.7726035025075517749 ] 
dist 166=[-.79219463887470941316,1.8273623798982165903 ] 
dist 167=[-.88604757863827784616,1.8644930062342425655 ] 
dist 168=[-.9682740345439837288 ,1.8898825024394589623 ] 
dist 169=[-1.0561324242652745348 ,1.8977793502865152108 ] 
dist 170=[-1.1408927905140486053 ,1.8969549918374890844 ] 
dist 171=[-1.2107565990176425159 ,1.8923187991282231668 ] 
dist 172=[-1.2830997755307776743 ,1.8150132167007173094 ] 
dist 173=[-1.3777595912747141420 ,1.8031038593493785945 ] 
dist 174=[-1.4665049806367771106 ,1.7594664640162736410 ] 
dist 175=[-1.5152423093378629228 ,1.7515227218499277269 ] 
dist 176=[-1.5440158262195575111 ,1.6294476970885733070 ] 
dist 177=[-1.5539538643535109914 ,1.6008690510903865730 ] 
dist 178=[-1.5764487668822098632 ,1.5757144835100887146 ] 
dist 179=[-1.5961479188788455395 ,1.5657920531278302454 ] 
dist 180=[-1.7132929957617500549 ,1.1656931179733258434 ] 
dist 181=[-1.7799651703773103864 ,1.1118011550097713090 ] 
dist 182=[-1.8224543578165594689 ,1.0062759224530754224 ] 
dist 183=[-1.8430690733496617674 ,.97846174752055201859] 
dist 184=[-1.8708931832251277918 ,.87835038017659919298] 
dist 185=[-1.8792666416158255906 ,.85457624040665738908] 
dist 186=[-1.8791742042358811601 ,.81847625618560539009] 
dist 187=[-1.8749675873229093699 ,.80740552175823006004] 
dist 188=[-1.7801361642708119459 ,.40129531728947744803] 
dist 189=[-1.7751005374973020402 ,.54315074482421499963] 
dist 190=[-1.4658968110357671787 ,.66330690225051730113] 
dist 191=[-1.4343304962776107833 ,.78527594515349792651] 
dist 192=[-1.3481575536091452353 ,.89908774666448084564] 
dist 193=[-1.3341693511124073801 ,.98668731159253900835] 
dist 194=[-1.1710460963811597302 ,1.0718756477447969108 ] 
dist 195=[-1.1370932326936423480 ,1.1760657981567430906 ] 
dist 196=[-1.1011319638479856823 ,1.2743487989731322403 ] 
dist 197=[-1.0898737348091140957 ,1.3359608651228863054 ] 
dist 198=[-.70935091493088450507,1.3943410279373600200 ] 
dist 199=[-.65986862739682518924,1.4577809644623146490 ] 
dist 200=[-.5592889202637340783 ,1.5004938094271689956 ] 
dist 201=[-.53274187530326113422,1.5260920734595673763 ] 
dist 202=[-.43518218633820901447,1.5425393798259528112 ] 
dist 203=[-.41430437057932937997,1.5499504128200567971 ] 
dist 204=[-.37772688031776290602,1.5523594122428955745 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 0, 0, 0, 1] 
dist 0=[42.307941683764859194  ,42.307941683764859194  ] 
dist 1=[41.311480954539257313  ,43.003775601830464318  ] 
dist 2=[39.641434925426715452  ,43.473234391073475086  ] 
dist 3=[37.908443921840442624  ,43.823164226178296019  ] 
dist 4=[36.660526162504669750  ,44.041613489657037237  ] 
dist 5=[35.526012583658695278  ,44.205753423698598029  ] 
dist 6=[34.245676683952512601  ,44.338694019173590857  ] 
dist 7=[32.965109027352785635  ,44.414863130284227493  ] 
dist 8=[31.829444174415799208  ,44.352120605191536785  ] 
dist 9=[30.578560517590391889  ,43.380702088769080543  ] 
dist 10=[28.837415910061535841  ,43.175340507046387472  ] 
dist 11=[27.078732213157478483  ,42.846638283909156924  ] 
dist 12=[25.757581577419945390  ,42.731695597028432772  ] 
dist 13=[24.498480503595062883  ,42.318864167860801775  ] 
dist 14=[22.987370583221867039  ,42.179240737126738117  ] 
dist 15=[21.421143529649439403  ,41.893054251492584907  ] 
dist 16=[19.941494387236999696  ,41.676867715354741701  ] 
dist 17=[18.234047918479711924  ,30.521903567825003853  ] 
dist 18=[15.757023983632695094  ,29.527581958621731557  ] 
dist 19=[13.295485555966360538  ,27.138143984850971070  ] 
dist 20=[11.649834530450069989  ,26.763332914299564521  ] 
dist 21=[10.277705524478337209  ,23.308674523395408132  ] 
dist 22=[8.9094284817299605286 ,22.661876046319097867  ] 
dist 23=[7.6390933483093195564 ,21.841147679202389381  ] 
dist 24=[6.6583989949844438586 ,21.609675197449077512  ] 
dist 25=[5.6963452105748918652 ,16.186630144319976377  ] 
dist 26=[4.2905904158272917445 ,15.496396406294079662  ] 
dist 27=[2.4638197879360166459 ,14.052733625219064633  ] 
dist 28=[.82656148599497412162,13.670302419675848156  ] 
dist 29=[-.99436915740176312352,12.226902497007674355  ] 
dist 30=[-3.5558395429547279381 ,11.947250597086409749  ] 
dist 31=[-6.0569184738163716088 ,11.373466335216942451  ] 
dist 32=[-7.6367030342788009809 ,11.223424180935107125  ] 
dist 33=[-8.8537367410471296457 ,3.4122317149424704020 ] 
dist 34=[-9.9050469555899805782 ,2.7157964376173176627 ] 
dist 35=[-10.778411451637844348  ,1.1702418771692581040 ] 
dist 36=[-11.284436166556272423  ,.89011653289503696056] 
dist 37=[-11.623239571741167535  ,.29219621355570533136] 
dist 38=[-11.828783712361671629  ,.24741993836874088836] 
dist 39=[-11.968693466242012966  ,-.11174271101961611669] 
dist 40=[-12.045132464439896302  ,-.17870519998803423455] 
dist 41=[-12.092754580212292344  ,-.26841628252662472227] 
dist 42=[-12.116847686095346610  ,-.29636715109208663048] 
dist 43=[-12.126289938603553608  ,-.84893907961343517582] 
dist 44=[-12.115036012923599913  ,-.92301611395206859306] 
dist 45=[-12.087285600156934057  ,-1.0737394216452353976 ] 
dist 46=[-12.046316550032915831  ,-1.1143550821198657586 ] 
dist 47=[-11.160573282502960936  ,-1.2706736571310351392 ] 
dist 48=[-11.143869562088208393  ,-1.3030262172510766776 ] 
dist 49=[-4.3289252642017684670 ,-1.3760273202553771307 ] 
dist 50=[-3.9049992285347451660 ,-1.3976758422177069534 ] 
dist 51=[-2.8914201900989581119 ,-.45636862409559450998] 
dist 52=[-2.7451580414553306653 ,.27277205375509804243] 
dist 53=[-1.3426548848623956752 ,.98387864772162666637] 
dist 54=[-1.0933679104550030941 ,1.8572794045212458449 ] 
dist 55=[-.78262521465171967317,2.6846803710489221311 ] 
dist 56=[-.72818188464793673647,3.2122393294409323015 ] 
dist 57=[-.27061653293175863603,3.6220871211948079723 ] 
dist 58=[-.24343551978793829271,3.9796533726366297756 ] 
dist 59=[.16470783040992435614,4.2775677700899082311 ] 
dist 60=[.21909737121896102865,4.4493800661479661597 ] 
dist 61=[.32066616621801916089,4.5628029967475219739 ] 
dist 62=[.34291819151556099491,4.6278429191929332278 ] 
dist 63=[.39858696531019840764,4.6640124527104274031 ] 
dist 64=[.39956098554725131494,4.6672860239972221553 ] 
dist 65=[.38031547043192856698,4.6471626501660563993 ] 
dist 66=[.32881356870183794078,4.6303268245356297367 ] 
dist 67=[.26959882532585365293,4.4820963457929477979 ] 
dist 68=[.21956154930625918309,4.4402935349570153900 ] 
dist 69=[.16690287914186643446,4.3789708046186021006 ] 
dist 70=[.09717238157482329228,4.3545863158281287098 ] 
dist 71=[.02201574149242446178,3.8302786280140088052 ] 
dist 72=[-.05232392039119251357,3.7796449597110441088 ] 
dist 73=[-.1402028042755485515 ,3.6547149038138205658 ] 
dist 74=[-.26941582066100822555,3.6168499425227540633 ] 
dist 75=[-.4019980556328062379 ,3.4032247304519212978 ] 
dist 76=[-.50333838046625186795,3.3556216831097890110 ] 
dist 77=[-.6011700362133085503 ,3.2614104659995251915 ] 
dist 78=[-.75905995228020348851,3.2329845867083876510 ] 
dist 79=[-1.3061330451492469240 ,3.1105560838300193409 ] 
dist 80=[-2.1101171152214547509 ,3.1000807102213038057 ] 
dist 81=[-2.9040215628367994955 ,1.6226955989754539318 ] 
dist 82=[-3.4108813412583150892 ,1.6097038592066789484 ] 
dist 83=[-3.8048664247179619967 ,1.0250070837301934635 ] 
dist 84=[-4.1482101131466733097 ,.94552295900434149105] 
dist 85=[-4.4330624411243953758 ,.81342055864621856553] 
dist 86=[-4.5935759511748831565 ,.78104611462860169511] 
dist 87=[-4.6939553498287581475 ,.20707488735966479613] 
dist 88=[-4.7387945148315228350 ,.13221520689160396268] 
dist 89=[-4.7618234491538826210 ,-.04621658885406301515] 
dist 90=[-4.7751366069117122892 ,-.07268727283137341725] 
dist 91=[-4.7840252334962339611 ,-.32099171274246827898] 
dist 92=[-4.7893500181430391135 ,-.36574423032893142154] 
dist 93=[-4.7920618314147848881 ,-.42223814197596194294] 
dist 94=[-4.7904950704250093836 ,-.43415939393519934407] 
dist 95=[-4.7854966626056910066 ,-.89895544326682146162] 
dist 96=[-4.7744786361159909874 ,-.60817120588401853646] 
dist 97=[-2.3263900131953408921 ,-.32897195849762781385] 
dist 98=[-2.3194250260942771061 ,-.04610162556160873996] 
dist 99=[-1.7783131966277515810 ,.25877411701747838142] 
dist 100=[-1.7183102031404851134 ,.50077912282922490928] 
dist 101=[-1.5635249559630759753 ,.7010146445619070859 ] 
dist 102=[-1.5390534929607599829 ,.89656291908969404941] 
dist 103=[-1.2776970246514674781 ,1.0789674058570469847 ] 
dist 104=[-1.2257801024364351407 ,1.3098433086723612668 ] 
dist 105=[-1.1667403396168716646 ,1.6822370819438475073 ] 
dist 106=[-1.1498096181671623786 ,1.9186961929892821808 ] 
dist 107=[-.63030469206904875917,2.1009042319273943405 ] 
dist 108=[-.5640810014698805574 ,2.2567523153581908233 ] 
dist 109=[-.4266300352062617734 ,2.3842121645851088632 ] 
dist 110=[-.39033339656199146613,2.4531104704857381190 ] 
dist 111=[-.25547016997969159268,2.4923091215849822913 ] 
dist 112=[-.22829580079539291858,2.5017129366380923027 ] 
dist 113=[-.17805678479161422258,1.9462847807881298189 ] 
dist 114=[-.16621742041062398133,2.0004536770268156031 ] 
dist 115=[.39095166839076839463,2.0790009281505932137 ] 
dist 116=[.33709205364205498546,2.1254233907453425635 ] 
dist 117=[.26138896088462803953,2.1573401768082482418 ] 
dist 118=[.13620263096838887095,2.1779914279296090255 ] 
dist 119=[.00198676394342212460,2.1886976606868620400 ] 
dist 120=[-.10976959190937261885,2.1891250415114488614 ] 
dist 121=[-.2264471035386065246 ,2.1696021508768126079 ] 
dist 122=[-.4085702086021491956 ,2.1662209403911715757 ] 
dist 123=[-.59999337734471293477,2.0589112510882673083 ] 
dist 124=[-.78045114637498730157,2.0314400666394793741 ] 
dist 125=[-.98749802388961912841,2.0144764993981828199 ] 
dist 126=[-1.2850684497343831642 ,2.0087684035055583826 ] 
dist 127=[-1.5768106769128405031 ,1.1273588603027947767 ] 
dist 128=[-1.7605993889495332637 ,1.1169121449461890572 ] 
dist 129=[-1.9005870412082799987 ,.24569751734270650866] 
dist 130=[-2.0441255643526076894 ,.16353857524829036913] 
dist 131=[-2.1894083019789011512 ,-.00800352881823892898] 
dist 132=[-2.2797695298605471379 ,-.05075159824429459734] 
dist 133=[-2.3472300072343104042 ,-.21184765583409745059] 
dist 134=[-2.4011061774053300429 ,-.24268880870173007142] 
dist 135=[-2.4427241554057240695 ,-.29196592630526228238] 
dist 136=[-2.4612569253877080099 ,-.3031590695084467984 ] 
dist 137=[-2.4664402830975398912 ,-.31079415158250005919] 
dist 138=[-2.4689964022036102357 ,-.29362220988592083278] 
dist 139=[-2.4940780414495689532 ,-.25817935172323683755] 
dist 140=[-2.5015287359459480989 ,-.18859519988375282062] 
dist 141=[-2.4975628461454137835 ,-.10244024012962017358] 
dist 142=[-2.4926100727626395708 ,-.00085661209318285662] 
dist 143=[-2.0300832217883285803 ,.28629707879292402396] 
dist 144=[-2.0266154083834665358 ,.58163156049007211558] 
dist 145=[-1.0596266446733511544 ,.82321818402681460682] 
dist 146=[-1.0216933726998697451 ,1.0546550182821597878 ] 
dist 147=[-.77292581388585929266,1.2618882601603941168 ] 
dist 148=[-.72645796950724567587,1.4068724384385633735 ] 
dist 149=[-.64070398816832449854,1.5340514773480566324 ] 
dist 150=[-.62002478893574949749,1.6702221966498352519 ] 
dist 151=[-.31679688266899791774,1.7941210661393408901 ] 
dist 152=[-.2745828364606155259 ,1.8723174497069897936 ] 
dist 153=[-.18531414788752538646,1.9320262558282165472 ] 
dist 154=[-.16277426603283681293,1.9821265852356727970 ] 
dist 155=[-.07263472485148776444,2.0222070222941998318 ] 
dist 156=[-.05567978807853010470,2.0419166165890820259 ] 
dist 157=[-.02168937982343982449,2.0504552644914453488 ] 
dist 158=[-.01321293580318336378,2.0485076823068071986 ] 
dist 159=[.13397328053722132776,1.4366595258951223911 ] 
dist 160=[-.1520002810051686154 ,1.4386247598435903328 ] 
dist 161=[-.4393072739505302673 ,1.2785056157236193249 ] 
dist 162=[-.63032919468903602313,1.2563853007836255934 ] 
dist 163=[-.78738181608598590775,1.1999971852714638747 ] 
dist 164=[-.93911107592495267909,1.1850847450432552626 ] 
dist 165=[-1.0757762460926850180 ,1.0847020585540480216 ] 
dist 166=[-1.1727042470697784046 ,1.0627137224649597378 ] 
dist 167=[-1.2590668208756358785 ,1.0235541537643097905 ] 
dist 168=[-1.3535602987566966215 ,1.0128800186924689279 ] 
dist 169=[-1.4387504206597945455 ,.78870077789676379186] 
dist 170=[-1.4879816115396442496 ,.75723949337523856124] 
dist 171=[-1.5202776462415617961 ,.68271729644810254416] 
dist 172=[-1.5378796545650794182 ,.6667466004952416784 ] 
dist 173=[-1.5471765237352233610 ,.55944745351675642236] 
dist 174=[-1.5463586493220712218 ,.53849664241441757292] 
dist 175=[-1.5404220635791874254 ,.50069587286873483145] 
dist 176=[-1.5345072393692595136 ,.4913601549731605094 ] 
dist 177=[-1.5088397522471064862 ,.4293712332857378106 ] 
dist 178=[-1.5775122929848992786 ,.47136203693733427913] 
dist 179=[-1.6312890364162829263 ,.5150867946083469951 ] 
dist 180=[-1.6563607668852987646 ,.55628627012895839658] 
dist 181=[-1.6682198104661411002 ,.60351842115185371745] 
dist 182=[-1.6692545893971793559 ,.67131842482752888648] 
dist 183=[-1.6178238071255291974 ,.74024274736149813033] 
dist 184=[-1.6043524998729294280 ,.7919614232875342621 ] 
dist 185=[-1.5837950995892781272 ,.84096672761085982122] 
dist 186=[-1.6101228642013722945 ,.89906126711264574387] 
dist 187=[-1.6227781100383867964 ,.95852903607270971224] 
dist 188=[-1.6236249738899902930 ,1.0130138966939424910 ] 
dist 189=[-1.6022374507669602542 ,1.0742651356027401700 ] 
dist 190=[-1.5922554460637004246 ,1.1607352584987346612 ] 
dist 191=[-1.5819264602830582270 ,1.2441684076373699333 ] 
dist 192=[-1.5743552804659328286 ,1.2932986792587129241 ] 
dist 193=[-1.3879408173232664471 ,1.3266860519528281411 ] 
dist 194=[-1.4544636675999667222 ,1.3472903595332225483 ] 
dist 195=[-1.5001362637899227280 ,1.3599226355569147927 ] 
dist 196=[-1.5293254521218664763 ,1.3614938840357124369 ] 
dist 197=[-1.5489335815476560683 ,1.3579464732215178327 ] 
dist 198=[-1.5563624804285517919 ,1.3529794767891351019 ] 
dist 199=[-1.5563004712550209508 ,1.2449974893262814675 ] 
dist 200=[-1.5537387872779876622 ,1.2893817270175078238 ] 
dist 201=[-1.4101919690775021434 ,1.3397803176620255286 ] 
dist 202=[-1.3861411603978612838 ,1.3736067452344972063 ] 
dist 203=[-1.3401432822134234130 ,1.3978316535551537902 ] 
dist 204=[-1.3263948527292618436 ,1.4099065472696519404 ] 
dist 205=[-1.2693830902495137307 ,1.4181653648426544882 ] 
dist 206=[-1.2546536627673493483 ,1.4265932636875918787 ] 
dist 207=[-1.2197779607768450652 ,1.4273767932622913566 ] 
dist 208=[-1.2071870370554397032 ,1.4254733706483617569 ] 
dist 209=[-.34327106355996537336,1.1653694589537849769 ] 
dist 210=[-.26609127356648414419,1.1355206981575262902 ] 
dist 211=[-.09387536193038991523,1.0605295683203708785 ] 
dist 212=[-.13523810760909069608,1.0446519752985274772 ] 
dist 213=[-.24688602152307346542,.95511058392071980152] 
dist 214=[-.39817454840757518208,.94460483534677966607] 
dist 215=[-.54825056471366643453,.85436039470181437677] 
dist 216=[-.65505994712877694086,.84256084801485414162] 
dist 217=[-.75064873051579867578,.88187897468869774812] 
dist 218=[-.85594058619826609378,.94520028856224782014] 
dist 219=[-.95943820402816507494,1.0014923026376401928 ] 
dist 220=[-1.0478668937582809695 ,1.0629205965810495852 ] 
dist 221=[-1.1422176009875251333 ,1.1229558798653427322 ] 
dist 222=[-1.2693548443380662988 ,1.1736860842732726826 ] 
dist 223=[-1.3911000713364853551 ,1.2273176485649996974 ] 
dist 224=[-1.4639289383053725466 ,1.2989303725116188263 ] 
dist 225=[-1.5148904689198722056 ,1.3666002636727771772 ] 
dist 226=[-1.5493514961013317729 ,1.4044939168680757289 ] 
dist 227=[-1.5734890968878886653 ,1.4278245291561758462 ] 
dist 228=[-1.5832447654390082344 ,1.4373691036188104846 ] 
dist 229=[-1.5843359624786473770 ,1.4401374637409426487 ] 
dist 230=[-1.5824125783621658175 ,1.4371163634457708236 ] 
dist 231=[-1.4496467292903487286 ,1.4288865240615119016 ] 
dist 232=[-1.4132308446699111702 ,1.4232296125180470001 ] 
dist 233=[-1.4207642048892399142 ,1.2793367163485437560 ] 
dist 234=[-1.4441781491829061941 ,1.2555582364643259011 ] 
dist 235=[-1.4556628762614059232 ,1.2037619756338963850 ] 
dist 236=[-1.4582349181274885091 ,1.1872623583584974982 ] 
dist 237=[-1.4280513380202112767 ,1.1116864643692640864 ] 
dist 238=[-1.4200316133118864055 ,1.0953105136102688533 ] 
dist 239=[-1.4150428291438608631 ,1.0494086269893664358 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 1, 1, 2, 2, 0, 1] 
dist 0=[56.097320746523164516  ,56.097320746523164516  ] 
dist 1=[55.759386077918805825  ,56.363263721894984905  ] 
dist 2=[54.675996197360900293  ,56.673238607028204809  ] 
dist 3=[53.410736148597109092  ,56.732405004226982108  ] 
dist 4=[52.191674180495491724  ,56.606444791234935222  ] 
dist 5=[50.770502841655667441  ,56.485284141488603613  ] 
dist 6=[48.697888853927371821  ,56.305916275558507630  ] 
dist 7=[46.359147294012453968  ,56.199890113249553800  ] 
dist 8=[43.875016777256620870  ,52.740296151095141755  ] 
dist 9=[40.802358206905288374  ,52.169781441961045257  ] 
dist 10=[36.113022982973664728  ,51.299742060766063681  ] 
dist 11=[31.384049863646322939  ,51.028378616244528121  ] 
dist 12=[28.152981304850941592  ,50.426589616527182853  ] 
dist 13=[25.392234284725873378  ,50.165315356182577546  ] 
dist 14=[22.541449582443811417  ,48.405178729980529641  ] 
dist 15=[19.841394816362777531  ,44.396784526517077416  ] 
dist 16=[17.682421512627157687  ,33.376712719370299048  ] 
dist 17=[15.499594351008240419  ,32.423427421303172295  ] 
dist 18=[12.703823820995861113  ,30.491602729664882652  ] 
dist 19=[9.9881016577869398953 ,29.977788773639467339  ] 
dist 20=[8.1247499975076525202 ,28.061740370113282471  ] 
dist 21=[6.5218126870662245738 ,27.651932601476924276  ] 
dist 22=[4.8459204253819480120 ,26.870058906613133512  ] 
dist 23=[3.2416504369921263307 ,26.663349880173430261  ] 
dist 24=[1.9243237607242195935 ,11.141343651287994711  ] 
dist 25=[.55706398651811021374,9.7956775295524857669 ] 
dist 26=[-1.2477126864493611621 ,6.7631931355550296197 ] 
dist 27=[-3.7835142210609422056 ,6.3006065633571509104 ] 
dist 28=[-6.1206027874900545870 ,5.2427443296300750809 ] 
dist 29=[-7.8209942999365654758 ,5.0387579113389192263 ] 
dist 30=[-9.3859640770211393195 ,4.3916604520272232773 ] 
dist 31=[-11.182200299510719236  ,3.5746116575883407131 ] 
dist 32=[-12.841409054780236110  ,-2.5232710571679606066 ] 
dist 33=[-13.859094601549128493  ,-2.9459411892209933910 ] 
dist 34=[-14.605242252777894066  ,-3.6593093790903262906 ] 
dist 35=[-15.179914670840622574  ,-3.8068078706763723066 ] 
dist 36=[-15.613823851773006826  ,-3.9974854526408263394 ] 
dist 37=[-15.797650815885030849  ,-3.8634100679095743736 ] 
dist 38=[-15.867603264330889870  ,-3.5382518736641232298 ] 
dist 39=[-15.846618425761010845  ,-2.8719732768773918816 ] 
dist 40=[-9.0211156951340411513 ,-2.1572905045466917744 ] 
dist 41=[-8.9532468391964549850 ,-1.6387570239776201010 ] 
dist 42=[-8.8330164386794992699 ,-1.1672996552331797002 ] 
dist 43=[-8.7891272068874872752 ,-.63981977614295582461] 
dist 44=[-8.5920204423028143843 ,-.11883522469188443269] 
dist 45=[-8.5315607923209337896 ,.32702545976076799309] 
dist 46=[-8.3792192858890875804 ,.80239539001934594525] 
dist 47=[-8.3182992883988001019 ,1.4414492125535914584 ] 
dist 48=[-3.9941293923157230635 ,2.0723306888788396331 ] 
dist 49=[-3.6081820686321854697 ,2.5152629214092777113 ] 
dist 50=[-2.7755537547333145721 ,2.9054246537613318594 ] 
dist 51=[-2.5885612722036947298 ,3.3259336700617434776 ] 
dist 52=[-1.1012275745421818097 ,3.7346338508110218409 ] 
dist 53=[-.83909735865203624977,4.0778651013464891175 ] 
dist 54=[-.07228561721590915624,4.4399612931381814076 ] 
dist 55=[.84730420830097148528,4.9243095390883979597 ] 
dist 56=[2.0016756001927055383 ,5.3890432048627071022 ] 
dist 57=[1.9689635513916248209 ,5.6728960580200793980 ] 
dist 58=[1.8595025519822263104 ,5.8801133632166426842 ] 
dist 59=[1.7325860999942371033 ,6.0387526140779147638 ] 
dist 60=[1.6301932169185685852 ,6.1556783510461874228 ] 
dist 61=[1.5268512380838309400 ,6.1963376778626398221 ] 
dist 62=[1.3959915911362592510 ,6.2013234139974713437 ] 
dist 63=[1.2580719933751910702 ,6.1192237599793885072 ] 
dist 64=[1.1264793681261272099 ,5.6191060338939224246 ] 
dist 65=[.97460243461091030694,5.7511086839876975656 ] 
dist 66=[.75566319924751728995,5.8480474164061195415 ] 
dist 67=[.53295193016951067112,5.9232798461966941602 ] 
dist 68=[.36597437180908462986,5.9793943752549006307 ] 
dist 69=[.16462030759075080983,5.9999451545665555684 ] 
dist 70=[-.62482397143514791269,5.9986242959174715571 ] 
dist 71=[-1.8126066404381860531 ,5.9880388482413049866 ] 
dist 72=[-3.0458918450047424771 ,1.3509517272130937742 ] 
dist 73=[-3.8660756100848155492 ,1.2338850963213362194 ] 
dist 74=[-4.5235154350785020592 ,.97354112949632627681] 
dist 75=[-5.1312354390383561938 ,.92193762887760847098] 
dist 76=[-5.6609360617934410242 ,.72768100230635754007] 
dist 77=[-6.0069696399176176082 ,.70286810433628511239] 
dist 78=[-6.2850398102112678534 ,.69609111850750232294] 
dist 79=[-6.5434944580661937546 ,.67089117186546982745] 
dist 80=[-6.7637487450184953434 ,.66358005327106522585] 
dist 81=[-6.8893301060714076926 ,.64842946466475135136] 
dist 82=[-6.9698344879308740671 ,.64288872264570530847] 
dist 83=[-7.0100987431020150467 ,.61529398284237758429] 
dist 84=[-7.0215230622180184078 ,.60747734862920664548] 
dist 85=[-7.0120020987654847760 ,.59115966365270077254] 
dist 86=[-6.9419878729506540080 ,.58516449166154514428] 
dist 87=[-6.9125690302878650803 ,.55460097579163065493] 
dist 88=[-4.3528631585888172683 ,.54716697625319534919] 
dist 89=[-4.1227522454360603340 ,.52390982484479299721] 
dist 90=[-3.5561919114465299631 ,.57102084078987782089] 
dist 91=[-3.4668155965678979798 ,1.2359905345220821388 ] 
dist 92=[-2.8681290276864325766 ,1.8555406684480967271 ] 
dist 93=[-2.8523210632819398103 ,2.3308652844908075069 ] 
dist 94=[-2.8399775654631868345 ,2.7916601825816754469 ] 
dist 95=[-2.8292492409407735438 ,3.3532283848769609678 ] 
dist 96=[-.80607623999790981994,3.8819781239536047432 ] 
dist 97=[-.63434954405429752312,4.2117864360771156623 ] 
dist 98=[-.26272224489818426622,4.4591029442844500748 ] 
dist 99=[-.1812406448402387289 ,4.6585980152382502878 ] 
dist 100=[.21766323079637374611,4.8146405004000962388 ] 
dist 101=[.28626877797822256063,4.8885099989804384383 ] 
dist 102=[.38824779419363345331,4.9231415116958813801 ] 
dist 103=[.33654496873976381626,4.9231496422305770420 ] 
dist 104=[.2652903374961546225 ,2.4914710282838998531 ] 
dist 105=[.16613658119829814926,2.6815857912110802715 ] 
dist 106=[.00309812527446947806,2.8192526957606395420 ] 
dist 107=[-.16437815709680490995,2.9216236537509807833 ] 
dist 108=[-.2812448832091135509 ,2.9997032483667038524 ] 
dist 109=[-.38333460501046069998,3.0403870188185662205 ] 
dist 110=[-.49185033572570645849,3.0615548248505984202 ] 
dist 111=[-.9531429202184864001 ,3.0616987031325583090 ] 
dist 112=[-1.4731118578670642948 ,3.0059740286893449771 ] 
dist 113=[-1.8182320776441329286 ,3.0526260691611549816 ] 
dist 114=[-2.1015443979075268299 ,3.0767505281854001636 ] 
dist 115=[-2.3747967772275020684 ,3.0793746906186412658 ] 
dist 116=[-2.6208615326416609069 ,2.9290822112606132417 ] 
dist 117=[-2.7956521725715004124 ,2.9138018055953116259 ] 
dist 118=[-2.9518300230072021806 ,2.7270196912485271285 ] 
dist 119=[-3.1236055732518552333 ,2.6698646706993814779 ] 
dist 120=[-3.2762084335321732991 ,2.2157240897952332760 ] 
dist 121=[-3.3558555795426633692 ,2.1507108762725775512 ] 
dist 122=[-3.3998142829490923279 ,2.0218515588332714687 ] 
dist 123=[-3.4099364345734286869 ,1.9862833401946396362 ] 
dist 124=[-3.3861660106970141349 ,1.8493125596034693225 ] 
dist 125=[-3.3789607766404309789 ,1.8173602172973429566 ] 
dist 126=[-3.3736822832061321809 ,1.7521146109348019497 ] 
dist 127=[-3.3696235328475401187 ,1.7322281821717816802 ] 
dist 128=[-1.6915749998427226126 ,-.8693185763576797317 ] 
dist 129=[-1.8364134174554210956 ,-.94289677908237239756] 
dist 130=[-1.9448274828903750702 ,-.95671580625941884581] 
dist 131=[-2.0319225116467843692 ,-.99898302026113288836] 
dist 132=[-2.0998079742461522729 ,-.90598187851407283443] 
dist 133=[-2.1315485028013212268 ,-.79495989864561945397] 
dist 134=[-2.1461328622957124671 ,-.6476845809613090923 ] 
dist 135=[-2.1457091741816516571 ,-.48834769474301278604] 
dist 136=[-1.6401877397177587987 ,-.32918110497488979263] 
dist 137=[-1.6365202377884915649 ,-.13962044879197804281] 
dist 138=[-1.6312708390809532998 ,.14103373945751898239] 
dist 139=[-1.5150140419387324506 ,.4211946782131065412 ] 
dist 140=[-1.4966374468445018209 ,.60878682158290949262] 
dist 141=[-1.4419785715931884875 ,.76452753410421710831] 
dist 142=[-1.4313751399902895053 ,.91755496014966859498] 
dist 143=[-1.3102017124206704462 ,1.0571519492144980265 ] 
dist 144=[-1.2831976324317494975 ,1.1592850011278422219 ] 
dist 145=[-1.2534000073534710531 ,1.2535476466078646445 ] 
dist 146=[-1.2399939315382071024 ,1.3617282547098676609 ] 
dist 147=[-.90740764632024250506,1.4601916345156584552 ] 
dist 148=[-.86229906585191173948,1.5156676959565956368 ] 
dist 149=[-.77006033556447153891,1.5502734316286483216 ] 
dist 150=[-.74502326539421062174,1.5654337916104425116 ] 
dist 151=[-.64932250326019729693,1.5727527486352199845 ] 
dist 152=[-.71200034252520860582,1.5814651189871508345 ] 
dist 153=[-.80495558355928999123,1.6846623960517848877 ] 
dist 154=[-.88308052421707600166,1.7583582528092814412 ] 
dist 155=[-.96128185168575460038,1.8112034165030463139 ] 
dist 156=[-1.0334482874602880103 ,1.8502893108399613912 ] 
dist 157=[-1.0874917033703537910 ,1.8690534174397516479 ] 
dist 158=[-1.1385504046938917605 ,1.8765669782222325120 ] 
dist 159=[-1.1988046683300685991 ,1.8753945458950128543 ] 
dist 160=[-1.2544004433292847060 ,1.7258552977436050412 ] 
dist 161=[-1.2868695558051148913 ,1.6999895076201705464 ] 
dist 162=[-1.3085693287899808521 ,1.6546254608384869035 ] 
dist 163=[-1.3211920772433047142 ,1.6413467806898456630 ] 
dist 164=[-1.3269709325467748146 ,1.5909093103902837978 ] 
dist 165=[-1.3267111222653092891 ,1.5752578268335286920 ] 
dist 166=[-1.3602875268253896852 ,1.5459162302055792817 ] 
dist 167=[-1.3979745367452667458 ,1.5359320740314138844 ] 
dist 168=[-1.4212178044124837961 ,.29624104616955961426] 
dist 169=[-1.4383437251452201130 ,.19637735436508405943] 
dist 170=[-1.4516176871796261429 ,.36241049738713288248] 
dist 171=[-1.4599198618960416399 ,.63480222612433904884] 
dist 172=[-1.4597113579508718808 ,.81601739488471899706] 
dist 173=[-1.4507581737641350722 ,.96518117214234863915] 
dist 174=[-1.4441826770143182509 ,1.1096392408416385211 ] 
dist 175=[-1.3918668083332211153 ,1.2400380664319072040 ] 
dist 176=[-1.3769789157779819417 ,1.3330830131346471291 ] 
dist 177=[-1.3934613854167705248 ,1.4165913393033106897 ] 
dist 178=[-1.4617217449204876177 ,1.5089212501756063800 ] 
dist 179=[-1.5154643985088789918 ,1.5914433812804439972 ] 
dist 180=[-1.5563368139040955399 ,1.6358049061749813296 ] 
dist 181=[-1.5732240286601674332 ,1.6607005774956902015 ] 
dist 182=[-1.5797767792150238906 ,1.6666545853155514878 ] 
dist 183=[-1.5793983914700101880 ,1.6635248479471097289 ] 
dist 184=[-1.6127633004248105108 ,1.6611322700337329459 ] 
dist 185=[-1.6316503544380841122 ,1.6579878619739201360 ] 
dist 186=[-1.6391235654190530550 ,1.6529758114716186541 ] 
dist 187=[-1.6380530279091281137 ,1.3394082724703991450 ] 
dist 188=[-1.6105421495717650916 ,1.3011424243748908157 ] 
dist 189=[-1.5996798154602858816 ,1.2004846356558060097 ] 
dist 190=[-1.5822927637780734031 ,1.1844552027563654714 ] 
dist 191=[-1.5747377545351481878 ,1.0070316025187695155 ] 
dist 192=[-1.3534280711817522702 ,.97110613946772955594] 
dist 193=[-1.3199736614279345836 ,.97283002746372404661] 
dist 194=[-1.2486949499537626196 ,1.0561668610640434638 ] 
dist 195=[-1.2273218320792829828 ,1.1459792560390434143 ] 
dist 196=[-1.1345607164945878080 ,1.2331207487115947376 ] 
dist 197=[-1.1153865173852153805 ,1.3058010205208009788 ] 
dist 198=[-1.0604402373636166440 ,1.3818472600899272678 ] 
dist 199=[-1.0520114442791119819 ,1.4824313593720800563 ] 
dist 200=[-.1385920171922523774 ,1.5774062844227210572 ] 
dist 201=[-.2682353034144399709 ,1.6310646787250512672 ] 
dist 202=[-.47033686773659142072,1.6647734168038032570 ] 
dist 203=[-.67446171310821789028,1.6959087453795024212 ] 
dist 204=[-.81218047728238249746,1.7603772199875492303 ] 
dist 205=[-.92764456049871956741,1.8011754325277859618 ] 
dist 206=[-1.0429428692938999409 ,1.8203806415287829953 ] 
dist 207=[-1.1493229791454120818 ,1.8303298279332934811 ] 
dist 208=[-1.2291910643013698671 ,1.8341794384072097886 ] 
dist 209=[-1.3049425615910600833 ,1.8343080714965102686 ] 
dist 210=[-1.3948912287170373024 ,1.8294009430975771382 ] 
dist 211=[-1.4783696366647988779 ,1.8015106092351179758 ] 
dist 212=[-1.5282957618585572493 ,1.8079555549220234620 ] 
dist 213=[-1.5632055421537344996 ,1.8096939316942411808 ] 
dist 214=[-1.5867482681487289024 ,1.8083134682834817566 ] 
dist 215=[-1.6011757225409538500 ,1.8023046130849272543 ] 
dist 216=[-1.6035858107531345462 ,1.4797823894981799484 ] 
dist 217=[-1.5940883399297792163 ,1.4404732527104828050 ] 
dist 218=[-1.5919873538036494003 ,1.3374685759248555677 ] 
dist 219=[-1.5146835768703726048 ,1.3200187988070986519 ] 
dist 220=[-1.4987616824371692800 ,1.1385371756993731538 ] 
dist 221=[-1.4532322777421701806 ,1.1015110670884554703 ] 
dist 222=[-1.4410467694170144905 ,1.0580553575992520576 ] 
dist 223=[-1.3425181430596913371 ,1.0427105021942614743 ] 
dist 224=[-1.4613902770409831419 ,.65738483147068275834] 
dist 225=[-1.5302368584199982982 ,.60700001161185970626] 
dist 226=[-1.5756302093120402902 ,.50184248929761639057] 
dist 227=[-1.6008876161437004638 ,.47355884649294150772] 
dist 228=[-1.6169459071862820649 ,.36563189736960844115] 
dist 229=[-1.6256229591457960593 ,.34392603667924262562] 
dist 230=[-1.6305560186988316624 ,.29949503167188352155] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 2, 0, 2, 0, 1] 
dist 0=[47.146930701096367502  ,47.146930701096367502  ] 
dist 1=[46.769959841758354611  ,47.526132458479725495  ] 
dist 2=[45.643932332705318776  ,48.046765526428800101  ] 
dist 3=[44.271787348515033614  ,48.439058161941479691  ] 
dist 4=[42.739765364920967758  ,48.733428473205866392  ] 
dist 5=[40.793537384497412866  ,48.863015278619182728  ] 
dist 6=[37.766975246206886329  ,48.896086143067754319  ] 
dist 7=[34.692765106943089557  ,48.862700434925752306  ] 
dist 8=[32.556119898248648682  ,48.642507863369028917  ] 
dist 9=[30.691609538486361787  ,48.557801853820453333  ] 
dist 10=[28.704051180640177075  ,48.157635580258162184  ] 
dist 11=[26.782505568192610086  ,48.096535762369181692  ] 
dist 12=[25.181422127323292780  ,46.721759349202900875  ] 
dist 13=[23.503126176640861123  ,46.407324284530573315  ] 
dist 14=[21.272768003732183031  ,45.230758141383903594  ] 
dist 15=[19.066778663215905287  ,43.187364961018934952  ] 
dist 16=[17.485587142954977585  ,31.975308948282008895  ] 
dist 17=[16.052862937294891033  ,31.314565478119304724  ] 
dist 18=[14.439606676597999788  ,30.514718235705484721  ] 
dist 19=[12.824255598600269565  ,30.272998151642129992  ] 
dist 20=[11.382733000933078221  ,24.107492537432429097  ] 
dist 21=[9.7843665425727495930 ,23.306607627243723605  ] 
dist 22=[7.5415364065202617874 ,21.666000569684430989  ] 
dist 23=[5.3391984547954178504 ,21.231465067141293816  ] 
dist 24=[3.9024860474696582994 ,19.609150378001568472  ] 
dist 25=[2.7425229417467892484 ,19.274713058794332292  ] 
dist 26=[1.6463533324294601949 ,18.625682222577077049  ] 
dist 27=[.6659573459013072475 ,18.456771121668045212  ] 
dist 28=[-.03137873054382673253,11.525681359132595016  ] 
dist 29=[-.66047753259936375864,11.163218893323512743  ] 
dist 30=[-2.4577451925734024769 ,9.6133583851854284649 ] 
dist 31=[-4.3574952818109883664 ,7.0422723140243920171 ] 
dist 32=[-6.0733507613520008803 ,.60272675390704635885] 
dist 33=[-7.3111830755388362399 ,.12685467688131737402] 
dist 34=[-8.4405961833170374093 ,-.67829020153362732196] 
dist 35=[-9.7234474133738221046 ,-.85218347966169772763] 
dist 36=[-10.905079200265191877  ,-1.6446416657475234376 ] 
dist 37=[-11.630158095995830576  ,-1.3900407694045817965 ] 
dist 38=[-12.162712381352986835  ,-.93246408074036321095] 
dist 39=[-12.575187401622659518  ,-.45534625238073881709] 
dist 40=[-12.885474837121505964  ,-.12261463546413829301] 
dist 41=[-13.009762573775686667  ,.16610005621829746754] 
dist 42=[-13.055447395777068077  ,.46799881325566725098] 
dist 43=[-13.051624340050771300  ,.75357313591030921387] 
dist 44=[-11.697744677911017651  ,.97733360873396309891] 
dist 45=[-11.676468739924607936  ,1.1978524992478412955 ] 
dist 46=[-11.629063559357138394  ,1.4706284502513677543 ] 
dist 47=[-11.593688854900712104  ,1.7282469937566298080 ] 
dist 48=[-5.7572096598465201847 ,1.8883673227632556346 ] 
dist 49=[-5.2643763541157581518 ,2.0074104510199700084 ] 
dist 50=[-4.1845014137822600428 ,2.1012359381289483365 ] 
dist 51=[-4.1311183470060388641 ,2.1742488275316370133 ] 
dist 52=[-2.2199441803653640121 ,2.2102265393045135730 ] 
dist 53=[-1.9165497822499104322 ,2.2264832986204794559 ] 
dist 54=[-1.5499437415695936313 ,2.2278926474642164305 ] 
dist 55=[-1.4872104080021585403 ,2.1036298353741418004 ] 
dist 56=[-.34443434915153676174,2.7960040531505985693 ] 
dist 57=[-.24373117470387780372,3.3271681006070177423 ] 
dist 58=[-.10194289475731061274,3.7467382357139357132 ] 
dist 59=[-.07341972905579154543,4.1248991179931332799 ] 
dist 60=[1.7099745802126270994 ,4.4487858370765142419 ] 
dist 61=[1.5873950498025732048 ,4.6517769790296531022 ] 
dist 62=[1.4025842442809988780 ,4.8061237671744409178 ] 
dist 63=[1.2108418009377267670 ,4.9360174971870149405 ] 
dist 64=[1.0605668142206102514 ,5.0363650557085130500 ] 
dist 65=[.91182406312845446244,5.0727542758860967087 ] 
dist 66=[.72615756044350230112,5.0825843736041705808 ] 
dist 67=[.53074618124829068693,5.0765358440478624106 ] 
dist 68=[.3430732904865987207 ,4.9500189577068114882 ] 
dist 69=[.12488021898108259446,4.9097067793303956960 ] 
dist 70=[-.19241151927612006428,4.9606246535713397362 ] 
dist 71=[-.50787697759845953357,5.0552543761465418526 ] 
dist 72=[-.71878488725741372125,5.1315626308684755546 ] 
dist 73=[-.8937933857415806682 ,5.1710854067246785367 ] 
dist 74=[-1.0659205376200663530 ,5.1914744367343167857 ] 
dist 75=[-1.2233175289505639642 ,5.1913509794632920832 ] 
dist 76=[-1.8457198324722813949 ,3.9380685209095178380 ] 
dist 77=[-2.4881767298544031808 ,3.8972366690180989605 ] 
dist 78=[-3.0134757778126325804 ,3.8021763720973818670 ] 
dist 79=[-3.5167571230378074689 ,3.7687440514729913985 ] 
dist 80=[-3.9678551926939524571 ,2.2799894718582542221 ] 
dist 81=[-4.2848635904977981606 ,2.1290317283704941484 ] 
dist 82=[-4.5646886585487606274 ,1.7676883250859813614 ] 
dist 83=[-4.8673909425902534671 ,1.7073212308756881638 ] 
dist 84=[-5.1373353907555312427 ,1.1893178106852866501 ] 
dist 85=[-5.2863910484907355345 ,1.0923493657958144976 ] 
dist 86=[-5.3756641619197452867 ,.95717932674913583866] 
dist 87=[-5.4069165526143429447 ,.91669262570265780223] 
dist 88=[-5.4136497078706682357 ,.63519420648296369598] 
dist 89=[-5.4050402474262857384 ,.78273327971008621374] 
dist 90=[-5.3836259703856739039 ,.93432396051401890275] 
dist 91=[-5.3657859850829610488 ,1.0770152310987665688 ] 
dist 92=[-4.6287917204338927472 ,1.1890292448105723944 ] 
dist 93=[-4.5428526360632667098 ,1.3000858104051105249 ] 
dist 94=[-4.3092135838469172053 ,1.4389540693240251869 ] 
dist 95=[-4.2676686855794078068 ,1.9149620377356849141 ] 
dist 96=[-3.8249719501108481596 ,2.4012806991769373291 ] 
dist 97=[-3.7318560135291660607 ,2.7740294884844425522 ] 
dist 98=[-3.6238781567385322055 ,3.1350886742980546846 ] 
dist 99=[-3.5816871567541632834 ,3.5747628951675923465 ] 
dist 100=[-2.5528356389687163109 ,3.9886865453430886129 ] 
dist 101=[-2.4158468554354055173 ,4.2469683413772532523 ] 
dist 102=[-2.1326259399960710343 ,4.4408105744166740536 ] 
dist 103=[-2.0560907838724624884 ,4.5975270972620791818 ] 
dist 104=[-1.7635668836105228737 ,4.7185068949120909487 ] 
dist 105=[-1.7030096909795664081 ,4.7697120764578603038 ] 
dist 106=[-1.5793605957167004664 ,4.7898018544274405910 ] 
dist 107=[-1.5453087078391133288 ,4.7865483767321085284 ] 
dist 108=[-1.5851690147856703654 ,2.7996059640525658335 ] 
dist 109=[-1.6900911872391226696 ,2.8070536646716610342 ] 
dist 110=[-1.8188826044197866591 ,2.8058621137108362354 ] 
dist 111=[-1.9407970973771037356 ,2.4760432420500070491 ] 
dist 112=[-2.0182739250803112745 ,2.4255346068820993894 ] 
dist 113=[-2.0781384233480320197 ,2.3416267109083697522 ] 
dist 114=[-2.1297520493283997920 ,2.3173808991517191159 ] 
dist 115=[-2.1722511189838744985 ,2.2444769967329819183 ] 
dist 116=[-2.1971276723067922572 ,2.1896921987315943169 ] 
dist 117=[-2.2130285538573237796 ,2.1665865970980953452 ] 
dist 118=[-2.2152367514310761563 ,2.0201598215900737043 ] 
dist 119=[-.22622349047966541448,2.0374532642937024215 ] 
dist 120=[-.42908894614227882167,2.1340512816403791058 ] 
dist 121=[-.58163681946933336014,2.1892206101702406404 ] 
dist 122=[-.72651961857394565176,2.2247247986524164586 ] 
dist 123=[-.89880519319207558559,2.2428118450759007124 ] 
dist 124=[-1.0755267485285620848 ,2.2501106602990279064 ] 
dist 125=[-1.2381234165393814039 ,2.2483706442234421074 ] 
dist 126=[-1.4215430188595512333 ,2.2308303685697416964 ] 
dist 127=[-1.6813866714620956766 ,2.2216198533911037826 ] 
dist 128=[-1.9343233619648233837 ,-.76519588798305519705] 
dist 129=[-2.0901768868505849634 ,-.7474079085969849721 ] 
dist 130=[-2.2047949008025687259 ,-.69603650028121899204] 
dist 131=[-2.2931417794300312932 ,-.62700555816586408596] 
dist 132=[-2.3613021153333790122 ,-.53872858320098197562] 
dist 133=[-2.3953466899341080176 ,-.41942813180615639431] 
dist 134=[-2.4109293462682040944 ,-.22656711377226687857] 
dist 135=[-2.4120225817625257042 ,-.02908872514982578820] 
dist 136=[-2.2668657862273785627 ,.10864304200083431923] 
dist 137=[-2.3344359942916913369 ,.22901292582823676613] 
dist 138=[-2.3795353504984715718 ,.35719468024550640723] 
dist 139=[-2.4057931345312541840 ,.48062425185031012833] 
dist 140=[-2.4192158511300195733 ,.58202782530500883108] 
dist 141=[-2.4193948136721891087 ,.68674846383193602685] 
dist 142=[-2.4016716292927666673 ,.82342079153299736786] 
dist 143=[-2.3940130640425561022 ,.95667699248843442063] 
dist 144=[-1.8934075562034415773 ,1.0477634831866067459 ] 
dist 145=[-1.8465859376844374891 ,1.1254360575932020875 ] 
dist 146=[-1.7264148061765600938 ,1.2051518435973570402 ] 
dist 147=[-1.7032729507470742156 ,1.2801224316359230730 ] 
dist 148=[-1.4973304095432284998 ,1.3388562712979953228 ] 
dist 149=[-1.4550338909657799476 ,1.3969783502213586496 ] 
dist 150=[-1.3969708929703048554 ,1.5433182957982467094 ] 
dist 151=[-1.3774057182368074551 ,1.7156476969231403703 ] 
dist 152=[-.95523072100274927035,1.8740375644862497517 ] 
dist 153=[-.89886085706334127569,1.9661949681997306706 ] 
dist 154=[-.77586993200643603343,2.0275036999053220985 ] 
dist 155=[-.74378597983112280525,2.0627548658086584014 ] 
dist 156=[-.60013828146860629524,2.0857601730189382396 ] 
dist 157=[-.57332497539172473026,2.0981923114184985630 ] 
dist 158=[-.50794774468990241835,2.1052688295126036168 ] 
dist 159=[-.49664602318481996461,2.1069115836171929604 ] 
dist 160=[1.0615505940679027550 ,1.5463552234754537817 ] 
dist 161=[1.0232898086563070946 ,1.5343020172162478494 ] 
dist 162=[.91342939970375071265,1.5166487345739135150 ] 
dist 163=[.76117229879242975673,1.5222509474360839773 ] 
dist 164=[.60661586239281502492,1.5249764875742982587 ] 
dist 165=[.42069873358980922266,1.5261178048518379943 ] 
dist 166=[.14325896372060286804,1.5254001919004053580 ] 
dist 167=[-.13472403695158088761,1.3195687449465654154 ] 
dist 168=[-.32280946484325045296,1.2739734384660852739 ] 
dist 169=[-.48114081140939960669,1.1962167550504530513 ] 
dist 170=[-.64035391115755460299,1.1832277748968112704 ] 
dist 171=[-.78802359882549910052,1.0391394563260650170 ] 
dist 172=[-.90027630358406502069,1.0092417756744191030 ] 
dist 173=[-1.0081271048554242757 ,.97615084506029257402] 
dist 174=[-1.1382238744624074406 ,.96490182455923154891] 
dist 175=[-1.2600685792894045584 ,.67404445098430580401] 
dist 176=[-1.3349789828973089953 ,.59366011825437950319] 
dist 177=[-1.3898738453943825422 ,.50554299303637207248] 
dist 178=[-1.4318224911351214974 ,.48206949179782381488] 
dist 179=[-1.4629694986275330179 ,.39431234201983646652] 
dist 180=[-1.4747498955101466398 ,.37590981171907861848] 
dist 181=[-1.4782614818545666025 ,.34117540167425643317] 
dist 182=[-1.4764019077720100864 ,.33233848523530330464] 
dist 183=[-1.3996008576039757578 ,.06549545054214729863] 
dist 184=[-1.4099318403682015900 ,.19057676833611439868] 
dist 185=[-1.4430224367557169798 ,.29951213519953579722] 
dist 186=[-1.4904178836443072962 ,.41492927532128810232] 
dist 187=[-1.5263058888263618764 ,.52570989580782643586] 
dist 188=[-1.5520583455283209842 ,.61613804508501457324] 
dist 189=[-1.5589957148399700438 ,.70899656649014595074] 
dist 190=[-1.5590770573506706856 ,.82947674201189096663] 
dist 191=[-1.5574653682841248012 ,.94658152046588770438] 
dist 192=[-1.0611151864222943834 ,1.0259666860896325150 ] 
dist 193=[-.99383459661610540938,1.0929362154646788590 ] 
dist 194=[-.97565572040863445752,1.1604839049976007037 ] 
dist 195=[-.90845410846739846466,1.2232406937806390724 ] 
dist 196=[-.89180895682050368776,1.2710866310512725368 ] 
dist 197=[-.86244683823505885524,1.3171752237862846897 ] 
dist 198=[-.8543458310082634674 ,1.3729155487498774170 ] 
dist 199=[-.43165578114169341313,1.4229810775371215532 ] 
dist 200=[-.56543742462057499265,1.4464189863590672148 ] 
dist 201=[-.67805790359868508128,1.4578972237164867378 ] 
dist 202=[-.79128444097469896432,1.4602301216785690913 ] 
dist 203=[-.89626765592333987304,1.4308820377735241307 ] 
dist 204=[-.97598451836401607925,1.4472022125695604594 ] 
dist 205=[-1.0524803553619586816 ,1.4546980335280493865 ] 
dist 206=[-1.1446061593242087047 ,1.4549366453468906643 ] 
dist 207=[-1.2307952876004494037 ,1.4515177818895813494 ] 
dist 208=[-1.2835945550221444000 ,1.3486910623560262220 ] 
dist 209=[-1.3220550635837774708 ,1.3317418507726184308 ] 
dist 210=[-1.3510107532877519744 ,1.3631035829265415160 ] 
dist 211=[-1.3716404106916346818 ,1.3858787165409920030 ] 
dist 212=[-1.3768670460230546829 ,1.3933890676383670989 ] 
dist 213=[-1.3761768735039568437 ,1.3940923123535614339 ] 
dist 214=[-1.3731922029444394142 ,1.3904176369638262705 ] 
dist 215=[-1.3258011985555061025 ,1.0995193009024630795 ] 
dist 216=[-1.3149775637985249212 ,.78638462250325875295] 
dist 217=[-1.2792881061798134531 ,.74483170654865349453] 
dist 218=[-1.2718263384808512026 ,.66165683261180086797] 
dist 219=[-1.1809930751837391050 ,.63963719750328762938] 
dist 220=[-1.1599104246478400662 ,.55901530608756450487] 
dist 221=[-1.1321976998917556423 ,.54096189438700528698] 
dist 222=[-1.0486185008093317419 ,.51025939727915969769] 
dist 223=[-.98688556931807608146,.50231420246840464392] 
dist 224=[-1.0569732835424638600 ,-.42974701326461565456] 
dist 225=[-1.1149504246032014034 ,-.38986596333881968136] 
dist 226=[-1.1715852694184201025 ,-.31114744343354574749] 
dist 227=[-1.2230444574112955327 ,-.21809798079971156081] 
dist 228=[-1.2603624790676980228 ,-.11379004914643024853] 
dist 229=[-1.2944812778427913676 ,.01878113395354523905] 
dist 230=[-1.3331704135070341430 ,.22464486021760133982] 
dist 231=[-1.3666889728577666278 ,.43237338219583562033] 
dist 232=[-1.3801689650915277426 ,.57238811373795938048] 
dist 233=[-1.3851345617005472732 ,.68965593970099595121] 
dist 234=[-1.3846674052809785761 ,.80658933117311747838] 
dist 235=[-1.3488500514689687602 ,.91439921972005593375] 
dist 236=[-1.3285442826700690712 ,.99525029120345605546] 
dist 237=[-1.3197113171211407257 ,1.0718633918805144636 ] 
dist 238=[-1.3122615816546473472 ,1.1627574140054924551 ] 
dist 239=[-1.0773154639448148201 ,1.2471105495951307431 ] 
dist 240=[-1.0437012344624121029 ,1.2976154609502991010 ] 
dist 241=[-.97880400515113109738,1.3330119994482239135 ] 
dist 242=[-.96122884147944742061,1.3570593604455987685 ] 
dist 243=[-.89610732671242408191,1.3727676061125020486 ] 
dist 244=[-.87991190361877379103,1.3755471985623589487 ] 
dist 245=[-.85113137901272890943,1.3721407446976728174 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 1, 0, 1, 1, 2] 
dist 0=[59.913238057883724816  ,59.913238057883724816  ] 
dist 1=[59.790451685927027074  ,59.929240018420035334  ] 
dist 2=[59.464110709282236730  ,59.913238057883724816  ] 
dist 3=[58.757148913932790165  ,59.773621548645399208  ] 
dist 4=[57.384962951687082414  ,59.514163529453679524  ] 
dist 5=[55.832248103309770707  ,59.431946850482450805  ] 
dist 6=[54.129054852206541094  ,59.398185475548326045  ] 
dist 7=[52.640519995059177428  ,58.617595650676864953  ] 
dist 8=[50.497449120894538226  ,53.918844052363943674  ] 
dist 9=[47.935606382278645132  ,52.928536818563790336  ] 
dist 10=[45.249661249094478759  ,52.376274963610423151  ] 
dist 11=[41.951363872277769105  ,51.727494330433611523  ] 
dist 12=[36.943743744164696803  ,51.515017601757840430  ] 
dist 13=[31.901074042047080264  ,50.634972978438684214  ] 
dist 14=[28.462810895535982105  ,50.299495548949524958  ] 
dist 15=[25.532912110394066819  ,48.057351610319363359  ] 
dist 16=[22.520756902570564524  ,34.544322586786639038  ] 
dist 17=[19.677729572796231656  ,34.000704271896413202  ] 
dist 18=[16.427366502171725293  ,32.133542731719025732  ] 
dist 19=[12.987995041480563719  ,31.682849696546005761  ] 
dist 20=[9.8017287421172063050 ,31.184042655155517637  ] 
dist 21=[7.3726244658034358800 ,31.025677441156890839  ] 
dist 22=[5.0259563993089259392 ,10.136122137407772255  ] 
dist 23=[2.1683146975447725457 ,8.4296241501545952178 ] 
dist 24=[-.53651433290743442641,6.4536431028523822088 ] 
dist 25=[-2.2732139240996692667 ,4.6103513380429902354 ] 
dist 26=[-3.6403131561966299924 ,4.2848854327658905584 ] 
dist 27=[-4.8910872397447605797 ,3.7840445849055701637 ] 
dist 28=[-6.8154429423413566176 ,3.6846693100374092419 ] 
dist 29=[-9.1310850688398374016 ,-.89325475640230015003] 
dist 30=[-11.306675745101626491  ,-1.2542300031672350648 ] 
dist 31=[-12.671669894890304304  ,-2.3009548756582652964 ] 
dist 32=[-13.708183574047893746  ,-4.0806623144155703689 ] 
dist 33=[-14.571816004068538037  ,-5.1481922889848037004 ] 
dist 34=[-15.261483443821428758  ,-5.3062204420281645458 ] 
dist 35=[-15.603215440748708840  ,-5.5917571195418922764 ] 
dist 36=[-15.775808525706227655  ,-5.6397527890462459429 ] 
dist 37=[-15.794255832427008810  ,-5.7608547225511242748 ] 
dist 38=[-7.9689248505597382299 ,-5.1621914110179788295 ] 
dist 39=[-7.9227011870415427012 ,-4.1159442931288295658 ] 
dist 40=[-6.5938160682745516982 ,-3.1778870700226695044 ] 
dist 41=[-6.4007021470119922560 ,-2.1453692170446932896 ] 
dist 42=[-6.3026108091953167166 ,-1.1334920718441900131 ] 
dist 43=[-6.2599221280813782046 ,-.2775123721706910831 ] 
dist 44=[-6.2337509883394583803 ,.6271571412317604858 ] 
dist 45=[-5.0993894907701445929 ,1.8335995898666730007 ] 
dist 46=[-4.8240230573191123857 ,3.0200227856309412334 ] 
dist 47=[-4.7405443591270204550 ,3.8449431030865787384 ] 
dist 48=[-2.4879628770861066315 ,4.5627519394480953090 ] 
dist 49=[-1.6310244619916643825 ,5.3218917006935974310 ] 
dist 50=[-1.4750644078137314741 ,6.0497204456446399791 ] 
dist 51=[-1.2862577890213051014 ,6.6427094109833312207 ] 
dist 52=[-1.2504290798632762758 ,7.3912571540447777527 ] 
dist 53=[-.01588821367754623408,8.0400955548488735332 ] 
dist 54=[.13095301832976064107,8.7841332943144152544 ] 
dist 55=[.44325482544105296224,9.2125835608242289778 ] 
dist 56=[.50824225807028479527,9.4926502484828467912 ] 
dist 57=[.81385735843842779945,9.6443106033600255256 ] 
dist 58=[.86632036633560732013,9.7421481239111377374 ] 
dist 59=[.95288194685587161464,9.7641997960014085880 ] 
dist 60=[.96992142470759791394,9.6343925931570294112 ] 
dist 61=[1.1206543969024313798 ,9.3532701491295298872 ] 
dist 62=[.8454545227367441333 ,7.6996410823074357351 ] 
dist 63=[0                     ,7.0133609178276932393 ] 
dist 64=[.3602460471569547286 ,4.1247285279432779312 ] 
dist 65=[.0244385150339366623 ,4.1126455744740014089 ] 
dist 66=[-.3404880977074374659 ,4.0117168191980344695 ] 
dist 67=[-.7069758704651073795 ,3.9803200405982397803 ] 
dist 68=[-1.1448417866596951963 ,3.9312569946595939675 ] 
dist 69=[-1.7947665175183884154 ,3.9120041521371231577 ] 
dist 70=[-2.4384448069893562702 ,2.2129237263922516880 ] 
dist 71=[-2.8514127836037836667 ,2.1918484260685085658 ] 
dist 72=[-3.1747014168191825835 ,2.1826272535310633118 ] 
dist 73=[-3.4604352477712198610 ,2.1310573658992903829 ] 
dist 74=[-3.7004762515212604612 ,2.1179221478300406211 ] 
dist 75=[-3.8413986773183157255 ,2.0740128872216321285 ] 
dist 76=[-3.9369440684853476440 ,2.0651598931078313841 ] 
dist 77=[-3.9959023331342092954 ,1.2477248507397403387 ] 
dist 78=[-4.0346617813837088687 ,1.1684876959672653278 ] 
dist 79=[-4.0495742119602788519 ,.97857804298247141172] 
dist 80=[-4.0689500726959335984 ,.94627076853567242158] 
dist 81=[-4.1278240272435814856 ,.6716348429710082994 ] 
dist 82=[-4.1757418450898092071 ,.6197683754790374527 ] 
dist 83=[-4.2011697424253275023 ,.5468789469347768390 ] 
dist 84=[-4.2150863061591031616 ,.5250148792403128327 ] 
dist 85=[-4.2170522212980237840 ,.1898180075749323958 ] 
dist 86=[-1.9389832138996819165 ,.1763400858618330374 ] 
dist 87=[-1.9698433303067572164 ,.1755124206448852110 ] 
dist 88=[-1.9997479243989322410 ,.59263404823604597547] 
dist 89=[-2.0213947404590252833 ,1.0037466892145036954 ] 
dist 90=[-2.0278921514880119323 ,1.3793680294436690115 ] 
dist 91=[-2.0258857090287860517 ,1.6549667772729875194 ] 
dist 92=[-2.0217730707694016470 ,1.9100060949985153426 ] 
dist 93=[-1.3955814255723229324 ,2.2035474333343766244 ] 
dist 94=[-1.3946529820016320163 ,2.4767917294491321716 ] 
dist 95=[-1.3798360231609814095 ,2.6508249609834392193 ] 
dist 96=[-1.3773557231175076927 ,2.7854353191199710324 ] 
dist 97=[-1.3076989602987899956 ,2.9013687131415431315 ] 
dist 98=[-1.2901912407971138720 ,2.9964067739553888933 ] 
dist 99=[-1.2789052650807590905 ,3.0476418406243774793 ] 
dist 100=[-1.2752227198723176457 ,3.0766420467415924387 ] 
dist 101=[-.99483340746077329118,3.0829685097531232956 ] 
dist 102=[-.95719581016343865851,2.1336972789704084520 ] 
dist 103=[-.8859172940254616794 ,2.2190632513210591468 ] 
dist 104=[-.86755648695488558026,2.2726826606379724982 ] 
dist 105=[-.80484958847342053245,2.2972331444439236734 ] 
dist 106=[-.78854991218901895872,2.3099960478908259997 ] 
dist 107=[-.77199269756563179972,2.3165428872011383318 ] 
dist 108=[-.76608013546125405104,2.3198618494543525417 ] 
dist 109=[.07812801627112888525,2.3197074182746036337 ] 
dist 110=[.14720608950644733508,1.9932816644073880514 ] 
dist 111=[.29612581267982657786,1.9458276112390035114 ] 
dist 112=[.32650967036460155406,1.8631079306086618244 ] 
dist 113=[.4810475848197787866 ,1.8412752532377206371 ] 
dist 114=[.50692143839881039713,1.7716637277819308860 ] 
dist 115=[.55814357937056654452,1.7489786177288789628 ] 
dist 116=[.56904734580974835088,1.7336724273052998369 ] 
dist 117=[.50854945171222641664,1.7272882662106738013 ] 
dist 118=[.1290512977853314975 ,1.0648408023826617750 ] 
dist 119=[-.12916630040514535732,1.1119410767516353191 ] 
dist 120=[-.34808834434287678514,1.1513269674614839308 ] 
dist 121=[-.57073523133088442932,1.1827779424353061007 ] 
dist 122=[-.77883849426351849604,1.1982019208149582417 ] 
dist 123=[-.9397089257925573836 ,1.2048538105371152764 ] 
dist 124=[-1.0968574343582728808 ,1.2053119737790335062 ] 
dist 125=[-1.2901055946495696088 ,-.00993154448178411130] 
dist 126=[-1.4729966388707055717 ,-.06736181877360328232] 
dist 127=[-1.5888035920631307335 ,-.19036826714989955692] 
dist 128=[-1.6776949448949750436 ,-.21655837754081635585] 
dist 129=[-1.7531481328148384345 ,-.34122762591794029306] 
dist 130=[-1.8142247885290825397 ,-.36154220045543203722] 
dist 131=[-1.8457300401744595127 ,-.3940217217028306787 ] 
dist 132=[-1.8616204445318594416 ,-.40078976063550675943] 
dist 133=[-1.8635707336586207860 ,-.40299041315329249887] 
dist 134=[-.82530392976177084421,-.20886291812040850863] 
dist 135=[-.87261838487026956311,-.05920365827743148098] 
dist 136=[-.91611925638505292869,.07087239236499215296] 
dist 137=[-.95475453095086144692,.20819650044698010125] 
dist 138=[-.98117851080176455866,.33965477722475107491] 
dist 139=[-1.0033390433509711820 ,.44632733457648173749] 
dist 140=[-1.0255216011171150288 ,.55528417833726793939] 
dist 141=[-1.0432981666387277228 ,.6958708378003090773 ] 
dist 142=[-1.0478718667458129368 ,.8332277697526609128 ] 
dist 143=[-1.0479249675554851782 ,.92563058407347675468] 
dist 144=[-1.0476477355264054000 ,1.0024954730024096155 ] 
dist 145=[-1.0076401046414964334 ,1.0783096007824419799 ] 
dist 146=[-.99715874466626153743,1.1485975699535839275 ] 
dist 147=[-.99077533309462408247,1.2019429935329823422 ] 
dist 148=[-.98832326249105211951,1.2527593674710241943 ] 
dist 149=[-.77989071919886661407,1.3135306637193113405 ] 
dist 150=[-.75148840631370542715,1.3682095946714011969 ] 
dist 151=[-.69830713154346345286,1.3947100415160490106 ] 
dist 152=[-.68457529447292104011,1.4083587768121009697 ] 
dist 153=[-.63785955970486682972,1.4117113621896112116 ] 
dist 154=[-.72813558398810246509,1.3871382659385375934 ] 
dist 155=[-.80183693726227208092,1.3808237013617387750 ] 
dist 156=[-.87399270682980271571,1.3771037799731833214 ] 
dist 157=[-.96285740290307896988,1.3759777863859913857 ] 
dist 158=[-1.0468903916596159701 ,1.1221210141665564207 ] 
dist 159=[-1.0997643316889809350 ,1.0870148365959693659 ] 
dist 160=[-1.1399133175734582260 ,1.0231062936229071437 ] 
dist 161=[-1.1731646378861803811 ,1.0067437312718283356 ] 
dist 162=[-1.1994159008940787341 ,.95283286124499460652] 
dist 163=[-1.2116295495818902939 ,.93706325613671028195] 
dist 164=[-1.2158918455646278324 ,.92554324383594469531] 
dist 165=[-1.2152265185301586588 ,.92238059566265169448] 
dist 166=[-.11082951648628502839,.90093477692645237336] 
dist 167=[-.26947811262034035486,.93934971037529409919] 
dist 168=[-.40343091734480036989,.97139613508425937516] 
dist 169=[-.53875940300878368095,.99691359195386566214] 
dist 170=[-.66466732647194389206,1.0092680877876336099 ] 
dist 171=[-.76101935156379782859,1.0143552207257770339 ] 
dist 172=[-.85421212667308119857,1.0144971839853207179 ] 
dist 173=[-.96751277854156784951,1.0030660386736265021 ] 
dist 174=[-1.0740992608728569297 ,.99898174717517631959] 
dist 175=[-1.1404933379919131719 ,.98001378699450947251] 
dist 176=[-1.1901935592568638818 ,.97692326761655828068] 
dist 177=[-1.2301463444772942633 ,.91529034725272569911] 
dist 178=[-1.2608117892276765537 ,.90262444341673478832] 
dist 179=[-1.2734427967579467851 ,.89162262349546454681] 
dist 180=[-1.2779861287498871845 ,.88581359151886414435] 
dist 181=[-1.2763607361000191150 ,.69125122000317510743] 
dist 182=[-1.2452093146096343592 ,.66441134529896540046] 
dist 183=[-1.2372361295852731304 ,.61173220341861586947] 
dist 184=[-1.2082581825865017554 ,.59762747971213485026] 
dist 185=[-1.2024928899195629775 ,.54571302382854697279] 
dist 186=[-1.1226997872634535210 ,.53338906719095725097] 
dist 187=[-1.1060348843722954402 ,.57590300291557574636] 
dist 188=[-1.0879155222171106479 ,.66357398860752248785] 
dist 189=[-1.0788177458578943809 ,.7746959257267655165 ] 
dist 190=[-.98464403057648358262,.88147488285504919538] 
dist 191=[-.97992702916271814159,.95181310038301877388] 
dist 192=[-.97933132149003671347,1.0089478260603500904 ] 
dist 193=[-.94458606719120218916,1.0630284542046570927 ] 
dist 194=[-.93488432307338881485,1.1110364231696057782 ] 
dist 195=[-.92843409980154119292,1.1439351555731051042 ] 
dist 196=[-.92473463022282417896,1.1720921307466569040 ] 
dist 197=[-.90417222564553826619,1.2011789232472036549 ] 
dist 198=[-.94705868150420661548,1.2251084063448281045 ] 
dist 199=[-.97781986271928764898,1.2326805200534079246 ] 
dist 200=[-1.0000829075587710259 ,1.2405392260430479220 ] 
dist 201=[-1.0156431664597495745 ,1.2415937267360673096 ] 
dist 202=[-1.0196505563243888649 ,1.2164249305096690760 ] 
dist 203=[-1.0193013253528565031 ,1.2086827170636052810 ] 
dist 204=[-1.0174718706645332762 ,1.2029379061146963765 ] 
dist 205=[-.98891266909396349459,1.1984213700163722057 ] 
dist 206=[-.98376186393280110249,1.1866157163545057439 ] 
dist 207=[-.9621125715221341555 ,1.2323538232053079776 ] 
dist 208=[-.95891546858639823506,1.2625322410405180984 ] 
dist 209=[-.89236837333798295521,1.2793699249462148495 ] 
dist 210=[-.87673127018228819969,1.2892596212191621234 ] 
dist 211=[-.86565978140291506302,1.2917059070600226082 ] 
dist 212=[-.86292868050291315727,1.2891664968270410693 ] 
dist 213=[-.63334248935468300908,1.2862312546689053145 ] 
dist 214=[-.60303117363963350127,1.1790292430709767420 ] 
dist 215=[-.54527725730603396497,1.1644839317205034193 ] 
dist 216=[-.53050055362581538455,1.1192672680126650000 ] 
dist 217=[-.54754251069073961549,1.1125691760458457488 ] 
dist 218=[-.65947651467257575828,1.0088517855764943491 ] 
dist 219=[-.74515764909252924538,.99053039418411638114] 
dist 220=[-.82804559833802916607,.98977407832375089579] 
dist 221=[-.92882877493041765237,.96251350138962475138] 
dist 222=[-1.0236144826025563862 ,.6668036756097342233 ] 
dist 223=[-1.0825622082739176235 ,.6283257119942904359 ] 
dist 224=[-1.1265585631176620304 ,.55363044506012933761] 
dist 225=[-1.1616637849849514013 ,.53446787893142616386] 
dist 226=[-1.1883657176569992621 ,.46846385528075180279] 
dist 227=[-1.1988184427596515226 ,.45252975911106369376] 
dist 228=[-1.2039310640697818834 ,.4353985485910896299 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 0, 1, 0, 0, 2] 
dist 0=[49.607989467186813282  ,49.607989467186813282  ] 
dist 1=[48.908555056493690031  ,50.029991531094260765  ] 
dist 2=[48.018363135070859145  ,50.330539352725954058  ] 
dist 3=[46.834422890143870262  ,50.544669828093830427  ] 
dist 4=[45.205116850394378029  ,50.689282327014301424  ] 
dist 5=[42.536190273590539268  ,50.712054878075140400  ] 
dist 6=[39.784310403605910828  ,50.649208989318073209  ] 
dist 7=[37.823659526483878490  ,50.595843034192041744  ] 
dist 8=[36.061853125320073012  ,50.223658224092915770  ] 
dist 9=[34.104012082928167174  ,50.066011769578163114  ] 
dist 10=[32.163014523063136162  ,49.849191066153189798  ] 
dist 11=[30.468328760923921977  ,49.740024815431421756  ] 
dist 12=[28.624064072091589662  ,49.337135186145097014  ] 
dist 13=[26.085337786130467787  ,49.190853482326537313  ] 
dist 14=[23.535222817795048250  ,48.823965818434341546  ] 
dist 15=[21.645306322122348452  ,48.223885972107973415  ] 
dist 16=[19.870318004853801755  ,35.736270098493826445  ] 
dist 17=[17.779040962118454185  ,34.577060458358991744  ] 
dist 18=[15.634347992058706783  ,31.745740710850314051  ] 
dist 19=[13.645675071573775907  ,31.330610983571279536  ] 
dist 20=[11.381722144395706540  ,27.108099301183462230  ] 
dist 21=[8.1367233690296535246 ,26.314952180366673879  ] 
dist 22=[4.9323826001590639869 ,25.408075812697120702  ] 
dist 23=[2.8307617579203779664 ,25.223089813472344024  ] 
dist 24=[1.1248973010812538685 ,18.166012682993947277  ] 
dist 25=[-.49812166291356380989,17.288867093578699372  ] 
dist 26=[-1.9531874159944826866 ,15.511833873442310970  ] 
dist 27=[-2.9880667752925993253 ,15.057118455723523666  ] 
dist 28=[-5.5375807722143778705 ,13.447389723396638155  ] 
dist 29=[-8.0834018061939797395 ,13.112608745263443876  ] 
dist 30=[-9.6818298879769104398 ,12.630207294629023509  ] 
dist 31=[-10.901956710122591495  ,12.495932066656282654  ] 
dist 32=[-11.935958859161334970  ,1.6423350607012271546 ] 
dist 33=[-12.780265907836131986  ,.7421849148846226789 ] 
dist 34=[-13.242501026441943929  ,-1.2257788816828330196 ] 
dist 35=[-13.518390185112466942  ,-1.5854689810502816270 ] 
dist 36=[-13.618566330366121441  ,-3.7441339669191510558 ] 
dist 37=[-13.647582908116831434  ,-4.0977821976330441953 ] 
dist 38=[-13.639050931637952269  ,-3.4786090709603524942 ] 
dist 39=[-13.604470863002297153  ,-2.8557899781014099413 ] 
dist 40=[-13.555877862578275624  ,-2.2866268562615360938 ] 
dist 41=[-13.434520101973501547  ,-1.6437957758657178569 ] 
dist 42=[-13.365888086238013138  ,-1.0042620203018413434 ] 
dist 43=[-13.207811314843672171  ,-.4480943356647781503 ] 
dist 44=[-13.136706482561165883  ,.1528054141287183086 ] 
dist 45=[-12.425603914352933076  ,.9709705832450823194 ] 
dist 46=[-12.468950375904152156  ,1.7830016405770584147 ] 
dist 47=[-12.461871146633112054  ,2.3594791414471115407 ] 
dist 48=[-3.5354182423856079309 ,2.8733925877551456627 ] 
dist 49=[-2.8768888547849707980 ,3.4358036452195558775 ] 
dist 50=[-1.8294588895878366964 ,3.9859453166268292970 ] 
dist 51=[-1.6387938558781818737 ,4.4509138915692438804 ] 
dist 52=[-1.3138107705440048562 ,5.4037680767319427597 ] 
dist 53=[-1.2810200196220629568 ,6.3219988738934193164 ] 
dist 54=[.2400275886592608785 ,6.8959905650788070283 ] 
dist 55=[.3275499204723386787 ,7.3279386840468177619 ] 
dist 56=[1.2723352958822174769 ,7.6792264044017033257 ] 
dist 57=[1.4085761215801316076 ,7.9520236509967116176 ] 
dist 58=[1.5528430822808051407 ,8.0706945601883355923 ] 
dist 59=[1.5372869595057132154 ,8.1239795002178149629 ] 
dist 60=[1.4551407308938649962 ,8.1357248463742124318 ] 
dist 61=[1.2811914689036612382 ,4.7994500122176287380 ] 
dist 62=[.9512005320024164794 ,5.0295311121251735086 ] 
dist 63=[.2658210721358575303 ,5.2868091733984955429 ] 
dist 64=[-.4351814903045413589 ,5.5153837778375782877 ] 
dist 65=[-.9152542414430488979 ,5.6308967319419145138 ] 
dist 66=[-1.3244439103696049118 ,5.6898854774445497327 ] 
dist 67=[-1.7427006373509024918 ,5.6990555607441653543 ] 
dist 68=[-2.1337337382769023969 ,5.6462947511065076286 ] 
dist 69=[-2.4343241218553758931 ,5.6179816907798050816 ] 
dist 70=[-2.7255998960095144004 ,5.5863827258476965598 ] 
dist 71=[-3.0794592086701285516 ,5.5615995408880738284 ] 
dist 72=[-3.4106141570216237849 ,4.7693269495271423108 ] 
dist 73=[-3.6113025110332626700 ,4.6523835549646763169 ] 
dist 74=[-3.7543404229681466136 ,4.4148795508500254970 ] 
dist 75=[-3.8554883628656501834 ,4.3468334431063962296 ] 
dist 76=[-3.9269082306710601326 ,4.0711072470646578562 ] 
dist 77=[-3.9513664687457057068 ,4.0089386284800629698 ] 
dist 78=[-3.9528720493475990397 ,3.8629689355706085740 ] 
dist 79=[-3.9422301797815892198 ,3.8141448378218254696 ] 
dist 80=[-2.5369467030507276691 ,1.1235682849511653922 ] 
dist 81=[-2.6742304494325913644 ,1.1477959990263902426 ] 
dist 82=[-2.7464575575812781935 ,1.1760171132649719095 ] 
dist 83=[-2.7866202582720124766 ,1.2122779440867303345 ] 
dist 84=[-2.7958609456619133085 ,1.2685682674976089926 ] 
dist 85=[-2.7717300236197979342 ,1.3268982083746352783 ] 
dist 86=[-2.7621525130250974824 ,1.3713009908195256740 ] 
dist 87=[-2.7521210184887059673 ,1.4137003936578678689 ] 
dist 88=[-2.7399009885565488186 ,1.4640638973867441230 ] 
dist 89=[-2.7252000648215265649 ,1.5153063152940055478 ] 
dist 90=[-2.7120750132237254829 ,1.5612140730805127078 ] 
dist 91=[-2.6970807109651199880 ,1.6117254438605763238 ] 
dist 92=[-2.6856967611374942123 ,1.6813133262767511788 ] 
dist 93=[-2.6004105818873573494 ,1.7459118166364918497 ] 
dist 94=[-2.6050818357124660220 ,1.7765186049523870817 ] 
dist 95=[-2.5992684282615816532 ,1.7907544088521938547 ] 
dist 96=[-2.4534796081432786060 ,1.7905509007387209665 ] 
dist 97=[-2.4273011182226893274 ,1.7566654545714944277 ] 
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