8 phat 1 dirichlet min maxes function [0, 1, 0, 1, 2, 2, 0, 2] 
dist 0=[3.6662870895019277789 ,3.6662870895019277789 ] 
dist 1=[3.6624116094839698118 ,3.6705330345524536332 ] 
dist 2=[3.6579847975656627067 ,3.6764416569217440805 ] 
dist 3=[3.6534982123574186233 ,3.6823093111793103902 ] 
dist 4=[3.6493836305384502235 ,3.6863913865548849530 ] 
dist 5=[3.6447192206120261999 ,3.6899801064222137114 ] 
dist 6=[3.6380333467356391411 ,3.6938743966407618361 ] 
dist 7=[3.6311453653125951327 ,3.6977056251057523585 ] 
dist 8=[3.6256725301475617598 ,3.7010421149101547810 ] 
dist 9=[3.6201432251900446970 ,3.7046828597167199082 ] 
dist 10=[3.6130293556791381930 ,3.7097311010406553571 ] 
dist 11=[3.6053690605168376373 ,3.7148588918896248262 ] 
dist 12=[3.5976540764375442583 ,3.7188178381351854766 ] 
dist 13=[3.5883564026141337770 ,3.7227111946473506732 ] 
dist 14=[3.5743654278376018977 ,3.7275766437258624891 ] 
dist 15=[3.5600129157571404952 ,3.7327438865855599674 ] 
dist 16=[3.5492691165870755325 ,3.7378444112719435036 ] 
dist 17=[3.5390235145926851759 ,3.7439158722826942363 ] 
dist 18=[3.5266637834500162244 ,3.7529668224253449639 ] 
dist 19=[3.5137664627143854114 ,3.7619466547856578702 ] 
dist 20=[3.5013705504222444263 ,3.7677336526729036052 ] 
dist 21=[3.4868639125415339685 ,3.7723364009172014456 ] 
dist 22=[3.4655238414163552631 ,3.7765792967337838798 ] 
dist 23=[3.4433042480309895941 ,3.7803072455443649288 ] 
dist 24=[3.4252795875223451047 ,3.7828502367127558573 ] 
dist 25=[3.4067274178799454908 ,3.7850327912441532659 ] 
dist 26=[3.3823978352041072179 ,3.7873190243108432187 ] 
dist 27=[3.3559689354860362058 ,3.7893631912465886720 ] 
dist 28=[3.3290196486932459477 ,3.7905774934158613782 ] 
dist 29=[3.2963006749872226017 ,3.7914260946367142036 ] 
dist 30=[3.2467934333623357072 ,3.7920074634554251978 ] 
dist 31=[3.1970426551937517412 ,3.7923842760789993138 ] 
dist 32=[3.1633495554087774753 ,3.7924593213554940319 ] 
dist 33=[3.1346956333833051014 ,3.7923401979389320344 ] 
dist 34=[3.1051012207849904579 ,3.7922976096487698878 ] 
dist 35=[3.0768760179389489131 ,3.7824178173046002491 ] 
dist 36=[3.0536988441458756322 ,3.7813627870413204255 ] 
dist 37=[3.0295896679741686580 ,3.7791516775052273405 ] 
dist 38=[2.9976365287888270780 ,3.7785047926912398360 ] 
dist 39=[2.9658348127967406372 ,3.7757465354715808508 ] 
dist 40=[2.9423313230445343142 ,3.7751800145585679397 ] 
dist 41=[2.9202140734835014119 ,3.7735485503281937662 ] 
dist 42=[2.8939572260221833690 ,3.7733056882919075077 ] 
dist 43=[2.8667852795615749024 ,3.7696918598103267643 ] 
dist 44=[2.8410077057288590191 ,3.7690268043570858107 ] 
dist 45=[2.8110989533280973941 ,3.7674660182124864285 ] 
dist 46=[2.7674025999736948775 ,3.7669763820759787623 ] 
dist 47=[2.7234647017078932124 ,3.7645048004342117583 ] 
dist 48=[2.6925897903263976854 ,3.7639455856029919763 ] 
dist 49=[2.6651215261011610514 ,3.7627942599252312320 ] 
dist 50=[2.6348099710670799747 ,3.7624298126095594580 ] 
dist 51=[2.6046893968625750471 ,3.6011873470463502296 ] 
dist 52=[2.5779850461771861503 ,3.5931546502812328411 ] 
dist 53=[2.5484469419326730290 ,3.5745204168135338619 ] 
dist 54=[2.5069915695530681334 ,3.5715075492722461816 ] 
dist 55=[2.4646627208794056097 ,3.5466385655631358031 ] 
dist 56=[2.4316307795690510380 ,3.5420963360671088589 ] 
dist 57=[2.3988125034815331100 ,3.5357651495181034291 ] 
dist 58=[2.3573383039386879617 ,3.5339250749494666640 ] 
dist 59=[2.3130543972620258516 ,3.4998299138497271908 ] 
dist 60=[2.2689975065973809849 ,3.4954113703899598190 ] 
dist 61=[2.2162988990802967350 ,3.4860300892233283428 ] 
dist 62=[2.1374487785345488026 ,3.4836454538252203697 ] 
dist 63=[2.0582655896935677807 ,3.4734637260038126764 ] 
dist 64=[2.0042347352051549711 ,3.4715970645834132366 ] 
dist 65=[1.9578465237291609548 ,3.4669623926953649252 ] 
dist 66=[1.9092333320142934322 ,3.4662933695212236443 ] 
dist 67=[1.8624312977174312911 ,3.4155750087099383430 ] 
dist 68=[1.8232875805256279570 ,3.4107800694466463072 ] 
dist 69=[1.7819340156481086652 ,3.3995884563247764713 ] 
dist 70=[1.7262927594276552944 ,3.3977514452184639819 ] 
dist 71=[1.6705290490026293526 ,3.3825032215450547888 ] 
dist 72=[1.6286856775328720642 ,3.3796781363157836046 ] 
dist 73=[1.5886848422644408250 ,3.3757636776091720272 ] 
dist 74=[1.5402911384989352806 ,3.3745978716188831391 ] 
dist 75=[1.4897191703250058044 ,3.3523842091305816744 ] 
dist 76=[1.4410054434655284416 ,3.3494677230869947596 ] 
dist 77=[1.3839152173780616424 ,3.3433320548417081633 ] 
dist 78=[1.2998378884927103701 ,3.3416638634831782321 ] 
dist 79=[1.2150192350433122649 ,3.3350906418778490568 ] 
dist 80=[1.1549637672051687869 ,3.3338327431907271797 ] 
dist 81=[1.1010611074254456704 ,3.3307351263199254514 ] 
dist 82=[1.0408532195008162923 ,3.3301977058576763436 ] 
dist 83=[.98060103478078614362,3.2472953856177086308 ] 
dist 84=[.92652119116881024589,3.2412889177707860241 ] 
dist 85=[.86615566585866885403,3.2270820788499543052 ] 
dist 86=[.78076123110146875041,3.2249884744489611103 ] 
dist 87=[.69327233618532589709,3.2051989660160085198 ] 
dist 88=[.62452912890752250461,3.2015568642403460691 ] 
dist 89=[.55578901617764736172,3.1972227219319595403 ] 
dist 90=[.4683124986322838435 ,3.1963056535518082414 ] 
dist 91=[.37460086368961117331,3.1658041933985555898 ] 
dist 92=[.28092075367666535976,3.1619489751899593573 ] 
dist 93=[.16853455841315831557,3.1543155290465351427 ] 
dist 94=[0                     ,3.1523709126918045634 ] 
dist 95=[1.4550996546376402610 ,3.1455532753971242951 ] 
dist 96=[1.4148007064728945897 ,3.1440667915620465971 ] 
dist 97=[1.3743660934417331524 ,3.1418949858733632339 ] 
dist 98=[1.3460994219254053044 ,3.1412626046337488977 ] 
dist 99=[1.3211050737043247216 ,3.0828689013650652776 ] 
dist 100=[1.2937594417464225443 ,3.0778093187963140660 ] 
dist 101=[1.2667245488533840024 ,3.0666684317744271377 ] 
dist 102=[1.2429731272540799739 ,3.0642888048927088568 ] 
dist 103=[1.2168814513685564334 ,3.0510463242358701049 ] 
dist 104=[1.1804857645394693279 ,3.0486297013503589373 ] 
dist 105=[1.1434219753265999523 ,3.0437426330564220772 ] 
dist 106=[1.1146579536282325282 ,3.0424534508940258713 ] 
dist 107=[1.0862301976700860849 ,3.0293840531603668666 ] 
dist 108=[1.0505114393457387900 ,3.0274009906884480247 ] 
dist 109=[1.0124792276799856008 ,3.0232227033824070250 ] 
dist 110=[.9747978790088239062 ,3.0200054692726075428 ] 
dist 111=[.9298410078152197716 ,3.0100992161149625420 ] 
dist 112=[.8627073999846586036 ,3.0094081477390867736 ] 
dist 113=[.79560663266801155628,3.0059836435669135658 ] 
dist 114=[.75078112039780057987,3.0003238821074480399 ] 
dist 115=[.71332963653075653244,1.5240974767569805397 ] 
dist 116=[.67572427950651916369,1.4878963624301415838 ] 
dist 117=[.6405308190678091297 ,1.4034534271200962370 ] 
dist 118=[.61272669150094399293,1.3913102230345942233 ] 
dist 119=[.5847830750997827378 ,1.2787618626416078708 ] 
dist 120=[.5490316726280576157 ,1.2586519508937229344 ] 
dist 121=[.51404650278042795838,1.2342912937780482592 ] 
dist 122=[.48916774379389494965,1.2300095341609914757 ] 
dist 123=[.46672680611214678224,1.0764318428360580559 ] 
dist 124=[.44149268896907756679,1.0576912137767462331 ] 
dist 125=[.41614354627803223596,1.0200318032639348155 ] 
dist 126=[.3932425173752890828 ,1.0105701938289842324 ] 
dist 127=[.36755864537733373752,.9778027107155576599 ] 
dist 128=[.33107839572751517081,.9710559512496289453 ] 
dist 129=[.29483038064114532664,.9621797678604929079 ] 
dist 130=[.27007542474691110425,.9600441420081780454 ] 
dist 131=[.2487999048899790367 ,.7436869388950358882 ] 
dist 132=[.22646930209108392832,.7256346700240618307 ] 
dist 133=[.20494987484204382147,.6853330830556613421 ] 
dist 134=[.18691897981621069487,.6780301284028487482 ] 
dist 135=[.16784178856841433106,.66139712507859438325] 
dist 136=[.14213727622518744839,.65976177501383342122] 
dist 137=[.11636046782596655766,.63825064878945003856] 
dist 138=[.09699409924964912535,.63527744163530276362] 
dist 139=[.07845717320393005059,.62919099046314704369] 
dist 140=[.05599805581651299741,.62763307868649152421] 
dist 141=[.03251104707790339809,.62203178491202379963] 
dist 142=[.00986265366566010465,.62093011592182215184] 
dist 143=[-.01669836614888004594,.61898525947465591052] 
dist 144=[-.05583550731810216071,.61856219115434356814] 
dist 145=[-.09489217724767672885,.5117342084826523404 ] 
dist 146=[-.12113131977881451953,.5105011556694619820 ] 
dist 147=[-.14321646056391990201,.44155049358957850455] 
dist 148=[-.16565751970984308   ,.43864220947263039665] 
dist 149=[-.18682946564336610902,.41383819766584613001] 
dist 150=[-.20383827462438133144,.40942981157068948165] 
dist 151=[-.22119435093023560895,.40352796109084977824] 
dist 152=[-.24375533304144361513,.40205172205358842428] 
dist 153=[-.26600356420896722698,.37096761258826968511] 
dist 154=[-.28210866656965094161,.36710733951976660324] 
dist 155=[-.2969283979194324019 ,.35896014071795520887] 
dist 156=[-.3140352676394941275 ,.35707862978525617586] 
dist 157=[-.33147374339472832157,.34874804736182239416] 
dist 158=[-.34761986725727127415,.34726955738187803192] 
dist 159=[-.36604602209960858492,.34405458037390096765] 
dist 160=[-.39260440430917069303,.34341559111762363227] 
dist 161=[-.41915839009482999344,.31013346845780978117] 
dist 162=[-.43756695966087829828,.30709833287996515196] 
dist 163=[-.45368231107199495061,.30016878675033233932] 
dist 164=[-.47106364296054386696,.29907092174899755207] 
dist 165=[-.48810019002406771938,.29029821810833807731] 
dist 166=[-.50283643501997943384,.28875083641514823635] 
dist 167=[-.51883170811708769875,.28651271469388962213] 
dist 168=[-.54090424750178529677,.28591682861880021714] 
dist 169=[-.56327640094274739741,.27580665155319181632] 
dist 170=[-.58047010168831702308,.27454356347292144167] 
dist 171=[-.59730347362122593497,.27175373477216052932] 
dist 172=[-.61823434617899532446,.27124211905703523241] 
dist 173=[-.64040813139743181374,.26800091475143715942] 
dist 174=[-.66221303542645554209,.2674413253388819213 ] 
dist 175=[-.68810641352868010491,.26640470539050099168] 
dist 176=[-.72663370508934164164,.26617158230471635284] 
dist 177=[-.76507138388477192173,-.1954757365794850632 ] 
dist 178=[-.79060632069593266864,-.1958406652170665633 ] 
dist 179=[-.81178399398653794126,-.4056660420395143180 ] 
dist 180=[-.8327930379550737252 ,-.4142843321600805668 ] 
dist 181=[-.8522905751847721527 ,-.4339230591740966300 ] 
dist 182=[-.8674223693519949425 ,-.4370277189044916446 ] 
dist 183=[-.8823776459688906783 ,-.4617245004008828388 ] 
dist 184=[-.9011691371668298076 ,-.4660600742486507899 ] 
dist 185=[-.91939339649624135455,-.4723672174282120393 ] 
dist 186=[-.93207980340441394119,-.4740246457568536467 ] 
dist 187=[-.94324132107865203225,-.5017484429069606793 ] 
dist 188=[-.9553661725708652532 ,-.5051881463303008117 ] 
dist 189=[-.96730227916257693852,-.5128486277311397866 ] 
dist 190=[-.97770884255865212143,-.5141488571970653878 ] 
dist 191=[-.98907418710374790167,-.5231739704115034671 ] 
dist 192=[-1.0048453451514049490 ,-.5247167619159981369 ] 
dist 193=[-1.0203581486543113252 ,-.5273668787572160640 ] 
dist 194=[-1.0306901033081553136 ,-.5279206288536779126 ] 
dist 195=[-1.0392883546146784753 ,-.5441405314669498749 ] 
dist 196=[-1.0478665027176781254 ,-.54589963943929517445] 
dist 197=[-1.0558590391966219478 ,-.54913601843541133602] 
dist 198=[-1.0621149034762723773 ,-.54984847569582243359] 
dist 199=[-1.0683479335720532314 ,-.55164537663207393421] 
dist 200=[-1.0762491537053153959 ,-.55171637836684594024] 
dist 201=[-1.0839460758700574927 ,-.5511532264382317135 ] 
dist 202=[-1.0893619408394981654 ,-.54957257603212289367] 
dist 203=[-1.0941878798231890894 ,-.54761381979472050833] 
dist 204=[-1.0995251578845582516 ,-.54553829580397295227] 
dist 205=[-1.1048358222751409620 ,-.54296286429260999621] 
dist 206=[-1.1095553272805746798 ,-.53900451703449995922] 
dist 207=[-1.1147850207813456393 ,-.53442026501442553761] 
dist 208=[-1.1221364414158365264 ,-.52934132817893799634] 
dist 209=[-1.1293545631003219512 ,-.52288515318444021296] 
dist 210=[-1.1340510722920887776 ,-.51279225057578468088] 
dist 211=[-1.1378375535925296570 ,-.5024887472342100349 ] 
dist 212=[-1.1414155959169008431 ,-.49519019495250961406] 
dist 213=[-1.1446206423056590572 ,-.48863720685082575986] 
dist 214=[-1.1469151536052931539 ,-.48131573510225211056] 
dist 215=[-1.1490007736969557731 ,-.47398900695057077098] 
dist 216=[-1.1513702642701537295 ,-.46741495638101665338] 
dist 217=[-1.1535455915170292587 ,-.46007938814951269874] 
dist 218=[-1.1548545658961806162 ,-.44970670393371486211] 
dist 219=[-1.1557899794678177928 ,-.43908352689086930306] 
dist 220=[-1.1564710772445932562 ,-.4307460126960731059 ] 
dist 221=[-1.1569779039369352436 ,-.42241866440411775621] 
dist 222=[-1.1572162436377887697 ,-.41183611241135362518] 
dist 223=[-1.1573053832267856357 ,-.40050797188925082483] 
dist 224=[-1.1573001173628611992 ,-.38919838230860687536] 
dist 225=[-1.1557093274904631347 ,-.37564242536847786615] 
dist 226=[-1.1552140060400367312 ,-.35532919239592324102] 
dist 227=[-1.1347661754566754215 ,-.33469798582698134309] 
dist 228=[-1.1336348595769933622 ,-.31987017902955796285] 
dist 229=[-1.1315984444102395165 ,-.3063350414390768613 ] 
dist 230=[-1.1311003106597735536 ,-.29087426827190746671] 
dist 231=[-1.1295640309705894362 ,-.27520627591165060067] 
dist 232=[-1.1291407281588844496 ,-.26084228218856729957] 
dist 233=[-1.1289698117770106061 ,-.24456406487602402954] 
dist 234=[-1.1279194295929199165 ,-.22123948349319861306] 
dist 235=[-1.1006068671867166274 ,-.19721703657351925925] 
dist 236=[-1.0979662614398187426 ,-.17814746477195847998] 
dist 237=[-1.0950567322432942072 ,-.15889905822983934884] 
dist 238=[-1.0914994938503398397 ,-.13416128993061256177] 
dist 239=[-1.0722047168366198494 ,-.10753983533044741409] 
dist 240=[-1.0609042564320329975 ,-.08075698563386291170] 
dist 241=[-1.0144873495510618262 ,-.04850342198914075374] 

8 phat 1 dirichlet min maxes function [0, 2, 2, 0, 0, 2, 1, 0, 1] 
dist 0=[3.5586299203039998963 ,3.5586299203039998963 ] 
dist 1=[3.5575584190833588077 ,3.5605960831782416082 ] 
dist 2=[3.5552386945956223232 ,3.5627593639930803160 ] 
dist 3=[3.5516207160047089032 ,3.5641337242504887061 ] 
dist 4=[3.5459422601356464262 ,3.5652043569751473705 ] 
dist 5=[3.5398563257987949691 ,3.5661528025944713614 ] 
dist 6=[3.5346084811543653893 ,3.5670154020824189989 ] 
dist 7=[3.5289262735871302860 ,3.5677426674225553078 ] 
dist 8=[3.5211029098793430380 ,3.5685162076043357537 ] 
dist 9=[3.5124222686387039980 ,3.5695638829368660087 ] 
dist 10=[3.5033110289126873430 ,3.5707184109171383642 ] 
dist 11=[3.4920627093667208901 ,3.5719193477056813211 ] 
dist 12=[3.4748339604072337792 ,3.5733944976762196234 ] 
dist 13=[3.4571819960083547257 ,3.5756458599610626619 ] 
dist 14=[3.4442408512443752309 ,3.5779497315337628801 ] 
dist 15=[3.4321673226765680699 ,3.5796349098216001743 ] 
dist 16=[3.4179857211032153810 ,3.5812033586213174056 ] 
dist 17=[3.4033926641321519069 ,3.5830403041673207046 ] 
dist 18=[3.3896733455351679807 ,3.5849277041044807740 ] 
dist 19=[3.3738522023544214221 ,3.5866979579744485319 ] 
dist 20=[3.3508520436785206862 ,3.5887362420355360492 ] 
dist 21=[3.3270194398700123895 ,3.5916957333353228219 ] 
dist 22=[3.3078685917115195477 ,3.5947608730015626298 ] 
dist 23=[3.2883226104952907199 ,3.5972217366076419767 ] 
dist 24=[3.2629095044481990789 ,3.5997314455192971862 ] 
dist 25=[3.2354124070052291605 ,3.6029919540544220509 ] 
dist 26=[3.2075306551244995011 ,3.6065186053203821465 ] 
dist 27=[3.1737930366904518246 ,3.6100928559232414097 ] 
dist 28=[3.1228730277064850475 ,3.6144165432552446845 ] 
dist 29=[3.0718324213191939013 ,3.6209408661092810133 ] 
dist 30=[3.0376124234912275872 ,3.6274463248407927687 ] 
dist 31=[3.0088865511025624902 ,3.6316945549159940997 ] 
dist 32=[2.9798219224536481864 ,3.6351367520611062130 ] 
dist 33=[2.9524797484469743708 ,3.6384181521013837783 ] 
dist 34=[2.9306435303429510147 ,3.6413767978800639731 ] 
dist 35=[2.9084797293204159600 ,3.6435280049144812138 ] 
dist 36=[2.8798272548839068150 ,3.6455171167702099634 ] 
dist 37=[2.8516467100656637589 ,3.6478273895998043721 ] 
dist 38=[2.8313705825044786014 ,3.6499753259711350636 ] 
dist 39=[2.8128376016623242437 ,3.6513151036328516781 ] 
dist 40=[2.7916294774623147788 ,3.6523300252926795216 ] 
dist 41=[2.7701135623107913796 ,3.6531785648029163411 ] 
dist 42=[2.7503494470190740467 ,3.6538631401460352322 ] 
dist 43=[2.7279189589334479540 ,3.6542222130938332037 ] 
dist 44=[2.6957378069196578553 ,3.6544142893238369769 ] 
dist 45=[2.6636244469761248935 ,3.6544308745159514440 ] 
dist 46=[2.6414651207056536441 ,3.6543378817215625749 ] 
dist 47=[2.6221755111111107462 ,3.6542505344899454136 ] 
dist 48=[2.6015407441633851909 ,3.6538342857480248405 ] 
dist 49=[2.5814169827496028546 ,3.6536967825439113697 ] 
dist 50=[2.5641713465521347509 ,3.6521874074666651496 ] 
dist 51=[2.5455887665917261428 ,3.6517125334709669798 ] 
dist 52=[2.5201173576412361017 ,3.6508617417234937127 ] 
dist 53=[2.4943765875268914427 ,3.6495203149578169819 ] 
dist 54=[2.4747165886021999140 ,3.6419186482717887388 ] 
dist 55=[2.4555855784021124241 ,3.6388972381719743887 ] 
dist 56=[2.4319607127322846473 ,3.5985491113344943646 ] 
dist 57=[2.4070174002418298333 ,3.5952877890727155776 ] 
dist 58=[2.3826127285100866992 ,3.5890184887733942909 ] 
dist 59=[2.3537243563341270702 ,3.5867197586318719651 ] 
dist 60=[2.3108466697132948682 ,3.5692291196816102869 ] 
dist 61=[2.2679300790348804916 ,3.5596024678641831969 ] 
dist 62=[2.2388860943391843026 ,3.3557791844115030327 ] 
dist 63=[2.2142091164675648655 ,3.3445746555337981793 ] 
dist 64=[2.1887601365689758082 ,3.3185845299999654365 ] 
dist 65=[2.1645129840724537810 ,3.3145100531851448336 ] 
dist 66=[2.1446432011811796631 ,3.2800028403790224201 ] 
dist 67=[2.1240113205433488588 ,3.2737551394020947742 ] 
dist 68=[2.0967158497479772499 ,3.2653087998851382460 ] 
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dist 70=[2.0495540464156943060 ,3.2165260411272345296 ] 
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dist 72=[1.9207791917685373378 ,3.1981479976724926707 ] 
dist 73=[1.8692361893238812143 ,3.1949739748428335647 ] 
dist 74=[1.8250370877451502551 ,3.1820920016894304158 ] 
dist 75=[1.7788023294192477478 ,3.1796924107768340408 ] 
dist 76=[1.7343418629544389521 ,3.1742070123680109960 ] 
dist 77=[1.6972397987872873705 ,3.1731118041526041547 ] 
dist 78=[1.6581160591847917999 ,3.1080753864641314515 ] 
dist 79=[1.6055690397853314417 ,3.1020665307181293104 ] 
dist 80=[1.5529491506422059622 ,3.0881162305143254469 ] 
dist 81=[1.5135339374902919142 ,3.0858554478183398218 ] 
dist 82=[1.4759218176684628387 ,3.0671859392917835534 ] 
dist 83=[1.4305141693123104974 ,3.0637691562637463005 ] 
dist 84=[1.3831137554809091417 ,3.0590089439844411994 ] 
dist 85=[1.3375307200547647016 ,3.0576211899714718431 ] 
dist 86=[1.2841670263434943700 ,3.0318055624759204616 ] 
dist 87=[1.2056445507315127535 ,3.0284534742559462732 ] 
dist 88=[1.1264567212460090310 ,3.0213447358604107385 ] 
dist 89=[1.0704316606012101562 ,3.0195174539096128914 ] 
dist 90=[1.0201914394195662536 ,3.0118134781017049658 ] 
dist 91=[.96414254208741912813,3.0103936586139493188 ] 
dist 92=[.9080915624978354951 ,3.0068580563332429909 ] 
dist 93=[.85784301156635608794,3.0063446111827943021 ] 
dist 94=[.80180337079905985963,2.9170969085118171347 ] 
dist 95=[.72258845540567903286,2.9106818500160352601 ] 
dist 96=[.64145641494788189961,2.8956566270382314672 ] 
dist 97=[.57774841365415884729,2.8933659073425622763 ] 
dist 98=[.51408082564710593868,2.8729185730325882573 ] 
dist 99=[.43311043392978677877,2.8691825450327412415 ] 
dist 100=[.34639424219493342337,2.8644318263641040054 ] 
dist 101=[.25974387372933776979,2.8632277867506690361 ] 
dist 102=[.15581778994610316001,2.8336485688340800210 ] 
dist 103=[0                     ,2.8298848566149580405 ] 
dist 104=[.96681798373957247145,2.8222185230457627378 ] 
dist 105=[.94126644331743680429,2.8202205926269184140 ] 
dist 106=[.91802930571372652654,2.8128760417822530442 ] 
dist 107=[.89184408030202563901,2.8113864205794709031 ] 
dist 108=[.85450046983071724672,2.8085241862160796560 ] 
dist 109=[.81733017244581315629,2.8077915361694388707 ] 
dist 110=[.79183818284946976088,2.7579180075140665241 ] 
dist 111=[.76981413767060792851,2.7534640514910970787 ] 
dist 112=[.74651528718994419808,2.7434453600708256827 ] 
dist 113=[.72395067044736365087,2.7415100738674727523 ] 
dist 114=[.70486349019107145673,2.7289781656182162709 ] 
dist 115=[.68451071658941107556,2.7266853305337005156 ] 
dist 116=[.65688384717515025307,2.7225439911597989564 ] 
dist 117=[.62908635663379515559,2.7207344594992567618 ] 
dist 118=[.60805111479726362991,2.7069096592319099727 ] 
dist 119=[.5877696842907951087 ,2.7028936045694659473 ] 
dist 120=[.56298736717265689636,2.6772785409062107723 ] 
dist 121=[.53695935972623899711,2.6755879643945559808 ] 
dist 122=[.51169528671813375923,2.6737563184004717620 ] 
dist 123=[.48194092544120460757,2.6713917976682010591 ] 
dist 124=[.43795219319431333816,2.6583330662859129073 ] 
dist 125=[.39399419324380931493,2.6505574690034822223 ] 
dist 126=[.3643627582212434454 ,1.2033885684029392100 ] 
dist 127=[.33931379370101428634,1.1684177888320149074 ] 
dist 128=[.31368523869287553932,1.0868591614789879334 ] 
dist 129=[.28939449763092250968,1.0751510951673190763 ] 
dist 130=[.26969666129738554903,.96653188844692861504] 
dist 131=[.24942915832198572468,.94713892316125640121] 
dist 132=[.22285980502625988135,.92367763499548576189] 
dist 133=[.19655290356520320521,.91961205985988251251] 
dist 134=[.17733518289634266309,.77620174566571789834] 
dist 135=[.15947435921505306844,.76779435569419324861] 
dist 136=[.13859491628612673191,.76568552488518485658] 
dist 137=[.11716438918321070781,.75841281818277320935] 
dist 138=[.09709928136728193729,.75690198010389033719] 
dist 139=[.07402428684339783427,.75498735800408297372] 
dist 140=[.04055449998570715892,.75456997925344133473] 
dist 141=[.00700177038596806901,.70482540497215890498] 
dist 142=[-.01640498719519485032,.70068638567625433722] 
dist 143=[-.03705064674072799838,.69146852888101732274] 
dist 144=[-.05955924754602272115,.68976887356262613295] 
dist 145=[-.08176539465323705346,.67873355431751305648] 
dist 146=[-.10120126825388471559,.67678882902248033384] 
dist 147=[-.12249102303034994307,.67326397447624792265] 
dist 148=[-.15211251802131125117,.6724734456165988416 ] 
dist 149=[-.18224430479337894058,.66191016038468080228] 
dist 150=[-.20557517802364794671,.66045614604074899184] 
dist 151=[-.22858280207295190442,.65746303752623035019] 
dist 152=[-.25742162295202754136,.65669299608155842612] 
dist 153=[-.28809255624621784245,.65389587407746324568] 
dist 154=[-.3184284552127185522 ,.65335318543543099881] 
dist 155=[-.35458306690588544372,.65234863233360575246] 
dist 156=[-.40852829612941836073,.6521167085402433226 ] 
dist 157=[-.46239203190813785763,.23354007155948130177] 
dist 158=[-.49822067887769799473,-.03885835719150956368] 
dist 159=[-.52798617806348579127,-.05401967144858444437] 
dist 160=[-.55759790484687625333,-.08910371203903370831] 
dist 161=[-.58513326524486992274,-.09427660806677722905] 
dist 162=[-.60659350077676259549,-.14008421250643160369] 
dist 163=[-.62788879435533138373,-.14820372494256762022] 
dist 164=[-.65476441036651676484,-.15858717459827890692] 
dist 165=[-.68088638552024544312,-.1607516784230990012 ] 
dist 166=[-.69916719139405109194,-.21928421705254486661] 
dist 167=[-.71535239526679603728,-.2264340038157836266 ] 
dist 168=[-.73309216612832219339,-.24120557942914223218] 
dist 169=[-.75064927370948878188,-.24484923663989449922] 
dist 170=[-.76610384956499462086,-.25867477693060192348] 
dist 171=[-.78310616309886341448,-.26128990123488826466] 
dist 172=[-.80685409298096497263,-.26604003532965009025] 
dist 173=[-.83028024202308713989,-.26708046904514176662] 
dist 174=[-.84599546671375665963,-.33326018423425559838] 
dist 175=[-.85919778378631456276,-.33894414895897806183] 
dist 176=[-.87257253430165262663,-.35206961239174482465] 
dist 177=[-.88516546839331449579,-.35394695648103710001] 
dist 178=[-.89524059813208473412,-.37089559631107038911] 
dist 179=[-.90548357801494081208,-.37386277213495474425] 
dist 180=[-.91874791578212194305,-.37756164307195315459] 
dist 181=[-.93180486384061452655,-.37817419327874159335] 
dist 182=[-.94121831228881936739,-.39907011801820848277] 
dist 183=[-.94984187846455543882,-.40155460381116145696] 
dist 184=[-.95973937652014593888,-.40665048057681017326] 
dist 185=[-.96979720679096214198,-.40785914601813252843] 
dist 186=[-.97906210559619988594,-.41236858531252011043] 
dist 187=[-.98959790216167133527,-.41321862787459888103] 
dist 188=[-1.0047392556877136898 ,-.4143917194378631486 ] 
dist 189=[-1.0197104122548135404 ,-.41459252347989201273] 
dist 190=[-1.0295654359346014178 ,-.57556409156326619209] 
dist 191=[-1.0376390457263712107 ,-.58212508657483685526] 
dist 192=[-1.0454846593704214100 ,-.59694070804142264487] 
dist 193=[-1.0526597236329081332 ,-.59935661251348477635] 
dist 194=[-1.0580511769453611984 ,-.61753469113498025723] 
dist 195=[-1.0632126012325702917 ,-.62069727534178205487] 
dist 196=[-1.0694675598895827018 ,-.62561704848445432792] 
dist 197=[-1.0754211850629209709 ,-.62679990101257473275] 
dist 198=[-1.0793772926920555218 ,-.645462351559727386  ] 
dist 199=[-1.0826595152772029268 ,-.64780322511927092701] 
dist 200=[-1.0859176416023632056 ,-.65294670513372951547] 
dist 201=[-1.0889427487340521619 ,-.653830576164579609  ] 
dist 202=[-1.0912929052952765905 ,-.65961446603136744262] 
dist 203=[-1.0936179430691897795 ,-.66057520368418244391] 
dist 204=[-1.0965425659702702437 ,-.66231910361662332754] 
dist 205=[-1.0993275549208737761 ,-.66267991754760395802] 
dist 206=[-1.1010940714022968981 ,-.66635423833971893166] 
dist 207=[-1.1024668773652706993 ,-.66686260506804664148] 
dist 208=[-1.1036770768446032406 ,-.66681777731557021451] 
dist 209=[-1.1047017563588770459 ,-.66600717961854699593] 
dist 210=[-1.1053325152044588568 ,-.66475800148776731195] 
dist 211=[-1.1058005883839737320 ,-.66295888497897930769] 
dist 212=[-1.1061745708422086014 ,-.66039738654040607391] 
dist 213=[-1.1064391931987971767 ,-.65609881029016499906] 
dist 214=[-1.1064918387076786960 ,-.65140297675921463258] 
dist 215=[-1.1064255520476645427 ,-.64725250303568857372] 
dist 216=[-1.1063905207965933372 ,-.64267290858364892385] 
dist 217=[-1.1055119323268471222 ,-.63626062402465496427] 
dist 218=[-1.1052630661682819790 ,-.62909649383662396661] 
dist 219=[-1.1050865603924697966 ,-.62150964526357493608] 
dist 220=[-1.1049716900334260098 ,-.61209702249374932998] 
dist 221=[-1.0186111361739278669 ,-.59763014874865439582] 
dist 222=[-1.0145999266826438520 ,-.58295470494374631808] 
dist 223=[-1.0052445528249696142 ,-.57270782765904025142] 
dist 224=[-1.0037396107673918150 ,-.56366114301091100456] 
dist 225=[-.99106803737206637668,-.55378619368227995791] 
dist 226=[-.98873745872268483166,-.54403802283392504514] 
dist 227=[-.98555955831304811405,-.53549840081936315191] 
dist 228=[-.98460473179316451053,-.52613866517738352041] 
dist 229=[-.96655169773423764258,-.51311016205685870277] 
dist 230=[-.96420227590164387784,-.49985641955331860108] 
dist 231=[-.95927590182453327282,-.48959574938709526743] 
dist 232=[-.95794914474835088842,-.47947958973609278478] 
dist 233=[-.95278978008889470778,-.46680383606819653286] 
dist 234=[-.95180130344730718731,-.45332616089927015281] 
dist 235=[-.94946487642454095766,-.44000243549918797   ] 
dist 236=[-.94900415486241744431,-.42412903634327277591] 
dist 237=[-.91946958368295015012,-.40045308007774840923] 
dist 238=[-.88382265088114930235,-.37645044675677705054] 
dist 239=[-.87425996192462013039,-.35927038543646376326] 
dist 240=[-.87185646817461037205,-.34366019698777141527] 
dist 241=[-.86197445110310231847,-.32593677937461750293] 
dist 242=[-.86014670444771394364,-.30803640338629023922] 
dist 243=[-.85599518411484244827,-.29171839923353571488] 
dist 244=[-.85516839689405709073,-.2732997360650725697 ] 
dist 245=[-.8495099398026194695 ,-.24699705317385211975] 
dist 246=[-.802402678254176338  ,-.21994533193790786219] 
dist 247=[-.79764431074787939171,-.19853062995270871815] 
dist 248=[-.79394478178130122561,-.176970044747678695  ] 
dist 249=[-.79216648240275724667,-.14933480509812733937] 
dist 250=[-.75879224434554293546,-.11963227247864360867] 
dist 251=[-.75322604417469783823,-.08980284097966054594] 
dist 252=[-.72456961690305398499,-.05391904168485449845] 

8 phat 1 dirichlet min maxes function [2, 0, 0, 2, 2, 1, 1, 2] 
dist 0=[3.5711328272112337564 ,3.5711328272112337564 ] 
dist 1=[3.5707064575851692039 ,3.5715708124696265097 ] 
dist 2=[3.5700383761883362668 ,3.5722854178346928504 ] 
dist 3=[3.5689441555569462813 ,3.5730591549267327921 ] 
dist 4=[3.5668133015365006052 ,3.5737336538325671060 ] 
dist 5=[3.5642258578584121358 ,3.5744703492520444525 ] 
dist 6=[3.5613053208950081372 ,3.5754928473558198865 ] 
dist 7=[3.5575567402629683601 ,3.5766313982063007464 ] 
dist 8=[3.5516572468595067915 ,3.5778322897504570491 ] 
dist 9=[3.5453388663571359125 ,3.5793190687118992454 ] 
dist 10=[3.5399147862362926462 ,3.5816011496955638550 ] 
dist 11=[3.5340623330166043734 ,3.5839415924374804760 ] 
dist 12=[3.5260304818655771062 ,3.5856618090391504095 ] 
dist 13=[3.5171306305963632777 ,3.5872711765353946204 ] 
dist 14=[3.5078062558988037806 ,3.5891682142182555440 ] 
dist 15=[3.4963066489124791977 ,3.5911240496398287285 ] 
dist 16=[3.4787060836889796002 ,3.5929685947998627903 ] 
dist 17=[3.4606783251709267065 ,3.5951003158276515695 ] 
dist 18=[3.4474699819248901135 ,3.5982048234918595690 ] 
dist 19=[3.4351554756730531837 ,3.6014241113855586004 ] 
dist 20=[3.4207029606694712106 ,3.6040149385390564458 ] 
dist 21=[3.4058377887606064545 ,3.6066628565535185625 ] 
dist 22=[3.3918726865629915516 ,3.6101104947502993898 ] 
dist 23=[3.3757759350292937978 ,3.6138433061360989700 ] 
dist 24=[3.3523843652504819356 ,3.6176318858589555961 ] 
dist 25=[3.3281500975370417233 ,3.6222187390525734054 ] 
dist 26=[3.3086826307949508288 ,3.6291445643345097690 ] 
dist 27=[3.2888191022284700807 ,3.6360521065789786920 ] 
dist 28=[3.2630006172975028642 ,3.6405658268002961813 ] 
dist 29=[3.2350686085052781731 ,3.6442264203264494669 ] 
dist 30=[3.2067511822290718611 ,3.6477215333106382912 ] 
dist 31=[3.1724902348512554931 ,3.6508766034372046525 ] 
dist 32=[3.1207847046847271777 ,3.6531770541170586871 ] 
dist 33=[3.0689584296804967883 ,3.6553106458375466801 ] 
dist 34=[3.0342145131851608819 ,3.6577982883457649242 ] 
dist 35=[3.0050519344438333855 ,3.6601161988261146539 ] 
dist 36=[2.9755504781186703657 ,3.6615708747790904396 ] 
dist 37=[2.9478005669457022051 ,3.6626832753265689765 ] 
dist 38=[2.9256440017542385782 ,3.6636321129923643049 ] 
dist 39=[2.9031598989867070250 ,3.6644121059992137683 ] 
dist 40=[2.8740998687493539528 ,3.6648491363319317210 ] 
dist 41=[2.8455215803668698158 ,3.6651219501978410246 ] 
dist 42=[2.8249643990712278069 ,3.6652450737901765598 ] 
dist 43=[2.8061797511827119343 ,3.6652544754551811301 ] 
dist 44=[2.7846914273679984927 ,3.6652023849512930530 ] 
dist 45=[2.7628956354075095913 ,3.6648581205361058358 ] 
dist 46=[2.7428811442615960684 ,3.6647386798857828796 ] 
dist 47=[2.7201718618969539419 ,3.6632944941086136483 ] 
dist 48=[2.6875971620854121707 ,3.6629109115851881611 ] 
dist 49=[2.6550937985640945358 ,3.6625063823391209993 ] 
dist 50=[2.6326698545564345543 ,3.6622240760088379176 ] 
dist 51=[2.6131546766192525229 ,3.6533789944205900929 ] 
dist 52=[2.5922860999474865999 ,3.6522059380059178394 ] 
dist 53=[2.5719388302137762118 ,3.6486091910182460086 ] 
dist 54=[2.5545088303075906705 ,3.6434470197026415073 ] 
dist 55=[2.5357337365437078420 ,3.6107378334907420715 ] 
dist 56=[2.5100062196716025525 ,3.6075241363697842025 ] 
dist 57=[2.4840101198288361771 ,3.5989197418411918455 ] 
dist 58=[2.4641607197992220298 ,3.5888314955163671535 ] 
dist 59=[2.4448507927974437350 ,3.3704139520622703530 ] 
dist 60=[2.4210125336121493734 ,3.3593106108605053312 ] 
dist 61=[2.3958478589263453979 ,3.3335550951355710747 ] 
dist 62=[2.3608521968216040936 ,3.3295140221763226380 ] 
dist 63=[2.3196912991496430128 ,3.2953133734330083682 ] 
dist 64=[2.2876638704169130313 ,3.2891196972669024294 ] 
dist 65=[2.2555884604691881755 ,3.2807394281036348617 ] 
dist 66=[2.2159484784881411572 ,3.2783298006675864390 ] 
dist 67=[2.1733183384761936331 ,3.2323605506920731114 ] 
dist 68=[2.1309953518387152210 ,3.2264819140012485984 ] 
dist 69=[2.0804359952944481177 ,3.2141250026841098930 ] 
dist 70=[2.0048609821114959700 ,3.2109754521295616236 ] 
dist 71=[1.9289961022064131261 ,3.1981747229092149293 ] 
dist 72=[1.8772773005884752297 ,3.1957913966665296910 ] 
dist 73=[1.8329253777832806160 ,3.1903291297949622236 ] 
dist 74=[1.7865274721080105088 ,3.1892484036508614047 ] 
dist 75=[1.7419080976902270195 ,3.1246433282098344100 ] 
dist 76=[1.7046701694824843770 ,3.1186703226184386528 ] 
dist 77=[1.6654003040833011734 ,3.1048011497496277823 ] 
dist 78=[1.6126533306800081523 ,3.1025525467408385668 ] 
dist 79=[1.5598315265165329614 ,3.0839818609316234005 ] 
dist 80=[1.5202623436887202018 ,3.0805818862987285468 ] 
dist 81=[1.4825006338318056069 ,3.0758455466980553685 ] 
dist 82=[1.4369085886055102693 ,3.0744639495868466784 ] 
dist 83=[1.3893136601289152894 ,3.0487439725014450074 ] 
dist 84=[1.3435405645273078296 ,3.0454030914915882150 ] 
dist 85=[1.2899520824736430616 ,3.0383197104921818202 ] 
dist 86=[1.2110961828408062638 ,3.0364951245588014151 ] 
dist 87=[1.1315710277155974326 ,3.0288212128156042897 ] 
dist 88=[1.0753055726233669251 ,3.0274052281738016395 ] 
dist 89=[1.0248479821564503182 ,3.0238798365332826319 ] 
dist 90=[.96855385765208086287,3.0233651557314826688 ] 
dist 91=[.91225607306678040533,2.9342040262452406790 ] 
dist 92=[.86178384170643110139,2.9277937270634268535 ] 
dist 93=[.8054927626295121556 ,2.9127743599579853735 ] 
dist 94=[.72592001334962681657,2.9104873541282003531 ] 
dist 95=[.64442044143327468223,2.8900306643959418880 ] 
dist 96=[.5804222124615507673 ,2.8862919492260788572 ] 
dist 97=[.51646306654012981737,2.8815492847428915760 ] 
dist 98=[.43511982254559686394,2.8803543635746090869 ] 
dist 99=[.34800328663384055485,2.8506903608780051467 ] 
dist 100=[.26095139526202150705,2.8469169026227215797 ] 
dist 101=[.15654265614412143642,2.8392391592004611841 ] 
dist 102=[0                     ,2.8372399936589389940 ] 
dist 103=[1.0916691751152776627 ,2.8299037217119817105 ] 
dist 104=[1.0563561548878551712 ,2.8284117952576733054 ] 
dist 105=[1.0217355496212068631 ,2.8255655762630971064 ] 
dist 106=[.9970089581911616738 ,2.8248416821194936048 ] 
dist 107=[.9745948513569934183 ,2.7745608367457830821 ] 
dist 108=[.9492239639136415539 ,2.7700765362469960190 ] 
dist 109=[.9236417542567706204 ,2.7599988190861534663 ] 
dist 110=[.9003823787240212422 ,2.7580434296271754224 ] 
dist 111=[.8741766527303910985 ,2.7454644004086088512 ] 
dist 112=[.8368093222470820830 ,2.7431632032204341566 ] 
dist 113=[.7996177547646047187 ,2.7389867399808865923 ] 
dist 114=[.7741150640103734681 ,2.7380033084832759339 ] 
dist 115=[.7520859289014782861 ,2.7233771866146437744 ] 
dist 116=[.7287882526994714793 ,2.7213830507200519651 ] 
dist 117=[.7062287686632516748 ,2.7166300924785616695 ] 
dist 118=[.6871523318101943944 ,2.7122476912111456366 ] 
dist 119=[.6668165637793268250 ,2.6941001125905938312 ] 
dist 120=[.6392198751443851704 ,2.6924380930232628580 ] 
dist 121=[.6114559662991193885 ,2.6874011140793666160 ] 
dist 122=[.5904513333760885454 ,2.6801944324681784832 ] 
dist 123=[.5702044507440405835 ,1.2176057703353620087 ] 
dist 124=[.5454714707899808861 ,1.1825369690314510946 ] 
dist 125=[.5194990367218582044 ,1.1007491313374700657 ] 
dist 126=[.4942944558502425486 ,1.0890074053859668344 ] 
dist 127=[.4646143534176009947 ,.99924844619061541949] 
dist 128=[.4207402599717775963 ,.99856355782081187525] 
dist 129=[.3768987941757781003 ,.93710109951955300524] 
dist 130=[.3473491992304713877 ,.93302149382794157494] 
dist 131=[.3223729932361552520 ,.83944226205356067807] 
dist 132=[.2968246470433169205 ,.83676379936065476823] 
dist 133=[.2726135601238981750 ,.81172208079178800604] 
dist 134=[.2529862636781133053 ,.80724129552690704668] 
dist 135=[.2327967183880262278 ,.80186877874353491023] 
dist 136=[.2063366897175824189 ,.80095916988240849142] 
dist 137=[.1801413754418243774 ,.76639401464327016011] 
dist 138=[.1610106624825444799 ,.76217745973965837656] 
dist 139=[.1432362153143527396 ,.75374412549657810704] 
dist 140=[.1224658348449961500 ,.75163269134299723021] 
dist 141=[.1011517071601206692 ,.74437848937240877404] 
dist 142=[.0812023229913883377 ,.74286498613240365186] 
dist 143=[.0582656906877395917 ,.74101401277667868561] 
dist 144=[.0250028553810227690 ,.74066428547644797672] 
dist 145=[-.0083397991703886597 ,.6903076669518570012 ] 
dist 146=[-.0315957008398139915 ,.6861347320120996181 ] 
dist 147=[-.0521037740441236571 ,.6768559070587709260 ] 
dist 148=[-.0744553768175217221 ,.6751333638132309040 ] 
dist 149=[-.0965024998062215026 ,.6640705530337820815 ] 
dist 150=[-.1157926829124182430 ,.6621226343490264727 ] 
dist 151=[-.1369174003302670205 ,.6585625495666723163 ] 
dist 152=[-.1663024855913173374 ,.6577563556610163035 ] 
dist 153=[-.1961907919185379837 ,.6473437791683388571 ] 
dist 154=[-.2193283456048371499 ,.6458981784511237238 ] 
dist 155=[-.2421407882014184120 ,.6429669507142371247 ] 
dist 156=[-.2707286811782207601 ,.6422239886054853450 ] 
dist 157=[-.3011295173697883822 ,.6396030277522794904 ] 
dist 158=[-.3311935599104892846 ,.6390759541626415252 ] 
dist 159=[-.3670206786269889265 ,.6382611117009448504 ] 
dist 160=[-.4204732698509336785 ,.6380582543208780076 ] 
dist 161=[-.4738439509997224958 ,-.14915971649394422798] 
dist 162=[-.5093434385111347851 ,-.15133857930740799006] 
dist 163=[-.5388341650980581245 ,-.21014765603791337692] 
dist 164=[-.5681703795017965214 ,-.21733253076950322962] 
dist 165=[-.5954481478265822112 ,-.23217812247311323382] 
dist 166=[-.6167052902766394859 ,-.23583994576610793774] 
dist 167=[-.6377968562898482899 ,-.24974249401232222247] 
dist 168=[-.6644123423551552473 ,-.25237165168884169688] 
dist 169=[-.6902800133701451595 ,-.25715391293315100323] 
dist 170=[-.7083803943519511798 ,-.25820360222026404522] 
dist 171=[-.7244032824617016228 ,-.32473667107073796822] 
dist 172=[-.7419611839737514903 ,-.33045351104031315509] 
dist 173=[-.75933596544204797799,-.34365590199257753599] 
dist 174=[-.77462639852545988892,-.34554484892045101878] 
dist 175=[-.79144509009042304157,-.36259771120623595701] 
dist 176=[-.81493277893257180404,-.36558384454156933814] 
dist 177=[-.83810058539777883664,-.36930663332181891051] 
dist 178=[-.8536397817910752248 ,-.36992491989262762   ] 
dist 179=[-.86669124424911123367,-.39096972369490174363] 
dist 180=[-.87990834451700661729,-.39347300690304152736] 
dist 181=[-.89234977599879563831,-.3986071112740753325 ] 
dist 182=[-.90229864108742338345,-.39982682748160949033] 
dist 183=[-.91240862262055146043,-.40437120036674456489] 
dist 184=[-.92549452362402976476,-.40522856370343246348] 
dist 185=[-.93837288193686430922,-.40641567655253569095] 
dist 186=[-.94765272012301464625,-.40662393130740446521] 
dist 187=[-.95614895086788631562,-.56972929347919944505] 
dist 188=[-.96589295790454265318,-.57637906768681353565] 
dist 189=[-.97579069096030278842,-.59140207933775672977] 
dist 190=[-.98490183018253388761,-.59384794794304969766] 
dist 191=[-.99525777690710939251,-.61230384479933193205] 
dist 192=[-1.0101346746813092696 ,-.61551625919735495788] 
dist 193=[-1.0248424859571484500 ,-.62049641377019451088] 
dist 194=[-1.0345221015323019958 ,-.62169929379577163118] 
dist 195=[-1.0424497243287542128 ,-.64074093519481888678] 
dist 196=[-1.0501496743058937276 ,-.64312562136328941719] 
dist 197=[-1.0571890098280002715 ,-.64838774010836735383] 
dist 198=[-1.0624742149009685393 ,-.64927493409598615446] 
dist 199=[-1.0675297698676120965 ,-.65526441700342126146] 
dist 200=[-1.0736505154224242479 ,-.65626304355660937475] 
dist 201=[-1.0794733986069027662 ,-.65803109702009759111] 
dist 202=[-1.0833375210364069515 ,-.65838514349625698076] 
dist 203=[-1.0865377911809236961 ,-.66249333508296254163] 
dist 204=[-1.0897053055935983115 ,-.66309852360993029706] 
dist 205=[-1.0926402709165734388 ,-.66313681683740625244] 
dist 206=[-1.0949103554060567463 ,-.66241331630112394667] 
dist 207=[-1.0971466984295600626 ,-.66124798197169435386] 
dist 208=[-1.0999466896283052550 ,-.65951897331454510119] 
dist 209=[-1.1026088833115354619 ,-.65703152501434463017] 
dist 210=[-1.1042940506073821887 ,-.65283256134312529375] 
dist 211=[-1.1055996384932793272 ,-.64823654671410533458] 
dist 212=[-1.1067435657932244228 ,-.6441609484027985369 ] 
dist 213=[-1.1077070079543676883 ,-.63965290595603089841] 
dist 214=[-1.1082906875494724951 ,-.63332714698708642385] 
dist 215=[-1.1087126524566871040 ,-.62625341427256657002] 
dist 216=[-1.1090292813854554362 ,-.61875360487606305149] 
dist 217=[-1.1092391193595085052 ,-.60944295852728390048] 
dist 218=[-1.1092730884394516053 ,-.59512622983024834343] 
dist 219=[-1.1091654821757277180 ,-.58060057598981236566] 
dist 220=[-1.1091223367414696691 ,-.57045425482636206277] 
dist 221=[-1.1081947630334022947 ,-.56149212397701457255] 
dist 222=[-1.1079371749603703973 ,-.55170295683007380697] 
dist 223=[-1.1077431953136285992 ,-.54203563189304662468] 
dist 224=[-1.1076193108203351258 ,-.53356081906198178031] 
dist 225=[-1.0196024753167351440 ,-.52426708844566869814] 
dist 226=[-1.0155182002041325982 ,-.51132421449631024817] 
dist 227=[-1.0059902647469286666 ,-.49815483390749871502] 
dist 228=[-1.0044623527341033930 ,-.48795509986223991285] 
dist 229=[-.99155472863222450451,-.47789487932595340716] 
dist 230=[-.98918185234303461142,-.4652835000197206547 ] 
dist 231=[-.98595879219179628653,-.45187133673938989007] 
dist 232=[-.98498677929767892649,-.438608100458445457  ] 
dist 233=[-.96660008250036625612,-.42280359949218916546] 
dist 234=[-.96420911069089052257,-.39922679061554432476] 
dist 235=[-.95920339684900152835,-.37532322223933274702] 
dist 236=[-.95785774656963241964,-.35821172934182892222] 
dist 237=[-.95264043092641844402,-.3426614529612123797 ] 
dist 238=[-.95163809988623310007,-.32500247568456809533] 
dist 239=[-.94929285922476094053,-.30716515541416853547] 
dist 240=[-.94881073248794575459,-.2909015249873332055 ] 
dist 241=[-.88792537011842280859,-.27254173870461995598] 
dist 242=[-.88335055058475558413,-.24632012375641575011] 
dist 243=[-.87372128551906777738,-.21935049159050786674] 
dist 244=[-.87130897585513151623,-.19799875090685751093] 
dist 245=[-.86133254569867918507,-.17649968676320648053] 
dist 246=[-.85747359282068013258,-.1489407753604449724 ] 
dist 247=[-.84760086164199255168,-.11931901668061234633] 
dist 248=[-.84022892720057238506,-.08956888860565368497] 
dist 249=[-.80650950870272539801,-.05377916800966605989] 

8 phat 1 dirichlet min maxes function [2, 0, 2, 1, 0, 2, 2, 0, 2] 
dist 0=[3.7070983188127068899 ,3.7070983188127068899 ] 
dist 1=[3.7029453803693313117 ,3.7091398609007524867 ] 
dist 2=[3.6981406778287420331 ,3.7106329810904204177 ] 
dist 3=[3.6934921272564947723 ,3.7136246652894369149 ] 
dist 4=[3.6880286357407368175 ,3.7170988421117289629 ] 
dist 5=[3.6799642329188186867 ,3.7206521067248614444 ] 
dist 6=[3.6707619132532970606 ,3.7239601311547475801 ] 
dist 7=[3.6607468344006329263 ,3.7277497133658237971 ] 
dist 8=[3.6481333461413919622 ,3.7332291706617743651 ] 
dist 9=[3.6285375654352929184 ,3.7388383759688138888 ] 
dist 10=[3.6084840868563033832 ,3.7431469439636473288 ] 
dist 11=[3.5940398401974880698 ,3.7473631669079861986 ] 
dist 12=[3.5808210747836630695 ,3.7526030116753020554 ] 
dist 13=[3.5656694438606024093 ,3.7581528561827282562 ] 
dist 14=[3.5502834633765732588 ,3.7636090702487447832 ] 
dist 15=[3.5361273188860093130 ,3.7700875893918923753 ] 
dist 16=[3.5200427403014879318 ,3.7797266110299173572 ] 
dist 17=[3.4969431582583829980 ,3.7892824417196722490 ] 
dist 18=[3.4731263809815145438 ,3.7954282062211881484 ] 
dist 19=[3.4541730724768132468 ,3.8003021385570982785 ] 
dist 20=[3.4349968674347830249 ,3.8047707112121628120 ] 
dist 21=[3.4102885222146346929 ,3.8086799400412911850 ] 
dist 22=[3.3836642160950237230 ,3.8113165323438747695 ] 
dist 23=[3.3568243012234769006 ,3.8135471016835009423 ] 
dist 24=[3.3244600690211877516 ,3.8158322738300956056 ] 
dist 25=[3.2757388766208090883 ,3.8178745921497875285 ] 
dist 26=[3.2268218866299305731 ,3.8191337584714147966 ] 
dist 27=[3.1936744796233771077 ,3.8200704477224914351 ] 
dist 28=[3.1654640749633474547 ,3.8208228594552206306 ] 
dist 29=[3.1362947579825959331 ,3.8214063607476768193 ] 
dist 30=[3.1084543980313537806 ,3.8216674098145791212 ] 
dist 31=[3.0855597343593766122 ,3.8217442125160681802 ] 
dist 32=[3.0617145037866519069 ,3.8217112209593929086 ] 
dist 33=[3.0300719512542978670 ,3.8083214855943880262 ] 
dist 34=[2.9985611448206292682 ,3.8070386533221949239 ] 
dist 35=[2.9752428941267773793 ,3.8044504118213336309 ] 
dist 36=[2.9532704260505843016 ,3.8037281643918683527 ] 
dist 37=[2.9271426615190642859 ,3.8008474643029802406 ] 
dist 38=[2.9000810653633581287 ,3.8002209406319796891 ] 
dist 39=[2.8743733443777905343 ,3.7986989035553103983 ] 
dist 40=[2.8445187138322815835 ,3.7982550735100720289 ] 
dist 41=[2.8008697887345356049 ,3.7956923027014999515 ] 
dist 42=[2.7569664878521114852 ,3.7951028238754449346 ] 
dist 43=[2.7260943760680109268 ,3.7940628874836931716 ] 
dist 44=[2.6986061559884010726 ,3.7937684079094377904 ] 
dist 45=[2.6682381783164721755 ,3.7926478424269761831 ] 
dist 46=[2.6380414523570905070 ,3.7923120689298728793 ] 
dist 47=[2.6112382311901428599 ,3.7916504427673058856 ] 
dist 48=[2.5815648337692287576 ,3.7914183219335278027 ] 
dist 49=[2.5398876225914492122 ,3.6739402920722586867 ] 
dist 50=[2.4973182739100822391 ,3.6672412154889744780 ] 
dist 51=[2.4640763964385718347 ,3.6524071697458138570 ] 
dist 52=[2.4310286325227937570 ,3.6493396741065070013 ] 
dist 53=[2.3892357281269545351 ,3.6229589910458869836 ] 
dist 54=[2.3445969084144803105 ,3.6180502142878405124 ] 
dist 55=[2.3001657009049945437 ,3.5974257826078051774 ] 
dist 56=[2.2470037222348148585 ,3.5955244482794615724 ] 
dist 57=[2.1674424807393743183 ,3.5644995449277903341 ] 
dist 58=[2.0875380838155526494 ,3.5604619395037076543 ] 
dist 59=[2.0330035106304160226 ,3.5518615339879587366 ] 
dist 60=[1.9861703783112323808 ,3.5496743970585960347 ] 
dist 61=[1.9370711635749391799 ,3.5402161171201387823 ] 
dist 62=[1.8897890777612668285 ,3.5384691106484276095 ] 
dist 63=[1.8502243249945585067 ,3.5341872134058818924 ] 
dist 64=[1.8084088374516370013 ,3.5334987320175256537 ] 
dist 65=[1.7521239854549582747 ,3.4863587704640421330 ] 
dist 66=[1.6957052026105786154 ,3.4818705173997730123 ] 
dist 67=[1.6533540030045526068 ,3.4713805461723692232 ] 
dist 68=[1.6128518022690942180 ,3.4696485522729253937 ] 
dist 69=[1.5638288759630419395 ,3.4552860329588217118 ] 
dist 70=[1.5125873113525805618 ,3.4526150880201527513 ] 
dist 71=[1.4632107274946218725 ,3.4489095059040711523 ] 
dist 72=[1.4053300803135168364 ,3.4478024297723586007 ] 
dist 73=[1.3200729115646633038 ,3.4265805577893893048 ] 
dist 74=[1.2340576039754032938 ,3.4237847334227405001 ] 
dist 75=[1.1731444596105577801 ,3.4179087391365286218 ] 
dist 76=[1.1184612529319230259 ,3.4163081681158937489 ] 
dist 77=[1.0573652214412530134 ,3.4099900707834112355 ] 
dist 78=[.99621486602661376555,3.4087756842474542330 ] 
dist 79=[.94131436796205372079,3.4057743757789691227 ] 
dist 80=[.88002098198874739981,3.4052476355939586930 ] 
dist 81=[.79329956251330074028,3.3238014024489477738 ] 
dist 82=[.70444492561468647564,3.3178981618805301972 ] 
dist 83=[.6346188325121233139 ,3.3038962799966089180 ] 
dist 84=[.56478678785154029561,3.3018550361138276321 ] 
dist 85=[.47590834476525490361,3.2822258584738529387 ] 
dist 86=[.38068863698885227507,3.2786068713453311773 ] 
dist 87=[.28549201658984899174,3.2743851437955440084 ] 
dist 88=[.1712799687461830061 ,3.2735496261513589261 ] 
dist 89=[0                     ,3.2427913407053724336 ] 
dist 90=[1.6677283556538135163 ,3.2389120853375388119 ] 
dist 91=[1.6370665256069977563 ,3.2312901997919725652 ] 
dist 92=[1.6079740916597688761 ,3.2293614517605567380 ] 
dist 93=[1.5843314603031570112 ,3.2226960085522614009 ] 
dist 94=[1.5599589500870059293 ,3.2212120548375201122 ] 
dist 95=[1.5279470703160235662 ,3.2192800990247685591 ] 
dist 96=[1.4962227336413389607 ,3.2186360311012011209 ] 
dist 97=[1.4730003683850865696 ,3.1580079435348531517 ] 
dist 98=[1.4513703741534207355 ,3.1527933769479062284 ] 
dist 99=[1.4260153696998805546 ,3.1413697372053018189 ] 
dist 100=[1.3999529128818088620 ,3.1388745898915608751 ] 
dist 101=[1.3754931766674255876 ,3.1254705923282002880 ] 
dist 102=[1.3473190497054685769 ,3.1230267651135574104 ] 
dist 103=[1.3063993841683518196 ,3.1179490566354535148 ] 
dist 104=[1.2653559213134241347 ,3.1144888701943537369 ] 
dist 105=[1.2366866168877669647 ,3.1039960248980768012 ] 
dist 106=[1.2113603702928423171 ,3.0938289168738038980 ] 
dist 107=[1.1836888199065946989 ,3.0905463760093515890 ] 
dist 108=[1.1563536250862502215 ,3.0897828911794820847 ] 
dist 109=[1.1323727686740088999 ,3.0874055152166495540 ] 
dist 110=[1.1060577607271581029 ,3.0758002907063386323 ] 
dist 111=[1.0693861823951368197 ,3.0738376288321890050 ] 
dist 112=[1.0320571440837055511 ,3.0627132853534825037 ] 
dist 113=[1.0031123589264485108 ,1.6084084825819067128 ] 
dist 114=[.9745296588957585842 ,1.5721080611967256145 ] 
dist 115=[.9386489265556318793 ,1.4874284460712053403 ] 
dist 116=[.9004610262127934527 ,1.4752472390746467515 ] 
dist 117=[.8626498742243817834 ,1.4182702770636193192 ] 
dist 118=[.8175562333459053138 ,1.4155455529560340160 ] 
dist 119=[.7502390720322078463 ,1.4150106681249886837 ] 
dist 120=[.6829631571645831392 ,1.3134326058361143453 ] 
dist 121=[.6380344981363931876 ,1.1592873302456513404 ] 
dist 122=[.6005120476668389168 ,1.1404714452914853401 ] 
dist 123=[.5628602606442192554 ,1.1026603421829954195 ] 
dist 124=[.5276392826236726761 ,1.0931584449235380124 ] 
dist 125=[.4998398363166513885 ,1.0602398825413876931 ] 
dist 126=[.4719254492505299234 ,1.0534611003010755492 ] 
dist 127=[.4362447191564051153 ,1.0445141258797090508 ] 
dist 128=[.4013446969200812838 ,1.0423314713259735650 ] 
dist 129=[.3765530668227909246 ,.82474153451659941254] 
dist 130=[.3542181287532417425 ,.80657367303196122944] 
dist 131=[.3291446403134514298 ,.76601466340200195618] 
dist 132=[.3039806050987263899 ,.75865626763896697782] 
dist 133=[.2812834885656107731 ,.7413104096633940623 ] 
dist 134=[.2558580828599884623 ,.73760400647142790262] 
dist 135=[.2197811511740668308 ,.73693069876200290553] 
dist 136=[.1839493047008821553 ,.68254928999753740769] 
dist 137=[.1595042164704643660 ,.63493698164805419419] 
dist 138=[.1385225561742771546 ,.62848166047378004111] 
dist 139=[.1165440911031021470 ,.61498015320218989437] 
dist 140=[.0953908441183739933 ,.6117369781296029327 ] 
dist 141=[.0777099774603037407 ,.59837459243618250066] 
dist 142=[.0590409435964981688 ,.59592899070966245537] 
dist 143=[.0339351220382642066 ,.59091428483539677697] 
dist 144=[.0087809280200851133 ,.58963675000511990393] 
dist 145=[-.0100815910698313371 ,.54737959902529171099] 
dist 146=[-.0281010372659396760 ,.54157989981368119619] 
dist 147=[-.0498830201195130248 ,.54011957969533911105] 
dist 148=[-.0726352231108283385 ,.53503870706078210608] 
dist 149=[-.0945354573202249514 ,.53399928691064723604] 
dist 150=[-.1201889621570837023 ,.53257622739353180875] 
dist 151=[-.1579538896787115720 ,.53219404038612306652] 
dist 152=[-.1956268749274271234 ,.38164368152907124473] 
dist 153=[-.2209126194419089145 ,.37339677510749328434] 
dist 154=[-.2421693103557167810 ,.35443841447919106111] 
dist 155=[-.2637264654849076687 ,.35149023968218139462] 
dist 156=[-.2840377928643363774 ,.32703377796982640051] 
dist 157=[-.3003112916036845475 ,.32268656402626308943] 
dist 158=[-.3168769548060319534 ,.31667173231021537195] 
dist 159=[-.3383569121713884400 ,.31501012351218847915] 
dist 160=[-.3595137657690187763 ,.28505229681559041081] 
dist 161=[-.3747870447174604949 ,.28129408555169417252] 
dist 162=[-.3887990019817798312 ,.27322881303267996704] 
dist 163=[-.4049106891452905019 ,.27148099990149752058] 
dist 164=[-.4212996630921826132 ,.26275026547558197364] 
dist 165=[-.4364207410429622304 ,.26123787170948506767] 
dist 166=[-.4536348687952036150 ,.25786389944964053724] 
dist 167=[-.4783958423169885912 ,.25725730869315629325] 
dist 168=[-.5031315387343165078 ,.2273888675887709011 ] 
dist 169=[-.5202445604796099285 ,.2245460955142332155 ] 
dist 170=[-.5351887131642418357 ,.2181962637296506555 ] 
dist 171=[-.5512491402013690256 ,.21705847794161286758] 
dist 172=[-.5669565094068523559 ,.20942153041903634101] 
dist 173=[-.5804884644388671653 ,.20808140880683578811] 
dist 174=[-.5951302834031918587 ,.20571046253496737697] 
dist 175=[-.6152770024812859485 ,.20519868308090110898] 
dist 176=[-.6356712951955960825 ,.19782105783320178393] 
dist 177=[-.65841768837718783737,.19682714546846741277] 
dist 178=[-.68889283065777608659,.19477265079563966181] 
dist 179=[-.71417800179941561557,.19426943231857103749] 
dist 180=[-.73927874685552465673,.19235136333650326086] 
dist 181=[-.76258458628198018888,.1919894796479535451 ] 
dist 182=[-.78069030974926608464,.19134438458571743548] 
dist 183=[-.79860216167106114205,.19120847418328258136] 
dist 184=[-.82113254070483244099,-.42349946548957669313] 
dist 185=[-.84299451237506427426,-.45362640370663297199] 
dist 186=[-.8595690804029931346 ,-.4573684321484074747 ] 
dist 187=[-.8784087721879830006 ,-.4656179352142922904 ] 
dist 188=[-.8958809823438516701 ,-.46710693712573978355] 
dist 189=[-.9094208004288198907 ,-.47659099431118139407] 
dist 190=[-.9227836390078754588 ,-.47821062624786433794] 
dist 191=[-.9395479553182432821 ,-.48120283112147735072] 
dist 192=[-.9557933922800996669 ,-.48186324274028985145] 
dist 193=[-.9670807666010130593 ,-.50196477472156290628] 
dist 194=[-.97763647259234765454,-.50405481737413403994] 
dist 195=[-.98812832030284447057,-.50812774234079518276] 
dist 196=[-.99863643971678131325,-.50909402572852904204] 
dist 197=[-1.0084535161397330196 ,-.51208243370738516444] 
dist 198=[-1.0173863435585507280 ,-.5127048430777342726 ] 
dist 199=[-1.0311905938580522694 ,-.5127372406440978872 ] 
dist 200=[-1.0447537380869872238 ,-.51197467980831254799] 
dist 201=[-1.0537620687360650325 ,-.51084344798781247183] 
dist 202=[-1.0612311799500731312 ,-.50940121190498599199] 
dist 203=[-1.0686375859142393530 ,-.50744322611511441082] 
dist 204=[-1.0755091673862605722 ,-.50424903608085604559] 
dist 205=[-1.0808390352395843855 ,-.50047245598764527138] 
dist 206=[-1.0861039220857098957 ,-.49618501927412413605] 
dist 207=[-1.0927156038505573045 ,-.49066670863962229132] 
dist 208=[-1.0991261728281440561 ,-.48196692012470303314] 
dist 209=[-1.1035866349340566427 ,-.47305820862851551772] 
dist 210=[-1.1087898039021434276 ,-.46670423152652087834] 
dist 211=[-1.1139436452983731649 ,-.4609544866870165206 ] 
dist 212=[-1.1189319894140301117 ,-.45446249333838259665] 
dist 213=[-1.1234808379032372046 ,-.44792675746679986645] 
dist 214=[-1.1268767169834930011 ,-.44200200953141776764] 
dist 215=[-1.1301060934902007071 ,-.43534163674850118047] 
dist 216=[-1.1345270380470735314 ,-.42586351339801401352] 
dist 217=[-1.1380167814680669861 ,-.41613047228156460536] 
dist 218=[-1.1407998656975820221 ,-.40845045419471223329] 
dist 219=[-1.1433783019977742456 ,-.4007414364545750862 ] 
dist 220=[-1.1456529318321626709 ,-.39089236208100064514] 
dist 221=[-1.1472207974465239664 ,-.38032292085536700546] 
dist 222=[-1.1485839390951918350 ,-.36973254592836132676] 
dist 223=[-1.1500396817384076952 ,-.35701062119360001759] 
dist 224=[-1.1513348872084121505 ,-.33791534598651511121] 
dist 225=[-1.1520558893614424431 ,-.31850852220305400148] 
dist 226=[-1.1525000499458704353 ,-.30454044700957456053] 
dist 227=[-1.1526879080579800905 ,-.29176949512406795239] 
dist 228=[-1.1527677114287209011 ,-.27715093084034943761] 
dist 229=[-1.1527796477112073110 ,-.26231918371160519071] 
dist 230=[-1.1527015843770426120 ,-.24869552165031103696] 
dist 231=[-1.1519080327606389061 ,-.23323529376549633522] 
dist 232=[-1.1290126849239792091 ,-.21105758067752781214] 
dist 233=[-1.1273561694937792396 ,-.18820561692003819326] 
dist 234=[-1.1241168069673283814 ,-.17004849156448466126] 
dist 235=[-1.1232800964397947267 ,-.15170570604940792445] 
dist 236=[-1.1201642468394636928 ,-.1281111198849641827 ] 
dist 237=[-1.1123233996360792873 ,-.10270959440438583935] 
dist 238=[-1.1110307955986937499 ,-.07713934576231930608] 
dist 239=[-1.1031577009260373406 ,-.04633540998756553043] 

8 phat 1 dirichlet min maxes function [2, 2, 0, 2, 2, 2, 1, 2] 
dist 0=[1.4936466728740699411 ,1.4936466728740699411 ] 
dist 1=[1.4604202716387563961 ,1.5210887186877463704 ] 
dist 2=[1.4102476123207047059 ,1.5481244059357757962 ] 
dist 3=[1.3597550577916830024 ,1.5730934807443977437 ] 
dist 4=[1.3252491010918973343 ,1.5922692374921755746 ] 
dist 5=[1.2955679410756050279 ,1.6110303157877433630 ] 
dist 6=[1.2643741997908877479 ,1.6343407091747877228 ] 
dist 7=[1.2342880197296673210 ,1.6568192536394540968 ] 
dist 8=[1.2090370199970271405 ,1.6722530010273814766 ] 
dist 9=[1.1822834842071742386 ,1.6856062040039816532 ] 
dist 10=[1.1461872796130979771 ,1.6997627327528869882 ] 
dist 11=[1.1099664089729520884 ,1.7134919465480308666 ] 
dist 12=[1.0827142200711669662 ,1.7251359232194607181 ] 
dist 13=[1.0565906244490845460 ,1.7407783480219777444 ] 
dist 14=[1.0248840404436304736 ,1.7572520706100386541 ] 
dist 15=[.99169617385415143244,1.7756546307747317206 ] 
dist 16=[.95964756569753170159,1.8017045628323245675 ] 
dist 17=[.92202710550638536807,1.8275522933747470457 ] 
dist 18=[.86655227061479851543,1.8451460654285509258 ] 
dist 19=[.81055957416564466972,1.8602044851074993021 ] 
dist 20=[.77086770914390464543,1.8759109991981888162 ] 
dist 21=[.73519431847864242453,1.8909867749626571424 ] 
dist 22=[.69527520379982824763,1.9035222927400792363 ] 
dist 23=[.6552848219126217491 ,1.9167012049258341285 ] 
dist 24=[.6193263687182802741 ,1.9343505194627630257 ] 
dist 25=[.57913567106414702655,1.9520009166115960070 ] 
dist 26=[.52221664590387930609,1.9651841636946477853 ] 
dist 27=[.46387387419440354418,1.9777272864529266955 ] 
dist 28=[.41798830300548098886,1.9928172385098051919 ] 
dist 29=[.37206429992885876297,2.0085412879539793896 ] 
dist 30=[.3135678040381999218 ,2.0236207621932492916 ] 
dist 31=[.25087415195694188191,2.0412424625812077973 ] 
dist 32=[.18816185554754945031,2.0671352502233621994 ] 
dist 33=[.11289817957255793749,2.0929095087600239880 ] 
dist 34=[0                     ,2.1100571022680933777 ] 
dist 35=[1.4477689097935193707 ,2.1243069300205435006 ] 
dist 36=[1.4640794139937919856 ,2.1384903205534489828 ] 
dist 37=[1.5017311564960475327 ,2.1516842649088299047 ] 
dist 38=[1.5073434319116247462 ,2.1619763746241323183 ] 
dist 39=[1.5562169245116518234 ,2.1721982449216687664 ] 
dist 40=[1.5648664155875270440 ,2.1851112365782961251 ] 
dist 41=[1.5761523207006399276 ,2.1976687504007145344 ] 
dist 42=[1.5786646556957891417 ,2.2064687334306025013 ] 
dist 43=[1.6398919599656026837 ,2.2142726427195527698 ] 
dist 44=[1.6473926281345769251 ,2.2228459288034052329 ] 
dist 45=[1.6630530088831005686 ,2.2313428292314382332 ] 
dist 46=[1.6667394064645423905 ,2.2388412013813926499 ] 
dist 47=[1.6819936887362852604 ,2.2471065177257649871 ] 
dist 48=[1.6847690616667315049 ,2.2586711441567739348 ] 
dist 49=[1.6902166467645959494 ,2.2700883318431169745 ] 
dist 50=[1.6915195836197383729 ,2.2777639033496534165 ] 
dist 51=[1.7990163415637747605 ,2.2842302651310582302 ] 
dist 52=[1.8071314473793983433 ,2.2908106951097804523 ] 
dist 53=[1.8247734692000286829 ,2.2970254480053786414 ] 
dist 54=[1.8282616379486055328 ,2.3020291263711242465 ] 
dist 55=[1.8478950254828172067 ,2.3071451077947233415 ] 
dist 56=[1.8512599062989210197 ,2.3138090664688874882 ] 
dist 57=[1.8581044884060941654 ,2.3203874536844855371 ] 
dist 58=[1.8625315262163956961 ,2.3251611555203436173 ] 
dist 59=[1.9123113558456149175 ,2.3295658711547259772 ] 
dist 60=[1.9178319477512651073 ,2.3346683387541352341 ] 
dist 61=[1.9323867168901940045 ,2.3398799252078305798 ] 
dist 62=[1.9492366432725585991 ,2.3447211100685715338 ] 
dist 63=[2.0358816588444275419 ,2.3502586067401871150 ] 
dist 64=[2.0432918187202597942 ,2.3582553966776567925 ] 
dist 65=[2.0600591688599892140 ,2.3661702107463049732 ] 
dist 66=[2.0627464236390674847 ,2.3713798097580284408 ] 
dist 67=[2.0833944545784270894 ,2.3756471984288849921 ] 
dist 68=[2.0869812165974605144 ,2.3797932323374855156 ] 
dist 69=[2.0924240617998522786 ,2.3835843651552677401 ] 
dist 70=[2.0937672415035863912 ,2.3864321730873906642 ] 
dist 71=[2.1069562023203947244 ,2.3891576062086636475 ] 
dist 72=[2.0938937644792974265 ,2.3924592494434459599 ] 
dist 73=[2.0805352414198819640 ,2.3956012630693302601 ] 
dist 74=[2.0700784730416740616 ,2.3976881888925589708 ] 
dist 75=[2.0596593120032768041 ,2.3994186563867374982 ] 
dist 76=[2.0464512044654178318 ,2.4011348604439397983 ] 
dist 77=[2.0323278555870563799 ,2.4027273551756126414 ] 
dist 78=[2.0182478144458909394 ,2.4039629951321555532 ] 
dist 79=[2.0013848682315426281 ,2.4051840142626984149 ] 
dist 80=[1.9761301686354944357 ,2.4067180312319344252 ] 
dist 81=[1.9504813873314992412 ,2.4081571842749954887 ] 
dist 82=[1.9320421498196795334 ,2.4089987546963544031 ] 
dist 83=[1.9152037499254544576 ,2.4095703891421594089 ] 
dist 84=[1.8959581561030917480 ,2.4099298137249474669 ] 
dist 85=[1.8764464467554002563 ,2.4101596899425356054 ] 
dist 86=[1.8585436060203203781 ,2.4102131370982370551 ] 
dist 87=[1.8382416873920516452 ,2.4101776883964615680 ] 
dist 88=[1.8091338932321843963 ,2.4101156736846863537 ] 
dist 89=[1.7791443783758856424 ,2.4084177157513450285 ] 
dist 90=[1.7553156589963851169 ,2.4081070011457474314 ] 
dist 91=[1.7312412655854849654 ,2.4074842224913183961 ] 
dist 92=[1.7002690739076659574 ,2.4072827864234505062 ] 
dist 93=[1.6669198862952912289 ,2.4063520469547465437 ] 
dist 94=[1.6333377337950851695 ,2.4061347382969315698 ] 
dist 95=[1.5928713907458291169 ,2.4054459714393732615 ] 
dist 96=[1.5319860954730924886 ,2.4053217897639720187 ] 
dist 97=[1.4710321560117488080 ,2.3924585150012062077 ] 
dist 98=[1.4302912420669609091 ,2.3912075315001242507 ] 
dist 99=[1.3962286153993446024 ,2.3882984452997532856 ] 
dist 100=[1.3619871880848430683 ,2.3876942683695474411 ] 
dist 101=[1.3299169705953139436 ,2.3836049954735263530 ] 
dist 102=[1.3045389761418844726 ,2.3827985602811737659 ] 
dist 103=[1.2789952884774380524 ,2.3814056499667394812 ] 
dist 104=[1.2462623139473321883 ,2.3810575628224211034 ] 
dist 105=[1.2142058594921911225 ,2.3742864705712617801 ] 
dist 106=[1.1913681876024559469 ,2.3733332250832782768 ] 
dist 107=[1.1707254465290466533 ,2.3711803040722278607 ] 
dist 108=[1.1474485059910450313 ,2.3706330734967708809 ] 
dist 109=[1.1240283029088892427 ,2.3677292570198755580 ] 
dist 110=[1.1028125253229616580 ,2.3671388532745458182 ] 
dist 111=[1.0789720976074343123 ,2.3659334594935689563 ] 
dist 112=[1.0450535443408225404 ,2.3655815220932331641 ] 
dist 113=[1.0113267915251796834 ,2.3161157730026330918 ] 
dist 114=[.98825354731997998122,2.3125988402700415011 ] 
dist 115=[.96838026313129150583,2.3054125966974121444 ] 
dist 116=[.94745304517583029207,2.3035351229497825196 ] 
dist 117=[.92724403383107199112,2.2965992929135788861 ] 
dist 118=[.9102435075840678125 ,2.2952030733818762608 ] 
dist 119=[.89219729865355787358,2.2924661924126913340 ] 
dist 120=[.86780565630992461886,2.2914576693274806764 ] 
dist 121=[.84331060990269525492,2.2462962766663244248 ] 
dist 122=[.82485079458027613899,2.2417905583781603491 ] 
dist 123=[.80712649906201009078,2.2360925921911366950 ] 
dist 124=[.78557346171896746253,2.2307579394213154540 ] 
dist 125=[.76299225210809608126,2.2008675725973185866 ] 
dist 126=[.74115536558355426159,2.1837846218273022572 ] 
dist 127=[.71549893276721606738,1.2720541731379719379 ] 
dist 128=[.67763990228993708838,1.2498064716465788531 ] 
dist 129=[.63983635030298923879,1.1978911290423761090 ] 
dist 130=[.61440182615654677987,1.1904064679979055318 ] 
dist 131=[.59295325731625485737,1.1211056686458330195 ] 
dist 132=[.57109314638136828809,1.1087063315014620327 ] 
dist 133=[.5504275109147243977 ,1.0936636362342117672 ] 
dist 134=[.53375673002069330985,1.0909648559277312435 ] 
dist 135=[.51668285060255642068,.99597388762955856082] 
dist 136=[.49440485948623003285,.9843553079307539592 ] 
dist 137=[.47239604686695239703,.96100197746526913371] 
dist 138=[.45639885576329736328,.95512417807927225906] 
dist 139=[.44161217030877733166,.93471083084947761335] 
dist 140=[.42444526483040284524,.9305054463643990382 ] 
dist 141=[.40689077760556202487,.92483082804963535453] 
dist 142=[.39055380213195777541,.92332158672258496024] 
dist 143=[.37184376060019929187,.78770250290110151556] 
dist 144=[.34479723548109299121,.77632701644658620171] 
dist 145=[.31772204807070471538,.75093025155399116094] 
dist 146=[.29889736010757103724,.74629300859860480357] 
dist 147=[.28235976499724845713,.71568198851927117063] 
dist 148=[.26443273085970756075,.71027752224229908209] 
dist 149=[.24680735993078277049,.70060556235846667082] 
dist 150=[.23147638888288386284,.69846713025218887907] 
dist 151=[.21476317075056263469,.66833028632483749157] 
dist 152=[.19160894331994415894,.66423422335327839054] 
dist 153=[.16809989203548433723,.65559856539017877618] 
dist 154=[.14996741233019577389,.65355861956140410529] 
dist 155=[.13215287735656791502,.6447107710994637482 ] 
dist 156=[.10991557467381066321,.64312287797906341737] 
dist 157=[.08631298318403292877,.63963312647795435168] 
dist 158=[.06303742320087174690,.63893601164265732524] 
dist 159=[.03534870314531146126,.44711279885117321166] 
dist 160=[-.00590610771557537300,.43623542540170880622] 
dist 161=[-.04710356418865319702,.41106942812158648891] 
dist 162=[-.07456287216332561886,.40729409471875307564] 
dist 163=[-.09743698425339104099,.37436929504855053238] 
dist 164=[-.12029409451496400725,.36850759826688157026] 
dist 165=[-.14161398954914185638,.36086716550462593583] 
dist 166=[-.15833938734617766605,.35909936194379604157] 
dist 167=[-.17503906841440540945,.31678456630517201251] 
dist 168=[-.19625609898616177115,.31155469000808939722] 
dist 169=[-.21694692592989200014,.3006707326321398743 ] 
dist 170=[-.2315418426742774773 ,.29800012657002456223] 
dist 171=[-.24458411619991708738,.28742584350329352815] 
dist 172=[-.25906451835670603449,.28545626900739569904] 
dist 173=[-.27350477941976715876,.2815521656595086462 ] 
dist 174=[-.2863864923990736782 ,.28058933941736124988] 
dist 175=[-.30070044445846843906,.2311688336751948992 ] 
dist 176=[-.32086952523774916978,.2268029156466863448 ] 
dist 177=[-.34084128936580974796,.21666355874620749355] 
dist 178=[-.35436599363999619572,.21519695059658193627] 
dist 179=[-.36586660297700044346,.20184987904107461542] 
dist 180=[-.37774218041050772484,.19948044064207244568] 
dist 181=[-.38906641942204199694,.19654899624981415711] 
dist 182=[-.39836172765672345243,.19601290109679838115] 
dist 183=[-.40802737848549879643,.17848856565938568319] 
dist 184=[-.42083295255086379405,.17636029811624283182] 
dist 185=[-.43357513135878489909,.17203441174195625975] 
dist 186=[-.44298720720429905902,.17094259688878010529] 
dist 187=[-.45183878491538287876,.16711111531751464244] 
dist 188=[-.46233902464478714279,.16634897960293923573] 
dist 189=[-.47320056816939180487,.16522584343955139903] 
dist 190=[-.48349732660083516561,.16493752368948199349] 
dist 191=[-.49543832225338657403,-.01615866298375935759] 
dist 192=[-.512876657838326285  ,-.01644790291681235660] 
dist 193=[-.53021525016862116366,-.03996995086358477473] 
dist 194=[-.54175728231590777824,-.04173016425573746138] 
dist 195=[-.55135589504381716515,-.04554841031077748268] 
dist 196=[-.56092099505610716306,-.04631510205425467317] 
dist 197=[-.56982579931490568868,-.05054735300001140198] 
dist 198=[-.57678329200655341231,-.05127466400824877338] 
dist 199=[-.58370363173961838636,-.05277497590973158570] 
dist 200=[-.59245982770766168896,-.05313268561114213848] 
dist 201=[-.60098137763046058936,-.05585975132055383355] 
dist 202=[-.6069631555626240908 ,-.05631011575753457836] 
dist 203=[-.61227826021588324598,-.05679575686239905376] 
dist 204=[-.6181331806090447595 ,-.05680844491330583699] 
dist 205=[-.62394501805783294108,-.05662148486225875902] 
dist 206=[-.62908779504276487096,-.05614506832397548537] 
dist 207=[-.63476801701891973978,-.05536165893387520543] 
dist 208=[-.64272958317215840376,-.05394684835217018388] 
dist 209=[-.65059516435815530864,-.05241446785885992367] 
dist 210=[-.65589145562019965036,-.05116079802886232674] 
dist 211=[-.66036239276270515123,-.04986150734642293616] 
dist 212=[-.66492663619119171724,-.04814658017600017718] 
dist 213=[-.66924623650754474506,-.04627907147397038280] 
dist 214=[-.67273862453509271467,-.04436946971086331504] 
dist 215=[-.67632255401143650647,-.04204781943273007804] 
dist 216=[-.68100831139193032301,-.03853222506797656837] 
dist 217=[-.68564190359642763422,-.03483143701334117006] 
dist 218=[-.68901717734419681314,-.03176905277117826399] 
dist 219=[-.69214443899176315042,-.02856333994733042089] 
dist 220=[-.69578600645035314131,-.02428925153229408328] 
dist 221=[-.69951584586413646796,-.01961318333002475046] 
dist 222=[-.70299618691327148637,-.01479965858412002485] 
dist 223=[-.70698931383296905413,-.00892405918037265353] 
dist 224=[-.71277024782049950722,0                     ] 
dist 225=[-.71849136574200185725,-.18080603622702941208] 
dist 226=[-.7222452347909759008 ,-.17984578847307020558] 
dist 227=[-.7253069017376179821 ,-.1787203260775981465 ] 
dist 228=[-.72825927933531457104,-.17745604137617148574] 
dist 229=[-.73094409659557007291,-.1758376256983782411 ] 
dist 230=[-.73293554977608242017,-.17329569678667769023] 
dist 231=[-.73481666196208642502,-.17058272894686110727] 
dist 232=[-.73706012989623999451,-.16828017468801357136] 
dist 233=[-.73917711349411627579,-.16581872027657627086] 
dist 234=[-.74055230246112071026,-.16247014582310526795] 
dist 235=[-.7416584500429430287 ,-.1587740974623234083 ] 
dist 236=[-.74269929581945576016,-.15492280404326064345] 
dist 237=[-.74362860203512344331,-.15018827215687056211] 
dist 238=[-.7442886061331011162 ,-.14295944576455766596] 
dist 239=[-.74488310672987749061,-.13556402940630092203] 
dist 240=[-.74555041549235181591,-.13016316153809500662] 
dist 241=[-.74614811597229750094,-.12514588164667544334] 
dist 242=[-.74646418938980905041,-.11928471299112876726] 
dist 243=[-.74663697121463682927,-.11327184531883661772] 
dist 244=[-.74667153870496958061,-.1076477843220231015 ] 
dist 245=[-.74663006897550314644,-.10118511310468536614] 
dist 246=[-.74657896047842212281,-.09181795363228988755] 
dist 247=[-.74650323388157380156,-.08212504649242004085] 
dist 248=[-.74645053618407787103,-.07435943880644336711] 
dist 249=[-.74304931389831235569,-.06645546933902699569] 
dist 250=[-.74260488076992916016,-.05620912856601357402] 
dist 251=[-.74197603513120831802,-.04513859866378714137] 
dist 252=[-.74140323813211241762,-.03393802017588657810] 
dist 253=[-.73755927326853922351,-.02040397354758102650] 

8 phat 1 dirichlet min maxes function [2, 2, 0, 2] 
dist 0=[1.3315824796456996138 ,1.3315824796456996138 ] 
dist 1=[1.2839566826522532350 ,1.3789770010124176354 ] 
dist 2=[1.2514082932846996608 ,1.4106003069871589280 ] 
dist 3=[1.2234093348670092258 ,1.4369804507006191829 ] 
dist 4=[1.1939809093550932578 ,1.4634027326737460039 ] 
dist 5=[1.1655957653743692929 ,1.4880883840358692509 ] 
dist 6=[1.1417698533668928233 ,1.5075221423187136011 ] 
dist 7=[1.1165239564373939976 ,1.5269898560845736174 ] 
dist 8=[1.0824589859780150218 ,1.5518113307061898572 ] 
dist 9=[1.0482750497935429093 ,1.5760603320882267996 ] 
dist 10=[1.0225533005403843340 ,1.5932381994441668895 ] 
dist 11=[.99789469191654600101,1.6086649243361311562 ] 
dist 12=[.967963236765125492  ,1.6259094941589837615 ] 
dist 13=[.93663186729545380007,1.6431744384577801740 ] 
dist 14=[.90637371281863879164,1.6586826637801104131 ] 
dist 15=[.87085323184789753384,1.6760031676268323496 ] 
dist 16=[.81847297209687162062,1.7005170953044025494 ] 
dist 17=[.76560290911523299209,1.7248389117766076782 ] 
dist 18=[.72812325441506586892,1.7413909878677309199 ] 
dist 19=[.69443671247858959209,1.7555545371460835732 ] 
dist 20=[.65673880241882770945,1.7703224282756261516 ] 
dist 21=[.61897237670543997295,1.7844940379119222340 ] 
dist 22=[.58501177822546120132,1.7962725098484968554 ] 
dist 23=[.54705255037535289791,1.8086509072697404963 ] 
dist 24=[.49329192352450785493,1.8252221828079079246 ] 
dist 25=[.43818574910582035574,1.8417917299689832960 ] 
dist 26=[.39484443754668040987,1.8541632183322100600 ] 
dist 27=[.3514656454562947122 ,1.8659296183307009272 ] 
dist 28=[.29620955220888469076,1.8800788614179542670 ] 
dist 29=[.23698799568387183073,1.8948193121095385427 ] 
dist 30=[.17774766386064449248,1.9089505072315145117 ] 
dist 31=[.10664998959567449944,1.9254602370647868406 ] 
dist 32=[0                     ,1.9497146713487231472 ] 
dist 33=[1.3682616841909744259 ,1.9738575083550983992 ] 
dist 34=[1.3836908626755846586 ,1.9899208580626203884 ] 
dist 35=[1.4193045882237657284 ,2.0032709261478229498 ] 
dist 36=[1.4246161382017502180 ,2.0165608188671891176 ] 
dist 37=[1.4708339734129717744 ,2.0289249367376099545 ] 
dist 38=[1.4790132328051247603 ,2.0385719676541212770 ] 
dist 39=[1.4896958927146734020 ,2.0481552667763795925 ] 
dist 40=[1.4920819148745060062 ,2.0602644619228561792 ] 
dist 41=[1.5499374004791583570 ,2.0720417160483875139 ] 
dist 42=[1.5570265074125422622 ,2.0802972734888915171 ] 
dist 43=[1.5718349861718727494 ,2.0876208516690752814 ] 
dist 44=[1.5753137273424402079 ,2.0956702514969833039 ] 
dist 45=[1.5897658143336178654 ,2.1036501631055409737 ] 
dist 46=[1.5923907701682257932 ,2.1106957933405442669 ] 
dist 47=[1.5975624713582834077 ,2.1184649628384996690 ] 
dist 48=[1.5988044639746591117 ,2.1293389835497621484 ] 
dist 49=[1.7008017878717111996 ,2.1400759231763264946 ] 
dist 50=[1.7084942967549904726 ,2.1472967777187747889 ] 
dist 51=[1.7252114419954161766 ,2.1533828966598146765 ] 
dist 52=[1.7285225860243396348 ,2.1595809699757602528 ] 
dist 53=[1.7471080203686977535 ,2.1654375228154274286 ] 
dist 54=[1.7502928293296442072 ,2.1701575830492656312 ] 
dist 55=[1.7567855995829095744 ,2.1749879334432931263 ] 
dist 56=[1.7583813229133613726 ,2.1812856404127210581 ] 
dist 57=[1.8083093164575103377 ,2.1875052174482967493 ] 
dist 58=[1.8135538763444101132 ,2.1920230537561728900 ] 
dist 59=[1.8217541125582659359 ,2.1961962383481039759 ] 
dist 60=[1.8237301608064704361 ,2.2010372319762333247 ] 
dist 61=[1.8541788121976934316 ,2.2059854974959125700 ] 
dist 62=[1.8573684937586959323 ,2.2105877633917284706 ] 
dist 63=[1.8764743179515541046 ,2.2158564653670486349 ] 
dist 64=[1.9047708640987229038 ,2.2234704329638835901 ] 
dist 65=[1.9258677109035035359 ,2.2310085677791765906 ] 
dist 66=[1.9329209856219329978 ,2.2359739439754796024 ] 
dist 67=[1.9488869654561524657 ,2.2400454124829499305 ] 
dist 68=[1.9514411242730371429 ,2.2440079748229461591 ] 
dist 69=[1.9711215215678878281 ,2.2476359005918571549 ] 
dist 70=[1.9745410099153817699 ,2.2503688451073574678 ] 
dist 71=[1.9797124683207533176 ,2.2529918990584393581 ] 
dist 72=[1.9703207871121401940 ,2.2561802711575056997 ] 
dist 73=[1.9575621327086553839 ,2.2592199428863861524 ] 
dist 74=[1.9475805211884197651 ,2.2612482056919658064 ] 
dist 75=[1.9376400462801211784 ,2.2629403096267374764 ] 
dist 76=[1.9250459247522052189 ,2.2646353682859043248 ] 
dist 77=[1.9115827501188966201 ,2.2662192207603724874 ] 
dist 78=[1.8981661437624413638 ,2.2674665086478215084 ] 
dist 79=[1.8821016463372724698 ,2.2687163803085689136 ] 
dist 80=[1.8580471638831903855 ,2.2703105715332585758 ] 
dist 81=[1.8336191132358759610 ,2.2718176785858840828 ] 
dist 82=[1.8160603767361131396 ,2.2727192199324304524 ] 
dist 83=[1.8000289952138854612 ,2.2733569568592113961 ] 
dist 84=[1.7817102091018439528 ,2.2738088616951515331 ] 
dist 85=[1.7631406138791277449 ,2.2741228110295209515 ] 
dist 86=[1.7461060159568367285 ,2.2742087332858947263 ] 
dist 87=[1.7267917359363634671 ,2.2742047323025158278 ] 
dist 88=[1.6991036278146909758 ,2.2741589914310420693 ] 
dist 89=[1.6705783738190527872 ,2.2730570959003366945 ] 
dist 90=[1.6479155882068892904 ,2.2728275778739208178 ] 
dist 91=[1.6250214365844990772 ,2.2723238860167282558 ] 
dist 92=[1.5955707367298265060 ,2.2721439113052827750 ] 
dist 93=[1.5638613557470132976 ,2.2712437954036207325 ] 
dist 94=[1.5319326930975978751 ,2.2710277793675531374 ] 
dist 95=[1.4934604204813678885 ,2.2704274857631426975 ] 
dist 96=[1.4355772218045075645 ,2.2702527641167750018 ] 
dist 97=[1.3776295328351169504 ,2.2598423262133392885 ] 
dist 98=[1.3388993045518990388 ,2.2587828361487885405 ] 
dist 99=[1.3065192428730647108 ,2.2563179540879197606 ] 
dist 100=[1.2739716146548656146 ,2.2557892919376520075 ] 
dist 101=[1.2434893342503590640 ,2.2522976849883022713 ] 
dist 102=[1.2193704668375015697 ,2.2516019650015911216 ] 
dist 103=[1.1950964913361597842 ,2.2503758836434525696 ] 
dist 104=[1.1639937933716190560 ,2.2500683499848037469 ] 
dist 105=[1.1335354579028099757 ,2.2441453470703582672 ] 
dist 106=[1.1118388709263731973 ,2.2433040281817280850 ] 
dist 107=[1.0922301722413694751 ,2.2413925764523490308 ] 
dist 108=[1.0701231907996330436 ,2.2409063147274330715 ] 
dist 109=[1.0478824127567061432 ,2.2382808651201421663 ] 
dist 110=[1.0277385404281959853 ,2.2377430457517419402 ] 
dist 111=[1.0051054538097414205 ,2.2366601994018415320 ] 
dist 112=[.972908056023377188  ,2.2363456214623483767 ] 
dist 113=[.94089418514796909765,2.1904692905707253610 ] 
dist 114=[.91899518866890498325,2.1872143001885261702 ] 
dist 115=[.90013589969215264858,2.1805720047094651211 ] 
dist 116=[.88028056890469655924,2.1788377938593898436 ] 
dist 117=[.86110917789053096302,2.1724411992044503461 ] 
dist 118=[.84498558277411648752,2.1711490855281203388 ] 
dist 119=[.8278737733173629215 ,2.1686327933472697715 ] 
dist 120=[.80474961919577203664,2.1679803201745778492 ] 
dist 121=[.78152949655069854522,2.1254974152609188794 ] 
dist 122=[.76403382215330268945,2.1212913129206334924 ] 
dist 123=[.74723850229136576338,2.1159859349326402354 ] 
dist 124=[.72681973098969629718,2.1147303059091134798 ] 
dist 125=[.70542934315030208162,2.0830346985007010991 ] 
dist 126=[.68474764980833161528,2.0802711359782389238 ] 
dist 127=[.66045121566321649208,2.0589834923487988985 ] 
dist 128=[.62460220937807873693,2.0266749580109094002 ] 
dist 129=[.58880703618200960545,1.2102125200732829514 ] 
dist 130=[.56472592925867531569,1.1892709000320717059 ] 
dist 131=[.54442103673371296484,1.1404024600281711671 ] 
dist 132=[.52373036096326406013,1.1333565830842890557 ] 
dist 133=[.50417267265009531064,1.0681189520032528220 ] 
dist 134=[.48839962189214868519,1.0564460234530997694 ] 
dist 135=[.47224877880745285789,1.0422843452314242435 ] 
dist 136=[.45117995722037290999,1.0397422022712338258 ] 
dist 137=[.43036796199173272026,.95030414371882245823] 
dist 138=[.41524439984520534576,.93936392133600619563] 
dist 139=[.40126898662512988908,.91737424137597798014] 
dist 140=[.38504947759412150433,.91183939535662836792] 
dist 141=[.36846684786147574337,.89261581683158933719] 
dist 142=[.35303898646858577891,.88865530189977090123] 
dist 143=[.335373787209703455  ,.88330789370369481517] 
dist 144=[.3098420194059529423 ,.88188212231526899796] 
dist 145=[.28428502444000478243,.75412110433664501269] 
dist 146=[.26651891893844875172,.74340313154894666478] 
dist 147=[.25091448184664705642,.71947464909172905323] 
dist 148=[.23400395434405476602,.71510402619248803465] 
dist 149=[.21738092620254444952,.68626213825518733566] 
dist 150=[.20292645913394968785,.68116952966505923665] 
dist 151=[.18717268463585707397,.67205363777884042352] 
dist 152=[.16535255070173054692,.67003728584778568019] 
dist 153=[.14320020950936017464,.6416357754582143873 ] 
dist 154=[.12611763766356403068,.63777486385331204987] 
dist 155=[.10933790989587137861,.62963344211841571951] 
dist 156=[.08839691613124522346,.62771052382440747223] 
dist 157=[.06617259327194235266,.61936171149589096469] 
dist 158=[.04425967152693603425,.6178638912684343101 ] 
dist 159=[.01819453041508765426,.6145662135446944787 ] 
dist 160=[-.02063827388110502558,.61391167777591277775] 
dist 161=[-.05941590020112643675,.43287187437505620154] 
dist 162=[-.08526033467105607774,.42260362368129153722] 
dist 163=[-.10678704215895957756,.39884750402384835534] 
dist 164=[-.12829417236714415457,.39528199895061645566] 
dist 165=[-.14835257110623851394,.36420195676062726029] 
dist 166=[-.16408449089492597585,.3586682309375922715 ] 
dist 167=[-.17978863413091402793,.35145106754695921054] 
dist 168=[-.19973592930848345815,.3497767980472966196 ] 
dist 169=[-.2191861407561484042 ,.30983464458173079901] 
dist 170=[-.23290199648338244225,.30489662883906456988] 
dist 171=[-.24515461462340009526,.29461753294245196677] 
dist 172=[-.25875201528290921726,.29209661867747105579] 
dist 173=[-.27230808135773884243,.28209881547522403165] 
dist 174=[-.28439536510144951781,.28023781934195143324] 
dist 175=[-.2978219023900171169 ,.27654021165863934166] 
dist 176=[-.31673485490891768914,.27562580910565627189] 
dist 177=[-.33546032578763998866,.22897214764009909715] 
dist 178=[-.34813695439712287396,.22484758763232481652] 
dist 179=[-.35891197394765038842,.21526649008879892084] 
dist 180=[-.37003118996226567435,.21388141583313698103] 
dist 181=[-.3806297426305712612 ,.20126114909609071325] 
dist 182=[-.38932215845570112115,.19902008859338660421] 
dist 183=[-.39835444159532650668,.1962514213339965979 ] 
dist 184=[-.41031243110574131543,.19574713136852687319] 
dist 185=[-.42220729330755139448,.1791431060117948401 ] 
dist 186=[-.43098707323371581607,.17712639048396633185] 
dist 187=[-.43923763402378603246,.1730303478382672374 ] 
dist 188=[-.44901567015709475623,.17199700382234780341] 
dist 189=[-.45912513821762040909,.16837461392659741139] 
dist 190=[-.46870139510523603281,.16765251875418413304] 
dist 191=[-.479801008857000127  ,.1665979446364453123 ] 
dist 192=[-.49600375907935210825,.16632403020341317766] 
dist 193=[-.5121110108039015016 ,-.00623821941518019363] 
dist 194=[-.52282863967291326048,-.01330451312104079952] 
dist 195=[-.53173646172579011717,-.02957344559034422066] 
dist 196=[-.54060465880159785221,-.03204984197643931567] 
dist 197=[-.54885515614216971349,-.05306298575390104736] 
dist 198=[-.55529223816908324958,-.05651266078054362327] 
dist 199=[-.56168632237570574286,-.05784953321307268460] 
dist 200=[-.56976483253616056878,-.05809404390218876536] 
dist 201=[-.57762111239591402882,-.06006022852649389262] 
dist 202=[-.58312629659561801267,-.06041229902742004430] 
dist 203=[-.58800789369092209215,-.06058679257676062803] 
dist 204=[-.59336988460958174618,-.06038728636342170957] 
dist 205=[-.59868341419790031274,-.05998965623318920497] 
dist 206=[-.60337117059398597108,-.05932670641044392188] 
dist 207=[-.60853715321373706292,-.05833714417698958449] 
dist 208=[-.61576354208444512365,-.05663318177151908519] 
dist 209=[-.62289659296431060937,-.05481492643016164952] 
dist 210=[-.62768923252308453185,-.05336821087763323956] 
dist 211=[-.63172367639678185788,-.05190532104854823192] 
dist 212=[-.63582401685154720821,-.05002230649692136062] 
dist 213=[-.63969302719848222538,-.04799499760717481921] 
dist 214=[-.64280217270466679601,-.04595494465200671129] 
dist 215=[-.6459756338893754476 ,-.04349825408964389310] 
dist 216=[-.65010190081610445833,-.03980449954749743361] 
dist 217=[-.65417149621222718325,-.03592669468936905450] 
dist 218=[-.65711827667972929817,-.03273384219076405401] 
dist 219=[-.65983075390246596817,-.02940567298545961065] 
dist 220=[-.66296315866690741644,-.02498661448533208362] 
dist 221=[-.66615701406235982178,-.02016068243624396267] 
dist 222=[-.66911528794810056028,-.01520512268237422376] 
dist 223=[-.67249218766699983127,-.00916477721296100048] 
dist 224=[-.67736050646738160357,0                     ] 
dist 225=[-.6821723988650750736 ,-.16613803282171774587] 
dist 226=[-.6853235990028833592 ,-.16585862800575132426] 
dist 227=[-.68788692424718563506,-.16542300087403685036] 
dist 228=[-.690347375084578111  ,-.16465622591029526302] 
dist 229=[-.69257724680664020974,-.1637278295470743617 ] 
dist 230=[-.69421827952480688916,-.16264571244099547461] 
dist 231=[-.695755569464079356  ,-.16123493157097633233] 
dist 232=[-.69757048385070625342,-.15899193372521634013] 
dist 233=[-.6992735438076318658 ,-.15658742609882904352] 
dist 234=[-.70036342863770038151,-.15453062228078740372] 
dist 235=[-.70122155600430681073,-.15231803375567291747] 
dist 236=[-.70199761014975417396,-.14929038224340867009] 
dist 237=[-.70266899532370734599,-.14594022710396765283] 
dist 238=[-.70310846066649860447,-.14243767693093817362] 
dist 239=[-.7034657458676438757 ,-.13812366488173562199] 
dist 240=[-.70380842801196056818,-.13152782584918449259] 
dist 241=[-.70409008569396450185,-.12477644871288160252] 
dist 242=[-.70420327821842793549,-.11984030660702829176] 
dist 243=[-.70423775090860373187,-.1152491238555257757 ] 
dist 244=[-.70421585002760972773,-.10987748758837090248] 
dist 245=[-.70393830194267568769,-.10436229952559451497] 
dist 246=[-.7038381259462252614 ,-.09919692374717928577] 
dist 247=[-.70369340897255946056,-.09325600400405199524] 
dist 248=[-.70362654030619197549,-.08463877909058546765] 
dist 249=[-.69985300166446617181,-.07571924262136306514] 
dist 250=[-.69937062081428141338,-.06856912726242113696] 
dist 251=[-.69866786308221791871,-.06128787423151626145] 
dist 252=[-.69845284946472737876,-.05184379986065261782] 
dist 253=[-.69412742815293791232,-.04163760763481897024] 
dist 254=[-.69367553193919963448,-.03130802071381110469] 
dist 255=[-.69043968539361891085,-.01882390553376311107] 

8 phat 1 dirichlet min maxes function [2, 1, 2, 2, 0, 2, 0, 1, 2] 
dist 0=[3.3954416020357425129 ,3.3954416020357425129 ] 
dist 1=[3.3855879305731637734 ,3.4010196792608896084 ] 
dist 2=[3.3704210138216205323 ,3.4134779386493212339 ] 
dist 3=[3.3486518184444407147 ,3.4277973442526706575 ] 
dist 4=[3.3262120909223986568 ,3.4403033048641017718 ] 
dist 5=[3.3083630932453304344 ,3.4539798026981500931 ] 
dist 6=[3.2903119835150112227 ,3.4729812826294737332 ] 
dist 7=[3.2670638241949505772 ,3.4916824440510170514 ] 
dist 8=[3.2420181915031443273 ,3.5041576899906450707 ] 
dist 9=[3.2167773138217795804 ,3.5145615538998942389 ] 
dist 10=[3.1863467557474574452 ,3.5249773281868919031 ] 
dist 11=[3.1405427616233680353 ,3.5347056323413649881 ] 
dist 12=[3.0945517143294667959 ,3.5423596647825712521 ] 
dist 13=[3.0633729584949283086 ,3.5500229141626539977 ] 
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dist 23=[2.8115622401291880820 ,3.6275731564780739502 ] 
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dist 45=[1.9567075377333596008 ,3.6380496342378747804 ] 
dist 46=[1.9117798419629514852 ,3.6376065549110853011 ] 
dist 47=[1.8646647491364206387 ,3.6352817137815375819 ] 
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dist 65=[.9069690532423301761 ,3.4243825121270740761 ] 
dist 66=[.84793485477933620508,3.4224218050072491962 ] 
dist 67=[.76440057217738689529,3.4138253453479979561 ] 
dist 68=[.67880750040959402824,3.4122283703534994765 ] 
dist 69=[.61153830331061985295,3.4083646168782759572 ] 
dist 70=[.54425762608031134764,3.4076842695138933086 ] 
dist 71=[.45861863439168121441,3.3650233303954178507 ] 
dist 72=[.36686561207834431466,3.3609365392054466617 ] 
dist 73=[.27512928133008309119,3.3513696069040444736 ] 
dist 74=[.16506468370195357103,3.3497875105594489513 ] 
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dist 76=[2.2076758429054462242 ,3.3341694888428236773 ] 
dist 77=[2.1809743232052605556 ,3.3307759205043927844 ] 
dist 78=[2.1508630272828184984 ,3.3297543327971099633 ] 
dist 79=[2.1078934981857909090 ,3.3100505964868487286 ] 
dist 80=[2.0651120164381751620 ,3.3074491386476947580 ] 
dist 81=[2.0357528919777958701 ,3.3019967474879548421 ] 
dist 82=[2.0103675961116961256 ,3.3005122405230740162 ] 
dist 83=[1.9834810497252795196 ,3.2946626789879031407 ] 
dist 84=[1.9574223736736479970 ,3.2935302350215217743 ] 
dist 85=[1.9353484801860519238 ,3.2907531954076533310 ] 
dist 86=[1.9117839743128793494 ,3.2902359167505079070 ] 
dist 87=[1.8797629908906057138 ,3.2138670391482086066 ] 
dist 88=[1.8475286202356599104 ,3.2083159238316355151 ] 
dist 89=[1.8231105857842512658 ,3.1951283266257187558 ] 
dist 90=[1.7995431037807244414 ,3.1932151178185841027 ] 
dist 91=[1.7707108617932941300 ,3.1746576062284077952 ] 
dist 92=[1.7404110965261437768 ,3.1712317871592143773 ] 
dist 93=[1.7109736613732073842 ,3.1672747248418321913 ] 
dist 94=[1.6762838037672320261 ,3.1665159381628514496 ] 
dist 95=[1.6249748496536006125 ,3.1371591269346618906 ] 
dist 96=[1.5736921377746413609 ,3.1334586778047698663 ] 
dist 97=[1.5391072466044221627 ,3.1262156656511559066 ] 
dist 98=[1.5098534920768346983 ,3.1243882295282582950 ] 
dist 99=[1.4798948182951237172 ,3.1181152585101392826 ] 
dist 100=[1.4514823319309985675 ,3.1155640615703105857 ] 
dist 101=[1.4284131796014538006 ,3.1139179130921284234 ] 
dist 102=[1.4046507155345972709 ,3.1092136430809400068 ] 
dist 103=[1.3734650483479285932 ,3.0502138198612018679 ] 
dist 104=[1.3425711824163639077 ,3.0448678166638028629 ] 
dist 105=[1.3199758955384962344 ,3.0332998629278249163 ] 
dist 106=[1.2989491850087712405 ,3.0274039316516432219 ] 
dist 107=[1.2743294748620646889 ,3.0072425071424635994 ] 
dist 108=[1.2490382853570391106 ,2.8066692504277211117 ] 
dist 109=[1.2253257214384123657 ,2.7967045087835917684 ] 
dist 110=[1.1980304633124492125 ,2.7752011100559997079 ] 
dist 111=[1.1584088386883721051 ,2.7704407474831866814 ] 
dist 112=[1.1186763337366412639 ,2.7465216004062238776 ] 
dist 113=[1.0909375648756097297 ,2.7422787560610675305 ] 
dist 114=[1.0664489021156774906 ,2.7318173858592820132 ] 
dist 115=[1.0397165115796461075 ,2.7180802651404927968 ] 
dist 116=[1.0133232237773770815 ,2.6443921119048907910 ] 
dist 117=[.99019093960954559145,2.6352536307520153991 ] 
dist 118=[.96482569583024328264,2.6033548146261364449 ] 
dist 119=[.92950078255736640371,1.5738813074414583182 ] 
dist 120=[.893552748208169574  ,1.5390275865408922608 ] 
dist 121=[.8656950795556444369 ,1.4577217490906636779 ] 
dist 122=[.83820130444024662471,1.4460219695105933868 ] 
dist 123=[.8037088095321125766 ,1.3376212029891929057 ] 
dist 124=[.7670093342926307140 ,1.3182465769934261647 ] 
dist 125=[.7306878483492646625 ,1.2947653176954634428 ] 
dist 126=[.6873825803417661034 ,1.2906161234594100522 ] 
dist 127=[.6227486429450875577 ,1.2654378954959109931 ] 
dist 128=[.5581597321053970445 ,1.1244875647621347053 ] 
dist 129=[.5150345660313065834 ,1.0881586454337294472 ] 
dist 130=[.4790282402200021668 ,1.0790270606855910710 ] 
dist 131=[.4429140114505383737 ,1.0473782304181328739 ] 
dist 132=[.4091417353320734262 ,1.0408620928836680289 ] 
dist 133=[.3825029967539482324 ,1.0322293524373637476 ] 
dist 134=[.3557701590332573925 ,1.0300941366215940390 ] 
dist 135=[.3216214953195201395 ,.82096064624527477703] 
dist 136=[.2882304958524462092 ,.80348772068372481086] 
dist 137=[.2645282428538899553 ,.76447665165616527766] 
dist 138=[.2431927204221882392 ,.75739750795902967996] 
dist 139=[.2192684174884476461 ,.71043040156007663642] 
dist 140=[.1952733482374973959 ,.70215659928146719188] 
dist 141=[.1736547672865085540 ,.68740112029470697669] 
dist 142=[.1494571905641499517 ,.68416378346626513619] 
dist 143=[.1151463842072412468 ,.63827354918603750481] 
dist 144=[.0810788617383611895 ,.63205294138368932989] 
dist 145=[.0578543973641806654 ,.61902282021143995326] 
dist 146=[.0379386644079864294 ,.61590679314168420246] 
dist 147=[.0171057520307869205 ,.60293107756432293417] 
dist 148=[-.0029271223971375310 ,.60056653169654508879] 
dist 149=[-.0196427798622702668 ,.59565859768840944791] 
dist 150=[-.0372674364204798468 ,.5944563396768045108 ] 
dist 151=[-.0609362205221743561 ,.47880957793232345054] 
dist 152=[-.0846357159836495469 ,.45900088827628444194] 
dist 153=[-.1023832150517930420 ,.45629441511119838723] 
dist 154=[-.1193138344605370662 ,.45068391739582320411] 
dist 155=[-.1397458891967821340 ,.44928281600392134191] 
dist 156=[-.1610700427403051859 ,.44391046173042664621] 
dist 157=[-.1815689722915396924 ,.44289501908554676054] 
dist 158=[-.2055606524990157474 ,.44093610993149113342] 
dist 159=[-.2408554755358490651 ,.44046613765156145692] 
dist 160=[-.2760546826372487859 ,.31119401957000654276] 
dist 161=[-.2996639082226494387 ,.30395983492355433757] 
dist 162=[-.3194935809429328623 ,.28727163634976846732] 
dist 163=[-.3395749370701475559 ,.28473151268575476672] 
dist 164=[-.3584775745491644751 ,.26304140023765833174] 
dist 165=[-.3735924851005123211 ,.25918408193882240999] 
dist 166=[-.3889513546809389118 ,.25402938575903313619] 
dist 167=[-.4088298050079406777 ,.25274169809586176449] 
dist 168=[-.4283918354522559933 ,.22545236005313608516] 
dist 169=[-.4424850556814399479 ,.22206094847370001339] 
dist 170=[-.4553852081281231751 ,.21491441311627594555] 
dist 171=[-.4701750812348831770 ,.21324744757248956658] 
dist 172=[-.4851951677430096549 ,.20596990086577995466] 
dist 173=[-.4990161518378594643 ,.20467012433568350918] 
dist 174=[-.5147207341349070660 ,.20185719604475434816] 
dist 175=[-.5372750337979501713 ,.20127844464578430081] 
dist 176=[-.5597914523849019519 ,.17147278580316695515] 
dist 177=[-.5753445139906064388 ,.16876198194703629629] 
dist 178=[-.5889003522306054797 ,.16254866466761045769] 
dist 179=[-.6034280678459535893 ,.16158051923907682017] 
dist 180=[-.6176120171468781076 ,.15364003621302846786] 
dist 181=[-.6297928229169345703 ,.1522365793393585954 ] 
dist 182=[-.6429397170450574164 ,.15026694663826907901] 
dist 183=[-.6609879276346488620 ,.14972289922158102274] 
dist 184=[-.6792393662394095516 ,.14033365567789025654] 
dist 185=[-.6931991530447228640 ,.13916295328517100473] 
dist 186=[-.70887586958810960567,.13661760418102757656] 
dist 187=[-.73206729807938263037,.13611469736381121649] 
dist 188=[-.75008257224154385092,.13328230958027480919] 
dist 189=[-.76790346356048014271,.13279686513709836828] 
dist 190=[-.7903173860595780159 ,.1318102729100629865 ] 
dist 191=[-.81206535364099516771,.13156513515469538579] 
dist 192=[-.8406390117066535205 ,-.42282172845271939886] 
dist 193=[-.8609162384870350517 ,-.43098293830829184272] 
dist 194=[-.8777139799940685649 ,-.43248492843679743754] 
dist 195=[-.8943460818646371418 ,-.44179843698318800976] 
dist 196=[-.9097608679196502705 ,-.44338926160345931876] 
dist 197=[-.9216894656906483868 ,-.44639003418850175054] 
dist 198=[-.9334461989077618030 ,-.44707086099419043132] 
dist 199=[-.9481735499802107533 ,-.46785497088758273136] 
dist 200=[-.9624342776065449981 ,-.469991402158337348  ] 
dist 201=[-.9723245649625583929 ,-.47422610933352392397] 
dist 202=[-.9809870861462374480 ,-.47525170514906000182] 
dist 203=[-.9903368695969919507 ,-.47857664749261588733] 
dist 204=[-.99950529646886460309,-.4792745264984251235 ] 
dist 205=[-1.0074424154641966589 ,-.47964003281918427614] 
dist 206=[-1.0160633515286223010 ,-.47921540646602856674] 
dist 207=[-1.0279669985321670733 ,-.47843958475067740861] 
dist 208=[-1.0396498898226055744 ,-.47729103916475519676] 
dist 209=[-1.0473878274912366546 ,-.47564015481324398249] 
dist 210=[-1.0537798032321777068 ,-.4728550179082891091 ] 
dist 211=[-1.0600789683142989115 ,-.46952581688715064781] 
dist 212=[-1.0658978341788412970 ,-.46569877835858098586] 
dist 213=[-1.0703686622314292166 ,-.46074239767422675958] 
dist 214=[-1.0747448004639937777 ,-.45289609496421495767] 
dist 215=[-1.0801849330679485476 ,-.44484918675458689613] 
dist 216=[-1.0854324771744402939 ,-.43909040838946317445] 
dist 217=[-1.0890382865600870070 ,-.43385927726728479275] 
dist 218=[-1.0921611459854467352 ,-.42792276403591924069] 
dist 219=[-1.0954769396471252186 ,-.42192910629023465462] 
dist 220=[-1.0986958955295771466 ,-.41646936771449404044] 
dist 221=[-1.1014314300200663632 ,-.41031040137522433349] 
dist 222=[-1.1043595320403579253 ,-.40151993839910270537] 
dist 223=[-1.1083487871768743683 ,-.3924818920858177221 ] 
dist 224=[-1.1122256535262842603 ,-.38533261736763228153] 
dist 225=[-1.1147042099769608345 ,-.37813994524775382984] 
dist 226=[-1.1166530804296906126 ,-.36892827840112840265] 
dist 227=[-1.1184112023844875476 ,-.35903163022816225546] 
dist 228=[-1.1199292352010463871 ,-.34909913704791522395] 
dist 229=[-1.1209177516332023744 ,-.33715561850425109284] 
dist 230=[-1.1217156993108268061 ,-.31921521248387167861] 
dist 231=[-1.1224714651109358206 ,-.30097665240746706229] 
dist 232=[-1.1231035399595056790 ,-.28784055932340960748] 
dist 233=[-1.1234067298970105672 ,-.27582123784887519785] 
dist 234=[-1.1235418923906459132 ,-.26204954563365115826] 
dist 235=[-1.1235484654120964816 ,-.24806941453870749207] 
dist 236=[-1.1232806991546082722 ,-.23521635824253875719] 
dist 237=[-1.1231564400981844216 ,-.22062131718191150011] 
dist 238=[-1.1222058567438423792 ,-.1996735276877905708 ] 
dist 239=[-1.1199250573942515842 ,-.17808406645105410925] 
dist 240=[-1.0967089634844772152 ,-.16092243795719604511] 
dist 241=[-1.0948551224461368648 ,-.14357827667551264084] 
dist 242=[-1.0911779694969232520 ,-.12125870218754362554] 
dist 243=[-1.0902229850977159495 ,-.09722503946442485549] 
dist 244=[-1.0800687243400064760 ,-.07302480289177659928] 
dist 245=[-1.0781711370661342964 ,-.04386622261991717880] 

8 phat 1 dirichlet min maxes function [0, 1, 0, 1, 2, 2, 1, 0, 1] 
dist 0=[3.6583492091530817932 ,3.6583492091530817932 ] 
dist 1=[3.6553816539198195687 ,3.6597767387952138919 ] 
dist 2=[3.6517763342928538160 ,3.6625191513788333054 ] 
dist 3=[3.6486799288682407150 ,3.6664713803932109056 ] 
dist 4=[3.6453377933342197965 ,3.6721926370953728140 ] 
dist 5=[3.6407495985937943668 ,3.6779233292483482971 ] 
dist 6=[3.6361099383650547015 ,3.6819133064646525136 ] 
dist 7=[3.6325619567212746675 ,3.6854244168886667375 ] 
dist 8=[3.6273026832075602396 ,3.6892396984932374579 ] 
dist 9=[3.6218135938274894612 ,3.6929962924375220256 ] 
dist 10=[3.6162576774306029275 ,3.6962726687631969498 ] 
dist 11=[3.6090958182468599506 ,3.6998519316124380205 ] 
dist 12=[3.6013769608685798702 ,3.7048200646491883793 ] 
dist 13=[3.5935930761629722705 ,3.7098687687255518948 ] 
dist 14=[3.5842051462361944123 ,3.7137703189833602887 ] 
dist 15=[3.5700701893154047204 ,3.7176107120863916751 ] 
dist 16=[3.5555715549119683504 ,3.7224148042926710593 ] 
dist 17=[3.5447289391193565104 ,3.7275193785122298262 ] 
dist 18=[3.5343994564217481481 ,3.7325616928603243049 ] 
dist 19=[3.5219533452404606284 ,3.7385665763627839679 ] 
dist 20=[3.5089738013648781952 ,3.7475213900267273834 ] 
dist 21=[3.4965106355651663954 ,3.7564070791329307599 ] 
dist 22=[3.4819342769584922207 ,3.7621354722211387262 ] 
dist 23=[3.4605021140158782195 ,3.7666939615645230225 ] 
dist 24=[3.4381910129212397610 ,3.7709000963107299477 ] 
dist 25=[3.4200989680496800173 ,3.7745985707647297174 ] 
dist 26=[3.4014836332392447906 ,3.7771264491779509008 ] 
dist 27=[3.3770794192287948576 ,3.7793014016503395119 ] 
dist 28=[3.3505734818621047798 ,3.7815882024258958856 ] 
dist 29=[3.3235514048356411046 ,3.7836330973706510349 ] 
dist 30=[3.2907482037109845380 ,3.7848404386575136381 ] 
dist 31=[3.2411181766735870752 ,3.7856750490803557458 ] 
dist 32=[3.1912458699249965006 ,3.7862290268929595299 ] 
dist 33=[3.1574735699290408375 ,3.7865830033206397703 ] 
dist 34=[3.1287556547632504147 ,3.7866429656603646146 ] 
dist 35=[3.0991005405246015073 ,3.7865423916575845721 ] 
dist 36=[3.0708208097909968562 ,3.7864570095432046686 ] 
dist 37=[3.0476043373114998159 ,3.7771196952153514238 ] 
dist 38=[3.0234591738551197381 ,3.7761023235052738703 ] 
dist 39=[2.9914647520608888725 ,3.7739539751604838307 ] 
dist 40=[2.9596249245628591335 ,3.7733197811030022750 ] 
dist 41=[2.9360981316417400910 ,3.7705925619812749969 ] 
dist 42=[2.9139637793387919975 ,3.7700270053843527699 ] 
dist 43=[2.8876936215199191215 ,3.7684428922887875865 ] 
dist 44=[2.8605116968580749498 ,3.7681686960098433377 ] 
dist 45=[2.8347303485785411929 ,3.7643873047920202379 ] 
dist 46=[2.8048216161220574193 ,3.7637104308728988315 ] 
dist 47=[2.7611304617000253904 ,3.7620663247176990642 ] 
dist 48=[2.7171999295665556094 ,3.7616131400235032427 ] 
dist 49=[2.6863337067205937783 ,3.7588720104779646430 ] 
dist 50=[2.6588768371967505472 ,3.7582615123916936787 ] 
dist 51=[2.6285834727635474106 ,3.7571395005913900076 ] 
dist 52=[2.5984842533893404054 ,3.7568155021559567292 ] 
dist 53=[2.5718039540279334815 ,3.5912532736405927364 ] 
dist 54=[2.5422966861543737275 ,3.5830943582713565599 ] 
dist 55=[2.5008898081027107864 ,3.5641676022862935006 ] 
dist 56=[2.4586127581956683065 ,3.5611122671812840746 ] 
dist 57=[2.4256248706837259524 ,3.5358604494279533942 ] 
dist 58=[2.3928537750274471430 ,3.5312504554171321695 ] 
dist 59=[2.3514438804911684634 ,3.5248344880805897751 ] 
dist 60=[2.3072310197272962054 ,3.5229677401251825750 ] 
dist 61=[2.2632482724329037294 ,3.4883901351162758400 ] 
dist 62=[2.2106409009425804644 ,3.4839118110533972476 ] 
dist 63=[2.1319301951697104027 ,3.4744082313124376038 ] 
dist 64=[2.0528881634272813359 ,3.4719925542489126476 ] 
dist 65=[1.9989555140977283250 ,3.4616996424205454778 ] 
dist 66=[1.9526536412481365426 ,3.4598133302608588472 ] 
dist 67=[1.9041341417562264899 ,3.4551315314006183156 ] 
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dist 141=[-.03870381644681223133,.63268615719304913502] 
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dist 168=[-.58524414641856246694,.28471719037784281633] 
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dist 170=[-.62900228425847427629,.28096759915771111756] 
dist 171=[-.65114675226699891941,.28042529154116229677] 
dist 172=[-.67744842210231579311,.27928743094846225588] 
dist 173=[-.71658902838702941264,.27903668223785692801] 
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dist 175=[-.7815844910021423281 ,-.1965807574961325771 ] 
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dist 179=[-.8596534301378183816 ,-.2058464612265902563 ] 
dist 180=[-.8748598270520285506 ,-.2062086938539397683 ] 
dist 181=[-.8939711737709937159 ,-.4139192168208620186 ] 
dist 182=[-.91250774591091031829,-.4224516687955148603 ] 
dist 183=[-.92541510299663473717,-.4418885078509107783 ] 
dist 184=[-.93677474208142011004,-.4449648648300546670 ] 
dist 185=[-.94912059349639034924,-.4693868929736016426 ] 
dist 186=[-.9612776866239730779 ,-.4736729769067918662 ] 
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dist 188=[-.98346851894717509396,-.4815606720120766290 ] 
dist 189=[-.99955181593904130207,-.5088979731480671756 ] 
dist 190=[-1.0153741089076307412 ,-.5122890580507245285 ] 
dist 191=[-1.0259163224149016691 ,-.5198541995734836874 ] 
dist 192=[-1.0346940967754215376 ,-.5211245667748355564 ] 
dist 193=[-1.0434587940720463795 ,-.5300733668600728393 ] 
dist 194=[-1.0516299510852039966 ,-.5316033394796742800 ] 
dist 195=[-1.0580336245402989104 ,-.5341852465757493335 ] 
dist 196=[-1.0644214174281146316 ,-.5347360945486544327 ] 
dist 197=[-1.0725290719132067473 ,-.55034723796948875663] 
dist 198=[-1.0804320546358409288 ,-.55205417687241637225] 
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dist 200=[-1.0909723191131029083 ,-.55583217562603322984] 
dist 201=[-1.0964833593402206371 ,-.55744377677919793661] 
dist 202=[-1.1019745942096393502 ,-.55742943331162406272] 
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dist 204=[-1.1122971402395374984 ,-.55506810196558343637] 
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dist 206=[-1.1274543335345844526 ,-.55081003145200059298] 
dist 207=[-1.1323459366056939803 ,-.5481404895595221762 ] 
dist 208=[-1.1362946446955978667 ,-.54406609599780202234] 
dist 209=[-1.1400343187025756055 ,-.53935941116437558816] 
dist 210=[-1.1433898206866049013 ,-.53416081856088362819] 
dist 211=[-1.1458018554749572058 ,-.52756310475595894152] 
dist 212=[-1.1480043431260972240 ,-.51726023938710535958] 
dist 213=[-1.1505216656314939357 ,-.50674663439916985751] 
dist 214=[-1.1528408446205653165 ,-.49930598778005594089] 
dist 215=[-1.1542507661701198209 ,-.49263237181321400655] 
dist 216=[-1.1552758441260439265 ,-.4851866621374421012 ] 
dist 217=[-1.1560556635592959037 ,-.47774166635137744213] 
dist 218=[-1.1566476404314437389 ,-.47107086848879497726] 
dist 219=[-1.1569213598994297406 ,-.46363499437485999976] 
dist 220=[-1.1570332489664983428 ,-.45312980853982713902] 
dist 221=[-1.1570277623525344379 ,-.44237496770706106215] 
dist 222=[-1.1558400709290134359 ,-.43394049886833667532] 
dist 223=[-1.1556096866030834353 ,-.42552226761603084888] 
dist 224=[-1.1550799223767813189 ,-.41483233795866986893] 
dist 225=[-1.1548829220449197830 ,-.40339336099844334575] 
dist 226=[-1.1538719903407192615 ,-.39197905372639279861] 
dist 227=[-1.1536243082859293527 ,-.37830193290592015184] 
dist 228=[-1.1524452972858320819 ,-.35781208043745706061] 
dist 229=[-1.1356233650076306369 ,-.33700345518535828544] 
dist 230=[-1.1345031076218391451 ,-.32205128784611069179] 
dist 231=[-1.1324791220242205009 ,-.30840583877855385635] 
dist 232=[-1.1319816377612044680 ,-.29282384175175393968] 
dist 233=[-1.1302457352775842728 ,-.27703568893121479639] 
dist 234=[-1.1232790737485887459 ,-.26256563722771982791] 
dist 235=[-1.1220854327230344662 ,-.24617050256442616827] 
dist 236=[-1.1150891538581064771 ,-.22268232437329234589] 
dist 237=[-1.1012095134284110374 ,-.19849305618665988175] 
dist 238=[-1.0165809756116642669 ,-.17929366953998109337] 
dist 239=[-1.0107586814639789557 ,-.15991663584817116659] 
dist 240=[-.99712675096219268909,-.13501679695083802935] 
dist 241=[-.99505779883141510509,-.10822254348156257204] 
dist 242=[-.97545325795446282589,-.08126815467179938396] 
dist 243=[-.97186633272793978264,-.04880968500798952125] 

8 phat 1 dirichlet min maxes function [0, 0, 0, 2, 1, 2, 1, 1, 2] 
dist 0=[.91466780556222681552,.91466780556222681552] 
dist 1=[.90946084802135067955,.92082747515407097622] 
dist 2=[.90486961891671774217,.9289172673757789292 ] 
dist 3=[.90117281540136304663,.94184456515019544762] 
dist 4=[.8973928362266866638 ,.95573352492679256236] 
dist 5=[.89071446136555751832,.96766989032514280813] 
dist 6=[.88168296750931593285,.9805607449464232119 ] 
dist 7=[.87148557210511323235,.99826758743767796831] 
dist 8=[.85691821986427931934,1.0178959996372145621 ] 
dist 9=[.84160597623992638399,1.0384729835664931124 ] 
dist 10=[.82842907446429887847,1.0638594397853338011 ] 
dist 11=[.81418369589403007674,1.1027253668112570897 ] 
dist 12=[.79459762951037647682,1.1417531871202409973 ] 
dist 13=[.77287733108804945158,1.1677872044651226961 ] 
dist 14=[.75009519291099564653,1.1894973693396633313 ] 
dist 15=[.7219796781370353725 ,1.2112301180857730971 ] 
dist 16=[.67892629447619056005,1.2315266768491417466 ] 
dist 17=[.63514031810420059605,1.2474921953254035570 ] 
dist 18=[.60409449055910059681,1.2634735639770557061 ] 
dist 19=[.57618455183947573209,1.2838335256707755929 ] 
dist 20=[.54494188381459992503,1.3037160052472392272 ] 
dist 21=[.51363712137498044377,1.3177874843740856356 ] 
dist 22=[.48547881053880230647,1.3304108616913442004 ] 
dist 23=[.45399835534450741328,1.3445010486156992590 ] 
dist 24=[.40940527905188301645,1.3585959526707589639 ] 
dist 25=[.36369257725465032828,1.3712382017226909213 ] 
dist 26=[.32773370899263719766,1.3853427200351872668 ] 
dist 27=[.29173855332051855242,1.4052865961797690382 ] 
dist 28=[.24588070511568704732,1.4250663069013004340 ] 
dist 29=[.19672829834049391664,1.4385141781493538952 ] 
dist 30=[.14755516949737359818,1.4500073570051193258 ] 
dist 31=[.08853595788211831314,1.4619684469866820389 ] 
dist 32=[0                     ,1.4734326892213875437 ] 
dist 33=[1.3114690954931127769 ,1.4829385177270089195 ] 
dist 34=[1.3236580821252143859 ,1.4929086985670884380 ] 
dist 35=[1.3258519242167964839 ,1.5062303232038869880 ] 
dist 36=[1.3302618695884939531 ,1.5195387611004737971 ] 
dist 37=[1.3313436966673603780 ,1.5294561997481624493 ] 
dist 38=[1.3807411032737743106 ,1.5388697496824826590 ] 
dist 39=[1.3851451900608581947 ,1.5501626739639257649 ] 
dist 40=[1.3950720647775560471 ,1.5619130049663269971 ] 
dist 41=[1.3966807599708906217 ,1.5731561554386758685 ] 
dist 42=[1.4087692058867337639 ,1.5862752830602652078 ] 
dist 43=[1.4108588017875655668 ,1.6055294023939708667 ] 
dist 44=[1.4141175078941947364 ,1.6246925431554679228 ] 
dist 45=[1.4148914823992428594 ,1.6374477638061526169 ] 
dist 46=[1.4268470622786193696 ,1.6480541081799609108 ] 
dist 47=[1.4283479391821906915 ,1.6586218860501043968 ] 
dist 48=[1.4315329359824050016 ,1.6684595044111400698 ] 
dist 49=[1.4321474154398155565 ,1.6761452590316382283 ] 
dist 50=[1.4367723084311631339 ,1.6837896528133027416 ] 
dist 51=[1.4386427589500656724 ,1.6934618304322545736 ] 
dist 52=[1.4440413494481793056 ,1.7028751733054185752 ] 
dist 53=[1.4461426387968539107 ,1.7094842452069434086 ] 
dist 54=[1.6109814488748227248 ,1.7153582592235830133 ] 
dist 55=[1.6170836139856072378 ,1.7218314192459224530 ] 
dist 56=[1.6309252282960167383 ,1.7282586620728907783 ] 
dist 57=[1.6331181501347212592 ,1.7339490102986237833 ] 
dist 58=[1.6502691843201416594 ,1.7402366797757725873 ] 
dist 59=[1.6532530483527242062 ,1.7490531678901944785 ] 
dist 60=[1.6576848968827617871 ,1.7577654465799525504 ] 
dist 61=[1.6588080415664586820 ,1.7636362852738323564 ] 
dist 62=[1.6769821298162017267 ,1.7685972090186635098 ] 
dist 63=[1.6792149223724545418 ,1.7736698883737315317 ] 
dist 64=[1.6842536475306487174 ,1.7784760295176529520 ] 
dist 65=[1.6849917999663981458 ,1.7823708181591604411 ] 
dist 66=[1.6910487321634608505 ,1.7863759958211187905 ] 
dist 67=[1.6920645714080918306 ,1.7916236858017689607 ] 
dist 68=[1.6934859053862845470 ,1.7968184462336673580 ] 
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dist 76=[1.6599583619251805621 ,1.8341213775707816572 ] 
dist 77=[1.6518109089214425177 ,1.8384460592442519688 ] 
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dist 90=[1.5260885376121382447 ,1.8692710364511483644 ] 
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dist 100=[1.3438735951511270350 ,1.8786257993773152025 ] 
dist 101=[1.3244219162322141259 ,1.8787631522870897224 ] 
dist 102=[1.3047813095301233055 ,1.8788005623086769625 ] 
dist 103=[1.2795289554416257226 ,1.8787784964783360346 ] 
dist 104=[1.2523464354252016324 ,1.8784745358504272723 ] 
dist 105=[1.2249853475150853296 ,1.8783628839541943002 ] 
dist 106=[1.1920236021054089931 ,1.8781361362891425219 ] 
dist 107=[1.1424389846783539335 ,1.8780430563129073173 ] 
dist 108=[1.0928024429174715825 ,1.8759049995916597024 ] 
dist 109=[1.0596330045942223003 ,1.8755686445351384205 ] 
dist 110=[1.0319084728773257726 ,1.8747802228593127424 ] 
dist 111=[1.0040510382174214436 ,1.8745287605044499775 ] 
dist 112=[.97796810701517246421,1.8732784319399415778 ] 
dist 113=[.95734141988026395697,1.8727922867254208030 ] 
dist 114=[.93659249028494445441,1.8714833562561980082 ] 
dist 115=[.91002060090029581736,1.8702072658693376266 ] 
dist 116=[.88400597409470104854,1.8637436760625346027 ] 
dist 117=[.86548604166499337812,1.8612867605364836400 ] 
dist 118=[.8487598736849095018 ,1.0450990026341968333 ] 
dist 119=[.82992013359210117777,1.0280798890191525840 ] 
dist 120=[.8109763491657852335 ,.98836057007646405471] 
dist 121=[.79383401377521381573,.98263190304675252702] 
dist 122=[.77458583055126394889,.92958840465333623035] 
dist 123=[.74721885564303940803,.92009472354211640478] 
dist 124=[.72001430471789402935,.90857681105594488715] 
dist 125=[.70141580193458225408,.90650361437080991164] 
dist 126=[.68541034147697119589,.8337037237854762693 ] 
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dist 181=[-.25121920290356182916,.18856876885989921954] 
dist 182=[-.26107019495707958461,.03868696720674120849] 
dist 183=[-.27197444301044387994,.03257210460785571556] 
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dist 185=[-.29248283564351093127,.01633838543800743037] 
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dist 193=[-.37564595681083153247,-.04350698857649650726] 
dist 194=[-.38269339526931007652,-.04949975654434354464] 
dist 195=[-.39198571876281866002,-.05056759162805920351] 
dist 196=[-.40121138890333747022,-.05282561245972798875] 
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dist 209=[-.50174192576365406214,-.08066801288475369212] 
dist 210=[-.50640507010959690678,-.08079060142456546037] 
dist 211=[-.51224311656451947718,-.08062323756122239035] 
dist 212=[-.51789451578965666328,-.08032383765641130947] 
dist 213=[-.52181108901850193319,-.07988669473563675108] 
dist 214=[-.52523842505207305966,-.07926148648594836683] 
dist 215=[-.52893292215859062592,-.07820982688735455028] 
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dist 220=[-.54835324205329766652,-.06763419336971488158] 
dist 221=[-.55139161849695054365,-.06533547420636244698] 
dist 222=[-.55389694833939929359,-.06313621287281359962] 
dist 223=[-.55635835498502080938,-.06047363926070954723] 
dist 224=[-.55862709848102834941,-.05769086583288999534] 
dist 225=[-.56036179410085170465,-.05501081708092121438] 
dist 226=[-.56205163875043715135,-.05187077027307206376] 
dist 227=[-.56414098264328997327,-.04724810177553887085] 
dist 228=[-.56615063051907306643,-.04243479667106248075] 
dist 229=[-.5675216987016282272 ,-.03853223945493673942] 
dist 230=[-.56869856780873026345,-.03451795056739539085] 
dist 231=[-.57035111622276878342,-.02925772966220084058] 
dist 232=[-.57198663081173618582,-.02354669912087978847] 
dist 233=[-.57349415291758274618,-.01772926780420630264] 
dist 234=[-.57481853804511719096,-.01067161981674652599] 
dist 235=[-.57572152377981090075,0                     ] 
dist 236=[-.57649601059559767877,-.06605130661594937171] 
dist 237=[-.57730641548640767201,-.06002549085686030266] 
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dist 239=[-.5784788697576238006 ,-.04874499150240935927] 
dist 240=[-.57880447683197502647,-.04360410728144166359] 
dist 241=[-.57905667429471745522,-.03691179950935534680] 
dist 242=[-.57924472527508364402,-.02966744048952158214] 
dist 243=[-.5793137493546313331 ,-.02231845704916282833] 
dist 244=[-.57932496913792149268,-.01342438939393328718] 

8 phat 1 dirichlet min maxes function [1, 1, 1, 2, 1, 1, 1, 0, 2] 
dist 0=[.59310168175457002045,.59310168175457002045] 
dist 1=[.58137831978835459501,.60532265871563863987] 
dist 2=[.54670677498335987505,.62549271138664992729] 
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dist 4=[.48644379537649783654,.66630978226570590884] 
dist 5=[.46396793024588809562,.68272864759836447675] 
dist 6=[.43880857774108160808,.69984817403854187219] 
dist 7=[.41359942909759697994,.72259039239973723194] 
dist 8=[.39092438385659925792,.74524908414953001456] 
dist 9=[.36557438022232035036,.76203451160421214608] 
dist 10=[.32966561035743596485,.77786873541704594589] 
dist 11=[.292855400741576662  ,.79672268870373128907] 
dist 12=[.2638997097590054237 ,.81626406420014037251] 
dist 13=[.23491501618840397057,.83484792430528586839] 
dist 14=[.19798879880340473396,.85644499195317276199] 
dist 15=[.15840984950164812124,.88803896389970217727] 
dist 16=[.1188144386259490917 ,.91947640606893618873] 
dist 17=[.07129088637882791859,.94044736760031885358] 
dist 18=[0                     ,.95793559721927721148] 
dist 19=[.58079233694325660923,.97544238443177337271] 
dist 20=[.59248191512988401608,.99179248488408644412] 
dist 21=[.61850530408592268884,1.0046540589573404442 ] 
dist 22=[.62324959069331659051,1.0175287621294232085 ] 
dist 23=[.65429612024138363178,1.0339313807282453267 ] 
dist 24=[.65974075754534189418,1.0499495597741159960 ] 
dist 25=[.66955650928066870466,1.0612865361044425076 ] 
dist 26=[.67172863807905545603,1.0714572215244936307 ] 
dist 27=[.74291484378490671573,1.0828103292740176901 ] 
dist 28=[.75075640188874560928,1.0941675892909119621 ] 
dist 29=[.7641941068261990079 ,1.1043548863245727504 ] 
dist 30=[.77826738209204115384,1.1157209437909366027 ] 
dist 31=[.81445140541830588264,1.1317931608246394910 ] 
dist 32=[.91672064840859462963,1.1477333103605868614 ] 
dist 33=[.92710705304351701475,1.1585711096052292865 ] 
dist 34=[.95106906069504964541,1.1678340047693065210 ] 
dist 35=[.95465321413666405124,1.1774746579994048210 ] 
dist 36=[.98571543595824859378,1.1867152506684196000 ] 
dist 37=[.99121177893795217885,1.1943779363244690619 ] 
dist 38=[.99842536244076131606,1.2024155080563979532 ] 
dist 39=[1.0000636155140676002 ,1.2131556232066041968 ] 
dist 40=[1.0387956269370018269 ,1.2238854457276694138 ] 
dist 41=[1.0435466447456641284 ,1.2318818507436176052 ] 
dist 42=[1.0534961083421647979 ,1.2394725107987369262 ] 
dist 43=[1.0558092974732867275 ,1.2485793866983462174 ] 
dist 44=[1.0656129743526241867 ,1.2580555402728997831 ] 
dist 45=[1.0673785407600480222 ,1.2671232896821566414 ] 
dist 46=[1.0709227523619179740 ,1.2777045103505150799 ] 
dist 47=[1.0717909513207074762 ,1.2932344517108850480 ] 
dist 48=[1.1116015136483650627 ,1.3086910525901626436 ] 
dist 49=[1.1151488696647699756 ,1.3189789172376889176 ] 
dist 50=[1.1231467924749705651 ,1.3275333186999913789 ] 
dist 51=[1.1244410173713241197 ,1.3360561817969169614 ] 
dist 52=[1.1341868068324683280 ,1.3439898933481025370 ] 
dist 53=[1.1358716310283863308 ,1.3501877276704044653 ] 
dist 54=[1.1384924398881887186 ,1.3563517657522759812 ] 
dist 55=[1.1391168124849475627 ,1.3641502944959170827 ] 
dist 56=[1.1549868144021772986 ,1.3717398319555652800 ] 
dist 57=[1.1567733574389305493 ,1.3770679187450646574 ] 
dist 58=[1.1600972666315362739 ,1.3818028971398675201 ] 
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dist 62=[1.1744213542259997613 ,1.4018505510344636305 ] 
dist 63=[1.1809635731894204708 ,1.4089529537958850658 ] 
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dist 65=[1.3013365221245123641 ,1.4206997569893265583 ] 
dist 66=[1.3124431085430674148 ,1.4246949443447122498 ] 
dist 67=[1.3142040473909001660 ,1.4287791706533013653 ] 
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dist 106=[1.0517551483850950541 ,1.5128039945515713000 ] 
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dist 108=[1.0095603359029311724 ,1.5124590863896569291 ] 
dist 109=[.9875423124618595144 ,1.5123525959787017541 ] 
dist 110=[.96101715648729945684,1.5121727789757967562 ] 
dist 111=[.92111496004083115719,1.5121039079512526064 ] 
dist 112=[.88117086141758552913,1.5101391913512055624 ] 
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dist 117=[.77215664777055557379,1.5076137020554444672 ] 
dist 118=[.75545739009719070479,1.5071182340434038313 ] 
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dist 121=[.6982264424928053937 ,1.4992098527189076250 ] 
dist 122=[.68476324587343951424,1.4980446620555253630 ] 
dist 123=[.66959801727001685355,1.4977002528647340447 ] 
dist 124=[.65434859128163447813,1.4911759589156666202 ] 
dist 125=[.64054861315300994393,1.4905148054444795855 ] 
dist 126=[.62505282094869422504,1.4858270708903797955 ] 
dist 127=[.60302030040094272745,1.4785156482982783298 ] 
dist 128=[.58111825552418910065,.83852749005443255289] 
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dist 135=[.48826937659480921475,.72666599019433817601] 
dist 136=[.47248702417082619049,.66791642268779277583] 
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dist 146=[.31206037673175055735,.51591081804277126226] 
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dist 152=[.23530981897433203698,.46455244680650142275] 
dist 153=[.22516815022304816557,.46200184812099508679] 
dist 154=[.21580903431874775645,.45661884870647491318] 
dist 155=[.20496570375609115607,.45534781301069015443] 
dist 156=[.19388995359441194472,.44980491622635495874] 
dist 157=[.18360118146174318634,.44881188173695437305] 
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dist 167=[.05906582399076160014,.27039968029690648386] 
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dist 174=[-.03770338373506671494,.22152801464463075392] 
dist 175=[-.06317550768708582413,.22089982542795730883] 
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dist 177=[-.10555050929566041861,.1870932138178562275 ] 
dist 178=[-.119655604498421588  ,.1806829924368795491 ] 
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dist 185=[-.20198516579739773086,.15496668094788597123] 
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dist 189=[-.2353177775538465806 ,.14858325313097577155] 
dist 190=[-.24396579388927549464,.14790541311798066894] 
dist 191=[-.25612822111737651229,.14773063038443133862] 
dist 192=[-.26816176056623249239,.02755137833971441042] 
dist 193=[-.27629423807774295868,.02264395253096891670] 
dist 194=[-.28319171581802035816,.01132893906917777998] 
dist 195=[-.29028537397378189529,.00961660813533358344] 
dist 196=[-.29703178518294683239,-.00505146214478026113] 
dist 197=[-.30254030825656543891,-.00765276568515716738] 
dist 198=[-.30824225585710645546,-.01111563769588760930] 
dist 199=[-.31576234672551186083,-.01195448627128249333] 
dist 200=[-.32322935884206814016,-.03024157929657651589] 
dist 201=[-.32871899649775912038,-.03250186627187671432] 
dist 202=[-.3338559986832297964 ,-.03726298158180337062] 
dist 203=[-.33991250255257920194,-.03835903736338209051] 
dist 204=[-.34615714366215431773,-.04317647697012964706] 
dist 205=[-.3520466768643696205 ,-.04403269004000876589] 
dist 206=[-.35885316753840276582,-.04585185478372374648] 
dist 207=[-.36876555107765749478,-.04624039491424845918] 
dist 208=[-.37860984932408262451,-.06085469187848232873] 
dist 209=[-.38514400532063806668,-.06151587855490045432] 
dist 210=[-.39055698043547096784,-.06281943011471314151] 
dist 211=[-.3959166620910229822 ,-.06313583962366362611] 
dist 212=[-.40088411295529733273,-.06416233764751045425] 
dist 213=[-.4047282023152174038 ,-.06438223252925284216] 
dist 214=[-.40851696723044804001,-.06450480964192622678] 
dist 215=[-.41326312559270086461,-.06438938875380084723] 
dist 216=[-.41785891807848078285,-.06416758736255079199] 
dist 217=[-.42104623382941996904,-.06382988517409510757] 
dist 218=[-.42383784810226287499,-.06333994839151653128] 
dist 219=[-.42685087241688274804,-.06250921004336341364] 
dist 220=[-.42980538839233105317,-.06151470146192450702] 
dist 221=[-.43236297488889746516,-.06036971390377369525] 
dist 222=[-.43514076574756209459,-.05888580102444942588] 
dist 223=[-.43897607816874633551,-.05653568019497334724] 
dist 224=[-.44274006907530925196,-.05409855840667091224] 
dist 225=[-.44523258067799371689,-.05226665493874505811] 
dist 226=[-.44729095738659284891,-.05051274014762732666] 
dist 227=[-.44931845012374278236,-.04838752376298503819] 
dist 228=[-.45119065669936498157,-.04616540586058279208] 
dist 229=[-.45262790357274041806,-.04402389454583324578] 
dist 230=[-.45403350090864155925,-.04151373773711641247] 
dist 231=[-.45577911235303692223,-.03781711580004464768] 
dist 232=[-.45746197494045145317,-.03396752623857403591] 
dist 233=[-.45861658283329125351,-.03084552784394643362] 
dist 234=[-.4596146236164019653 ,-.02763341662534410376] 
dist 235=[-.46067123269796169147,-.02342338454598628156] 
dist 236=[-.46169503097453215326,-.01885207380825343966] 
dist 237=[-.46256183166711555304,-.01419492506459208366] 
dist 238=[-.46348678270131049848,-.00854443870340717390] 
dist 239=[-.4647431767980624648 ,0                     ] 
dist 240=[-.46596216482520751403,-.07192156983041925962] 
dist 241=[-.46673749557481334051,-.06920071930569670718] 
dist 242=[-.46734247774278646267,-.06664985786913913471] 
dist 243=[-.46788008896921528914,-.06363589946373682   ] 
dist 244=[-.46833839262598212449,-.06052522870660460869] 
dist 245=[-.46862615335756547459,-.05758752739249318343] 
dist 246=[-.46884638417220648061,-.05418974758093810708] 
dist 247=[-.46903457715776382489,-.04923884949593012103] 
dist 248=[-.46917768960614803628,-.04410485620555156217] 
dist 249=[-.46921760214566752299,-.03997472735770795452] 
dist 250=[-.46921812235333097506,-.03575555031372244162] 
dist 251=[-.4692036671004182664 ,-.03026537291524586253] 
dist 252=[-.46877886398915206964,-.02432341677895572478] 
dist 253=[-.46869208915923763752,-.01829721052387577893] 
dist 254=[-.46817309768282280585,-.01100514494289430880] 

8 phat 1 dirichlet min maxes function [1, 1, 2, 0, 2, 1, 2, 0, 2] 
dist 0=[2.3005366442532759593 ,2.3005366442532759593 ] 
dist 1=[2.2973146946218190176 ,2.3075188811603541611 ] 
dist 2=[2.2925674075243136840 ,2.3155088576231533814 ] 
dist 3=[2.2848129326329225992 ,2.3227616951701717148 ] 
dist 4=[2.2739424444566329929 ,2.3309240479705224812 ] 
dist 5=[2.2628484048024607437 ,2.3425520272628868095 ] 
dist 6=[2.2541997436279266695 ,2.3542767959289991911 ] 
dist 7=[2.2456152358635086326 ,2.3628263014375535267 ] 
dist 8=[2.2347778096392382378 ,2.3707566358804053608 ] 
dist 9=[2.2232119516218054996 ,2.3800047641087513598 ] 
dist 10=[2.2117137752230423590 ,2.3894848727839946461 ] 
dist 11=[2.1979664427209281458 ,2.3983431143610178775 ] 
dist 12=[2.1774041360892199496 ,2.4085163950785298719 ] 
dist 13=[2.1564211629720650482 ,2.4232565725363470281 ] 
dist 14=[2.1409911979551230812 ,2.4385100714996364750 ] 
dist 15=[2.1265485567169913609 ,2.4507366042913866685 ] 
dist 16=[2.1095148031818458710 ,2.4631878927236171813 ] 
dist 17=[2.0919483175676207386 ,2.4793404001992910836 ] 
dist 18=[2.0753747896808506660 ,2.4968000431374187757 ] 
dist 19=[2.0562159501127207276 ,2.5144797863000973549 ] 
dist 20=[2.0283084182907698240 ,2.5358557446200530609 ] 
dist 21=[1.9993666145387443893 ,2.5681000009148818463 ] 
dist 22=[1.9760707675285174852 ,2.6003667804829978758 ] 
dist 23=[1.9522578177933030359 ,2.6218328306162661856 ] 
dist 24=[1.9212476434225698166 ,2.6396702290130343870 ] 
dist 25=[1.8876693920818399427 ,2.6574226450685340029 ] 
dist 26=[1.8535843334553418154 ,2.6739354634884465615 ] 
dist 27=[1.8123131415696955360 ,2.6868145546251529081 ] 
dist 28=[1.7499909137889389505 ,2.6996039209960897457 ] 
dist 29=[1.6872715893442602110 ,2.7157578467316984259 ] 
dist 30=[1.6444120422025530912 ,2.7314658608774250651 ] 
dist 31=[1.6075474953235575180 ,2.7424716110091122289 ] 
dist 32=[1.5688077095179975742 ,2.7522295017357985717 ] 
dist 33=[1.5314454955970943234 ,2.7629461622310001790 ] 
dist 34=[1.5000911313966883758 ,2.7735654385236075327 ] 
dist 35=[1.4668739582965951789 ,2.7829337994555564019 ] 
dist 36=[1.4220606566547577757 ,2.7932579022623171207 ] 
dist 37=[1.3770942597281196174 ,2.8077000831285927299 ] 
dist 38=[1.3432647190585819979 ,2.8219568304941022781 ] 
dist 39=[1.3108387692818577127 ,2.8315392120360804437 ] 
dist 40=[1.2714866287516107861 ,2.8396096148912840778 ] 
dist 41=[1.2302979696883319902 ,2.8478185486447550718 ] 
dist 42=[1.1905260913171808993 ,2.8555688845233769194 ] 
dist 43=[1.1438417941295933650 ,2.8618049270515687399 ] 
dist 44=[1.0750040035233798369 ,2.8681773105012990362 ] 
dist 45=[1.0055245923654740669 ,2.8764730024351073957 ] 
dist 46=[.95627386408266108553,2.8846598969103282772 ] 
dist 47=[.91201094851433993603,2.8905970984862328525 ] 
dist 48=[.86248239780329400554,2.8960716065667675634 ] 
dist 49=[.8128667816212308986 ,2.9024077585695994590 ] 
dist 50=[.76825561185114662377,2.9088763150639261498 ] 
dist 51=[.71839547136433201206,2.9148804338023819771 ] 
dist 52=[.64778438576979746839,2.9217444229709460679 ] 
dist 53=[.5754079191948393747 ,2.9316524077551627801 ] 
dist 54=[.51848639397834907752,2.9414570051499635576 ] 
dist 55=[.4615183924849728116 ,2.9479074520941150587 ] 
dist 56=[.38895602486188649951,2.9531879031055393474 ] 
dist 57=[.31118805919587436549,2.9583125921965933632 ] 
dist 58=[.23339807511362394932,2.9629948979403773872 ] 
dist 59=[.14003982105705697088,2.9665058448548627074 ] 
dist 60=[0                     ,2.9698597841185466932 ] 
dist 61=[2.6088368941517786752 ,2.9739140716962686928 ] 
dist 62=[2.5925143576065414865 ,2.9777679107349738505 ] 
dist 63=[2.5797284528141675879 ,2.9803200698035032189 ] 
dist 64=[2.5669801318793354578 ,2.9824279607091635975 ] 
dist 65=[2.5508079142458490776 ,2.9845047565360700990 ] 
dist 66=[2.5335092210399957116 ,2.9864229390805094451 ] 
dist 67=[2.5162551026895001532 ,2.9878963894173129986 ] 
dist 68=[2.4955844981234554586 ,2.9893383308735186878 ] 
dist 69=[2.4646201911455914047 ,2.9911304861333029304 ] 
dist 70=[2.4331698517824069007 ,2.9928024837948459534 ] 
dist 71=[2.4105551614422845180 ,2.9937638037288766532 ] 
dist 72=[2.3898990789936703713 ,2.9943962041019592393 ] 
dist 73=[2.3662829713874451331 ,2.9947525418904843977 ] 
dist 74=[2.3423363362547289296 ,2.9949609333252674102 ] 
dist 75=[2.3203581700254676690 ,2.9950015545899229306 ] 
dist 76=[2.2954299449494473848 ,2.9949356226585934868 ] 
dist 77=[2.2596833532029110896 ,2.9948705354042584552 ] 
dist 78=[2.2228514345070916153 ,2.9923219906085881850 ] 
dist 79=[2.1935820025482263606 ,2.9918832603284143487 ] 
dist 80=[2.1640071531501589942 ,2.9910442297860208162 ] 
dist 81=[2.1259535886194275766 ,2.9907879030457175102 ] 
dist 82=[2.0849770933380304770 ,2.9896845667902221057 ] 
dist 83=[2.0437107971161159264 ,2.9894068074209794046 ] 
dist 84=[1.9939825069492175165 ,2.9886544527582473474 ] 
dist 85=[1.9191588403711044052 ,2.9884117096526164274 ] 
dist 86=[1.8442498628985132902 ,2.9709434521148102702 ] 
dist 87=[1.7941803364220984790 ,2.9692875931036365669 ] 
dist 88=[1.7523169075485432576 ,2.9654362515900075533 ] 
dist 89=[1.7102315378060163643 ,2.9646527731096711245 ] 
dist 90=[1.6708133478205624032 ,2.9592578618795966056 ] 
dist 91=[1.6396183835849640210 ,2.9582002982902797807 ] 
dist 92=[1.6082175890903136397 ,2.9564050803177648430 ] 
dist 93=[1.5679760977003350708 ,2.9559505448675060428 ] 
dist 94=[1.5285649086078045806 ,2.9471292649120432093 ] 
dist 95=[1.5004852441103540594 ,2.9458945370637977292 ] 
dist 96=[1.4751019208088907278 ,2.9431199917321571973 ] 
dist 97=[1.4464758393286136850 ,2.9424117206008776869 ] 
dist 98=[1.4176715053953863346 ,2.9387237257909250841 ] 
dist 99=[1.3915751892834885099 ,2.9379774833242338160 ] 
dist 100=[1.3622478596219646972 ,2.9364315442144874195 ] 
dist 101=[1.3205197796579212865 ,2.9358234149157725398 ] 
dist 102=[1.2790263291234163846 ,2.8741976076613953047 ] 
dist 103=[1.2506374948015552456 ,2.8697947276681759121 ] 
dist 104=[1.2261834504276132258 ,2.8607885022928157832 ] 
dist 105=[1.2004287843922947006 ,2.8584339481578549875 ] 
dist 106=[1.1755556997002884029 ,2.8497230025924495212 ] 
dist 107=[1.1546278966161087710 ,2.8457434304477996847 ] 
dist 108=[1.1324096272045338038 ,2.8339257743211070605 ] 
dist 109=[1.1023748002850745158 ,2.8254192354528874229 ] 
dist 110=[1.0722107636992194845 ,2.7871117451390567654 ] 
dist 111=[1.0494756679458242080 ,2.7735510364816514577 ] 
dist 112=[1.0276434711382749356 ,1.5798668936020776398 ] 
dist 113=[1.0010909442190865924 ,1.5523351103591030343 ] 
dist 114=[.97326951501620400259,1.4880883194389151457 ] 
dist 115=[.94636183009927021615,1.4788272750924210934 ] 
dist 116=[.91474514450082688237,1.3930635314005511712 ] 
dist 117=[.86808816170708613533,1.3777188425603535264 ] 
dist 118=[.82149836324229151094,1.3591069869464804436 ] 
dist 119=[.79015040855172412899,1.3557718533210367649 ] 
dist 120=[.76371297549057314153,1.2382063490743408958 ] 
dist 121=[.736764795187594257  ,1.2238276330906678275 ] 
dist 122=[.71128690997576914205,1.1949290769765069684 ] 
dist 123=[.69073051704539273758,1.1876564111820666765 ] 
dist 124=[.66967378660323399506,1.1624042810653923288 ] 
dist 125=[.64219459906548273651,1.1572009096551572657 ] 
dist 126=[.61504537366596746803,1.1501931502385062940 ] 
dist 127=[.59530846030561594509,1.1483398671079684968 ] 
dist 128=[.57706161351907268112,.98044966392477133897] 
dist 129=[.55587251229518500599,.96637105241210230095] 
dist 130=[.5342022157064797933 ,.93494201213048552507] 
dist 131=[.51403063335612943523,.92920152713996661   ] 
dist 132=[.490925627810456066  ,.89132856268054065325] 
dist 133=[.45752191822456674358,.88464242751407520662] 
dist 134=[.42408113915928633924,.87267178271840346383] 
dist 135=[.40082785923166233813,.87002388072926756187] 
dist 136=[.38039681173891935876,.83277280822938940503] 
dist 137=[.35824469323421012515,.82770773938115941802] 
dist 138=[.33646265003637128851,.81703787307991971603] 
dist 139=[.31751186847405839573,.81450968691164500738] 
dist 140=[.2968489039155847272 ,.80361089023231467594] 
dist 141=[.26821829203773369281,.80164997667778432811] 
dist 142=[.23914695127388978334,.79736399636687552713] 
dist 143=[.21672111320729488131,.79648684468776305312] 
dist 144=[.1946854816541241691 ,.55918889747054384449] 
dist 145=[.16717492972685081489,.55781527940124403007] 
dist 146=[.13797316661071005012,.55295204601120642244] 
dist 147=[.1091728516064510617 ,.55198058433490779518] 
dist 148=[.07490950302868758960,.5504435993367809486 ] 
dist 149=[.02385612667187619437,.55007285790106038585] 
dist 150=[-.02712735975010199764,.45213501861913839987] 
dist 151=[-.06111115525449653872,.44994102451951122744] 
dist 152=[-.08942228071007061047,.39761558583626688156] 
dist 153=[-.11771562798482700343,.39114771968604882428] 
dist 154=[-.14410826089624044104,.37768213794224976307] 
dist 155=[-.16481671018482286123,.37438365530687016979] 
dist 156=[-.1854965928468069984 ,.36128229035438859346] 
dist 157=[-.2117749619764557011 ,.35884544480401436322] 
dist 158=[-.23740376516845665654,.35400224154968228546] 
dist 159=[-.25548544603416539721,.35280469028686723909] 
dist 160=[-.27164730547919806204,.29185099427307362188] 
dist 161=[-.28959700609726825689,.28646251059294915992] 
dist 162=[-.30750027194636121059,.2739418639437288996 ] 
dist 163=[-.32347639674434142038,.27213699487502623936] 
dist 164=[-.34123306079992611718,.25563741730447818717] 
dist 165=[-.36625831385512096828,.25270816304770276677] 
dist 166=[-.39104098146822862693,.24910399761327842196] 
dist 167=[-.40782732689278467189,.24846166761906450557] 
dist 168=[-.42210549241786845168,.22672054050731388005] 
dist 169=[-.4368556796583297053 ,.22408338982803406231] 
dist 170=[-.45092512370830792668,.21873677599809113676] 
dist 171=[-.46248038139939993882,.2173908270963495571 ] 
dist 172=[-.47450191405202422999,.21269220860908857568] 
dist 173=[-.49043641347574709404,.21175167964795440238] 
dist 174=[-.5062956129659334173 ,.21042603270780230033] 
dist 175=[-.51801595306637041336,.21007686657385069027] 
dist 176=[-.52904415431377484837,.00802379669166794764] 
dist 177=[-.5421348644066670653 ,.00712037248310667976] 
dist 178=[-.55568059741785502125,.00274802812031167261] 
dist 179=[-.56852884693925558889,.00200218121959286512] 
dist 180=[-.58343408707678114723,.00032237976607799633] 
dist 181=[-.60520758636076870666,6.61541499047162400000e-05] 
dist 182=[-.62685912249858346143,-.03290360038069398582] 
dist 183=[-.64127652168402168436,-.03528591346721429374] 
dist 184=[-.65327109897672642395,-.04051419886168924006] 
dist 185=[-.66523157862757188561,-.04151266454752407320] 
dist 186=[-.67637143670341648878,-.04749961313629477084] 
dist 187=[-.68508360596538207228,-.04853555820200179681] 
dist 188=[-.69375712373393478574,-.05053518952099816672] 
dist 189=[-.70474237952263097507,-.05100947050899046685] 
dist 190=[-.71543849902213624833,-.05563375760996591409] 
dist 191=[-.72295549921117322793,-.05632414771617692887] 
dist 192=[-.72964387990965971908,-.05744401331244303989] 
dist 193=[-.73702560047905269752,-.05769983981911464134] 
dist 194=[-.74436122310816665838,-.05801939002431796226] 
dist 195=[-.75086521644226753321,-.05782003105999113151] 
dist 196=[-.75805955742931476434,-.05730835529960709518] 
dist 197=[-.76815650482621913649,-.05623230133615002000] 
dist 198=[-.77813739699028418275,-.05501696207410630981] 
dist 199=[-.78486752811509289333,-.05394816848908914541] 
dist 200=[-.79055920123297543643,-.05277395265041795326] 
dist 201=[-.79638636041540852326,-.05113684911211105337] 
dist 202=[-.80191172853590072256,-.04931171483205306861] 
dist 203=[-.80639626619025486516,-.04738539458220514136] 
dist 204=[-.81101403258414287783,-.04500049713810834473] 
dist 205=[-.81707230295567664047,-.04134118500124662447] 
dist 206=[-.82307292673968056127,-.03746996611763441720] 
dist 207=[-.82746011228166681595,-.03423749108431346170] 
dist 208=[-.83154115681209331183,-.03082811998832976591] 
dist 209=[-.83631724574898294595,-.02624933409946330428] 
dist 210=[-.84122232342493239658,-.02122409349007389657] 
dist 211=[-.84581931060890710838,-.01602903301079341846] 
dist 212=[-.85110934350933918434,-.00967215191173606453] 
dist 213=[-.85878653794978711158,0                     ] 
dist 214=[-.86639007032012925065,-.21439308939094303632] 
dist 215=[-.87138546283426979284,-.211334798158558333  ] 
dist 216=[-.87546686289151585262,-.20806560837316073735] 
dist 217=[-.87941451521411672938,-.2052832692350352176 ] 
dist 218=[-.88301238991729618453,-.20230228349301307903] 
dist 219=[-.8856947154624984924 ,-.19823849954168580276] 
dist 220=[-.88824188043103560872,-.19374905919002511321] 
dist 221=[-.89129913092711836858,-.18906551807074374404] 
dist 222=[-.89419402796414925186,-.18330400546718279297] 
dist 223=[-.8960917971834830504 ,-.17450289756323063067] 
dist 224=[-.89763775703554757241,-.16549737165788066521] 
dist 225=[-.89912545275595111969,-.15891821663067040559] 
dist 226=[-.90047631783973351327,-.15280392699014494061] 
dist 227=[-.90147497339569477282,-.14565773297697882601] 
dist 228=[-.90241503765907869408,-.13832468081517642616] 
dist 229=[-.90353155616179663487,-.13146297702409381017] 
dist 230=[-.90455757893725164074,-.12357592561858049703] 
dist 231=[-.9051356680544985408 ,-.11214166797668979085] 
dist 232=[-.90550090009639207862,-.10030875021588335774] 
dist 233=[-.90567549926635551227,-.09082712554465253897] 
dist 234=[-.90576222685587509805,-.08117520417358426374] 
dist 235=[-.90577597661071492098,-.06866111622939052562] 
dist 236=[-.9055012754112716835 ,-.05513958610828858804] 
dist 237=[-.90500984716097285951,-.04145807903425759759] 
dist 238=[-.90215442357286725684,-.02492545713274080569] 

8 phat 1 dirichlet min maxes function [1, 1, 1, 2, 1, 1, 0, 1] 
dist 0=[.61513923310833420726,.61513923310833420726] 
dist 1=[.59208054782795414908,.63382345115704872158] 
dist 2=[.55677023306722098371,.65163624262714651562] 
dist 3=[.52085907208108984038,.66769835693163224361] 
dist 4=[.49539704955627964817,.67938000466065603381] 
dist 5=[.47250719386848146708,.69018477982592376726] 
dist 6=[.44688449754451485874,.70273947320576672966] 
dist 7=[.4212111310109601903 ,.71468341338464287035] 
dist 8=[.3981185990068373474 ,.73589614461515631539] 
dist 9=[.37230191214665382327,.75897293000371154639] 
dist 10=[.33573214243871080301,.77606815460199189384] 
dist 11=[.29824436798533113126,.79219469490862753471] 
dist 12=[.268755735113087636  ,.8113968206307762776 ] 
dist 13=[.2392376077024869956 ,.83129912184303906681] 
dist 14=[.20163185772217965822,.85022631058882444653] 
dist 15=[.16132458776109104454,.87222244249478864135] 
dist 16=[.1210005946508898388 ,.90440027830729558728] 
dist 17=[.07260260723513918918,.93641872458746709014] 
dist 18=[0                     ,.95777731159357155629] 
dist 19=[.59147372435897545872,.97558885298869591157] 
dist 20=[.60337810524561315492,.99341939454783839562] 
dist 21=[.62987981236540387026,1.0100719227207571889 ] 
dist 22=[.6347111906993728289 ,1.0231715037506131424 ] 
dist 23=[.6663287370449460449 ,1.0362845561225730183 ] 
dist 24=[.67187352339773331938,1.0529909714382113208 ] 
dist 25=[.68186956513954180199,1.0693058922005982363 ] 
dist 26=[.68660000479955322773,1.0808529983041655729 ] 
dist 27=[.75657338028171342239,1.0912123091260478989 ] 
dist 28=[.7645588334030334083 ,1.1027761428067703941 ] 
dist 29=[.78555997400146809857,1.1143443047425312191 ] 
dist 30=[.80967661827425664633,1.1247209311664883929 ] 
dist 31=[.933565678480792011  ,1.1362983505465210044 ] 
dist 32=[.94414241772316282773,1.1526695980056115506 ] 
dist 33=[.96854366351802027102,1.1689063863414679894 ] 
dist 34=[.97219340733254053095,1.1799459812106211069 ] 
dist 35=[1.0038253818748558408 ,1.1893814656631624946 ] 
dist 36=[1.0094225487928399723 ,1.1992019345741217124 ] 
dist 37=[1.0167680881179370883 ,1.2086149973782052647 ] 
dist 38=[1.0184360251609778641 ,1.2164208907395302252 ] 
dist 39=[1.0578800674878184576 ,1.2246088428752499990 ] 
dist 40=[1.0627183713169619876 ,1.2355501185291166340 ] 
dist 41=[1.0728503626079402143 ,1.2464810082568606401 ] 
dist 42=[1.0752062421009165896 ,1.2546274205498987095 ] 
dist 43=[1.0851887846661676892 ,1.2623606355987673995 ] 
dist 44=[1.0869867208932396030 ,1.2716387701808028690 ] 
dist 45=[1.0905952200557630451 ,1.2812932496230448337 ] 
dist 46=[1.0914789907430083735 ,1.2905318223506127241 ] 
dist 47=[1.1320281441961271584 ,1.3013125180940056002 ] 
dist 48=[1.1356410235705851238 ,1.3171353904905481611 ] 
dist 49=[1.1437870293926920353 ,1.3328835596687842367 ] 
dist 50=[1.1451049195944210559 ,1.3433654485522016262 ] 
dist 51=[1.1550322189885584699 ,1.3520811348305852251 ] 
dist 52=[1.1567484572193928701 ,1.3607646107347287791 ] 
dist 53=[1.1594170550063211641 ,1.3688477824387595388 ] 
dist 54=[1.1600531249652726015 ,1.3751622917050310221 ] 
dist 55=[1.1698995536594572971 ,1.3814422899143995945 ] 
dist 56=[1.1723848785023378322 ,1.3893874195933254091 ] 
dist 57=[1.1814136964557212945 ,1.3971195767800811331 ] 
dist 58=[1.1821733775387071813 ,1.4025476991310481848 ] 
dist 59=[1.1841976822897882103 ,1.4073714856126342841 ] 
dist 60=[1.1857627285362432589 ,1.4126863394443571304 ] 
dist 61=[1.1912836742165259855 ,1.4179629327216206033 ] 
dist 62=[1.1945005111823864966 ,1.4226336794986748604 ] 
dist 63=[1.3201967712099498148 ,1.4277939930480530923 ] 
dist 64=[1.3251821847258741603 ,1.4350288208310029329 ] 
dist 65=[1.3364885127236822419 ,1.4421777458123489424 ] 
dist 66=[1.3382812821535021967 ,1.4469944538754796481 ] 
dist 67=[1.3522840547564072827 ,1.4510639153618392709 ] 
dist 68=[1.3547198694872145064 ,1.4552239037778409018 ] 
dist 69=[1.3583435521191369545 ,1.4591645873334476954 ] 
dist 70=[1.3592600319058424603 ,1.4623568440135619330 ] 
dist 71=[1.3740717117440876319 ,1.4656385058647169479 ] 
dist 72=[1.3758926394985831974 ,1.4699368042626708309 ] 
dist 73=[1.3799956836047598366 ,1.4741910814012077080 ] 
dist 74=[1.3806015844482872862 ,1.4772966612056273760 ] 
dist 75=[1.3855144283257716526 ,1.4801807870151680260 ] 
dist 76=[1.3863374850865932602 ,1.4835492629875498627 ] 
dist 77=[1.3875065827378139594 ,1.4870050548078744249 ] 
dist 78=[1.3871520765437538937 ,1.4902384383403855224 ] 
dist 79=[1.3811222611172023233 ,1.4939551950680659049 ] 
dist 80=[1.3718014214895320744 ,1.4993444478516269789 ] 
dist 81=[1.3623222711244579659 ,1.5046875088248683084 ] 
dist 82=[1.3556592265843134082 ,1.5082195014536104462 ] 
dist 83=[1.3497294028938058132 ,1.5111295611676642772 ] 
dist 84=[1.3431830479185368783 ,1.5139849317252979645 ] 
dist 85=[1.3366766027791315324 ,1.5166144895546446602 ] 
dist 86=[1.3309064081772222366 ,1.5186213134447875696 ] 
dist 87=[1.3245226709601496096 ,1.5205727075096889147 ] 
dist 88=[1.3155621126100810802 ,1.5229805500563644204 ] 
dist 89=[1.3064125946821376899 ,1.5252942310199503867 ] 
dist 90=[1.2992730345983875719 ,1.5268689851556701052 ] 
dist 91=[1.2921802156188868495 ,1.5282167163827086810 ] 
dist 92=[1.2832176511854213080 ,1.5296223209001209401 ] 
dist 93=[1.2736486842610442316 ,1.5309714134598630634 ] 
dist 94=[1.2641303118722453124 ,1.5320931009630965597 ] 
dist 95=[1.2527462736728448864 ,1.5332722960360232275 ] 
dist 96=[1.2357148240648397666 ,1.5348514160048391924 ] 
dist 97=[1.2184247890589986915 ,1.5363798221747709536 ] 
dist 98=[1.2060064326373021670 ,1.5373561655948261750 ] 
dist 99=[1.1946781026757461475 ,1.5381228777615617071 ] 
dist 100=[1.1817480630478737464 ,1.5388127724144059556 ] 
dist 101=[1.1686492538778477228 ,1.5394071261858798094 ] 
dist 102=[1.1566458592456849871 ,1.5397916813407365696 ] 
dist 103=[1.1430461970157469156 ,1.5400992776722692001 ] 
dist 104=[1.1235624684051721932 ,1.5403858021923304213 ] 
dist 105=[1.1034948626116476607 ,1.5406147894989638407 ] 
dist 106=[1.0875597460384242583 ,1.5406922411640329260 ] 
dist 107=[1.0714695374515461627 ,1.5407005510325041383 ] 
dist 108=[1.0507815757926417085 ,1.5406662069866684426 ] 
dist 109=[1.0285121116853897404 ,1.5403351178258001811 ] 
dist 110=[1.0060960428439166358 ,1.5402238076913819569 ] 
dist 111=[.97909130635080555828,1.5400437684918341238 ] 
dist 112=[.93846760799302256848,1.5399721899392046812 ] 
dist 113=[.89780122368178074243,1.5379291505468379286 ] 
dist 114=[.87062574701210460269,1.5376232759015481560 ] 
dist 115=[.84791089831970688129,1.5369073603576752646 ] 
dist 116=[.82508660047169644283,1.5366905649641425506 ] 
dist 117=[.80371583813338061497,1.5355748310818604386 ] 
dist 118=[.78681499284441660313,1.5353256645083310833 ] 
dist 119=[.76981343294375710454,1.5348176532769861502 ] 
dist 120=[.74803982176461998149,1.5346592024051379171 ] 
dist 121=[.72672248430768445755,1.5275707709314289747 ] 
dist 122=[.71154597577734532719,1.5267415962460039538 ] 
dist 123=[.69783878543702704726,1.5255501336970075332 ] 
dist 124=[.68239858059950932882,1.5246004653905102971 ] 
dist 125=[.66687257358126835033,1.5185435156218238850 ] 
dist 126=[.65282218270169948262,1.5149420329924719870 ] 
dist 127=[.63704510800737170733,.85364104007906689072] 
dist 128=[.61461253041778542869,.83964880999563761704] 
dist 129=[.59231274714398248654,.80699410545577512721] 
dist 130=[.57706683704712861923,.80228434264180047529] 
dist 131=[.56394593038529450338,.75867713617441959035] 
dist 132=[.55014595817294193487,.75087254144809297567] 
dist 133=[.5368298544834162943 ,.74140339045649737034] 
dist 134=[.5256443757624663058 ,.73969895054971872439] 
dist 135=[.51378526842726116307,.67985732356617769751] 
dist 136=[.49777471453008104557,.67253457310864305492] 
dist 137=[.48170468758666079772,.65781668905130074031] 
dist 138=[.46960769373891676549,.65411131364356261891] 
dist 139=[.45800593772827463112,.64123776190864400886] 
dist 140=[.44391681489845566055,.63858459571946329341] 
dist 141=[.42916554620139995182,.63499222211486809692] 
dist 142=[.41491526987597528374,.63402284793963106662] 
dist 143=[.39818363387653707833,.54829413613303620979] 
dist 144=[.37350716315060976897,.5410969899592299985 ] 
dist 145=[.34887214931213658927,.52503028767892338933] 
dist 146=[.33230633690843889591,.52209038557478843288] 
dist 147=[.31834623507111422732,.5027231588826297168 ] 
dist 148=[.30413381497060820204,.49930183064907367135] 
dist 149=[.29070781255911473548,.49317011275605851196] 
dist 150=[.27989330647087508288,.49181073963511283969] 
dist 151=[.2688319678556280021 ,.47271969989820527245] 
dist 152=[.25441865887850350869,.47012184513657939223] 
dist 153=[.24018869964270221485,.46463915971467483112] 
dist 154=[.22986074250521190347,.46334458422757557104] 
dist 155=[.22032957968268640107,.45769927628907823655] 
dist 156=[.20928672171007704485,.45668788084340200757] 
dist 157=[.19800705813406021419,.45444253275112994186] 
dist 158=[.18752869548395533996,.45400985229150537545] 
dist 159=[.17554323463676164996,.33137026039686270489] 
dist 160=[.15823532201643757345,.32440687100199588088] 
dist 161=[.14091652179201694924,.30829902879089865257] 
dist 162=[.12888751156687523351,.30587548130289286038] 
dist 163=[.11833294191862447062,.28480304862342656242] 
dist 164=[.10691176337253892401,.28104960326041775622] 
dist 165=[.09569475357555409933,.27613913517510834778] 
dist 166=[.08595683945049437192,.27498437986034028859] 
dist 167=[.07535689363164391184,.24791241952382011702] 
dist 168=[.06069183927837573848,.24456068082662434426] 
dist 169=[.04581090209952073111,.23757444753392477321] 
dist 170=[.03434744556880025581,.23586594045823975003] 
dist 171=[.02309847520553273559,.22903076442402959421] 
dist 172=[.00907546223922272103,.22776288162395554208] 
dist 173=[-.00579885324992999826,.22521253664853605269] 
dist 174=[-.02045295250901587960,.22457297027098677926] 
dist 175=[-.03787503953406481327,.20693829660926069858] 
dist 176=[-.06382104208186615927,.20682610810660836213] 
dist 177=[-.08972612246605613011,.18361465623477269809] 
dist 178=[-.10698452473973466626,.18267411397635252377] 
dist 179=[-.12135219227161927292,.17404596275026316211] 
dist 180=[-.13569460940120111535,.17251155282136775208] 
dist 181=[-.14906305508281603459,.17063106581930385435] 
dist 182=[-.15953492971830509093,.17029687902397674648] 
dist 183=[-.16997608922018783355,.15882175752649354392] 
dist 184=[-.18322167729692624808,.15742749403599624186] 
dist 185=[-.19612910365317924836,.15460742907538053022] 
dist 186=[-.20521764852631702736,.15389784169351559807] 
dist 187=[-.21332258463451209827,.15142573717430917288] 
dist 188=[-.22229566974565465853,.15092712824674137815] 
dist 189=[-.23122904738094078356,.15023650951460460167] 
dist 190=[-.23917515737293069867,.1500581728366001233 ] 
dist 191=[-.24798577263803572516,.02771940857718514880] 
dist 192=[-.26037708891097760557,.02272364349592748466] 
dist 193=[-.27263718325886140228,.01120511671820817005] 
dist 194=[-.28092292333942201184,.00946188452842412022] 
dist 195=[-.28795055494893912707,-.00546945853583337800] 
dist 196=[-.29517833540854889593,-.00811742222332209822] 
dist 197=[-.30205247042522828835,-.01164281316797337218] 
dist 198=[-.30766555399302744203,-.01249706829905908159] 
dist 199=[-.31347597834987958173,-.03111002385318876835] 
dist 200=[-.32113945770079640301,-.03341062133188134259] 
dist 201=[-.32874899653305636208,-.03825695808408983452] 
dist 202=[-.33434366396002113612,-.03937229291723696837] 
dist 203=[-.33957919476517205836,-.04427705412783695194] 
dist 204=[-.34575222136391794604,-.04514859141777864976] 
dist 205=[-.35211720045340531724,-.04700104821120932122] 
dist 206=[-.35812052291347290407,-.04739597380057411804] 
dist 207=[-.36505874792907863173,-.05401046878659524859] 
dist 208=[-.37516324807156018339,-.05414863981624895825] 
dist 209=[-.38519845490632158065,-.06166391579494461127] 
dist 210=[-.39185951330010545768,-.06234119850463169025] 
dist 211=[-.39737782225985420674,-.06367840038447244128] 
dist 212=[-.40284214035165804105,-.06400350553289166961] 
dist 213=[-.40790679123711893572,-.06506204054160476296] 
dist 214=[-.41182646949096432607,-.06528787296033285544] 
dist 215=[-.41569008615352226522,-.06542298805115324329] 
dist 216=[-.42053049602087715453,-.06531385776832706590] 
dist 217=[-.42521779212763930011,-.06509640775012290756] 
dist 218=[-.42846896835151419728,-.06475881851596104696] 
dist 219=[-.43131693790194510866,-.06426591409995051152] 
dist 220=[-.43439144577198708899,-.06342720482458151171] 
dist 221=[-.43740664461700730502,-.06242204036226757217] 
dist 222=[-.44001738372412877119,-.06126334588199224597] 
dist 223=[-.4428534307129774586 ,-.05976075443695412304] 
dist 224=[-.44676983959548600789,-.05738009267914690994] 
dist 225=[-.45061370886173067329,-.05491094018660001542] 
dist 226=[-.45315960430420908625,-.05305439928326173683] 
dist 227=[-.45526260760893504174,-.05127635054232964124] 
dist 228=[-.45733495056634682265,-.04912111657067331758] 
dist 229=[-.45924915664732415962,-.04686720255529595513] 
dist 230=[-.4607196275290951357 ,-.04469444336218417086] 
dist 231=[-.46215865533179065313,-.04214720048808916761] 
dist 232=[-.4639470920954449064 ,-.03839543104094531953] 
dist 233=[-.46567188809524028857,-.03448819309892426900] 
dist 234=[-.46685635891243062451,-.03131910566139030257] 
dist 235=[-.46788138086619238248,-.02805824349733287559] 
dist 236=[-.46896839662019097581,-.02378391558913992462] 
dist 237=[-.47002277868993738603,-.01914259754505660218] 
dist 238=[-.47091726901922673138,-.01441385328234471121] 
dist 239=[-.47187332272157283749,-.00867630555429159910] 
dist 240=[-.47317395241175341745,0                     ] 
dist 241=[-.47443648430581353787,-.06798738882101483227] 
dist 242=[-.47524015089140192957,-.06491180450023770947] 
dist 243=[-.47586798105379237266,-.06173773602950595221] 
dist 244=[-.47642718532802384203,-.05874047014405554372] 
dist 245=[-.47690483157923675784,-.05527403573690889137] 
dist 246=[-.47720643873017949759,-.05022338150241155931] 
dist 247=[-.4774392536374936266 ,-.04498605969724472579] 
dist 248=[-.47764174007859131368,-.04077298739919611408] 
dist 249=[-.47779780079530712893,-.03646924286620735167] 
dist 250=[-.47784491679905601435,-.03086924095604838845] 
dist 251=[-.47784983892346374541,-.02480853017299650865] 
dist 252=[-.47783712597658995093,-.01866203753205104924] 
dist 253=[-.4774196674783667278 ,-.01122452741586060412] 

8 phat 1 dirichlet min maxes function [1, 0, 0, 1, 2, 2, 0, 0, 2] 
dist 0=[3.5806020345178120748 ,3.5806020345178120748 ] 
dist 1=[3.5777465951909268236 ,3.5827028355526952230 ] 
dist 2=[3.5745954455525565581 ,3.5846702804171147917 ] 
dist 3=[3.5713118431644150430 ,3.5869923311543127535 ] 
dist 4=[3.5672746654715501756 ,3.5892242962265565465 ] 
dist 5=[3.5611092981794632741 ,3.5908314083239307209 ] 
dist 6=[3.5545954691900089060 ,3.5923016690597814994 ] 
dist 7=[3.5491644857374039636 ,3.5939862222671742279 ] 
dist 8=[3.5434418976419319061 ,3.5956964760810461026 ] 
dist 9=[3.5357616895843369757 ,3.5972695290039264965 ] 
dist 10=[3.5273328323652628147 ,3.5990564839145329406 ] 
dist 11=[3.5186157307169680312 ,3.6016223213874057854 ] 
dist 12=[3.5079447016843129455 ,3.6042675993991595719 ] 
dist 13=[3.4917003446624495422 ,3.6063723049913373321 ] 
dist 14=[3.4750691471491873757 ,3.6085013728438758153 ] 
dist 15=[3.4628507943475974787 ,3.6112440897731492822 ] 
dist 16=[3.4514260384357923554 ,3.6141991408999601334 ] 
dist 17=[3.4379691333185961559 ,3.6171775213898293710 ] 
dist 18=[3.4241013106947790335 ,3.6207684214502717191 ] 
dist 19=[3.4110329161613761198 ,3.6261734885369196328 ] 
dist 20=[3.3959383292399833355 ,3.6315575737540733900 ] 
dist 21=[3.3739659264280786364 ,3.6350645457365912299 ] 
dist 22=[3.3511862355700741408 ,3.6378960495404459469 ] 
dist 23=[3.3328625695647499827 ,3.6405783225662182953 ] 
dist 24=[3.3141435973045950258 ,3.6429853007912297566 ] 
dist 25=[3.2897827113304978386 ,3.6447156477483124460 ] 
dist 26=[3.2634127060306139164 ,3.6462956902611128536 ] 
dist 27=[3.2366574441923407060 ,3.6481014572444371237 ] 
dist 28=[3.2042710692388886271 ,3.6497647631890914473 ] 
dist 29=[3.1553771446611820198 ,3.6507749712377936079 ] 
dist 30=[3.1063623370601450749 ,3.6515081490668634772 ] 
dist 31=[3.0734924402423769796 ,3.6520633566652292622 ] 
dist 32=[3.0458910586138851091 ,3.6524667181885125323 ] 
dist 33=[3.0179498092693848795 ,3.6525925184124170280 ] 
dist 34=[2.9916552858776656828 ,3.6525758972846426114 ] 
dist 35=[2.9706406509988304931 ,3.6525032636185054120 ] 
dist 36=[2.9492968934967051348 ,3.6518199998107846654 ] 
dist 37=[2.9216859110028907283 ,3.6516241932649611100 ] 
dist 38=[2.8945208453838088595 ,3.6509794186101820416 ] 
dist 39=[2.8749607128499432702 ,3.6507896921664362127 ] 
dist 40=[2.8570672409142700451 ,3.6490478018980922354 ] 
dist 41=[2.8365686587251630942 ,3.6486142916570429307 ] 
dist 42=[2.8157600380624040516 ,3.6480567531966967190 ] 
dist 43=[2.7966264418029794426 ,3.6478203319516413752 ] 
dist 44=[2.7748962173758706942 ,3.6417148856022950202 ] 
dist 45=[2.7437013317036387992 ,3.6408131341387332371 ] 
dist 46=[2.7125644002358773867 ,3.6390488136304955303 ] 
dist 47=[2.6910659870990930631 ,3.6385528483317916881 ] 
dist 48=[2.6723380371061440085 ,3.6365847254117632211 ] 
dist 49=[2.6522826939724234391 ,3.6361219715021659005 ] 
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dist 102=[.85305452910249842328,2.7194626048273153786 ] 
dist 103=[.79731133700221895952,2.7175581781992003919 ] 
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dist 108=[.43063939510937785196,2.6829229359592261514 ] 
dist 109=[.34441267960808638405,2.6809284980482913013 ] 
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dist 113=[.81348691616630816757,2.6669061489727267392 ] 
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dist 118=[.69527628422705698396,1.0894507463860947048 ] 
dist 119=[.67406301127915466221,1.0859452435561995405 ] 
dist 120=[.65359553662811512161,1.0778651560609739522 ] 
dist 121=[.628565531813192715  ,1.0765804579203899144 ] 
dist 122=[.60226665084338280603,1.0660331039938663976 ] 
dist 123=[.57672379259569361378,1.0641368555454289096 ] 
dist 124=[.54662911268943799799,1.0614796368765932970 ] 
dist 125=[.50212337922911780314,1.0607274381042006818 ] 
dist 126=[.45764309327336171702,.93111538638063688562] 
dist 127=[.42765020095822983424,.92314975474510272932] 
dist 128=[.40228546067992469039,.90457141842733337246] 
dist 129=[.37631734144747950057,.90188118807818448897] 
dist 130=[.35169438021224124333,.87710412734108756749] 
dist 131=[.33171014362425208359,.87267013424463679851] 
dist 132=[.31113258751073511277,.86725561353231769123] 
dist 133=[.28413640476302955836,.8662517648849096326 ] 
dist 134=[.257397337009467387  ,.83239307423928565616] 
dist 135=[.23784821634940386596,.82824460586640606102] 
dist 136=[.21966363758403685753,.81988197366594647007] 
dist 137=[.19838260726195115082,.81777046951142567329] 
dist 138=[.17652715091725335787,.81039033948883624749] 
dist 139=[.15604492284905697738,.80888079327952703154] 
dist 140=[.13247514875119715445,.80672836012646117732] 
dist 141=[.09826980277188492037,.8061356218516599677 ] 
dist 142=[.06397222979338036826,.75827994009897010455] 
dist 143=[.04003355649518021588,.75424351192003117407] 
dist 144=[.01890579221037227926,.74520141668857103577] 
dist 145=[-.00414841281351076025,.7435771317659286107 ] 
dist 146=[-.02690465292680388011,.73258863998308997668] 
dist 147=[-.0504625842367016328 ,.73064654124827930545] 
dist 148=[-.1002739681671049321 ,.72723391806174523776] 
dist 149=[-.1335618898491255332 ,.72649711443484997701] 
dist 150=[-.1613872613594785217 ,.7153448937939511341 ] 
dist 151=[-.1893489656104527623 ,.71385472387275286246] 
dist 152=[-.2155314141765646953 ,.7106276334136835874 ] 
dist 153=[-.2362399326493598718 ,.70994621225505282657] 
dist 154=[-.2570740827325069999 ,.70634925608663255173] 
dist 155=[-.2837590457575319914 ,.70571933356783547949] 
dist 156=[-.3098862648233212142 ,.70437947190282873241] 
dist 157=[-.36305428679223348669,.7040699010575727169 ] 
dist 158=[-.41855926431324487286,-.2558678772273653791 ] 
dist 159=[-.45548365648014224439,-.2594753351716151076 ] 
dist 160=[-.48616392277635030784,-.2731824288612548828 ] 
dist 161=[-.51669299626854071096,-.2757731467130972229 ] 
dist 162=[-.54508611118644222629,-.2804763965691996788 ] 
dist 163=[-.56722275080980550152,-.2815049650898137282 ] 
dist 164=[-.58919667868263048749,-.3468967614871016677 ] 
dist 165=[-.6169389699178030535 ,-.3525118441118908392 ] 
dist 166=[-.64390828847856113362,-.3654708685999176070 ] 
dist 167=[-.66279040327540529758,-.3673269032136570346 ] 
dist 168=[-.67951669990041465559,-.3840337407375611748 ] 
dist 169=[-.6978629552818651629 ,-.3869561850848058503 ] 
dist 170=[-.71602819153083898145,-.3906127236148786050 ] 
dist 171=[-.73203043667880265558,-.3912251046088744027 ] 
dist 172=[-.74964556786286343043,-.4116997589830074118 ] 
dist 173=[-.77426221389371251198,-.4141321020097003626 ] 
dist 174=[-.7985508282423363192 ,-.4191341786278825069 ] 
dist 175=[-.81485386786293771516,-.4203016365083073754 ] 
dist 176=[-.82856010222450945671,-.4247691611760848403 ] 
dist 177=[-.84246173537852668092,-.4256009622720364181 ] 
dist 178=[-.85556117165043149231,-.4267866077732867586 ] 
dist 179=[-.86605869884039471592,-.4270154333637067442 ] 
dist 180=[-.87674684241948140067,-.5846937111214190978 ] 
dist 181=[-.89060874543801905637,-.5910948954942576821 ] 
dist 182=[-.90426391907940551621,-.6055382756774454588 ] 
dist 183=[-.91412517259162922687,-.6078986521605542961 ] 
dist 184=[-.92317575878914591543,-.6255801470970544270 ] 
dist 185=[-.93358834429259588796,-.6286533960019645959 ] 
dist 186=[-.94418362450508206741,-.6334600050021914592 ] 
dist 187=[-.95396499143616067108,-.6346069803860799344 ] 
dist 188=[-.96510511929540483832,-.6525964269351282685 ] 
dist 189=[-.98113536778823545319,-.6548584861705028139 ] 
dist 190=[-.99699132502486064695,-.6597902265165334751 ] 
dist 191=[-1.0074343031822601809 ,-.6606661827188173517 ] 
dist 192=[-1.0159957232563389896 ,-.6660863390602191931 ] 
dist 193=[-1.0243255695538096397 ,-.6669798113371729297 ] 
dist 194=[-1.0319502304053309328 ,-.6686774284532133561 ] 
dist 195=[-1.0376909527315266807 ,-.6690483775246351321 ] 
dist 196=[-1.0431978969792333459 ,-.67196140923601822124] 
dist 197=[-1.0498874562127455308 ,-.67229915473854353174] 
dist 198=[-1.0562627853234168222 ,-.67210826356494009751] 
dist 199=[-1.0605128274290349710 ,-.67114528423319355888] 
dist 200=[-1.0640540489895782189 ,-.66974983861717270889] 
dist 201=[-1.0675941402647450200 ,-.66782911458048780837] 
dist 202=[-1.0708971853067184193 ,-.66513978973436692106] 
dist 203=[-1.0734902329109878157 ,-.6606700718544728299 ] 
dist 204=[-1.0760810172425376120 ,-.6558031324351595479 ] 
dist 205=[-1.0793749977747714587 ,-.65152497548481068586] 
dist 206=[-1.0825236690703271313 ,-.64682402498726467979] 
dist 207=[-1.0845332315222377715 ,-.6402659425375415341 ] 
dist 208=[-1.0861092048707294593 ,-.63295001292147534942] 
dist 209=[-1.0875235763653325881 ,-.62521780350441677352] 
dist 210=[-1.0887394430157826171 ,-.61563549485080007959] 
dist 211=[-1.0895214311755937687 ,-.60091952629758247705] 
dist 212=[-1.0901416648423253053 ,-.58599595867899849672] 
dist 213=[-1.0907105594530366508 ,-.57558327947574294011] 
dist 214=[-1.0911609853726175404 ,-.56639803086945761209] 
dist 215=[-1.0913073466095151324 ,-.55638390475204370641] 
dist 216=[-1.0913420137269763013 ,-.54650547132188254693] 
dist 217=[-1.0913456522643286798 ,-.53786294078868628292] 
dist 218=[-1.0905736131064528104 ,-.52839979434683287848] 
dist 219=[-1.0903739087777731198 ,-.51523902017180989673] 
dist 220=[-1.0902535785960000959 ,-.50185588228678535573] 
dist 221=[-1.0902088696622029152 ,-.491503303759404777  ] 
dist 222=[-1.0101375422222257526 ,-.48130436378085733183] 
dist 223=[-1.0063842484605509155 ,-.46853572545376277361] 
dist 224=[-.99763383768651794795,-.4549648721049502074 ] 
dist 225=[-.99621246401969457493,-.4415571929235301518 ] 
dist 226=[-.9843561051621894522 ,-.42558983453531697329] 
dist 227=[-.98217117121101234594,-.40178068158471862683] 
dist 228=[-.97915893881745349114,-.37764586288987065925] 
dist 229=[-.97826271767665427754,-.36037588769016660669] 
dist 230=[-.96132207515377719587,-.34468882528720821193] 
dist 231=[-.9591112339410428599 ,-.32688537902629620401] 
dist 232=[-.95445605960457879885,-.30890830454694874529] 
dist 233=[-.95320411083877367676,-.29252674676186984504] 
dist 234=[-.94825176558299602545,-.27404147898115037899] 
dist 235=[-.94634922669941733683,-.2476498957386761641 ] 
dist 236=[-.94128240128644855208,-.22050944591423413934] 
dist 237=[-.9384308694057976401 ,-.19902882694347266998] 
dist 238=[-.88516335998227850652,-.17740589389935838507] 
dist 239=[-.88072834902780787833,-.14969620191437783911] 
dist 240=[-.87142060662286171652,-.11991641648058826763] 
dist 241=[-.86905774020742248375,-.09001343725723706375] 
dist 242=[-.85014469193324280711,-.05404412980582423294] 

8 phat 1 dirichlet min maxes function [0, 0, 0, 2, 0, 1, 2, 1, 2] 
dist 0=[.76258199268003595948,.76258199268003595948] 
dist 1=[.76009838961350324498,.76545063261542753052] 
dist 2=[.75303281230324982307,.77115612668759879822] 
dist 3=[.74274461348454158398,.78243463175810049881] 
dist 4=[.72554016727407343468,.79573067031377448103] 
dist 5=[.70570658716720500292,.81938129165012890734] 
dist 6=[.68490206075309717398,.84508242690965108062] 
dist 7=[.65922618533968809585,.8641223275333325314 ] 
dist 8=[.61990759404265834403,.88208390952594236397] 
dist 9=[.57991995707073112517,.90347185650818903081] 
dist 10=[.55156795201151543056,.92564011932013543635] 
dist 11=[.52608042419107343688,.94672290498920138307] 
dist 12=[.49755047050479052007,.97122465857198827782] 
dist 13=[.46896441518608333896,1.0070685278911000865 ] 
dist 14=[.44325248584032285587,1.0427350944883994088 ] 
dist 15=[.41450779937994135326,1.0665276518954180823 ] 
dist 16=[.37379095628299952363,1.0863694067793469360 ] 
dist 17=[.33205221526478480154,1.1062330725597504982 ] 
dist 18=[.29922001832307458689,1.1247848820918602160 ] 
dist 19=[.2663552907437026806 ,1.1393793157259046425 ] 
dist 20=[.22448643006948940249,1.1539895018453308374 ] 
dist 21=[.17961000713961027894,1.1726043232269714807 ] 
dist 22=[.1347152689625473484 ,1.1907834182451240312 ] 
dist 23=[.08083156675965977401,1.2036507344544285049 ] 
dist 24=[0                     ,1.2151952968038227033 ] 
dist 25=[.65847701514852339808,1.2280834810897351655 ] 
dist 26=[.67172863807905545602,1.2409772310327221346 ] 
dist 27=[.70832433152726759178,1.2525440588181874815 ] 
dist 28=[1.0392179704234133367 ,1.2654503514732886106 ] 
dist 29=[1.0509879626321596543 ,1.2837018646089190163 ] 
dist 30=[1.0781430340190638583 ,1.3018039675635538175 ] 
dist 31=[1.0822038860018300155 ,1.3141126328060041770 ] 
dist 32=[1.1174083576766081515 ,1.3246336691912475272 ] 
dist 33=[1.1236377283312606901 ,1.3355853929307357645 ] 
dist 34=[1.1318102886960316341 ,1.3460836532161753776 ] 
dist 35=[1.1336639709168534178 ,1.3547908728803831749 ] 
dist 36=[1.1775744055824169821 ,1.3639255165120854169 ] 
dist 37=[1.1829601791371674946 ,1.3761334477224914299 ] 
dist 38=[1.1942367257498306571 ,1.3883305377069784576 ] 
dist 39=[1.1968605768756653859 ,1.3974218206699282212 ] 
dist 40=[1.2079636626899371102 ,1.4060531771617481169 ] 
dist 41=[1.2099645584208227272 ,1.4164105989090185799 ] 
dist 42=[1.2139754115278421123 ,1.4271890662907943166 ] 
dist 43=[1.2149564538191818038 ,1.4375045809178536918 ] 
dist 44=[1.2601461564111598135 ,1.4495430369075259887 ] 
dist 45=[1.2641704135894006695 ,1.4672131588934820507 ] 
dist 46=[1.2732465326952219218 ,1.4848000137935351586 ] 
dist 47=[1.2747127371897880714 ,1.4965054081419885289 ] 
dist 48=[1.2857813118491904458 ,1.5062380933814808734 ] 
dist 49=[1.2876951134485885600 ,1.5159342427961215178 ] 
dist 50=[1.2906630666216579778 ,1.5249597128602601452 ] 
dist 51=[1.2913727648846199280 ,1.5320097251926141659 ] 
dist 52=[1.3023807250276476845 ,1.5390206310530869154 ] 
dist 53=[1.3051529332160801531 ,1.5478896777454535546 ] 
dist 54=[1.3151119081041057911 ,1.5565206017373698158 ] 
dist 55=[1.3159585792450173526 ,1.5625790325928788984 ] 
dist 56=[1.3182236121658952247 ,1.5679622808017991201 ] 
dist 57=[1.3199611529506746831 ,1.5738925190755793915 ] 
dist 58=[1.3260722579063949149 ,1.5797794634802112324 ] 
dist 59=[1.3296350983193101767 ,1.5849895390754795809 ] 
dist 60=[1.4691424210793008389 ,1.5907449300243640237 ] 
dist 61=[1.4746791344116818718 ,1.5988130995628827635 ] 
dist 62=[1.4872342219025593054 ,1.6067850552596903922 ] 
dist 63=[1.4892261492366601935 ,1.6121555972613732833 ] 
dist 64=[1.5047707712687124318 ,1.6166922144819880391 ] 
dist 65=[1.5074745961166890098 ,1.6213285265913634921 ] 
dist 66=[1.5115012846586050288 ,1.6257196515198317956 ] 
dist 67=[1.5125183504930065776 ,1.6292755363994770446 ] 
dist 68=[1.5289429421001874293 ,1.6329298664294028651 ] 
dist 69=[1.5309630683507464862 ,1.6377147655633226360 ] 
dist 70=[1.5355106970228804832 ,1.6424499479147912422 ] 
dist 71=[1.5361856318144446539 ,1.6459054142103949118 ] 
dist 72=[1.5416176612388694722 ,1.6491133019854918392 ] 
dist 73=[1.5425271123485916641 ,1.6528581868356257738 ] 
dist 74=[1.5438311376456150258 ,1.6566991933978198988 ] 
dist 75=[1.5441080389549219985 ,1.6602915618178164619 ] 
dist 76=[1.5393423320271892421 ,1.6644198428783012933 ] 
dist 77=[1.5290205292451020172 ,1.6704044648142656804 ] 
dist 78=[1.5185225936408412409 ,1.6763372399483516671 ] 
dist 79=[1.5111420932251417737 ,1.6802581373379616546 ] 
dist 80=[1.5045723718593952386 ,1.6834875993643450616 ] 
dist 81=[1.4973174549733184562 ,1.6866546788421393501 ] 
dist 82=[1.4901055230283883991 ,1.6895701846093005288 ] 
dist 83=[1.4837077301386423830 ,1.6917933685989872740 ] 
dist 84=[1.4766280565807346940 ,1.6939533508477835620 ] 
dist 85=[1.4666886655854413809 ,1.6966160542652927718 ] 
dist 86=[1.4565388073881818730 ,1.6991733759094092227 ] 
dist 87=[1.4486172822225925678 ,1.7009118382419771108 ] 
dist 88=[1.4407463221186241260 ,1.7023973928813682696 ] 
dist 89=[1.4307987121383240510 ,1.7039431006678854755 ] 
dist 90=[1.4201771455688178904 ,1.7054244162603613679 ] 
dist 91=[1.4096104219582142527 ,1.7066524068347289072 ] 
dist 92=[1.3969715777633637525 ,1.7079401520754491133 ] 
dist 93=[1.3780617294071947995 ,1.7096604835496115083 ] 
dist 94=[1.3588643293752371567 ,1.7113236930750438772 ] 
dist 95=[1.3450753044604055093 ,1.7123829545260855526 ] 
dist 96=[1.3324958750158858997 ,1.7132111154904517469 ] 
dist 97=[1.3181367342521887541 ,1.7139499378669281041 ] 
dist 98=[1.3035895445565698464 ,1.7145818867120773096 ] 
dist 99=[1.2902579344227815001 ,1.7149825608472039016 ] 
dist 100=[1.2751526572136562033 ,1.7152937513547568107 ] 
dist 101=[1.2535109669381762901 ,1.7155677727770087745 ] 
dist 102=[1.2312203348458265950 ,1.7157763105177429273 ] 
dist 103=[1.2135193508141374442 ,1.7158255710950558279 ] 
dist 104=[1.1956455106260287593 ,1.7158113799873794728 ] 
dist 105=[1.1726634674926429642 ,1.7157661126864773290 ] 
dist 106=[1.1479241587917516786 ,1.7153008629864534210 ] 
dist 107=[1.1230214224868772241 ,1.7151560213076894905 ] 
dist 108=[1.0930205763863810732 ,1.7149782036052262676 ] 
dist 109=[1.0478893132991024519 ,1.7148879790351864565 ] 
dist 110=[1.0027104340236732284 ,1.7123048813023774342 ] 
dist 111=[.97251912722824312528,1.7119324778444152936 ] 
dist 112=[.94728310195195206656,1.7110616122909084582 ] 
dist 113=[.92192487612811934615,1.7108092844666480239 ] 
dist 114=[.89818116873785829125,1.7094703012433114738 ] 
dist 115=[.8794030632062759836 ,1.7091756696520814654 ] 
dist 116=[.86051246152306729572,1.7085850457947614620 ] 
dist 117=[.83631878025596136983,1.7084047472723943759 ] 
dist 118=[.81263169916071254227,1.7003725393399127656 ] 
dist 119=[.79576744984640889628,1.6994322966401062240 ] 
dist 120=[.78053525561129469381,1.6980705035578342933 ] 
dist 121=[.76337623917061512293,1.6970048655052431948 ] 
dist 122=[.74612129698710275952,1.6901860330968536441 ] 
dist 123=[.73050540892986518955,1.6861383535404843218 ] 
dist 124=[.71296973431010617739,.94818992259159007199] 
dist 125=[.6880358289819568865 ,.93259263224654608473] 
dist 126=[.66324915553906565725,.89619230349694015924] 
dist 127=[.64630239441765260565,.8909424451516712075 ] 
dist 128=[.63171704530244311416,.84233439172832665553] 
dist 129=[.61637579465755511607,.83363492341898288494] 
dist 130=[.60157181438429657384,.82308011813694323888] 
dist 131=[.58913549551181850416,.82118064731831587134] 
dist 132=[.57594931953398076558,.75448074926609427364] 
dist 133=[.55814598235917254195,.74631898224225610311] 
dist 134=[.54027598637030448808,.72991473826432782101] 
dist 135=[.52682318149401339639,.72578487640194890797] 
dist 136=[.51392028906922592714,.71143689052197566033] 
dist 137=[.49824989043680936398,.70847991102609290406] 
dist 138=[.48184240391704182658,.70447705585417046624] 
dist 139=[.46599123024483667268,.703397876404481735  ] 
dist 140=[.4473792319623007701 ,.6078623491809967969 ] 
dist 141=[.41992871032320619084,.59984232744907846854] 
dist 142=[.39252397191484351784,.58193858305441768267] 
dist 143=[.3740951021885211607 ,.57866291967600038498] 
dist 144=[.35856438493157136111,.5570814564105492152 ] 
dist 145=[.34275197998064312977,.55326910015867829639] 
dist 146=[.32781390345390385877,.54643710192699527423] 
dist 147=[.31578041650199247176,.54492270293846548607] 
dist 148=[.30347134540264200074,.52365077388947716081] 
dist 149=[.28743095857081782317,.52075632964330589009] 
dist 150=[.27159403472870630086,.51464812553398175557] 
dist 151=[.26009879618230853429,.51320575904535776798] 
dist 152=[.24948943372484913078,.50691838724037927366] 
dist 153=[.23719592974538018617,.50579181510394222764] 
dist 154=[.22463800121893745324,.503292364542738271  ] 
dist 155=[.21297096579387368488,.50280957640810206668] 
dist 156=[.19962490673799866849,.36622743318999100076] 
dist 157=[.18035104383026710503,.35847303007242088561] 
dist 158=[.16106457764669973058,.34053525092143120545] 
dist 159=[.14766810668955701563,.33783680547087835575] 
dist 160=[.13591285554598119014,.3143704022366314318 ] 
dist 161=[.12319111208037860084,.31019065969094117737] 
dist 162=[.11069601338269155828,.30472356169454516491] 
dist 163=[.09984731969384780543,.30343903149522297634] 
dist 164=[.08803723241259501123,.27329115878207764445] 
dist 165=[.07169665104109293667,.26955895331442340202] 
dist 166=[.05511494702297588805,.26178033171121853993] 
dist 167=[.04234039215306477435,.25987772850566113766] 
dist 168=[.02980397792253217779,.25227013477801802402] 
dist 169=[.01417481374854557907,.25085867376045044067] 
dist 170=[-.00240378825396452875,.24802173694275347141] 
dist 171=[-.01873786324308716318,.24731092749637050305] 
dist 172=[-.03815793958827585491,.23458137659786240638] 
dist 173=[-.06708025267833877914,.23444769749322432716] 
dist 174=[-.09595726650382654711,.20170409264360154695] 
dist 175=[-.1151961501112689577 ,.20065689143319321667] 
dist 176=[-.13121315617127947615,.19105402334872180531] 
dist 177=[-.14720296710335372965,.18934643800990470864] 
dist 178=[-.16210755041467541959,.18725275978207904762] 
dist 179=[-.17378374949854174473,.18688020565477340818] 
dist 180=[-.18542666079204029621,.17411725218735213328] 
dist 181=[-.20019809611681456005,.17256657701532215261] 
dist 182=[-.21459305075123569345,.16942940215147993889] 
dist 183=[-.22473007519130604437,.16863991585314428824] 
dist 184=[-.23377112488718155124,.16588852777023868264] 
dist 185=[-.24378228507672876702,.16533397084053740948] 
dist 186=[-.25375012841283547466,.16456360608529185996] 
dist 187=[-.26261791482642483593,.16436332025278056166] 
dist 188=[-.27245174608087290066,.02851928542032161738] 
dist 189=[-.28628367664096640249,.02297116449028206332] 
dist 190=[-.29996979845020387331,.01018026325820267114] 
dist 191=[-.30922040860817835292,.00824376985536347683] 
dist 192=[-.3170676172061523137 ,-.00833314444946865008] 
dist 193=[-.32514026662905538473,-.01127272778088166408] 
dist 194=[-.33281915428680308762,-.01518913041044356636] 
dist 195=[-.33909135338037466411,-.01613990701196522911] 
dist 196=[-.34558585651599405956,-.03678783737109251037] 
dist 197=[-.35415393913901277977,-.03934018428309694869] 
dist 198=[-.36266281354085645662,-.04471897005198051735] 
dist 199=[-.368920489438938819  ,-.04595450545171464311] 
dist 200=[-.37477826486672531917,-.05140558786834601884] 
dist 201=[-.38168757552910220189,-.05237285985715954931] 
dist 202=[-.38881316445602988903,-.05443379710976111822] 
dist 203=[-.39553603231382609916,-.05486821619109314848] 
dist 204=[-.40330753229657052266,-.05732742260590721549] 
dist 205=[-.41462754970683107938,-.05746987430715874621] 
dist 206=[-.42587075413222277348,-.06628691970537492166] 
dist 207=[-.4333350095017624611 ,-.06707079574739305977] 
dist 208=[-.43952023042240215526,-.06863294116807252204] 
dist 209=[-.44564741904397224348,-.06901671849575106164] 
dist 210=[-.45132807358219051364,-.07029512534366716409] 
dist 211=[-.45572720075896145577,-.07056091556565219465] 
dist 212=[-.46006597307820743206,-.07078951240521788337] 
dist 213=[-.46550521394285288854,-.07073199325407391916] 
dist 214=[-.47077413931646636782,-.07055402361354304387] 
dist 215=[-.47443166591593942698,-.07022629735427536509] 
dist 216=[-.47763868212006712469,-.06972353973486945165] 
dist 217=[-.48110560888109045891,-.06884544647234097939] 
dist 218=[-.48450852931476531687,-.06778454185954661439] 
dist 219=[-.48745952631429613553,-.06655057278287086150] 
dist 220=[-.49066904525052975432,-.06494337073079307438] 
dist 221=[-.49510602877370432844,-.06238963421066055201] 
dist 222=[-.49946294739982610279,-.05973822922788212278] 
dist 223=[-.50235221438428019542,-.05774036826002045396] 
dist 224=[-.50474280292230310545,-.05582280955203610358] 
dist 225=[-.50710505532566498299,-.05349255841096774351] 
dist 226=[-.50929131025415902215,-.05105248655465104796] 
dist 227=[-.51097792567900196106,-.04869565580664044706] 
dist 228=[-.51263531105552843627,-.04592911475680095179] 
dist 229=[-.5147046485786608707 ,-.04185028934865912553] 
dist 230=[-.51670506089126414722,-.03760077466324048382] 
dist 231=[-.51808675199962437512,-.03415150904714131804] 
dist 232=[-.51929093039383850408,-.03060004861170795279] 
dist 233=[-.52058130878066929522,-.02594176460415217391] 
dist 234=[-.52184107334073034404,-.02088204694408948425] 
dist 235=[-.52292279934775180807,-.01572493861694967482] 
dist 236=[-.52409021118776317355,-.00946615773356838894] 
dist 237=[-.52569271090723839232,0                     ] 
dist 238=[-.52725277572841878725,-.07645387011875061650] 
dist 239=[-.52825045250647708589,-.07298737576653918453] 
dist 240=[-.52903516141234608801,-.06941130254498341963] 
dist 241=[-.52974337650876313029,-.06603655494323690762] 
dist 242=[-.53035501400433960182,-.06213520132971679111] 
dist 243=[-.53075342316948833787,-.05645280286583888398] 
dist 244=[-.53107512071645610996,-.05056119746877540594] 
dist 245=[-.53137992195794788539,-.04582305233909850692] 
dist 246=[-.53162926242392814017,-.04098407350064500739] 
dist 247=[-.53172912167471952732,-.03468914309385475255] 
dist 248=[-.53176679437277281995,-.02787707605386358162] 
dist 249=[-.53176739213919800213,-.02096964843644928653] 
dist 250=[-.531413971031977363  ,-.01261213338670970319] 

8 phat 1 dirichlet min maxes function [2, 1, 0, 1, 1, 0, 1, 0, 2] 
dist 0=[3.8170960045271912620 ,3.8170960045271912620 ] 
dist 1=[3.8143813434517314461 ,3.8204122668981676694 ] 
dist 2=[3.8068392204398778058 ,3.8255569816131765694 ] 
dist 3=[3.7980071724169836260 ,3.8313987156296284928 ] 
dist 4=[3.7886610333623538282 ,3.8368342107673599610 ] 
dist 5=[3.7770695258706223882 ,3.8403540073966306254 ] 
dist 6=[3.7592562182581263307 ,3.8431726039456629828 ] 
dist 7=[3.7411800980218224220 ,3.8458033616903544830 ] 
dist 8=[3.7285373651014083189 ,3.8481373841148645213 ] 
dist 9=[3.7173516880770252150 ,3.8497690637347906725 ] 
dist 10=[3.7051036524537330788 ,3.8512118592302997137 ] 
dist 11=[3.6929888512443647515 ,3.8547510626704132775 ] 
dist 12=[3.6823360991680417555 ,3.8580827397676877146 ] 
dist 13=[3.6706259309004955702 ,3.8605940755767869848 ] 
dist 14=[3.6542815657805013548 ,3.8630057897807717049 ] 
dist 15=[3.6376329119736390597 ,3.8659389702403137006 ] 
dist 16=[3.6247056179810742373 ,3.8686879743692494226 ] 
dist 17=[3.6119230192286286613 ,3.8703630021343014710 ] 
dist 18=[3.5958531325814972677 ,3.8715852169282724938 ] 
dist 19=[3.5787378709381393382 ,3.8725230360314414476 ] 
dist 20=[3.5617738719065891015 ,3.8732148912920970911 ] 
dist 21=[3.5415295511657376803 ,3.8734532860126174921 ] 
dist 22=[3.5112933155557777416 ,3.8735173236509589293 ] 
dist 23=[3.4806183843973795990 ,3.8735117738071875260 ] 
dist 24=[3.4586193233046899124 ,3.8723976794881043831 ] 
dist 25=[3.4385847064815687448 ,3.8721218822827601773 ] 
dist 26=[3.4157673650366319837 ,3.8714483275999653793 ] 
dist 27=[3.3926803578707507050 ,3.8711797476294318105 ] 
dist 28=[3.3715671038840350738 ,3.8697434424037011257 ] 
dist 29=[3.3476805370633822564 ,3.8693800515444090337 ] 
dist 30=[3.3135005430748502780 ,3.8685349488461268034 ] 
dist 31=[3.2783139782749110020 ,3.8682244494052208263 ] 
dist 32=[3.2504012242133640075 ,3.8202498864420875797 ] 
dist 33=[3.2222425505660506217 ,3.8168633453414965524 ] 
dist 34=[3.1860723308783699362 ,3.8091869905931896180 ] 
dist 35=[3.1471544643210936344 ,3.8076199968224259596 ] 
dist 36=[3.1080054652605268654 ,3.7976620146011666001 ] 
dist 37=[3.0608607554775897876 ,3.7957794326152938658 ] 
dist 38=[2.9899608086459214526 ,3.7923490127195875781 ] 
dist 39=[2.9189685322514764540 ,3.7915062038483544310 ] 
dist 40=[2.8714545130236439774 ,3.7781373846447981550 ] 
dist 41=[2.8316592598600681734 ,3.7762849837876357435 ] 
dist 42=[2.7915413115219949145 ,3.7717955397567689707 ] 
dist 43=[2.7538942414952718791 ,3.7710228011219094521 ] 
dist 44=[2.7239822659096060816 ,3.7641944989516168599 ] 
dist 45=[2.6937629808787573377 ,3.7628476052844248286 ] 
dist 46=[2.6548867023818701570 ,3.7610988939655881711 ] 
dist 47=[2.6167411061336540347 ,3.7604976871052201143 ] 
dist 48=[2.5894444804064604732 ,3.7422004715331556461 ] 
dist 49=[2.5646468624219647640 ,3.7400785018034129965 ] 
dist 50=[2.5364970587941195849 ,3.7350447360584381033 ] 
dist 51=[2.5080666815246144864 ,3.7341248169627801157 ] 
dist 52=[2.4821467957340386292 ,3.7250108572248610566 ] 
dist 53=[2.4528863150760304367 ,3.7232339522672185044 ] 
dist 54=[2.4110938769561334485 ,3.7154165109785020100 ] 
dist 55=[2.3694686332160923423 ,3.6295585160724445394 ] 
dist 56=[2.3408769141308381040 ,3.6244504443104000640 ] 
dist 57=[2.3161272933207569340 ,3.6149497801629952993 ] 
dist 58=[2.2898700762296665898 ,3.6126875846374428549 ] 
dist 59=[2.2643946172986918388 ,3.6051464887653974583 ] 
dist 60=[2.2427719545665244818 ,3.5807947671865196174 ] 
dist 61=[2.2196520952338996636 ,3.5768566151175673522 ] 
dist 62=[2.1881879927007483647 ,3.5542694575249547351 ] 
dist 63=[2.1564927989033173552 ,3.5102825671786037186 ] 
dist 64=[2.1324485965546018472 ,3.3073889966738760967 ] 
dist 65=[2.1092084272165431960 ,3.3036598479635593927 ] 
dist 66=[2.0807292887746598254 ,3.2993453407438941403 ] 
dist 67=[2.0507756693424606286 ,3.2985313612597038964 ] 
dist 68=[2.0216377166762219607 ,3.2668100187454956214 ] 
dist 69=[1.9872729911803820851 ,3.2628220055923084525 ] 
dist 70=[1.9364127789490424590 ,3.2550084302978939210 ] 
dist 71=[1.8855655021064020941 ,3.2530392568890554278 ] 
dist 72=[1.8512525169316074492 ,3.2462873998222775168 ] 
dist 73=[1.8222051045838703987 ,3.2447737950646122534 ] 
dist 74=[1.7924196168295289224 ,3.2429336552851816359 ] 
dist 75=[1.7641473853913357809 ,3.2423823747861767577 ] 
dist 76=[1.7411528539767948264 ,3.1798969906053978186 ] 
dist 77=[1.7174317970404211034 ,3.1745590392296783408 ] 
dist 78=[1.6862535328094655489 ,3.1628878021503041495 ] 
dist 79=[1.6553450118810897898 ,3.1603268451218163916 ] 
dist 80=[1.6327029024274520619 ,3.1467132864075825059 ] 
dist 81=[1.6115964197679243948 ,3.1442362528660172453 ] 
dist 82=[1.5868302595509396513 ,3.1390452797170666543 ] 
dist 83=[1.5613594298095792971 ,3.1376335139084160003 ] 
dist 84=[1.5374343362625359980 ,3.1251948235748688665 ] 
dist 85=[1.5098599433917795012 ,3.1232186582851208388 ] 
dist 86=[1.4697922644185248492 ,3.1193027957697184945 ] 
dist 87=[1.4295954284289877899 ,3.1182787421855470981 ] 
dist 88=[1.4015044198118426640 ,3.1145509003263531988 ] 
dist 89=[1.3766753010620935729 ,3.1137279300816972191 ] 
dist 90=[1.3495257134295305848 ,3.1122269934652225874 ] 
dist 91=[1.3226936322057739704 ,3.1118342573626578159 ] 
dist 92=[1.2991345088081164939 ,2.9438738531361782512 ] 
dist 93=[1.2732658633567010476 ,2.9344035389858206021 ] 
dist 94=[1.2371959141955624337 ,2.9131093837125276702 ] 
dist 95=[1.2004702896152190701 ,2.9091687251703027870 ] 
dist 96=[1.1719790050240104977 ,2.8827964788930301782 ] 
dist 97=[1.1438305289081103448 ,2.8780475401732927031 ] 
dist 98=[1.1084761055326056737 ,2.8696568225453845454 ] 
dist 99=[1.0708387127373931108 ,2.8677842548243816354 ] 
dist 100=[1.0335585766877735033 ,2.8384740364913193539 ] 
dist 101=[.9890878126085142598 ,2.8345531078303378184 ] 
dist 102=[.9226885935226359629 ,2.8254556340530563240 ] 
dist 103=[.8563252694016435272 ,2.8239062400605329033 ] 
dist 104=[.8119980817583369073 ,2.8116506170401115010 ] 
dist 105=[.7749691899216999303 ,2.8093775543962910296 ] 
dist 106=[.7377983529303534365 ,2.8060508578790445169 ] 
dist 107=[.7030180846733976049 ,2.8051176629359149428 ] 
dist 108=[.6755512397666011477 ,2.7877176785103372710 ] 
dist 109=[.6479566652394433109 ,2.7853305586988677345 ] 
dist 110=[.6126654906836407577 ,2.7788378349920727296 ] 
dist 111=[.5781372487458643381 ,2.7710025660619190436 ] 
dist 112=[.5535943319238054809 ,2.5935032868422010167 ] 
dist 113=[.5314675787480990027 ,2.5839553097981108088 ] 
dist 114=[.5066037609468178425 ,2.5655310068828586392 ] 
dist 115=[.4816363532982901246 ,2.5610459233780412782 ] 
dist 116=[.4590952506137923540 ,2.5466405071696985832 ] 
dist 117=[.4338272641412348639 ,2.5432962277061354960 ] 
dist 118=[.3979525814252556606 ,2.5328573747537426092 ] 
dist 119=[.3623126072371186700 ,2.5172285743375753800 ] 
dist 120=[.3379834324898944282 ,2.4020969980974576460 ] 
dist 121=[.3170851551862136678 ,2.3896723109810810260 ] 
dist 122=[.2951684435400318804 ,2.3542866454516219251 ] 
dist 123=[.2740588877377852698 ,2.3076080574459932597 ] 
dist 124=[.2563891568249157604 ,2.0376410891013020887 ] 
dist 125=[.2377096110830036852 ,2.0132514131890279673 ] 
dist 126=[.17214018552946311517,1.9545201524088299476 ] 
dist 127=[0                     ,1.8995806555394572589 ] 
dist 128=[.16461792291925267115,.66616475852588212808] 
dist 129=[.14085495768912831077,.65988666786136692034] 
dist 130=[.11678428856969976096,.65831280203737835204] 
dist 131=[.08573223211443884072,.65227271400009916947] 
dist 132=[.05522279701219073426,.65113055512830883325] 
dist 133=[.03332256155066100790,.64889582415955359356] 
dist 134=[.01335763527164795974,.64834837991841964693] 
dist 135=[-.0185442941776866999 ,.50193213051459002039] 
dist 136=[-.0440755906063786423 ,.49374559821478868756] 
dist 137=[-.0655542790911823912 ,.47483361778724335256] 
dist 138=[-.0873618295853359239 ,.47198161143980999011] 
dist 139=[-.11171028866458238643,.4473344790722404704 ] 
dist 140=[-.14584151974561983465,.4429525351717380806 ] 
dist 141=[-.1693480122417563824 ,.4371785603488349250 ] 
dist 142=[-.18976225252152786549,.4358048109415537714 ] 
dist 143=[-.2115247696700111704 ,.4045366827654988598 ] 
dist 144=[-.23270298729459819562,.4006686777282559871 ] 
dist 145=[-.25078008520811857445,.3925713824281085962 ] 
dist 146=[-.27019681540766990123,.3906397808844757754 ] 
dist 147=[-.29673343440490038494,.3826075881400323365 ] 
dist 148=[-.3235156179601583865 ,.3811440443684498569 ] 
dist 149=[-.34391458297035747409,.3781350518382692288 ] 
dist 150=[-.36371049226353051062,.3773798163921158936 ] 
dist 151=[-.38808051046894696091,.3425341544637531195 ] 
dist 152=[-.4137709364027991506 ,.3394139143780202848 ] 
dist 153=[-.43884835067183512728,.3322093650485495854 ] 
dist 154=[-.46848941416581599564,.3311386554696414810 ] 
dist 155=[-.51243400172760243248,.3217821041891205438 ] 
dist 156=[-.5562486112826766386 ,.3201261687900549621 ] 
dist 157=[-.58536977646397196963,.3179760547574350587 ] 
dist 158=[-.60953742696965681625,.3175060610158394240 ] 
dist 159=[-.63353845422989553936,.30574090519634993763] 
dist 160=[-.65582948255527286855,.30429997928965196516] 
dist 161=[-.67315730436824044436,.30130312949876444549] 
dist 162=[-.69030947926982988558,.30058457667434949232] 
dist 163=[-.71189794460204486608,.29770461561378369378] 
dist 164=[-.73285262458370115427,.29717306630244739678] 
dist 165=[-.74746972247887983123,.29615614683012152641] 
dist 166=[-.7603614332066253794 ,.29591957646351805273] 
dist 167=[-.77441473302239551972,-.40852422790980029526] 
dist 168=[-.78827828542930074943,-.41801807359051232397] 
dist 169=[-.8004110325059680665 ,-.41963347238029229709] 
dist 170=[-.81370005444267615469,-.42280693468901846245] 
dist 171=[-.8321886157255191985 ,-.42356029783707994985] 
dist 172=[-.85039520189953768479,-.44641235189411980566] 
dist 173=[-.86255635422292601697,-.44871251610515591031] 
dist 174=[-.87271546046663981444,-.45336140602925189014] 
dist 175=[-.88291404533685883493,-.45451083602827348988] 
dist 176=[-.89245722274736000886,-.45841015682579653955] 
dist 177=[-.89999476555745369038,-.45918593582108303247] 
dist 178=[-.90756846408787936772,-.46000918493012534814] 
dist 179=[-.91725628054833752753,-.45995906399055107251] 
dist 180=[-.92673580741498747538,-.45956006129956421932] 
dist 181=[-.93347637525896195174,-.4586969840963409982 ] 
dist 182=[-.93955605704222263081,-.4573217376726012572 ] 
dist 183=[-.94639210654940659658,-.45487409766582810845] 
dist 184=[-.95325938686846568788,-.45189986161121410426] 
dist 185=[-.95946400848869387749,-.44841833941646044765] 
dist 186=[-.96642329155045242301,-.44386974038843721216] 
dist 187=[-.97630920050992566087,-.43662748263545950732] 
dist 188=[-.98605237684524679781,-.42918545496559964665] 
dist 189=[-.99244074170683465032,-.42383780131032110139] 
dist 190=[-.99764630873548938765,-.41895803993647213142] 
dist 191=[-1.0026583477484235319 ,-.41338737086563563031] 
dist 192=[-1.0072112654539197968 ,-.40774461402202574718] 
dist 193=[-1.0105803675242971143 ,-.40257646819355857674] 
dist 194=[-1.0137550048614059093 ,-.3967239999520553026 ] 
dist 195=[-1.0175300704326125761 ,-.38834406391410638213] 
dist 196=[-1.0210867639004186274 ,-.37971682792739386015] 
dist 197=[-1.0233879218826632831 ,-.37287518504334312335] 
dist 198=[-1.0252284735811399938 ,-.36597609048612847604] 
dist 199=[-1.0269427622886735931 ,-.35711901279425636949] 
dist 200=[-1.0284612824461145707 ,-.34759275176822498887] 
dist 201=[-1.0295187668358069247 ,-.33801703263432763216] 
dist 202=[-1.0304495863166007967 ,-.32649175895922539912] 
dist 203=[-1.0314614471368108514 ,-.30916764100242827258] 
dist 204=[-1.0323662625358077876 ,-.2915514456297089695 ] 
dist 205=[-1.0328689117646546945 ,-.2788579054449157912 ] 
dist 206=[-1.0331771468021627203 ,-.26723790331899482895] 
dist 207=[-1.0333043394305300060 ,-.25391562838692969172] 
dist 208=[-1.0333307470952538486 ,-.24038738325455777539] 
dist 209=[-1.0332927482443649530 ,-.2279435209155886625 ] 
dist 210=[-1.0331032764423719038 ,-.21380831285573109703] 
dist 211=[-1.0329816365233640571 ,-.19351497838922351914] 
dist 212=[-1.0312457622080994419 ,-.17259810234405239401] 
dist 213=[-1.0309257327472616733 ,-.15596883171000666709] 
dist 214=[-1.0295197044216842070 ,-.13916080075202385964] 
dist 215=[-1.0168052133119014964 ,-.11752890102726030559] 
dist 216=[-1.0156321769797284239 ,-.09423493994352373678] 
dist 217=[-1.0133918682740071190 ,-.07077895390377531801] 
dist 218=[-1.0111534675385881396 ,-.04251699585020034769] 

8 phat 1 dirichlet min maxes function [1, 2, 0, 0, 1, 1, 1, 2] 
dist 0=[3.9528419951458709648 ,3.9528419951458709648 ] 
dist 1=[3.9525005395108584539 ,3.9530681201856030139 ] 
dist 2=[3.9519088407414858389 ,3.9531984879747707991 ] 
dist 3=[3.9511954771156581666 ,3.9532440659057532785 ] 
dist 4=[3.9503673658202843071 ,3.9531732289053546865 ] 
dist 5=[3.9487482620658283269 ,3.9529409601933194274 ] 
dist 6=[3.9467864902632711833 ,3.9527884887200637196 ] 
dist 7=[3.9442173631612507994 ,3.9517943731016422410 ] 
dist 8=[3.9401197215798194495 ,3.9515094317872362557 ] 
dist 9=[3.9357204414699525188 ,3.9508295786584994676 ] 
dist 10=[3.9319447851012439766 ,3.9505603854558828718 ] 
dist 11=[3.9278716926797054681 ,3.9464922828356865841 ] 
dist 12=[3.9222826888759186850 ,3.9458191030631412948 ] 
dist 13=[3.9160900101300879529 ,3.9442424901607405616 ] 
dist 14=[3.9096022715913078759 ,3.9437358494444411808 ] 
dist 15=[3.9016012125288926178 ,3.9412356181565806353 ] 
dist 16=[3.8893553920989021268 ,3.9406661655735515237 ] 
dist 17=[3.8769529797656321814 ,3.9394782545804036346 ] 
dist 18=[3.8683255667164160437 ,3.9390975603681817241 ] 
dist 19=[3.8607417666113193332 ,3.9219270321754591621 ] 
dist 20=[3.8525137065167866622 ,3.9200006397618348835 ] 
dist 21=[3.8444198862745218005 ,3.9164220206359232777 ] 
dist 22=[3.8373730327749644756 ,3.9155253161981193055 ] 
dist 23=[3.8296852218716530681 ,3.9125780791435748327 ] 
dist 24=[3.8190276331476225171 ,3.9117969356885972155 ] 
dist 25=[3.8082036095538787873 ,3.9090271978683464994 ] 
dist 26=[3.7998500750459436647 ,3.9043597878354087001 ] 
dist 27=[3.7916382727022540291 ,3.8671608742966210712 ] 
dist 28=[3.7813811642473584836 ,3.8630074135670544014 ] 
dist 29=[3.7704909081413604215 ,3.8507991097611908990 ] 
dist 30=[3.7597465755816325834 ,3.8340050006879625711 ] 
dist 31=[3.7326356047245869665 ,3.8082327086190568093 ] 
dist 32=[3.7136522755490344481 ,3.8069153682668605374 ] 
dist 33=[3.6970701459256682990 ,3.8040765881186041651 ] 
dist 34=[3.6792420385137189364 ,3.8032463494439104215 ] 
dist 35=[3.6618014391943462744 ,3.7716745008804821029 ] 
dist 36=[3.6467693049815307728 ,3.7685007498006183482 ] 
dist 37=[3.6304983106990033764 ,3.7609511931398837593 ] 
dist 38=[3.6081023892608086016 ,3.7597214613114018273 ] 
dist 39=[3.5854279018557086299 ,3.7488808709319499141 ] 
dist 40=[3.5680426702746319244 ,3.7468193953160815894 ] 
dist 41=[3.5510607337053748075 ,3.7441465130219934091 ] 
dist 42=[3.5299993878820718721 ,3.7432627533875499156 ] 
dist 43=[3.5077155002162428453 ,3.7253439217605224556 ] 
dist 44=[3.4858435128805065640 ,3.7229544127302252449 ] 
dist 45=[3.4599011880123770033 ,3.7181052600101005595 ] 
dist 46=[3.4213363384377257246 ,3.7168078085106951623 ] 
dist 47=[3.3822855555085657681 ,3.7118791282536097641 ] 
dist 48=[3.3543995435697646477 ,3.7108493482235676510 ] 
dist 49=[3.3291263008322260056 ,3.7086465996076857744 ] 
dist 50=[3.3005263455073523699 ,3.7079928211154733236 ] 
dist 51=[3.2716922905129461684 ,3.6404330290512918133 ] 
dist 52=[3.2454826714252411636 ,3.6351784346671659744 ] 
dist 53=[3.2159580957653658853 ,3.6241014237465658586 ] 
dist 54=[3.1738645306562861005 ,3.6212453405877587165 ] 
dist 55=[3.1305975214457297848 ,3.6095652193039074626 ] 
dist 56=[3.0963792813007280598 ,3.6073897112346589411 ] 
dist 57=[3.0619562250166906174 ,3.6019105864065333969 ] 
dist 58=[3.0178699707849500575 ,3.5963075665585988610 ] 
dist 59=[2.9705002816175710924 ,3.5416058187005589643 ] 
dist 60=[2.9229437987585161340 ,3.5354351128368892663 ] 
dist 61=[2.8657433930393928976 ,3.5246613718295919112 ] 
dist 62=[2.7797989322500468539 ,3.5231947733622705938 ] 
dist 63=[2.6937736898028007007 ,3.5209503030528465862 ] 
dist 64=[2.6362501651568719329 ,3.5203227977371400228 ] 
dist 65=[2.5881282569205507776 ,3.4616714481055662919 ] 
dist 66=[2.5397085834041394901 ,3.4565586934534934566 ] 
dist 67=[2.4943301924474935921 ,3.4452960584409468960 ] 
dist 68=[2.4583731243787130095 ,3.4428702417970359048 ] 
dist 69=[2.4221368372496825030 ,3.4294382584550586931 ] 
dist 70=[2.3756415966833991405 ,3.4269768300759465747 ] 
dist 71=[2.3300784177748410998 ,3.4219847217682397748 ] 
dist 72=[2.2975702883785127176 ,3.4206590442133890589 ] 
dist 73=[2.2681371185330933445 ,3.4071567325399381045 ] 
dist 74=[2.2348734845446054845 ,3.4051075070798257249 ] 
dist 75=[2.2013625307689090767 ,3.4007272371119167034 ] 
dist 76=[2.1709401053635281127 ,3.3995165660670754726 ] 
dist 77=[2.1367008789877256400 ,3.3945021125745830938 ] 
dist 78=[2.0879230853692777697 ,3.3935280323381773630 ] 
dist 79=[2.0393936813126429563 ,3.3911046207008898549 ] 
dist 80=[2.0061479894931871227 ,3.3906465939105992587 ] 
dist 81=[1.9774641488773236168 ,3.1650260772754873983 ] 
dist 82=[1.9332961899758327199 ,3.1534238192464466515 ] 
dist 83=[1.8742390190510400295 ,3.1271541452003128352 ] 
dist 84=[1.8149862184870891133 ,3.1224821873876116437 ] 
dist 85=[1.7595638899823954987 ,3.0894472348533271207 ] 
dist 86=[1.7158282419517760027 ,3.0834999750535199269 ] 
dist 87=[1.6719196170018218768 ,3.0735798619941092615 ] 
dist 88=[1.6158053973179865074 ,3.0712705659771602514 ] 
dist 89=[1.5609241082253810971 ,3.0328638067271987435 ] 
dist 90=[1.5219470880458632834 ,3.0278648345501905391 ] 
dist 91=[1.4868412485981682836 ,3.0160211564678809665 ] 
dist 92=[1.4474443132072853684 ,3.0142583936580050211 ] 
dist 93=[1.4079127580052141016 ,2.9976584380942093096 ] 
dist 94=[1.3722684521525372784 ,2.9945879219686687666 ] 
dist 95=[1.3323491703321058687 ,2.9909140679981862190 ] 
dist 96=[1.2757181189977767215 ,2.9900884777244460141 ] 
dist 97=[1.2194767775808047176 ,2.9611553010712691878 ] 
dist 98=[1.1811162982600400289 ,2.9534538284218544127 ] 
dist 99=[1.1481997388138372751 ,2.7505435426652331567 ] 
dist 100=[1.1137335576647925433 ,2.7436723279216872091 ] 
dist 101=[1.0805701969413132656 ,2.7204024175354601982 ] 
dist 102=[1.0528647949369345067 ,2.7159243680020666254 ] 
dist 103=[1.0236233130443527834 ,2.7050699875384844023 ] 
dist 104=[.98431577927632609522,2.7030612344288608602 ] 
dist 105=[.92835512880910400733,2.6980922690163453673 ] 
dist 106=[.83700995384936828256,2.6909855749635834618 ] 
dist 107=[.74339656676915280722,2.5477313299881649851 ] 
dist 108=[.66979698619307528885,2.5345015586088329567 ] 
dist 109=[.59615952584103996016,2.5199240363988755133 ] 
dist 110=[.50239462270698561498,2.5027955623074295502 ] 
dist 111=[.40191793697449955578,2.4132636565765148631 ] 
dist 112=[.30143385535687663457,2.3621408406146844774 ] 
dist 113=[.18085485131581348236,2.1560021401683666898 ] 
dist 114=[0                     ,2.1019097820089274013 ] 
dist 115=[.55287962847063901342,1.2070299539094386578 ] 
dist 116=[.51924657508789852212,1.2036129259906109334 ] 
dist 117=[.48756613874221829578,1.1989328778493316950 ] 
dist 118=[.46219833368287192241,1.1976405682299174026 ] 
dist 119=[.43638850781073868801,1.1735265632218107849 ] 
dist 120=[.40294003037298270893,1.1704891510687013143 ] 
dist 121=[.37000321039835992417,1.1640205606528731468 ] 
dist 122=[.34623996557788166686,1.1625398815042745958 ] 
dist 123=[.32445346995985538447,1.1556512601932202037 ] 
dist 124=[.29942345825660761945,1.1544484623055558643 ] 
dist 125=[.27397458202338566907,1.1516129966496629502 ] 
dist 126=[.25051266823593383867,1.1512078991236841855 ] 
dist 127=[.22381761140465304971,.74841914314191053129] 
dist 128=[.18543647136691010521,.7328826445016889742 ] 
dist 129=[.14710178624286154051,.69670914536422033733] 
dist 130=[.1205925446355803982 ,.69147365909438584191] 
dist 131=[.09745578865974458628,.64347791015273848828] 
dist 132=[.07261072440046183665,.63491491634215474028] 
dist 133=[.04832377865546713946,.62440811200500368837] 
dist 134=[.02741944350454248472,.62247130379217026484] 
dist 135=[.00481671210890858072,.55784916426640854071] 
dist 136=[-.02626365662524531834,.54995560723933558402] 
dist 137=[-.05771687160123181770,.53400106284663483356] 
dist 138=[-.08181095240285832062,.52997380619013120603] 
dist 139=[-.10532499788197613092,.51588191618438307677] 
dist 140=[-.13445812689055077298,.51302596824330445651] 
dist 141=[-.16526702420721606262,.50891503337324254826] 
dist 142=[-.19548398308722655091,.50780708068276540318] 
dist 143=[-.2313074830719125206 ,.42016317413448109208] 
dist 144=[-.28454201006646767936,.41278398974614655419] 
dist 145=[-.33764582959287289461,.39622222317111651668] 
dist 146=[-.37294651217157912484,.39331172043410900047] 
dist 147=[-.40224859357307117463,.37313320784264189694] 
dist 148=[-.43135858052534673369,.36957898628394275177] 
dist 149=[-.45840098839491256597,.36349408059624919033] 
dist 150=[-.47943295066717308796,.36216020121552873331] 
dist 151=[-.50026176285774680644,.34158130461474356611] 
dist 152=[-.52649158977661879172,.33887259686333809696] 
dist 153=[-.55195800545538121034,.33298049290186481115] 
dist 154=[-.56973324549817224609,.33179434468811323395] 
dist 155=[-.58542176595865457575,.32519491502957876693] 
dist 156=[-.60254150233537258025,.32405323810467291406] 
dist 157=[-.61944040418252600551,.32171421806774755776] 
dist 158=[-.63424560758751108048,.32112602445193457894] 
dist 159=[-.65047513229790750735,.21479524707287575897] 
dist 160=[-.6730711835177546845 ,.20860059455246884242] 
dist 161=[-.69532933572089816838,.19419873465684316202] 
dist 162=[-.71020729659262034897,.19211918832209107394] 
dist 163=[-.72264740024644887113,.17309715309650758947] 
dist 164=[-.73515435609602196657,.16971351875609000172] 
dist 165=[-.74686925503634894809,.1655544685319454293 ] 
dist 166=[-.7561412065980159171 ,.16480209508886846685] 
dist 167=[-.76547522236674739668,.13952063659745226506] 
dist 168=[-.77743837221577098994,.13644440878837681777] 
dist 169=[-.78915526239057450476,.13021714670024265573] 
dist 170=[-.79750426295018678957,.12864771339977679085] 
dist 171=[-.80505253771663970622,.12316324882409548261] 
dist 172=[-.81356660109044966826,.1220591633927458378 ] 
dist 173=[-.82213452947766912757,.12048405362915880218] 
dist 174=[-.82989825916022149203,.12005978839394944094] 
dist 175=[-.83862428398895901569,.08715951216865455388] 
dist 176=[-.85104130117910956084,.08440523749382770503] 
dist 177=[-.86330809271850656735,.07820444985127383422] 
dist 178=[-.87143323058156503189,.07715313195643213119] 
dist 179=[-.87814547453132416854,.06957069899244993884] 
dist 180=[-.88476082910369370319,.06824304362926741292] 
dist 181=[-.89087203259790111265,.06607181521996723737] 
dist 182=[-.8955677242463342688 ,.06557429798906144369] 
dist 183=[-.90016411662511955369,.05780851820197666294] 
dist 184=[-.90587814036316657577,.05681035997017822590] 
dist 185=[-.91138970030529047901,.05462171787347237146] 
dist 186=[-.9151762607336127166 ,.05421694606297525483] 
dist 187=[-.91845484520763209421,.05173455046868092433] 
dist 188=[-.92193455369815939031,.05131086089265149604] 
dist 189=[-.92531160263996193166,.05050654792927621684] 
dist 190=[-.92817956654924191178,.05032285565069309011] 
dist 191=[-.93124761591554209586,-.22796575290152560806] 
dist 192=[-.93542500720075719909,-.21690945473155183352] 
dist 193=[-.9394993640983813525 ,-.20560232664955769865] 
dist 194=[-.9421552896454016186 ,-.19735242867182725011] 
dist 195=[-.94430209522662655134,-.18969641824323308532] 
dist 196=[-.94634001293188099813,-.18076465509788527019] 
dist 197=[-.94817183025753529409,-.17160860330346499019] 
dist 198=[-.94949425784791376381,-.16305546060820268307] 
dist 199=[-.95070762190070273545,-.15323567606253862535] 
dist 200=[-.95210321497607465823,-.13901330910449222514] 
dist 201=[-.95339388396849366093,-.12430144270445818754] 
dist 202=[-.95418756947189050256,-.112523751077467627  ] 
dist 203=[-.95477563517419664496,-.10054465639812388485] 
dist 204=[-.95524384839984013249,-.08502719756100809178] 
dist 205=[-.95560383425914002234,-.06826779591524522375] 
dist 206=[-.95575902026780227081,-.05132117948378670927] 
dist 207=[-.95579529283377915946,-.03085138506355222452] 

8 phat 1 dirichlet min maxes function [1, 1, 2, 1, 0, 0, 2, 1, 2] 
dist 0=[1.9780946872313063366 ,1.9780946872313063366 ] 
dist 1=[1.9742293861534329095 ,1.9810354504245434959 ] 
dist 2=[1.9685340940892822112 ,1.9889329719413120182 ] 
dist 3=[1.9561371537218526829 ,2.0003391829480165364 ] 
dist 4=[1.9398524993869782548 ,2.0190621131702757493 ] 
dist 5=[1.9244872464964089236 ,2.0381187404282255424 ] 
dist 6=[1.9067243087338258592 ,2.0508597152365722828 ] 
dist 7=[1.8808491012747514594 ,2.0615165011157075254 ] 
dist 8=[1.8540145248827553403 ,2.0722365358668475140 ] 
dist 9=[1.8324141860145973172 ,2.0822817408726985279 ] 
dist 10=[1.8103337983436141154 ,2.0902392620849823283 ] 
dist 11=[1.7815790642216319686 ,2.0982567545572410112 ] 
dist 12=[1.7504426589979134232 ,2.1085418443114093255 ] 
dist 13=[1.7188357718619548702 ,2.1186200060846387746 ] 
dist 14=[1.6805648449170357140 ,2.1258098048135705445 ] 
dist 15=[1.6227727977199333307 ,2.1323189392401642205 ] 
dist 16=[1.5646124192819877364 ,2.1415983563794649407 ] 
dist 17=[1.5248681965556462494 ,2.1597478463848542232 ] 
dist 18=[1.4906831658228757034 ,2.1771725141750476925 ] 
dist 19=[1.4547591256295441217 ,2.1916676392853935660 ] 
dist 20=[1.4201124922858068049 ,2.2069124721902732228 ] 
dist 21=[1.3910369914899871448 ,2.2273359257416120508 ] 
dist 22=[1.3602340319508445997 ,2.2477640488734324406 ] 
dist 23=[1.3186777010221868268 ,2.2630275649328460665 ] 
dist 24=[1.2769793910233551066 ,2.2775554061015968021 ] 
dist 25=[1.2456085277968716913 ,2.2950408895825166381 ] 
dist 26=[1.2155392490687900012 ,2.3132653248168986665 ] 
dist 27=[1.1790471774493894023 ,2.3307489284993679767 ] 
dist 28=[1.1408520765685293959 ,2.3511848398357345155 ] 
dist 29=[1.1039708160067565182 ,2.3812183122910572451 ] 
dist 30=[1.0606795592108208119 ,2.4111150754137566609 ] 
dist 31=[.99684497858335027964,2.4310041604149531360 ] 
dist 32=[.93241545052598380718,2.4475308647400083394 ] 
dist 33=[.88674445148957939993,2.4639783315338102576 ] 
dist 34=[.84569884378896275611,2.4792769934296590043 ] 
dist 35=[.79977051830073941391,2.4912085556242526167 ] 
dist 36=[.75376156663429185809,2.5030564711014168647 ] 
dist 37=[.71239346133942549743,2.5180205521036014658 ] 
dist 38=[.66615812176667185361,2.5325712091756820548 ] 
dist 39=[.60068061711531173341,2.5427654569621066859 ] 
dist 40=[.53356618083096789328,2.5518032198216846153 ] 
dist 41=[.48078324403776090029,2.5617280152876236482 ] 
dist 42=[.42795739316933380347,2.5715620445327310734 ] 
dist 43=[.36067130433409925588,2.5802367490780124662 ] 
dist 44=[.28855827921827045387,2.5897956727322285919 ] 
dist 45=[.21642506375419923727,2.6031665200160863569 ] 
dist 46=[.1298558561232277976 ,2.6163652764829244998 ] 
dist 47=[0                     ,2.6252358487366516730 ] 
dist 48=[1.6646419730410285630 ,2.6327059887673314857 ] 
dist 49=[1.6833826319009199705 ,2.6403031103367302880 ] 
dist 50=[1.7266476968757315966 ,2.6474750223355979982 ] 
dist 51=[1.7396047535298541870 ,2.6532443530928589649 ] 
dist 52=[1.7937949223335239016 ,2.6591386324026662200 ] 
dist 53=[2.3393478018297431788 ,2.6668103316309087503 ] 
dist 54=[2.3478271109787789462 ,2.6743806650109163206 ] 
dist 55=[2.3670087954073233299 ,2.6798694883757673016 ] 
dist 56=[2.3700869071274897079 ,2.6849293028826382856 ] 
dist 57=[2.3936931751506975276 ,2.6907836301522536654 ] 
dist 58=[2.3977932720140379297 ,2.6967592556278852399 ] 
dist 59=[2.4040294231869178240 ,2.7023042562779015002 ] 
dist 60=[2.4055640581573583817 ,2.7086421269998457527 ] 
dist 61=[2.4299625758132886540 ,2.7177891834013875645 ] 
dist 62=[2.4329910075781298806 ,2.7268401666068208507 ] 
dist 63=[2.4396795788441666001 ,2.7327937513852786664 ] 
dist 64=[2.4407746638034663675 ,2.7376662807076354139 ] 
dist 65=[2.4483662661130423738 ,2.7423931119703800757 ] 
dist 66=[2.4496195412917430636 ,2.7467105964449003346 ] 
dist 67=[2.4433222099982331044 ,2.7499457658034779125 ] 
dist 68=[2.4327954816124758255 ,2.7530340861968225003 ] 
dist 69=[2.4179558284660453977 ,2.7567641864847854016 ] 
dist 70=[2.4027753281343444247 ,2.7603082876971835393 ] 
dist 71=[2.3908852387782845478 ,2.7626526247899419311 ] 
dist 72=[2.3790312469338590080 ,2.7645858786284992325 ] 
dist 73=[2.3639951213226012352 ,2.7664856741492166774 ] 
dist 74=[2.3479124497041198055 ,2.7682371442401642760 ] 
dist 75=[2.3318723712896045869 ,2.7695771081479433452 ] 
dist 76=[2.3126570446265810685 ,2.7708832379610630752 ] 
dist 77=[2.2838736876704376348 ,2.7724993797078699433 ] 
dist 78=[2.2546389175462854530 ,2.7740036568629020946 ] 
dist 79=[2.2336179788868619698 ,2.7748623365990857310 ] 
dist 80=[2.2144182523462843992 ,2.7754192981046960042 ] 
dist 81=[2.1924681450489937226 ,2.7757167191698143814 ] 
dist 82=[2.1702113610314413920 ,2.7758813130201377659 ] 
dist 83=[2.1497849520826462182 ,2.7759069711649879427 ] 
dist 84=[2.1266174232161681694 ,2.7758362155001161892 ] 
dist 85=[2.0933964185839084138 ,2.7757775281521705789 ] 
dist 86=[2.0591671031340907454 ,2.7732742941832696654 ] 
dist 87=[2.0319664247773768621 ,2.7728501500804493265 ] 
dist 88=[2.0044824027767752586 ,2.7720467399378371842 ] 
dist 89=[1.9691197349909912310 ,2.7718049228367575756 ] 
dist 90=[1.9310411557064207934 ,2.7707839015813756118 ] 
dist 91=[1.8926937443559588384 ,2.7705223592988914139 ] 
dist 92=[1.8464832253550421726 ,2.7698442465985652667 ] 
dist 93=[1.7769529630428783458 ,2.7695968701262788018 ] 
dist 94=[1.7073434149204123228 ,2.7529670047156886417 ] 
dist 95=[1.6608157594425577036 ,2.7513999126163144799 ] 
dist 96=[1.6219133880049831011 ,2.7477563909190175751 ] 
dist 97=[1.5828042487591129198 ,2.7470178713652747443 ] 
dist 98=[1.5461733326692259955 ,2.7419230980332832034 ] 
dist 99=[1.5171836174875567646 ,2.7409259460474065297 ] 
dist 100=[1.4880021059159633205 ,2.7392362291768503474 ] 
dist 101=[1.4506040225595402261 ,2.7388083112042673408 ] 
dist 102=[1.4139772376414580490 ,2.7305180863868249994 ] 
dist 103=[1.3878808462583073094 ,2.7293590406429615041 ] 
dist 104=[1.3642897787625151836 ,2.7267545149140280657 ] 
dist 105=[1.3376840504410255980 ,2.7260919165266109766 ] 
dist 106=[1.3109121553660389774 ,2.7226327591843729350 ] 
dist 107=[1.2866564367049153156 ,2.7219337061924768885 ] 
dist 108=[1.2593969731377133393 ,2.7192719849542937554 ] 
dist 109=[1.2206103849296672128 ,2.7145472120744276172 ] 
dist 110=[1.1820415680056470561 ,2.6623648504666487074 ] 
dist 111=[1.1556531688039542043 ,2.6582541061611648490 ] 
dist 112=[1.1329217245094248596 ,2.6498446950021704360 ] 
dist 113=[1.1089803784209258173 ,2.6476462676793188543 ] 
dist 114=[1.0858579937325627028 ,2.6284364149773826957 ] 
dist 115=[1.0664023169276569896 ,2.6248604062084548181 ] 
dist 116=[1.0457461788688452187 ,2.6087234568112736568 ] 
dist 117=[1.0178220636624801640 ,1.4569097875519012126 ] 
dist 118=[.98977736908053504727,1.4312800833993449772 ] 
dist 119=[.96863892502002560684,1.3714731824630131330 ] 
dist 120=[.94833926158869802295,1.3628516113823126361 ] 
dist 121=[.92364960952224134933,1.2830191952642849289 ] 
dist 122=[.89777954541156686741,1.2687360549864878618 ] 
dist 123=[.87275834638873633747,1.2514093759771885191 ] 
dist 124=[.84335769352017379106,1.2483031480788622926 ] 
dist 125=[.79997023173022526276,1.1388869707811808769 ] 
dist 126=[.75664496284093622934,1.1255049711953144021 ] 
dist 127=[.72749307564317569028,1.0986078339867970196 ] 
dist 128=[.70290719133451155918,1.0918385451038428798 ] 
dist 129=[.67784549850527500267,1.0683317664241553616 ] 
dist 130=[.65415064814330790476,1.0634889478108803059 ] 
dist 131=[.63503200333698795689,1.0569607673277493947 ] 
dist 132=[.61544723122214583975,1.0552304687183690940 ] 
dist 133=[.58988791608439168585,.89905969364339501072] 
dist 134=[.56463501798308521919,.88596275223157992395] 
dist 135=[.54627588478858239331,.85672322928675521019] 
dist 136=[.52930198388747497729,.85138496930201399625] 
dist 137=[.5095898828390312209 ,.81614533588899546138] 
dist 138=[.48942945987999595062,.80992419572058183257] 
dist 139=[.47066231409658042879,.79879083773205027873] 
dist 140=[.44916518408420633341,.7963296147932823202 ] 
dist 141=[.41808508458983808691,.76165142078617506791] 
dist 142=[.38697009613752421132,.75693806414919201176] 
dist 143=[.36533341362100746841,.7470047899757849542 ] 
dist 144=[.34632206509749437037,.74465580173738813797] 
dist 145=[.32570816221802647306,.73449418302755540338] 
dist 146=[.30543799755678870353,.7326686336845214752 ] 
dist 147=[.28780156912112408735,.72866826782816258286] 
dist 148=[.2685708574249130391 ,.72785956218443303325] 
dist 149=[.2419237117810766339 ,.54118097440311341816] 
dist 150=[.21486589793601373993,.52090324303449015144] 
dist 151=[.19399255260361829069,.51842150634511586061] 
dist 152=[.17348168176796174162,.51338413068618615229] 
dist 153=[.14787373133775319759,.5121072115280386932 ] 
dist 154=[.12069101719160241274,.50760100281081776861] 
dist 155=[.09388124169002839899,.50669715755535689727] 
dist 156=[.06198545151882068078,.50530310822994386692] 
dist 157=[.01445916378816431899,.50495653628012672712] 
dist 158=[-.03300232097772772726,.35132973580792279409] 
dist 159=[-.06463890547065691211,.33881938332692181916] 
dist 160=[-.09099509730296357930,.33575035184560223768] 
dist 161=[-.11733551505978348583,.32359920733168202278] 
dist 162=[-.14190691470815167262,.3213359878134014592 ] 
dist 163=[-.16118720283210307049,.3168529320166749323 ] 
dist 164=[-.18044167290248717624,.31574838521384834181] 
dist 165=[-.20490980279906112724,.25898301601332377024] 
dist 166=[-.22877362774067327411,.25396957867845334287] 
dist 167=[-.24561093562862266296,.24232630167006837687] 
dist 168=[-.26066143488681908703,.24064337381115220939] 
dist 169=[-.2773781957316957523 ,.22531769866912089431] 
dist 170=[-.29405250059053618245,.22259747437455013557] 
dist 171=[-.30893317995395572099,.21923481384763147591] 
dist 172=[-.32547332023547357427,.21862323414540810329] 
dist 173=[-.34878531049060398464,.19850496123736978841] 
dist 174=[-.37187185439607156384,.19606280256638398504] 
dist 175=[-.387510230781565442  ,.19110048864890309386] 
dist 176=[-.40081291471105838175,.18984871686581261976] 
dist 177=[-.4145569115662533394 ,.18546014448964783677] 
dist 178=[-.42766756286265539089,.18458667139585096989] 
dist 179=[-.43843692496422461441,.18330982455083977176] 
dist 180=[-.44964224487589407801,.18297920392726705078] 
dist 181=[-.46449668583190261356,.02376482173414888137] 
dist 182=[-.47928177893317578981,.00900377830508494538] 
dist 183=[-.49020971404016516964,.00718292503340769383] 
dist 184=[-.50049368084352414387,.00331795549412458550] 
dist 185=[-.51270296215070001865,.00246975103996160166] 
dist 186=[-.52533771079007150604,-.00153171220260459261] 
dist 187=[-.53732350634197950791,-.00222119887099754700] 
dist 188=[-.55122946929680810202,-.00374140796792913190] 
dist 189=[-.57154470440608931248,-.00400141263485303351] 
dist 190=[-.59174675212422342278,-.03386709759952653277] 
dist 191=[-.60519997631005332606,-.03604105670945904055] 
dist 192=[-.61639352489644022318,-.04080103345891772857] 
dist 193=[-.62755708574019587181,-.04171952414143778970] 
dist 194=[-.63795588693716847125,-.04713587179298437895] 
dist 195=[-.64609046987768711908,-.04807192487338316954] 
dist 196=[-.65419081417666236949,-.04990277550516056284] 
dist 197=[-.6644526640730753543 ,-.05034314358282599136] 
dist 198=[-.6744456483016602553 ,-.05438871767688720464] 
dist 199=[-.68147055557319929022,-.05500427234716349124] 
dist 200=[-.68772323269973220756,-.05594287341685502784] 
dist 201=[-.69462737000207794454,-.05617342087513100142] 
dist 202=[-.70149031097125193857,-.05632186422806028109] 
dist 203=[-.70757820669432273792,-.05605969630253632839] 
dist 204=[-.71431476320863393466,-.05549391081158187871] 
dist 205=[-.7237722854747850011 ,-.05436077817437880364] 
dist 206=[-.73312241910209628656,-.05309693315419916892] 
dist 207=[-.73942943130356453238,-.05200831986422247136] 
dist 208=[-.74476566800887699158,-.05083129565282778411] 
dist 209=[-.75023279224221370497,-.04921373699275725060] 
dist 210=[-.75541920292580074482,-.04742117028021838377] 
dist 211=[-.75963261220601819603,-.04554413112219101695] 
dist 212=[-.76397479020010720137,-.04323056504271697773] 
dist 213=[-.77035080751834865926,-.03969201238001783036] 
dist 214=[-.77905119307881851374,-.03595298900329246151] 
dist 215=[-.78619785170414957049,-.03283758600403716255] 
dist 216=[-.79317399331933007614,-.02955752746061709237] 
dist 217=[-.79957443693354286276,-.02515989795482307100] 
dist 218=[-.8044183608569276316 ,-.02033701261298720275] 
dist 219=[-.80908920421663696076,-.01535605114237261694] 
dist 220=[-.81479734686940249232,-.00926457977888465341] 
dist 221=[-.82025452187149794759,0                     ] 
dist 222=[-.82392152095602312477,-.19605730333740029279] 
dist 223=[-.8270088292871146016 ,-.19315803643427447745] 
dist 224=[-.8301472989518110793 ,-.18922537488223183236] 
dist 225=[-.83310922177548107462,-.18489007547107284727] 
dist 226=[-.83549036435854603752,-.18038032275370439938] 
dist 227=[-.83792166525016352284,-.17484169575806106395] 
dist 228=[-.84108422846895221126,-.16639110354853203258] 
dist 229=[-.84412900224864848174,-.15774810282764620411] 
dist 230=[-.84608915582056715875,-.15143986940391448455] 
dist 231=[-.84764583494903784274,-.14558342280818127364] 
dist 232=[-.84907673509918356406,-.13874744792207662934] 
dist 233=[-.85033107466067507042,-.13173757570749062029] 
dist 234=[-.85118152110415155071,-.12518555695513394489] 
dist 235=[-.85190580857251017124,-.11766014517419181319] 
dist 236=[-.85265551709457442027,-.10675687378611884116] 
dist 237=[-.85330412878032038348,-.09547623191589620253] 
dist 238=[-.85362403376442725467,-.08644140101502936086] 
dist 239=[-.85379170239784120313,-.07724816573290859628] 
dist 240=[-.85383138876862936137,-.06533392178903713209] 
dist 241=[-.85359606514390529827,-.05246303374124876476] 
dist 242=[-.85351370039789162686,-.03944339314319622791] 
dist 243=[-.85340145197982519883,-.02371308009471511649] 

8 phat 1 dirichlet min maxes function [1, 0, 1, 1, 0, 2, 1, 0, 1] 
dist 0=[3.4005111448320879776 ,3.4005111448320879776 ] 
dist 1=[3.3932754160584370528 ,3.4052589591643324913 ] 
dist 2=[3.3848375310174129841 ,3.4091315940938163091 ] 
dist 3=[3.3752811764099126384 ,3.4128666857277566468 ] 
dist 4=[3.3629939563670068745 ,3.4169658634193425392 ] 
dist 5=[3.3436327834595878259 ,3.4222948337171123222 ] 
dist 6=[3.3231821501043908864 ,3.4295911972792011971 ] 
dist 7=[3.3065371623573312001 ,3.4415598409703575314 ] 
dist 8=[3.2893550291309211095 ,3.4537384771060252478 ] 
dist 9=[3.2667558622129175927 ,3.4618747949018095295 ] 
dist 10=[3.2421741181904024268 ,3.4686736190464121515 ] 
dist 11=[3.2170618194926595281 ,3.4755023410087781294 ] 
dist 12=[3.1865396496819914503 ,3.4818946546284276628 ] 
dist 13=[3.1403188016317751592 ,3.4944829849876061426 ] 
dist 14=[3.0938556337323074562 ,3.5070144276028082590 ] 
dist 15=[3.0623642046993576569 ,3.5174579643384521400 ] 
dist 16=[3.0355557881033585025 ,3.5279016958696837107 ] 
dist 17=[3.0078243500426661000 ,3.5376485424860896706 ] 
dist 18=[2.9813490338516331500 ,3.5453045894346858933 ] 
dist 19=[2.9595650222657367898 ,3.5529581368753569985 ] 
dist 20=[2.9368659515159871732 ,3.5626949927932432056 ] 
dist 21=[2.9067304712069333893 ,3.5721971567859108382 ] 
dist 22=[2.8767140442856114600 ,3.5789119557194482484 ] 
dist 23=[2.8544911833172226886 ,3.5849252743522189776 ] 
dist 24=[2.8335405228281917061 ,3.5916215673811656927 ] 
dist 25=[2.8086128139789181905 ,3.5983111493406263045 ] 
dist 26=[2.7827860491882714380 ,3.6042976313609472939 ] 
dist 27=[2.7582392360971284693 ,3.6109654988001172699 ] 
dist 28=[2.7297234105130440101 ,3.6203805951874484149 ] 
dist 29=[2.6880208930543135531 ,3.6296115489017654624 ] 
dist 30=[2.6460708241822543799 ,3.6355428598744024429 ] 
dist 31=[2.6165648143303031335 ,3.6402404285355041028 ] 
dist 32=[2.5902852696565717868 ,3.6445364829214705118 ] 
dist 33=[2.5612408283401752204 ,3.6482871759581363404 ] 
dist 34=[2.5323533233020946217 ,3.6508033342015893545 ] 
dist 35=[2.5067015166852002405 ,3.6529173256035969666 ] 
dist 36=[2.4782940184433452990 ,3.6550593862811150208 ] 
dist 37=[2.4383839588955885182 ,3.6569706189540698252 ] 
dist 38=[2.3976148633701436021 ,3.6581613101075962000 ] 
dist 39=[2.3657712888966126411 ,3.6590617429369085115 ] 
dist 40=[2.3341066365043144273 ,3.6598119426115459799 ] 
dist 41=[2.2940532203206344946 ,3.6604153138412333869 ] 
dist 42=[2.2512674517211124235 ,3.6607284331997961590 ] 
dist 43=[2.2086735996079686964 ,3.6608913270933399063 ] 
dist 44=[2.1577048178601111221 ,3.6608937970933821923 ] 
dist 45=[2.0814199694396210799 ,3.6467853165155725052 ] 
dist 46=[2.0048038116745914103 ,3.6454752418905542317 ] 
dist 47=[1.9525098189363034200 ,3.6428515863663063934 ] 
dist 48=[1.9075969597353836279 ,3.6421278892542315534 ] 
dist 49=[1.8605047765532876767 ,3.6392905243008685346 ] 
dist 50=[1.8151516773756025719 ,3.6386654189702368541 ] 
dist 51=[1.7771950233538132586 ,3.6372208548351045667 ] 
dist 52=[1.7370738336267974788 ,3.6367443711877618998 ] 
dist 53=[1.6830627587365744441 ,3.6345299254186059040 ] 
dist 54=[1.6289200884221710666 ,3.6339797942704483929 ] 
dist 55=[1.5882725281868093442 ,3.6331715519183189942 ] 
dist 56=[1.5493947733249821940 ,3.6328915301966727823 ] 
dist 57=[1.5023311909563355035 ,3.6322020304335578189 ] 
dist 58=[1.4531340179892833323 ,3.6319273116601460859 ] 
dist 59=[1.4057220651117761135 ,3.6317224164585210740 ] 
dist 60=[1.3501403569406718176 ,3.6315568870374147076 ] 
dist 61=[1.2682647894086631780 ,3.5085195157945502962 ] 
dist 62=[1.1856592914700154209 ,3.5017896154664398583 ] 
dist 63=[1.1271579179748859142 ,3.4861773121144254916 ] 
dist 64=[1.0746367900611045848 ,3.4836149504885143437 ] 
dist 65=[1.0159518167210727284 ,3.4627270100907204627 ] 
dist 66=[.95721205017317985782,3.4588956649885998554 ] 
dist 67=[.90447175383292428259,3.4534768036370655558 ] 
dist 68=[.84558685431218996899,3.4519190536169136267 ] 
dist 69=[.76226914598208556142,3.4229776502646577684 ] 
dist 70=[.67690027580779416796,3.4192060116753940568 ] 
dist 71=[.60981088600641011225,3.4111593531677868376 ] 
dist 72=[.54271339931955738944,3.4091172146580923556 ] 
dist 73=[.4573121418825965305 ,3.4002174775336756388 ] 
dist 74=[.36581611910708002271,3.3985697386967766312 ] 
dist 75=[.27434003760243186764,3.3945592789209379838 ] 
dist 76=[.16459008960851774818,3.3938839170745293691 ] 
dist 77=[0                     ,3.3497232870458004905 ] 
dist 78=[1.9511776463489304856 ,3.3455064790212636753 ] 
dist 79=[1.9195135283744097599 ,3.3356413243064443284 ] 
dist 80=[1.8876319289154224458 ,3.3340140975386201780 ] 
dist 81=[1.8634706659349944261 ,3.3204708324341387162 ] 
dist 82=[1.8401408870794309214 ,3.3179490879308843701 ] 
dist 83=[1.8115851448145888495 ,3.3144649205692911952 ] 
dist 84=[1.7815684179457543100 ,3.3134176051168475832 ] 
dist 85=[1.7523948400200455642 ,3.2932708235594075954 ] 
dist 86=[1.7180075208733275107 ,3.2906147651589199184 ] 
dist 87=[1.6671363263967910653 ,3.2850454216719355606 ] 
dist 88=[1.6162871978254456634 ,3.2835302498068651785 ] 
dist 89=[1.5819881401948893496 ,3.2775642219566433651 ] 
dist 90=[1.5529690109781040317 ,3.2764114342990656036 ] 
dist 91=[1.5232390924727036312 ,3.2735885687660542627 ] 
dist 92=[1.4950363036778297477 ,3.2730653834815256199 ] 
dist 93=[1.4721255476485363123 ,3.1958861929155224990 ] 
dist 94=[1.4485155240778727485 ,3.1902771012682327046 ] 
dist 95=[1.4175157318122746980 ,3.1769670305138295759 ] 
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dist 177=[-.6688890391626707458 ,.16264750727475141919] 
dist 178=[-.68313250223750659783,.16022451524853198427] 
dist 179=[-.700774566642478722  ,.15986188445478066381] 
dist 180=[-.7194287592049187024 ,.15677627543166774462] 
dist 181=[-.73772063837484228124,.15623706076280415906] 
dist 182=[-.75940352464570510198,.15551132406330252175] 
dist 183=[-.79162142218434538055,.15534574544502279995] 
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dist 185=[-.84508204383224450507,-.1221658869345352399 ] 
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dist 187=[-.88026770548913317245,-.1247890147754592852 ] 
dist 188=[-.89650167847621869334,-.1251552409867304631 ] 
dist 189=[-.9090735291454759723 ,-.3395351421612137610 ] 
dist 190=[-.9214730900308239627 ,-.3483590905382017247 ] 
dist 191=[-.9370179271921748401 ,-.3685047506922518915 ] 
dist 192=[-.9520762395273570682 ,-.3716689625109488987 ] 
dist 193=[-.9625297509477143568 ,-.3971321471929407954 ] 
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dist 200=[-1.0340979047456014286 ,-.4518381514683178773 ] 
dist 201=[-1.0423630564828605681 ,-.4610097480518453056 ] 
dist 202=[-1.0492040515206230874 ,-.4625769255711102357 ] 
dist 203=[-1.0559680112285473380 ,-.4654651013890008002 ] 
dist 204=[-1.0622308023384496589 ,-.4661009300643356612 ] 
dist 205=[-1.0670671741744943498 ,-.48548359926566408775] 
dist 206=[-1.0718244528628395986 ,-.48750181947442709346] 
dist 207=[-1.0777708960041897868 ,-.49143367225537387145] 
dist 208=[-1.0835228745000874927 ,-.49236647892052618109] 
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dist 210=[-1.0909775914271404160 ,-.49585140998253813033] 
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dist 212=[-1.0983666678118111134 ,-.49514586544055397829] 
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dist 215=[-1.1096159124792102091 ,-.49076947897980753073] 
dist 216=[-1.1141914714718974341 ,-.48768468504094596421] 
dist 217=[-1.1171347307479294155 ,-.48403742960441550906] 
dist 218=[-1.1194696125070358442 ,-.47989675196511321427] 
dist 219=[-1.1216116682638974543 ,-.47456727513664329248] 
dist 220=[-1.1234866605453123494 ,-.4661650963951122356 ] 
dist 221=[-1.1247532933994867921 ,-.45756098070128110503] 
dist 222=[-1.1258271383286320405 ,-.45142378053586089505] 
dist 223=[-1.1269309870691733111 ,-.4458696910614744317 ] 
dist 224=[-1.1278942274849378412 ,-.43959781808444017948] 
dist 225=[-1.1284056467640873970 ,-.43328320747991639486] 
dist 226=[-1.1286880672389280712 ,-.42755813653991925383] 
dist 227=[-1.1287476392467050296 ,-.42112158725211490584] 
dist 228=[-1.1286957485283001208 ,-.41196117045653174175] 
dist 229=[-1.1286308078324677276 ,-.40255399074433079685] 
dist 230=[-1.1285343176184495674 ,-.39513041468875080731] 
dist 231=[-1.1284519074044930859 ,-.38767815272218818665] 
dist 232=[-1.1234845533142994477 ,-.37815619684990442692] 
dist 233=[-1.1228826066230523960 ,-.36793731225022910126] 
dist 234=[-1.1214993816331978304 ,-.35769744096549855953] 
dist 235=[-1.1210634988565045902 ,-.34539599735537385803] 
dist 236=[-1.1190079761589819260 ,-.32693117268850128188] 
dist 237=[-1.0970832443527391596 ,-.30816472077545048454] 
dist 238=[-1.0958709873365681899 ,-.29465681026601221043] 
dist 239=[-1.0937379336467355392 ,-.28230580076603378875] 
dist 240=[-1.0932340162907023875 ,-.26816672989066035795] 
dist 241=[-1.0918067434594328297 ,-.25382075800724480692] 
dist 242=[-1.0913482878714362505 ,-.24064216503000529948] 
dist 243=[-1.0887225833499715583 ,-.22568607079173250307] 
dist 244=[-1.0831050873828395372 ,-.20423037851914795785] 
dist 245=[-1.0608952639094728229 ,-.18212182469316910612] 
dist 246=[-1.0581077672801364062 ,-.16455438504962940183] 
dist 247=[-1.0473417676682229262 ,-.14680636603777070004] 
dist 248=[-.9701279277645617445 ,-.12397551245487891812] 
dist 249=[-.96393850632887298932,-.09939549510598610856] 
dist 250=[-.94943463742769177842,-.07465110263215454661] 
dist 251=[-.9449660512327801666 ,-.04484120620864268414] 

8 phat 1 dirichlet min maxes function [0, 2, 0, 1, 2, 2, 0, 0, 1] 
dist 0=[3.7116873296618437033 ,3.7116873296618437033 ] 
dist 1=[3.7109220342323231616 ,3.7125101501494631647 ] 
dist 2=[3.7086837423491961908 ,3.7143467876853211028 ] 
dist 3=[3.7051637279559151435 ,3.7180666510028252584 ] 
dist 4=[3.6989363456197883568 ,3.7222282727878170140 ] 
dist 5=[3.6924349122420891619 ,3.7258319082119365469 ] 
dist 6=[3.6878187102607367585 ,3.7297468220850916680 ] 
dist 7=[3.6836621605546057603 ,3.7351535498383918903 ] 
dist 8=[3.6789992780974095556 ,3.7406358492711354498 ] 
dist 9=[3.6743213844976205798 ,3.7448530535762029146 ] 
dist 10=[3.6701047773159383255 ,3.7489857130405920760 ] 
dist 11=[3.6623342899028952072 ,3.7541298520775348620 ] 
dist 12=[3.6496651508025864175 ,3.7595825577238653810 ] 
dist 13=[3.6299938548092119988 ,3.7649494760210700935 ] 
dist 14=[3.6098637520640197298 ,3.7713266009635383392 ] 
dist 15=[3.5953594191068725694 ,3.7808200914102991245 ] 
dist 16=[3.5820806815478112780 ,3.7902337695013270668 ] 
dist 17=[3.5668528832372635689 ,3.7962916538555204354 ] 
dist 18=[3.5513853824860282333 ,3.8010999386696565002 ] 
dist 19=[3.5371478548276318475 ,3.8055152868806601045 ] 
dist 20=[3.5209657227643801177 ,3.8093828522551592969 ] 
dist 21=[3.4977199405327504706 ,3.8120000398100423326 ] 
dist 22=[3.4737498141257255443 ,3.8142236488265625658 ] 
dist 23=[3.4546703569797157853 ,3.8165169340140499765 ] 
dist 24=[3.4353627298020689772 ,3.8185669349543025482 ] 
dist 25=[3.4104799419638285031 ,3.8198174192638377469 ] 
dist 26=[3.3836651143780113287 ,3.8207316907789448635 ] 
dist 27=[3.3566294632925740058 ,3.8214368434166188435 ] 
dist 28=[3.3240265383971529200 ,3.8219602331722122421 ] 
dist 29=[3.2749430020662572565 ,3.8221474558966481988 ] 
dist 30=[3.2256633317999112519 ,3.8221642979667981966 ] 
dist 31=[3.1922758867385399985 ,3.8220973571167203181 ] 
dist 32=[3.1638673915586617306 ,3.8097722907065529473 ] 
dist 33=[3.1345031810440061457 ,3.8085541860855196934 ] 
dist 34=[3.1064829978249853711 ,3.8060726289826844171 ] 
dist 35=[3.0834505234377941632 ,3.8053714135185849248 ] 
dist 36=[3.0594707391140416869 ,3.8025218864188146186 ] 
dist 37=[3.0276613907899411306 ,3.8019126456881599141 ] 
dist 38=[2.9959899307347912604 ,3.8003514646424821108 ] 
dist 39=[2.9725616944212061766 ,3.7999703774215338402 ] 
dist 40=[2.9504944075231087471 ,3.7970971399757140275 ] 
dist 41=[2.9242666552930935869 ,3.7964846256379417982 ] 
dist 42=[2.8971084139409444306 ,3.7952908975338293812 ] 
dist 43=[2.8713192437535339127 ,3.7949311097088313054 ] 
dist 44=[2.8413780227738128768 ,3.7933921183196223606 ] 
dist 45=[2.7976118876542300904 ,3.7930200592141406603 ] 
dist 46=[2.7535945744731723391 ,3.7920067969587187859 ] 
dist 47=[2.7226486628320997318 ,3.7917098290792724833 ] 
dist 48=[2.6951013757196635817 ,3.6802811546204133766 ] 
dist 49=[2.6646783159950352308 ,3.6738085885645855622 ] 
dist 50=[2.6344327507621068354 ,3.6594817547624988044 ] 
dist 51=[2.6075954331211329195 ,3.6529308583210084497 ] 
dist 52=[2.5778919319505027019 ,3.6294245192619535613 ] 
dist 53=[2.5361818517738938507 ,3.5938037321419153135 ] 
dist 54=[2.4935830456700156740 ,3.5878445356756295590 ] 
dist 55=[2.4603247103609080022 ,3.5861211582830312078 ] 
dist 56=[2.4272667286464484525 ,3.5541338281312673562 ] 
dist 57=[2.3854693264270209329 ,3.5499764156828303490 ] 
dist 58=[2.3408299910131042422 ,3.5411299870786917462 ] 
dist 59=[2.2964044935728564899 ,3.5388803439710913536 ] 
dist 60=[2.2432539281961834276 ,3.5291917834503305038 ] 
dist 61=[2.1637149825914541540 ,3.5274063262986206795 ] 
dist 62=[2.0838350484452942764 ,3.5230121314932955704 ] 
dist 63=[2.0293205558700154925 ,3.5223283943706699684 ] 
dist 64=[1.9825083004400410562 ,3.4740370022964720818 ] 
dist 65=[1.9334367342094970929 ,3.4694492203741108888 ] 
dist 66=[1.8861848096546913451 ,3.4587313665000826876 ] 
dist 67=[1.8466509847165424939 ,3.4569646467857840652 ] 
dist 68=[1.8048731666165873954 ,3.4423129092438024691 ] 
dist 69=[1.7486454415063743972 ,3.4395912810395409020 ] 
dist 70=[1.6922868457192902814 ,3.4358159272544638458 ] 
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dist 72=[1.6095357024400210764 ,3.4131355081622484814 ] 
dist 73=[1.5605827127517739516 ,3.4102988140224921846 ] 
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dist 75=[1.4601201488213165616 ,3.4027106266932423913 ] 
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dist 90=[.37979390064207573606,3.2165502976838529528 ] 
dist 91=[.28481932928290744644,3.2146123896041451111 ] 
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dist 93=[0                     ,3.2063998555143974392 ] 
dist 94=[1.5081280915537855107 ,3.2043962275686493579 ] 
dist 95=[1.4865871856958563627 ,3.2037539189408187143 ] 
dist 96=[1.4613240488649115117 ,3.1436134518391904439 ] 
dist 97=[1.4353491163376226922 ,3.1384305020388439508 ] 
dist 98=[1.4109610955839846819 ,3.1270601602966604596 ] 
dist 99=[1.3828614275803508851 ,3.1245918830356123684 ] 
dist 100=[1.3420402600626594219 ,3.1112026909406115696 ] 
dist 101=[1.3010915762500332530 ,3.1087609784527667040 ] 
dist 102=[1.2724818552289128741 ,3.1037254846883076937 ] 
dist 103=[1.2472012933830853490 ,3.1023732013171650082 ] 
dist 104=[1.2195689287430068653 ,3.0896275683351365616 ] 
dist 105=[1.1922661149359749694 ,3.0876472301353468473 ] 
dist 106=[1.1683037249904265325 ,3.0835914305526830225 ] 
dist 107=[1.1420006712121865960 ,3.0824989046967132958 ] 
dist 108=[1.1053354253222799205 ,3.0782951068037036091 ] 
dist 109=[1.0680082773482369135 ,3.0766810990653707325 ] 
dist 110=[1.0390576783643645202 ,3.0724806552536289074 ] 
dist 111=[1.0104623526093176730 ,3.0701548810617152149 ] 
dist 112=[.97455626366531830405,1.5883429401769634241 ] 
dist 113=[.93633649572805175654,1.5519979981357780006 ] 
dist 114=[.89848667467406675155,1.4672158631708665068 ] 
dist 115=[.85334164676105997998,1.4550211404682683742 ] 
dist 116=[.78594174719012127515,1.4501396364258193149 ] 
dist 117=[.71858072107817193698,1.3218054460333363542 ] 
dist 118=[.67359118329344892835,1.2973371221626780127 ] 
dist 119=[.63601345420670089414,1.2930284996613848501 ] 
dist 120=[.59829895596298355205,1.1387341849161921895 ] 
dist 121=[.56301466440826745479,1.1199018712728419681 ] 
dist 122=[.53515753028921248443,1.0820580999534504373 ] 
dist 123=[.50717804861973420416,1.0725486696232928748 ] 
dist 124=[.47140437853259246948,1.0396076999155833780 ] 
dist 125=[.43640876772135352844,1.0328244672539805353 ] 
dist 126=[.41154144894573013058,1.0238807528032359331 ] 
dist 127=[.38913028450653493873,1.0217081557163831435 ] 
dist 128=[.36395905677786156732,.80402596502240665541] 
dist 129=[.33868994515632065521,.78585426749299732581] 
dist 130=[.31588725448162758494,.77038492223768678221] 
dist 131=[.2903348044708746574 ,.76669735453748461997] 
dist 132=[.25406691777170627469,.76606769664694074591] 
dist 133=[.21804085733737876512,.6805117347886796524 ] 
dist 134=[.19345568932107803835,.6651805978104520046 ] 
dist 135=[.17234564411300321104,.66181893150668135337] 
dist 136=[.15021974346123268351,.63297051549177909791] 
dist 137=[.1289166289400644731 ,.61063397276710769808] 
dist 138=[.11109764977868360135,.60670306219700651344] 
dist 139=[.09227151382979207008,.59947495636928380066] 
dist 140=[.06693986821920547678,.59782619963502240077] 
dist 141=[.04155276071791333036,.57705280736018272189] 
dist 142=[.02250478249604513049,.57415014884478023412] 
dist 143=[.00429760183829411084,.56900560821188809225] 
dist 144=[-.01772639560013956613,.56686879850257282921] 
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dist 175=[-.646361708648518589  ,.21731267406261187396] 
dist 176=[-.66973496037476838865,.21686286423589256841] 
dist 177=[-.69976932678402699821,.21455881490433723269] 
dist 178=[-.72468871227274913158,.21416980038039339071] 
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dist 189=[-.94578039934221415771,-.49187160561137139194] 
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dist 204=[-1.0888304560669901700 ,-.51070621190637783   ] 
dist 205=[-1.0956331096554042232 ,-.50619244687374493091] 
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dist 207=[-1.1045812564053050464 ,-.49130497400197593616] 
dist 208=[-1.1091664881357600907 ,-.48199502238383778947] 
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dist 217=[-1.1464373303780717343 ,-.41530255747356764962] 
dist 218=[-1.1482229765349275153 ,-.4074093380206534684 ] 
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dist 222=[-1.1539690032344940606 ,-.36276173248974816355] 
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dist 237=[-1.0929413313623379963 ,-.07826801240713771155] 
dist 238=[-1.0900649220087491029 ,-.04701196252545419580] 

8 phat 1 dirichlet min maxes function [1, 2, 0, 1, 0, 1, 0, 2] 
dist 0=[3.9538026979212241210 ,3.9538026979212241210 ] 
dist 1=[3.9534547612424311197 ,3.9540422020581160436 ] 
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dist 5=[3.9439169525374946712 ,3.9558633759292092650 ] 
dist 6=[3.9408132681327579348 ,3.9558479518161757135 ] 
dist 7=[3.9373480284801597787 ,3.9533825404230620392 ] 
dist 8=[3.9324448833078125006 ,3.9529665934435556006 ] 
dist 9=[3.9269422413978991554 ,3.9519183551049712587 ] 
dist 10=[3.9210790527263867918 ,3.9515471591629692563 ] 
dist 11=[3.9137791187437225212 ,3.9495437720264421938 ] 
dist 12=[3.9025295786697884257 ,3.9490578939788575641 ] 
dist 13=[3.8911002021625598483 ,3.9481141347573668380 ] 
dist 14=[3.8830809358282425615 ,3.9478132843418158794 ] 
dist 15=[3.8759589724116502167 ,3.9407646872614321731 ] 
dist 16=[3.8681187646334689717 ,3.9401700669016295550 ] 
dist 17=[3.8603388787960518182 ,3.9386353120761748293 ] 
dist 18=[3.8534582053265417446 ,3.9382566941066725478 ] 
dist 19=[3.8458612056812924249 ,3.9354096257634786159 ] 
dist 20=[3.8352160646326679557 ,3.9347700824251126201 ] 
dist 21=[3.8243538011617275632 ,3.9337901552089926458 ] 
dist 22=[3.8158883289310065669 ,3.9334727345303289050 ] 
dist 23=[3.8074879011265092638 ,3.9261246689017332151 ] 
dist 24=[3.7968858171724508298 ,3.9249888430916097931 ] 
dist 25=[3.7855724715596463588 ,3.9231965127863074613 ] 
dist 26=[3.7743270462093226487 ,3.9226906685030883130 ] 
dist 27=[3.7608830368981819117 ,3.9126607466666372316 ] 
dist 28=[3.7407755008768761105 ,3.9115487041734863206 ] 
dist 29=[3.7203634933081535233 ,3.9039933364009339703 ] 
dist 30=[3.7057016194654338700 ,3.8919554764268354472 ] 
dist 31=[3.6923250232298681699 ,3.7832741708794860358 ] 
dist 32=[3.6770540456199902070 ,3.7822392101611838891 ] 
dist 33=[3.6615814564231997223 ,3.7718851419141586938 ] 
dist 34=[3.6473984296787496691 ,3.7699015785078926288 ] 
dist 35=[3.6313253697588233955 ,3.7676687721468229275 ] 
dist 36=[3.6082927758391297306 ,3.7671440372574904682 ] 
dist 37=[3.5845665955240584282 ,3.7483604101701992334 ] 
dist 38=[3.5657192376614949107 ,3.7476745449538950423 ] 
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dist 43=[3.4372853629349689162 ,3.7334302261911840170 ] 
dist 44=[3.3891486652873444466 ,3.7329733210446303984 ] 
dist 45=[3.3408132936485430543 ,3.6776590213734370259 ] 
dist 46=[3.3080263200722748985 ,3.6740370548109764141 ] 
dist 47=[3.2800861502197040203 ,3.6634222833450772332 ] 
dist 48=[3.2511376743983705382 ,3.6608441212326654115 ] 
dist 49=[3.2234715240735324959 ,3.6508438122101868185 ] 
dist 50=[3.2006605760861983010 ,3.6489333739148702450 ] 
dist 51=[3.1768494002673588462 ,3.6444902697913548441 ] 
dist 52=[3.1451824173637405667 ,3.6435827969614242701 ] 
dist 53=[3.1136149516212884215 ,3.6374417780993720564 ] 
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dist 55=[3.0680875101371278433 ,3.5816209379265312080 ] 
dist 56=[3.0417150617110132816 ,3.5769165806906578415 ] 
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dist 62=[2.8375918101660706347 ,3.5046012004376554354 ] 
dist 63=[2.7812191579055717064 ,3.4735315735297286849 ] 
dist 64=[2.7261246816912135460 ,3.4696108431841374065 ] 
dist 65=[2.6800182996495634960 ,3.4619421416136925210 ] 
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dist 106=[.2992822074008132667 ,2.7107524049612227538 ] 
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dist 111=[.79834694063074508507,1.3770886648116216957 ] 
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dist 154=[-.5539860121992478103 ,.42480758231371728373] 
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dist 207=[-1.0367510370175460789 ,-.15055746192748344314] 
dist 208=[-1.0368318682497675103 ,-.13616569805733536554] 
dist 209=[-1.0368171703458594779 ,-.12157640056641332082] 
dist 210=[-1.0367516415139247646 ,-.10274244178597271635] 
dist 211=[-1.0361896172597335962 ,-.08243281540077855445] 
dist 212=[-1.0360079618474681552 ,-.06194111790631837366] 
dist 213=[-1.0356961148741975589 ,-.03722130326623885119] 

8 phat 1 dirichlet min maxes function [1, 1, 0, 1, 1, 1, 2, 0, 1] 
dist 0=[1.5382553395354917878 ,1.5382553395354917878 ] 
dist 1=[1.5157842741399570655 ,1.5493148691374490781 ] 
dist 2=[1.4820575113851046116 ,1.5710810626638450748 ] 
dist 3=[1.4311287937263420660 ,1.5964248625742382673 ] 
dist 4=[1.3798753825167893297 ,1.6158877367614556364 ] 
dist 5=[1.3448498713156936304 ,1.6349290896658785535 ] 
dist 6=[1.3147222378955060305 ,1.6585868373731231183 ] 
dist 7=[1.2830599587035393173 ,1.6813999039995974603 ] 
dist 8=[1.2525222982225705004 ,1.6970625983593413160 ] 
dist 9=[1.2268930537375315784 ,1.7128470708819050508 ] 
dist 10=[1.1997393580679446527 ,1.7294742111550328058 ] 
dist 11=[1.1631040142662054738 ,1.7480671147148915886 ] 
dist 12=[1.1263424887199095418 ,1.7666857129104559466 ] 
dist 13=[1.0986840772762295516 ,1.7834156340986800674 ] 
dist 14=[1.0721716278030522623 ,1.8021053166576187330 ] 
dist 15=[1.0399938623285235045 ,1.8285628188790196382 ] 
dist 16=[1.0063132129813327659 ,1.8548154393093575674 ] 
dist 17=[.97378934751263567577,1.8726856128886132191 ] 
dist 18=[.93561146592037773505,1.8879814706451143760 ] 
dist 19=[.87931519832100849881,1.9039370237866854243 ] 
dist 20=[.82249361942852688326,1.9192526914827216344 ] 
dist 21=[.78221453464919825934,1.9319890595961340290 ] 
dist 22=[.74601374203721600941,1.9453803478862316278 ] 
dist 23=[.70550501150933429841,1.9633156566803211352 ] 
dist 24=[.66492428049610655892,1.9812527897930324107 ] 
dist 25=[.62843549230947145707,1.9946513798076644904 ] 
dist 26=[.58765244233251532418,2.0074005448511565668 ] 
dist 27=[.52989500356001848741,2.0227400310353519131 ] 
dist 28=[.47069305790272370744,2.0387249868554188667 ] 
dist 29=[.42413209466741336329,2.0540559916395621280 ] 
dist 30=[.37753244396199239001,2.0719726362913317102 ] 
dist 31=[.3181757518136255175 ,2.0982999822325924582 ] 
dist 32=[.25456039621039030257,2.1245069600922774917 ] 
dist 33=[.19092642790566511178,2.1419421421076884543 ] 
dist 34=[.1145568377772311477 ,2.1564306284595943221 ] 
dist 35=[0                     ,2.1708510220800391574 ] 
dist 36=[1.4688772501550511488 ,2.1842650840423073829 ] 
dist 37=[1.4854217918631472114 ,2.1947283116123566999 ] 
dist 38=[1.5236147210859345984 ,2.2051195791199665841 ] 
dist 39=[1.5293068642270247977 ,2.2182458059419263843 ] 
dist 40=[1.5788855218609679372 ,2.2310103147672575209 ] 
dist 41=[1.5876598746530931741 ,2.2399547347990987981 ] 
dist 42=[1.5991059978294293778 ,2.2478860834551726498 ] 
dist 43=[1.6016519108078723610 ,2.2565983751899675894 ] 
dist 44=[1.6637743984644585323 ,2.2652324573001730898 ] 
dist 45=[1.6713843379670501598 ,2.2728509730880054663 ] 
dist 46=[1.6872709281874269692 ,2.2812479595279338672 ] 
dist 47=[1.6910124418256346863 ,2.2929958727219164085 ] 
dist 48=[1.7064798333938696244 ,2.3045936026738442592 ] 
dist 49=[1.7092951498918499584 ,2.3123898664868976296 ] 
dist 50=[1.7148160669615734715 ,2.3189571616275375330 ] 
dist 51=[1.7161352231665919578 ,2.3256390994340896870 ] 
dist 52=[1.8250936481852071225 ,2.3319489556465003437 ] 
dist 53=[1.8333210460956475652 ,2.3370279497826907598 ] 
dist 54=[1.8512088004146486789 ,2.3422197946673230492 ] 
dist 55=[1.8547440280639891441 ,2.3489810474349246671 ] 
dist 56=[1.8746557754533447636 ,2.3556547604652561096 ] 
dist 57=[1.8780684861558741988 ,2.3604964528051506972 ] 
dist 58=[1.8855582122776191122 ,2.3649627072059528723 ] 
dist 59=[1.8938349569083954757 ,2.3701346941287451846 ] 
dist 60=[1.9399270408446581109 ,2.3754163035257935972 ] 
dist 61=[1.9455210341058744640 ,2.3803210416506588919 ] 
dist 62=[1.9639017282807389665 ,2.3859300542730443446 ] 
dist 63=[2.0650968372953078881 ,2.3940287174947882678 ] 
dist 64=[2.0726019671778405750 ,2.4020437780989614744 ] 
dist 65=[2.0895826004185945763 ,2.4073183861903257350 ] 
dist 66=[2.0923052555047917341 ,2.4116379416272579764 ] 
dist 67=[2.1132109227160866657 ,2.4158328535943328793 ] 
dist 68=[2.1168422270196817890 ,2.4196674837007393486 ] 
dist 69=[2.1223572468031374655 ,2.4225459356730434713 ] 
dist 70=[2.1237168363803400278 ,2.4252987146060134488 ] 
dist 71=[2.1266850062326111270 ,2.4286306624986458949 ] 
dist 72=[2.1131670826034900646 ,2.4318000842898532562 ] 
dist 73=[2.1025840624350067996 ,2.4339027701670906954 ] 
dist 74=[2.0920377207838503418 ,2.4356436075282626377 ] 
dist 75=[2.0786664973148395179 ,2.4373656593567319764 ] 
dist 76=[2.0643677678781434513 ,2.4389606984618885929 ] 
dist 77=[2.0501114887534854950 ,2.4401934949775852420 ] 
dist 78=[2.0330364451864612662 ,2.4414071520773881642 ] 
dist 79=[2.0074629310403108306 ,2.4429256395562776201 ] 
dist 80=[1.9814898890858687376 ,2.4443472045648450077 ] 
dist 81=[1.9628167703073773974 ,2.4451731789431599862 ] 
dist 82=[1.9457640126514990896 ,2.4457275611247810674 ] 
dist 83=[1.9262722501757179996 ,2.4460627727855508414 ] 
dist 84=[1.9065103106839626489 ,2.4462706217812753642 ] 
dist 85=[1.8883768665476595955 ,2.4463155591683385102 ] 
dist 86=[1.8678126381562437454 ,2.4462718536390856186 ] 
dist 87=[1.8383277913965530634 ,2.4462119431746096155 ] 
dist 88=[1.8079493878843700709 ,2.4443508345591503457 ] 
dist 89=[1.7838110156141693783 ,2.4440187528437707590 ] 
dist 90=[1.7594231729896577714 ,2.4433646166305333916 ] 
dist 91=[1.7280469076619253248 ,2.4431575176576466542 ] 
dist 92=[1.6942622271362443546 ,2.4422244556879040336 ] 
dist 93=[1.6602409513333225757 ,2.4420009360189655531 ] 
dist 94=[1.6192450383361366036 ,2.4413297297863940956 ] 
dist 95=[1.5575624721636127528 ,2.4411779110849070914 ] 
dist 96=[1.4958101603907453516 ,2.4276684829289173358 ] 
dist 97=[1.4545352709453826754 ,2.4263670190202291137 ] 
dist 98=[1.4200258116586932828 ,2.4233408298997165729 ] 
dist 99=[1.3853345752471589510 ,2.4227167318406187185 ] 
dist 100=[1.3528426660460481313 ,2.4184698641028552458 ] 
dist 101=[1.3271303058335693208 ,2.4176342276280303913 ] 
dist 102=[1.3012494482762776382 ,2.4161985686877698540 ] 
dist 103=[1.2680835657668591280 ,2.4158385076383976344 ] 
dist 104=[1.2356027469341683273 ,2.4088436131501393570 ] 
dist 105=[1.2124620787437676801 ,2.4078608229825403732 ] 
dist 106=[1.1915447722344960224 ,2.4056441552956301363 ] 
dist 107=[1.1679571880664773891 ,2.4050808222166122538 ] 
dist 108=[1.1442238344046774216 ,2.4021034773571237091 ] 
dist 109=[1.1227234638234867042 ,2.4014991778995524252 ] 
dist 110=[1.0985624925945283185 ,2.4002614079116040355 ] 
dist 111=[1.0641869901044901238 ,2.3998995990539634756 ] 
dist 112=[1.0300054886995577567 ,2.3494840403085866164 ] 
dist 113=[1.0066205033075825291 ,2.3458977987591964631 ] 
dist 114=[.9864780293032565143 ,2.3385676421890591509 ] 
dist 115=[.96526626418459203697,2.3366522663440188221 ] 
dist 116=[.944781809281965543  ,2.3295737864404777570 ] 
dist 117=[.92754850677238021926,2.3281500197394577434 ] 
dist 118=[.90925427668281973535,2.3253547906040070314 ] 
dist 119=[.88452621264946878947,2.3246258352175584861 ] 
dist 120=[.8596927766321644601 ,2.2783812104567918553 ] 
dist 121=[.84097706865696205716,2.2737961463237407843 ] 
dist 122=[.8230062225597741722 ,2.2679942369738941154 ] 
dist 123=[.80115216301107383474,2.2661317620418763030 ] 
dist 124=[.77825492852000968149,2.2321669208024551984 ] 
dist 125=[.7561114821493312259 ,2.2263937201626078050 ] 
dist 126=[.73009414654388053788,2.1972944776116436264 ] 
dist 127=[.69170172459762787493,1.2885132795025224680 ] 
dist 128=[.65336522126082874265,1.2659193237055921393 ] 
dist 129=[.62757155475978570278,1.2131962135503065175 ] 
dist 130=[.60581950665535180363,1.2055952267131454225 ] 
dist 131=[.58364909142341279114,1.1352172158518103921 ] 
dist 132=[.5626894736422965272 ,1.1226252940544388917 ] 
dist 133=[.54578049985768529527,1.1073490312747881202 ] 
dist 134=[.52846172262260611586,1.1046087263082040959 ] 
dist 135=[.5058629301258613974 ,1.0081455065794527895 ] 
dist 136=[.48353659915978069531,.99634707141100046906] 
dist 137=[.46730764206051516984,.97263219675670361326] 
dist 138=[.45230574307197615661,.96666347070563235009] 
dist 139=[.43488752751442356549,.94593468717457654741] 
dist 140=[.41707524950133483085,.94166437871481574429] 
dist 141=[.40049713827554958684,.93590301720493531866] 
dist 142=[.38150996949333634116,.93437165334301223782] 
dist 143=[.35406169102568504242,.7966687771822991984 ] 
dist 144=[.32658384383192062331,.78511893233990290051] 
dist 145=[.30747840296546156576,.75933281724046846692] 
dist 146=[.29069332757785550832,.75462486392685406542] 
dist 147=[.27249672098762875118,.72354473041641791558] 
dist 148=[.25460554117169618523,.71805756892665295975] 
dist 149=[.23904214375026468286,.70823813853532922734] 
dist 150=[.22207451552063016213,.70606732444218831892] 
dist 151=[.19856654640464525439,.67547036949511037583] 
dist 152=[.17469776189706640394,.67131195093380646487] 
dist 153=[.15628690651491519282,.6625452454758974339 ] 
dist 154=[.13819800783219824688,.66047425607644391975] 
dist 155=[.11561701941476265047,.65149411990726102054] 
dist 156=[.09164901829626139312,.64988234238131331304] 
dist 157=[.06801220109981249854,.64634167925142472909] 
dist 158=[.03989305054076822154,.64563325561852727264] 
dist 159=[-.00200385651201551779,.45094884883596690775] 
dist 160=[-.04384282930273618592,.43990986130132017209] 
dist 161=[-.07173024833918361531,.41436979958219380494] 
dist 162=[-.09496155885459661063,.4105387842242736017 ] 
dist 163=[-.11817654165160982241,.37712455706428552922] 
dist 164=[-.13983084708694382074,.37117584602349287128] 
dist 165=[-.15681959700996282499,.36342308339079550178] 
dist 166=[-.17378316762639550867,.36163042835130157517] 
dist 167=[-.19533675823693673277,.31868623430453222521] 
dist 168=[-.21635642096825718885,.31337892783386968497] 
dist 169=[-.23118433099279288145,.30233448059978400004] 
dist 170=[-.24443589130632586782,.29962417256883600045] 
dist 171=[-.25915030554275607279,.28889684512935834442] 
dist 172=[-.27382488648214609109,.28689845714465464542] 
dist 173=[-.28691711740673949184,.28293949276224262846] 
dist 174=[-.30146621714695848246,.28196378368547649411] 
dist 175=[-.32196813439558199428,.23180959221747578089] 
dist 176=[-.34227012339966678874,.2273796531075600494 ] 
dist 177=[-.35601952923049181721,.21709219374933061817] 
dist 178=[-.367712376854060896  ,.21560397040370968687] 
dist 179=[-.37978832917957994764,.20206401325677140042] 
dist 180=[-.39130480673298521034,.19966050164938559048] 
dist 181=[-.40075980862969737637,.19668590958834711898] 
dist 182=[-.41059321122022582018,.19614142419649861331] 
dist 183=[-.42362325545778573553,.1783725500968004125 ] 
dist 184=[-.43658982502680836486,.17621464682498101448] 
dist 185=[-.44616933499727612385,.17182773911547687228] 
dist 186=[-.45518005053818061694,.17072040955342405255] 
dist 187=[-.46587149663943893829,.16683351163017477771] 
dist 188=[-.47693214484208841518,.16606074621267594191] 
dist 189=[-.4874196335747906419 ,.16491956707070107868] 
dist 190=[-.49958334697575377817,.1646274147822867338 ] 
dist 191=[-.51734873397645024916,-.01375391164811942308] 
dist 192=[-.53501324849188453189,-.02638752541740833427] 
dist 193=[-.54677348157281723616,-.03999678067880080120] 
dist 194=[-.55655492063387643561,-.04394484547841375487] 
dist 195=[-.56630444780328022421,-.04473028154175492428] 
dist 196=[-.57538239591343617148,-.04913409444754556451] 
dist 197=[-.58247758279138763855,-.04989193419692891502] 
dist 198=[-.58953714677477791804,-.05143553414318376862] 
dist 199=[-.5984726067043304083 ,-.05182207166539904549] 
dist 200=[-.60717012576289321196,-.05475159263592458469] 
dist 201=[-.61327794895665485006,-.05522797012575490974] 
dist 202=[-.61870768590149459857,-.05579591145521761131] 
dist 203=[-.62469292463889636963,-.05586471060015290182] 
dist 204=[-.630636487115895391  ,-.05573344908622655910] 
dist 205=[-.6358995229941235051 ,-.05530633483644574547] 
dist 206=[-.64171563621468295716,-.05457740115175677803] 
dist 207=[-.64987145530958329708,-.05323898371195977005] 
dist 208=[-.65793058045345609068,-.05178212434296143064] 
dist 209=[-.66335992709238333898,-.05057944235599859354] 
dist 210=[-.66794616064740689889,-.04932335108691250235] 
dist 211=[-.67263291387012489262,-.04765279100883030133] 
dist 212=[-.67707149203572473579,-.04582745110275338150] 
dist 213=[-.68066504903272224809,-.04395225578481532243] 
dist 214=[-.68435731229224413077,-.04166620657918076582] 
dist 215=[-.68919070609353317856,-.03819756048493890473] 
dist 216=[-.69397311104090022259,-.03454340999391082754] 
dist 217=[-.69746142374795022309,-.03151538438754898541] 
dist 218=[-.7006980879463266641 ,-.02834190540601036531] 
dist 219=[-.70447392286073697103,-.02410595558789471414] 
dist 220=[-.70834508783698787273,-.01946930192978353896] 
dist 221=[-.71196306319033376631,-.01469311576933935982] 
dist 222=[-.71611863177677758574,-.00886081235714209471] 
dist 223=[-.7221401184108399006 ,0                     ] 
dist 224=[-.72810089052820342579,-.18550495643550271821] 
dist 225=[-.73201360753768276453,-.18485773289030774031] 
dist 226=[-.73520662021248214899,-.18384690255610673577] 
dist 227=[-.73828864573200300196,-.18266987562422597684] 
dist 228=[-.74109335986618300837,-.18135786018474755897] 
dist 229=[-.74317715554552961162,-.17968498985444957306] 
dist 230=[-.74514886413030383378,-.17706460175863699826] 
dist 231=[-.74750524476913515063,-.17427064779389359187] 
dist 232=[-.74973128144545996182,-.17190353137307340577] 
dist 233=[-.75118162870665073415,-.16937665916060391277] 
dist 234=[-.75235310380566161908,-.16594367577711030977] 
dist 235=[-.75346368052242583389,-.16215662596407341662] 
dist 236=[-.75446089985470867077,-.15821354565055313707] 
dist 237=[-.7551789604130749995 ,-.15336830991948436677] 
dist 238=[-.75583589596503132778,-.14597281750887522287] 
dist 239=[-.7565886315666055716 ,-.1384078137956962571 ] 
dist 240=[-.75726949366527277336,-.13288455713977557443] 
dist 241=[-.7576389413617535724 ,-.12775504341828152174] 
dist 242=[-.75785392433611933901,-.12176490521372338745] 
dist 243=[-.75791692971701746788,-.11562090659020784446] 
dist 244=[-.75791809399604170516,-.10987596636831964711] 
dist 245=[-.75788571496269116796,-.10327577783084827617] 
dist 246=[-.75782228934460181853,-.09371093769308349757] 
dist 247=[-.75777330806232860118,-.08381416321966474357] 
dist 248=[-.75446969137154707482,-.07588629249219327397] 
dist 249=[-.75403519214059731691,-.06781814283048747671] 
dist 250=[-.75342570618026376805,-.05736026630022299752] 
dist 251=[-.75322604417469783837,-.04606182581931722790] 
dist 252=[-.74904103576873044923,-.03463157048911099710] 
dist 253=[-.74827046327606261088,-.02082065289521149365] 

8 phat 1 dirichlet min maxes function [1, 0, 1, 1, 0, 0, 2, 1, 2] 
dist 0=[3.4304732306524103703 ,3.4304732306524103703 ] 
dist 1=[3.4279445160449787756 ,3.4324244216521971210 ] 
dist 2=[3.4240730837770659086 ,3.4377003798582090310 ] 
dist 3=[3.4143619860047481583 ,3.4452141790114120916 ] 
dist 4=[3.4025014889357451735 ,3.4575219508922593357 ] 
dist 5=[3.3910271888184248922 ,3.4700393128789805724 ] 
dist 6=[3.3775419336042243955 ,3.4783914569911200804 ] 
dist 7=[3.3576377612405094613 ,3.4853591305194873911 ] 
dist 8=[3.3368853944653607352 ,3.4923386744630548173 ] 
dist 9=[3.3200074259664182839 ,3.4988601245235256965 ] 
dist 10=[3.3025961511293567469 ,3.5039954391123930935 ] 
dist 11=[3.2797106069635829698 ,3.5091410255993695455 ] 
dist 12=[3.2548247172830807195 ,3.5157035487349761945 ] 
dist 13=[3.2294122046023241163 ,3.5221157209945524750 ] 
dist 14=[3.1985326827791769767 ,3.5266599047566177934 ] 
dist 15=[3.1517791411508272660 ,3.5307427678888495250 ] 
dist 16=[3.1047838554876549276 ,3.5353096744855972399 ] 
dist 17=[3.0729373776178931063 ,3.5432307260642703094 ] 
dist 18=[3.0458327772476017569 ,3.5530311110189666282 ] 
dist 19=[3.0178046772294676614 ,3.5607201657422307759 ] 
dist 20=[2.9910521928835518760 ,3.5683982660169927133 ] 
dist 21=[2.9690499712191644992 ,3.5781548413828025903 ] 
dist 22=[2.9461322991640438997 ,3.5876706877714837853 ] 
dist 23=[2.9157180856937737477 ,3.5943858918778048334 ] 
dist 24=[2.8854293446959390263 ,3.6003899621998208853 ] 
dist 25=[2.8630135582188123927 ,3.6070613244574296183 ] 
dist 26=[2.8418896179911780248 ,3.6137175368878315170 ] 
dist 27=[2.8167681766184482433 ,3.6196610164362723480 ] 
dist 28=[2.7907474292028584985 ,3.6262702229626406909 ] 
dist 29=[2.7660263358562983356 ,3.6355893178992737597 ] 
dist 30=[2.7373158333878819573 ,3.6447243951569668264 ] 
dist 31=[2.6953377479835024855 ,3.6505975451503510082 ] 
dist 32=[2.6531142480915014026 ,3.6552529860416108504 ] 
dist 33=[2.6234221088336764300 ,3.6595172948383328302 ] 
dist 34=[2.5969832410382782451 ,3.6632450549571573845 ] 
dist 35=[2.5677725919708137046 ,3.6657543351185051431 ] 
dist 36=[2.5387255344516771348 ,3.6678718482539253820 ] 
dist 37=[2.5129410252314698258 ,3.6700325742528083328 ] 
dist 38=[2.4843939811037120510 ,3.6719610656975408904 ] 
dist 39=[2.4442969961276683680 ,3.6731496524256536346 ] 
dist 40=[2.4033409388371145975 ,3.6740333615628835359 ] 
dist 41=[2.3713576730022105902 ,3.6747423440840506821 ] 
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dist 138=[.05483811509244775642,1.0049789693158180562 ] 
dist 139=[.03678503992963189560,.9984250337414604540 ] 
dist 140=[.01250754304925666377,.9897625023135816230 ] 
dist 141=[-.01181673345137511817,.9876405044064363267 ] 
dist 142=[-.03005692263346943583,.7774110648422561026 ] 
dist 143=[-.04748185934028806259,.7598552151344739555 ] 
dist 144=[-.06854520369698723638,.7206590130890483317 ] 
dist 145=[-.09054676214287972200,.7135515667465059625 ] 
dist 146=[-.11172446572146567666,.6663686570808275442 ] 
dist 147=[-.1365316166264125645 ,.6580591258022346106 ] 
dist 148=[-.17305061820823457139,.6432459797430645042 ] 
dist 149=[-.20948071287651716616,.6399990136704076630 ] 
dist 150=[-.23393224460707213971,.5939429924722291546 ] 
dist 151=[-.25448765066866782878,.5877018437032114164 ] 
dist 152=[-.27533361426588085906,.5746397413068353926 ] 
dist 153=[-.29497485500316295423,.5715108498573909790 ] 
dist 154=[-.31071148452912075469,.5585521424589781902 ] 
dist 155=[-.32673064565371496808,.5561857812384793828 ] 
dist 156=[-.34750198583823711856,.5513120968686228535 ] 
dist 157=[-.36796088500591368383,.5500871233505042366 ] 
dist 158=[-.38273031186313236075,.2649593010184970564 ] 
dist 159=[-.39628003306836962461,.25604907002408019189] 
dist 160=[-.41186022596123548957,.2543616758613952719 ] 
dist 161=[-.42770856357840037864,.24610838022512539161] 
dist 162=[-.44233083810571978898,.2446807344196673892 ] 
dist 163=[-.45897712458478723603,.24143975436918211992] 
dist 164=[-.48292131696268375606,.24090762132715069845] 
dist 165=[-.50684106916408562052,.21182908190876358778] 
dist 166=[-.52338959726823018612,.20908332252982577801] 
dist 167=[-.53784080454619911853,.20292135464444106574] 
dist 168=[-.55337147348121455249,.20184323494720941877] 
dist 169=[-.56856073543217077178,.19434642495115944672] 
dist 170=[-.5816463473366263666 ,.19302886444398280384] 
dist 171=[-.59580522192559178471,.19077896932417439474] 
dist 172=[-.61528743224891321248,.19028585037737210777] 
dist 173=[-.63500905426928976348,.18272025330516761764] 
dist 174=[-.65012555281186108581,.18172522303265711857] 
dist 175=[-.66488690959019293273,.17958698417914977371] 
dist 176=[-.68318799842633129658,.17914102871904349692] 
dist 177=[-.70254815853766507047,.17684128722896233511] 
dist 178=[-.72154569940465305154,.17645046850428923343] 
dist 179=[-.74407509081047354226,.17559398127753033687] 
dist 180=[-.77756231621621188612,.17544385164074600026] 
dist 181=[-.81096140108175759708,-.1002781337202410811 ] 
dist 182=[-.83313823989074198693,-.1239662775269230345 ] 
dist 183=[-.85151885435904271943,-.1268210997144222923 ] 
dist 184=[-.86973340740985564293,-.1326861877562947061 ] 
dist 185=[-.8866247066348948781 ,-.1341203460669044700 ] 
dist 186=[-.8997124354803973436 ,-.1394214092486063826 ] 
dist 187=[-.9126272755782765719 ,-.1404311183116633734 ] 
dist 188=[-.9288270432433703476 ,-.1420331799061920545 ] 
dist 189=[-.9445241723500897582 ,-.1423974361400029947 ] 
dist 190=[-.9554285096227847907 ,-.3547363901617544201 ] 
dist 191=[-.9649980770045435418 ,-.3634759991073390828 ] 
dist 192=[-.97535625731689689938,-.3834197096244789117 ] 
dist 193=[-.98553106083765498057,-.3865574868471969721 ] 
dist 194=[-.99436714547262177911,-.4117341476222257022 ] 
dist 195=[-1.0039879917191568270 ,-.4161602039318751634 ] 
dist 196=[-1.0173017841629367223 ,-.4225325881404346887 ] 
dist 197=[-1.0303815542046703218 ,-.4242302014780993594 ] 
dist 198=[-1.0390663366146667773 ,-.4528565353463862026 ] 
dist 199=[-1.0462644190626319555 ,-.4564119631999760626 ] 
dist 200=[-1.0533975240816461905 ,-.4642727482592225680 ] 
dist 201=[-1.0600125829005712936 ,-.4656691821882648364 ] 
dist 202=[-1.0651385333796106792 ,-.4747723730422924315 ] 
dist 203=[-1.0701973093724304798 ,-.4763281472201652799 ] 
dist 204=[-1.0765436938896784796 ,-.4791510549183670723 ] 
dist 205=[-1.0826938692336223000 ,-.4797595018722477792 ] 
dist 206=[-1.0869678341204066479 ,-.49828452994862713834] 
dist 207=[-1.0907204739067666571 ,-.50023120953326224636] 
dist 208=[-1.0947854019541673929 ,-.50397640613870932365] 
dist 209=[-1.0987803882821476464 ,-.50485124780563128339] 
dist 210=[-1.1022532850550037822 ,-.50745580294057421235] 
dist 211=[-1.1060378010881435351 ,-.50792331615654263228] 
dist 212=[-1.1112792829307906696 ,-.50780734962937244644] 
dist 213=[-1.1164011707545153756 ,-.50686484916833710653] 
dist 214=[-1.1197073209613427498 ,-.50556221620441872278] 
dist 215=[-1.1223431210970615443 ,-.50400576840016858266] 
dist 216=[-1.1247836209062298494 ,-.50195264649760796621] 
dist 217=[-1.1269355365841550367 ,-.49866335635552863839] 
dist 218=[-1.1284170070552491660 ,-.49479800218186428228] 
dist 219=[-1.1297031095054002678 ,-.49044073022858621387] 
dist 220=[-1.1310735614104124402 ,-.48485247064539211516] 
dist 221=[-1.1322902326872645066 ,-.47606344490592816845] 
dist 222=[-1.1329612214770194524 ,-.46707106420720563902] 
dist 223=[-1.1333662806637810229 ,-.46066940944261012773] 
dist 224=[-1.1335192517711462451 ,-.454888800705816924  ] 
dist 225=[-1.1335714759864000788 ,-.44838039911882526704] 
dist 226=[-1.1335735423373440137 ,-.44183861300139132629] 
dist 227=[-1.1335392712790160854 ,-.43592443397154825105] 
dist 228=[-1.1334645516290795882 ,-.42928889447025544303] 
dist 229=[-1.1293134225340126099 ,-.41986177497307384158] 
dist 230=[-1.1287844406710815746 ,-.41018780311600322457] 
dist 231=[-1.1275678200440281415 ,-.40256487909496859523] 
dist 232=[-1.1271963064414075446 ,-.39492288306237157652] 
dist 233=[-1.1253820376007474177 ,-.38517258940036168964] 
dist 234=[-1.1249811725796938940 ,-.37471574611199699878] 
dist 235=[-1.1241320729588492630 ,-.36424765844430419126] 
dist 236=[-1.1231587941743831875 ,-.35167952824940033967] 
dist 237=[-1.1201441022500112044 ,-.33282286916522179706] 
dist 238=[-1.1040741611252294600 ,-.31366155392681113862] 
dist 239=[-1.1028773286465376121 ,-.29987484161226090434] 
dist 240=[-1.1007601307231514214 ,-.28727441584419675043] 
dist 241=[-1.1002560997634237824 ,-.27285801994835167205] 
dist 242=[-1.0917787934157568530 ,-.2582352675150508487 ] 
dist 243=[-1.0902229850977159496 ,-.24480943610772409805] 
dist 244=[-1.0823935219201801576 ,-.22957835109236590823] 
dist 245=[-.97865827743670224205,-.20773487259209921213] 
dist 246=[-.97254201072182470594,-.18522958670971918611] 
dist 247=[-.95821234517683702658,-.16735137418339899212] 
dist 248=[-.95606099796432508219,-.14929350319538032261] 
dist 249=[-.93659470084886846346,-.12606960109928901305] 
dist 250=[-.93193280855629085535,-.10106918350621194632] 
dist 251=[-.92703901019913224556,-.07590553580103325391] 
dist 252=[-.91706190070847513932,-.04559342638997798762] 

8 phat 1 dirichlet min maxes function [2, 0, 1, 1, 2, 0, 2, 0, 2] 
dist 0=[3.9499011727116908602 ,3.9499011727116908602 ] 
dist 1=[3.9491101461014220438 ,3.9505256250964036724 ] 
dist 2=[3.9480388822446492637 ,3.9510009508130985164 ] 
dist 3=[3.9462935036763576238 ,3.9511954771156581668 ] 
dist 4=[3.9444055223771172493 ,3.9512228924820999402 ] 
dist 5=[3.9427638572649003079 ,3.9511735680617016003 ] 
dist 6=[3.9409746695472857337 ,3.9507470607963268703 ] 
dist 7=[3.9384966040250238101 ,3.9505666473170535526 ] 
dist 8=[3.9357400986624254449 ,3.9500808317378243350 ] 
dist 9=[3.9328371742039249665 ,3.9498565077071127247 ] 
dist 10=[3.9292465659300675860 ,3.9485654752781994929 ] 
dist 11=[3.9237393869586298173 ,3.9482217596944021116 ] 
dist 12=[3.9180006767557284544 ,3.9474564034130354953 ] 
dist 13=[3.9134839643265001876 ,3.9471739862692165603 ] 
dist 14=[3.9089604458687121180 ,3.9426890796466537610 ] 
dist 15=[3.9031945122007170983 ,3.9419639792244563943 ] 
dist 16=[3.8930032709208390925 ,3.9402798547036729679 ] 
dist 17=[3.8814013236563201780 ,3.9397467670023049072 ] 
dist 18=[3.8733092873628155136 ,3.9371430026661680150 ] 
dist 19=[3.8661734941581032608 ,3.9365561663110988412 ] 
dist 20=[3.8583964280441777178 ,3.9353201925401140691 ] 
dist 21=[3.8507254121101606709 ,3.9349243174253529357 ] 
dist 22=[3.8409145898500740915 ,3.9172950752008567690 ] 
dist 23=[3.8275920766292828112 ,3.9153228353472732421 ] 
dist 24=[3.8130383194403106243 ,3.9116762613975136185 ] 
dist 25=[3.7980819848698085364 ,3.9100538612156068904 ] 
dist 26=[3.7798405323175995764 ,3.8976350440987890729 ] 
dist 27=[3.7521466165298616132 ,3.8904317858256133465 ] 
dist 28=[3.7241767082628893869 ,3.8389771725725392642 ] 
dist 29=[3.7048313121173606832 ,3.8379551752798617101 ] 
dist 30=[3.6879431881314119130 ,3.8187899301751582448 ] 
dist 31=[3.6698021341329964021 ,3.8162231312267769211 ] 
dist 32=[3.6520650046801732920 ,3.8105998640408178384 ] 
dist 33=[3.6367925403510691212 ,3.8092040855009124329 ] 
dist 34=[3.6202743848752116837 ,3.8023822344014255099 ] 
dist 35=[3.5975546096469356027 ,3.8010674558132434810 ] 
dist 36=[3.5745595416465424336 ,3.7981769461769786374 ] 
dist 37=[3.5569402413390972719 ,3.7973342246671580891 ] 
dist 38=[3.5397408851439529187 ,3.7649769666001819732 ] 
dist 39=[3.5184255535393233602 ,3.7617401274678894871 ] 
dist 40=[3.4958810754196383162 ,3.7540680432667928603 ] 
dist 41=[3.4737652503978378372 ,3.7528005188037553972 ] 
dist 42=[3.4475426278752176692 ,3.7418682790969063684 ] 
dist 43=[3.4085713514504844790 ,3.7397923314081373114 ] 
dist 44=[3.3691131924201470088 ,3.7370341504525680618 ] 
dist 45=[3.3409430859130105655 ,3.7361479026274400221 ] 
dist 46=[3.3154193612749560366 ,3.7183416027608922261 ] 
dist 47=[3.2865464773142727934 ,3.7159646985823880617 ] 
dist 48=[3.2574432528664828649 ,3.7122568716763974207 ] 
dist 49=[3.2309981882494221044 ,3.7097800402990680197 ] 
dist 50=[3.2012158301469665153 ,3.7047109588759570884 ] 
dist 51=[3.1587637500620554288 ,3.7036740122974578897 ] 
dist 52=[3.1151321162381135320 ,3.7013328851309739600 ] 
dist 53=[3.0806316556830395364 ,3.7006620203437581798 ] 
dist 54=[3.0459303899030617482 ,3.6307029699399104966 ] 
dist 55=[3.0014955543319102419 ,3.6253238098354516617 ] 
dist 56=[2.9537552102964932223 ,3.6139730860369186426 ] 
dist 57=[2.9058322259323190290 ,3.6110645462402232692 ] 
dist 58=[2.8481950977345102228 ,3.5874433697753814033 ] 
dist 59=[2.7615991048803984870 ,3.5753094743892675496 ] 
dist 60=[2.6749235751489752633 ,3.5439784941340407330 ] 
dist 61=[2.6169683070279906987 ,3.5372660456066027889 ] 
dist 62=[2.5684886100383337054 ,3.5358069678874206122 ] 
dist 63=[2.5197144610709699593 ,3.5334771726861529380 ] 
dist 64=[2.4740073995659864548 ,3.5328567186347341692 ] 
dist 65=[2.4377957598931088215 ,3.4751440728505345152 ] 
dist 66=[2.4013083488402375029 ,3.4700943902275287175 ] 
dist 67=[2.3544982281178085585 ,3.4589508168465941985 ] 
dist 68=[2.3086299982006101878 ,3.4565650300950962396 ] 
dist 69=[2.2759100605329773344 ,3.4432100048238853342 ] 
dist 70=[2.2462911174911790887 ,3.4407601270537945230 ] 
dist 71=[2.2128265703105792928 ,3.4358333031779948559 ] 
dist 72=[2.1791183624482375631 ,3.4345342154539211973 ] 
dist 73=[2.1485247999193459341 ,3.4208536195674446894 ] 
dist 74=[2.1140993769165490814 ,3.4187983074471564985 ] 
dist 75=[2.0650640926338667143 ,3.4143420695346460864 ] 
dist 76=[2.0162818075235085148 ,3.4131723991989456957 ] 
dist 77=[1.9828683570794472017 ,3.4078787699984310269 ] 
dist 78=[1.9540456439757594865 ,3.4068506045320900054 ] 
dist 79=[1.9236258703714394364 ,3.4044610980039663302 ] 
dist 80=[1.8942081517708491169 ,3.4038696273852261045 ] 
dist 81=[1.8693935631080541260 ,3.1734526579771243240 ] 
dist 82=[1.8429939242550593998 ,3.1616988909170320320 ] 
dist 83=[1.8072361560726252259 ,3.1350739181309875086 ] 
dist 84=[1.7712924800651334826 ,3.1303521154090598924 ] 
dist 85=[1.7441492276434294801 ,3.0968377050427032734 ] 
dist 86=[1.7180333905926663113 ,3.0908044996535378576 ] 
dist 87=[1.6861992780760899924 ,3.0807848244678922283 ] 
dist 88=[1.6441003063344030155 ,3.0784408561848675821 ] 
dist 89=[1.5895202433731558654 ,3.0393753939486360005 ] 
dist 90=[1.5507523093446499964 ,3.0342939540922111311 ] 
dist 91=[1.5158297854787398063 ,3.0222877807143527562 ] 
dist 92=[1.4700326039999638688 ,3.0204757030650010015 ] 
dist 93=[1.4322178389737757366 ,3.0037440777046149420 ] 
dist 94=[1.4002899331137578736 ,3.0006517060061107626 ] 
dist 95=[1.3620823202284048452 ,2.9968659458356055896 ] 
dist 96=[1.3057047456399291005 ,2.9959499048776340476 ] 
dist 97=[1.2497122956568222454 ,2.9661255430606914202 ] 
dist 98=[1.2115168482319272432 ,2.9625137187343473238 ] 
dist 99=[1.1787368155597881251 ,2.9550631159832004634 ] 
dist 100=[1.1444055080761465316 ,2.9501772641241288151 ] 
dist 101=[1.1113669496638479953 ,2.9347696983537592832 ] 
dist 102=[1.0837577899772291492 ,2.7529380146193345191 ] 
dist 103=[1.0546108462643839034 ,2.7431471970290725839 ] 
dist 104=[1.0154212984179815331 ,2.7245281740759082919 ] 
dist 105=[.97615935166377853663,2.7200633138438721893 ] 
dist 106=[.94672281922499555193,2.7062336220186446562 ] 
dist 107=[.91860690861470230793,2.7028698583544057641 ] 
dist 108=[.88462732321615781725,2.6878761097349423506 ] 
dist 109=[.83761672138633971769,2.6597777005886844763 ] 
dist 110=[.7439462683240553348 ,2.5516193294619957486 ] 
dist 111=[.67029915430682304492,2.5383640598603205589 ] 
dist 112=[.59661164513474578959,2.4892312463102131770 ] 
dist 113=[.50277961474152446302,2.1588736017138918153 ] 
dist 114=[.40222927274951092146,2.1325314678446474011 ] 
dist 115=[.30166902659297334133,2.0743137608695981862 ] 
dist 116=[.1809967878036303519 ,2.0502415794472593702 ] 
dist 117=[0                     ,1.9631854202541192604 ] 
dist 118=[.49418438335871816092,1.1383677571587405235 ] 
dist 119=[.46837979412512998107,1.1368860492860020592 ] 
dist 120=[.43492779779825679843,1.1300199748400616580 ] 
dist 121=[.4019826240241111423 ,1.1288194889405407179 ] 
dist 122=[.3782052766616994688 ,1.1260049739692828175 ] 
dist 123=[.35639764358161590852,1.1255922016817881812 ] 
dist 124=[.33133113906932660579,.72599839740800616581] 
dist 125=[.30583831136110613612,.71057707938630570616] 
dist 126=[.28232542615916192264,.67468047835752432975] 
dist 127=[.25556406039253792006,.66947987895005906117] 
dist 128=[.21707762025925556575,.62187951547900556778] 
dist 129=[.17863357062339677396,.6133885735570785703 ] 
dist 130=[.15204176280334514054,.60295038611082468592] 
dist 131=[.12882558682502020478,.60101235568405399563] 
dist 132=[.10388374259497337759,.53704038935139620415] 
dist 133=[.07949529198664976704,.5292248022390202966 ] 
dist 134=[.05849263771362756174,.51341361241748156808] 
dist 135=[.03577426856113183274,.50941957628202948614] 
dist 136=[.00452312207640908427,.49542155431933439626] 
dist 137=[-.02710818056020324753,.49259139667833511377] 
dist 138=[-.05134713806171473047,.48846289047899178008] 
dist 139=[-.07501066785016680866,.48736798740546977542] 
dist 140=[-.10434031451769975011,.40107576001649584627] 
dist 141=[-.13536291690280490738,.39380292613555735057] 
dist 142=[-.16579810809077478224,.37746448584287082906] 
dist 143=[-.20188678680606613787,.37460912681825965699] 
dist 144=[-.2555228000819881362 ,.35465994630232172727] 
dist 145=[-.3090301199870611166 ,.35114596876518346961] 
dist 146=[-.3446040374934758147 ,.34518396033413670406] 
dist 147=[-.3741384487314483285 ,.3438632633525984508 ] 
dist 148=[-.4034883195989264101 ,.32336646043328610166] 
dist 149=[-.4307594614641501039 ,.32068158959574239277] 
dist 150=[-.4519791549581697392 ,.31480390649811457659] 
dist 151=[-.4730031590202816306 ,.31365700938147307467] 
dist 152=[-.4994915618223456826 ,.30696159707909508971] 
dist 153=[-.5252152617677653521 ,.30580106583414727384] 
dist 154=[-.5431805273391471303 ,.30351242928996334302] 
dist 155=[-.5590477384447841098 ,.30295496701639487565] 
dist 156=[-.5763794206355137785 ,.20044469331550665995] 
dist 157=[-.5934975464460624207 ,.19443963028992868238] 
dist 158=[-.6085105523995608492 ,.18046115465009391062] 
dist 159=[-.6249810455192460562 ,.17845983483353272918] 
dist 160=[-.6479289809822958913 ,.1599497701311225202 ] 
dist 161=[-.6705408755983165487 ,.15665696670524058253] 
dist 162=[-.6856672373807970197 ,.15266399857156279763] 
dist 163=[-.6983281497075060970 ,.15198819699289644782] 
dist 164=[-.7110784816501385515 ,.12718110219720020661] 
dist 165=[-.7230350486129581858 ,.12417177060376426469] 
dist 166=[-.7325209767281512805 ,.1181170129450541221 ] 
dist 167=[-.7420914378911329419 ,.11660069156478122598] 
dist 168=[-.7543861289825117816 ,.11136994869616539152] 
dist 169=[-.7664414043847578039 ,.11030062156836034422] 
dist 170=[-.7750542256262035405 ,.10894137918808230515] 
dist 171=[-.7828643809252610261 ,.10867593774257069953] 
dist 172=[-.7917090691146455634 ,.07545356976170305722] 
dist 173=[-.8006298460259914650 ,.07271232547019481333] 
dist 174=[-.8087443489557024584 ,.06658004139978112135] 
dist 175=[-.8178897477084182245 ,.06550706289507587129] 
dist 176=[-.8309340095869766661 ,.05812639637485659604] 
dist 177=[-.8438256185476108023 ,.05683760764697206641] 
dist 178=[-.8523604215008708764 ,.05460795576229455799] 
dist 179=[-.8594064492370093821 ,.05413105638010238078] 
dist 180=[-.8663431032629308800 ,.04701538672735378202] 
dist 181=[-.8727461065726119164 ,.04607234337623136676] 
dist 182=[-.8776575862789213120 ,.04411211474114443336] 
dist 183=[-.8824571632239515301 ,.04365553356244467692] 
dist 184=[-.8884125740334257250 ,.04179207633813926235] 
dist 185=[-.8941514246062455906 ,.04145261829098378295] 
dist 186=[-.8980847851925618599 ,.04082183400727846120] 
dist 187=[-.9014804907672531434 ,.04068223072908937712] 
dist 188=[-.9050687765000834664 ,-.23363665252341132982] 
dist 189=[-.9085416468630373977 ,-.22840114117689262823] 
dist 190=[-.9114757098253572492 ,-.2229203678003508441 ] 
dist 191=[-.9146012760233185188 ,-.21616506252228177146] 
dist 192=[-.9188401607136050282 ,-.20583171980784683817] 
dist 193=[-.9229670174232709898 ,-.19525365175975452126] 
dist 194=[-.9256444862977596420 ,-.18751948373116687054] 
dist 195=[-.9277944409882883507 ,-.18032586451957160794] 
dist 196=[-.9298112833668527357 ,-.17190981123300154358] 
dist 197=[-.9316078221035300884 ,-.16326939714436729056] 
dist 198=[-.9328765871187908186 ,-.15517835706345235524] 
dist 199=[-.9340120798512656156 ,-.14587379745188025886] 
dist 200=[-.9352755617164740626 ,-.13237955275308803083] 
dist 201=[-.9364213435867153515 ,-.1184133364895569419 ] 
dist 202=[-.9370860553604663694 ,-.10722097974810228063] 
dist 203=[-.9375310345357881948 ,-.09582667347868561530] 
dist 204=[-.9377979108058830743 ,-.08105267892922056593] 
dist 205=[-.9379479174562968490 ,-.06508935842142549547] 
dist 206=[-.9379579536871478044 ,-.04893799312282494217] 
dist 207=[-.9378459338733745810 ,-.02942182347075819574] 

8 phat 1 dirichlet min maxes function [1, 1, 2, 0, 0, 0, 0, 0, 2] 
dist 0=[2.2605379509042677379 ,2.2605379509042677379 ] 
dist 1=[2.2601991129904866132 ,2.2610421687561425570 ] 
dist 2=[2.2597654031510166696 ,2.2617684715879024256 ] 
dist 3=[2.2587043206451792951 ,2.2629956357248738824 ] 
dist 4=[2.2566122778525381259 ,2.2644636658197759642 ] 
dist 5=[2.2539955004912855265 ,2.2661534169941836608 ] 
dist 6=[2.2508355206014261390 ,2.2683436036183873486 ] 
dist 7=[2.2466454330891823669 ,2.2718133427479117567 ] 
dist 8=[2.2399083051756431891 ,2.2755296671134171428 ] 
dist 9=[2.2326540414326191889 ,2.2787061786398167065 ] 
dist 10=[2.2263954507768679975 ,2.2821219302170384738 ] 
dist 11=[2.2196157611236368875 ,2.2867951994317872938 ] 
dist 12=[2.2102771419588922505 ,2.2919669573928095733 ] 
dist 13=[2.1999128541280289901 ,2.2973766313518982005 ] 
dist 14=[2.1890305693539755405 ,2.3040423684855309303 ] 
dist 15=[2.1755927752902448887 ,2.3142382967024979098 ] 
dist 16=[2.1550066483281208057 ,2.3246801220714558361 ] 
dist 17=[2.1339120702693031204 ,2.3323294318011836014 ] 
dist 18=[2.1184405112086639956 ,2.3394602897543099646 ] 
dist 19=[2.1039993050934553303 ,2.3478283424300557180 ] 
dist 20=[2.0870260589410315553 ,2.3564351975581894631 ] 
dist 21=[2.0695541128064287972 ,2.3645212499213254430 ] 
dist 22=[2.0531181453010692514 ,2.3738420844217721146 ] 
dist 23=[2.0341559175931508729 ,2.3873879874936133487 ] 
dist 24=[2.0065791261222527868 ,2.4014229963197233472 ] 
dist 25=[1.9779990382154040413 ,2.4127002220074770383 ] 
dist 26=[1.9550237023221495921 ,2.4242098236744966745 ] 
dist 27=[1.9315651251090578910 ,2.4391743215469540417 ] 
dist 28=[1.9010521090899357692 ,2.4553665385639423683 ] 
dist 29=[1.8680298425005029862 ,2.4717869367845802841 ] 
dist 30=[1.8345344569710989727 ,2.4916577163435859577 ] 
dist 31=[1.7939955308580537687 ,2.5216512335440875259 ] 
dist 32=[1.7327996465757825761 ,2.5516733120855103418 ] 
dist 33=[1.6712132369559412199 ,2.5716583351413725826 ] 
dist 34=[1.6291122403481925938 ,2.5882786515476421392 ] 
dist 35=[1.5928833625865013303 ,2.6048421230609339741 ] 
dist 36=[1.5547849762620975290 ,2.6202635127863513695 ] 
dist 37=[1.5180250358019423036 ,2.6323155764689793024 ] 
dist 38=[1.4871498400300669583 ,2.6443064735707486601 ] 
dist 39=[1.4544173556779141229 ,2.6594832006555179044 ] 
dist 40=[1.4102284086285352087 ,2.6742562727741317725 ] 
dist 41=[1.3658750368113381622 ,2.6846325762597329283 ] 
dist 42=[1.3324848680514403482 ,2.6938592126678411238 ] 
dist 43=[1.3004587868846340464 ,2.7040336915282975018 ] 
dist 44=[1.2615616616916528874 ,2.7141399434249390928 ] 
dist 45=[1.2208331828780787917 ,2.7230936762414997535 ] 
dist 46=[1.1814818326524323168 ,2.7329924165623248090 ] 
dist 47=[1.1352730610765425579 ,2.7468786362136331324 ] 
dist 48=[1.0671154368155872707 ,2.7606034789574312477 ] 
dist 49=[.99831391861609378877,2.7698567221552342394 ] 
dist 50=[.94952962274325455047,2.7776808796604741044 ] 
dist 51=[.90567132368643835516,2.7856894734131571993 ] 
dist 52=[.8565734071459446669 ,2.7932824260567359820 ] 
dist 53=[.80737644870185155211,2.7994440463613569153 ] 
dist 54=[.7631219908631751329 ,2.8057879652079780069 ] 
dist 55=[.71364445465953998952,2.8141100999366070010 ] 
dist 56=[.64355559485419282091,2.8223530716183176665 ] 
dist 57=[.57170590656996370936,2.8283803434421854343 ] 
dist 58=[.51518519558144927962,2.8339878534074738539 ] 
dist 59=[.45860577316204709686,2.8405518052304567701 ] 
dist 60=[.38652124438541737646,2.8472940381320644306 ] 
dist 61=[.30925674996867277782,2.8536146606602106898 ] 
dist 62=[.23195787323717708206,2.8608898295255749465 ] 
dist 63=[.13917985222157916621,2.8714501849503919859 ] 
dist 64=[0                     ,2.8819247842978168334 ] 
dist 65=[2.5936631523913757742 ,2.8888569345375126144 ] 
dist 66=[2.5822789417927101960 ,2.8945772986268447773 ] 
dist 67=[2.5697147753228595256 ,2.9002048332478261610 ] 
dist 68=[2.5572293567605484668 ,2.9053969606413988156 ] 
dist 69=[2.5456200547176864416 ,2.9093757246126767464 ] 
dist 70=[2.5327510603293396645 ,2.9132601970076149748 ] 
dist 71=[2.5167345594420719329 ,2.9180751645836573288 ] 
dist 72=[2.4991916197668943900 ,2.9227127370974032316 ] 
dist 73=[2.4855049169071583936 ,2.9258876410711566438 ] 
dist 74=[2.4719100943686994072 ,2.9286247105733833377 ] 
dist 75=[2.4547346544467441937 ,2.9315109741922868812 ] 
dist 76=[2.4363987313587584454 ,2.9343007555222751981 ] 
dist 77=[2.4181620843063533186 ,2.9366519025367157873 ] 
dist 78=[2.3963526481752171578 ,2.9391514704947481914 ] 
dist 79=[2.3637259147035098839 ,2.9425349266086475493 ] 
dist 80=[2.3306046157366910004 ,2.9458260346693473780 ] 
dist 81=[2.3068169622392641424 ,2.9479562166660325773 ] 
dist 82=[2.2851186244018303547 ,2.9496609648162590521 ] 
dist 83=[2.2603543759653395630 ,2.9512503652333185807 ] 
dist 84=[2.2352680294379867772 ,2.9526593600502815985 ] 
dist 85=[2.2122813248248621479 ,2.9536424978735293784 ] 
dist 86=[2.1862391382156509509 ,2.9545099131089788801 ] 
dist 87=[2.1489311525654017652 ,2.9554560260477552489 ] 
dist 88=[2.1105058667100616819 ,2.9563032709154349469 ] 
dist 89=[2.0799945832775600900 ,2.9567752207275264391 ] 
dist 90=[2.0491874012013930368 ,2.9570663232186888961 ] 
dist 91=[2.0095785438519351986 ,2.9571901909098287223 ] 
dist 92=[1.9669424836095465405 ,2.9571980314960723664 ] 
dist 93=[1.9240267761190139586 ,2.9571607748685743427 ] 
dist 94=[1.8723267893529237979 ,2.9568341886876428343 ] 
dist 95=[1.7945544472637399306 ,2.9567706366367749635 ] 
dist 96=[1.7167014035408838064 ,2.9553037435218511420 ] 
dist 97=[1.6646786170799711356 ,2.9544626501099920449 ] 
dist 98=[1.6211980391923040916 ,1.6779533403310662270 ] 
dist 99=[1.5775130150234561358 ,1.6516058900017380309 ] 
dist 100=[1.5366132598243526863 ,1.5901107700346393289 ] 
dist 101=[1.5042734921622130171 ,1.5812426923845287157 ] 
dist 102=[1.4717459945941454838 ,1.5082697904402064349 ] 
dist 103=[1.4300953376766380526 ,1.5051039852957453934 ] 
dist 104=[1.3893207305600900370 ,1.4665645680840548574 ] 
dist 105=[1.3602973486399612228 ,1.4633582906035175410 ] 
dist 106=[1.3340894282571131966 ,1.3527475501454507299 ] 
dist 107=[1.3045763987565302511 ,1.3458536146182694822 ] 
dist 108=[1.2749041610306817440 ,1.3219077341600990579 ] 
dist 109=[1.2480594229317374035 ,1.3169669762205572972 ] 
dist 110=[1.2179216745430969329 ,1.3102906368121005841 ] 
dist 111=[1.1750777097392783600 ,1.3084900984617384677 ] 
dist 112=[1.1324904682165459114 ,1.2659921280502946926 ] 
dist 113=[1.1033795884664906730 ,1.2641787523226893664 ] 
dist 114=[1.0783317664229290131 ,1.1047443547754495350 ] 
dist 115=[1.0519963681997554222 ,1.0992308694952000115 ] 
dist 116=[1.0265897359711839982 ,1.0630545251093950461 ] 
dist 117=[1.0051512857119022189 ,1.0566608432749057823 ] 
dist 118=[.97952697624097134071,1.0451685409363566453 ] 
dist 119=[.95213151909381560201,1.0426092696766843469 ] 
dist 120=[.921507259280031712  ,1.0070014714413223224 ] 
dist 121=[.89846146491575506663,1.0021433569647481182 ] 
dist 122=[.87370553490123431223,.99190402013716138436] 
dist 123=[.84954350998876267245,.9894648257407069811 ] 
dist 124=[.82146558857662093127,.97895985268035028414] 
dist 125=[.79434906044681969945,.97706702833308124213] 
dist 126=[.76251672436918039033,.97288596162729411641] 
dist 127=[.71557602095012998376,.97205255663965664445] 
dist 128=[.66871698087650415809,.92500071352680453256] 
dist 129=[.63721129039167465253,.92415849853914598827] 
dist 130=[.61066635894725725513,.69571229566099114506] 
dist 131=[.58364988188788503203,.6910992710340101712 ] 
dist 132=[.55813352303389256743,.65119773086358382986] 
dist 133=[.53456408553045127106,.64408772514513821445] 
dist 134=[.50900014423905518199,.63472715975243405125] 
dist 135=[.48843193825257045372,.63247253917411692692] 
dist 136=[.46221456753414048208,.58548052743740954763] 
dist 137=[.44005856026568551165,.58324552228057656886] 
dist 138=[.41306298092961430595,.56173781389477627096] 
dist 139=[.39349183767409291371,.55852286079994497932] 
dist 140=[.37545279071127650852,.54539086147403047562] 
dist 141=[.35458545041770827011,.54297596351685167967] 
dist 142=[.3332888693849015364 ,.53800247492601837644] 
dist 143=[.30696218934680246291,.53672870617829368817] 
dist 144=[.27419153667617266478,.48851760902446310521] 
dist 145=[.25143686748660144017,.48726287819802832795] 
dist 146=[.22579821716681315391,.45981044314086326701] 
dist 147=[.20318437237119615092,.45803571309302854353] 
dist 148=[.1833614487649391058 ,.44166648600859681737] 
dist 149=[.16194053424291686286,.43875103140662963089] 
dist 150=[.14092018608051796638,.43520031291085563242] 
dist 151=[.1226298452675257668 ,.43457928563889469283] 
dist 152=[.0945566383794463335 ,.41259600489524353574] 
dist 153=[.0729383063631046239 ,.40992321259651647572] 
dist 154=[.04774376082283682019,.40453354277195901063] 
dist 155=[.0253059352830377074 ,.4031795782705941795 ] 
dist 156=[-.0027189128484977593 ,.39848193710680284247] 
dist 157=[-.03032112152473074679,.39752598881714626684] 
dist 158=[-.06313131204507721427,.39624796661137841139] 
dist 159=[-.11198759082604926423,.39594370671913871723] 
dist 160=[-.16076415330074183205,.34634606516379578275] 
dist 161=[-.19325548619915414387,.34611903959674100234] 
dist 162=[-.22029972634980822121,.11471501713546336486] 
dist 163=[-.24728843736641069362,.11124295502776296762] 
dist 164=[-.2724392218751992284 ,.08106897605262160244] 
dist 165=[-.29213193129239613333,.07571053462912033389] 
dist 166=[-.31415503032633439701,.06869970328077242781] 
dist 167=[-.33664637997818705002,.06708434302147277547] 
dist 168=[-.36089321174977918284,.02880278825605249240] 
dist 169=[-.37795730077231509755,.02561171305236420683] 
dist 170=[-.40106323891173730457,.01423587269867894030] 
dist 171=[-.41780037880295698891,.01187116554851496348] 
dist 172=[-.43270091592791705314,.00223654305706091582] 
dist 173=[-.44915893243572959182,.00046711286388825771] 
dist 174=[-.46552166790332040267,-.00306849021667557478] 
dist 175=[-.4812627956035314389 ,-.00394120891915942539] 
dist 176=[-.50418371989300312464,-.04250721930495947172] 
dist 177=[-.51966499348605030651,-.04338171518011048947] 
dist 178=[-.5409887042553351375 ,-.05905740399290178579] 
dist 179=[-.55604204119374927768,-.06034386669411628735] 
dist 180=[-.56878200845226422882,-.07163306289597888533] 
dist 181=[-.58184032965429185348,-.07362458528322167569] 
dist 182=[-.59423185218934151459,-.07619675418842076466] 
dist 183=[-.60430468837788387539,-.07673415000505475623] 
dist 184=[-.61469081622902201015,-.09078452516496519280] 
dist 185=[-.62833547553331505139,-.09249333826571122103] 
dist 186=[-.64185901594654401753,-.09604536928411839371] 
dist 187=[-.65176067978550635145,-.09688317583171803755] 
dist 188=[-.66098575304798136776,-.10026651490366672889] 
dist 189=[-.67180299568713330805,-.10088711313199925371] 
dist 190=[-.68292396908903007821,-.10204123522532556858] 
dist 191=[-.69413068676780844397,-.10229704514050330005] 
dist 192=[-.71255023261193351638,-.11666854852254967452] 
dist 193=[-.72476510035511545518,-.11795870076292207025] 
dist 194=[-.74019586564517807452,-.12050857651087682439] 
dist 195=[-.75166978710897490726,-.12112897752463055266] 
dist 196=[-.76114086373514490363,-.12315291822350863285] 
dist 197=[-.77046262519719567977,-.12358328311390482422] 
dist 198=[-.77906571309632147546,-.12385009927492368814] 
dist 199=[-.7856621640164558852 ,-.12365069442202293136] 
dist 200=[-.79210578180722611551,-.12324557197563718821] 
dist 201=[-.80009755176581707439,-.12261037079351860907] 
dist 202=[-.80779681714073495277,-.12168000397615584718] 
dist 203=[-.81307044449532206354,-.12009422078527938092] 
dist 204=[-.81761953071813922051,-.1181927227997500261 ] 
dist 205=[-.82242070067127874085,-.11599955616338698187] 
dist 206=[-.82706372781922946282,-.11315470756986483363] 
dist 207=[-.83098025790463969506,-.10864665800554261421] 
dist 208=[-.83514697612155621197,-.10397085984809852275] 
dist 209=[-.84079073193308246009,-.10045504283774645388] 
dist 210=[-.84628167064267650018,-.09708779178071437754] 
dist 211=[-.84983713502725740141,-.09300615903987301471] 
dist 212=[-.85268403285011130284,-.08873764412292084138] 
dist 213=[-.85534077289447587631,-.08462288279978177887] 
dist 214=[-.85769756878135918873,-.07979900118489534051] 
dist 215=[-.85934471858236909793,-.07269415880375869188] 
dist 216=[-.86080074551033890101,-.06529503055432526943] 
dist 217=[-.86239306813398376076,-.05929406234834878501] 
dist 218=[-.86384174939924152086,-.05311964123346236739] 
dist 219=[-.86472322545118768889,-.04502671826061478306] 
dist 220=[-.86536497308722341202,-.03623924172385310612] 
dist 221=[-.86585476612542648813,-.02728675840497796701] 
dist 222=[-.86621487147399810315,-.01642482754464375636] 
dist 223=[-.8663378798635677208 ,0                     ] 
dist 224=[-.86637213089504105948,-.01866137719900066528] 

8 phat 1 dirichlet min maxes function [1, 0, 2, 2, 2, 2, 0, 2] 
dist 0=[3.9111887666588487235 ,3.9111887666588487235 ] 
dist 1=[3.9095040327410210621 ,3.9122366828069593503 ] 
dist 2=[3.9064869483242774825 ,3.9127065555661184757 ] 
dist 3=[3.9032697852127391712 ,3.9131465868772974816 ] 
dist 4=[3.9007847555988431380 ,3.9140751361284844505 ] 
dist 5=[3.8983398402206310523 ,3.9150083518836088984 ] 
dist 6=[3.8952831302258119982 ,3.9154670448149903593 ] 
dist 7=[3.8920362704215132158 ,3.9156694300300330462 ] 
dist 8=[3.8888307739414953112 ,3.9156867665768021040 ] 
dist 9=[3.8850148044761899518 ,3.9153530036134733893 ] 
dist 10=[3.8793261109564483955 ,3.9152083417746733826 ] 
dist 11=[3.8733717987965204888 ,3.9147020777398830742 ] 
dist 12=[3.8684933801046507684 ,3.9144924965737604173 ] 
dist 13=[3.8634287051459983247 ,3.9129597251073573242 ] 
dist 14=[3.8567293856836942101 ,3.9125549861941211076 ] 
dist 15=[3.8494239933923493380 ,3.9119261034626101093 ] 
dist 16=[3.8419350849235627022 ,3.9117002988001156464 ] 
dist 17=[3.8328145032590672729 ,3.9001606108362178577 ] 
dist 18=[3.8189825738106524536 ,3.8988496316522551951 ] 
dist 19=[3.8048650152407273580 ,3.8957394884785681938 ] 
dist 20=[3.7946019443329320334 ,3.8950579332381875867 ] 
dist 21=[3.7851137954674223528 ,3.8903909984142476204 ] 
dist 22=[3.7740958511561066852 ,3.8894343158064420669 ] 
dist 23=[3.7628277732998828459 ,3.8878117790813489416 ] 
dist 24=[3.7523391141119837302 ,3.8873805498576522498 ] 
dist 25=[3.7403252515310152502 ,3.8784747337016957156 ] 
dist 26=[3.7229565055733997891 ,3.8771997178856691690 ] 
dist 27=[3.7049998942207467856 ,3.8743942716213010248 ] 
dist 28=[3.6906346261290678953 ,3.8735687835586675969 ] 
dist 29=[3.6760312455871967423 ,3.8699414629369237720 ] 
dist 30=[3.6435061217932366899 ,3.8691846620872845534 ] 
dist 31=[3.6098004776218567482 ,3.8674283435503212120 ] 
dist 32=[3.5865879861553854303 ,3.8668904503286333403 ] 
dist 33=[3.5664300248279310026 ,3.8071040648440641883 ] 
dist 34=[3.5449422098775697048 ,3.8065962166443386518 ] 
dist 35=[3.5156115509006828378 ,3.7838033843565994175 ] 
dist 36=[3.4895864692441073138 ,3.7819726354289796570 ] 
dist 37=[3.4670516577723006728 ,3.7667589357393382947 ] 
dist 38=[3.4431332480330799561 ,3.7639235198111253721 ] 
dist 39=[3.4199203330676874319 ,3.7599995122310644665 ] 
dist 40=[3.4002074334024960903 ,3.7588208163874318777 ] 
dist 41=[3.3791204114369509450 ,3.7361222063417559870 ] 
dist 42=[3.3504111383312129540 ,3.7331265130620701967 ] 
dist 43=[3.3214857288360105179 ,3.7268438557229312348 ] 
dist 44=[3.2995341819272693357 ,3.7251329582790308637 ] 
dist 45=[3.2783084512218311477 ,3.7183876433244426756 ] 
dist 46=[3.2479444218295236766 ,3.7170839304933636432 ] 
dist 47=[3.2040816565092523270 ,3.7138795545147072054 ] 
dist 48=[3.1728379031463237358 ,3.7132914731610004192 ] 
dist 49=[3.1446021110398762664 ,3.6718712007918453692 ] 
dist 50=[3.1127709038521284837 ,3.6679593791796577134 ] 
dist 51=[3.0733084130733548852 ,3.6589896257955180336 ] 
dist 52=[3.0398616212235350439 ,3.6573082770214510219 ] 
dist 53=[3.0096836467734923918 ,3.6454510275867668691 ] 
dist 54=[2.9728105323232979873 ,3.6432309701179368180 ] 
dist 55=[2.9252113461727830886 ,3.6395355267100622610 ] 
dist 56=[2.8876377804203728710 ,3.6386287546006277007 ] 
dist 57=[2.8499049912347018348 ,3.6222224903263023057 ] 
dist 58=[2.8016689265375601022 ,3.6200038933460017598 ] 
dist 59=[2.7498851555008262400 ,3.6149266827498168533 ] 
dist 60=[2.6979618793300071007 ,3.6138550815701622277 ] 
dist 61=[2.6355563994075010916 ,3.6070240749128933143 ] 
dist 62=[2.5418448131359007859 ,3.6056991948333382457 ] 
dist 63=[2.4480665426828575098 ,3.6032985962091323909 ] 
dist 64=[2.3853943323947850779 ,3.6026958793153358112 ] 
dist 65=[2.3330043051144912720 ,3.5223369082248360438 ] 
dist 66=[2.2803537859982647798 ,3.5219591407660461834 ] 
dist 67=[2.2310510796642398270 ,3.2436174248514465229 ] 
dist 68=[2.1920519842049842802 ,3.2351897498564038516 ] 
dist 69=[2.1521271209859177757 ,3.2004032503272486184 ] 
dist 70=[2.0967318266136392813 ,3.1952111829836614322 ] 
dist 71=[2.0448843009366643911 ,3.1746841146904258189 ] 
dist 72=[2.0039143568283729781 ,3.1717655163636161878 ] 
dist 73=[1.9627309899830544996 ,3.1392840083850123175 ] 
dist 74=[1.9100297937138102832 ,3.1366063168755234363 ] 
dist 75=[1.8584529623590298836 ,3.1005405075798166532 ] 
dist 76=[1.8217669479318628743 ,3.0978855962023568222 ] 
dist 77=[1.7886669147968236926 ,3.0790685229077412200 ] 
dist 78=[1.7514336665867448494 ,3.0756330719655269988 ] 
dist 79=[1.7140230637389984278 ,3.0699283229498488344 ] 
dist 80=[1.6802136289690238219 ,3.0685685722031935654 ] 
dist 81=[1.6422862335709797064 ,3.0432654860721353469 ] 
dist 82=[1.5884041809739028762 ,3.0419337959217814344 ] 
dist 83=[1.5348601874542313935 ,3.0061735268033244862 ] 
dist 84=[1.4982849961224018702 ,3.0037440182110366118 ] 
dist 85=[1.4668417814368992154 ,2.9908189446466699491 ] 
dist 86=[1.4338252050247434506 ,2.9884595808564921864 ] 
dist 87=[1.4019993544895577655 ,2.9835223379204824870 ] 
dist 88=[1.3753189297428541552 ,2.9821774560133536746 ] 
dist 89=[1.3470781381461595358 ,2.9701105769030819796 ] 
dist 90=[1.3090109690357166870 ,2.9685494855599452792 ] 
dist 91=[1.2708295842000886861 ,2.9643539059959333176 ] 
dist 92=[1.2421319405963236370 ,2.9633275008998162402 ] 
dist 93=[1.2146520711343060151 ,2.9594560022578024319 ] 
dist 94=[1.1813416667167764023 ,2.9586358576163058376 ] 
dist 95=[1.1464981615573061985 ,2.9569269408413907689 ] 
dist 96=[1.1128860353516455783 ,2.9564270158302649716 ] 
dist 97=[1.0734575638850660111 ,2.9544626501099920447 ] 
dist 98=[1.0153492324334379274 ,2.9524784219606735235 ] 
dist 99=[.9573557854066880168 ,2.1782518974538931894 ] 
dist 100=[.9183868406821717093 ,2.1513020185839712412 ] 
dist 101=[.8855788397070067999 ,2.0916557816486807551 ] 
dist 102=[.8522285800590216747 ,2.0801978134662561173 ] 
dist 103=[.8207558005227278189 ,2.0097243208009452991 ] 
dist 104=[.7954575409239848290 ,1.9972739907280314896 ] 
dist 105=[.7696298825763278328 ,1.9737797502259773061 ] 
dist 106=[.7360395585373845331 ,1.9682209220992944588 ] 
dist 107=[.7029067346268796159 ,1.9037746834151143718 ] 
dist 108=[.6789090331575179179 ,1.8945357876289068056 ] 
dist 109=[.6568130126492560789 ,1.8762826489089885831 ] 
dist 110=[.6312867312045782441 ,1.8717403644480933266 ] 
dist 111=[.6052543792719204399 ,1.8563914983011090408 ] 
dist 112=[.5811341250797418735 ,1.8530679891226379488 ] 
dist 113=[.5535942197979355825 ,1.8496162670414572266 ] 
dist 114=[.5138835896663305888 ,1.8450488193019132251 ] 
dist 115=[.4741727256854303452 ,1.3041551496242038725 ] 
dist 116=[.4466318850287471397 ,1.2735230534766856676 ] 
dist 117=[.4225099940253242011 ,1.2123650027326068422 ] 
dist 118=[.3964746025648029318 ,1.1970801747243425772 ] 
dist 119=[.3709445806019141578 ,1.1447607573675008796 ] 
dist 120=[.3488441193878771256 ,1.1337951586799073265 ] 
dist 121=[.3248405760123542639 ,1.1208571323663402484 ] 
dist 122=[.2916984069157382515 ,1.1074317184546224251 ] 
dist 123=[.2580980389291602117 ,.8295470276961983757 ] 
dist 124=[.2322617436958939659 ,.8283671273856604054 ] 
dist 125=[.2069541524605828719 ,.8258550365926103951 ] 
dist 126=[.1754685500390828325 ,.8252963787275560368 ] 
dist 127=[.1421040738776397047 ,.6042344601772714733 ] 
dist 128=[0                     ,.6030728394524188387 ] 
dist 129=[.0702938306754490131 ,.6007919318783579496 ] 
dist 130=[.0122722255908713250 ,.6002393401928529187 ] 
dist 131=[-.0456414822216196723 ,.3697844063859052039 ] 
dist 132=[-.0841972396346734276 ,.36213621785064302442] 
dist 133=[-.1162649274670754735 ,.35249529044030988576] 
dist 134=[-.1482269757762158297 ,.35053583069812862994] 
dist 135=[-.1779867157754229959 ,.29417099426287610415] 
dist 136=[-.2012453804199071281 ,.28726573985809581187] 
dist 137=[-.2243862399542833085 ,.27312471338311675963] 
dist 138=[-.2536747707490772863 ,.26951633994020782097] 
dist 139=[-.2821826964556781985 ,.25659809870671039671] 
dist 140=[-.3022012100898529548 ,.25406713454837657471] 
dist 141=[-.3199960858253095204 ,.24971007356380371879] 
dist 142=[-.3396096720232265478 ,.24876730262172564815] 
dist 143=[-.35908561236774113552,.17826622995951779916] 
dist 144=[-.37632991781797745169,.17223170352907019673] 
dist 145=[-.39538498924742002841,.1584893723884884992 ] 
dist 146=[-.42210382080147862876,.15627762125667566927] 
dist 147=[-.44850513946172574708,.13897913815619390769] 
dist 148=[-.46629018959967480194,.13592938596440231368] 
dist 149=[-.48131208649285678168,.13140173639609792854] 
dist 150=[-.49666105571813210268,.13023203626452423238] 
dist 151=[-.51119588912253621947,.11064688248427943768] 
dist 152=[-.52296132038289924665,.10819813348799344016] 
dist 153=[-.53504788567133889366,.10269483530711797096] 
dist 154=[-.55086722455892045107,.10177324638762052053] 
dist 155=[-.56651841308422504923,.09509818510900758784] 
dist 156=[-.57793239296140614903,.09393854912873781181] 
dist 157=[-.5885208679113965403 ,.09205046656808451290] 
dist 158=[-.60087011546296706473,.09162052230328146564] 
dist 159=[-.61352944864892185868,.03278829527289172335] 
dist 160=[-.62535823656109424832,.02893701971803716563] 
dist 161=[-.63894263842965559721,.02023718544447276400] 
dist 162=[-.65862425999417615458,.01878896822653878720] 
dist 163=[-.67812875688904469751,.00805823351638716069] 
dist 164=[-.69100467697279898189,.00617592155270509360] 
dist 165=[-.70159369355860193475,.00319754113223549858] 
dist 166=[-.71195079458200187127,.00248694312653409702] 
dist 167=[-.72146685825874895173,-.00888734227463807732] 
dist 168=[-.72869180567442071636,-.01032584243372017242] 
dist 169=[-.7356809456228355381 ,-.01357800463434686052] 
dist 170=[-.7442538019214051184 ,-.01409617652579720839] 
dist 171=[-.7524655450499025532 ,-.01809098351667103441] 
dist 172=[-.7580102667602893950 ,-.01878400950259866226] 
dist 173=[-.7627076286357347231 ,-.01982784878362090871] 
dist 174=[-.7675300132439727788 ,-.02008714286173980554] 
dist 175=[-.7721109566466144192 ,-.02418115731301339643] 
dist 176=[-.7758425767278591880 ,-.02474239538773755604] 
dist 177=[-.77969734816598535527,-.02544737126994521671] 
dist 178=[-.78477088525021951578,-.02556633739391906453] 
dist 179=[-.78968072980502557004,-.02545835232271511173] 
dist 180=[-.79288074805524615452,-.02501162348267741246] 
dist 181=[-.79546662200768270488,-.02422826125573785699] 
dist 182=[-.79791995189844372111,-.02277390697845663050] 
dist 183=[-.80012406860211352779,-.02113627275413396876] 
dist 184=[-.80171311752611211803,-.01961985248884547410] 
dist 185=[-.80316880978349825709,-.01789053451125847743] 
dist 186=[-.80483952043962182331,-.01540133030986247438] 
dist 187=[-.80638238162292197885,-.01259078099314536237] 
dist 188=[-.80732669212973082196,-.00957624503542604829] 
dist 189=[-.80802089158661088686,-.00581138383052189197] 
dist 190=[-.80856333636517788565,0                     ] 
dist 191=[-.80897184938069406972,-.03500792333023887136] 
dist 192=[-.80913034244627945315,-.02638409596719604331] 
dist 193=[-.80917454124812943997,-.01589336960910246269] 

8 phat 1 dirichlet min maxes function [0, 2, 0, 1, 1, 1, 1, 0, 1] 
dist 0=[3.8368501536164156676 ,3.8368501536164156676 ] 
dist 1=[3.8294822852490949400 ,3.8472873886365088260 ] 
dist 2=[3.8228920738625696938 ,3.8575335779310342540 ] 
dist 3=[3.8155654337846825042 ,3.8641372779750215614 ] 
dist 4=[3.8082531158372099695 ,3.8693902567549117360 ] 
dist 5=[3.8017201992736972800 ,3.8742336377044073675 ] 
dist 6=[3.7944526236265816988 ,3.8784899237816448108 ] 
dist 7=[3.7842017212256301553 ,3.8813945604758151528 ] 
dist 8=[3.7737121816111537819 ,3.8838888208308388025 ] 
dist 9=[3.7654900763884139299 ,3.8865036370349004803 ] 
dist 10=[3.7572868149993389221 ,3.8888578062761376363 ] 
dist 11=[3.7468726566653206560 ,3.8903094924574405803 ] 
dist 12=[3.7357287464700269794 ,3.8913896824763199401 ] 
dist 13=[3.7246065291264563242 ,3.8922578726122659160 ] 
dist 14=[3.7112764698140332841 ,3.8929315586419234715 ] 
dist 15=[3.6913013402473933232 ,3.8932337358404805787 ] 
dist 16=[3.6710084043485979385 ,3.8933239149068382857 ] 
dist 17=[3.6564071428886272293 ,3.8933050516358238276 ] 
dist 18=[3.6430604203044064391 ,3.8810115484892586777 ] 
dist 19=[3.6277855609377381381 ,3.8798132885277456977 ] 
dist 20=[3.6122876139025418554 ,3.8774113334301920960 ] 
dist 21=[3.5980485586466727807 ,3.8767387991635322206 ] 
dist 22=[3.5818857915201650050 ,3.8740535435547970822 ] 
dist 23=[3.5586931299725623720 ,3.8734590523922172346 ] 
dist 24=[3.5347885827216607886 ,3.8720201559953265022 ] 
dist 25=[3.5157783227960579413 ,3.8715764227871306653 ] 
dist 26=[3.4965563676974436041 ,3.8691445542250135492 ] 
dist 27=[3.4718050568053652669 ,3.8685744038111246132 ] 
dist 28=[3.4451424266967306706 ,3.8675584622502440123 ] 
dist 29=[3.4182753266653169780 ,3.8672651654737340890 ] 
dist 30=[3.3858866238132362713 ,3.8661160992596411094 ] 
dist 31=[3.3371379611156518377 ,3.8657807048522852405 ] 
dist 32=[3.2881912984406457142 ,3.8650689045747514662 ] 
dist 33=[3.2550106113580603807 ,3.8648103606776056536 ] 
dist 34=[3.2267576055583842068 ,3.7479977247450921105 ] 
dist 35=[3.1975213363518257880 ,3.7413942801950745771 ] 
dist 36=[3.1696027783670097184 ,3.7260680490830267196 ] 
dist 37=[3.1466205325233413682 ,3.7235387128049310988 ] 
dist 38=[3.1226633144141140932 ,3.7029856293561775058 ] 
dist 39=[3.0908449442720212074 ,3.6992068293274147157 ] 
dist 40=[3.0591464187112590641 ,3.6938423407340611231 ] 
dist 41=[3.0356685757754709542 ,3.6923020980403543340 ] 
dist 42=[3.0135252230898779990 ,3.6635997244392239783 ] 
dist 43=[2.9871645721696013226 ,3.6598493903163362109 ] 
dist 44=[2.9598456649763702717 ,3.6518433972161352042 ] 
dist 45=[2.9338693626758457302 ,3.6497991524125392299 ] 
dist 46=[2.9036841786839505138 ,3.6409068705431179221 ] 
dist 47=[2.8595300574824805169 ,3.6392531905295696654 ] 
dist 48=[2.8151095148289026050 ,3.6352287627212637345 ] 
dist 49=[2.7838586680104485938 ,3.6345358207929043526 ] 
dist 50=[2.7560175534342835864 ,3.5898592183887991613 ] 
dist 51=[2.7252356959276254432 ,3.5855826978672083033 ] 
dist 52=[2.6946134048207538420 ,3.5755843155616891320 ] 
dist 53=[2.6674105492594172398 ,3.5739171475104346394 ] 
dist 54=[2.6372766277339426297 ,3.5601927953264885873 ] 
dist 55=[2.5949302968417028557 ,3.5576323762140249748 ] 
dist 56=[2.5516677281014771417 ,3.5540500248011117199 ] 
dist 57=[2.5178689270164341461 ,3.5529856773085136803 ] 
dist 58=[2.4842528375070434452 ,3.5325299313036980908 ] 
dist 59=[2.4417211064633459351 ,3.5298254874546846630 ] 
dist 60=[2.3962828910931513866 ,3.5241279107470895806 ] 
dist 61=[2.3510410861991151700 ,3.5225689148848788897 ] 
dist 62=[2.2968982263370691965 ,3.5163752900790161149 ] 
dist 63=[2.2158564653670486349 ,3.5151878766130940313 ] 
dist 64=[2.1344600658985786025 ,3.5121957406614304566 ] 
dist 65=[2.0788986801793006235 ,3.5117086160439541873 ] 
dist 66=[2.0311745746129930126 ,3.4299989151787095406 ] 
dist 67=[1.9811267058812874847 ,3.4240986523328599894 ] 
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dist 85=[.96372016738862250436,3.2403307617684793389 ] 
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dist 128=[.43544355576724466782,1.3685657047279166084 ] 
dist 129=[.37703716574977521074,.94460080683486748288] 
dist 130=[.31880304126797694837,.92833156147463693305] 
dist 131=[.27976696599814232787,.890368718862760821  ] 
dist 132=[.24700568099838667942,.88492412613832787921] 
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dist 139=[.04485734161734165797,.7177502590471561108 ] 
dist 140=[.02379303670788548230,.71350150205741684058] 
dist 141=[-.00029309050392940634,.69884932101377550801] 
dist 142=[-.02471824316580139208,.69581506627269125781] 
dist 143=[-.04713861753990844172,.69197245412712551843] 
dist 144=[-.07257085761906647244,.69115801459142227208] 
dist 145=[-.10904318583534287016,.59229610582640207927] 
dist 146=[-.14543216630481516503,.58407718075236056072] 
dist 147=[-.17053102334630017741,.56577786350117972035] 
dist 148=[-.19236801118928066387,.56241010204908524548] 
dist 149=[-.21570982597537356442,.54052456642395289177] 
dist 150=[-.23846277078683631149,.53667125155401473883] 
dist 151=[-.25794433489655075825,.52969227707364737224] 
dist 152=[-.27892143910179521446,.52813011942234904796] 
dist 153=[-.30765640165371886913,.50726662378507825585] 
dist 154=[-.33668687045075670582,.5043957976811136531 ] 
dist 155=[-.35884597145165614978,.4985101049585946644 ] 
dist 156=[-.38039591017104764314,.49700406616450018477] 
dist 157=[-.40698978794274838395,.49158838675462315225] 
dist 158=[-.43505834988502209135,.4905283172555174078 ] 
dist 159=[-.46250688463424323285,.48865721745574043143] 
dist 160=[-.49498793092779528899,.48825351085365889246] 
dist 161=[-.54318605905638578263,.34662609081733776186] 
dist 162=[-.59124924538766259489,.33877065174665203776] 
dist 163=[-.62319053861389549926,.32067423303895012141] 
dist 164=[-.64969456551215147789,.31789775840570171071] 
dist 165=[-.67600920888142012349,.2944487599585034956 ] 
dist 166=[-.70044469569508029991,.29028004976830051457] 
dist 167=[-.71943227935460437763,.28463518286308528814] 
dist 168=[-.73822057457622950605,.28316909092219402719] 
dist 169=[-.76185893415170022695,.25397895877211579657] 
dist 170=[-.78479872626056898094,.2503394795919553008 ] 
dist 171=[-.80079282199364293743,.24261714575058360935] 
dist 172=[-.81489085564727329666,.24086577905209696661] 
dist 173=[-.83024658402443146212,.23280395861174936257] 
dist 174=[-.84538752579921251501,.23139499358690360483] 
dist 175=[-.85862644102271915331,.22820718371053117602] 
dist 176=[-.87311719841257801784,.22767829927777959998] 
dist 177=[-.89326540819044026655,.19691151684115442817] 
dist 178=[-.91310093959432775752,.19406760870656291997] 
dist 179=[-.92634101704286654371,.18761381643838987933] 
dist 180=[-.93739138497271611865,.18655187824052266388] 
dist 181=[-.9484682796113742845 ,.17849208833783134096] 
dist 182=[-.95882276449573808703,.17707194391963094354] 
dist 183=[-.96698356601008506306,.17488529583480327321] 
dist 184=[-.97516721078158165242,.17434371293174790878] 
dist 185=[-.98561308515488771614,.16544851916156506941] 
dist 186=[-.99582368363244248108,.16433445038408159229] 
dist 187=[-1.0030662546936267060 ,.16176765363465508131] 
dist 188=[-1.0095803041708090716 ,.16139420626613933826] 
dist 189=[-1.0168768894547788467 ,.15809563633603973219] 
dist 190=[-1.0241908035312376482 ,.15751792442155888355] 
dist 191=[-1.0307741851182260316 ,.15677889002714931311] 
dist 192=[-1.0381381593637836324 ,.15664025201864162971] 
dist 193=[-1.0485744217409003922 ,-.43984186766151094378] 
dist 194=[-1.0588639498110838453 ,-.4327339524954598202 ] 
dist 195=[-1.0656409995726828777 ,-.42760164059338243349] 
dist 196=[-1.0711973174726065013 ,-.4228931183586710789 ] 
dist 197=[-1.0766039786551335148 ,-.41748016381268543497] 
dist 198=[-1.0815534266833523333 ,-.41197581589655809035] 
dist 199=[-1.0852809132280315758 ,-.40690169066518878076] 
dist 200=[-1.0888575984800170247 ,-.40112944807948502081] 
dist 201=[-1.0932038445574477335 ,-.3928327402667068898 ] 
dist 202=[-1.0973467556676756168 ,-.38427752886614108007] 
dist 203=[-1.1001101092621222500 ,-.37747129807232584695] 
dist 204=[-1.1024143003035543837 ,-.37058780458214207802] 
dist 205=[-1.1047205826132434583 ,-.36172351129185227486] 
dist 206=[-1.1068742784435773192 ,-.35217575410823979488] 
dist 207=[-1.1085681269278625077 ,-.34255851292657746799] 
dist 208=[-1.1102633953284668412 ,-.33096868215886154009] 
dist 209=[-1.1124227594933835028 ,-.31353092132314783053] 
dist 210=[-1.1144625409916625844 ,-.2957922611263197379 ] 
dist 211=[-1.1156794826674080591 ,-.28299887614697669595] 
dist 212=[-1.1165362761352172098 ,-.27127559882995562968] 
dist 213=[-1.1171354879567104499 ,-.25781714426609113087] 
dist 214=[-1.1175724986268659956 ,-.24414053619675405879] 
dist 215=[-1.1177805115857630561 ,-.23154466656102098531] 
dist 216=[-1.1178621897782309648 ,-.21722433726034392115] 
dist 217=[-1.1178446619896269444 ,-.19665018064661163117] 
dist 218=[-1.1159986767324778213 ,-.17543723012287660825] 
dist 219=[-1.1156709044629068405 ,-.15856182817041461296] 
dist 220=[-1.1151527396906575879 ,-.14149501908298846986] 
dist 221=[-1.1149802914554396118 ,-.11951645881354548664] 
dist 222=[-1.1144242039028641491 ,-.09584224469432948238] 
dist 223=[-1.1142281370534897013 ,-.07199310719359500595] 
dist 224=[-1.1138897133803192438 ,-.04324985017645742867] 

8 phat 1 dirichlet min maxes function [2, 0, 0, 2, 2, 0, 0, 1, 2] 
dist 0=[3.5485093312119369917 ,3.5485093312119369917 ] 
dist 1=[3.5467448149941307153 ,3.5502255088189096194 ] 
dist 2=[3.5414031574016872390 ,3.5529342861883329585 ] 
dist 3=[3.5356307276388764617 ,3.5553814272470627270 ] 
dist 4=[3.5306200248171663599 ,3.5574965471527637618 ] 
dist 5=[3.5251663671095667627 ,3.5588773022665640145 ] 
dist 6=[3.5176221409160722725 ,3.5599956154893014989 ] 
dist 7=[3.5092345984560520044 ,3.5610610388931940989 ] 
dist 8=[3.5004077523180382501 ,3.5620471340312319847 ] 
dist 9=[3.4894942954375810703 ,3.5628481507224747662 ] 
dist 10=[3.4727605167659785955 ,3.5636737071650028506 ] 
dist 11=[3.4556086110830476267 ,3.5647579398323414909 ] 
dist 12=[3.4430226822061217453 ,3.5659366220982276148 ] 
dist 13=[3.4312691632785518659 ,3.5671399641283793991 ] 
dist 14=[3.4174467987647479851 ,3.5686020511713876277 ] 
dist 15=[3.4032142706047700211 ,3.5708156965514934989 ] 
dist 16=[3.3898201285201522917 ,3.5730739308681428852 ] 
dist 17=[3.3743632426831219947 ,3.5747143655732376659 ] 
dist 18=[3.3518799324108527599 ,3.5762297816555500043 ] 
dist 19=[3.3285775168016694514 ,3.5779879341704180358 ] 
dist 20=[3.3098442838919323425 ,3.5797852018206105234 ] 
dist 21=[3.2907168500916392782 ,3.5814570670205467632 ] 
dist 22=[3.2658376608128536871 ,3.5833712391321795429 ] 
dist 23=[3.2389131758340322085 ,3.5861377074753396192 ] 
dist 24=[3.2116047504564725589 ,3.5889975116429278284 ] 
dist 25=[3.1785555949656181538 ,3.5912850143003876333 ] 
dist 26=[3.1286687332189893803 ,3.5936101537613345024 ] 
dist 27=[3.0786613924514099717 ,3.5966204938476665585 ] 
dist 28=[3.0451303310830349205 ,3.5998714075146216174 ] 
dist 29=[3.0169786137955756074 ,3.6031588144992423436 ] 
dist 30=[2.9884881362804502814 ,3.6071301714308208503 ] 
dist 31=[2.9616817725314596845 ,3.6131168157976897589 ] 
dist 32=[2.9402663496810960793 ,3.6190837625597068778 ] 
dist 33=[2.9185231209263251998 ,3.6229763283810587382 ] 
dist 34=[2.8904055648251849265 ,3.6261258479869396449 ] 
dist 35=[2.8627469520576285324 ,3.6291206769032299093 ] 
dist 36=[2.8428394528640848849 ,3.6318158221580434501 ] 
dist 37=[2.8246363707143337090 ,3.6337666318478675137 ] 
dist 38=[2.8037952635580174886 ,3.6355615604157345183 ] 
dist 39=[2.7826457784338568058 ,3.6376331883448727525 ] 
dist 40=[2.7632092138252090010 ,3.6395523013907831093 ] 
dist 41=[2.7411432453288361288 ,3.6407371811226077947 ] 
dist 42=[2.7094763954411222961 ,3.6416204508101420967 ] 
dist 43=[2.6778725961824773495 ,3.6423331486027968322 ] 
dist 44=[2.6560588241887356102 ,3.6428882528016823767 ] 
dist 45=[2.6370635779022771024 ,3.6431411554521558753 ] 
dist 46=[2.6167336126473525199 ,3.6432229240552128854 ] 
dist 47=[2.5969010269235752782 ,3.6431944656222228033 ] 
dist 48=[2.5798952513226292740 ,3.6428599434555986786 ] 
dist 49=[2.5615628514169824038 ,3.6427242494261075231 ] 
dist 50=[2.5364238950052064767 ,3.6422085067522851574 ] 
dist 51=[2.5110143958859333272 ,3.6420466000687976904 ] 
dist 52=[2.4915998509541264190 ,3.6396505104398185759 ] 
dist 53=[2.4727004312212118400 ,3.6391617522144789655 ] 
dist 54=[2.4493513837658844235 ,3.6368727327676190133 ] 
dist 55=[2.4246939736788080398 ,3.6327927534893794496 ] 
dist 56=[2.4005612282079400892 ,3.5853347785575424038 ] 
dist 57=[2.3719888935762432550 ,3.5820085062746990299 ] 
dist 58=[2.3295735502850928838 ,3.5756184413178340050 ] 
dist 59=[2.2871169920549908941 ,3.5740237227444315156 ] 
dist 60=[2.2583798015984870226 ,3.5554907355861269788 ] 
dist 61=[2.2339585751405794308 ,3.5528287468900543047 ] 
dist 62=[2.2087654612567447060 ,3.5405359778914398407 ] 
dist 63=[2.1847571634515424366 ,3.5214764786451099957 ] 
dist 64=[2.1650750883027482804 ,3.3391598155928662772 ] 
dist 65=[2.1446309323749515085 ,3.3278134242453784038 ] 
dist 66=[2.1175743841394976094 ,3.3014942315803288621 ] 
dist 67=[2.0906652248790995843 ,3.2973727997146083282 ] 
dist 68=[2.0708106107938571080 ,3.2624348540490326457 ] 
dist 69=[2.0521601741257796585 ,3.2561111359669317039 ] 
dist 70=[2.0300676096819791427 ,3.2475717534076736949 ] 
dist 71=[1.9866695008858609965 ,3.2451363431761861162 ] 
dist 72=[1.9113392131432879038 ,3.1982181351417107804 ] 
dist 73=[1.8599893722365523404 ,3.1922257574590570901 ] 
dist 74=[1.8159587052822987494 ,3.1796382684030792196 ] 
dist 75=[1.7699045770867941370 ,3.1764293146935313635 ] 
dist 76=[1.7256205368961843919 ,3.1634319937070542895 ] 
dist 77=[1.6886700923848411299 ,3.1610092217998007619 ] 
dist 78=[1.6497100900635870911 ,3.1554903819322042201 ] 
dist 79=[1.5973879662223466728 ,3.1543746056706480219 ] 
dist 80=[1.5449955540599015958 ,3.0887137852313081677 ] 
dist 81=[1.5057544036307135016 ,3.0826527744436769515 ] 
dist 82=[1.4683119719317951687 ,3.0685845491011758768 ] 
dist 83=[1.4231143026298208067 ,3.0663056637298176711 ] 
dist 84=[1.3759358097679544434 ,3.0474923862825865966 ] 
dist 85=[1.3305702289255438568 ,3.0440510220672154149 ] 
dist 86=[1.2774641841409852011 ,3.0392549573360137186 ] 
dist 87=[1.1993244027964580055 ,3.0378581607227014226 ] 
dist 88=[1.1205239554194883301 ,3.0119018140843010785 ] 
dist 89=[1.0647752945976303419 ,3.0085330321594719143 ] 
dist 90=[1.0147853400787871588 ,3.0013860422487821105 ] 
dist 91=[.95901929488456362277,2.9995547191196973335 ] 
dist 92=[.90325327733991046726,2.9918031631369581380 ] 
dist 93=[.85326343249672744423,2.9903772906818918462 ] 
dist 94=[.79751495968624834649,2.9868238831319254608 ] 
dist 95=[.71871485053443187789,2.9863130828284647535 ] 
dist 96=[.63800903994287570883,2.8968581324609300524 ] 
dist 97=[.57463789995441831342,2.8904310322150063862 ] 
dist 98=[.51130897650696209685,2.8753843332429570256 ] 
dist 99=[.43077202750044069936,2.8730869207593790940 ] 
dist 100=[.34452141069030402797,2.8526326120893852638 ] 
dist 101=[.25833823239452490839,2.8488966239557699555 ] 
dist 102=[.15497391594156807296,2.8441317337935259549 ] 
dist 103=[0                     ,2.8429155371108602672 ] 
dist 104=[.9436966388924327443 ,2.8134176274796147788 ] 
dist 105=[.9175260915736464068 ,2.8096630939506297608 ] 
dist 106=[.8801959818599716795 ,2.8020049246095245997 ] 
dist 107=[.8430359702438386823 ,2.8000069976815941175 ] 
dist 108=[.8175457990915988359 ,2.7926466889612170178 ] 
dist 109=[.7955177265687566589 ,2.7911588683500324556 ] 
dist 110=[.7722057792620881641 ,2.7882749069266117658 ] 
dist 111=[.7496230955809675992 ,2.7875310054912738348 ] 
dist 112=[.7305120080045935597 ,2.7381350529172644856 ] 
dist 113=[.7101262649034818170 ,2.7337163728367994234 ] 
dist 114=[.6824450806975356737 ,2.7237654792776270668 ] 
dist 115=[.6545886091595369488 ,2.7218543132993203296 ] 
dist 116=[.6335017334487742438 ,2.7093739610379182581 ] 
dist 117=[.6131637348577937338 ,2.7070902908950262672 ] 
dist 118=[.5883027003725038833 ,2.7008322903409925516 ] 
dist 119=[.5621869581816564834 ,2.6931697376829411335 ] 
dist 120=[.5368302484399874335 ,2.6572343525127041716 ] 
dist 121=[.5069611368081577934 ,2.6555077539084681757 ] 
dist 122=[.4627962174406438241 ,2.6535841063037126012 ] 
dist 123=[.4186594920457650016 ,2.6532156823440339902 ] 
dist 124=[.3889031536153905498 ,2.6380594113785371629 ] 
dist 125=[.3637437855479116143 ,2.6368123103411659957 ] 
dist 126=[.3379945031546652435 ,2.6262936869733810181 ] 
dist 127=[.3135844431654410387 ,2.6100964841953438125 ] 
dist 128=[.2937818369816641713 ,1.1862680078225159241 ] 
dist 129=[.2733992889973081659 ,1.1514120046029336689 ] 
dist 130=[.2466695171194703867 ,1.0701217280550713297 ] 
dist 131=[.2201992785546496031 ,1.0584532852139132103 ] 
dist 132=[.2008548390685870226 ,.95019561531174588209] 
dist 133=[.1828688175556427403 ,.93086795788773268098] 
dist 134=[.1618321213200731040 ,.9074874537828861795 ] 
dist 135=[.1402341838459950563 ,.90343901974776961157] 
dist 136=[.1200032509090974469 ,.77713265946332398386] 
dist 137=[.0967304439288523019 ,.77512610332539988838] 
dist 138=[.0629653004093196335 ,.77461209136228176129] 
dist 139=[.0291129650282027938 ,.7257138414725798187 ] 
dist 140=[.0054913989178084317 ,.7216210490649347366 ] 
dist 141=[-.0153498271538467545 ,.7124853022652804321 ] 
dist 142=[-.0380810675633458420 ,.7108175406642960938 ] 
dist 143=[-.0605124344381970447 ,.6998155370600199795 ] 
dist 144=[-.0801541949726058760 ,.6978743585253424890 ] 
dist 145=[-.1016768179458082159 ,.6943981614634195661 ] 
dist 146=[-.1316314551828906189 ,.6936297044857527475 ] 
dist 147=[-.1621061624089075825 ,.6828457685283418640 ] 
dist 148=[-.1857090157346002766 ,.6813790574761887065 ] 
dist 149=[-.2089909685767947639 ,.6782962394837040685 ] 
dist 150=[-.2381821044756729176 ,.6775610296553570749 ] 
dist 151=[-.2692320839367327205 ,.6744376191036524677 ] 
dist 152=[-.2999492337348279123 ,.6738724424340292099 ] 
dist 153=[-.3365629282557466385 ,.6726524585172180972 ] 
dist 154=[-.3911985242073164693 ,.6723891228622993294 ] 
dist 155=[-.4457531683895768672 ,.23930825567762861948] 
dist 156=[-.4820430648390467165 ,.22745945856685377444] 
dist 157=[-.5121936062858131777 ,.22523721909839168759] 
dist 158=[-.5421914198709316499 ,.22104471143749983158] 
dist 159=[-.5700877597037876044 ,.22007656447661300183] 
dist 160=[-.5918326104293033883 ,-.05095935378279659218] 
dist 161=[-.6134134163201368139 ,-.06603738479497855276] 
dist 162=[-.6406536001660159794 ,-.10092841334398932262] 
dist 163=[-.6671319837445077551 ,-.10607134150057543632] 
dist 164=[-.6856656650744948137 ,-.15162376767505375716] 
dist 165=[-.7020783729731102855 ,-.15969727583861330861] 
dist 166=[-.7200730689634346925 ,-.17001894587002654091] 
dist 167=[-.73788575039921435427,-.17216646997572418636] 
dist 168=[-.75357042513278900515,-.2303605118489013027 ] 
dist 169=[-.77083015489718150897,-.23746736017482259233] 
dist 170=[-.79494292546527683725,-.25214880696496646661] 
dist 171=[-.81873126003070281218,-.25576979472669930241] 
dist 172=[-.83469328055976560198,-.26950304946601179483] 
dist 173=[-.84810711192331421357,-.27210104826647875699] 
dist 174=[-.86170292512654885283,-.27681293808689220356] 
dist 175=[-.87450831415721317566,-.27784252741385826687] 
dist 176=[-.88476052801772638382,-.3435721132392216353 ] 
dist 177=[-.89519005445461040053,-.34921453440051607364] 
dist 178=[-.90870469601432226298,-.3622434094152655498 ] 
dist 179=[-.92201217409664905081,-.3641055609145858355 ] 
dist 180=[-.93161307401324350195,-.38092499349414509513] 
dist 181=[-.94041530786473426323,-.38386866040949365934] 
dist 182=[-.95052820161667786184,-.3875358937367916316 ] 
dist 183=[-.96081071375536803615,-.38813924913914813921] 
dist 184=[-.97029142406357673291,-.40885762224335089014] 
dist 185=[-.98107967014496168849,-.41131930246282267153] 
dist 186=[-.99659225417139369974,-.41636745982890303336] 
dist 187=[-1.0119330404108704718 ,-.41756355208917044651] 
dist 188=[-1.0220341104453988608 ,-.42202408385694925901] 
dist 189=[-1.0303123268493037956 ,-.42286482160638982667] 
dist 190=[-1.0383618150671261111 ,-.42401409242228441445] 
dist 191=[-1.0457266690193443669 ,-.42419934757820766888] 
dist 192=[-1.0512663907189128780 ,-.58260785634131015509] 
dist 193=[-1.0565752750393100998 ,-.5890597047481779678 ] 
dist 194=[-1.0630167900313353844 ,-.60362046516998667986] 
dist 195=[-1.0691519616729777357 ,-.60599936079658946124] 
dist 196=[-1.0732354903301600342 ,-.6238362215050116414 ] 
dist 197=[-1.0766309150055864945 ,-.62693757260204959381] 
dist 198=[-1.0800137133718519813 ,-.63178263004943838495] 
dist 199=[-1.0831625593696229182 ,-.63294087329117632227] 
dist 200=[-1.0856221853938860325 ,-.65113799433653457096] 
dist 201=[-1.0880681124077931255 ,-.65342499071884575453] 
dist 202=[-1.0911621521774257414 ,-.65842273770255256407] 
dist 203=[-1.0941140340253104593 ,-.65930232450010714282] 
dist 204=[-1.0959913441040520090 ,-.66483395381460048842] 
dist 205=[-1.0974559531855948922 ,-.66574817438239776708] 
dist 206=[-1.0987570854796712620 ,-.66746207052355174158] 
dist 207=[-1.0998660651294138864 ,-.66783099775877641964] 
dist 208=[-1.1005620970302582196 ,-.67097347652849817601] 
dist 209=[-1.1010945389748643566 ,-.67136307119162779797] 
dist 210=[-1.1015492045364885875 ,-.6712163135801295823 ] 
dist 211=[-1.1018908523558266326 ,-.67029896744140410553] 
dist 212=[-1.1019712252550468891 ,-.66894706473915134097] 
dist 213=[-1.1019605895678931175 ,-.66706211345600930139] 
dist 214=[-1.1019381904263563654 ,-.66441000766638663113] 
dist 215=[-1.1011219021693548783 ,-.65998961707315999521] 
dist 216=[-1.1008915181750562282 ,-.65517175155228283181] 
dist 217=[-1.1007351616877668646 ,-.65092979993314951677] 
dist 218=[-1.1006373122969969450 ,-.64626284743740515492] 
dist 219=[-1.0166772866186949854 ,-.63974500989042299553] 
dist 220=[-1.0127698242579582090 ,-.63247065098338603904] 
dist 221=[-1.0036590183241846346 ,-.62477774196831246939] 
dist 222=[-1.0021869597680681506 ,-.61524091434021011391] 
dist 223=[-.9898485840220912159 ,-.6005912361937634182 ] 
dist 224=[-.98757766184472173899,-.58573345713746519998] 
dist 225=[-.98446455743191023653,-.5753642515577903665 ] 
dist 226=[-.98353390739364057182,-.56621479029814016498] 
dist 227=[-.96594746409499547181,-.55623571035964792838] 
dist 228=[-.96365614957664343331,-.54638949116896937216] 
dist 229=[-.95884144529508625794,-.53777142097775122014] 
dist 230=[-.95754284161831923116,-.52833192910191488327] 
dist 231=[-.95246554995619873547,-.51520014559698133586] 
dist 232=[-.95149660797442759125,-.50184474324106364546] 
dist 233=[-.94917463411776360865,-.4915107988166914814 ] 
dist 234=[-.94874260030665249343,-.48132753379876506758] 
dist 235=[-.91997563723398542447,-.46857479519949643283] 
dist 236=[-.91728024153219383121,-.4550189106177705706 ] 
dist 237=[-.91106030604762231227,-.44162318210345332994] 
dist 238=[-.90926164632232194495,-.42566793838976445189] 
dist 239=[-.90140585450410901391,-.40187440811627838791] 
dist 240=[-.86057552285302975353,-.37775439018709723708] 
dist 241=[-.85648855610496109735,-.36049324191092558767] 
dist 242=[-.8556522505687531132 ,-.34481237616370684521] 
dist 243=[-.85053407525224775458,-.32701321140139742933] 
dist 244=[-.84942408434728375902,-.3090388810172636277 ] 
dist 245=[-.84847865614802190421,-.29265737040968242616] 
dist 246=[-.84427986497780894765,-.27417016854064295489] 
dist 247=[-.83499572364914805183,-.24777340293188325733] 
dist 248=[-.80241423767763051801,-.22062654700840571936] 
dist 249=[-.79840070066360937757,-.19913909860368408644] 
dist 250=[-.78293551005985827165,-.17750764412003186572] 
dist 251=[-.67331749632771880951,-.14978477816828691245] 
dist 252=[-.66448358484360458002,-.11998967460851472495] 
dist 253=[-.64466898199195649115,-.09006959593088861275] 
dist 254=[-.63698370180062674992,-.05407844166398016298] 

8 phat 1 dirichlet min maxes function [2, 1, 2, 2, 1, 0, 0, 0, 2] 
dist 0=[3.4158106247772727639 ,3.4158106247772727639 ] 
dist 1=[3.4125002119055252677 ,3.4184960520203632914 ] 
dist 2=[3.4080696424453293869 ,3.4211632632991596577 ] 
dist 3=[3.4009036522860665613 ,3.4244008130484778761 ] 
dist 4=[3.3924531530566487209 ,3.4287038751670575247 ] 
dist 5=[3.3828846264373728051 ,3.4356330746893139584 ] 
dist 6=[3.3705831247974792235 ,3.4437921537562880174 ] 
dist 7=[3.3512008993810844873 ,3.4530146571354077548 ] 
dist 8=[3.3307278884010846639 ,3.4648609021939441656 ] 
dist 9=[3.3140633186577944924 ,3.4835147784880652475 ] 
dist 10=[3.2968597379932108457 ,3.5023461283787480385 ] 
dist 11=[3.2742307318545418323 ,3.5149022588167514200 ] 
dist 12=[3.2496157316843720220 ,3.5253670233317556611 ] 
dist 13=[3.2244683180699666479 ,3.5358330520037806169 ] 
dist 14=[3.1939026491509309664 ,3.5456013967702281126 ] 
dist 15=[3.1476150087026372721 ,3.5532754755767052656 ] 
dist 16=[3.1010843291603646893 ,3.5609481181540795211 ] 
dist 17=[3.0695465241025996789 ,3.5707107252507082925 ] 
dist 18=[3.0426979582516137262 ,3.5802387241727184452 ] 
dist 19=[3.0149239152983903314 ,3.5869729532307034056 ] 
dist 20=[2.9884072549690171503 ,3.5930048898876238069 ] 
dist 21=[2.9665881371026717422 ,3.5997237694873510584 ] 
dist 22=[2.9438515153540922697 ,3.6064369878938060240 ] 
dist 23=[2.9136649122355478468 ,3.6124462873576774453 ] 
dist 24=[2.8835969760215285473 ,3.6191409335420723636 ] 
dist 25=[2.8613350181741960284 ,3.6285955112841414901 ] 
dist 26=[2.8403465463385415938 ,3.6378654267703741866 ] 
dist 27=[2.8153724702815907511 ,3.6438214381995290764 ] 
dist 28=[2.7894969193971170619 ,3.6485381874799147590 ] 
dist 29=[2.7649026196149795445 ,3.6528511247155432673 ] 
dist 30=[2.7363307661502499036 ,3.6566160930416319556 ] 
dist 31=[2.6945452984839420334 ,3.6591410018765169132 ] 
dist 32=[2.6525113677505147402 ,3.6612614420919777259 ] 
dist 33=[2.6229456834850566816 ,3.6634085711595397889 ] 
dist 34=[2.5966122710375953006 ,3.6653243509560751141 ] 
dist 35=[2.5675071940209506788 ,3.6665194058855072856 ] 
dist 36=[2.5385587392646979407 ,3.6674249406108443321 ] 
dist 37=[2.5128518088488605512 ,3.6681826397619111734 ] 
dist 38=[2.4843824383469254711 ,3.6687945549364778953 ] 
dist 39=[2.4443844357738606227 ,3.6691169539366278111 ] 
dist 40=[2.4035250590266128188 ,3.6692915221158158446 ] 
dist 41=[2.3716102597002490297 ,3.6693121143799460974 ] 
dist 42=[2.3398741172928860386 ,3.6550378891031061318 ] 
dist 43=[2.2997293592806547304 ,3.6537179767643937557 ] 
dist 44=[2.2568455531111584606 ,3.6510773122213842245 ] 
dist 45=[2.2141534285500157578 ,3.6503498752667150578 ] 
dist 46=[2.1630665549558603792 ,3.6475037081645064779 ] 
dist 47=[2.0866043929280539248 ,3.6468754270089628643 ] 
dist 48=[2.0098099252313224451 ,3.6454325961243023162 ] 
dist 49=[1.9573938554333314809 ,3.6449584127870294739 ] 
dist 50=[1.9123757500185257476 ,3.6427647617921161786 ] 
dist 51=[1.8651725789845137228 ,3.6422161667509139876 ] 
dist 52=[1.8197122008263583663 ,3.6414312467297507254 ] 
dist 53=[1.7816651357959257890 ,3.6411507084141584856 ] 
dist 54=[1.7414478294261087834 ,3.6405074088458229247 ] 
dist 55=[1.6873066534807674941 ,3.6402598742049887895 ] 
dist 56=[1.6330332418456614164 ,3.6400895518194384783 ] 
dist 57=[1.5922870039633798994 ,3.6399780955299540265 ] 
dist 58=[1.5533143565831281733 ,3.5174802846829780984 ] 
dist 59=[1.5061351731204060975 ,3.5107641700794738498 ] 
dist 60=[1.4568167708463955772 ,3.4951837349826263550 ] 
dist 61=[1.4092874130539934149 ,3.4926254930210940153 ] 
dist 62=[1.3535676324761164439 ,3.4717782561108814942 ] 
dist 63=[1.2714881673219712708 ,3.4679538619568008764 ] 
dist 64=[1.1886767468768437024 ,3.4625426811151263955 ] 
dist 65=[1.1300292016028705084 ,3.4609875672904307396 ] 
dist 66=[1.0773764955755889175 ,3.4320920633032526923 ] 
dist 67=[1.0185439732339496720 ,3.4283257692849826024 ] 
dist 68=[.95965621537640600619,3.4202895335946482773 ] 
dist 69=[.90678257173094720827,3.4182499361698041370 ] 
dist 70=[.84774840451788553321,3.4093573020885553086 ] 
dist 71=[.76421902460752799224,3.4077104038383841054 ] 
dist 72=[.67863306911670277596,3.4037038242499854982 ] 
dist 73=[.61137275711368582849,3.4030266667329167346 ] 
dist 74=[.54410402958252916524,3.3588972094209547537 ] 
dist 75=[.45848441228771147707,3.3546822659998288108 ] 
dist 76=[.36675424164779251564,3.3448210457808870712 ] 
dist 77=[.27504376853865764899,3.3431940278408354293 ] 
dist 78=[.16501238989317575999,3.3296538696942946900 ] 
dist 79=[0                     ,3.3271323496101426568 ] 
dist 80=[1.9206707386665278840 ,3.3236480683647889698 ] 
dist 81=[1.8886874031592200926 ,3.3226006822854005259 ] 
dist 82=[1.8644499721220541823 ,3.3024485635713478110 ] 
dist 83=[1.8410475482488050894 ,3.2997914496379309880 ] 
dist 84=[1.8124041617558312447 ,3.2942199102999962287 ] 
dist 85=[1.7822959770782306623 ,3.2927039906706539699 ] 
dist 86=[1.7530345001760310324 ,3.2867343155547176181 ] 
dist 87=[1.7185443200904912163 ,3.2855807142310846024 ] 
dist 88=[1.6675218213829076166 ,3.2827549809914904992 ] 
dist 89=[1.6165218055621064278 ,3.2822315063649288387 ] 
dist 90=[1.5821215548793229403 ,3.2049395515801596874 ] 
dist 91=[1.5530174453185648213 ,3.1993224446904344356 ] 
dist 92=[1.5232014888503900466 ,3.1859919311949870360 ] 
dist 93=[1.4949177256239919497 ,3.1840502383543758462 ] 
dist 94=[1.4719422428927767514 ,3.1653357303959068848 ] 
dist 95=[1.4482664680909855720 ,3.1618831740488643061 ] 
dist 96=[1.4171816033747574686 ,3.1578658139122072411 ] 
dist 97=[1.3863815219623531469 ,3.1570749181422156406 ] 
dist 98=[1.3638448532137883081 ,3.1276455364582908390 ] 
dist 99=[1.3428626906395175215 ,3.1239331043687104619 ] 
dist 100=[1.3182804856585622048 ,3.1166465186222200273 ] 
dist 101=[1.2930197583732993233 ,3.1148036516574235596 ] 
dist 102=[1.2693235712979149058 ,3.1084442121641596987 ] 
dist 103=[1.2420376347097243814 ,3.1064616247733225562 ] 
dist 104=[1.2024182517564522716 ,3.1044650403490580372 ] 
dist 105=[1.1626832903562215013 ,3.1020282433690780993 ] 
dist 106=[1.1349350510038402243 ,3.0393955276885655716 ] 
dist 107=[1.1104298809405571012 ,3.0339891882025756188 ] 
dist 108=[1.0836668873791784468 ,3.0223040364866985303 ] 
dist 109=[1.0572359563407871845 ,3.0196227911791334006 ] 
dist 110=[1.0340590046979863423 ,2.9973120112256711424 ] 
dist 111=[1.0086350129807338445 ,2.9861388169926228310 ] 
dist 112=[.97321613596277811789,2.7931575299219309446 ] 
dist 113=[.93716711744091872281,2.7830854818844096481 ] 
dist 114=[.90922261980970303655,2.7613466754937696440 ] 
dist 115=[.88163503824375304729,2.7565417127331934654 ] 
dist 116=[.8470136499410074011 ,2.7323540900022846275 ] 
dist 117=[.8101712769728846401 ,2.7241823371795873413 ] 
dist 118=[.7736999685785549173 ,2.7068907669248355400 ] 
dist 119=[.7302098492682675530 ,2.6932468720772988301 ] 
dist 120=[.6652929020766302425 ,2.6294177478653400729 ] 
dist 121=[.6004183160945459783 ,2.6078065198335605781 ] 
dist 122=[.5570976375821423390 ,1.5534791794256746630 ] 
dist 123=[.5209228334130985314 ,1.5184729588635826838 ] 
dist 124=[.4846310632450789510 ,1.4368130781133232256 ] 
dist 125=[.4506872603744444747 ,1.4250637345657145322 ] 
dist 126=[.4239041014504598365 ,1.3161996008327481052 ] 
dist 127=[.3970178503742238185 ,1.2967434773706553786 ] 
dist 128=[.3626616887273095952 ,1.2731648480017602018 ] 
dist 129=[.3290622474704963930 ,1.2690024368466340105 ] 
dist 130=[.3052028057801689299 ,1.1203522089270379847 ] 
dist 131=[.2837162565468021176 ,1.1022049067666253889 ] 
dist 132=[.2596081587960378028 ,1.0657335994058402547 ] 
dist 133=[.2354204507623124363 ,1.0565669809334963170 ] 
dist 134=[.2136154679901728974 ,1.0248007655194231100 ] 
dist 135=[.1891987998768227363 ,1.0182607523089952001 ] 
dist 136=[.1545645995756420451 ,1.0096063808763495347 ] 
dist 137=[.1201705436518797182 ,1.0074761573617408320 ] 
dist 138=[.0967144301437068215 ,.79764504266789019709] 
dist 139=[.0765903205887032572 ,.78011822761284480043] 
dist 140=[.0555239626776652368 ,.74098666892872505431] 
dist 141=[.0352570756349740042 ,.73388862126554125337] 
dist 142=[.0183307733014059210 ,.68677967512604979858] 
dist 143=[.0004704983672232742 ,.6784820845455140412 ] 
dist 144=[-.0235321899974650915 ,.66368775920556853073] 
dist 145=[-.0475740269892926918 ,.66044360475349852189] 
dist 146=[-.0655908926981135766 ,.61443665637103291935] 
dist 147=[-.0827912130185002401 ,.6082014007215861186 ] 
dist 148=[-.1035669463370766122 ,.59514594906496561712] 
dist 149=[-.1252595030681336749 ,.59202157533022755426] 
dist 150=[-.1461270295936376577 ,.57904464539760191076] 
dist 151=[-.1705611345293310349 ,.57667757440191736191] 
dist 152=[-.2065196647279444582 ,.57178322655206013242] 
dist 153=[-.2423860330386804660 ,.57056907463026762967] 
dist 154=[-.2664514992130829349 ,.32862280748168370984] 
dist 155=[-.2866739452639191400 ,.31122409965081837243] 
dist 156=[-.3071685996200556819 ,.3085500304022563902 ] 
dist 157=[-.3264701646303971293 ,.28601132471257096916] 
dist 158=[-.3419203670925572166 ,.28200382662642995784] 
dist 159=[-.3576348906025660948 ,.27656394272888460181] 
dist 160=[-.3779937145938834588 ,.27513936220571903923] 
dist 161=[-.3980380024221424307 ,.24711281725741212343] 
dist 162=[-.4124944112797554498 ,.24361517749449501983] 
dist 163=[-.4257430405966717263 ,.23618492648035974043] 
dist 164=[-.4409563254577697511 ,.23450634110864945508] 
dist 165=[-.4564198410855934167 ,.22671424371489867208] 
dist 166=[-.4706693696028961819 ,.22535682138828655987] 
dist 167=[-.4868772506307685782 ,.22226015445907574536] 
dist 168=[-.5101739895170780082 ,.22176703741261835752] 
dist 169=[-.5334398646713230661 ,.19231343939796237463] 
dist 170=[-.5495242937146597510 ,.18958276689183537883] 
dist 171=[-.5635577937695618102 ,.18339130725041480638] 
dist 172=[-.5786201485836226525 ,.18236606006650566922] 
dist 173=[-.5933397550193864559 ,.17464728032591673419] 
dist 174=[-.6060022942517634103 ,.1732868306158427964 ] 
dist 175=[-.6196876807878811635 ,.17117202331541849605] 
dist 176=[-.6384985788814534730 ,.17065368153249490862] 
dist 177=[-.6575317896895608359 ,.16217529693745140839] 
dist 178=[-.6721064058800713792 ,.16111076446057331351] 
dist 179=[-.6863250068937315398 ,.15865318049002100728] 
dist 180=[-.7039341909504614546 ,.15829804621212219294] 
dist 181=[-.7225525314960772076 ,.15512589263326305374] 
dist 182=[-.7408076622139288995 ,.1545704521349571685 ] 
dist 183=[-.7624457963277096519 ,.15386602733462547054] 
dist 184=[-.7945958277928625471 ,.15373821786071239445] 
dist 185=[-.8266576214234856023 ,-.12275150441762009809] 
dist 186=[-.8479428137641668360 ,-.33804120954099869364] 
dist 187=[-.8655803370294834220 ,-.3469015780695751407 ] 
dist 188=[-.8830518057131602485 ,-.36713188320290597417] 
dist 189=[-.8992496435015005371 ,-.37030848712581986153] 
dist 190=[-.9117927681082532918 ,-.39588355747216130697] 
dist 191=[-.9241632937062588875 ,-.40038187077881586806] 
dist 192=[-.9396707588133773059 ,-.40683188562615043714] 
dist 193=[-.9546923925974080535 ,-.40855929523586674362] 
dist 194=[-.9651196426837817356 ,-.43777524533199859027] 
dist 195=[-.9742622467083866104 ,-.44140508171212647093] 
dist 196=[-.98414542220949813321,-.44940816597889913397] 
dist 197=[-.99384597900925304691,-.45085360437067272153] 
dist 198=[-1.0022581325266494091 ,-.46005939156606803687] 
dist 199=[-1.0114071974903193915 ,-.46163233442185203003] 
dist 200=[-1.0240553469930919051 ,-.46453824745012786121] 
dist 201=[-1.0364756064473206912 ,-.46518005549471087985] 
dist 202=[-1.0447131363791344504 ,-.48474748699554358724] 
dist 203=[-1.0515302105281385644 ,-.48678208841143816018] 
dist 204=[-1.0582687754076705823 ,-.49075321929233665467] 
dist 205=[-1.0645069178259493834 ,-.49169746419045911443] 
dist 206=[-1.0693223532562291574 ,-.49463263394789111544] 
dist 207=[-1.0740572327120277484 ,-.49525556647066609662] 
dist 208=[-1.0799731760298369890 ,-.49530947272295045907] 
dist 209=[-1.0856944238791501225 ,-.49460285745292818554] 
dist 210=[-1.0896505468551041946 ,-.49353995786114500644] 
dist 211=[-1.0931032663681327707 ,-.49216877509194388777] 
dist 212=[-1.0968109517376192283 ,-.49029800695072796685] 
dist 213=[-1.1004356079378338382 ,-.48723680542139396995] 
dist 214=[-1.1035562357644663762 ,-.48361377584875677477] 
dist 215=[-1.1069313044967921251 ,-.47949579989009741627] 
dist 216=[-1.1115737479056110992 ,-.47419244694097974188] 
dist 217=[-1.1160999714030832991 ,-.46582818286625858502] 
dist 218=[-1.1190101704257779045 ,-.45726167830287526798] 
dist 219=[-1.1213173184866040682 ,-.451149387911200687  ] 
dist 220=[-1.1234313443534655494 ,-.44561587560196880713] 
dist 221=[-1.1252799880220179929 ,-.4393642834324434105 ] 
dist 222=[-1.1265256120833202192 ,-.43306841056789634568] 
dist 223=[-1.1275781644802564768 ,-.42735774459689575742] 
dist 224=[-1.1286545296562767796 ,-.42093530405393020891] 
dist 225=[-1.1295914366097122538 ,-.41179244021215429379] 
dist 226=[-1.1300861636436858030 ,-.40240220130994496561] 
dist 227=[-1.1303556253106016214 ,-.39499028548517436741] 
dist 228=[-1.1304118248644217918 ,-.38754814384829167721] 
dist 229=[-1.1303417999273365106 ,-.37803696925468990165] 
dist 230=[-1.1302690742521155634 ,-.36782857410043216728] 
dist 231=[-1.1301649453376402284 ,-.35759765592190480102] 
dist 232=[-1.1300816053720681962 ,-.34530583036721084203] 
dist 233=[-1.1250028383244660276 ,-.32685415519813637675] 
dist 234=[-1.1034196001938911505 ,-.30810055843504965499] 
dist 235=[-1.0999705315038038480 ,-.29460108864560766566] 
dist 236=[-1.0990776340845483494 ,-.28225697215239814161] 
dist 237=[-1.0958831728956542722 ,-.26812456548628338472] 
dist 238=[-1.0951693473163720324 ,-.25378466799924696868] 
dist 239=[-1.0939724832771825999 ,-.2406106088352291942 ] 
dist 240=[-1.0936588022048901406 ,-.22565882697461627761] 
dist 241=[-1.0925979188828632255 ,-.20420832361784438937] 
dist 242=[-1.0621245924655622912 ,-.18210469479095199166] 
dist 243=[-1.0593279112111404264 ,-.16454051196387345264] 
dist 244=[-1.0563333663363532918 ,-.14679517998237725405] 
dist 245=[-1.0551561397034048356 ,-.12396697230955266999] 
dist 246=[-1.0320728521629049362 ,-.09938940157570863634] 
dist 247=[-1.0281552302651334497 ,-.07464689921100339568] 
dist 248=[-1.0079849270981509718 ,-.04483886609181720990] 

8 phat 1 dirichlet min maxes function [0, 2, 1, 0, 0, 1, 1, 0, 2] 
dist 0=[3.9331357286683542765 ,3.9331357286683542765 ] 
dist 1=[3.9311306414773127301 ,3.9343440778724348643 ] 
dist 2=[3.9278626221471453369 ,3.9371723502196536267 ] 
dist 3=[3.9231839396218623540 ,3.9400389900821342382 ] 
dist 4=[3.9179083301062105821 ,3.9417738015097241293 ] 
dist 5=[3.9122526406606866539 ,3.9430255339778270325 ] 
dist 6=[3.9051873646111448467 ,3.9439598733936442211 ] 
dist 7=[3.8942734896177913504 ,3.9446397195651300369 ] 
dist 8=[3.8831749783609946753 ,3.9448734918341840459 ] 
dist 9=[3.8753711711283239517 ,3.9449292119778319105 ] 
dist 10=[3.8684231110613449351 ,3.9448968474328324480 ] 
dist 11=[3.8607475491347986527 ,3.9433474146595122575 ] 
dist 12=[3.8531153521379188025 ,3.9430228094004990604 ] 
dist 13=[3.8463407555250309073 ,3.9421641244022274362 ] 
dist 14=[3.8388405252119953762 ,3.9412723843139775396 ] 
dist 15=[3.8283058439504067378 ,3.9378475735640436884 ] 
dist 16=[3.8175452635604176143 ,3.9311481380879952546 ] 
dist 17=[3.8091414547046188222 ,3.9297733113824027272 ] 
dist 18=[3.8007856720163481851 ,3.9294915454650975739 ] 
dist 19=[3.7902171996650489961 ,3.9265462615056376501 ] 
dist 20=[3.7789281142215077001 ,3.9259598261200418160 ] 
dist 21=[3.7676899293010782060 ,3.9246177895397846062 ] 
dist 22=[3.7542421296161937702 ,3.9241688167072456735 ] 
dist 23=[3.7341147321354428942 ,3.9220251358097283680 ] 
dist 24=[3.7136768353660407293 ,3.9215310287256543616 ] 
dist 25=[3.6989870608208653681 ,3.9203924495452595744 ] 
dist 26=[3.6855755146438459320 ,3.9199991442930369359 ] 
dist 27=[3.6702504511998186716 ,3.9153001289667767304 ] 
dist 28=[3.6547150602824482966 ,3.9144347715391210844 ] 
dist 29=[3.6404622209102874490 ,3.9131537298039645592 ] 
dist 30=[3.6243002542396004201 ,3.9103546993279985834 ] 
dist 31=[3.6011284843625866676 ,3.9029691359779546688 ] 
dist 32=[3.5772539010524435714 ,3.7766356740318789781 ] 
dist 33=[3.5582807293219432705 ,3.7717417607678962205 ] 
dist 34=[3.5391084879499862486 ,3.7703441243186894284 ] 
dist 35=[3.5144376418370907023 ,3.7441913024261738551 ] 
dist 36=[3.4878698995922951413 ,3.7407577415991596670 ] 
dist 37=[3.4611102029097461264 ,3.7334104846874891682 ] 
dist 38=[3.4288595335471535503 ,3.7315238646336066722 ] 
dist 39=[3.3803282724159316888 ,3.7302054100988494603 ] 
dist 40=[3.3315979826442984480 ,3.7217261320363359285 ] 
dist 41=[3.2985512144120150044 ,3.7179890298320737266 ] 
dist 42=[3.2703984113969120090 ,3.7172996352019555828 ] 
dist 43=[3.2412436577291056045 ,3.6753868492205282556 ] 
dist 44=[3.2133891065287660546 ,3.6713515895029596245 ] 
dist 45=[3.1904370312073348342 ,3.6619157292389311003 ] 
dist 46=[3.1664911871967826914 ,3.6603234009474731347 ] 
dist 47=[3.1346616395094527901 ,3.6508603594623649213 ] 
dist 48=[3.1029397797418331097 ,3.6449089578106171857 ] 
dist 49=[3.0794246856381059428 ,3.6414706226592813433 ] 
dist 50=[3.0572264151224759202 ,3.6404571500870218630 ] 
dist 51=[3.0307717661213292450 ,3.6389138784390275747 ] 
dist 52=[3.0033399341092016907 ,3.6251334687879956938 ] 
dist 53=[2.9772330084079238739 ,3.6239045454145312816 ] 
dist 54=[2.9468780943701233464 ,3.6138697862495509728 ] 
dist 55=[2.9024546231383406106 ,3.6053246756123158108 ] 
dist 56=[2.8577543454287648992 ,3.6041724483314024185 ] 
dist 57=[2.8262922293875083714 ,3.6011991300628877576 ] 
dist 58=[2.7982478017857664331 ,3.6007627325683779814 ] 
dist 59=[2.7672180354199177956 ,3.5191442613791195460 ] 
dist 60=[2.7363356302583095280 ,3.5132738584955609556 ] 
dist 61=[2.7088806422831896131 ,3.4993020497231681989 ] 
dist 62=[2.6784500235298195744 ,3.4972908532303809682 ] 
dist 63=[2.6356653220997268852 ,3.4775500206423010968 ] 
dist 64=[2.5919455000696075416 ,3.4739022595153618786 ] 
dist 65=[2.5577744721353676452 ,3.4697462760123497738 ] 
dist 66=[2.5237740792689565528 ,3.4689911704283771118 ] 
dist 67=[2.4807367902907214495 ,3.4374471802903355549 ] 
dist 68=[2.4347486085933363658 ,3.4334780430880515924 ] 
dist 69=[2.3889448695352644070 ,3.4257470353629039854 ] 
dist 70=[2.3341189406568080994 ,3.4238053711293159163 ] 
dist 71=[2.2520426808531311995 ,3.4172061516395695236 ] 
dist 72=[2.1696023276101325924 ,3.4157008850638660705 ] 
dist 73=[2.1133200538613222144 ,3.4140095730412671049 ] 
dist 74=[2.0649678340470072667 ,3.4135806419914952734 ] 
dist 75=[2.0142471020146053832 ,3.3491631728978256062 ] 
dist 76=[1.9653857044790821195 ,3.3436876335471065291 ] 
dist 77=[1.9244706845634584561 ,3.3317508285745174473 ] 
dist 78=[1.8812029237719034150 ,3.3290901774576640775 ] 
dist 79=[1.8229307430537897828 ,3.3152642508215812108 ] 
dist 80=[1.7645050114793276141 ,3.3127470316496960951 ] 
dist 81=[1.7206230603806790821 ,3.3073793741246295570 ] 
dist 82=[1.6786332631792122197 ,3.3059458962943013204 ] 
dist 83=[1.6277760062212068079 ,3.2936124560215648814 ] 
dist 84=[1.5745990901185735221 ,3.2916164757330785388 ] 
dist 85=[1.5233308337521394497 ,3.2877475735146744533 ] 
dist 86=[1.4632123331066980755 ,3.2867532365647819717 ] 
dist 87=[1.3746351130226226343 ,3.2832635778358499725 ] 
dist 88=[1.2852604230221418242 ,3.2824478673575308392 ] 
dist 89=[1.2219521038516336885 ,3.2812453158633088001 ] 
dist 90=[1.1651019249082870639 ,3.2808712369988249228 ] 
dist 91=[1.1015593060765136105 ,3.0867704738061638157 ] 
dist 92=[1.0379454649919271234 ,3.0762216653085457461 ] 
dist 93=[.98081040291038190168,3.0524161518538586127 ] 
dist 94=[.91700356320796999732,3.0480970691787002182 ] 
dist 95=[.82670311899634734251,3.0183720829110451108 ] 
dist 96=[.73417145427445233256,3.0130185771177897635 ] 
dist 97=[.66143990215929723474,3.0038078400334540744 ] 
dist 98=[.58868731426098333703,3.0017375636041433526 ] 
dist 99=[.49607150786036487571,2.9304372906152981706 ] 
dist 100=[.39683750244222539218,2.9223351058288257122 ] 
dist 101=[.29761262111236542967,2.9084093353903548246 ] 
dist 102=[.17855669166154115161,2.8931117362738470737 ] 
dist 103=[0                     ,2.8531581736926184406 ] 
dist 104=[1.1758845327109073498 ,1.5381693705861114403 ] 
dist 105=[1.1351606345388410807 ,1.5306301417352455879 ] 
dist 106=[1.0774319236049654205 ,1.5145805803493773213 ] 
dist 107=[1.0201191522461243406 ,1.5109034079506325769 ] 
dist 108=[.98105897270270162218,1.4938369728114382810 ] 
dist 109=[.9475754361710433131 ,1.4908544277758783867 ] 
dist 110=[.9125687049700688385 ,1.4838426345213804516 ] 
dist 111=[.87891791918986174488,1.4828266860225692554 ] 
dist 112=[.85085803501387807205,1.4158639973033309394 ] 
dist 113=[.82128869746379267994,1.4096166983076403280 ] 
dist 114=[.78160024215585885679,1.3952230642359160442 ] 
dist 115=[.74187002637568073331,1.3929582154313518605 ] 
dist 116=[.71213365091964946474,1.3742297167832023287 ] 
dist 117=[.68378146733576374148,1.3708764740377850423 ] 
dist 118=[.64958788702268219319,1.3662157161309168396 ] 
dist 119=[.61391317943648701813,1.3648914754927345864 ] 
dist 120=[.57963662802713939497,1.3412844465758547375 ] 
dist 121=[.53953320924779461355,1.3382924710412616372 ] 
dist 122=[.48055158793670668475,1.3318801976754450356 ] 
dist 123=[.42173614094742410278,1.3304325729071049633 ] 
dist 124=[.38229740360592225453,1.3234535315971690800 ] 
dist 125=[.34918397735445301759,1.3222240288962190925 ] 
dist 126=[.31566917142962790884,1.3194159379682497423 ] 
dist 127=[.2841336195542201503 ,1.3189202628262006249 ] 
dist 128=[.25893702072308008192,.89721140823800891768] 
dist 129=[.23335192908146349452,.88101530312998740795] 
dist 130=[.20026244301782626391,.84324532836904314574] 
dist 131=[.16771126039087303828,.83781553602201924753] 
dist 132=[.14427933115367436616,.78750753024477879408] 
dist 133=[.12285054833031063119,.77852175008041407421] 
dist 134=[.09831176030255041483,.76763535831288725144] 
dist 135=[.07340734512437543181,.76572689092039284707] 
dist 136=[.05051608857214775971,.69717407229445788172] 
dist 137=[.02452497851549039469,.68881106053404730416] 
dist 138=[-.01277855502250140730,.67200760206502824471] 
dist 139=[-.05000938158287748671,.66778705384517666766] 
dist 140=[-.07570967066371981606,.65317678522266100085] 
dist 141=[-.09809201997986315227,.65016838839759770825] 
dist 142=[-.12205140393998177647,.6462241573089917776 ] 
dist 143=[-.14542721316319311207,.64528819564536095157] 
dist 144=[-.16547531919191255686,.54880367504053823145] 
dist 145=[-.18709091907032669014,.54075447427028378893] 
dist 146=[-.21673655418785075727,.52279675586744001762] 
dist 147=[-.24670323812769637931,.51953004267501648025] 
dist 148=[-.26960300267439444967,.49795166725507319984] 
dist 149=[-.29189826673627165901,.49415220768151971342] 
dist 150=[-.3194470063928955873 ,.48735453663115437774] 
dist 151=[-.3485417018159487644 ,.48585745796655092589] 
dist 152=[-.37702064149333677082,.46492128554729382506] 
dist 153=[-.41074121171786590273,.46207438398276566406] 
dist 154=[-.46080192939311944069,.45614551010371808372] 
dist 155=[-.51072793825460888142,.45469646505866803411] 
dist 156=[-.5439096873571111549 ,.44892367044150806056] 
dist 157=[-.57144575013494281135,.4478514778144663261 ] 
dist 158=[-.59878955602627838724,.44572010341591823457] 
dist 159=[-.62418363299408644484,.4451937095433523961 ] 
dist 160=[-.64392096989248550319,.31249036541101039723] 
dist 161=[-.66345575540014526058,.30503884428672557721] 
dist 162=[-.6880396538294279857 ,.28783702104814434262] 
dist 163=[-.71190014255073394946,.28523369706312490318] 
dist 164=[-.72854136207357415688,.26284581233976355854] 
dist 165=[-.74321526809160235866,.25886534952626151254] 
dist 166=[-.75920669427519911518,.25359168034010708442] 
dist 167=[-.77497944122383238562,.25231246179949173461] 
dist 168=[-.78877865885214957297,.22400659592724948281] 
dist 169=[-.80388929502815911764,.22049842386755696481] 
dist 170=[-.82490761032173288819,.21313709681183178024] 
dist 171=[-.84560331231728127847,.21139427843796935554] 
dist 172=[-.85942352990269103403,.20401940155989765606] 
dist 173=[-.87096466205043077064,.20268528399941777763] 
dist 174=[-.88254423192858264855,.19988511492702084378] 
dist 175=[-.89337550608286310488,.19923268910698138243] 
dist 176=[-.90192353050423482442,.16786960801752639045] 
dist 177=[-.91050612902997216195,.16504476650425891463] 
dist 178=[-.92147571543939280294,.15854345226323223711] 
dist 179=[-.93220519420805163937,.15755728008691462356] 
dist 180=[-.93982739270214169554,.14917620545853169432] 
dist 181=[-.94669484682344939691,.14769465973835074344] 
dist 182=[-.95440542384184615965,.14570262638844112173] 
dist 183=[-.96214473685290007206,.14521415632130484583] 
dist 184=[-.96912715129165237069,.13498420455507665576] 
dist 185=[-.97695059981313153833,.13372411574374258162] 
dist 186=[-.98805402244413915835,.13104698048701713664] 
dist 187=[-.99900899846276106443,.13046420883385663796] 
dist 188=[-1.0062386734084728792 ,.12768841305185069044] 
dist 189=[-1.0121820388019871882 ,.12721225346415917761] 
dist 190=[-1.0179918419381444402 ,.12616075747149155855] 
dist 191=[-1.0233278910531459639 ,.12598505599488274281] 
dist 192=[-1.0273762626067761580 ,-.36493441987055490037] 
dist 193=[-1.0312897928713673952 ,-.36018167638881105329] 
dist 194=[-1.0360864782307878891 ,-.35324678944733896169] 
dist 195=[-1.0406795396928975596 ,-.3460518698552614302 ] 
dist 196=[-1.0437785823093838512 ,-.34025902209957282229] 
dist 197=[-1.0464016342282404333 ,-.33433711915546621071] 
dist 198=[-1.0490907553205318473 ,-.32662595162111562256] 
dist 199=[-1.0516429572576673659 ,-.31827778210582899427] 
dist 200=[-1.0537183341238790682 ,-.3098079758249297404 ] 
dist 201=[-1.0558589520623265372 ,-.2995567417131647465 ] 
dist 202=[-1.0586721005725417949 ,-.28408320176770579608] 
dist 203=[-1.0613705454514141591 ,-.26832316164049135534] 
dist 204=[-1.0630523521421300599 ,-.25692596904807572683] 
dist 205=[-1.0643248232546888403 ,-.24645091496865841597] 
dist 206=[-1.0653859533692525469 ,-.23437921471697310418] 
dist 207=[-1.0662399736831625069 ,-.22208607192651737334] 
dist 208=[-1.0666840138557300733 ,-.21072526973275436549] 
dist 209=[-1.0669161015171540967 ,-.19777811161123307406] 
dist 210=[-1.0669602616111976686 ,-.17913982539777346858] 
dist 211=[-1.0668390501313233774 ,-.15990734863211886247] 
dist 212=[-1.0667466426695067747 ,-.14458352815559547633] 
dist 213=[-1.0665507278218924688 ,-.12906399120837179055] 
dist 214=[-1.0664525715806683398 ,-.10904866777940590912] 
dist 215=[-1.0658678572600908102 ,-.08747471125419014547] 
dist 216=[-1.0657088462845358154 ,-.06572091917351852398] 
dist 217=[-1.0651907395604710153 ,-.03948833050242131430] 

8 phat 1 dirichlet min maxes function [2, 1, 2, 1, 0, 0, 0, 0, 1] 
dist 0=[3.6749303117277368259 ,3.6749303117277368259 ] 
dist 1=[3.6708131674594640319 ,3.6808826325956300168 ] 
dist 2=[3.6672187690964780762 ,3.6868415661234919401 ] 
dist 3=[3.6633573929337625621 ,3.6909851676962873902 ] 
dist 4=[3.6595818645130533647 ,3.6946258946660957963 ] 
dist 5=[3.6563308598705128797 ,3.6985733886876973230 ] 
dist 6=[3.6528146663102290205 ,3.7024550395380417754 ] 
dist 7=[3.6479784293888941656 ,3.7058324110432216539 ] 
dist 8=[3.6421885056856089420 ,3.7095152137376597713 ] 
dist 9=[3.6353011913301495994 ,3.7146185820907667568 ] 
dist 10=[3.6298359975505345238 ,3.7198009517182466796 ] 
dist 11=[3.6243209759469587350 ,3.7237997629051329833 ] 
dist 12=[3.6172343407392484547 ,3.7277301637000245572 ] 
dist 13=[3.6096078072018105092 ,3.7326389091954779377 ] 
dist 14=[3.6019332151305870331 ,3.7378505865400942522 ] 
dist 15=[3.5926888701490986684 ,3.7429927076801720598 ] 
dist 16=[3.5787834030740109268 ,3.7491119995024515998 ] 
dist 17=[3.5645176124040117530 ,3.7582323209857545614 ] 
dist 18=[3.5538319967924830232 ,3.7672802117059356099 ] 
dist 19=[3.5436352820525512213 ,3.7731097886072292308 ] 
dist 20=[3.5313250880045438690 ,3.7777449431936533712 ] 
dist 21=[3.5184744151828513389 ,3.7820152076349286989 ] 
dist 22=[3.5061158336967252810 ,3.7857654512008993037 ] 
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dist 32=[3.2519446491778646518 ,3.7978778605086369983 ] 
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dist 34=[3.1685913892647019409 ,3.7876237238597538715 ] 
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dist 36=[3.1103964213261369598 ,3.7842924275060206056 ] 
dist 37=[3.0821932978494664326 ,3.7836373454448489712 ] 
dist 38=[3.0590307415683584387 ,3.7808630144723140709 ] 
dist 39=[3.0349336329090184411 ,3.7802921060884806835 ] 
dist 40=[3.0029923733323937100 ,3.7786563209507504046 ] 
dist 41=[2.9712005714015111258 ,3.7784073102078405140 ] 
dist 42=[2.9477012871619074839 ,3.7749035422761362175 ] 
dist 43=[2.9255848974219567340 ,3.7742462141993744000 ] 
dist 44=[2.8993245815887932323 ,3.7727399681232306104 ] 
dist 45=[2.8721466088975948430 ,3.7722468898739298904 ] 
dist 46=[2.8463596636895285092 ,3.7699311586503717492 ] 
dist 47=[2.8164372132214072281 ,3.7694054636193976425 ] 
dist 48=[2.7727175272508679405 ,3.7682347143830360916 ] 
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dist 59=[2.4037572435598003884 ,3.5046138525077074419 ] 
dist 60=[2.3622227006722075638 ,3.4953101443413788751 ] 
dist 61=[2.3178728265445812805 ,3.4929450426119864850 ] 
dist 62=[2.2737480759759255593 ,3.4828345785310752526 ] 
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dist 64=[2.1419907526823464535 ,3.4763796564812502005 ] 
dist 65=[2.0626805052569535768 ,3.4757083458585432691 ] 
dist 66=[2.0085617287111148592 ,3.4253386867526012893 ] 
dist 67=[1.9620967183069822002 ,3.4205734084050975910 ] 
dist 68=[1.9134009595175987933 ,3.4094496167989507038 ] 
dist 69=[1.8665181539303159348 ,3.4076225793931933882 ] 
dist 70=[1.8273048207884888701 ,3.3924595800865355053 ] 
dist 71=[1.7858759033926300284 ,3.3896492324369183293 ] 
dist 72=[1.7301309301410220947 ,3.3857544155350855857 ] 
dist 73=[1.6742622123057058815 ,3.3845941853085733510 ] 
dist 74=[1.6323383269236337590 ,3.3624738579332421506 ] 
dist 75=[1.5922588437866224536 ,3.3595685971603364253 ] 
dist 76=[1.5437675966208805495 ,3.3534569635663863150 ] 
dist 77=[1.4930924211890509094 ,3.3517949422145468383 ] 
dist 78=[1.4442773915560148084 ,3.3452445079180919895 ] 
dist 79=[1.3870670077065960962 ,3.3439904867450820051 ] 
dist 80=[1.3028110533514381566 ,3.3409007485506575579 ] 
dist 81=[1.2178115209180669151 ,3.3403645159139397336 ] 
dist 82=[1.1576268814712948587 ,3.2575584008814495933 ] 
dist 83=[1.1036071455787630993 ,3.2515589190669802211 ] 
dist 84=[1.0432667595416423324 ,3.2373643503826704580 ] 
dist 85=[.98288098527341888952,3.2352750023168666661 ] 
dist 86=[.92867969990962071075,3.2154890633750177828 ] 
dist 87=[.86817736356369141476,3.2118469433415455483 ] 
dist 88=[.78258786354556601631,3.2075220895032537096 ] 
dist 89=[.69489845943837649811,3.2066133729374525909 ] 
dist 90=[.62599666590921547111,3.1760629390829739066 ] 
dist 91=[.55709700694611520814,3.1722024864574310786 ] 
dist 92=[.46941614037361310971,3.1645651517955236496 ] 
dist 93=[.37548492867060103168,3.1626209708427143170 ] 
dist 94=[.28158436290138651359,3.1558154888377267052 ] 
dist 95=[.16893299571254116044,3.1543283046246452389 ] 
dist 96=[0                     ,3.1521814693306481601 ] 
dist 97=[1.3356357147915862022 ,3.1515473967962088406 ] 
dist 98=[1.3105925833210440368 ,3.0928719159006518209 ] 
dist 99=[1.2831975235457734488 ,3.0877921897334079057 ] 
dist 100=[1.2561160879459054349 ,3.0766133556177465093 ] 
dist 101=[1.2323274232641194366 ,3.0742196204296987617 ] 
dist 102=[1.2061978787472029174 ,3.0609511972379117171 ] 
dist 103=[1.1697531470753059237 ,3.0585301030548633538 ] 
dist 104=[1.1326410781262591694 ,3.0536191736612371339 ] 
dist 105=[1.1038422481500544465 ,3.0523200681747581400 ] 
dist 106=[1.0753826044180144088 ,3.0392963720018702808 ] 
dist 107=[1.0396272480947126572 ,3.0373132005119394467 ] 
dist 108=[1.0015578468152134304 ,3.0331524492002794242 ] 
dist 109=[.9638422439674188679 ,3.0320100833766175948 ] 
dist 110=[.9188464235309932858 ,3.0274621681918469580 ] 
dist 111=[.8516568462697378973 ,3.0265776861927500850 ] 
dist 112=[.7845010186664312575 ,3.0239613546261519638 ] 
dist 113=[.7396401936428249841 ,3.0199378723360542594 ] 
dist 114=[.7021608190871245663 ,1.5342711965145976127 ] 
dist 115=[.6645300893272814422 ,1.4980398664947913482 ] 
dist 116=[.6293145730323001846 ,1.4135258752346015353 ] 
dist 117=[.6014958219777594078 ,1.4013720556748579987 ] 
dist 118=[.5735401090804303710 ,1.2887261604751343956 ] 
dist 119=[.5377767584774460024 ,1.2685984052392384038 ] 
dist 120=[.5027815919913916577 ,1.2442158106898208697 ] 
dist 121=[.4778985422938995724 ,1.2399290415926310566 ] 
dist 122=[.4554566404575582473 ,1.0862068452973455691 ] 
dist 123=[.4302258325842476467 ,1.0674479526555294627 ] 
dist 124=[.4048825321094243782 ,1.0297518568354158378 ] 
dist 125=[.3819906705963544289 ,1.0202808130046548883 ] 
dist 126=[.3563202370631826106 ,.98747953266187008163] 
dist 127=[.3198629135226606940 ,.98072568567879964257] 
dist 128=[.2836393133955127483 ,.97183738458608630598] 
dist 129=[.2589037512237594818 ,.96969583770672580587] 
dist 130=[.2376478198539695162 ,.7530866700131140744 ] 
dist 131=[.2153424110543646218 ,.73501207829661442435] 
dist 132=[.1938501078582442360 ,.69466079276286484882] 
dist 133=[.1758465213499865379 ,.68734782595864624632] 
dist 134=[.1568022330955870284 ,.65244372854184362908] 
dist 135=[.1311472221749755203 ,.65080597851802601585] 
dist 136=[.1054224125153603143 ,.62939753727858351827] 
dist 137=[.0860989359622118170 ,.62643391040829918997] 
dist 138=[.0676067982238881008 ,.62038474594768816014] 
dist 139=[.0452072645321185841 ,.61884090113283333822] 
dist 140=[.0217853954324504672 ,.61332174633283572306] 
dist 141=[-.0007959864291365766 ,.61222874708714934496] 
dist 142=[-.0272752257968889853 ,.61036699597659973239] 
dist 143=[-.0662881531512717782 ,.60995366442057552732] 
dist 144=[-.1052193492261695488 ,.52080879807641317905] 
dist 145=[-.1313716712713498048 ,.5195705848173713239 ] 
dist 146=[-.1533809809480058047 ,.4324439430735024986 ] 
dist 147=[-.1757405227011396815 ,.4295300374746222336 ] 
dist 148=[-.1968327300698138096 ,.4047293151662771163 ] 
dist 149=[-.2137728230844801561 ,.4003222515337848369 ] 
dist 150=[-.2310545296820093182 ,.3944075651188767728 ] 
dist 151=[-.2535131587997062034 ,.3929180572506661395 ] 
dist 152=[-.2756577691848285352 ,.3619133808491821542 ] 
dist 153=[-.2916834308025456972 ,.3580612607970407267 ] 
dist 154=[-.3064255723892508301 ,.3499203236160918369 ] 
dist 155=[-.3234362250699293718 ,.3480515280241817270 ] 
dist 156=[-.3407729046138035046 ,.3396879959990773194 ] 
dist 157=[-.3568191225574930183 ,.3382103011799838480 ] 
dist 158=[-.3751267856457572723 ,.3349701690300319295 ] 
dist 159=[-.4015090300757610853 ,.3343516209747648811 ] 
dist 160=[-.4278846617015442106 ,.3014429549856473252 ] 
dist 161=[-.4461658742036419127 ,.2984326025612134317 ] 
dist 162=[-.4621658063020236524 ,.2915763044749734713 ] 
dist 163=[-.4794165338969600329 ,.2904765309793453972 ] 
dist 164=[-.4963214119821391143 ,.2818466376036681611 ] 
dist 165=[-.5109379790279345009 ,.2803260524428534304 ] 
dist 166=[-.5267984428772419860 ,.2780783595178999175 ] 
dist 167=[-.5486787895360502787 ,.2774952943205168577 ] 
dist 168=[-.5708533953076836543 ,.26772379968153921078] 
dist 169=[-.5878908675424387452 ,.26650227506761975275] 
dist 170=[-.6045670799855702210 ,.26376698206337108612] 
dist 171=[-.6252966810469542137 ,.26330032333022120312] 
dist 172=[-.6472542073905560140 ,.26001157990482682655] 
dist 173=[-.6688420038454716788 ,.25944123626315158152] 
dist 174=[-.6944742503643995704 ,.2584805700546206712 ] 
dist 175=[-.7326091912123949928 ,.25827073151710865818] 
dist 176=[-.7706543455440920696 ,-.18799721734721980927] 
dist 177=[-.7959274557846857536 ,-.18836418193888803175] 
dist 178=[-.8168868053456994950 ,-.39975268336992325925] 
dist 179=[-.8376773320664669245 ,-.40843336491925256187] 
dist 180=[-.8569708185985451444 ,-.42821881073645496383] 
dist 181=[-.8719421538582555121 ,-.43134399076935338078] 
dist 182=[-.8867368614846717867 ,-.45624029274576816463] 
dist 183=[-.9053238616661765971 ,-.46061177612879925221] 
dist 184=[-.9233484657928719118 ,-.46696001835089289056] 
dist 185=[-.9358936465054832930 ,-.46863202586558277471] 
dist 186=[-.9469285532085548600 ,-.49663580256463132267] 
dist 187=[-.9589122090029334185 ,-.50011069054657602241] 
dist 188=[-.9707071492902792475 ,-.50784011447745247948] 
dist 189=[-.9809872192888100362 ,-.50916193256135923983] 
dist 190=[-.99221154339110763536,-.51824196934544279537] 
dist 191=[-1.0077834283453213036 ,-.51979395479775476756] 
dist 192=[-1.0230986644738080694 ,-.52249335188733121421] 
dist 193=[-1.0332964213995310032 ,-.52304915336490875725] 
dist 194=[-1.0417801183731838205 ,-.53970765321595974265] 
dist 195=[-1.0502392708066520241 ,-.54150429011481806215] 
dist 196=[-1.0581178953446789500 ,-.54483498269189115214] 
dist 197=[-1.0642795397223004222 ,-.54557592802249749822] 
dist 198=[-1.0704139552886072858 ,-.54750582884451851976] 
dist 199=[-1.0781836853966671062 ,-.54763801381608759651] 
dist 200=[-1.0857493787142176775 ,-.54714063858095009368] 
dist 201=[-1.0910676738438466533 ,-.54564996006887443951] 
dist 202=[-1.0958012210373005272 ,-.5437820428051163552 ] 
dist 203=[-1.1010279819571494332 ,-.54177576374888439741] 
dist 204=[-1.1062238284521671312 ,-.53926758456716968918] 
dist 205=[-1.1108337390677101900 ,-.53539210605028318421] 
dist 206=[-1.1159357599494687444 ,-.5308952533110797685 ] 
dist 207=[-1.1231000515139116580 ,-.52590169055053552544] 
dist 208=[-1.1301319544341392368 ,-.51954647178835546357] 
dist 209=[-1.1347044321428050691 ,-.50960329566332985298] 
dist 210=[-1.1383876906703999221 ,-.49944960861400499218] 
dist 211=[-1.1418627470678234804 ,-.49225237179247193865] 
dist 212=[-1.1449718370200717383 ,-.48578538638629215163] 
dist 213=[-1.1471912428305461043 ,-.47855248127816732145] 
dist 214=[-1.1492020338038499819 ,-.47131005848741899721] 
dist 215=[-1.1514766733935828669 ,-.46480496588872556853] 
dist 216=[-1.1535596084966730285 ,-.45754088652126022483] 
dist 217=[-1.1548035888778592608 ,-.44726263101232861996] 
dist 218=[-1.1556811074081662821 ,-.43673328419431855016] 
dist 219=[-1.1562982081829939316 ,-.42846486499302628956] 
dist 220=[-1.1567498327677617249 ,-.42020228564324069826] 
dist 221=[-1.1569654561637960529 ,-.40969626006949116746] 
dist 222=[-1.1570511609696222711 ,-.39844711323936872645] 
dist 223=[-1.1570350637646754649 ,-.38721216147196495836] 
dist 224=[-1.1551791683133977329 ,-.37374256911136516091] 
dist 225=[-1.1546269257513298679 ,-.35355523583415655941] 
dist 226=[-1.1337875808613646778 ,-.33305050485160995596] 
dist 227=[-1.1326506036111859344 ,-.31831136614793203806] 
dist 228=[-1.1306092526002385961 ,-.30485489730815564182] 
dist 229=[-1.1301114987804958630 ,-.28948060326708959735] 
dist 230=[-1.1285881687866028876 ,-.27389834918373606219] 
dist 231=[-1.1282292703037989193 ,-.25961006088552311892] 
dist 232=[-1.1280215922057073138 ,-.24341532614811277593] 
dist 233=[-1.1269477328154427385 ,-.2202075909442331859 ] 
dist 234=[-1.0994278470255966115 ,-.19630431011465788927] 
dist 235=[-1.0967710070223070403 ,-.17732750032590996601] 
dist 236=[-1.0938513681755429530 ,-.15817103734507017169] 
dist 237=[-1.0902670698684576928 ,-.13354916140805880191] 
dist 238=[-1.0708483276021523703 ,-.10705129457953875149] 
dist 239=[-1.0594757127051096508 ,-.08039116939061073729] 
dist 240=[-1.0127639715615356066 ,-.04828423147672449973] 

8 phat 1 dirichlet min maxes function [1, 0, 2, 2, 0, 1, 0, 0, 2] 
dist 0=[3.9318533079063155418 ,3.9318533079063155418 ] 
dist 1=[3.9297389086406398579 ,3.9326620106698777290 ] 
dist 2=[3.9271425810021012516 ,3.9337823361120497038 ] 
dist 3=[3.9244192091156537276 ,3.9353566025854230501 ] 
dist 4=[3.9210582555947796754 ,3.9371853086564448872 ] 
dist 5=[3.9159116582806876270 ,3.9388856348528577222 ] 
dist 6=[3.9105399687929091504 ,3.9399463901278229156 ] 
dist 7=[3.9062786667296985760 ,3.9407501391281715411 ] 
dist 8=[3.9019797705400168778 ,3.9414224608010762430 ] 
dist 9=[3.8964577081320074037 ,3.9419651088207496285 ] 
dist 10=[3.8905161314468923917 ,3.9422501676936153296 ] 
dist 11=[3.8845392181612313351 ,3.9424032343084137676 ] 
dist 12=[3.8773415562291224387 ,3.9424179061761790573 ] 
dist 13=[3.8665171013908097719 ,3.9423472572001722494 ] 
dist 14=[3.8551482674971273600 ,3.9422375289176592452 ] 
dist 15=[3.8457731412653380939 ,3.9419191603271555394 ] 
dist 16=[3.8359858861179282830 ,3.9417434753333385548 ] 
dist 17=[3.8229685758698052992 ,3.9406584175580247517 ] 
dist 18=[3.8087389406290826313 ,3.9403566800122146793 ] 
dist 19=[3.7941025011404363295 ,3.9396470982411871053 ] 
dist 20=[3.7762417937243942587 ,3.9393718318359435127 ] 
dist 21=[3.7491153942983922886 ,3.9352266333362942626 ] 
dist 22=[3.7217144875225444086 ,3.9345443787898535793 ] 
dist 23=[3.7027557768890873014 ,3.9329425502779167518 ] 
dist 24=[3.6861979430408340617 ,3.9324373497051389764 ] 
dist 25=[3.6684003144149180055 ,3.9298940682544348448 ] 
dist 26=[3.6509921432063658182 ,3.9293173601957588719 ] 
dist 27=[3.6359921018818891545 ,3.9281287704929691321 ] 
dist 28=[3.6197593702994486043 ,3.9265988898345455302 ] 
dist 29=[3.5974205556306018852 ,3.8673521517540761404 ] 
dist 30=[3.5748058687787137210 ,3.8631780663582821401 ] 
dist 31=[3.5574696747762510880 ,3.8535160763488640743 ] 
dist 32=[3.5405386860408368860 ,3.8517878270369796321 ] 
dist 33=[3.5195447816094647603 ,3.8387544480433644163 ] 
dist 34=[3.4973344609399112144 ,3.8363119820417784555 ] 
dist 35=[3.4755379232711484962 ,3.8325402837496558180 ] 
dist 36=[3.4496875117066132036 ,3.8315315445874879939 ] 
dist 37=[3.4112620821044510977 ,3.8126745215591855573 ] 
dist 38=[3.3723536092282915757 ,3.8101459982043705270 ] 
dist 39=[3.3445710706394796014 ,3.8045824979914431791 ] 
dist 40=[3.3193935064786186342 ,3.8032214152082018170 ] 
dist 41=[3.2909046828569496242 ,3.7963959283271185305 ] 
dist 42=[3.2621842973124716564 ,3.7950790444866764322 ] 
dist 43=[3.2360805075462934904 ,3.7922399416033503090 ] 
dist 44=[3.2066771680112240922 ,3.7914097138101715775 ] 
dist 45=[3.1647588980957182533 ,3.7598678791451829174 ] 
dist 46=[3.1216731261005064832 ,3.7566982154678053117 ] 
dist 47=[3.0875998896006547440 ,3.7491581691821291079 ] 
dist 48=[3.0533242533901626253 ,3.7479314190634083937 ] 
dist 49=[3.0094289018568737989 ,3.7371055595572967927 ] 
dist 50=[2.9622653895396989629 ,3.7350473965161022427 ] 
dist 51=[2.9149174219043804987 ,3.7323820909076604243 ] 
dist 52=[2.8579689301519024916 ,3.7315041906069767471 ] 
dist 53=[2.7724042370451091739 ,3.7136130289619807617 ] 
dist 54=[2.6867596237513913096 ,3.7112284611226916222 ] 
dist 55=[2.6294914588738446229 ,3.7063912620779236031 ] 
dist 56=[2.5815840956651043417 ,3.7050977129442711668 ] 
dist 57=[2.5333817962318458441 ,3.7001882326259692244 ] 
dist 58=[2.4882080875656271395 ,3.6991616848809752434 ] 
dist 59=[2.4524147985640431574 ,3.6969725805714648700 ] 
dist 60=[2.4163450359173087688 ,3.6963244041443159976 ] 
dist 61=[2.3700654590399984021 ,3.5182112740056814306 ] 
dist 62=[2.3247145759469668630 ,3.5159177172774056150 ] 
dist 63=[2.2923594998603697374 ,3.5152955268440227365 ] 
dist 64=[2.2630665358953175560 ,3.4573524621979000303 ] 
dist 65=[2.2299638092302623656 ,3.4522906285278127124 ] 
dist 66=[2.1966163589799935082 ,3.4411271874539184151 ] 
dist 67=[2.1663445240153386438 ,3.4387332420659738427 ] 
dist 68=[2.1322765228775315147 ,3.4253785806157672310 ] 
dist 69=[2.0837447700054819823 ,3.4229301250408415286 ] 
dist 70=[2.0354610498269528582 ,3.4179927514992036075 ] 
dist 71=[2.0023851558063591670 ,3.4166881670486364980 ] 
dist 72=[1.9738494077573943300 ,3.4031060588426888995 ] 
dist 73=[1.9437258384352291639 ,3.4010586472207342863 ] 
dist 74=[1.9145904994248221942 ,3.3966433636963168967 ] 
dist 75=[1.8900075783674357482 ,3.3954621851335075964 ] 
dist 76=[1.8638487310054129586 ,3.3902900690604552619 ] 
dist 77=[1.8284098370851975264 ,3.3892858046651410167 ] 
dist 78=[1.7927833921010740719 ,3.3868919629271358607 ] 
dist 79=[1.7658743583716690695 ,3.3863533148774993570 ] 
dist 80=[1.7399786871947195744 ,3.1587237760302184106 ] 
dist 81=[1.7084055957679002981 ,3.1470766753404195059 ] 
dist 82=[1.6752820679926628893 ,3.1207000022765902608 ] 
dist 83=[1.6431847992995961202 ,3.1160157804794239986 ] 
dist 84=[1.6054235983824914516 ,3.0828327501987795370 ] 
dist 85=[1.5496448819257660626 ,3.0768593349536076795 ] 
dist 86=[1.4939243798490349495 ,3.0669166976448776963 ] 
dist 87=[1.4563960308995348521 ,3.0645967879964472960 ] 
dist 88=[1.4247062295527223935 ,3.0259789131405448620 ] 
dist 89=[1.3923393610176084436 ,3.0209543454785197670 ] 
dist 90=[1.3616974331774688670 ,3.0090652461869820640 ] 
dist 91=[1.3369072300891188943 ,3.0072847547987582279 ] 
dist 92=[1.3114524788915210864 ,2.9906664661596994074 ] 
dist 93=[1.2781524219976756853 ,2.9875939893097336769 ] 
dist 94=[1.2452138656714963961 ,2.9838795699308852867 ] 
dist 95=[1.2212050822653532155 ,2.9830163988233273880 ] 
dist 96=[1.1989451762786956639 ,2.9537752600339600465 ] 
dist 97=[1.1730019628259863971 ,2.9502204843472623600 ] 
dist 98=[1.1464174484997092218 ,2.9429092916551606967 ] 
dist 99=[1.1215924001847901498 ,2.9409762759448876074 ] 
dist 100=[1.0930948776538983926 ,2.9336974566849585042 ] 
dist 101=[1.0518208167370643994 ,2.9322470189662901762 ] 
dist 102=[1.0104699063503863910 ,2.9291934876979206631 ] 
dist 103=[.9816649932698691540 ,2.9269549835453213569 ] 
dist 104=[.9563020426438463573 ,2.8813669420956200730 ] 
dist 105=[.9287186537875685083 ,2.8766236925135131394 ] 
dist 106=[.9015462006181187612 ,2.8697410798906783284 ] 
dist 107=[.8717584126253348844 ,2.8581616091694964411 ] 
dist 108=[.8364472610494517745 ,2.8302286894068530861 ] 
dist 109=[.8024693177292890069 ,2.7416896922659644752 ] 
dist 110=[.7626765733081210591 ,2.7319229118536507028 ] 
dist 111=[.7041067719324562152 ,2.7010611979713129212 ] 
dist 112=[.6456835374167981214 ,2.1501805923565688257 ] 
dist 113=[.6064770464563996827 ,2.1239638932866329520 ] 
dist 114=[.5735249872820725292 ,2.0660286404966637449 ] 
dist 115=[.5401188833753545587 ,2.0548174983383598032 ] 
dist 116=[.5086508361577026679 ,1.9866285644531020100 ] 
dist 117=[.4834508188916224241 ,1.9745870965233583280 ] 
dist 118=[.44120337283863385048,1.9516688653086625349 ] 
dist 119=[.39790619335470569089,1.9461941210581744202 ] 
dist 120=[.36179930459919990545,1.7645449858025123988 ] 
dist 121=[.32565453232538299662,1.7447085689799933296 ] 
dist 122=[.29189887478235764613,1.7117580572826882434 ] 
dist 123=[.18032398329476559928,1.6733767419300124777 ] 
dist 124=[0                     ,1.5760923414107907352 ] 
dist 125=[.20492147483620710715,.62388129042218046736] 
dist 126=[.17186614237926588472,.55944643104323304096] 
dist 127=[.14847798774159392214,.55157689828402326486] 
dist 128=[.12750353772920504178,.53567552291428470382] 
dist 129=[.1041027935590184621 ,.53166288479493862218] 
dist 130=[.08070103394495167456,.51763060837223531086] 
dist 131=[.05972252225389299461,.51478469347117409544] 
dist 132=[.03632726009015652546,.51070885968611133347] 
dist 133=[.00325872909026317534,.50960391739961912549] 
dist 134=[-.02953068805713800190,.42211686214069302257] 
dist 135=[-.05180952143223350141,.41475428730525111646] 
dist 136=[-.07083439588127421642,.39823472744909329537] 
dist 137=[-.09060828768062881000,.39532743062332426196] 
dist 138=[-.10954448793564947511,.37521518927660504794] 
dist 139=[-.125218676104718698  ,.37167305979526049291] 
dist 140=[-.14163414804604158053,.36559322667482575553] 
dist 141=[-.1705957900900142177 ,.36426464127110728978] 
dist 142=[-.2062592577945329212 ,.34380897753738753257] 
dist 143=[-.2592579902059295970 ,.34111268137078595767] 
dist 144=[-.3121274090384951116 ,.335261150847572536  ] 
dist 145=[-.3472736347613627951 ,.33407093925382438355] 
dist 146=[-.3764490069834374880 ,.32755889230160291974] 
dist 147=[-.4054355813010395572 ,.32643356523181173101] 
dist 148=[-.4323649416704272848 ,.32409667362146683533] 
dist 149=[-.4533116543126459435 ,.32353974227870203123] 
dist 150=[-.4740585596573068223 ,.21687064080253705912] 
dist 151=[-.5001887098936886521 ,.21067045506949154486] 
dist 152=[-.5255600435092668820 ,.19626142054120109535] 
dist 153=[-.5432717547451432338 ,.1941759742056336259 ] 
dist 154=[-.5589071852814130008 ,.17516078285261426091] 
dist 155=[-.5759735941301152952 ,.17177873074189208057] 
dist 156=[-.5928225762182866372 ,.16760546883008012452] 
dist 157=[-.6075883204501673787 ,.16683732220206111355] 
dist 158=[-.62377816878675784765,.14163494088598523555] 
dist 159=[-.64632343146553261689,.13856599873357521187] 
dist 160=[-.66853348887717764454,.13234234681068826825] 
dist 161=[-.68338254811646516075,.13077107570515662783] 
dist 162=[-.69580204730268444485,.12526047049591066159] 
dist 163=[-.70829409622869360133,.12415611771662307396] 
dist 164=[-.71999875530276720887,.1225324350072093458 ] 
dist 165=[-.72926877018093249371,.12211025609308032593] 
dist 166=[-.73860655104763749251,.08958362903673247308] 
dist 167=[-.75058226761248387358,.08685310782077513965] 
dist 168=[-.76231517903594983901,.08069388246967086185] 
dist 169=[-.77068176249540777752,.07966035361210308717] 
dist 170=[-.77825228033134897807,.07209366533465872289] 
dist 171=[-.78680100518791413914,.07076795421148298868] 
dist 172=[-.79540928336287706179,.06863821592696686817] 
dist 173=[-.80321800879233147652,.06813968613329428381] 
dist 174=[-.81200143140064851039,.06026008904774725143] 
dist 175=[-.8245084053263709876 ,.05925623360666335971] 
dist 176=[-.83686569064283634178,.05702337582461112714] 
dist 177=[-.84505037440756620494,.05663874704879553175] 
dist 178=[-.85181137313134363679,.05400899012777165465] 
dist 179=[-.85847405802138903647,.05355707510649492990] 
dist 180=[-.86462851355554824433,.05277043021940006643] 
dist 181=[-.8693566472780607921 ,.05260728822827385077] 
dist 182=[-.87398404008015336195,-.25519503447896371561] 
dist 183=[-.87973554943651678367,-.25160572405743452271] 
dist 184=[-.88528274610496598237,-.24776044341318037992] 
dist 185=[-.88909291158693301916,-.24447561044579927348] 
dist 186=[-.89239099708088609983,-.24094593053923563476] 
dist 187=[-.89588992657624935365,-.23612124502005471523] 
dist 188=[-.89928473308160057834,-.23078535900697559406] 
dist 189=[-.90216634442912505246,-.22521097079347044949] 
dist 190=[-.90524775586079969212,-.21834829637048688148] 
dist 191=[-.90944176335501415925,-.20785956359253135916] 
dist 192=[-.91353162648040519495,-.19712587678970562725] 
dist 193=[-.91619647429559102766,-.18928342491880144909] 
dist 194=[-.91834915821274650546,-.18199459043644093247] 
dist 195=[-.92039040666299598569,-.1734751910488072783 ] 
dist 196=[-.92222369142387685946,-.16473309624571276065] 
dist 197=[-.92354454431049509274,-.15655350228441852406] 
dist 198=[-.92475378865934904835,-.14715231560060388865] 
dist 199=[-.9261406695211311238 ,-.13352409858442567195] 
dist 200=[-.92742116120345877981,-.11942181796493284764] 
dist 201=[-.92820486680017563532,-.10812446632854410824] 
dist 202=[-.92878110322275848277,-.09662696389835118241] 
dist 203=[-.92923174184394413765,-.08172409975968569368] 
dist 204=[-.92957162570001401419,-.06562397644958328020] 
dist 205=[-.92970487318379613739,-.04933768328775517422] 
dist 206=[-.92972371264704425979,-.02966099314874298763] 

8 phat 1 dirichlet min maxes function [1, 0, 2, 0, 1, 2, 2, 0, 1] 
dist 0=[3.8998850008689875163 ,3.8998850008689875163 ] 
dist 1=[3.8992804354854345021 ,3.9007517916379418763 ] 
dist 2=[3.8983287242427907691 ,3.9018598257499160999 ] 
dist 3=[3.8960733739570655250 ,3.9034293218060344018 ] 
dist 4=[3.8931285166585562138 ,3.9051913116845960426 ] 
dist 5=[3.8894188510091207065 ,3.9070692948602679460 ] 
dist 6=[3.8844067539752045044 ,3.9094076827188310120 ] 
dist 7=[3.8762523071823309732 ,3.9130112277481214819 ] 
dist 8=[3.8675506013852144042 ,3.9165941250962631752 ] 
dist 9=[3.8603495218445440225 ,3.9188499255133016924 ] 
dist 10=[3.8528093642215736794 ,3.9205833946190046685 ] 
dist 11=[3.8427513705566461026 ,3.9220770401500975464 ] 
dist 12=[3.8317424444929856287 ,3.9233163308815399573 ] 
dist 13=[3.8203986440328728105 ,3.9240324168551585511 ] 
dist 14=[3.8065415582396451213 ,3.9245079500699699128 ] 
dist 15=[3.7854797266146959206 ,3.9247850645185488936 ] 
dist 16=[3.7641730681014117009 ,3.9249107719354284840 ] 
dist 17=[3.7493366967922132394 ,3.9248961716438404181 ] 
dist 18=[3.7362792403359069294 ,3.9245946868582191086 ] 
dist 19=[3.7220880715648077771 ,3.9244967225957357641 ] 
dist 20=[3.7081139053997456719 ,3.9229518154099131644 ] 
dist 21=[3.6959244386703077844 ,3.9225378012802281540 ] 
dist 22=[3.6826069614216641165 ,3.9221724010938488197 ] 
dist 23=[3.6641208607671932671 ,3.9219370619862747503 ] 
dist 24=[3.6453353730123338233 ,3.9128876568884679184 ] 
dist 25=[3.6308203759170858254 ,3.9117205093710545040 ] 
dist 26=[3.6165353708119045458 ,3.9073622683993828945 ] 
dist 27=[3.5986698290811304257 ,3.8531267478561106796 ] 
dist 28=[3.5796898372352018089 ,3.8421498427176372666 ] 
dist 29=[3.5609471379634523768 ,3.8400803939325679269 ] 
dist 30=[3.5386316278162837885 ,3.8364773315838666434 ] 
dist 31=[3.5053607332363199809 ,3.8356303499275384817 ] 
dist 32=[3.4716309272191467817 ,3.8204154534086496281 ] 
dist 33=[3.4474798150932066999 ,3.8183337309053713372 ] 
dist 34=[3.4255249983772132643 ,3.8134744526850685164 ] 
dist 35=[3.4005801645215103220 ,3.8125030049935823837 ] 
dist 36=[3.3753741405957484475 ,3.8056482682127966997 ] 
dist 37=[3.3523745885113120548 ,3.8043049877986514059 ] 
dist 38=[3.3263952953633400390 ,3.8020838233702394815 ] 
dist 39=[3.2892705913852503540 ,3.8015046916987109476 ] 
dist 40=[3.2510740082194030219 ,3.7786563209507504044 ] 
dist 41=[3.2208073005541193164 ,3.7761833364620817399 ] 
dist 42=[3.1903052075479419348 ,3.7701885020305934977 ] 
dist 43=[3.1511671054691085920 ,3.7692493610753623186 ] 
dist 44=[3.1090771114475174985 ,3.7602510663730746563 ] 
dist 45=[3.0667677322159296855 ,3.7585134602304269187 ] 
dist 46=[3.0158394701982118874 ,3.7564555868849154071 ] 
dist 47=[2.9392747670841101096 ,3.7558622492283439672 ] 
dist 48=[2.8626204327069999628 ,3.7394855259310155620 ] 
dist 49=[2.8113336541861014435 ,3.7373169799042455628 ] 
dist 50=[2.7683969074057562027 ,3.7330624251170216133 ] 
dist 51=[2.7251419035813313928 ,3.7319519509588153203 ] 
dist 52=[2.6845701116074976896 ,3.7279412242819456204 ] 
dist 53=[2.6523659563100725854 ,3.7270307068556752233 ] 
dist 54=[2.6198601252510551579 ,3.7254222432103021672 ] 
dist 55=[2.5780816590040901924 ,3.7244368676757592192 ] 
dist 56=[2.5371072461306587992 ,3.5473888274717278208 ] 
dist 57=[2.5078175518767537006 ,3.5443442739000567810 ] 
dist 58=[2.4812413100672462859 ,3.5438817292333802108 ] 
dist 59=[2.4511204481676732560 ,3.4604184410102376423 ] 
dist 60=[2.4207266175319872631 ,3.4544407757660692137 ] 
dist 61=[2.3930585268132466627 ,3.4402123088448736454 ] 
dist 62=[2.3618582076153796277 ,3.4381774394115738506 ] 
dist 63=[2.3173357999601605635 ,3.4180862929707475168 ] 
dist 64=[2.2730087371019931157 ,3.4143788330419174933 ] 
dist 65=[2.2425897784607318042 ,3.4101857484974654977 ] 
dist 66=[2.2162889895335251113 ,3.4094608137878468013 ] 
dist 67=[2.1884342127486863019 ,3.3773977653639993619 ] 
dist 68=[2.1614379733544064150 ,3.3733754905893206275 ] 
dist 69=[2.1385712521038355692 ,3.3655597959774169154 ] 
dist 70=[2.1141615638906977383 ,3.3636042626196991676 ] 
dist 71=[2.0809936038112899031 ,3.3570065390297861503 ] 
dist 72=[2.0476052971763579745 ,3.3554923930821016055 ] 
dist 73=[2.0223142437573428320 ,3.3539105412023916417 ] 
dist 74=[1.9979052227134132179 ,3.3536075411737699407 ] 
dist 75=[1.9680449614523183609 ,3.2882472945108074501 ] 
dist 76=[1.9366656484794361940 ,3.2827277106642790308 ] 
dist 77=[1.9061805654725079702 ,3.2707144761780085144 ] 
dist 78=[1.8702570193620666691 ,3.2680280168258649397 ] 
dist 79=[1.8171243726849966214 ,3.2541857275415574816 ] 
dist 80=[1.7640193187373414858 ,3.2516704978554991990 ] 
dist 81=[1.7282061409128198245 ,3.2462689709440913936 ] 
dist 82=[1.6979141912216069441 ,3.2448713592194372216 ] 
dist 83=[1.6668935232033575069 ,3.2327813115310706675 ] 
dist 84=[1.6374746192991699694 ,3.2308095742019223395 ] 
dist 85=[1.6135895732911085705 ,3.2270687698524524860 ] 
dist 86=[1.5889878276410146946 ,3.2261282644976226142 ] 
dist 87=[1.5567021935260929095 ,3.2229771523607749542 ] 
dist 88=[1.5247193553819346680 ,3.2221954045595844653 ] 
dist 89=[1.5013287647348135986 ,3.2214086629369099904 ] 
dist 90=[1.4795631172443633244 ,3.2211786361556973953 ] 
dist 91=[1.4540798967430208627 ,3.0360414768595249998 ] 
dist 92=[1.4279025781205060685 ,3.0258575253890517336 ] 
dist 93=[1.4033606043470737265 ,3.0029034560747468195 ] 
dist 94=[1.3751117240556757127 ,2.9987122606419882798 ] 
dist 95=[1.3341071329187170799 ,2.9701307490253504049 ] 
dist 96=[1.2929883352253226293 ,2.9649840190680919901 ] 
dist 97=[1.2642826396009770255 ,2.9560354293844347521 ] 
dist 98=[1.2389412852882291123 ,2.9540487418874796300 ] 
dist 99=[1.2112795319569990510 ,2.9217557419272912003 ] 
dist 100=[1.1839695293663588861 ,2.9174837302574090978 ] 
dist 101=[1.1600351444666799801 ,2.9074455569722386392 ] 
dist 102=[1.1337915027339200429 ,2.9058578419650441638 ] 
dist 103=[1.0972446930633094086 ,2.8919905169687017374 ] 
dist 104=[1.0600538285470681585 ,2.8894188862197046156 ] 
dist 105=[1.0312340288604642846 ,2.8860594402432149159 ] 
dist 106=[1.0027916286075832783 ,2.8850594247119948734 ] 
dist 107=[.9671103258306212510 ,2.6947369935650267604 ] 
dist 108=[.9291466433173778365 ,2.6825094073993511580 ] 
dist 109=[.89157494180824055394,2.6576760481419722977 ] 
dist 110=[.84677979008011986587,2.6513244161215305092 ] 
dist 111=[.77992299564935120068,2.6286106167607430058 ] 
dist 112=[.71311310730093207464,2.6240299912945898816 ] 
dist 113=[.653016347299875584  ,2.6161582646825545003 ] 
dist 114=[.5811747663001063798 ,2.6072912753776610002 ] 
dist 115=[.4897290911874220034 ,2.4723030707640418227 ] 
dist 116=[.39175402320058353924,2.4587063097599864427 ] 
dist 117=[.29379536197333480837,2.4392652134893093154 ] 
dist 118=[.1762640796127702851 ,2.4068396308072683181 ] 
dist 119=[0                     ,2.3301290805696807157 ] 
dist 120=[.43392892270529021109,.79747831720401744995] 
dist 121=[.40941768930499351188,.78885822043107781497] 
dist 122=[.38735506764006080007,.77161929119020541392] 
dist 123=[.36261711175496245526,.76730752961991383217] 
dist 124=[.33780694260435911729,.7525163958930396236 ] 
dist 125=[.3154554747649650041 ,.74943206563261974011] 
dist 126=[.2854135366498037475 ,.7457164870438332961 ] 
dist 127=[.2546554635793286746 ,.745076997966494046  ] 
dist 128=[.21974936016305000807,.64275946223989634448] 
dist 129=[.19574119912095757608,.63429705557983700337] 
dist 130=[.1730255775804538219 ,.61550251655706113863] 
dist 131=[.1413877556039207064 ,.61199946518465191286] 
dist 132=[.1186385270520196867 ,.58965924623977610712] 
dist 133=[.0978597735621776534 ,.58572833318200604876] 
dist 134=[.0741036638938627169 ,.5785065970410742897 ] 
dist 135=[.0500151474797557636 ,.57686135405074893101] 
dist 136=[.0279067987110442433 ,.55607769321149165095] 
dist 137=[.0028309131613666882 ,.55317590164279620625] 
dist 138=[-.0331274673388100778 ,.54735609770833372725] 
dist 139=[-.0690024512386540089 ,.545897973240502323  ] 
dist 140=[-.0937447583412031726 ,.54087515511582346512] 
dist 141=[-.1152693786320438825 ,.53983631087267182949] 
dist 142=[-.1382739221816639605 ,.53853730661390740122] 
dist 143=[-.1606960680168082646 ,.5382821788142175193 ] 
dist 144=[-.1798911529976890684 ,.38612717377881442774] 
dist 145=[-.2005570093812689036 ,.37788134890975698221] 
dist 146=[-.2288621005479391830 ,.35890319855941839057] 
dist 147=[-.2574566990710502473 ,.35599076827585248002] 
dist 148=[-.2792805572677536310 ,.33147619481535468212] 
dist 149=[-.3005020280705160188 ,.32712701079937851318] 
dist 150=[-.3266871344723824187 ,.32121216731010355543] 
dist 151=[-.3543224704210638135 ,.31967570062374848128] 
dist 152=[-.3813447210910576546 ,.28952224993028741094] 
dist 153=[-.4133193562084875360 ,.28577085416850849291] 
dist 154=[-.4607637575982703913 ,.27778136255143710695] 
dist 155=[-.5080760015273327883 ,.27601678522631198976] 
dist 156=[-.5395220207205338270 ,.26759720938371818172] 
dist 157=[-.5656192526760371644 ,.26614876339714328154] 
dist 158=[-.5915368617520843738 ,.26283246452225074979] 
dist 159=[-.6156081168245241727 ,.26233774342733761273] 
dist 160=[-.6343201128074583816 ,.23231444186842046411] 
dist 161=[-.6528427342092855086 ,.22951673597082029688] 
dist 162=[-.6761565168986789584 ,.22325832923589767032] 
dist 163=[-.6987860586232389304 ,.2221672169886250262 ] 
dist 164=[-.7145717853637778363 ,.21463852440870875256] 
dist 165=[-.7284945097744388885 ,.21332513246888143488] 
dist 166=[-.7436722237986784422 ,.21106171822185365193] 
dist 167=[-.7586452986817852115 ,.21057608159548034227] 
dist 168=[-.7717494939123873003 ,.20333062454028570834] 
dist 169=[-.7861029109689921227 ,.20237245076739378762] 
dist 170=[-.8060727736761474464 ,.20038171478647566088] 
dist 171=[-.82573823316391781472,.1999196468444685481 ] 
dist 172=[-.83887407029402353635,.1980337335812702069 ] 
dist 173=[-.8498476406919200212 ,.19769047772948927105] 
dist 174=[-.86086423156766210143,.19705906921155107317] 
dist 175=[-.87117307560474607112,.19692175719335110631] 
dist 176=[-.87931573003528853101,-.40970595441954977376] 
dist 177=[-.88749776761153774701,-.41167170654427338095] 
dist 178=[-.89796416004187480197,-.41213449384131407616] 
dist 179=[-.90820570013665633815,-.41348163389899669047] 
dist 180=[-.91548835761909812602,-.41343564530962795504] 
dist 181=[-.92205722118822625687,-.41285527290452723256] 
dist 182=[-.92944365754950343627,-.41138889831930489851] 
dist 183=[-.93686401486273387541,-.4094505181220542204 ] 
dist 184=[-.94356857852230987405,-.406982226333015476  ] 
dist 185=[-.9510887803621202991 ,-.40363281683300454645] 
dist 186=[-.96177166731387709759,-.39817023321800862371] 
dist 187=[-.972308522923588677  ,-.39250938717877450942] 
dist 188=[-.97924461200966354401,-.38836695286292859051] 
dist 189=[-.98492703196042947777,-.38451097338838468424] 
dist 190=[-.9904492719488255455 ,-.37999575391884629264] 
dist 191=[-.99549981228530360702,-.37535837474023410626] 
dist 192=[-.99929545515996600073,-.37101372794496837462] 
dist 193=[-1.0029297758706453274 ,-.36601600476291466842] 
dist 194=[-1.0073350312190744408 ,-.35876642739872584776] 
dist 195=[-1.0115286207795445483 ,-.35126299649945242029] 
dist 196=[-1.0143162867877147469 ,-.34524988495061500779] 
dist 197=[-1.0166303198421564854 ,-.33912841804858230897] 
dist 198=[-1.0189293992654652445 ,-.33119153568310165105] 
dist 199=[-1.0210653921959182613 ,-.32261589668522004527] 
dist 200=[-1.0227270830836257484 ,-.31393950899610544481] 
dist 201=[-1.0243731664699124004 ,-.30345573546422094574] 
dist 202=[-1.0264467191308674215 ,-.28765090031939367093] 
dist 203=[-1.0283963092118672645 ,-.27156133278953899197] 
dist 204=[-1.0295465553216228499 ,-.25993867213170675992] 
dist 205=[-1.0303405864081029148 ,-.24926941222788838943] 
dist 206=[-1.0308653657832891125 ,-.23699322771002511134] 
dist 207=[-1.0312405153991285265 ,-.22450266288903479294] 
dist 208=[-1.0314360326643022042 ,-.21297590316060417246] 
dist 209=[-1.0315389017548771713 ,-.19985270870619119196] 
dist 210=[-1.0315434249320874688 ,-.18097668913868874338] 
dist 211=[-1.0292622549022690634 ,-.16150562424759364898] 
dist 212=[-1.0288899160572413799 ,-.1460023494076768091 ] 
dist 213=[-1.0283507586923710055 ,-.13031087785640631813] 
dist 214=[-1.0281604508888016217 ,-.11008704463462208976] 
dist 215=[-1.0277078952728740057 ,-.08829497814011501358] 
dist 216=[-1.0275294244071216681 ,-.06633085456439731260] 
dist 217=[-1.0273158428613677902 ,-.03985163318350435486] 

8 phat 1 dirichlet min maxes function [2, 0, 1, 2, 0, 1, 0, 0, 1] 
dist 0=[3.9498940926494692882 ,3.9498940926494692882 ] 
dist 1=[3.9483164320468241605 ,3.9509004667358320652 ] 
dist 2=[3.9464760249466849658 ,3.9516890597745215542 ] 
dist 3=[3.9444187016042450655 ,3.9523956286338908680 ] 
dist 4=[3.9417911034826533442 ,3.9529417575006347968 ] 
dist 5=[3.9376696750009941799 ,3.9530886136555721140 ] 
dist 6=[3.9333378354733305829 ,3.9530860606353447492 ] 
dist 7=[3.9298686145352472386 ,3.9530345579871648633 ] 
dist 8=[3.9263385420738576866 ,3.9518981383818922172 ] 
dist 9=[3.9217632828100841133 ,3.9515553173683676573 ] 
dist 10=[3.9168200710316878740 ,3.9512810390235949592 ] 
dist 11=[3.9118182158286110343 ,3.9510657938576648169 ] 
dist 12=[3.9057734911866070784 ,3.9447478304021023408 ] 
dist 13=[3.8966588972338868378 ,3.9438335142295552565 ] 
dist 14=[3.8870761794685156575 ,3.9419799356522690536 ] 
dist 15=[3.8791590003324822331 ,3.9414388895354897308 ] 
dist 16=[3.8708805229765189738 ,3.9391652508788283153 ] 
dist 17=[3.8598526390008893184 ,3.9386653833753450774 ] 
dist 18=[3.8477893549030229251 ,3.9372979651692400115 ] 
dist 19=[3.8353693719166534231 ,3.9369895026595304095 ] 
dist 20=[3.8202049610672714669 ,3.9341609596434351820 ] 
dist 21=[3.7971642233788393075 ,3.9335820409687253732 ] 
dist 22=[3.7738672517836791470 ,3.9323021221998589279 ] 
dist 23=[3.7576779284475325811 ,3.9318805117469770794 ] 
dist 24=[3.7434644469527816552 ,3.9298908965385625885 ] 
dist 25=[3.7280706542713134811 ,3.9289882222635323082 ] 
dist 26=[3.7129441384304914726 ,3.9259060229901844609 ] 
dist 27=[3.6997997388059882882 ,3.9231640984937250727 ] 
dist 28=[3.6854812004027747565 ,3.8346120701696120811 ] 
dist 29=[3.6656582414341479794 ,3.8277708851525678803 ] 
dist 30=[3.6455375953951497030 ,3.8264350187483396454 ] 
dist 31=[3.6300283371032547193 ,3.8239872992491152176 ] 
dist 32=[3.6148002983402702528 ,3.8233612034609577119 ] 
dist 33=[3.5958045035947510673 ,3.7976932544032417332 ] 
dist 34=[3.5756490805363458972 ,3.7950044413256324736 ] 
dist 35=[3.5557826391248745544 ,3.7884132219320293640 ] 
dist 36=[3.5321566462505709457 ,3.7874656556009929474 ] 
dist 37=[3.4969633759194263765 ,3.7774037170012892478 ] 
dist 38=[3.4612974438824469179 ,3.7754693996010939822 ] 
dist 39=[3.4357808492663432774 ,3.7734316189941072790 ] 
dist 40=[3.4126060463989650691 ,3.7730525138800606681 ] 
dist 41=[3.3863070580014177204 ,3.7540794193417768396 ] 
dist 42=[3.3597508397087502572 ,3.7516305344345506938 ] 
dist 43=[3.3355471417949707032 ,3.7469901726023464898 ] 
dist 44=[3.3082300851151609171 ,3.7458263984698436002 ] 
dist 45=[3.2692207287043796436 ,3.7419464318565051655 ] 
dist 46=[3.2290967061072055489 ,3.7409802559258275181 ] 
dist 47=[3.1973210909964827604 ,3.7400583623097033455 ] 
dist 48=[3.1653153676557630651 ,3.7398301271378698486 ] 
dist 49=[3.1242709340858696284 ,3.6905246097693649156 ] 
dist 50=[3.0801423894141820855 ,3.6862705558726708886 ] 
dist 51=[3.0358005158227086628 ,3.6773923244252402893 ] 
dist 52=[2.9824378879099072475 ,3.6718173252956119127 ] 
dist 53=[2.9022271863346299221 ,3.6539361575540847327 ] 
dist 54=[2.8219280884752817512 ,3.6156861148975084744 ] 
dist 55=[2.7682118838572598580 ,3.6141679154236481316 ] 
dist 56=[2.7232512868628638015 ,3.6080799911397370199 ] 
dist 57=[2.6779737844054648903 ,3.6069197704101719962 ] 
dist 58=[2.6355154149500967689 ,3.6039207576241364604 ] 
dist 59=[2.6018310810804887370 ,3.6034874210074154397 ] 
dist 60=[2.5678471942023171198 ,3.5212529341368442380 ] 
dist 61=[2.5241906412834687003 ,3.5153474538585537990 ] 
dist 62=[2.4813846189585753795 ,3.5012950808634865844 ] 
dist 63=[2.4508027733342967534 ,3.4992720137337988984 ] 
dist 64=[2.4230716668985472300 ,3.4794284332393567079 ] 
dist 65=[2.3916683294298995708 ,3.4757627244833758684 ] 
dist 66=[2.3599954229250113711 ,3.4715831852527596457 ] 
dist 67=[2.3311860660552616966 ,3.4708232216983641164 ] 
dist 68=[2.2987173914406190831 ,3.4391580787809804032 ] 
dist 69=[2.2524075629746548367 ,3.4351743987807529434 ] 
dist 70=[2.2063104611113817286 ,3.4274127273712169845 ] 
dist 71=[2.1746926726180606520 ,3.4254631928518418349 ] 
dist 72=[2.1473722802324260087 ,3.4188351315810280143 ] 
dist 73=[2.1184643529227495246 ,3.4173247009013703428 ] 
dist 74=[2.0904636672793647202 ,3.4156227630204238294 ] 
dist 75=[2.0667721550279793725 ,3.4151891280138591301 ] 
dist 76=[2.0415045390214486576 ,3.3506835194576896023 ] 
dist 77=[2.0071995886831441751 ,3.3452002462338897822 ] 
dist 78=[1.9726797528780491600 ,3.3332445696925544667 ] 
dist 79=[1.9465526154997075249 ,3.3305827029576950108 ] 
dist 80=[1.9213570279509409005 ,3.3167302918535495816 ] 
dist 81=[1.8905633026147639238 ,3.3142086251113076293 ] 
dist 82=[1.8582181915370615879 ,3.3088373069207995483 ] 
dist 83=[1.8268172089903000216 ,3.3073983236934813103 ] 
dist 84=[1.7898312592158069287 ,3.2950335691257330308 ] 
dist 85=[1.7351468119103167916 ,3.2930341649451357069 ] 
dist 86=[1.6804987127807158290 ,3.2891551550856760634 ] 
dist 87=[1.6436581522429622431 ,3.2881576682587847855 ] 
dist 88=[1.6125115861268524033 ,3.2846523114210118316 ] 
dist 89=[1.5806389216018898055 ,3.2838349734220167399 ] 
dist 90=[1.5504266006856097098 ,3.2826186206918959087 ] 
dist 91=[1.5259212506439373167 ,3.2822446203064058276 ] 
dist 92=[1.5007021452203099633 ,3.0880570626300057215 ] 
dist 93=[1.4676348708527879796 ,3.0775071578348120004 ] 
dist 94=[1.4348910933837862041 ,3.0537014905893947606 ] 
dist 95=[1.4109659446997447328 ,3.0493809544470752535 ] 
dist 96=[1.3756104979976193831 ,3.0196634095418518342 ] 
dist 97=[1.2861564011536572273 ,3.0143116336881011688 ] 
dist 98=[1.2227932340294939247 ,3.0050975967392424833 ] 
dist 99=[1.1658952396311181584 ,3.0030284061285694652 ] 
dist 100=[1.1023013446715119399 ,2.9691892697222703782 ] 
dist 101=[1.0386374056805415820 ,2.9647348728500856036 ] 
dist 102=[.98145924090724162029,2.9542061409173279119 ] 
dist 103=[.91760580006620173529,2.9508307123907020216 ] 
dist 104=[.82724126307205412608,2.9362414996690773298 ] 
dist 105=[.73464470081789593926,2.9044037866117697065 ] 
dist 106=[.66186332816575434572,2.9005250400585417866 ] 
dist 107=[.5890620019311361598 ,2.8830370247468641104 ] 
dist 108=[.49638562669167339119,2.7371781578939166533 ] 
dist 109=[.39708744998043815587,2.7246696654486635789 ] 
dist 110=[.29779941942286626653,2.6992350976928699502 ] 
dist 111=[.17866844580902738743,2.6833206261023551447 ] 
dist 112=[0                     ,2.6343394100582960982 ] 
dist 113=[.85508886449817961589,1.3571631967558991810 ] 
dist 114=[.82558408986608582878,1.3501477126597616764 ] 
dist 115=[.78598631781850589394,1.3489093285874882961 ] 
dist 116=[.7463487247081126938 ,1.3461358762758397292 ] 
dist 117=[.6799706198635244643 ,1.3455960743912900227 ] 
dist 118=[.6126315061036994425 ,.92038857195559327091] 
dist 119=[.5676811312345385551 ,.90409238177451479486] 
dist 120=[.5301630443494684475 ,.86607949872966907386] 
dist 121=[.4925523736490648006 ,.86062159113135358485] 
dist 122=[.4573934509896482131 ,.80996104491637440814] 
dist 123=[.4296821224256428411 ,.80282726617040804074] 
dist 124=[.4018925808083938251 ,.78997106684088944198] 
dist 125=[.3664208133958091314 ,.78807164654231424751] 
dist 126=[.3317489333408472803 ,.71891547405232921425] 
dist 127=[.3071588648624140395 ,.71048148815220889134] 
dist 128=[.2850462900589915440 ,.69355225151430597941] 
dist 129=[.2602841484056214709 ,.68930395919265677051] 
dist 130=[.2354680137105325241 ,.67462604556790088569] 
dist 131=[.20635925869121728118,.67159573452719250246] 
dist 132=[.17392997701770137531,.66769187946504946238] 
dist 133=[.15058945508816572465,.66681683545092282071] 
dist 134=[.1176875610841181293 ,.56893278946138315322] 
dist 135=[.0937732286134047612 ,.56078251103254537925] 
dist 136=[.0732884787191163796 ,.54261694441693412491] 
dist 137=[.0518962311420859993 ,.53929524968069394082] 
dist 138=[.0313476097104707558 ,.51751808590604369912] 
dist 139=[-.00575193427389385688,.513684304372561631  ] 
dist 140=[-.04279821126096133191,.50678635460781948762] 
dist 141=[-.06836790912792933501,.50525598553475687566] 
dist 142=[-.09063313001945645154,.48431436963547489451] 
dist 143=[-.11446181427924466069,.4814511362260070063 ] 
dist 144=[-.13770690540677339786,.47553518633515472597] 
dist 145=[-.15763780943122240247,.47404299325272004062] 
dist 146=[-.17912268933882383365,.46845757535237826456] 
dist 147=[-.20858353578381319265,.46739075772836898314] 
dist 148=[-.23836096120678038753,.46539187693439726842] 
dist 149=[-.26111212683161580114,.46492872142817068664] 
dist 150=[-.28325890253672540207,.32792123135812906391] 
dist 151=[-.31061882592630561652,.32027809740380827198] 
dist 152=[-.33951132460153931178,.30265246234832779186] 
dist 153=[-.36778825527526045383,.29996764100105004803] 
dist 154=[-.40126657086959773005,.27708001920357465804] 
dist 155=[-.45096411312948015272,.27301135188665459776] 
dist 156=[-.50052741613685003723,.26756369982127242576] 
dist 157=[-.5334687888235481208 ,.26619779679342884153] 
dist 158=[-.56080612934276491804,.23748799769140887931] 
dist 159=[-.58795384207834678499,.23392015184774484296] 
dist 160=[-.61316661428954273015,.2263931795225521584 ] 
dist 161=[-.63276438115789662393,.22464845294498376746] 
dist 162=[-.65216230083589247852,.2169550107682367884 ] 
dist 163=[-.67657571113713581488,.2155869501041409011 ] 
dist 164=[-.70027158643312729271,.21260792180034680819] 
dist 165=[-.71679943841933661669,.21201452085055016849] 
dist 166=[-.73137489421924260408,.18100274001421150784] 
dist 167=[-.74726137487115297126,.17817533897470769413] 
dist 168=[-.7629319990519134032 ,.17171423440232131503] 
dist 169=[-.77664405733296373248,.1706933614677868328 ] 
dist 170=[-.7916610842126593195 ,.16249668318901159951] 
dist 171=[-.81255147776945765288,.16105051679839003241] 
dist 172=[-.83312222129539571616,.15896843956568750511] 
dist 173=[-.84686068241276925814,.15841098989478555677] 
dist 174=[-.85833539664112344569,.14893420587457328256] 
dist 175=[-.86985136069594233725,.14775289031774089285] 
dist 176=[-.88062509005565560702,.14514325726576827464] 
dist 177=[-.88913094013649854316,.14466889713595880879] 
dist 178=[-.89767420617837160611,.14164315361806261479] 
dist 179=[-.90859761515983880979,.14112241093193515403] 
dist 180=[-.91928390156830340024,.14016295732016815737] 
dist 181=[-.92687870764899721479,.13995002532213301675] 
dist 182=[-.9337248817006947914 ,-.39869977054105429635] 
dist 183=[-.94141671519246343714,-.39762054244581066906] 
dist 184=[-.94914017383768412545,-.39608768309494916777] 
dist 185=[-.95611286478492393744,-.39401138693337889423] 
dist 186=[-.96392914462807967671,-.39112240761661051463] 
dist 187=[-.97502693249234367648,-.38633907447809605812] 
dist 188=[-.98597643265697458652,-.38135635016899177199] 
dist 189=[-.99319957454604943066,-.37766983109137349453] 
dist 190=[-.99913432866137859442,-.3741979462621845328 ] 
dist 191=[-1.0049303426230626845 ,-.37007357486545452957] 
dist 192=[-1.0102501894080491684 ,-.36580528417391878021] 
dist 193=[-1.0142802970385166025 ,-.36175769620859561548] 
dist 194=[-1.0181704020208265376 ,-.35706358632948441459] 
dist 195=[-1.0229302399796641572 ,-.35020931421147851968] 
dist 196=[-1.0274839420486670360 ,-.34309599147899104265] 
dist 197=[-1.0305495115257731619 ,-.3373657053936050465 ] 
dist 198=[-1.0331367162517732467 ,-.33150492063427186626] 
dist 199=[-1.0357769817101009021 ,-.32386957571952779841] 
dist 200=[-1.0382752080159485747 ,-.31560165447099130666] 
dist 201=[-1.0402942580616293563 ,-.30721066902465808061] 
dist 202=[-1.0423655650491287518 ,-.2970529764804900924 ] 
dist 203=[-1.0450728025180507046 ,-.28171856821532785   ] 
dist 204=[-1.0476628315616021492 ,-.26609948670515554304] 
dist 205=[-1.0492653082796660814 ,-.25480314341759913858] 
dist 206=[-1.0504639199399277170 ,-.24441969867164513248] 
dist 207=[-1.0514385156520848282 ,-.23245199664081818906] 
dist 208=[-1.0522036110386244712 ,-.22026390699121252712] 
dist 209=[-1.0525642297603302533 ,-.20899893372040818332] 
dist 210=[-1.0527422316781787448 ,-.19616000880086770015] 
dist 211=[-1.0527769094580705722 ,-.17767639308357418834] 
dist 212=[-1.0523512768621720226 ,-.15860308437032224571] 
dist 213=[-1.0522067748392434042 ,-.14340548736791898543] 
dist 214=[-1.0519460197174285458 ,-.12801326252045001581] 
dist 215=[-1.0518416088317090469 ,-.10816146154868599496] 
dist 216=[-1.0512924477664617279 ,-.08676346640867108095] 
dist 217=[-1.0511402391413848681 ,-.06518674237134658712] 
dist 218=[-1.0506183630201975572 ,-.03916745105987837420] 

8 phat 1 dirichlet min maxes function [2, 2, 0, 2, 1, 1, 1, 0, 1] 
dist 0=[2.0228642380162044408 ,2.0228642380162044408 ] 
dist 1=[2.0113148520502647978 ,2.0418185671155526673 ] 
dist 2=[2.0028866972699079664 ,2.0611094059315713730 ] 
dist 3=[1.9941116755560577957 ,2.0740048062424679224 ] 
dist 4=[1.9781366212304263720 ,2.0847883819112895140 ] 
dist 5=[1.9616631232966247213 ,2.0956320875882959562 ] 
dist 6=[1.9461225776961189076 ,2.1057906983289717235 ] 
dist 7=[1.9281592388815779027 ,2.1138339494281687932 ] 
dist 8=[1.9019947563546818939 ,2.1219340162339689277 ] 
dist 9=[1.8748612968753753060 ,2.1323198898740106105 ] 
dist 10=[1.8530221255960747833 ,2.1424943427482097539 ] 
dist 11=[1.8306991933912954743 ,2.1497487450813611935 ] 
dist 12=[1.8016307279481952111 ,2.1563121623622612920 ] 
dist 13=[1.7701556586772227718 ,2.1637227307180261236 ] 
dist 14=[1.7382064979866016744 ,2.1711845964287931414 ] 
dist 15=[1.6995222208494841411 ,2.1779532036829738831 ] 
dist 16=[1.6411072084483804188 ,2.1855666908205629504 ] 
dist 17=[1.5823198654956159839 ,2.1964080220331626192 ] 
dist 18=[1.5421462956455932434 ,2.2073389311188910487 ] 
dist 19=[1.5075909980531326838 ,2.2153107253368125352 ] 
dist 20=[1.4712763099427740368 ,2.2227063512301011135 ] 
dist 21=[1.4362519712695390531 ,2.2313326278140619271 ] 
dist 22=[1.4068579730151383071 ,2.2401762303669085608 ] 
dist 23=[1.3757162587710506204 ,2.2517838911722301959 ] 
dist 24=[1.3337011951389977484 ,2.2723874706300650768 ] 
dist 25=[1.2915418014757052510 ,2.2877795797020682110 ] 
dist 26=[1.2598227799131391902 ,2.3024273588440264554 ] 
dist 27=[1.2294185482777479063 ,2.3200536791988430212 ] 
dist 28=[1.1925182137366955278 ,2.3384230212030938661 ] 
dist 29=[1.1538948597909872578 ,2.3560428423586988121 ] 
dist 30=[1.1165986873370029780 ,2.3766358354756974256 ] 
dist 31=[1.0728193507297717040 ,2.4068976709735802173 ] 
dist 32=[1.0082638510963403428 ,2.4370214692007272288 ] 
dist 33=[.94310618060478040369,2.4570623243328300358 ] 
dist 34=[.89691820862460480663,2.4737159511805692366 ] 
dist 35=[.85540712851682562206,2.4902910639113507376 ] 
dist 36=[.80895665874672285979,2.5057093206016993372 ] 
dist 37=[.76242389716670026793,2.5177356011409628716 ] 
dist 38=[.72058365709006349017,2.5296789311030778171 ] 
dist 39=[.67381968606470254838,2.5447653913710456406 ] 
dist 40=[.60759238926699257175,2.5594359589152039619 ] 
dist 41=[.53970891402904758746,2.5697157461137112976 ] 
dist 42=[.48632036007594042517,2.5788309463737386234 ] 
dist 43=[.43288765590512144968,2.5888432446608943262 ] 
dist 44=[.36482758366020243903,2.5987654240372540609 ] 
dist 45=[.29188453838335426778,2.6075201551369371664 ] 
dist 46=[.21892032702111103017,2.6171691488563529414 ] 
dist 47=[.1313532714278582339 ,2.6306683196604564776 ] 
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dist 59=[2.4635336125446845599 ,2.7192825429556572861 ] 
dist 60=[2.4703600160708654533 ,2.7253467931087838960 ] 
dist 61=[2.4714665807563323043 ,2.7309777793416304410 ] 
dist 62=[2.4792583000358654206 ,2.7374168915177527080 ] 
dist 63=[2.4805467082252515558 ,2.7467135949346139330 ] 
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dist 73=[2.4139689838566894265 ,2.7924651038121996269 ] 
dist 74=[2.4019265390082577022 ,2.7944594443092116564 ] 
dist 75=[2.3866553780608029558 ,2.7964307330158106150 ] 
dist 76=[2.3703233474090971156 ,2.7982556297701681864 ] 
dist 77=[2.3540375225410119546 ,2.7996644140344846233 ] 
dist 78=[2.3345299725840105561 ,2.8010497447989043887 ] 
dist 79=[2.3053113537221750461 ,2.8027808346543861679 ] 
dist 80=[2.2756354922222005521 ,2.8044003760436135531 ] 
dist 81=[2.2542990129164207190 ,2.8053395211751662203 ] 
dist 82=[2.2348127368001668224 ,2.8059675155678886782 ] 
dist 83=[2.2125374995047894017 ,2.8063424715939554111 ] 
dist 84=[2.1899524339778617326 ,2.8065728411630846291 ] 
dist 85=[2.1692268696528780868 ,2.8066224962640858967 ] 
dist 86=[2.1457217410288551910 ,2.8065705694865646042 ] 
dist 87=[2.1120186810005971847 ,2.8065039969560186825 ] 
dist 88=[2.0772935554975918359 ,2.8043159994558780187 ] 
dist 89=[2.0497002600384726206 ,2.8039288621969716167 ] 
dist 90=[2.0218208077646182879 ,2.8031721047002524001 ] 
dist 91=[1.9859510774545378557 ,2.8029345301406193157 ] 
dist 92=[1.9473273552791727158 ,2.8018755023033581379 ] 
dist 93=[1.9084321957934733542 ,2.8016186583563113815 ] 
dist 94=[1.8615625187483714115 ,2.8008656438605589643 ] 
dist 95=[1.7910414845076514132 ,2.8006788498553453777 ] 
dist 96=[1.7204404997874831730 ,2.7849887474706654401 ] 
dist 97=[1.6732510276429111586 ,2.7834833224335332086 ] 
dist 98=[1.6337962557103843225 ,2.7799822716527047069 ] 
dist 99=[1.5941333341179743146 ,2.7792629134167662609 ] 
dist 100=[1.5569847233917626888 ,2.7743507630609332165 ] 
dist 101=[1.5275869551140272340 ,2.7733850852069780060 ] 
dist 102=[1.4979962201957036130 ,2.7717319002838122172 ] 
dist 103=[1.4600757613119162006 ,2.7713160171431117635 ] 
dist 104=[1.4229383682689419756 ,2.7632363928405885150 ] 
dist 105=[1.3964798220265985435 ,2.7610788498405544295 ] 
dist 106=[1.3725630665180435587 ,2.7490926472186140858 ] 
dist 107=[1.3455925939792455050 ,2.7482735509597775727 ] 
dist 108=[1.3184551411285735428 ,2.7468431479036973053 ] 
dist 109=[1.2938704802987751189 ,2.7444125208656646503 ] 
dist 110=[1.2662431674293084780 ,2.7330744667235247277 ] 
dist 111=[1.2269353966221029212 ,2.7258951921307228524 ] 
dist 112=[1.1878492662489458392 ,2.6951696976528743831 ] 
dist 113=[1.1611084939760464595 ,2.6862360641354610164 ] 
dist 114=[1.1380751893488437834 ,1.4805121119484367568 ] 
dist 115=[1.1138185759475354146 ,1.4546524929736937759 ] 
dist 116=[1.0903933357300661615 ,1.3943083046633166372 ] 
dist 117=[1.0706854445434884653 ,1.3856090983129187744 ] 
dist 118=[1.0497638087966369687 ,1.3050561245013384609 ] 
dist 119=[1.0214837061026303179 ,1.2906436549848062735 ] 
dist 120=[.9930828179789262697 ,1.2731604382585977850 ] 
dist 121=[.97167805203356079662,1.2700255879587419080 ] 
dist 122=[.95112473195965621519,1.1596081134742912367 ] 
dist 123=[.92612954611257096817,1.1461031503511827227 ] 
dist 124=[.89994091876648235016,1.1189593287259096936 ] 
dist 125=[.87461394652465622344,1.1121278620615948189 ] 
dist 126=[.84485577304396208535,1.0884049111965487150 ] 
dist 127=[.80094276338161954579,1.0835172261571387172 ] 
dist 128=[.75709353825063934646,1.0769279028513891714 ] 
dist 129=[.72759049681175200611,1.0751800767572162840 ] 
dist 130=[.70270997978818712698,.91752143996626302055] 
dist 131=[.67735041143125213301,.90429898761485319832] 
dist 132=[.65337548609375026865,.87477985875355307168] 
dist 133=[.63403340908340276507,.86938918814047688543] 
dist 134=[.6142220764060525252 ,.83381327499029868598] 
dist 135=[.58837017315721798688,.8275324558756830235 ] 
dist 136=[.56282964892645217931,.81629008380780295667] 
dist 137=[.54426380262266140309,.81380393872644288366] 
dist 138=[.527101200549334863  ,.77879459544110400345] 
dist 139=[.50717351940176410454,.77403541721959324354] 
dist 140=[.48679458990605536473,.76400556048337882348] 
dist 141=[.46782703747935267975,.76163292687968169409] 
dist 142=[.44610271096954572373,.75137128937044706014] 
dist 143=[.41469694807708456976,.74952751053967302671] 
dist 144=[.38325710737170681697,.74548581800209597396] 
dist 145=[.36139647286050792435,.74466920703114230822] 
dist 146=[.34219039524472579328,.56270833567093536345] 
dist 147=[.32136852893462379821,.56102774086365493051] 
dist 148=[.30089575878147159943,.54571350494352387324] 
dist 149=[.28308603249738701694,.54298118749658881371] 
dist 150=[.2636688713114025934 ,.53960294049765214006] 
dist 151=[.23676651486461568767,.53895803290112576933] 
dist 152=[.20945095200510968726,.51843223220646282792] 
dist 153=[.18838100457906003574,.51592116111157671983] 
dist 154=[.16767906986704976885,.51082629276407521067] 
dist 155=[.14183552276337583405,.50953550930110470537] 
dist 156=[.11440424542210940987,.50498502812169139608] 
dist 157=[.08735154119430189754,.50407151272266387939] 
dist 158=[.05516839069809756059,.50267390875468259906] 
dist 159=[.00721581761507117234,.50232331748763701587] 
dist 160=[-.04067060743390520179,.32920886399292612508] 
dist 161=[-.07258917210297826135,.32808743738932179237] 
dist 162=[-.09917887794624660430,.27073743858809446142] 
dist 163=[-.12575037594802910874,.26566953680839384297] 
dist 164=[-.1505358573187367447 ,.25389718474480408676] 
dist 165=[-.16998166698444272175,.25219701217021759567] 
dist 166=[-.18939913730016701778,.23669292935061967087] 
dist 167=[-.21407126397389913293,.23394052141801974766] 
dist 168=[-.23813252830009493798,.23054370449183735462] 
dist 169=[-.25510660748851764023,.22992967942132046343] 
dist 170=[-.2702767302929743284 ,.20954105618070005304] 
dist 171=[-.28712234114110136777,.2070663366604306324 ] 
dist 172=[-.30392283798208094787,.20204201992370698952] 
dist 173=[-.31891250906083265543,.2007754169395999574 ] 
dist 174=[-.33557081601612188149,.19634107108281575036] 
dist 175=[-.35904569721205885065,.19545652599524276438] 
dist 176=[-.38229198793841860389,.194178715727640147  ] 
dist 177=[-.39803595481790626058,.1938429965476696586 ] 
dist 178=[-.41142562342258174212,.03738611884084809396] 
dist 179=[-.42525494559801016045,.03596246989025228730] 
dist 180=[-.43844415537215432764,.02380304526217847599] 
dist 181=[-.44927343542434877868,.02165336984371381904] 
dist 182=[-.46053698180495944176,.01878238949364164222] 
dist 183=[-.47546321547330416094,.01809343898842695351] 
dist 184=[-.49031726378257566708,.00316915475465784898] 
dist 185=[-.50129207561179038779,.00133210068988135899] 
dist 186=[-.5116160994591971413 ,-.00255125972835920340] 
dist 187=[-.52386705791210852778,-.00341777895884837318] 
dist 188=[-.53654174479180787559,-.00737813319881639583] 
dist 189=[-.5485606419319864131 ,-.00806918189844011752] 
dist 190=[-.56250131026629114055,-.00955038064877343158] 
dist 191=[-.58286289862775616595,-.00984043052477611360] 
dist 192=[-.6031092509841572056 ,-.03893250205913707593] 
dist 193=[-.61658898628918844742,-.04107102274764414232] 
dist 194=[-.62780129733876552945,-.04573741088927929881] 
dist 195=[-.63897816893579499147,-.04665108828913441072] 
dist 196=[-.64938587883395801509,-.05191056606759848229] 
dist 197=[-.6575216164491923198 ,-.05281763018536746523] 
dist 198=[-.66561766002189931388,-.05462636703092616565] 
dist 199=[-.6758665975358924362 ,-.05506999245245943221] 
dist 200=[-.68584338545429780898,-.05879373646610321172] 
dist 201=[-.69285085660174446574,-.05937763720217045598] 
dist 202=[-.6990817027879327508 ,-.06017783354200943407] 
dist 203=[-.70595206493425883303,-.06036824039325878093] 
dist 204=[-.71277578884568489667,-.06033470361179087325] 
dist 205=[-.72038625339571601462,-.05995828111653733219] 
dist 206=[-.72929355881779838011,-.05925576300455042321] 
dist 207=[-.73756692557303179914,-.05791798228462594304] 
dist 208=[-.74702932435925391735,-.05644637444648181795] 
dist 209=[-.76069264449776548715,-.05520857000007899517] 
dist 210=[-.77422089196520172398,-.05389549050568337610] 
dist 211=[-.78314301375728282785,-.05212271035057660767] 
dist 212=[-.790470953954621912  ,-.05017294586368040344] 
dist 213=[-.7976226295144522086 ,-.04815194650055138347] 
dist 214=[-.80418318219123179933,-.04567535648048682562] 
dist 215=[-.80914668965750901905,-.04190335385770442374] 
dist 216=[-.81393130406940311718,-.03792395064659864550] 
dist 217=[-.81977630643232241438,-.03461780518453208958] 
dist 218=[-.82536322780123215754,-.03114528316563556712] 
dist 219=[-.829115545271035614  ,-.02650038994296445181] 
dist 220=[-.83227264798028354289,-.02141145191181818708] 
dist 221=[-.83547876949190266442,-.01616287380316413405] 
dist 222=[-.83850244667379995892,-.00974915353256601840] 
dist 223=[-.84092979429867350104,0                     ] 
dist 224=[-.84340513486524229613,-.17359761523852829395] 
dist 225=[-.84662079132123110985,-.16524929903592006752] 
dist 226=[-.84971724674051562818,-.15670804737388732869] 
dist 227=[-.8517157937222307284 ,-.15046955494388302199] 
dist 228=[-.85330879746097091156,-.14467332711916568284] 
dist 229=[-.85478310408201474254,-.13790101239137988293] 
dist 230=[-.8560825159422292257 ,-.13095277746749889278] 
dist 231=[-.85697595006442702282,-.12445288621532997523] 
dist 232=[-.85775029028029580528,-.11698305655256237412] 
dist 233=[-.85857333061840575954,-.10615524153561499852] 
dist 234=[-.85929816832322743903,-.09495054605976209362] 
dist 235=[-.85967970253493157135,-.08597325763731904722] 
dist 236=[-.85988574539774900192,-.07683558162169679052] 
dist 237=[-.85993147534098115818,-.06498935141766605472] 
dist 238=[-.85986785641295769772,-.05218997672784746058] 
dist 239=[-.85981930070817180699,-.03923989447013808038] 
dist 240=[-.8597553371675732976 ,-.02359162483487070507] 

8 phat 1 dirichlet min maxes function [0, 1, 1, 2, 2, 1, 1, 2] 
dist 0=[3.6212213609002868587 ,3.6212213609002868587 ] 
dist 1=[3.6144706275085269003 ,3.6271345671620768413 ] 
dist 2=[3.6047375161376227877 ,3.6335176498947837577 ] 
dist 3=[3.5946862857650072662 ,3.6397773113096338107 ] 
dist 4=[3.5866631067079634546 ,3.6451968440716777580 ] 
dist 5=[3.5785232494806703795 ,3.6510836988674054167 ] 
dist 6=[3.5680053175555911280 ,3.6592126038447381704 ] 
dist 7=[3.5566572083954642547 ,3.6671712567034241925 ] 
dist 8=[3.5451967214086449449 ,3.6723771179457387420 ] 
dist 9=[3.5313627767827011944 ,3.6766049754029131171 ] 
dist 10=[3.5105210634417762345 ,3.6806517024498854137 ] 
dist 11=[3.4893041406138628194 ,3.6843114674465605691 ] 
dist 12=[3.4739693938267047059 ,3.6869915096597565643 ] 
dist 13=[3.4598826551479896805 ,3.6894888342902222112 ] 
dist 14=[3.4436576457213012960 ,3.6924177384836097502 ] 
dist 15=[3.4271380796347867739 ,3.6951558693960514981 ] 
dist 16=[3.4118731424109993706 ,3.6968901151516262905 ] 
dist 17=[3.3944766675677717501 ,3.6982348298903098386 ] 
dist 18=[3.3694311543053425916 ,3.6994148699480010568 ] 
dist 19=[3.3435826022813129789 ,3.7004099083980879979 ] 
dist 20=[3.3229740489839338221 ,3.7010146264646805435 ] 
dist 21=[3.3020882999751396991 ,3.7014539195162776421 ] 
dist 22=[3.2751309915438294403 ,3.7017872539650247979 ] 
dist 23=[3.2460610380746513847 ,3.7019943402905005021 ] 
dist 24=[3.2167249104142952069 ,3.7020137317648451511 ] 
dist 25=[3.1813290508320776009 ,3.7017944460371779542 ] 
dist 26=[3.1280207476407105296 ,3.7017275332627767633 ] 
dist 27=[3.0746122152864897195 ,3.7003288847455644628 ] 
dist 28=[3.0388154486125166595 ,3.6999503568596814085 ] 
dist 29=[3.0087777741692295321 ,3.6996676390463490680 ] 
dist 30=[2.9784050614469154387 ,3.6995008723424531670 ] 
dist 31=[2.9498445452380428645 ,3.6930578742411508701 ] 
dist 32=[2.9270554840047992571 ,3.6921251207209146484 ] 
dist 33=[2.9039430558790669799 ,3.6904421244896309210 ] 
dist 34=[2.8740891029423349612 ,3.6900013749140803208 ] 
dist 35=[2.8447386955295839121 ,3.6884769163182092847 ] 
dist 36=[2.8236404014725984412 ,3.6880384244082736326 ] 
dist 37=[2.8043758707487399215 ,3.6874504634331921631 ] 
dist 38=[2.7823603417677734750 ,3.6872122910084291480 ] 
dist 39=[2.7600420523032993429 ,3.6583228817097067316 ] 
dist 40=[2.7395665085221067457 ,3.6557514907371272081 ] 
dist 41=[2.7163490643379932550 ,3.6501259317165487660 ] 
dist 42=[2.6830634347788779939 ,3.6487397678583805619 ] 
dist 43=[2.6498582842431547992 ,3.6419607056540160708 ] 
dist 44=[2.6269627484766793499 ,3.6406612040069104060 ] 
dist 45=[2.6070505118043819843 ,3.6378013293216809430 ] 
dist 46=[2.5857782731041985118 ,3.6369839768568070323 ] 
dist 47=[2.5650500400814060565 ,3.6293846259121076690 ] 
dist 48=[2.5473137742324862042 ,3.6281651036533573263 ] 
dist 49=[2.5282259668955773416 ,3.6253818476259516334 ] 
dist 50=[2.5020916968281853281 ,3.6246702994211344384 ] 
dist 51=[2.4756943593829913851 ,3.6207907357166193857 ] 
dist 52=[2.4555543076257214796 ,3.6194283575564740181 ] 
dist 53=[2.4359767206748750529 ,3.6163178532643618805 ] 
dist 54=[2.4118291888085932179 ,3.6133568992876388222 ] 
dist 55=[2.3863490763308902597 ,3.5030658775448888799 ] 
dist 56=[2.3614412940332648828 ,3.4959259814310971892 ] 
dist 57=[2.3319739405773579263 ,3.4816923766763108247 ] 
dist 58=[2.2882559783494160292 ,3.4780829136549249216 ] 
dist 59=[2.2445060826577622378 ,3.4654648999224409796 ] 
dist 60=[2.2149109983927583738 ,3.4589397898020486748 ] 
dist 61=[2.1897797001233632512 ,3.4381851528851934832 ] 
dist 62=[2.1638845226670565926 ,3.4239198572725240462 ] 
dist 63=[2.1392262015660874318 ,3.3610842334847219531 ] 
dist 64=[2.1190422107491271539 ,3.3388320802991116788 ] 
dist 65=[2.0981044131692465309 ,3.0997232442300811614 ] 
dist 66=[2.0704309369131955189 ,3.0979465417545713607 ] 
dist 67=[2.0429251081375515463 ,3.0903443858434045132 ] 
dist 68=[2.0226578844894136707 ,3.0889407003148174920 ] 
dist 69=[2.0036473300975152898 ,3.0854708235152066162 ] 
dist 70=[1.9811680584881988112 ,3.0849375359084811520 ] 
dist 71=[1.9579544732633817496 ,2.9954520175209741819 ] 
dist 72=[1.9360067344468626836 ,2.9890459961593460192 ] 
dist 73=[1.9105997357078305730 ,2.9740073619710555926 ] 
dist 74=[1.8735494407303372567 ,2.9717390811588938351 ] 
dist 75=[1.8363247642733595357 ,2.9511683006467848396 ] 
dist 76=[1.8102202562485507436 ,2.9474058730912162773 ] 
dist 77=[1.7870519468670201198 ,2.9427096004283161995 ] 
dist 78=[1.7615717849343303961 ,2.9415811651848225537 ] 
dist 79=[1.7363032079351226746 ,2.9113864994828624155 ] 
dist 80=[1.7139812181069671962 ,2.9075569580580259466 ] 
dist 81=[1.6893576835351400153 ,2.8998189590473514366 ] 
dist 82=[1.6548831470780352928 ,2.8978168074388102549 ] 
dist 83=[1.6197198964930062623 ,2.8905595115038713852 ] 
dist 84=[1.5923415710976744752 ,2.8890590517665499952 ] 
dist 85=[1.5651989764969393789 ,2.8863386414575979344 ] 
dist 86=[1.5309786266067597270 ,2.8856810106486204589 ] 
dist 87=[1.4944821914161904368 ,2.8331981675307022530 ] 
dist 88=[1.4582354727024152011 ,2.8285611690725136844 ] 
dist 89=[1.4149258527147609546 ,2.8181977302027991794 ] 
dist 90=[1.3501784860742428536 ,2.8161375493724737095 ] 
dist 91=[1.2854332077036103896 ,2.8033746363489846734 ] 
dist 92=[1.2421319405963236369 ,2.8010434477567059872 ] 
dist 93=[1.2058998385767165272 ,2.7966930623939284142 ] 
dist 94=[1.1694305463138052207 ,2.7956368091047455273 ] 
dist 95=[1.1352435991821339718 ,2.7814209012963407255 ] 
dist 96=[1.1081406600019183824 ,2.7794342476792356583 ] 
dist 97=[1.0808145027206621877 ,2.7748442871112431710 ] 
dist 98=[1.0457347044749299178 ,2.7739644736568897188 ] 
dist 99=[1.0113498602846167649 ,2.7677310392108451047 ] 
dist 100=[.98680345294169246035,2.7665423427985782506 ] 
dist 101=[.96456479445566519235,2.7645773292409728894 ] 
dist 102=[.93941072558441432022,2.7640805270243229037 ] 
dist 103=[.91405751685421947321,2.6465880437969328895 ] 
dist 104=[.89102231792598255348,2.6393640831195655012 ] 
dist 105=[.86508204553003633582,2.6232911580211142695 ] 
dist 106=[.82810882000917123258,2.6201419382367756625 ] 
dist 107=[.79131611666311297579,2.6007083299468976175 ] 
dist 108=[.76609791574854582276,2.5972085899159042771 ] 
dist 109=[.74432626873850910209,2.5906438441145221720 ] 
dist 110=[.72131945228507154125,2.5890662783105680237 ] 
dist 111=[.69905291181805501293,2.5690891058720706353 ] 
dist 112=[.68024229814764162179,2.5662689334144594548 ] 
dist 113=[.6602056055083911535 ,2.5601132886201857750 ] 
dist 114=[.63303486610701563733,2.5586897128663158716 ] 
dist 115=[.60570858821606693051,2.5514559846428193095 ] 
dist 116=[.58504975645347749185,2.5489673109772062518 ] 
dist 117=[.56515046236435958903,2.5435034932332086025 ] 
dist 118=[.54086226272409457471,2.5389403376678092362 ] 
dist 119=[.51536754246008724593,2.3808629999557210044 ] 
dist 120=[.49064228095155309769,2.3707998928805360230 ] 
dist 121=[.46153849526510984956,2.3506058150183856841 ] 
dist 122=[.41853009590445026092,2.3454988341310159698 ] 
dist 123=[.37555928162210455241,2.3276510821561938568 ] 
dist 124=[.34660583266412632296,2.3188114093685676556 ] 
dist 125=[.32214364519538823554,2.2919679282059197412 ] 
dist 126=[.26447817122089785706,2.2736827381586418586 ] 
dist 127=[.15866009921586901957,2.1935442961951853530 ] 
dist 128=[0                     ,2.1655339900975146300 ] 
dist 129=[.2291660952099096321 ,.78654099958702544275] 
dist 130=[.1990960020333498465 ,.7856373686712212158 ] 
dist 131=[.1678301439254685282 ,.75130320624350475909] 
dist 132=[.1379484236946864938 ,.74711646069811146324] 
dist 133=[.1031081199409806054 ,.73874065804526582445] 
dist 134=[.0520084006813021431 ,.73664383214401032347] 
dist 135=[.0011104192934479573 ,.72943984110112020191] 
dist 136=[-.0329229522143204063 ,.72793818323081453456] 
dist 137=[-.0613926227886547902 ,.7261020260655863428 ] 
dist 138=[-.0900363310975742317 ,.72575823681947439151] 
dist 139=[-.1168795418386345062 ,.67595575687655123177] 
dist 140=[-.1381473938694324663 ,.67183102821297495188] 
dist 141=[-.1595783127532090617 ,.6626568141031163823 ] 
dist 142=[-.1870737753531896599 ,.66095894674509664083] 
dist 143=[-.2140167011967135374 ,.65001709560656257652] 
dist 144=[-.2332375257545272709 ,.64809156854393700063] 
dist 145=[-.2506379366842858987 ,.64458118939852917903] 
dist 146=[-.2702993816430440655 ,.64378939603278642778] 
dist 147=[-.2901050312461042646 ,.63348677148096869921] 
dist 148=[-.3080822469991169947 ,.63205972567020633855] 
dist 149=[-.3283124215446326238 ,.62916513484324460304] 
dist 150=[-.3571296914349466280 ,.62843194278310002829] 
dist 151=[-.3857989480685594598 ,.62584741047838144698] 
dist 152=[-.4054370837044823478 ,.62532854768080962174] 
dist 153=[-.4223782913625120991 ,.62453088164228644329] 
dist 154=[-.4402600933122137937 ,.62433169931956223825] 
dist 155=[-.4575540037374158294 ,-.2866454758110059003 ] 
dist 156=[-.4828578895251930951 ,-.2896405888103451875 ] 
dist 157=[-.51121276643948704703,-.2934122916784997706 ] 
dist 158=[-.53941739334836191128,-.2940753602682690699 ] 
dist 159=[-.56564188190793449889,-.3150796971110438878 ] 
dist 160=[-.58607639823716789178,-.3175859615784760882 ] 
dist 161=[-.60635003319919157179,-.3227530274840603567 ] 
dist 162=[-.63193101953408042699,-.3239586080763557744 ] 
dist 163=[-.65679211705951350637,-.3286402210773160233 ] 
dist 164=[-.67418626939197249166,-.3295076446572724956 ] 
dist 165=[-.68958199969752740404,-.3308380234858674892 ] 
dist 166=[-.70644960366077247527,-.3311425399968228925 ] 
dist 167=[-.72313949454026446756,-.5066452286205280940 ] 
dist 168=[-.73782439734749149736,-.5137231678941682005 ] 
dist 169=[-.75397470711119031229,-.5297656295223848184 ] 
dist 170=[-.77652610576821862532,-.5323438279714854402 ] 
dist 171=[-.79876914948888732194,-.5522224698901875658 ] 
dist 172=[-.81368607284523833184,-.5556918894072220942 ] 
dist 173=[-.82621269112319956478,-.5609321923186157662 ] 
dist 174=[-.83889473457647004179,-.5622410648431098221 ] 
dist 175=[-.85083025965791105062,-.5834237569930530559 ] 
dist 176=[-.86037087954384031839,-.5860462545147339253 ] 
dist 177=[-.87006262486182630631,-.5919940129116238885 ] 
dist 178=[-.88260265687482077588,-.5928708866207010421 ] 
dist 179=[-.89494167759837056143,-.6001529258493840144 ] 
dist 180=[-.90382940475328142384,-.6013919252031716862 ] 
dist 181=[-.91196310757852036385,-.6030988156112476292 ] 
dist 182=[-.92128610675017095717,-.6034476153176939736 ] 
dist 183=[-.93075326520893380977,-.61066571557597117953] 
dist 184=[-.93946361100147477444,-.61160320913611037792] 
dist 185=[-.94936048807817278684,-.61258193773725980937] 
dist 186=[-.96357371335775146068,-.61250838923838482107] 
dist 187=[-.97762233813328538892,-.61198414473731774806] 
dist 188=[-.9868608275759384026 ,-.61081607772802631843] 
dist 189=[-.99441905613163611073,-.6089429481608885441 ] 
dist 190=[-1.0017467388148935696 ,-.60559857907632985903] 
dist 191=[-1.0084368202122372215 ,-.60187185761562174082] 
dist 192=[-1.0134446809184839819 ,-.5984693713849763522 ] 
dist 193=[-1.0182201851220839573 ,-.59462515478366982526] 
dist 194=[-1.0239808509214984561 ,-.5891315446881454096 ] 
dist 195=[-1.0294505232313643812 ,-.58294289432832989933] 
dist 196=[-1.0330620694618238109 ,-.57631864115692010371] 
dist 197=[-1.0360330716503661989 ,-.56805161998506021377] 
dist 198=[-1.0389406053291330626 ,-.55529223816908324963] 
dist 199=[-1.0416131594159072252 ,-.54232887486026363172] 
dist 200=[-1.0436442538677675888 ,-.53324595315908414005] 
dist 201=[-1.0456110067413348909 ,-.52519398218748342184] 
dist 202=[-1.0480261888688546110 ,-.51635415756450113511] 
dist 203=[-1.0503111560458625230 ,-.50759806470060705074] 
dist 204=[-1.0517570627601695738 ,-.49988097253949799512] 
dist 205=[-1.0528767344138328450 ,-.49138388380252357369] 
dist 206=[-1.0538568079160272808 ,-.47950792421883444959] 
dist 207=[-1.0546815571882650604 ,-.46740555077575474642] 
dist 208=[-1.0551799621857695925 ,-.4580028297616734831 ] 
dist 209=[-1.0555387808690574980 ,-.44870097954530929325] 
dist 210=[-1.0558052290910217756 ,-.4370020391795284578 ] 
dist 211=[-1.0559737302639188757 ,-.42454070442025885569] 
dist 212=[-1.0559954558305089321 ,-.41218939428082544415] 
dist 213=[-1.0558553496978273185 ,-.39745061840512696609] 
dist 214=[-1.0553057173022583883 ,-.37543982370447070551] 
dist 215=[-1.0497126488374165238 ,-.3531146779889045944 ] 
dist 216=[-1.0490714356131329044 ,-.33711854333219583229] 
dist 217=[-1.0471476124141815178 ,-.32256704775541059147] 
dist 218=[-1.0444916774155897683 ,-.3060201911679648631 ] 
dist 219=[-.97026798086086403764,-.28929380775228346909] 
dist 220=[-.96628928797689404366,-.27402422292863148931] 
dist 221=[-.9569908133010182501 ,-.25677150886897843437] 
dist 222=[-.95551305673302404003,-.23211292989034350725] 
dist 223=[-.9428669878968515711 ,-.20674336786860529346] 
dist 224=[-.9405410313252175041 ,-.1866468337176344564 ] 
dist 225=[-.93742840868960271757,-.16640104006687109786] 
dist 226=[-.93648612290567553329,-.14043445484839650502] 
dist 227=[-.91222742562532342453,-.11251724899742682408] 
dist 228=[-.90927124390289060921,-.08446929069491461639] 
dist 229=[-.90137635043176448063,-.05072031935176510610] 

8 phat 1 dirichlet min maxes function [1, 0, 0, 2, 1, 0, 1] 
dist 0=[3.5977136278799123834 ,3.5977136278799123834 ] 
dist 1=[3.5962405618578480804 ,3.5988974234393703063 ] 
dist 2=[3.5940228712395907883 ,3.5999580689718873143 ] 
dist 3=[3.5908158417245608593 ,3.6011404258330141513 ] 
dist 4=[3.5853855105536639045 ,3.6028110865438603282 ] 
dist 5=[3.5794338894287858560 ,3.6045998339773508844 ] 
dist 6=[3.5741417458877333894 ,3.6062545356408170820 ] 
dist 7=[3.5682753003267648922 ,3.6081417757023516725 ] 
dist 8=[3.5600265180323978857 ,3.6108606506261317390 ] 
dist 9=[3.5507933148808364142 ,3.6136675708835877428 ] 
dist 10=[3.5409892758497392831 ,3.6159069799525322269 ] 
dist 11=[3.5288067260517537207 ,3.6181779249892553862 ] 
dist 12=[3.5100597027560758858 ,3.6211109782443711224 ] 
dist 13=[3.4908839246578555462 ,3.6242748848710154531 ] 
dist 14=[3.4769863952320165316 ,3.6274692174420476585 ] 
dist 15=[3.4641813100732836229 ,3.6313244444034484275 ] 
dist 16=[3.4493752048483121770 ,3.6371318616225463300 ] 
dist 17=[3.4342682455186960571 ,3.6429185169906633831 ] 
dist 18=[3.4202597726362544664 ,3.6466906959054265128 ] 
dist 19=[3.4042564366443859585 ,3.6497396916634438978 ] 
dist 20=[3.3811702151431637043 ,3.6526336794461388008 ] 
dist 21=[3.3573239640817418868 ,3.6552345122406036755 ] 
dist 22=[3.3382805823391927625 ,3.6571109120727775310 ] 
dist 23=[3.3189523374691460806 ,3.6588311502302111891 ] 
dist 24=[3.2939666610674162458 ,3.6608073433544905604 ] 
dist 25=[3.2670035621352609605 ,3.6626331253586950054 ] 
dist 26=[3.2397658157461660478 ,3.6637517294520404722 ] 
dist 27=[3.2068816078885716492 ,3.6645753139400782301 ] 
dist 28=[3.1573332016307558954 ,3.6652210417385076884 ] 
dist 29=[3.1076825497768775928 ,3.6657089515438101181 ] 
dist 30=[3.0743893692870159146 ,3.6659012712588826946 ] 
dist 31=[3.0464359622364505285 ,3.6659267109435127166 ] 
dist 32=[3.0181438948427181300 ,3.6658843676161466477 ] 
dist 33=[2.9915227569628935638 ,3.6653603639563582897 ] 
dist 34=[2.9702529085980042219 ,3.6651932503848822035 ] 
dist 35=[2.9486552785009660506 ,3.6646003608001140322 ] 
dist 36=[2.9207230449557200839 ,3.6644304162354513215 ] 
dist 37=[2.8932453224596411951 ,3.6627139058698296762 ] 
dist 38=[2.8734656932089055784 ,3.6622837656041077218 ] 
dist 39=[2.8553771620901259109 ,3.6617717049340297848 ] 
dist 40=[2.8346636708282725982 ,3.6615346089931837447 ] 
dist 41=[2.8136416995649049811 ,3.6553196157572677539 ] 
dist 42=[2.7943192778622810846 ,3.6544050526477485155 ] 
dist 43=[2.7723804651314170372 ,3.6526434938364657849 ] 
dist 44=[2.7408931793012951098 ,3.6521551754705405029 ] 
dist 45=[2.7094673570438346384 ,3.6502638956181285316 ] 
dist 46=[2.6877743927413423065 ,3.6498036751469081923 ] 
dist 47=[2.6688821808742630823 ,3.6488050985432419457 ] 
dist 48=[2.6486591012282220307 ,3.6484712609619340555 ] 
dist 49=[2.6289287457616003663 ,3.6229943342515546658 ] 
dist 50=[2.6120073836171400796 ,3.6206137843927610220 ] 
dist 51=[2.5937632066047140847 ,3.6144034630170498980 ] 
dist 52=[2.5687417178336978160 ,3.6075241493130525887 ] 
dist 53=[2.5434493763804800000 ,3.2833171751231063610 ] 
dist 54=[2.5241218144726414408 ,3.2769674233493065940 ] 
dist 55=[2.5053046385506681321 ,3.2684025982050947834 ] 
dist 56=[2.4820537923613045074 ,3.2659676537635971985 ] 
dist 57=[2.4574983097068416713 ,3.2188244772722688845 ] 
dist 58=[2.4334627123581196014 ,3.2128054850618109086 ] 
dist 59=[2.4050034417846068300 ,3.2001687155461078867 ] 
dist 60=[2.3627536881521922044 ,3.1969416258031829983 ] 
dist 61=[2.3204619675737709146 ,3.1839191652254244527 ] 
dist 62=[2.2918348332189558699 ,3.1814878625095793068 ] 
dist 63=[2.2675054912641516798 ,3.1759679503197991075 ] 
dist 64=[2.2424045303708271197 ,3.1748357804440677868 ] 
dist 65=[2.2184824051612385732 ,3.1087738211469276655 ] 
dist 66=[2.1988682935063602979 ,3.1026803195020407485 ] 
dist 67=[2.1784923343383123424 ,3.0885439721422451108 ] 
dist 68=[2.1515228917395554733 ,3.0862486927773136360 ] 
dist 69=[2.1246989010297112833 ,3.0673664856444598664 ] 
dist 70=[2.1049047355444002931 ,3.0639132584042128959 ] 
dist 71=[2.0863087038757514319 ,3.0590810370497113537 ] 
dist 72=[2.0642771341569198337 ,3.0576804766141405046 ] 
dist 73=[2.0415027376379403304 ,3.0317027407225550900 ] 
dist 74=[2.0199354696180522240 ,3.0283306339976329184 ] 
dist 75=[1.9949419416210626757 ,3.0211620549890295816 ] 
dist 76=[1.9584628319835837421 ,3.0193394486731617462 ] 
dist 77=[1.9217988522009439058 ,3.0115187275960397964 ] 
dist 78=[1.8960658612558598897 ,3.0100805753591914833 ] 
dist 79=[1.8732046080134585630 ,3.0065281482529652097 ] 
dist 80=[1.8480273051408819472 ,3.0059920242996493725 ] 
dist 81=[1.8230386593962479674 ,2.9156005398906502249 ] 
dist 82=[1.8009320166718731074 ,2.9091240610350240191 ] 
dist 83=[1.7765195176616392871 ,2.8939562217006801610 ] 
dist 84=[1.7423076667015856472 ,2.8916465623517789384 ] 
dist 85=[1.7073979561826658371 ,2.8710138033822555951 ] 
dist 86=[1.6801940854974330930 ,2.8672455833957995894 ] 
dist 87=[1.6532028252174411748 ,2.8624587172145357085 ] 
dist 88=[1.6191435360411243350 ,2.8612527692639779862 ] 
dist 89=[1.5828036748814641425 ,2.8314384976471260630 ] 
dist 90=[1.5466903441845481814 ,2.8276478815597637042 ] 
dist 91=[1.5035237746938618881 ,2.8199289241633097312 ] 
dist 92=[1.4389716310830993388 ,2.8179186450335223721 ] 
dist 93=[1.3744140850391346521 ,2.8105365779739793974 ] 
dist 94=[1.3312259063309132130 ,2.8090388510277143909 ] 
dist 95=[1.2950747616931735664 ,2.8061728874059133319 ] 
dist 96=[1.2586646807527315646 ,2.8054429385213699651 ] 
dist 97=[1.2245189773763872683 ,2.7553244456168263974 ] 
dist 98=[1.1974251270231807833 ,2.7508532548274986897 ] 
dist 99=[1.1700862954530962876 ,2.7407974485556243903 ] 
dist 100=[1.1349606905750643324 ,2.7388562100179673572 ] 
dist 101=[1.1005168023273868904 ,2.7262863164834560469 ] 
dist 102=[1.0699161317870266201 ,2.7239877413789095892 ] 
dist 103=[1.0196823085083911073 ,2.7198356068745032829 ] 
dist 104=[.96364497091073708715,2.7188639138151328672 ] 
dist 105=[.90760807435801611344,2.7041940286578107962 ] 
dist 106=[.85737601427794336967,2.7022015289141739694 ] 
dist 107=[.80135790333730729618,2.6974387113645633158 ] 
dist 108=[.72217722353932336369,2.6966776952947399529 ] 
dist 109=[.64108183907039509278,2.6897683409500161064 ] 
dist 110=[.57740504798827869272,2.6884522437165966296 ] 
dist 111=[.51377088645342887094,2.6868000288057762601 ] 
dist 112=[.43284601554372438041,2.6862878053342535708 ] 
dist 113=[.34618005277522439464,2.5803371299111139014 ] 
dist 114=[.25958194011456440304,2.5736406588322059543 ] 
dist 115=[.15572000384117083625,2.5573183597296022150 ] 
dist 116=[0                     ,2.5416243411310237919 ] 
dist 117=[.69051004943615586653,1.0821142070870258712 ] 
dist 118=[.66941239514433066789,1.0786156948112451796 ] 
dist 119=[.64906176228325487493,1.0705614041139398318 ] 
dist 120=[.6241821188515800759 ,1.0692734495606646462 ] 
dist 121=[.59804516005080477541,1.0587891481683660970 ] 
dist 122=[.57266538563358243008,1.0569052400337678512 ] 
dist 123=[.54276724326814868585,1.0542386406290596736 ] 
dist 124=[.49855724362753440886,1.0534927701396792977 ] 
dist 125=[.45437458999212721376,.92384734925503818595] 
dist 126=[.42458582903931385545,.91588992873268677588] 
dist 127=[.39939746100954220194,.89733064839007419117] 
dist 128=[.37361594028991518825,.89464441536266603202] 
dist 129=[.34917370775727412986,.86989404115658237824] 
dist 130=[.32934236473678545188,.8654653137339170926 ] 
dist 131=[.3089278546730921684 ,.86006001880440134312] 
dist 132=[.28215300958895293243,.85906131057240585018] 
dist 133=[.25563665499353264403,.82524369391795863151] 
dist 134=[.2362560822304031128 ,.82110142843744812039] 
dist 135=[.21823402470742632113,.81275289078133997922] 
dist 136=[.19715160150011780657,.81064562717607359059] 
dist 137=[.17550474528472138283,.80328463243616668203] 
dist 138=[.15522500956389794771,.80177843214316018604] 
dist 139=[.13189372874604838466,.79964130951145416622] 
dist 140=[.09804098319288895983,.79904969014882553773] 
dist 141=[.06409966643750694392,.75128154191684295458] 
dist 142=[.04041410925851326809,.7472548930016963413 ] 
dist 143=[.01951442580780347560,.73823611803939222421] 
dist 144=[-.0237080754516984299 ,.7366159197266414409 ] 
dist 145=[-.0736280360189738719 ,.72566153667588699815] 
dist 146=[-.1069915881597807537 ,.72372606662447246785] 
dist 147=[-.1348835490025702162 ,.72032348162941623939] 
dist 148=[-.1629176662473421386 ,.71958867899270126646] 
dist 149=[-.1891714454454433796 ,.70849664708937943513] 
dist 150=[-.2099422239066750657 ,.70701380658368805294] 
dist 151=[-.2308444285353411953 ,.70380870724543031174] 
dist 152=[-.2576238998680120582 ,.70312740850000519744] 
dist 153=[-.2838471760874124303 ,.699575277889035651  ] 
dist 154=[-.3025246533117874606 ,.69895415216330791003] 
dist 155=[-.3194023842678112057 ,.69761946248706562999] 
dist 156=[-.35766770985697719976,.6973249432762606405 ] 
dist 157=[-.41243497081370363744,-.2473467512263285961 ] 
dist 158=[-.44886817268380228784,-.2499477079395674790 ] 
dist 159=[-.47913983979580168319,-.2546973213193238404 ] 
dist 160=[-.50926155332936080969,-.2557443906081637518 ] 
dist 161=[-.53727530807092869196,-.3211723466224726716 ] 
dist 162=[-.55911534500137429252,-.3268007997592545619 ] 
dist 163=[-.58079406522633724065,-.3397861950644257310 ] 
dist 164=[-.60816257639765979809,-.3416518821136360879 ] 
dist 165=[-.63476800642630259425,-.3583824047728890603 ] 
dist 166=[-.65339447879142194764,-.3613095283218149839 ] 
dist 167=[-.66989340798093260593,-.3649891898992991096 ] 
dist 168=[-.68798887215093584122,-.3656217523834263624 ] 
dist 169=[-.7059049692339050518 ,-.3860785165530366992 ] 
dist 170=[-.72168645503578334848,-.3885123746151015055 ] 
dist 171=[-.73905750755208089732,-.3935289952174305819 ] 
dist 172=[-.76333173951741309376,-.3946908277169250293 ] 
dist 173=[-.78728193877641935436,-.3992178374726143993 ] 
dist 174=[-.80335689528391742712,-.4000542050185131934 ] 
dist 175=[-.81687036103710680753,-.4013016714993703583 ] 
dist 176=[-.83057483368654060694,-.4015894745921398134 ] 
dist 177=[-.84348744561365152991,-.5635691026443431171 ] 
dist 178=[-.85383354788074415173,-.5701218027161350070 ] 
dist 179=[-.86436595574346598453,-.5849252773008845231 ] 
dist 180=[-.87802379181659347544,-.5873329000553813947 ] 
dist 181=[-.89147696031641746267,-.6055150207485965428 ] 
dist 182=[-.90119072519569765481,-.6086786442306404026 ] 
dist 183=[-.91010431830547170478,-.6135783795243613168 ] 
dist 184=[-.92035687987894734543,-.6147625400934401957 ] 
dist 185=[-.93078798211429875577,-.6334989299839129056 ] 
dist 186=[-.94041574032699928788,-.6358442346828598345 ] 
dist 187=[-.95137930457115691211,-.6410147112247644640 ] 
dist 188=[-.967153558142963882  ,-.6418879197694220605 ] 
dist 189=[-.98275513854904577489,-.6477551485159963754 ] 
dist 190=[-.99302802528805915607,-.6487317045855165625 ] 
dist 191=[-1.0014471622858124546 ,-.6504673939206671859 ] 
dist 192=[-1.0096338619824547572 ,-.6508161445331769648 ] 
dist 193=[-1.0171243804217066245 ,-.65476056265231976978] 
dist 194=[-1.0227588353725450002 ,-.65533046613493893323] 
dist 195=[-1.0281587112022787156 ,-.65534391335328472057] 
dist 196=[-1.0347109238323143242 ,-.65460304683362436312] 
dist 197=[-1.0409516781669317032 ,-.65342634364069514999] 
dist 198=[-1.0451057388025817158 ,-.65169647668629832158] 
dist 199=[-1.0485600936096484731 ,-.64921571857519030881] 
dist 200=[-1.0520020679106016994 ,-.6450355805230578312 ] 
dist 201=[-1.0552062982310431784 ,-.6404629521700383666 ] 
dist 202=[-1.0577096880617048547 ,-.63641228659295539202] 
dist 203=[-1.0601996065069167543 ,-.6319353099521943122 ] 
dist 204=[-1.0633499408382793716 ,-.62565746876157417268] 
dist 205=[-1.0663576937977337064 ,-.61863933661309433069] 
dist 206=[-1.0682773015723211868 ,-.61120132469346557644] 
dist 207=[-1.0697827107002289808 ,-.60196939371286742703] 
dist 208=[-1.0711337239640297501 ,-.58777593949149268385] 
dist 209=[-1.0722951074743915015 ,-.5733764071955340079 ] 
dist 210=[-1.0730420310577273896 ,-.56332018953285855806] 
dist 211=[-1.0736344313697130435 ,-.55443978478607855279] 
dist 212=[-1.0741777672929930553 ,-.54474322681842300658] 
dist 213=[-1.0746066683999397502 ,-.53516936591290957684] 
dist 214=[-1.0747413557291157025 ,-.52677969764555225232] 
dist 215=[-1.0747681589257850727 ,-.51758204880908442686] 
dist 216=[-1.0747654632390230384 ,-.50477638768540726822] 
dist 217=[-1.0739984580821411050 ,-.49174818264547854114] 
dist 218=[-1.0737940356507920063 ,-.48166038092861592374] 
dist 219=[-1.0736652641325712344 ,-.47171304195294862439] 
dist 220=[-1.0736044552852203582 ,-.45924663416226811327] 
dist 221=[-.99453812337115763974,-.445990467109443321  ] 
dist 222=[-.99080643617579292803,-.43288421115273831315] 
dist 223=[-.98210069761204722138,-.41726881499336636036] 
dist 224=[-.98069153649156241833,-.39397650098434702865] 
dist 225=[-.96887956746702426421,-.37036247267614691847] 
dist 226=[-.96670260444145779358,-.35346026523515676724] 
dist 227=[-.96371816241271593928,-.33810228466999940228] 
dist 228=[-.96282453150597488757,-.32066488773189041562] 
dist 229=[-.94589762657859707282,-.3030532548915189808 ] 
dist 230=[-.94368951883341424978,-.28699834827469131385] 
dist 231=[-.93905198291651770306,-.26887659486043942942] 
dist 232=[-.93558685055041031429,-.24299790362724208258] 
dist 233=[-.92646573017887816692,-.21638234906888990465] 
dist 234=[-.92587287724174292759,-.19531325671303764678] 
dist 235=[-.92191894298719122328,-.17410099296206751143] 
dist 236=[-.91561321472163118746,-.14691276704256913413] 
dist 237=[-.87072442878369151688,-.11769104566018376747] 
dist 238=[-.8663410419041903593 ,-.08834512527307004578] 
dist 239=[-.85535750146917689888,-.05304351593464948766] 

8 phat 1 dirichlet min maxes function [0, 2, 2, 0, 2, 0, 1, 0, 2] 
dist 0=[3.5185916322193623712 ,3.5185916322193623712 ] 
dist 1=[3.5163203826588317842 ,3.5201606888561670989 ] 
dist 2=[3.5129238084112143437 ,3.5221400935901527310 ] 
dist 3=[3.5068535668439931071 ,3.5260526538836947792 ] 
dist 4=[3.4997328145926118409 ,3.5301403794274077846 ] 
dist 5=[3.4921343145990867175 ,3.5328204336119619496 ] 
dist 6=[3.4826665694059829890 ,3.5350038741321729852 ] 
dist 7=[3.4680690224442412443 ,3.5371052387824259778 ] 
dist 8=[3.4530750167771073724 ,3.5398965679064053884 ] 
dist 9=[3.4420214707140848776 ,3.5428757665532121526 ] 
dist 10=[3.4316479634895859053 ,3.5457435433631310437 ] 
dist 11=[3.4193740289279046508 ,3.5483480844486242910 ] 
dist 12=[3.4066950703199344847 ,3.5502743769429307686 ] 
dist 13=[3.3947014977864508080 ,3.5520884457920576592 ] 
dist 14=[3.3808129686537092151 ,3.5542441262732029515 ] 
dist 15=[3.3605543605122500987 ,3.5563085853751644636 ] 
dist 16=[3.3395337827134525206 ,3.5577577787030730896 ] 
dist 17=[3.3225974437461563361 ,3.5590455815152037208 ] 
dist 18=[3.3052704963736488094 ,3.5604644745592809325 ] 
dist 19=[3.2826875144426107846 ,3.5618731890484392398 ] 
dist 20=[3.2582253672623293290 ,3.5631202708574824418 ] 
dist 21=[3.2333819342398395509 ,3.5644981736013573958 ] 
dist 22=[3.2032924905931753955 ,3.5664301554787271545 ] 
dist 23=[3.1578467973855036068 ,3.5684020601840761776 ] 
dist 24=[3.1122810167347765012 ,3.5699396465517467331 ] 
dist 25=[3.0817112334745921430 ,3.5714661420287606844 ] 
dist 26=[3.0560272493019897815 ,3.5733936764624575997 ] 
dist 27=[3.0300041990037280117 ,3.5754509657573131792 ] 
dist 28=[3.0055003055651186688 ,3.5774964644191227490 ] 
dist 29=[2.9858928039369465908 ,3.5799422372575320178 ] 
dist 30=[2.9659562493430723955 ,3.5836005811966063123 ] 
dist 31=[2.9401361754260762443 ,3.5872355545702533368 ] 
dist 32=[2.9147190779529145108 ,3.5895878447859879528 ] 
dist 33=[2.8963943906992810536 ,3.5914697473241219510 ] 
dist 34=[2.8796074935710341669 ,3.5932232109671936505 ] 
dist 35=[2.8603414099280352243 ,3.5947767990319481909 ] 
dist 36=[2.8407641379894362004 ,3.5958592144364744816 ] 
dist 37=[2.8227325173593137168 ,3.5968124666806182199 ] 
dist 38=[2.8022296901167971857 ,3.5978494066563166347 ] 
dist 39=[2.7727678274274255670 ,3.5987762670713264104 ] 
dist 40=[2.7433484921509800565 ,3.5992892076915255626 ] 
dist 41=[2.7230157705039873476 ,3.5996011058835712719 ] 
dist 42=[2.7052818174276508271 ,3.5997238118873235204 ] 
dist 43=[2.6862573085684189584 ,3.5997163202419789456 ] 
dist 44=[2.6676714688506559699 ,3.5996686058151734901 ] 
dist 45=[2.6516921505007990653 ,3.5992821688178832950 ] 
dist 46=[2.6344298618117036494 ,3.5992092073016242961 ] 
dist 47=[2.6107122631041624272 ,3.5974972829169269042 ] 
dist 48=[2.5867187634687561973 ,3.5971508976042159304 ] 
dist 49=[2.5683528973830860709 ,3.5962007503600552680 ] 
dist 50=[2.5504424304249761728 ,3.5959327985536314376 ] 
dist 51=[2.5282704838647419366 ,3.5939216794180607231 ] 
dist 52=[2.5048328231762833480 ,3.5934450035124869404 ] 
dist 53=[2.4818596204265885438 ,3.5927161103816745729 ] 
dist 54=[2.4546344797597088089 ,3.5924690770092252615 ] 
dist 55=[2.4141894729439472230 ,3.5810892306910937088 ] 
dist 56=[2.3736931872851086772 ,3.5796727837436110255 ] 
dist 57=[2.3462629361367958290 ,3.5773888541224867466 ] 
dist 58=[2.3229308108303441791 ,3.5737910051982733884 ] 
dist 59=[2.2988266376678055143 ,3.5642955199917063981 ] 
dist 60=[2.2758344643621344543 ,3.5323922505488238143 ] 
dist 61=[2.2569502324228041845 ,3.5287820524134048632 ] 
dist 62=[2.2373033439205861584 ,3.5169086071420618277 ] 
dist 63=[2.2112606171040400345 ,3.2712401082756719923 ] 
dist 64=[2.1853405656840142024 ,3.2592683919892819625 ] 
dist 65=[2.1661843670673404297 ,3.2314985461476720904 ] 
dist 66=[2.1481587927015466933 ,3.2271698847475200447 ] 
dist 67=[2.1267611304483340677 ,3.1903322437814316591 ] 
dist 68=[2.1046192020478700232 ,3.1836731006161951218 ] 
dist 69=[2.0836166340797050686 ,3.1747227886716531501 ] 
dist 70=[2.0592509983453075424 ,3.1722195609490903284 ] 
dist 71=[2.0236571196426713441 ,3.1228472148366702777 ] 
dist 72=[1.9878699247071443991 ,3.1165600740898075016 ] 
dist 73=[1.9627310424793041878 ,3.1033749189339204074 ] 
dist 74=[1.9403753715078672210 ,3.1000112669315577604 ] 
dist 75=[1.9157207561407632357 ,3.0865027309594456824 ] 
dist 76=[1.8726437844846970868 ,3.0839772154011055804 ] 
dist 77=[1.8220712608361483469 ,3.0783089526657455441 ] 
dist 78=[1.7787192957398447755 ,3.0771024767577481820 ] 
dist 79=[1.7333944000268357637 ,3.0086653915998990091 ] 
dist 80=[1.6898234528680459907 ,3.0023720354307609628 ] 
dist 81=[1.6534871542639233885 ,2.9877784124880594113 ] 
dist 82=[1.6151915041577800912 ,2.9854184784087566999 ] 
dist 83=[1.5637832934402648145 ,2.9659639132759435533 ] 
dist 84=[1.5123159141923510603 ,2.9624127049639670251 ] 
dist 85=[1.4737835940687519272 ,2.9574556965772428309 ] 
dist 86=[1.4370331403763211571 ,2.9560184080463549898 ] 
dist 87=[1.3926930967144014843 ,2.9294301027816896242 ] 
dist 88=[1.3464217015001012210 ,2.9259860610766773694 ] 
dist 89=[1.3019459816265775150 ,2.9186664326491091866 ] 
dist 90=[1.2498950407948031003 ,2.9168164779127488148 ] 
dist 91=[1.1733233119110302670 ,2.9088539395109097323 ] 
dist 92=[1.0961104717429798549 ,2.9073952075232395197 ] 
dist 93=[1.0414951318826335578 ,2.9037957813308307489 ] 
dist 94=[.99253190966643127461,2.9032607339489868503 ] 
dist 95=[.93792712821721170871,2.8127861922819308934 ] 
dist 96=[.88333151706202081684,2.8062990321776754387 ] 
dist 97=[.83440497421997703235,2.7911404872680093774 ] 
dist 98=[.77985381560629274798,2.7888115450776729266 ] 
dist 99=[.70276014781740885456,2.7683005867756131207 ] 
dist 100=[.62380807520021741089,2.7645599493718953746 ] 
dist 101=[.56182343099929842703,2.7597285780744774744 ] 
dist 102=[.49988885670356941311,2.7584592686783065531 ] 
dist 103=[.42113705837472948615,2.7292717918264213146 ] 
dist 104=[.33680421807167479844,2.7255519160965084402 ] 
dist 105=[.25254587857142663288,2.7179194211784595891 ] 
dist 106=[.15149635667035556763,2.7159191707587003552 ] 
dist 107=[0                     ,2.7084832829614951156 ] 
dist 108=[.86303496905199751554,2.7070014710502874757 ] 
dist 109=[.84380384245839886906,2.7040219553833463713 ] 
dist 110=[.823257645999973824  ,2.7032294483259461658 ] 
dist 111=[.79531715702894406237,2.6558200186043331274 ] 
dist 112=[.76718098091687396358,2.6515474468255811829 ] 
dist 113=[.74585205455854040511,2.6418759027589917907 ] 
dist 114=[.72525122996139625045,2.6400658883429419179 ] 
dist 115=[.7000273914491765113 ,2.6277932251786076419 ] 
dist 116=[.67350864232266544169,2.6255464685751835777 ] 
dist 117=[.64772829877437161698,2.6216252027020668526 ] 
dist 118=[.61733573914031289658,2.6207392814381437754 ] 
dist 119=[.57236856557479878007,2.6057815203450198969 ] 
dist 120=[.52741859416941522089,2.6037870418630746777 ] 
dist 121=[.49709484153517068794,2.5990022929242440406 ] 
dist 122=[.47143490326369900099,2.5974073328820071028 ] 
dist 123=[.44513974448400858675,2.5903903732086658361 ] 
dist 124=[.42019106178599460443,2.5737350341650110185 ] 
dist 125=[.39991689941700060733,2.5718537411390776328 ] 
dist 126=[.37901770882137172007,2.5646279866163202281 ] 
dist 127=[.35156897283077537961,1.1143386017630446128 ] 
dist 128=[.32436732549436049144,1.0799510027816053002 ] 
dist 129=[.30445646594862982408,.99975590784751023435] 
dist 130=[.28591178276018821427,.98824953834607434131] 
dist 131=[.26417471054972815818,.88146799103713145986] 
dist 132=[.24183183911687687092,.86798226536245137445] 
dist 133=[.22086401681880311124,.86648545141668229003] 
dist 134=[.19671290939041953649,.86407326027754394013] 
dist 135=[.1616372010517745574 ,.86349667974847291006] 
dist 136=[.12645578618535405452,.81791119833845260887] 
dist 137=[.10188186272794812777,.8140179717712724395 ] 
dist 138=[.08017415522696255304,.80523505879226420878] 
dist 139=[.05645733081220916749,.8037060821726131181 ] 
dist 140=[.03302943805966668009,.79284092285084475698] 
dist 141=[.01247742964979368363,.79091367665192431026] 
dist 142=[-.01007413751589363684,.78771013424520944454] 
dist 143=[-.0415000745777304127 ,.78697641465498904951] 
dist 144=[-.07348896036221198508,.77521400069908781479] 
dist 145=[-.09829226872554171077,.77369033099616765327] 
dist 146=[-.12278459604142872356,.7702109700242695551 ] 
dist 147=[-.15352958729689725155,.76963676786556734805] 
dist 148=[-.18625101421272044493,.76519819494392515025] 
dist 149=[-.21864889566149826537,.76440481990547960104] 
dist 150=[-.25728612261412309601,.76321238499762875375] 
dist 151=[-.31496433644888909962,.76290283070170418503] 
dist 152=[-.37256389980850161968,.1969751817466430882 ] 
dist 153=[-.41088653365704138448,.18478201898936834347] 
dist 154=[-.44273391455804187221,.18177541358367481574] 
dist 155=[-.47443308760914839958,.17027258552978310218] 
dist 156=[-.50392009346137754797,.16810299382502090045] 
dist 157=[-.52691902044308149152,.16408554517044801632] 
dist 158=[-.54975777313615149362,.16318013410954440461] 
dist 159=[-.5786041048778049501 ,-.10222684660562659033] 
dist 160=[-.60665263535856807034,-.11695869360769312543] 
dist 161=[-.62630026298114555   ,-.15104710771259752149] 
dist 162=[-.64371506096729104069,-.15606542429881857677] 
dist 163=[-.66283248973887815835,-.20055544903272534306] 
dist 164=[-.68177068102122853369,-.20843729200421437177] 
dist 165=[-.69846855389996687375,-.21850193851619637833] 
dist 166=[-.71686166819253342437,-.22057882832633086902] 
dist 167=[-.74258068282930119292,-.27735830816944048706] 
dist 168=[-.76796352027527933083,-.28428562430828596318] 
dist 169=[-.78501196173040170814,-.29859060322861733892] 
dist 170=[-.79935680982436137666,-.30211629940030241066] 
dist 171=[-.81392552388604074715,-.31546513124609199327] 
dist 172=[-.82766584190132948444,-.31799148418413965716] 
dist 173=[-.83869718864890620796,-.32254395979795724692] 
dist 174=[-.84994735480636077095,-.32352841378104667768] 
dist 175=[-.8645629488782937818 ,-.38735269278704756022] 
dist 176=[-.87897230061212011997,-.39282100874526488227] 
dist 177=[-.88939752477931680621,-.40543227725673383538] 
dist 178=[-.89898533933032922241,-.40723968922295555781] 
dist 179=[-.91004513625463987722,-.42346323979224015184] 
dist 180=[-.92131528618032982419,-.42629761086153998063] 
dist 181=[-.93174451191343252984,-.42985566360547071091] 
dist 182=[-.94364220214924935633,-.43045425680454896338] 
dist 183=[-.96078612395792567994,-.45018743819907394656] 
dist 184=[-.97775113478191052879,-.45252838359550688162] 
dist 185=[-.98893319684813568612,-.45735327028189968014] 
dist 186=[-.99811014030197658291,-.45846119744291119323] 
dist 187=[-1.0070548101044829906 ,-.46280056562486577933] 
dist 188=[-1.0152527881368868165 ,-.46359927945136130817] 
dist 189=[-1.0214430126045994455 ,-.46475925466512019924] 
dist 190=[-1.0273985208418753822 ,-.4649922387346473242 ] 
dist 191=[-1.0346576447877028473 ,-.61263191673973158944] 
dist 192=[-1.0415882481277345556 ,-.61862240918253292748] 
dist 193=[-1.0462296937039305390 ,-.63210580507705847498] 
dist 194=[-1.0501203925021385382 ,-.63432816374267652639] 
dist 195=[-1.0540480571735933822 ,-.65072216716838060371] 
dist 196=[-1.0577373458037585004 ,-.65356452006965875335] 
dist 197=[-1.0606745515900195266 ,-.65809342500601715391] 
dist 198=[-1.0636474317957276501 ,-.65914754544237693427] 
dist 199=[-1.0674794031162851414 ,-.67537504636917273756] 
dist 200=[-1.0711581599397763533 ,-.67743394777506725866] 
dist 201=[-1.0735181979731023702 ,-.68181442503643672867] 
dist 202=[-1.0753829971736545070 ,-.68267593786111722525] 
dist 203=[-1.0770808610933803897 ,-.68712511691329113803] 
dist 204=[-1.0785578529139838914 ,-.68785513672680065499] 
dist 205=[-1.0795391999739130263 ,-.68935062626710625522] 
dist 206=[-1.0803533508446875712 ,-.68961639113899152123] 
dist 207=[-1.0811616042294727681 ,-.69073033930513871669] 
dist 208=[-1.0818407356195183236 ,-.69061560942109080468] 
dist 209=[-1.0821384019005516304 ,-.6900358932211182155 ] 
dist 210=[-1.0822747933068701873 ,-.68866488644158797975] 
dist 211=[-1.0823088191149230231 ,-.68687628098884045252] 
dist 212=[-1.0817594985621175348 ,-.68462620099044871318] 
dist 213=[-1.0816221145385130669 ,-.6815884657578896393 ] 
dist 214=[-1.0815435431657193147 ,-.67664937191245620242] 
dist 215=[-1.0815236589783711276 ,-.67131176241239227532] 
dist 216=[-1.0081100518894190492 ,-.66668001866886846134] 
dist 217=[-1.0046563931915713200 ,-.66164065372778394556] 
dist 218=[-.99661499017598909012,-.65467258918805264162] 
dist 219=[-.9952869188058886907 ,-.64692792887790306345] 
dist 220=[-.98440430421999113544,-.63878231214281682404] 
dist 221=[-.98239395702509476502,-.62871518571822927   ] 
dist 222=[-.97956462313727000789,-.61328485069169422568] 
dist 223=[-.97873951318511153219,-.59764836212034899133] 
dist 224=[-.96318755435895387457,-.58675664706512943541] 
dist 225=[-.9611495711400464565 ,-.57716810880541871301] 
dist 226=[-.95682220665911041084,-.56674404000728703783] 
dist 227=[-.95568190601282271609,-.55647874498219348886] 
dist 228=[-.95093227953454732302,-.54752524710765521684] 
dist 229=[-.95004489045986475705,-.53774462022817550298] 
dist 230=[-.94781294378483817188,-.5241709325029635873 ] 
dist 231=[-.94747936062739118949,-.51038049135501979515] 
dist 232=[-.92204233365354149323,-.49973287299736517015] 
dist 233=[-.9196214593463140848 ,-.48926223443805654774] 
dist 234=[-.91399185541620266742,-.47617965579129343966] 
dist 235=[-.91302298757131578931,-.46228859835723001489] 
dist 236=[-.90537868288457090833,-.44858416593989460382] 
dist 237=[-.90395254715497987218,-.43227792380534818121] 
dist 238=[-.89862616541336427679,-.40798004800398649136] 
dist 239=[-.85946386236959637216,-.38335645486952653821] 
dist 240=[-.85747415003832835691,-.36574738950825170484] 
dist 241=[-.85425311943339450072,-.34976321238838721806] 
dist 242=[-.85346086128576942786,-.33163889001087183747] 
dist 243=[-.85159961326775605013,-.31334704691811017346] 
dist 244=[-.83931748229947507143,-.29669280384236702654] 
dist 245=[-.83726587679593312069,-.27791119490336806134] 
dist 246=[-.82608759439889624122,-.25111022127340457167] 
dist 247=[-.80464979105628752903,-.22355460853314940596] 
dist 248=[-.67746614899211772451,-.20175455865395573224] 
dist 249=[-.66870884256100400012,-.17981853479973743742] 
dist 250=[-.64909144973750671088,-.1517190396851525852 ] 
dist 251=[-.6454830638849184566 ,-.12152603511128925185] 
dist 252=[-.6142835497988896062 ,-.09121630271116797845] 
dist 253=[-.60860635341884663879,-.05476366232916357199] 

8 phat 1 dirichlet min maxes function [1, 0, 0, 0, 0, 0, 0, 0, 2] 
dist 0=[3.2272675315746325760 ,3.2272675315746325760 ] 
dist 1=[3.2224353837635314032 ,3.2303151151691669429 ] 
dist 2=[3.2174970243558038113 ,3.2326632688722878169 ] 
dist 3=[3.2140246031878791397 ,3.2346977638279759919 ] 
dist 4=[3.2109330211862627780 ,3.2363942767387529042 ] 
dist 5=[3.2075179781688597588 ,3.2373905344982883211 ] 
dist 6=[3.2041225027102904559 ,3.2380724371917267922 ] 
dist 7=[3.2011091851272283255 ,3.2385115598206809626 ] 
dist 8=[3.1977737019711240325 ,3.2388262477440677149 ] 
dist 9=[3.1930895870482936220 ,3.2390104221664360069 ] 
dist 10=[3.1883055662609503876 ,3.2391357002932278995 ] 
dist 11=[3.1845704652289324830 ,3.2392148047004998259 ] 
dist 12=[3.1808578400866875401 ,3.2392588507869124284 ] 
dist 13=[3.1761637167748459656 ,3.2392438950235948557 ] 
dist 14=[3.1711504478515002668 ,3.2391826575600861016 ] 
dist 15=[3.1661612628159549554 ,3.2390937151434092801 ] 
dist 16=[3.1601922778177802647 ,3.2387843408621285194 ] 
dist 17=[3.1512598827760323536 ,3.2220644538171241866 ] 
dist 18=[3.1421905138899696096 ,3.2191121416453021300 ] 
dist 19=[3.1356736426510240597 ,3.2182769479515561688 ] 
dist 20=[3.1297256955234470543 ,3.2149746546394493393 ] 
dist 21=[3.1229319767564151917 ,3.2143104237436252187 ] 
dist 22=[3.1160467104573945857 ,3.2126202908721727295 ] 
dist 23=[3.1097325780396465904 ,3.2122842130634200248 ] 
dist 24=[3.1025749031031340678 ,3.2093203805919056281 ] 
dist 25=[3.0923155275671022892 ,3.2087186371803140960 ] 
dist 26=[3.0817462778358162511 ,3.2076279554658579038 ] 
dist 27=[3.0733491278508311025 ,3.2073298795373312370 ] 
dist 28=[3.0648660064597214566 ,3.2062312516399455095 ] 
dist 29=[3.0539528754542823832 ,3.2059207882129511722 ] 
dist 30=[3.0422022126532321674 ,3.2053516452994082648 ] 
dist 31=[3.0303690243933247228 ,3.2051686473696707802 ] 
dist 32=[3.0161095137157512068 ,3.2042455478035299263 ] 
dist 33=[2.9946537378086775673 ,3.1056458537171982273 ] 
dist 34=[2.9730589109189211788 ,3.0879475391086109491 ] 
dist 35=[2.9582432057392130287 ,3.0856002026748843654 ] 
dist 36=[2.9454367171713152537 ,3.0702986208526137628 ] 
dist 37=[2.9318786084460023933 ,3.0666635964906133596 ] 
dist 38=[2.9187411142594845692 ,3.0615962044725969443 ] 
dist 39=[2.9076170517991800814 ,3.0604483005173802802 ] 
dist 40=[2.8957454561083410750 ,3.0432259668760961509 ] 
dist 41=[2.8796178811538475039 ,3.0385963185731777547 ] 
dist 42=[2.8633842054095454920 ,3.0324561273809368896 ] 
dist 43=[2.8510882130141166105 ,3.0315219060545044420 ] 
dist 44=[2.8392214837525059178 ,3.0226027546024647350 ] 
dist 45=[2.8247048277506938087 ,3.0209157964916802989 ] 
dist 46=[2.8094494161914455822 ,3.0189191549697662357 ] 
dist 47=[2.7946277160988491309 ,3.0184131020806485931 ] 
dist 48=[2.7771607431895644564 ,3.0008445211047137444 ] 
dist 49=[2.7513244273308465322 ,2.9987208060594668800 ] 
dist 50=[2.7252138098652062840 ,2.9941126960464457772 ] 
dist 51=[2.7066496491856545673 ,2.9929614892398026812 ] 
dist 52=[2.6899079497875712435 ,2.9875505626399853410 ] 
dist 53=[2.6710870464449676617 ,2.9865222387470716811 ] 
dist 54=[2.6521824602276673033 ,2.9841836070621325637 ] 
dist 55=[2.6351060338652061525 ,2.9836028199177433792 ] 
dist 56=[2.6159561202688991197 ,2.9780202330924261662 ] 
dist 57=[2.5887577297206122358 ,2.9770957934196945720 ] 
dist 58=[2.5608448661071752509 ,2.9751208529415793291 ] 
dist 59=[2.5388371095724862006 ,2.9745469717030982801 ] 
dist 60=[2.5167596676831206093 ,2.9721157002421590105 ] 
dist 61=[2.4885680659924157272 ,2.9716197078244170198 ] 
dist 62=[2.4583179609114991658 ,2.9703256886685863331 ] 
dist 63=[2.4280066487894428155 ,2.9700632574911886195 ] 
dist 64=[2.3915902284800586911 ,2.9667649741855013288 ] 
dist 65=[2.3369201172321164056 ,2.8117733289889559882 ] 
dist 66=[2.2821525872011557908 ,2.4493201123649896568 ] 
dist 67=[2.2453464976773937916 ,2.4435097832392785553 ] 
dist 68=[2.2143532895799141997 ,2.3928913637795362209 ] 
dist 69=[2.1828368764225462642 ,2.3838085187543150909 ] 
dist 70=[2.1530868582346938137 ,2.3719438636440137927 ] 
dist 71=[2.1291591044285180530 ,2.3690282889500449101 ] 
dist 72=[2.1047170261815631465 ,2.3019407083760523100 ] 
dist 73=[2.0729097423555924898 ,2.2935488597782645360 ] 
dist 74=[2.0415254145953303816 ,2.2761272595657948302 ] 
dist 75=[2.0187751289836613607 ,2.2716602268370128764 ] 
dist 76=[1.9978078778749221020 ,2.2546819270630475139 ] 
dist 77=[1.9735555611325680417 ,2.2514445952216582725 ] 
dist 78=[1.9488049270121092201 ,2.2448761089394993093 ] 
dist 79=[1.9258444371642191900 ,2.2431800517931417608 ] 
dist 80=[1.8996061145429722548 ,2.1551938436214403791 ] 
dist 81=[1.8617443686304307058 ,2.1473188219034726161 ] 
dist 82=[1.8238683574258408694 ,2.1291754031060852756 ] 
dist 83=[1.7975729724406362848 ,2.1262707573105481737 ] 
dist 84=[1.7745126183740086579 ,2.1025978393682029216 ] 
dist 85=[1.7495765079560253153 ,2.0983379991203935153 ] 
dist 86=[1.7250958891515116274 ,2.0923141059110036667 ] 
dist 87=[1.7038574671828856278 ,2.0906241854035610885 ] 
dist 88=[1.6807503173597226530 ,2.0603836857890425234 ] 
dist 89=[1.6487949069722110295 ,2.0565218710130728688 ] 
dist 90=[1.6163735953174993663 ,2.0481973017894896995 ] 
dist 91=[1.5914028684892024714 ,2.0463140561746567487 ] 
dist 92=[1.5669033060299668618 ,2.0370385964075722409 ] 
dist 93=[1.5363666161963154779 ,2.0353798801569778994 ] 
dist 94=[1.5039774324730493906 ,2.0316727318665038520 ] 
dist 95=[1.4720680129470675381 ,2.0308993471538514457 ] 
dist 96=[1.4341305398321118048 ,1.9369457041186158312 ] 
dist 97=[1.3776295328351169504 ,1.9303313842006963327 ] 
dist 98=[1.3209935860870045765 ,1.9151121991676369415 ] 
dist 99=[1.2825163608511662935 ,1.9126572628338849298 ] 
dist 100=[1.2496624043684022450 ,1.8928532525569525952 ] 
dist 101=[1.2155191621987590337 ,1.8892897035220390807 ] 
dist 102=[1.1828237667405247133 ,1.8841902609266954841 ] 
dist 103=[1.1557610992503292541 ,1.8827786697743965231 ] 
dist 104=[1.1274182138841295431 ,1.8576360451128707718 ] 
dist 105=[1.0896020238373952345 ,1.8544209635010009462 ] 
dist 106=[1.0518477758773483872 ,1.8474499147263916612 ] 
dist 107=[1.0237526513844357314 ,1.8459067589701766617 ] 
dist 108=[.99712353366103349537,1.8380079856525134231 ] 
dist 109=[.9652332134469115361 ,1.8365910950844671752 ] 
dist 110=[.93208068596760461063,1.8335215859608747165 ] 
dist 111=[.90040281463508226295,1.8327893659216305114 ] 
dist 112=[.86347269198968654387,1.8037702607917524411 ] 
dist 113=[.8093114849163286157 ,1.8009405073938482135 ] 
dist 114=[.75476401667997231618,1.7943549992008919460 ] 
dist 115=[.71628887092695911522,1.7933088378995692182 ] 
dist 116=[.68190730071808832625,1.7844570244540004152 ] 
dist 117=[.64373387362590802832,1.7828385957793504148 ] 
dist 118=[.60566440887084319257,1.7806484606275456140 ] 
dist 119=[.57169867715155017659,1.7799897296042579955 ] 
dist 120=[.52571161990039623641,1.7676287297622107683 ] 
dist 121=[.46632319277098027324,1.7660279943234319293 ] 
dist 122=[.41977937626944152531,1.7626814386605779440 ] 
dist 123=[.37334898858308127952,1.7617856952263582231 ] 
dist 124=[.31441426532940551529,1.7583327109663993287 ] 
dist 125=[.25135455173201448309,1.7576697346659805339 ] 
dist 126=[.18842446427233118502,1.7561452111519858834 ] 
dist 127=[.11300728495284611978,1.7558172966014824483 ] 
dist 128=[0                     ,1.7360086697867775740 ] 
dist 129=[0                     ,1.5532752235051456469 ] 
dist 130=[.2916542424003601287 ,.3572698145898035655 ] 
dist 131=[.2385238662908373467 ,.3478727179115348540 ] 
dist 132=[.1943055100166557078 ,.2604706505324893106 ] 
dist 133=[.1501858671004923252 ,.2448973402735085538 ] 
dist 134=[.1090758587507347710 ,.2261229494151975405 ] 
dist 135=[.0768957497387129914 ,.2229932607988175848 ] 
dist 136=[.0448310696011189978 ,.1047142498807209146 ] 
dist 137=[.0041827578400864155 ,.0903570560101709616 ] 
dist 138=[-.0354139540922500827 ,.0615426933349457878 ] 
dist 139=[-.0632723391612597032 ,.0543362470494099255 ] 
dist 140=[-.0880918748395526105 ,.0295682726588641624 ] 
dist 141=[-.1155334829883566182 ,.0244647651530720939 ] 
dist 142=[-.1428325320708050015 ,.0182176920673144127 ] 
dist 143=[-.1670818529674391292 ,.0171644384871064395 ] 
dist 144=[-.1939424534722662655 ,-.1151442622566932445 ] 
dist 145=[-.2316863916480665821 ,-.1162574053647060075 ] 
dist 146=[-.2690167882389644797 ,-.1885500889451298326 ] 
dist 147=[-.2942232657747672897 ,-.1938829211574946975 ] 
dist 148=[-.3155780557963472597 ,-.2295932067403507005 ] 
dist 149=[-.3375020617602837278 ,-.2358365965447174036 ] 
dist 150=[-.3583290861730266305 ,-.2469046877910116487 ] 
dist 151=[-.3752960585116037798 ,-.2492879704278144386 ] 
dist 152=[-.3928243163092179366 ,-.2829932449539588915 ] 
dist 153=[-.4158964486411825508 ,-.2875454127396815552 ] 
dist 154=[-.4387849740777103938 ,-.2967893578484259644 ] 
dist 155=[-.4555788296282843675 ,-.2991051012278284833 ] 
dist 156=[-.4712607057044046501 ,-.3071381452024881038 ] 
dist 157=[-.4897014231509606180 ,-.3087305612370348187 ] 
dist 158=[-.5086889347508486101 ,-.3108509891868352539 ] 
dist 159=[-.5265579548566320428 ,-.3112581668171364304 ] 
dist 160=[-.5471791739810866692 ,-.4204826863811865889 ] 
dist 161=[-.5771752740095523024 ,-.4210214865319958624 ] 
dist 162=[-.6069525671633482547 ,-.5459184458588223166 ] 
dist 163=[-.6266985834923031050 ,-.5495109310680951513 ] 
dist 164=[-.6430361036920062887 ,-.5819666291361978310 ] 
dist 165=[-.6591796940721089488 ,-.5876861992062106412 ] 
dist 166=[-.6741206871803615753 ,-.5948179528475030999 ] 
dist 167=[-.6856479249242193655 ,-.5960812179572960261 ] 
dist 168=[-.6969764001296137186 ,-.6372201627606569917 ] 
dist 169=[-.7111223811856708399 ,-.6421666632590353950 ] 
dist 170=[-.7247986344996134101 ,-.6522875653247036655 ] 
dist 171=[-.7342482472032932099 ,-.6547986266551154498 ] 
dist 172=[-.7424876815480832040 ,-.6637821288433425283 ] 
dist 173=[-.7513233287014004856 ,-.6655186945562101600 ] 
dist 174=[-.7599536014269845863 ,-.6680860672175699225 ] 
dist 175=[-.7673715767113355325 ,-.6687199774800074040 ] 
dist 176=[-.7753838003196116413 ,-.7130872700362952524 ] 
dist 177=[-.7863910749962764990 ,-.7167490931275039441 ] 
dist 178=[-.7971708620784116805 ,-.7250826078601013492 ] 
dist 179=[-.8042731645108093317 ,-.7262946822169613028 ] 
dist 180=[-.8100989018438933936 ,-.7365883766765351921 ] 
dist 181=[-.8157725074651119578 ,-.7383446593257266155 ] 
dist 182=[-.8209697546964646648 ,-.7407003572896641916 ] 
dist 183=[-.8248901073513051934 ,-.7411387161695535718 ] 
dist 184=[-.8286581943372000935 ,-.7518426898375178132 ] 
dist 185=[-.8332464465762870717 ,-.7530753728723829151 ] 
dist 186=[-.8376256117288894677 ,-.7557510291360489814 ] 
dist 187=[-.8405573891339699625 ,-.7561438639208874952 ] 
dist 188=[-.8430143647699244165 ,-.7589222855898734833 ] 
dist 189=[-.8454943714366903462 ,-.7593367576001692606 ] 
dist 190=[-.8478244442348444270 ,-.7600472934259747819 ] 
dist 191=[-.8496817517045774077 ,-.7601629381052435328 ] 
dist 192=[-.8515643958707894850 ,-.7875122781493360900 ] 
dist 193=[-.8539959687491657671 ,-.7896082940948103516 ] 
dist 194=[-.8563409047921212426 ,-.8193247118792465791 ] 
dist 195=[-.8578770085627634197 ,-.8201042665292026126 ] 
dist 196=[-.8591278998606060055 ,-.8234481234250236085 ] 
dist 197=[-.86033185355327380852,-.8240339731094424209 ] 
dist 198=[-.86142600424238360727,-.8248363141907846814 ] 
dist 199=[-.86223763704049234373,-.82490881919048322965] 
dist 200=[-.86300484087928585426,-.82471392011270171692] 
dist 201=[-.86392126876405971627,-.8241355070195147724 ] 
dist 202=[-.86478774100916524645,-.82316078356397994922] 
dist 203=[-.86535510428445859866,-.82138063776760955624] 
dist 204=[-.86581693957829875828,-.81920106898439630206] 
dist 205=[-.8662612528620394754 ,-.81662870843292383669] 
dist 206=[-.86666505218078195148,-.81325466353472719361] 
dist 207=[-.86696482414491145511,-.80786852715955413578] 
dist 208=[-.86724854484794868817,-.8022661350231242161 ] 
dist 209=[-.86758816375390954164,-.79802709026230718195] 
dist 210=[-.86789968889898709374,-.7939410784741945601 ] 
dist 211=[-.86807102580528938563,-.78895071796944448077] 
dist 212=[-.86817408892518833907,-.78371159265941153106] 
dist 213=[-.86821246803927461968,-.77863053628884994607] 
dist 214=[-.86820686104055385799,-.77265022572201253932] 
dist 215=[-.86816090626071655676,-.76381422779638482048] 
dist 216=[-.86802746780642028001,-.75459976269523466573] 
dist 217=[-.86794797317830255487,-.74710563589683487467] 
dist 218=[-.86744041201419549049,-.73937562411530596394] 
dist 219=[-.8673026638939146211 ,-.72921763229634127391] 
dist 220=[-.86692127697605709284,-.71817431535504857258] 
dist 221=[-.86677545573368382528,-.70690314572026248371] 
dist 222=[-.86590601972816950151,-.6932125988666213029 ] 
dist 223=[-.86568611407115132951,-.6724921876669998313 ] 
dist 224=[-.8652860173195691538 ,-.65159658701176576424] 
dist 225=[-.86516038719123729653,-.63720530503159759695] 
dist 226=[-.6603624076889488979 ,-.62470794538072720586] 
dist 227=[-.65293434285776176988,-.61138768750168052854] 
dist 228=[-.63650936536761945793,-.59842775370611605165] 
dist 229=[-.63327997305362537674,-.58737161578248395952] 
dist 230=[-.61384661777910900188,-.5755021547548188684 ] 
dist 231=[-.61039045884010746822,-.55928905130540722214] 
dist 232=[-.60376508156674088429,-.54293168184466537815] 
dist 233=[-.60215656598778232739,-.5304851720970355467 ] 
dist 234=[-.58413420469272196921,-.51841926404472174182] 
dist 235=[-.58151494313871504694,-.50358422457149431288] 
dist 236=[-.5762811904469254624 ,-.48795644606949783705] 
dist 237=[-.57495116495452842972,-.47271970244720504177] 
dist 238=[-.57028196536534170012,-.45472474275598810261] 
dist 239=[-.56929415085988436532,-.42806453834340278623] 
dist 240=[-.56783735220877338854,-.40110916076136434461] 
dist 241=[-.56678319609987565369,-.38193355184181901818] 
dist 242=[-.40337475849793475246,-.36463085672567590502] 
dist 243=[-.39402335494328949627,-.3451668263176757581 ] 
dist 244=[-.3753422634829717216 ,-.32561110152969893478] 
dist 245=[-.37066324616562403152,-.30794163858243968127] 
dist 246=[-.3545912246546224664 ,-.28812422713484984572] 
dist 247=[-.35122250799838502253,-.25997704544673721118] 
dist 248=[-.34711594635918643269,-.23109403789588644056] 
dist 249=[-.34307007804314773678,-.20833343744789847267] 
dist 250=[-.23344246819391912608,-.1855138801526121848 ] 
dist 251=[-.22307266596500471741,-.15639505140211328403] 
dist 252=[-.21062253224304100754,-.12516330034165232954] 
dist 253=[-.19814821088195644113,-.09389238716476261931] 
dist 254=[-.13145793926143432074,-.05634333066093050109] 

8 phat 1 dirichlet min maxes function [1, 2, 0, 1, 0, 2, 1, 0, 1] 
dist 0=[3.9570911942166854262 ,3.9570911942166854262 ] 
dist 1=[3.9563809839603403181 ,3.9574067088772066297 ] 
dist 2=[3.9554143569435447018 ,3.9575044639920119474 ] 
dist 3=[3.9540731880898592265 ,3.9574832896129341974 ] 
dist 4=[3.9521891515623361589 ,3.9570129070393291772 ] 
dist 5=[3.9490510746420984302 ,3.9568090312580629787 ] 
dist 6=[3.9456109588303612247 ,3.9564161997026032518 ] 
dist 7=[3.9425187839516507092 ,3.9560009334182110568 ] 
dist 8=[3.9390634461450224471 ,3.9532838702975470254 ] 
dist 9=[3.9341707094675914791 ,3.9512892466936730385 ] 
dist 10=[3.9286781071430809736 ,3.9508047125217420853 ] 
dist 11=[3.9228233446867289201 ,3.9498688057863614360 ] 
dist 12=[3.9155323379069624707 ,3.9495711998692117620 ] 
dist 13=[3.9042948412432739160 ,3.9469340375039942282 ] 
dist 14=[3.8928770276259151642 ,3.9455995847271749643 ] 
dist 15=[3.8848647664533496759 ,3.9454089310559104323 ] 
dist 16=[3.8777478658514249682 ,3.9421887473482625237 ] 
dist 17=[3.8699114518219362979 ,3.9415953992254495725 ] 
dist 18=[3.8621342880904082185 ,3.9400771357023027732 ] 
dist 19=[3.8552543909780857052 ,3.9396892778125540838 ] 
dist 20=[3.8476568956773560488 ,3.9369028185139620147 ] 
dist 21=[3.8370093887779355553 ,3.9362749204268541967 ] 
dist 22=[3.8261439772066741681 ,3.9352707177802910528 ] 
dist 23=[3.8176748803917491080 ,3.9349596908660347923 ] 
dist 24=[3.8092697536140150309 ,3.9278200444511150284 ] 
dist 25=[3.7986602241176144043 ,3.9267055481308126767 ] 
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dist 39=[3.5672306050270893037 ,3.7479381664287992641 ] 
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dist 42=[3.4972396892423124710 ,3.7378343474444045241 ] 
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dist 46=[3.3419991936448617737 ,3.6802209052228689914 ] 
dist 47=[3.3091650652569863573 ,3.6756458937285097865 ] 
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dist 57=[3.0425381215144272949 ,3.5754554048735267704 ] 
dist 58=[3.0046154580189255888 ,3.5343618261348581400 ] 
dist 59=[2.9499508629425670572 ,3.5323499778128084746 ] 
dist 60=[2.8677932234888600781 ,3.5127933347445565384 ] 
dist 61=[2.7855490670216914634 ,3.5091783352605690012 ] 
dist 62=[2.7305384121433081768 ,3.5050118387765837050 ] 
dist 63=[2.6845017014595065886 ,3.5042109186052653217 ] 
dist 64=[2.6381524658535999745 ,3.4730970382363664950 ] 
dist 65=[2.5946967500169894584 ,3.4691713045424112412 ] 
dist 66=[2.5602338424321742542 ,3.4614938416302987483 ] 
dist 67=[2.5254761700959978537 ,3.4595565991072142416 ] 
dist 68=[2.4808414233680220837 ,3.4529089459960458142 ] 
dist 69=[2.4370838407134570627 ,3.4514089578867184981 ] 
dist 70=[2.4058347410087476108 ,3.4495690559246423726 ] 
dist 71=[2.3775114799727308932 ,3.4489836828141002482 ] 
dist 72=[2.3454569729322260384 ,3.3859848058698551530 ] 
dist 73=[2.3131383470276345010 ,3.3805882822316578499 ] 
dist 74=[2.2837586357264064124 ,3.3687932421170768629 ] 
dist 75=[2.2506608551174996535 ,3.3661866614948862406 ] 
dist 76=[2.2034703066042971103 ,3.3524243532341991620 ] 
dist 77=[2.1565035573048663587 ,3.3499147143991377590 ] 
dist 78=[2.1243009522055199845 ,3.3446306010001530577 ] 
dist 79=[2.0964877073295696347 ,3.3431846895577517656 ] 
dist 80=[2.0670779802752182355 ,3.3305509378963422829 ] 
dist 81=[2.0243768536428526398 ,3.3285359399652934458 ] 
dist 82=[1.9753514099458133557 ,3.3245244193112664167 ] 
dist 83=[1.9342912818592157424 ,3.3234676099599538565 ] 
dist 84=[1.8908632847008653029 ,3.3195710308464733469 ] 
dist 85=[1.8323665460471467884 ,3.3187195625182899880 ] 
dist 86=[1.7737116577189790060 ,3.3170869521321803847 ] 
dist 87=[1.7296510754047330528 ,3.3166375931197118019 ] 
dist 88=[1.6874839808471525726 ,3.1141412797110067108 ] 
dist 89=[1.6364029028347826882 ,3.1032977382109355817 ] 
dist 90=[1.5829871185667456950 ,3.0788053548496819162 ] 
dist 91=[1.5314813774039412683 ,3.0743855106141592258 ] 
dist 92=[1.4710789217889456744 ,3.0437448419234016523 ] 
dist 93=[1.3820769555966088873 ,3.0382271271735545121 ] 
dist 94=[1.2922710593440209761 ,3.0288125506275707877 ] 
dist 95=[1.2286529450979244253 ,3.0266764576291505402 ] 
dist 96=[1.1715200631673395552 ,2.9915639980055997964 ] 
dist 97=[1.1076546050948255727 ,2.9869624731965645408 ] 
dist 98=[1.0437136031815046032 ,2.9760329960092697732 ] 
dist 99=[.98627855216387789792,2.9744154648350311779 ] 
dist 100=[.92213166868867716332,2.9584954523362473134 ] 
dist 101=[.83134384685273152303,2.9510640696689232927 ] 
dist 102=[.73831008153025780347,2.9257921635452353170 ] 
dist 103=[.665179594716670412  ,2.9149498995522955510 ] 
dist 104=[.59202396292468034279,2.7563884184688309915 ] 
dist 105=[.49888961952899899436,2.7437017720796060348 ] 
dist 106=[.39909725425707277144,2.7178762984594567251 ] 
dist 107=[.29931004013161672893,2.7107449007131218451 ] 
dist 108=[.17957643116894091611,2.6558625204154766381 ] 
dist 109=[0                     ,2.6281590933348850793 ] 
dist 110=[.8761965608333331384 ,1.3764697203119455838 ] 
dist 111=[.83653913749098703149,1.3619833811396487254 ] 
dist 112=[.79683348055389672443,1.3597085428872461743 ] 
dist 113=[.76710491531688413138,1.3408642076333453756 ] 
dist 114=[.73874982107707739388,1.3374920490306912075 ] 
dist 115=[.70453791712986077113,1.3328149220106006304 ] 
dist 116=[.66883617687737430316,1.3314838280781668530 ] 
dist 117=[.63452187951413107028,1.3077621509887084220 ] 
dist 118=[.59436531271253387781,1.3047581630545150870 ] 
dist 119=[.53529505193074629659,1.2983251490526189130 ] 
dist 120=[.47638693164514630761,1.2968723372709253569 ] 
dist 121=[.43687891136365934701,1.2898918413899694532 ] 
dist 122=[.40369950468736342279,1.2886642501558867644 ] 
dist 123=[.3701052352118672375 ,1.2858513481123892704 ] 
dist 124=[.33848683695844843976,1.2853669566304173137 ] 
dist 125=[.31321072671576922071,.86670887848602554902] 
dist 126=[.28753267427864133236,.85062117371072997485] 
dist 127=[.25430654558388012831,.81311661648834285418] 
dist 128=[.22161314003530548953,.80771761276810641224] 
dist 129=[.19806592937284283807,.75780373169539229204] 
dist 130=[.17651857629782959606,.74889057493138214748] 
dist 131=[.15182441035658761745,.73806401194992260946] 
dist 132=[.12675127252518267736,.73614620211458297976] 
dist 133=[.1036880680351076271 ,.6683005213744180488 ] 
dist 134=[.07748827101159697058,.66002183904998923468] 
dist 135=[.03986906220844754915,.64336772693492331392] 
dist 136=[.00231636536667477327,.63918051743770391033] 
dist 137=[-.02361739015510874832,.62465392533369000496] 
dist 138=[-.04621504897761891290,.62167253507870923413] 
dist 139=[-.07042367721260931984,.61768655589088290902] 
dist 140=[-.09405395624964190789,.61668516475059311352] 
dist 141=[-.11433827344212448073,.52194450687041138002] 
dist 142=[-.13622391554376415494,.51402445681467895248] 
dist 143=[-.16625934148621952481,.49633382522006617455] 
dist 144=[-.19662874719433275887,.49313774424968917412] 
dist 145=[-.21985027650427378346,.47182155500541467691] 
dist 146=[-.24247226093341897453,.46806810809512734628] 
dist 147=[-.27044354430175490587,.46140094843962826126] 
dist 148=[-.29999431989791280533,.45994686757184559453] 
dist 149=[-.32893412258949825026,.43905409397796627121] 
dist 150=[-.36321119361547593215,.43623227626681155112] 
dist 151=[-.41411053349109546954,.4303027098333521452 ] 
dist 152=[-.46487580873531438594,.42890732292592228011] 
dist 153=[-.49861663531991942891,.42293901535276580565] 
dist 154=[-.52661807009569903909,.42186420833502971622] 
dist 155=[-.55442632940851039801,.41959312140802520996] 
dist 156=[-.5802532546636285699 ,.41908027859672082643] 
dist 157=[-.60032954607566254959,.29189336035715969947] 
dist 158=[-.62020219144007104052,.28470081327132943327] 
dist 159=[-.64521455970934143909,.26807531346134766317] 
dist 160=[-.66949251377775397232,.26558063480553353763] 
dist 161=[-.68642757627328340948,.24388410832250573289] 
dist 162=[-.70136341187946347539,.24002631311284237248] 
dist 163=[-.71764465295366574012,.2349843076287364937 ] 
dist 164=[-.7337058336319055869 ,.23381622008515460642] 
dist 165=[-.74776145641180412467,.20612429719143333004] 
dist 166=[-.76315626867803970269,.2027045202540846716 ] 
dist 167=[-.78457409899631624218,.19557721783963500868] 
dist 168=[-.80566502313122203442,.19384608758074833093] 
dist 169=[-.81975224571262020216,.18689033103622824847] 
dist 170=[-.83151973549734307503,.18560395547979685171] 
dist 171=[-.84333194187952668863,.18303485537439468077] 
dist 172=[-.85438436622008605532,.18239776185323451407] 
dist 173=[-.86311280414034282649,.15073490012432573937] 
dist 174=[-.87188201023516896726,.14793184446019939802] 
dist 175=[-.88309752270918210862,.1414286514176593957 ] 
dist 176=[-.89407110923837549152,.14048937448703763144] 
dist 177=[-.90187264233382622395,.1319578410377319822 ] 
dist 178=[-.90890778331660957628,.13044705836949927098] 
dist 179=[-.91681587828388398893,.12857336961038301511] 
dist 180=[-.92475874686121107115,.12823446393116510449] 
dist 181=[-.93193299824297261574,.11716660986974929192] 
dist 182=[-.93997804235932181349,.11582821964401740701] 
dist 183=[-.951404052852175186  ,.11309844957618396409] 
dist 184=[-.96268125922129264697,.1124097860147164998 ] 
dist 185=[-.97013109973793127021,.10998988896217632843] 
dist 186=[-.97626379962374717624,.10951421213805698853] 
dist 187=[-.98227251117213398362,.10880246811480260391] 
dist 188=[-.98780035908430769003,.10862546934798513591] 
dist 189=[-.99200962712238909568,-.34056034187667019103] 
dist 190=[-.99609355836674349214,-.3363841169944000499 ] 
dist 191=[-1.0011200594853030856 ,-.33022156576650421401] 
dist 192=[-1.0059436851574507788 ,-.32379913553718082142] 
dist 193=[-1.0092161223729545873 ,-.31858342097804797654] 
dist 194=[-1.0120053088265276534 ,-.31321077319569797441] 
dist 195=[-1.0148959543380139424 ,-.30616058515522997264] 
dist 196=[-1.0176590310541897780 ,-.29850126865530561952] 
dist 197=[-1.0199379428896171533 ,-.29069220939482384426] 
dist 198=[-1.0223174019168038514 ,-.28121320976662517356] 
dist 199=[-1.0254826462036403667 ,-.26687446373802541111] 
dist 200=[-1.0285364205886064627 ,-.25225819158887460944] 
dist 201=[-1.0304700029021309113 ,-.24166912901572181396] 
dist 202=[-1.0319686427873279812 ,-.23191763613048879354] 
dist 203=[-1.0332826773365497891 ,-.22065143538060463302] 
dist 204=[-1.0343899433193384636 ,-.20916282302795393545] 
dist 205=[-1.0350615170558167944 ,-.19852170587387010397] 
dist 206=[-1.0355477681059509226 ,-.1863758949325050286 ] 
dist 207=[-1.0359137378146332085 ,-.16886878119909531369] 
dist 208=[-1.0361737914272918276 ,-.15079415685690659996] 
dist 209=[-1.0362363971381822128 ,-.13637840121439210308] 
dist 210=[-1.0362085619460142058 ,-.12176529619208159246] 
dist 211=[-1.0361407729305813967 ,-.10290129371137797872] 
dist 212=[-1.0355812545476025603 ,-.08255961403908477921] 
dist 213=[-1.0354029618696136621 ,-.06203607104580337546] 
dist 214=[-1.0350693866883612839 ,-.03727819980493173551] 

8 phat 1 dirichlet min maxes function [2, 2, 1, 1, 2, 0, 0, 1, 2] 
dist 0=[2.4024054621553612659 ,2.4024054621553612659 ] 
dist 1=[2.3964860465088911239 ,2.4054520149264372893 ] 
dist 2=[2.3874542430739610741 ,2.4117185789128281209 ] 
dist 3=[2.3739749951771713689 ,2.4189406148468159803 ] 
dist 4=[2.3585294183749031976 ,2.4247790559206135087 ] 
dist 5=[2.3416324441198933999 ,2.4307701400850739012 ] 
dist 6=[2.3202929320712989623 ,2.4386027458935697880 ] 
dist 7=[2.2870775327337353211 ,2.4607351464850410471 ] 
dist 8=[2.2532268403261577851 ,2.4841040376603590933 ] 
dist 9=[2.2293462044102749810 ,2.5016066769595387149 ] 
dist 10=[2.2080024691375032418 ,2.5183067727788855799 ] 
dist 11=[2.1842991958802891574 ,2.5384655550096935249 ] 
dist 12=[2.1606575825096576101 ,2.5595077383853666159 ] 
dist 13=[2.1395604871129966902 ,2.5797413838372667396 ] 
dist 14=[2.1161114723816659695 ,2.6034275014734579792 ] 
dist 15=[2.0830623660827295708 ,2.6382793437927499764 ] 
dist 16=[2.0492558829784951506 ,2.6729779265020666046 ] 
dist 17=[2.0227774220736600180 ,2.6960510180102098227 ] 
dist 18=[1.9963790553205375096 ,2.7152119200622949833 ] 
dist 19=[1.9628929475283353718 ,2.7342620116709448719 ] 
dist 20=[1.9270745754608092294 ,2.7519692310678976972 ] 
dist 21=[1.8913473342821515217 ,2.7657587361279627310 ] 
dist 22=[1.8485441194883314162 ,2.7794322732751139876 ] 
dist 23=[1.7844224022008485994 ,2.7966756298225449274 ] 
dist 24=[1.7199990676436921386 ,2.8134296715320710115 ] 
dist 25=[1.6759894084475061273 ,2.8251459831339127493 ] 
dist 26=[1.6381509944368687739 ,2.8355104871636480077 ] 
dist 27=[1.5984121653990194432 ,2.8468573911872689029 ] 
dist 28=[1.5601013656686072130 ,2.8580800679809663633 ] 
dist 29=[1.5279749601850457199 ,2.8679476725837972175 ] 
dist 30=[1.4939608539344627789 ,2.8787944505320731246 ] 
dist 31=[1.4480994002987268317 ,2.8939337565792091761 ] 
dist 32=[1.4020935544676521442 ,2.9088639503771119778 ] 
dist 33=[1.3675018921376550690 ,2.9188742941442782903 ] 
dist 34=[1.3343648174971865744 ,2.9272782018961509122 ] 
dist 35=[1.2941772113613828234 ,2.9357827602023613591 ] 
dist 36=[1.2521287168452241194 ,2.9437845793484044999 ] 
dist 37=[1.2115482354623146715 ,2.9501775653826445560 ] 
dist 38=[1.1639312351305879102 ,2.9566689445639026558 ] 
dist 39=[1.0937372161533503065 ,2.9650643324828607185 ] 
dist 40=[1.0228967177691105189 ,2.9733235494890508110 ] 
dist 41=[.97269385101565750606,2.9792702555022490474 ] 
dist 42=[.92758832101684373328,2.9847101080442574464 ] 
dist 43=[.87713677191289872229,2.9909419464252417499 ] 
dist 44=[.8266079529878502376 ,2.9972682732755517491 ] 
dist 45=[.78119335042990546867,3.0030860761976657687 ] 
dist 46=[.73044963527980258609,3.0096941805131361802 ] 
dist 47=[.65860478389711785601,3.0191816671866030940 ] 
dist 48=[.58497128372218496569,3.0285489285752879344 ] 
dist 49=[.527073113747335405  ,3.0346761405984403526 ] 
dist 50=[.46913881169661178871,3.0396524196071730605 ] 
dist 51=[.3953607862773380116 ,3.0444160212250356933 ] 
dist 52=[.31629759253305891175,3.0487246796664266771 ] 
dist 53=[.23722303117686649986,3.0518812159876880346 ] 
dist 54=[.14233116685739431178,3.0548240058835510843 ] 
dist 55=[0                     ,3.0582776963793416790 ] 
dist 56=[1.8189356275684276182 ,3.0615079871892882773 ] 
dist 57=[1.8392826170236664289 ,3.0635571943031745963 ] 
dist 58=[1.8935810832759507495 ,3.0651500285905545663 ] 
dist 59=[2.5400612123211327881 ,3.0665548582158361183 ] 
dist 60=[2.5488771798302816200 ,3.0677448309539717584 ] 
dist 61=[2.5687649597139102836 ,3.0684782555243308881 ] 
dist 62=[2.5719985660047445979 ,3.0690235714159482972 ] 
dist 63=[2.5856067241528787830 ,3.0694611328043234367 ] 
dist 64=[2.5554593465207501807 ,3.0697773191886755757 ] 
dist 65=[2.5337545058881682118 ,3.0698371439564330487 ] 
dist 66=[2.5139018827664482588 ,3.0697919699715497878 ] 
dist 67=[2.4911631850407064429 ,3.0696911945725403186 ] 
dist 68=[2.4680830297501510001 ,3.0688941613498519246 ] 
dist 69=[2.4468646035468847937 ,3.0686443401085891236 ] 
dist 70=[2.4227697230244194895 ,3.0682719778088468173 ] 
dist 71=[2.3881840221150665650 ,3.0681178040058663546 ] 
dist 72=[2.3525336212470595827 ,3.0638247966504776854 ] 
dist 73=[2.3241800397417775404 ,3.0631642394892991639 ] 
dist 74=[2.2955093069293790055 ,3.0618500003931982637 ] 
dist 75=[2.2585903256835521011 ,3.0614658585430694565 ] 
dist 76=[2.2188211731410464052 ,3.0598613984586064056 ] 
dist 77=[2.1787500242858775617 ,3.0594935032564845285 ] 
dist 78=[2.1304468585419201856 ,3.0585174624708738290 ] 
dist 79=[2.0577504208974866388 ,3.0582497491371911082 ] 
dist 80=[1.9849638517937565856 ,3.0203825756934248814 ] 
dist 81=[1.9363001679090379055 ,3.0175373398198379602 ] 
dist 82=[1.8955981450166336110 ,3.0109312608234940334 ] 
dist 83=[1.8546574605146678706 ,3.0097342872008540126 ] 
dist 84=[1.8162967453208630186 ,3.0007230952300534066 ] 
dist 85=[1.7859143535887276777 ,2.9990203436865181127 ] 
dist 86=[1.7553089784503575076 ,2.9963867714604086075 ] 
dist 87=[1.7160563508993300121 ,2.9956766499962068830 ] 
dist 88=[1.6775989904333774996 ,2.9822180997357473864 ] 
dist 89=[1.6501746077843041328 ,2.9804013603592008671 ] 
dist 90=[1.6253586305489094167 ,2.9764185197522608371 ] 
dist 91=[1.5973346429531173523 ,2.9754081997387934711 ] 
dist 92=[1.5691145912463397817 ,2.9705360986760953970 ] 
dist 93=[1.5435143762672105260 ,2.9695872472891653056 ] 
dist 94=[1.5147176570406999314 ,2.9674863730609273791 ] 
dist 95=[1.4737118932206558389 ,2.9668685950243982477 ] 
dist 96=[1.4329228137992128287 ,2.9427779699244216903 ] 
dist 97=[1.4049928115001767932 ,2.9403612436717198311 ] 
dist 98=[1.3809092633116476606 ,2.9346521856112705119 ] 
dist 99=[1.3555056334650397827 ,2.9336781678514460597 ] 
dist 100=[1.3309476043111096336 ,2.9255772665366936565 ] 
dist 101=[1.3102463782415682533 ,2.9240334520948313795 ] 
dist 102=[1.2882350968886297422 ,2.9218965508301766177 ] 
dist 103=[1.2584369715515953360 ,2.9212376753631030382 ] 
dist 104=[1.2284910504864339147 ,2.9080912087279084751 ] 
dist 105=[1.2058886003174518478 ,2.9063255322842532422 ] 
dist 106=[1.1841528887284638974 ,2.9005250400585417866 ] 
dist 107=[1.1576738393154658548 ,2.8667060044654805973 ] 
dist 108=[1.1299061543966881537 ,2.8638988489722781919 ] 
dist 109=[1.1030160236920897713 ,2.8590155963209706229 ] 
dist 110=[1.0713938624159766298 ,2.8534165607023440303 ] 
dist 111=[1.0246985065428653263 ,2.8384327608232240048 ] 
dist 112=[.97805804161623928382,2.6202117667091085082 ] 
dist 113=[.94665543889067717519,2.6083850792413567420 ] 
dist 114=[.92014951339963489258,2.5819982650721915296 ] 
dist 115=[.89309529037568934491,2.5770063549311349152 ] 
dist 116=[.86749424482720871123,2.5450427386059186128 ] 
dist 117=[.84680089063682994965,2.5393324364404539166 ] 
dist 118=[.82556969864556493378,2.5286428719202092408 ] 
dist 119=[.79781735319144596616,2.5176287617278116220 ] 
dist 120=[.77037682226807394866,2.4438968473089105828 ] 
dist 121=[.75039285865954293505,2.4347110725240963195 ] 
dist 122=[.73188202774570660186,2.4037338948924185539 ] 
dist 123=[.71033388709662779188,1.5209287003174004894 ] 
dist 124=[.68826726914307425864,1.4921879368555768144 ] 
dist 125=[.66768257846267982432,1.4251287380105068217 ] 
dist 126=[.64406957042615392528,1.4154665232168405679 ] 
dist 127=[.60988997188300001594,1.3259893363881459329 ] 
dist 128=[.57565509938950401664,1.3099858170951870920 ] 
dist 129=[.55182100082352992031,1.2905757016126272030 ] 
dist 130=[.53084942412175900566,1.2871099366932383947 ] 
dist 131=[.50806436606339665992,1.1646194667798478098 ] 
dist 132=[.48563209524140254899,1.1496461883287705304 ] 
dist 133=[.46607163383695507572,1.1195501260836878662 ] 
dist 134=[.44470684403987092759,1.1119783648359052804 ] 
dist 135=[.41505743174060686043,1.0856982459413821741 ] 
dist 136=[.38493104165997458317,1.0802858220626172986 ] 
dist 137=[.36165838623061587516,1.0730227303806858802 ] 
dist 138=[.33875935331144156181,1.0711327514778133407 ] 
dist 139=[.31012741763617011891,.89691171797296779345] 
dist 140=[.27971289858021541645,.88231655766503657939] 
dist 141=[.24968370215758853552,.84973012985430474626] 
dist 142=[.21393398316291373077,.8437934481978255788 ] 
dist 143=[.1606379194309065201 ,.80452831060742647801] 
dist 144=[.1074035522076125853 ,.79760101585623666989] 
dist 145=[.0719006133632997957 ,.78522057445067942808] 
dist 146=[.0423032571952805644 ,.78249099275084549182] 
dist 147=[.0126906574143546109 ,.74391969211026849379] 
dist 148=[-.0149544165551884807 ,.73868286035551705262] 
dist 149=[-.0366818571364003285 ,.72766281130691686253] 
dist 150=[-.0584132412354789547 ,.72505189873149580431] 
dist 151=[-.0860740889003642180 ,.71385472387275286262] 
dist 152=[-.1130736043842409023 ,.71183696986956272178] 
dist 153=[-.1321597228358418469 ,.70747552580109982694] 
dist 154=[-.1492582166033173303 ,.70654934601696233305] 
dist 155=[-.1683074229264070018 ,.46329141625346914405] 
dist 156=[-.1873417352512918740 ,.4495261645153659921 ] 
dist 157=[-.2043806544465082789 ,.41767464253041535368] 
dist 158=[-.2233625234339008485 ,.41291161662970342471] 
dist 159=[-.2501684496127784646 ,.37124386015665154396] 
dist 160=[-.2767376791884891081 ,.3638303840776232992 ] 
dist 161=[-.2947727843388680856 ,.35420420272857895882] 
dist 162=[-.3101549627636882511 ,.3520170057393470112 ] 
dist 163=[-.3261127384680725549 ,.29847321901381596233] 
dist 164=[-.3413758826879236131 ,.29186863048281676357] 
dist 165=[-.3539796014271892013 ,.27814523300675966891] 
dist 166=[-.3671526836949868506 ,.27476898821744031149] 
dist 167=[-.3846932277241978625 ,.2615335251235848835 ] 
dist 168=[-.4021878344132756171 ,.25905868303639686488] 
dist 169=[-.4151771717019529666 ,.25423042623626211089] 
dist 170=[-.4274593553483442419 ,.25306223491682309552] 
dist 171=[-.4421254149151947666 ,.19067121985891865767] 
dist 172=[-.4573484034689606956 ,.18518722511783520826] 
dist 173=[-.4718582499442273054 ,.1724693244820260081 ] 
dist 174=[-.4887457714336611567 ,.17062604143674570402] 
dist 175=[-.5134792332661514786 ,.15395232709275878273] 
dist 176=[-.5381006129484341023 ,.15099858309042432115] 
dist 177=[-.5545398165272111744 ,.14731832759981299839] 
dist 178=[-.5682651520910483674 ,.14663616031926192595] 
dist 179=[-.5820313185569401452 ,.12502731977059881713] 
dist 180=[-.5949045768090564881 ,.12240722061143884161] 
dist 181=[-.6050583646816129868 ,.11705997406071383589] 
dist 182=[-.6152477217387655326 ,.11570811500160312316] 
dist 183=[-.6282632533367475224 ,.11094174039159531324] 
dist 184=[-.6409898113059460546 ,.11000504543728840908] 
dist 185=[-.6500233014096984727 ,.10856992369805161604] 
dist 186=[-.6581544392485441992 ,.10822117687086897529] 
dist 187=[-.6672716742226919465 ,.00500519575396342636] 
dist 188=[-.6764155854887463123 ,.00113829445319296970] 
dist 189=[-.6846534259508865033 ,.00046382189973295156] 
dist 190=[-.6938736348322358662 ,-.00058326153960343313] 
dist 191=[-.7069469260787682520 ,-.00083652813118970677] 
dist 192=[-.7199273289738391816 ,-.00754200438751132280] 
dist 193=[-.7287759933088501348 ,-.00829964556081083923] 
dist 194=[-.7363636684669596216 ,-.00974370761435940552] 
dist 195=[-.7443002349250806679 ,-.01008290959219973576] 
dist 196=[-.7519316814992468462 ,-.01109812692686500769] 
dist 197=[-.7582989062232684764 ,-.01129617804675158285] 
dist 198=[-.7650119059782093815 ,-.01127779915236352275] 
dist 199=[-.7740264196967134608 ,-.01096037324187308043] 
dist 200=[-.78305234877329166202,-.01051043251585321948] 
dist 201=[-.78981100887175475856,-.00996203725189021863] 
dist 202=[-.79625813456975330917,-.00923274201336800606] 
dist 203=[-.80403795575800885204,-.00805921903004407832] 
dist 204=[-.81215711568819947414,-.00667924171653629047] 
dist 205=[-.81996156398847966787,-.00512423894284356498] 
dist 206=[-.82909540109082323102,-.00313132206792633676] 
dist 207=[-.84253198943479025798,0                     ] 
dist 208=[-.85589273531484460455,-.28255667385114703333] 
dist 209=[-.86472321069537755586,-.28477534431463351125] 
dist 210=[-.87199681055050802329,-.28530819882402856917] 
dist 211=[-.87913020552094180015,-.28922270139562124856] 
dist 212=[-.88569693767965729214,-.28986671187187378682] 
dist 213=[-.89070394303485536904,-.29043130417245943535] 
dist 214=[-.89556811920951492536,-.29028978415962812595] 
dist 215=[-.90156355366746028013,-.28982460329370940538] 
dist 216=[-.90732106148446916855,-.28890652917466070791] 
dist 217=[-.91123355648553444966,-.28747343116661586538] 
dist 218=[-.9145752276925877322 ,-.28494832951836180703] 
dist 219=[-.91804949747012434382,-.28226358021953472255] 
dist 220=[-.92137728481538990749,-.28019191092740573994] 
dist 221=[-.92413304565440349787,-.27815641916163369533] 
dist 222=[-.92702027979383714013,-.27561626313940945042] 
dist 223=[-.93087396127733437522,-.2729213079149560306 ] 
dist 224=[-.93459807175452671119,-.27026660660476829235] 
dist 225=[-.93696703691124328787,-.26711126648604503569] 
dist 226=[-.93881589095962600785,-.26241383465979683257] 
dist 227=[-.94045960118688038671,-.25750096793391855788] 
dist 228=[-.94186145684470301888,-.25348390983433148913] 
dist 229=[-.94274291834403221332,-.24932129393057953998] 
dist 230=[-.94341905588423700882,-.24382618219820130268] 
dist 231=[-.9439996486955336001 ,-.23784010534779924119] 
dist 232=[-.94448004194273786468,-.23171370650811255703] 
dist 233=[-.94475538450181931598,-.22426035779104552124] 
dist 234=[-.94493546870384588647,-.21296672778806215438] 
dist 235=[-.94503480535793641945,-.20144652226965882852] 
dist 236=[-.9450754797663675569 ,-.19308690355488281973] 
dist 237=[-.94504608617200933017,-.18537466848772338947] 
dist 238=[-.9449252189740277406 ,-.17644384737796814341] 
dist 239=[-.94484163190648316035,-.16732506633850539963] 
dist 240=[-.93623874349448225785,-.15886101012432261909] 
dist 241=[-.93543341131295145616,-.14918578333064412907] 
dist 242=[-.93350472425530201933,-.13522252586148767161] 
dist 243=[-.93312294533523111146,-.1207989821399561774 ] 
dist 244=[-.93021367930729341957,-.10928268449151224521] 
dist 245=[-.92962797583786143663,-.09759706943117145008] 
dist 246=[-.92873662473617729744,-.08249627259826334472] 
dist 247=[-.92770420445537060557,-.06620443056808347855] 
dist 248=[-.91866324897940729637,-.04975483841255192214] 
dist 249=[-.9174706260622080203 ,-.02990244652456979307] 

8 phat 1 dirichlet min maxes function [1, 1, 1, 2, 0, 1, 1, 2] 
dist 0=[.84988809654981010018,.84988809654981010018] 
dist 1=[.8400583845355418977 ,.85859376999226521663] 
dist 2=[.82601604242143400779,.86814004754322781698] 
dist 3=[.81125564586012482368,.8775907756988966679 ] 
dist 4=[.79855377310160337081,.88591426006555091418] 
dist 5=[.78482206079093833551,.89507517734421385705] 
dist 6=[.76594238740504193531,.9078755729359640055 ] 
dist 7=[.74500552603326580769,.92126187850291384103] 
dist 8=[.72304522427956741283,.93276639043145082714] 
dist 9=[.69594401060826964638,.94519097312296546525] 
dist 10=[.65444390761090931762,.96225749022105897302] 
dist 11=[.61223763744752106288,.98117615548724831267] 
dist 12=[.58231181110357660304,1.0010091866932571449 ] 
dist 13=[.55540867513145849711,1.0254778708639470263 ] 
dist 14=[.52529292835988641091,1.0629387871000432700 ] 
dist 15=[.4951172677123114517 ,1.1005557294036519148 ] 
dist 16=[.46797448158474808896,1.1256485062701657011 ] 
dist 17=[.4376292901996812947 ,1.1465736505044161529 ] 
dist 18=[.39464426266078243644,1.1675203884501566178 ] 
dist 19=[.35057994652494528915,1.1870827671049653664 ] 
dist 20=[.31591768651834595246,1.2024705836359234730 ] 
dist 21=[.28122039480185092246,1.2178735022187301852 ] 
dist 22=[.23701595494796710516,1.2374962912420917910 ] 
dist 23=[.18963570710417404666,1.2566587708224138250 ] 
dist 24=[.14223543518597607981,1.2702204891845107924 ] 
dist 25=[.08534402977507185324,1.2823863649194838670 ] 
dist 26=[0                     ,1.2959655844675014100 ] 
dist 27=[1.1387711086061993907 ,1.3095491736615701232 ] 
dist 28=[1.1430651029875525618 ,1.3217325310896863953 ] 
dist 29=[1.1802673799033623578 ,1.3353248556273749460 ] 
dist 30=[1.1868501355915749837 ,1.3545442121083687361 ] 
dist 31=[1.1954928874411213235 ,1.3736052487495061938 ] 
dist 32=[1.1974583351082653025 ,1.3865643080362596982 ] 
dist 33=[1.2438329495548187662 ,1.3976395112350061649 ] 
dist 34=[1.2495219701284241868 ,1.4091652669943645954 ] 
dist 35=[1.2614381282424343783 ,1.4202120462608458559 ] 
dist 36=[1.2642063696259139268 ,1.4293713826716902793 ] 
dist 37=[1.2759568012964067373 ,1.4389778416063927079 ] 
dist 38=[1.2780715835634074635 ,1.4518130850311235907 ] 
dist 39=[1.2823230859413857814 ,1.4646354409199912225 ] 
dist 40=[1.2833661602131195971 ,1.4741903543207124616 ] 
dist 41=[1.3309759788987984445 ,1.4832595056368083624 ] 
dist 42=[1.3352208989755226218 ,1.4941388529500892686 ] 
dist 43=[1.3447886578036438043 ,1.5054586293693538830 ] 
dist 44=[1.3463394284626885494 ,1.5162894717407786946 ] 
dist 45=[1.3579894658779621470 ,1.5289272366736924497 ] 
dist 46=[1.3600032329227607684 ,1.5474745874798907257 ] 
dist 47=[1.3631447110408082421 ,1.5659342521777623714 ] 
dist 48=[1.3638905390091286422 ,1.5782212797317823234 ] 
dist 49=[1.3754082743773673445 ,1.5884383616707617561 ] 
dist 50=[1.3768544131587937619 ,1.5986183809275552935 ] 
dist 51=[1.3799221983820373556 ,1.6080950890946456246 ] 
dist 52=[1.3805149453729131085 ,1.6154989731907763148 ] 
dist 53=[1.3849741122720657443 ,1.6228631022088119018 ] 
dist 54=[1.3867783116753596513 ,1.6321807925730983697 ] 
dist 55=[1.3919885047582653870 ,1.6412491934576150156 ] 
dist 56=[1.3940158810247813749 ,1.6476161810309748839 ] 
dist 57=[1.5529431798099075412 ,1.6532751376137765112 ] 
dist 58=[1.5588258135817805791 ,1.6595114614428858530 ] 
dist 59=[1.5721694868925879325 ,1.6657036397416276715 ] 
dist 60=[1.5742834715387141021 ,1.6711860170761664362 ] 
dist 61=[1.5908175445395509342 ,1.6772440031759613614 ] 
dist 62=[1.5936940617549957795 ,1.6857385782473455688 ] 
dist 63=[1.5979663435170436525 ,1.6941328114657552087 ] 
dist 64=[1.5990490808754765989 ,1.6997894368125146907 ] 
dist 65=[1.6165694147118055504 ,1.7045694611288568904 ] 
dist 66=[1.6187218608713431485 ,1.7094573484878104342 ] 
dist 67=[1.6235792722074501544 ,1.7140885222732324542 ] 
dist 68=[1.6242908292692214371 ,1.7178417093850425639 ] 
dist 69=[1.6301297755067297255 ,1.7217014422532276747 ] 
dist 70=[1.6311090414644693645 ,1.7267587920636301417 ] 
dist 71=[1.6324791308424999146 ,1.7317652377253585684 ] 
dist 72=[1.6327454832361189750 ,1.7354213574321275818 ] 
dist 73=[1.6380195365818130136 ,1.7388182361026131420 ] 
dist 74=[1.6387052054699889676 ,1.7427877349181342663 ] 
dist 75=[1.6346928120671102241 ,1.7468613206845670702 ] 
dist 76=[1.6289983142724236260 ,1.7506745403617799916 ] 
dist 77=[1.6218788019161792148 ,1.7550592279439730492 ] 
dist 78=[1.6108754153352578689 ,1.7614186476434339075 ] 
dist 79=[1.5996858774168674687 ,1.7677242536656459468 ] 
dist 80=[1.5918217759781612749 ,1.7718936901841536297 ] 
dist 81=[1.5848243164241690351 ,1.7753302359921792292 ] 
dist 82=[1.5771012421056734303 ,1.7787043277937601725 ] 
dist 83=[1.5694263720172891550 ,1.7818129827362808805 ] 
dist 84=[1.5626217171944998718 ,1.7841877988332905082 ] 
dist 85=[1.5550949722324992722 ,1.7864992836882536360 ] 
dist 86=[1.5445318089654058261 ,1.7893546182096025342 ] 
dist 87=[1.5337466710489676863 ,1.7920998712752871203 ] 
dist 88=[1.5253320456262866155 ,1.7939710377721395919 ] 
dist 89=[1.5169736770766315567 ,1.7955753284661537296 ] 
dist 90=[1.5064135536760427082 ,1.7972530961639863390 ] 
dist 91=[1.4951397554654852317 ,1.7988662429488059063 ] 
dist 92=[1.4839267542342289174 ,1.8002120546435629692 ] 
dist 93=[1.4705168044851021492 ,1.8016309026656942877 ] 
dist 94=[1.4504554248226137688 ,1.8035361908728927335 ] 
dist 95=[1.4300898606675246986 ,1.8053826522781761625 ] 
dist 96=[1.4154632004367134035 ,1.8065661971796339355 ] 
dist 97=[1.4021210726869835690 ,1.8075002457825589321 ] 
dist 98=[1.3868935082899339331 ,1.8083487381400586109 ] 
dist 99=[1.3714677523656664892 ,1.8090854731691073252 ] 
dist 100=[1.3573328743505020096 ,1.8095725000577419652 ] 
dist 101=[1.3413189684883622729 ,1.8099737892564869804 ] 
dist 102=[1.3183772788656735750 ,1.8103675801749853238 ] 
dist 103=[1.2947484445066677458 ,1.8106954827485577530 ] 
dist 104=[1.2759860237066444656 ,1.8108332233207770835 ] 
dist 105=[1.2570415165755090040 ,1.8108726543864503436 ] 
dist 106=[1.2326843511944254182 ,1.8108538798844708165 ] 
dist 107=[1.2064655431344098962 ,1.8105735134682594608 ] 
dist 108=[1.1800746413147584582 ,1.8104689500771206351 ] 
dist 109=[1.1482817779087370938 ,1.8102500790733843708 ] 
dist 110=[1.1004556371987820819 ,1.8101586681939897059 ] 
dist 111=[1.0525794523128655615 ,1.8081433109900388669 ] 
dist 112=[1.0205864164651277935 ,1.8078237584102979173 ] 
dist 113=[.9938452309861317293 ,1.8070746587793872330 ] 
dist 114=[.96697594666407149345,1.8068338016989272892 ] 
dist 115=[.94181827903454433744,1.8056429987251236542 ] 
dist 116=[.9219233970750626081 ,1.8051779708736447731 ] 
dist 117=[.90191069858691901279,1.8039181532805148976 ] 
dist 118=[.87628177607985209135,1.8026910037552510840 ] 
dist 119=[.85119039824379616473,1.7964767826951668771 ] 
dist 120=[.83332782716974801441,1.7941132401572032341 ] 
dist 121=[.81719545029254206886,1.0073844129135096341 ] 
dist 122=[.79902468422135132458,.99097672223587257568] 
dist 123=[.78075365386864325093,.95268438034588299187] 
dist 124=[.76422022942837703716,.94716146562129043929] 
dist 125=[.74565586576084977567,.89602369411418156999] 
dist 126=[.71926127220606787834,.88687108785784107784] 
dist 127=[.69302338681341571805,.87576681220612068351] 
dist 128=[.67508584084789255603,.87376790721421337361] 
dist 129=[.6596492838648709767 ,.80358381467437910247] 
dist 130=[.64341511586283794191,.79499522403630989258] 
dist 131=[.62775096300860593233,.77773353799576020599] 
dist 132=[.61459441224987000417,.77338771734497903695] 
dist 133=[.6006466461226287322 ,.75828917615752825452] 
dist 134=[.58181770725893375666,.75517720815365411977] 
dist 135=[.56291948100086614308,.75096385233985743259] 
dist 136=[.54869457190462908242,.74982662512422154601] 
dist 137=[.53505304903562296384,.6492454336957539794 ] 
dist 138=[.5184883120442535351 ,.6408011302120343257 ] 
dist 139=[.5011458629154257027 ,.621950781438012127  ] 
dist 140=[.48439356567323288379,.61850065507256003569] 
dist 141=[.46472511666759366001,.59577875896083470362] 
dist 142=[.43571833862177309949,.59447271662399723556] 
dist 143=[.40676070820525096289,.58456904069826715337] 
dist 144=[.38728884502920166796,.58297327682677750497] 
dist 145=[.37088055306692230929,.56057689303276017626] 
dist 146=[.35417691530811115551,.5575286914488580661 ] 
dist 147=[.33839831539797190909,.55109595758472123023] 
dist 148=[.32569008660209804562,.54957623605752467616] 
dist 149=[.3126929590054743349 ,.54295352742695660812] 
dist 150=[.29575879144693245207,.54176664604658976073] 
dist 151=[.27904076856661967076,.53913200483623496319] 
dist 152=[.26690819906746005791,.53862359652771292711] 
dist 153=[.25571285932844231648,.39457421146958097073] 
dist 154=[.24274366609757446167,.38639522768005026657] 
dist 155=[.22949735372540025449,.36747606043645457828] 
dist 156=[.21719356385223321498,.36462856709973698513] 
dist 157=[.20312131894786485941,.33987951323189903969] 
dist 158=[.18280135512263180268,.33547103633898849227] 
dist 159=[.16246920498056193885,.32970091960665183969] 
dist 160=[.14834821597115317497,.32834150945496715252] 
dist 161=[.1359591288538585463 ,.29655159941163438795] 
dist 162=[.1225544210948649863 ,.2926150453883930003 ] 
dist 163=[.10939030258101220168,.2844081051029846005 ] 
dist 164=[.09796354949735387681,.28240230506479892563] 
dist 165=[.08552654752455838580,.27436565726184354084] 
dist 166=[.06832152980969973399,.27287584368788211105] 
dist 167=[.05086395366855505938,.2698737353254442794 ] 
dist 168=[.03741674207913912179,.26911943499830491133] 
dist 169=[.02422222454032298873,.24487758387663485843] 
dist 170=[.00777540050011830886,.24404032907460733137] 
dist 171=[-.00966908591991738433,.24116008557405183806] 
dist 172=[-.02685415782299115984,.24056730212239631819] 
dist 173=[-.04728443514990142905,.23983488030095561789] 
dist 174=[-.07770943374400228696,.23970551110649196717] 
dist 175=[-.10808605122963314247,.20578369160081497667] 
dist 176=[-.12832280873715792704,.20539453958998936942] 
dist 177=[-.14516924056746871413,.19188376440824922466] 
dist 178=[-.16198487870680739962,.19024246465981404549] 
dist 179=[-.17765782649006496715,.18692571565342313282] 
dist 180=[-.18993360588359949279,.18609177474112393816] 
dist 181=[-.20217218481345069748,.18319113746416010334] 
dist 182=[-.21769633429008169921,.18260469218797795414] 
dist 183=[-.23282335848580328868,.18180386689080043519] 
dist 184=[-.24347347416904141911,.18160511351569961456] 
dist 185=[-.25296960385474487218,.03713751956792402176] 
dist 186=[-.26348079412523192426,.03124261506768656154] 
dist 187=[-.27394424572631060152,.01764864555619575662] 
dist 188=[-.28324942528760051173,.01559284917802817261] 
dist 189=[-.29356539760386548109,-.00203626373107972916] 
dist 190=[-.3080719238174287487 ,-.00516301830924612350] 
dist 191=[-.32242399587391115539,-.00932002895135644917] 
dist 192=[-.3321221662933849825 ,-.01032342237093126001] 
dist 193=[-.34034625514289761057,-.03233136289735922750] 
dist 194=[-.34880214151452258315,-.03505101063413381450] 
dist 195=[-.356842772330470291  ,-.04077568776994050910] 
dist 196=[-.36340587856352821661,-.04209785676735882384] 
dist 197=[-.37019749772700976482,-.04787585007859539715] 
dist 198=[-.37915215846954020001,-.04890528748513788802] 
dist 199=[-.38804242237455790462,-.05108272859411924886] 
dist 200=[-.39457646033003164454,-.05155730154138794948] 
dist 201=[-.40068882555217332431,-.06195831692876083330] 
dist 202=[-.40789243874217486949,-.06246061948816377585] 
dist 203=[-.41531827050881941891,-.06456977263502057829] 
dist 204=[-.42231948884276437844,-.06495023235989139014] 
dist 205=[-.43040892966814824083,-.06568634289401453349] 
dist 206=[-.44218754760803749241,-.06585752314217921172] 
dist 207=[-.45388437637591900369,-.07432494068849829300] 
dist 208=[-.46164666831416151595,-.07509646838720667512] 
dist 209=[-.46807540924864592591,-.07660812967238589225] 
dist 210=[-.47443816119295467384,-.07697244375066617841] 
dist 211=[-.48033352204451717716,-.07813545852202098683] 
dist 212=[-.48489274318685547153,-.07838914413192233665] 
dist 213=[-.48938356494465560695,-.07848497993872132117] 
dist 214=[-.49500533478186361475,-.07830531570179856556] 
dist 215=[-.50044710847524657361,-.07799830316726989752] 
dist 216=[-.50421796282542303937,-.07756305591803517907] 
dist 217=[-.50751731396540772925,-.07694708258417182652] 
dist 218=[-.51107311978906808369,-.07591716723922408283] 
dist 219=[-.51455675741679168127,-.07468972344688248172] 
dist 220=[-.51756744265628926779,-.07328367259599301605] 
dist 221=[-.52083316093381146941,-.07146594384633728603] 
dist 222=[-.52533690638908630484,-.06859189572868396342] 
dist 223=[-.52975459954706621416,-.06561323375879228798] 
dist 224=[-.53267611684290678821,-.06337706551232391554] 
dist 225=[-.5350844852455455385 ,-.06123881316692261505] 
dist 226=[-.5374496317738456058 ,-.05865175525952847412] 
dist 227=[-.53962899477016587293,-.05594878199569467224] 
dist 228=[-.54129424676455159499,-.05334687964621324518] 
dist 229=[-.54291538565284053626,-.05029937243363847097] 
dist 230=[-.54491830043219457243,-.04581407351873829948] 
dist 231=[-.54684407979418262764,-.04114426905439926046] 
dist 232=[-.54815668437003133411,-.03735877441603683066] 
dist 233=[-.54928203258429562535,-.03346554184848085002] 
dist 234=[-.55063755447509967105,-.02836479616291756858] 
dist 235=[-.552220155156001402  ,-.02282731837039543656] 
dist 236=[-.5536784403094915819 ,-.01718725017400609728] 
dist 237=[-.55495924545916513674,-.01034518757062518437] 
dist 238=[-.55583194458508077938,0                     ] 
dist 239=[-.55657983825423799632,-.06373432199517715544] 
dist 240=[-.55736143654523918899,-.05791965074691788406] 
dist 241=[-.55806349418011342644,-.05188854256578337211] 
dist 242=[-.55849323230020844614,-.04703455855597969023] 
dist 243=[-.5588091892852489665 ,-.04207396498635199925] 
dist 244=[-.55905612863457991372,-.03561642895384977097] 
dist 245=[-.55924210288568252046,-.02862624230236855285] 
dist 246=[-.55931420222736358604,-.02153514820434508795] 
dist 247=[-.55932821932069285344,-.01295322153561823133] 

8 phat 1 dirichlet min maxes function [2, 1, 0, 1, 2, 0, 0, 1, 2] 
dist 0=[3.8998850008689875165 ,3.8998850008689875165 ] 
dist 1=[3.8992804354854345022 ,3.9007517916379418765 ] 
dist 2=[3.8983287242427907692 ,3.9018598257499161001 ] 
dist 3=[3.8960733739570655251 ,3.9034293218060344019 ] 
dist 4=[3.8931285166585562140 ,3.9051913116845960428 ] 
dist 5=[3.8894188510091207067 ,3.9070692948602679462 ] 
dist 6=[3.8844067539752045045 ,3.9094076827188310121 ] 
dist 7=[3.8762523071823309735 ,3.9130112277481214821 ] 
dist 8=[3.8675506013852144043 ,3.9165941250962631753 ] 
dist 9=[3.8603495218445440227 ,3.9188499255133016925 ] 
dist 10=[3.8528093642215736796 ,3.9205833946190046686 ] 
dist 11=[3.8427513705566461028 ,3.9220770401500975464 ] 
dist 12=[3.8317424444929856289 ,3.9233163308815399575 ] 
dist 13=[3.8203986440328728108 ,3.9240324168551585512 ] 
dist 14=[3.8065415582396451216 ,3.9245079500699699128 ] 
dist 15=[3.7854797266146959209 ,3.9247850645185488937 ] 
dist 16=[3.7641730681014117011 ,3.9249107719354284841 ] 
dist 17=[3.7493366967922132396 ,3.9248961716438404182 ] 
dist 18=[3.7362792403359069296 ,3.9245946868582191087 ] 
dist 19=[3.7220880715648077773 ,3.9244967225957357643 ] 
dist 20=[3.7081139053997456720 ,3.9229518154099131646 ] 
dist 21=[3.6959244386703077845 ,3.9225378012802281542 ] 
dist 22=[3.6826069614216641166 ,3.9221724010938488199 ] 
dist 23=[3.6641208607671932672 ,3.9219370619862747506 ] 
dist 24=[3.6453353730123338235 ,3.9128876568884679187 ] 
dist 25=[3.6308203759170858256 ,3.9117205093710545043 ] 
dist 26=[3.6165353708119045459 ,3.9073622683993828948 ] 
dist 27=[3.5986698290811304258 ,3.8531267478561106798 ] 
dist 28=[3.5796898372352018091 ,3.8421498427176372667 ] 
dist 29=[3.5609471379634523771 ,3.8400803939325679271 ] 
dist 30=[3.5386316278162837886 ,3.8364773315838666436 ] 
dist 31=[3.5053607332363199812 ,3.8356303499275384818 ] 
dist 32=[3.4716309272191467820 ,3.8204154534086496283 ] 
dist 33=[3.4474798150932067002 ,3.8183337309053713374 ] 
dist 34=[3.4255249983772132645 ,3.8134744526850685166 ] 
dist 35=[3.4005801645215103224 ,3.8125030049935823839 ] 
dist 36=[3.3753741405957484477 ,3.8056482682127966999 ] 
dist 37=[3.3523745885113120550 ,3.8043049877986514060 ] 
dist 38=[3.3263952953633400393 ,3.8020838233702394816 ] 
dist 39=[3.2892705913852503543 ,3.8015046916987109477 ] 
dist 40=[3.2510740082194030221 ,3.7786563209507504046 ] 
dist 41=[3.2208073005541193166 ,3.7761833364620817400 ] 
dist 42=[3.1903052075479419350 ,3.7701885020305934979 ] 
dist 43=[3.1511671054691085922 ,3.7692493610753623188 ] 
dist 44=[3.1090771114475174986 ,3.7602510663730746565 ] 
dist 45=[3.0667677322159296857 ,3.7585134602304269188 ] 
dist 46=[3.0158394701982118875 ,3.7564555868849154073 ] 
dist 47=[2.9392747670841101098 ,3.7558622492283439674 ] 
dist 48=[2.8626204327069999629 ,3.7394855259310155621 ] 
dist 49=[2.8113336541861014436 ,3.7373169799042455630 ] 
dist 50=[2.7683969074057562027 ,3.7330624251170216135 ] 
dist 51=[2.7251419035813313929 ,3.7319519509588153203 ] 
dist 52=[2.6845701116074976898 ,3.7279412242819456206 ] 
dist 53=[2.6523659563100725856 ,3.7270307068556752234 ] 
dist 54=[2.6198601252510551581 ,3.7254222432103021673 ] 
dist 55=[2.5780816590040901926 ,3.7244368676757592192 ] 
dist 56=[2.5371072461306587994 ,3.5473888274717278210 ] 
dist 57=[2.5078175518767537007 ,3.5443442739000567811 ] 
dist 58=[2.4812413100672462861 ,3.5438817292333802109 ] 
dist 59=[2.4511204481676732561 ,3.4604184410102376424 ] 
dist 60=[2.4207266175319872632 ,3.4544407757660692137 ] 
dist 61=[2.3930585268132466629 ,3.4402123088448736455 ] 
dist 62=[2.3618582076153796278 ,3.4381774394115738508 ] 
dist 63=[2.3173357999601605637 ,3.4180862929707475169 ] 
dist 64=[2.2730087371019931158 ,3.4143788330419174933 ] 
dist 65=[2.2425897784607318043 ,3.4101857484974654978 ] 
dist 66=[2.2162889895335251114 ,3.4094608137878468015 ] 
dist 67=[2.1884342127486863020 ,3.3773977653639993621 ] 
dist 68=[2.1614379733544064152 ,3.3733754905893206276 ] 
dist 69=[2.1385712521038355693 ,3.3655597959774169156 ] 
dist 70=[2.1141615638906977384 ,3.3636042626196991676 ] 
dist 71=[2.0809936038112899032 ,3.3570065390297861505 ] 
dist 72=[2.0476052971763579746 ,3.3554923930821016056 ] 
dist 73=[2.0223142437573428321 ,3.3539105412023916418 ] 
dist 74=[1.9979052227134132180 ,3.3536075411737699410 ] 
dist 75=[1.9680449614523183610 ,3.2882472945108074503 ] 
dist 76=[1.9366656484794361941 ,3.2827277106642790308 ] 
dist 77=[1.9061805654725079702 ,3.2707144761780085145 ] 
dist 78=[1.8702570193620666693 ,3.2680280168258649398 ] 
dist 79=[1.8171243726849966216 ,3.2541857275415574817 ] 
dist 80=[1.7640193187373414859 ,3.2516704978554991990 ] 
dist 81=[1.7282061409128198246 ,3.2462689709440913936 ] 
dist 82=[1.6979141912216069443 ,3.2448713592194372218 ] 
dist 83=[1.6668935232033575070 ,3.2327813115310706675 ] 
dist 84=[1.6374746192991699695 ,3.2308095742019223397 ] 
dist 85=[1.6135895732911085706 ,3.2270687698524524860 ] 
dist 86=[1.5889878276410146946 ,3.2261282644976226142 ] 
dist 87=[1.5567021935260929096 ,3.2229771523607749543 ] 
dist 88=[1.5247193553819346681 ,3.2221954045595844653 ] 
dist 89=[1.5013287647348135988 ,3.2214086629369099905 ] 
dist 90=[1.4795631172443633245 ,3.2211786361556973953 ] 
dist 91=[1.4540798967430208629 ,3.0360414768595250000 ] 
dist 92=[1.4279025781205060687 ,3.0258575253890517337 ] 
dist 93=[1.4033606043470737267 ,3.0029034560747468197 ] 
dist 94=[1.3751117240556757128 ,2.9987122606419882798 ] 
dist 95=[1.3341071329187170800 ,2.9701307490253504050 ] 
dist 96=[1.2929883352253226294 ,2.9649840190680919902 ] 
dist 97=[1.2642826396009770257 ,2.9560354293844347523 ] 
dist 98=[1.2389412852882291125 ,2.9540487418874796302 ] 
dist 99=[1.2112795319569990511 ,2.9217557419272912005 ] 
dist 100=[1.1839695293663588862 ,2.9174837302574090981 ] 
dist 101=[1.1600351444666799802 ,2.9074455569722386394 ] 
dist 102=[1.1337915027339200430 ,2.9058578419650441639 ] 
dist 103=[1.0972446930633094087 ,2.8919905169687017376 ] 
dist 104=[1.0600538285470681587 ,2.8894188862197046158 ] 
dist 105=[1.0312340288604642846 ,2.8860594402432149159 ] 
dist 106=[1.0027916286075832784 ,2.8850594247119948735 ] 
dist 107=[.9671103258306212510 ,2.6947369935650267605 ] 
dist 108=[.9291466433173778365 ,2.6825094073993511582 ] 
dist 109=[.8915749418082405540 ,2.6576760481419722976 ] 
dist 110=[.8467797900801198659 ,2.6513244161215305093 ] 
dist 111=[.7799229956493512008 ,2.6286106167607430059 ] 
dist 112=[.7131131073009320748 ,2.6240299912945898817 ] 
dist 113=[.65301634729987558404,2.6161582646825545005 ] 
dist 114=[.58117476630010637984,2.6072912753776610004 ] 
dist 115=[.48972909118742200345,2.4723030707640418229 ] 
dist 116=[.39175402320058353928,2.4587063097599864427 ] 
dist 117=[.2937953619733348084 ,2.4392652134893093157 ] 
dist 118=[.17626407961277028509,2.4068396308072683182 ] 
dist 119=[0                     ,2.3301290805696807158 ] 
dist 120=[.4339289227052902111 ,.79747831720401745003] 
dist 121=[.4094176893049935119 ,.78885822043107781509] 
dist 122=[.3873550676400608002 ,.77161929119020541407] 
dist 123=[.3626171117549624554 ,.7673075296199138323 ] 
dist 124=[.3378069426043591174 ,.75251639589303962377] 
dist 125=[.3154554747649650042 ,.74943206563261974018] 
dist 126=[.28541353664980374749,.74571648704383329634] 
dist 127=[.25465546357932867454,.74507699796649404607] 
dist 128=[.2197493601630500080 ,.64275946223989634456] 
dist 129=[.1957411991209575761 ,.63429705557983700353] 
dist 130=[.17302557758045382185,.61550251655706113868] 
dist 131=[.14138775560392070634,.61199946518465191295] 
dist 132=[.11863852705201968661,.58965924623977610719] 
dist 133=[.09785977356217765336,.58572833318200604883] 
dist 134=[.07410366389386271681,.57850659704107428976] 
dist 135=[.05001514747975576356,.57686135405074893118] 
dist 136=[.02790679871104424310,.55607769321149165109] 
dist 137=[.00283091316136668814,.55317590164279620626] 
dist 138=[-.03312746733881007788,.54735609770833372727] 
dist 139=[-.06900245123865400895,.54589797324050232307] 
dist 140=[-.09374475834120317267,.54087515511582346524] 
dist 141=[-.1152693786320438827 ,.5398363108726718296 ] 
dist 142=[-.13827392218166396071,.53853730661390740135] 
dist 143=[-.16069606801680826463,.53828217881421751942] 
dist 144=[-.17989115299768906848,.3861271737788144278 ] 
dist 145=[-.20055700938126890365,.3778813489097569824 ] 
dist 146=[-.22886210054793918309,.3589031985594183906 ] 
dist 147=[-.2574566990710502475 ,.3559907682758524802 ] 
dist 148=[-.27928055726775363112,.3314761948153546823 ] 
dist 149=[-.30050202807051601895,.3271270107993785132 ] 
dist 150=[-.32668713447238241878,.3212121673101035555 ] 
dist 151=[-.35432247042106381365,.3196757006237484813 ] 
dist 152=[-.38134472109105765476,.2895222499302874111 ] 
dist 153=[-.41331935620848753609,.2857708541685084930 ] 
dist 154=[-.46076375759827039138,.2777813625514371070 ] 
dist 155=[-.50807600152733278843,.2760167852263119898 ] 
dist 156=[-.53952202072053382711,.2675972093837181818 ] 
dist 157=[-.56561925267603716456,.2661487633971432817 ] 
dist 158=[-.591536861752084374  ,.2628324645222507499 ] 
dist 159=[-.61560811682452417285,.2623377434273376129 ] 
dist 160=[-.63432011280745838169,.2323144418684204642 ] 
dist 161=[-.65284273420928550871,.2295167359708202970 ] 
dist 162=[-.67615651689867895848,.2232583292358976705 ] 
dist 163=[-.6987860586232389306 ,.2221672169886250263 ] 
dist 164=[-.71457178536377783644,.2146385244087087527 ] 
dist 165=[-.72849450977443888861,.2133251324688814350 ] 
dist 166=[-.74367222379867844231,.2110617182218536520 ] 
dist 167=[-.75864529868178521165,.2105760815954803423 ] 
dist 168=[-.77174949391238730031,.20333062454028570836] 
dist 169=[-.78610291096899212279,.20237245076739378759] 
dist 170=[-.80607277367614744647,.20038171478647566086] 
dist 171=[-.82573823316391781489,.19991964684446854818] 
dist 172=[-.83887407029402353649,.19803373358127020702] 
dist 173=[-.84984764069192002128,.19769047772948927108] 
dist 174=[-.86086423156766210158,.19705906921155107319] 
dist 175=[-.87117307560474607127,.19692175719335110629] 
dist 176=[-.87931573003528853118,-.40970595441954977379] 
dist 177=[-.88749776761153774721,-.41167170654427338099] 
dist 178=[-.89796416004187480214,-.4121344938413140762 ] 
dist 179=[-.90820570013665633831,-.41348163389899669054] 
dist 180=[-.9154883576190981261 ,-.41343564530962795505] 
dist 181=[-.92205722118822625705,-.41285527290452723252] 
dist 182=[-.92944365754950343646,-.41138889831930489856] 
dist 183=[-.93686401486273387555,-.40945051812205422047] 
dist 184=[-.94356857852230987432,-.40698222633301547603] 
dist 185=[-.95108878036212029934,-.40363281683300454643] 
dist 186=[-.96177166731387709779,-.39817023321800862371] 
dist 187=[-.97230852292358867718,-.39250938717877450941] 
dist 188=[-.97924461200966354422,-.38836695286292859048] 
dist 189=[-.98492703196042947789,-.38451097338838468424] 
dist 190=[-.9904492719488255456 ,-.37999575391884629261] 
dist 191=[-.99549981228530360719,-.37535837474023410631] 
dist 192=[-.99929545515996600082,-.37101372794496837468] 
dist 193=[-1.0029297758706453275 ,-.36601600476291466846] 
dist 194=[-1.0073350312190744409 ,-.35876642739872584781] 
dist 195=[-1.0115286207795445486 ,-.35126299649945242034] 
dist 196=[-1.0143162867877147471 ,-.34524988495061500782] 
dist 197=[-1.0166303198421564854 ,-.33912841804858230899] 
dist 198=[-1.0189293992654652447 ,-.33119153568310165109] 
dist 199=[-1.0210653921959182614 ,-.32261589668522004532] 
dist 200=[-1.0227270830836257486 ,-.31393950899610544486] 
dist 201=[-1.0243731664699124005 ,-.30345573546422094579] 
dist 202=[-1.0264467191308674216 ,-.28765090031939367097] 
dist 203=[-1.0283963092118672646 ,-.27156133278953899196] 
dist 204=[-1.0295465553216228500 ,-.25993867213170675992] 
dist 205=[-1.0303405864081029148 ,-.24926941222788838944] 
dist 206=[-1.0308653657832891126 ,-.23699322771002511134] 
dist 207=[-1.0312405153991285267 ,-.22450266288903479292] 
dist 208=[-1.0314360326643022044 ,-.21297590316060417243] 
dist 209=[-1.0315389017548771714 ,-.19985270870619119193] 
dist 210=[-1.0315434249320874690 ,-.18097668913868874337] 
dist 211=[-1.0292622549022690635 ,-.16150562424759364898] 
dist 212=[-1.0288899160572413800 ,-.14600234940767680911] 
dist 213=[-1.0283507586923710056 ,-.13031087785640631814] 
dist 214=[-1.0281604508888016218 ,-.11008704463462208974] 
dist 215=[-1.0277078952728740058 ,-.08829497814011501358] 
dist 216=[-1.0275294244071216681 ,-.06633085456439731259] 
dist 217=[-1.0273158428613677902 ,-.03985163318350435487] 

8 phat 1 dirichlet min maxes function [2, 0, 0, 0, 1, 0, 0, 1, 2] 
dist 0=[3.3413029787336678902 ,3.3413029787336678902 ] 
dist 1=[3.3376244337088492044 ,3.3452223727547107249 ] 
dist 2=[3.3268299984829729697 ,3.3515227390738885985 ] 
dist 3=[3.3153836563375307990 ,3.3580127579902920882 ] 
dist 4=[3.3060639026283385277 ,3.3641916305991734589 ] 
dist 5=[3.2964405343815639688 ,3.3692474413647828451 ] 
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dist 8=[3.2559358199460199358 ,3.3881199164026498220 ] 
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dist 10=[3.2129331614020284191 ,3.3959415748860521347 ] 
dist 11=[3.1869284040663372999 ,3.3991932724245763410 ] 
dist 12=[3.1694050650801485370 ,3.4020810113208382274 ] 
dist 13=[3.1545983084511520524 ,3.4041047183676500133 ] 
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dist 17=[3.1015538721664039532 ,3.4106451160152776509 ] 
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dist 19=[3.0704226563255916758 ,3.4115902610557449201 ] 
dist 20=[3.0591205398632598638 ,3.4117562079717882756 ] 
dist 21=[3.0486266283718753115 ,3.4118166364360723844 ] 
dist 22=[3.0363741316781061706 ,3.4118117540431017767 ] 
dist 23=[3.0238064985402096873 ,3.4117298851164744290 ] 
dist 24=[3.0120520713294070994 ,3.4082169277626291236 ] 
dist 25=[2.9985441800978651006 ,3.4077108207634235422 ] 
dist 26=[2.9789628581189444333 ,3.4064312690398500274 ] 
dist 27=[2.9593378425500511961 ,3.4060987496476820414 ] 
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dist 31=[2.9075079757155074804 ,3.3939284879549194995 ] 
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dist 38=[2.8053777400529821319 ,3.3417096713262245868 ] 
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dist 45=[2.6468465370163308051 ,3.3231103223316084759 ] 
dist 46=[2.6278587472851173035 ,3.3215692040810172888 ] 
dist 47=[2.6096532207664877218 ,3.3211175948788846702 ] 
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dist 52=[2.5205505887454251990 ,3.3080451841265231367 ] 
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dist 56=[2.4509568374744085696 ,3.2944482141842833167 ] 
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dist 58=[2.3993814898593171666 ,3.2902206822876695618 ] 
dist 59=[2.3684801025365358418 ,3.2894910660523253319 ] 
dist 60=[2.3466753435154016404 ,3.2802448072993300847 ] 
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dist 62=[2.3055281761753018186 ,3.2723752990734685932 ] 
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dist 64=[2.2646465807653411311 ,2.7449172374677934825 ] 
dist 65=[2.2432135991430925197 ,2.7375599291119881727 ] 
dist 66=[2.2130025954957684052 ,2.7222177401842546169 ] 
dist 67=[2.1820987159371424881 ,2.7182921601430862205 ] 
dist 68=[2.1578942967548219667 ,2.7030011114311027400 ] 
dist 69=[2.1337640992904942631 ,2.7001111334297646383 ] 
dist 70=[2.1031570995247188180 ,2.6939670111250991402 ] 
dist 71=[2.0704200085650981811 ,2.6924096554473226289 ] 
dist 72=[2.0377696494892787269 ,2.6140531168817724286 ] 
dist 73=[1.9986558109139985870 ,2.6069440192213342126 ] 
dist 74=[1.9400654184304380516 ,2.5905170897625285010 ] 
dist 75=[1.8814304611442254943 ,2.5878744021881710877 ] 
dist 76=[1.8421383676088400844 ,2.5662289166829564280 ] 
dist 77=[1.8091760804170679753 ,2.5623077984754839131 ] 
dist 78=[1.7758597447808872455 ,2.5567943712072986404 ] 
dist 79=[1.7445399121810043175 ,2.5552241511631611088 ] 
dist 80=[1.7195634467119088992 ,2.5266801801382901377 ] 
dist 81=[1.6942457319136831174 ,2.5230097300569036751 ] 
dist 82=[1.6615609345449654418 ,2.5151502238801684647 ] 
dist 83=[1.6294358496783170277 ,2.5132730293964595314 ] 
dist 84=[1.6063569315040958356 ,2.5046110780777527424 ] 
dist 85=[1.5852981332489421917 ,2.5030439277101202076 ] 
dist 86=[1.5612533353835178411 ,2.4993694006328896843 ] 
dist 87=[1.5368898375339377784 ,2.4987112409058302519 ] 
dist 88=[1.5145562697391360258 ,2.4058513733053893730 ] 
dist 89=[1.4892466340547740785 ,2.3992547924843537199 ] 
dist 90=[1.4529791484984278440 ,2.3839552794872219890 ] 
dist 91=[1.4168067812607660017 ,2.3815484716012311333 ] 
dist 92=[1.3918776097789443404 ,2.3612300023199763597 ] 
dist 93=[1.3702098157826149248 ,2.3575479944114002754 ] 
dist 94=[1.3470826474231819711 ,2.3525522029865482024 ] 
dist 95=[1.3245593072249836620 ,2.3511001237488036436 ] 
dist 96=[1.3053067682816559700 ,2.3237681741658198224 ] 
dist 97=[1.2846040483823486917 ,2.3202664763109087408 ] 
dist 98=[1.2562801226756260666 ,2.3129005388607400506 ] 
dist 99=[1.2276807060686975126 ,2.3110217782447997006 ] 
dist 100=[1.2058760488443442119 ,2.3033609709110598056 ] 
dist 101=[1.1846952312517350418 ,2.3019359690865168285 ] 
dist 102=[1.1585911136711916400 ,2.2986445774123275232 ] 
dist 103=[1.1310573520480565570 ,2.2980102151937209380 ] 
dist 104=[1.1041580946417044729 ,2.2592899197470960084 ] 
dist 105=[1.0723467472459468409 ,2.2557005130257146158 ] 
dist 106=[1.0251650941706264820 ,2.2473701307511724063 ] 
dist 107=[.9779546032500891316 ,2.2460076030938089031 ] 
dist 108=[.9460279072239602265 ,2.2348520762079032171 ] 
dist 109=[.9189268014038070238 ,2.2328059356658080767 ] 
dist 110=[.8910182110519139884 ,2.2299271812791212414 ] 
dist 111=[.8644528199615091337 ,2.2290947641800474645 ] 
dist 112=[.8427243830756172515 ,2.2135997762337617653 ] 
dist 113=[.8201993132219762329 ,2.2115815039005395450 ] 
dist 114=[.7904474662418531535 ,2.2072861761840842633 ] 
dist 115=[.7608849402350993422 ,2.2061868533744718759 ] 
dist 116=[.7391171362178750550 ,2.2014694703642921904 ] 
dist 117=[.7187138378049282440 ,2.2005965251699355157 ] 
dist 118=[.68967256665797713144,2.1984457928962368261 ] 
dist 119=[.62133112754777072672,2.1981056035557642606 ] 
dist 120=[.55136769773689856123,2.1418790130806068486 ] 
dist 121=[.49647977112965119012,2.1377617637669379463 ] 
dist 122=[.44167318715812164313,2.1288805612090288628 ] 
dist 123=[.37203511956547148636,2.1268557163112387723 ] 
dist 124=[.29748708375313567501,2.1101031939027396413 ] 
dist 125=[.22304096337593196484,2.1069905600988673828 ] 
dist 126=[.13378527804098702962,2.0971994719034483592 ] 
dist 127=[0                     ,2.0823733384531083100 ] 
dist 128=[.4088529350205072835 ,1.1670535444183442867 ] 
dist 129=[.37561653224757914015,1.1647893904533969918 ] 
dist 130=[.34549629755562811612,1.1641409831827969993 ] 
dist 131=[.3083586155855838418 ,1.1524206237538817696 ] 
dist 132=[.27862604991522794769,1.1509238978319886824 ] 
dist 133=[.24880494148395834625,1.1477234019967041429 ] 
dist 134=[.2138495651508420330 ,1.1469724968467510804 ] 
dist 135=[.16889312151421916611,1.1434840133614460878 ] 
dist 136=[.12258631663826257307,1.1428607631585697139 ] 
dist 137=[.08189752107474366076,1.1414012349973163590 ] 
dist 138=[0                     ,1.1411546295454228874 ] 
dist 139=[-.0473251874281346500 ,.07191726521317173147] 
dist 140=[-.0931339500184074729 ,.03106191010222351912] 
dist 141=[-.1312346025284239324 ,.02390047722383665538] 
dist 142=[-.1692105357290470920 ,.01116143028442545258] 
dist 143=[-.2045703149233904087 ,.00839523217622227002] 
dist 144=[-.2322066048822959542 ,-.03055498647928332533] 
dist 145=[-.2597038102483713959 ,-.03582914842120874385] 
dist 146=[-.2945072722365027914 ,-.04663810221909101405] 
dist 147=[-.3283838418286074769 ,-.04937194334442451585] 
dist 148=[-.35217356996237090233,-.05913140839672599685] 
dist 149=[-.37332216725093682091,-.06102785874183636497] 
dist 150=[-.39663446930792032499,-.06412300754532601758] 
dist 151=[-.41978455671033475384,-.06482023788708098219] 
dist 152=[-.44028431873898608272,-.300769174837952597  ] 
dist 153=[-.46293868443848203112,-.31372093153915519261] 
dist 154=[-.49470700074142038746,-.34368142598040885255] 
dist 155=[-.52609927573292777201,-.34806781485644312173] 
dist 156=[-.54724951598052683796,-.38710230145764408589] 
dist 157=[-.56511722758821521151,-.39400337178271910171] 
dist 158=[-.58337969316487486633,-.40277264531552569104] 
dist 159=[-.60067724419024414928,-.40451599611346966678] 
dist 160=[-.61468539351819711575,-.45406173436352987411] 
dist 161=[-.62908180745005912966,-.46007914154247160261] 
dist 162=[-.64793239947624405678,-.47248679567235587406] 
dist 163=[-.66658673116428148391,-.4755296882076572906 ] 
dist 164=[-.6801981302850085106 ,-.48699187751535189134] 
dist 165=[-.69283261649190307881,-.48916246048810477406] 
dist 166=[-.70757939355001666139,-.49296352855822059615] 
dist 167=[-.72270296759867694033,-.49374576212865735394] 
dist 168=[-.73684462539780601959,-.54802130496199350253] 
dist 169=[-.7530935052336460136 ,-.55263313238926825654] 
dist 170=[-.77664582129888576184,-.56318907481267313835] 
dist 171=[-.7999939669643353921 ,-.5647349100335710778 ] 
dist 172=[-.81542618335726626521,-.57803439638172740587] 
dist 173=[-.82813875729367871386,-.58033625442997451583] 
dist 174=[-.84060853372360351159,-.58337867671940249398] 
dist 175=[-.85208945581907940583,-.58397811382425090474] 
dist 176=[-.86084668321405970244,-.59894465926950053847] 
dist 177=[-.86935734403795157619,-.60071298329934080697] 
dist 178=[-.87985201161722860904,-.60447987542284159382] 
dist 179=[-.88993269655417229879,-.60518268550530040136] 
dist 180=[-.89678745452441580118,-.6089732856412357215 ] 
dist 181=[-.90264696971486700231,-.60958131886715832393] 
dist 182=[-.90874675490001336496,-.61077327460842958006] 
dist 183=[-.91459413931556470376,-.61099399418392633678] 
dist 184=[-.91944406372069113183,-.71263330753510391436] 
dist 185=[-.9245320900612670028 ,-.71662240471513503656] 
dist 186=[-.9313318477262382824 ,-.72544777834300040678] 
dist 187=[-.9379364703119158944 ,-.72698394814362356994] 
dist 188=[-.9422439761700401268 ,-.73718967863715592776] 
dist 189=[-.9457280740265221714 ,-.73892381935563818161] 
dist 190=[-.9490391585925436435 ,-.74202587540402578087] 
dist 191=[-.9520177345005497844 ,-.74267553581939446429] 
dist 192=[-.9541718448879173323 ,-.75063729920061761215] 
dist 193=[-.9561520731126735365 ,-.75173270431751713879] 
dist 194=[-.9584351678474542537 ,-.75348041726253761379] 
dist 195=[-.9605493178340055420 ,-.75386500544553017547] 
dist 196=[-.9618537986136088757 ,-.75410807604674917442] 
dist 197=[-.9628254850465075798 ,-.75357447006682177167] 
dist 198=[-.9636085047950557143 ,-.75246296122186626082] 
dist 199=[-.9642179875474980745 ,-.75026129930345968359] 
dist 200=[-.9644955733900338419 ,-.74781070220231946405] 
dist 201=[-.9646187254847530956 ,-.74570347892569840216] 
dist 202=[-.9646103554192542469 ,-.74342748445966787769] 
dist 203=[-.9381619589199863451 ,-.74030173303602633193] 
dist 204=[-.93673935409418925747,-.73683789006878374626] 
dist 205=[-.93347772297875675082,-.73320955258696978185] 
dist 206=[-.93280297783380553638,-.72873582745491774887] 
dist 207=[-.92841427614220395183,-.72189057291770866172] 
dist 208=[-.92756773007996164999,-.7146545540139735366 ] 
dist 209=[-.92605237298866458167,-.708617825058991542  ] 
dist 210=[-.92567935687610507269,-.70225445886495418579] 
dist 211=[-.91917743711874065618,-.69371191287560361639] 
dist 212=[-.91826933365651894454,-.68433650624204814322] 
dist 213=[-.91613318412439231043,-.67464183510245270125] 
dist 214=[-.91569051014808403842,-.6627759074108084148 ] 
dist 215=[-.91259356009177653563,-.6447158655182519001 ] 
dist 216=[-.91197510567151820517,-.62646366278309115393] 
dist 217=[-.91094445178227769453,-.61382911603556478588] 
dist 218=[-.91067255810415606691,-.60278946488245790563] 
dist 219=[-.89951246404841399296,-.59091652650693113089] 
dist 220=[-.89830812407568731283,-.57930057403644358644] 
dist 221=[-.89534105156119282527,-.5692888017535718137 ] 
dist 222=[-.8949044670903796932 ,-.55845276784911972816] 
dist 223=[-.89030703525578793576,-.54353989269724150138] 
dist 224=[-.88941422919001425627,-.52844433677087314744] 
dist 225=[-.88846063144705337853,-.51687759875771834173] 
dist 226=[-.88825477991310776248,-.50558717498710632161] 
dist 227=[-.87884537049814497858,-.49159680918447164782] 
dist 228=[-.87763476810886300425,-.47680188982909123282] 
dist 229=[-.87538308475792926886,-.46229337351879459235] 
dist 230=[-.87308343622001701341,-.44509549065131530782] 
dist 231=[-.8665448246141625143 ,-.41954353686306629362] 
dist 232=[-.84636564870707958418,-.39367918379062594877] 
dist 233=[-.84409760108578041723,-.37523174887863874191] 
dist 234=[-.83648899967117491439,-.35853670812780738683] 
dist 235=[-.67207267316050448927,-.33968163515720213249] 
dist 236=[-.6639270696488564581 ,-.32069504505101424794] 
dist 237=[-.6457845023340930331 ,-.30347394924484514344] 
dist 238=[-.64234582131272732688,-.28410597530442272257] 
dist 239=[-.62049801145240965757,-.25653220965842117739] 
dist 240=[-.6166078208360391076 ,-.22820955979388520623] 
dist 241=[-.60945091851345712533,-.20584616467472442322] 
dist 242=[-.60779353102278031368,-.18338357349890512047] 
dist 243=[-.55147604521482555372,-.15466414943520836937] 
dist 244=[-.54524045136100946266,-.12383248186732862407] 
dist 245=[-.5347531277924848749 ,-.09292124996638724394] 
dist 246=[-.52279241869007158959,-.05577415003203277900] 

8 phat 1 dirichlet min maxes function [0, 0, 0, 0, 2] 
dist 0=[.5039462403018273706 ,.5039462403018273706 ] 
dist 1=[.47144683871468920236,.53614180943829698713] 
dist 2=[.44840345629134624866,.5579698864802962736 ] 
dist 3=[.42768750395139932585,.57655915819134811352] 
dist 4=[.40449763926856972518,.59579976268630303324] 
dist 5=[.38126156121183301072,.61417569367047121186] 
dist 6=[.3603607595029809631 ,.62930634042068909736] 
dist 7=[.33699390822224266044,.64508211737485456235] 
dist 8=[.30389382768547884033,.66603851970845411352] 
dist 9=[.26996260618972502464,.68691761661186946868] 
dist 10=[.24327125715558993356,.70238417875207885924] 
dist 11=[.21655286522326279976,.71697372893104626162] 
dist 12=[.18251347454529163223,.734344848172967959  ] 
dist 13=[.14602852625061456679,.75234889728528111578] 
dist 14=[.10952809782433970614,.76947011856771110749] 
dist 15=[.06571900929314506411,.78936689953631134149] 
dist 16=[0                     ,.81847297209687162057] 
dist 17=[.53543630353476255408,.84743460201700407187] 
dist 18=[.5462143618254301362 ,.86675362441679750584] 
dist 19=[.5702076004389152932 ,.88286381917256710282] 
dist 20=[.574582595205478573  ,.89899038978628835295] 
dist 21=[.6032043395278258228 ,.91405100239816844981] 
dist 22=[.60822367097255022324,.92589744947607661681] 
dist 23=[.61727462334847617   ,.93775527183245552511] 
dist 24=[.61927805127917258237,.95286138723931693763] 
dist 25=[.68493166529288911966,.96761297842148508757] 
dist 26=[.69216325954758858679,.97805273281451997766] 
dist 27=[.70440287427201842027,.98741768392952970102] 
dist 28=[.70711997768261466278,.99787014711168718665] 
dist 29=[.74783297319933280622,1.0083257189287403625 ] 
dist 30=[.75252939339538581586,1.0177031069946291900 ] 
dist 31=[.77819551205003276232,1.0281646362994042731 ] 
dist 32=[.81654007909120912575,1.0429566951922630484 ] 
dist 33=[.84523976441312097734,1.0576267328935089040 ] 
dist 34=[.85482021739005401902,1.0676001883082998785 ] 
dist 35=[.87692190864132926387,1.0761234932906881725 ] 
dist 36=[.8802286268344206233 ,1.0849930397663879537 ] 
dist 37=[.90887658650757783441,1.0934936859135780059 ] 
dist 38=[.91394567501001534399,1.1005414197746487247 ] 
dist 39=[.92060128932022991384,1.1079327540434631935 ] 
dist 40=[.92211496617726286762,1.1178077818820456382 ] 
dist 41=[.95782467298502173432,1.1276726291420526818 ] 
dist 42=[.96220537672025171589,1.1350232446636742216 ] 
dist 43=[.97138132376426008331,1.1419997358769544538 ] 
dist 44=[.97351277612609767648,1.1503681165424312914 ] 
dist 45=[.98256169403697083071,1.1590749449659670478 ] 
dist 46=[.98419015387179012096,1.1674052077097206383 ] 
dist 47=[.9874643430642230995 ,1.1771248405286740086 ] 
dist 48=[.98826772516972326893,1.1913890601163532768 ] 
dist 49=[1.0249216472593164104 ,1.2055857704983080353 ] 
dist 50=[1.0281899043022444622 ,1.2150353719279930655 ] 
dist 51=[1.0355559395011595418 ,1.2228931028329638842 ] 
dist 52=[1.0367501327209101228 ,1.2307224365511595548 ] 
dist 53=[1.0457180284602889579 ,1.2380109307201837615 ] 
dist 54=[1.0472681144091634626 ,1.2437053392188865523 ] 
dist 55=[1.0496873579586997535 ,1.2493692785439179511 ] 
dist 56=[1.0502613848020160119 ,1.2565358979396108373 ] 
dist 57=[1.0649315263504949527 ,1.2635108491212052229 ] 
dist 58=[1.0665813895605169874 ,1.2684081282624837573 ] 
dist 59=[1.0696467478912549913 ,1.2727609352972961298 ] 
dist 60=[1.0703334272001424019 ,1.2775580341443564391 ] 
dist 61=[1.0777021523444056198 ,1.2823212846828899617 ] 
dist 62=[1.0787239391549174055 ,1.2865387006849101907 ] 
dist 63=[1.0829106338567418766 ,1.2911990548742107594 ] 
dist 64=[1.0889781469134015737 ,1.2977340286735776939 ] 
dist 65=[1.1958461877031305035 ,1.3041918825319097097 ] 
dist 66=[1.2003755213830609882 ,1.3085437620765112656 ] 
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dist 68=[1.2122770417610235872 ,1.3159821782559047920 ] 
dist 69=[1.2250068736490419200 ,1.3195456037630183879 ] 
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dist 71=[1.2305109523159333406 ,1.3254039635082359115 ] 
dist 72=[1.2313445235507570667 ,1.3292961336873799988 ] 
dist 73=[1.2448318090669198600 ,1.3331492518589770371 ] 
dist 74=[1.2464888196296076224 ,1.3359633200944396594 ] 
dist 75=[1.2502277415779447293 ,1.3385780579498385330 ] 
dist 76=[1.2507757445158355291 ,1.3416338679089011257 ] 
dist 77=[1.2552687437578721139 ,1.3447699711974473102 ] 
dist 78=[1.2538507763626436820 ,1.3477058771169736328 ] 
dist 79=[1.2483530881673708334 ,1.3510819671364119842 ] 
dist 80=[1.2398570776500781129 ,1.3559787777576254071 ] 
dist 81=[1.2312176457116565610 ,1.3608342457682776527 ] 
dist 82=[1.2251462843688282434 ,1.3640449681463559069 ] 
dist 83=[1.2197445264557432364 ,1.3666914925970273004 ] 
dist 84=[1.2137834280272224038 ,1.3692902063665150378 ] 
dist 85=[1.2078600058773181950 ,1.3716846689899203679 ] 
dist 86=[1.2026089436547423615 ,1.3735142025068645317 ] 
dist 87=[1.1968012597195526485 ,1.3752952487648456885 ] 
dist 88=[1.1886514026617242163 ,1.3774957658300701690 ] 
dist 89=[1.1803306107615930318 ,1.3796116570001389243 ] 
dist 90=[1.1738392014298472566 ,1.3810542054181752952 ] 
dist 91=[1.1673916791458160462 ,1.3822913921126174261 ] 
dist 92=[1.1592464254056478228 ,1.3835858501302692162 ] 
dist 93=[1.1505510401383557996 ,1.3848308251110702438 ] 
dist 94=[1.1419030430561102979 ,1.3858700832175265098 ] 
dist 95=[1.1315610208913227947 ,1.3869662717338044615 ] 
dist 96=[1.1160896992312983650 ,1.3884389652886528526 ] 
dist 97=[1.1003839587232019972 ,1.3898664969400294963 ] 
dist 98=[1.0891042823542355087 ,1.3907820409795758202 ] 
dist 99=[1.0788154804621517464 ,1.3915051845843963950 ] 
dist 100=[1.0670731374785407058 ,1.3921631269722473858 ] 
dist 101=[1.0551781991209398986 ,1.3927351451074493094 ] 
dist 102=[1.0442790279372657864 ,1.3931145975470825204 ] 
dist 103=[1.0319312571754866431 ,1.3934287068900487214 ] 
dist 104=[1.0142420574961345990 ,1.3937393576969816030 ] 
dist 105=[.99602318308860528568,1.3939995406272504600 ] 
dist 106=[.98155676275752288209,1.3941117821011637917 ] 
dist 107=[.96695016453237025415,1.3941460308607774489 ] 
dist 108=[.948170589564746407  ,1.3941344737967493008 ] 
dist 109=[.927955819231554515  ,1.3939332926694797826 ] 
dist 110=[.90760857525317856892,1.3938563471587936866 ] 
dist 111=[.88309660160450313777,1.3936873579411171024 ] 
dist 112=[.84622330863652535358,1.3936149454072909719 ] 
dist 113=[.80931148491632861567,1.3921165538306647177 ] 
dist 114=[.78464539154132080454,1.3918759450096044558 ] 
dist 115=[.7640284519923709701 ,1.3913118785207076556 ] 
dist 116=[.74331285737611532504,1.3911281552622135987 ] 
dist 117=[.72391694792330242004,1.3902282316614304750 ] 
dist 118=[.70857862315916035065,1.3900222716636898631 ] 
dist 119=[.69314957072647768053,1.3895909784649911943 ] 
dist 120=[.67339075925292812041,1.3894520204061064510 ] 
dist 121=[.6540464403349621507 ,1.3831968954656584817 ] 
dist 122=[.64027531859113292688,1.3824659303297080896 ] 
dist 123=[.6278382045189611225 ,1.3814277193136143956 ] 
dist 124=[.61382978905260910304,1.3811165202984665120 ] 
dist 125=[.59974417786565738757,1.3751820981527498717 ] 
dist 126=[.58699828827386209162,1.3745848195445474669 ] 
dist 127=[.57268684066178450272,1.3703111888946862912 ] 
dist 128=[.55233914671353405266,1.3636425788466524944 ] 
dist 129=[.53211232506659450201,.77543214366112702949] 
dist 130=[.51828435513119925523,.76279132858703254762] 
dist 131=[.50638450247831229238,.73329022623653402981] 
dist 132=[.49386996606138942534,.72903517734055554877] 
dist 133=[.48179495408795365191,.68963795144498542706] 
dist 134=[.47165315728804214277,.68258665690952323604] 
dist 135=[.46090160693521736572,.67403147198665005734] 
dist 136=[.44638763890721752666,.67249116927379754167] 
dist 137=[.43182035500941511365,.61842137365122810509] 
dist 138=[.42085554626254235064,.61180466904658009635] 
dist 139=[.4103405688845016698 ,.59850595864196758593] 
dist 140=[.39757256755800049178,.59515780643065071536] 
dist 141=[.38420522129311232338,.58352504986024834248] 
dist 142=[.37129292132585960075,.58112750554065026962] 
dist 143=[.35613304099084120166,.57788048982727592403] 
dist 144=[.33377558762466459328,.57700338615814782389] 
dist 145=[.31145607476622795548,.49952012244321666444] 
dist 146=[.29644795284347878079,.4930147650475429428 ] 
dist 147=[.28380121471860704825,.47849255080231925724] 
dist 148=[.27092701182755962445,.47583475278590680109] 
dist 149=[.25876588494120663259,.45832927864051307397] 
dist 150=[.24897138282333233606,.45523669269667485837] 
dist 151=[.23895438486924926328,.44969339584849564626] 
dist 152=[.22590329585927437299,.4484641723625403414 ] 
dist 153=[.21301889217342497119,.43120700985616071024] 
dist 154=[.20366861961772700687,.4288584361837831352 ] 
dist 155=[.19504081938154638805,.42390154024294372663] 
dist 156=[.18504623606578413579,.4227310461958520052 ] 
dist 157=[.17483823531027126438,.41762546023518257392] 
dist 158=[.16535678567042186037,.41671082194192843042] 
dist 159=[.15451271316653025813,.41467889091510635015] 
dist 160=[.13885435091912482777,.41428823690957066085] 
dist 161=[.12318668293563664175,.3033355983791068334 ] 
dist 162=[.11230538837497673641,.29703521911143100436] 
dist 163=[.10275880390783970568,.28246131291177627189] 
dist 164=[.09242984899643168095,.28026799006222426605] 
dist 165=[.08228641650305445645,.2612025136145094852 ] 
dist 166=[.07348190401327898675,.25780641393667064428] 
dist 167=[.06389916021195253428,.2533619698472091745 ] 
dist 168=[.05064287669853609185,.25231532464488360185] 
dist 169=[.03719210153249150813,.22782305418299593987] 
dist 170=[.02683140967088200329,.22479025081092596554] 
dist 171=[.01666556691231733704,.21846788939269974651] 
dist 172=[.00399416957412968046,.2169222490906043167 ] 
dist 173=[-.00944576143731222026,.21073269164597908127] 
dist 174=[-.02268566558767072814,.20958501198400871267] 
dist 175=[-.03842565336171245839,.20727345575887436426] 
dist 176=[-.06186568041485137897,.20669293602054816199] 
dist 177=[-.08526837740048113179,.17808472161656311995] 
dist 178=[-.10085904846495426598,.17554459826924580287] 
dist 179=[-.1138376635052174588 ,.16963565265984952408] 
dist 180=[-.1267923855267496208 ,.16878468981614362145] 
dist 181=[-.13886667267401452028,.16097200281741281585] 
dist 182=[-.14832363219134723397,.1595824071280081523 ] 
dist 183=[-.15775176297277166949,.15788103011305986132] 
dist 184=[-.16971073792603132159,.15757965656457925711] 
dist 185=[-.18136367581951232728,.14717688626754795707] 
dist 186=[-.18956768755103221055,.14591291516997625176] 
dist 187=[-.19688256278239059075,.14335761313382789852] 
dist 188=[-.20497903947930803859,.14271485866496424934] 
dist 189=[-.2130385695178900255 ,.14047730325470334371] 
dist 190=[-.22020566163980582739,.14002539486894679572] 
dist 191=[-.22815106790603697471,.13940363003170715669] 
dist 192=[-.23932378028781520479,.13924579673730649916] 
dist 193=[-.25037741540804042451,.02805711482977417760] 
dist 194=[-.25784652398541344103,.02351828590211289792] 
dist 195=[-.2641801434194983923 ,.01305180550126816978] 
dist 196=[-.27069193026728211471,.01146870907046945198] 
dist 197=[-.27688371589009380687,-.00210368595582270923] 
dist 198=[-.28193736094537515339,-.00451090768284142417] 
dist 199=[-.28716664407154001575,-.00771220326131715477] 
dist 200=[-.29406096522587363065,-.00848559285871281189] 
dist 201=[-.3009055104852132887 ,-.02542527004587583235] 
dist 202=[-.30593569477892883128,-.02751873843735095052] 
dist 203=[-.31064093705395871541,-.03192600305280006704] 
dist 204=[-.31618574523088339753,-.03294327741650852007] 
dist 205=[-.32190134562237706827,-.03739401005617846416] 
dist 206=[-.32728974046585896607,-.03818659296698295675] 
dist 207=[-.33351537252416747576,-.03986473388867244540] 
dist 208=[-.34257984192093642188,-.04022890564367303725] 
dist 209=[-.3515812231432433958 ,-.05797356257472114041] 
dist 210=[-.35755450852092943489,-.05888170204377127937] 
dist 211=[-.36250132224595612526,-.06001453253479232121] 
dist 212=[-.3673969147604636302 ,-.06028575028660336785] 
dist 213=[-.37193260095043489904,-.06113842842092189607] 
dist 214=[-.37543982370447070546,-.06132766541455402422] 
dist 215=[-.37889397077005339869,-.06136753506200458398] 
dist 216=[-.38321735926846650206,-.06120131133138127880] 
dist 217=[-.3874020108469686723 ,-.06093690184147396470] 
dist 218=[-.39030122346536091041,-.06058063537807923274] 
dist 219=[-.39283736717347776405,-.06008603394803668859] 
dist 220=[-.39556977773967363532,-.05926828572076876337] 
dist 221=[-.3982462146441435245 ,-.05829724702757717042] 
dist 222=[-.40055846904401370115,-.05718951174291955050] 
dist 223=[-.40306589806175838351,-.05576038006948102342] 
dist 224=[-.40652301482235690696,-.05350383870389579288] 
dist 225=[-.40991369390676761036,-.05116631538188841673] 
dist 226=[-.41215537855645528662,-.04941326816426852388] 
dist 227=[-.41400260724257198639,-.04773873287239699905] 
dist 228=[-.41581550009512914552,-.04571521120866395259] 
dist 229=[-.41748521198007481562,-.04360234114020425790] 
dist 230=[-.4187597304520633249 ,-.04157042103231738641] 
dist 231=[-.41999923026507465914,-.03919198779811076623] 
dist 232=[-.42152887085412212571,-.03569313767352670220] 
dist 233=[-.42299872695299510795,-.03205106161836654688] 
dist 234=[-.42399909450743504383,-.02909975151248094855] 
dist 235=[-.42485515576041753868,-.02606541099137425681] 
dist 236=[-.42574780041711064084,-.02209122136335403763] 
dist 237=[-.42660441510774004297,-.01777737352578467824] 
dist 238=[-.42731635993293470568,-.01338447184198749140] 
dist 239=[-.42806453834340278621,-.00805598431433074275] 
dist 240=[-.42906608391923809366,0                     ] 
dist 241=[-.4300331794979158514 ,-.06532694454360248982] 
dist 242=[-.43064356159796996447,-.06286761659056645836] 
dist 243=[-.43111437851199708353,-.06055989616294910115] 
dist 244=[-.43152322783529294075,-.05783025666776777373] 
dist 245=[-.43186484907772346586,-.05501141906288783799] 
dist 246=[-.43206676125741993231,-.05234691498503245105] 
dist 247=[-.43220659232544315847,-.04926325299459828222] 
dist 248=[-.4322998973960586637 ,-.04476786311727401194] 
dist 249=[-.43235546954660605942,-.04010531052946946066] 
dist 250=[-.43235899063884941937,-.03635302683078232313] 
dist 251=[-.43231234300806914282,-.03251855857841664542] 
dist 252=[-.43228418828469518125,-.02752727578324564075] 
dist 253=[-.4317806282399682928 ,-.02212443121332173779] 
dist 254=[-.43168157937843234809,-.01664379439547050050] 
dist 255=[-.4311370381810483203 ,-.01001104946605160907] 

8 phat 1 dirichlet min maxes function [2, 1, 1, 1, 0, 1] 
dist 0=[3.3145612579434577400 ,3.3145612579434577400 ] 
dist 1=[3.3048292386717346979 ,3.3238584059250573871 ] 
dist 2=[3.2968545230269196938 ,3.3300936778865431608 ] 
dist 3=[3.2885742711029892262 ,3.3353300796386399420 ] 
dist 4=[3.2776201358562508942 ,3.3406318420529504285 ] 
dist 5=[3.2656743226677590128 ,3.3456217053490764458 ] 
dist 6=[3.2534274535610968809 ,3.3496105403767569325 ] 
dist 7=[3.2385115598206809626 ,3.3536626969980435719 ] 
dist 8=[3.2158899026634695205 ,3.3589058406291057266 ] 
dist 9=[3.1931629878715782004 ,3.3639519708432297868 ] 
dist 10=[3.1778260736317079769 ,3.3672160912703776169 ] 
dist 11=[3.1648424613169204149 ,3.3698259372195440502 ] 
dist 12=[3.1515285297720722437 ,3.3722550279739278668 ] 
dist 13=[3.1388907542178433172 ,3.3744054143871586621 ] 
dist 14=[3.1286117013751104326 ,3.3759004656035168128 ] 
dist 15=[3.1180074921331920748 ,3.3772137914313711071 ] 
dist 16=[3.1040691219949961028 ,3.3786372857235867284 ] 
dist 17=[3.0902511044090942219 ,3.3799067939947281307 ] 
dist 18=[3.0801282938973636073 ,3.3806041864784817038 ] 
dist 19=[3.0706916400478524743 ,3.3810213999875861346 ] 
dist 20=[3.0596181836665619224 ,3.3811702151431637044 ] 
dist 21=[3.0482293420096631131 ,3.3811956189338618458 ] 
dist 22=[3.0375311771385433396 ,3.3811258465829048837 ] 
dist 23=[3.0252008501796321991 ,3.3809713500617314752 ] 
dist 24=[3.0072835158439627101 ,3.3808712013932420982 ] 
dist 25=[2.9893082438206727478 ,3.3779452398132293148 ] 
dist 26=[2.9767461716372618765 ,3.3774719625742991135 ] 
dist 27=[2.9656424761081646982 ,3.3763790778934341311 ] 
dist 28=[2.9535005716050459687 ,3.3760114247857191686 ] 
dist 29=[2.9415003774484168760 ,3.3720781100488962140 ] 
dist 30=[2.9309635097892254170 ,3.3714036481494489496 ] 
dist 31=[2.9193933289362141647 ,3.3681854066641878085 ] 
dist 32=[2.9032599805596765036 ,3.3627802374831994660 ] 
dist 33=[2.8868331569073619370 ,3.3054253487459000285 ] 
dist 34=[2.8740891029423349612 ,3.3040736659555392500 ] 
dist 35=[2.8614980762965868140 ,3.3007504037896507170 ] 
dist 36=[2.8456833473259442316 ,3.3001971921347441678 ] 
dist 37=[2.8288471818786892258 ,3.2949855708421297649 ] 
dist 38=[2.8121705067490841709 ,3.2939490808698798782 ] 
dist 39=[2.7922769819740349637 ,3.2926914562832459268 ] 
dist 40=[2.7625737247617660481 ,3.2922476816038639393 ] 
dist 41=[2.7327720992646068068 ,3.2819170026529473890 ] 
dist 42=[2.7124851107321689351 ,3.2805560007804441822 ] 
dist 43=[2.6951199139004725725 ,3.2775154892227118753 ] 
dist 44=[2.6770051765315604032 ,3.2767431269008331926 ] 
dist 45=[2.6596170053120608764 ,3.2727798128089029730 ] 
dist 46=[2.6451580037795714465 ,3.2719853154561700928 ] 
dist 47=[2.6299565625089697911 ,3.2703184361547515057 ] 
dist 48=[2.6095987031494565258 ,3.2698268634474363408 ] 
dist 49=[2.5892403862892500041 ,3.2640359338653001385 ] 
dist 50=[2.5740371150595108361 ,3.2631695426055089656 ] 
dist 51=[2.5595749112839775231 ,3.2608979161343813788 ] 
dist 52=[2.5421807935590449877 ,3.2605660138326295972 ] 
dist 53=[2.5240587382733829910 ,3.2565277981905219341 ] 
dist 54=[2.5066848536841779746 ,3.2556966487908475510 ] 
dist 55=[2.4863864360981873958 ,3.2549179111782034230 ] 
dist 56=[2.4565665277615615165 ,3.2547490833460083496 ] 
dist 57=[2.4265152986833381130 ,3.2447621900795300025 ] 
dist 58=[2.4052916201938726836 ,3.2434486426179393253 ] 
dist 59=[2.3862986227888721497 ,3.2409817382853816901 ] 
dist 60=[2.3651699052905543123 ,3.2403494211476561805 ] 
dist 61=[2.3440757146379269664 ,3.2314032797279069079 ] 
dist 62=[2.3252208213225860820 ,3.2301990793426148026 ] 
dist 63=[2.3042388109946542809 ,3.2237817719170487474 ] 
dist 64=[2.2746363551718807533 ,3.2136012069194142616 ] 
dist 65=[2.2443431508588786654 ,2.6926185703071387206 ] 
dist 66=[2.2205982124522587060 ,2.6743151750254706493 ] 
dist 67=[2.1969084749923906727 ,2.6534583573905910076 ] 
dist 68=[2.1668360692014390658 ,2.6494451907284489497 ] 
dist 69=[2.1346585379612578137 ,2.6338775260895108269 ] 
dist 70=[2.1025484994871768271 ,2.6309309395473722395 ] 
dist 71=[2.0640688876130328531 ,2.6247151933305367286 ] 
dist 72=[2.0064136702899242934 ,2.6231023795342463301 ] 
dist 73=[1.9487086425408794380 ,2.5432173661753739353 ] 
dist 74=[1.9100297937138102831 ,2.5359833874390021339 ] 
dist 75=[1.8775711107626421078 ,2.5192760098723677667 ] 
dist 76=[1.8447461532500709570 ,2.5165906474267755564 ] 
dist 77=[1.8138770086658272960 ,2.4946116580752918561 ] 
dist 78=[1.7892413908863966577 ,2.4906345901787992156 ] 
dist 79=[1.7642521133259773575 ,2.4850378764538662442 ] 
dist 80=[1.7319683633491501302 ,2.4834477194247711702 ] 
dist 81=[1.7002265240861386649 ,2.4546148782107665172 ] 
dist 82=[1.6774048376946093436 ,2.4509115176284693692 ] 
dist 83=[1.6565622847985803652 ,2.4429734104885985289 ] 
dist 84=[1.6327367907517282322 ,2.4410934158194810663 ] 
dist 85=[1.6085799239065567700 ,2.4323307028622472503 ] 
dist 86=[1.5864119114229331884 ,2.4307484055585469099 ] 
dist 87=[1.5612708050742503501 ,2.4270655422999397502 ] 
dist 88=[1.5252218463366598874 ,2.4263899397501234736 ] 
dist 89=[1.4892577374981481805 ,2.3333200304849775364 ] 
dist 90=[1.4644560226529646546 ,2.3267172875886085149 ] 
dist 91=[1.4428819109067699742 ,2.3114228416686999068 ] 
dist 92=[1.4198279066218078021 ,2.3090070100641675584 ] 
dist 93=[1.3973596225351640181 ,2.2887600771186604293 ] 
dist 94=[1.3781283357174077564 ,2.2850949959925579391 ] 
dist 95=[1.3574263270767704192 ,2.2800797497465092693 ] 
dist 96=[1.3290752959731436592 ,2.2786087413486860256 ] 
dist 97=[1.3004358928490639259 ,2.2516351688423611072 ] 
dist 98=[1.2785804236309681841 ,2.2481771347867505323 ] 
dist 99=[1.2573306976935387292 ,2.2408697458942483913 ] 
dist 100=[1.2311142099175269813 ,2.2390433698875451914 ] 
dist 101=[1.2034475734119783155 ,2.2313276496696737628 ] 
dist 102=[1.1763973908687215234 ,2.2299147129298361433 ] 
dist 103=[1.1443917104045974043 ,2.2265740419057631388 ] 
dist 104=[1.0969035548611790757 ,2.2260058794622447176 ] 
dist 105=[1.0493789625506370214 ,2.1888021745880043156 ] 
dist 106=[1.0172275384932848495 ,2.1853355279816358099 ] 
dist 107=[.9899223194314316101 ,2.1772479245450428006 ] 
dist 108=[.9617820848814289014 ,2.1759642179910980885 ] 
dist 109=[.9349827756313195604 ,2.1650164800744727381 ] 
dist 110=[.9130411298742343529 ,2.1630076216339095370 ] 
dist 111=[.8902754155595014715 ,2.1603119409965531451 ] 
dist 112=[.8601799106768321075 ,2.1594990172171434822 ] 
dist 113=[.8302639016647650377 ,2.1439216300032133959 ] 
dist 114=[.8082161537124798797 ,2.1419016683733827677 ] 
dist 115=[.7875308763314748729 ,2.1376956290799425683 ] 
dist 116=[.7630646196547775578 ,2.1365716718689982017 ] 
dist 117=[.7377954973399418743 ,2.1322558305960660180 ] 
dist 118=[.7138988339821215002 ,2.1314186362519942944 ] 
dist 119=[.67342144933620818627,2.1295220486730306454 ] 
dist 120=[.6066595772723223008 ,2.1290784769960769621 ] 
dist 121=[.53831799926909001187,2.0792321741401244950 ] 
dist 122=[.48470996624609197283,2.0754645370771743653 ] 
dist 123=[.43118837046601135024,2.0673908262322143814 ] 
dist 124=[.36319253262387774451,2.0654943751176372629 ] 
dist 125=[.29040728530658515124,2.0499196942286513930 ] 
dist 126=[.2177283765983904652 ,2.0470211832983139016 ] 
dist 127=[.13059642705719907489,2.0378553201491038056 ] 
dist 128=[0                     ,2.0238850434976507844 ] 
dist 129=[.35273356620115712501,1.2138815016564954310 ] 
dist 130=[.31734065612624484706,1.2125637078121843066 ] 
dist 131=[.2821018222644129725 ,1.2095880115466630650 ] 
dist 132=[.23746495622368980434,1.2090285230487169427 ] 
dist 133=[.18975016848198290365,1.2052812400314785832 ] 
dist 134=[.14219980955041597935,1.2045974519634881045 ] 
dist 135=[.08526241796217444538,1.2033918224321177956 ] 
dist 136=[0                     ,1.2031190405481360804 ] 
dist 137=[.0046386137623999160 ,.08368171158883089156] 
dist 138=[-.0423526448090861626 ,.06868355095710935172] 
dist 139=[-.0814411575673047323 ,.03522654897570875558] 
dist 140=[-.1204088317799041572 ,.02921203594608400153] 
dist 141=[-.1566966304332509641 ,-.01087251683667104572] 
dist 142=[-.1850659005061600160 ,-.01789624250744702291] 
dist 143=[-.2132995874482145882 ,-.03038847662115753279] 
dist 144=[-.2490450744094028012 ,-.03309913633979501222] 
dist 145=[-.2838433646626286968 ,-.07124185871626937256] 
dist 146=[-.30828835906127060767,-.07640646419087261129] 
dist 147=[-.33002781789995677427,-.08697252541233625084] 
dist 148=[-.35400422790187950464,-.08964830045010626486] 
dist 149=[-.37782128027690246459,-.09911835818618476972] 
dist 150=[-.39892333169396677849,-.10096720937332265149] 
dist 151=[-.42225296121774543222,-.10388824475968509463] 
dist 152=[-.45498013327689666854,-.10457080048865229251] 
dist 153=[-.48732504941568667139,-.33525019461555438178] 
dist 154=[-.50912569564464087808,-.34788642202130933652] 
dist 155=[-.52755219793493475745,-.37711573628639882166] 
dist 156=[-.54640085220185076899,-.38139007254625347499] 
dist 157=[-.56426310588115719779,-.41946011696230954772] 
dist 158=[-.57874410379579038792,-.42618797049391247084] 
dist 159=[-.59364053375068697698,-.43472765897672955931] 
dist 160=[-.61316449558533156017,-.43641160645040017834] 
dist 161=[-.63249393162234776686,-.48468645399304085785] 
dist 162=[-.64661228476286106691,-.49054405889443499598] 
dist 163=[-.65973176034813671639,-.5026177967782055586 ] 
dist 164=[-.67506578528460764322,-.50557668685193339785] 
dist 165=[-.69080329273685490667,-.51670462901191308245] 
dist 166=[-.70553667947035176191,-.51881271575839015662] 
dist 167=[-.72247929673323703985,-.52246810323948572381] 
dist 168=[-.74705357044419246384,-.52322655420215291652] 
dist 169=[-.77141977661237943972,-.5758582630937387347 ] 
dist 170=[-.78753014223212517259,-.58032197954671376109] 
dist 171=[-.80080716733211901362,-.59052404269160011683] 
dist 172=[-.81384022285530007043,-.59202378199113937271] 
dist 173=[-.82584605638087653459,-.60482440859270828476] 
dist 174=[-.83501426794590987697,-.60703559101050993433] 
dist 175=[-.84393452630874425517,-.60998670191687238707] 
dist 176=[-.85494855892576523411,-.61058297053626299494] 
dist 177=[-.8655352293638923851 ,-.62475453425348222114] 
dist 178=[-.87274606800278132673,-.62642700305156148246] 
dist 179=[-.87892291826290973032,-.63001459761084835608] 
dist 180=[-.88537371024850723727,-.63065131173691730389] 
dist 181=[-.8915703624129551450 ,-.63433904344766482832] 
dist 182=[-.8967306658472387285 ,-.63491551219872456812] 
dist 183=[-.9021626004897517350 ,-.63608589291223164356] 
dist 184=[-.9094457397966146413 ,-.6362565040211485372 ] 
dist 185=[-.9165270153937615362 ,-.72986340176712909857] 
dist 186=[-.9211515156739145530 ,-.73350517683596125611] 
dist 187=[-.9248988959972222850 ,-.74152218891437949035] 
dist 188=[-.9284728521222770041 ,-.74293949805674041096] 
dist 189=[-.9316988227772194900 ,-.75207154924805230312] 
dist 190=[-.9340461532147843938 ,-.753613499498697419  ] 
dist 191=[-.9362185017038974019 ,-.75644034170956299603] 
dist 192=[-.9387445149535693345 ,-.75704815216582452632] 
dist 193=[-.9410946754029616529 ,-.76357723041193714501] 
dist 194=[-.9425635985947086683 ,-.76450575961066699599] 
dist 195=[-.9436798748550614418 ,-.76572074976994902759] 
dist 196=[-.9446194349127488298 ,-.76587161650427420415] 
dist 197=[-.9453821353617560279 ,-.76561525997212437357] 
dist 198=[-.9457909437638713270 ,-.76475472972951908629] 
dist 199=[-.9460216731578916262 ,-.76327971256099115712] 
dist 200=[-.9460719819907707296 ,-.76056556026556757166] 
dist 201=[-.92691422809916188773,-.75760736259746202242] 
dist 202=[-.9258199803378937044 ,-.75515618977113151893] 
dist 203=[-.92333161738081242544,-.75258749691476691219] 
dist 204=[-.92276229845210275941,-.74915914467219792958] 
dist 205=[-.91942590781366282468,-.74540652532507475996] 
dist 206=[-.91876805608398654221,-.74154078589043603603] 
dist 207=[-.91750572778607448378,-.73681987437005977541] 
dist 208=[-.91716507738527374211,-.72964670664503038024] 
dist 209=[-.91213569808843994305,-.72208419962500757421] 
dist 210=[-.91141149738793951155,-.7158059844321463016 ] 
dist 211=[-.90963129852648247194,-.70921519097191215539] 
dist 212=[-.90930283552465912922,-.70040239141195370384] 
dist 213=[-.90647216668828009249,-.69074717859159042437] 
dist 214=[-.90589702652742903201,-.68078687063294323669] 
dist 215=[-.90512680690899692975,-.66861259386160164581] 
dist 216=[-.9048629083212664432 ,-.65010190081610445838] 
dist 217=[-.89599459166349866754,-.63140148220403981415] 
dist 218=[-.89498324095882777497,-.61846832724877733112] 
dist 219=[-.89250162163278169396,-.60718008481578281487] 
dist 220=[-.89210458343813122553,-.59505899350184967428] 
dist 221=[-.88825501032788658488,-.58321174073328254624] 
dist 222=[-.88749797208380368804,-.57301878612388130818] 
dist 223=[-.88660876685049548553,-.56200210284644021288] 
dist 224=[-.88633170882279295375,-.54686005916046061659] 
dist 225=[-.87715919004014701049,-.53154118645048744706] 
dist 226=[-.87599181671602278246,-.5198172055082239129 ] 
dist 227=[-.87389354016023339898,-.50838655831597592952] 
dist 228=[-.87339260234607393995,-.49424095213575945312] 
dist 229=[-.86560712864294387433,-.47929148106290861929] 
dist 230=[-.86462860678192079414,-.464645495906383314  ] 
dist 231=[-.85918945725466284717,-.44729519034035175141] 
dist 232=[-.85068246093487122153,-.4215288708541221257 ] 
dist 233=[-.67127827809464052198,-.39545242341692899299] 
dist 234=[-.66323188027755846825,-.376861650922885026  ] 
dist 235=[-.64532903477623303712,-.36004503935994574661] 
dist 236=[-.64191760283272936408,-.34106493702645463029] 
dist 237=[-.62041293621574896344,-.32195943748717758429] 
dist 238=[-.61658452258665470451,-.30464125000439408051] 
dist 239=[-.60949942276276106817,-.28517277448838781213] 
dist 240=[-.60784704539018192066,-.25746646014054624905] 
dist 241=[-.55177723167963475005,-.22901219678737417323] 
dist 242=[-.54557957272759122526,-.2065520408568816512 ] 
dist 243=[-.53544214989099126085,-.18399890396550250386] 
dist 244=[-.53306403394817660391,-.15517272620348179914] 
dist 245=[-.495635936624917154  ,-.12423098843325738351] 
dist 246=[-.49147654750049333867,-.09321594511888663117] 
dist 247=[-.46720084604892239562,-.05594887075430504051] 

8 phat 1 dirichlet min maxes function [1, 2, 2, 0, 2, 2, 2, 1, 2] 
dist 0=[3.4777317412115046364 ,3.4777317412115046364 ] 
dist 1=[3.4637080640040504849 ,3.4868395458578950936 ] 
dist 2=[3.4493353776631543425 ,3.4941631343559538142 ] 
dist 3=[3.4388315684536794873 ,3.5010501131939268172 ] 
dist 4=[3.4290651078426167206 ,3.5071958369640855857 ] 
dist 5=[3.4176417455685166153 ,3.5115544719399221691 ] 
dist 6=[3.4059134101386517482 ,3.5154738915995687706 ] 
dist 7=[3.3949270859922669061 ,3.5198627880969617225 ] 
dist 8=[3.3822886392160862137 ,3.5239280808304050802 ] 
dist 9=[3.3639519708432297870 ,3.5280198193881909517 ] 
dist 10=[3.3449670589978968825 ,3.5312765164418506193 ] 
dist 11=[3.3297357001599917581 ,3.5338622705199647934 ] 
dist 12=[3.3142120426694633898 ,3.5362379830991364856 ] 
dist 13=[3.2940579640925054181 ,3.5383197031753625028 ] 
dist 14=[3.2722656737815138502 ,3.5397295152821179806 ] 
dist 15=[3.2501893256042491898 ,3.5409284330550275002 ] 
dist 16=[3.2234914221095946809 ,3.5421665959105545216 ] 
dist 17=[3.1832133513238577140 ,3.5432758600166886558 ] 
dist 18=[3.1428318917479515577 ,3.5439591937690166982 ] 
dist 19=[3.1157204429536388018 ,3.5444667804909532322 ] 
dist 20=[3.0929204324103603536 ,3.5448730692867609913 ] 
dist 21=[3.0697843146221304330 ,3.5451869287318136102 ] 
dist 22=[3.0479764886946744636 ,3.5453248029160495691 ] 
dist 23=[3.0304895189046388405 ,3.5453611604046608700 ] 
dist 24=[3.0126753530087092908 ,3.5452966217724923793 ] 
dist 25=[2.9895587738649956570 ,3.5451119830165967432 ] 
dist 26=[2.9667815037217973088 ,3.5449836037450021221 ] 
dist 27=[2.9503245414653069076 ,3.5446411355914693134 ] 
dist 28=[2.9352125405062329953 ,3.5444724319212786452 ] 
dist 29=[2.9178149872729496960 ,3.5434742510514589857 ] 
dist 30=[2.9001062602074859562 ,3.5432037336579731045 ] 
dist 31=[2.8837495935988355182 ,3.5425571532546831194 ] 
dist 32=[2.8651145925891227060 ,3.5423074936674770273 ] 
dist 33=[2.8382927452224426631 ,3.5387411156876773855 ] 
dist 34=[2.8114910980557216029 ,3.5381592423792213165 ] 
dist 35=[2.7929368959191895657 ,3.5367146498379358211 ] 
dist 36=[2.7767216191505048283 ,3.5363360439250570432 ] 
dist 37=[2.7592754503730930920 ,3.5338326494236056231 ] 
dist 38=[2.7422010078668724718 ,3.5332745523769272554 ] 
dist 39=[2.7274726007284349836 ,3.5323079008276193084 ] 
dist 40=[2.7115202697665190446 ,3.5320364784348446382 ] 
dist 41=[2.6895502487018204360 ,3.5259445392227116990 ] 
dist 42=[2.6673012785469761913 ,3.5250435671074814127 ] 
dist 43=[2.6502331778300907248 ,3.5231007389451232285 ] 
dist 44=[2.6335522866917742882 ,3.5225181805508570831 ] 
dist 45=[2.6128521179199216856 ,3.5199764855275851748 ] 
dist 46=[2.5909440406706411447 ,3.5194408412403187764 ] 
dist 47=[2.5694316308305367097 ,3.5180582040870934126 ] 
dist 48=[2.5439088620082098947 ,3.5177282569656077669 ] 
dist 49=[2.5059597313301551023 ,3.4980391018391753055 ] 
dist 50=[2.4679490722468174239 ,3.4960210696303975649 ] 
dist 51=[2.4421801956718167811 ,3.4917858533373431433 ] 
dist 52=[2.4202371222049187179 ,3.4906156846400742818 ] 
dist 53=[2.3975293106564506826 ,3.4859208591306457302 ] 
dist 54=[2.3758449690642137027 ,3.4850042704590910628 ] 
dist 55=[2.3579956778056978106 ,3.4826465224800534873 ] 
dist 56=[2.3393905052343727188 ,3.4822511867459561521 ] 
dist 57=[2.3146827104853649379 ,3.4513872595114138752 ] 
dist 58=[2.2900700127341668950 ,3.4481279291902944141 ] 
dist 59=[2.2718452190839170158 ,3.4438318444319249658 ] 
dist 60=[2.2546615523899519458 ,3.4424845197691321029 ] 
dist 61=[2.2342132631632613132 ,3.4174735503843960784 ] 
dist 62=[2.2130265682456273495 ,3.4131427028831362441 ] 
dist 63=[2.1928893492155646707 ,3.3911088552633241508 ] 
dist 64=[2.1694961382880485114 ,2.9895087033912157126 ] 
dist 65=[2.1352857863306739760 ,2.9185782168227542963 ] 
dist 66=[2.1008743058397392457 ,2.9120824580353504399 ] 
dist 67=[2.0766765999612244085 ,2.8970393529717593433 ] 
dist 68=[2.0551315962938633150 ,2.8946058044202438779 ] 
dist 69=[2.0313306716380483919 ,2.8746307758116921949 ] 
dist 70=[2.0076652465986607087 ,2.8709924178614020049 ] 
dist 71=[1.9866622284733229081 ,2.8658885230210489449 ] 
dist 72=[1.9634129423689173793 ,2.8644208568599984854 ] 
dist 73=[1.9307626596578600095 ,2.8374309649033500328 ] 
dist 74=[1.8974162908358591986 ,2.8339409984304260283 ] 
dist 75=[1.8713827266789977048 ,2.8264980263596689996 ] 
dist 76=[1.8455075041186303329 ,2.8246546219647004739 ] 
dist 77=[1.8127944865802974199 ,2.8164951708734292371 ] 
dist 78=[1.7778593706856897485 ,2.8150047129032572724 ] 
dist 79=[1.7430959666395737066 ,2.8114043956872306448 ] 
dist 80=[1.7015089856046767226 ,2.8108168600859279271 ] 
dist 81=[1.6392802125742351072 ,2.7193284252786144872 ] 
dist 82=[1.5770306624932796392 ,2.7127975874465835850 ] 
dist 83=[1.5353605752380012680 ,2.6975602672002830875 ] 
dist 84=[1.5004517437281433863 ,2.6952106172908704614 ] 
dist 85=[1.4652465717536570979 ,2.6746745802024546366 ] 
dist 86=[1.4322012165200845113 ,2.6709353263415617862 ] 
dist 87=[1.4059314459748284802 ,2.6660630107097256874 ] 
dist 88=[1.3793788399312760614 ,2.6647617488788408212 ] 
dist 89=[1.3452021696808088703 ,2.6358730595995785994 ] 
dist 90=[1.3116595019525430121 ,2.6321901742591360403 ] 
dist 91=[1.2876428455278881453 ,2.6246001045095711491 ] 
dist 92=[1.2658107298243622625 ,2.6226051492669397823 ] 
dist 93=[1.2410060166234350054 ,2.6151438101993020716 ] 
dist 94=[1.2159419826735230394 ,2.6136729629973738398 ] 
dist 95=[1.1930726087075589426 ,2.6106420816744322798 ] 
dist 96=[1.1672408554386558085 ,2.6098209921351931951 ] 
dist 97=[1.1303275868228719562 ,2.5641898768894088635 ] 
dist 98=[1.0935543504533426834 ,2.5600560238082930805 ] 
dist 99=[1.0682827128134589237 ,2.5506597077469892330 ] 
dist 100=[1.0463934844365570863 ,2.5489406315196571292 ] 
dist 101=[1.0231495625114436305 ,2.5369097936701153089 ] 
dist 102=[1.0005847242123198588 ,2.5347075390918754778 ] 
dist 103=[.98141176556972237899,2.5309990136721580857 ] 
dist 104=[.96089332470001773204,2.5301261534366004583 ] 
dist 105=[.93294668582190144564,2.5151227030911442998 ] 
dist 106=[.9047844726475395074 ,2.5131323461722304373 ] 
dist 107=[.8834037551539026558 ,2.5084620003347214831 ] 
dist 108=[.86272189980192695258,2.5076576141967642648 ] 
dist 109=[.83735506853811948645,2.5011444982441280419 ] 
dist 110=[.81066294472701512512,2.4999117129319713852 ] 
dist 111=[.78468004558963622933,2.4981547064582767845 ] 
dist 112=[.75402303867557129311,2.4976344557201071601 ] 
dist 113=[.70863492956488648911,2.4113672837623423553 ] 
dist 114=[.66325211863614135833,2.4056651779659396608 ] 
dist 115=[.63261630394450499087,2.3931189472425922483 ] 
dist 116=[.60667048904877125932,2.3905166860055474172 ] 
dist 117=[.5800472299807235646 ,2.3757438470894488985 ] 
dist 118=[.5547651453739845546 ,2.3730840042710464934 ] 
dist 119=[.5341839004049155996 ,2.3677708854921784569 ] 
dist 120=[.51293553944322086786,2.3664044725524658242 ] 
dist 121=[.48498505449418390877,2.3194507124607786522 ] 
dist 122=[.4572659752582919454 ,2.3143130341404183878 ] 
dist 123=[.40943503779491789815,2.3064117488315661236 ] 
dist 124=[.32743388792711842002,2.3043963399881969632 ] 
dist 125=[.24551396635568711507,2.2709039306495595747 ] 
dist 126=[.14727523349071515884,2.2651240696946681380 ] 
dist 127=[0                     ,2.2367734863685875463 ] 
dist 128=[.32637906808562825573,.96701229450444344083] 
dist 129=[.29024379178897492613,.96634490188713667422] 
dist 130=[.25398406289948162799,.92535247537373785904] 
dist 131=[.22863131152143063119,.92175455443811606953] 
dist 132=[.20620870281088009959,.91351155669871028263] 
dist 133=[.18166926512017098875,.91217831938466343202] 
dist 134=[.15740427540225306386,.90159442482420880544] 
dist 135=[.13607943240656194035,.89970427569329314492] 
dist 136=[.11264765978271387162,.89694690253095914159] 
dist 137=[.07995515250695281400,.8962074360635163646 ] 
dist 138=[.04665936461758318521,.88335185262238387913] 
dist 139=[.02081452707901367772,.88171974853840402297] 
dist 140=[-.00473293497914839543,.87812597129890581679] 
dist 141=[-.03683924930997399358,.87740734946099572436] 
dist 142=[-.07102841512623084535,.87320192651893647665] 
dist 143=[-.10490708446785895896,.87245562387904315484] 
dist 144=[-.1453306904738410373 ,.87099351081430222465] 
dist 145=[-.20569897870438747439,.8706305598163513095 ] 
dist 146=[-.26599219194614321023,-.14667091181507660797] 
dist 147=[-.30611550647458450846,-.17966844668002517746] 
dist 148=[-.33946870175956348323,-.18452442556707333532] 
dist 149=[-.37268208769923045756,-.22756210986566563574] 
dist 150=[-.40358760910225413616,-.23518306831376269709] 
dist 151=[-.4277095703106279508 ,-.2449175622727521003 ] 
dist 152=[-.45167917748088958752,-.24692124283312119499] 
dist 153=[-.48197530516218651944,-.30172867466831781426] 
dist 154=[-.51144398631043881815,-.30841095486065959342] 
dist 155=[-.53210389021536683896,-.3222147842882376001 ] 
dist 156=[-.55043422288548078047,-.32560463146337059092] 
dist 157=[-.57058484522420560964,-.33849345935525144544] 
dist 158=[-.59056306393106219423,-.34092724989081538919] 
dist 159=[-.60820380640386938969,-.34531179228157214901] 
dist 160=[-.62765703086417018703,-.3462576662420220758 ] 
dist 161=[-.6548850243690367557 ,-.40730935650758810294] 
dist 162=[-.68176862234054031614,-.41254038898276148108] 
dist 163=[-.69984430144290430481,-.42457453815060406085] 
dist 164=[-.71507449583164148884,-.42631629478560382259] 
dist 165=[-.73057641840904677901,-.44169920455251069846] 
dist 166=[-.74521847729750639694,-.44438068052664527256] 
dist 167=[-.7570093028363433019 ,-.44781411632357755875] 
dist 168=[-.76906645154307675857,-.44843785216120658087] 
dist 169=[-.78477379731883524742,-.46672125466930936204] 
dist 170=[-.8002799971617604496 ,-.46889228651805896728] 
dist 171=[-.81153258914459413834,-.47341800896413250342] 
dist 172=[-.82191555519539789575,-.47439679173139558349] 
dist 173=[-.83394333810278903601,-.47864560214620182331] 
dist 174=[-.84622822200245071211,-.47939254754513034282] 
dist 175=[-.85763958706875213462,-.48065979445882841366] 
dist 176=[-.8706918562758835755 ,-.48090884295491079087] 
dist 177=[-.88954025508508060169,-.61976134268985385425] 
dist 178=[-.90820352492154152778,-.62532560607679176425] 
dist 179=[-.92051529457784623176,-.63782488138234661277] 
dist 180=[-.93063085487418024707,-.63989590442660661305] 
dist 181=[-.94050943793729283672,-.65500567964163840001] 
dist 182=[-.9495759415472489831 ,-.65761871628802397664] 
dist 183=[-.95644323796688181733,-.66183858885959579742] 
dist 184=[-.96307077506216963457,-.66280214236077372948] 
dist 185=[-.97117825249363879986,-.6773952969710082292 ] 
dist 186=[-.97893353027613094244,-.67925952175441075841] 
dist 187=[-.98415229059845584692,-.6831377557630686031 ] 
dist 188=[-.9885543204111769269 ,-.68396741000710534221] 
dist 189=[-.99304273049647805867,-.68756054845156796232] 
dist 190=[-.9972871666093256848 ,-.68819078594458398737] 
dist 191=[-1.0007133120215568039 ,-.68919186591696972433] 
dist 192=[-1.0042243234718938016 ,-.68940107375839477596] 
dist 193=[-1.0088082038601242058 ,-.68941432771809025972] 
dist 194=[-1.0132288785359499670 ,-.6889590852158204308 ] 
dist 195=[-1.0160870839260315030 ,-.68809641494773204541] 
dist 196=[-1.0183708900859723422 ,-.68644382311260821443] 
dist 197=[-1.0204940380781833421 ,-.68439333077161604046] 
dist 198=[-1.0223719625906200631 ,-.68193908734313564181] 
dist 199=[-1.0236749136693227899 ,-.67869871447578347284] 
dist 200=[-1.0248167877239907427 ,-.67350383775835888442] 
dist 201=[-1.0260504503961795045 ,-.667917621011672498  ] 
dist 202=[-1.0271487929825232797 ,-.663111941725352902  ] 
dist 203=[-1.0277494150345222751 ,-.65791864027492700079] 
dist 204=[-1.0281052955534300004 ,-.65078196255904304117] 
dist 205=[-1.0282247107579206893 ,-.64287050754549645814] 
dist 206=[-1.0282476553647412943 ,-.63457822899580677238] 
dist 207=[-1.0282176227324426991 ,-.62434990115990030611] 
dist 208=[-1.0281427660416759504 ,-.6086946175170766909 ] 
dist 209=[-1.0280696748127819792 ,-.59283887547697604029] 
dist 210=[-.97019745318255788518,-.58180873915790064582] 
dist 211=[-.96738757330847352051,-.57211340246034062486] 
dist 212=[-.96085411191326115546,-.56159656569569743557] 
dist 213=[-.95973888965852405511,-.55125375860837759785] 
dist 214=[-.95088591874626411303,-.54225448378239024743] 
dist 215=[-.9492392145936973748 ,-.53244221418482980357] 
dist 216=[-.9468355806498509332 ,-.51884755074153826992] 
dist 217=[-.94615692512559809121,-.50504598838953220612] 
dist 218=[-.93337619671737486767,-.49440614445624921724] 
dist 219=[-.9316852067776378759 ,-.48395870506199721089] 
dist 220=[-.92804455514824518276,-.47092670202281933059] 
dist 221=[-.92710946127831372872,-.45710050499627392563] 
dist 222=[-.92292620294751572559,-.44347641033577529013] 
dist 223=[-.92213309966251412964,-.4272779325774603276 ] 
dist 224=[-.92025697064104281887,-.40315462398861644431] 
dist 225=[-.91985940250075188551,-.37871371116637737297] 
dist 226=[-.86506228817941104684,-.36124486206317682861] 
dist 227=[-.86106831490039473371,-.34539781129629574808] 
dist 228=[-.85276330757130760249,-.32744380773251793121] 
dist 229=[-.85057355922100953341,-.30933232502969151541] 
dist 230=[-.84231565404348403157,-.29285537366981340022] 
dist 231=[-.84072552087470286157,-.27428426637090722365] 
dist 232=[-.8373336344123681174 ,-.2477964918806293655 ] 
dist 233=[-.83643988341859638973,-.22056849847646250268] 
dist 234=[-.79136446048030339435,-.19903663039092001453] 
dist 235=[-.78682204725538003201,-.17737883583511067109] 
dist 236=[-.78084793958405739012,-.14964714912684371677] 
dist 237=[-.77902293454241367561,-.11985515617216990376] 
dist 238=[-.74649989365409914032,-.08995646496867000617] 
dist 239=[-.7409778945256432342 ,-.05400442315080114328] 

8 phat 1 dirichlet min maxes function [0, 2, 0, 2, 2, 2, 1, 1, 2] 
dist 0=[3.5954794656899869286 ,3.5954794656899869286 ] 
dist 1=[3.5928370842584101282 ,3.5982244851530753675 ] 
dist 2=[3.5897419640226559996 ,3.6008520995395539216 ] 
dist 3=[3.5851860880400644597 ,3.6030248940662417164 ] 
dist 4=[3.5804782696841225796 ,3.6052983791712068449 ] 
dist 5=[3.5767753956904084552 ,3.6083287573591254859 ] 
dist 6=[3.5730695120564909605 ,3.6113524035776782018 ] 
dist 7=[3.5683496036411711190 ,3.6135989725584105303 ] 
dist 8=[3.5632916665223506721 ,3.6157247138174823697 ] 
dist 9=[3.5582336818407961902 ,3.6182650829135558166 ] 
dist 10=[3.5521646895199876174 ,3.6209029549657188949 ] 
dist 11=[3.5430628146378975776 ,3.6234187098712987795 ] 
dist 12=[3.5335138103447325549 ,3.6263478104770626657 ] 
dist 13=[3.5256563356407688155 ,3.6306390370297827783 ] 
dist 14=[3.5174686566454068544 ,3.6349586729640423477 ] 
dist 15=[3.5065988481605808192 ,3.6380014158026328829 ] 
dist 16=[3.4947265615801168373 ,3.6407160646183401385 ] 
dist 17=[3.4825290621405010545 ,3.6437233668779433207 ] 
dist 18=[3.4676547923881960846 ,3.6467185119729438150 ] 
dist 19=[3.4450756873546212366 ,3.6493845444115554627 ] 
dist 20=[3.4220221505382377562 ,3.6523422607843274882 ] 
dist 21=[3.4052501951969144780 ,3.6565041360355855716 ] 
dist 22=[3.3897319225270798000 ,3.6607585592216777022 ] 
dist 23=[3.3716929782063748996 ,3.6640864696178957322 ] 
dist 24=[3.3532342550726174137 ,3.6674003513044678638 ] 
dist 25=[3.3360368997425392002 ,3.6715986720820061490 ] 
dist 26=[3.3163266882587537844 ,3.6760868509152931614 ] 
dist 27=[3.2878167764618696418 ,3.6805601593824579209 ] 
dist 28=[3.2583358885169875874 ,3.6859170435143852108 ] 
dist 29=[3.2347418613250228472 ,3.6939394962488950631 ] 
dist 30=[3.2107482062534625567 ,3.7019135291741337612 ] 
dist 31=[3.1796688374480807645 ,3.7070767399306401988 ] 
dist 32=[3.1460985408559549475 ,3.7112111449022946991 ] 
dist 33=[3.1121414084876468384 ,3.7150700010279704749 ] 
dist 34=[3.0711122898676464637 ,3.7184938861938358953 ] 
dist 35=[3.0092547190505703862 ,3.7208884303387752577 ] 
dist 36=[2.9472770804601004342 ,3.7230069824501022121 ] 
dist 37=[2.9057677009548735020 ,3.7253269221709286934 ] 
dist 38=[2.8709701554219639487 ,3.7274097867762279473 ] 
dist 39=[2.8358392125593017943 ,3.7285800536520271155 ] 
dist 40=[2.8028392493437874784 ,3.7293151633465222899 ] 
dist 41=[2.7765654191508413435 ,3.7296574222107366961 ] 
dist 42=[2.7499716777032671190 ,3.7298362707733349056 ] 
dist 43=[2.7156920999817437666 ,3.7299177362698121752 ] 
dist 44=[2.6820245704048682560 ,3.7299441130857977373 ] 
dist 45=[2.6578789631599427667 ,3.7299025749717309569 ] 
dist 46=[2.6358891197294435179 ,3.7254793958618436778 ] 
dist 47=[2.6108444397977801313 ,3.7248566222384651985 ] 
dist 48=[2.5855034654213747993 ,3.7233723451009250878 ] 
dist 49=[2.5623284724718864322 ,3.7229177847385795806 ] 
dist 50=[2.5361089736709439212 ,3.7204922033402087315 ] 
dist 51=[2.4985902662676741916 ,3.7190414495841273776 ] 
dist 52=[2.4611921492726086437 ,3.6868567374723738886 ] 
dist 53=[2.4354550006028080116 ,3.6849039820571223181 ] 
dist 54=[2.4131240715017968343 ,3.6813796836660274142 ] 
dist 55=[2.3893505079033973141 ,3.6805278676431589980 ] 
dist 56=[2.3662347224653902421 ,3.6779517534417867870 ] 
dist 57=[2.3465348432683676883 ,3.6756628176004201761 ] 
dist 58=[2.3254017653018109580 ,3.6660035697401402267 ] 
dist 59=[2.2965533214813338231 ,3.6594775911543420059 ] 
dist 60=[2.2674531638814836377 ,3.6309250027422891390 ] 
dist 61=[2.2453132548053975966 ,3.6203337129454947216 ] 
dist 62=[2.2050760170184524874 ,3.4931378184760634424 ] 
dist 63=[2.1533859098044730082 ,3.4837205752624382695 ] 
dist 64=[2.0760777535429414124 ,3.4618761514348756485 ] 
dist 65=[1.9984561132814000528 ,3.4583990396273492420 ] 
dist 66=[1.9455120943149634612 ,3.4293255989136789622 ] 
dist 67=[1.9000798495775334121 ,3.4240393185766230329 ] 
dist 68=[1.8525047463984366736 ,3.4167825416703095848 ] 
dist 69=[1.8067243865665464043 ,3.4146495039973055191 ] 
dist 70=[1.7684709820282180387 ,3.3752476514248158109 ] 
dist 71=[1.7280893673654946793 ,3.3701720037239316969 ] 
dist 72=[1.6737963273584978597 ,3.3594499218529111452 ] 
dist 73=[1.6194022156939276169 ,3.3567221666291302706 ] 
dist 74=[1.5786163225629274556 ,3.3453529894045848906 ] 
dist 75=[1.5396554653929504114 ,3.3432543013325367319 ] 
dist 76=[1.4925613617323696551 ,3.3382352001731984616 ] 
dist 77=[1.4433695037802033240 ,3.3373903879485195101 ] 
dist 78=[1.3960177871012594248 ,3.2804579021420137904 ] 
dist 79=[1.3405485598595933446 ,3.2751350306566828000 ] 
dist 80=[1.2588872683996710844 ,3.2627417124561931663 ] 
dist 81=[1.1765176061798632182 ,3.2607215526328663004 ] 
dist 82=[1.1182149490206375574 ,3.2439769087382882971 ] 
dist 83=[1.0659049557497392518 ,3.2408927522260577161 ] 
dist 84=[1.0075054996827958574 ,3.2366133653682066419 ] 
dist 85=[.94908001353778992113,3.2353500503268991321 ] 
dist 86=[.89666590154692190979,3.2115386740626121090 ] 
dist 87=[.83818104339481491183,3.2084288567495008438 ] 
dist 88=[.75547302678150780345,3.2018656752582327276 ] 
dist 89=[.67074760618916904883,3.2001133779117759758 ] 
dist 90=[.60419328274367381855,3.1930680096423486368 ] 
dist 91=[.53765824662284773556,3.1917390674913208865 ] 
dist 92=[.45300997295491375916,3.1884592604693997577 ] 
dist 93=[.36233928260141851739,3.1879248589515544297 ] 
dist 94=[.27171502968515203005,3.1023924324385030930 ] 
dist 95=[.16300648908221274017,3.0962127329315893100 ] 
dist 96=[0                     ,3.0816619990399375605 ] 
dist 97=[1.1904076385870593612 ,3.0794827739832795495 ] 
dist 98=[1.1460650280470198929 ,3.0594274699784923215 ] 
dist 99=[1.0798113127308095173 ,3.0557481401766639350 ] 
dist 100=[1.0135749795486226389 ,3.0512321128453134032 ] 
dist 101=[.96930189588680356303,3.0501856679184353878 ] 
dist 102=[.93228447396393452027,3.0201314551486707492 ] 
dist 103=[.89507009570686827766,3.0163207605744673842 ] 
dist 104=[.8602137427955498889 ,3.0086790740117267071 ] 
dist 105=[.83262819735187423629,3.0067118799406867707 ] 
dist 106=[.80485994170895285895,2.9996607278095939607 ] 
dist 107=[.76927276542718934102,2.9981735420615584423 ] 
dist 108=[.73441940696493846176,2.9956231793090438618 ] 
dist 109=[.70958635260997403547,2.9950114967778860034 ] 
dist 110=[.68713711196900074936,2.9404561314987811358 ] 
dist 111=[.6618187809992727988 ,2.9356684607628294103 ] 
dist 112=[.63634212859025396184,2.9237405802815751832 ] 
dist 113=[.6132596172925031678 ,2.9006169747631819638 ] 
dist 114=[.58731840346337851449,2.8867945495486912306 ] 
dist 115=[.55040721358626289578,2.8843106323554155219 ] 
dist 116=[.51370313972049237649,2.8785637110100302812 ] 
dist 117=[.48859037018243221917,2.8775059352307014062 ] 
dist 118=[.46695755244008583927,2.8674947950184876648 ] 
dist 119=[.44417295384624452844,2.8657110943124164457 ] 
dist 120=[.42216753092435389532,2.8589157750193342552 ] 
dist 121=[.40365134155357428527,2.8108214800643183266 ] 
dist 122=[.38399235582884135737,2.8063227677228416534 ] 
dist 123=[.35741585648879553106,2.8011222756902336632 ] 
dist 124=[.33072441953370505992,2.7877269383941139725 ] 
dist 125=[.31060569431131615926,2.7575503553293160343 ] 
dist 126=[.29128500740931409121,1.3802038631865495692 ] 
dist 127=[.26778564762045287316,1.3444778141395586506 ] 
dist 128=[.24316257334620569228,1.2611500184015729648 ] 
dist 129=[.2193471356803269334 ,1.2491755471762746326 ] 
dist 130=[.19136305211601685914,1.1381526490262260629 ] 
dist 131=[.15006579184525297805,1.1183218848917649200 ] 
dist 132=[.10882761660324822086,1.0943110511703571232 ] 
dist 133=[.08107986751856135059,1.0901147387063912647 ] 
dist 134=[.05767799124205420569,.93877510062236643915] 
dist 135=[.03382289273200733665,.92031869793319474865] 
dist 136=[.01126862292441584587,.88323462655279497584] 
dist 137=[-.00693006261274099144,.87392218177750389793] 
dist 138=[-.02557275519123385607,.84169738138983023603] 
dist 139=[-.04990301081565520950,.83506238299538816171] 
dist 140=[-.07394177774893710003,.8263977032663312232 ] 
dist 141=[-.09141854336448749334,.8243761991836118373 ] 
dist 142=[-.10757697487070870826,.6118275578471881497 ] 
dist 143=[-.12634253110677620951,.59411870542029609117] 
dist 144=[-.14553514493271783954,.5545862268598423602 ] 
dist 145=[-.16340176606652651143,.54743471842543973863] 
dist 146=[-.18386769042362638768,.5171925525403974388 ] 
dist 147=[-.21345726922632761295,.51657852815130810099] 
dist 148=[-.24308022061658425222,.47663339443414937788] 
dist 149=[-.26367963214089432835,.47337768781348970575] 
dist 150=[-.28177984228982574713,.46399747128361101687] 
dist 151=[-.30140622654745652731,.46270780107495592333] 
dist 152=[-.32070559141170038952,.45235831963739949707] 
dist 153=[-.33749775517754768769,.45052409877010780607] 
dist 154=[-.35580821808795576365,.44788308392163990377] 
dist 155=[-.38118063471807048295,.44717168967933117838] 
dist 156=[-.4069442601607956574 ,.43494761494150996121] 
dist 157=[-.4268195210089220347 ,.43341325019572644172] 
dist 158=[-.44634992259026021685,.4300387760520041786 ] 
dist 159=[-.4707341438578280355 ,.42939164649113600243] 
dist 160=[-.49661807824528717373,.42549640081551300425] 
dist 161=[-.52214718926651668655,.42481833640420819346] 
dist 162=[-.55251958372948146018,.42351447696300497366] 
dist 163=[-.597776189941077281  ,.42320461990776027699] 
dist 164=[-.64294644503769618665,-.02510717225811021712] 
dist 165=[-.67297344452023004843,-.02743169502174175863] 
dist 166=[-.69789815461254182989,-.08889562971839806048] 
dist 167=[-.72265974252480800833,-.09642170442166438118] 
dist 168=[-.74566280093097714092,-.11198733026941758903] 
dist 169=[-.76355356445351213676,-.11583135508431198792] 
dist 170=[-.78127188610457502821,-.13049224855611536387] 
dist 171=[-.80358520092985572941,-.13326130257267172819] 
dist 172=[-.82524943780396839235,-.13837362727486807986] 
dist 173=[-.84037151328410556461,-.13952186164684885661] 
dist 174=[-.85371912494457594766,-.20977114353249705877] 
dist 175=[-.868285679504426631  ,-.21583782170595470701] 
dist 176=[-.88266517036952871   ,-.2298550915105370169 ] 
dist 177=[-.89526455253847714682,-.23187516186381632844] 
dist 178=[-.9090773338775833564 ,-.2500280778141045457 ] 
dist 179=[-.92831032430820123816,-.25321623929155985814] 
dist 180=[-.94725679517105816064,-.25721544317732271583] 
dist 181=[-.95992352927494049154,-.25792135243560357469] 
dist 182=[-.97051746068141541054,-.28051708964542502644] 
dist 183=[-.9811729109618853658 ,-.28322275183517074767] 
dist 184=[-.99115664203732629044,-.28878183466066644348] 
dist 185=[-.99906376436701745155,-.29011580909993820805] 
dist 186=[-1.0070288704891240285 ,-.29510667680439925586] 
dist 187=[-1.0172445497241480284 ,-.29604920161597800629] 
dist 188=[-1.0272536253084289540 ,-.29746987052593206404] 
dist 189=[-1.0343923439181861302 ,-.29780674123930418753] 
dist 190=[-1.0408534032336173515 ,-.48559637409708696258] 
dist 191=[-1.0481519099085630114 ,-.49330038437403509442] 
dist 192=[-1.0555030020180096459 ,-.51079320779067298167] 
dist 193=[-1.0621744165300942942 ,-.51359344409803457425] 
dist 194=[-1.0696813139314416090 ,-.53538273096933658858] 
dist 195=[-1.0803743096968498601 ,-.53919493699487525252] 
dist 196=[-1.0909179460306787388 ,-.5448898133608471648 ] 
dist 197=[-1.0978274187078379818 ,-.54633516650034102734] 
dist 198=[-1.1034533952104391002 ,-.57001069514949770842] 
dist 199=[-1.1088631137474907457 ,-.57294088941037842071] 
dist 200=[-1.1137724935724069708 ,-.5795941970831984672 ] 
dist 201=[-1.1173971407440977874 ,-.58058734426011793844] 
dist 202=[-1.1208043955403007677 ,-.58877923045713553336] 
dist 203=[-1.1248442155057217129 ,-.5901812719413301268 ] 
dist 204=[-1.1286441851600676692 ,-.59213186886327808697] 
dist 205=[-1.1310920504772704575 ,-.59256520289782991282] 
dist 206=[-1.1330378160624316579 ,-.60266368056592263218] 
dist 207=[-1.1348294124380382076 ,-.60388689625666276377] 
dist 208=[-1.1364020907009518653 ,-.60564509646865936434] 
dist 209=[-1.1374721935935296995 ,-.60606907006916784611] 
dist 210=[-1.1383876906703999219 ,-.60601551324822922745] 
dist 211=[-1.1393419492925631929 ,-.6052276532596677905 ] 
dist 212=[-1.1401874521602586722 ,-.6037443532746629921 ] 
dist 213=[-1.1406679377469066805 ,-.60090915793211199551] 
dist 214=[-1.1409768195229710673 ,-.59768562443013105952] 
dist 215=[-1.1411359381035358451 ,-.594649024303770234  ] 
dist 216=[-1.1411879956906363253 ,-.59114311217193098926] 
dist 217=[-1.1411724033518191062 ,-.58604236664571395028] 
dist 218=[-1.1409253555397723600 ,-.58025544930823429416] 
dist 219=[-1.1408815162757652390 ,-.57400497031805852965] 
dist 220=[-1.1396422122532003607 ,-.5661658898200840623 ] 
dist 221=[-1.1393943171621418044 ,-.5540248915485800902 ] 
dist 222=[-1.1386837672858378612 ,-.54167334415983851292] 
dist 223=[-1.1385072274676596225 ,-.5329920929265749169 ] 
dist 224=[-1.1369319701105552600 ,-.52526792451508703802] 
dist 225=[-1.1365620028680010666 ,-.51674446050417880892] 
dist 226=[-1.1360774014442105813 ,-.50827616421585629308] 
dist 227=[-1.1358842512517742619 ,-.5007726234435730422 ] 
dist 228=[-1.0236773149947697672 ,-.49247728676679556178] 
dist 229=[-1.0185565951258867874 ,-.48084192504242781611] 
dist 230=[-1.0065837417515181698 ,-.46896646880594355324] 
dist 231=[-1.0047311049672120609 ,-.45971077845843823481] 
dist 232=[-.98849122463685491343,-.45052672236540123255] 
dist 233=[-.98552272459054106323,-.43893775808623587704] 
dist 234=[-.98166323746254570558,-.42657395192056777028] 
dist 235=[-.98061617304060504026,-.41429064460669154428] 
dist 236=[-.95740156970896004556,-.39961175899238529955] 
dist 237=[-.95443167368640851509,-.37766603359950626073] 
dist 238=[-.94832007980391432112,-.35539680501249982942] 
dist 239=[-.94671171578134810491,-.339423951917799926  ] 
dist 240=[-.94069185663209528281,-.32487639401699271856] 
dist 241=[-.93949811446589821392,-.30830808809572262186] 
dist 242=[-.93703728287161509219,-.29154524673943448981] 
dist 243=[-.93636658428171039994,-.27621956654337748008] 
dist 244=[-.87224815641920738378,-.25888508207060520111] 
dist 245=[-.86730827203341668672,-.23408734004235682385] 
dist 246=[-.85680799801652807148,-.20856484128965697149] 
dist 247=[-.85429097316069535026,-.18833144083820983689] 
dist 248=[-.84305235761839134325,-.16793312907400008688] 
dist 249=[-.83896585134074368163,-.14175100133384981588] 
dist 250=[-.82908053847042215028,-.11359191148029034874] 
dist 251=[-.82155045594253820605,-.08528606428058225591] 
dist 252=[-.78681739996884621339,-.05121580711067445398] 

8 phat 1 dirichlet min maxes function [2, 2, 2, 0, 2, 1, 2, 0, 2] 
dist 0=[.72342455308718169479,.72342455308718169479] 
dist 1=[.70666788291455496287,.73344459391265575277] 
dist 2=[.68735048619739866187,.74052772944964011828] 
dist 3=[.66708774179256252532,.74847102336446469211] 
dist 4=[.64208073601827988134,.76208472987176562191] 
dist 5=[.60378666862343368909,.77503617343295823604] 
dist 6=[.56484098645047373466,.78410379715351903305] 
dist 7=[.53722757324001147216,.79805572677956493621] 
dist 8=[.51240383544140338078,.82308482801450086554] 
dist 9=[.48461663512144969271,.84162659661541154509] 
dist 10=[.45677463695190290704,.85911798467218846668] 
dist 11=[.43173171264412792884,.87994564775271658124] 
dist 12=[.40373474382129036252,.90153297119811131978] 
dist 13=[.36407680205123698488,.92206294265046317435] 
dist 14=[.32342343440481163333,.94592198542721585075] 
dist 15=[.29144484118623781055,.98082533598203653229] 
dist 16=[.25943441039527788496,1.0155559161371336695 ] 
dist 17=[.21865369529336511739,1.0387238916524545286 ] 
dist 18=[.17494347794299818722,1.0580445563302097010 ] 
dist 19=[.13121527042101679772,1.0773861943290784757 ] 
dist 20=[.07873155501923528324,1.0954502191612892460 ] 
dist 21=[0                     ,1.1096605322160439124 ] 
dist 22=[.64138775116453979432,1.1238858218175077743 ] 
dist 23=[.65429612024138363179,1.1420097547282161416 ] 
dist 24=[.68303334464946216524,1.1597092141524962285 ] 
dist 25=[.68827189383804858047,1.1722366444381486951 ] 
dist 26=[.73275505953582523613,1.1834758508641808750 ] 
dist 27=[.7407501997770313317 ,1.1960225168323500642 ] 
dist 28=[.77169332445792688722,1.2085742411613920612 ] 
dist 29=[1.0123002311059211790 ,1.2198336837986259186 ] 
dist 30=[1.0237672557348696449 ,1.2323965392162934571 ] 
dist 31=[1.0502228775592075419 ,1.2501618209860450219 ] 
dist 32=[1.0541795316712632782 ,1.2677814346215021489 ] 
dist 33=[1.0884758925979763720 ,1.2797616304812939149 ] 
dist 34=[1.0945445442340153850 ,1.2900014740530668756 ] 
dist 35=[1.1025075997544630015 ,1.3006598111493214772 ] 
dist 36=[1.1043148020096078257 ,1.3108764099280194948 ] 
dist 37=[1.1470867182753412636 ,1.3193493363694724974 ] 
dist 38=[1.1523330476093142547 ,1.3282375808425314606 ] 
dist 39=[1.1633185976809900990 ,1.3401154275381251634 ] 
dist 40=[1.1658738114783021993 ,1.3519823647911198219 ] 
dist 41=[1.1766939878022553563 ,1.3608269756504130009 ] 
dist 42=[1.1786433240407484610 ,1.3692235609329691700 ] 
dist 43=[1.1825533549713104360 ,1.3792984325560057676 ] 
dist 44=[1.1835103822905529926 ,1.3897824180699856924 ] 
dist 45=[1.2275038050559152148 ,1.3998154352341544071 ] 
dist 46=[1.2314225873645077048 ,1.4115237012389048607 ] 
dist 47=[1.2402595348760192143 ,1.4287085744008321100 ] 
dist 48=[1.2416881881100339627 ,1.4458123923583009891 ] 
dist 49=[1.2524612017114471541 ,1.4571964440694820454 ] 
dist 50=[1.2543237717149767085 ,1.4666621139474390278 ] 
dist 51=[1.2572161998094416882 ,1.4760925318562453355 ] 
dist 52=[1.2579066965988338501 ,1.4848708333497065759 ] 
dist 53=[1.2686059682425825487 ,1.4917280808065468964 ] 
dist 54=[1.2699464049569061992 ,1.4985475770483140163 ] 
dist 55=[1.2734932624574623610 ,1.5071748761001393290 ] 
dist 56=[1.2818749605200066015 ,1.5155707340588615771 ] 
dist 57=[1.2840755085205188582 ,1.5214644812709656704 ] 
dist 58=[1.2846494981003370002 ,1.5267017331313097618 ] 
dist 59=[1.2873889138163610620 ,1.5324716532862321000 ] 
dist 60=[1.2924122408969595448 ,1.5381997501078172293 ] 
dist 61=[1.4313267199335191939 ,1.5432697113910458441 ] 
dist 62=[1.4367266902130897182 ,1.5488707118069621284 ] 
dist 63=[1.4489724903897721457 ,1.5567229298236204179 ] 
dist 64=[1.4509147539319195853 ,1.5644817165783140684 ] 
dist 65=[1.4660789077777597178 ,1.5697089981736581532 ] 
dist 66=[1.4687166592979121826 ,1.5741249779863355152 ] 
dist 67=[1.4726427213200131950 ,1.5786386116253143222 ] 
dist 68=[1.4736350657035832709 ,1.5829139304783882768 ] 
dist 69=[1.4896670610991046085 ,1.5863766670601504178 ] 
dist 70=[1.4916384289044476962 ,1.5899358406290635914 ] 
dist 71=[1.4960785238816535296 ,1.5945969011472919584 ] 
dist 72=[1.4967357338643607684 ,1.5992098869829860302 ] 
dist 73=[1.5020462029557792559 ,1.6025767650962936788 ] 
dist 74=[1.5029356113488093162 ,1.6057029985472309862 ] 
dist 75=[1.5042044974478937872 ,1.6093534218391148976 ] 
dist 76=[1.5044692981651478466 ,1.6130980177243513822 ] 
dist 77=[1.5050541121756006266 ,1.6166009354527229856 ] 
dist 78=[1.4985336730522263538 ,1.6206269851441412618 ] 
dist 79=[1.4884533893339777593 ,1.6264640744904581753 ] 
dist 80=[1.4782014925729982163 ,1.6322508714995914481 ] 
dist 81=[1.4709946162757182394 ,1.6360757552679640853 ] 
dist 82=[1.4645801215186223301 ,1.6392266471898963605 ] 
dist 83=[1.4574976557253191207 ,1.6423175214800043150 ] 
dist 84=[1.4504577567978439701 ,1.6451634317988105505 ] 
dist 85=[1.4442135184457961162 ,1.6473344842013948558 ] 
dist 86=[1.4373045438609830344 ,1.6494447183644487982 ] 
dist 87=[1.4276057620269920550 ,1.6520473601491738108 ] 
dist 88=[1.4177020276355985759 ,1.6545476275933142281 ] 
dist 89=[1.4099732595715153471 ,1.6562483713606620162 ] 
dist 90=[1.4022944538181717823 ,1.6577028451783633383 ] 
dist 91=[1.3925905568886249524 ,1.6592180492968535268 ] 
dist 92=[1.3822296541340205546 ,1.6606712685131726233 ] 
dist 93=[1.3719228863518016164 ,1.6618778072416246104 ] 
dist 94=[1.3595954451346408252 ,1.6631446838099938608 ] 
dist 95=[1.3411520442064263918 ,1.6648392514693960634 ] 
dist 96=[1.3224284010341563191 ,1.6664785088360549441 ] 
dist 97=[1.3089800161650141506 ,1.6675241481041270359 ] 
dist 98=[1.2967117046174777546 ,1.6683435380071036781 ] 
dist 99=[1.2827082351263218511 ,1.6690778124403508080 ] 
dist 100=[1.2685216777628364904 ,1.6697082376545766813 ] 
dist 101=[1.2555210293679811200 ,1.6701122377658409740 ] 
dist 102=[1.2407911172432103003 ,1.6704309750064055866 ] 
dist 103=[1.2196876684847908656 ,1.6707203554610070508 ] 
dist 104=[1.1979516092414307972 ,1.6709466629576569834 ] 
dist 105=[1.1806913141025730191 ,1.6710131129707271254 ] 
dist 106=[1.1632627458616069631 ,1.6710110044862852371 ] 
dist 107=[1.1408536074342147870 ,1.6709656228987164239 ] 
dist 108=[1.1167311983988336823 ,1.6705655155859338098 ] 
dist 109=[1.0924497097214630521 ,1.6704348794393641656 ] 
dist 110=[1.0631974922845793442 ,1.6702504166079135265 ] 
dist 111=[1.0191926408963484691 ,1.6701677943775277903 ] 
dist 112=[.97514145717376445444,1.6678057645518937309 ] 
dist 113=[.94570391434750402254,1.6674589417050427383 ] 
dist 114=[.92109812301751338368,1.6666475378351353737 ] 
dist 115=[.89637348443709835275,1.6664072475481843490 ] 
dist 116=[.87322321815161791825,1.6651513349433290586 ] 
dist 117=[.85491476584084712922,1.6648729509299643479 ] 
dist 118=[.83649692813033966911,1.6643101833036869321 ] 
dist 119=[.81290913067887583223,1.6641365210252817862 ] 
dist 120=[.7898154399324718401 ,1.6563834269089779172 ] 
dist 121=[.77337398191528258394,1.6554761780319059077 ] 
dist 122=[.75852399378289852916,1.6540659399384419454 ] 
dist 123=[.74179603078446246958,1.6517736220822608328 ] 
dist 124=[.72497483756808385622,1.6458927449247975789 ] 
dist 125=[.70975193745604355137,.92471042310934544248] 
dist 126=[.69265792126509209533,.9095286525711326101 ] 
dist 127=[.66835244219642316459,.87409792558744108696] 
dist 128=[.64419066881882006129,.86898784819744329126] 
dist 129=[.62767146168576706338,.82167400874642206958] 
dist 130=[.61345441917430572568,.81320609041735387274] 
dist 131=[.59850108470715672603,.8029322018575492007 ] 
dist 132=[.58407175491124379882,.80108310882886455891] 
dist 133=[.57195068110619664021,.73615683556234822296] 
dist 134=[.55909920680538233759,.72821198987260832541] 
dist 135=[.54174834469055685177,.71224376640523661343] 
dist 136=[.52433278066121591963,.70822364282173171555] 
dist 137=[.51122250487348058757,.69425675844440846244] 
dist 138=[.4986485546930812479 ,.69137828286533327615] 
dist 139=[.48337824193940763539,.68748132116586337992] 
dist 140=[.46738997303181332914,.68643025452355742085] 
dist 141=[.4519442667129704966 ,.59342540157783187448] 
dist 142=[.43380870870469477614,.58561762299613434885] 
dist 143=[.40706128959210791803,.56818774251001894533] 
dist 144=[.38035864779068464206,.56499856830824864866] 
dist 145=[.36240219475629179122,.54398826533877516797] 
dist 146=[.3472699039913726176 ,.54027673997968323494] 
dist 147=[.33186364190482732397,.53362513797904214615] 
dist 148=[.31730956114862674022,.53215060326867045253] 
dist 149=[.30558591442571502569,.5114409306344909902 ] 
dist 150=[.29359424303525912618,.5086228865657266039 ] 
dist 151=[.27796808917254497706,.50267574278694477378] 
dist 152=[.26254043562703118758,.50127141159714617806] 
dist 153=[.25134274657280870817,.49514897720768869593] 
dist 154=[.24100848847669715077,.49405200575647160319] 
dist 155=[.22903447641128840167,.49161753834061083451] 
dist 156=[.21680331070710636278,.49114777320347548766] 
dist 157=[.20544046258270757792,.35813791497208062378] 
dist 158=[.19244284521556834062,.35058604900834181547] 
dist 159=[.17367275846148456597,.33311688051159918929] 
dist 160=[.15489063665292504103,.33048869583749967665] 
dist 161=[.14184488021576251747,.30763540191316698015] 
dist 162=[.13039779359720228636,.30356480441579338864] 
dist 163=[.11801019858508359964,.29823986867853728557] 
dist 164=[.10584368074201944801,.2969881294217479232 ] 
dist 165=[.09528088171377382083,.26762834143804890549] 
dist 166=[.08378253894658295515,.26399350859947310816] 
dist 167=[.06787393537805103884,.25641746645074262932] 
dist 168=[.05173086972902309289,.25456460890309921693] 
dist 169=[.03929470100237805016,.24715355803094656081] 
dist 170=[.02709080158370697003,.24577873761476367333] 
dist 171=[.01187679101318724346,.24301422105712629407] 
dist 172=[-.00426112396861135578,.24232121314772166198] 
dist 173=[-.02016055291222081075,.2271635918202069215 ] 
dist 174=[-.03906352380515999665,.22648098181263923332] 
dist 175=[-.06721532011238138170,.22635476332555734708] 
dist 176=[-.09532286601127824975,.19688510193643915453] 
dist 177=[-.11404883949143587488,.18753037735686234105] 
dist 178=[-.12963854089947021025,.18586682987590766335] 
dist 179=[-.14520129764130689442,.18382775980149485103] 
dist 180=[-.15970750424772788636,.18346527089071776146] 
dist 181=[-.17107110588576362867,.17102725019328464529] 
dist 182=[-.18240183303838506277,.16951603944529779998] 
dist 183=[-.19677654483865228092,.16645917331573970664] 
dist 184=[-.21078457058610083285,.16568997332427088235] 
dist 185=[-.22064858850123874959,.1630099099259758588 ] 
dist 186=[-.22944559760895498167,.16246949551712412756] 
dist 187=[-.23918568989590844085,.16172030115289824708] 
dist 188=[-.24888314840453152678,.1615264873420606482 ] 
dist 189=[-.25750962646525179852,.02902201125852860739] 
dist 190=[-.26707523232964246163,.02361087328646804712] 
dist 191=[-.28052911248079291232,.01113515376747045969] 
dist 192=[-.29384083633342563582,.00924675757738937876] 
dist 193=[-.30283783056233224248,-.00692370433746556499] 
dist 194=[-.31046929588365634627,-.00979132127146708888] 
dist 195=[-.31831903434740798262,-.01361035174384773467] 
dist 196=[-.32578527661981361319,-.01453652429138803336] 
dist 197=[-.33188279375286263713,-.03468689904974124738] 
dist 198=[-.3381955341015122109 ,-.03717761649594677178] 
dist 199=[-.34652264870875501695,-.04242537981097960392] 
dist 200=[-.35479167429458780229,-.04363207045128757565] 
dist 201=[-.3608720640980133715 ,-.04894634353730790776] 
dist 202=[-.36656299132316028672,-.04989005898345039898] 
dist 203=[-.37327420374204959531,-.05189810138575450687] 
dist 204=[-.38019478378260429259,-.05232403639671858092] 
dist 205=[-.38672316152534271772,-.05652049647570842591] 
dist 206=[-.39426900486791034987,-.05717708743638865329] 
dist 207=[-.40525935026392347226,-.05732126413759086188] 
dist 208=[-.41617471534036924055,-.06569375912905048606] 
dist 209=[-.42342064455614217582,-.06644297167717939631] 
dist 210=[-.42942420297007534565,-.06792937254073864394] 
dist 211=[-.43537020333403421077,-.06829272551526527285] 
dist 212=[-.44088207388403145627,-.06949008740258569722] 
dist 213=[-.445149154448561964  ,-.06974209152730777497] 
dist 214=[-.44935642340131719608,-.06992734959082127110] 
dist 215=[-.45462905320892668251,-.06984072112597027490] 
dist 216=[-.45973572448506240542,-.06963670598243109379] 
dist 217=[-.46327917514071938186,-.06929448483963770460] 
dist 218=[-.4663846409562046162 ,-.06878279699596150874] 
dist 219=[-.46973941464578196964,-.06790091673078886313] 
dist 220=[-.47303083822952947215,-.06683978098138087669] 
dist 221=[-.47588290966390321724,-.06561110436808102284] 
dist 222=[-.47898294583142243   ,-.06401429383592184112] 
dist 223=[-.48326620469736553327,-.06148072021300906316] 
dist 224=[-.48747113528710293747,-.05885161220792233430] 
dist 225=[-.49025786582059556162,-.05687267872945254134] 
dist 226=[-.49256168414559411123,-.05497534893369834651] 
dist 227=[-.4948350119605674303 ,-.05267260159695802661] 
dist 228=[-.49693689180128289093,-.05026287111112736736] 
dist 229=[-.49855493458161901067,-.04793761926015828733] 
dist 230=[-.50014162740796099319,-.04520986698391987734] 
dist 231=[-.50211811042279656942,-.04119022047789202448] 
dist 232=[-.50402650043789407271,-.03700317910284046288] 
dist 233=[-.50534082775985952729,-.03360587914830054451] 
dist 234=[-.50648225850886427785,-.03010905399743828526] 
dist 235=[-.50769907872265245173,-.02552392153216167200] 
dist 236=[-.50888323025729574874,-.02054438244912556824] 
dist 237=[-.50989398940559505587,-.01547001559228978655] 
dist 238=[-.51097965466849356876,-.00931237789438225377] 
dist 239=[-.51246342351713649271,0                     ] 
dist 240=[-.51390587290280681754,-.07070537080369549601] 
dist 241=[-.51482626472583432962,-.06724483537497880778] 
dist 242=[-.51554781410500748566,-.06397800713679509765] 
dist 243=[-.51619491409354416704,-.06020054956296330759] 
dist 244=[-.51675083465976336708,-.05469759278565623542] 
dist 245=[-.5171076764589937609 ,-.04899161218283314808] 
dist 246=[-.51738987298075712875,-.04440209450295009151] 
dist 247=[-.51764722238178225955,-.03971431065841974698] 
dist 248=[-.51785243459661515299,-.03361527497198786631] 
dist 249=[-.51792608687530070364,-.02701480703583845518] 
dist 250=[-.51794674881845203635,-.02032138916539572220] 
dist 251=[-.5178858457681097956 ,-.01222241556482492587] 

8 phat 1 dirichlet min maxes function [0, 0, 0, 0, 2, 1, 0, 1, 2] 
dist 0=[.31625479040857823606,.31625479040857823606] 
dist 1=[.31306671112613128918,.3206869979427158802 ] 
dist 2=[.30474685412872157909,.32764221512722193487] 
dist 3=[.29450697245798683268,.3364435262378474649 ] 
dist 4=[.28234841882021485921,.34648662371546827606] 
dist 5=[.26635206508552691497,.35840888831939169386] 
dist 6=[.24076128723410649725,.37409274555013588172] 
dist 7=[.21388358692213720185,.39918191615260655714] 
dist 8=[.19273964543234230615,.42466995324714805544] 
dist 9=[.171573247084115521  ,.441949245112232352  ] 
dist 10=[.14460572134698687313,.45666338715978845494] 
dist 11=[.11570000480443846499,.47189102837880069404] 
dist 12=[.08678099706164718169,.48643305796314880964] 
dist 13=[.05207064288282013988,.49840480828642231462] 
dist 14=[0                     ,.51088514759017661409] 
dist 15=[.45540505604970379315,.52746149412036399895] 
dist 16=[.47808860711173991499,.5439755695776115059 ] 
dist 17=[.4820663356463492196 ,.55620683016036240412] 
dist 18=[.48924567940915468932,.5677427163970726747 ] 
dist 19=[.4908366661879447529 ,.58147535015590620536] 
dist 20=[.51206969137956445537,.59570692158386494733] 
dist 21=[.51498533885784462714,.6092385203819532041 ] 
dist 22=[.52086363429968193038,.62496211596120691589] 
dist 23=[.52233453197449629319,.64796150449952750033] 
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dist 85=[.98822104702501945844,1.0641820016869348796 ] 
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dist 89=[.96490461958751153477,1.0773212760742155592 ] 
dist 90=[.96052563004998901686,1.0794561063166093598 ] 
dist 91=[.95569983550488642597,1.0815581345649572616 ] 
dist 92=[.95090841171748140402,1.0834987313397831444 ] 
dist 93=[.94666689732604437222,1.0849878464786139884 ] 
dist 94=[.94198077150696108974,1.0864436051763225867 ] 
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dist 97=[.92347950781789610198,1.0911874895548380017 ] 
dist 98=[.91829236960409546045,1.0922199156013942746 ] 
dist 99=[.91174491823208263849,1.0933124274396306868 ] 
dist 100=[.90475807642054157005,1.0943707451139331985 ] 
dist 101=[.89781341744019638148,1.0952663968495022085 ] 
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dist 106=[.84719198200531108104,1.1002651580732807157 ] 
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dist 108=[.82824366173940958662,1.1014429621909935618 ] 
dist 109=[.81951045720507799786,1.1018380310356592337 ] 
dist 110=[.80961892513835078267,1.1021943010898710609 ] 
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dist 112=[.78086083272923880622,1.1029601518769260820 ] 
dist 113=[.76927738913198184718,1.1031758439632946015 ] 
dist 114=[.75758350692784027879,1.1033249116618056552 ] 
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dist 122=[.59519520217813629229,1.1026998588386573590 ] 
dist 123=[.57862279138655146831,1.1020839947492056374 ] 
dist 124=[.56310744199983804025,.62290492671897524932] 
dist 125=[.55084005544884720712,.61296818628423330278] 
dist 126=[.53850213083056547851,.589776898530475685  ] 
dist 127=[.52270463590246994373,.58643158623221120749] 
dist 128=[.50723985226423331621,.55545653931788234864] 
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dist 130=[.48629414315301766658,.54318526221461056546] 
dist 131=[.47510331069476574218,.54197310242302577637] 
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dist 133=[.4536752821228774448 ,.49423978844781082752] 
dist 134=[.44225015965951470582,.48377870291421424338] 
dist 135=[.42600913690981300269,.48114478039894417256] 
dist 136=[.40986585036098677767,.47199276832028274592] 
dist 137=[.3988316633792402382 ,.47010616847281889991] 
dist 138=[.38933828551943944146,.46754922317671600245] 
dist 139=[.37935808849906676999,.46685599824000785878] 
dist 140=[.36973058783898235375,.40583852182282832294] 
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dist 142=[.35308244748744087079,.38927603895307420501] 
dist 143=[.34152343994315376354,.38718100758849177205] 
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dist 146=[.31282831238999999514,.36658757547863683109] 
dist 147=[.3026722268957744305 ,.36561770139150072462] 
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dist 149=[.28177590772173834205,.35112089035118160917] 
dist 150=[.26972579223465266173,.34951948763144586679] 
dist 151=[.25195734418955378471,.34921461234559418365] 
dist 152=[.23422018860033912308,.3413115743503700845 ] 
dist 153=[.22229523995217769589,.34058984470145730505] 
dist 154=[.21224863666061103034,.33898291413013373293] 
dist 155=[.20202468334490690779,.33867610030962992085] 
dist 156=[.19236913389452527715,.25096014356342418532] 
dist 157=[.18459609185101106902,.24597776563532190757] 
dist 158=[.1766496449858527753 ,.23445349493527970605] 
dist 159=[.16630049278790404337,.2327173102396504014 ] 
dist 160=[.15608551233562950548,.21764239500341855227] 
dist 161=[.14867573965613200849,.21495671963889145737] 
dist 162=[.1418418230513418379 ,.21143719764081199527] 
dist 163=[.13393021197388208987,.21060361963041157641] 
dist 164=[.12585239237883846156,.19124314433838286629] 
dist 165=[.11835365755635274953,.18884436903480549657] 
dist 166=[.10978052036809597501,.18584664207574972845] 
dist 167=[.09740519378434272834,.18537647563980937575] 
dist 168=[.08502414853001387177,.17770810315148050986] 
dist 169=[.07642813720489015720,.17679894750861902735] 
dist 170=[.06888937496093615005,.17495809189678593208] 
dist 171=[.06073722519295788214,.17449309605996371225] 
dist 172=[.05273414156516352336,.15188997142796492647] 
dist 173=[.04579162966431125628,.14987967449773412244] 
dist 174=[.03823899601602757639,.14686527307826156431] 
dist 175=[.02779548359071423780,.14663623044222998495] 
dist 176=[.01720071154712750991,.13833149472041773738] 
dist 177=[.00904305385259377522,.13728431418340232779] 
dist 178=[.00104181118351279353,.13588425518133287882] 
dist 179=[-.00892731567681897436,.13564969149014217199] 
dist 180=[-.01949892690234606194,.13296979154726489544] 
dist 181=[-.02991004956844007720,.13260879665637200419] 
dist 182=[-.04228475304221235952,.13214526885575305447] 
dist 183=[-.06071050021599510841,.13205013535861686327] 
dist 184=[-.07910581819596114020,.12203841086064577936] 
dist 185=[-.09135880779674293232,.12167873105354833427] 
dist 186=[-.1015569435195013839 ,.12119871162510432665] 
dist 187=[-.11173304197527655464,.12108681600373215529] 
dist 188=[-.12121544103301157299,.03158360155278795862] 
dist 189=[-.12863884532728725228,.02793575956274499311] 
dist 190=[-.13603633611754444041,.01951917963225669010] 
dist 191=[-.14541508363078430238,.01824906457637674892] 
dist 192=[-.15455164651435844991,.00731976345452714955] 
dist 193=[-.16098042188504420184,.00538052802789404576] 
dist 194=[-.16670867236400526328,.00281295125333153819] 
dist 195=[-.17304320249536058656,.00220010512980558091] 
dist 196=[-.17934545554695218581,-.01150594656812688621] 
dist 197=[-.18494460078538243944,-.01310273267611908417] 
dist 198=[-.19114745506857303015,-.01443796773084342344] 
dist 199=[-.1998644867186302155 ,-.01476923157182039689] 
dist 200=[-.20848632064685449663,-.02114358101696566111] 
dist 201=[-.21430839312248406845,-.02178292391078054353] 
dist 202=[-.21924120878584157014,-.02311598620878864983] 
dist 203=[-.22430610028053515647,-.02342564868326719919] 
dist 204=[-.2291179026577792135 ,-.03803955331964824246] 
dist 205=[-.23303838599047851691,-.03935564806433786801] 
dist 206=[-.23708897947649855426,-.04052401329057045463] 
dist 207=[-.24242121005737622055,-.04076813441151407919] 
dist 208=[-.24771116640271546026,-.04544306274048859803] 
dist 209=[-.25159266697861484318,-.04601883714484420354] 
dist 210=[-.25521725485435890457,-.04725693918021829336] 
dist 211=[-.25947958490290254029,-.04750750351217548727] 
dist 212=[-.26386828215157006952,-.04883502818469247807] 
dist 213=[-.26799832677515585831,-.04905844451615240535] 
dist 214=[-.2727643254371489743 ,-.04953775560976869720] 
dist 215=[-.27969677818340627221,-.04962545251262340796] 
dist 216=[-.28657817096679002545,-.05335205967924881316] 
dist 217=[-.29113993464728732741,-.05372135798267525385] 
dist 218=[-.2949125887502840002 ,-.05439425461828707814] 
dist 219=[-.29863761848737746072,-.05454238040984377003] 
dist 220=[-.30208322287175122604,-.05491269628510785252] 
dist 221=[-.30473820221490711683,-.05492798870087066028] 
dist 222=[-.30734414833005262185,-.05481188736825135008] 
dist 223=[-.3105936244790772422 ,-.05448522504675631549] 
dist 224=[-.31373280336490350075,-.05408040347852555338] 
dist 225=[-.31589757094719057534,-.05365167298217362366] 
dist 226=[-.31778053256656466375,-.05311989760929134265] 
dist 227=[-.31979251447883487249,-.05230289683102780338] 
dist 228=[-.32175329292250495   ,-.05135691974657000541] 
dist 229=[-.32343144555116417058,-.05030926202832496955] 
dist 230=[-.32523781815489847323,-.04897783466261313693] 
dist 231=[-.32771146426950101863,-.04689684731801375209] 
dist 232=[-.33013016291764536558,-.04474917522919696519] 
dist 233=[-.33171675089632764926,-.04315101884771336906] 
dist 234=[-.33301030270396427405,-.04163662768548017553] 
dist 235=[-.33425688461713694128,-.03982397802196598017] 
dist 236=[-.33538995860405933084,-.03794049942783865059] 
dist 237=[-.33622948953285655947,-.03614279952069999611] 
dist 238=[-.33702158698372460833,-.03404888248953503916] 
dist 239=[-.33796493158304167539,-.03098059478028342762] 
dist 240=[-.33885438575646537579,-.02779165640611251649] 
dist 241=[-.33943092664372229248,-.02521515864375734768] 
dist 242=[-.33989325543054972161,-.02257303565071494254] 
dist 243=[-.34032587209557992775,-.01912160274632249105] 
dist 244=[-.34088280640638611844,-.01537959491824512450] 
dist 245=[-.34126179959503937125,-.01157523097861972408] 
dist 246=[-.34152984857897244914,-.00696506123291621253] 
dist 247=[-.34171968269209343322,0                     ] 
dist 248=[-.3418605922412189248 ,-.01647382934033417959] 
dist 249=[-.34193294732543958636,-.01239566244906864230] 
dist 250=[-.34196949470333511905,-.00745718711212252455] 

8 phat 1 dirichlet min maxes function [0, 0, 2, 1, 0, 2, 0, 2] 
dist 0=[2.2090097018320747248 ,2.2090097018320747248 ] 
dist 1=[2.2006104680650608147 ,2.2174615045108142811 ] 
dist 2=[2.1899930307757167342 ,2.2282892181941507118 ] 
dist 3=[2.1786548495402594884 ,2.2388921296274227110 ] 
dist 4=[2.1673726980664606110 ,2.2464447430957964882 ] 
dist 5=[2.1538760362257018173 ,2.2532704798498709294 ] 
dist 6=[2.1336799869821525005 ,2.2609659430393311859 ] 
dist 7=[2.1130708428269549445 ,2.2687082381168078373 ] 
dist 8=[2.0979218342112726886 ,2.2757213036689579890 ] 
dist 9=[2.0837482155830052335 ,2.2836017478292245219 ] 
dist 10=[2.0670405565179886871 ,2.2948135024623975529 ] 
dist 11=[2.0498151783674445658 ,2.3061170379044091376 ] 
dist 12=[2.0335707238607190863 ,2.3143646008801685971 ] 
dist 13=[2.0147979244246539788 ,2.3220201055753180716 ] 
dist 14=[1.9874593627891693074 ,2.3309554495135608462 ] 
dist 15=[1.9591104253433181645 ,2.3401191935026856828 ] 
dist 16=[1.9362962011226334592 ,2.3486882839031980354 ] 
dist 17=[1.9129795866774513717 ,2.3585345602473134088 ] 
dist 18=[1.8826211274368870896 ,2.3728069629035514738 ] 
dist 19=[1.8497512210628436827 ,2.3875789579839806501 ] 
dist 20=[1.8163890128164253776 ,2.3994235710125123012 ] 
dist 21=[1.7759958270401811117 ,2.4114896103110019855 ] 
dist 22=[1.7150025555551630713 ,2.4271472965551601918 ] 
dist 23=[1.6536205052921831890 ,2.4440745347941597562 ] 
dist 24=[1.6116722351717470732 ,2.4612186976013422638 ] 
dist 25=[1.5755887600827756108 ,2.4819496677767335348 ] 
dist 26=[1.5376654372265250891 ,2.5132238960276816578 ] 
dist 27=[1.5010879942786575537 ,2.5445210998432519022 ] 
dist 28=[1.4703879363246777520 ,2.5653439709325133562 ] 
dist 29=[1.4378602105807145224 ,2.5826489546244448396 ] 
dist 30=[1.3939722417415892926 ,2.5998748442782465090 ] 
dist 31=[1.3499321562024210068 ,2.6159000750187338864 ] 
dist 32=[1.3167959771604338714 ,2.6284025034968242772 ] 
dist 33=[1.2850311833177836624 ,2.6408212448226879711 ] 
dist 34=[1.2464765338074375179 ,2.6565117328114952590 ] 
dist 35=[1.2061199918045206410 ,2.6717713870732337730 ] 
dist 36=[1.1671477709651032168 ,2.6824668224823017451 ] 
dist 37=[1.1213992023034077582 ,2.6919535888173690862 ] 
dist 38=[1.0539378026364152321 ,2.7023786478882273588 ] 
dist 39=[.98584623911444198108,2.7127125894056439762 ] 
dist 40=[.93757706530300231283,2.7218348920015265608 ] 
dist 41=[.89419399909527950091,2.7318925433834401961 ] 
dist 42=[.84564648315111141371,2.7459678183608347049 ] 
dist 43=[.79701162475366976312,2.7598648912061887093 ] 
dist 44=[.75327919645707439389,2.7692097462318297364 ] 
dist 45=[.70439867181733063905,2.7770847069337427841 ] 
dist 46=[.63517183405342626515,2.7851023006788871752 ] 
dist 47=[.56421290170046235805,2.7926767098479139150 ] 
dist 48=[.50840413544913879712,2.7987789622608838794 ] 
dist 49=[.45254786548485097526,2.8050217053443553516 ] 
dist 50=[.38139892244674692775,2.8131580690347129837 ] 
dist 51=[.30514445634443703395,2.8211921807499279335 ] 
dist 52=[.22886649632747138663,2.8270259233292817609 ] 
dist 53=[.13732148181565110172,2.8324124562943336194 ] 
dist 54=[0                     ,2.8386577598991859469 ] 
dist 55=[2.5492236931499782462 ,2.8450396770469204051 ] 
dist 56=[2.5508768298939004205 ,2.8509726563413882958 ] 
dist 57=[2.5772878902969913855 ,2.8577626466688411736 ] 
dist 58=[2.5805571241298173495 ,2.8675725540783281958 ] 
dist 59=[2.5878214049237087423 ,2.8772837229178023058 ] 
dist 60=[2.5889757304519419635 ,2.8836787659180569155 ] 
dist 61=[2.5973594449576199545 ,2.8889206169389622878 ] 
dist 62=[2.5939780601134948924 ,2.8940190925868249500 ] 
dist 63=[2.5825950188923849700 ,2.8986849127853293199 ] 
dist 64=[2.5724446906065741829 ,2.9021961706946653857 ] 
dist 65=[2.5611693163273884554 ,2.9055627976622201578 ] 
dist 66=[2.5452861959627605715 ,2.9096501054135308277 ] 
dist 67=[2.5290434525569758851 ,2.9135443180775799164 ] 
dist 68=[2.5163296153843673762 ,2.9161385780841856083 ] 
dist 69=[2.5036621014350380390 ,2.9182982507101414695 ] 
dist 70=[2.4876046338927642593 ,2.9204541426902885809 ] 
dist 71=[2.4704348998737444679 ,2.9224637395264632853 ] 
dist 72=[2.4533184235999839447 ,2.9240382430266454157 ] 
dist 73=[2.4328193425756628579 ,2.9256085057251193900 ] 
dist 74=[2.4021195172826278142 ,2.9276011448610106679 ] 
dist 75=[2.3709408524431543911 ,2.9294801044111225989 ] 
dist 76=[2.3485264563787871033 ,2.9305956570839510103 ] 
dist 77=[2.3280583621501591412 ,2.9313744533877878224 ] 
dist 78=[2.3046647063423249289 ,2.9319064069041955155 ] 
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