8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 1, 0, 0, 0, 1] 
dist 0=[57.042600517755135768  ,57.042600517755135768  ] 
dist 1=[55.533535765720615042  ,57.759462819757074624  ] 
dist 2=[53.792572005536312725  ,58.174815451355596364  ] 
dist 3=[52.149586542679228968  ,58.677001614525023005  ] 
dist 4=[50.261837056550857868  ,59.109012687172723046  ] 
dist 5=[47.543208540747224834  ,59.368699471284384582  ] 
dist 6=[44.493289464315983225  ,59.411293788610850658  ] 
dist 7=[41.282497095894615640  ,59.216483611925406938  ] 
dist 8=[37.333178488634298355  ,59.182154891728923038  ] 
dist 9=[31.334044412201597572  ,57.703602715636652193  ] 
dist 10=[25.306886253885642853  ,57.366106755072334951  ] 
dist 11=[21.245481879381621865  ,56.701502043330591800  ] 
dist 12=[17.838584724653935979  ,56.479383186562071907  ] 
dist 13=[14.424599292027172028  ,55.422806273070352524  ] 
dist 14=[11.258108889542596452  ,51.826994321219864242  ] 
dist 15=[8.8391146659754849023 ,51.159893382987019453  ] 
dist 16=[6.4977289081558990549 ,46.918112690792933971  ] 
dist 17=[3.6403795329134202821 ,38.426747987369695718  ] 
dist 18=[.9324993166552941178 ,36.969472317994815804  ] 
dist 19=[-.8124013811859349915 ,33.439418992388027050  ] 
dist 20=[-2.1934495191879214241 ,32.920741918573443147  ] 
dist 21=[-3.4487443382135944214 ,27.791325512116908983  ] 
dist 22=[-4.5375741771886376377 ,26.845028713050523106  ] 
dist 23=[-5.2545769794534463385 ,25.717484020880889963  ] 
dist 24=[-5.8450948616725576821 ,25.483440192634969241  ] 
dist 25=[-6.4305267476799697068 ,17.634802837789364720  ] 
dist 26=[-6.9300878899689828090 ,16.684855805394123761  ] 
dist 27=[-7.1777310387845756247 ,14.685060762748358516  ] 
dist 28=[-7.3008930036555158416 ,14.222117305085647632  ] 
dist 29=[-8.7118362827432336436 ,12.279548003223812948  ] 
dist 30=[-10.292322209289868179  ,11.927601445771000423  ] 
dist 31=[-12.145702087304650408  ,11.278472965223395367  ] 
dist 32=[-13.863364442930217753  ,11.136709486980158242  ] 
dist 33=[-14.901843567027338068  ,-5.2738661198348575821 ] 
dist 34=[-15.645207110846825647  ,-4.4424271985279593602 ] 
dist 35=[-16.184206370830528286  ,-3.7773786497023953175 ] 
dist 36=[-16.580366041401342092  ,-3.1104868043949653954 ] 
dist 37=[-16.753170211061171686  ,-2.2709679114341984849 ] 
dist 38=[-16.805081532709228649  ,-1.3882353851275666158 ] 
dist 39=[-16.789515935490427724  ,-.5485945935842422645 ] 
dist 40=[-4.0102761999328688478 ,.4183157873644714989 ] 
dist 41=[-3.9489592681065398710 ,1.8091027374949572843 ] 
dist 42=[-.62313241074563780116,3.1885553076872063024 ] 
dist 43=[-.29782548940120539072,4.1103971751985416973 ] 
dist 44=[.35970265964433091688,4.8723084815546286108 ] 
dist 45=[.52336648735077210886,5.6138554690918975407 ] 
dist 46=[1.0751641935104086165 ,6.2848252035913417332 ] 
dist 47=[1.1902177380423882372 ,6.7652693172412040208 ] 
dist 48=[1.2819896776726858596 ,7.1981134804470128407 ] 
dist 49=[1.2478856990376290075 ,7.6793530299153363032 ] 
dist 50=[1.1620461444495626408 ,8.1100168966454524950 ] 
dist 51=[1.0175684942837780086 ,8.3411259715551166282 ] 
dist 52=[.8030137980534289125 ,8.4709408306437795647 ] 
dist 53=[.4374239785914330234 ,8.4974345359955547414 ] 
dist 54=[.0033998164959688126 ,8.4771662475277161807 ] 
dist 55=[-.4842977161023738713 ,8.3188813635013202227 ] 
dist 56=[-1.1042528270698779953 ,7.2020625100085270632 ] 
dist 57=[-2.0661029292629792042 ,6.8301332174156840775 ] 
dist 58=[-3.0257650875904158032 ,2.0058039264189180912 ] 
dist 59=[-3.6370234068382022858 ,1.9557414190406587651 ] 
dist 60=[-4.1097342331025645679 ,1.4080517615437493831 ] 
dist 61=[-4.5165707480082115838 ,1.3048358746300438412 ] 
dist 62=[-4.8502148018670327421 ,1.1871160084150281984 ] 
dist 63=[-5.0308560837699085945 ,1.1645441585055245720 ] 
dist 64=[-5.1339627722103325284 ,.25421068017725795352] 
dist 65=[-5.1594455359716452442 ,.14674854201097512343] 
dist 66=[-5.1401157205179637095 ,-.08648333575909664517] 
dist 67=[-5.1341949882625159036 ,-.13094309837507012447] 
dist 68=[-5.1285891073952738441 ,-.36972947762604379457] 
dist 69=[-5.1222313932084451474 ,-.40869531297586260657] 
dist 70=[-5.1160951348874271512 ,-.47824404748387060597] 
dist 71=[-5.1113444861522379519 ,-.49067747261831087607] 
dist 72=[-5.1067911018210145850 ,-1.2603790384130097334 ] 
dist 73=[-5.1014126249556126131 ,-1.3190208124288179577 ] 
dist 74=[-1.4752643960025980470 ,-1.0920534350894733640 ] 
dist 75=[-1.5633841850607712027 ,-.43749405163182323152] 
dist 76=[-1.6415884636658727387 ,.12490986000601560279] 
dist 77=[-1.6955804388494422878 ,.70757138853556073469] 
dist 78=[-1.7423589259768382063 ,1.2577690259924246165 ] 
dist 79=[-1.7917471513085787904 ,1.6906564863734758104 ] 
dist 80=[-1.8346804929595783060 ,2.1199998312883796447 ] 
dist 81=[-1.8556712644544694090 ,2.6560696137227058293 ] 
dist 82=[-1.8646700161294632856 ,3.1660207342004330736 ] 
dist 83=[-1.8638016353237832744 ,3.4911569175614250893 ] 
dist 84=[-1.8477291690001020375 ,3.7428159799500688177 ] 
dist 85=[-1.8398829853213782637 ,3.9595990849599183357 ] 
dist 86=[-1.8102241802033809878 ,4.1370970548219308643 ] 
dist 87=[-1.7992894414477231468 ,4.2320126547148581897 ] 
dist 88=[-1.6396553966109906838 ,4.2845314392341919661 ] 
dist 89=[-1.6108225096446457147 ,4.2928733442118833023 ] 
dist 90=[-1.5390660088751190308 ,1.6238675644879357911 ] 
dist 91=[-1.5173073141419596647 ,1.8131937531186501158 ] 
dist 92=[-1.3905739620526989022 ,1.9721423256407193573 ] 
dist 93=[-1.3618664932414538900 ,2.0649285139124483416 ] 
dist 94=[-1.3068458353656486755 ,2.1270708722414119787 ] 
dist 95=[-1.2904732811208932553 ,2.1637574125392823160 ] 
dist 96=[-1.3929314736176788111 ,2.1883777297477392039 ] 
dist 97=[-1.6197597187954484734 ,2.2023659729472855303 ] 
dist 98=[-1.8296699464595636047 ,2.2113522898451463375 ] 
dist 99=[-1.9554041808551458707 ,2.2159790885168822260 ] 
dist 100=[-2.0506870476247359478 ,2.2175251523403278550 ] 
dist 101=[-2.1349700480738159083 ,2.2141983893657693386 ] 
dist 102=[-2.1984185777840343750 ,2.2066807926510877139 ] 
dist 103=[-2.2246433903135640683 ,2.1974878704444754726 ] 
dist 104=[-2.2338357443201288912 ,.48665915979850855781] 
dist 105=[-2.2295356915250315347 ,.35210347293028047871] 
dist 106=[-2.0982476672003256943 ,.05695369517810286511] 
dist 107=[-2.0732910693010628575 ,.12153087111662651642] 
dist 108=[-1.9989832546257701135 ,.30589191318040990103] 
dist 109=[-1.9807321712148207336 ,.49557483387865851763] 
dist 110=[-1.8117154620293245885 ,.67378620755025350833] 
dist 111=[-1.7729555298521119841 ,.81238677089612161683] 
dist 112=[-1.7205952118808241867 ,.94830339641987764872] 
dist 113=[-1.7007901993011372585 ,1.1158145542681539798 ] 
dist 114=[-1.2294719284522028157 ,1.2740095475887474465 ] 
dist 115=[-1.1647536313780322834 ,1.3727625981440870475 ] 
dist 116=[-1.1012136781718264843 ,1.4467554213743297807 ] 
dist 117=[-1.1056568570371178669 ,1.5061717945448285892 ] 
dist 118=[-1.1078166525377429671 ,1.5516057969948990330 ] 
dist 119=[-1.1074283061538219972 ,1.5698198412902610921 ] 
dist 120=[-.32783889945304949339,1.5762182816341682699 ] 
dist 121=[-.26454394426206651226,1.5744940429350212345 ] 
dist 122=[-.11993758930462192289,1.0671406307036094441 ] 
dist 123=[-.09387758247598863265,1.2295361230035780567 ] 
dist 124=[.08548761570563292605,1.3531900681182183294 ] 
dist 125=[.11645577512836414004,1.4561664250711439890 ] 
dist 126=[.1727347183690134905 ,1.5394661210331452879 ] 
dist 127=[.18474011157173941385,1.5846037974684246826 ] 
dist 128=[.32931308364993102585,1.6104030933677599112 ] 
dist 129=[.34971395319169758877,1.6165312813364114011 ] 
dist 130=[.37091334739941631445,1.5566210997562900355 ] 
dist 131=[.36753721678857771626,1.5429835699711176833 ] 
dist 132=[.3536869618943069583 ,1.5322248281593474244 ] 
dist 133=[.32528646603212285963,1.5226344912174995748 ] 
dist 134=[.28086504509342651764,1.5145678313089305554 ] 
dist 135=[.2031067608851155947 ,1.5098844792288252941 ] 
dist 136=[.12251971624479461733,1.5067970139326166851 ] 
dist 137=[.06681256373027711053,1.5050935402811718286 ] 
dist 138=[.01878630626627534440,.27222750012248842725] 
dist 139=[-.03116639314914815777,.17231136718472418522] 
dist 140=[-.12676686393074290534,-.04958108931531117848] 
dist 141=[-.30874307095633828207,-.06451288786354979079] 
dist 142=[-.48055203054185574189,-.08854149917133739750] 
dist 143=[-.61571095989576754959,-.09386267636377675188] 
dist 144=[-.74975403156637780208,-.14361033641477937578] 
dist 145=[-.91711140299165913224,-.15111073425643147438] 
dist 146=[-1.0763123574591869745 ,-.15404312970296951166] 
dist 147=[-1.1778115589177014629 ,-.14752374929589013406] 
dist 148=[-1.2563655401676517099 ,-.13609401506332919363] 
dist 149=[-1.3240150965860511397 ,-.11844292932680161288] 
dist 150=[-1.3793832172423137585 ,-.09289929706767055034] 
dist 151=[-1.4089342172791326167 ,-.04998863439864298340] 
dist 152=[-1.4251987202967081161 ,-.00581356754327161731] 
dist 153=[-1.4275535720283969069 ,.02477353193970134423] 
dist 154=[-.32377861864195872894,.05119070600906356200] 
dist 155=[-.32164330116011558703,.13757770866936617719] 
dist 156=[-.30119123933215848975,.24007339233344001833] 
dist 157=[-.29610330003773727933,.34102379905297829079] 
dist 158=[-.28927975987461603748,.43367680191021802142] 
dist 159=[-.2865157986975923441 ,.50129567275747459036] 
dist 160=[-.21727368497099912047,.56311704311186856128] 
dist 161=[-.20761873308345747012,.6330869520038608712 ] 
dist 162=[-.18671231276563633184,.69722797629630375302] 
dist 163=[-.18069934272445928034,.73579322985702720785] 
dist 164=[-.15563418211820989357,.76296583516715983607] 
dist 165=[-.15073960628139617783,.78164947826410028941] 
dist 166=[-.13782806929995955922,.79428032398947831195] 
dist 167=[-.13586762444431255084,.79730355037316987305] 
dist 168=[.1732345864442500528 ,.79629008682003846255] 
dist 169=[.19365920382715718909,.79296963130130191753] 
dist 170=[.16230238476657434167,.57311504258136586532] 
dist 171=[.08132209901696620205,.55039230731837232083] 
dist 172=[.01171624176982740016,.49228370172676607736] 
dist 173=[-.06042434111480783144,.48276547284331566405] 
dist 174=[-.1285460291024463014 ,.38668250139829296777] 
dist 175=[-.18211788042781390941,.3677816433945838088 ] 
dist 176=[-.23521491542777957414,.34471894580238007733] 
dist 177=[-.30144229795268763112,.34359385907970699958] 
dist 178=[-.36437627628479707636,.34368511686894931304] 
dist 179=[-.4043336520121435161 ,.34253194160898269675] 
dist 180=[-.43505507024608160291,.34002505583637387605] 
dist 181=[-.46114039116084496496,.33824098781070486778] 
dist 182=[-.48220290548249934528,.3331507090441760056 ] 
dist 183=[-.49288478445545018409,.3306544048635861579 ] 
dist 184=[-.49820584436423357874,.14194281266732444207] 
dist 185=[-.49899335365707395907,.12470362508618570175] 
dist 186=[-.38817640590966912697,.08559829911274607970] 
dist 187=[-.43350603637352868562,.07777188318603751920] 
dist 188=[-.46782348849395293437,.02929565347829175693] 
dist 189=[-.49604326762643254957,.02070109593754894587] 
dist 190=[-.5184271930362351108 ,.00393363119624027173] 
dist 191=[-.5294581295630889047 ,-.00011129934899996794] 
dist 192=[-.5349730837163079806 ,-.04116827676166716271] 
dist 193=[-.53545736802832384919,-.04737040516144530681] 
dist 194=[-.5170698329369954331 ,-.05518452620337738501] 
dist 195=[-.51212570305587147774,-.05616414101845496096] 
dist 196=[-.50457720982263296649,-.05446506991771749149] 
dist 197=[-.50139153661319000498,-.04881816471503157930] 
dist 198=[-.48913823735993372216,-.03921262418138393953] 
dist 199=[-.48493935420770356498,-.01713115839327039837] 
dist 200=[-.47484612802844035999,.00874913746193727651] 
dist 201=[-.47074631623442378315,.02665014885324244661] 
dist 202=[-.1559987106823997346 ,.05362642833687065035] 
dist 203=[-.12767831665236467094,.10972492012285101179] 
dist 204=[-.06522888928383150930,.17075479423052602176] 
dist 205=[-.05189829776427273725,.23190630448960472327] 
dist 206=[.01940369836153903894,.28904818998003072066] 
dist 207=[.02092155686280065518,.33277223328548173363] 
dist 208=[.01526113921980908042,.37445113342887710333] 
dist 209=[.00912768190624978658,.42417349733485747578] 
dist 210=[.00148129125657997511,.47034307196687565213] 
dist 211=[-.01021427697474080353,.49784643951393046816] 
dist 212=[-.02359468856358864268,.51691434879111352228] 
dist 213=[-.03796228959757379124,.52942632199323924804] 
dist 214=[-.05578086667349249246,.53795774503445614398] 
dist 215=[-.08292824665083609938,.54114297825980120471] 
dist 216=[-.10994865014354677578,.54105461728818102705] 
dist 217=[-.12726041260369720375,.54009353718512878471] 
dist 218=[-.14074571706925302229,.1787903151331605348 ] 
dist 219=[-.15250045284151437647,.17929094635945790026] 
dist 220=[-.16221642622646964283,.17814430547601511805] 
dist 221=[-.19203101891648931411,.1772868316536628649 ] 
dist 222=[-.23542378506050675324,.17617619185174313807] 
dist 223=[-.26653956142732046147,.1753230627965439004 ] 
dist 224=[-.29458345150452709458,.14712178349468278921] 
dist 225=[-.32571986256923981734,.14288026348014111155] 
dist 226=[-.354083122164985313  ,.13428158505582034839] 
dist 227=[-.37106243652747355513,.1317922604665053463 ] 
dist 228=[-.38293405100331667688,.12160642985556497689] 
dist 229=[-.39091800142224127657,.11928759796595615151] 
dist 230=[-.39606842774424466736,.11377824822313661458] 
dist 231=[-.39692597070505093007,.11191980443431156936] 
dist 232=[-.39557315896489571269,.00560377064573745686] 
dist 233=[-.39423005586826678047,.04364672268518967852] 
dist 234=[-.27041443108768945256,.09890220996240238916] 
dist 235=[-.25974043657667529237,.13511291849299437026] 
dist 236=[-.24934887884256226497,.16426060764378207653] 
dist 237=[-.24692316007131044426,.19133573423203097821] 
dist 238=[-.22466803229159413321,.21496282289799517456] 
dist 239=[-.21966377211758219524,.23035330539789945335] 
dist 240=[-.21287803853420439635,.24263706538362531817] 
dist 241=[-.2103625835340200418 ,.25386861924890317533] 
dist 242=[-.15136897886930051358,.2634469152236885459 ] 
dist 243=[-.14329070269579914686,.26913435852595210597] 
dist 244=[-.1257481648126013977 ,.27305215650324778606] 
dist 245=[-.12075141599298519353,.27556981945197531614] 
dist 246=[-.10009230633186053046,.27698857874451698082] 
dist 247=[-.09612313377131491363,.27662752476574205122] 
dist 248=[-.08581431264842975381,.2750922182866993199 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 2, 1, 2] 
dist 0=[55.717341781707705762  ,55.717341781707705762  ] 
dist 1=[54.608682216804797522  ,56.578373880110521230  ] 
dist 2=[53.114406641859192935  ,57.083855805448048149  ] 
dist 3=[51.048849492107999515  ,57.426304874622171813  ] 
dist 4=[47.659124321500617199  ,57.636228041741483016  ] 
dist 5=[44.167158861416763638  ,57.738908054744828557  ] 
dist 6=[41.693296801805387045  ,57.705925680138830829  ] 
dist 7=[39.487271785096791369  ,57.497554531267465784  ] 
dist 8=[37.064538067500037686  ,56.893510838952036988  ] 
dist 9=[34.682113284291735432  ,56.338532112432749618  ] 
dist 10=[32.636808032972434746  ,56.034478643664002172  ] 
dist 11=[30.442016872154139087  ,55.608978824516339930  ] 
dist 12=[27.462237886152576723  ,55.427166749860899301  ] 
dist 13=[24.491604037213765040  ,54.882573488472401446  ] 
dist 14=[22.333080801944532904  ,54.666237379384493721  ] 
dist 15=[20.349918561039101138  ,53.682632213811655094  ] 
dist 16=[18.079215299571819538  ,51.747082896806302459  ] 
dist 17=[15.787906337063442792  ,35.110580163142771288  ] 
dist 18=[13.236091013516286029  ,33.472210117355925494  ] 
dist 19=[10.568228390129913543  ,29.544517439111395513  ] 
dist 20=[7.1280335847198496357 ,28.956370447362485205  ] 
dist 21=[3.7799606942981385090 ,23.391598611741381351  ] 
dist 22=[1.4796171757922589414 ,22.374369334469343646  ] 
dist 23=[-.50080357260673283718,21.108373587805512224  ] 
dist 24=[-2.5717862117279522769 ,20.823307575248317191  ] 
dist 25=[-4.5528531031463097705 ,12.761771646381037820  ] 
dist 26=[-6.1748601971695247945 ,11.778229358336958197  ] 
dist 27=[-7.8532787539908350074 ,9.6977048477957602060 ] 
dist 28=[-10.061085032636552242  ,9.2236492374372309556 ] 
dist 29=[-12.172617467439634004  ,7.1593203163032109836 ] 
dist 30=[-13.466669980417696905  ,6.7902449395055889007 ] 
dist 31=[-14.419130665583640720  ,6.0948278270614487885 ] 
dist 32=[-15.165362834293203038  ,5.9432559214280256134 ] 
dist 33=[-15.736037084918612842  ,-1.6958457212424558709 ] 
dist 34=[-15.986664099904932081  ,-2.3656941849616063747 ] 
dist 35=[-16.096621827410656532  ,-3.7182748805196978546 ] 
dist 36=[-16.104645756895262966  ,-4.0353579526970201812 ] 
dist 37=[-15.481883597345815427  ,-3.2244107440027868927 ] 
dist 38=[-15.334096075244965177  ,-2.6440736892655465806 ] 
dist 39=[-15.010586644664062074  ,-2.1368769965759375116 ] 
dist 40=[-14.890886278017828261  ,-1.6002510105685678386 ] 
dist 41=[-14.282352803110164917  ,-1.0884933099021590071 ] 
dist 42=[-14.139729709858538653  ,-.68030724450634015535] 
dist 43=[-13.687463118751003700  ,-.27127723003268617139] 
dist 44=[-13.674789844106346701  ,.24397543259485093162] 
dist 45=[-13.753732667765250000  ,2.0531126852001993797 ] 
dist 46=[-13.756016913744674924  ,4.1289468774370671593 ] 
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dist 87=[.07745826096419744551,1.6374977360547833382 ] 
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dist 120=[-2.1174686199437339080 ,.49699222908206144802] 
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dist 123=[-2.0930125662449364742 ,.51228181693475947495] 
dist 124=[-2.0881412510464839700 ,.51090592755183629759] 
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dist 127=[-2.0749414631947176792 ,.55901981137707441384] 
dist 128=[-2.0692313470863644010 ,.60909391091785693795] 
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dist 132=[.01130607672766708601,.68653436953256145157] 
dist 133=[.35442247825533843077,.69250284751782255056] 
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dist 138=[.42896996352985561285,1.5112884196452664424 ] 
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dist 141=[.07888007201312738229,1.7705351614007472115 ] 
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dist 143=[-.09155543249744462821,1.8228682627981871133 ] 
dist 144=[-.17280102564192435518,1.8252386338108654114 ] 
dist 145=[-.24932447311653340982,.05895833579430178344] 
dist 146=[-.30916799631341489363,-.01730056789038341646] 
dist 147=[-.36816414766277539041,-.05283266916742438040] 
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dist 151=[-.64242759032856665722,-.17422117463327288116] 
dist 152=[-.73293449042651985225,-.17357649859635109316] 
dist 153=[-.81626196836604440946,-.16679004977906012657] 
dist 154=[-.86694736307473931338,-.15130056996868093267] 
dist 155=[-.90336429970417137876,-.10200192362113055192] 
dist 156=[-.92976165146018595339,-.02046925963272863721] 
dist 157=[-.94832238916016557783,.06225023834465701198] 
dist 158=[-.95347438929068967131,.12191511056326293053] 
dist 159=[-.95333961244817027287,.17402816888287801297] 
dist 160=[-.95080448135197517865,.22411094221818454204] 
dist 161=[-.7457534436750338385 ,.2689539810888507407 ] 
dist 162=[-.72377349609950821675,.30016389840301167527] 
dist 163=[-.66542479532008179124,.32731357213075291152] 
dist 164=[-.65571636615109539144,.35595912024516306048] 
dist 165=[-.55138740684872305828,.3817076451839039835 ] 
dist 166=[-.53019087248330839925,.39729981124113199261] 
dist 167=[-.50564031929799755285,.40841375544409690098] 
dist 168=[-.49747594118295732439,.41999995019510025452] 
dist 169=[-.27842558941287249376,.48984253854090388447] 
dist 170=[-.25030972604809146721,.53307648842289086917] 
dist 171=[-.1907519845363854228 ,.56502662438611293055] 
dist 172=[-.17476289177476398687,.58985264976844805832] 
dist 173=[-.13653202995993962983,.60877934197853239626] 
dist 174=[-.16682872651868519623,.61719393109427061388] 
dist 175=[-.19114690090220728972,.62047782917230392358] 
dist 176=[-.2135981768193252316 ,.61985198826040701541] 
dist 177=[-.23307771386855504804,.49954267253755867593] 
dist 178=[-.24554050503693036763,.55511980633834127498] 
dist 179=[-.25522412915143922916,.59650583567805976444] 
dist 180=[-.26361606090201080593,.62929308290232824328] 
dist 181=[-.27037230490077881635,.65505335675759211524] 
dist 182=[-.27353047861870562237,.66840035562839619275] 
dist 183=[-.27464707711663928685,.67520118365453051578] 
dist 184=[-.27443358488602713305,.67600454121473976842] 
dist 185=[-.27072302098089083672,.64871394160044669372] 
dist 186=[-.26916082815065575569,.64672948952049200947] 
dist 187=[-.26388484683720380539,.64364683737706782041] 
dist 188=[-.26169016069029560671,.64072220119344763665] 
dist 189=[-.13027893600123407977,.63185553172637907407] 
dist 190=[-.13335085302451048814,.6277471164485750239 ] 
dist 191=[-.13655891752133301137,.61720722137303743735] 
dist 192=[-.14078502975720658255,.61247551078409354605] 
dist 193=[-.14533532805574158306,.20821509602696015026] 
dist 194=[-.14983717122119442241,.17233635362048625604] 
dist 195=[-.16684112521468268471,.09223737387216949837] 
dist 196=[-.24540666870149623274,.07593729298278987958] 
dist 197=[-.31901385451638035876,-.00649778383651311320] 
dist 198=[-.37597172113073279393,.01945000652875986268] 
dist 199=[-.43157250123115858399,.04579316010277432745] 
dist 200=[-.49976506108043894258,.07951084734738210053] 
dist 201=[-.56402277845395239327,.11532730884116385318] 
dist 202=[-.6039238586655171777 ,.15004367100190266695] 
dist 203=[-.63357544962966105425,.19055177749400549014] 
dist 204=[-.65693851192599922654,.24947495334812860701] 
dist 205=[-.67443524248393558496,.30739214884329080837] 
dist 206=[-.68068055478331746634,.34388662242450599018] 
dist 207=[-.68248174327425905725,.37162274813624537667] 
dist 208=[-.68224740382147637667,.39459715633511371927] 
dist 209=[-.24952186371282014113,.4128214478942789598 ] 
dist 210=[-.24949545356394303732,.42160638428134442679] 
dist 211=[-.24847176991702888306,.42599348572812055548] 
dist 212=[-.2473900014824428501 ,.42667212691454753542] 
dist 213=[-.2393974825968866454 ,.41356640354731963943] 
dist 214=[-.23723392148516487455,.40976690133572354618] 
dist 215=[-.23066161979178652702,.4034774691592164296 ] 
dist 216=[-.22860357942380437264,.4318507529578185786 ] 
dist 217=[-.21261321878483316126,.46000137499711057366] 
dist 218=[-.20876091757441454801,.47688177513628182966] 
dist 219=[-.20275568974767003616,.48871893362701817702] 
dist 220=[-.20073906608463064028,.49674715577236457446] 
dist 221=[-.15275675566038575651,.50170008347592229621] 
dist 222=[-.14559320880752546913,.50227714340452476854] 
dist 223=[-.13270574146848422291,.49915123772461440531] 
dist 224=[-.12952621622248480549,.4973923236522371227 ] 
dist 225=[-.13169364333501807139,.33088523709585941163] 
dist 226=[-.17049122163697551547,.33012591145616497407] 
dist 227=[-.20175137561623210887,.3252615573679111555 ] 
dist 228=[-.23083532143253640958,.32389391205505111507] 
dist 229=[-.25624375444732528739,.30448236372673263243] 
dist 230=[-.2728394179699934759 ,.29956046552031056079] 
dist 231=[-.28613338832408621474,.2946563218756737121 ] 
dist 232=[-.29836856899837227143,.29188958799700761445] 
dist 233=[-.30868565427302225177,.21876311280274516165] 
dist 234=[-.31432679362818194582,.20863302400890469175] 
dist 235=[-.31761289426222631163,.18808907960211814863] 
dist 236=[-.31853396468628758373,.18246806064246407266] 
dist 237=[-.31785908614806266406,.1609183431235925897 ] 
dist 238=[-.31706876872343500324,.15614940755179092294] 
dist 239=[-.31163209478314036992,.14661015449537666233] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 0, 0, 2, 1, 2] 
dist 0=[51.304508078108793068  ,51.304508078108793068  ] 
dist 1=[50.932195745680267359  ,51.899703125685583023  ] 
dist 2=[50.040646782213743260  ,52.507812109407280492  ] 
dist 3=[48.599938090026642038  ,52.775577648016894110  ] 
dist 4=[46.250640780186093448  ,52.875474858946974049  ] 
dist 5=[43.823546256016998703  ,52.853445131383804057  ] 
dist 6=[42.072058424455820892  ,52.406103570966991870  ] 
dist 7=[40.475886679887868036  ,51.860733906502356193  ] 
dist 8=[38.668910971068873065  ,50.728832569509883155  ] 
dist 9=[36.858896967288575064  ,50.560219271957625053  ] 
dist 10=[35.250426745577694973  ,49.799042878137575416  ] 
dist 11=[33.476800103572754246  ,49.590860350081749980  ] 
dist 12=[31.006875243620414402  ,49.022375418809684217  ] 
dist 13=[28.514286802583152980  ,48.814733781366904498  ] 
dist 14=[26.649970509700066874  ,47.632820652181486954  ] 
dist 15=[24.882643672714334494  ,46.533851083635029931  ] 
dist 16=[22.777194305917738830  ,30.146602606814250468  ] 
dist 17=[20.605921649082215990  ,29.690829964876626935  ] 
dist 18=[18.575351184101614237  ,25.049440085987585599  ] 
dist 19=[16.162873324252002982  ,24.186072666637198706  ] 
dist 20=[12.903418431060712858  ,23.847237967036065095  ] 
dist 21=[9.5861092638094818485 ,23.015504928935830963  ] 
dist 22=[7.3804728081085311104 ,15.520974915694194774  ] 
dist 23=[5.5574699424913340763 ,14.601910291164059105  ] 
dist 24=[2.7027570570521931043 ,12.730946340110846794  ] 
dist 25=[.6919934387994566460 ,12.254900432637212850  ] 
dist 26=[-1.0410945253741380921 ,10.580261436958771981  ] 
dist 27=[-2.8582494621688472711 ,10.238179694292033344  ] 
dist 28=[-4.6012703083437401377 ,9.7744560806818527644 ] 
dist 29=[-6.0389364294217091015 ,9.6604610604973434886 ] 
dist 30=[-7.5374387961790739255 ,-.1565448612827604411 ] 
dist 31=[-9.5249007573271267212 ,-1.4304211964285136236 ] 
dist 32=[-11.425505155396893151  ,-3.0329006757467057881 ] 
dist 33=[-12.577210268993700305  ,-3.3829689296305129310 ] 
dist 34=[-13.410666882019064443  ,-3.3806692103022038382 ] 
dist 35=[-14.039057369446228644  ,-3.2495410628359770694 ] 
dist 36=[-14.516730330811236147  ,-2.9133935912695706542 ] 
dist 37=[-14.747427706534408004  ,-2.5365752159104333250 ] 
dist 38=[-14.846244426569128456  ,-2.2429604246320286340 ] 
dist 39=[-14.854385286025758216  ,-1.9571450054690761816 ] 
dist 40=[-13.945678359932641207  ,-1.6107545971051746548 ] 
dist 41=[-13.774534445368795201  ,-1.2546330289955465146 ] 
dist 42=[-13.457497639757109032  ,-.9296703235673032815 ] 
dist 43=[-13.358680408986102418  ,-.5666040995270611189 ] 
dist 44=[-12.998798509813157138  ,-.0581828582853877500 ] 
dist 45=[-12.998082611977847134  ,.4516116667894598158 ] 
dist 46=[-12.556551758646730013  ,.82032119730215002234] 
dist 47=[-12.458610870697100510  ,1.7761592039367113597 ] 
dist 48=[-4.6925255601834647599 ,2.7128378348508194120 ] 
dist 49=[-4.0076088569499555230 ,3.6508577450259475279 ] 
dist 50=[-3.5461134728102748486 ,4.4811817417723306202 ] 
dist 51=[-3.4212623661821363150 ,5.0452059355828740192 ] 
dist 52=[-3.3795749027044588545 ,5.5224025195518491858 ] 
dist 53=[.0265179806380997233 ,6.0063505019186908303 ] 
dist 54=[.6387804143147406808 ,6.7759160033050717702 ] 
dist 55=[.7774704321832181156 ,7.8163247206310470449 ] 
dist 56=[2.2683073410476420281 ,8.7763014430510201708 ] 
dist 57=[2.4857725107577244791 ,9.3445578342498358755 ] 
dist 58=[2.7595123784855047577 ,9.7351584653712616891 ] 
dist 59=[2.7877369403560232119 ,9.9859839702839994597 ] 
dist 60=[2.7208403339001730811 ,10.161718523870239645  ] 
dist 61=[2.5159388576931798319 ,10.252560567768022552  ] 
dist 62=[1.8308437460161661841 ,10.298807446275884551  ] 
dist 63=[1.0949974672386312874 ,10.296484387683278516  ] 
dist 64=[.46821046841616266199,3.8625628694485703052 ] 
dist 65=[-.17225907579743162738,3.6935144489905918842 ] 
dist 66=[-.77135734808831533135,3.6518409758508400232 ] 
dist 67=[-1.2331081144340999166 ,3.5346820894176694826 ] 
dist 68=[-1.6820440793335342967 ,3.5016600413793391489 ] 
dist 69=[-2.2300364912820555416 ,1.5776022022432348728 ] 
dist 70=[-2.7463356603609596800 ,.90413761025669564345] 
dist 71=[-3.0688232420179888764 ,.43027599268206108748] 
dist 72=[-3.3106657226276708932 ,.32311002044095962189] 
dist 73=[-3.5051893594461731501 ,-.18659087923397419256] 
dist 74=[-3.6589413186240951915 ,-.27559125690358255644] 
dist 75=[-3.7381162084701026672 ,-.46890987628591135463] 
dist 76=[-3.7777127285420822634 ,-.50526512534728773395] 
dist 77=[-4.0047708697858658994 ,-.6975014261339168167 ] 
dist 78=[-4.1893122820369533476 ,-.71578499604775677239] 
dist 79=[-4.3076099977323286721 ,-.68545895575509426673] 
dist 80=[-4.3664080126941506210 ,-.58109341109441154193] 
dist 81=[-4.3983700903536286176 ,-.43742946364879626586] 
dist 82=[-4.4095708652293051687 ,-.25028884657948358074] 
dist 83=[-4.4077394199383830153 ,.00424571440945794637] 
dist 84=[-4.3927382773492741576 ,.41682034895436706449] 
dist 85=[-2.8982946759599148593 ,.8353642727243505281 ] 
dist 86=[-2.5432343673195036673 ,1.1137254394860782306 ] 
dist 87=[-2.4862750154581847182 ,1.4387310009181533327 ] 
dist 88=[-2.3557274492743787705 ,1.8710888314351926477 ] 
dist 89=[-2.3137718706761945923 ,2.2659322085165363589 ] 
dist 90=[-2.1203972376241926698 ,2.5545678357189288054 ] 
dist 91=[-2.0784891891164507107 ,2.8203784656507409226 ] 
dist 92=[-1.9787975488514460218 ,3.1241632091224531289 ] 
dist 93=[-1.9470568310123652319 ,3.4011224015235676671 ] 
dist 94=[-.63396392904395824787,3.5598959396333128488 ] 
dist 95=[-.50133677904579251026,3.6623408164954425731 ] 
dist 96=[-.22984366371565276353,3.7145265321308068236 ] 
dist 97=[-.16050403029103004832,3.7435840702989130729 ] 
dist 98=[.08361670810427964704,3.7537500917155438665 ] 
dist 99=[.13368993452345802271,3.7520272019881245934 ] 
dist 100=[-.07122863660988705511,3.7395134501109294631 ] 
dist 101=[-.55841178926055105549,2.9562763641188810350 ] 
dist 102=[-.88009586102164644245,2.8639501618835471003 ] 
dist 103=[-1.1416939871879561112 ,2.6156745343359624345 ] 
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dist 110=[-2.1798744880812403508 ,.55856905459059416302] 
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dist 119=[-1.2560764420715631789 ,.124070276490568727  ] 
dist 120=[-1.2923209326578012562 ,.0557548781687687517 ] 
dist 121=[-1.3197937845531819063 ,.0458409950694804795 ] 
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dist 123=[-1.3447801985305018365 ,.0188048949390507652 ] 
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dist 125=[-1.3385288506923572796 ,-.0114547418515136318 ] 
dist 126=[-.79532709604733123836,-.0223560296563336416 ] 
dist 127=[-.74691897659144971911,-.0246594206998874098 ] 
dist 128=[-.62579855984103090841,.0260424243560402107 ] 
dist 129=[-.6081899023324651991 ,.0866517230509364641 ] 
dist 130=[-.42048490624684564753,.14843501620907388222] 
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dist 134=[-.02609784517841213482,.53682843756322228601] 
dist 135=[.01119601718453681848,.60165881369362996667] 
dist 136=[.09031889308714537510,.65093755105715746724] 
dist 137=[.10791777431798127513,.69179299888489564174] 
dist 138=[.18463488634235636732,.72436172280549919932] 
dist 139=[.19832482841266994672,.74057598997450979313] 
dist 140=[.22023341351193437011,.74885441896669298172] 
dist 141=[.22487081960409165707,.74976024606329901859] 
dist 142=[.21172504352380142622,.563344270496191377  ] 
dist 143=[.15472181386460735531,.59669612977288471024] 
dist 144=[.09639442046705906881,.61963209276321140849] 
dist 145=[.05614347967741174118,.63436931851426285514] 
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dist 147=[-.01429222583515235996,.64886277843543856881] 
dist 148=[-.04803969908972674951,.64994720095241201064] 
dist 149=[-.07435692547460073040,.64871949927768504871] 
dist 150=[-.10019824898245150513,.58913557070464455966] 
dist 151=[-.13204670160724999016,.58097053290013000594] 
dist 152=[-.16204631657932536623,.56560837163147247543] 
dist 153=[-.1805131730640995212 ,.56071183875382277679] 
dist 154=[-.1940136067824960574 ,.5392467022110068226 ] 
dist 155=[-.2042044399451497573 ,.53346395521799626456] 
dist 156=[-.2120099561185818939 ,.51857094143209989291] 
dist 157=[-.2159985691995369702 ,.51283901381936433937] 
dist 158=[-.2179445434717660844 ,.14781012836563686078] 
dist 159=[-.2179207992300834454 ,.1147741283076865971 ] 
dist 160=[-.24336575753162304954,.04289328634464653314] 
dist 161=[-.31614335118171054491,.02708383454967171521] 
dist 162=[-.38364932875402766901,-.0017655327977925924 ] 
dist 163=[-.43482122674779201948,.0062973721653136243 ] 
dist 164=[-.48379048568091481065,.0136468113884764204 ] 
dist 165=[-.54250742629317670606,.0189328597704052140 ] 
dist 166=[-.5972158966136693301 ,.0259228561370551603 ] 
dist 167=[-.63018981735754718227,.0396461111911988923 ] 
dist 168=[-.65353331337203875673,.0526507670010927297 ] 
dist 169=[-.66981235889019642726,.0608389418229741706 ] 
dist 170=[-.68103517986042738726,.0670586957969922441 ] 
dist 171=[-.68420253123282582839,.0722140528188197551 ] 
dist 172=[-.68383626609077288387,.07630525075865600285] 
dist 173=[-.68142472520317110505,.07827791575681536988] 
dist 174=[-.09136158893341189649,.1613807165295495255 ] 
dist 175=[-.09027270680709922806,.21833783478461707526] 
dist 176=[-.07811022541540999918,.26422492225060630216] 
dist 177=[-.07597108720457815108,.30794726712081858129] 
dist 178=[-.07140638253665086788,.3624271303435965279 ] 
dist 179=[-.06999811211008423268,.40037021227692704976] 
dist 180=[-.06370502949875560017,.43343100294329771128] 
dist 181=[-.06235913086113253734,.46843102622810089133] 
dist 182=[-.0585419572031555825 ,.49982927653512886932] 
dist 183=[-.0578199399941265857 ,.51851849713545348912] 
dist 184=[-.0480596565857996659 ,.53146195092011873032] 
dist 185=[-.05284081162039079920,.53993263589416623749] 
dist 186=[-.05802844438176753084,.54487147275320227699] 
dist 187=[-.06328196908259119834,.54558077547934199068] 
dist 188=[-.06814884807095614815,.54112424815847161294] 
dist 189=[-.07179388070295062748,.54028718429141043331] 
dist 190=[-.09798553612258688574,.3301855872618871644 ] 
dist 191=[-.14518014776458224071,.31033290658368006206] 
dist 192=[-.18344170826580383933,.28941962983482685993] 
dist 193=[-.21945506263175095492,.28548179345589491424] 
dist 194=[-.25121734761857010053,.25301141951271000847] 
dist 195=[-.27251681231158591717,.24612356879127648972] 
dist 196=[-.29020661198432568123,.2358573520213230636 ] 
dist 197=[-.30756584287196012421,.2325990472164409728 ] 
dist 198=[-.32281390400646064469,.16159199924850114653] 
dist 199=[-.33207989180098745184,.1519797413872998593 ] 
dist 200=[-.33872616588155151727,.13033040465495224397] 
dist 201=[-.3435213438545413374 ,.12512643869467416015] 
dist 202=[-.34674962594776117447,.09770248695808206638] 
dist 203=[-.34714366751423894776,.09252959215066747945] 
dist 204=[-.34604144669467657858,.08135562664157755943] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 2, 0, 0, 1] 
dist 0=[54.454558419079516310  ,54.454558419079516310  ] 
dist 1=[54.231545673626253566  ,54.638569087984277569  ] 
dist 2=[53.875303348946432774  ,54.838956748926073342  ] 
dist 3=[53.252239164080072415  ,55.034277091061245518  ] 
dist 4=[51.963752176524723436  ,55.197881103493278940  ] 
dist 5=[50.343084318892313526  ,55.368976555321554002  ] 
dist 6=[48.393540999149397685  ,55.593887482721748024  ] 
dist 7=[45.825879457613014327  ,55.797173745958533724  ] 
dist 8=[41.736916465961409235  ,55.881957905928719820  ] 
dist 9=[37.567541413840889850  ,55.895312168847264773  ] 
dist 10=[34.678673135408975853  ,55.816386072762795515  ] 
dist 11=[32.168891549184367984  ,55.677146036938857547  ] 
dist 12=[29.512995682231288305  ,55.558846530490810889  ] 
dist 13=[26.768613183812256494  ,54.890390163408576226  ] 
dist 14=[23.751132473614195916  ,53.436855335071363272  ] 
dist 15=[20.865447625797825245  ,40.044785934036688684  ] 
dist 16=[18.514892097677568412  ,38.701993183610484368  ] 
dist 17=[16.099736325885139944  ,35.395516793001047157  ] 
dist 18=[12.955499447983857302  ,34.919688584904666415  ] 
dist 19=[9.8787747008419224328 ,29.909753581237436312  ] 
dist 20=[7.7329259514810744654 ,28.965657480180583013  ] 
dist 21=[5.8505123711660099838 ,27.920161600631480564  ] 
dist 22=[3.8254849861043751306 ,27.730542328198839897  ] 
dist 23=[1.8528412168810989352 ,19.154048958285371127  ] 
dist 24=[.17905927304299589384,18.095685374476547799  ] 
dist 25=[-1.6055133286473329233 ,15.962040520540355744  ] 
dist 26=[-4.0219459692673544079 ,15.420383759359705872  ] 
dist 27=[-6.3581863161295846002 ,13.532495268695374647  ] 
dist 28=[-7.8225622169525326821 ,13.134669310466219461  ] 
dist 29=[-8.9384289703309011910 ,12.639950355582271931  ] 
dist 30=[-9.8817040421559261988 ,12.536029178219477684  ] 
dist 31=[-10.650978607574709725  ,-.56208419566860202726] 
dist 32=[-11.071559288311291290  ,-1.6263904305066105481 ] 
dist 33=[-11.322223915032251450  ,-3.8974006847211014534 ] 
dist 34=[-11.412893587872307550  ,-4.3460496606389117459 ] 
dist 35=[-11.441443109275071140  ,-5.5276907507317570393 ] 
dist 36=[-11.443774210446900781  ,-5.3045662112138197674 ] 
dist 37=[-11.430395814987492263  ,-4.9798563400454071787 ] 
dist 38=[-12.085046570112230612  ,-4.5406796829569796044 ] 
dist 39=[-13.397187000468678728  ,-3.9352667892968551597 ] 
dist 40=[-14.221688712781987469  ,-2.9468997579613896855 ] 
dist 41=[-14.849736026170005576  ,-1.9356698018523914979 ] 
dist 42=[-15.377051638641483700  ,-1.2388507125077364030 ] 
dist 43=[-15.801479404819661818  ,-.63990664008099688381] 
dist 44=[-16.018505565229792059  ,-.01902566152953930088] 
dist 45=[-16.125970436529506576  ,.56772006902802140317] 
dist 46=[-16.129962395471892980  ,1.0305521290811134666 ] 
dist 47=[-2.3606053660819111000 ,1.4909953571012666788 ] 
dist 48=[-2.3035965050871181815 ,2.0683066118763041869 ] 
dist 49=[-1.2920956659020355138 ,3.1116835368869686004 ] 
dist 50=[-1.1644705779924042793 ,4.2326686216457202711 ] 
dist 51=[-.86999190233430788816,5.2346168228657693246 ] 
dist 52=[-.82506514209015709037,5.9321306219893880108 ] 
dist 53=[-.45007743823606089008,6.5475137442846825043 ] 
dist 54=[-.38465091590057688734,7.2064732871049610861 ] 
dist 55=[-.29411342009321579292,7.8009243271459057276 ] 
dist 56=[-.27351968531293778596,8.1658011912983879917 ] 
dist 57=[3.8648956954417941669 ,8.4328333749465253567 ] 
dist 58=[3.4649619034748158974 ,8.6366536853352397860 ] 
dist 59=[3.0358127558805028431 ,8.7845919129088466154 ] 
dist 60=[2.7205001551685297367 ,8.8285251233204785244 ] 
dist 61=[2.4291613372452259129 ,8.8234175380965869594 ] 
dist 62=[2.0954987636042557841 ,8.7941849923494403377 ] 
dist 63=[1.7610793636213185537 ,5.1690146323716970258 ] 
dist 64=[1.4666328783299680178 ,4.8497071850024994519 ] 
dist 65=[.7710534356041882109 ,4.0532763197564909076 ] 
dist 66=[-.01786502323947678283,3.9372714976214081074 ] 
dist 67=[-.76079055445685125773,2.7141114130239798060 ] 
dist 68=[-1.3416659925623766993 ,2.4853693753182364001 ] 
dist 69=[-1.9142798590983007947 ,2.2216429988811988556 ] 
dist 70=[-2.6242665663558943893 ,2.1711475512470959678 ] 
dist 71=[-3.2970255237064736645 ,.31628852550043616004] 
dist 72=[-3.7211141554447144686 ,.27044274378739595369] 
dist 73=[-4.0437061807893705754 ,.18781530044522035095] 
dist 74=[-4.3115098170379494333 ,.17020450879843427912] 
dist 75=[-4.5255262055127856058 ,-.05842267748538860625] 
dist 76=[-4.6335113572017682954 ,-.09281712094373114785] 
dist 77=[-4.6891270159354810502 ,-.12164834945491007754] 
dist 78=[-4.6965008563236823566 ,-.11480718876853139564] 
dist 79=[-3.4708797112854939581 ,-.09193645392172655834] 
dist 80=[-3.7015010647027438872 ,-.04767941821132814734] 
dist 81=[-3.8655245103696158900 ,.02039857264341331956] 
dist 82=[-3.9818298913723646109 ,.13835338821898657996] 
dist 83=[-4.0657919741694891441 ,.26629645703670705246] 
dist 84=[-4.1007033590817371981 ,.37426332923820109356] 
dist 85=[-4.1085816366522645209 ,.48805363105190021878] 
dist 86=[-4.1032546864718399674 ,.6392991792360088137 ] 
dist 87=[-3.7692348711691385736 ,.80288511897420098215] 
dist 88=[-3.7096027227652677434 ,.96596098784034969163] 
dist 89=[-3.5928236376853480418 ,1.1598549054942636931 ] 
dist 90=[-3.5562219489859064806 ,1.4464777806667659394 ] 
dist 91=[-3.3959690810059707147 ,1.7291864442387143860 ] 
dist 92=[-3.3558819157827242841 ,1.9074729031740639585 ] 
dist 93=[-3.2496142826488597915 ,2.1644651167180937737 ] 
dist 94=[-3.2144497035960186462 ,2.5636694138376058510 ] 
dist 95=[-.92295241607871569106,2.9285679174316521118 ] 
dist 96=[-.71376413023517850086,3.1962673151205657806 ] 
dist 97=[-.26320641792163414985,3.4438842334450531559 ] 
dist 98=[-.16060247249501196295,3.7286422562871014628 ] 
dist 99=[.31510236048708385576,3.9878405194998821404 ] 
dist 100=[.39889843742938608716,4.1334579199036677855 ] 
dist 101=[.57387399838669758326,4.2236739369360365621 ] 
dist 102=[.61193388827252687336,4.2617848770546370073 ] 
dist 103=[.75920356846736530402,4.2768883857157313144 ] 
dist 104=[.76408942007551186241,4.2752907997933274065 ] 
dist 105=[.44727931835695940874,4.2611509151396257736 ] 
dist 106=[-.05074834969929312587,4.2462682878110580118 ] 
dist 107=[-.54969425229341231627,3.6701608056909159494 ] 
dist 108=[-.88290747265384537118,3.5881087975134251706 ] 
dist 109=[-1.1582313553871025948 ,3.3667685159683458506 ] 
dist 110=[-1.4261903346708899790 ,3.1101133602032789987 ] 
dist 111=[-1.6686280432431326255 ,.3046895548696297376 ] 
dist 112=[-1.8421198907565510961 ,.25642925641321710056] 
dist 113=[-1.9982000333084022930 ,.14760692364808766792] 
dist 114=[-2.1711673184421759217 ,.12632606402537483801] 
dist 115=[-2.3269516913255307099 ,-.05649924322209759935] 
dist 116=[-2.4144675135873352523 ,-.08926271797901989415] 
dist 117=[-2.4686813469614220375 ,-.11090145826284365474] 
dist 118=[-2.4915753657705913270 ,-.09873673357717447154] 
dist 119=[-2.5005115810785976593 ,-.06975003445659084444] 
dist 120=[-2.4990284851288821270 ,-.01817291963048336584] 
dist 121=[-2.4896441247042018017 ,.05975420047612237106] 
dist 122=[-2.4670542150487262648 ,.19388297799884200856] 
dist 123=[-1.8853912954451268228 ,.33057270739134654736] 
dist 124=[-1.8902069150399798326 ,.41872122442772729075] 
dist 125=[-1.8864785727553882568 ,.48809072476430342085] 
dist 126=[-1.8792239280530335500 ,.54985602559193948766] 
dist 127=[-1.1507981400871113863 ,.60192750113234660776] 
dist 128=[-1.0840455074681294142 ,.63262146968903323567] 
dist 129=[-.91690747017506213927,.65351081080095647606] 
dist 130=[-.89212309601006037025,.66646638099431093237] 
dist 131=[-.63202683859819989624,.67555227606585615066] 
dist 132=[-.58290959450770140907,.68100182163711627406] 
dist 133=[-.52595384135935172394,.68484110827781813566] 
dist 134=[-.5137683068540564268 ,.68749815308854067115] 
dist 135=[-.07919037274127102713,.76305567512156681596] 
dist 136=[-.02667276362666117886,.85638429217567934548] 
dist 137=[.08536415781305092903,.92786102331220556355] 
dist 138=[.11016950204966581477,.98807779976289057764] 
dist 139=[.14917507266255663355,1.0363574742051688920 ] 
dist 140=[.06329732886149896108,1.0602060003694728038 ] 
dist 141=[-.01039912814344953829,1.0725645669809677316 ] 
dist 142=[-.08658070729293267044,1.0749995964438808030 ] 
dist 143=[-.15838690027896265735,.81309748815699353319] 
dist 144=[-.21462762758034983106,.87318385925136729976] 
dist 145=[-.27015208193702555734,.91626240851075116138] 
dist 146=[-.33910082422942632507,.94739357739659930756] 
dist 147=[-.40446122310399887371,.97039926723181433853] 
dist 148=[-.44566961992872151065,.98104932738593370909] 
dist 149=[-.47701545530178048789,.98469725405970388026] 
dist 150=[-.50302799543666109744,.98408069463419242183] 
dist 151=[-.52357228906049748581,.8995995185788896554 ] 
dist 152=[-.53310176844383542397,.88471875325784175682] 
dist 153=[-.53750186403360372551,.85852424414836995392] 
dist 154=[-.53758287684905607977,.85157570902537385809] 
dist 155=[-.06443492345902165886,.82060756998263583122] 
dist 156=[-.04265726207800138830,.81213245960498583634] 
dist 157=[.00735314569116005854,.78981500554822498486] 
dist 158=[.01558822560292081794,.78107845038483243553] 
dist 159=[-.12150065754193952336,.23173547498594731318] 
dist 160=[-.25020492766330556989,.18189472818296878054] 
dist 161=[-.35812345925633987975,.14119180930327011326] 
dist 162=[-.4657637231041668173 ,.17132145302508364555] 
dist 163=[-.56708896733293122853,.19940361597161218405] 
dist 164=[-.6450028232101625465 ,.21645597256972581743] 
dist 165=[-.71932321769066291415,.22866995585144413792] 
dist 166=[-.80809058769847530276,.23744837907945157159] 
dist 167=[-.89061567980320955936,.24542653833429743462] 
dist 168=[-.94002779027261493014,.24922013889715619709] 
dist 169=[-.9746100771187234959 ,.25081697428720830097] 
dist 170=[-.99795937929999078383,.2506612083017480305 ] 
dist 171=[-1.0138963429309088299 ,.24376351011921008037] 
dist 172=[-1.0189005488719400267 ,.24196146624967297336] 
dist 173=[-1.0183668690337996796 ,.23534640290209427857] 
dist 174=[-1.0155112979528707604 ,.23397127355087405709] 
dist 175=[-.10600478029000008872,.21544833881342788309] 
dist 176=[-.12122890948066105565,.26907435607866770319] 
dist 177=[-.13573585529387568345,.33366588226640896292] 
dist 178=[-.15301553286595105514,.42126509222593717066] 
dist 179=[-.16901574572200616181,.50271580904658182575] 
dist 180=[-.17841842478634266915,.56003994800676905713] 
dist 181=[-.18476770983998714176,.61061087795785153299] 
dist 182=[-.18858725859101282608,.66511643488736666052] 
dist 183=[-.19104926894148313726,.71433542825606077149] 
dist 184=[-.19198335624300147822,.74381253708946621358] 
dist 185=[-.19197283846942883802,.7644448122986770205 ] 
dist 186=[-.19148230034627717742,.77837151159239150466] 
dist 187=[-.15817270670084103444,.78692143832068132853] 
dist 188=[-.18129205991636656651,.78845455314289987469] 
dist 189=[-.19916995811675037673,.78292124831013631284] 
dist 190=[-.21454106182338157281,.78206658212487235362] 
dist 191=[-.22710510326375331778,.50132202434020900048] 
dist 192=[-.23378312718279447293,.47898578313073314826] 
dist 193=[-.27710607714154134523,.42876409007409113822] 
dist 194=[-.33092768912922688809,.42270361473741902783] 
dist 195=[-.3782656070879115142 ,.37357181846800588149] 
dist 196=[-.40977550326461391692,.36318587893261152945] 
dist 197=[-.43568798755154916607,.34745056444802885732] 
dist 198=[-.46069189537335995596,.34256223528094927202] 
dist 199=[-.48256009022992888433,.23689109043940588078] 
dist 200=[-.49596087885571540821,.22258960956882026442] 
dist 201=[-.50570741332806239513,.19015418735445661962] 
dist 202=[-.51299488504854984035,.18259075839319186044] 
dist 203=[-.51812860280371211947,.14089586833980756024] 
dist 204=[-.51928123690686033706,.13304231854106889767] 
dist 205=[-.51792417654297749444,.11661337359236421427] 
dist 206=[-.51648271574095332308,.11209872521698102219] 
dist 207=[-.13391850239469017576,.13635039473694824514] 
dist 208=[-.15296142150021958179,.15595556426244079534] 
dist 209=[-.16799398897874467151,.17443924901940955829] 
dist 210=[-.18147023525265295934,.19619180446584325752] 
dist 211=[-.19290372942294445187,.21622903241282501791] 
dist 212=[-.19978444945601744406,.22786890206851084813] 
dist 213=[-.20464289146006725346,.23557157069200457704] 
dist 214=[-.2080061380752790426 ,.23990008332243887622] 
dist 215=[-.21025893985176470479,.24259214017886284608] 
dist 216=[-.21068637002186181963,.24376565214999376438] 
dist 217=[-.21016233579906561107,.24405016110322547375] 
dist 218=[-.2094441072594527066 ,.24331313936747395031] 
dist 219=[-.20377517979495457753,.05418530271905896529] 
dist 220=[-.20203444545848349621,.04334400239681425075] 
dist 221=[-.19778359126387256627,.02125411598473570638] 
dist 222=[-.19605771805333845056,.02672221252279616941] 
dist 223=[-.11111788180923013503,.04186847109904624415] 
dist 224=[-.12080361661941954166,.07143858869531871472] 
dist 225=[-.13498595799380534964,.09575114641596903001] 
dist 226=[-.1512921594705073516 ,.11921322874559577749] 
dist 227=[-.16623247330823675076,.14030791432929757241] 
dist 228=[-.1749652049034538811 ,.15517467107549263443] 
dist 229=[-.18081163341663644508,.16831548922273544304] 
dist 230=[-.18423596883279943684,.18252435740908499738] 
dist 231=[-.1863842528952129755 ,.19529898038208529585] 
dist 232=[-.18713957312646187915,.2027168104411712312 ] 
dist 233=[-.187018394050263782  ,.20762767137140273148] 
dist 234=[-.18652735642656741095,.21039778087080225981] 
dist 235=[-.15385983882154373757,.21185971417594702214] 
dist 236=[-.15491712775870525904,.21180915870240949518] 
dist 237=[-.15501993940936525704,.21054848959587060799] 
dist 238=[-.15462093941312257176,.20942535009756881452] 
dist 239=[-.15061891670729146833,.10123498627830570293] 
dist 240=[-.14928582514074502996,.10789745531373866797] 
dist 241=[-.14656447450239101481,.1129639699108811698 ] 
dist 242=[-.14550679334866545504,.11716559170481260177] 
dist 243=[-.12265521653779906913,.12063398330882002948] 
dist 244=[-.11915908426249699871,.12277512977426408813] 
dist 245=[-.11102328417226937758,.12435022568235996215] 
dist 246=[-.10865033518073753763,.12556045341672836619] 
dist 247=[-.09673186148412920757,.12644076659438004079] 
dist 248=[-.09422142662599598911,.12714594160250811631] 
dist 249=[-.08877598343819514976,.12779854554838080467] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 0, 0, 0, 1] 
dist 0=[42.202744858797354786  ,42.202744858797354786  ] 
dist 1=[41.998967107445564177  ,42.265654505486101982  ] 
dist 2=[41.655292418996607366  ,42.313195535777239697  ] 
dist 3=[40.873885869724114770  ,42.269833950559441895  ] 
dist 4=[39.807555051284712104  ,42.210402752173399910  ] 
dist 5=[38.497466747263832876  ,41.711742594841779945  ] 
dist 6=[36.752491762146950591  ,41.556029162317612982  ] 
dist 7=[33.948687791904554672  ,41.093122548921715502  ] 
dist 8=[30.930509989049596637  ,40.909833629869472690  ] 
dist 9=[28.329215431053510965  ,38.654203257653682994  ] 
dist 10=[25.525556468432402543  ,38.258014478651591445  ] 
dist 11=[21.699332933437207387  ,37.372915695223652044  ] 
dist 12=[17.492512558344913646  ,37.093982949134799475  ] 
dist 13=[13.168636227066527942  ,35.829377814826926325  ] 
dist 14=[7.9161680440997549186 ,35.560300086593971227  ] 
dist 15=[0                     ,34.861536613004156010  ] 
dist 16=[24.715641739546497045  ,34.693983049507186130  ] 
dist 17=[21.869147851945702144  ,32.771864775925343527  ] 
dist 18=[18.947993663317936496  ,32.441410947546865910  ] 
dist 19=[16.696387160530708613  ,31.708934259384545809  ] 
dist 20=[14.499576527162633913  ,31.487125116363699303  ] 
dist 21=[11.796685675015579435  ,30.514527467394402379  ] 
dist 22=[8.9670246457107266558 ,30.313412041627973662  ] 
dist 23=[6.2634834191985244278 ,29.809621348809818129  ] 
dist 24=[3.1265851473438605562 ,29.689213617486052630  ] 
dist 25=[-1.4345396800099877107 ,28.319006784995586270  ] 
dist 26=[-5.9354161703347408429 ,-2.5119040803212675647 ] 
dist 27=[-8.8318922778459293740 ,-6.0827016638605982591 ] 
dist 28=[-11.117117495154337465  ,-6.6040626182236178801 ] 
dist 29=[-13.176644634947151640  ,-10.711748354035775832  ] 
dist 30=[-14.942793989647483782  ,-11.365997580453716420  ] 
dist 31=[-16.056454079103989689  ,-12.368007664260335203  ] 
dist 32=[-16.910947247468108211  ,-12.550217357665596006  ] 
dist 33=[-17.642540265750286014  ,-14.879979944362545007  ] 
dist 34=[-18.250442230692282421  ,-15.157681667305939020  ] 
dist 35=[-18.610859262403145024  ,-15.116958039638809169  ] 
dist 36=[-18.862805780519809598  ,-14.635979200137223484  ] 
dist 37=[-19.036755316336090496  ,-13.913082542656136498  ] 
dist 38=[-19.150071989523365799  ,-12.906580989228001607  ] 
dist 39=[-19.159489839994866613  ,-11.502203293397512545  ] 
dist 40=[-19.095494919287048260  ,-9.1913419215170818858 ] 
dist 41=[-19.041275836114906026  ,-6.8202025326550019647 ] 
dist 42=[-8.8800384353398673802 ,-5.1750944316175637930 ] 
dist 43=[-8.0164722165885016480 ,-3.7489339209805869095 ] 
dist 44=[-5.9566320296852216601 ,-2.1369817478930413087 ] 
dist 45=[-5.6359642583779975734 ,-.40749002066116097993] 
dist 46=[-2.8249674928474185513 ,1.2034913564053383545 ] 
dist 47=[-2.2726981249174517079 ,2.4365497165467291285 ] 
dist 48=[-2.1756570600252872235 ,3.6283347437329485355 ] 
dist 49=[-1.3850823957818339436 ,5.0747012670408545023 ] 
dist 50=[1.8282088087414623486 ,6.4397379047399206058 ] 
dist 51=[2.6239894642947574098 ,7.3069700474609443763 ] 
dist 52=[2.8883755859131535940 ,7.9753130024141249880 ] 
dist 53=[3.7207440345728883992 ,8.5465836635123736348 ] 
dist 54=[3.9555769067442801932 ,9.0113573280107599337 ] 
dist 55=[4.2045860819071139716 ,9.2546510530985829082 ] 
dist 56=[4.2456334972230208977 ,9.3850584724130028126 ] 
dist 57=[5.1506729847823460954 ,9.4110283973146779161 ] 
dist 58=[5.2088570060996498249 ,5.8639780886840565142 ] 
dist 59=[5.1816208188339628360 ,5.9597657802439861217 ] 
dist 60=[5.1112684291064442011 ,5.9817799358968540082 ] 
dist 61=[4.9651233187846340739 ,5.9623695286603372904 ] 
dist 62=[4.7826505837480680018 ,5.9493553768938044888 ] 
dist 63=[4.5672129100325176756 ,5.9335248285319264650 ] 
dist 64=[4.2870335475291704027 ,5.9101404693282348151 ] 
dist 65=[3.8461131224405399237 ,4.9674143374784182072 ] 
dist 66=[3.3823905647900859732 ,4.8302670793168484669 ] 
dist 67=[3.0111421859149162376 ,4.5693921034556276082 ] 
dist 68=[2.6369259905010823205 ,4.4986480308998845655 ] 
dist 69=[2.1612282605122096102 ,4.2393928711206004475 ] 
dist 70=[1.6569193176990628773 ,4.1716696364685813687 ] 
dist 71=[1.1684347437375208464 ,4.0626728806379230125 ] 
dist 72=[.46562104886398294442,4.0283063963047539264 ] 
dist 73=[-.57306727503101443787,2.7042967832843965910 ] 
dist 74=[-1.2768551839030799187 ,.03949802120235897330] 
dist 75=[-1.8700374409278996513 ,-.23606914282513215951] 
dist 76=[-2.4673023767734798966 ,-.72711758887737558968] 
dist 77=[-3.0214580648908535708 ,-.84242979620679342518] 
dist 78=[-3.4425972643543525613 ,-1.2932482923442386208 ] 
dist 79=[-3.8469805904277801605 ,-1.3773141280115427219 ] 
dist 80=[-4.3342781508885464177 ,-1.4919555813770157125 ] 
dist 81=[-4.7902661672076766340 ,-1.5080374542291451858 ] 
dist 82=[-5.0696921582780588220 ,-1.4879938804956835068 ] 
dist 83=[-5.2733471663294790062 ,-1.4156836953279043391 ] 
dist 84=[-5.4269162709295762371 ,-1.2915393562827988920 ] 
dist 85=[-5.5373375480160303197 ,-1.0645837798709392743 ] 
dist 86=[-5.5687797215922470723 ,-.78928533371370524513] 
dist 87=[-5.5720892697975783172 ,-.46787442770815915974] 
dist 88=[-5.5702137007507269932 ,.26018595689213844253] 
dist 89=[-4.7618482036836033648 ,.99478153127514579052] 
dist 90=[.92947624960322145018,1.4796862478966179506 ] 
dist 91=[1.2103704676235977489 ,1.8741463284065771557 ] 
dist 92=[1.8072659128581473257 ,2.2677362161718118327 ] 
dist 93=[1.9391034671990702667 ,2.6785925580964370249 ] 
dist 94=[2.4641590570168420079 ,2.9593463795897874384 ] 
dist 95=[2.5391199190121826144 ,3.1983764027836863817 ] 
dist 96=[2.6817623278126804970 ,3.4427559650097406511 ] 
dist 97=[2.7040993965095658778 ,3.6610937708108850683 ] 
dist 98=[2.7458050718856211732 ,3.7962090014139701307 ] 
dist 99=[2.7006827604633884757 ,3.8961815299483441044 ] 
dist 100=[2.5909103336042689112 ,3.9742748524644486296 ] 
dist 101=[2.3562855973504761075 ,4.0322931929846728863 ] 
dist 102=[2.0716030648439255372 ,4.0521525706764319728 ] 
dist 103=[1.6960563573987630942 ,4.0491294679831628512 ] 
dist 104=[1.0988717935718430064 ,4.0405829078268436194 ] 
dist 105=[.49344763512723331493,3.9511846508872343529 ] 
dist 106=[.08502138382841415450,2.3014982694686483143 ] 
dist 107=[-.25686603878631543617,2.1489433608807419278 ] 
dist 108=[-.5967989215522395814 ,1.7702757056214316530 ] 
dist 109=[-.90899857949993072721,1.7144090576237012865 ] 
dist 110=[-1.1402292614714637052 ,1.1365006601433423227 ] 
dist 111=[-1.3561771749857446274 ,1.0282979314395335995 ] 
dist 112=[-1.6073966430809716180 ,.90171746302513275332] 
dist 113=[-1.8415528765589834655 ,.87545409451299090292] 
dist 114=[-1.9894166112847851275 ,-.00606460144545056353] 
dist 115=[-2.1022155640005470545 ,-.13997382833699510777] 
dist 116=[-2.1964598551945192871 ,-.24530543021800684983] 
dist 117=[-2.2714174664819574343 ,-.34136729233799193368] 
dist 118=[-2.3072591664350012837 ,-.52794230065085791935] 
dist 119=[-2.3226862723896026461 ,-.56752532607425089028] 
dist 120=[-2.3230421809523882906 ,-.61330096959535078615] 
dist 121=[-2.2380753063104132286 ,-.63909736724328142333] 
dist 122=[-1.0184001804132639379 ,-.72603042973041607703] 
dist 123=[-1.0606072276014073580 ,-.73674776234316257162] 
dist 124=[-1.0876531556952143198 ,-.75186692595685906776] 
dist 125=[-1.1066310790540521478 ,-.74922174634688392777] 
dist 126=[-1.1166325332064428017 ,-.739932927754424319  ] 
dist 127=[-1.1220002065112027015 ,-.72156015315734747078] 
dist 128=[-1.1224712948132908842 ,-.69307202733555651355] 
dist 129=[-.98214213322038566348,-.64341164755280407518] 
dist 130=[-.96065827365356636356,-.58929694465379764947] 
dist 131=[-.92515756815496734692,-.54302781196409616002] 
dist 132=[-.9147587481383478914 ,-.49369220755923485241] 
dist 133=[-.88408530493254096524,-.42732922504877497067] 
dist 134=[-.87316397842461282393,-.35514562528319547339] 
dist 135=[-.86581723511607416957,-.28257470737113310286] 
dist 136=[-.86157768816233757501,-.19584382342269454177] 
dist 137=[-.48809136199822043839,-.01546032699132014613] 
dist 138=[.00696480676224107798,.12110299160397727741] 
dist 139=[.06103806133170452284,.2376263434891930025 ] 
dist 140=[.14985552191855795004,.35717047342684564792] 
dist 141=[.16928418293078287435,.46942331891751804244] 
dist 142=[.25618008117954058988,.55685073693165070818] 
dist 143=[.27149439417523787128,.6427896387266970936 ] 
dist 144=[.2974495538764962292 ,.74910325189232978874] 
dist 145=[.30257603693369336585,.84986280557989420256] 
dist 146=[.30644955318123880935,.91363777985142115342] 
dist 147=[.29714520571974893822,.96250015672050666107] 
dist 148=[.27830183482832582472,1.0037489882439670382 ] 
dist 149=[.24155717278622265593,1.0369201163870409570 ] 
dist 150=[.19616920165485824702,1.0535473628830579161 ] 
dist 151=[.14283225410898169868,1.0612318110929074753 ] 
dist 152=[.01563476557206280277,1.0617438727277877930 ] 
dist 153=[-.13468635425393603709,.73535379459025560261] 
dist 154=[-.23432778655325081061,-.13335604336678390522] 
dist 155=[-.31583332287204455571,-.17240659501594870514] 
dist 156=[-.39379050266603946921,-.26110555169747568547] 
dist 157=[-.46561767584388930259,-.27409467012627346376] 
dist 158=[-.51526169753296382662,-.36912148795593295318] 
dist 159=[-.55781396749998043582,-.38365864931317733724] 
dist 160=[-.60176978570514351417,-.40925425156915465074] 
dist 161=[-.64113611437733451556,-.41374619573205824311] 
dist 162=[-.66537520491106781154,-.44849658415141729588] 
dist 163=[-.68316103861797749876,-.44866480160379573214] 
dist 164=[-.69677448964287005199,-.44013876943321681313] 
dist 165=[-.70665238475380176271,-.41753431581952299494] 
dist 166=[-.70953066942253629567,-.3876405042760572589 ] 
dist 167=[-.70867539881804261655,-.35002732381984133736] 
dist 168=[-.70665122549826610608,-.27584532319579900206] 
dist 169=[-.54227091716606125966,-.16882564846688363481] 
dist 170=[-.38527273956596280646,-.09553341755404060482] 
dist 171=[-.32068671213268923722,-.03299035788340152959] 
dist 172=[-.31138481554073600099,.03113978439455022176] 
dist 173=[-.2115479786971797936 ,.09129733504358963109] 
dist 174=[-.1928185171707044728 ,.13798967010579887027] 
dist 175=[-.17169883930598722193,.18371121802936848496] 
dist 176=[-.16790656592311714246,.23999543204655790952] 
dist 177=[-.08399182169397022756,.2931514376877204667 ] 
dist 178=[.01718034961564049256,.32639121722461382641] 
dist 179=[.04686961819581476000,.35137217790466562345] 
dist 180=[.06831517839462734928,.37157476227743594856] 
dist 181=[.08285917697138875926,.38758256450184615424] 
dist 182=[.11470890820970605535,.3958257353853335879 ] 
dist 183=[.11981739390857304978,.39994966830976755195] 
dist 184=[.12808582850267758447,.40063147115125876776] 
dist 185=[.1315928641407901983 ,.3196987891074779009 ] 
dist 186=[.18760955653879940064,.3368632017739282926 ] 
dist 187=[.19224621174573642634,.34835382086640107106] 
dist 188=[.20003738173889127394,.35510748855730149272] 
dist 189=[.20126309271625108329,.35946885280632399883] 
dist 190=[.20026891608679159926,.36141177225610820777] 
dist 191=[.19596316802651574732,.36195895462514501368] 
dist 192=[.18841753144025596177,.36102357314528598906] 
dist 193=[.17449390307800919444,.31504998118726326286] 
dist 194=[.15904502620436545647,.30784975030059509501] 
dist 195=[.14541205311073376486,.29476721390636182144] 
dist 196=[.13051139010493708343,.29115365668074129194] 
dist 197=[.11000202189948456988,.27927729548311295641] 
dist 198=[.08747462684737334162,.27618969960687397766] 
dist 199=[.06451988400429649924,.26797921667943117842] 
dist 200=[.01517925786472431064,.26563838571552366766] 
dist 201=[-.05131993284469197649,.15250194449035324613] 
dist 202=[-.09618376433332868367,.05909228571743676001] 
dist 203=[-.13375619367225914185,.02720595545304436058] 
dist 204=[-.17116024321790146657,.01348831570741065746] 
dist 205=[-.20782857426203418763,-.00039597657497729799] 
dist 206=[-.23682740702547963909,-.02336762206506720998] 
dist 207=[-.26488116299981669747,-.02748986534429218360] 
dist 208=[-.29895063955092376892,-.03563503911902181697] 
dist 209=[-.33091323777529774878,-.03754465305348235833] 
dist 210=[-.35055987484053953165,-.04293029294088965929] 
dist 211=[-.36493272916561565344,-.04248329353133736429] 
dist 212=[-.37585098733093670597,-.03967282658641202760] 
dist 213=[-.38370391077213824354,-.03290923213926931568] 
dist 214=[-.38584502678189412091,-.0241319304543761231 ] 
dist 215=[-.38601347995107210604,-.00939684112905191197] 
dist 216=[-.38599425739084514008,.03911808484977313058] 
dist 217=[-.2670426168410928384 ,.09288525096961126859] 
dist 218=[.02080307592153939512,.12818532066748874406] 
dist 219=[.03374516225764693101,.15668434175774897361] 
dist 220=[.06298826276496770125,.18895468389752739177] 
dist 221=[.06765687940777894930,.21873938164122764552] 
dist 222=[.08933558970722150752,.23902059686668873795] 
dist 223=[.09188380991522047661,.2562052917521495434 ] 
dist 224=[.09389117330933568877,.27363454453695157368] 
dist 225=[.09239712174010840443,.28909485962699900775] 
dist 226=[.08952117194115917986,.29842314538919086541] 
dist 227=[.08519055544135257006,.30503765739886973313] 
dist 228=[.07896951044459174397,.30966932145544819961] 
dist 229=[.06855006458829501875,.31266683237331513898] 
dist 230=[.05152500941636918325,.31288474913838538896] 
dist 231=[.02608699077660794452,.31165768719514514629] 
dist 232=[-.01330110910920564532,.31016795159717526025] 
dist 233=[-.05283660388089685288,.22623834179866003542] 
dist 234=[-.07886276486393478699,.16832848212195407349] 
dist 235=[-.09994978196365101893,.15435022073164465953] 
dist 236=[-.11977761949327008745,.15208043476373196305] 
dist 237=[-.1372525750974335127 ,.13387938442396558679] 
dist 238=[-.14895133580446312586,.13005842449059012499] 
dist 239=[-.15864672179268706569,.12421172659170113961] 
dist 240=[-.16812792955341812505,.1224270625570966797 ] 
dist 241=[-.176457335762874755  ,.08422617717910851118] 
dist 242=[-.18155684134547318716,.07906354172724649691] 
dist 243=[-.18526083504682270581,.06730117376986536502] 
dist 244=[-.18802186646248588612,.06462692200358770516] 
dist 245=[-.18996020264367169609,.04937195011304519804] 
dist 246=[-.19038138027760377726,.04650444199969229678] 
dist 247=[-.18989998564001187326,.04065030824867691689] 
dist 248=[-.18934012930682425092,.03907865402708403629] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 0, 1, 1, 2] 
dist 0=[50.529039094121523685  ,50.529039094121523685  ] 
dist 1=[50.015264354196885335  ,50.734714965736911249  ] 
dist 2=[49.051321274991424791  ,51.041970151651870586  ] 
dist 3=[47.219506764539636613  ,51.507729785731942042  ] 
dist 4=[45.037664894592680037  ,52.311326391424112905  ] 
dist 5=[42.676063770698106657  ,53.120525231888418458  ] 
dist 6=[39.726787508060960554  ,53.608558497506762869  ] 
dist 7=[35.198214824893662985  ,53.954218698860643592  ] 
dist 8=[30.623155863782429230  ,54.195188590994917888  ] 
dist 9=[27.488080946455750539  ,54.349549949413898443  ] 
dist 10=[24.801953999593674279  ,54.349490637327753360  ] 
dist 11=[22.019153453643285879  ,54.262044589700505490  ] 
dist 12=[19.379882536045317247  ,54.179136021770263844  ] 
dist 13=[17.266488049526964316  ,53.512862760698040161  ] 
dist 14=[15.127815742110320078  ,41.301672690852893823  ] 
dist 15=[12.386866403812628232  ,38.772028587521938657  ] 
dist 16=[9.7241502755864904725 ,38.307014234912346970  ] 
dist 17=[7.8975009490887029050 ,34.657714093755570189  ] 
dist 18=[6.3262876814461163963 ,33.960162307026963353  ] 
dist 19=[4.6831928051554997630 ,32.889070071393206093  ] 
dist 20=[3.1087579306061452219 ,32.593934862591786539  ] 
dist 21=[1.8110368032298554277 ,26.976033348323206721  ] 
dist 22=[.45813085420309740063,26.244700329337815504  ] 
dist 23=[-1.3383111851371732009 ,24.553966929297343255  ] 
dist 24=[-3.0645410256518962547 ,24.247468045876819489  ] 
dist 25=[-4.1371320154243281943 ,22.023388658835504452  ] 
dist 26=[-4.9465668386090157084 ,21.616494837318813008  ] 
dist 27=[-5.6204860284599316400 ,20.944711501668283107  ] 
dist 28=[-6.1656569558756345437 ,20.783178297329330762  ] 
dist 29=[-6.4604550280216135883 ,11.523755912403936305  ] 
dist 30=[-6.6339454765102367931 ,1.3223834106234988961 ] 
dist 31=[-6.6946383007184901433 ,.45005598160740863733] 
dist 32=[-6.7020169810978550841 ,-1.4239401414698699691 ] 
dist 33=[-6.7132587234469340813 ,-1.7934835263589317173 ] 
dist 34=[-8.1236300951807641331 ,-3.7447226205161434729 ] 
dist 35=[-9.1519993821830826394 ,-3.4010191492801894540 ] 
dist 36=[-10.101738305650815211  ,-2.5728465297765738163 ] 
dist 37=[-11.198098935588397826  ,-1.7079626475881264831 ] 
dist 38=[-12.207503828414229512  ,-.6535550255456154131 ] 
dist 39=[-12.809900849420995687  ,.9309816144917953938 ] 
dist 40=[-13.232462644828990740  ,2.5173168823162132452 ] 
dist 41=[-13.523441053338326198  ,3.5790850953078469843 ] 
dist 42=[-13.723290581555958681  ,4.4575538694871052934 ] 
dist 43=[-13.781743918770095113  ,5.3129106728216079845 ] 
dist 44=[-13.777644509991582636  ,6.0860607392518200067 ] 
dist 45=[-13.737760056186576522  ,6.6367129969718768474 ] 
dist 46=[-.31980769778080654501,7.1290874728873495761 ] 
dist 47=[-.24449538122271608071,7.6698926642042227675 ] 
dist 48=[.01458959655137731472,8.1486208652783440414 ] 
dist 49=[.03954169623205551922,8.3933877883441130561 ] 
dist 50=[-.0096074907899751627 ,8.5250927613646957056 ] 
dist 51=[-.1725079531388185667 ,8.5525721082913268234 ] 
dist 52=[-.3956888137933088140 ,8.4388550917560440834 ] 
dist 53=[-.6853714727322754967 ,8.4024881765920408424 ] 
dist 54=[-1.0788580851498283979 ,8.3743696356554914891 ] 
dist 55=[-1.7162320501342032733 ,8.3499266090643546750 ] 
dist 56=[-2.3571194132815748620 ,4.8465589221154003676 ] 
dist 57=[-2.7646359196015144864 ,4.9715313832831212057 ] 
dist 58=[-3.0787699903932718687 ,5.0669813027181230637 ] 
dist 59=[-3.3470783156323100732 ,5.1058543442382518352 ] 
dist 60=[-3.5661498278743564831 ,5.1109237658822278544 ] 
dist 61=[-3.6838331497884840971 ,5.1019832649865981099 ] 
dist 62=[-3.7497190626755179235 ,2.4940573448617035655 ] 
dist 63=[-3.7653529162974631004 ,2.2721662371038416348 ] 
dist 64=[-3.7148966657960601168 ,1.7388877490577748412 ] 
dist 65=[-3.7007455938120224530 ,1.6538262029536958680 ] 
dist 66=[-3.6881641637836037022 ,.9022444880824518285 ] 
dist 67=[-3.6745176136197696997 ,.76615594317953690388] 
dist 68=[-3.6613059809541379364 ,.5760134809761863363 ] 
dist 69=[-3.6504563766266632482 ,.52151562091997976364] 
dist 70=[-3.6393029009021365633 ,-.4391715544471205280 ] 
dist 71=[-3.6248761384942634092 ,-.5568746704386966215 ] 
dist 72=[-1.8504749844720401311 ,-.63126104809923557015] 
dist 73=[-1.9942314390608243826 ,-.14906518988160409752] 
dist 74=[-2.1083290375168916441 ,.26408122012578093315] 
dist 75=[-2.1672506490097284060 ,.69031700700090325936] 
dist 76=[-2.1969278183894084373 ,1.0917327803236750007 ] 
dist 77=[-2.2019539001692708805 ,1.4058537313625932980 ] 
dist 78=[-1.3528784052600077501 ,1.7158344467194674524 ] 
dist 79=[-1.3031928041598373930 ,2.1007382535373208455 ] 
dist 80=[-1.2117567520607284574 ,2.4658796490026307882 ] 
dist 81=[-1.2065101676165920444 ,2.6970116278064421888 ] 
dist 82=[-1.2009315703000105962 ,2.8739991207946010055 ] 
dist 83=[-1.1961709925636763523 ,3.0231061848707240421 ] 
dist 84=[-1.1913223307032469359 ,3.1427079994412059411 ] 
dist 85=[-1.1860105033144163069 ,3.2019724352616366352 ] 
dist 86=[-1.1799929404218884768 ,3.2295624752950139885 ] 
dist 87=[-1.1775640201983923581 ,3.2325201030975305835 ] 
dist 88=[-1.1768642288434941369 ,.23281093859787491972] 
dist 89=[-1.1783455537038292365 ,.10885592082678840897] 
dist 90=[-1.1810002820699280650 ,.25850851426203261979] 
dist 91=[-1.1849359485266579117 ,.44692164391879715821] 
dist 92=[-1.1903729361056610422 ,.66520147270562374726] 
dist 93=[-1.1989416649289495059 ,.98128383835759447022] 
dist 94=[-1.2062586914422769660 ,1.2916846843753338008 ] 
dist 95=[-1.3067020896959964177 ,1.4873066897226732396 ] 
dist 96=[-1.4686561116954776251 ,1.6363579398519043784 ] 
dist 97=[-1.5661498055412398106 ,1.7609040224363789913 ] 
dist 98=[-1.6349838115509572017 ,1.8613668563655527612 ] 
dist 99=[-1.7141837558290338270 ,1.9142933568591402165 ] 
dist 100=[-1.7823025807017746295 ,1.9428389814260593266 ] 
dist 101=[-1.8186662634534122386 ,1.9489247247674085501 ] 
dist 102=[-1.8386983228137607993 ,1.8986132055025468686 ] 
dist 103=[-1.8416549893799221547 ,1.8839036259136428926 ] 
dist 104=[-1.8352186986490470040 ,1.8704859647233541917 ] 
dist 105=[-1.8290295211001088155 ,1.8594927189345452474 ] 
dist 106=[-1.7994795085815392423 ,1.8407504835625755530 ] 
dist 107=[-1.7896477618741546684 ,1.8283046775142754977 ] 
dist 108=[-1.6841181220370559660 ,1.8151878772626951243 ] 
dist 109=[-1.6572413206359018956 ,1.8057193946092993463 ] 
dist 110=[-1.6245709414852045378 ,.97875488526018444197] 
dist 111=[-1.6096197392820039661 ,1.0988064948690554512 ] 
dist 112=[-1.2234260629757055911 ,1.2103489733296822668 ] 
dist 113=[-1.1693556311780751278 ,1.2769029672825737209 ] 
dist 114=[-1.0557174095742156793 ,1.3231829879918818919 ] 
dist 115=[-1.0725981500671460530 ,1.3538397646241527974 ] 
dist 116=[-1.1109863065005069795 ,1.3742386157383630127 ] 
dist 117=[-1.1358188703420976854 ,1.3795863118320663043 ] 
dist 118=[-1.1538809812983891923 ,1.3777059132550787203 ] 
dist 119=[-1.1652549740853512284 ,1.3728601854138244175 ] 
dist 120=[-1.1739337263034916775 ,.92308877735414857887] 
dist 121=[-1.1812324731727189183 ,1.0545121645118218820 ] 
dist 122=[-1.1871068042277987500 ,1.1541016372992221634 ] 
dist 123=[-1.1900970907728935778 ,1.2361752640544974830 ] 
dist 124=[-1.1915553256389104137 ,1.3022703967094518463 ] 
dist 125=[-1.1913112806092178794 ,1.3381003446358456883 ] 
dist 126=[-.32457051920555066302,1.3585995019687474135 ] 
dist 127=[-.25435250518285002808,1.3635158864624211001 ] 
dist 128=[-.09488499757891644620,1.3017924404460583120 ] 
dist 129=[-.0657710934754560994 ,1.2879162697385929646 ] 
dist 130=[.1288122209289659535 ,1.2769496950827359931 ] 
dist 131=[.1621935989469128877 ,1.2679199419974579693 ] 
dist 132=[.2241779954350225499 ,1.2592609903631882061 ] 
dist 133=[.2376852914153624314 ,1.2546905695410099056 ] 
dist 134=[.38263930810155163938,1.2518039737850978925 ] 
dist 135=[.40368961850662408495,1.2504712013343313853 ] 
dist 136=[.1983140417667472037 ,.7653427599658551847 ] 
dist 137=[.0262078243414976292 ,.8143342544293556549 ] 
dist 138=[-.12158481623201786464,.8544724231896447338 ] 
dist 139=[-.27460352645827532183,.8759386452209734953 ] 
dist 140=[-.419060801199125855  ,.8878045620992327566 ] 
dist 141=[-.53269353481415329729,.8896415567064274764 ] 
dist 142=[-.64538385741207492975,.1135533118581538718 ] 
dist 143=[-.7860813242187902319 ,.0801355557553967175 ] 
dist 144=[-.91992983302047850328,.0040800024932019519 ] 
dist 145=[-1.0052927066338194148 ,-.0091634264772731394 ] 
dist 146=[-1.0713923531399574436 ,-.0999541968117612038 ] 
dist 147=[-1.1283798767620725113 ,-.1150378107064592137 ] 
dist 148=[-1.1750712261835047561 ,-.1428564453385509951 ] 
dist 149=[-1.2000887085181252715 ,-.1487098117730998731 ] 
dist 150=[-1.2139925427919832840 ,-.2078433186353404450 ] 
dist 151=[-1.2163399060115164224 ,-.13203135668722692999] 
dist 152=[-.3564350788054689359 ,.02651387490472509678] 
dist 153=[-.3720908326929778212 ,.13289206018388693025] 
dist 154=[-.3842288673781968264 ,.22129040497271445891] 
dist 155=[-.3898013075209005285 ,.30810100589743530649] 
dist 156=[-.3919047457938156918 ,.3871127687468810825 ] 
dist 157=[-.3917051783123524169 ,.44478125744166678709] 
dist 158=[-.36172698274635300312,.49730877019612863218] 
dist 159=[-.35671892970992026388,.55644946612157160411] 
dist 160=[-.34204950333187237586,.61057377462511336797] 
dist 161=[-.33876544329437599486,.64308660248476694678] 
dist 162=[-.30676058017337238928,.66595959176909009985] 
dist 163=[-.29960506966648599334,.68162000797409611175] 
dist 164=[-.29029905737200491779,.69209631488304714998] 
dist 165=[-.28670575440385602158,.69428551870397829548] 
dist 166=[-.20234579663606082595,.69314676277710667924] 
dist 167=[-.19092518839460526268,.69034310327118619137] 
dist 168=[-.16614862929995514656,.48978237261006059479] 
dist 169=[-.15917762652706554316,.46930335849538151715] 
dist 170=[-.1305377581374389367 ,.41718925144427020938] 
dist 171=[-.1250662896275712444 ,.40871476944979957382] 
dist 172=[-.1112040543789953523 ,.32352965167011290772] 
dist 173=[-.1530064300874507945 ,.30686720589880753583] 
dist 174=[-.19941136016801224925,.28648439458945016475] 
dist 175=[-.25733708878645951869,.28012053655518807917] 
dist 176=[-.31241042449189339983,.28279263529261449217] 
dist 177=[-.34743501536433363154,.30977930858586061632] 
dist 178=[-.37443287760359974307,.3322573100461436815 ] 
dist 179=[-.39748150864842751207,.34500487446334762134] 
dist 180=[-.41618839915915079842,.3530562022863837561 ] 
dist 181=[-.42586371496975811707,.35679739624230297655] 
dist 182=[-.43076216369879744684,.3586167915249159469 ] 
dist 183=[-.43166028345163811872,.35900016012353935078] 
dist 184=[-.3349608722595532692 ,.35841035553545333307] 
dist 185=[-.37318654486696491183,.3570528018337071566 ] 
dist 186=[-.40211064311719552769,.35349943660190857415] 
dist 187=[-.4258683140285684046 ,.35147423306336476207] 
dist 188=[-.44467950499788283173,.34588355847528319163] 
dist 189=[-.45386585659310498356,.34323461600834526283] 
dist 190=[-.45842289700919967778,.1357001420922072806 ] 
dist 191=[-.45876161093503516802,.11707479698096928437] 
dist 192=[-.44308707184845470749,.07514999731513582213] 
dist 193=[-.43886176582525290924,.06665032331024648425] 
dist 194=[-.43213804382218939525,.01584529127208631692] 
dist 195=[-.42942758174496481997,.00692410233102693915] 
dist 196=[-.41835006188933419774,-.01097269912467966784] 
dist 197=[-.41471583321914422975,-.01537871920831437006] 
dist 198=[-.40556540417680409005,-.05379202987211813396] 
dist 199=[-.4018264803577522173 ,-.05414046308013748551] 
dist 200=[-.3170866120875343326 ,.03815610001542834857] 
dist 201=[-.3253569097588497154 ,.10061784722315878333] 
dist 202=[-.3310773805434972803 ,.15311779302811477713] 
dist 203=[-.3336301180533408354 ,.20566674614263844257] 
dist 204=[-.3343483931156776216 ,.25438422876599032112] 
dist 205=[-.3336877035926138458 ,.29168544993954783664] 
dist 206=[-.01754664840275944843,.32712758518364645154] 
dist 207=[-.00076629663016341009,.36924695703319694855] 
dist 208=[.02985948650721159408,.40827514296711016056] 
dist 209=[.03372089357518536135,.43138346886595584718] 
dist 210=[.0460239904421423238 ,.447231685843466628  ] 
dist 211=[.0485836167979169752 ,.4572917782532262868 ] 
dist 212=[.0487154867182553511 ,.46401989830979961387] 
dist 213=[.04556460884636218090,.46657320271367765934] 
dist 214=[.02846230510172099794,.46655525796474405801] 
dist 215=[-.01376404724547412842,.46561748699691879251] 
dist 216=[-.06037198632920666431,.2113289268520041839 ] 
dist 217=[-.09182060650495418230,.2166681273415101522 ] 
dist 218=[-.12346901344868356658,.2203063985616860005 ] 
dist 219=[-.16517719648353833145,.2214999653365864432 ] 
dist 220=[-.20300388210274758035,.2213862761133454122 ] 
dist 221=[-.2302017952852148991 ,.2207912296358920781 ] 
dist 222=[-.25479016912681132673,.17256275682701432829] 
dist 223=[-.28220509547897886073,.17391214707843903099] 
dist 224=[-.30720393407025530018,.1741763255165854438 ] 
dist 225=[-.32215232151248006966,.17372171840889034679] 
dist 226=[-.33258356314105226422,.16830218328113011021] 
dist 227=[-.33955929130901827626,.16653487527254585611] 
dist 228=[-.34407640108453945231,.16439939181649308333] 
dist 229=[-.34479981258980736092,.16327345863528872883] 
dist 230=[-.34384671324708167264,.13137711737159364642] 
dist 231=[-.34248783050457605619,.12676009306619929466] 
dist 232=[-.23898515525002124944,.11714459618991194185] 
dist 233=[-.22928942537489532899,.11683530310678044194] 
dist 234=[-.21427543193972062267,.14250291301528019707] 
dist 235=[-.21203274442975172232,.16634507953362922316] 
dist 236=[-.19206371882085255539,.18715153568940453611] 
dist 237=[-.18762280112373648328,.20070699609691683621] 
dist 238=[-.18144551367545380702,.21152919568265724629] 
dist 239=[-.17923908774473599879,.22143014112743082338] 
dist 240=[-.12821814422348850968,.22988708864642544756] 
dist 241=[-.12124152593897937215,.23494786079146705609] 
dist 242=[-.10596490702142366748,.23848257475278752105] 
dist 243=[-.10172264583467074633,.24085071851763327303] 
dist 244=[-.08343469514327150255,.24228230391394612221] 
dist 245=[-.07992514887094327256,.2420801657092497113 ] 
dist 246=[-.07116698968990188744,.2409538820616891963 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 0, 2, 1, 2] 
dist 0=[56.760783085482964434  ,56.760783085482964434  ] 
dist 1=[55.417781387820895541  ,57.446746474322974485  ] 
dist 2=[53.753524577212970943  ,57.820819454056463635  ] 
dist 3=[51.784791604904695560  ,57.918417905057186538  ] 
dist 4=[49.212472302521564896  ,57.889405998715580729  ] 
dist 5=[45.138004368557602514  ,57.597994809113328599  ] 
dist 6=[40.979381646179963344  ,57.456843790908110149  ] 
dist 7=[38.070947466680468930  ,57.301648495078541431  ] 
dist 8=[35.516152625108552647  ,57.166980375126155468  ] 
dist 9=[32.769445873695649756  ,56.847422993794088188  ] 
dist 10=[30.102950767784247318  ,56.676610575031343452  ] 
dist 11=[27.868246846154280166  ,56.327863218738599382  ] 
dist 12=[25.516765777899728609  ,56.177336389698616074  ] 
dist 13=[22.383564266291497762  ,55.417691940596398863  ] 
dist 14=[19.287028613545674984  ,55.126702309646762898  ] 
dist 15=[17.081728960863763091  ,53.172822525285009362  ] 
dist 16=[15.100797701591633236  ,32.453217849314733002  ] 
dist 17=[12.899906202606987277  ,29.846756627402122900  ] 
dist 18=[10.716862951866369400  ,25.962841995043932819  ] 
dist 19=[8.8067277087359484068 ,24.869807848386870416  ] 
dist 20=[6.7227889982628340220 ,24.568155430082915993  ] 
dist 21=[3.8445956571964711505 ,18.717797240027144425  ] 
dist 22=[1.0314321913635958792 ,17.075124186236731012  ] 
dist 23=[-.79290382231050654447,16.720960427721240819  ] 
dist 24=[-2.2509267524576592603 ,12.386976546808612450  ] 
dist 25=[-3.6004320515418060574 ,11.261075441235371154  ] 
dist 26=[-4.7854960585491913828 ,10.173129221031685432  ] 
dist 27=[-5.5866079254916516609 ,9.6868489421986838029 ] 
dist 28=[-6.2649733421634753085 ,9.4101646075325424525 ] 
dist 29=[-6.9599888315498094234 ,5.5861105896879095144 ] 
dist 30=[-7.5692083831618567321 ,1.3985027976026443180 ] 
dist 31=[-9.8239163543468419571 ,.0253812579785503416 ] 
dist 32=[-12.284452769687516360  ,-3.3279267357731547821 ] 
dist 33=[-13.793792679754091428  ,-4.6120728528922245955 ] 
dist 34=[-14.904594787359267914  ,-3.9202709481676074903 ] 
dist 35=[-15.772607951198607387  ,-3.1053679954377818255 ] 
dist 36=[-16.451970452749726736  ,-2.0481173581851260571 ] 
dist 37=[-16.808689153674010030  ,-.38941040772457165433] 
dist 38=[-17.000587353920012318  ,1.2856727290269042148 ] 
dist 39=[-17.025234653984396570  ,2.4084369844126457579 ] 
dist 40=[-16.049815812394803248  ,3.3380260419416317886 ] 
dist 41=[-15.861015285221893404  ,4.2429185179573199896 ] 
dist 42=[-15.601187553246693865  ,5.0595050679223904086 ] 
dist 43=[-15.492375578254801624  ,5.6370120344210995701 ] 
dist 44=[-15.223550013028214818  ,6.1484734326453497729 ] 
dist 45=[-15.102801471868329362  ,6.7017372493415200832 ] 
dist 46=[-14.999148345245922745  ,7.1959818924108270957 ] 
dist 47=[-14.918046716638494492  ,7.4720314163591940813 ] 
dist 48=[-4.3340817277759206243 ,7.6403871867632030274 ] 
dist 49=[-3.4562824970792391832 ,7.7049622767180866686 ] 
dist 50=[-1.4676457671697916224 ,7.7201962635576665902 ] 
dist 51=[-1.1126858055968964875 ,7.6946041320453442131 ] 
dist 52=[-.42687085609546487088,7.6343812878584279857 ] 
dist 53=[-.46898856400894295275,7.5943613074431778909 ] 
dist 54=[-.52347239835753043263,6.7875462831535335650 ] 
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dist 56=[-.58103990262778697169,8.4904946414887931938 ] 
dist 57=[-.59838420402506164579,9.2941618830073696581 ] 
dist 58=[-.61134852367866823392,9.8981400739424671533 ] 
dist 59=[-.61802941669096157341,10.387771556411100893  ] 
dist 60=[-.6212807436661317089 ,10.767499474447042894  ] 
dist 61=[-.62060811937222776779,10.932819736284766139  ] 
dist 62=[-.5577483898076357621 ,11.006876363140768746  ] 
dist 63=[-.54707536570839001424,11.022302845876180044  ] 
dist 64=[-.53074482256400946468,2.8411975657129477289 ] 
dist 65=[-.9435929860637388718 ,1.8622534627273572409 ] 
dist 66=[-1.3990102636037974672 ,1.6247033470364713320 ] 
dist 67=[-1.8311570099810917881 ,1.3651750221262943152 ] 
dist 68=[-2.3433718546290282710 ,1.2872330955461589089 ] 
dist 69=[-2.8229876726012801642 ,-.07390697465423132822] 
dist 70=[-3.1251072901090080922 ,.05179488474782034326] 
dist 71=[-3.3545413579451581314 ,.1380290787900694816 ] 
dist 72=[-3.5442328072916212162 ,.21176508246932787669] 
dist 73=[-3.6935890930029649489 ,.28759736113736086833] 
dist 74=[-3.8696275951524870968 ,.35885629953734962686] 
dist 75=[-4.1708157691960352880 ,.4143436975703324199 ] 
dist 76=[-4.5183828794802732298 ,.46883255083232317828] 
dist 77=[-4.7792694676203985325 ,.53610594387430696185] 
dist 78=[-5.0269264330066057053 ,.5997031966329463637 ] 
dist 79=[-5.3218298406739598939 ,.87273318202442942627] 
dist 80=[-5.5880867510922962089 ,1.5256824603864668252 ] 
dist 81=[-5.7214415736634277269 ,1.9660106873433953912 ] 
dist 82=[-5.7911893558662585422 ,2.3339096630634536169 ] 
dist 83=[-5.8033999554850818913 ,2.6979548348766460268 ] 
dist 84=[-5.7244917621962912745 ,3.0306321202505399206 ] 
dist 85=[-5.6973039708560463042 ,3.2734070150205122485 ] 
dist 86=[-5.6750319557751179966 ,3.4962410869253364528 ] 
dist 87=[-5.6538262683354567189 ,3.7493659213015246205 ] 
dist 88=[-4.6046719369907810988 ,3.9772597477621098512 ] 
dist 89=[-4.4557116262983407038 ,4.0994436228815566423 ] 
dist 90=[-4.1728323447800302834 ,4.1672415937355374945 ] 
dist 91=[-4.0972318243132484488 ,4.1820680234287226378 ] 
dist 92=[-3.8255105721521861410 ,4.1686208201839884615 ] 
dist 93=[-3.7545126276187686344 ,4.1545906527845301976 ] 
dist 94=[-3.6510434945213961502 ,4.1345379378027178303 ] 
dist 95=[-3.6242856619155887444 ,4.2360963105264130805 ] 
dist 96=[-3.6267593636655833273 ,4.5396942643165741249 ] 
dist 97=[-3.6055374408477927806 ,4.7845365712796659050 ] 
dist 98=[-3.5896665249219101138 ,4.9151261413502952098 ] 
dist 99=[-3.5388992968088719023 ,4.9870068039240673896 ] 
dist 100=[-3.5126227496290766290 ,5.0013709593714912415 ] 
dist 101=[-3.1216579673466870396 ,4.8308774922078120527 ] 
dist 102=[-3.0551650249509005849 ,4.7875786806453349062 ] 
dist 103=[-2.8915991546977054948 ,4.7513440733275451541 ] 
dist 104=[-2.8438430963839024584 ,4.6144072267110847392 ] 
dist 105=[-2.5673817305616692676 ,4.5936602415401403113 ] 
dist 106=[-2.5063863028863454233 ,4.5614039631253898744 ] 
dist 107=[-2.3875572422056859001 ,4.2708510863726567698 ] 
dist 108=[-2.3525688616581024047 ,3.5552140025558093976 ] 
dist 109=[-1.5258052045610718053 ,.21100123955712662795] 
dist 110=[-1.8081761751412310780 ,.24746264186330522775] 
dist 111=[-2.0260418617118704885 ,.27000575940045567266] 
dist 112=[-2.2125615537622789170 ,.28665017686138397737] 
dist 113=[-2.3651347221815646112 ,.29957359760090600064] 
dist 114=[-2.4475471733682179826 ,.30955212032050789043] 
dist 115=[-2.4942864178286159930 ,.31444581736785576295] 
dist 116=[-2.5054463650843758345 ,.31654759462057884186] 
dist 117=[-2.4782810072144806852 ,.31673479414795848199] 
dist 118=[-2.4710798790013807788 ,.26024764597041857842] 
dist 119=[-2.4648616733409179108 ,.26814888785290780337] 
dist 120=[-2.4584359664501897810 ,.27253974209337564851] 
dist 121=[-2.4524261304917203246 ,.27347337342699446394] 
dist 122=[-2.4478595291916876881 ,.27198731085302646396] 
dist 123=[-2.4434984251180936494 ,.27138654794126997073] 
dist 124=[-2.4383002055494424543 ,.27083349331806161194] 
dist 125=[-.53164144895467002922,.27020495485037908772] 
dist 126=[-.3762042216462932490 ,.22094335932228986272] 
dist 127=[-.0287827483522296690 ,.21402924275198497176] 
dist 128=[.0377307544353281203 ,.4267363812168464057 ] 
dist 129=[.14608391007957539094,.6969677110163411258 ] 
dist 130=[.12216236490296110313,.9093531812434881143 ] 
dist 131=[.09374072144133083521,1.1197695136085644475 ] 
dist 132=[.05971233584925584125,1.3821457041881307931 ] 
dist 133=[.00917573471076197910,1.6315112709137055556 ] 
dist 134=[-.04153159931909610965,1.7900175552702144992 ] 
dist 135=[-.07624152371611240141,1.9121220054969638705 ] 
dist 136=[-.105849951742962692  ,2.0162494917506680109 ] 
dist 137=[-.13620115660561556449,2.1006904291832075766 ] 
dist 138=[-.16467505497954833763,2.1442482435914570300 ] 
dist 139=[-.18679272337964028298,2.1661440367995861842 ] 
dist 140=[-.20847211879212585952,2.1689286042678517007 ] 
dist 141=[-.23519756200921788858,.0600120353291877374 ] 
dist 142=[-.26046864195596724885,-.0327433714683277066 ] 
dist 143=[-.2842144461541359713 ,-.05423843380163256575] 
dist 144=[-.4362569312652859612 ,-.05326049054713160875] 
dist 145=[-.5767336914598089065 ,-.04822724466836115613] 
dist 146=[-.6796199884210920929 ,-.04098011394868359495] 
dist 147=[-.7745332315802680599 ,-.03116788207316225945] 
dist 148=[-.8832053750957272589 ,-.00057301565744289874] 
dist 149=[-.9832604403606046043 ,.04966500051887627115] 
dist 150=[-1.0437945993376865395 ,.10281123843875212526] 
dist 151=[-1.0868958025794523792 ,.13937307686810258533] 
dist 152=[-1.1173945478050460342 ,.16896868647020484644] 
dist 153=[-1.1386811837437936427 ,.19674932058250541565] 
dist 154=[-1.1450294869047754763 ,.2211998616896060545 ] 
dist 155=[-1.1448374725304222665 ,.23750814437979869026] 
dist 156=[-1.1406486657444972338 ,.25095727548565442953] 
dist 157=[-.88477145353816024918,.2639995133670177183 ] 
dist 158=[-.85715441509823445797,.27527115240257496355] 
dist 159=[-.78457494029761278966,.28165556125093111952] 
dist 160=[-.77240448642220746101,.28567551486630597593] 
dist 161=[-.64503473044566308933,.2875131714390880981 ] 
dist 162=[-.61930858371455030321,.32140724761542798325] 
dist 163=[-.58879559678625267274,.39531248515494403392] 
dist 164=[-.57842328750514756097,.48659612188538932022] 
dist 165=[-.3181074023536598474 ,.57287221261016345243] 
dist 166=[-.2846743257642066265 ,.6267996591476475892 ] 
dist 167=[-.2133577561033704866 ,.6672712367970531204 ] 
dist 168=[-.1947565398364885864 ,.6998647838223996480 ] 
dist 169=[-.1200483112763400716 ,.7250467002376440483 ] 
dist 170=[-.1058809534708238920 ,.7359490844207674876 ] 
dist 171=[-.10409215575950107496,.7406336343342133338 ] 
dist 172=[-.12086640563750160417,.7410101423504633416 ] 
dist 173=[-.14086451904449545639,.5941006322740647318 ] 
dist 174=[-.15942277646627235317,.6643592975791143870 ] 
dist 175=[-.171084137679502094  ,.7171965649085438748 ] 
dist 176=[-.17991438190317691065,.7600032502482053533 ] 
dist 177=[-.18717592250553992095,.7939125559076848602 ] 
dist 178=[-.19286306710762592334,.8112477668754632393 ] 
dist 179=[-.19541107801726498175,.8198081435872800648 ] 
dist 180=[-.19638537029793689355,.8212424511048524207 ] 
dist 181=[-.19622028917063608979,.78371111386063200251] 
dist 182=[-.10375701501831302471,.78033163037825051087] 
dist 183=[-.09616340754038213307,.77573812976906359311] 
dist 184=[-.08356136421316729727,.77206895186322772284] 
dist 185=[-.08042952521583101120,.75963564088759793809] 
dist 186=[-.07406772117136441406,.75444644115959545274] 
dist 187=[-.07408145904674254907,.74071599930229826108] 
dist 188=[-.07681473297039323153,.73462896064636870031] 
dist 189=[-.08396802641986100500,.24934765542486527089] 
dist 190=[-.1199316192984516693 ,.20603831728582456659] 
dist 191=[-.2125246652262236889 ,.1367967613450992169 ] 
dist 192=[-.3081671477364297024 ,.16555584899708233828] 
dist 193=[-.3974711238431241180 ,.19981469436142526837] 
dist 194=[-.4660767138358267312 ,.23492946258226218696] 
dist 195=[-.5325776238135341669 ,.26710310132978939054] 
dist 196=[-.6134845408563717484 ,.30323964379998081844] 
dist 197=[-.6894023597245809773 ,.3541648453894472127 ] 
dist 198=[-.7359972834557976713 ,.4035060175109090656 ] 
dist 199=[-.7699811174823403710 ,.4333225529008458482 ] 
dist 200=[-.7955816037022059894 ,.4545044867538388575 ] 
dist 201=[-.8142371216033743486 ,.4693959514309714317 ] 
dist 202=[-.8205109595065691898 ,.4802600444303780350 ] 
dist 203=[-.8217775333576336132 ,.4853738751571116785 ] 
dist 204=[-.8204541631972863561 ,.4872466862036181062 ] 
dist 205=[-.3300059848940612508 ,.4867033737959957409 ] 
dist 206=[-.3300834178537003314 ,.4371923691947896797 ] 
dist 207=[-.3294845679783754068 ,.4287865923679946403 ] 
dist 208=[-.3245703050377432033 ,.4137367198719718500 ] 
dist 209=[-.3235047022487490566 ,.4093870242141106665 ] 
dist 210=[-.3026956831356709733 ,.4253946832737093616 ] 
dist 211=[-.2974712106503148211 ,.4637094157258864500 ] 
dist 212=[-.2932855699072150257 ,.5046894897799546285 ] 
dist 213=[-.2913572915873224851 ,.5416318025461843058 ] 
dist 214=[-.19703292746459948983,.5638366035407394530 ] 
dist 215=[-.18508229904968881577,.5794703433213595808 ] 
dist 216=[-.16142170496860371162,.5901949167584779441 ] 
dist 217=[-.1552082944538055196 ,.5969264326365210914 ] 
dist 218=[-.1329094196129280111 ,.5980358531419777925 ] 
dist 219=[-.12774186804666092003,.5943301429430988109 ] 
dist 220=[-.12028058813447673918,.5930817586886461223 ] 
dist 221=[-.15631748308589122571,.39770246254414215255] 
dist 222=[-.20540007763395552287,.39540337556672199473] 
dist 223=[-.24490934250188733558,.38656218729404816063] 
dist 224=[-.28160473150819073784,.3842956134923458287 ] 
dist 225=[-.3136194916875397403 ,.35783279305729008397] 
dist 226=[-.3344540679932586619 ,.35141431333411335814] 
dist 227=[-.3510587337602621943 ,.34416984918534063874] 
dist 228=[-.3661968338702838399 ,.34069855032777518395] 
dist 229=[-.3789770795751994091 ,.25241831815175085956] 
dist 230=[-.3861743523241075351 ,.24023059552577098966] 
dist 231=[-.3906478512842784697 ,.21496204873044814869] 
dist 232=[-.3925608754103635991 ,.2079534689377875282 ] 
dist 233=[-.3926742812035538554 ,.18036075816945248417] 
dist 234=[-.3918265583880706806 ,.17454525321142899541] 
dist 235=[-.3867205545366037661 ,.16174523057741177094] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 2, 2, 0, 0, 1] 
dist 0=[50.237956231830199099  ,50.237956231830199099  ] 
dist 1=[49.890850739265611410  ,50.786527901876313008  ] 
dist 2=[49.053257292996035029  ,51.348648407859685536  ] 
dist 3=[47.699111417446125155  ,51.599019454555225914  ] 
dist 4=[45.485205569165418064  ,51.690359068523924142  ] 
dist 5=[43.194610578640442610  ,51.673258730480221452  ] 
dist 6=[41.534108467528398055  ,51.283840271954586079  ] 
dist 7=[40.012929106726863336  ,50.781924998834099282  ] 
dist 8=[38.278636804902953744  ,49.539130489475069709  ] 
dist 9=[36.534188571803918458  ,49.378971691481379062  ] 
dist 10=[34.972310880505278227  ,48.675395624501569470  ] 
dist 11=[33.240269957756223246  ,48.477306071905898582  ] 
dist 12=[30.815934994330102431  ,47.966144347746477620  ] 
dist 13=[28.363662489872071897  ,47.765478349476445765  ] 
dist 14=[26.519888219665118124  ,46.755558339530028431  ] 
dist 15=[24.762548539746233479  ,45.747908047762451901  ] 
dist 16=[22.655298146440218072  ,29.689398577941740543  ] 
dist 17=[20.474808460980180093  ,29.242834855664576306  ] 
dist 18=[18.424634208376995483  ,24.971065042739288154  ] 
dist 19=[16.068919887288473656  ,24.399656512801354521  ] 
dist 20=[12.667351064712539140  ,24.259567348991202517  ] 
dist 21=[9.2963190203981215255 ,22.826516943569187699  ] 
dist 22=[7.0625233290784565537 ,15.793861422053115657  ] 
dist 23=[5.2247371106090476394 ,14.924907648872843777  ] 
dist 24=[3.4359837916054708812 ,13.141337936509611686  ] 
dist 25=[1.7845435689490728714 ,12.682842445986141970  ] 
dist 26=[.00150421308863410344,11.182148607203526506  ] 
dist 27=[-1.9093664821358562800 ,10.708579965357353939  ] 
dist 28=[-3.7669280381456224327 ,10.184160516490759787  ] 
dist 29=[-5.3376389733727180501 ,10.057832936330038978  ] 
dist 30=[-7.0080741660833463026 ,1.1038920286062222397 ] 
dist 31=[-9.2652423048959031879 ,-.27035859590757483983] 
dist 32=[-11.436492817223344600  ,-1.9858762349186206009 ] 
dist 33=[-12.763881284379302285  ,-2.3203820093414257105 ] 
dist 34=[-13.736907045001029596  ,-4.0888695531742790538 ] 
dist 35=[-14.491846194528931098  ,-4.0056438648876697505 ] 
dist 36=[-15.078217950038265815  ,-3.6972572177776368223 ] 
dist 37=[-15.377263697116092199  ,-3.3462467215655707583 ] 
dist 38=[-15.526417653366345146  ,-3.0664902346532719767 ] 
dist 39=[-15.546635337028263102  ,-2.7884515346789848617 ] 
dist 40=[-14.693497924936735384  ,-2.4435939722872281156 ] 
dist 41=[-14.526352870740183155  ,-2.0848954193519975097 ] 
dist 42=[-14.262688866797041061  ,-1.7513057399889062907 ] 
dist 43=[-14.167537264734068573  ,-1.3735424847679851025 ] 
dist 44=[-13.854354725487294808  ,-.83831811299609674949] 
dist 45=[-13.741368303550769318  ,-.2988656126588163956 ] 
dist 46=[-13.555116583112159853  ,.09593573096137344535] 
dist 47=[-13.484968611389075025  ,.71136529134362419315] 
dist 48=[-4.5875459049916158863 ,1.4878646017432720214 ] 
dist 49=[-3.8312605040569847332 ,2.3477599535237126232 ] 
dist 50=[-2.6956515974848943749 ,3.1688019551929125555 ] 
dist 51=[-2.5506696350447833050 ,3.7499309973772184174 ] 
dist 52=[-2.5086851874350881235 ,4.2668503104411064799 ] 
dist 53=[.67927890178725046398,5.0663234958055711510 ] 
dist 54=[1.3368826174024016402 ,5.8530115639098945978 ] 
dist 55=[1.4759276064947988650 ,6.9751823459224158376 ] 
dist 56=[3.2555844736029766104 ,8.0558832504783013599 ] 
dist 57=[3.0010716857316011887 ,8.7137166810620445753 ] 
dist 58=[2.6263551459088946277 ,9.1881637681191561365 ] 
dist 59=[2.1639084874154326764 ,9.5368604332046029843 ] 
dist 60=[1.5495522441619232377 ,9.7996235333881764183 ] 
dist 61=[.56870738984622525869,9.9310395245741003588 ] 
dist 62=[-.425871014705781897  ,9.9915519148104168747 ] 
dist 63=[-1.0950511572894472537 ,9.9878857736156086964 ] 
dist 64=[-1.6529715942551434939 ,4.8284980672008990080 ] 
dist 65=[-2.2036939737036709171 ,4.7782132719374758745 ] 
dist 66=[-2.7066226554606858700 ,4.2736763592444404668 ] 
dist 67=[-3.0738751015022456009 ,4.1664996564779485729 ] 
dist 68=[-3.4115351166062586507 ,4.0325045973789395555 ] 
dist 69=[-3.7964065098462165585 ,3.9808584483551131584 ] 
dist 70=[-4.1486234676396968636 ,2.8073605947434482229 ] 
dist 71=[-4.3559942002480749228 ,2.6504514261778135904 ] 
dist 72=[-4.4966332588845034410 ,2.3164828039337180257 ] 
dist 73=[-4.5825810155585464068 ,2.2242263038208200146 ] 
dist 74=[-4.6370103434021591355 ,1.8583276318823979716 ] 
dist 75=[-4.6519069380258701695 ,1.7866097011854747564 ] 
dist 76=[-4.6427045081260416483 ,1.6211836115757726073 ] 
dist 77=[-4.6304351798349962122 ,1.5830597728727358502 ] 
dist 78=[-3.2120224786223920168 ,-.74199095308159313534] 
dist 79=[-3.4771524495506324878 ,-.5451818068930017945 ] 
dist 80=[-3.6690822152720468601 ,-.3366500883335435823 ] 
dist 81=[-3.8115131803883686578 ,-.1854121593869186506 ] 
dist 82=[-3.9193046738721949383 ,-.0478809073830453498 ] 
dist 83=[-3.9729621418781218779 ,.1060755521555069312 ] 
dist 84=[-3.9973270975524650228 ,.2581156904616847603 ] 
dist 85=[-3.9966097910530008613 ,.3880551078680876370 ] 
dist 86=[-3.6728635956012529607 ,.5263182448449979930 ] 
dist 87=[-3.6156283238538542861 ,.7116159533196191306 ] 
dist 88=[-3.5200395129240797321 ,.89380874361151628886] 
dist 89=[-3.4899254761770625948 ,1.1094214095269150586 ] 
dist 90=[-3.3850928034314258316 ,1.2683368212434030091 ] 
dist 91=[-3.3501233623609122842 ,1.4096263571447125837 ] 
dist 92=[-3.2904717373398895136 ,1.5636203752980404541 ] 
dist 93=[-3.2695766007376374322 ,1.7037263262464298179 ] 
dist 94=[-1.6035798810880538189 ,1.7896040485445198687 ] 
dist 95=[-1.5786833643381886769 ,1.8521443341396666285 ] 
dist 96=[-.0015157666940187873 ,1.8991214054303535779 ] 
dist 97=[.0984864274034106136 ,1.9324529601110645578 ] 
dist 98=[.6252043311857662769 ,1.9405396580717984955 ] 
dist 99=[.7132201953224564445 ,2.2473148807659994486 ] 
dist 100=[.74624813890196930711,2.5319996216766545004 ] 
dist 101=[.45978986300672061459,2.8299222706010182922 ] 
dist 102=[.26274077865887731445,3.1636349721517320915 ] 
dist 103=[.09375225613886653827,3.3667901768095794430 ] 
dist 104=[-.08075853046546636336,3.5130755763631897572 ] 
dist 105=[-.24513815523407248132,3.6198325090289941114 ] 
dist 106=[-.3737087972986402555 ,3.6976814894092075866 ] 
dist 107=[-.5004792382517898119 ,3.7286103734067886391 ] 
dist 108=[-.65767805324736832864,3.7359765483354522384 ] 
dist 109=[-.80659495673807624468,3.7197939966251185182 ] 
dist 110=[-.90032396287988840019,1.3087726369909431983 ] 
dist 111=[-.97143760671127648859,1.2901212346420247139 ] 
dist 112=[-1.0301272840952021930 ,.47453464343399533633] 
dist 113=[-1.2314823459195524365 ,.3925798473176628328 ] 
dist 114=[-1.4477309049275948693 ,.22161738734245508752] 
dist 115=[-1.6042403920180542864 ,.1770197874446625982 ] 
dist 116=[-1.7468163773521363805 ,.01364754863894017039] 
dist 117=[-1.9074730443987157859 ,-.01848937331796172502] 
dist 118=[-2.0529081889160810416 ,-.0745238194759502501 ] 
dist 119=[-2.1347454770868065287 ,-.0865494346201728143 ] 
dist 120=[-2.1855872604153126586 ,-.1088633244962060028 ] 
dist 121=[-2.2073334436204921415 ,-.0982881388318005027 ] 
dist 122=[-2.2167253028031652997 ,-.0696970863341459126 ] 
dist 123=[-2.2182739334672188973 ,-.0091434898214961622 ] 
dist 124=[-2.1891165452747988332 ,.0672010278949455845 ] 
dist 125=[-2.1225169778904071655 ,.1588078111763728640 ] 
dist 126=[-1.7224504163115955330 ,.2790330730774254846 ] 
dist 127=[-1.6020472716234118818 ,.4695775023555843028 ] 
dist 128=[-.90485325827295602692,.6604560483852420211 ] 
dist 129=[-.87783364180305337997,.782018454693814713  ] 
dist 130=[-.86965808409846612819,.87596806842045133664] 
dist 131=[-.84917906127091758303,.95667122409399777272] 
dist 132=[-.84105592326076803267,1.0226768194778611532 ] 
dist 133=[-.2533143971801053099 ,1.0579810662062647345 ] 
dist 134=[-.20068696171048296642,1.0779258257487992526 ] 
dist 135=[-.08518989258332248697,1.0826444181307819364 ] 
dist 136=[-.06051339122554568674,1.0756844873375994835 ] 
dist 137=[.06924834524352836914,1.0730446891928999596 ] 
dist 138=[.09137528560946057251,1.0703355526519326731 ] 
dist 139=[.14058516922865586978,1.0668544850022935438 ] 
dist 140=[.14876014901492768937,1.0631679208433841774 ] 
dist 141=[.21233242146699466015,1.0596357486254769509 ] 
dist 142=[.22157483940564837403,1.0555512224407930412 ] 
dist 143=[.21888802651874836153,1.0501315396823233259 ] 
dist 144=[.16662656849141308988,1.0207850834759664070 ] 
dist 145=[.02536326042162179826,1.0423258870405894132 ] 
dist 146=[-.09562814001420878572,1.0489389095361645857 ] 
dist 147=[-.22036292456061734982,1.0497185586838492338 ] 
dist 148=[-.33775710501673043451,1.0479818029534021188 ] 
dist 149=[-.42946131661067298318,-.03055395619325048025] 
dist 150=[-.51979099540281323374,-.08317856140137456075] 
dist 151=[-.63170149417437993358,-.20248976098749458182] 
dist 152=[-.7377024500273530060 ,-.22084509217966148948] 
dist 153=[-.8044541658024271423 ,-.28050661633714005001] 
dist 154=[-.8551522198886211530 ,-.29120606630135422281] 
dist 155=[-.8971016664394469707 ,-.30221990545761262147] 
dist 156=[-.9301500951666707594 ,-.299299711318294008  ] 
dist 157=[-.9453344336073977891 ,-.28652595932301129063] 
dist 158=[-.9520055957244753981 ,-.22130810118342409491] 
dist 159=[-.9514733224905292547 ,-.1128541115407066744 ] 
dist 160=[-.786987243914324389  ,-.00195210866170273005] 
dist 161=[-.7954176231958476582 ,.0730334417706730798 ] 
dist 162=[-.79657562136807001893,.1359547726187179182 ] 
dist 163=[-.79216517683200110531,.2022732684902890374 ] 
dist 164=[-.78961361979059641566,.2651037227061658692 ] 
dist 165=[-.47411491234688151725,.3104553463673605635 ] 
dist 166=[-.46566676861767535311,.3516260252322660246 ] 
dist 167=[-.44272300732682348439,.3977776685518337699 ] 
dist 168=[-.43763213068830900971,.4401693965846420833 ] 
dist 169=[-.39305888619808860866,.4663393623222449949 ] 
dist 170=[-.38336258717868795057,.4856048656632614519 ] 
dist 171=[-.36967408138007893338,.5004486168378380135 ] 
dist 172=[-.36495462308752232933,.5112900877959297180 ] 
dist 173=[-.25821468041199579971,.5145869004715282817 ] 
dist 174=[-.24370362878683569615,.5148849058546322405 ] 
dist 175=[-.21171306164615037295,.5137627288781780552 ] 
dist 176=[-.20320511908252935696,.49949055492404826398] 
dist 177=[-.16447380996984425287,.5032346354445623975 ] 
dist 178=[-.15710638031188984257,.50310020958318297619] 
dist 179=[-.13940887544176214578,.50072472790605601625] 
dist 180=[-.15147080887692953488,.49835218276452295576] 
dist 181=[-.18355439991930021862,.28646320610136528982] 
dist 182=[-.2142711096807897076 ,.2744550515461930137 ] 
dist 183=[-.2510845758268730934 ,.27120484633471220748] 
dist 184=[-.28531835442222472352,.19209164324354644906] 
dist 185=[-.30574307877975289854,.19583879169203417289] 
dist 186=[-.3199291689817635252 ,.19747082903369141487] 
dist 187=[-.32927352022771458653,.19786807186048673331] 
dist 188=[-.33594657292140151984,.19760144662903115715] 
dist 189=[-.3394756115100917889 ,.19474781957315770209] 
dist 190=[-.34136980671478443645,.19367769246348452377] 
dist 191=[-.34152133315074112428,.18967107676637640228] 
dist 192=[-.29222500154571707091,.18848432881920256819] 
dist 193=[-.31826678408548301181,.17650756520336635493] 
dist 194=[-.33709931126077986366,.17355116653603618975] 
dist 195=[-.35099062009655286797,.16982797876229442876] 
dist 196=[-.36153303506005298154,.16822244668098953557] 
dist 197=[-.36700307668138940201,.1276208727648242572 ] 
dist 198=[-.36980081693072207284,.12188211426859720676] 
dist 199=[-.3696796672290847412 ,.11019810514692393133] 
dist 200=[-.33443539215045854824,.10697187358298690822] 
dist 201=[-.32839564903634151632,.09442063499801244493] 
dist 202=[-.32103779441889307051,.09166741592622312129] 
dist 203=[-.31966919517372346733,.08584454111565291116] 
dist 204=[-.31671042600286881436,.08409930442753914221] 
dist 205=[-.314842091206765879  ,.07697318923634047959] 
dist 206=[-.31597456293378547141,.07518587297285649344] 
dist 207=[-.31696013393219520265,.07457179565036374368] 
dist 208=[-.31675113062240255215,.07539770981038876662] 
dist 209=[-.31170702584186174702,.07708422709047596006] 
dist 210=[-.30972842075415495935,.10429435664543729528] 
dist 211=[-.30410049780434305546,.14744806864397406096] 
dist 212=[-.30152347841702781557,.18797722007739889434] 
dist 213=[.01948097287475242186,.21950269884108457629] 
dist 214=[.03614395606646575419,.25043172829976905442] 
dist 215=[.04015534994584668662,.2885810861725244815 ] 
dist 216=[.07398305201040788973,.32463615306625721472] 
dist 217=[.07934349879857477278,.34720913533686106254] 
dist 218=[.08262268034118815359,.36420106562419866701] 
dist 219=[.07106685090946482170,.37798821327179461192] 
dist 220=[.05193889951321210394,.38863862817395088522] 
dist 221=[.03144886161780763639,.39311521372730837213] 
dist 222=[.01445844201706434185,.3946449791607157634 ] 
dist 223=[-.03902766310957556943,.39400502613843646832] 
dist 224=[-.09700276303512318541,.14725737562749850134] 
dist 225=[-.13486202013083488347,.15026178875943861466] 
dist 226=[-.16518682937646270534,.15259632145200966595] 
dist 227=[-.19310091298095425687,.15488592435413644678] 
dist 228=[-.21728419343495827571,.15771111481928463407] 
dist 229=[-.23272379888469966328,.16027278714132749891] 
dist 230=[-.24469510066103460581,.16151083160999088017] 
dist 231=[-.25504049115875111412,.16201579834108412796] 
dist 232=[-.26374732454109578978,.16165208689049470699] 
dist 233=[-.26918105446899776933,.16075840198128715882] 
dist 234=[-.27539776001767626928,.16005812864562008323] 
dist 235=[-.27935481708317763738,.15747112925435457645] 
dist 236=[-.28005339018349599865,.15630848916388613803] 
dist 237=[-.27726702438381246437,.14791336680182432747] 
dist 238=[-.27556768305664740929,.14598160119351645604] 
dist 239=[-.26112968240272313727,.14082522246252446942] 
dist 240=[-.16524504506999963855,.13916805425729926126] 
dist 241=[-.16590391234739898727,.12873723310078823606] 
dist 242=[-.16571053419426183158,.12629312787500897061] 
dist 243=[-.1655019403104960718 ,.12180678997048510634] 
dist 244=[-.15813540058500011402,.12171795926834655938] 
dist 245=[-.15605286251739523647,.12936406643098000504] 
dist 246=[-.1546368245466482846 ,.1355923810544132433 ] 
dist 247=[-.1537854356463035703 ,.14150069944588663827] 
dist 248=[-.11711968198456230975,.14649385018536786583] 
dist 249=[-.11207117596334665287,.14907081903347367353] 
dist 250=[-.10226163425553094053,.15036660686028514428] 
dist 251=[-.09965338701927281342,.15042845654150519107] 
dist 252=[-.09022604956245159515,.14944233732380695092] 
dist 253=[-.08791455855392345669,.14877626876387185836] 
dist 254=[-.08443104286939812904,.14645464221184717744] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 0, 1, 1, 1, 2] 
dist 0=[54.039408756576070273  ,54.039408756576070273  ] 
dist 1=[52.740159389779849807  ,54.890344989782933951  ] 
dist 2=[50.481743347564926963  ,55.358015904933972227  ] 
dist 3=[48.091896658004241226  ,55.657366862302339603  ] 
dist 4=[46.267703711028359983  ,55.835726098200196219  ] 
dist 5=[44.501421354573722307  ,55.960948393993706998  ] 
dist 6=[42.343018456063245368  ,56.047330870015428998  ] 
dist 7=[40.087577549747270283  ,56.083534965227357771  ] 
dist 8=[37.933620038803216732  ,55.688516181816640452  ] 
dist 9=[35.433018998410862150  ,52.685843137874750162  ] 
dist 10=[31.792616705311215287  ,52.160423820627633118  ] 
dist 11=[28.044765967837234616  ,51.271286809607973929  ] 
dist 12=[25.114799080864158693  ,51.017537405987371240  ] 
dist 13=[22.211267394210550577  ,50.205026706824311749  ] 
dist 14=[18.568815286407739189  ,49.931867541181802973  ] 
dist 15=[14.711674804359125349  ,49.654042190663671328  ] 
dist 16=[10.950130858427481744  ,49.083222067766673275  ] 
dist 17=[6.5217886107739499905 ,29.450835743069220977  ] 
dist 18=[0                     ,27.779548999496508284  ] 
dist 19=[15.066323718527349394  ,23.824569100046184481  ] 
dist 20=[12.565005758456937215  ,23.231193351346118261  ] 
dist 21=[9.9882373222369574136 ,17.821640544005349583  ] 
dist 22=[6.6258530253591139679 ,16.850809420367341245  ] 
dist 23=[3.3337908965980628958 ,15.596354020136403312  ] 
dist 24=[1.0374842314895504643 ,15.312633311576299713  ] 
dist 25=[-.9765327354659569405 ,11.529864163355202142  ] 
dist 26=[-3.1417512131532794277 ,9.9689252724326818091 ] 
dist 27=[-5.2494764764882732859 ,5.4633383400901936213 ] 
dist 28=[-7.0345431867094400531 ,5.1016680328417446993 ] 
dist 29=[-8.9345234278710729783 ,3.1680859899512387181 ] 
dist 30=[-11.502607918885644100  ,2.8522211410967540706 ] 
dist 31=[-13.973965376202185512  ,2.2093044556313985439 ] 
dist 32=[-15.487776412798210407  ,2.0947807902360702588 ] 
dist 33=[-16.600181898458267286  ,-2.4880101170393300074 ] 
dist 34=[-17.467401031191944247  ,-2.9098472725764113311 ] 
dist 35=[-18.134876850514702214  ,-3.7077183038286133588 ] 
dist 36=[-18.448827501132771879  ,-3.8833702943561250987 ] 
dist 37=[-18.591147170687364294  ,-4.3448330891179887077 ] 
dist 38=[-18.592084862018024516  ,-4.3781782790171298693 ] 
dist 39=[-17.736625105264349510  ,-4.2699924839452125980 ] 
dist 40=[-17.549951144341103417  ,-3.9451901970889166837 ] 
dist 41=[-17.189721363185609158  ,-3.5492606737389758056 ] 
dist 42=[-17.067359406209580928  ,-3.1568766964825314160 ] 
dist 43=[-16.500396432635631869  ,-2.6941946369635961282 ] 
dist 44=[-16.350194914359115198  ,-2.0170513242048666720 ] 
dist 45=[-15.933136715527442594  ,-1.2554556727970176930 ] 
dist 46=[-15.794212948923755380  ,-.4553768280521540687 ] 
dist 47=[-10.831360499032913337  ,.5256997064904354310 ] 
dist 48=[-10.764093689038795612  ,2.8942701207468834421 ] 
dist 49=[-3.4497808547191711705 ,5.3204652540758331234 ] 
dist 50=[-3.0644656986783216410 ,6.9425343530029254354 ] 
dist 51=[-.72277729715477133799,8.2848689690544299758 ] 
dist 52=[-.31394680460756872657,9.5949328823865112090 ] 
dist 53=[.49159233111628649227,10.782953347507627856  ] 
dist 54=[.68540769827368293218,11.838649799068572532  ] 
dist 55=[2.4672985714429841503 ,13.067596411179950077  ] 
dist 56=[2.7419879197102470998 ,13.776141318621061138  ] 
dist 57=[3.0466389786730715911 ,14.239467651454216430  ] 
dist 58=[3.0469559085625638688 ,14.489621301215377633  ] 
dist 59=[2.9213562903731238571 ,14.711225540822555301  ] 
dist 60=[2.6167457696867336877 ,14.760077079832187598  ] 
dist 61=[2.1235468879320330606 ,14.726203197315769426  ] 
dist 62=[1.2453793653408235738 ,14.407899360259775551  ] 
dist 63=[.3394244440416533164 ,7.1013756711396010188 ] 
dist 64=[-.2647150072126126510 ,7.0889329440052987682 ] 
dist 65=[-.7625844428486046832 ,1.9757139318955720172 ] 
dist 66=[-1.2446241386501508006 ,1.5590369168382202176 ] 
dist 67=[-1.6789220604766208532 ,.61316316722182272848] 
dist 68=[-1.9863635039640811154 ,.44137030237451749698] 
dist 69=[-2.2595396429199484526 ,-.7113743014889819639 ] 
dist 70=[-2.5572012873639426181 ,-.9089909995118211126 ] 
dist 71=[-2.8282094163814407008 ,-1.2743376585968967980 ] 
dist 72=[-3.1357978970219116870 ,-1.3534717300165629488 ] 
dist 73=[-3.7995656024535315060 ,-2.2169743039338146817 ] 
dist 74=[-4.2213736111736641271 ,-2.3415783661049929011 ] 
dist 75=[-4.5462534068298652135 ,-2.4408737780224629388 ] 
dist 76=[-4.8232825614931751954 ,-2.2461146382931300088 ] 
dist 77=[-5.0479955238690372925 ,-1.9679129203717447798 ] 
dist 78=[-5.1641359953214880376 ,-1.5042653821793726113 ] 
dist 79=[-5.2228783081918430885 ,-1.0286890494554310180 ] 
dist 80=[-5.2321674144067361157 ,-.70288942949375274127] 
dist 81=[-1.4498273975603008925 ,-.42533133686023379882] 
dist 82=[-1.4019554455484944019 ,-.14214116146683366432] 
dist 83=[-.9294307202265576772 ,.12203882728406410642] 
dist 84=[-.8414592113895608763 ,.44708599616151636273] 
dist 85=[-.7318485794324739004 ,.77149197961023848775] 
dist 86=[-.7050452240884657146 ,1.0177990102870736136 ] 
dist 87=[.0178953067840776102 ,1.2536684460739321414 ] 
dist 88=[.1048057238989872825 ,1.5364687246026888475 ] 
dist 89=[.2966250601254172731 ,1.8000594617403100980 ] 
dist 90=[.33087215484651890923,1.9592976407740362596 ] 
dist 91=[.5407484781932821298 ,2.0765650137311972802 ] 
dist 92=[.5737990432864339086 ,2.1924414248297594696 ] 
dist 93=[.64074708304214536011,2.2845812756246870339 ] 
dist 94=[.6511349231122132558 ,2.3288410412118459285 ] 
dist 95=[.6193997503915808782 ,2.3492660914317021230 ] 
dist 96=[.3045158730710470911 ,2.3500925297379464083 ] 
dist 97=[-.0183142752514276152 ,2.3063009689739132815 ] 
dist 98=[-.2400172869629584367 ,2.2922002610983146613 ] 
dist 99=[-.4296040767368678098 ,2.2393242195560611587 ] 
dist 100=[-.6243327394906500570 ,2.2250037196565812107 ] 
dist 101=[-.8069386974753814557 ,2.0700582771024341173 ] 
dist 102=[-.9481728183953350093 ,2.0325670798258252528 ] 
dist 103=[-1.0858442435702071381 ,1.9871292552367215123 ] 
dist 104=[-1.2542427117634440315 ,1.9669941706488542297 ] 
dist 105=[-1.4124472839560810066 ,1.4666792345491635581 ] 
dist 106=[-1.5094575612772524685 ,1.4930547097610702330 ] 
dist 107=[-1.5800197629674870406 ,1.5164033789819838613 ] 
dist 108=[-1.6327257409707498761 ,1.5320874501208828995 ] 
dist 109=[-1.6707725102072966220 ,1.5450380509007441955 ] 
dist 110=[-1.6828547554664740669 ,1.5574374180350404657 ] 
dist 111=[-1.6845936909242922471 ,1.5661561949206653164 ] 
dist 112=[-1.6813860061912538211 ,1.5644609591373734482 ] 
dist 113=[-1.8479844160802318467 ,1.5571028087320116189 ] 
dist 114=[-2.0015661964175390636 ,1.5503650212999430290 ] 
dist 115=[-2.1264551450076770762 ,1.5029706188810835354 ] 
dist 116=[-2.1929659754768066794 ,1.4889867799422664919 ] 
dist 117=[-2.2297868564652392906 ,1.4539061731593976375 ] 
dist 118=[-2.2380825511179130920 ,1.4397050849019958482 ] 
dist 119=[-2.2010482411337090813 ,1.2382748452964433264 ] 
dist 120=[-2.1899766556875813723 ,1.2058326879995234797 ] 
dist 121=[-2.1797716947677572413 ,1.1235904966213750596 ] 
dist 122=[-2.1681722919660029126 ,1.1046374976914798166 ] 
dist 123=[-2.1566130092945387908 ,.96319616929572645627] 
dist 124=[-2.1009158416455468152 ,.93328071565201407242] 
dist 125=[-1.7754877961364365115 ,.88451224270158453036] 
dist 126=[-1.7511162694430036918 ,.8705428184506607661 ] 
dist 127=[-1.7484882478945659156 ,.57676199368944261516] 
dist 128=[-1.7469966749088975090 ,.72125292614394375086] 
dist 129=[-.34144112794204039565,.83442210668850897014] 
dist 130=[-.22761630041744165897,.93424948661436650757] 
dist 131=[.02602649925625478742,1.0177329291035514853 ] 
dist 132=[.0747413990838279231 ,1.0656943243026275029 ] 
dist 133=[.36811836860920701857,1.0967837739855876558 ] 
dist 134=[.41745100287723545078,1.1129554163279217319 ] 
dist 135=[.51672796674419102744,1.1228859767806245407 ] 
dist 136=[.54009752750625108396,1.1290738688371898121 ] 
dist 137=[.69667068336589495654,1.1914375806039056010 ] 
dist 138=[.72000126510253633284,1.3073675899309398260 ] 
dist 139=[.71691997163876099079,1.3971511498612902825 ] 
dist 140=[.67702074474950985342,1.4745753416991155394 ] 
dist 141=[.61660775635292449204,1.5380185579439746778 ] 
dist 142=[.47655966090806150145,1.5720184513722996742 ] 
dist 143=[.2699672664635874565 ,1.5909216531668031864 ] 
dist 144=[.1273713313422641494 ,1.5941294158756929927 ] 
dist 145=[.00456226870280159154,.05966135681095769444] 
dist 146=[-.1230896199005107079 ,.03053119863274427396] 
dist 147=[-.24384882589645423973,-.1576256454415273825 ] 
dist 148=[-.3432533617306833557 ,-.18972749389925598735] 
dist 149=[-.4460118404477947389 ,-.2509007768854658446 ] 
dist 150=[-.55258342633893583775,-.26459803790956339526] 
dist 151=[-.66552559389409238589,-.39284923140968872879] 
dist 152=[-.73755889335443161472,-.41221659884610966253] 
dist 153=[-.79331406761502506857,-.4224561603938583201 ] 
dist 154=[-.84131257920527412981,-.40879415006861443403] 
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dist 173=[-.0460599743350627076 ,.52171774960219767829] 
dist 174=[-.0357835019851190147 ,.53348379013202629984] 
dist 175=[-.0131547539507250446 ,.5393358382855765322 ] 
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dist 177=[-.03178352176780310550,.41565935472438096839] 
dist 178=[-.07046887554290374303,.4672021088696091717 ] 
dist 179=[-.10704025382348770677,.5064124003125762783 ] 
dist 180=[-.13583747359461302208,.53899736713563187391] 
dist 181=[-.16440122081770756082,.5649831794528697741 ] 
dist 182=[-.20004119097819888219,.57786114558704099223] 
dist 183=[-.23388828708359355046,.58447075931361262504] 
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dist 185=[-.27166233209616910141,.5691212191549005571 ] 
dist 186=[-.28536773351697895739,.56419647042848147682] 
dist 187=[-.29628410785406961   ,.55784308363755862353] 
dist 188=[-.30152042852368455531,.55489370943113046691] 
dist 189=[-.30385431390025020875,.54297930515585497189] 
dist 190=[-.30392305937351478289,.53881385443824959781] 
dist 191=[-.23735689580143549713,.5274316708603088998 ] 
dist 192=[-.27625385859494557426,.52254310211565299123] 
dist 193=[-.30648506185948760349,.17463377321509783967] 
dist 194=[-.33274739306085919565,.14329767945313095863] 
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dist 196=[-.36631862535523710388,.05938336910117322654] 
dist 197=[-.37333727570990358216,-.02018984356311242323] 
dist 198=[-.37551967842548031547,-.03389284411638499044] 
dist 199=[-.4027425762962694577 ,-.06357263517971443283] 
dist 200=[-.4571483165288009849 ,-.06943896624267468090] 
dist 201=[-.5076668387749093872 ,-.11436634368475279911] 
dist 202=[-.5377571819549578447 ,-.1220515068362468955 ] 
dist 203=[-.5586131620272395055 ,-.12256326003196619227] 
dist 204=[-.5722866543182843160 ,-.1134229813877034376 ] 
dist 205=[-.5816321947069164317 ,-.09879802237223202915] 
dist 206=[-.5852195147150656536 ,-.06528825090896932688] 
dist 207=[-.5852726517154900664 ,.01086207155505207733] 
dist 208=[-.5842535435602187283 ,.06237860373362160843] 
dist 209=[-.08202567352091535254,.10564805961448914646] 
dist 210=[-.07306079646553622672,.148894389793269339  ] 
dist 211=[-.02052619527459255337,.18970635438188940124] 
dist 212=[-.01128456275932041826,.2205457026297398473 ] 
dist 213=[.00751841784588878207,.24984172525463568755] 
dist 214=[.01222728686570991347,.2846384694907872281 ] 
dist 215=[.05133201597226448240,.31685764260465124354] 
dist 216=[.05762719604656125925,.3447853960541915830 ] 
dist 217=[.06337742988000607207,.3758234555973686222 ] 
dist 218=[.06214269689628788232,.3943967305174282635 ] 
dist 219=[.05776721898375432786,.4073736362535280125 ] 
dist 220=[.04904698005148903284,.4160827092079939052 ] 
dist 221=[.03549003796567400188,.4217444528380941973 ] 
dist 222=[.00546385325500923126,.4226677159984893867 ] 
dist 223=[-.02598698659209902951,.4215467176856810699 ] 
dist 224=[-.04906082188030655165,.4198883669046083027 ] 
dist 225=[-.10811998354900764445,.2897955022505121203 ] 
dist 226=[-.14682191228641547304,.28306135904564972023] 
dist 227=[-.17797168919315802098,.27256117156021144091] 
dist 228=[-.20689922403444719289,.2700848723625039561 ] 
dist 229=[-.23213618253673889302,.24669697889339894105] 
dist 230=[-.24856118645953575791,.24138246974341950714] 
dist 231=[-.26165389436743357423,.23434599517864921458] 
dist 232=[-.2735953858377444188 ,.23164563422108002798] 
dist 233=[-.2837580565939192597 ,.16750988084445291348] 
dist 234=[-.2897535337859963022 ,.15871643939151474274] 
dist 235=[-.2938349228867356602 ,.13975783554622148447] 
dist 236=[-.2963607691776821747 ,.13437954348052962906] 
dist 237=[-.2976865715693461813 ,.11229495949983141182] 
dist 238=[-.2972559663177662706 ,.10800257662087430034] 
dist 239=[-.2953163000812542473 ,.11480620179542917467] 
dist 240=[-.2938149708899900083 ,.13692552442646300339] 
dist 241=[-.20188009653843619738,.15433311841928149048] 
dist 242=[-.20151286998075113934,.16982358894385978277] 
dist 243=[-.19643523722289140858,.1828663886831850502 ] 
dist 244=[-.19460390249558149916,.19050846350352205936] 
dist 245=[-.19238140881402005886,.19564481638868817337] 
dist 246=[-.19116063521213730356,.19869025648842315661] 
dist 247=[-.15563859003848508456,.20064812600458596061] 
dist 248=[-.14648467247862169011,.20144538603563817826] 
dist 249=[-.11098296348282678685,.20154148883747419965] 
dist 250=[-.10787837965444543268,.20090519773723459557] 
dist 251=[-.10055565245521736014,.19932416825750604358] 
dist 252=[-.09118672803639057608,.19829709813326534371] 
dist 253=[-.07005590723427587736,.19510880685560953785] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 0, 1, 2] 
dist 0=[65.737539591960360379  ,65.737539591960360379  ] 
dist 1=[65.585946979158718609  ,65.723608640001392638  ] 
dist 2=[65.147516166281321749  ,65.737539591960360379  ] 
dist 3=[64.414150995968864986  ,65.236973282397840230  ] 
dist 4=[63.084839199936123892  ,65.057052913407135066  ] 
dist 5=[61.548507373468263873  ,63.544228031681191380  ] 
dist 6=[59.988476048467851181  ,63.344332040272333420  ] 
dist 7=[58.109378671068813349  ,60.889789307045919316  ] 
dist 8=[55.298955596147602605  ,60.597490101536578596  ] 
dist 9=[52.098441220076348902  ,59.849530994139681498  ] 
dist 10=[48.661635371080550660  ,59.553664543685153058  ] 
dist 11=[44.386885167902366274  ,59.334890840401754057  ] 
dist 12=[37.840289932534805760  ,59.163750889184459484  ] 
dist 13=[31.241441033647691191  ,42.442571107641055819  ] 
dist 14=[26.757949646877497917  ,41.457298299139910693  ] 
dist 15=[22.957006837781663288  ,40.368513096091930065  ] 
dist 16=[19.083465430674693213  ,40.118939070992511771  ] 
dist 17=[15.450027134322222526  ,30.566901349747479780  ] 
dist 18=[12.607607554237604684  ,29.359427545298066166  ] 
dist 19=[9.7935168805134894642 ,26.923087754096596954  ] 
dist 20=[6.2726843878142280706 ,26.294419362645888318  ] 
dist 21=[2.8969680341790599298 ,24.052942013393931051  ] 
dist 22=[.6620765385009577784 ,23.575186034172705633  ] 
dist 23=[-1.1721125237675488356 ,22.867297041357920378  ] 
dist 24=[-2.9480564638826067806 ,22.669558879599375664  ] 
dist 25=[-4.5600958975852437152 ,5.8706443567251226064 ] 
dist 26=[-5.7403307709556858956 ,4.4691645803912913907 ] 
dist 27=[-6.8378603912430820096 ,1.3905477305711519774 ] 
dist 28=[-8.1209663517325741889 ,.82683094115257136192] 
dist 29=[-9.3034217416595303270 ,-2.6029567678818685002 ] 
dist 30=[-9.9990773686442085083 ,-3.1701644428878030011 ] 
dist 31=[-10.479122630452444546  ,-4.2795337075925082927 ] 
dist 32=[-11.759918768326570540  ,-4.5294428237299333527 ] 
dist 33=[-13.467542004740629973  ,-6.2997341457355483729 ] 
dist 34=[-14.517433894893356622  ,-6.5841877646663863780 ] 
dist 35=[-15.290554659205604388  ,-6.6339939657483667066 ] 
dist 36=[-15.892617124357135038  ,-6.3344655422851434390 ] 
dist 37=[-16.342576550874271352  ,-5.8457486519369633359 ] 
dist 38=[-16.508112582173067886  ,-5.1281843300760994203 ] 
dist 39=[-16.564089781211220809  ,-4.1083591928207277071 ] 
dist 40=[-16.576246251113560250  ,-2.2556182474519168712 ] 
dist 41=[-9.2822357433221411083 ,.1299476596522942903 ] 
dist 42=[-9.2052365998836579289 ,1.7424317892052949534 ] 
dist 43=[-9.1591550995159039508 ,3.0944403736011563801 ] 
dist 44=[-9.1438438977638596681 ,4.4411428478118037436 ] 
dist 45=[-2.8394362437968555213 ,5.6789727976989779472 ] 
dist 46=[-2.3198188812309569508 ,6.5968062665707568688 ] 
dist 47=[-1.1922570546164081533 ,7.4550601972612491235 ] 
dist 48=[-.93887909257047330233,8.4554162069522190229 ] 
dist 49=[.29463391581831314156,9.3733668283089105562 ] 
dist 50=[.50818329014104470349,9.9029233943689648904 ] 
dist 51=[.99220160377452833091,10.249455552745939662  ] 
dist 52=[1.0688402695876989978 ,10.437193353402635202  ] 
dist 53=[1.6290865506380507034 ,10.550455800427435464  ] 
dist 54=[1.7104307932507288875 ,10.599681433162293218  ] 
dist 55=[1.6801615209396744104 ,10.611476437276672167  ] 
dist 56=[1.4902595308417355596 ,10.576043548920371405  ] 
dist 57=[1.2128877669832085878 ,8.9648832682247111365 ] 
dist 58=[.83351613721724795114,8.7430268692930051770 ] 
dist 59=[.3072263158868441642 ,8.1566538063719435986 ] 
dist 60=[-.5564642304550851982 ,7.4983222561309070707 ] 
dist 61=[-1.4308242393419236488 ,.58723275277313205482] 
dist 62=[-1.9997258132102947687 ,.41976973696665907393] 
dist 63=[-2.4533872754558737244 ,.18507930158699729765] 
dist 64=[-2.8679434323039950776 ,.1201169781667781441 ] 
dist 65=[-3.2253911876865064105 ,-1.0186456590524279542 ] 
dist 66=[-3.4512020321810989889 ,-1.1580318628265741219 ] 
dist 67=[-3.6238372178265330436 ,-1.4424850567651107861 ] 
dist 68=[-3.7691472221609501330 ,-1.5033287131802835755 ] 
dist 69=[-3.8890943432089856362 ,-1.7192245106933660173 ] 
dist 70=[-3.9605235185298903928 ,-1.7549325165725487466 ] 
dist 71=[-4.0102651439915783360 ,-1.7445332554283514400 ] 
dist 72=[-4.0436229025550120689 ,-1.6480112984726459756 ] 
dist 73=[-4.0640734705720323087 ,-1.5195760974589747720 ] 
dist 74=[-4.0622861172094994600 ,-1.4130841007946640356 ] 
dist 75=[-4.0439630826695232752 ,-1.3029096837858518510 ] 
dist 76=[-4.0303963518295109682 ,-1.1596822966238078430 ] 
dist 77=[-2.3585488813287703952 ,-.8626918042241934326 ] 
dist 78=[-2.2570986294614194199 ,-.42227476494081370982] 
dist 79=[-1.9967544993641824351 ,-.01520967901596570451] 
dist 80=[-1.9566704801312717600 ,.40088374306576138191] 
dist 81=[-1.5282001479522746967 ,.79014697380106986014] 
dist 82=[-1.4450648483119659391 ,1.0901823021654710149 ] 
dist 83=[-1.3488467742561156904 ,1.3818756482570124757 ] 
dist 84=[-1.3242177011443532014 ,1.7378706622463453395 ] 
dist 85=[-1.0797269950306215449 ,2.0723520079860358980 ] 
dist 86=[-1.0782589317651338856 ,2.2782179982220726635 ] 
dist 87=[-1.0830307696889745139 ,2.4290192218983801413 ] 
dist 88=[-1.0972865863058837482 ,2.5438121144694615707 ] 
dist 89=[-1.1130811641842916482 ,2.6318056926359021785 ] 
dist 90=[-1.1239822201992501755 ,2.6756854023080146406 ] 
dist 91=[-1.1331308815590705762 ,2.6956079318437906142 ] 
dist 92=[-1.1419712390837093562 ,2.6961462283129488281 ] 
dist 93=[-1.1496626386126600065 ,2.6938372201521037329 ] 
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dist 95=[-1.1572552813207987866 ,2.7853354331067395898 ] 
dist 96=[-1.1587071150059040629 ,2.7884163381196519290 ] 
dist 97=[-1.1586431771706712001 ,2.7449745368340886708 ] 
dist 98=[-1.1556216425765096335 ,2.7266995602602064832 ] 
dist 99=[-1.1497559821637266696 ,2.6886388319349317266 ] 
dist 100=[-1.1444048794891230395 ,2.6721268569116021995 ] 
dist 101=[-1.1242785112544939955 ,2.5801954281526147466 ] 
dist 102=[-1.1161884015474364302 ,2.5568639720255071808 ] 
dist 103=[-1.0916243049524215228 ,2.4757405031129519593 ] 
dist 104=[-1.0804306956435407583 ,2.4614974406859885662 ] 
dist 105=[-1.2246065507760921832 ,1.6885777537781576319 ] 
dist 106=[-1.3859357468932202694 ,1.6746738109084562209 ] 
dist 107=[-1.5639050155727670807 ,1.6415351165826635098 ] 
dist 108=[-1.8108861098327656906 ,1.6280761598306346520 ] 
dist 109=[-2.0491306935224906091 ,1.1290352049239902354 ] 
dist 110=[-2.1922456008814175539 ,1.2347173311915631987 ] 
dist 111=[-2.2929683622084656460 ,1.3181351041905780912 ] 
dist 112=[-2.3620684906719704954 ,1.3927021695028776108 ] 
dist 113=[-2.4115674474343400807 ,1.4556569278113875203 ] 
dist 114=[-2.4340743010614534586 ,1.4927533359249135100 ] 
dist 115=[-2.4411119007142637455 ,1.5179150926859133673 ] 
dist 116=[-2.4377772239021171821 ,1.5332605408781582892 ] 
dist 117=[-2.1830812489479689704 ,1.5401658719641091140 ] 
dist 118=[-2.1403921355348988338 ,1.5395907572210947141 ] 
dist 119=[-1.9925130563636758258 ,1.5204721375966069003 ] 
dist 120=[-1.7570978926094701470 ,1.5167139333630489141 ] 
dist 121=[-1.7774287920565177107 ,1.4197064655050647404 ] 
dist 122=[-1.7901831194468007696 ,1.3949578213060722799 ] 
dist 123=[-1.7918971728388874859 ,1.3779688228073092227 ] 
dist 124=[-1.7874428768059068016 ,1.3712055926777440731 ] 
dist 125=[.01811823039170902848,.90117301567394150938] 
dist 126=[.10914092795452444717,1.0616259069259756026 ] 
dist 127=[.29759694434741820518,1.1852804993387934344 ] 
dist 128=[.32250476746902630654,1.2908882712466162642 ] 
dist 129=[.43000239873477588669,1.3771425581172250416 ] 
dist 130=[.44910635686901093022,1.4235728717786167031 ] 
dist 131=[.47271297481854368633,1.4496874995147922879 ] 
dist 132=[.47194176881556516477,1.4558919877567491874 ] 
dist 133=[.46202389338538167975,1.4370249461444267212 ] 
dist 134=[.43994929532923608762,1.4318607881064541542 ] 
dist 135=[.40477758484156771663,1.4273245654265496020 ] 
dist 136=[.34260506423838183907,1.4225001663823751837 ] 
dist 137=[.26794743079187184688,1.4178908887770105377 ] 
dist 138=[.18296336093639544368,1.4142091252109383555 ] 
dist 139=[.07426022361807391382,1.4105147598921045248 ] 
dist 140=[-.09502970209078840767,1.4058510367165002831 ] 
dist 141=[-.26513118954362481254,.8213062748569868048 ] 
dist 142=[-.37707216349177174479,.80912046979291535298] 
dist 143=[-.46768678827194370418,.77461671048970455049] 
dist 144=[-.55270204873896549641,.76683087539335297959] 
dist 145=[-.62745915843738931809,.69490490487299312748] 
dist 146=[-.67714613608494447855,.67893133368743086369] 
dist 147=[-.71790872274771051294,.65737510223787019931] 
dist 148=[-.81788058019618756078,.64942546736166394206] 
dist 149=[-.96108108911886705274,.4646932661603847783 ] 
dist 150=[-1.0518191766039203353 ,.43951116201814671536] 
dist 151=[-1.1213928859886186737 ,.38480989823928581066] 
dist 152=[-1.1801497209187399819 ,.36928138497122353918] 
dist 153=[-1.2273679049561545991 ,.30523396997127631247] 
dist 154=[-1.2509035311442553893 ,.29298030522197980964] 
dist 155=[-1.2618531589554958346 ,.26130330011012719424] 
dist 156=[-1.2631624166168152391 ,.25670008393997705397] 
dist 157=[-.20344973488068371653,-.02490038658936786174] 
dist 158=[-.24382718961080426654,.07708782622311588109] 
dist 159=[-.27658437163351293811,.16281161493924166082] 
dist 160=[-.30747728723810278236,.25236805990939190558] 
dist 161=[-.33478364600878890446,.33531228035591891341] 
dist 162=[-.35322849511375017256,.396174078202584868  ] 
dist 163=[-.36870310228823060206,.45243540553212056426] 
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dist 165=[-.39717796913706708746,.57655400683973543909] 
dist 166=[-.40294808076965951736,.61260171981193050252] 
dist 167=[-.40542001072009255281,.63831082059262003051] 
dist 168=[-.40527925694780689937,.65658606878121191096] 
dist 169=[-.39571749312000836071,.66942575243404870656] 
dist 170=[-.39228557167191793657,.6734486472657946005 ] 
dist 171=[-.3893643511904269094 ,.67353680646832551721] 
dist 172=[-.38690657015531018143,.67122755111334771893] 
dist 173=[-.28005951963894013539,.5453149492330761105 ] 
dist 174=[-.26733870209229471753,.53121813756894762086] 
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dist 176=[-.23054993940438647861,.48675168353364894732] 
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dist 185=[-.44902246805260190375,.40025820172362897466] 
dist 186=[-.45451962657817325223,.40030445957407796611] 
dist 187=[-.45646500920365609922,.39859646140798253698] 
dist 188=[-.45589233538918074167,.3967245863174892059 ] 
dist 189=[-.36227731262746218156,.10026272253033872701] 
dist 190=[-.40629904398908225667,.07855302768623114402] 
dist 191=[-.43991036715300003323,.05327448446639227937] 
dist 192=[-.46805810721401631063,.07000530848720915427] 
dist 193=[-.49051064882516690603,.08797625970175311360] 
dist 194=[-.50139775232756272049,.10568828535304362403] 
dist 195=[-.50697840143002954549,.12657845850737731589] 
dist 196=[-.50825566802200485141,.15722969897019109559] 
dist 197=[-.49962759675550767324,.18861435552672543283] 
dist 198=[-.5023366879131866887 ,.21243083386332484767] 
dist 199=[-.50210628243637977033,.23523269020810571786] 
dist 200=[-.50115545535722434179,.26256944722798302948] 
dist 201=[-.4914110122180025996 ,.29068453410964571802] 
dist 202=[-.48813681875084012921,.31659191307360071154] 
dist 203=[-.47759969284428539855,.34580999676376332099] 
dist 204=[-.47372437562467595487,.38713430932244605802] 
dist 205=[-.33364797797200243187,.42706457830043520266] 
dist 206=[-.33715057730794788082,.45072070768948849252] 
dist 207=[-.33817226936176401714,.46695495691962079634] 
dist 208=[-.33771931851458416669,.47727323603159291009] 
dist 209=[-.33075503674360364218,.4841200650632433137 ] 
dist 210=[-.32818566399389976328,.48650361784170251416] 
dist 211=[-.32263618408893800468,.48607800107163310386] 
dist 212=[-.32033293496402182379,.4851106023846295473 ] 
dist 213=[-.27259119500892756697,.47235611753047741694] 
dist 214=[-.26515431547825203521,.49665314651269630571] 
dist 215=[-.24779691318912262253,.51263816487905218981] 
dist 216=[-.24260002571813879906,.52143229068746844612] 
dist 217=[-.21676414659789224663,.52677381512652909234] 
dist 218=[-.21125447448123556652,.52898298169530004464] 
dist 219=[-.19926484634578833592,.52931877872573720875] 
dist 220=[-.19554497336523368031,.52769788306432508546] 
dist 221=[-.07640093219393965903,.27000842477135615281] 
dist 222=[-.10886399768329857195,.27400556008902623841] 
dist 223=[-.14341805319825379162,.27564001589510921992] 
dist 224=[-.19309092315235495237,.27568744780396369063] 
dist 225=[-.23844205994734909588,.27219189057801540282] 
dist 226=[-.27156200042021820289,.27058358083348443398] 
dist 227=[-.3020242856027411181 ,.26632459309105738619] 
dist 228=[-.3367720447464917468 ,.26433600473733651557] 
dist 229=[-.36854857392844809131,.23095970180511945948] 
dist 230=[-.38715601076294981346,.22553016151842047795] 
dist 231=[-.39965746700482530193,.21231841040116235384] 
dist 232=[-.40707153039086226181,.20861113442448141826] 
dist 233=[-.4116905974043137942 ,.1871270412656870631 ] 
dist 234=[-.4130404092831209099 ,.1824948038934003144 ] 
dist 235=[-.4122526317337534315 ,.17340340938107918937] 
dist 236=[-.41124972325447736991,.17075907939609512335] 
dist 237=[-.31154480329810393467,.09671373070905323744] 
dist 238=[-.3004662468382838761 ,.13435490437883241432] 
dist 239=[-.27165032298956061877,.16453040707722549961] 
dist 240=[-.26701467782884060223,.19234950759742003485] 
dist 241=[-.2176417136426136285 ,.21647904334295557115] 
dist 242=[-.20779883160682008684,.23193375259609848556] 
dist 243=[-.19641786376538031222,.24397238728124753964] 
dist 244=[-.19298097071831222027,.25447215771255756296] 
dist 245=[-.13119237983293684325,.26333924863526142111] 
dist 246=[-.12348426145629608817,.2688637718620042922 ] 
dist 247=[-.10601997627869713765,.27298919554377606324] 
dist 248=[-.10183726525147381945,.27627433442506311268] 
dist 249=[-.07933487038488632708,.27876112696485685819] 
dist 250=[-.07506342950378857837,.27970135863327994703] 
dist 251=[-.06598186466321546323,.27968653376075613001] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 1, 2, 1, 2] 
dist 0=[65.068589130221285085  ,65.068589130221285085  ] 
dist 1=[64.489920103064357288  ,65.270090324822473953  ] 
dist 2=[63.563477420371664225  ,65.496029568669065807  ] 
dist 3=[62.203696204401873458  ,65.652277679396608009  ] 
dist 4=[60.263273590497455040  ,65.605821881577007268  ] 
dist 5=[57.018129348734910945  ,65.458924182618849090  ] 
dist 6=[53.642659963037381379  ,65.306620025725106875  ] 
dist 7=[51.181780721585795837  ,64.937762444595288687  ] 
dist 8=[48.914781184534105270  ,63.916372606955770177  ] 
dist 9=[46.313468459778661109  ,60.812916717045273448  ] 
dist 10=[43.689873031426481904  ,60.108314789378473444  ] 
dist 11=[39.346583046516135610  ,59.102168655955542147  ] 
dist 12=[33.085435755680941684  ,58.757057960950460005  ] 
dist 13=[28.825861567477238902  ,58.103919531684303528  ] 
dist 14=[25.208348217977811124  ,57.776226202451372384  ] 
dist 15=[21.510920012777438351  ,55.440973307528003037  ] 
dist 16=[18.035400576034685081  ,50.042031826010138554  ] 
dist 17=[15.303796177947054007  ,28.756909363201376693  ] 
dist 18=[12.587239659169610156  ,26.457374033387428783  ] 
dist 19=[9.1713226648719641968 ,25.789710732239717857  ] 
dist 20=[5.8873616452033237600 ,24.974719399264014822  ] 
dist 21=[3.6974837040986755141 ,24.777331320594193234  ] 
dist 22=[1.8827081366755768457 ,11.969284039099719198  ] 
dist 23=[.09635432044440793519,10.270459100335309187  ] 
dist 24=[-2.0316622336994095180 ,9.8739248790728214114 ] 
dist 25=[-4.5878356060878019177 ,2.7803260428424641784 ] 
dist 26=[-6.9187112823601722987 ,1.0486532233548763755 ] 
dist 27=[-8.6360912006873161980 ,-.74597855528505946503] 
dist 28=[-10.238665476275991772  ,-1.2553676431021346882 ] 
dist 29=[-12.111146735489157094  ,-2.7418281390780984358 ] 
dist 30=[-13.844276319011286360  ,-3.0069979517258547639 ] 
dist 31=[-14.890307061999699807  ,-3.7633672348651091596 ] 
dist 32=[-15.637398005086853825  ,-4.5424244245923284960 ] 
dist 33=[-16.176498462665848673  ,-5.3663569821917397014 ] 
dist 34=[-16.568193616704314867  ,-5.0207612777808598922 ] 
dist 35=[-16.726438388288568173  ,-4.4401173766879973600 ] 
dist 36=[-16.766765938074421893  ,-3.5791309162965732687 ] 
dist 37=[-16.737372779856417526  ,-2.1146194554842831876 ] 
dist 38=[-11.094888112468809148  ,-.10855243608947258861] 
dist 39=[-11.035211064769668623  ,1.5799667274464831861 ] 
dist 40=[-10.992634611132868501  ,2.9950355760680276217 ] 
dist 41=[-9.6719247398632294270 ,4.4030437476645635688 ] 
dist 42=[-9.4639859099909202978 ,5.6959324650535851984 ] 
dist 43=[-9.0010254136108269352 ,6.6519361605051744925 ] 
dist 44=[-8.8560814403575653570 ,7.5430815990983887381 ] 
dist 45=[-8.2032461449358373447 ,8.5774575393983674152 ] 
dist 46=[-8.0662226035152762650 ,9.5248822901182834735 ] 
dist 47=[-7.6998654215590946576 ,10.069112673567592504  ] 
dist 48=[-7.6235562766673246440 ,10.421788725169340453  ] 
dist 49=[-2.6548747839949048588 ,10.604707391106837633  ] 
dist 50=[-2.1729358294002822778 ,10.713363323680013878  ] 
dist 51=[-1.1412865337121226282 ,10.769782226921083828  ] 
dist 52=[-.89727434662121780803,10.798929030340349157  ] 
dist 53=[.18335969505654086704,10.799130953588502323  ] 
dist 54=[.37754954339530430183,8.8662854591526985298 ] 
dist 55=[.78835768418786947827,8.6205052566406158315 ] 
dist 56=[.87999960078046853772,7.9716046439202221116 ] 
dist 57=[.43489285838737546634,7.8566960129376672362 ] 
dist 58=[-.03111441260252833342,6.7040085346439769531 ] 
dist 59=[-.40439273167704310874,6.4689603223322159156 ] 
dist 60=[-.780085255902687947  ,6.1760657655967547231 ] 
dist 61=[-1.2557547609491263453 ,6.0670887381673685527 ] 
dist 62=[-1.7100625699965885886 ,3.6932995301518176287 ] 
dist 63=[-2.0005740636986601804 ,3.3843363142883915119 ] 
dist 64=[-2.2259119909141747507 ,2.4283945612007028894 ] 
dist 65=[-2.4203022084986651807 ,-1.3073315886339914319 ] 
dist 66=[-2.5792599795721875580 ,-1.3416405176687881689 ] 
dist 67=[-2.9300186984316065558 ,-1.2931241857186326940 ] 
dist 68=[-3.3271775109688486957 ,-1.1888871010502656286 ] 
dist 69=[-3.6646436115572573640 ,-.98209044067044229274] 
dist 70=[-3.8689779980644532538 ,-.76192983522408353414] 
dist 71=[-4.0150062911777496578 ,-.60438786908997015894] 
dist 72=[-4.1198732260039695971 ,-.4599345138173616992 ] 
dist 73=[-4.1987756837006400431 ,-.29942622022186727781] 
dist 74=[-4.2411958288376034378 ,-.14398195233094182506] 
dist 75=[-4.2652752579634627754 ,-.0159941174167149311 ] 
dist 76=[-4.2709280391811425100 ,.11598160357449840889] 
dist 77=[-4.2645588664160480874 ,.28736659649941848631] 
dist 78=[-4.2481339720830647829 ,.4531948712080247222 ] 
dist 79=[-4.2064779011883934339 ,.56303047280482805258] 
dist 80=[-4.1830839309344064275 ,.65264057123900100325] 
dist 81=[-1.5569742425933665985 ,.82270912664428922175] 
dist 82=[-1.3272149109576493155 ,.99786025855330668705] 
dist 83=[-1.0134140027240935940 ,1.2043690641134985963 ] 
dist 84=[-.70584673861322772176,1.3971730175956736387 ] 
dist 85=[-.27006600994274514495,1.5176536988953639038 ] 
dist 86=[-.13357418622768389434,1.8195089760649390137 ] 
dist 87=[-.19927423344751913167,2.1456971254411274895 ] 
dist 88=[-.25672940393256806627,2.5393773425907935210 ] 
dist 89=[-.31757215841636512011,2.9069767801068975459 ] 
dist 90=[-.37558387198650022865,3.1291172589465388010 ] 
dist 91=[-.4217542144876866954 ,3.2869183939002261580 ] 
dist 92=[-.46787244747282231055,3.3978308069377369814 ] 
dist 93=[-.52567549862427692716,3.4783414867465876405 ] 
dist 94=[-.58040982993013518306,3.5148534046142925509 ] 
dist 95=[-.61429417838246368036,3.5260848573908469152 ] 
dist 96=[-.63922891577351734052,3.5220328913610696321 ] 
dist 97=[-.65828534204044644057,1.3156239465619212608 ] 
dist 98=[-.67197552964084859661,1.2815399288695163943 ] 
dist 99=[-.67551578057690473844,1.2693061590213090707 ] 
dist 100=[-.74209296167567291359,1.0500907032858809250 ] 
dist 101=[-1.0097393486761165105 ,1.0318366233433081695 ] 
dist 102=[-1.2082114049759490643 ,1.0139398628506020254 ] 
dist 103=[-1.3936837673559950867 ,1.0059327496527432519 ] 
dist 104=[-1.6094812462979890521 ,.98862377990175799704] 
dist 105=[-1.8087817355498880927 ,.98077608381639784537] 
dist 106=[-1.9284418299838979469 ,.97438328087734874349] 
dist 107=[-2.0124872590547679791 ,.96839225442094951911] 
dist 108=[-2.0696970892483937957 ,.19537459870583323886] 
dist 109=[-2.1096404087761343891 ,.13951949831688968802] 
dist 110=[-2.1248055654154222659 ,.03508633818413573729] 
dist 111=[-2.1258097844709456908 ,.08493847416313418401] 
dist 112=[-2.1215967170628559069 ,.37376089787230377606] 
dist 113=[-1.6370313027832701831 ,.66371303396581101669] 
dist 114=[-1.6337418437292841353 ,.8532091426198609886 ] 
dist 115=[-1.6104706365848631091 ,1.0050261499067975331 ] 
dist 116=[-1.6034103436351858095 ,1.1446678426325646964 ] 
dist 117=[-1.5071535801843383111 ,1.2654288076327663517 ] 
dist 118=[-1.4825898963661882080 ,1.3419236862379233825 ] 
dist 119=[-1.4571270989558460242 ,1.4004572722286507186 ] 
dist 120=[-1.4432949962050847969 ,1.4495588640235866615 ] 
dist 121=[-1.0786997134158867585 ,1.4895726427087908767 ] 
dist 122=[-1.0281663255625556507 ,1.5118532227229424510 ] 
dist 123=[-.97809597056961453345,1.5253218351998525963 ] 
dist 124=[-.89612761691605178092,1.5301914313506958944 ] 
dist 125=[-.78535701329721373795,1.5291029948251720920 ] 
dist 126=[-.76131762561039856201,1.5244070660868427822 ] 
dist 127=[-.71126162893151995801,1.5056938754746939015 ] 
dist 128=[-.6966661506417696545 ,1.4946917523157139966 ] 
dist 129=[.27985318565214033715,.95331716313147851686] 
dist 130=[.27162373074423632616,.98291882744776926169] 
dist 131=[.24272427816161684812,.9945059273712827288 ] 
dist 132=[.18057975455409551989,.99856131029990988529] 
dist 133=[.07642583257092923899,.99811524633158348496] 
dist 134=[-.03014965838392611930,.53502761833825490669] 
dist 135=[-.11276665950749346662,.54966345769156188252] 
dist 136=[-.19292768371029965831,.56110815972048219786] 
dist 137=[-.27137693662175167247,.56620307905646672929] 
dist 138=[-.34254683002995357232,.56761395975716504436] 
dist 139=[-.39366960581131037657,.56682372669232889666] 
dist 140=[-.43980706458204777738,.37464128280121878006] 
dist 141=[-.49109060142859764922,.35814853813959484487] 
dist 142=[-.53789162486594056851,.31555279986074070784] 
dist 143=[-.56614716556983953695,.30940001437161091074] 
dist 144=[-.58618064707053974763,.23856490414172437455] 
dist 145=[-.60018036519069052201,.2248280569366631455 ] 
dist 146=[-.60941218649312529333,.21023258337206988307] 
dist 147=[-.61125321856273747919,.2075003696488643426 ] 
dist 148=[-.60882482114626638649,.08859735558135021935] 
dist 149=[-.60762892728462273233,.16099289496456951577] 
dist 150=[-.51081804114563664731,.23360824456020139461] 
dist 151=[-.520530552761728748  ,.2809442738915060444 ] 
dist 152=[-.52518928838482903074,.31873135261586461521] 
dist 153=[-.52613781274958167817,.35325447302312290021] 
dist 154=[-.51250353484586519512,.38294723128404970892] 
dist 155=[-.50875919962191947733,.40146477964233968842] 
dist 156=[-.50633353437764254704,.41529922766458697862] 
dist 157=[-.50509032472282872275,.42630899391501550932] 
dist 158=[-.39131944901621017205,.43474893453795319362] 
dist 159=[-.37561937167137121364,.43833166508795265602] 
dist 160=[-.34620086908918491228,.43902564966291605252] 
dist 161=[-.33853895755779351924,.43834622970751848382] 
dist 162=[-.31223112667351557007,.43110036931143912012] 
dist 163=[-.30510606683664792526,.42842409269590433802] 
dist 164=[-.29781921919562615835,.41888831543708318342] 
dist 165=[-.29476149030588430179,.41576814625608689572] 
dist 166=[-.26004302773217050064,.15023406069660613459] 
dist 167=[-.25852277749504484086,.17357707989216095246] 
dist 168=[-.25353361015238418836,.19225579415484819263] 
dist 169=[-.25157670287864638682,.20941878057345050815] 
dist 170=[-.24726769532060010142,.22426891207697782769] 
dist 171=[-.24550906963295434357,.2337203213915609904 ] 
dist 172=[-.07507239592560475789,.24101779529285621414] 
dist 173=[-.06015589578723733251,.24727509484803738014] 
dist 174=[-.02694489397822275416,.25203276657622507938] 
dist 175=[-.02025338236085745680,.25334696391253783203] 
dist 176=[.01852794718141230826,.25328230935706306581] 
dist 177=[.02518734492839472732,.25253751964736944514] 
dist 178=[.03890156514917759751,.24320469603588183238] 
dist 179=[.04216737439106673788,.24778306622033971086] 
dist 180=[.01162734982353249896,.27579068090461488491] 
dist 181=[-.04774348637097660571,.29336117180177412803] 
dist 182=[-.10714753394774363624,.30663619334752005884] 
dist 183=[-.14646594161931781484,.31750458700892324338] 
dist 184=[-.17854350060557757399,.32598592047763554634] 
dist 185=[-.20905882152703724047,.32973667949988693874] 
dist 186=[-.23617869768439773169,.33096555295598082175] 
dist 187=[-.2547093398311155263 ,.33067034364083669365] 
dist 188=[-.27046845131235414827,.08040663465696320926] 
dist 189=[-.28653034627729326948,.07828759010899872630] 
dist 190=[-.30056245164534664656,.05666136260043929230] 
dist 191=[-.3082234144578331132 ,.0527401224572995858 ] 
dist 192=[-.31267137155262843423,.04755162288028410907] 
dist 193=[-.31388526301528811369,.04587651911429184307] 
dist 194=[-.31346174784893398213,.04549733713031632330] 
dist 195=[-.31242143154850246402,.04721353364392149922] 
dist 196=[-.30872808727615965631,.05077748378480690612] 
dist 197=[-.30661095468098825173,.05777949836965158501] 
dist 198=[-.25332683555787002339,.06527361123589943394] 
dist 199=[-.2554242519486736222 ,.07080093791445215976] 
dist 200=[-.25668759644125121434,.07593177364400259826] 
dist 201=[-.25650083145428543445,.08184560569964017938] 
dist 202=[-.25528500030762854792,.08779459133803494039] 
dist 203=[-.25440164481074309183,.09306652549162088217] 
dist 204=[-.14148785508228787   ,.09884281833220864674] 
dist 205=[-.14133873359553430861,.10680494085831837054] 
dist 206=[-.1396203556820239038 ,.114742566855951731  ] 
dist 207=[-.13916365249861753696,.12042172678209210613] 
dist 208=[-.13123687805806722182,.12552728966191117755] 
dist 209=[-.12920572008537691284,.13117731128776377955] 
dist 210=[-.12742380680782038408,.13673957870114138438] 
dist 211=[-.1264554545833214533 ,.14149583725184941193] 
dist 212=[-.09509675645356122265,.14657096716401785957] 
dist 213=[-.09078775663296632133,.15340694585745860664] 
dist 214=[-.08222365114961377094,.15989712460542781279] 
dist 215=[-.07991916801978540825,.16359268488812708285] 
dist 216=[-.07135060819497725723,.16595008683815475   ] 
dist 217=[-.06936824827163503205,.16710010778739484261] 
dist 218=[-.06581503549955320500,.16739010394597011617] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 1, 1, 0, 1] 
dist 0=[39.252816266720789620  ,39.252816266720789620  ] 
dist 1=[37.873064985846476822  ,40.343464159023458549  ] 
dist 2=[35.735288998850460481  ,41.326703452044083693  ] 
dist 3=[33.557545458335334260  ,42.166633750473769430  ] 
dist 4=[32.018037763446813377  ,42.684901728038455569  ] 
dist 5=[30.648299354833489451  ,43.066620245864593336  ] 
dist 6=[29.148095291266533495  ,43.361013170273397285  ] 
dist 7=[27.674129324000336125  ,43.583682658021269427  ] 
dist 8=[26.408817652463024101  ,43.678977050488650758  ] 
dist 9=[25.049827654629507602  ,43.697995296570693767  ] 
dist 10=[23.201133623161591221  ,43.674580782033868548  ] 
dist 11=[21.352157797527205500  ,43.482359646884164858  ] 
dist 12=[19.991722004289077881  ,43.409686661986435826  ] 
dist 13=[18.722529359640557701  ,43.118466247989754480  ] 
dist 14=[17.237601495030168825  ,43.044904679362804988  ] 
dist 15=[15.717723352311390521  ,41.831254621299262049  ] 
dist 16=[14.308380994684581455  ,41.051014774346291032  ] 
dist 17=[12.701205928189583235  ,34.156826975910478049  ] 
dist 18=[10.389897127159475976  ,33.777380298486616921  ] 
dist 19=[8.1072583684658983331 ,31.852308166500107838  ] 
dist 20=[6.6145140223918623175 ,31.477553739920285562  ] 
dist 21=[5.4043671529432801911 ,30.665081093017156425  ] 
dist 22=[4.2514791896118344154 ,30.426382968743135038  ] 
dist 23=[3.2133718288787161879 ,28.116985916366319347  ] 
dist 24=[2.4619943368888459465 ,27.750100433463515484  ] 
dist 25=[1.7705970421738206323 ,26.749692408761274836  ] 
dist 26=[.97199563557968754877,25.565799229415221505  ] 
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dist 162=[-.13041964559147603757,.4448588992660394095 ] 
dist 163=[-.1349426707606426635 ,.28432778986818882367] 
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dist 186=[-.26332350537177123451,.13927746106437746482] 
dist 187=[-.24523375392613374904,.1404819486418245432 ] 
dist 188=[-.2417567079855902851 ,.14104874792247568747] 
dist 189=[-.23554205841964966484,.14116461582462591409] 
dist 190=[-.23361179154962397867,.14073131389608027866] 
dist 191=[-.22553116248126295531,.1395668394540948237 ] 
dist 192=[-.22313794281603743958,.13883838863814465018] 
dist 193=[-.21766737499829314703,.06944172033479721341] 
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dist 195=[-.06715957421687023353,.04869566526458400949] 
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dist 201=[-.09097526502510028567,.19558916753593392461] 
dist 202=[-.09827391018564124364,.21966889078761487576] 
dist 203=[-.10347883428653044668,.2420221308435901367 ] 
dist 204=[-.10717485409829570817,.25533868355625467371] 
dist 205=[-.10988387041862944581,.26457412931724100481] 
dist 206=[-.11115124894694114422,.27064303937829684085] 
dist 207=[-.11160357022314533199,.27473273081243493275] 
dist 208=[-.11148816860772370214,.27607056210649867417] 
dist 209=[-.02530115259781994666,.27587844386357865486] 
dist 210=[-.02074774062176115001,.27520555696279486398] 
dist 211=[-.04828878607043717015,.00967265223093098091] 
dist 212=[-.06889009430482134706,.01870761039115998849] 
dist 213=[-.08757027259621862949,.02705873953014255970] 
dist 214=[-.11235555755259720173,.03332040958660957391] 
dist 215=[-.13467984844522452219,.03923887420948816196] 
dist 216=[-.15047180381479401218,.04622120919772371038] 
dist 217=[-.16448599067448935963,.05269333205975498647] 
dist 218=[-.17971688250914701111,.05657651052332120885] 
dist 219=[-.19350479182784584946,.05930000969575124567] 
dist 220=[-.20176140999905619662,.06114577512098359683] 
dist 221=[-.20753851341454602766,.06245529848883057974] 
dist 222=[-.21143306129507316593,.06303967550023535331] 
dist 223=[-.21385686649689101457,.06320417290779521167] 
dist 224=[-.21428185468639581697,.06309934520991299243] 
dist 225=[-.21297761137238564076,.06184121896195946753] 
dist 226=[-.2126214883547018277 ,.06694223082208252377] 
dist 227=[-.14098701535796703917,.07065037577561442820] 
dist 228=[-.13504221971694798824,.07342788155558773781] 
dist 229=[-.12011478980453304727,.08064745316811015245] 
dist 230=[-.11855129047518680407,.09520044940765818359] 
dist 231=[-.10564735128374749315,.10794228376273289543] 
dist 232=[-.10287655793953604627,.11632143973006377364] 
dist 233=[-.09875234665783611654,.12309973556800494163] 
dist 234=[-.09742662097366756413,.12945409562070026797] 
dist 235=[-.06817677572313582500,.13494947022463685141] 
dist 236=[-.06420082976903207045,.1383003767414254736 ] 
dist 237=[-.05660967143943453323,.14071786446454406336] 
dist 238=[-.05589845742820286651,.14248883121098598024] 
dist 239=[-.05392430213436624225,.14370527536545431447] 
dist 240=[-.05331484126528624315,.14391012772594243759] 
dist 241=[-.03492657615611751814,.14345100959659477683] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 2, 0, 0, 0, 1] 
dist 0=[53.653897937541877541  ,53.653897937541877541  ] 
dist 1=[53.314187313601139589  ,53.877886927581389524  ] 
dist 2=[52.855623125390567345  ,54.060054697658819986  ] 
dist 3=[52.156978549342251683  ,54.232701457571822721  ] 
dist 4=[51.147382377618283959  ,54.385643300597902819  ] 
dist 5=[49.447039454893727570  ,54.489038215825605492  ] 
dist 6=[47.428643604276013859  ,54.575372923260950561  ] 
dist 7=[45.148929214756164387  ,54.659989664625134584  ] 
dist 8=[42.110697536142994135  ,54.723950122851195593  ] 
dist 9=[37.691226706783952806  ,54.727856713322884843  ] 
dist 10=[33.076819095243706423  ,54.687838247301617408  ] 
dist 11=[29.888011376667508783  ,54.594492386889151229  ] 
dist 12=[27.126216929424849758  ,54.428311226632303733  ] 
dist 13=[24.216741350348176945  ,53.946209443043245001  ] 
dist 14=[21.426644438203684835  ,51.047833839444498855  ] 
dist 15=[19.141285894084374545  ,48.864586376308565124  ] 
dist 16=[16.781664638672396024  ,38.700967567036336339  ] 
dist 17=[13.694443486315964548  ,37.362786404546914536  ] 
dist 18=[10.666234494999604753  ,34.100012035293730238  ] 
dist 19=[8.5419860765263601669 ,33.614468772526760124  ] 
dist 20=[6.6656633305922993590 ,28.770117852710551561  ] 
dist 21=[4.6272305299183282485 ,27.861611496549286322  ] 
dist 22=[2.6297253516635676491 ,26.796284176025953349  ] 
dist 23=[.9163009759656411405 ,26.560975379531578215  ] 
dist 24=[-.92631973252374358746,18.612258806976464786  ] 
dist 25=[-3.4410848100862808799 ,17.623630629825806839  ] 
dist 26=[-5.8778475440905492065 ,15.596065106596607164  ] 
dist 27=[-7.4090311478722073084 ,15.072890678223822078  ] 
dist 28=[-8.5798686050399454480 ,13.188324646684135610  ] 
dist 29=[-9.5764683695761360910 ,12.807885886503459166  ] 
dist 30=[-10.394171844783847217  ,12.187578309321971828  ] 
dist 31=[-10.850226474883689403  ,12.040229199098281124  ] 
dist 32=[-11.133945465979368186  ,.69581060080529690308] 
dist 33=[-11.263468942393948890  ,-.26072258793513294481] 
dist 34=[-11.327636880017584726  ,-2.3119413510431400306 ] 
dist 35=[-11.350092006182636672  ,-2.7166410299012391606 ] 
dist 36=[-11.349607202681029280  ,-4.8297474800014988481 ] 
dist 37=[-11.321325717312408739  ,-5.1769191131088754853 ] 
dist 38=[-11.279819052016024310  ,-5.8861097787990889236 ] 
dist 39=[-12.165007232850130675  ,-6.0137421623125971601 ] 
dist 40=[-13.294379099552267529  ,-4.8760121448155850450 ] 
dist 41=[-13.977905861412973213  ,-3.4784585871682464980 ] 
dist 42=[-14.468731406764655371  ,-2.5241175278309010469 ] 
dist 43=[-14.828264925859773987  ,-1.4705949273193186098 ] 
dist 44=[-15.084868617221180005  ,-.3941311157619844086 ] 
dist 45=[-15.164476209502605845  ,.6882678032727369305 ] 
dist 46=[-15.174396473879032440  ,1.6914406139327158171 ] 
dist 47=[-15.152477088625098672  ,2.4517593104145142882 ] 
dist 48=[-1.6354119283444162258 ,3.1797790409289826191 ] 
dist 49=[.0633831333352332869 ,4.0540851007872041487 ] 
dist 50=[.6821388558952774404 ,4.8735677222011749769 ] 
dist 51=[1.2386908612557419935 ,5.3827974698345082968 ] 
dist 52=[1.3313363292524770302 ,5.7623709793653802184 ] 
dist 53=[1.9597366798104920638 ,6.0643921591154513650 ] 
dist 54=[2.0601022064821829632 ,6.3009088040915661974 ] 
dist 55=[2.2452495177524767505 ,6.4190128096447504464 ] 
dist 56=[2.2811851517912051759 ,6.7245378044779656925 ] 
dist 57=[2.3246436676477705873 ,7.1033284346697084921 ] 
dist 58=[2.0486362598862069332 ,7.3955843019367697111 ] 
dist 59=[1.8499830651726947314 ,7.6466288966790017347 ] 
dist 60=[1.6708486588502603920 ,7.8522452579581445943 ] 
dist 61=[1.4725466562724287877 ,7.9631069705751151970 ] 
dist 62=[1.2778983912967998426 ,8.0258109081624232236 ] 
dist 63=[.7150577606516680636 ,8.0391172321397051914 ] 
dist 64=[-.53228216926180904918,6.2541573822244168780 ] 
dist 65=[-1.3695810609433633734 ,6.1234639076819222731 ] 
dist 66=[-2.0655428145595826964 ,5.7738719054334890064 ] 
dist 67=[-2.7490361720576094926 ,5.7056627026280495191 ] 
dist 68=[-3.3709314423353607408 ,5.0608060439221379084 ] 
dist 69=[-3.8211537917540718696 ,4.9256139431516477888 ] 
dist 70=[-4.2311772121197058521 ,4.7473688846075407959 ] 
dist 71=[-4.6927010371103330266 ,4.6833287687908121528 ] 
dist 72=[-5.1143233914763436971 ,3.2628479421619193173 ] 
dist 73=[-5.3651433150652676444 ,3.0732858156419272243 ] 
dist 74=[-5.5384658703493090568 ,2.6627577520910175031 ] 
dist 75=[-5.6508626012295519322 ,2.5520259523780962905 ] 
dist 76=[-5.7231851102045229138 ,2.0842665323211564123 ] 
dist 77=[-5.7366322651507152621 ,1.9964822707279514344 ] 
dist 78=[-5.7235418603485992712 ,1.7791326883384118822 ] 
dist 79=[-5.7001179873295994644 ,1.7447628490594764821 ] 
dist 80=[-4.0217367368974882327 ,.04027556708447259402] 
dist 81=[-4.2561397548984142410 ,.09330257380406841376] 
dist 82=[-4.4191517584272259233 ,.16084972963156043468] 
dist 83=[-4.5276962303598648359 ,.25176663973577787541] 
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dist 88=[-4.1933712065972777032 ,1.3540192552162973478 ] 
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dist 91=[-3.9270709003619101225 ,2.2599651851470587161 ] 
dist 92=[-3.7281050532384113011 ,2.7574636361391214746 ] 
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dist 164=[-.3284959999637198991 ,.27411699585388208782] 
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dist 166=[-.3339561052228742316 ,.28037729358467219762] 
dist 167=[-.3337506528440881122 ,.28003378387676952012] 
dist 168=[-.3322545325574446354 ,.27974250522281541126] 
dist 169=[-.3308393922201241372 ,.20982560296804897941] 
dist 170=[-.18629859584888139063,.20287933883280263669] 
dist 171=[-.17615542861773493934,.18458026113732272711] 
dist 172=[-.1509839823818483492 ,.18169730127245784934] 
dist 173=[-.14703219738796229918,.14964352066276783672] 
dist 174=[-.10825417769190560579,.14322064962102171372] 
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dist 176=[-.12750849051851962974,.13947845475021007349] 
dist 177=[-.1474852104009321867 ,.15620350629882555444] 
dist 178=[-.15970213929657803496,.17160317817518439006] 
dist 179=[-.16855557891653263394,.18115715781598411822] 
dist 180=[-.17511291514890100731,.18824874671379377619] 
dist 181=[-.1800460141991490447 ,.19382399009730693832] 
dist 182=[-.18241940855661654448,.19799299999035932597] 
dist 183=[-.18336792261799654146,.19947419542661240215] 
dist 184=[-.18330434677197308223,.1997930552976764964 ] 
dist 185=[-.15841881205253213676,.19932221597521825274] 
dist 186=[-.17432615910221928843,.07169411111357697646] 
dist 187=[-.18595605416321449923,.06836033846305075221] 
dist 188=[-.19477127500753978974,.06130934134549041622] 
dist 189=[-.2016006734378735973 ,.05933087744421737351] 
dist 190=[-.2053069604623508005 ,.05138160566878067021] 
dist 191=[-.20743144629801316472,.04976861051837873742] 
dist 192=[-.20794888207267666348,.04597460249863450392] 
dist 193=[-.18870118010594929759,.04502630704186983809] 
dist 194=[-.1854512860023325913 ,.03964523365108137265] 
dist 195=[-.18108506761081537774,.03840136284726858239] 
dist 196=[-.17933813194227399265,.03759205937011983326] 
dist 197=[-.17579101606237617352,.03771805991766323791] 
dist 198=[-.17447152781714711979,.03833918416440607491] 
dist 199=[-.17368766429756494922,.03964391024804286146] 
dist 200=[-.173429473792062381  ,.04169076184145216501] 
dist 201=[-.09612199574034721918,.04527101481807425660] 
dist 202=[-.11306437293624713656,.04897978010551120352] 
dist 203=[-.12363431197694225294,.05153934296197910014] 
dist 204=[-.13155577632393456526,.06573332418316416603] 
dist 205=[-.13792980112257574413,.08672445785445725652] 
dist 206=[-.14285952068000752611,.10445901984688908634] 
dist 207=[-.14501725131307288483,.12204941578108020674] 
dist 208=[-.14596296510210624502,.14401364931356420587] 
dist 209=[-.14605592066348593114,.16490556370914755606] 
dist 210=[-.14047876544741597434,.17821724169889880884] 
dist 211=[-.1390922844651177196 ,.18850881789357239697] 
dist 212=[-.13623413362352892562,.19735038501602414883] 
dist 213=[-.13517369120326639367,.20456794759213078071] 
dist 214=[-.1297662207742242839 ,.20837951025049509615] 
dist 215=[-.12847230318420103861,.21041902734177322867] 
dist 216=[-.12402365415729157457,.21056557837890444803] 
dist 217=[-.12336348701990165013,.06709947185655197883] 
dist 218=[-.06188621689672712201,.06595885006685660895] 
dist 219=[-.07886085488446668952,.06547621468665977768] 
dist 220=[-.09470679078732982922,.06508090817533214810] 
dist 221=[-.10858913221476458867,.06470819935032895682] 
dist 222=[-.11772910388424552085,.06438428761043516963] 
dist 223=[-.12513306502543853413,.06418329292180547347] 
dist 224=[-.1320886169790943089 ,.06403699097609232330] 
dist 225=[-.13814525951178100799,.06393107704653513157] 
dist 226=[-.14196272232084098085,.06387316299521181011] 
dist 227=[-.14486507138201611188,.06391808310471294837] 
dist 228=[-.14727096141916211541,.06404843375966270195] 
dist 229=[-.14916942769395666994,.06433073724703125315] 
dist 230=[-.15004749698450561618,.06468913368465447531] 
dist 231=[-.1503454274216077595 ,.06512266958111524265] 
dist 232=[-.14993106154083980032,.06569313735444244513] 
dist 233=[-.08822932606085071314,.06659728789895100131] 
dist 234=[-.08772520705644605048,.06750502876208590971] 
dist 235=[-.08577207540948026093,.06808964521026720833] 
dist 236=[-.08527797395045428261,.06854704164157737457] 
dist 237=[-.07940849459979543045,.06894725749407531443] 
dist 238=[-.07798614337393799800,.07271192805809953473] 
dist 239=[-.07640145533668339140,.07643960080397796674] 
dist 240=[-.07563199234316192767,.07989137346327987212] 
dist 241=[-.05603879478167523125,.08282260689502417795] 
dist 242=[-.05333622435619667972,.08447341885433527389] 
dist 243=[-.04774721098242291729,.08549970864808986398] 
dist 244=[-.04620086675008632116,.08593913805244117707] 
dist 245=[-.04013781150659941190,.08596589361742245100] 
dist 246=[-.03885366662822374598,.08579247285931768553] 
dist 247=[-.03606668042130398300,.08462195075193868638] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 1, 1, 2] 
dist 0=[56.310698864672515561  ,56.310698864672515561  ] 
dist 1=[54.997691031172266726  ,57.344132374348862058  ] 
dist 2=[53.371981701390613779  ,57.853531641275592338  ] 
dist 3=[51.203091745757216475  ,58.100944584890278152  ] 
dist 4=[47.721078138608731971  ,58.124340079434732172  ] 
dist 5=[44.149960471237320245  ,57.714913972974068878  ] 
dist 6=[41.625184658660190355  ,57.581019704230774162  ] 
dist 7=[39.378925118667895681  ,56.949983357251287915  ] 
dist 8=[36.919726536123537335  ,56.156743020609484485  ] 
dist 9=[34.505847801468573380  ,55.563383639212792550  ] 
dist 10=[32.440340444028179310  ,55.349034135627017607  ] 
dist 11=[30.229644446056371713  ,54.876142859117645501  ] 
dist 12=[27.235596163540673625  ,54.687470917093486436  ] 
dist 13=[24.254080543312964910  ,53.760420637598287569  ] 
dist 14=[22.093195578333357183  ,53.524156655668926111  ] 
dist 15=[20.113501899760700655  ,51.986815622364541421  ] 
dist 16=[17.855221239917626446  ,49.144731224051001646  ] 
dist 17=[15.581310294029086691  ,28.748655509914175021  ] 
dist 18=[13.538731682243834916  ,26.812174344306054289  ] 
dist 19=[11.266255533120815232  ,22.827038875323551921  ] 
dist 20=[8.0732109887036124990 ,22.536907102717749500  ] 
dist 21=[4.9375278575872135290 ,16.448874956145083877  ] 
dist 22=[2.8940220978431108696 ,15.552003263995109689  ] 
dist 23=[1.2501256090447312444 ,13.864741786264657453  ] 
dist 24=[-.2889837476141688170 ,13.485110313331196551  ] 
dist 25=[-1.6521461005140295826 ,9.5317535298427200992 ] 
dist 26=[-2.5932221884006070230 ,8.9519663265804538502 ] 
dist 27=[-3.4108974918033660110 ,7.8100487210887479984 ] 
dist 28=[-4.4816180611716965876 ,7.6501521173018945257 ] 
dist 29=[-6.4973134758167704508 ,-.44502928092797136027] 
dist 30=[-8.1362773374866779774 ,-1.1568830271563815558 ] 
dist 31=[-9.8215147932330357956 ,-2.6217802453649263883 ] 
dist 32=[-12.023356928002717294  ,-2.9483248394619469414 ] 
dist 33=[-14.117911781343647780  ,-4.2271665202050251106 ] 
dist 34=[-15.374825715837003233  ,-4.4607482715396646402 ] 
dist 35=[-16.267725874418723521  ,-4.4609158028948879393 ] 
dist 36=[-16.907618344301099217  ,-3.6369781641875002607 ] 
dist 37=[-17.381418744400216126  ,-2.7811462485221237897 ] 
dist 38=[-17.610318934983268021  ,-2.1835727076225076025 ] 
dist 39=[-17.706796430598632192  ,-1.6637739393234496250 ] 
dist 40=[-17.699092910207503507  ,-1.1177293252084551124 ] 
dist 41=[-16.159514023732717474  ,-.5994501157346419796 ] 
dist 42=[-15.896464643632212562  ,-.1902142299593979955 ] 
dist 43=[-15.417399755158991870  ,.2159892944217861494 ] 
dist 44=[-15.277318086903465102  ,.73078643445289911785] 
dist 45=[-14.729404591129038940  ,3.2698795485702322153 ] 
dist 46=[-14.568779580744586056  ,4.9872959409646885868 ] 
dist 47=[-14.259445194158379488  ,6.4303463558664512113 ] 
dist 48=[-14.156146987984961110  ,7.8747346868637326796 ] 
dist 49=[-3.6421177865699284378 ,9.2083405741736004318 ] 
dist 50=[-2.7332545975283671743 ,10.209396084362514997  ] 
dist 51=[-.74046608662426818001,11.158134726689369694  ] 
dist 52=[-.33029987439533139107,12.283069385954958906  ] 
dist 53=[1.3278303919298682464 ,13.325767962201272155  ] 
dist 54=[1.2830746718485666702 ,13.946366828789239217  ] 
dist 55=[1.1856805357584687752 ,14.376590125856972127  ] 
dist 56=[1.0656435026772956171 ,14.659569057886011465  ] 
dist 57=[.9412436794801837249 ,14.838620439667958455  ] 
dist 58=[.8263680839235722279 ,14.865477053004789879  ] 
dist 59=[.6970423333328716569 ,14.810535357669788100  ] 
dist 60=[.5149366727842937466 ,14.754504571351613730  ] 
dist 61=[.3323226207211066914 ,13.668307085365076139  ] 
dist 62=[.2009191169389949273 ,13.470108928925704107  ] 
dist 63=[.0822206134415699060 ,12.911099266301056609  ] 
dist 64=[-.21953453585115541352,12.191055801061195955  ] 
dist 65=[-.8991081779613830592 ,1.3955182317544131310 ] 
dist 66=[-1.4328274729632384786 ,1.4024098879498544093 ] 
dist 67=[-1.9610834209817883746 ,1.4110433664954571306 ] 
dist 68=[-2.6188903195946413776 ,1.4239945909219021476 ] 
dist 69=[-3.2434260820706012067 ,1.4354354382141823359 ] 
dist 70=[-3.6389535621423343792 ,1.4380262816173671803 ] 
dist 71=[-3.9419077799797143256 ,1.4343386667225774560 ] 
dist 72=[-4.1971141937588734393 ,1.4306266124842787426 ] 
dist 73=[-4.4016707162437767413 ,1.4025136430248377522 ] 
dist 74=[-4.5025517119615602041 ,1.3934649539176379095 ] 
dist 75=[-4.5523457403625069224 ,1.3602361153574704271 ] 
dist 76=[-4.5568079761890038958 ,1.3517758697936024086 ] 
dist 77=[-2.3431925966065424422 ,1.2153539196227570252 ] 
dist 78=[-2.3245873844175234195 ,1.1914705010809044278 ] 
dist 79=[-2.3026969850714183528 ,1.1229072304591688793 ] 
dist 80=[-2.2893838043184782790 ,1.1111129240859937200 ] 
dist 81=[-2.2495158313465125251 ,.9685450142422568767 ] 
dist 82=[-2.2324755490049624758 ,.9377640428089833771 ] 
dist 83=[-2.1965433743079381022 ,.9057474831810758335 ] 
dist 84=[-2.1817573318103023474 ,.9528137019078946210 ] 
dist 85=[.0107435234306850048 ,1.2069995015931133801 ] 
dist 86=[.1728911231621312008 ,1.3671196100632048395 ] 
dist 87=[.3774918322975808511 ,1.5042411634041497909 ] 
dist 88=[.3355240675869129980 ,1.6630439697905051240 ] 
dist 89=[.2683514034266034962 ,1.8080266721663471380 ] 
dist 90=[.1703862675975836323 ,1.9140799648156630900 ] 
dist 91=[.0314081843973365548 ,2.0119339653606361162 ] 
dist 92=[-.1993377475833559286 ,2.1242551478557060943 ] 
dist 93=[-.4355942993773209649 ,2.2246554688468416288 ] 
dist 94=[-.5965525337413461097 ,2.2749551450983703699 ] 
dist 95=[-.7327187117215834970 ,2.2998802126540222526 ] 
dist 96=[-.8701019284625290953 ,2.3031400873006877521 ] 
dist 97=[-.9972739940001391443 ,2.2744481207799682948 ] 
dist 98=[-1.0927165081640928333 ,2.2589529397309520563 ] 
dist 99=[-1.1829209183981156478 ,2.1749897105928019576 ] 
dist 100=[-1.2892014583699677396 ,1.9949233965775303902 ] 
dist 101=[-1.3868773803320934546 ,1.1201880343655576838 ] 
dist 102=[-1.4427637957043179604 ,1.0763007158059573432 ] 
dist 103=[-1.4785756956701818847 ,.97407366513967518652] 
dist 104=[-1.4961883542766178404 ,.94930864331974294042] 
dist 105=[-1.5041697891401217930 ,.80643905650115886881] 
dist 106=[-1.5017561043022648320 ,.77830392209865744844] 
dist 107=[-1.4931560408437243212 ,.72171476428899605911] 
dist 108=[-1.4859587763972453075 ,.70612587337651609944] 
dist 109=[-1.0378123519469206357 ,-.4672633284375308408 ] 
dist 110=[-1.2429633268081530880 ,-.49061034274564992075] 
dist 111=[-1.4016597031192611218 ,-.50338551621780156304] 
dist 112=[-1.5382541430019185360 ,-.48734903972356286864] 
dist 113=[-1.6503198483905348842 ,-.45693215091845018757] 
dist 114=[-1.7111414486229968404 ,-.40789751953967318759] 
dist 115=[-1.7460299432292580973 ,-.33593303294008702738] 
dist 116=[-1.7546099849497146201 ,-.21404086596911453038] 
dist 117=[-1.7450551024049989098 ,-.0887996167954392965 ] 
dist 118=[-1.7426898890748067301 ,-.0034731274144738184 ] 
dist 119=[-1.7407084298455646640 ,.0687994696488858601 ] 
dist 120=[-1.7387900404244135732 ,.1421914406141076886 ] 
dist 121=[-1.7371009612850172354 ,.2106532632913833519 ] 
dist 122=[-1.7360281757284689393 ,.2624937293231594153 ] 
dist 123=[-1.7352168848577781824 ,.3120016119621822493 ] 
dist 124=[-1.7345643945284705377 ,.3711614008715064074 ] 
dist 125=[-.37706287966727724574,.4261368267218365003 ] 
dist 126=[-.26725227805349352526,.4589518299881546757 ] 
dist 127=[-.02120890862105478274,.4817687195203133590 ] 
dist 128=[.02534708245093550745,.4968547528548816963 ] 
dist 129=[.2881551144440081246 ,.5076656440445646615 ] 
dist 130=[.2577186268742991429 ,.58940910138396279022] 
dist 131=[.2145578383845213809 ,.73777001347552855848] 
dist 132=[.1428545986128399964 ,.9233904201873150405 ] 
dist 133=[.0691970934206347502 ,1.1001046025147259848 ] 
dist 134=[.01824023377881244385,1.2129316180665145098 ] 
dist 135=[-.02575039231276161808,1.3004217546236287416 ] 
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dist 137=[-.11507651422675287285,1.4381360871838441915 ] 
dist 138=[-.14945362640389779958,1.4716259614352094977 ] 
dist 139=[-.18369751888022141124,1.4905358203811504563 ] 
dist 140=[-.22662422387032579865,1.4944537781106939156 ] 
dist 141=[-.26748819051883756465,.21523586880810808008] 
dist 142=[-.29350340211982664462,.2001931498587178545 ] 
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dist 150=[-.69086286504278023437,-.2910978972412476160 ] 
dist 151=[-.72059034041339694709,-.3414538954645730794 ] 
dist 152=[-.7406484587418823124 ,-.3499678032107780984 ] 
dist 153=[-.75464297636461917196,-.39502777387229576161] 
dist 154=[-.76017939878829715169,-.40216591236197630341] 
dist 155=[-.76062316976096659814,-.35682303400893487306] 
dist 156=[-.75940114992790550869,-.24940621541190073696] 
dist 157=[-.59544412852709851364,-.13919253892244548828] 
dist 158=[-.5769435361539697743 ,-.06303599130869858317] 
dist 159=[-.52869219086855774094,.00262905011827000907] 
dist 160=[-.52022457126567910393,.07098821239739371695] 
dist 161=[-.43639955900973915682,.13570623455518433347] 
dist 162=[-.42685931563917912834,.18684547712333011882] 
dist 163=[-.41873209887575124573,.23774620303314594184] 
dist 164=[-.41500738159338295741,.30151288415688060937] 
dist 165=[-.22201935939651548534,.36221929866638178174] 
dist 166=[-.20017671138736765409,.40091136749888433257] 
dist 167=[-.15278871860595970831,.43082285869796117505] 
dist 168=[-.14108295707397994077,.45649976205039173298] 
dist 169=[-.08843672807526232156,.47743703544835012703] 
dist 170=[-.07890992309575246755,.4884400464767631392 ] 
dist 171=[-.05673648318625249953,.49425441829388845775] 
dist 172=[-.05293752609473403550,.49508446033376361919] 
dist 173=[.07314538851159620505,.3786246751248275813 ] 
dist 174=[.08020285428498419225,.43210460477831177832] 
dist 175=[.08479266576721395360,.4732103807192265762 ] 
dist 176=[.08141920092461043066,.50812204448861851521] 
dist 177=[.07412944151593354539,.53634434559097792219] 
dist 178=[.06164260802930387568,.55075930395179503729] 
dist 179=[.04284994064758556730,.55850455901301248391] 
dist 180=[.00709983574125231568,.56011149535839146184] 
dist 181=[-.02965186673948389502,.55282973958759948472] 
dist 182=[-.0548432243792881703 ,.54951004922500412869] 
dist 183=[-.08600096165430482622,.54587331915927279899] 
dist 184=[-.12362587706714315476,.5432415592847350161 ] 
dist 185=[-.1580339699815278356 ,.53353578402314383112] 
dist 186=[-.1832488918232565321 ,.52976877304469164974] 
dist 187=[-.2065238196205180799 ,.51945399935525690029] 
dist 188=[-.2331922149127700519 ,.51490643372739481487] 
dist 189=[-.2576888255127281218 ,.17583519464893631947] 
dist 190=[-.2722989720605917102 ,.14539292549153895724] 
dist 191=[-.2824453166551108431 ,.07784552464946393714] 
dist 192=[-.2891323681952943086 ,.06372455718518370139] 
dist 193=[-.2936206311771168286 ,-.01473182223723637156] 
dist 194=[-.33223095408248045207,.00142926284914999195] 
dist 195=[-.37600526108657690786,.02815706898431008223] 
dist 196=[-.4281950195898782052 ,.06928508013301867484] 
dist 197=[-.47663006461329098425,.11041127978583041106] 
dist 198=[-.50542351048776854873,.13713174162561595667] 
dist 199=[-.52530965123005834006,.15837726974769015149] 
dist 200=[-.53820528180845132727,.17766024695775383785] 
dist 201=[-.54701625695336109276,.19416991681076293519] 
dist 202=[-.55060484233562036199,.20435073460687981321] 
dist 203=[-.5510516875952359292 ,.21182886696795487003] 
dist 204=[-.55000798643548637166,.21755537998944082008] 
dist 205=[-.15785244991748577345,.22199901033370673307] 
dist 206=[-.15145058983024131812,.22435880414255000918] 
dist 207=[-.13808601518609871151,.2256384608197880297 ] 
dist 208=[-.13429449168012627212,.2257728589920576962 ] 
dist 209=[-.11893175077562061931,.2251576746876259415 ] 
dist 210=[-.11570140331832408651,.24957580387622123914] 
dist 211=[-.10798843657925794729,.27870861469996282981] 
dist 212=[-.10589121230450644046,.31159112983971552579] 
dist 213=[.01611500086770411660,.34168487995051277875] 
dist 214=[.02733435250382404206,.35969112641764633164] 
dist 215=[.04923016049717670685,.37226840800642280364] 
dist 216=[.05439672285323014933,.38070143914341971925] 
dist 217=[.06540514357455165765,.38628266997407791217] 
dist 218=[.03763494664916876061,.38748183290921275889] 
dist 219=[.00239826158198174663,.38679823419649150804] 
dist 220=[-.05217610340196896767,.38517571130083741333] 
dist 221=[-.10689834852146545945,.27444299830444342217] 
dist 222=[-.14272497058978207159,.2717574930878671877 ] 
dist 223=[-.17152084398054760953,.26328254036080619074] 
dist 224=[-.19819224132427274692,.26121785416096612949] 
dist 225=[-.2214099782451071133 ,.24046743622005606326] 
dist 226=[-.23642655510888830792,.23563648477588344085] 
dist 227=[-.24828926444564333809,.22954559335809089368] 
dist 228=[-.25892361969553381045,.22703275158538569367] 
dist 229=[-.26789244298270421592,.16578327524316833378] 
dist 230=[-.27311004455700510579,.15735904450967112591] 
dist 231=[-.27656984480023734057,.13944090513746223511] 
dist 232=[-.27852556929226121225,.13439411736017042142] 
dist 233=[-.27935867576324685433,.11394959141683958235] 
dist 234=[-.27884097959493205383,.10986373480982945313] 
dist 235=[-.27654836756227512171,.09992477210740986367] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 1, 0, 2] 
dist 0=[57.568003788906772731  ,57.568003788906772731  ] 
dist 1=[56.823628632385900395  ,58.021840937221799859  ] 
dist 2=[55.486643864163100472  ,58.198679585642977504  ] 
dist 3=[53.832228080450738059  ,58.257224565566802698  ] 
dist 4=[51.820344317204881844  ,58.238652624798043512  ] 
dist 5=[49.157765989347862111  ,58.159559258506951270  ] 
dist 6=[44.905128519581724506  ,58.055855315645530600  ] 
dist 7=[40.557914007261197709  ,57.776573605194298090  ] 
dist 8=[37.517620412755030448  ,57.631921137388792228  ] 
dist 9=[34.847250331401397529  ,57.499175943002802136  ] 
dist 10=[31.976929837511816390  ,57.351628330122091221  ] 
dist 11=[29.191034116296856243  ,57.194159984694329006  ] 
dist 12=[26.857555691756118520  ,57.057057955787171667  ] 
dist 13=[24.403396952700118899  ,56.905392568306032720  ] 
dist 14=[21.135187912404115189  ,56.393089960196318388  ] 
dist 15=[17.906307999831806480  ,37.095511821916228104  ] 
dist 16=[15.608948070724149474  ,35.442462301315724730  ] 
dist 17=[13.547671444223191227  ,31.446385633674119309  ] 
dist 18=[11.261184218044091751  ,30.871916489202343678  ] 
dist 19=[8.9954400637320605975 ,25.116713764998847798  ] 
dist 20=[7.0164918849986448860 ,24.062723275782479247  ] 
dist 21=[4.8604759444818019954 ,22.831202400265077284  ] 
dist 22=[1.8864973244893861687 ,22.614809720832036853  ] 
dist 23=[-1.0167815955955179918 ,13.931907734586642118  ] 
dist 24=[-2.8905605071729700798 ,12.886311840930478758  ] 
dist 25=[-4.3779770464187380942 ,11.822294888516373890  ] 
dist 26=[-5.7375065838169888330 ,11.240164231152343039  ] 
dist 27=[-6.9195937770756582925 ,9.1687095689826465211 ] 
dist 28=[-7.6981743376710463470 ,8.1002186050336873778 ] 
dist 29=[-10.331364309773172857  ,7.3331456628902418200 ] 
dist 30=[-12.017448236028025585  ,7.2265942577546434286 ] 
dist 31=[-13.281376620003636059  ,-2.0153034022760345526 ] 
dist 32=[-14.310638292321692418  ,-2.7688454143609282894 ] 
dist 33=[-15.132572123421628594  ,-4.3098467032844238604 ] 
dist 34=[-15.567846136650235402  ,-4.6443971556538499013 ] 
dist 35=[-15.806573544324023781  ,-4.9361572186978521411 ] 
dist 36=[-15.854563376134249249  ,-3.9190898039370633443 ] 
dist 37=[-15.329388956146719292  ,-2.6189209020080140551 ] 
dist 38=[-15.196619569528592674  ,-.59790363889758791516] 
dist 39=[-15.066501552621300530  ,1.4388451678643926649 ] 
dist 40=[-14.977282062796323826  ,2.8019595568721117951 ] 
dist 41=[-14.822535226868107432  ,3.9292631118687298307 ] 
dist 42=[-14.737523406986471384  ,5.0256212690162002457 ] 
dist 43=[-14.660758978090498583  ,6.0152181325143284266 ] 
dist 44=[-14.586980321768359795  ,6.7167687407682501554 ] 
dist 45=[-12.645535358269490530  ,7.3402952203953329842 ] 
dist 46=[-12.640210178986891943  ,8.0187585710435706363 ] 
dist 47=[-1.7120827802704621500 ,8.6272536199896797993 ] 
dist 48=[-1.3757964375546718358 ,8.9716569247118102317 ] 
dist 49=[-.59813937680054589824,9.1879230502308114714 ] 
dist 50=[-.51090641880193798891,9.2851237210881400498 ] 
dist 51=[-.25629266354718708137,9.3223734154705186087 ] 
dist 52=[-.21330464020900379157,9.3006308926774986910 ] 
dist 53=[-.23195547075744440431,9.2404828323713415897 ] 
dist 54=[-.33923174225697895091,9.1950128310787401366 ] 
dist 55=[-.46152182100680819068,9.0556828233297809396 ] 
dist 56=[-.5400754909363177896 ,9.5368849460881963136 ] 
dist 57=[-.60127096361490993954,9.9124380094577474116 ] 
dist 58=[-.65436196279529148325,10.079187700826483812  ] 
dist 59=[-.69794376194367377169,10.156571408029019778  ] 
dist 60=[-.7212321922173802081 ,10.175424500327918000  ] 
dist 61=[-.73433239329862709436,7.9013257785139268823 ] 
dist 62=[-.7372984002448338019 ,7.8637110645496619818 ] 
dist 63=[-.73008480861380231106,3.9857822093521983281 ] 
dist 64=[-.7276673362760392411 ,3.6401010054437833210 ] 
dist 65=[-.72534575868835349545,2.8138472685668841210 ] 
dist 66=[-.8989524004426459583 ,2.6769497117458113284 ] 
dist 67=[-1.4110261365199619685 ,1.5197891635918608726 ] 
dist 68=[-2.0544083626910832168 ,1.3091253037340614378 ] 
dist 69=[-2.6687610929986754837 ,1.0014708314900690833 ] 
dist 70=[-3.0650547675155306242 ,.9169745526870375807 ] 
dist 71=[-3.3772921343738992456 ,-.05089520330460487343] 
dist 72=[-3.6997959073439914849 ,.05392334593591393492] 
dist 73=[-4.0600842918895169783 ,.14393138198559225544] 
dist 74=[-4.3405790295449459582 ,.23704701936733250807] 
dist 75=[-4.6165722853371128840 ,.42012668343273314977] 
dist 76=[-4.9590218077724064296 ,.97318902621756333939] 
dist 77=[-5.2747862223960927601 ,1.5365723757932688017 ] 
dist 78=[-5.4443067811488915975 ,1.9171358839582842644 ] 
dist 79=[-5.5396096077314730953 ,2.2357264099697910311 ] 
dist 80=[-5.5618158018207220440 ,2.5519238073544167913 ] 
dist 81=[-5.5520726208825314790 ,2.8414203910232942308 ] 
dist 82=[-5.5412722851714120711 ,3.0535073446843855321 ] 
dist 83=[-5.5258741917904378872 ,3.2489599774926096967 ] 
dist 84=[-5.5004234665651362446 ,3.4720960110050773186 ] 
dist 85=[-4.6028710243942600986 ,3.6735102302236308058 ] 
dist 86=[-4.4708240256202864712 ,3.7823143854877577737 ] 
dist 87=[-4.2189578019950272051 ,3.8437787733021303256 ] 
dist 88=[-4.1501006997151072721 ,3.8563608364797193891 ] 
dist 89=[-3.8943660528158505349 ,3.8494573236620559237 ] 
dist 90=[-3.8281042198682238009 ,3.8331972616491083370 ] 
dist 91=[-3.7120282847018801948 ,3.8069071968501443023 ] 
dist 92=[-3.6785312753406138208 ,3.7899378830345321054 ] 
dist 93=[-2.9068897665838327968 ,2.4485122189890533821 ] 
dist 94=[-3.0846684019796718371 ,3.0281804894981684657 ] 
dist 95=[-3.2564538515266131233 ,3.5567632580296214981 ] 
dist 96=[-3.3557739526370242620 ,3.9921761219442761839 ] 
dist 97=[-3.4205871523371709178 ,4.3182075840045895419 ] 
dist 98=[-3.4547448794928482024 ,4.5800360750063698685 ] 
dist 99=[-3.4688608369540418418 ,4.7882669693593419128 ] 
dist 100=[-3.4660034586825478397 ,4.9004091447983646730 ] 
dist 101=[-3.4311504827912097608 ,4.9636408692763912905 ] 
dist 102=[-3.4154795420762880540 ,4.9766904685064476264 ] 
dist 103=[-3.1348980868289110682 ,4.6449796479849869091 ] 
dist 104=[-3.0828596784143330576 ,4.5835486961915385726 ] 
dist 105=[-2.9480723650710316230 ,4.5186419636506609617 ] 
dist 106=[-2.9082688173990371895 ,4.3935138935692393719 ] 
dist 107=[-2.6539649013262508426 ,3.5419344454799769594 ] 
dist 108=[-2.5961273097512581519 ,2.9941397054342223984 ] 
dist 109=[-2.4905951674509527014 ,1.7562517031337182941 ] 
dist 110=[-2.4603431943076330764 ,1.7455628654784615585 ] 
dist 111=[-1.6158178670934096852 ,.253532160592375969  ] 
dist 112=[-1.9112888233209208111 ,.27440729413267013522] 
dist 113=[-2.1390891171773776199 ,.28944509721111098908] 
dist 114=[-2.3338173566080634851 ,.30042005174222849477] 
dist 115=[-2.4930036126418756715 ,.3086757402497423398 ] 
dist 116=[-2.5789835270482007769 ,.31286403433638716512] 
dist 117=[-2.6277425766293822795 ,.3148693549619417526 ] 
dist 118=[-2.6392707195904196004 ,.31468470558496128992] 
dist 119=[-2.6067192357681320863 ,.2631716278723396722 ] 
dist 120=[-2.5982396096852681771 ,.27717351040212870356] 
dist 121=[-2.5909963439842288713 ,.28638419628195178958] 
dist 122=[-2.5836302764768298690 ,.29145725893528896997] 
dist 123=[-2.5768115548881138159 ,.2946084114211245676 ] 
dist 124=[-2.5717438903650974723 ,.29614979119608845885] 
dist 125=[-2.5670132190542641621 ,.2968081361223393865 ] 
dist 126=[-2.5615301629800356983 ,.2964348743162009221 ] 
dist 127=[-.55536850322951107845,.25314220227263289027] 
dist 128=[-.3918284855702810967 ,.24804855436187416331] 
dist 129=[-.0263943242634582665 ,.24501880805841269187] 
dist 130=[.0436016342501894393 ,.4523196575411355950 ] 
dist 131=[.15103991583923198689,.7365092751304374454 ] 
dist 132=[.12022428158926619512,.9598396138291055716 ] 
dist 133=[.08287027593343708763,1.1810783968910570423 ] 
dist 134=[.02687971571531751207,1.4569245433520413919 ] 
dist 135=[-.02942095005801875437,1.7190859762518410435 ] 
dist 136=[-.06801251994462683688,1.8857250504192777045 ] 
dist 137=[-.10098177103581591242,2.0140958631341689455 ] 
dist 138=[-.13484913042887442487,2.1235719330956814257 ] 
dist 139=[-.16665851651309701637,2.2123556920264674222 ] 
dist 140=[-.19141645338944439919,2.2581667503565387321 ] 
dist 141=[-.21572547875476251173,2.2812144827074941550 ] 
dist 142=[-.24574396169047504231,2.2841289105566840365 ] 
dist 143=[-.27414382427788922115,.0604235826582369558 ] 
dist 144=[-.2919945088242894805 ,-.0373676232480927679 ] 
dist 145=[-.30551878608796914551,-.06284889491813506038] 
dist 146=[-.4625175390338863649 ,-.05889231229917791543] 
dist 147=[-.6104253458993667123 ,-.05248827111435605015] 
dist 148=[-.7186667529561922193 ,-.04030301476922109811] 
dist 149=[-.8184334437600140586 ,-.00728534697103918579] 
dist 150=[-.9325354750008507478 ,.04443572703338158202] 
dist 151=[-1.0375627953582995310 ,.09666452076562792302] 
dist 152=[-1.1011245559682252152 ,.13450322957610700931] 
dist 153=[-1.1464055004875311333 ,.16519880947368540875] 
dist 154=[-1.1784933850373594068 ,.19411959015114126001] 
dist 155=[-1.2008726198857199800 ,.21964399089166077816] 
dist 156=[-1.2074195910275720469 ,.2367881667003004009 ] 
dist 157=[-1.2071403730126189558 ,.25105656806428639739] 
dist 158=[-1.2025939349084373660 ,.26510672633542184161] 
dist 159=[-.92986102769808019035,.27733391984482676269] 
dist 160=[-.90052692878459315494,.28432880377799128995] 
dist 161=[-.82351157772842177798,.28882209189553093576] 
dist 162=[-.81063523665250395214,.29106815324552726765] 
dist 163=[-.67580125907688086035,.29169473738340022354] 
dist 164=[-.6486027182174440787 ,.33681480178176346778] 
dist 165=[-.61637158490936190717,.41475593386813495891] 
dist 166=[-.60549968179981434395,.51102770287722664913] 
dist 167=[-.3308774298267349290 ,.60202062569156727478] 
dist 168=[-.2956448780964418731 ,.6589016048216661029 ] 
dist 169=[-.2204972822725460174 ,.7015962034471410395 ] 
dist 170=[-.2009374575335151224 ,.7359921511773583966 ] 
dist 171=[-.1223082790090928791 ,.7625797286181761536 ] 
dist 172=[-.11083564811037420059,.7741222642116416640 ] 
dist 173=[-.11937332337847025618,.7790990298042342890 ] 
dist 174=[-.13962303335355194134,.7794931202760744866 ] 
dist 175=[-.15843388244157461258,.6237064658071020498 ] 
dist 176=[-.1702945363343136569 ,.6969168583814519360 ] 
dist 177=[-.17932152342960487162,.7519385466269131198 ] 
dist 178=[-.18682587531120610655,.7964518835603659742 ] 
dist 179=[-.1927654715656187251 ,.8316859152540675120 ] 
dist 180=[-.19554891192058396582,.8496814752866458892 ] 
dist 181=[-.19666485615848149394,.8585357932667113294 ] 
dist 182=[-.1966296817922140037 ,.8600074774730699574 ] 
dist 183=[-.10825269474586209779,.82176666571531728922] 
dist 184=[-.10080929657816630764,.81809483523892813638] 
dist 185=[-.08897030253708105428,.81317807582008559568] 
dist 186=[-.08585838423789162446,.80930965257853400139] 
dist 187=[-.08058718168936773307,.79613270449402461423] 
dist 188=[-.08112601186498954854,.79066887910802619178] 
dist 189=[-.08445518671277506397,.77622907139733063228] 
dist 190=[-.09245585028870565371,.76983909087368048556] 
dist 191=[-.10194533219982161441,.26093625605474538517] 
dist 192=[-.1264202097442281116 ,.21551839147790526425] 
dist 193=[-.2243210264989461641 ,.16873737719587567051] 
dist 194=[-.3244485839958508965 ,.20476499586207986059] 
dist 195=[-.4179288034680565291 ,.24178055863444760871] 
dist 196=[-.4897241523419884331 ,.2758279747606811062 ] 
dist 197=[-.5592995450882766807 ,.3141741338070704143 ] 
dist 198=[-.6439227316352041984 ,.3683398616952561024 ] 
dist 199=[-.7233157947030881614 ,.4208677660074012630 ] 
dist 200=[-.7720234903193543104 ,.4526792754916298193 ] 
dist 201=[-.8075242245111907977 ,.4753616263645591510 ] 
dist 202=[-.8342223907475643279 ,.4914667953614485887 ] 
dist 203=[-.8536588543268844701 ,.5032893261689021173 ] 
dist 204=[-.8601858497617791713 ,.5088852372026973050 ] 
dist 205=[-.8614752381507001172 ,.5109825038426364257 ] 
dist 206=[-.8600137153140591293 ,.5104789290279341239 ] 
dist 207=[-.3457535041434926274 ,.4597510160353360787 ] 
dist 208=[-.3449854294613464321 ,.4510733358612013621 ] 
dist 209=[-.3395155207651325534 ,.4355991488117390379 ] 
dist 210=[-.3383530050585583417 ,.4311165766706127791 ] 
dist 211=[-.3161696364097313766 ,.4137918407300971806 ] 
dist 212=[-.3106353239531425769 ,.4468453343873995069 ] 
dist 213=[-.3061582733005697013 ,.4870786836095335575 ] 
dist 214=[-.3041230927845058007 ,.5301238793775875708 ] 
dist 215=[-.20504313780592003726,.5689269781457101427 ] 
dist 216=[-.19249247381609577462,.5922351149301983244 ] 
dist 217=[-.16767642966240190239,.6086275041817871124 ] 
dist 218=[-.16117137733766037873,.6198375122939469020 ] 
dist 219=[-.13789963624241352083,.6268410366526208516 ] 
dist 220=[-.13249129964272200255,.6279983965825827328 ] 
dist 221=[-.12485357541390206189,.6239919197795941737 ] 
dist 222=[-.12239481978096198257,.6227486068475916473 ] 
dist 223=[-.16373691404129375497,.41733325000950945043] 
dist 224=[-.21529205885130254314,.41488884241768489084] 
dist 225=[-.25679704100014992125,.40554193617867650843] 
dist 226=[-.2953554544596072521 ,.40315132012628551845] 
dist 227=[-.3290023254045644831 ,.37531022561066694288] 
dist 228=[-.3509112999679339320 ,.3685639703056607113 ] 
dist 229=[-.3683861109962435103 ,.36093726833269438586] 
dist 230=[-.3843413614230329649 ,.35729163813455194315] 
dist 231=[-.3978201438577372733 ,.26464865598422980278] 
dist 232=[-.4054143062480536766 ,.25186011033850583702] 
dist 233=[-.4101390886557768311 ,.22533782604383499436] 
dist 234=[-.4121697091580160269 ,.21798049191869980532] 
dist 235=[-.4123053915830552578 ,.18900589825137457327] 
dist 236=[-.4114235957082603180 ,.18290343138499862724] 
dist 237=[-.4060662922245026298 ,.16945617355537425858] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 1, 2] 
dist 0=[54.324271060782021370  ,54.324271060782021370  ] 
dist 1=[52.888415146641368968  ,55.600263558108410030  ] 
dist 2=[51.477438197336288612  ,56.372906543887305606  ] 
dist 3=[49.813194519372531236  ,56.924816175626940688  ] 
dist 4=[47.365693396992161456  ,57.319770971154545198  ] 
dist 5=[44.597585204435688303  ,57.583485292979317052  ] 
dist 6=[41.652953810125014383  ,57.611544722210850300  ] 
dist 7=[38.009955951639166621  ,57.537630236396962787  ] 
dist 8=[32.453007983004409911  ,57.428659781120771142  ] 
dist 9=[26.861543402554284386  ,56.604540087884400520  ] 
dist 10=[23.080530306297725802  ,56.357267378472613755  ] 
dist 11=[19.894590017230002312  ,55.878935707316199038  ] 
dist 12=[16.678944866024006576  ,55.706594671671722329  ] 
dist 13=[13.681641093110613338  ,51.984167468964023228  ] 
dist 14=[11.367182584985196824  ,51.502179445932873554  ] 
dist 15=[9.1032718814463250228 ,48.367571089234956280  ] 
dist 16=[6.3070554988909254571 ,43.206687416371858614  ] 
dist 17=[3.6403795329134202715 ,39.240015411222786840  ] 
dist 18=[1.8933733947693496063 ,37.887643679347443984  ] 
dist 19=[.4781656409843520953 ,34.625818151908317672  ] 
dist 20=[-.86393212798200238794,34.121304820649776022  ] 
dist 21=[-2.0668650802821707591 ,29.400690609530575552  ] 
dist 22=[-2.9270425753890993257 ,28.524393365843695129  ] 
dist 23=[-3.7096549468248188637 ,27.412706888811646479  ] 
dist 24=[-4.6045287139705229856 ,27.114535745289231573  ] 
dist 25=[-5.4190695167581911887 ,19.974438544064114177  ] 
dist 26=[-5.8809285121924874795 ,19.091493832342667866  ] 
dist 27=[-6.1822420255580277025 ,17.189538142959115843  ] 
dist 28=[-6.3541144655916524225 ,16.776403788152895722  ] 
dist 29=[-7.2668161435905969970 ,14.748465459588545112  ] 
dist 30=[-8.7898476531093682165 ,14.402148445913236667  ] 
dist 31=[-10.213162092685485722  ,13.626293001005545410  ] 
dist 32=[-11.878925597927188252  ,13.014283601611953407  ] 
dist 33=[-13.421541349459726567  ,-4.2074491691360833161 ] 
dist 34=[-14.353028197558244206  ,-3.6328161311762032487 ] 
dist 35=[-15.018600183104990164  ,-3.0364858086937282326 ] 
dist 36=[-15.499130971206596227  ,-2.2592724477301178476 ] 
dist 37=[-15.849660166417040770  ,-1.4291854747898117624 ] 
dist 38=[-15.995930014350149753  ,-.6215638811549379532 ] 
dist 39=[-16.035626108662166726  ,.3219661264237907357 ] 
dist 40=[-16.014450296183162835  ,1.6945317366953447729 ] 
dist 41=[-1.6489522195701690290 ,3.0592041409194205104 ] 
dist 42=[-1.1351403005245354861 ,3.9714034710086679566 ] 
dist 43=[-.13430309722351738164,4.7252228701971166278 ] 
dist 44=[.02321994380452813411,5.4582438725392882219 ] 
dist 45=[.56801122266575758463,6.1206865901401752102 ] 
dist 46=[.68053802475945365684,6.5930573998338463643 ] 
dist 47=[.80083568290293538465,7.0163880025603872557 ] 
dist 48=[.80163705804492360243,7.4833551339869833216 ] 
dist 49=[.7549090783299119068 ,7.8987747247011465787 ] 
dist 50=[.6449507972660896036 ,8.1165029139415741242 ] 
dist 51=[.4680145649319671675 ,8.2315619558250766711 ] 
dist 52=[.1539446374464367348 ,8.2518780343535103835 ] 
dist 53=[-.2236789651403945251 ,8.2005202781705909340 ] 
dist 54=[-.6542587650638667397 ,8.1551341780884026550 ] 
dist 55=[-1.2056701721602843003 ,7.8820990553357208196 ] 
dist 56=[-2.0654976210485472981 ,7.2758166843651820767 ] 
dist 57=[-2.9238504353087603070 ,2.4972142997605304296 ] 
dist 58=[-3.4694029240160391617 ,2.3464297205250682620 ] 
dist 59=[-3.8898971783998186063 ,1.9668980886198515439 ] 
dist 60=[-4.2492543895155110415 ,1.9116780732729930036 ] 
dist 61=[-4.5430756431168492736 ,1.3208959052099855274 ] 
dist 62=[-4.7020589803693863767 ,1.2103609481657373204 ] 
dist 63=[-4.7926515462513441546 ,1.0828928669943718346 ] 
dist 64=[-4.8139972856023595581 ,1.0589796920739676176 ] 
dist 65=[-4.7564678241052860066 ,.1027962373248587695 ] 
dist 66=[-4.7418769598771101982 ,-.0106371181383899443 ] 
dist 67=[-4.7295883278379960284 ,-.2542341377811190528 ] 
dist 68=[-4.7174563719753093497 ,-.30372138379214209033] 
dist 69=[-4.7065313672043113804 ,-.5458061449361387752 ] 
dist 70=[-4.6990379763883130410 ,-.5868591131150665896 ] 
dist 71=[-4.6927010371103330173 ,-.65199267672635553341] 
dist 72=[-4.6863694330297472604 ,-.6639607862351734851 ] 
dist 73=[-1.4149613948003239887 ,-.9468498501754235548 ] 
dist 74=[-1.4066515374064824423 ,-.3370553407283955360 ] 
dist 75=[-1.4408620059833493651 ,.1866247597597530155 ] 
dist 76=[-1.5134681358330706444 ,.7287893098604119865 ] 
dist 77=[-1.5775906773944741440 ,1.2405421135389581645 ] 
dist 78=[-1.6214353539481891190 ,1.6428904266081665214 ] 
dist 79=[-1.6590138039651659631 ,2.0416906735905805448 ] 
dist 80=[-1.6980976195779107596 ,2.5392979832594648345 ] 
dist 81=[-1.7317922239702542137 ,3.0125329079748313459 ] 
dist 82=[-1.7478341334296432682 ,3.3140920338564118512 ] 
dist 83=[-1.7540763161502806109 ,3.5473216745679474252 ] 
dist 84=[-1.7523935886807094178 ,3.7479247188952765432 ] 
dist 85=[-1.7367650269833969189 ,3.9119583665338721700 ] 
dist 86=[-1.7297492358106894328 ,3.9992789560687942659 ] 
dist 87=[-1.6994562968637944893 ,4.0470598765130390615 ] 
dist 88=[-1.6918894182913803855 ,4.0533362188718144669 ] 
dist 89=[-1.5578495608393940728 ,1.1347938064156695906 ] 
dist 90=[-1.5326142828246675593 ,1.3940956842914052049 ] 
dist 91=[-1.4699141338100717914 ,1.5967919792721900777 ] 
dist 92=[-1.4497508482144208713 ,1.7751701510670293981 ] 
dist 93=[-1.3375572782100318945 ,1.9242697184166491717 ] 
dist 94=[-1.3116958064498212895 ,2.0101371064873345828 ] 
dist 95=[-1.3781456233507741490 ,2.0661990973804930754 ] 
dist 96=[-1.5913907471163309763 ,2.0963805701117037870 ] 
dist 97=[-1.7884590886413851387 ,2.1151052274067238513 ] 
dist 98=[-1.9065149750711176135 ,2.1254437943072591857 ] 
dist 99=[-1.9924461944912878721 ,2.1317356020943178152 ] 
dist 100=[-2.0717545315291393262 ,2.1342767557574552168 ] 
dist 101=[-2.1312481453016600514 ,2.1342951227391929448 ] 
dist 102=[-2.1555537875694785925 ,2.1304995382254050677 ] 
dist 103=[-2.1637690336198031081 ,2.1232013323792452090 ] 
dist 104=[-2.1594180620752016040 ,2.1141336393064733986 ] 
dist 105=[-2.0302993121949563882 ,.4645381707028117993 ] 
dist 106=[-2.0059321143083062428 ,.3345229135019441433 ] 
dist 107=[-1.9334320225196795336 ,.3132006033079208255 ] 
dist 108=[-1.9158648425037693998 ,.4974334244949120946 ] 
dist 109=[-1.7513303053259620794 ,.6702815053527963400 ] 
dist 110=[-1.7136660204050229668 ,.8043393697956898227 ] 
dist 111=[-1.6633383154212494281 ,.9354639374300603448 ] 
dist 112=[-1.6441019154611743011 ,1.0966167232527440661 ] 
dist 113=[-1.1858408857902433000 ,1.2486093433705697215 ] 
dist 114=[-1.1229680926541197135 ,1.3431918607310183956 ] 
dist 115=[-1.0793707982723360720 ,1.4137191874804492611 ] 
dist 116=[-1.0897659189768989367 ,1.4697437365639037104 ] 
dist 117=[-1.0981469161806905951 ,1.5121063627543107054 ] 
dist 118=[-1.1024138668526828134 ,1.5281321719751906195 ] 
dist 119=[-1.1044884961340900845 ,1.5333527984351824678 ] 
dist 120=[-1.1041177213350968563 ,1.5325870957450801628 ] 
dist 121=[-.32536727197275223909,1.0347421160994217243 ] 
dist 122=[-.26215548540260436354,1.1874201170937349249 ] 
dist 123=[-.11778857539543286589,1.3034194521211562672 ] 
dist 124=[-.09176552916242003845,1.3995656204868156918 ] 
dist 125=[.08713096404234163062,1.4771807151473011331 ] 
dist 126=[.11800488246330397315,1.5192347711272538283 ] 
dist 127=[.17415748222238682593,1.5432676395776702308 ] 
dist 128=[.18614293702941972297,1.5489673421829327376 ] 
dist 129=[.32977155771324112419,1.4857999132995132870 ] 
dist 130=[.35005984419834795254,1.4714584007938900927 ] 
dist 131=[.37094784408328482508,1.4601634134039572452 ] 
dist 132=[.36738206792536789757,1.4501472527789457636 ] 
dist 133=[.35336020615365153772,1.4416951753496242698 ] 
dist 134=[.32483844559236782229,1.4368284323740463756 ] 
dist 135=[.28030982029159886135,1.4336522635761956081 ] 
dist 136=[.2024357582695304638 ,1.4319655346629399350 ] 
dist 137=[.1217515012209108569 ,.25208049233338344726] 
dist 138=[.03836271531177612288,.15645691183678059963] 
dist 139=[-.1297757359038988558 ,.03451809573312070487] 
dist 140=[-.3038577282434830190 ,.02306685881059645726] 
dist 141=[-.4681944965462224585 ,-.05290870663184016968] 
dist 142=[-.5974500456915748129 ,-.06559975134480404681] 
dist 143=[-.7256175405988914641 ,-.08958906021435052669] 
dist 144=[-.8856135611580826469 ,-.09487238319976945012] 
dist 145=[-1.0378044254013566026 ,-.14502497739096756595] 
dist 146=[-1.1348293996809858468 ,-.1525459844673646391 ] 
dist 147=[-1.2099167055267690801 ,-.15560449922195803663] 
dist 148=[-1.2745758638923121773 ,-.14917070659324006931] 
dist 149=[-1.3274941628348868658 ,-.13782937080238199419] 
dist 150=[-1.3557351578203869584 ,-.12026101469575232612] 
dist 151=[-1.3712757158230153819 ,-.09481200231967965788] 
dist 152=[-1.3735188843823814445 ,-.05203719174234228637] 
dist 153=[-.32873806938388192811,.0214218895489279852 ] 
dist 154=[-.32690913901153668735,.1405363988784916350 ] 
dist 155=[-.31997414522418685748,.2396133800697933544 ] 
dist 156=[-.3178083170491341352 ,.3370625282878816060 ] 
dist 157=[-.2969631053168137594 ,.4263089939150155270 ] 
dist 158=[-.29182722958544085446,.4913846062658588428 ] 
dist 159=[-.28497152704522699206,.5507458140552769309 ] 
dist 160=[-.28219920987352658595,.6177313855894933399 ] 
dist 161=[-.21307872543182227145,.6790862631480451451 ] 
dist 162=[-.20346471560920091869,.7159819624681727486 ] 
dist 163=[-.18264955424354144515,.7419857417385470292 ] 
dist 164=[-.17667312904107208921,.7598809833206122566 ] 
dist 165=[-.15180712645487936243,.7719301006911907518 ] 
dist 166=[-.146956750829157794  ,.7746089379157791600 ] 
dist 167=[-.13421727087489883622,.7734833988593331221 ] 
dist 168=[-.13226582096386715821,.7703514667101320848 ] 
dist 169=[.16004234202731441162,.55170278499285934513] 
dist 170=[.08127716159937665578,.52927915414327436172] 
dist 171=[.01358656343221514974,.4720477227618191273 ] 
dist 172=[-.05655349707445037763,.46272367191697446025] 
dist 173=[-.12277863860527214731,.3685532897927201308 ] 
dist 174=[-.17484994915159647669,.35007911584009767742] 
dist 175=[-.22645261130502669883,.32955883434352764873] 
dist 176=[-.29080803775109430769,.33438203433191230188] 
dist 177=[-.3519619365480244321 ,.33734163900713659128] 
dist 178=[-.39079141212083105062,.33850453147185680334] 
dist 179=[-.42064923595400134375,.33857776796829670424] 
dist 180=[-.44600873846995607608,.33743477444583105916] 
dist 181=[-.46649159383868842701,.33497307720926126216] 
dist 182=[-.4768928840912962081 ,.3332128642623930331 ] 
dist 183=[-.48209104293440986211,.32822957485808633629] 
dist 184=[-.48287214096104548366,.32578805923140294105] 
dist 185=[-.37581007399746435539,.13881568782277710572] 
dist 186=[-.41890943999359818784,.12180079368150032499] 
dist 187=[-.45149444532400932132,.08322011585188380405] 
dist 188=[-.47821073919653772137,.07549912166104231453] 
dist 189=[-.49936634113383794841,.02773756316215754297] 
dist 190=[-.50976273955392173903,.01927619419696057150] 
dist 191=[-.51491787670874795116,.00275100382004748827] 
dist 192=[-.51534286542568914985,-.00123686935914502571] 
dist 193=[-.49678626434496213787,-.04142466075136430076] 
dist 194=[-.49192826262812718166,-.04750664404815370276] 
dist 195=[-.48437373619522818984,-.05506214977553556195] 
dist 196=[-.48127945374253044379,-.05590641798943747649] 
dist 197=[-.46918987275971887953,-.05410077957001107822] 
dist 198=[-.4651107268041564195 ,-.04840513523085823645] 
dist 199=[-.45526310170776413269,-.03878396041728930374] 
dist 200=[-.45127550733818052675,-.01736308866862814334] 
dist 201=[-.14896109794378941503,.03829875263187780176] 
dist 202=[-.12176965153444513597,.10810863934239912366] 
dist 203=[-.06185965883083196854,.1668096182005204112 ] 
dist 204=[-.04903384119463662538,.2256049698951670407 ] 
dist 205=[.01921127852910958507,.2804755209508084786 ] 
dist 206=[.02715147811917638594,.3225020943175626385 ] 
dist 207=[.02617383777209382442,.3625416465804494740 ] 
dist 208=[.02201354501089745621,.4102784734863716377 ] 
dist 209=[.01661383294146930680,.4545900649915294444 ] 
dist 210=[.01069185652912881088,.4809629854430313603 ] 
dist 211=[.00326112115917285628,.4992184271181922803 ] 
dist 212=[-.00815709203117010949,.5111410698366819048 ] 
dist 213=[-.02124216787714214513,.5192438772235117517 ] 
dist 214=[-.03532237808017752405,.5222578501462105436 ] 
dist 215=[-.05280473088437294294,.5221301459075691255 ] 
dist 216=[-.07946194512315427640,.5212047690953401609 ] 
dist 217=[-.10600267317756153684,.16741926757714649708] 
dist 218=[-.12302006549588080417,.17165255131968223166] 
dist 219=[-.14031261672741139061,.17385475324965786969] 
dist 220=[-.18664163489324741268,.17427017568329076796] 
dist 221=[-.2286072906714393665 ,.17286695109726928906] 
dist 222=[-.2586913353666688691 ,.17194472636373867936] 
dist 223=[-.2857970810061618057 ,.17080596293969478983] 
dist 224=[-.3158797287723279548 ,.16995757305802991437] 
dist 225=[-.3432790752141975433 ,.14229491846077165461] 
dist 226=[-.3596787064751740342 ,.13814510869324327642] 
dist 227=[-.3711419146066092077 ,.12970475615380441089] 
dist 228=[-.3788452917865690111 ,.12726017123365279092] 
dist 229=[-.3838090460085887696 ,.11723898625877142661] 
dist 230=[-.3846326487609599203 ,.11497386046542990129] 
dist 231=[-.3833041139193592850 ,.10955393677673797277] 
dist 232=[-.3820053588305247134 ,.10776615031151776977] 
dist 233=[-.26223482209932187747,.09491993275895920859] 
dist 234=[-.25152840691717114797,.13006308238133898004] 
dist 235=[-.23983344405760625899,.15835452430740794464] 
dist 236=[-.23743531241088943019,.18464000337513172442] 
dist 237=[-.21567493366757206451,.20758236697775022414] 
dist 238=[-.21080295098720279133,.22253519201000969312] 
dist 239=[-.20413487282952404757,.23447926134327551029] 
dist 240=[-.20169678272956098899,.24541694113326143902] 
dist 241=[-.14481863160277898655,.2547544634978225019 ] 
dist 242=[-.13703458439456193008,.2603140625667047409 ] 
dist 243=[-.1200805939614279613 ,.2641625794675447351 ] 
dist 244=[-.11526517017682655196,.2666731002372751433 ] 
dist 245=[-.09521265364881492695,.2681253831464871166 ] 
dist 246=[-.09135608176923795427,.2677934980916265300 ] 
dist 247=[-.08148289472016992216,.2664160426106509514 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 0, 0, 0, 0, 2] 
dist 0=[59.439116306790806492  ,59.439116306790806492  ] 
dist 1=[58.508338369231373671  ,59.842052704204031625  ] 
dist 2=[57.445241928775279305  ,60.018323449777742284  ] 
dist 3=[56.513856591090452839  ,60.043954570080632006  ] 
dist 4=[55.498556847019671104  ,59.922367268723104976  ] 
dist 5=[54.100289946193851919  ,59.074684603257648607  ] 
dist 6=[52.558925146256047800  ,58.874732058765156936  ] 
dist 7=[50.972102607553490665  ,58.782079159245704652  ] 
dist 8=[49.044239337851746942  ,58.546384655279176591  ] 
dist 9=[46.140803642548891297  ,52.111477295096632186  ] 
dist 10=[43.118114371149044060  ,51.204888252670346841  ] 
dist 11=[40.713929360501574297  ,50.095914780801822013  ] 
dist 12=[38.296482881396156219  ,49.217504684691324644  ] 
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dist 21=[4.0039803133098853272 ,10.099875252230143850  ] 
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dist 70=[-1.9760819080085278671 ,-1.3940973817134027996 ] 
dist 71=[-2.1908306668791840954 ,-1.4287819050922504772 ] 
dist 72=[-2.3857949560956273070 ,-1.4839636533880140657 ] 
dist 73=[-2.5068631172110185602 ,-1.4888040548512198580 ] 
dist 74=[-2.5969819974923015080 ,-1.4766456751808663485 ] 
dist 75=[-2.6684273132476752260 ,-1.4407037651112157829 ] 
dist 76=[-2.7224120466310515313 ,-1.3806252452408546955 ] 
dist 77=[-2.7428458968953039377 ,-1.2721263499194828545 ] 
dist 78=[-2.7453402033692630399 ,-1.1410503589606917391 ] 
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dist 80=[-2.2881290940826222732 ,-.57379717317592891699] 
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dist 83=[-1.4952401287431592517 ,.19891614693344787219] 
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dist 86=[-.97967642512434673027,.84541460570233332068] 
dist 87=[-.92211249261566889468,.99037817409359118526] 
dist 88=[-.85148171577257634398,1.1604092011322648467 ] 
dist 89=[-.83058888487603758749,1.2809410459660177650 ] 
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dist 101=[.03819195065930100125,1.0781656555013697625 ] 
dist 102=[.00518349038446211586,1.0880275791550079147 ] 
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dist 106=[-.10019641427181196633,.94802636731585132923] 
dist 107=[-.11747828093763031606,.93916711899907019466] 
dist 108=[-.13075976718848306725,.9188644948823190505 ] 
dist 109=[-.1420262028197416017 ,.91128956084722785131] 
dist 110=[-.1511149667988021311 ,.90646185903582811038] 
dist 111=[-.15570827663381026214,.9041392195700165374 ] 
dist 112=[-.15799589488254010965,.11332158274828004123] 
dist 113=[-.158317689774850471  ,.04907126783975210316] 
dist 114=[-.15244885739450886898,-.09185272828766251371] 
dist 115=[-.26859770455577035483,-.08608847261529326951] 
dist 116=[-.37787366288345343565,-.07649066677650737233] 
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dist 118=[-.54758088317381162923,-.05373826580839882763] 
dist 119=[-.65223127940483318716,-.04352645361082739117] 
dist 120=[-.75159106225895376992,-.03231129859815290941] 
dist 121=[-.8147530242740815202 ,-.01685156858161892786] 
dist 122=[-.86345466627524547855,-.00148258546325085882] 
dist 123=[-.90511023533968000502,.00937452131709036075] 
dist 124=[-.93901555909602532405,.01898064818595821042] 
dist 125=[-.95678963301750905561,.02936617296734245226] 
dist 126=[-.96613967314095813335,.03944762646814205868] 
dist 127=[-.96690396297083385079,.04784612017772215632] 
dist 128=[-.01743163003246137024,.05940297175200487828] 
dist 129=[-.01678563700598390569,.14633667340404031093] 
dist 130=[.07358500124821462670,.21797496112261825837] 
dist 131=[.07843374302151712555,.28735579320027481899] 
dist 132=[.08795774183819928867,.35088428936277615423] 
dist 133=[.09002827289048090767,.39583298339458086818] 
dist 134=[.09463707258016301648,.43557635999593359749] 
dist 135=[.09415298867149933265,.47855803973829503665] 
dist 136=[.09207690072131448086,.51752318450701087678] 
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dist 138=[.08174088620155115874,.55831278721392341049] 
dist 139=[.07646341812017287553,.57076188232222677008] 
dist 140=[.07040462612529345118,.57927393049402944759] 
dist 141=[.06107149623321355088,.58089640730046439686] 
dist 142=[.04977287074303409417,.57945610816808858198] 
dist 143=[.03784892562581951830,.577830690083729803  ] 
dist 144=[.02319442645694392337,.36691119884879558092] 
dist 145=[.00099785875934860356,.34730032958150049734] 
dist 146=[-.02119350201695579357,.29795085187789846446] 
dist 147=[-.03582808823882119900,.2905347226217015819 ] 
dist 148=[-.07371988324340214000,.21269973269770957286] 
dist 149=[-.11249870348651798743,.19788101320803928896] 
dist 150=[-.15076654891680711414,.18065781282022468886] 
dist 151=[-.19827543264295078104,.17670428163222758289] 
dist 152=[-.24332571958629322714,.04320776726307048452] 
dist 153=[-.2717841618222552331 ,.03166898690492633066] 
dist 154=[-.2935024565661190672 ,.01296183459411430709] 
dist 155=[-.31166046206035705029,.01048767261491274882] 
dist 156=[-.32611144378013926593,.00464788440583421413] 
dist 157=[-.33303914733679674746,.00370277669766085029] 
dist 158=[-.33655287206957532311,-.00423447113365838291] 
dist 159=[-.33738248571647244944,-.00565851490711559335] 
dist 160=[-.25978551946831786381,-.00772584382684823099] 
dist 161=[-.28086887769191547002,-.00828664981532322938] 
dist 162=[-.29615203132150316351,.00304098364350077982] 
dist 163=[-.30750933027551376629,.01251450893929281075] 
dist 164=[-.31606304623909491613,.02027166947246946794] 
dist 165=[-.3201578299144814573 ,.02769259600521007461] 
dist 166=[-.32177164146196588461,.03431239694649087425] 
dist 167=[-.32170391440912733936,.03887421000592318303] 
dist 168=[-.29590227500000847793,.04279468309440934983] 
dist 169=[-.29124232808863013646,.04685677028857681525] 
dist 170=[-.2830037789810995033 ,.05049651837237107464] 
dist 171=[-.28054882327079617669,.05273229434980822290] 
dist 172=[-.27120711736961736052,.05436563911652714356] 
dist 173=[-.2685899810404997143 ,.05614851570756051022] 
dist 174=[-.26173776984801873657,.05786119875651368713] 
dist 175=[-.25957906715802670933,.05872273934899821614] 
dist 176=[-.07910045588149286360,.05912600114603537646] 
dist 177=[-.06282517688929010455,.07561316787417062705] 
dist 178=[-.02724951464580202015,.11072895867287497817] 
dist 179=[-.01949591093342232444,.1458070889256833863 ] 
dist 180=[-.00096881081095705932,.17877748297943656371] 
dist 181=[-.00581508781711013564,.20456550589089588979] 
dist 182=[-.01037534807067510242,.22927443782684479192] 
dist 183=[-.01392547508036967591,.258941491922949174  ] 
dist 184=[-.01740766724789195071,.28659746871161942118] 
dist 185=[-.02169785479992950396,.30328184271033504064] 
dist 186=[-.02574676775262965286,.3151106391917714616 ] 
dist 187=[-.02842822039874686142,.32339169215521752819] 
dist 188=[-.03038981647223742859,.3291671920975275944 ] 
dist 189=[-.03180008577758504850,.33099807643743415159] 
dist 190=[-.03285959394192443726,.33099151829509202658] 
dist 191=[-.03342231292035035653,.32997583299011933873] 
dist 192=[-.05890640435365435603,.01430833718358539753] 
dist 193=[-.08498600441591097319,.01388076581288524991] 
dist 194=[-.10743802616779208061,-.00699064762606748911] 
dist 195=[-.1365138751822828107 ,-.00403659159739427105] 
dist 196=[-.16261447970045046461,-.00146368450988948854] 
dist 197=[-.18092535976737487366,.00124970392346455505] 
dist 198=[-.19701731503934563918,.00383525092441016596] 
dist 199=[-.21426447508356445211,.00589860669904232471] 
dist 200=[-.22981985556549671196,.00796863535236908993] 
dist 201=[-.2391615440211791986 ,.01058115577577338327] 
dist 202=[-.24573090857863446984,.01307382226637493430] 
dist 203=[-.2502244588588288962 ,.01466604389628116393] 
dist 204=[-.25303420215053387952,.01590005397235546074] 
dist 205=[-.25351380983563778767,.01696431663406629850] 
dist 206=[-.25192096291245564638,.01783646664267153567] 
dist 207=[-.2514791547937579574 ,.01830453486598893239] 
dist 208=[-.15927125299738086786,.05052986910126376061] 
dist 209=[-.15225020954783344327,.07292885523395408640] 
dist 210=[-.14099679493583395155,.09103699742449850412] 
dist 211=[-.13920244090883377847,.10799291997950617704] 
dist 212=[-.12416223960912665252,.12288547341482830407] 
dist 213=[-.12093091928778500987,.13276081922864297851] 
dist 214=[-.11618670603199396929,.14084009560059018071] 
dist 215=[-.11463760454255465398,.14856629638847087893] 
dist 216=[-.08032501763241876449,.15529096437095845951] 
dist 217=[-.07566572457704971964,.15937409974886675762] 
dist 218=[-.06524423626852633009,.16229855803229857484] 
dist 219=[-.06263916916504885489,.16440006789244839294] 
dist 220=[-.04961007010955482089,.16580713622137344705] 
dist 221=[-.04714100977058037799,.16596066688274052552] 
dist 222=[-.04160505847593385707,.1653915205335104488 ] 
dist 223=[-.04017983151697040702,.16481386544082442156] 
dist 224=[-.02591918158423254655,.07235998596448769501] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 2, 1, 0, 1] 
dist 0=[60.314766809524483292  ,60.314766809524483292  ] 
dist 1=[59.973006598090449215  ,60.633162062415572073  ] 
dist 2=[59.457943524281015140  ,61.054543565076127726  ] 
dist 3=[58.583061933532055280  ,61.435563302432922440  ] 
dist 4=[56.804487795157794312  ,61.592826574056824387  ] 
dist 5=[54.634571146393934532  ,61.615690663812628497  ] 
dist 6=[52.197068108126163674  ,61.548268097710981446  ] 
dist 7=[49.092464774254348985  ,61.201964595536843541  ] 
dist 8=[44.258617739789049112  ,61.060485905671620226  ] 
dist 9=[39.356166401286219346  ,60.455329269268134157  ] 
dist 10=[35.977481662683966946  ,60.321271801312783674  ] 
dist 11=[33.061761184682678191  ,58.380216894350943449  ] 
dist 12=[30.007692641604014202  ,57.907593338134940538  ] 
dist 13=[27.090588079172035689  ,56.096771323652966390  ] 
dist 14=[24.721493048571768015  ,52.892547626562635466  ] 
dist 15=[22.294183087741472685  ,34.041472973255075544  ] 
dist 16=[19.144050370574124652  ,33.031562676017517759  ] 
dist 17=[16.067475950380768869  ,31.785031123614158735  ] 
dist 18=[13.933605919986191658  ,31.436782427165632992  ] 
dist 19=[12.074665962271890020  ,22.583926473947182834  ] 
dist 20=[10.095633135987706216  ,21.460989946931169409  ] 
dist 21=[8.1806754248395750941 ,19.110898447400240292  ] 
dist 22=[6.5770485336063178420 ,18.489293247196476312  ] 
dist 23=[3.4183764131361754949 ,16.153721051004361300  ] 
dist 24=[1.0992933215786093721 ,15.699439451393224520  ] 
dist 25=[-.8611346310667087934 ,14.795417889134283277  ] 
dist 26=[-2.8543796146858115208 ,14.567731281476365619  ] 
dist 27=[-4.7265652632226295724 ,5.3028461545139843787 ] 
dist 28=[-6.8830780631246309053 ,4.7100351046244080712 ] 
dist 29=[-9.0964858318979489932 ,2.6448813568992650608 ] 
dist 30=[-11.235999469546186909  ,1.6952158504003040241 ] 
dist 31=[-13.171661927549111664  ,-4.0513312114159229818 ] 
dist 32=[-14.570946597652452699  ,-4.4426811808720953483 ] 
dist 33=[-15.849666009880764975  ,-5.1006326517742876493 ] 
dist 34=[-17.303970903113291052  ,-5.2330599752249118480 ] 
dist 35=[-18.629018059433872668  ,-5.3633307642957846262 ] 
dist 36=[-19.391566719505810222  ,-5.1745074333440215533 ] 
dist 37=[-19.891201720841537433  ,-4.7731848711342598004 ] 
dist 38=[-20.166237997948076613  ,-3.9808818723133395815 ] 
dist 39=[-20.321319743667205347  ,-3.0011163172658672310 ] 
dist 40=[-20.341753912823407319  ,-1.8513335606115572819 ] 
dist 41=[-20.279561737150729007  ,-.35860228768153280642] 
dist 42=[-20.220734604711303028  ,1.9900288056836229016 ] 
dist 43=[-12.919683317210767679  ,4.3580134656217510443 ] 
dist 44=[-12.781229287023387796  ,5.9281485113774022039 ] 
dist 45=[-12.392729951996778173  ,7.2133427147931972485 ] 
dist 46=[-12.287729496345168388  ,8.4444582673548231144 ] 
dist 47=[-6.0350207795329789800 ,9.5458929516695563080 ] 
dist 48=[-5.4214404703432970588 ,10.313708505696295038  ] 
dist 49=[-4.0434541695873413712 ,10.984134702698876032  ] 
dist 50=[-3.7561782681942550902 ,11.697093701602838845  ] 
dist 51=[-2.0745884751940670567 ,12.322250453431280281  ] 
dist 52=[-1.7736716174897668175 ,12.642266679860057471  ] 
dist 53=[-1.1678731602486263729 ,12.811062305730275781  ] 
dist 54=[-1.0146065787091656993 ,12.838369748488040024  ] 
dist 55=[.42870534230986113701,12.702145545881908543  ] 
dist 56=[.65272530419711078826,12.641598304677276299  ] 
dist 57=[.70553767640122325404,12.581380685756934486  ] 
dist 58=[.52249654693343001398,12.506514821932714462  ] 
dist 59=[.36494073665509634473,9.3916429909014463434 ] 
dist 60=[.201976483068023381  ,9.0151763200390467990 ] 
dist 61=[.04881568342368586989,8.1120629352411043612 ] 
dist 62=[-.06969349639069459459,7.2465980038584408464 ] 
dist 63=[-.18511127927295801914,.03530018770729104712] 
dist 64=[-.42673441536672253071,.01827810813855259945] 
dist 65=[-.6690663099342299009 ,-.23311590141005179026] 
dist 66=[-.89596795159732775541,-.26605812377582654126] 
dist 67=[-1.0954746201973793475 ,-.314770884268016707  ] 
dist 68=[-1.2285281030051337618 ,-.32403339537393192791] 
dist 69=[-1.3384378453283541541 ,-.31920527707241378477] 
dist 70=[-1.4456484603336566553 ,-.2932913490548025962 ] 
dist 71=[-1.5398138197818418601 ,-.24720079264666525645] 
dist 72=[-1.5976709353420756709 ,-.16194979866849677959] 
dist 73=[-1.6401769420201689972 ,-.07247281918932637074] 
dist 74=[-1.6730388510082194942 ,-.00953178893321040366] 
dist 75=[-1.6973381235911285810 ,.04564380772019491598] 
dist 76=[-1.7056510034330556192 ,.10418517608494845849] 
dist 77=[-1.7039140230922192691 ,.15999448518491361396] 
dist 78=[-1.6996532112974701932 ,.20428714559311649869] 
dist 79=[-.72051184290126375405,.24837488380265438095] 
dist 80=[-.63705607242059293415,.30337088181210662089] 
dist 81=[-.46152368713338088466,.35525338598860213125] 
dist 82=[-.43806300929267029005,.38693250764722223612] 
dist 83=[-.3881180025532988358 ,.40970225669566376168] 
dist 84=[-.37429325434225949272,.42607394030392741215] 
dist 85=[-.31964124189605019667,.46173666041590084353] 
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dist 201=[-.06889172942274849090,.02557689307504816539] 
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dist 220=[-.00302576588102180610,.02322748105755131286] 
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dist 222=[-.00414502268041871128,.02491615758935877964] 
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dist 234=[-.02234533171104521017,.00926813056245613163] 
dist 235=[-.02311949945638333584,.00901495224914696275] 
dist 236=[-.02355246700181819044,.00893728267657056832] 
dist 237=[-.02381915502337700674,.00879768845179770130] 
dist 238=[-.02393032400893973254,.00874917227018405540] 
dist 239=[-.02393352634241596042,.00748287679087981862] 
dist 240=[-.02387818227192454040,.00729499702356720970] 
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dist 248=[-.01515169211419176945,.01312647375831187807] 
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dist 250=[-.01140674423202380612,.01329364075783213679] 
dist 251=[-.01124245508006499256,.01302235509670059683] 
dist 252=[-.01117133792736364840,.01293849304139296811] 
dist 253=[-.01110204603999684255,.01287580602309946705] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 0, 0, 1, 2] 
dist 0=[62.019012087182448125  ,62.019012087182448125  ] 
dist 1=[61.664399970153711144  ,62.302188211988659020  ] 
dist 2=[60.531750193706290063  ,62.606021409121429153  ] 
dist 3=[59.176037897969409906  ,62.653286043261310902  ] 
dist 4=[57.824763389416998209  ,62.431848574278872778  ] 
dist 5=[56.215610420256646526  ,62.279260999046417848  ] 
dist 6=[53.829943312495889733  ,61.968301294667612755  ] 
dist 7=[51.121887881166673915  ,61.818007790872130988  ] 
dist 8=[48.225225909090933545  ,57.927650394981473249  ] 
dist 9=[44.629484236667283758  ,57.257669677805611360  ] 
dist 10=[39.129610723483000332  ,56.290227637494785081  ] 
dist 11=[33.584841476277131391  ,55.966886292307851137  ] 
dist 12=[29.809690978927356134  ,55.362767356791470370  ] 
dist 13=[26.599802579777238577  ,55.059921996073946583  ] 
dist 14=[23.312098565699476028  ,52.903845563460595029  ] 
dist 15=[20.216419833642073854  ,47.940008405014639829  ] 
dist 16=[17.773086881487127600  ,32.021265997969424326  ] 
dist 17=[15.332851195331755933  ,30.822024081002368385  ] 
dist 18=[12.248967167022331394  ,28.468148041594233950  ] 
dist 19=[9.2744904952117970026 ,27.870945526650386330  ] 
dist 20=[7.2708814746481748741 ,25.824963864048473470  ] 
dist 21=[5.5873914743062737422 ,25.354694895119333881  ] 
dist 22=[3.8910169913221987988 ,24.855789154281669769  ] 
dist 23=[2.3060102003924529352 ,24.758096663530590106  ] 
dist 24=[1.0667268975988987922 ,5.3425204572034037744 ] 
dist 25=[-.16488217422509308117,3.7738714483295528627 ] 
dist 26=[-1.7205578059387722910 ,3.2819613354052024950 ] 
dist 27=[-3.2566453529336064648 ,1.6827947003038242159 ] 
dist 28=[-5.6782859150480957182 ,.57101272388084123846] 
dist 29=[-7.5141524242240031430 ,.34871059238873976431] 
dist 30=[-9.2778066255576016751 ,-.39247188121523838531] 
dist 31=[-11.410954440476048136  ,-1.3136402393491933897 ] 
dist 32=[-13.420453302389462468  ,-5.8258246631339974314 ] 
dist 33=[-14.690206736401580489  ,-5.9216578440190535035 ] 
dist 34=[-15.664696329097422795  ,-5.8212972776733027388 ] 
dist 35=[-16.494845938990751051  ,-5.6525720552610755852 ] 
dist 36=[-17.171352736076538582  ,-5.4317602154447482735 ] 
dist 37=[-17.532165455780949648  ,-5.1333787668848785217 ] 
dist 38=[-17.731779534292121726  ,-4.6543427640463945123 ] 
dist 39=[-17.764439153907594448  ,-3.5995706301617450636 ] 
dist 40=[-8.8035494619002194486 ,-1.5173075846659012038 ] 
dist 41=[-8.6294391330189670892 ,-.11867990882723733574] 
dist 42=[-8.2941460915211705212 ,1.0447460245672586133 ] 
dist 43=[-8.1988925326893580067 ,2.1888786495904742546 ] 
dist 44=[-7.8302734837732927960 ,3.2313320142707310077 ] 
dist 45=[-7.7341623142398756298 ,3.9892363357611843571 ] 
dist 46=[-7.5522843885331243758 ,4.6832706362466465704 ] 
dist 47=[-7.4970468954281417896 ,5.4710981077288370921 ] 
dist 48=[-2.4427876501744025020 ,6.2017745347003549029 ] 
dist 49=[-2.2410211728044882890 ,6.6529586772087142933 ] 
dist 50=[-2.1879881653541585509 ,6.9807828921520771029 ] 
dist 51=[-.70779817677395979093,7.2260058815292722888 ] 
dist 52=[-.52245111005134864369,7.4021742100934026871 ] 
dist 53=[-.13239580389663903324,7.4544516786557756822 ] 
dist 54=[-.03301483255547089919,7.4603840960480143912 ] 
dist 55=[.35335970750284987982,7.4515046957660558097 ] 
dist 56=[.4269325319055223934 ,5.5004831176907693198 ] 
dist 57=[.5669105429032454595 ,5.8795738124064104759 ] 
dist 58=[.59922586592582800776,6.1529339988867350894 ] 
dist 59=[-.01666682986647633760,6.3546012187814274616 ] 
dist 60=[-.64685111342563002048,6.4997168314606299207 ] 
dist 61=[-1.1465001615963184353 ,6.5472426686129025618 ] 
dist 62=[-1.6451060198794522204 ,6.5554508602216465450 ] 
dist 63=[-2.2711564254456592251 ,6.5435690756201529980 ] 
dist 64=[-2.8673785587069045325 ,1.1355112268821765555 ] 
dist 65=[-3.2470091214622592946 ,.92857670630460697679] 
dist 66=[-3.5398834470458468491 ,.66661206630641507322] 
dist 67=[-3.7900372727060485768 ,.38179522625092511284] 
dist 68=[-3.9929300428409269739 ,.01727318063418357452] 
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dist 70=[-4.1512543388161980077 ,-.16302962980213317894] 
dist 71=[-4.1603889863917378989 ,-.25513556267286055055] 
dist 72=[-3.0375158261666952108 ,-.2645705701444209146 ] 
dist 73=[-3.3803528638021673017 ,-.24744036183203454028] 
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dist 78=[-4.1291512323861735247 ,.06998944689279353128] 
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dist 80=[-3.9373030850020023141 ,.23303607737845818229] 
dist 81=[-3.8935397304246295401 ,.32665505750108976429] 
dist 82=[-3.8291371507808578864 ,.46248861022166956769] 
dist 83=[-3.8027361353963318352 ,.60064521194173401348] 
dist 84=[-3.7165833565500482164 ,.70356249323911003878] 
dist 85=[-3.6843563715466668265 ,.80017754989410228048] 
dist 86=[-3.6220672929077129709 ,.91324353723177488512] 
dist 87=[-3.5985619227861617472 ,1.0281140000962228581 ] 
dist 88=[-2.0191003414313804868 ,1.1319680384207044697 ] 
dist 89=[-1.9581656296330112875 ,1.2476425270709499177 ] 
dist 90=[-1.9399740269754896719 ,1.4097367615335491536 ] 
dist 91=[-.11286658184947250222,1.5664963492177738137 ] 
dist 92=[.45361838690092324799,1.9099903546981146525 ] 
dist 93=[.54935660900624984149,2.2369742321797663656 ] 
dist 94=[.75759281883699961549,2.5507293270454311409 ] 
dist 95=[.79408770818568658569,2.9281119711621882815 ] 
dist 96=[1.0626763873896085025 ,3.2802659388381379762 ] 
dist 97=[1.0986097895186903260 ,3.4933470339038581355 ] 
dist 98=[1.0823507092716596009 ,3.6451721795950369007 ] 
dist 99=[.99072388506221254907,3.7528879507406980407 ] 
dist 100=[.85787954531583438677,3.8304569044499157464 ] 
dist 101=[.67715730924924176932,3.8619884882243561621 ] 
dist 102=[.42700559247243713606,3.8682888912923030596 ] 
dist 103=[.01713636559535930769,3.8624338997087356933 ] 
dist 104=[-.40039284028365066616,1.4675562337548188988 ] 
dist 105=[-.68111214391459708142,1.4088299363678929761 ] 
dist 106=[-.91502092357718817592,1.3957324104628975705 ] 
dist 107=[-1.1457874033717122692 ,.49984155720192773402] 
dist 108=[-1.3565279811638724239 ,.41254109082105036874] 
dist 109=[-1.5105395303996049669 ,.22730385062219913263] 
dist 110=[-1.6523136859755560646 ,.18096920783189666427] 
dist 111=[-1.8142339754559814567 ,-.00660161619853362634] 
dist 112=[-1.9610872552346763089 ,-.04174004052871381314] 
dist 113=[-2.0427435450182448021 ,-.11063907940492951234] 
dist 114=[-2.0921855904564825545 ,-.12712656893099060754] 
dist 115=[-2.1104957699358081362 ,-.17510348672120298553] 
dist 116=[-2.1171549044822994350 ,-.17315363540337070962] 
dist 117=[-2.1201121390991418463 ,-.15165814868237213872] 
dist 118=[-2.1209261199846605378 ,-.09793865561842664402] 
dist 119=[-2.1061817625681149508 ,-.02772144956864427662] 
dist 120=[-1.7141143830920659855 ,.05960526387875986138] 
dist 121=[-1.6632778716116976706 ,.17608287059288171278] 
dist 122=[-1.5039921903497542490 ,.36261791556230602558] 
dist 123=[-.96458778157260494666,.55004948488626191258] 
dist 124=[-.72853687585499505134,.67010709679533684658] 
dist 125=[-.68320551836497119885,.76367295451570204917] 
dist 126=[-.62987571110111131397,.84540510031757739355] 
dist 127=[-.61636989318966592472,.91317761555784462823] 
dist 128=[-.20229047610612315134,.951046980896445594  ] 
dist 129=[-.15130998784451448156,.97423792610002320156] 
dist 130=[-.04215969180745638208,.98344811164259028642] 
dist 131=[-.01711743465333639875,.98739631791757320785] 
dist 132=[.09456030547853021418,1.0296221891408067725 ] 
dist 133=[.11450152055577642662,1.0530508807798005475 ] 
dist 134=[.15297901763551122698,1.0649881822686225734 ] 
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dist 197=[-.53002481235477584311,.16079105439947806169] 
dist 198=[-.52795062272251995016,.14244617711927947343] 
dist 199=[-.5258973769559193262 ,.13838125919644706171] 
dist 200=[-.33518749579232112535,-.1262571921716797649 ] 
dist 201=[-.32815936865037503114,-.10474624446588896283] 
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dist 212=[-.24389770458881636037,.32976933259686347417] 
dist 213=[-.24182758128260526274,.34108966602367542747] 
dist 214=[-.24024231536674670714,.34758907865219499368] 
dist 215=[-.23890296013197832723,.35169391657278609769] 
dist 216=[-.17614095186809769061,.3534601668375586989 ] 
dist 217=[-.16849254334438440934,.3538497363353204809 ] 
dist 218=[-.15018336138625834953,.35283598285124605941] 
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dist 224=[-.1717348379249308394 ,.23669419251165112295] 
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dist 226=[-.21498527443256194081,.24769108036051067446] 
dist 227=[-.23613546234785555325,.25074864866823473308] 
dist 228=[-.24857462064398211811,.25262542068972092858] 
dist 229=[-.25699897421305163718,.2525620819405191567 ] 
dist 230=[-.26213059252794632267,.25133893550929808134] 
dist 231=[-.26540897907923777186,.25013181874148464262] 
dist 232=[-.26643933253066002496,.05941979362060423446] 
dist 233=[-.26601923735984724747,.04542920126789875392] 
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dist 237=[-.19799500015532258006,.11301778790596210686] 
dist 238=[-.19596278824909049436,.13092203087765777004] 
dist 239=[-.1809039819744161406 ,.14641991459161809927] 
dist 240=[-.17738292231657802544,.15628695984455489453] 
dist 241=[-.17162993546799292603,.16390454199473752664] 
dist 242=[-.16983724291679295715,.17042742182815148864] 
dist 243=[-.12829688066954243086,.1758710850139196234 ] 
dist 244=[-.12245838983750823026,.17918285218546069123] 
dist 245=[-.10914083203214425057,.18156157769923059897] 
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dist 248=[-.05918847713354774027,.18459669956948454165] 
dist 249=[-.05259893486019294554,.18403453958825507583] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 2, 1, 2] 
dist 0=[61.134446074730061245  ,61.134446074730061245  ] 
dist 1=[60.927474476654512210  ,61.250561503717881771  ] 
dist 2=[60.480383018829633796  ,61.334735775077321225  ] 
dist 3=[59.685198702262096785  ,61.380065253445595440  ] 
dist 4=[58.088242887979885338  ,61.341090321107139802  ] 
dist 5=[56.119940741396022879  ,61.232578535012210847  ] 
dist 6=[53.841945993532591782  ,61.118024390520823263  ] 
dist 7=[50.896563654071090191  ,60.705924526188360467  ] 
dist 8=[46.263261263916295773  ,60.531544559424671521  ] 
dist 9=[41.545624669099825752  ,60.002894002192252342  ] 
dist 10=[38.263408290182154819  ,59.757826030311523013  ] 
dist 11=[35.398086872477975080  ,58.390253586984657974  ] 
dist 12=[32.344968808411765363  ,57.985015346177911264  ] 
dist 13=[29.397247901882719357  ,56.294176591649040339  ] 
dist 14=[26.952580814905216017  ,53.145922055890820813  ] 
dist 15=[24.402545811408064164  ,30.944091910192392348  ] 
dist 16=[21.033646947301646504  ,29.654512270050360984  ] 
dist 17=[17.717169235771673896  ,28.392082638626899760  ] 
dist 18=[15.376222016419446195  ,28.103824259116505814  ] 
dist 19=[13.294926808170872709  ,19.249859413412294592  ] 
dist 20=[11.014996755444082604  ,18.155586640627046158  ] 
dist 21=[8.7721550097233238906 ,15.876426809208932784  ] 
dist 22=[6.1242617167100130571 ,15.292680712524008181  ] 
dist 23=[2.5104306384207571626 ,13.122096591974877480  ] 
dist 24=[.05055419058479488773,12.702893396200400512  ] 
dist 25=[-2.0421236015449630167 ,11.953217282842726392  ] 
dist 26=[-4.1900167917022344344 ,11.793086694272626793  ] 
dist 27=[-6.2188754807067602752 ,6.0317275903695519754 ] 
dist 28=[-7.8367870480800701740 ,5.4116718183943824516 ] 
dist 29=[-9.4716417355442859897 ,2.9086780129881831151 ] 
dist 30=[-11.569476934686746895  ,1.7452270060428046987 ] 
dist 31=[-13.555419361600685776  ,-4.2659071963698923611 ] 
dist 32=[-14.743556248426779686  ,-4.5913976248781583159 ] 
dist 33=[-15.583331595384506284  ,-5.1886528079543923764 ] 
dist 34=[-16.177151026716427620  ,-5.3100853476016418546 ] 
dist 35=[-16.613707700881904512  ,-5.5488222255344092054 ] 
dist 36=[-16.824771226582700591  ,-5.4524680347058614788 ] 
dist 37=[-16.914102228392215305  ,-5.1882953271093615492 ] 
dist 38=[-16.903005236832353646  ,-4.6300803670551145745 ] 
dist 39=[-15.338121482280854286  ,-3.9286494945141491172 ] 
dist 40=[-15.074928725649900600  ,-3.0925039544422965112 ] 
dist 41=[-14.992509410995852176  ,-1.9989781703056333503 ] 
dist 42=[-14.946837478871328164  ,-.23735319773869684846] 
dist 43=[-13.923556933476526239  ,2.3466479820221476793 ] 
dist 44=[-13.766295673436756022  ,4.0988508222766035941 ] 
dist 45=[-13.474114710541210752  ,5.5756079075421416859 ] 
dist 46=[-13.379016077665137434  ,7.0606808925016093768 ] 
dist 47=[-3.1077710949198865942 ,8.4360921495099284985 ] 
dist 48=[-2.2236411932397415092 ,9.4753694348011026601 ] 
dist 49=[-.28976822420281461415,10.466932569367167314  ] 
dist 50=[.11026304435608986896,11.652082415526969668  ] 
dist 51=[2.1395734489298241151 ,12.755455327577018911  ] 
dist 52=[2.1997491637172018577 ,13.420734311724253217  ] 
dist 53=[2.2499020727541066501 ,13.892507345825893024  ] 
dist 54=[2.1682062609852359758 ,14.223695942058240143  ] 
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dist 56=[1.6543656950479751262 ,14.491174963015397537  ] 
dist 57=[1.2903734497770704874 ,14.453956432420734264  ] 
dist 58=[.96538487012730816798,14.424701593414082843  ] 
dist 59=[.66394989947509056082,13.515552450522365929  ] 
dist 60=[.34794332642927368201,13.341422878019078343  ] 
dist 61=[.0478378617393137177 ,12.834288748925191417  ] 
dist 62=[-.1902287095474482075 ,12.153522226495248693  ] 
dist 63=[-.7541788637105272521 ,.3437499107463532050 ] 
dist 64=[-1.2680983871593141302 ,.3095706823441724979 ] 
dist 65=[-1.7737614826794002442 ,.14565650179740740176] 
dist 66=[-2.3991102350615612038 ,.11898988453476189335] 
dist 67=[-2.9904154742309100025 ,.12274546770485770722] 
dist 68=[-3.3602776402408839074 ,.1689762389835136353 ] 
dist 69=[-3.6381274717282516718 ,.23873906462766239314] 
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dist 71=[-4.0382328142229183626 ,.4726474207712694008 ] 
dist 72=[-4.1231201576271156373 ,.6968210376120400569 ] 
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dist 98=[-1.6625064785733119627 ,2.7886234596065915309 ] 
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dist 100=[-1.6976347075657864685 ,2.4217675146977773332 ] 
dist 101=[-1.6928682408104441049 ,2.3264940377304253500 ] 
dist 102=[-1.6908998473268106076 ,2.2684859853254433243 ] 
dist 103=[-1.6037979658814265314 ,1.8904969764356695822 ] 
dist 104=[-1.5802181780970301245 ,1.8901965879922941262 ] 
dist 105=[-1.5651558072470317906 ,.98786549362477426872] 
dist 106=[-1.5577615854017146989 ,.97412117086174411865] 
dist 107=[-1.0887212684534179235 ,.0075614665482070335 ] 
dist 108=[-1.3128146308448067405 ,-.0436370045877900288 ] 
dist 109=[-1.4865326118388034114 ,-.3593582854847897531 ] 
dist 110=[-1.6366935695728201230 ,-.4126646818704489922 ] 
dist 111=[-1.7601190946084313591 ,-.5179702904474609854 ] 
dist 112=[-1.8271585326439341636 ,-.5423282227045410021 ] 
dist 113=[-1.8656804468635205569 ,-.7253816095152613032 ] 
dist 114=[-1.8753091496068045262 ,-.75455488301090150028] 
dist 115=[-1.8738894886890903890 ,-.75569830234978056401] 
dist 116=[-1.8734385377853876605 ,-.71891425894868490968] 
dist 117=[-1.8729865211658837230 ,-.66066758883904875467] 
dist 118=[-1.8724723458274803168 ,-.57618079995220897025] 
dist 119=[-1.8719994240290605745 ,-.45643523852931140914] 
dist 120=[-1.8717054391961441997 ,-.2575181067355212421 ] 
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dist 122=[-1.8713808177221724780 ,.0830627229173438871 ] 
dist 123=[-.4127054258274813202 ,.1980353610634171276 ] 
dist 124=[-.29485187236111378826,.3123861929999232161 ] 
dist 125=[-.03047382598631820890,.4173772704475371714 ] 
dist 126=[.01936878112933842671,.4950112540300048935 ] 
dist 127=[.33101851288287044211,.5673654610442764670 ] 
dist 128=[.38378413673067234564,.6513228506970680665 ] 
dist 129=[.48689701026189121294,.77588964611839112264] 
dist 130=[.5105099433255105356 ,.97548448558898850669] 
dist 131=[.5961989151845781133 ,1.1655670920405181035 ] 
dist 132=[.5722763614239093002 ,1.2870222845000043109 ] 
dist 133=[.5357189514137484459 ,1.3813055882350800029 ] 
dist 134=[.4839805359653443049 ,1.4629779999285351702 ] 
dist 135=[.4113005952044189409 ,1.5301613910783677770 ] 
dist 136=[.2911973126462459004 ,1.5666364060729020387 ] 
dist 137=[.1679545124097322476 ,1.5875537225827102133 ] 
dist 138=[.08274922716161486674,1.5926648911347733399 ] 
dist 139=[.00923020682578399538,.57417725853188840321] 
dist 140=[-.06739127279501172834,.56441498093155378406] 
dist 141=[-.16436981397809114228,.46833202532794686536] 
dist 142=[-.27401353660305826441,.4490459709011855764 ] 
dist 143=[-.37500301583245430825,.42476620460928465586] 
dist 144=[-.45021015072285384382,.41597413798922462258] 
dist 145=[-.52082588561173217965,.22812232479592274562] 
dist 146=[-.60352836629206514928,.2038481745533989243 ] 
dist 147=[-.67999031013921409715,.1510617888253447635 ] 
dist 148=[-.72569587805981246461,.1383270547372864198 ] 
dist 149=[-.75756520960355368685,.0794962755376007792 ] 
dist 150=[-.77882206867859364503,.0689853332180189128 ] 
dist 151=[-.79368917274242645727,.0444839511572558784 ] 
dist 152=[-.80006646801360299263,.0404972488380560532 ] 
dist 153=[-.80144495651409864806,-.37528268403899975822] 
dist 154=[-.80005781984845092452,-.26275721505904615083] 
dist 155=[-.63556833350204617184,-.1472381245365163346 ] 
dist 156=[-.61655889319092890045,-.06733058594020447394] 
dist 157=[-.5873252277724249017 ,.00165650204727254131] 
dist 158=[-.60311957497740826779,.07361024235917554856] 
dist 159=[-.61159152854417064135,.14181305389963537082] 
dist 160=[-.61310936074520826827,.19583651068391751966] 
dist 161=[-.60623008101612509135,.24972762490732055134] 
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dist 163=[-.59765925045403182576,.38190640692650502834] 
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dist 172=[-.06791163600978928957,.45825353346350811231] 
dist 173=[.01732586128655066737,.5039356088281084166 ] 
dist 174=[.03203011570731099911,.543120210946309484  ] 
dist 175=[.06366527094975790111,.57508767847895675722] 
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dist 184=[-.00123546904336234739,.6048495574885830993 ] 
dist 185=[-.05559515677517660083,.5643331411708914401 ] 
dist 186=[-.0928580998083063790 ,.55935437350222279758] 
dist 187=[-.13369904780532283471,.19369897348253744556] 
dist 188=[-.1875850304024234503 ,.16085169608741525412] 
dist 189=[-.2367320287025685805 ,.08794899819621486372] 
dist 190=[-.2725331635291053166 ,.07268438639658444682] 
dist 191=[-.31132463095936701127,-.01209532049602838533] 
dist 192=[-.36046374929991927582,-.02675458201181358277] 
dist 193=[-.40722495879168414538,-.05793594639013900095] 
dist 194=[-.46272329374059220224,-.06470666463034313803] 
dist 195=[-.5140978185362765961 ,-.11591629034719796818] 
dist 196=[-.54440556314796138522,-.1062574759298211213 ] 
dist 197=[-.56504976182297337353,-.07815828611716104153] 
dist 198=[-.57786767257595907692,-.04671984253715723738] 
dist 199=[-.5864405394098754219 ,-.00685698716609460704] 
dist 200=[-.59014732129927418719,.05485345719525231986] 
dist 201=[-.59099588325190311929,.11672588613752021238] 
dist 202=[-.58962874580902008278,.15723495547631555756] 
dist 203=[-.28883409514719928446,.18979696314076791409] 
dist 204=[-.28629275553529072685,.21996245551287624349] 
dist 205=[-.26177885022299590068,.2462270349609381752 ] 
dist 206=[-.25625123261406642427,.2632252031349143371 ] 
dist 207=[-.2490031479957102605 ,.2766663499690108318 ] 
dist 208=[-.24617512714361075706,.2887389483086264125 ] 
dist 209=[-.17851956616313657189,.2989493211106758686 ] 
dist 210=[-.16923175507843318002,.32777722774689284803] 
dist 211=[-.1492643821289368086 ,.36134585027985710622] 
dist 212=[-.14360617009417066327,.38140430873103036827] 
dist 213=[-.12042839350787224714,.39538192447349793871] 
dist 214=[-.11589529628421334232,.40468898831650018303] 
dist 215=[-.10443109627010418481,.41092901608411106834] 
dist 216=[-.10241643793545547179,.41266980289596349294] 
dist 217=[-.00041901942739681344,.41219656408533112474] 
dist 218=[-.05964269811641941621,.41083192110576902713] 
dist 219=[-.11900522500674469569,.30127221730151475975] 
dist 220=[-.15783068918178234601,.2943972025957596982 ] 
dist 221=[-.18899268333904617389,.28511403353701923875] 
dist 222=[-.21778001546184325207,.28284828495197216034] 
dist 223=[-.24278670389360600418,.26044306648884120585] 
dist 224=[-.25886482399129061181,.25529131277365240864] 
dist 225=[-.27145759143378917403,.24865169199387416647] 
dist 226=[-.28255831446467942281,.24596826363262604146] 
dist 227=[-.29186089015363331702,.17923579684327353662] 
dist 228=[-.29727946520100203614,.17010518751082776103] 
dist 229=[-.30088074806902314077,.15065096725789606245] 
dist 230=[-.3029329642881713313 ,.14516465739753790313] 
dist 231=[-.30382569540073177993,.12289302265596083424] 
dist 232=[-.30322030048995274743,.11845650725182129061] 
dist 233=[-.30088937204343841038,.10758931439034911206] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 2, 2, 1, 0, 1] 
dist 0=[52.219433956882188525  ,52.219433956882188525  ] 
dist 1=[51.755803132143825011  ,52.895282193569255205  ] 
dist 2=[50.580451276461277911  ,53.658109554489566394  ] 
dist 3=[48.730286175646619112  ,54.120994877082208639  ] 
dist 4=[45.687820421052672742  ,54.453221771732421346  ] 
dist 5=[42.555218677865169309  ,54.694207431900310523  ] 
dist 6=[40.345043435567786329  ,54.847992311872840018  ] 
dist 7=[38.383408150269428698  ,54.831851515909568419  ] 
dist 8=[36.242936810651894364  ,53.927045801385160217  ] 
dist 9=[34.145718813435911236  ,53.691138807134991289  ] 
dist 10=[32.356512713873035788  ,53.346846906396520825  ] 
dist 11=[30.445610763775945226  ,53.197510297877806066  ] 
dist 12=[27.861911189764202657  ,52.662756900083331938  ] 
dist 13=[25.289160917537950381  ,52.471158230295432142  ] 
dist 14=[23.421704904319957471  ,52.030800220802115840  ] 
dist 15=[21.707039535511721715  ,51.738202980926391073  ] 
dist 16=[19.744112377054558503  ,35.463483761625612124  ] 
dist 17=[17.762094951130659059  ,34.007801399316741848  ] 
dist 18=[15.710601125422671860  ,30.522129031749106537  ] 
dist 19=[13.261573145467301510  ,29.971073999852756700  ] 
dist 20=[10.759913218602147792  ,24.997625143968572896  ] 
dist 21=[7.5232241008584938988 ,24.075255368022666265  ] 
dist 22=[4.3666112318680506106 ,22.867156056418133242  ] 
dist 23=[2.1844134345413700386 ,22.518199049855434619  ] 
dist 24=[.29086863038348797513,15.131172443083908368  ] 
dist 25=[-1.7134051751898884599 ,14.200995700960100255  ] 
dist 26=[-3.6459672095773685509 ,12.203807061367720143  ] 
dist 27=[-5.2537236385523656643 ,11.745755046224536770  ] 
dist 28=[-6.9402825807980841276 ,9.6099763577296042022 ] 
dist 29=[-9.1889143832319100358 ,9.2350694986107352241 ] 
dist 30=[-11.349257839145210164  ,8.3974553615461720861 ] 
dist 31=[-12.683306616340478416  ,8.2502435380806884602 ] 
dist 32=[-13.676899367564516721  ,.27255417052765851679] 
dist 33=[-14.476465808984236693  ,-.46945196212867333162] 
dist 34=[-15.098881955398908706  ,-1.9620245506184894150 ] 
dist 35=[-15.384333656363206582  ,-2.3253706020486410447 ] 
dist 36=[-15.523005079813704278  ,-2.5458586306038210975 ] 
dist 37=[-15.557401496297742094  ,-2.3690859730854116990 ] 
dist 38=[-15.175320618728037153  ,-2.2235333552487907742 ] 
dist 39=[-16.115269944356256109  ,-2.0759099507488002466 ] 
dist 40=[-16.949149118297766632  ,-1.8901998405852149394 ] 
dist 41=[-17.390972168253358742  ,-1.6967754930409775739 ] 
dist 42=[-17.632662630292875549  ,-1.5180674590830688002 ] 
dist 43=[-17.686601254648115547  ,-1.3171515515739473063 ] 
dist 44=[-17.628708887986959065  ,-.96426728606056281155] 
dist 45=[-17.578432357200162526  ,.08190431467683365903] 
dist 46=[-17.510518401935258903  ,1.4021939831743133051 ] 
dist 47=[-17.439069675071018562  ,3.4403781602048380564 ] 
dist 48=[-4.2808306731434093983 ,5.4866442403718677236 ] 
dist 49=[-3.9795767496116034331 ,6.8393139382577865327 ] 
dist 50=[-2.0595422143009668835 ,7.9423725043338921227 ] 
dist 51=[-1.7167707652789242360 ,8.9926189124302456326 ] 
dist 52=[-1.0677538930218401970 ,9.9283116766865038682 ] 
dist 53=[-.91466380964604563291,10.574290030107821960  ] 
dist 54=[.8819085510833863364 ,11.277511986873154022  ] 
dist 55=[1.0898990624235139825 ,11.827395526792512074  ] 
dist 56=[1.1158272072090128461 ,12.216410866200668110  ] 
dist 57=[1.2927606702384441341 ,12.448263316924408740  ] 
dist 58=[1.3182810589498403970 ,12.561403321035566026  ] 
dist 59=[1.3590278620926361675 ,12.588987559542891552  ] 
dist 60=[1.3616053326841942032 ,12.264976176432612634  ] 
dist 61=[1.1781062821576017286 ,11.825940117118803830  ] 
dist 62=[.76321229704649821583,1.3715046737243647919 ] 
dist 63=[.48356484522892571869,1.3676511308590344543 ] 
dist 64=[.24984550838470755011,1.3646147943200207020 ] 
dist 65=[.01813449074739616629,1.3614520519459099333 ] 
dist 66=[-.19428876931865480091,1.3588009990736347271 ] 
dist 67=[-.35109403450083113925,1.3561123831925510599 ] 
dist 68=[-.49714654269273754754,1.3527662157337675521 ] 
dist 69=[-.66672821644833167379,.50974303387756207933] 
dist 70=[-.82444271495300552449,.44099642986953326362] 
dist 71=[-.92314946410161275228,.2769478975726201779 ] 
dist 72=[-.99762108669508913982,.25343868117325280966] 
dist 73=[-1.0585891329097672683 ,.02745170867138112093] 
dist 74=[-1.1062850087930390353 ,-.01260714503101759533] 
dist 75=[-1.1277733571332545289 ,-.06226044689026760513] 
dist 76=[-1.1371184784907946248 ,-.07053580802907805289] 
dist 77=[-1.1363539445222626973 ,-.35616916133135090956] 
dist 78=[-.79918004133565635128,-.38594229661544722424] 
dist 79=[-.76796777593835402768,-.43380835715470703886] 
dist 80=[-.68780217173461612359,-.38893608266267333723] 
dist 81=[-.67485457159316780704,-.30327906190232508355] 
dist 82=[-.68478625463329609459,-.21967409394886309913] 
dist 83=[-.69543080463005900721,-.14983610816841025708] 
dist 84=[-.69794031051096061609,-.07692561358262041813] 
dist 85=[-.49938182469981215898,.01897204666786200978] 
dist 86=[-.49369658357588448508,.11242809928882139313] 
dist 87=[-.47863166947549238045,.17562110643178101739] 
dist 88=[-.47392091811794584574,.22866081157166193995] 
dist 89=[-.44449060566110026053,.28164440783151594938] 
dist 90=[-.43773497634965905686,.33055831953121115384] 
dist 91=[-.4251252376506767046 ,.36739060477849923177] 
dist 92=[-.42142347359633799643,.40252278393097881809] 
dist 93=[-.34902537504282272784,.44470475452662610748] 
dist 94=[-.33866491895018106927,.48360917062584735878] 
dist 95=[-.31372453215526348113,.50566846800289540533] 
dist 96=[-.30843969835162638687,.51978150496850624607] 
dist 97=[-.27103293434720043644,.52694248799561229036] 
dist 98=[-.26360166694689385105,.53099852287941109976] 
dist 99=[-.25082252232758200852,.53623784700925425674] 
dist 100=[-.2475878347235377227 ,.54938179206645030555] 
dist 101=[-.11899119854570182978,.55912638444900621101] 
dist 102=[-.10485866461591225311,.56627045565051651601] 
dist 103=[-.07675427491625847852,.5690262394839670587 ] 
dist 104=[-.06973025429625117302,.56915367604243610179] 
dist 105=[-.04607391897659813100,.56846607170047170524] 
dist 106=[-.04087850344773383713,.56091204776511158443] 
dist 107=[-.03652345021309519584,.55830809066519044862] 
dist 108=[-.03727330189759392676,.54954273262831745298] 
dist 109=[-.04019717496186230335,.54653145415286966493] 
dist 110=[-.04580522077582790165,.3564365055504349157 ] 
dist 111=[-.05444244126868597023,.33776781349106279932] 
dist 112=[-.09189603158390866352,.29159195522797057   ] 
dist 113=[-.14059021489471524089,.28475872066065700845] 
dist 114=[-.18549267272131383948,.2122081638027205491 ] 
dist 115=[-.21923258362191051257,.19849171246497017588] 
dist 116=[-.25128888833522365663,.19355287868830126014] 
dist 117=[-.28947012420914575226,-.09422471487298504875] 
dist 118=[-.32502028954338708619,-.10720539557215567323] 
dist 119=[-.34657220052730173522,-.13597966511366405304] 
dist 120=[-.36201382168588060282,-.13603066859344389466] 
dist 121=[-.37316865801939104559,-.12892040148970912438] 
dist 122=[-.38149270854407447433,-.11780451191267268803] 
dist 123=[-.38563453602611457071,-.10186786285044986556] 
dist 124=[-.3875108704293431804 ,-.07938540377766391940] 
dist 125=[-.38728295684866401547,-.04214706101426072792] 
dist 126=[-.20048784627155378555,-.00425200051612945099] 
dist 127=[-.20226017568006584446,.02085345116555216446] 
dist 128=[-.20363943359457237838,.04136386405583597850] 
dist 129=[-.20466931389941408803,.06092796977234322230] 
dist 130=[-.20504669579269211931,.07835993984480875649] 
dist 131=[-.20502367166741005177,.09036525988570324468] 
dist 132=[-.20445528824735735886,.10068621286123522902] 
dist 133=[-.07867097942550175020,.11140062818534712426] 
dist 134=[-.06834086865491222930,.12106172606978488058] 
dist 135=[-.04352757251545624670,.12718025707810085372] 
dist 136=[-.03993955281084152852,.13187733438524107353] 
dist 137=[-.00518409725945039372,.13586471132138673009] 
dist 138=[.00102743727941117790,.13909225440932447519] 
dist 139=[.00872438858550619263,.14075643534548254939] 
dist 140=[.01009326921119753565,.14159471410542166234] 
dist 141=[.05095318338394642060,.14152562480786382573] 
dist 142=[.05545143794589398745,.07462322760680055930] 
dist 143=[.04555999555377689395,.08242044364481017787] 
dist 144=[.03390140659039726697,.08906801208609470632] 
dist 145=[.02165995668237154317,.09449957305351254529] 
dist 146=[.01002133634354229657,.09744468306201314313] 
dist 147=[.00076668130333489340,.09913067354302112623] 
dist 148=[-.00848951249267987042,.09954000329299792694] 
dist 149=[-.02013459980149516234,.07233144226617647242] 
dist 150=[-.03122689931311892641,.07101064585418589288] 
dist 151=[-.03827840926221650079,.06737253043229252645] 
dist 152=[-.04370228139937282828,.06668867888416582962] 
dist 153=[-.04830275865138052056,.05964938502199547499] 
dist 154=[-.05202979357804255112,.05815870736079327521] 
dist 155=[-.05397032110536087076,.05633711772836627418] 
dist 156=[-.05502126651523608840,.05561938165100355980] 
dist 157=[-.05521666837785808301,.03929309462667528750] 
dist 158=[-.03915056004458394627,.03712133675582560193] 
dist 159=[-.03844888147552931496,.03250952037819782683] 
dist 160=[-.03664056979835658811,.03124217112220588192] 
dist 161=[-.03616195832051444540,.02625044427235031853] 
dist 162=[-.03309278724211045827,.02527040748380283870] 
dist 163=[-.03263804102779082241,.02305181607610607959] 
dist 164=[-.03156537015089483068,.02251201961388636605] 
dist 165=[-.03120037573790618869,-.00098502729626086013] 
dist 166=[-.03730470164722806053,-.00304356111494758695] 
dist 167=[-.04261230395342842976,-.00701233852892938838] 
dist 168=[-.04768433135762658606,-.00794107722590072001] 
dist 169=[-.05222150920252353824,-.00505039231838841801] 
dist 170=[-.05554298449263559214,-.00091495714692250988] 
dist 171=[-.05901793779815471467,.00303051327169917026] 
dist 172=[-.06298569397918292840,.00753245941205962860] 
dist 173=[-.06659318829654578893,.01397380856476255002] 
dist 174=[-.06863018405206859768,.02030306823588834118] 
dist 175=[-.06990963071139129232,.02435817091265619969] 
dist 176=[-.07049314644756324339,.02752808292375559731] 
dist 177=[-.07071668069901877138,.03032422283756726523] 
dist 178=[-.07060067541429435384,.03267202625144757688] 
dist 179=[-.07020205922612538795,.03405269540180752609] 
dist 180=[-.06990661822459466204,.03499402504761252476] 
dist 181=[-.01095173226901316198,.03558895543751274372] 
dist 182=[-.00910790573998506342,.03598283564162818199] 
dist 183=[-.00877250061988710827,.03998126819728024234] 
dist 184=[-.00802410623675138594,.04478686240620697211] 
dist 185=[-.00778792805678052249,.05065604354637523485] 
dist 186=[-.00671184651770637182,.05485464095462548393] 
dist 187=[-.00647714414993297580,.05838842388675330099] 
dist 188=[-.00591183949146123393,.06193755377190064329] 
dist 189=[-.00573284619949750766,.06506818832088759488] 
dist 190=[-.00545410936860215234,.06693183799122348383] 
dist 191=[-.01001851875030038882,.06822402161849381685] 
dist 192=[-.01370885113789777372,.06907396865662400294] 
dist 193=[-.01716440909781217317,.06957463581568003361] 
dist 194=[-.02019968064592284471,.06959109208989702585] 
dist 195=[-.02221334197258510953,.06916702760746882107] 
dist 196=[-.02386254727446437706,.06885306785755939599] 
dist 197=[-.02544402734418331157,.04320533620341941683] 
dist 198=[-.02682742664398022133,.04109753550152537448] 
dist 199=[-.02768635094857594762,.03580838212272773348] 
dist 200=[-.02832567870613749983,.03498094768619849293] 
dist 201=[-.02883268227948569971,.02661817003778707406] 
dist 202=[-.02954441691669659915,.02501004752841083189] 
dist 203=[-.03254745208141650784,.02307678088018555048] 
dist 204=[-.03583612979395121762,.02254640625147484369] 
dist 205=[-.03883851149834821870,.00793105753804885651] 
dist 206=[-.04069909156900177236,.00610993150789321725] 
dist 207=[-.04207784766667358263,.00221535179488176924] 
dist 208=[-.04315777661952418918,.00129434102539530572] 
dist 209=[-.04396210958964492562,.00105344520926818347] 
dist 210=[-.04424128361795329423,.00314362046551079869] 
dist 211=[-.04427091384214930069,.00471749461207943013] 
dist 212=[-.04415701796008863082,.00664725383627225585] 
dist 213=[-.01343896443544778834,.00920419224907825415] 
dist 214=[-.01396931660649330895,.01162317855315575208] 
dist 215=[-.01429892699865272657,.0131363255590877565 ] 
dist 216=[-.01444105605459127202,.01427272960191418674] 
dist 217=[-.01450858942118750286,.01518892430610645137] 
dist 218=[-.01454046915771834550,.01590760415239765227] 
dist 219=[-.01455255845743783493,.01625612994185666156] 
dist 220=[-.01454126718109216827,.01641966420392104296] 
dist 221=[-.01236431960045281660,.01642863748850050445] 
dist 222=[-.01204393227076690597,.00990166419254585824] 
dist 223=[-.01148539776198013025,.00959759477585731999] 
dist 224=[-.01133736353836492644,.00889860609451441850] 
dist 225=[-.01085973204956129994,.00947253191448403168] 
dist 226=[-.01070465376353154680,.01021337094198750970] 
dist 227=[-.01059108833014455861,.01077582850973435962] 
dist 228=[-.01053980010924484496,.01131623845029485649] 
dist 229=[-.00175905342033490841,.01196880632158288274] 
dist 230=[-.00266554938981453846,.01258069350372090056] 
dist 231=[-.00323483303616146393,.01295853070746867337] 
dist 232=[-.00366494368611548676,.01323712462108485520] 
dist 233=[-.00401650782578600498,.01345257457009996347] 
dist 234=[-.00460650392910885352,.01360967409450070529] 
dist 235=[-.00549938094724847786,.01365509043465478096] 
dist 236=[-.00648329568193700288,.01364176887994901432] 
dist 237=[-.00784812135890693664,.01360777448158494983] 
dist 238=[-.00916838274678529795,.01329443017713866782] 
dist 239=[-.00997456017296317806,.01321042030612725466] 
dist 240=[-.01055860036943226546,.01288363720803705187] 
dist 241=[-.01099248409933898435,.01283043129006819467] 
dist 242=[-.01131718487730165413,.01186521300338941829] 
dist 243=[-.01146546672750754404,.01163723239182915995] 
dist 244=[-.01151711782232445850,.01042297597051325663] 
dist 245=[-.01151128801042281038,.00612883933058058854] 
dist 246=[-.01124038705957975138,.00584724054439577509] 
dist 247=[-.01116945563052961920,.00577927347939590406] 
dist 248=[-.01104007566168293979,.00557716748261973376] 
dist 249=[-.01098606385763004916,.00551523400817665173] 
dist 250=[-.01070006353165308535,.00503505373763420903] 
dist 251=[-.01061860516119841595,.00491985396610339107] 
dist 252=[-.01035589801643949213,.00474103620669652726] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 2, 2, 0, 1] 
dist 0=[54.300623918928485002  ,54.300623918928485002  ] 
dist 1=[53.968437102963016064  ,54.536700780285135893  ] 
dist 2=[52.796613492325455884  ,55.324659413750102095  ] 
dist 3=[50.937459797274397145  ,56.157739196299568036  ] 
dist 4=[47.860961353106494345  ,56.573991925448965291  ] 
dist 5=[44.684626249721633187  ,56.764961371370750358  ] 
dist 6=[42.426761564270715216  ,56.779620634951154997  ] 
dist 7=[40.405929075844489252  ,54.994581933285792684  ] 
dist 8=[38.175729629729892298  ,54.646609422502812346  ] 
dist 9=[35.976641781481869758  ,54.125775654137262674  ] 
dist 10=[34.079762959432280092  ,53.930095341934085243  ] 
dist 11=[32.036727507535297622  ,53.324753383440405562  ] 
dist 12=[29.253550052916139153  ,53.096911940353411231  ] 
dist 13=[26.474711419593599014  ,52.708208290849032293  ] 
dist 14=[24.448725455832921474  ,52.563685895651142924  ] 
dist 15=[22.580386604485936219  ,33.442988026732965496  ] 
dist 16=[20.430697109613124337  ,31.804022951738458777  ] 
dist 17=[18.255357405839742718  ,27.890220970645826986  ] 
dist 18=[16.284067353204607035  ,27.300374310397963530  ] 
dist 19=[14.076431686058793078  ,21.810474654014987710  ] 
dist 20=[10.956117467076763311  ,21.262926973477206908  ] 
dist 21=[7.8845103042667723995 ,19.545281507070216995  ] 
dist 22=[5.8712758223020568440 ,19.251004687827104073  ] 
dist 23=[2.7647304080717487098 ,11.514821182409710535  ] 
dist 24=[.4705168638249787191 ,10.572267328984689497  ] 
dist 25=[-1.5070109210909253901 ,9.4370933812803133338 ] 
dist 26=[-3.5786473629742427199 ,8.7434016656709109720 ] 
dist 27=[-5.5624874908898861689 ,6.0747612695724166051 ] 
dist 28=[-7.1900626498244737300 ,5.7206201966165322699 ] 
dist 29=[-8.8770871811444473125 ,5.0207827421077813451 ] 
dist 30=[-11.099787028123215571  ,4.8611302993311203332 ] 
dist 31=[-13.225199851182619544  ,-1.6910341769244768896 ] 
dist 32=[-14.523813285593490156  ,-2.2796348839942312728 ] 
dist 33=[-15.474795711192275816  ,-3.4488836856117126285 ] 
dist 34=[-16.210805516118579200  ,-3.4618199646494187289 ] 
dist 35=[-16.770208793490540208  ,-3.2765981720498799168 ] 
dist 36=[-17.015180345597727716  ,-2.8796086840489303266 ] 
dist 37=[-17.118190405566211373  ,-2.4512853294453040648 ] 
dist 38=[-17.109796053032253451  ,-2.1408596465773854714 ] 
dist 39=[-16.360795994547374993  ,-1.8607565316877838057 ] 
dist 40=[-16.192977270985472744  ,-1.5527608206635887647 ] 
dist 41=[-15.834485290847912273  ,-1.2536304488749448823 ] 
dist 42=[-15.706197137718780715  ,-1.0086312811679679288 ] 
dist 43=[-15.067825867311789359  ,-.7581219493933680146 ] 
dist 44=[-14.920738944537237771  ,-.4368584649437442080 ] 
dist 45=[-14.434076387003623305  ,-.0322199715635207664 ] 
dist 46=[-14.362224121625471456  ,2.1302984890686113580 ] 
dist 47=[-6.3365480782764833773 ,4.7836881411280799367 ] 
dist 48=[-5.5748496535581230557 ,6.5521577402374206782 ] 
dist 49=[-3.8724848172818381497 ,8.0095455375041041126 ] 
dist 50=[-3.5201333794946381155 ,9.4217556726752119244 ] 
dist 51=[-1.4826347601512855662 ,10.695693733608401770  ] 
dist 52=[-1.1231205896624958762 ,11.601417445023654702  ] 
dist 53=[-.3897747665972417120 ,12.410514776268101367  ] 
dist 54=[-.2044900730159533267 ,13.299007301025941275  ] 
dist 55=[.7140232224268085841 ,14.086375734937384320  ] 
dist 56=[.6991747387837479172 ,14.491988449263360986  ] 
dist 57=[.6757808157270460802 ,14.713441382103118961  ] 
dist 58=[.6432948647307120088 ,14.765689389711175189  ] 
dist 59=[.5984676788599432944 ,14.598089759616953133  ] 
dist 60=[.5257853272905883526 ,14.551119718722368968  ] 
dist 61=[.4493231930673542463 ,13.906395051704239065  ] 
dist 62=[.3893626932791912206 ,12.597068851236309487  ] 
dist 63=[-.3223238047489198756 ,2.1630812345859884128 ] 
dist 64=[-.8192013196007761191 ,1.7139777036668381986 ] 
dist 65=[-1.2210287750357939470 ,.7975821146727631956 ] 
dist 66=[-1.5975720199946798974 ,.7875998709297545603 ] 
dist 67=[-1.9286592146615967129 ,.7702785138073960250 ] 
dist 68=[-2.1491586272749693130 ,.7652386610472129969 ] 
dist 69=[-2.4892961702895869692 ,.51279214054616894147] 
dist 70=[-3.2526816714168764032 ,.48554937402233244339] 
dist 71=[-3.9791074418996271104 ,.41812041820202608315] 
dist 72=[-4.4422041906755921216 ,.40790144266552239148] 
dist 73=[-4.8004686509084311169 ,.3036131202455447067 ] 
dist 74=[-5.1086418583985940300 ,.2836045641565437040 ] 
dist 75=[-5.3605298586998120542 ,.26447888446688177151] 
dist 76=[-5.4942295874113535114 ,.26001203988270766337] 
dist 77=[-5.5667808590199912439 ,.2057629382404925589 ] 
dist 78=[-5.5770177304950462733 ,.1976929977101944076 ] 
dist 79=[-1.1893516342726034450 ,.1770786367115507881 ] 
dist 80=[-1.0422393373247891314 ,.1737085042404806864 ] 
dist 81=[-.6971848465102237361 ,.1385841644737880707 ] 
dist 82=[-.63851348716219850744,.4974179706254249350 ] 
dist 83=[-.56219378960144930142,.8350038133167948108 ] 
dist 84=[-.56083551228623830886,1.0896646707492249205 ] 
dist 85=[-.17796641776230350545,1.3318898664420701442 ] 
dist 86=[-.14928262545210343908,1.6199027666388952035 ] 
dist 87=[-.08218906713209105825,1.8879241530366441617 ] 
dist 88=[-.07182357356615194079,2.0504032782046924003 ] 
dist 89=[-.0748862460472263589 ,2.1664410885873015929 ] 
dist 90=[-.0982481988186569049 ,2.2491756974464826359 ] 
dist 91=[-.1239249494506829760 ,2.3100056805920408178 ] 
dist 92=[-.1593506137621915840 ,2.3386650722528898148 ] 
dist 93=[-.1944879361823033182 ,2.3492497716268239006 ] 
dist 94=[-.2190008834923392814 ,2.3468315276788070717 ] 
dist 95=[-.2402820584358679267 ,1.9999316108936491699 ] 
dist 96=[-.26251490154148608403,1.9559170773460030625 ] 
dist 97=[-.28341701480832504924,1.8348775872243177532 ] 
dist 98=[-.29937239411094163228,1.8125973529118428528 ] 
dist 99=[-.48082456322802971697,1.5799253671774014236 ] 
dist 100=[-.63522486569596061244,1.5310086131860895575 ] 
dist 101=[-.78867430374093981713,1.4717108026625678231 ] 
dist 102=[-.9804426943376582418 ,1.4482988481926364794 ] 
dist 103=[-1.1625479454746805024 ,.9200133547587208677 ] 
dist 104=[-1.2774543069834229048 ,.8506277357958566730 ] 
dist 105=[-1.3648682990624174626 ,.7014539558080723093 ] 
dist 106=[-1.4373142669302309846 ,.6615808474547797609 ] 
dist 107=[-1.4943788461720304778 ,.4988607003760478863 ] 
dist 108=[-1.5204399000557052477 ,.4680024556692542381 ] 
dist 109=[-1.5320545270346288588 ,.3976752088064236393 ] 
dist 110=[-1.5314966997835027587 ,.3827971896280754786 ] 
dist 111=[-1.1813578636081141616 ,.4082721300895583057 ] 
dist 112=[-1.3603698582464418855 ,.44446730866817093867] 
dist 113=[-1.4976088081902889331 ,.47333119437434328813] 
dist 114=[-1.6135696226354284489 ,.4994998726874881123 ] 
dist 115=[-1.7072471626502828920 ,.5217379310001768042 ] 
dist 116=[-1.7555696361202763345 ,.5349319123288570731 ] 
dist 117=[-1.7817260943586871500 ,.5439275315573575189 ] 
dist 118=[-1.7869534832512115705 ,.5494234429451786935 ] 
dist 119=[-1.7741591374970411296 ,.5517759738015643753 ] 
dist 120=[-1.7732389347419764832 ,.5514676023037873129 ] 
dist 121=[-1.7685641366472833488 ,.5437496358091948170 ] 
dist 122=[-1.7612262653169950435 ,.5423467935869964902 ] 
dist 123=[-1.7434918250227025494 ,.5037676411939047915 ] 
dist 124=[-1.7331593430442950989 ,.4728215814163314429 ] 
dist 125=[-1.7075891040350152230 ,.3274259690978217828 ] 
dist 126=[-1.6957503734758554354 ,.2679783513684907246 ] 
dist 127=[-.58221172130676907026,-.02137083556852913188] 
dist 128=[-.48403764621265218345,.1789007001479153110 ] 
dist 129=[-.26415566240209572748,.3836920123304298863 ] 
dist 130=[-.2199814649872363523 ,.5921633647981957785 ] 
dist 131=[-.14173908244662280563,.7867153064416933289 ] 
dist 132=[-.14106924548026325639,.9359717546197825192 ] 
dist 133=[-.1256861919958122508 ,1.0804438384124127722 ] 
dist 134=[-.12330902656071478354,1.2559084258246204278 ] 
dist 135=[-.11656678828938193107,1.4203793443358975641 ] 
dist 136=[-.11543913543100622518,1.5209887950993782860 ] 
dist 137=[-.10166883476991770592,1.5939606840112883636 ] 
dist 138=[-.09870773992853230150,1.6481617288378546347 ] 
dist 139=[-.09570285877842832982,1.6877637763983997611 ] 
dist 140=[-.09468042061273857215,1.7024880411126288800 ] 
dist 141=[-.05916068300275969942,1.7059130317936061692 ] 
dist 142=[-.05447997853658188702,1.7013809535512166921 ] 
dist 143=[-.1601587367616864097 ,.12535080030772853168] 
dist 144=[-.2854406088886809148 ,.12640175469273549373] 
dist 145=[-.4137231993204143298 ,.12691613174604532229] 
dist 146=[-.5552960395401812776 ,.12673839263776208428] 
dist 147=[-.6832804061948227511 ,.12580906587989871357] 
dist 148=[-.7745345132070728374 ,.12512349233309221174] 
dist 149=[-.8562310393215123152 ,.06042416128130512542] 
dist 150=[-.9460861114436687108 ,.05467008440902448985] 
dist 151=[-1.0277793661984328443 ,.04113746919952377674] 
dist 152=[-1.0769130623725094989 ,.03880830723096827075] 
dist 153=[-1.1115402162117666652 ,.02059371765266743985] 
dist 154=[-1.1353552561580021582 ,.01732509521042736977] 
dist 155=[-1.1506796473244594965 ,.01212418843584355661] 
dist 156=[-1.1535800525397011194 ,.01085213800791486693] 
dist 157=[-1.1478149024372373426 ,.02231913137963690767] 
dist 158=[-1.1457053948784085520 ,.17042681301414358077] 
dist 159=[-.82548049673415203474,.31910965662617509359] 
dist 160=[-.822698679254960854  ,.41660149788585538667] 
dist 161=[-.80858039625513713371,.49511050075007105827] 
dist 162=[-.8047447906953464159 ,.5680599658925314745 ] 
dist 163=[-.75403706527188997709,.6317068887745178637 ] 
dist 164=[-.74137741255839886324,.6731022541187491016 ] 
dist 165=[-.72817134492457205083,.7060544909845643666 ] 
dist 166=[-.72114830452156399426,.7360155411620903954 ] 
dist 167=[-.5379749018186344324 ,.7612279666123657743 ] 
dist 168=[-.51264491211699306028,.7752348877299596895 ] 
dist 169=[-.46084156488401221469,.7836844719612454277 ] 
dist 170=[-.44659961232562833594,.7867259284034506775 ] 
dist 171=[-.39147778078180327388,.7860384742687097715 ] 
dist 172=[-.37950325584317302659,.7841392363905580505 ] 
dist 173=[-.35474052722425072808,.7724615309836764917 ] 
dist 174=[-.34755690662279932387,.7688983011334583602 ] 
dist 175=[-.08700375010449610049,.21670006946476530253] 
dist 176=[-.08832088404968579329,.25012802874631927186] 
dist 177=[-.08952196132381371582,.27559956574139961615] 
dist 178=[-.09038931136921227104,.29684393900260435372] 
dist 179=[-.09117145112719584355,.314040361770699539  ] 
dist 180=[-.09203032055450834630,.32335926692439047103] 
dist 181=[-.09268260105798148797,.32868621786355484363] 
dist 182=[-.09264024517654750928,.3299519567326448913 ] 
dist 183=[-.11184331224960241648,.31813145542713878844] 
dist 184=[-.13608534790740243655,.31543541747438657224] 
dist 185=[-.15908117392030196045,.31330440167669160399] 
dist 186=[-.17733139273855601662,.31139879739002296899] 
dist 187=[-.19557296434975826914,.30979121947079324744] 
dist 188=[-.21853504832869441442,.30884793633377956962] 
dist 189=[-.24045799654017641298,.30821190420833130697] 
dist 190=[-.25455423189106053338,.30782848891828361634] 
dist 191=[-.26559762114508515897,.12047894041560625165] 
dist 192=[-.27534135963516296386,.12084040769567915664] 
dist 193=[-.2834904819904007563 ,.12048439026531316499] 
dist 194=[-.28817248352241801445,.12002401317368275036] 
dist 195=[-.29120868511158051107,.11934066441506633583] 
dist 196=[-.29279275679268285558,.11881966284834186522] 
dist 197=[-.29320034319864836418,.10098416912229126506] 
dist 198=[-.29261368881622235698,.09842956262773120491] 
dist 199=[-.2893299562072802722 ,.10804308064346108696] 
dist 200=[-.28752008346989637046,.1200104567073288639 ] 
dist 201=[-.27392115553976746129,.1307091538657520111 ] 
dist 202=[-.27021322438531051513,.13812488001927208439] 
dist 203=[-.26430733911165164025,.14454326348827950555] 
dist 204=[-.25830633880518512807,.15126324337446175284] 
dist 205=[-.20841968277732341767,.15701557972032141969] 
dist 206=[-.19047959209778738104,.1595736944820114631 ] 
dist 207=[-.11820446140743003192,.16071497186215283139] 
dist 208=[-.11974647156986312024,.1608147093628893386 ] 
dist 209=[-.12092607419333761225,.15647475628978535023] 
dist 210=[-.12140060893852361917,.15512934720039426216] 
dist 211=[-.12144956944384761897,.15412304883633437841] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 2, 2, 1, 2] 
dist 0=[51.789781597146459658  ,51.789781597146459658  ] 
dist 1=[50.316136772531948195  ,52.837031103539023138  ] 
dist 2=[47.873082243131960872  ,53.577503213658319245  ] 
dist 3=[45.341621878850335886  ,54.121718617201648691  ] 
dist 4=[43.514866768009347375  ,54.385444731861063947  ] 
dist 5=[41.851850855399491766  ,54.494301380258512037  ] 
dist 6=[39.973868212965770235  ,54.470789497219221995  ] 
dist 7=[38.097189811444938731  ,54.269397082527794117  ] 
dist 8=[36.439112613055495501  ,53.782262284090988777  ] 
dist 9=[34.619820464331891541  ,51.008502523751274491  ] 
dist 10=[32.098940421017076455  ,50.796340833384140384  ] 
dist 11=[29.562664921097460181  ,50.084537190870633496  ] 
dist 12=[27.681632068128921867  ,49.843020400554887661  ] 
dist 13=[25.914835274763001571  ,49.458238979467762522  ] 
dist 14=[23.834378543729643226  ,49.312830302969762002  ] 
dist 15=[21.702515127213529784  ,48.816853348098596920  ] 
dist 16=[19.729939387915604583  ,47.893557854317386051  ] 
dist 17=[17.488148910668027645  ,26.600874800247490738  ] 
dist 18=[14.280107366525855504  ,24.890450361500330631  ] 
dist 19=[11.108745949184098793  ,20.983627338232102152  ] 
dist 20=[9.0133321060506220374 ,20.225588027487057599  ] 
dist 21=[7.2954569574814306190 ,17.505487509500110061  ] 
dist 22=[5.6325525579577924581 ,17.222776353966659454  ] 
dist 23=[4.1225863942870572981 ,13.485908537881163359  ] 
dist 24=[3.0156575595501683860 ,13.114367983531338655  ] 
dist 25=[1.9859773918373386705 ,10.492289261458273583  ] 
dist 26=[.03319397515724284769,9.4182052797214420341 ] 
dist 27=[-1.8616640649729055715 ,4.9365470419809347781 ] 
dist 28=[-3.8561181049285802644 ,4.6087254583352938412 ] 
dist 29=[-5.7721978023646361329 ,3.9479728401095895798 ] 
dist 30=[-7.3547288085751298012 ,3.8089373287090626608 ] 
dist 31=[-9.0047579734574616143 ,-1.8201841497375425015 ] 
dist 32=[-11.191850758002253180  ,-2.3316141047407878565 ] 
dist 33=[-13.285397599548862399  ,-2.4686824327876087387 ] 
dist 34=[-14.561950936388262243  ,-2.4401420715458360180 ] 
dist 35=[-15.493902685961482323  ,-2.3755579449577155729 ] 
dist 36=[-16.210120001972817083  ,-2.2999882991428405943 ] 
dist 37=[-16.753048334734892733  ,-2.2056698233599470855 ] 
dist 38=[-16.992218786216672750  ,-2.0654323350953253177 ] 
dist 39=[-17.091210510005920722  ,-1.9098114500677655784 ] 
dist 40=[-17.074092198920562103  ,-1.7537403571362284642 ] 
dist 41=[-16.277423227236297266  ,-1.5691755953908451864 ] 
dist 42=[-16.103874920722010712  ,-1.2995951681732138392 ] 
dist 43=[-15.739283749392272635  ,-1.0261071967963373586 ] 
dist 44=[-15.611426477705457724  ,-.7738862542276832376 ] 
dist 45=[-14.986794999465395332  ,.24476150418528525128] 
dist 46=[-14.841054901513485945  ,2.3578087273058844913 ] 
dist 47=[-14.371253074100892642  ,4.8767119608852798268 ] 
dist 48=[-14.292222261635344390  ,6.5558297350699316990 ] 
dist 49=[-6.2026309776103952366 ,7.9399027344587761769 ] 
dist 50=[-5.4410009940405909918 ,9.2816071048793756342 ] 
dist 51=[-3.7363062623677583672 ,10.492296315256370534  ] 
dist 52=[-3.3879160564604486946 ,11.353654790303774346  ] 
dist 53=[-1.3425891448573589710 ,12.123730853961531755  ] 
dist 54=[-.98231903227420809139,12.970287213305443765  ] 
dist 55=[-.25564638411231357228,13.720955828464953538  ] 
dist 56=[-.07448948365026131954,14.108438061267887650  ] 
dist 57=[1.1781737629694403961 ,14.318888030585310642  ] 
dist 58=[1.1862480967056217458 ,14.362894120086324619  ] 
dist 59=[1.1970549707353344614 ,14.215081867134247707  ] 
dist 60=[1.1797110894000867386 ,14.165808808210473145  ] 
dist 61=[1.1450118976179822800 ,14.126231266290587411  ] 
dist 62=[1.0779466982219777086 ,13.768261465994465680  ] 
dist 63=[.99548383038496227538,11.329705689283070514  ] 
dist 64=[.63534607425991971366,10.605249019335391640  ] 
dist 65=[-.10760534608693797042,1.3046974439346062272 ] 
dist 66=[-.59775821381585881442,1.2985000196651822413 ] 
dist 67=[-1.2948809230993842347 ,.70199214504956478302] 
dist 68=[-1.8801562636044852057 ,.64934929240809767242] 
dist 69=[-2.4610715071336158381 ,.52151814865439932868] 
dist 70=[-3.1868450218837015658 ,.50297602667399106415] 
dist 71=[-3.8772813511141283649 ,.31816656364645404499] 
dist 72=[-4.3172161410709446378 ,.28443624997917607738] 
dist 73=[-4.6573372778865826608 ,.24412637315326234706] 
dist 74=[-4.9495373300731298156 ,.23670415805575733849] 
dist 75=[-5.1881167196269287548 ,-.03428343819047230982] 
dist 76=[-5.3143004911132758715 ,-.06653634325083302190] 
dist 77=[-5.3821570722535182366 ,-.13477110267411511927] 
dist 78=[-5.3916191720586423158 ,-.14944147500458312203] 
dist 79=[-2.8083429480661528251 ,-.17732985019197740792] 
dist 80=[-2.8022155571134483592 ,-.13783257474339106367] 
dist 81=[-1.2319637635179167386 ,.20714213276519672284] 
dist 82=[-1.0999877694935552621 ,.5624604736016034437 ] 
dist 83=[-.78938843140862551137,.8908643352393187    ] 
dist 84=[-.7362206876552203001 ,1.1370925006704594081 ] 
dist 85=[-.50313979771484616012,1.3698511982370004986 ] 
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dist 163=[-.71942172120041788717,.6062773629577470023 ] 
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dist 175=[.05057321020697025637,.28825889189524101014] 
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dist 178=[-.06550649111614782353,.30032208042067070485] 
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dist 181=[-.13425576934866054544,.32763542077312228569] 
dist 182=[-.14927775059195374906,.32822652170085515042] 
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dist 188=[-.20638913612383964585,.30599759397744459807] 
dist 189=[-.20811597742699547257,.29785512083916448547] 
dist 190=[-.2081836694882612921 ,.29567108481146766481] 
dist 191=[-.20683519225204914381,.11027266466406672787] 
dist 192=[-.20576137372210340392,.09306759067304275566] 
dist 193=[-.18161139523156718563,.05521420148956970857] 
dist 194=[-.18983590883072923672,.04689018637796302330] 
dist 195=[-.20072449969975214906,.00372108909398302585] 
dist 196=[-.22721157419967745436,-.00376536584118222496] 
dist 197=[-.25197753901469109576,-.02053613095046343795] 
dist 198=[-.28082974920045518364,-.02349828448985295984] 
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dist 200=[-.32237141120240809363,-.05176612773830732743] 
dist 201=[-.33206426404079483921,-.05201966739515310800] 
dist 202=[-.33688367336368728296,-.04698969572463630930] 
dist 203=[-.33957466579932805553,-.03896045226900866503] 
dist 204=[-.34077508934133657231,-.02724719966295399566] 
dist 205=[-.3411130638691675001 ,-.01060935390133123764] 
dist 206=[-.34036221940026433856,.01706820353666520730] 
dist 207=[-.160082896992701647  ,.04539914130914321235] 
dist 208=[-.15946297562384354234,.06464410044738325630] 
dist 209=[-.05364813476190848863,.09604073838793350846] 
dist 210=[-.04487838776595643008,.12857137159286386138] 
dist 211=[-.02455616115145795027,.15900437245744086833] 
dist 212=[-.02107710415381012022,.18150665080245239695] 
dist 213=[.00511968716324300788,.20247834111253097778] 
dist 214=[.00970657978163762112,.2268048973920647316 ] 
dist 215=[.01731530880378157562,.24907678118619720887] 
dist 216=[.01744967602480081086,.26185088347557016965] 
dist 217=[.01540444964957967869,.27009685017271864489] 
dist 218=[.01127307506052298153,.27430251312505226678] 
dist 219=[.00482804226372313709,.27730650479232067967] 
dist 220=[-.00644804993018858269,.27830716112281771943] 
dist 221=[-.01994712623599412392,.27709300304226797893] 
dist 222=[-.04234312513475135674,.27025154757393645241] 
dist 223=[-.07898721009058920398,.22559881195501700686] 
dist 224=[-.10273927895768625754,.21144272348153015016] 
dist 225=[-.12156167460555472531,.15501234122459253148] 
dist 226=[-.13853801461983795162,.15322319371948724547] 
dist 227=[-.1529977252596947463 ,.14020708033906586086] 
dist 228=[-.16306629733016821502,.13724918361795020902] 
dist 229=[-.17373755101324158606,.13232333066750916391] 
dist 230=[-.17948179073923106014,.13085485045690398882] 
dist 231=[-.18270782525376625387,.09774698202790793484] 
dist 232=[-.18345299182291278705,.09311409312751183577] 
dist 233=[-.18302074933868584488,.08243766920953920423] 
dist 234=[-.18251620720860022135,.07986001493504699867] 
dist 235=[-.18177309189562813864,.06534229877181641208] 
dist 236=[-.17811893822353997424,.06251329938987855565] 
dist 237=[-.15128695586487003807,.05672592467771531964] 
dist 238=[-.13272884919478785754,.05512091253391662693] 
dist 239=[-.06389488521368185964,.02435822432900608580] 
dist 240=[-.07363945851628568355,.03013289862187096040] 
dist 241=[-.08303437360818506778,.03598932592002486923] 
dist 242=[-.08871857116233719604,.03992038512365263756] 
dist 243=[-.0927698693772954725 ,.04318673434972389832] 
dist 244=[-.09564898788851634308,.04639144188609427613] 
dist 245=[-.09773417375685767402,.04930401056378334576] 
dist 246=[-.09861725064126869072,.05140491954230748648] 
dist 247=[-.09882145140314733220,.05330966480334935357] 
dist 248=[-.09870471921394577654,.05543963909873044779] 
dist 249=[-.09019243868398543180,.05734126081625562689] 
dist 250=[-.08867994610341262894,.05833502604599081073] 
dist 251=[-.08576767396172581741,.05885202293011436314] 
dist 252=[-.08486506923105955758,.05886398516278220248] 
dist 253=[-.08097840968209327241,.05857490767325471081] 
dist 254=[-.07997810938994227575,.05834555553400747174] 
dist 255=[-.07743467797403337474,.05738147233688103279] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 2, 1, 2, 1, 2] 
dist 0=[57.354764866351718699  ,57.354764866351718699  ] 
dist 1=[56.305033960611497682  ,57.733892662547610519  ] 
dist 2=[54.902215471013904162  ,58.062061297047754822  ] 
dist 3=[53.113246532469121518  ,58.480160616723001804  ] 
dist 4=[50.695657925658047456  ,58.703252861606397596  ] 
dist 5=[46.782808382764121535  ,58.814743192423660065  ] 
dist 6=[42.769471915461137334  ,58.787125481717752550  ] 
dist 7=[39.950571582502362653  ,58.656609565611525285  ] 
dist 8=[37.462005301639952081  ,58.565559030443054601  ] 
dist 9=[34.767441872277186294  ,57.982318540727215516  ] 
dist 10=[32.140263896749853492  ,57.743442008347490045  ] 
dist 11=[29.920521743569868617  ,57.488272358415044049  ] 
dist 12=[27.569019228608751397  ,57.325634596473641428  ] 
dist 13=[24.415238703443283080  ,56.932640049592895708  ] 
dist 14=[21.288595738408296682  ,56.737744433247521693  ] 
dist 15=[19.045192755594985399  ,55.342348292261265024  ] 
dist 16=[17.012713155482710295  ,51.932120499516330736  ] 
dist 17=[14.727992079062070319  ,36.926003138842823368  ] 
dist 18=[12.311840688519066782  ,35.264372685562160387  ] 
dist 19=[8.7959038431885589272 ,31.260347918351765740  ] 
dist 20=[5.3705184016891246898 ,30.669918876407322811  ] 
dist 21=[3.0115214296655618822 ,24.930768057265680677  ] 
dist 22=[.9748827428102126069 ,23.877927195632992542  ] 
dist 23=[-1.1636735072792813209 ,22.605452523798422990  ] 
dist 24=[-3.2143856859952199726 ,22.342060734778494220  ] 
dist 25=[-4.9008638854134516070 ,13.780863948314238775  ] 
dist 26=[-6.6522367992155768484 ,12.739451961621222299  ] 
dist 27=[-8.9635196289775581611 ,10.562091972281077473  ] 
dist 28=[-11.178933754056152307  ,10.038139282239400293  ] 
dist 29=[-12.547558217939186584  ,7.9680945956897352623 ] 
dist 30=[-13.567308229261373005  ,7.5818613781858918946 ] 
dist 31=[-14.388384558056479063  ,6.9207006779794700924 ] 
dist 32=[-15.027694438458065505  ,6.7836771971905725666 ] 
dist 33=[-15.321206516990540885  ,-2.0999872084556957369 ] 
dist 34=[-15.462036455082878280  ,-2.8544762608132367343 ] 
dist 35=[-15.490039901836315734  ,-4.3930548946581056148 ] 
dist 36=[-15.092291563420242243  ,-4.7393352328865071658 ] 
dist 37=[-14.975967749553999102  ,-3.9258577924792245119 ] 
dist 38=[-14.715056060594768788  ,-2.7427030686873170486 ] 
dist 39=[-14.610725272115226499  ,-1.9284111721361182051 ] 
dist 40=[-14.055507237979191060  ,-1.2308939105853071997 ] 
dist 41=[-13.920730339627275846  ,-.51326624671104936201] 
dist 42=[-13.500194269964432756  ,.16007261155046827425] 
dist 43=[-13.748055578404660819  ,.68105016819309649313] 
dist 44=[-14.002297137393357818  ,2.0312514477697595205 ] 
dist 45=[-14.176384570071519259  ,4.0623106335913923697 ] 
dist 46=[-14.209288984676492068  ,5.7409062445135559780 ] 
dist 47=[-14.188752131203807215  ,7.3757254673941876509 ] 
dist 48=[-14.148912696365172478  ,8.8562455292420614369 ] 
dist 49=[-1.5401288491047420717 ,9.9192316220280763113 ] 
dist 50=[-.86157427275059947279,10.879705365318592803  ] 
dist 51=[-.68742361418056272665,11.951317481293681816  ] 
dist 52=[.7733009029160988232 ,12.918581052062697308  ] 
dist 53=[1.0085541769044009969 ,13.462635130385261102  ] 
dist 54=[1.2958355206940898540 ,13.801020478017009264  ] 
dist 55=[1.3358355311291693299 ,13.947351167654922410  ] 
dist 56=[1.2779595785148497219 ,14.010743483643116980  ] 
dist 57=[1.0758858257910191814 ,14.018145011134620153  ] 
dist 58=[.7300163102244150351 ,13.986242081788548289  ] 
dist 59=[.0983043956385698429 ,13.932270967983285532  ] 
dist 60=[-.5534458048320314395 ,8.5573202716480094145 ] 
dist 61=[-.9793186382687950170 ,8.6299270863431930727 ] 
dist 62=[-1.3207622913512470971 ,8.6584139026984275357 ] 
dist 63=[-1.6356976446020352350 ,8.6602782715776279739 ] 
dist 64=[-1.9091518052235180880 ,8.6307548945516051195 ] 
dist 65=[-2.0851230843236667612 ,3.1628102678903228256 ] 
dist 66=[-2.2233374476377232038 ,2.7102497392200899493 ] 
dist 67=[-2.3461967963152459641 ,1.8100416136513701692 ] 
dist 68=[-2.4510649906685687530 ,1.8788099236609045016 ] 
dist 69=[-2.5174970508341556573 ,1.9825738235867985907 ] 
dist 70=[-2.5686224845000590539 ,2.0840025103215886498 ] 
dist 71=[-2.8371854617921755228 ,2.1434401905348245806 ] 
dist 72=[-3.0625463543553697245 ,2.1830881015216981967 ] 
dist 73=[-3.6316598624471068537 ,2.2056114410134516200 ] 
dist 74=[-4.0917442596233827633 ,2.2151823871809800203 ] 
dist 75=[-4.4412154070554458331 ,2.2145383834175134996 ] 
dist 76=[-4.7304056763792069337 ,2.1876436976467211154 ] 
dist 77=[-4.9592306093602115685 ,2.1830743623621507968 ] 
dist 78=[-5.0678682515025952900 ,2.0312354619810604842 ] 
dist 79=[-5.1215963073424644085 ,2.0016350535139078103 ] 
dist 80=[-5.1313368277539323578 ,1.9173698921503286954 ] 
dist 81=[-3.1818630464739291135 ,1.8969969279096511697 ] 
dist 82=[-3.1195966008045802921 ,1.7163626687381151346 ] 
dist 83=[-3.0920548673112221617 ,1.6753734633404566849 ] 
dist 84=[-3.0576196718495123857 ,1.6185983922343761369 ] 
dist 85=[-3.0391090521420634233 ,1.5978808524036330398 ] 
dist 86=[-.8768690676646808075 ,1.4017157990034997875 ] 
dist 87=[-.75408851361686011164,1.5073857014291685841 ] 
dist 88=[-.7238741052566450265 ,1.5942868551315202428 ] 
dist 89=[-.58670020070308888165,1.6413095749793753792 ] 
dist 90=[-.56350016441391106479,1.7450357872090832632 ] 
dist 91=[-.5693292136694636934 ,1.8127966971663868438 ] 
dist 92=[-.61626317720232856382,1.9902376130934044264 ] 
dist 93=[-.68581848202089726609,2.2665053117129003560 ] 
dist 94=[-.78186328351102006795,2.5216148783430437995 ] 
dist 95=[-.91539803393925008729,2.6757232592110985014 ] 
dist 96=[-1.1344640563279760255 ,2.8607011458133235836 ] 
dist 97=[-1.3576795507606941064 ,3.2230864418298229862 ] 
dist 98=[-1.5077613773545283210 ,3.4411068533010509679 ] 
dist 99=[-1.6325481874088613074 ,3.5951588088065994875 ] 
dist 100=[-1.7548831333257359146 ,3.7022694284823157043 ] 
dist 101=[-1.8657920824317423111 ,3.7788903575169538556 ] 
dist 102=[-1.9450063076539031087 ,3.8112523420746105140 ] 
dist 103=[-2.0158930741251507788 ,3.8175826771707847500 ] 
dist 104=[-2.0935794099780993410 ,3.8132498833639727202 ] 
dist 105=[-2.1617889407525452109 ,3.4608894826257097201 ] 
dist 106=[-2.1948766265422720722 ,3.3998994341990033585 ] 
dist 107=[-2.2084008399012502109 ,3.2822238267096960541 ] 
dist 108=[-2.2088076056479008662 ,3.2462412889436853313 ] 
dist 109=[-2.1794359135993802704 ,3.0934196820489526908 ] 
dist 110=[-2.1658505064574666590 ,3.0542196176811687475 ] 
dist 111=[-2.1305252928465105304 ,2.9573110896371838082 ] 
dist 112=[-2.1140349168396708376 ,2.9215618823072628104 ] 
dist 113=[-1.4618099930027789270 ,.19473143794934120465] 
dist 114=[-1.5284233538535741395 ,.23292836129565288848] 
dist 115=[-1.5643892202038753372 ,.28139920482055328653] 
dist 116=[-1.5847441514052767363 ,.32772018796160921367] 
dist 117=[-1.5890731442789248958 ,.35734417741328243221] 
dist 118=[-.35372521601124067183,.38031673923194387891] 
dist 119=[-.3425510010785177701 ,.40011305755625796712] 
dist 120=[-.2954644534548928994 ,.41627591347595072653] 
dist 121=[-.2862351869849841269 ,.42475869072430427243] 
dist 122=[-.2627602849398099948 ,.42921231222639973661] 
dist 123=[-.2585814117567707492 ,.45793091156898737551] 
dist 124=[.32162099847610115405,.52824681622351041408] 
dist 125=[.35936236790411692471,.6105355308184957859 ] 
dist 126=[.44116072806726672977,.68656275402795899575] 
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dist 143=[-.4273460161616338898 ,.21799413074445435668] 
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dist 145=[-.48666076979379418086,.15519128570383120165] 
dist 146=[-.50907688785256897937,.09889818513928821949] 
dist 147=[-.52094634738303607848,.08873001694181478624] 
dist 148=[-.52734265894366507558,.06480480295009937692] 
dist 149=[-.52821180123942108129,.06087773676473510591] 
dist 150=[-.5144222114263811956 ,-.1328007518972530129 ] 
dist 151=[-.5300414578869478767 ,-.13063946207700726698] 
dist 152=[-.5411912835526709037 ,-.12305642212128674429] 
dist 153=[-.54813575637878227247,-.10798711573254057229] 
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dist 157=[-.60567786498106321129,.03263422020207558003] 
dist 158=[-.59962326944817403473,.07875272278414423916] 
dist 159=[-.59608475692557153653,.1245889197363627614 ] 
dist 160=[-.59181084125659193828,.16664343191855589663] 
dist 161=[-.58882247135770923719,.19767569785772050001] 
dist 162=[-.57820199116593721545,.2265274552725439102 ] 
dist 163=[-.57402727641026351694,.2598837876804549967 ] 
dist 164=[-.56310600763320300866,.2906450646488525646 ] 
dist 165=[-.55834820425437206413,.3091440169687766432 ] 
dist 166=[-.19034812641532371584,.3221751068554252174 ] 
dist 167=[-.15759035712120458376,.3311218929874122773 ] 
dist 168=[-.08492193816562374618,.3373394410690621064 ] 
dist 169=[-.0696987807650145976 ,.3394823441679302058 ] 
dist 170=[-.03081337644184530343,.3395085248868954954 ] 
dist 171=[-.07765927256764592000,.35966927296264532678] 
dist 172=[-.12459024355076932534,.40693581398914776268] 
dist 173=[-.15514650747570680259,.4632218805558670587 ] 
dist 174=[-.1795042179395006384 ,.51542437805415434692] 
dist 175=[-.20170672414246449693,.54639804644269170712] 
dist 176=[-.22077271986361679779,.56771706051311854448] 
dist 177=[-.23261735911062684283,.58139839157263119844] 
dist 178=[-.24141552861657591905,.5907017786831682925 ] 
dist 179=[-.24832708549655679477,.59455293725141587257] 
dist 180=[-.25374961071232569255,.59514408124790636358] 
dist 181=[-.25660740150415632883,.59395463683932241134] 
dist 182=[-.25812314100981944264,.16685123119899734354] 
dist 183=[-.25819243777989331357,.16235196079232261726] 
dist 184=[-.25731989349271556902,.14459405665732184972] 
dist 185=[-.25634537953885378024,.14072850878308983449] 
dist 186=[-.25256903302024537282,.13226852798455902635] 
dist 187=[-.26733980069595754435,.12967538900532852054] 
dist 188=[-.29901893493870463247,-.02477321865925611547] 
dist 189=[-.33486494660338299064,-.03862257475669311423] 
dist 190=[-.36769832810583415792,-.06617560312704068171] 
dist 191=[-.3873577495806643959 ,-.07279422304949381715] 
dist 192=[-.40110630231491709829,-.09355055170788357064] 
dist 193=[-.4103564847159669447 ,-.09766730298792024333] 
dist 194=[-.41651507878049739635,-.07076181747139306214] 
dist 195=[-.41792880346805654942,-.04061724824746033779] 
dist 196=[-.41726799969402283546,-.00238855093603966096] 
dist 197=[-.41557892911551350887,.05679749081383912779] 
dist 198=[-.30201695692525222348,.11613510865153850493] 
dist 199=[-.29854448343179606416,.15496848368753819569] 
dist 200=[-.28783746279192275449,.18616434302983397118] 
dist 201=[-.28550999541790073357,.21503028240869182845] 
dist 202=[-.25898773579238113606,.24013871826712876426] 
dist 203=[-.25374790905719302483,.25634302881761452626] 
dist 204=[-.24708745137815281838,.26910427817606895098] 
dist 205=[-.24436808282812463295,.28047552095080845968] 
dist 206=[-.17826947571266779659,.29004736446642032715] 
dist 207=[-.16917865740877891726,.29562941173361980373] 
dist 208=[-.14980187628627714051,.29934810960800999192] 
dist 209=[-.1443364503051719289 ,.3014857529413675882 ] 
dist 210=[-.12214158345140559455,.30243696868099031418] 
dist 211=[-.11772400531475400439,.30187002415778980618] 
dist 212=[-.10688859813619523154,.29953019854251751107] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 0, 0, 0, 1] 
dist 0=[60.001956069904515592  ,60.001956069904515592  ] 
dist 1=[59.711796618499726232  ,60.413626995167281958  ] 
dist 2=[59.078643806136977468  ,60.797528726544673040  ] 
dist 3=[57.939391797584180872  ,60.976801872416631818  ] 
dist 4=[56.032209601658684607  ,61.040481025800097316  ] 
dist 5=[53.773287429462317258  ,60.968912316785145496  ] 
dist 6=[51.229467471652077170  ,60.800121003076681234  ] 
dist 7=[47.985117173120944262  ,60.672940616533209511  ] 
dist 8=[42.928868218454845562  ,60.232728564633811962  ] 
dist 9=[37.799089625512898735  ,60.013174767487429930  ] 
dist 10=[34.261044750655035980  ,58.689381302332536565  ] 
dist 11=[31.205057852743670341  ,58.299250916253140962  ] 
dist 12=[27.999971882046741011  ,57.971763597118339976  ] 
dist 13=[24.936536693988836964  ,57.125877776485715316  ] 
dist 14=[22.445950438667091901  ,51.672655678414884600  ] 
dist 15=[19.892255166275712512  ,48.119151065742910242  ] 
dist 16=[16.576360923004208776  ,32.768319113221236561  ] 
dist 17=[13.338698952456675417  ,30.788495585995183563  ] 
dist 18=[11.097142517624155059  ,26.218243720450592514  ] 
dist 19=[9.1494468504057396625 ,25.445997852073664055  ] 
dist 20=[7.0849111253967291874 ,19.558898833016911144  ] 
dist 21=[5.0938506032837071576 ,18.520159337076481407  ] 
dist 22=[3.4390410417463119944 ,16.855974820182077762  ] 
dist 23=[1.7057311696951734240 ,16.461331809524029880  ] 
dist 24=[-.60001606254021802174,14.155344934785978965  ] 
dist 25=[-2.8269319515515655742 ,14.033565844441629531  ] 
dist 26=[-4.2455166474924839935 ,7.9315087496696719167 ] 
dist 27=[-5.3521034437222639092 ,7.5809006909142653777 ] 
dist 28=[-6.3321201740838490023 ,6.5035533902231126277 ] 
dist 29=[-7.1639870451834620053 ,4.3136673727895015787 ] 
dist 30=[-7.6786477550448806909 ,4.0044337710161188954 ] 
dist 31=[-9.1693505219200692859 ,2.6271385092100945671 ] 
dist 32=[-11.386835269191533045  ,-6.2754515749348979682 ] 
dist 33=[-12.743185674830791689  ,-6.4074575594162478516 ] 
dist 34=[-13.737285476704923535  ,-6.2366389563290727554 ] 
dist 35=[-14.507145916719207658  ,-5.7585625077608519349 ] 
dist 36=[-15.107040907738822139  ,-4.9865775047082842820 ] 
dist 37=[-15.421680542972591273  ,-4.0895556032179471260 ] 
dist 38=[-15.590680919750720425  ,-3.1123000682464164727 ] 
dist 39=[-15.609760119712586259  ,-1.8923633835758394278 ] 
dist 40=[-14.653183244337664909  ,-.02697569981605314997] 
dist 41=[-14.473161694369532530  ,1.8469089549147422542 ] 
dist 42=[-14.217156842876095302  ,3.1009135719090343489 ] 
dist 43=[-14.115407203766815762  ,4.1381271000945760536 ] 
dist 44=[-13.854635590593241436  ,5.1474409010689714934 ] 
dist 45=[-13.741924411895435908  ,6.0591772081634482312 ] 
dist 46=[-13.644073779700588536  ,6.7072623791432153695 ] 
dist 47=[-13.569415745946566057  ,7.2853029107786571382 ] 
dist 48=[-3.9086181155806532731 ,7.9177554262572654742 ] 
dist 49=[-3.1077348616964858713 ,8.4810438459182835051 ] 
dist 50=[-1.2943574732049633277 ,8.7831554691370448126 ] 
dist 51=[-.97068777057622406002,8.9514505212101426261 ] 
dist 52=[-.10834588397818486982,8.9892950079561969974 ] 
dist 53=[-.10802983812650388327,8.9606330150587623185 ] 
dist 54=[-.19368296235174578369,8.7670381221412460227 ] 
dist 55=[-.35849291322253868585,8.6863010621146298211 ] 
dist 56=[-.67399569375838801897,7.9831112017589812127 ] 
dist 57=[-1.0005385661405825320 ,8.4814234745202198770 ] 
dist 58=[-1.2094066123727442729 ,9.0306661993567916038 ] 
dist 59=[-1.3717274109000086985 ,9.4761302416394146508 ] 
dist 60=[-1.5125862701932335638 ,9.8216104228261796534 ] 
dist 61=[-1.6286174877799649353 ,9.9717811658802138106 ] 
dist 62=[-1.6918967038945289307 ,10.039096858680385440  ] 
dist 63=[-1.7285824206551121959 ,10.053834102026303212  ] 
dist 64=[-1.7385279204869117627 ,2.0868020223052377570 ] 
dist 65=[-2.1642694407768436777 ,1.7025688929485859953 ] 
dist 66=[-2.6416130480059882247 ,.8583373211209990017 ] 
dist 67=[-2.9422874528127405064 ,.7121693489218005324 ] 
dist 68=[-3.1705339147380131440 ,-.0342678861856050448 ] 
dist 69=[-3.3590025314996091941 ,-.1610771382879754153 ] 
dist 70=[-3.5071606927880563680 ,-.4449043116569238002 ] 
dist 71=[-3.5746404411783176130 ,-.4882731752810729708 ] 
dist 72=[-3.6051265093542715432 ,-.63055056557227535532] 
dist 73=[-3.6056431541293981062 ,-.29581704102426279972] 
dist 74=[-3.5481491174521053392 ,-.06521648895069474355] 
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dist 77=[-4.3685982343081154687 ,.53180723271065787898] 
dist 78=[-4.5921881030932452015 ,.68393792719027081727] 
dist 79=[-4.8576721908279250790 ,.83454719152792774218] 
dist 80=[-5.0970406460714352916 ,1.3725317621819079744 ] 
dist 81=[-5.2164259598562714249 ,1.7755408563737634639 ] 
dist 82=[-5.2785818380223047234 ,2.1125424136593649292 ] 
dist 83=[-5.2893722273767094481 ,2.4464883150691677339 ] 
dist 84=[-5.2145600884367586614 ,2.7519783929835187629 ] 
dist 85=[-5.1890723498130499638 ,2.9754711462184236525 ] 
dist 86=[-5.1683861556213975329 ,3.1811730411145703028 ] 
dist 87=[-5.1490090446660049416 ,3.4156871141041444753 ] 
dist 88=[-4.1911235924591057293 ,3.6272952796166768527 ] 
dist 89=[-4.0552227773218853844 ,3.7416214502521531630 ] 
dist 90=[-3.7970610765453274521 ,3.8062576889924616972 ] 
dist 91=[-3.7280839901058964791 ,3.8201070809137616649 ] 
dist 92=[-3.4802007435679101782 ,3.9372711587694583425 ] 
dist 93=[-3.4154947652067038534 ,4.2187710669443847238 ] 
dist 94=[-3.3212358392090676705 ,4.4457054324045765762 ] 
dist 95=[-3.3016215462501562315 ,4.5671220635636075101 ] 
dist 96=[-3.2537008054828612503 ,4.6344816473999415295 ] 
dist 97=[-3.2289754200387155451 ,4.6475677744248439414 ] 
dist 98=[-2.8744548016001180837 ,4.4804532434199817576 ] 
dist 99=[-2.8138224163671585018 ,4.4389449205871393696 ] 
dist 100=[-2.6634863024996254046 ,4.4046965572394136231 ] 
dist 101=[-2.6204496884536139993 ,4.3757854753985873861 ] 
dist 102=[-2.3629019233311351671 ,4.3417835861324153027 ] 
dist 103=[-2.3061038847426656618 ,4.3211229140193547416 ] 
dist 104=[-2.1977322285094647175 ,4.2705125118561901264 ] 
dist 105=[-2.1663269967688076102 ,4.1436622881124081582 ] 
dist 106=[-1.4255769497945832603 ,-.04490529631781499450] 
dist 107=[-1.6988606755458045657 ,.03071219650151374055] 
dist 108=[-1.9101997271875399620 ,.10812440002758463642] 
dist 109=[-2.0919751493426145777 ,.18061721724073783975] 
dist 110=[-2.2409272058933720251 ,.23660834732296405419] 
dist 111=[-2.3212962016827699713 ,.29114670044410156337] 
dist 112=[-2.3669476870828568120 ,.35784317156081458244] 
dist 113=[-2.3779886746980501286 ,.42055294561740243015] 
dist 114=[-2.3641450529531795280 ,.45918598426962491665] 
dist 115=[-2.3598342049938485607 ,.48751864632338377563] 
dist 116=[-2.3557754416435569147 ,.50913442184375473116] 
dist 117=[-2.3510688936687281947 ,.52568585664842999227] 
dist 118=[-2.3463584808376920196 ,.53381389681823317547] 
dist 119=[-2.3422770555707964598 ,.53731244831882784625] 
dist 120=[-2.3378960922437675128 ,.53742446506010263155] 
dist 121=[-2.3319827222931628663 ,.43508244045932872681] 
dist 122=[-.52534565454096961637,.47251161275980268831] 
dist 123=[-.3777418746605498134 ,.49941603945260963483] 
dist 124=[-.0475045839280320614 ,.51896821421035856288] 
dist 125=[.0156527160036188514 ,.53371803586062523583] 
dist 126=[.4025448218110611198 ,.6609148927315021588 ] 
dist 127=[.4680428202525546242 ,.8631921737942935269 ] 
dist 128=[.46513169236742284253,1.0634921801678682971 ] 
dist 129=[.44753637755972393417,1.3131049051881506862 ] 
dist 130=[.42703335366244287439,1.5502534566532938327 ] 
dist 131=[.40050420204395534294,1.7008240670810296283 ] 
dist 132=[.35886210962050902978,1.8166146331382778264 ] 
dist 133=[.31075447564103946031,1.9149969729534412937 ] 
dist 134=[.25842630272966493901,1.9945032438990326638 ] 
dist 135=[.19304274571940021676,2.0349815021000631525 ] 
dist 136=[.09284222370207371409,2.0545695000006537700 ] 
dist 137=[-.00814239328897751758,2.0572534822982885311 ] 
dist 138=[-.07665504924855952706,.12089658159463273406] 
dist 139=[-.13697631470160049142,.05935107689648745786] 
dist 140=[-.2598458265760320926 ,.04667230820250246197] 
dist 141=[-.4045792905334410944 ,-.02481978919053373776] 
dist 142=[-.5378916248659405977 ,-.03712334361439883374] 
dist 143=[-.6355330055264284633 ,-.06300559182218118397] 
dist 144=[-.7256075496720699871 ,-.06874821606906488179] 
dist 145=[-.8287358326618478193 ,-.11128118128640187739] 
dist 146=[-.9237289581693408496 ,-.11862361021291045942] 
dist 147=[-.9813473385442062057 ,-.12013951142100004562] 
dist 148=[-1.0225485414965727495 ,-.11309807964730475416] 
dist 149=[-1.0520387086142915186 ,-.10127379129113854007] 
dist 150=[-1.0727372197670512998 ,-.08345399549964522153] 
dist 151=[-1.0788632093994351027 ,-.04356721968489251338] 
dist 152=[-1.0788216725453790122 ,.03839763226795366763] 
dist 153=[-1.0749102815320597752 ,.12093151669799103798] 
dist 154=[-.84461885853260781235,.17489588547153315886] 
dist 155=[-.81963466994386781967,.21819889328399869514] 
dist 156=[-.75344926582020023966,.26139359738233009164] 
dist 157=[-.74234742407494129989,.30165985954721059104] 
dist 158=[-.62435445060321077587,.32880068957488694479] 
dist 159=[-.60038082896831504324,.35149293079555227789] 
dist 160=[-.5723227981721366032 ,.38834963544918648994] 
dist 161=[-.56278553321446741074,.47301948845545667942] 
dist 162=[-.3160588445123333732 ,.55286899639395578691] 
dist 163=[-.2843243454192175803 ,.6024683038313979424 ] 
dist 164=[-.2169204381211733954 ,.6393252685738294780 ] 
dist 165=[-.1989110084640367090 ,.6683391720673042382 ] 
dist 166=[-.1291473362448302892 ,.6905520746437523550 ] 
dist 167=[-.1156886671407862685 ,.7002762342611235832 ] 
dist 168=[-.0877681500653582914 ,.7041888477389258758 ] 
dist 169=[-.09210005903052674669,.7032846184516218694 ] 
dist 170=[-.12362257397840867779,.5699280199959602335 ] 
dist 171=[-.14913104722822125916,.6358364020998429973 ] 
dist 172=[-.17305347999059783555,.6851700716043214663 ] 
dist 173=[-.19408650694292157349,.7247159758509361150 ] 
dist 174=[-.20806659807026855454,.7559420676435207621 ] 
dist 175=[-.21953842405293546729,.7720784218595615816 ] 
dist 176=[-.23056359504607312143,.7802389221489865343 ] 
dist 177=[-.24006011353441944783,.7814228498988582146 ] 
dist 178=[-.24543274321905212354,.74299167706234352097] 
dist 179=[-.24880459425134875695,.74055042531661288456] 
dist 180=[-.25031826178343954428,.73684722990162564869] 
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dist 188=[-.1916950822692988179 ,.10574428621102299052] 
dist 189=[-.2826020691277398340 ,.08700398016764411875] 
dist 190=[-.3676983281058341361 ,-.02076639965657731496] 
dist 191=[-.4334246740784066729 ,-.02766078647516083054] 
dist 192=[-.4974700970725914658 ,.00981543577201124907] 
dist 193=[-.5758599692965095443 ,.04860210539846211827] 
dist 194=[-.6496491862364327680 ,.07869556664232699303] 
dist 195=[-.6953385207811393039 ,.10814338760501963513] 
dist 196=[-.7291390069224087765 ,.14435397681905823537] 
dist 197=[-.7554927830457083071 ,.18207911833529116297] 
dist 198=[-.7750046165296785928 ,.21756949284458716909] 
dist 199=[-.7815064037700232717 ,.25817104760648411674] 
dist 200=[-.7831851741468640985 ,.3162882676544878659 ] 
dist 201=[-.7834533400003718628 ,.3730372295965360207 ] 
dist 202=[-.2617243315944740363 ,.4081797466532378151 ] 
dist 203=[-.2723656100969411444 ,.4341761399813931975 ] 
dist 204=[-.2813539610878111726 ,.4544345213396641158 ] 
dist 205=[-.2885770370563734340 ,.4700294494943418539 ] 
dist 206=[-.2921751933478989443 ,.4774198704951500971 ] 
dist 207=[-.2938020076185971976 ,.4805246200306878031 ] 
dist 208=[-.2935291677050612102 ,.4805256683471329564 ] 
dist 209=[-.2912381660504316517 ,.4880646216128346304 ] 
dist 210=[-.2899816335035198216 ,.5211556166168146634 ] 
dist 211=[-.2843893463734721029 ,.5410716962123886444 ] 
dist 212=[-.2828918428361213859 ,.5551258674419850932 ] 
dist 213=[-.2641822146473483221 ,.5648284980301145986 ] 
dist 214=[-.2595475632782886085 ,.5709760510489649968 ] 
dist 215=[-.2545586383935565269 ,.5717973728190328908 ] 
dist 216=[-.2520064440924906542 ,.5686781765280339799 ] 
dist 217=[-.18609560086678575299,.5666970838288919544 ] 
dist 218=[-.17678438853017069862,.37745722217313302963] 
dist 219=[-.19501682880742167758,.3760677355059740527 ] 
dist 220=[-.23139923953997852682,.36938904313988025185] 
dist 221=[-.26520620951032846425,.36759036479886641119] 
dist 222=[-.2947112068292469620 ,.34426369332230289914] 
dist 223=[-.3139297406530739225 ,.33845810480408535061] 
dist 224=[-.3292655366837755015 ,.33234365003292090101] 
dist 225=[-.3432790752141975427 ,.32913173878120402043] 
dist 226=[-.3550870353558193118 ,.24555835988611719282] 
dist 227=[-.3616230133687643102 ,.23399602576765305094] 
dist 228=[-.3655372428782380730 ,.210331521320275056  ] 
dist 229=[-.3668850614680319949 ,.20381904860868084777] 
dist 230=[-.3664736646411533897 ,.17856661089489226173] 
dist 231=[-.3656017611963007424 ,.1730916192398631455 ] 
dist 232=[-.3599982756839964446 ,.16168161818787761547] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 2, 2, 1, 0, 1] 
dist 0=[51.304508078108793071  ,51.304508078108793071  ] 
dist 1=[50.932195745680267366  ,51.899703125685583030  ] 
dist 2=[50.040646782213743264  ,52.507812109407280495  ] 
dist 3=[48.599938090026642041  ,52.775577648016894115  ] 
dist 4=[46.250640780186093455  ,52.875474858946974052  ] 
dist 5=[43.823546256016998706  ,52.853445131383804065  ] 
dist 6=[42.072058424455820897  ,52.406103570966991877  ] 
dist 7=[40.475886679887868043  ,51.860733906502356196  ] 
dist 8=[38.668910971068873069  ,50.728832569509883161  ] 
dist 9=[36.858896967288575070  ,50.560219271957625056  ] 
dist 10=[35.250426745577694980  ,49.799042878137575421  ] 
dist 11=[33.476800103572754252  ,49.590860350081749981  ] 
dist 12=[31.006875243620414403  ,49.022375418809684220  ] 
dist 13=[28.514286802583152988  ,48.814733781366904501  ] 
dist 14=[26.649970509700066876  ,47.632820652181486959  ] 
dist 15=[24.882643672714334499  ,46.533851083635029930  ] 
dist 16=[22.777194305917738835  ,30.146602606814250471  ] 
dist 17=[20.605921649082215994  ,29.690829964876626941  ] 
dist 18=[18.575351184101614240  ,25.049440085987585606  ] 
dist 19=[16.162873324252002978  ,24.186072666637198707  ] 
dist 20=[12.903418431060712861  ,23.847237967036065099  ] 
dist 21=[9.5861092638094818534 ,23.015504928935830969  ] 
dist 22=[7.3804728081085311134 ,15.520974915694194771  ] 
dist 23=[5.5574699424913340803 ,14.601910291164059107  ] 
dist 24=[2.7027570570521930990 ,12.730946340110846795  ] 
dist 25=[.69199343879945663787,12.254900432637212854  ] 
dist 26=[-1.0410945253741380981 ,10.580261436958771981  ] 
dist 27=[-2.8582494621688472747 ,10.238179694292033347  ] 
dist 28=[-4.6012703083437401449 ,9.7744560806818527637 ] 
dist 29=[-6.0389364294217091061 ,9.6604610604973434898 ] 
dist 30=[-7.5374387961790739310 ,-.15654486128276044539] 
dist 31=[-9.5249007573271267262 ,-1.4304211964285136275 ] 
dist 32=[-11.425505155396893161  ,-3.0329006757467057861 ] 
dist 33=[-12.577210268993700307  ,-3.3829689296305129307 ] 
dist 34=[-13.410666882019064448  ,-3.3806692103022038386 ] 
dist 35=[-14.039057369446228653  ,-3.2495410628359770710 ] 
dist 36=[-14.516730330811236154  ,-2.9133935912695706563 ] 
dist 37=[-14.747427706534408009  ,-2.5365752159104333282 ] 
dist 38=[-14.846244426569128462  ,-2.2429604246320286380 ] 
dist 39=[-14.854385286025758221  ,-1.9571450054690761862 ] 
dist 40=[-13.945678359932641210  ,-1.6107545971051746603 ] 
dist 41=[-13.774534445368795205  ,-1.2546330289955465211 ] 
dist 42=[-13.457497639757109032  ,-.92967032356730328824] 
dist 43=[-13.358680408986102422  ,-.5666040995270611253 ] 
dist 44=[-12.998798509813157138  ,-.05818285828538775702] 
dist 45=[-12.998082611977847133  ,.45161166678945980765] 
dist 46=[-12.556551758646730016  ,.82032119730215001434] 
dist 47=[-12.458610870697100513  ,1.7761592039367113538 ] 
dist 48=[-4.6925255601834647610 ,2.7128378348508194166 ] 
dist 49=[-4.0076088569499555249 ,3.6508577450259475331 ] 
dist 50=[-3.5461134728102748476 ,4.4811817417723306245 ] 
dist 51=[-3.4212623661821363127 ,5.0452059355828740226 ] 
dist 52=[-3.3795749027044588526 ,5.5224025195518491891 ] 
dist 53=[.02651798063809972287,6.0063505019186908329 ] 
dist 54=[.63878041431474068015,6.7759160033050717756 ] 
dist 55=[.77747043218321811513,7.8163247206310470504 ] 
dist 56=[2.2683073410476420279 ,8.7763014430510201766 ] 
dist 57=[2.4857725107577244796 ,9.3445578342498358816 ] 
dist 58=[2.7595123784855047579 ,9.7351584653712616944 ] 
dist 59=[2.7877369403560232116 ,9.9859839702839994661 ] 
dist 60=[2.7208403339001730802 ,10.161718523870239651  ] 
dist 61=[2.5159388576931798328 ,10.252560567768022558  ] 
dist 62=[1.8308437460161661877 ,10.298807446275884557  ] 
dist 63=[1.0949974672386312911 ,10.296484387683278523  ] 
dist 64=[.46821046841616266724,3.8625628694485702981 ] 
dist 65=[-.17225907579743162158,3.6935144489905918780 ] 
dist 66=[-.7713573480883153249 ,3.6518409758508400159 ] 
dist 67=[-1.2331081144340999099 ,3.5346820894176694758 ] 
dist 68=[-1.6820440793335342893 ,3.5016600413793391416 ] 
dist 69=[-2.2300364912820555333 ,1.5776022022432348712 ] 
dist 70=[-2.7463356603609596709 ,.90413761025669563811] 
dist 71=[-3.0688232420179888670 ,.43027599268206108246] 
dist 72=[-3.3106657226276708839 ,.32311002044095961716] 
dist 73=[-3.5051893594461731408 ,-.18659087923397419697] 
dist 74=[-3.6589413186240951825 ,-.27559125690358256006] 
dist 75=[-3.7381162084701026579 ,-.46890987628591135774] 
dist 76=[-3.7777127285420822544 ,-.50526512534728773722] 
dist 77=[-4.0047708697858658913 ,-.69750142613391682007] 
dist 78=[-4.1893122820369533387 ,-.71578499604775677576] 
dist 79=[-4.3076099977323286631 ,-.6854589557550942693 ] 
dist 80=[-4.3664080126941506135 ,-.5810934110944115442 ] 
dist 81=[-4.3983700903536286098 ,-.43742946364879626833] 
dist 82=[-4.4095708652293051609 ,-.2502888465794835838 ] 
dist 83=[-4.4077394199383830070 ,.00424571440945794372] 
dist 84=[-4.3927382773492741496 ,.41682034895436706134] 
dist 85=[-2.8982946759599148740 ,.83536427272435052517] 
dist 86=[-2.5432343673195036802 ,1.1137254394860782279 ] 
dist 87=[-2.4862750154581847312 ,1.4387310009181533462 ] 
dist 88=[-2.3557274492743787824 ,1.8710888314351926605 ] 
dist 89=[-2.3137718706761946047 ,2.2659322085165363732 ] 
dist 90=[-2.1203972376241926815 ,2.5545678357189288188 ] 
dist 91=[-2.0784891891164507221 ,2.8203784656507409359 ] 
dist 92=[-1.9787975488514460333 ,3.1241632091224531415 ] 
dist 93=[-1.9470568310123652426 ,3.4011224015235676790 ] 
dist 94=[-.63396392904395825392,3.5598959396333128600 ] 
dist 95=[-.50133677904579251587,3.6623408164954425841 ] 
dist 96=[-.229843663715652768  ,3.7145265321308068350 ] 
dist 97=[-.16050403029103005232,3.7435840702989130839 ] 
dist 98=[.08361670810427964398,3.7537500917155438764 ] 
dist 99=[.13368993452345801957,3.7520272019881246035 ] 
dist 100=[-.07122863660988705579,3.7395134501109294732 ] 
dist 101=[-.55841178926055105639,2.9562763641188810410 ] 
dist 102=[-.8800958610216464429 ,2.8639501618835471061 ] 
dist 103=[-1.1416939871879561122 ,2.6156745343359624392 ] 
dist 104=[-1.3891512514260045411 ,2.5800565864933120838 ] 
dist 105=[-1.6081387352152551208 ,2.1313316583793510251 ] 
dist 106=[-1.7561490555063876776 ,2.1002324926193547842 ] 
dist 107=[-1.8802896160641427509 ,2.1372134721126464515 ] 
dist 108=[-2.0040394260942186272 ,2.1562537845137294307 ] 
dist 109=[-2.1133486346568245504 ,2.1575464874796013463 ] 
dist 110=[-2.1798744880812403504 ,.55856905459059416255] 
dist 111=[-2.2276853001725428753 ,.46471036992486073863] 
dist 112=[-2.2623286375037242063 ,.40954228092986144622] 
dist 113=[-2.2857678567434249685 ,.272166064989745713  ] 
dist 114=[-2.2888771606352600907 ,.22805544075352089444] 
dist 115=[-2.2817151300126149435 ,.21843965026460610511] 
dist 116=[-2.2727140921055536711 ,.16130504658205013709] 
dist 117=[-1.1257141488845153783 ,.15054010850447681487] 
dist 118=[-1.2064785309343226534 ,.12951854542870706516] 
dist 119=[-1.2560764420715631817 ,.12407027649056871163] 
dist 120=[-1.2923209326578012593 ,.05575487816876873349] 
dist 121=[-1.3197937845531819092 ,.04584099506948046044] 
dist 122=[-1.3395063318660434994 ,.02413503974922760947] 
dist 123=[-1.3447801985305018386 ,.01880489493905074557] 
dist 124=[-1.3430971187214774548 ,-.00673054444756616063] 
dist 125=[-1.3385288506923572808 ,-.01145474185151365247] 
dist 126=[-.79532709604733125461,-.02235602965633366286] 
dist 127=[-.74691897659144973583,-.02465942069988743079] 
dist 128=[-.62579855984103092697,.02604242435604024038] 
dist 129=[-.60818990233246521808,.08665172305093649404] 
dist 130=[-.42048490624684566821,.14843501620907390281] 
dist 131=[-.38520597832111171329,.23754535713514105986] 
dist 132=[-.34503184551232592828,.32527744813023277457] 
dist 133=[-.33736774778424882097,.43392292127867464722] 
dist 134=[-.02609784517841215268,.53682843756322230888] 
dist 135=[.01119601718453680055,.60165881369362999012] 
dist 136=[.09031889308714535823,.65093755105715749081] 
dist 137=[.10791777431798125906,.69179299888489566619] 
dist 138=[.18463488634235634905,.72436172280549922344] 
dist 139=[.19832482841266992867,.74057598997450981695] 
dist 140=[.22023341351193434962,.74885441896669300567] 
dist 141=[.22487081960409163667,.74976024606329904227] 
dist 142=[.21172504352380144112,.56334427049619135223] 
dist 143=[.15472181386460736721,.59669612977288468519] 
dist 144=[.09639442046705907746,.61963209276321138438] 
dist 145=[.05614347967741174853,.63436931851426283143] 
dist 146=[.02153423380280960535,.64446257587415520595] 
dist 147=[-.01429222583515235657,.64886277843543854477] 
dist 148=[-.04803969908972674889,.6499472009524119874 ] 
dist 149=[-.07435692547460073080,.64871949927768502536] 
dist 150=[-.10019824898245150745,.589135570704644537  ] 
dist 151=[-.13204670160724999455,.58097053290012998408] 
dist 152=[-.16204631657932537301,.56560837163147245436] 
dist 153=[-.18051317306409953013,.56071183875382275602] 
dist 154=[-.1940136067824960677 ,.53924670221100680292] 
dist 155=[-.20420443994514976885,.53346395521799624498] 
dist 156=[-.21200995611858190742,.51857094143209987382] 
dist 157=[-.21599856919953698307,.51283901381936432046] 
dist 158=[-.2179445434717660974 ,.1478101283656368553 ] 
dist 159=[-.2179207992300834588 ,.11477412830768659241] 
dist 160=[-.24336575753162304992,.04289328634464653108] 
dist 161=[-.31614335118171054402,.02708383454967171360] 
dist 162=[-.38364932875402766619,-.00176553279779261795] 
dist 163=[-.4348212267477920151 ,.00629737216531359873] 
dist 164=[-.4837904856809148057 ,.01364681138847639634] 
dist 165=[-.54250742629317669888,.01893285977040519015] 
dist 166=[-.59721589661366932176,.02592285613705515839] 
dist 167=[-.63018981735754717323,.03964611119119889083] 
dist 168=[-.65353331337203874713,.05265076700109272832] 
dist 169=[-.66981235889019641719,.06083894182297417036] 
dist 170=[-.68103517986042737588,.06705869579699224406] 
dist 171=[-.68420253123282581763,.07221405281881975604] 
dist 172=[-.68383626609077287231,.07630525075865600361] 
dist 173=[-.68142472520317109389,.07827791575681537126] 
dist 174=[-.09136158893341189557,.16138071652954954012] 
dist 175=[-.09027270680709922749,.2183378347846170903 ] 
dist 176=[-.07811022541540999928,.26422492225060631678] 
dist 177=[-.07597108720457815123,.30794726712081859424] 
dist 178=[-.07140638253665086853,.36242713034359653986] 
dist 179=[-.06999811211008423285,.40037021227692706142] 
dist 180=[-.06370502949875560055,.43343100294329772284] 
dist 181=[-.06235913086113253835,.46843102622810090216] 
dist 182=[-.05854195720315558305,.49982927653512887954] 
dist 183=[-.05781993999412658637,.51851849713545349883] 
dist 184=[-.0480596565857996673 ,.53146195092011873892] 
dist 185=[-.05284081162039080883,.53993263589416624657] 
dist 186=[-.05802844438176754033,.54487147275320228568] 
dist 187=[-.06328196908259120776,.54558077547934199926] 
dist 188=[-.06814884807095615769,.54112424815847162206] 
dist 189=[-.07179388070295063684,.54028718429141044221] 
dist 190=[-.09798553612258688698,.33018558726188716505] 
dist 191=[-.14518014776458224317,.31033290658368006196] 
dist 192=[-.18344170826580384264,.2894196298348268635 ] 
dist 193=[-.21945506263175095921,.28548179345589491798] 
dist 194=[-.25121734761857010655,.25301141951271001127] 
dist 195=[-.27251681231158592262,.24612356879127649187] 
dist 196=[-.29020661198432568804,.23585735202132306545] 
dist 197=[-.30756584287196013149,.23259904721644097535] 
dist 198=[-.32281390400646065294,.16159199924850114822] 
dist 199=[-.33207989180098746116,.1519797413872998608 ] 
dist 200=[-.33872616588155152659,.13033040465495224502] 
dist 201=[-.34352134385454134649,.12512643869467416104] 
dist 202=[-.34674962594776118344,.09770248695808206677] 
dist 203=[-.34714366751423895672,.09252959215066747966] 
dist 204=[-.34604144669467658764,.08135562664157755993] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 1, 1, 2] 
dist 0=[55.384657564515132945  ,55.384657564515132945  ] 
dist 1=[54.052392200739673910  ,56.438231131566951990  ] 
dist 2=[52.424159953562649163  ,56.953641087412077450  ] 
dist 3=[50.264219902912244553  ,57.210812176855419935  ] 
dist 4=[46.808655688322113379  ,57.233143610470673577  ] 
dist 5=[43.267191148757305809  ,56.778208859806680196  ] 
dist 6=[40.764154173592764582  ,56.642585316748373902  ] 
dist 7=[38.537642014879417505  ,56.027969919401155508  ] 
dist 8=[36.100238091630679340  ,55.657929054537175733  ] 
dist 9=[33.707522062351042880  ,55.084088580286615110  ] 
dist 10=[31.659289769768475263  ,54.882268671421025145  ] 
dist 11=[29.466240880240617269  ,54.392982627280254653  ] 
dist 12=[26.494897398624251690  ,54.191517256980948323  ] 
dist 13=[23.535407825163089882  ,53.163981764786521289  ] 
dist 14=[21.389498872542835171  ,52.892547626562635469  ] 
dist 15=[19.422591689802784709  ,51.378938488569349241  ] 
dist 16=[17.177652798310726834  ,48.594106986909701740  ] 
dist 17=[14.916753054132873759  ,28.800256599959803011  ] 
dist 18=[12.885694955123001027  ,26.926644469303161757  ] 
dist 19=[10.626217442662338791  ,23.992976516253506630  ] 
dist 20=[7.4521861230579383194 ,23.603803362349286054  ] 
dist 21=[4.3296273460082802062 ,16.881782930737302281  ] 
dist 22=[2.2756326117062342520 ,16.011028796406602066  ] 
dist 23=[.60244100727117138037,14.387050648968734960  ] 
dist 24=[-.99865828241888251817,14.025771539074159939  ] 
dist 25=[-2.4394726496770898766 ,10.645753741484935728  ] 
dist 26=[-3.4723636915579810654 ,10.254236455638603916  ] 
dist 27=[-4.4093925921748873543 ,9.4042188037604726034 ] 
dist 28=[-5.4674920962858158906 ,9.2374867956582761604 ] 
dist 29=[-6.4316240010925690714 ,2.1422189444625550817 ] 
dist 30=[-8.4043444182272197693 ,1.4540697974223992547 ] 
dist 31=[-10.028936300771778171  ,.04041493486756738037] 
dist 32=[-11.544654723943698714  ,-.30148564339233496659] 
dist 33=[-12.881326693567073199  ,-1.5622653800914830042 ] 
dist 34=[-13.790869831341914910  ,-1.8019276428041564287 ] 
dist 35=[-14.565899732140718185  ,-1.5211240113870780305 ] 
dist 36=[-15.365618674479740149  ,-.0708267190201753706 ] 
dist 37=[-16.054695300111964254  ,1.3975556431708737170 ] 
dist 38=[-16.387820942270301426  ,2.3709140294995143104 ] 
dist 39=[-16.558695833382139506  ,3.1643218831312328980 ] 
dist 40=[-16.599113130889311249  ,3.9153112190566340204 ] 
dist 41=[-16.299363746947728384  ,4.5782185157593697009 ] 
dist 42=[-16.219992670207272791  ,5.0204367262063774399 ] 
dist 43=[-16.171637684401054487  ,5.3840411276378075684 ] 
dist 44=[-16.154271285682909411  ,5.7334457567129858320 ] 
dist 45=[-13.475630057844037380  ,6.0386982784333400489 ] 
dist 46=[-13.360187909071591969  ,6.2262200054096326191 ] 
dist 47=[-13.289636502541063102  ,6.3625234545266957442 ] 
dist 48=[-13.262673424219991804  ,6.4635049002212873073 ] 
dist 49=[-2.8468789174179272027 ,6.5331201190353085921 ] 
dist 50=[-2.0038928186551942004 ,6.5442850313168768442 ] 
dist 51=[-1.4924459323114915893 ,6.5195270621140167605 ] 
dist 52=[-1.4440890872745079775 ,6.4945159088752942915 ] 
dist 53=[.1564938984571864118 ,3.3850803887279002733 ] 
dist 54=[.3248685060094042413 ,4.4661559168003335178 ] 
dist 55=[.6972289584642048347 ,5.5250356463233810424 ] 
dist 56=[.7617505206362384526 ,6.8308236289613539862 ] 
dist 57=[1.1742152255722603376 ,8.0681892800379766595 ] 
dist 58=[1.2400148054110803313 ,8.8539819654651972851 ] 
dist 59=[1.3668691095850447112 ,9.4597102534423311843 ] 
dist 60=[1.3933100930575969919 ,9.9783505436790401911 ] 
dist 61=[1.5355911222976326092 ,10.401524738471346365  ] 
dist 62=[1.5397929946821995671 ,10.626198564586773766  ] 
dist 63=[1.5065772046299090933 ,10.748581869774617140  ] 
dist 64=[1.4139174369095584969 ,10.763460402255804950  ] 
dist 65=[.92429591228284028973,2.1856404290390198796 ] 
dist 66=[.06268121660389340028,2.1914246229170544759 ] 
dist 67=[-.65713412573971131089,2.1874419362757536048 ] 
dist 68=[-1.3700717204019620776 ,2.1814654623923541173 ] 
dist 69=[-2.0228435809409864828 ,1.6715750726578055535 ] 
dist 70=[-2.5026795910358468674 ,1.6143332006585571542 ] 
dist 71=[-2.9472286061416698679 ,1.4636937740472852709 ] 
dist 72=[-3.4593044939273359798 ,1.4409375452300152784 ] 
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dist 150=[-.27590644142655373073,.55837156725402022518] 
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dist 162=[-.67868297103010922335,-.2840841798545848757 ] 
dist 163=[-.72706433824390611039,-.2369472672594889946 ] 
dist 164=[-.76591195788710675845,-.15975071497582736699] 
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dist 172=[-.75555697691105718546,.22682160741800471273] 
dist 173=[-.73589949752690511111,.2676900672416932942 ] 
dist 174=[-.72963642585923953668,.29336922637774526734] 
dist 175=[-.71301921582725337152,.31280049622173682952] 
dist 176=[-.70614444489942499183,.32874227649123706   ] 
dist 177=[-.22600194631748879761,.34119045683935572242] 
dist 178=[-.18276183474580924858,.34668352095291081025] 
dist 179=[-.08760921476738292039,.34914986344355445353] 
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dist 181=[.04061925674985327626,.44217962535772183414] 
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dist 188=[.15667456259837983567,.80644308013601048696] 
dist 189=[.1343332651367640388 ,.81966469824805470618] 
dist 190=[.10281511864143924498,.82443690672189479323] 
dist 191=[.05759134658596257812,.82431642686854441264] 
dist 192=[-.02828061082942432857,.82264347588274236371] 
dist 193=[-.11560053354965802291,.36883429031204645919] 
dist 194=[-.17410682412946189657,.36640914298608500779] 
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dist 206=[-.60700669730024344236,-.04228724856131408667] 
dist 207=[-.60448188984053670598,-.02967350232053442622] 
dist 208=[-.60268058698663002256,.05422704247242256641] 
dist 209=[-.40357368901389499237,.1384120387494277403 ] 
dist 210=[-.39693933696266835501,.19367870421286981027] 
dist 211=[-.39728807619889131311,.23827503696889382318] 
dist 212=[-.3961691545268371332 ,.2798868769969141696 ] 
dist 213=[-.33035141321158989449,.31632894298197471817] 
dist 214=[-.32255413543412707073,.34029846313291524211] 
dist 215=[-.31168046837640960747,.35968988473540166856] 
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dist 220=[-.17366359767777574855,.41391801486489572453] 
dist 221=[-.14193280579294510585,.41661676914666213654] 
dist 222=[-.13586305038162660183,.4162931032365394246 ] 
dist 223=[-.12086014486524302015,.41440042304728540099] 
dist 224=[-.1181397431063588636 ,.41259739310183410926] 
dist 225=[-.02426412677766098993,.29682389463896218924] 
dist 226=[-.04529597147275997495,.29786623287651632655] 
dist 227=[-.07116694870924330012,.29734697922007362144] 
dist 228=[-.11036088043389221396,.29649437741431588864] 
dist 229=[-.14933135240902191851,.22561354722750627863] 
dist 230=[-.17431065994573769575,.23005750546028265779] 
dist 231=[-.19379128121875858207,.2321872115095763489 ] 
dist 232=[-.21082294838895609108,.23245055304654898281] 
dist 233=[-.22494791264428563891,.22971788058774064685] 
dist 234=[-.23283119618277311476,.22827266358043068145] 
dist 235=[-.23764012877879537033,.22594616728033276114] 
dist 236=[-.23949868336466779375,.22285593257319467741] 
dist 237=[-.24012747981068305815,.15513695950787650884] 
dist 238=[-.24002980885239445405,.14671342792415773418] 
dist 239=[-.23937923414722484273,.12176209678479238967] 
dist 240=[-.23841367227438809337,.08820101762267683517] 
dist 241=[-.23574933980767680157,.06856884320711865350] 
dist 242=[-.23434607745107397145,.06547347515159973665] 
dist 243=[-.23054952075575123031,.05811015214263394402] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 2, 1, 0, 0, 2] 
dist 0=[65.054995073983131675  ,65.054995073983131675  ] 
dist 1=[64.811550099221720894  ,65.170126893058966492  ] 
dist 2=[64.426961080921754749  ,65.175504662754993665  ] 
dist 3=[63.748067655497237341  ,65.100836601425098616  ] 
dist 4=[62.382786331594353761  ,64.734548077322423150  ] 
dist 5=[60.791505760581617438  ,64.535432104303812045  ] 
dist 6=[59.202391165869303781  ,63.185115838218294023  ] 
dist 7=[56.078737019637091077  ,61.451589785892402539  ] 
dist 8=[52.595305032450413504  ,60.264274359113860402  ] 
dist 9=[50.073085152035212080  ,59.973308402916160477  ] 
dist 10=[47.766501056847954445  ,59.179156396388950686  ] 
dist 11=[43.652006421975726885  ,58.869382381324142028  ] 
dist 12=[37.172495236667906362  ,58.614891080081573448  ] 
dist 13=[30.645444663543142936  ,58.417993822596757851  ] 
dist 14=[26.217899753891746484  ,40.968884901961811452  ] 
dist 15=[22.472113126021089400  ,40.718195198197088778  ] 
dist 16=[18.667186370811262916  ,31.316572728168491689  ] 
dist 17=[15.105839668476474621  ,30.122759817887050483  ] 
dist 18=[12.332437389674264394  ,27.717125554476335263  ] 
dist 19=[9.5983524659331279184 ,27.095122958412039312  ] 
dist 20=[6.1934507434178714573 ,24.872493668896121849  ] 
dist 21=[2.9360669347322124162 ,24.396308076550029850  ] 
dist 22=[.7907569165061088870 ,23.678974515193845528  ] 
dist 23=[-.9577902675486645637 ,23.480538823851124831  ] 
dist 24=[-2.6311376445583777856 ,6.4163139787054958205 ] 
dist 25=[-4.1376249728522215086 ,4.9892767395352174094 ] 
dist 26=[-5.2204338184523258854 ,1.8439304985256461767 ] 
dist 27=[-6.2079208108783377912 ,1.2722032069714194471 ] 
dist 28=[-7.3351423840363942444 ,.25612443178157126801] 
dist 29=[-8.3892774690189459182 ,.15808624344425062554] 
dist 30=[-9.9771178073877042965 ,-3.9926636378731356812 ] 
dist 31=[-11.852059369823511215  ,-4.2450446561494165533 ] 
dist 32=[-13.597565576233619842  ,-6.2257287134798381164 ] 
dist 33=[-14.668432782239313719  ,-6.5336696698098511950 ] 
dist 34=[-15.454149045935318095  ,-6.6616881434357768885 ] 
dist 35=[-16.060657602238213934  ,-6.4158611556355161617 ] 
dist 36=[-16.513650016072470966  ,-5.9802116679330062520 ] 
dist 37=[-16.686142916360758624  ,-5.3083612550129694117 ] 
dist 38=[-16.744575927869839151  ,-4.3376006330747633204 ] 
dist 39=[-16.741803408007507928  ,-2.6502650304576660962 ] 
dist 40=[-10.440721784168658450  ,-.27714503252602307994] 
dist 41=[-10.362131108974656073  ,1.3250926993771581156 ] 
dist 42=[-10.144849655317056517  ,2.6664349401369663122 ] 
dist 43=[-10.057829529073281324  ,3.9990306671754002431 ] 
dist 44=[-9.9796211097786032119 ,5.2215616594033361745 ] 
dist 45=[-9.9236696469600733662 ,6.1239781786173536422 ] 
dist 46=[-2.8196370379010318422 ,6.9637494067606589192 ] 
dist 47=[-2.2311410664133695325 ,7.9365779768870217163 ] 
dist 48=[-1.0420164452180800376 ,8.8269787642132678180 ] 
dist 49=[-.66293975017314874666,9.3378794306495537519 ] 
dist 50=[.1554395535104968340 ,9.6683378058837792084 ] 
dist 51=[.5489705962892094929 ,9.8385770464483719804 ] 
dist 52=[.6308873305116736888 ,9.9389230878855883413 ] 
dist 53=[1.0275039989244204095 ,9.9905399945200511831 ] 
dist 54=[1.0752746097654312504 ,10.016569708142744358  ] 
dist 55=[1.0281124428689456060 ,10.015120767895981054  ] 
dist 56=[.8396465211882879934 ,8.1751513084120249708 ] 
dist 57=[.5753529393365617320 ,7.9415247601518220252 ] 
dist 58=[.2255490934221084956 ,7.3277253562913554118 ] 
dist 59=[-.2534652142729306355 ,7.3081086854076444375 ] 
dist 60=[-1.0334135932517933425 ,7.3567779146120769669 ] 
dist 61=[-1.8199454035637668159 ,7.3679571334233951434 ] 
dist 62=[-2.3252661608183083866 ,1.5137597707523794508 ] 
dist 63=[-2.7209901695914816427 ,1.2312117925367514293 ] 
dist 64=[-3.0702392043611059772 ,.5833340390699376497 ] 
dist 65=[-3.3627229723481763410 ,.47188087840192337385] 
dist 66=[-3.5319681483386926780 ,-.0864214492388408421 ] 
dist 67=[-3.6434198915721339501 ,-.1802577700678485637 ] 
dist 68=[-3.7053446987297096923 ,-.3910728916914889422 ] 
dist 69=[-3.7454427921802264207 ,-.4219810215873635504 ] 
dist 70=[-3.7697974887505325457 ,-.6511684923000289836 ] 
dist 71=[-3.7875126959767563907 ,-.67501554184833261312] 
dist 72=[-3.8010583914769355343 ,-.64631406063360647414] 
dist 73=[-3.8110799040644050546 ,-.53863881050037397068] 
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dist 75=[-3.8143987143718211630 ,-.19226308492069435467] 
dist 76=[-3.8087339418107414757 ,.07583170557767692041] 
dist 77=[-3.5371328826620792007 ,.51075557919148700341] 
dist 78=[-3.6969591403544925309 ,.95344061241301499178] 
dist 79=[-3.7743266002653164907 ,1.2525006762373551015 ] 
dist 80=[-3.8133531246556265148 ,1.5029643926713782030 ] 
dist 81=[-3.8200264403530194028 ,1.7518053162639375680 ] 
dist 82=[-3.7516468221990688690 ,1.9798780612295333487 ] 
dist 83=[-3.7300837004223193042 ,2.1474971651831206018 ] 
dist 84=[-3.7137644365915066991 ,2.3025461592253777406 ] 
dist 85=[-3.7004576037890113204 ,2.4804693576030887110 ] 
dist 86=[-2.9908440256494148401 ,2.6416485142074601288 ] 
dist 87=[-2.8909788487667401428 ,2.7299012662544748167 ] 
dist 88=[-2.7012930692205786801 ,2.7813897605194804635 ] 
dist 89=[-2.6508567004890832056 ,2.9056657132570730414 ] 
dist 90=[-2.4852769651999484943 ,2.9713312686471376495 ] 
dist 91=[-2.4831928162423754731 ,3.1396946145457469840 ] 
dist 92=[-2.4431866449071548885 ,3.3203894966731438254 ] 
dist 93=[-2.4276525189020836644 ,3.4177956342334286936 ] 
dist 94=[-2.3841606603593925668 ,3.4728386781832125384 ] 
dist 95=[-2.3642752221092570244 ,3.4844760875969941710 ] 
dist 96=[-2.0775188661516427128 ,3.3763664182428809546 ] 
dist 97=[-2.0297893334275582592 ,3.3504373289476252909 ] 
dist 98=[-1.9108854759670423654 ,3.3294672862621453958 ] 
dist 99=[-1.8792312223073298952 ,3.3099059290693957379 ] 
dist 100=[-1.6765038011033272654 ,3.2928802051262024913 ] 
dist 101=[-1.6325135061876229107 ,3.2820334129267969485 ] 
dist 102=[-1.5518264830943453421 ,3.2624958447007451442 ] 
dist 103=[-1.5294662588456861298 ,3.1729107490131688412 ] 
dist 104=[-1.3720139667985377433 ,-.8807958595723118510 ] 
dist 105=[-1.4039535142881856167 ,-.8209221781890007135 ] 
dist 106=[-1.4402398648675041965 ,-.7351098423570869592 ] 
dist 107=[-1.5916723870249582412 ,-.6140410000553876748 ] 
dist 108=[-1.7169756665391108147 ,-.4135254786614589178 ] 
dist 109=[-1.7864969763773983641 ,-.20784253442108181312] 
dist 110=[-1.8284255119213425976 ,-.06615987975812985368] 
dist 111=[-1.8436431303127900953 ,.05548973485581956136] 
dist 112=[-1.8490352478660769885 ,.18126002656963364306] 
dist 113=[-1.8517599001544063084 ,.29974286537962962026] 
dist 114=[-1.8530904600395591270 ,.39232237786219501828] 
dist 115=[-1.8529103181919871847 ,.4834702492830935305 ] 
dist 116=[-1.8518070719284214566 ,.59624180496100323648] 
dist 117=[-1.8494491631551058164 ,.70284102169063797226] 
dist 118=[-1.8457358031235830030 ,.76936664310360598962] 
dist 119=[-1.8392186104515954211 ,.81914169253331230867] 
dist 120=[-.45184048665861430666,.85892103969638040407] 
dist 121=[-.33783516651061652033,.88955041016676212166] 
dist 122=[-.1740725657601694973 ,.90282456482318980645] 
dist 123=[-.1370160013362954489 ,.90837174191773971071] 
dist 124=[-.1272790425084708686 ,.90817919137777729207] 
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dist 208=[-.20240854766341124766,.41641022787707254016] 
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dist 230=[-.26486100841643493453,.14234845339873483174] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 0, 0, 0, 2] 
dist 0=[61.548983411790816277  ,61.548983411790816277  ] 
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dist 5=[54.789325988592826289  ,61.878822395997066135  ] 
dist 6=[53.030561288685428204  ,61.789840025192116583  ] 
dist 7=[51.153891510446567412  ,61.710294626998031579  ] 
dist 8=[49.309758860569173669  ,61.002139497657972351  ] 
dist 9=[47.132063546868684470  ,56.123042843673691099  ] 
dist 10=[43.923232795990078702  ,55.321543265574909477  ] 
dist 11=[40.612127879273383433  ,53.876290443100538794  ] 
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dist 14=[29.844841225006132281  ,51.806922631418861848  ] 
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dist 17=[15.382437056924689354  ,34.824152684453744938  ] 
dist 18=[11.770942148099115785  ,34.611677507953534699  ] 
dist 19=[8.4401284187604720068 ,19.655971572969250516  ] 
dist 20=[5.9290869200353197673 ,18.949465375560093367  ] 
dist 21=[3.5324124414583685702 ,12.493532642536065012  ] 
dist 22=[.65825978239203823074,11.353977123020093388  ] 
dist 23=[-2.0428821961912596122 ,9.8831863310015125621 ] 
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dist 33=[-14.525662910307481700  ,-5.1264863103108349940 ] 
dist 34=[-14.530725431237085840  ,-4.2358164149649070014 ] 
dist 35=[-7.4629329504363504985 ,-3.0637296260272708644 ] 
dist 36=[-7.5409175998433720559 ,-1.9019659228405206771 ] 
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dist 44=[-5.8449130246365230750 ,4.9402365267924137755 ] 
dist 45=[-5.5720067966787212947 ,5.3481960420806026891 ] 
dist 46=[-5.4944888997622167712 ,5.6786916726749317633 ] 
dist 47=[-5.4289633131942809077 ,5.9363621287891487876 ] 
dist 48=[-5.4070495155512001070 ,6.0536618215532717048 ] 
dist 49=[-.8789761813036049757 ,6.1081768236997727599 ] 
dist 50=[-.51124571223318803008,6.1154239211521312752 ] 
dist 51=[.30094368160640417522,5.8715068460031706159 ] 
dist 52=[.45257110723300620672,5.8197862753843932440 ] 
dist 53=[.97899519034780154734,5.6418850183826240405 ] 
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dist 108=[-1.4971796937187215206 ,1.1549898977104343194 ] 
dist 109=[-1.5001462376011857085 ,1.1355240175216929585 ] 
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dist 111=[-1.2051856787203266472 ,1.1220544270699695883 ] 
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dist 113=[-1.0818575401272714517 ,.17510534123681497748] 
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dist 117=[-.83196621457410244165,.46806436701157980185] 
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dist 122=[-.95631733760185028115,.89276615786807738211] 
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dist 128=[-1.1360782554061640585 ,.83755575548905184524] 
dist 129=[.03148964205930617078,.91751826842345438098] 
dist 130=[.08308336562331439941,.98491952002031407988] 
dist 131=[.19820871434746855491,1.0391834942124084080 ] 
dist 132=[.21658565452301543487,1.0667242772331297027 ] 
dist 133=[.34503501478192254806,1.0814553511811577536 ] 
dist 134=[.36585935345872533862,1.0846037336539622902 ] 
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dist 146=[-.39927055854623153713,.43370820811354206688] 
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dist 149=[-.69233743727831787182,.29477538738375246221] 
dist 150=[-.79583281325256784058,.27887177736881973246] 
dist 151=[-.89238835415738096864,.26069613825772741101] 
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dist 196=[-.21633383742548669014,-.04527176266781139137] 
dist 197=[-.23021160632925686669,-.05013460608949689295] 
dist 198=[-.24587387298388164504,-.04852243970738930978] 
dist 199=[-.25996633564783857876,-.04355186551528577480] 
dist 200=[-.27164428914416254248,-.03270885910996092274] 
dist 201=[-.29585404786727398717,-.02012846893459563241] 
dist 202=[-.31003681511079570277,-.00822571381784263942] 
dist 203=[-.31957519749580426405,.00544418656940342483] 
dist 204=[-.32525371299139168149,.02507578144264339984] 
dist 205=[-.32873395731856936954,.04700650274012337542] 
dist 206=[-.32950122465902879328,.06984995217487825178] 
dist 207=[-.32866441591472838778,.09770908054009781085] 
dist 208=[-.32767477352531563623,.13965216261522103064] 
dist 209=[-.24210050801143828944,.18126848995104083884] 
dist 210=[-.23283938017514155397,.20782399757180007186] 
dist 211=[-.21456234353550910319,.22840051785668529521] 
dist 212=[-.21134143084686788986,.24616126953970346088] 
dist 213=[-.186042660389029322  ,.26072653200315216925] 
dist 214=[-.18068234839843956848,.26855337631473128268] 
dist 215=[-.172326144997525435  ,.27293381990043503041] 
dist 216=[-.1698057350607533387 ,.27386599701248821932] 
dist 217=[-.11562740825133550432,.27320014901970356798] 
dist 218=[-.10827638052044663007,.27214346134380799305] 
dist 219=[-.09141127513780000158,.27051303262527436325] 
dist 220=[-.08763873525888725636,.26614184902266199157] 
dist 221=[-.06539449655709499923,.22997413975458500917] 
dist 222=[-.06119849628980287429,.21952615610501116459] 
dist 223=[-.05283352431654367288,.2201142947776279038 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 1, 2, 0, 1, 2] 
dist 0=[54.895905105161461123  ,54.895905105161461123  ] 
dist 1=[54.542255448734091828  ,55.048864541171550744  ] 
dist 2=[53.873358839262061974  ,55.305833200339147218  ] 
dist 3=[52.745706716863256830  ,55.525412761305877227  ] 
dist 4=[51.347652645856032975  ,55.660154941484475092  ] 
dist 5=[49.598886267380475520  ,55.757961217794047669  ] 
dist 6=[47.254422882161725584  ,55.829819243906310130  ] 
dist 7=[43.477549831956739255  ,55.869970785459889492  ] 
dist 8=[39.612056570238052701  ,55.841225962270843878  ] 
dist 9=[36.913627675636426428  ,55.755669711384132185  ] 
dist 10=[34.547608310808058122  ,55.660049421501318417  ] 
dist 11=[32.009312527107445048  ,55.332144182962715972  ] 
dist 12=[29.547071144740338240  ,55.187946601022556766  ] 
dist 13=[27.484516956498989748  ,54.760124202247071863  ] 
dist 14=[24.656944583832679094  ,54.134047553757306404  ] 
dist 15=[21.544817943552361524  ,39.745074464798065659  ] 
dist 16=[18.579984508770997615  ,38.401843912575311115  ] 
dist 17=[16.183638369591098530  ,35.096194540354243569  ] 
dist 18=[13.738284605869846861  ,34.621976150074249929  ] 
dist 19=[10.577126550470940441  ,29.622523212072271338  ] 
dist 20=[7.4942774120706931657 ,28.681672731372147258  ] 
dist 21=[5.3613231213886152978 ,27.641772832581936970  ] 
dist 22=[3.5081291129594531600 ,27.457372137110476586  ] 
dist 23=[1.5421409926788649149 ,18.929821219852153912  ] 
dist 24=[-.35691257016119969138,17.879213844663186281  ] 
dist 25=[-1.9433998646545610343 ,15.762681788829709544  ] 
dist 26=[-3.6139923998164537337 ,15.226208228959360585  ] 
dist 27=[-5.8503366941027252223 ,13.361296786429277419  ] 
dist 28=[-8.0015392027960147512 ,12.967923360199770619  ] 
dist 29=[-9.3321854949773006760 ,12.490248589532076014  ] 
dist 30=[-10.326401208255353790  ,12.400573191528465114  ] 
dist 31=[-11.132851971668225356  ,-.56103776462231700542] 
dist 32=[-11.774752499599369664  ,-1.6103612717206129414 ] 
dist 33=[-12.110990506439132575  ,-3.8510193647011343533 ] 
dist 34=[-12.291125387179294554  ,-4.2911540118258292925 ] 
dist 35=[-12.329430390604232809  ,-6.3945979504692776707 ] 
dist 36=[-11.969709630455628467  ,-6.1724150489911185335 ] 
dist 37=[-11.874485911462825592  ,-5.8104399156941368621 ] 
dist 38=[-11.768261978975668400  ,-5.2790735625911864885 ] 
dist 39=[-12.945842344584115959  ,-4.3807643183587384510 ] 
dist 40=[-13.759257942706656247  ,-3.4538905715594159919 ] 
dist 41=[-14.381557487630418532  ,-2.8083488965529011062 ] 
dist 42=[-14.908910368148807706  ,-2.2469181770854584764 ] 
dist 43=[-15.337093024957906196  ,-1.6552967884358833146 ] 
dist 44=[-15.563208762966346204  ,-1.0907790636983572271 ] 
dist 45=[-15.685412298539502441  ,-.63730892575804059233] 
dist 46=[-15.698477183304248065  ,-.13277670605123211754] 
dist 47=[-1.9220390900973528071 ,1.0134753688588335310 ] 
dist 48=[-.55947293489925621598,2.0766878731997518476 ] 
dist 49=[-.38557405585501441561,2.9246500597662421247 ] 
dist 50=[.00788853424221503379,4.0246143432737551200 ] 
dist 51=[.07543569263609009086,5.0128536650655911080 ] 
dist 52=[.54356815897501738396,5.6982310321342016211 ] 
dist 53=[.62112625654478836095,6.2932302324582911682 ] 
dist 54=[.76261992258149557027,6.9209477098577146312 ] 
dist 55=[.79132787276662314643,7.4865824810502655156 ] 
dist 56=[2.9083407924323436018 ,7.8338212047216840496 ] 
dist 57=[2.9584326700208396986 ,8.0880370509691817219 ] 
dist 58=[2.7935219792801421930 ,8.2822772409706421311 ] 
dist 59=[2.3699420872114154172 ,8.4234399225002672330 ] 
dist 60=[1.9221944380780471267 ,8.4657439567340324886 ] 
dist 61=[1.6094086168337621612 ,8.4606050340134484963 ] 
dist 62=[1.3364981001105367519 ,8.4331266101304509198 ] 
dist 63=[1.0476912474642290349 ,4.9017018925472015510 ] 
dist 64=[.77155619572633678627,4.5887976200396981438 ] 
dist 65=[.54912028600990960107,3.8089219294339279144 ] 
dist 66=[.1749392431495610977 ,3.6963181658728164923 ] 
dist 67=[-.53862726814884567584,2.5022524865728495094 ] 
dist 68=[-1.0991021690708867567 ,2.2795941501243454678 ] 
dist 69=[-1.6539848129125531252 ,2.0952105092058694050 ] 
dist 70=[-2.3452673930768944546 ,2.0537348319081623294 ] 
dist 71=[-3.0019156535079497479 ,2.0360269719539579625 ] 
dist 72=[-3.4186238589968202108 ,.13195059763168406911] 
dist 73=[-3.7388320075439930252 ,-.02637182469465944300] 
dist 74=[-4.0104657088261362665 ,-.36688176870661442343] 
dist 75=[-4.2296605854396969624 ,-.4383493313849885416 ] 
dist 76=[-4.3406466358961564719 ,-.57725758932149167205] 
dist 77=[-4.3997640401510173939 ,-.56299774052957816677] 
dist 78=[-4.4120041753773214926 ,-.53904330027239335263] 
dist 79=[-3.0380866303675265788 ,-.49626815823366031064] 
dist 80=[-3.2221674418541003853 ,-.4452501294546801253 ] 
dist 81=[-3.3488159701233778499 ,-.38835816340160521447] 
dist 82=[-3.4305947547602348945 ,-.31660238828292472241] 
dist 83=[-3.4869819523291866045 ,-.20624278802943199718] 
dist 84=[-3.5122527420931068435 ,-.09150972314430512559] 
dist 85=[-3.5197228491391800658 ,-.00227023637948894981] 
dist 86=[-3.5133687870453072864 ,.08517487815292947894] 
dist 87=[-3.1315320556918881788 ,.19281256979888031748] 
dist 88=[-3.0703775274771884479 ,.35653797245939552147] 
dist 89=[-2.9766518026534798245 ,.59362601987630220855] 
dist 90=[-2.9481551920317811138 ,.78738885075715208214] 
dist 91=[-2.8291383534510624994 ,.97247468414427585241] 
dist 92=[-2.7970776560529207840 ,1.1376647395086126731 ] 
dist 93=[-2.7221479562040102133 ,1.2520433097320301296 ] 
dist 94=[-2.6948287015337373910 ,1.3510520892725566954 ] 
dist 95=[-.72194266946507606179,1.4549227385382768829 ] 
dist 96=[-.54613010529588617053,1.5621767177253397436 ] 
dist 97=[-.16291956432910924391,1.6289144221913731208 ] 
dist 98=[-.08045140839265827041,1.6777759880029135586 ] 
dist 99=[.34040271724829697562,1.8522385204322560551 ] 
dist 100=[.41174639735391299871,2.1181715707170499934 ] 
dist 101=[.57195115840755575909,2.3727055950650458701 ] 
dist 102=[.59591620423166785158,2.6780750925215185576 ] 
dist 103=[.57455824594957670329,2.9628505082853559576 ] 
dist 104=[.30402376628084742011,3.1352035896548373730 ] 
dist 105=[.11976660279508813017,3.2581485497927975296 ] 
dist 106=[-.03638650918299855325,3.3457533545912646178 ] 
dist 107=[-.19478178319194862127,3.4073565456664805108 ] 
dist 108=[-.34228961456150434835,3.4265364632645558193 ] 
dist 109=[-.45499921484041959086,3.4270981081456048985 ] 
dist 110=[-.56368081467443153617,3.4158904643993294927 ] 
dist 111=[-.69511333836335074536,.93453975290343442567] 
dist 112=[-.85334599445465117804,.74153566965653635713] 
dist 113=[-1.0769099055858390603 ,.70390697478176500502] 
dist 114=[-1.3670590533215356936 ,.65450990312708210135] 
dist 115=[-1.6322396895540701287 ,.63794424676098287475] 
dist 116=[-1.8178367095636505683 ,.29888493947168717667] 
dist 117=[-1.9805051608702255214 ,.25530055382299899928] 
dist 118=[-2.1542045781361990646 ,.15989154521951040313] 
dist 119=[-2.3107408684011851198 ,.13813305466278564613] 
dist 120=[-2.4049269246547227622 ,.02986569569037997249] 
dist 121=[-2.4714010667417573159 ,.01088327576710484676] 
dist 122=[-2.5173586663821687588 ,-.03278689701782528236] 
dist 123=[-2.5465696017246979862 ,0                     ] 
dist 124=[-2.5514372704727793472 ,-.50519520942068872694] 
dist 125=[-2.5371209420867583237 ,-.28458269447454536462] 
dist 126=[-2.5314197378118260927 ,.05889295172095774926] 
dist 127=[-1.5640100581670406786 ,.40418660951836706191] 
dist 128=[-1.4893690668392408108 ,.63205349186858250838] 
dist 129=[-1.3712707596351378195 ,.81725741086645153012] 
dist 130=[-1.3510553439785240892 ,.99233001088102084975] 
dist 131=[-1.1869667262376391472 ,1.1472199091973865810 ] 
dist 132=[-1.1526626725726838626 ,1.2518961083835680241 ] 
dist 133=[-1.1006620744142721565 ,1.3397005739280448477 ] 
dist 134=[-1.0846868615405793459 ,1.4272718890129729922 ] 
dist 135=[-.7435194233839741494 ,1.5047527807659933523 ] 
dist 136=[-.69756067083596108966,1.5522962822146165252 ] 
dist 137=[-.59302752487919940659,1.5869428980121647373 ] 
dist 138=[-.56932309837435982704,1.6129651159721832416 ] 
dist 139=[-.43461300188943983592,1.6313872299673837877 ] 
dist 140=[-.40940103510412600173,1.6357079352133894706 ] 
dist 141=[-.35770897396843055519,1.6320205376826292450 ] 
dist 142=[-.34382644545767156665,1.6270486336287750273 ] 
dist 143=[.1382581336791296106 ,.48620577460697427192] 
dist 144=[.17943591971207987885,.54095395224220536974] 
dist 145=[.1848005018866632826 ,.57394083606384714372] 
dist 146=[.18197065992313272749,.59728708088522964349] 
dist 147=[.16723633764462377635,.6135640926835663167 ] 
dist 148=[.14600761640799849427,.62507663430939989564] 
dist 149=[.11726232005660122725,.62940977745012971358] 
dist 150=[.07753836981704099829,.62992337696667671316] 
dist 151=[.01250136654289960671,.62866885634267576551] 
dist 152=[-.05382839834706018066,.55722241447543025225] 
dist 153=[-.09871173222720169732,.54626023688145856585] 
dist 154=[-.13643648631575453864,.54255969188037377501] 
dist 155=[-.18172817075152599185,.52670242803761159537] 
dist 156=[-.2281125127191222634 ,.52185122002905421287] 
dist 157=[-.2608411538567368916 ,.51001181300120641716] 
dist 158=[-.28980329404623861871,.50535386239353076602] 
dist 159=[-.3211594422663889198 ,.1542606274604935293 ] 
dist 160=[-.34975753286124356154,.12296222366114985067] 
dist 161=[-.36771485045084209265,.05390260376316206410] 
dist 162=[-.3813012652190858312 ,.03948013763511533554] 
dist 163=[-.39245880883563248479,-.03930458630584185462] 
dist 164=[-.40119156008117144641,-.05278565633028011109] 
dist 165=[-.40510288262171393719,-.08184271188058121060] 
dist 166=[-.4448966704776593505 ,-.05840956335780808183] 
dist 167=[-.49206408040309296308,.00584431721282794213] 
dist 168=[-.51991411580102560407,.07061297500957166545] 
dist 169=[-.53893081114187302359,.11367687449295022378] 
dist 170=[-.55084932110402806986,.14903943164363145594] 
dist 171=[-.5588530300493152639 ,.18307978703279583786] 
dist 172=[-.56224754741084117706,.21361696759702003797] 
dist 173=[-.56291578602030318704,.23500182966622509688] 
dist 174=[-.56172227386275369143,.25375318279176994244] 
dist 175=[-.24603854409393112542,.27378253728609479115] 
dist 176=[-.16884966480822472099,.29175675336353966819] 
dist 177=[-.1585039652103612327 ,.30230784028122288863] 
dist 178=[-.13670344533918508676,.30942825918177612724] 
dist 179=[-.13071420391590831103,.31371346276198609011] 
dist 180=[-.1072192633585407673 ,.31602882709653986574] 
dist 181=[-.10250946504564115612,.31615376082174553132] 
dist 182=[-.09207407561502371076,.31369074835529474385] 
dist 183=[-.08918683454170284266,.31257424058834724893] 
dist 184=[.05855230409333355777,.327858160750506026  ] 
dist 185=[.07192010769934829430,.34107919619183913871] 
dist 186=[.09562774059121869332,.35143622476110940709] 
dist 187=[.06953217535895309306,.35914985924933246549] 
dist 188=[.04020590863326487051,.36182357356239518795] 
dist 189=[.00293042758249302422,.36228647814691466292] 
dist 190=[-.05488244373909654361,.36118785184361723578] 
dist 191=[-.11292886491910958213,.30250164760868712304] 
dist 192=[-.15113621651843692664,.30038528150928001974] 
dist 193=[-.18208338172801529041,.29318735267558331074] 
dist 194=[-.21116173561473686011,.2911928750217152727 ] 
dist 195=[-.23677088504250605762,.27174903563308233804] 
dist 196=[-.25387585900167715285,.25733284276754452358] 
dist 197=[-.26800619495405814504,.25172077969478046408] 
dist 198=[-.28174627751090237916,.2227518134760390879 ] 
dist 199=[-.29363355149263518331,.20617891712784533464] 
dist 200=[-.30037096376074028207,.06786098115991125543] 
dist 201=[-.30461596145693033284,.05433615634157468974] 
dist 202=[-.30655812592997766771,.02608416280292875330] 
dist 203=[-.30686345407522613816,.01872535188706334485] 
dist 204=[-.30644537067777461767,-.00707787683510794080] 
dist 205=[-.30203393041213581714,-.01343326804304472979] 
dist 206=[-.30131744099490866455,-.01571612753367671041] 
dist 207=[-.30889763564706765708,-.02428912502459471478] 
dist 208=[-.32892225599909634476,-.02703233553689622206] 
dist 209=[-.33963826394791601678,-.02476655056464524666] 
dist 210=[-.34566621554704049049,-.01941704443552081518] 
dist 211=[-.34705122173313255782,-.00846971779019155572] 
dist 212=[-.34589964900661612812,.00522251322504839388] 
dist 213=[-.3453669706671290434 ,.02152481285882013983] 
dist 214=[-.34482021058305828328,.04284424561260260168] 
dist 215=[-.34411229356002028742,.07655572969181836345] 
dist 216=[-.2383799830753204493 ,.11050313531472992941] 
dist 217=[-.22877265545809592221,.13276407324609237871] 
dist 218=[-.22557069213793321839,.15070475767188911441] 
dist 219=[-.21038471829149515351,.18593211856592932509] 
dist 220=[-.20699537818575596208,.21979590514926600808] 
dist 221=[-.19806854704872147411,.24447622763970041274] 
dist 222=[-.19565274393957012069,.26713132495060126203] 
dist 223=[-.06623426947283987174,.29291441353762307637] 
dist 224=[-.05341074579110186178,.31631016163159195942] 
dist 225=[-.02678872385657762248,.32943940293230483012] 
dist 226=[-.01988824215473514676,.33754914719143335231] 
dist 227=[.00507155283460031247,.34091607177551527929] 
dist 228=[.01004416547574326338,.342371957971770414  ] 
dist 229=[.01781456776932469605,.34285648882322809671] 
dist 230=[.01970042368985944941,.34272191524967674842] 
dist 231=[-.00049581951356416557,.34170810625368661745] 
dist 232=[-.04586354833624757114,.2731401647688928731 ] 
dist 233=[-.07595525347498718649,.26478689842225527281] 
dist 234=[-.10058672963559283599,.24244407714791139136] 
dist 235=[-.12416794065950201129,.239072869341703277  ] 
dist 236=[-.14523743424070339241,.19885149057324425626] 
dist 237=[-.15984705463202204311,.19073312287632418322] 
dist 238=[-.17250657342970110753,.15521635484164815969] 
dist 239=[-.18579506572542119226,.06197253365844340549] 
dist 240=[-.19768782966424781548,.03088793800853435487] 
dist 241=[-.20477830392581530444,.02645060590032837906] 
dist 242=[-.20970090185365560178,.01723191716461882456] 
dist 243=[-.21294367682743376439,.01482120071913669793] 
dist 244=[-.21485360057194435865,.00599602326370116350] 
dist 245=[-.21508823865553402719,.00422674168210055860] 
dist 246=[-.21345623576725702432,.00122592287732249918] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 1, 0, 2, 0, 2] 
dist 0=[59.943850312882030487  ,59.943850312882030487  ] 
dist 1=[59.786936066977692888  ,60.060850501673213066  ] 
dist 2=[59.339045262653155100  ,60.143188181798218407  ] 
dist 3=[58.498611980534974121  ,60.161627016140800256  ] 
dist 4=[56.992846119799859691  ,60.136446523695461877  ] 
dist 5=[55.137592043537983294  ,60.044475025646956091  ] 
dist 6=[52.901689390838013831  ,59.935910046875491034  ] 
dist 7=[49.955058514000405846  ,59.844486784320718482  ] 
dist 8=[45.261949483407324966  ,59.747557422972411906  ] 
dist 9=[40.471625828580535183  ,59.617189645528059953  ] 
dist 10=[37.136753952547784758  ,59.474960371938488037  ] 
dist 11=[34.224049230809624126  ,59.330785290628648269  ] 
dist 12=[31.119165353122866953  ,59.157532982531021510  ] 
dist 13=[28.121520185924484213  ,58.648082368473907869  ] 
dist 14=[25.636774108127290650  ,38.511847532101294932  ] 
dist 15=[23.046603713889017437  ,36.780408042341890865  ] 
dist 16=[19.627539950646354073  ,32.605319916397804029  ] 
dist 17=[16.264018677811272004  ,31.993292850748030147  ] 
dist 18=[13.895363183865053762  ,26.009075420819905372  ] 
dist 19=[11.542760009700921312  ,24.913150974640849606  ] 
dist 20=[7.9394654905460083484 ,23.595303491027235530  ] 
dist 21=[5.4361334902990750039 ,23.332387668059221571  ] 
dist 22=[3.2519973138966368209 ,14.440877756773873394  ] 
dist 23=[.92291929687744998463,13.363839165421295948  ] 
dist 24=[-1.3315393683231546114 ,12.696344834091078972  ] 
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dist 138=[-.09809646423947695290,1.5120332237976615095 ] 
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dist 150=[-.85263893755814991008,.6180388306888926403 ] 
dist 151=[-.89854934147750209488,.6213455553988642408 ] 
dist 152=[-.93094764478776448026,.6211819622941197591 ] 
dist 153=[-.95330533877495496508,.00215773617464369165] 
dist 154=[-.96817429030074231073,-.02671347778519003061] 
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dist 160=[-.76152123191298154655,.46308832458903233976] 
dist 161=[-.75997116818285206558,.5238553861305821179 ] 
dist 162=[-.72378269595373078915,.57658213705184694586] 
dist 163=[-.71376241285301462906,.61033041196393317162] 
dist 164=[-.70577680618575864783,.6365724332715259255 ] 
dist 165=[-.70076360803865471193,.65935227037249218978] 
dist 166=[-.53166762048814567501,.67798744852797404686] 
dist 167=[-.50825242597591990104,.68769454283527028264] 
dist 168=[-.4619602558554314811 ,.69269199944167029253] 
dist 169=[-.44948631512626219435,.69253936543252286192] 
dist 170=[-.40319716916434522486,.68907208115869315561] 
dist 171=[-.39230373310620581216,.68666459889367410271] 
dist 172=[-.37309108303541781705,.672929931555611172  ] 
dist 173=[-.36803859511072710402,.67070509250144291581] 
dist 174=[-.23291572728558583183,.17249401578033478498] 
dist 175=[-.22562612647396243473,.21454130059285444416] 
dist 176=[-.22350343148598417104,.24818523436901138008] 
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dist 180=[-.09824501741642375440,.33622561463354924621] 
dist 181=[-.07681210837988429035,.34769249004968339254] 
dist 182=[-.07220752842505460779,.35700407254581898809] 
dist 183=[-.06485708298543430965,.36165543045339207426] 
dist 184=[-.06292919864760056667,.36378442120614296262] 
dist 185=[.13436119947530142443,.36352851795088591863] 
dist 186=[.1491736653460088961 ,.36066394984461785387] 
dist 187=[.17635274812237843392,.35914985924933245756] 
dist 188=[.13084045897343639527,.35222073788525005472] 
dist 189=[.06022895255198354009,.35052260532006417297] 
dist 190=[-.01096050765075292159,.25812182021045046479] 
dist 191=[-.05877904305430983075,.2597221920184531767 ] 
dist 192=[-.09857420108900136149,.26355559071211144776] 
dist 193=[-.13775176053425429396,.27220553971271905078] 
dist 194=[-.17347232043254632501,.27628310126494265923] 
dist 195=[-.19947463394712301602,.27798531692126180802] 
dist 196=[-.22330473860034954945,.27796263880885714591] 
dist 197=[-.25035853928596475012,.27352635144054760206] 
dist 198=[-.27514753283417811554,.27162518494662324758] 
dist 199=[-.28994154595101056061,.26802018712104211579] 
dist 200=[-.30022879649253371641,.26651179030236389121] 
dist 201=[-.30703690146916669294,.17419379747762361493] 
dist 202=[-.3115506995780281367 ,.164193169332809341  ] 
dist 203=[-.31268384478297342676,.14037793432846800557] 
dist 204=[-.31221418370410568932,.13569054581873796202] 
dist 205=[-.31108501535296738667,.10153223228355265002] 
dist 206=[-.20270027292836626203,.09500902042564881259] 
dist 207=[-.22221804495669799254,.08395464660095070833] 
dist 208=[-.24483577582459732572,.08123362122305427286] 
dist 209=[-.26549554776477579618,.03207950090877124503] 
dist 210=[-.27720115377492163749,.04372031776954073852] 
dist 211=[-.28457709298540137353,.06389730934356534452] 
dist 212=[-.28796150828351764485,.08373145213066299276] 
dist 213=[-.28963279752263853923,.10824778604355099306] 
dist 214=[-.29017321794525263291,.131442696996177701  ] 
dist 215=[-.28998868635954431002,.1460050203662108287 ] 
dist 216=[-.28890656254574212476,.15701514088109953168] 
dist 217=[-.06769266379079115065,.16603792541135820105] 
dist 218=[-.05448765170389370459,.17312930744583524945] 
dist 219=[-.02433471715536858942,.17643317189134077463] 
dist 220=[-.01887285427139628924,.1780151398467869389 ] 
dist 221=[.01860693809447588350,.1782365577953815058 ] 
dist 222=[.02510788656376266920,.1782278375240262403 ] 
dist 223=[.03691170545118252630,.19609289710539484235] 
dist 224=[.02484938814151704427,.21647696378683442153] 
dist 225=[.01061669474656639880,.23502408317935577825] 
dist 226=[-.00361915448714034453,.24555992241727992868] 
dist 227=[-.01612284813101732404,.25223215317240991109] 
dist 228=[-.02973392353395480286,.25536379016857582901] 
dist 229=[-.04838842834478286312,.2569526957752800397 ] 
dist 230=[-.06693909066362914274,.25746959318688550488] 
dist 231=[-.08013619679878200129,.25729970878246590655] 
dist 232=[-.09192137941277082515,.25635386619192372523] 
dist 233=[-.10483933248885549245,.20180096421456380477] 
dist 234=[-.11747708831211941831,.19529753780264507397] 
dist 235=[-.12814479212750115692,.1778721166623185739 ] 
dist 236=[-.13940034042972958212,.17532050764904505072] 
dist 237=[-.15438422873689325071,.14396897721467044793] 
dist 238=[-.16868998205695483518,.13766803280453527809] 
dist 239=[-.17723997309974411147,.13132964108135584189] 
dist 240=[-.18320255646410535477,.13001062537212095248] 
dist 241=[-.18718451495852901875,.06269920095912269001] 
dist 242=[-.1897920676987454362 ,.05430153533564398817] 
dist 243=[-.19027068874186243921,.03718719298808377144] 
dist 244=[-.18987676319263598461,.03277672467750254992] 
dist 245=[-.189027500063651634  ,.01863527997446966833] 
dist 246=[-.17434869000475088133,.01618793618173969033] 
dist 247=[-.17156878040136581944,.01297772112815298210] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 1, 1, 1, 0, 1] 
dist 0=[47.975490338651764392  ,47.975490338651764392  ] 
dist 1=[47.210272477561934809  ,48.315336450436197805  ] 
dist 2=[46.350105040387574743  ,48.484649529245172290  ] 
dist 3=[45.631145721719605601  ,48.568599822455055347  ] 
dist 4=[44.876040362707838573  ,48.582013193238310793  ] 
dist 5=[43.871722927523838338  ,48.324280445435269745  ] 
dist 6=[42.781468883388253904  ,48.207374271198889217  ] 
dist 7=[41.683313704401630644  ,48.088757937626584513  ] 
dist 8=[40.366972013166288599  ,47.987345142201436764  ] 
dist 9=[38.405598628841249349  ,44.735563938545656584  ] 
dist 10=[36.374665595850049382  ,44.246196746671731665  ] 
dist 11=[34.780625248413493555  ,43.310533907231696065  ] 
dist 12=[33.198787776522934753  ,43.049545255486349439  ] 
dist 13=[31.137900398991346220  ,42.046859386969158743  ] 
dist 14=[28.933892047985449817  ,41.791985126696853049  ] 
dist 15=[26.109539576643287337  ,41.284456808011055188  ] 
dist 16=[21.850794813373290440  ,41.124308683344210169  ] 
dist 17=[18.918878940008620486  ,32.245368773742023148  ] 
dist 18=[16.391861307473109376  ,25.515523765027906214  ] 
dist 19=[13.749596333558024076  ,22.522042604212054270  ] 
dist 20=[11.228162350386134793  ,22.087385554796930523  ] 
dist 21=[9.1833059643233859942 ,17.872302966318194632  ] 
dist 22=[7.0902401315993805964 ,17.105715303447577147  ] 
dist 23=[4.3756403327444668999 ,16.186648335153781403  ] 
dist 24=[1.7233217336410950151 ,16.014004419439109641  ] 
dist 25=[-.1213693028801062539 ,10.699784347141605937  ] 
dist 26=[-1.7347509731386220927 ,9.1449759564640216290 ] 
dist 27=[-3.4637224666693940265 ,7.6102620060580411915 ] 
dist 28=[-5.1452419096733114767 ,7.2333987410929862092 ] 
dist 29=[-6.5697458640481593399 ,5.8239931367246607407 ] 
dist 30=[-8.0878471507401628743 ,5.5551991123169324547 ] 
dist 31=[-10.144615524168238458  ,5.1428887401617475774 ] 
dist 32=[-12.121845796949849930  ,5.0458288883132395670 ] 
dist 33=[-13.322381438818404856  ,-1.4160212630295260313 ] 
dist 34=[-14.193634989214305315  ,-1.9532013990855142180 ] 
dist 35=[-14.854616369364959402  ,-2.5792827847118399850 ] 
dist 36=[-15.356423386660219550  ,-2.6377610433986242700 ] 
dist 37=[-15.591173366418606831  ,-2.5767911649673903380 ] 
dist 38=[-15.690447302550089825  ,-2.4625483923477061726 ] 
dist 39=[-15.690312804152832350  ,-2.2850044317557769828 ] 
dist 40=[-14.808709985015353725  ,-2.0292146079330245800 ] 
dist 41=[-14.635209560301767234  ,-1.6024404253481302178 ] 
dist 42=[-14.299457198585451725  ,-1.1465092541315160846 ] 
dist 43=[-14.190183242712207602  ,-.7741391462564913374 ] 
dist 44=[-13.701909416009708995  ,-.3927826468816854918 ] 
dist 45=[-13.573655133478355268  ,.0994013346804716430 ] 
dist 46=[-13.237380726880156886  ,.62458092995563302878] 
dist 47=[-13.113249973424742763  ,1.1378469369948679794 ] 
dist 48=[-9.3975126912046159584 ,1.7407482326222062492 ] 
dist 49=[-6.2374636451805279071 ,3.2031573558285358900 ] 
dist 50=[-2.8997073737417438422 ,4.9684073350793814027 ] 
dist 51=[-2.5882691383846298517 ,6.1466361741491124649 ] 
dist 52=[-.64795888213925134674,7.1196032417658056282 ] 
dist 53=[-.3095612547814042448 ,8.0658317877471680254 ] 
dist 54=[.3442780697935010539 ,8.9217216390742468961 ] 
dist 55=[.4979861337418449329 ,9.5342338427317788396 ] 
dist 56=[2.0216091277136032916 ,10.249464267440328458  ] 
dist 57=[2.2504177824750901864 ,10.833080701631788514  ] 
dist 58=[2.5300526491879146352 ,11.241952670791657015  ] 
dist 59=[2.5557811022813708006 ,11.527945099389186263  ] 
dist 60=[2.4814903805479645295 ,11.678995868252173610  ] 
dist 61=[2.2623289384836152030 ,11.709745524261203304  ] 
dist 62=[1.8959109274580073367 ,11.639987019521189951  ] 
dist 63=[1.2339833457043319284 ,11.378350410210034737  ] 
dist 64=[.5496352200409063538 ,6.0312799991277724464 ] 
dist 65=[.0936924396126252755 ,4.9350918416828838677 ] 
dist 66=[-.2814691877243574594 ,2.7195842669726010790 ] 
dist 67=[-.6436139718542355813 ,2.1752122762254443556 ] 
dist 68=[-1.2126135176014797884 ,2.0883201238841605615 ] 
dist 69=[-1.8120934958934248970 ,1.3062547554655352865 ] 
dist 70=[-2.3669453836333553996 ,1.1627662630429926132 ] 
dist 71=[-2.7852715251045233663 ,.96735037002019056546] 
dist 72=[-3.1833199225916987593 ,.91018551609308965764] 
dist 73=[-3.6572790742761106742 ,-.16606069588768122633] 
dist 74=[-4.0971123119948066645 ,-.29694548390290134418] 
dist 75=[-4.3589972956628066251 ,-.59591974379195441799] 
dist 76=[-4.5404802357643428344 ,-.63879548721987991398] 
dist 77=[-4.6594915361966771836 ,-.99680871915544133943] 
dist 78=[-4.7420688413660321321 ,-.99856641159398230599] 
dist 79=[-4.7781691186204111634 ,-.83146910779467036278] 
dist 80=[-4.7871327887228503566 ,-.58792337917321607207] 
dist 81=[-4.7783446557176153975 ,-.1769654426669932007 ] 
dist 82=[-2.2604479664923450607 ,.24510654438819669183] 
dist 83=[-2.1805818558426081875 ,.53300517605526305277] 
dist 84=[-2.1539694174535379650 ,.84208804118207920211] 
dist 85=[-1.9966982708629932428 ,1.2521773828086126588 ] 
dist 86=[-1.9600684271875132046 ,1.6270252475800381284 ] 
dist 87=[-1.8896159794506833096 ,1.9014768403028416779 ] 
dist 88=[-1.8683226118789346632 ,2.1546083906321179345 ] 
dist 89=[-1.4747494070681807902 ,2.4444100872808859773 ] 
dist 90=[-1.4181539312867141106 ,2.7110358657981077040 ] 
dist 91=[-1.2790305914274517575 ,2.8716981792756198683 ] 
dist 92=[-1.2518165632613550241 ,2.9853226357297958849 ] 
dist 93=[-1.0362735286480024543 ,3.0642546972603482458 ] 
dist 94=[-1.0163580760688477664 ,3.1188917390818928658 ] 
dist 95=[-1.0026704911379399089 ,3.1355864524142283523 ] 
dist 96=[-.99754656810325306139,3.1345863446174016209 ] 
dist 97=[-.34473059210029874008,3.1242836758602893225 ] 
dist 98=[-.78792141475735834773,2.2980268849968553801 ] 
dist 99=[-1.0785652290079829761 ,2.2111776591868194220 ] 
dist 100=[-1.3126464387263987469 ,2.0584482917871479771 ] 
dist 101=[-1.5301756168164046117 ,2.0394404160927429529 ] 
dist 102=[-1.7199506576779873211 ,1.8606063536440737394 ] 
dist 103=[-1.8433006886827456065 ,1.8200387912025765576 ] 
dist 104=[-1.9413748601571476513 ,1.7659599679699402580 ] 
dist 105=[-2.0302993121949563907 ,1.7453884594076101853 ] 
dist 106=[-2.1059620735128051862 ,1.2583986715634286083 ] 
dist 107=[-2.1511287920160564679 ,1.1917117902105816979 ] 
dist 108=[-2.1824814032569248315 ,1.2401622367896357652 ] 
dist 109=[-2.2030456097861858957 ,1.2794393459526700543 ] 
dist 110=[-2.2150184508056470592 ,1.2995064575673078471 ] 
dist 111=[-2.2121024950793213484 ,1.3093514866812279449 ] 
dist 112=[-2.2008124927756614598 ,1.3097798435424078464 ] 
dist 113=[-2.1911531171217102959 ,.70824191819711601636] 
dist 114=[-.419197688474312151  ,.18986261767689206905] 
dist 115=[-.45894110323816909243,.18483692683134505584] 
dist 116=[-.49661395566063014165,.16469106213949169614] 
dist 117=[-.58430244636102906293,.16048392616523902436] 
dist 118=[-.64367873673916409283,.14984976677294098048] 
dist 119=[-.69365634165775499435,.14737221142850309664] 
dist 120=[-.74384727730633848347,.12827248593296729426] 
dist 121=[-.78845587189798063429,.1242665295265895542 ] 
dist 122=[-.81615773776250907916,.1163008061632311382 ] 
dist 123=[-.83677888764783864957,.1138703688331046119 ] 
dist 124=[-.8531257910092869574 ,.1032700986135530386 ] 
dist 125=[-.86546872120517058643,.1008041010662554480 ] 
dist 126=[-.8701081586725038015 ,.0937997683288318633 ] 
dist 127=[-.86998701657613262348,.0921174380834997479 ] 
dist 128=[-.86824401342194552471,.1054326509149618239 ] 
dist 129=[-.47074256873611964511,.1724127696699187880 ] 
dist 130=[-.43687455006053713527,.2261170295540406199 ] 
dist 131=[-.35329315036689853776,.2756266521716989905 ] 
dist 132=[-.34107164548354408345,.3185657462865214264 ] 
dist 133=[-.21568734536468685291,.3460595111424082735 ] 
dist 134=[-.19246828279444768906,.3674748809021699687 ] 
dist 135=[-.16506142714878807657,.38936916868845551047] 
dist 136=[-.15971029889654830287,.412704473033955539  ] 
dist 137=[.03441117678405391985,.42723723280274165502] 
dist 138=[.05748106191721429954,.43810114598177046866] 
dist 139=[.10704927000662221401,.44679559320448962431] 
dist 140=[.11701618598917522638,.45343086382753662293] 
dist 141=[.16676641048732068364,.45607772350740038959] 
dist 142=[.17512373268848583263,.45859893557043719274] 
dist 143=[.18965719819372212083,.46425924148606212305] 
dist 144=[.1347992100128520718 ,.46530030183747950759] 
dist 145=[.08488722802806357091,.34559272006506382728] 
dist 146=[.04160773491440472719,.35694888668162685526] 
dist 147=[-.00379768780605708626,.36348784667044264907] 
dist 148=[-.04696886139414887509,.36519383067893890372] 
dist 149=[-.08133653005351691503,.36512337819833989987] 
dist 150=[-.11575952268889458827,.36456956525479560364] 
dist 151=[-.15915127734542932734,.36356843222389999756] 
dist 152=[-.20054720589947817455,.36199602707086875791] 
dist 153=[-.22700897235641406576,.31631590216103998055] 
dist 154=[-.2475380881331308933 ,.3106025436666093406 ] 
dist 155=[-.2652691682747637507 ,.29937196528850118972] 
dist 156=[-.2797918138710322236 ,.29595805824670724904] 
dist 157=[-.2875223414529646117 ,.28143006252210621859] 
dist 158=[-.2917355881690197922 ,.277846940597301071  ] 
dist 159=[-.2923788647349866926 ,.26881077746224062559] 
dist 160=[-.09788925081977854663,.26558461455525862609] 
dist 161=[-.0934308871971868865 ,.06849678293163672522] 
dist 162=[-.11085369335823133506,.05060281948107277253] 
dist 163=[-.1502634224346562218 ,.0349806790944778043 ] 
dist 164=[-.19000645072036037206,.0514010451266340015 ] 
dist 165=[-.22689532971978913019,.0633135636609247666 ] 
dist 166=[-.25491531592289349584,.0741693854796972355 ] 
dist 167=[-.28179024113028674146,.0863765292138294064 ] 
dist 168=[-.31410971500642363795,.0976042022023402603 ] 
dist 169=[-.34428247865188032486,.1045541088696515323 ] 
dist 170=[-.3625906422195777572 ,.1096819976508574701 ] 
dist 171=[-.37570394694004967147,.1136432320537773878 ] 
dist 172=[-.38514574804945649201,.1165383481234973128 ] 
dist 173=[-.39168262294753328561,.1174144147409265172 ] 
dist 174=[-.39320377586034838139,.1174673847545730701 ] 
dist 175=[-.3928943911149686166 ,.13504027965868036305] 
dist 176=[-.39212577371711677876,.15794382622884416206] 
dist 177=[-.09681396357950637659,.17197748637207830599] 
dist 178=[-.10065114342599217314,.18219791847605875437] 
dist 179=[-.10372491094867540947,.18988628295234199552] 
dist 180=[-.1060426597217013147 ,.20680349926241844814] 
dist 181=[-.10686567323130557984,.22998744465283574983] 
dist 182=[-.1069668328970452570 ,.25136828370046885712] 
dist 183=[-.1066459816041011162 ,.269610080045702749  ] 
dist 184=[-.1032580973000386498 ,.28831912043789649657] 
dist 185=[-.1023430715489125605 ,.30492633420997054632] 
dist 186=[-.0991398258739113424 ,.31478126112198814619] 
dist 187=[-.0984005138250763645 ,.32157173885469782272] 
dist 188=[-.0896128913794622308 ,.32594992614860027557] 
dist 189=[-.0875260911060381616 ,.32843938481422590084] 
dist 190=[-.0852446719628835545 ,.32861209309379922137] 
dist 191=[-.0841308477131222420 ,.32605387632054340606] 
dist 192=[-.07324179910506080168,.32498379997585492224] 
dist 193=[-.08275692415706338360,.18777407097432630456] 
dist 194=[-.09112549069930359412,.17507187505816990216] 
dist 195=[-.10009454641212278032,.15784746975342381972] 
dist 196=[-.11990484574271055726,.15527302610728150864] 
dist 197=[-.13883745935990855233,.13508403851692752229] 
dist 198=[-.15169747955948491177,.1309229052208499583 ] 
dist 199=[-.1625586552562794639 ,.12441136697133742738] 
dist 200=[-.17351532109525227701,.12250719440578282636] 
dist 201=[-.18324823588016421494,.08283806822376249592] 
dist 202=[-.18922634070205355074,.07750591556076459985] 
dist 203=[-.19359158803048911122,.06520151045641926848] 
dist 204=[-.19688886603922107298,.06261254180102077949] 
dist 205=[-.19924098474994429995,.04628814820231756423] 
dist 206=[-.1998347293223290627 ,.04324329221216531474] 
dist 207=[-.19945181650798620563,.03744454531503785150] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 1, 0, 1, 0, 0, 1] 
dist 0=[56.765779402657059248  ,56.765779402657059248  ] 
dist 1=[55.396159813533772028  ,57.477640545935703642  ] 
dist 2=[53.705769994924143002  ,57.867241397419611913  ] 
dist 3=[51.713000666628034975  ,57.950193785580608752  ] 
dist 4=[49.113520946515273020  ,57.896856618243874727  ] 
dist 5=[45.000442984212522534  ,57.583042761818063476  ] 
dist 6=[40.804022731849800452  ,57.438492671670140657  ] 
dist 7=[37.871672169435280385  ,57.307692504411061215  ] 
dist 8=[35.298492758085020733  ,56.990540856643894407  ] 
dist 9=[32.536078873054829381  ,56.821968085041096672  ] 
dist 10=[29.856747829091684483  ,56.463135971412417344  ] 
dist 11=[27.615124017816991477  ,56.306223549083287005  ] 
dist 12=[25.259704477522862613  ,55.501598486820641229  ] 
dist 13=[22.125570020275898881  ,55.265517811156284795  ] 
dist 14=[19.030055650375394454  ,54.974482692952340271  ] 
dist 15=[16.828620560186265334  ,53.192960176174312095  ] 
dist 16=[14.854365841940826261  ,48.735023220745279974  ] 
dist 17=[12.665725117395099567  ,31.646991709768265589  ] 
dist 18=[10.497580368387710167  ,29.786726771111500264  ] 
dist 19=[8.6046937060416322043 ,25.554476891118275486  ] 
dist 20=[6.5430405795311022309 ,24.790917688064521287  ] 
dist 21=[3.6998563006423501875 ,19.526272452003815869  ] 
dist 22=[.92211192461438723999,18.603579944624254873  ] 
dist 23=[-.87830031567984627907,16.957339751846858568  ] 
dist 24=[-2.3162159894934493886 ,16.604150559458137953  ] 
dist 25=[-3.6455365344465389022 ,11.750579783500966084  ] 
dist 26=[-4.8118811980398067198 ,11.085032164517853011  ] 
dist 27=[-5.5987341285180032960 ,9.9542349177751066539 ] 
dist 28=[-6.2633538303749743435 ,8.9320131328042584353 ] 
dist 29=[-6.9416952330489670400 ,6.4981097736242032023 ] 
dist 30=[-7.5352712526447266232 ,1.2688233246055382869 ] 
dist 31=[-7.8612447280891080804 ,.71267580135534429669] 
dist 32=[-9.8392581180270360971 ,-1.2594724308870517763 ] 
dist 33=[-12.276884926341623307  ,-4.5765752135225809895 ] 
dist 34=[-13.771378319103355713  ,-3.8834354907162644570 ] 
dist 35=[-14.870365427596751584  ,-3.0695767587064745850 ] 
dist 36=[-15.727573331822897915  ,-2.0152867226932213550 ] 
dist 37=[-16.397863609302606881  ,-.36288543802071009366] 
dist 38=[-16.749687962411075080  ,1.3055118324036785084 ] 
dist 39=[-16.938802035325005696  ,2.4237978869933451275 ] 
dist 40=[-16.962457238458818869  ,3.3497005064175167866 ] 
dist 41=[-15.976293229414252243  ,4.2510615906872312613 ] 
dist 42=[-15.786579493748387036  ,5.0645200050813849280 ] 
dist 43=[-15.523512159171591024  ,5.6399480889936383935 ] 
dist 44=[-15.414646023810814018  ,6.1497213110940338900 ] 
dist 45=[-15.143234417241211080  ,6.7014162190279969516 ] 
dist 46=[-15.022445265037868641  ,7.1940889356787299223 ] 
dist 47=[-14.917975584401047914  ,7.4684372551389320549 ] 
dist 48=[-14.837106427369021093  ,7.6346872859654345400 ] 
dist 49=[-4.3025667974336646216 ,7.6960731000120983291 ] 
dist 50=[-3.4288152181682681341 ,7.7086078736479593260 ] 
dist 51=[-1.4496869005502956854 ,7.6815178307542280293 ] 
dist 52=[-1.0962895623980656643 ,7.6222756346640499288 ] 
dist 53=[-.4835020207761930161 ,7.5835271672290102053 ] 
dist 54=[-.54935239865829985652,6.9249116020133748437 ] 
dist 55=[-.59007961524573783728,7.0596456058671951435 ] 
dist 56=[-.61988862074986093667,7.1843376224574938498 ] 
dist 57=[-.64222847270271478767,8.4643527548450202716 ] 
dist 58=[-.65932461212619143717,9.2638015598675554511 ] 
dist 59=[-.66824434655956903559,9.8645338569650926789 ] 
dist 60=[-.67277797003299233071,10.351405137380275286  ] 
dist 61=[-.67246359423673967635,10.728921156437176671  ] 
dist 62=[-.61112799322218554342,10.893182909152311667  ] 
dist 63=[-.60036963217304146665,10.966681677451105915  ] 
dist 64=[-.92600607019131465495,10.981893767768784687  ] 
dist 65=[-1.3775967784211711505 ,2.2667629926335926387 ] 
dist 66=[-1.8061031815048771223 ,1.8464418636795074509 ] 
dist 67=[-2.3139753879770167222 ,1.2959222000873028384 ] 
dist 68=[-2.7895692236831285310 ,.78192800205524006481] 
dist 69=[-3.0893283996031701890 ,-.02929812350126388944] 
dist 70=[-3.3171641785204726298 ,.03757438195045731813] 
dist 71=[-3.5058761106380038851 ,.13038623103275435509] 
dist 72=[-3.6547227507117280142 ,.20978185264456002969] 
dist 73=[-3.7235564581831509136 ,.29148891566633553362] 
dist 74=[-3.7542642867744476646 ,.36830115372516437938] 
dist 75=[-3.8624655978614272903 ,.42816568798247856127] 
dist 76=[-4.1607759593603818548 ,.48700251069953822526] 
dist 77=[-4.5056683351846267063 ,.55971299188149093876] 
dist 78=[-4.7641862482318925949 ,.62848520646636604479] 
dist 79=[-5.0092459304612232917 ,.67160874390253829416] 
dist 80=[-5.3005617022845298567 ,.86302458575399230633] 
dist 81=[-5.5633454562767535157 ,1.5149194471359286710 ] 
dist 82=[-5.6945596429111298179 ,1.9545265965226683159 ] 
dist 83=[-5.7629793853449905313 ,2.3218146763986650162 ] 
dist 84=[-5.7749601020281425654 ,2.6852445196269508485 ] 
dist 85=[-5.6938967563436904767 ,3.0173550366008080285 ] 
dist 86=[-5.6663036996107281838 ,3.2597125801520989007 ] 
dist 87=[-5.6439270980903364609 ,3.4821613285585060124 ] 
dist 88=[-5.6229992794449053800 ,3.7348471027743553880 ] 
dist 89=[-4.5753321212174396934 ,3.9623478279706558651 ] 
dist 90=[-4.4267422769262043310 ,4.0843295887077572245 ] 
dist 91=[-4.1446000625720926458 ,4.1520281698782100117 ] 
dist 92=[-4.0692490675975985772 ,4.1668710437062244473 ] 
dist 93=[-3.7987027489586590742 ,4.1535156806685060505 ] 
dist 94=[-3.7279956876621918873 ,4.2095826198827063386 ] 
dist 95=[-3.6256069001672849017 ,4.5130117494256547589 ] 
dist 96=[-3.5898215672486805045 ,4.7578215382533105816 ] 
dist 97=[-3.5723556202327314566 ,4.8883793211072343283 ] 
dist 98=[-3.5212274013252960505 ,4.9602222005997606256 ] 
dist 99=[-3.4950154221206440452 ,4.9747176247841740207 ] 
dist 100=[-3.1022567544788905388 ,4.8091857657486463089 ] 
dist 101=[-3.0356581510629683707 ,4.7669890893649824633 ] 
dist 102=[-2.8720142019024278215 ,4.7315929754973815651 ] 
dist 103=[-2.8243054852203092617 ,4.7012094583771441286 ] 
dist 104=[-2.5484976134378677753 ,4.6640707920368972596 ] 
dist 105=[-2.4877133398579974236 ,4.5746776536145098807 ] 
dist 106=[-2.3691671523445238292 ,4.5427186125950158071 ] 
dist 107=[-2.3342623781794339180 ,4.2537170882434526872 ] 
dist 108=[-1.5142568023144087043 ,.17748953417253365014] 
dist 109=[-1.7951562520956966539 ,.21785131583575531393] 
dist 110=[-2.0119201129172897529 ,.25565695586143483445] 
dist 111=[-2.1975546967842205119 ,.27899120872201151437] 
dist 112=[-2.3494222769189447381 ,.29617120648372473884] 
dist 113=[-2.4314493458695963480 ,.30941943177676329633] 
dist 114=[-2.4779639069317638919 ,.31963747141287689028] 
dist 115=[-2.4890955236484985057 ,.32472658317934991921] 
dist 116=[-2.4629191284652899404 ,.32702838099278438469] 
dist 117=[-2.4559397087187912626 ,.32717542360462920191] 
dist 118=[-2.4498916926447707777 ,.26862449190550446666] 
dist 119=[-2.4436095534487713147 ,.27779569480136705722] 
dist 120=[-2.4377146050439137158 ,.28300462916904509993] 
dist 121=[-2.4332038219200418319 ,.28428106486097176605] 
dist 122=[-2.4288657562116921848 ,.28397110760579189322] 
dist 123=[-2.4236516993884513882 ,.28372835923525286093] 
dist 124=[-.52948031952710630721,.28341134182634109429] 
dist 125=[-.37504424143596667899,.28291387640127487523] 
dist 126=[-.02983853104257936383,.23263176813013844455] 
dist 127=[.03624538762961253159,.42371257811772587741] 
dist 128=[.17724493007596237102,.69225505838874953311] 
dist 129=[.15557152556482237308,.90330919432871151705] 
dist 130=[.1311158752891662176 ,1.1124023404154092495 ] 
dist 131=[.10289904359802654059,1.3731221845781481893 ] 
dist 132=[.06752145729838815405,1.6209094128366956773 ] 
dist 133=[.01488358704347812554,1.7784037779795543407 ] 
dist 134=[-.03796157672064724952,1.8997183685682479606 ] 
dist 135=[-.07416659076869449735,2.0031535863433154736 ] 
dist 136=[-.10508372157903006724,2.0870187653045228414 ] 
dist 137=[-.13682910801800838352,2.1302516240617531097 ] 
dist 138=[-.16664328672367373435,2.1519442628076097071 ] 
dist 139=[-.18985460444273106142,2.1547137383934439815 ] 
dist 140=[-.21265508430362594902,.06024970221220667227] 
dist 141=[-.24083027578718797099,-.03189269494841997209] 
dist 142=[-.28169961127545322433,-.05512185866640418638] 
dist 143=[-.43275396414940641621,-.05716306671493571176] 
dist 144=[-.57231393607837463732,-.05625568083964745900] 
dist 145=[-.67453321160243049166,-.05109065374434232795] 
dist 146=[-.76883539139045729742,-.04359222897227264316] 
dist 147=[-.87681397458317267228,-.03337372184172164350] 
dist 148=[-.97623402132214874923,-.00397970299492075723] 
dist 149=[-1.0363906925989098392 ,.04812265605399241354] 
dist 150=[-1.0792311238098017211 ,.10376191471305265832] 
dist 151=[-1.1095605725387889582 ,.14110161699720794456] 
dist 152=[-1.1307359175526868523 ,.17130498563080533192] 
dist 153=[-1.1370548848513437215 ,.19961877168863790032] 
dist 154=[-1.1368752924783560917 ,.22451269038336863733] 
dist 155=[-1.1327126847717530822 ,.24107057378235964146] 
dist 156=[-.87933712867503400064,.25467477312614120827] 
dist 157=[-.851976900239278917  ,.26778324693845187745] 
dist 158=[-.78004125675876856023,.27909947896064911738] 
dist 159=[-.76797662706395808979,.28555261572034504717] 
dist 160=[-.64162501215376565199,.28967205568909388958] 
dist 161=[-.61609540165001522513,.32013142571121231434] 
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8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 1, 0, 0, 2] 
dist 0=[53.511426423276508079  ,53.511426423276508079  ] 
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dist 8=[36.188231280649917947  ,54.113478109418932391  ] 
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dist 10=[31.688842850334833515  ,53.429519915008064970  ] 
dist 11=[29.798220351755452177  ,52.862440446648816378  ] 
dist 12=[27.784157149052208838  ,52.731303444558951800  ] 
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dist 14=[22.362613757773503323  ,50.767201113845975030  ] 
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dist 18=[14.464138551137076747  ,29.414622873877789686  ] 
dist 19=[12.587945459274941061  ,28.421424642479090106  ] 
dist 20=[10.491718087635977474  ,28.204406138816949041  ] 
dist 21=[7.5339666293233718048 ,20.395673273981913894  ] 
dist 22=[4.6242181258165318513 ,19.419775637510060383  ] 
dist 23=[2.7196603720491783036 ,17.435164303793340776  ] 
dist 24=[1.1774370307287652562 ,16.924267152997898485  ] 
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dist 35=[-13.537894432805024427  ,-4.9751801065777939152 ] 
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dist 44=[-14.646107291806007596  ,-.58263311498556455028] 
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dist 48=[-3.8818730171272858632 ,2.3275011240794389240 ] 
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dist 103=[.27032958825444019184,4.1150112257232884258 ] 
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dist 106=[-.17921330797628419087,4.3668926480568242522 ] 
dist 107=[-.29252689885212260662,4.3749967462939365816 ] 
dist 108=[-.4040189960825550994 ,4.3666598692994531880 ] 
dist 109=[-.54198346161105634589,1.6092182238337545807 ] 
dist 110=[-.86910915256594881139,1.5430429977380485614 ] 
dist 111=[-1.1502359839249939398 ,1.5203935249312849223 ] 
dist 112=[-1.4255172639712490679 ,.595231028577998415  ] 
dist 113=[-1.6756183962179689644 ,.50144742136498022411] 
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dist 115=[-2.0204926865353219652 ,.2533864788265122621 ] 
dist 116=[-2.2049776395432938872 ,.06232086638852962476] 
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dist 128=[-.67099625178748643447,.73750214765880218023] 
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dist 130=[-.63811890642945687201,.97433112047377137172] 
dist 131=[-.63101619773882262405,1.0626874496506125819 ] 
dist 132=[-.61317150583389122756,1.1348982785527904502 ] 
dist 133=[-.60642729962274092361,1.1736350135588253794 ] 
dist 134=[-.16855093117745388736,1.1954370426856072540 ] 
dist 135=[-.12904485471933431534,1.2005359324938107661 ] 
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dist 138=[.06904056520253429429,1.1817799041116589866 ] 
dist 139=[.08508124828868567586,1.1777974482976346728 ] 
dist 140=[.12046403943882640495,1.1737867075824672731 ] 
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dist 143=[.16670451455668341233,1.1610899786308190572 ] 
dist 144=[.1613859896944076101 ,.79350872220396641809] 
dist 145=[.03538897758549531495,.81634377256900987323] 
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dist 148=[-.36613889725342749252,.8372958696473173893 ] 
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dist 226=[-.16485971623266264167,.13690886066509662519] 
dist 227=[-.19685854566505976756,.1402070803390658656 ] 
dist 228=[-.22489665726188894304,.14402791449946548542] 
dist 229=[-.24336497201484342177,.1495557252252785379 ] 
dist 230=[-.25833588877258428131,.15495260537646702739] 
dist 231=[-.27241994758399147876,.15825087569127696549] 
dist 232=[-.28463973892397909523,.16063952207282223717] 
dist 233=[-.29217254425361720509,.16240677746075628095] 
dist 234=[-.29770454512106357783,.1636358184320664759 ] 
dist 235=[-.30194149508066660538,.16387678804921796837] 
dist 236=[-.30517130792124059586,.16343859303411982943] 
dist 237=[-.30590291161503325773,.16294462073069930617] 
dist 238=[-.29948106682184433018,.16008648753618841633] 
dist 239=[-.29126198007604660549,.15895151031883979066] 
dist 240=[-.18609343298093487928,.15610572656353856837] 
dist 241=[-.18608138743337849436,.1548603531930030768 ] 
dist 242=[-.1842363513769142061 ,.14789006152356449199] 
dist 243=[-.1836610660042827803 ,.14610688963076339876] 
dist 244=[-.17366594902234574663,.14160892922143581383] 
dist 245=[-.17104753862240400317,.14968042878475902199] 
dist 246=[-.1687140660977248745 ,.15702563890902220421] 
dist 247=[-.16734625653733912852,.16389279803793379703] 
dist 248=[-.12617756647122471232,.16969987762254778227] 
dist 249=[-.12048533074982115764,.17281556783250130192] 
dist 250=[-.1091211476970806275 ,.1745508721594839204 ] 
dist 251=[-.10604451737837645684,.17485043638511497935] 
dist 252=[-.09449391873010993043,.17428552839908336929] 
dist 253=[-.09184379495669176739,.17374481122223037293] 
dist 254=[-.08693622384149537193,.17081035938524566319] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 1, 2, 2, 1, 2] 
dist 0=[57.042600517755135779  ,57.042600517755135779  ] 
dist 1=[55.533535765720615054  ,57.759462819757074639  ] 
dist 2=[53.792572005536312736  ,58.174815451355596378  ] 
dist 3=[52.149586542679228973  ,58.677001614525023016  ] 
dist 4=[50.261837056550857873  ,59.109012687172723061  ] 
dist 5=[47.543208540747224838  ,59.368699471284384595  ] 
dist 6=[44.493289464315983229  ,59.411293788610850670  ] 
dist 7=[41.282497095894615645  ,59.216483611925406950  ] 
dist 8=[37.333178488634298357  ,59.182154891728923049  ] 
dist 9=[31.334044412201597573  ,57.703602715636652203  ] 
dist 10=[25.306886253885642847  ,57.366106755072334962  ] 
dist 11=[21.245481879381621860  ,56.701502043330591810  ] 
dist 12=[17.838584724653935972  ,56.479383186562071916  ] 
dist 13=[14.424599292027172020  ,55.422806273070352534  ] 
dist 14=[11.258108889542596441  ,51.826994321219864250  ] 
dist 15=[8.8391146659754848935 ,51.159893382987019459  ] 
dist 16=[6.4977289081558990421 ,46.918112690792933979  ] 
dist 17=[3.6403795329134202714 ,38.426747987369695723  ] 
dist 18=[.9324993166552941035 ,36.969472317994815808  ] 
dist 19=[-.8124013811859350047 ,33.439418992388027053  ] 
dist 20=[-2.1934495191879214393 ,32.920741918573443153  ] 
dist 21=[-3.4487443382135944356 ,27.791325512116908984  ] 
dist 22=[-4.5375741771886376530 ,26.845028713050523105  ] 
dist 23=[-5.2545769794534463551 ,25.717484020880889961  ] 
dist 24=[-5.8450948616725577008 ,25.483440192634969240  ] 
dist 25=[-6.4305267476799697207 ,17.634802837789364719  ] 
dist 26=[-6.9300878899689828244 ,16.684855805394123757  ] 
dist 27=[-7.1777310387845756389 ,14.685060762748358513  ] 
dist 28=[-7.3008930036555158567 ,14.222117305085647629  ] 
dist 29=[-8.7118362827432336431 ,12.279548003223812944  ] 
dist 30=[-10.292322209289868180  ,11.927601445771000417  ] 
dist 31=[-12.145702087304650410  ,11.278472965223395362  ] 
dist 32=[-13.863364442930217757  ,11.136709486980158238  ] 
dist 33=[-14.901843567027338075  ,-5.2738661198348575963 ] 
dist 34=[-15.645207110846825652  ,-4.4424271985279593727 ] 
dist 35=[-16.184206370830528292  ,-3.7773786497023953309 ] 
dist 36=[-16.580366041401342100  ,-3.1104868043949654074 ] 
dist 37=[-16.753170211061171694  ,-2.2709679114341984969 ] 
dist 38=[-16.805081532709228657  ,-1.3882353851275666272 ] 
dist 39=[-16.789515935490427731  ,-.5485945935842422752 ] 
dist 40=[-4.0102761999328688555 ,.4183157873644714894 ] 
dist 41=[-3.9489592681065398793 ,1.8091027374949572757 ] 
dist 42=[-.6231324107456377973 ,3.1885553076872062953 ] 
dist 43=[-.29782548940120538736,4.1103971751985416913 ] 
dist 44=[.35970265964433092345,4.8723084815546286050 ] 
dist 45=[.52336648735077211586,5.6138554690918975361 ] 
dist 46=[1.0751641935104086265 ,6.2848252035913417293 ] 
dist 47=[1.1902177380423882477 ,6.7652693172412040173 ] 
dist 48=[1.2819896776726858715 ,7.1981134804470128384 ] 
dist 49=[1.2478856990376290208 ,7.6793530299153363018 ] 
dist 50=[1.1620461444495626549 ,8.1100168966454524951 ] 
dist 51=[1.0175684942837780242 ,8.3411259715551166287 ] 
dist 52=[.8030137980534289269 ,8.4709408306437795661 ] 
dist 53=[.4374239785914330387 ,8.4974345359955547440 ] 
dist 54=[.0033998164959688294 ,8.4771662475277161844 ] 
dist 55=[-.4842977161023738565 ,8.3188813635013202272 ] 
dist 56=[-1.1042528270698779782 ,7.2020625100085270722 ] 
dist 57=[-2.0661029292629791877 ,6.8301332174156840875 ] 
dist 58=[-3.0257650875904157857 ,2.0058039264189181195 ] 
dist 59=[-3.6370234068382022693 ,1.9557414190406587945 ] 
dist 60=[-4.1097342331025645522 ,1.4080517615437494155 ] 
dist 61=[-4.5165707480082115672 ,1.3048358746300438733 ] 
dist 62=[-4.8502148018670327266 ,1.1871160084150282315 ] 
dist 63=[-5.0308560837699085789 ,1.1645441585055246073 ] 
dist 64=[-5.1339627722103325134 ,.2542106801772579836 ] 
dist 65=[-5.1594455359716452290 ,.14674854201097515362] 
dist 66=[-5.1401157205179636948 ,-.08648333575909661601] 
dist 67=[-5.1341949882625158894 ,-.1309430983750700963 ] 
dist 68=[-5.1285891073952738295 ,-.36972947762604376228] 
dist 69=[-5.1222313932084451328 ,-.408695312975862574  ] 
dist 70=[-5.1160951348874271381 ,-.47824404748387057245] 
dist 71=[-5.1113444861522379407 ,-.49067747261831084132] 
dist 72=[-5.1067911018210145735 ,-1.2603790384130096845 ] 
dist 73=[-5.1014126249556126033 ,-1.3190208124288179091 ] 
dist 74=[-1.4752643960025979985 ,-1.0920534350894733746 ] 
dist 75=[-1.5633841850607711551 ,-.43749405163182324368] 
dist 76=[-1.6415884636658726918 ,.12490986000601558905] 
dist 77=[-1.6955804388494422426 ,.70757138853556071842] 
dist 78=[-1.7423589259768381622 ,1.2577690259924245992 ] 
dist 79=[-1.7917471513085787492 ,1.6906564863734757924 ] 
dist 80=[-1.8346804929595782679 ,2.1199998312883796261 ] 
dist 81=[-1.8556712644544693727 ,2.6560696137227058100 ] 
dist 82=[-1.8646700161294632520 ,3.1660207342004330543 ] 
dist 83=[-1.8638016353237832409 ,3.4911569175614250708 ] 
dist 84=[-1.8477291690001020098 ,3.7428159799500687988 ] 
dist 85=[-1.8398829853213782373 ,3.9595990849599183186 ] 
dist 86=[-1.8102241802033809610 ,4.1370970548219308479 ] 
dist 87=[-1.7992894414477231225 ,4.2320126547148581758 ] 
dist 88=[-1.6396553966109906762 ,4.2845314392341919535 ] 
dist 89=[-1.6108225096446457088 ,4.2928733442118832934 ] 
dist 90=[-1.5390660088751190296 ,1.6238675644879357895 ] 
dist 91=[-1.5173073141419596651 ,1.8131937531186501110 ] 
dist 92=[-1.3905739620526989078 ,1.9721423256407193492 ] 
dist 93=[-1.3618664932414538963 ,2.0649285139124483311 ] 
dist 94=[-1.3068458353656486836 ,2.1270708722414119662 ] 
dist 95=[-1.2904732811208932643 ,2.1637574125392823007 ] 
dist 96=[-1.3929314736176788353 ,2.1883777297477391864 ] 
dist 97=[-1.6197597187954484964 ,2.2023659729472855103 ] 
dist 98=[-1.8296699464595636266 ,2.2113522898451463167 ] 
dist 99=[-1.9554041808551458914 ,2.2159790885168822038 ] 
dist 100=[-2.0506870476247359442 ,2.2175251523403278314 ] 
dist 101=[-2.1349700480738159063 ,2.2141983893657693147 ] 
dist 102=[-2.1984185777840343751 ,2.2066807926510876898 ] 
dist 103=[-2.2246433903135640684 ,2.1974878704444754491 ] 
dist 104=[-2.2338357443201288916 ,.48665915979850853277] 
dist 105=[-2.2295356915250315346 ,.3521034729302804537 ] 
dist 106=[-2.0982476672003257052 ,.0569536951781028398 ] 
dist 107=[-2.0732910693010628697 ,.1215308711166265307 ] 
dist 108=[-1.9989832546257701269 ,.3058919131804099154 ] 
dist 109=[-1.9807321712148207472 ,.4955748338786585318 ] 
dist 110=[-1.8117154620293246045 ,.6737862075502535223 ] 
dist 111=[-1.7729555298521120007 ,.81238677089612163166] 
dist 112=[-1.7205952118808242042 ,.94830339641987766317] 
dist 113=[-1.7007901993011372762 ,1.1158145542681539946 ] 
dist 114=[-1.2294719284522028326 ,1.2740095475887474613 ] 
dist 115=[-1.1647536313780323013 ,1.3727625981440870626 ] 
dist 116=[-1.1012136781718264431 ,1.4467554213743297952 ] 
dist 117=[-1.1056568570371178269 ,1.5061717945448286037 ] 
dist 118=[-1.1078166525377429277 ,1.5516057969948990485 ] 
dist 119=[-1.1074283061538219594 ,1.5698198412902611073 ] 
dist 120=[-.32783889945304947552,1.5762182816341682856 ] 
dist 121=[-.26454394426206649624,1.5744940429350212495 ] 
dist 122=[-.1199375893046219121 ,1.0671406307036094559 ] 
dist 123=[-.0938775824759886223 ,1.2295361230035780676 ] 
dist 124=[.0854876157056329304 ,1.3531900681182183406 ] 
dist 125=[.1164557751283641428 ,1.4561664250711440006 ] 
dist 126=[.1727347183690134922 ,1.5394661210331452987 ] 
dist 127=[.1847401115717394151 ,1.5846037974684246936 ] 
dist 128=[.32931308364993102064,1.6104030933677599221 ] 
dist 129=[.34971395319169758316,1.6165312813364114121 ] 
dist 130=[.37091334739941630598,1.5566210997562900440 ] 
dist 131=[.36753721678857770718,1.5429835699711176909 ] 
dist 132=[.35368696189430694926,1.5322248281593474321 ] 
dist 133=[.32528646603212285006,1.5226344912174995822 ] 
dist 134=[.28086504509342650751,1.5145678313089305628 ] 
dist 135=[.20310676088511558489,1.5098844792288253011 ] 
dist 136=[.1225197162447946072 ,1.5067970139326166926 ] 
dist 137=[.0668125637302771004 ,1.5050935402811718367 ] 
dist 138=[.0187863062662753344 ,.27222750012248842594] 
dist 139=[-.0311663931491481676 ,.17231136718472418338] 
dist 140=[-.12676686393074290229,-.04958108931531118216] 
dist 141=[-.3087430709563382803 ,-.0645128878635497992 ] 
dist 142=[-.48055203054185574028,-.0885414991713374059 ] 
dist 143=[-.6157109598957675483 ,-.0938626763637767604 ] 
dist 144=[-.7497540315663778018 ,-.1436103364147793807 ] 
dist 145=[-.91711140299165913187,-.1511107342564314789 ] 
dist 146=[-1.0763123574591869757 ,-.1540431297029695147 ] 
dist 147=[-1.1778115589177014646 ,-.1475237492958901359 ] 
dist 148=[-1.2563655401676517111 ,-.1360940150633291938 ] 
dist 149=[-1.3240150965860511424 ,-.1184429293268016121 ] 
dist 150=[-1.3793832172423137619 ,-.0928992970676705481 ] 
dist 151=[-1.4089342172791326200 ,-.0499886343986429783 ] 
dist 152=[-1.4251987202967081202 ,-.0058135675432716095 ] 
dist 153=[-1.4275535720283969122 ,.02477353193970135343] 
dist 154=[-.32377861864195874027,.05119070600906357189] 
dist 155=[-.32164330116011559905,.13757770866936616506] 
dist 156=[-.30119123933215850088,.24007339233344000582] 
dist 157=[-.29610330003773729084,.34102379905297827804] 
dist 158=[-.28927975987461604862,.43367680191021801752] 
dist 159=[-.28651579869759235585,.50129567275747458588] 
dist 160=[-.21727368497099912858,.5631170431118685551 ] 
dist 161=[-.20761873308345747778,.63308695200386086367] 
dist 162=[-.1867123127656363390 ,.69722797629630374418] 
dist 163=[-.1806993427244592872 ,.73579322985702719861] 
dist 164=[-.1556341821182099010 ,.76296583516715982655] 
dist 165=[-.1507396062813961848 ,.78164947826410028051] 
dist 166=[-.1378280692999595670 ,.79428032398947830361] 
dist 167=[-.1358676244443125582 ,.79730355037316986348] 
dist 168=[.1732345864442500394 ,.79629008682003845326] 
dist 169=[.1936592038271571750 ,.7929696313013019075 ] 
dist 170=[.16230238476657436134,.57311504258136584026] 
dist 171=[.08132209901696622488,.55039230731837229513] 
dist 172=[.01171624176982742593,.49228370172676605072] 
dist 173=[-.06042434111480780266,.48276547284331563739] 
dist 174=[-.12854602910244626981,.38668250139829294119] 
dist 175=[-.18211788042781387623,.36778164339458378273] 
dist 176=[-.2352149154277795399 ,.34471894580238004972] 
dist 177=[-.30144229795268759465,.34359385907970701668] 
dist 178=[-.36437627628479703767,.34368511686894932867] 
dist 179=[-.40433365201214347628,.34253194160898271252] 
dist 180=[-.43505507024608156298,.34002505583637389127] 
dist 181=[-.46114039116084492275,.33824098781070488215] 
dist 182=[-.4822029054824993025 ,.3331507090441760211 ] 
dist 183=[-.49288478445545014135,.33065440486358617392] 
dist 184=[-.49820584436423353537,.14194281266732442467] 
dist 185=[-.49899335365707391609,.12470362508618568421] 
dist 186=[-.38817640590966917106,.08559829911274606138] 
dist 187=[-.43350603637352872904,.07777188318603750112] 
dist 188=[-.46782348849395297751,.02929565347829173891] 
dist 189=[-.49604326762643259207,.02070109593754892775] 
dist 190=[-.51842719303623515244,.00393363119624025368] 
dist 191=[-.52945812956308894646,-.00011129934899998590] 
dist 192=[-.53497308371630802197,-.04116827676166718093] 
dist 193=[-.53545736802832389005,-.04737040516144532571] 
dist 194=[-.51706983293699546972,-.05518452620337740318] 
dist 195=[-.51212570305587151393,-.05616414101845497928] 
dist 196=[-.50457720982263300085,-.05446506991771750994] 
dist 197=[-.50139153661319003856,-.04881816471503159788] 
dist 198=[-.48913823735993375412,-.03921262418138395806] 
dist 199=[-.48493935420770359685,-.01713115839327043276] 
dist 200=[-.47484612802844039019,.00874913746193724239] 
dist 201=[-.4707463162344238124 ,.02665014885324241261] 
dist 202=[-.15599871068239974752,.05362642833687065899] 
dist 203=[-.12767831665236468319,.10972492012285102039] 
dist 204=[-.0652288892838315188 ,.17075479423052603306] 
dist 205=[-.05189829776427274655,.23190630448960473707] 
dist 206=[.01940369836153903227,.28904818998003074256] 
dist 207=[.0209215568628006406 ,.33277223328548175786] 
dist 208=[.0152611392198090666 ,.37445113342887712931] 
dist 209=[.0091276819062497741 ,.42417349733485750348] 
dist 210=[.0014812912565799630 ,.47034307196687568195] 
dist 211=[-.01021427697474081371,.49784643951393049849] 
dist 212=[-.02359468856358865199,.51691434879111355309] 
dist 213=[-.03796228959757379864,.52942632199323927775] 
dist 214=[-.05578086667349249814,.5379577450344561737 ] 
dist 215=[-.08292824665083610274,.54114297825980123485] 
dist 216=[-.10994865014354677733,.5410546172881810567 ] 
dist 217=[-.12726041260369720304,.54009353718512881476] 
dist 218=[-.14074571706925301987,.17879031513316053308] 
dist 219=[-.15250045284151437323,.17929094635945790007] 
dist 220=[-.16221642622646963794,.17814430547601511859] 
dist 221=[-.1920310189164892725 ,.17728683165366286607] 
dist 222=[-.23542378506050671281,.17617619185174313973] 
dist 223=[-.26653956142732042168,.17532306279654390223] 
dist 224=[-.29458345150452705564,.1471217834946827939 ] 
dist 225=[-.32571986256923978043,.14288026348014111638] 
dist 226=[-.35408312216498527842,.13428158505582035445] 
dist 227=[-.37106243652747352178,.13179226046650535235] 
dist 228=[-.382934051003316644  ,.12160642985556498376] 
dist 229=[-.39091800142224124538,.11928759796595615828] 
dist 230=[-.39606842774424463729,.11377824822313662134] 
dist 231=[-.39692597070505090064,.11191980443431157627] 
dist 232=[-.39557315896489568435,.00560377064573746440] 
dist 233=[-.39423005586826675256,.04364672268518967844] 
dist 234=[-.27041443108768943966,.09890220996240238909] 
dist 235=[-.25974043657667529232,.1351129184929943706 ] 
dist 236=[-.24934887884256226494,.16426060764378207608] 
dist 237=[-.24692316007131044504,.19133573423203097801] 
dist 238=[-.22466803229159413325,.21496282289799517426] 
dist 239=[-.21966377211758219505,.23035330539789945255] 
dist 240=[-.21287803853420439634,.24263706538362531837] 
dist 241=[-.21036258353402004215,.25386861924890317533] 
dist 242=[-.1513689788693005142 ,.2634469152236885459 ] 
dist 243=[-.14329070269579914703,.26913435852595210597] 
dist 244=[-.12574816481260139786,.27305215650324778586] 
dist 245=[-.1207514159929851932 ,.27556981945197531614] 
dist 246=[-.10009230633186053046,.27698857874451698042] 
dist 247=[-.09612313377131491373,.27662752476574205102] 
dist 248=[-.08581431264842975418,.2750922182866993196 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 1, 0, 1, 1, 2] 
dist 0=[53.825060647609079315  ,53.825060647609079315  ] 
dist 1=[52.551675863100783398  ,54.437250407194478614  ] 
dist 2=[50.980852877494578864  ,54.782806470698784779  ] 
dist 3=[49.180957791894378672  ,55.072355830474695961  ] 
dist 4=[46.865141894044731672  ,55.298982240365902053  ] 
dist 5=[43.233943293833318260  ,55.405970607953615242  ] 
dist 6=[39.539492723001558601  ,55.400469789343654261  ] 
dist 7=[36.970950978681274516  ,55.310568996171097515  ] 
dist 8=[34.729982604716164440  ,55.230490665513061323  ] 
dist 9=[32.343355449987841585  ,54.778421331000372153  ] 
dist 10=[30.038745630815454285  ,54.632962957371752133  ] 
dist 11=[28.125015996116607631  ,54.063546214346140538  ] 
dist 12=[26.125618834847971955  ,53.947439482462626930  ] 
dist 13=[23.478351368726538673  ,52.254658074546221352  ] 
dist 14=[20.866372875108474767  ,51.845409033748486521  ] 
dist 15=[19.007618830778945808  ,49.652292484414352167  ] 
dist 16=[17.337839876879583020  ,35.939288196144682180  ] 
dist 17=[15.480233486625415782  ,31.189367912971667106  ] 
dist 18=[13.633792319320986531  ,30.287137606293482277  ] 
dist 19=[12.008078184907775971  ,29.305789953298117775  ] 
dist 20=[10.223910000210191191  ,29.128768394653045715  ] 
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dist 200=[-.51086262539022332821,.18715751817405434705] 
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dist 203=[-.51507279769889439174,.12153955636277731402] 
dist 204=[-.5135211967362016865 ,.11682717511100903204] 
dist 205=[-.2933576630222202987 ,-.12725715519352754766] 
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dist 210=[-.20478651621977867501,.10435296374066538255] 
dist 211=[-.21206008164061019421,.13705391865444724262] 
dist 212=[-.21878574380800993447,.1687000076362935668 ] 
dist 213=[-.22421748593388359874,.19361928033929033068] 
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dist 218=[-.21835517812631611839,.29548462907289648936] 
dist 219=[-.21569647046006983622,.30127296944957583498] 
dist 220=[-.21433884988336500138,.3049614501787436438 ] 
dist 221=[-.14552015995522377541,.30656413478131877435] 
dist 222=[-.13769256132664348592,.30694409729789244666] 
dist 223=[-.11927791228444693844,.30607888484603534255] 
dist 224=[-.11536081697038545745,.14235018597023131074] 
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dist 229=[-.14709202507044361587,.21496072095118910997] 
dist 230=[-.1645986110450074462 ,.22152475596277015596] 
dist 231=[-.1846833829687974471 ,.22599508667873445422] 
dist 232=[-.20309309830743507328,.22877440732962304376] 
dist 233=[-.21391656600190246633,.23025251703701479904] 
dist 234=[-.22124157037604537275,.23028137384989040673] 
dist 235=[-.22569289950208548676,.22824116612471498631] 
dist 236=[-.22854297081605562037,.22746089422088946297] 
dist 237=[-.22947935566970933097,.04423471304792042291] 
dist 238=[-.22919232139206675116,.03139969698749430768] 
dist 239=[-.22865747725907534926,.02872598759618920706] 
dist 240=[-.18309284045459321915,.06063615086075136257] 
dist 241=[-.18195068908066226626,.08145963698856551754] 
dist 242=[-.17822671454433226099,.09812015995843658321] 
dist 243=[-.17673944457414729553,.11342122572706505955] 
dist 244=[-.1665082338712399757 ,.12665016237032973296] 
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dist 248=[-.12436888006447719479,.15148006479363813409] 
dist 249=[-.11952801625249877826,.15423109903270186559] 
dist 250=[-.10846799671109521486,.15619908340055647992] 
dist 251=[-.10129409041469149339,.15760763352252305908] 
dist 252=[-.07605829851091163246,.15854531351504003838] 
dist 253=[-.05224718136018621706,.15863475426963568124] 
dist 254=[-.04649410911270210682,.15811926754247677491] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 0, 1, 0, 0, 2] 
dist 0=[53.005076223308530090  ,53.005076223308530090  ] 
dist 1=[52.095095876742542209  ,53.550710608306921143  ] 
dist 2=[50.949238398168521648  ,53.934853078266680849  ] 
dist 3=[49.461594688863520322  ,54.199727023593122541  ] 
dist 4=[47.435297023329850675  ,54.383535845071519601  ] 
dist 5=[44.138407680016526695  ,54.443811730130560934  ] 
dist 6=[40.752328826223103033  ,54.424350969762875299  ] 
dist 7=[38.369797579390319019  ,54.354739063527744575  ] 
dist 8=[36.260970439639051968  ,54.120431669016119774  ] 
dist 9=[33.967679358320449741  ,53.968856069128953530  ] 
dist 10=[31.724441477914896013  ,53.786487248710841337  ] 
dist 11=[29.815264365268924782  ,53.669540602528342600  ] 
dist 12=[27.779733309012194731  ,53.246462998207320463  ] 
dist 13=[25.031442162962228427  ,53.084784095439047842  ] 
dist 14=[22.295873941813101637  ,52.659303477757695705  ] 
dist 15=[20.310913025858795384  ,51.984213004123075653  ] 
dist 16=[18.488869808843703803  ,37.566262911211312744  ] 
dist 17=[16.403659059845142439  ,36.228763247729647309  ] 
dist 18=[14.298607990640991705  ,32.952135289369597594  ] 
dist 19=[12.396870344865343671  ,32.482010461583147903  ] 
dist 20=[9.8547736482099904020 ,27.581473373849146949  ] 
dist 21=[6.8251805749365544623 ,26.664169853103179243  ] 
dist 22=[4.3185713920640487285 ,25.639819438428598391  ] 
dist 23=[2.3915254498725496349 ,25.458790554808235542  ] 
dist 24=[.83612614797814581049,17.286281474721222070  ] 
dist 25=[-.95361666412460767874,16.282648650287755865  ] 
dist 26=[-2.5436008839821927216 ,14.254538874098642048  ] 
dist 27=[-4.2259656107745149215 ,13.740536495422076910  ] 
dist 28=[-6.4884712108685291634 ,11.950585681048684581  ] 
dist 29=[-8.6666036583086991500 ,11.576977183378251521  ] 
dist 30=[-10.012092145029781071  ,11.115282130541414429  ] 
dist 31=[-11.015158075136247920  ,11.028309928627607580  ] 
dist 32=[-11.824612932344366663  ,-.88942999675288958101] 
dist 33=[-12.466594277204510585  ,-1.8547669516876107598 ] 
dist 34=[-12.800013765391050325  ,-3.9083157835876652624 ] 
dist 35=[-12.974931389793407018  ,-4.3151899500259764796 ] 
dist 36=[-13.011154586955254024  ,-4.9422481027134414723 ] 
dist 37=[-12.590412179520539454  ,-4.2638758153151872102 ] 
dist 38=[-12.484818183755498665  ,-3.5524343120179168260 ] 
dist 39=[-12.351783937859480785  ,-3.0441879275440009357 ] 
dist 40=[-12.282414097929543945  ,-2.5895409634145462200 ] 
dist 41=[-13.002175896016313321  ,-2.0914975111566217221 ] 
dist 42=[-13.568454535541089492  ,-1.6053491799827054076 ] 
dist 43=[-14.047490945501903736  ,-1.1979340144612479883 ] 
dist 44=[-14.435915948489121198  ,-.7708645536764407718 ] 
dist 45=[-14.640186682195841277  ,-.20606854085777571759] 
dist 46=[-14.749450883547311633  ,.34714128851550238591] 
dist 47=[-14.758319110695606256  ,.7280913742500102106 ] 
dist 48=[-1.9749568330361395408 ,1.4215916850744424303 ] 
dist 49=[-.81287155581421545689,2.5468162792695479374 ] 
dist 50=[-.4358656482851097626 ,3.3985734908286348940 ] 
dist 51=[-.37114766251832932489,4.2134137180238734772 ] 
dist 52=[-.23111710867670682015,5.1913440448087466343 ] 
dist 53=[-.20385443272617937241,6.1049503966641669458 ] 
dist 54=[2.7149797732266200596 ,6.6630504053139691645 ] 
dist 55=[2.9905155095053031430 ,7.0678699697860398384 ] 
dist 56=[3.1501256524444581947 ,7.3696283963197077180 ] 
dist 57=[3.1932008159883105755 ,7.6010150218357491127 ] 
dist 58=[3.0790141319906579646 ,7.7494984325559775393 ] 
dist 59=[2.8471640192326365654 ,7.9308041226341205469 ] 
dist 60=[2.3954622209710189651 ,8.0630621214878190315 ] 
dist 61=[1.9185684177257658618 ,8.1037919484421193812 ] 
dist 62=[1.5861440611401594831 ,8.0988418238598502232 ] 
dist 63=[1.2967747853028099937 ,8.0743318561303154128 ] 
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dist 143=[-.31982397208980781615,1.5336345405402466272 ] 
dist 144=[-.07603014520924125370,.45125174322245227712] 
dist 145=[-.10875038964526112457,.48522699248002570495] 
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dist 150=[-.2210122910029416439 ,.54826813348311370301] 
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dist 152=[-.23972512197834949292,.49114756539743022974] 
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dist 156=[-.24667054149510574122,.44761387021195585254] 
dist 157=[-.07349971465885307264,.4425057139871531863 ] 
dist 158=[-.06217557454498549794,.43722388312133107484] 
dist 159=[-.03652647546993935648,.43410322331335147212] 
dist 160=[-.03543888573904088778,.05189111883578160008] 
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dist 164=[-.24068195902388305667,.0701638124449857074 ] 
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dist 166=[-.32600127005088017383,.1061856791714881477 ] 
dist 167=[-.3778127013223379239 ,.11789660499353200097] 
dist 168=[-.42673403138560249749,.12905155787243872521] 
dist 169=[-.45736931433462167693,.13898749572756202692] 
dist 170=[-.48045852089259563637,.14583754717527583008] 
dist 171=[-.49926784766542956221,.15174354298882906451] 
dist 172=[-.51387664786560623   ,.15791767207709140377] 
dist 173=[-.5202043322005136172 ,.16321955926448903508] 
dist 174=[-.52257143317926662196,.16564579305061793878] 
dist 175=[-.52191323589791109069,.16665134463998170945] 
dist 176=[-.17414997652913582337,.16657136606500001316] 
dist 177=[-.17724510109286127646,.16568720639377740892] 
dist 178=[-.17871557019581107007,.16807930228973149958] 
dist 179=[-.17926833529639481961,.20485114798609051735] 
dist 180=[-.17892010814036452509,.24136436503371181531] 
dist 181=[-.15752481784895538627,.26618392609047265613] 
dist 182=[-.15403752165872396355,.28716125560483151451] 
dist 183=[-.14795461896514164363,.30834399796611439052] 
dist 184=[-.14623806807360989868,.3271974810609199375 ] 
dist 185=[-.14010423280195212103,.33888153466713156924] 
dist 186=[-.13816791443324827256,.34753860697986025465] 
dist 187=[-.13984764993622438589,.35431579518949807022] 
dist 188=[-.14403142631099081078,.35936134610072672163] 
dist 189=[-.14783338521825365593,.36111034912831539977] 
dist 190=[-.15021046284195702721,.36078362568243362988] 
dist 191=[-.15198253112811216072,.36004031767749145917] 
dist 192=[-.15337402201249294427,.21336624413045049737] 
dist 193=[-.15440174645373480611,.20245082053261641824] 
dist 194=[-.1547242873956446507 ,.17479979780393707542] 
dist 195=[-.15458815684269064894,.17070427927967608384] 
dist 196=[-.15398278282159325135,.12644754283416485204] 
dist 197=[-.15271923593549171993,.11797273370995633715] 
dist 198=[-.15172658973190498587,.10843192355993148963] 
dist 199=[-.14998189727879488558,.10639296033915762912] 
dist 200=[-.16059779965058687953,.02784691976017023033] 
dist 201=[-.17406860053553790994,.01825600198391347244] 
dist 202=[-.18401488757204612893,-.00191965901204630473] 
dist 203=[-.19173589013451132836,-.00686193907497876915] 
dist 204=[-.19759641811031065757,-.02620670140119771288] 
dist 205=[-.20011969788521318641,-.02384392298903730639] 
dist 206=[-.20107166870992728979,-.01802368419448941635] 
dist 207=[-.20078910978758151786,-.01254646280120811898] 
dist 208=[-.11844279748934153661,-.00612319586290609136] 
dist 209=[-.13090388600080811082,.00040055210678016334] 
dist 210=[-.14030337462905384371,.00627959990626893583] 
dist 211=[-.14797669118024144485,.01280261152709263256] 
dist 212=[-.15403596933342518861,.02189663509945878213] 
dist 213=[-.15699422243015699783,.03100995892836551896] 
dist 214=[-.15844470900366688883,.03761062664580261496] 
dist 215=[-.15854543108239562839,.04362749569955404874] 
dist 216=[-.15289229280380197065,.05041251511859214601] 
dist 217=[-.15144169109199541993,.05716600382799501273] 
dist 218=[-.14912308677340618374,.06305794400506985021] 
dist 219=[-.14820940220773048497,.06944503994183643090] 
dist 220=[-.14451562617410114009,.07817574069806820629] 
dist 221=[-.14330385377653015217,.08654741912595614506] 
dist 222=[-.1403034384025842318 ,.09150206991268457648] 
dist 223=[-.13908454687129654608,.09490268203514817095] 
dist 224=[-.04493976353165660577,.10041050815409471855] 
dist 225=[-.03655739054432770893,.11109620429413867857] 
dist 226=[-.01791501467043938370,.11888475751006560238] 
dist 227=[-.01411748503215892975,.1260394573480567304 ] 
dist 228=[.00763750215282789458,.13419559452987558215] 
dist 229=[.01138494931503752552,.14158333876026013173] 
dist 230=[.01916167765344815585,.14567154469932598777] 
dist 231=[.02098689025931432518,.14812375038443778444] 
dist 232=[.03436935249297106684,.14898255178283541058] 
dist 233=[.03663925354185246999,.1490982767264895529 ] 
dist 234=[.03736211947125066801,.14867080759727575547] 
dist 235=[.02451889229631283660,.14765882154125475382] 
dist 236=[.00525656491848426314,.14702067254254113629] 
dist 237=[-.01407256689144696833,.12974229413365291713] 
dist 238=[-.02718253060092646382,.12707141480213592827] 
dist 239=[-.03823713827810923125,.11899235061336786655] 
dist 240=[-.04936487448650409825,-.00575510852632489506] 
dist 241=[-.05967783358187873568,-.01017845670970266870] 
dist 242=[-.06748136391595436515,-.01909181338659848649] 
dist 243=[-.07493599566282786006,-.02127342713078322885] 
dist 244=[-.08385703185242808726,-.02778108060958476860] 
dist 245=[-.09216248341379664053,-.02988878647817214728] 
dist 246=[-.09716080691501506175,-.03116629957663217129] 
dist 247=[-.10069136764337855958,-.03541385780235168164] 
dist 248=[-.10313989398449858111,-.04636164823335965233] 
dist 249=[-.10481805482390475882,-.03868723408880193397] 
dist 250=[-.10527432029676239666,-.02974614387302266549] 
dist 251=[-.10519992956324339465,-.01817377653572041400] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 2, 0, 2] 
dist 0=[61.025617946290246448  ,61.025617946290246448  ] 
dist 1=[60.829254957783738985  ,61.120579735368287149  ] 
dist 2=[60.350918690674068862  ,61.193969973977295576  ] 
dist 3=[59.505708562788753526  ,61.237029843050950981  ] 
dist 4=[57.844398254129413428  ,61.210896880349840078  ] 
dist 5=[55.802386270382566102  ,61.128948699453596343  ] 
dist 6=[53.437028868247825103  ,61.009064207065293954  ] 
dist 7=[50.377492190256205635  ,60.720024436044126771  ] 
dist 8=[45.563575447486495234  ,60.553094033032685229  ] 
dist 9=[40.662527379651435069  ,60.138942802643563498  ] 
dist 10=[37.255013307253814204  ,59.946570389439777976  ] 
dist 11=[34.283019546396975520  ,58.902528398330135222  ] 
dist 12=[31.120861546074173474  ,58.583646504804321234  ] 
dist 13=[28.071108583469547734  ,57.010150772369386457  ] 
dist 14=[25.547771708769226296  ,54.020043346693793548  ] 
dist 15=[22.921320253982973876  ,32.501300838621104001  ] 
dist 16=[19.459445016661434866  ,30.460779120585820953  ] 
dist 17=[16.056240245181824122  ,27.170418597447470943  ] 
dist 18=[13.663841312455246688  ,26.938476237775215760  ] 
dist 19=[11.547426428042583747  ,19.043526380692235048  ] 
dist 20=[9.2459576323323850334 ,18.003708931795747650  ] 
dist 21=[6.9925046397679175213 ,16.258020061512837387  ] 
dist 22=[5.0673466177710021273 ,15.868931697016531355  ] 
dist 23=[3.0062267494111382603 ,11.784006565357152230  ] 
dist 24=[.2087402069197057819 ,11.384934598556496111  ] 
dist 25=[-2.5090196373544074761 ,10.792709610931202402  ] 
dist 26=[-4.2518570997088676504 ,10.649343846184222839  ] 
dist 27=[-5.6226696939472422471 ,7.0159048071661573998 ] 
dist 28=[-6.8539927935534139748 ,6.3978864392462513454 ] 
dist 29=[-8.0520508263115554110 ,4.2119220768918591235 ] 
dist 30=[-10.353068501821781786  ,3.1593848857152921162 ] 
dist 31=[-12.543860496386159963  ,-5.2210900938069264200 ] 
dist 32=[-13.867431424202178569  ,-5.5252843136792555046 ] 
dist 33=[-14.818321614873566296  ,-6.0529027566382482358 ] 
dist 34=[-15.519827515758949393  ,-6.1491073739433604155 ] 
dist 35=[-16.055016730010430059  ,-6.2487991359249783419 ] 
dist 36=[-16.340973021469242143  ,-6.1024036063965734268 ] 
dist 37=[-16.502323374448995523  ,-5.4222036082517899283 ] 
dist 38=[-16.538646262873937638  ,-4.3636286310199982824 ] 
dist 39=[-15.074512063483068908  ,-3.0217575294755840920 ] 
dist 40=[-14.834663210431727895  ,-.9476342184985178545 ] 
dist 41=[-14.475835121951704100  ,1.1421908350400102872 ] 
dist 42=[-14.350431853965653100  ,2.5468798805993136641 ] 
dist 43=[-14.040014213202054239  ,3.7154324826443331873 ] 
dist 44=[-13.927876515375244850  ,4.8635383089370224531 ] 
dist 45=[-13.858524210831035169  ,5.9078005767443121044 ] 
dist 46=[-13.830181570575864232  ,6.6622361304918385352 ] 
dist 47=[-2.9196653501755592984 ,7.3475513086173528168 ] 
dist 48=[-2.0360042810699919970 ,8.1162168342331368798 ] 
dist 49=[-.1780634537283813974 ,8.8100167702323619239 ] 
dist 50=[.0107506823212386692 ,9.1966627495492522071 ] 
dist 51=[.3064807200409283461 ,9.4317911406956943860 ] 
dist 52=[.3786306563776363720 ,9.5209805368643949108 ] 
dist 53=[.4423218338164377548 ,9.5507158828212869996 ] 
dist 54=[.3711235389486496488 ,9.5486860938026513917 ] 
dist 55=[.2086688969001943735 ,9.3948093534683424984 ] 
dist 56=[-.1203466427278046070 ,9.4568530530950407759 ] 
dist 57=[-.4654082464733937847 ,10.098963756439197964  ] 
dist 58=[-.6918884207136583758 ,10.648450612000135077  ] 
dist 59=[-.8744580773457366503 ,11.096419274763838950  ] 
dist 60=[-1.0443580938448228987 ,11.333339266221927186  ] 
dist 61=[-1.1927436915465653264 ,11.461068945733193126  ] 
dist 62=[-1.2894896075798210353 ,11.475892805339835592  ] 
dist 63=[-1.3667700429523454055 ,.7525841457526382740 ] 
dist 64=[-1.4375029855784587141 ,.2854513583835188095 ] 
dist 65=[-1.5071653093730360720 ,-.2189515085962515392 ] 
dist 66=[-2.1313225134374472064 ,-.2906792048950894166 ] 
dist 67=[-2.7236112783005666318 ,-1.3736728938775749452 ] 
dist 68=[-3.0973639882284118826 ,-1.3800176996511629925 ] 
dist 69=[-3.4110001338108361607 ,-1.2924058953409853209 ] 
dist 70=[-3.9406535908878937584 ,-1.1798195019062923561 ] 
dist 71=[-4.4281046650410858270 ,-1.0275430103591114733 ] 
dist 72=[-4.7262724686929923806 ,-.78157889465419907141] 
dist 73=[-4.9427018638250057421 ,-.53053639719726618581] 
dist 74=[-5.1039712473568810737 ,-.35799696167453292896] 
dist 75=[-5.2188087553404152572 ,-.21016494291884634866] 
dist 76=[-5.2499830528820482964 ,-.05769352777855304106] 
dist 77=[-5.2510428317595604115 ,.08583611047828474284] 
dist 78=[-5.2456701888956048694 ,.19799630198288669489] 
dist 79=[-3.7427226710575614698 ,.30851394611056349541] 
dist 80=[-3.5940231274113175125 ,.4454954873263507411 ] 
dist 81=[-3.2094832591432569909 ,.5752965103580247058 ] 
dist 82=[-3.1498955837673165984 ,.6571676550564406425 ] 
dist 83=[-2.5058457623385514988 ,.7195168650029456949 ] 
dist 84=[-2.3798171438019170646 ,1.0260134367837233640 ] 
dist 85=[-2.2352862585953451908 ,1.3712819987862242921 ] 
dist 86=[-2.1972662134705511367 ,1.8020133651483260727 ] 
dist 87=[-.9856148066299328721 ,2.2109664226002638235 ] 
dist 88=[-.8352305607570756674 ,2.4693620446544010832 ] 
dist 89=[-.5151146894491996608 ,2.6664471524199230316 ] 
dist 90=[-.4699110437754590207 ,2.8308255345532227871 ] 
dist 91=[-.6229244207862672122 ,2.9611999249941249022 ] 
dist 92=[-.7263959250962910567 ,3.0226373177574404219 ] 
dist 93=[-.8129539345109307813 ,3.0527917305523911955 ] 
dist 94=[-.8985307059474154721 ,3.0583730050439624177 ] 
dist 95=[-.9764554336036713886 ,2.2432415720445497610 ] 
dist 96=[-1.0324987477735980750 ,2.4870486061365410558 ] 
dist 97=[-1.0829656957599183833 ,2.6684958092494441632 ] 
dist 98=[-1.1386423920266733214 ,2.8122801768535296000 ] 
dist 99=[-1.1875576124514925342 ,2.9249652235489574408 ] 
dist 100=[-1.2110602860603319993 ,2.9822960572581922217 ] 
dist 101=[-1.2220867686445914342 ,3.0100908732484444629 ] 
dist 102=[-1.2223164277915474702 ,3.0138151770444883734 ] 
dist 103=[-1.1991547466164651844 ,2.8542069870911635581 ] 
dist 104=[-1.1888422286847499234 ,2.8315392893876738471 ] 
dist 105=[-1.2867929517619889543 ,2.8012102884608304660 ] 
dist 106=[-1.4350486626763556088 ,2.7853289413127721302 ] 
dist 107=[-1.5484118464030892747 ,2.7297475804232354039 ] 
dist 108=[-1.6435678001567455834 ,2.7087260624053540687 ] 
dist 109=[-1.7195770381316993308 ,2.6593066382687689647 ] 
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dist 118=[-2.1552989559069891014 ,.79338151825823979942] 
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dist 126=[-2.8851160266324844232 ,.31218759890445259803] 
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dist 155=[-1.3194381591975275458 ,.54350677937010182463] 
dist 156=[-1.3179798385807872118 ,.52398860376909528386] 
dist 157=[-1.3051175725856416375 ,.47731944582509178807] 
dist 158=[-1.2979432009413473153 ,.46668060053957546243] 
dist 159=[-.49068216416027765746,.28555261572034505721] 
dist 160=[-.47613725269825438056,.32748755357101626283] 
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dist 164=[-.53624161167326157167,.47717987684400337517] 
dist 165=[-.54014748435363753061,.49334580193194610524] 
dist 166=[-.53996004377979910611,.50273835436984547167] 
dist 167=[-.52890728179931146806,.50861220349911144986] 
dist 168=[-.52515608921217743692,.5107415420946490458 ] 
dist 169=[-.51548010976969877335,.51052669115689818692] 
dist 170=[-.51126973357396555106,.5091164515309093769 ] 
dist 171=[-.48778293860496643682,.44700392592442663909] 
dist 172=[-.48180782329616016118,.4827595134450948693 ] 
dist 173=[-.4674000054580774871 ,.50863426177803386149] 
dist 174=[-.46206995253051612919,.5277484096214170498 ] 
dist 175=[-.22350182897945906217,.54198534186386659466] 
dist 176=[-.19901025589324214544,.54840017294894894942] 
dist 177=[-.14601974340027399277,.55048454326931974452] 
dist 178=[-.13286685890277181988,.55011633096024202371] 
dist 179=[-.07434335968382435815,.50512712510322550039] 
dist 180=[-.06371480705150231243,.49687909709808112727] 
dist 181=[-.03904687066054939392,.53340088907291286077] 
dist 182=[-.03472743048556410096,.57397043816366616011] 
dist 183=[-.00341781536798095795,.61013800540217279132] 
dist 184=[.00229740305036807783,.6296494010563546602 ] 
dist 185=[.00256078258198499394,.64068005755799512078] 
dist 186=[-.00454122948530297666,.643111008501617064  ] 
dist 187=[-.1122536124170798051 ,.6421403572523516821 ] 
dist 188=[-.19099552273125371934,.64041663914662019839] 
dist 189=[-.25744510247703067077,.63774191109861607203] 
dist 190=[-.32436339634532071658,.63476642337373182847] 
dist 191=[-.38634900712828616908,-.01233165368632646615] 
dist 192=[-.43311854910592293473,-.02521084560892676123] 
dist 193=[-.47763532702849133262,-.04893120046622215844] 
dist 194=[-.53063308684500335685,-.05416267838558916517] 
dist 195=[-.57976199745239301799,-.11639165069535535142] 
dist 196=[-.60884303560760493753,-.1248146161357280721 ] 
dist 197=[-.62876817120446084729,-.11094849504676436105] 
dist 198=[-.64136721997293004307,-.08351753460304461846] 
dist 199=[-.64937994890176954476,-.04951506389527453683] 
dist 200=[-.65100673620547939207,-.00943043321994244870] 
dist 201=[-.64949141502954206465,.04273007790689456629] 
dist 202=[-.64705440703601155434,.12491184099635415144] 
dist 203=[-.32852271954516342527,.2073810552623610253 ] 
dist 204=[-.32949616071660414865,.26068834697988474752] 
dist 205=[-.32883476886529852833,.30276702261371827466] 
dist 206=[-.32766803287867041405,.34043708637885536443] 
dist 207=[-.31808995547072593893,.37232332977227015666] 
dist 208=[-.31523447709132278169,.39132595879659474274] 
dist 209=[-.30800520671095992866,.40450131230104655477] 
dist 210=[-.30505982895756292134,.41313782619436883094] 
dist 211=[-.28917730951557167162,.41940327254204417536] 
dist 212=[-.2852326370908772765 ,.42311889651140503303] 
dist 213=[-.275980449509726478  ,.4256710436503872234 ] 
dist 214=[-.27265626271210114675,.42729556988174773555] 
dist 215=[-.22895064306685022694,.42819666744575431996] 
dist 216=[-.22218822417092399003,.42786324082799804153] 
dist 217=[-.20425304800224914083,.41409524911664689707] 
dist 218=[-.20128729654188839559,.38283565453127947925] 
dist 219=[-.16920542979574383637,.23750501338355404591] 
dist 220=[-.16267992205872466222,.24554154601518163404] 
dist 221=[-.15520074375121049179,.2500783994200090456 ] 
dist 222=[-.1527385423670122143 ,.25116784337895459442] 
dist 223=[-.16010092779667664327,.2507514250297949873 ] 
dist 224=[-.1685411643495776957 ,.25039054467248329737] 
dist 225=[-.17557144228976686947,.24990285867748656953] 
dist 226=[-.18249792027036853638,.24911753453823492611] 
dist 227=[-.18826042602847204871,.20509244135090510969] 
dist 228=[-.19064679686794175389,.1987127286442898375 ] 
dist 229=[-.19156269124166412396,.18684474856910210758] 
dist 230=[-.19145937491914541193,.18367412184717833877] 
dist 231=[-.18584198252032493593,.17241248574067859216] 
dist 232=[-.18398038583963183842,.16930755305033710465] 
dist 233=[-.18249798151211952211,.16512260623320717882] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 1, 0, 1, 0, 1] 
dist 0=[52.152894205316767781  ,52.152894205316767781  ] 
dist 1=[51.336373511465371444  ,52.433002608502784375  ] 
dist 2=[50.229652526920374184  ,52.735104893029763151  ] 
dist 3=[48.798768333481757074  ,53.093039482646880947  ] 
dist 4=[46.852924500624254621  ,53.324022554000635192  ] 
dist 5=[43.689713939781994885  ,53.473490781585279773  ] 
dist 6=[40.438761972472142120  ,53.505764369023730444  ] 
dist 7=[38.142464285295730462  ,53.457616700857038826  ] 
dist 8=[36.100457366571811405  ,53.390267746654875989  ] 
dist 9=[33.864837285290140095  ,53.083529757365468914  ] 
dist 10=[31.668882539733587724  ,52.922286717823637878  ] 
dist 11=[29.785079553331818832  ,52.736159234506066997  ] 
dist 12=[27.763698134146761107  ,52.617535568831765706  ] 
dist 13=[25.017905496303793217  ,52.238186963592617253  ] 
dist 14=[22.277273364895071178  ,52.081923784239693584  ] 
dist 15=[20.276288706249260443  ,51.040936176984494262  ] 
dist 16=[18.427139683996618128  ,48.493502596504447519  ] 
dist 17=[16.292648500291143103  ,36.763759436526310473  ] 
dist 18=[13.973613984262251115  ,35.451184648953649882  ] 
dist 19=[10.872928601577883162  ,32.259531660758269695  ] 
dist 20=[7.8324348352434731191 ,31.786363371722007448  ] 
dist 21=[5.7010417441789444385 ,27.081513545352143512  ] 
dist 22=[3.7153284960098578913 ,26.202622595426430839  ] 
dist 23=[1.7021824993741963445 ,25.169909868114538686  ] 
dist 24=[-.22008744428341607111,24.946735468947010666  ] 
dist 25=[-1.9322783717113369919 ,17.337006214599009555  ] 
dist 26=[-3.7715352275286147815 ,16.393491804791695628  ] 
dist 27=[-6.2790762996919502674 ,14.457551451231647127  ] 
dist 28=[-8.7029492034021123799 ,13.958877030633561037  ] 
dist 29=[-10.208144852930461874  ,12.166005734082287012  ] 
dist 30=[-11.338322998751435465  ,11.805320274323757465  ] 
dist 31=[-12.263463148924894731  ,11.223757060270586920  ] 
dist 32=[-13.004192978397461424  ,11.084779347878139640  ] 
dist 33=[-13.397145159921894532  ,.4913166855766621875 ] 
dist 34=[-13.613959389514776283  ,-.40010422256506503557] 
dist 35=[-13.660348625653732576  ,-2.3104740019874596045 ] 
dist 36=[-13.306304095227408772  ,-2.6863707704778411701 ] 
dist 37=[-13.208359503071417315  ,-4.6491712312991188726 ] 
dist 38=[-13.120728987370590877  ,-3.8916601575048020683 ] 
dist 39=[-13.049372779995877371  ,-3.2899915460074534108 ] 
dist 40=[-12.940658990953326399  ,-2.7577736705270560860 ] 
dist 41=[-12.876525420663530129  ,-2.1835950621776413610 ] 
dist 42=[-12.998958224640288370  ,-1.6281350396696117392 ] 
dist 43=[-13.454721455165219617  ,-1.1703778794694030348 ] 
dist 44=[-13.790810414661000238  ,-.69726141317394040163] 
dist 45=[-14.031452487524830120  ,-.08029311701123696313] 
dist 46=[-14.105878676702206892  ,.5199644838964413476 ] 
dist 47=[-14.116198733051013419  ,1.0415741798091352900 ] 
dist 48=[-14.100609350957898700  ,1.9046428172539453444 ] 
dist 49=[-.64293902864347333642,2.8206501332724427722 ] 
dist 50=[.02362586971219341890,3.7086847565346901283 ] 
dist 51=[.39643412908745808328,4.7910140056923151760 ] 
dist 52=[.53576123808582364738,5.8102780904288712563 ] 
dist 53=[.56028407363408857668,6.4465989510768818182 ] 
dist 54=[2.9687069982182380625 ,6.9244276344204164816 ] 
dist 55=[3.0525406935701668040 ,7.3110551170054502336 ] 
dist 56=[3.2105430554362757879 ,7.6161805538728237411 ] 
dist 57=[3.2336670297364002704 ,7.7687043683488812906 ] 
dist 58=[3.2795967273114154459 ,7.8432220881663814041 ] 
dist 59=[3.1164765746645841048 ,7.8524038291600203989 ] 
dist 60=[2.5797929619442310122 ,7.0802531230093154403 ] 
dist 61=[2.1960159278334371523 ,7.2625035716362795310 ] 
dist 62=[1.8516604582156886833 ,7.3503418046398006720 ] 
dist 63=[1.4721240383803293719 ,7.3858890281927364797 ] 
dist 64=[.65215099430318798917,7.3799880299762789143 ] 
dist 65=[-.50167692763365595036,5.9226803200257199196 ] 
dist 66=[-1.2772083389202817625 ,5.8085785299258706140 ] 
dist 67=[-1.9229464404297048248 ,5.4983978787336232052 ] 
dist 68=[-2.5589774238192361668 ,5.4383445616166331571 ] 
dist 69=[-3.1389296036325865927 ,4.8497050571792283839 ] 
dist 70=[-3.5609457328890551678 ,4.7252788775691452399 ] 
dist 71=[-3.9474790694587325895 ,4.5665121474245411992 ] 
dist 72=[-4.3858740489049396341 ,4.5069352421830997332 ] 
dist 73=[-4.7867539032057119163 ,3.1651337289843212364 ] 
dist 74=[-5.0236037089194602098 ,2.9858291598726521407 ] 
dist 75=[-5.1852722254121837527 ,2.6017854695453630615 ] 
dist 76=[-5.2861661175627087004 ,2.4952595341280333920 ] 
dist 77=[-5.3503668123277909555 ,2.0696162917502057179 ] 
dist 78=[-5.3656473997629339255 ,1.9872549394708832611 ] 
dist 79=[-5.3543172565294752031 ,1.7921095178433158267 ] 
dist 80=[-5.3372767692713181715 ,1.7525563354823016163 ] 
dist 81=[-3.7243032194687222748 ,.29572725215006703949] 
dist 82=[-3.9979981945878812661 ,.39488845084091673636] 
dist 83=[-4.1938029964646153231 ,.54198913371327403069] 
dist 84=[-4.3347768965832253259 ,.69299383749545448757] 
dist 85=[-4.4388970976471205752 ,.80776643195068188583] 
dist 86=[-4.4875886292886765046 ,.91777598698290726974] 
dist 87=[-4.5051145150654039162 ,1.0498378346955551556 ] 
dist 88=[-4.5022646931532721964 ,1.1858582727745018969 ] 
dist 89=[-4.1177085529196583935 ,1.3117074973444623642 ] 
dist 90=[-4.0505629494340831608 ,1.4542216032801478347 ] 
dist 91=[-3.9287775016854217417 ,1.6568058498152231509 ] 
dist 92=[-3.8926717853643008037 ,1.8539364521585572992 ] 
dist 93=[-3.7482472352894577977 ,1.9746990943288556065 ] 
dist 94=[-3.7063146343206327742 ,2.1872521347297372653 ] 
dist 95=[-3.6187127154103307301 ,2.5823577093852012218 ] 
dist 96=[-3.5877710257995220020 ,2.9461928845826684092 ] 
dist 97=[-.82902969751755389087,3.2176898980112674513 ] 
dist 98=[-.58770148123560703689,3.4733909426801974485 ] 
dist 99=[-.06421087106602706465,3.7741874278007638526 ] 
dist 100=[.04924224293872416798,4.0515552106664066585 ] 
dist 101=[.61203333970975538591,4.2137588299645680419 ] 
dist 102=[.46515294024952989341,4.3225572676476873196 ] 
dist 103=[.28600702000306170176,4.3868014979988745296 ] 
dist 104=[.13266062698411771397,4.4238709092544393132 ] 
dist 105=[-.02529592301553902469,4.4249065131361175990 ] 
dist 106=[-.1738854019743025474 ,4.4082301647551613594 ] 
dist 107=[-.33055471281163446795,4.3888969999333378616 ] 
dist 108=[-.81673695585593410354,3.9975382511381739256 ] 
dist 109=[-1.1403134123757293180 ,3.9325009693285264441 ] 
dist 110=[-1.4064669831145720423 ,3.7493148147013512312 ] 
dist 111=[-1.6635225960890750033 ,3.6816354797418699020 ] 
dist 112=[-1.8948065267915193185 ,3.3129406767392819910 ] 
dist 113=[-2.0581290304253955396 ,.19994970899336512293] 
dist 114=[-2.2028351866934973215 ,.1107748161408844486 ] 
dist 115=[-2.3598433435554197488 ,.09055027622454578689] 
dist 116=[-2.4993257606268161541 ,-.00345118394038844801] 
dist 117=[-2.5740989168318840559 ,-.01697005909590464479] 
dist 118=[-2.6157593769257410588 ,-.00916916245994988915] 
dist 119=[-2.6248549542916470192 ,.02971198785739965342] 
dist 120=[-2.6179659833177649517 ,.08551261867131572975] 
dist 121=[-2.6098215155893139207 ,.16083041059378378557] 
dist 122=[-2.5979412726846154506 ,.26478323930490180378] 
dist 123=[-2.5859828812679564667 ,.43484772029809505287] 
dist 124=[-.81025274556301998905,.60617838632703971176] 
dist 125=[-.80814568260571230354,.71518662172195997637] 
dist 126=[-.70693880979903727537,.79931176290124728846] 
dist 127=[-.6910754248467085588 ,.87135862234378222716] 
dist 128=[-.66925940495039428869,.93021920677070716127] 
dist 129=[-.66274500827757466486,.96172934575881914338] 
dist 130=[-.6346805790057130489 ,.97944548747516692278] 
dist 131=[-.62737709154451250272,.98352804540408739129] 
dist 132=[-.60891862286261275561,.97402810571171406068] 
dist 133=[-.60198625878541441071,.97094168365269442658] 
dist 134=[-.16504947535618000858,.96798944805008725803] 
dist 135=[-.12552586163001628597,.96447567204438361081] 
dist 136=[-.03985255908218089467,.96089103973381311348] 
dist 137=[-.02085717828987987303,.95765344208338504342] 
dist 138=[.07160383591083794682,.95405945405693268666] 
dist 139=[.08757987879382681940,.94909618097473082124] 
dist 140=[.1223240271499575631 ,.58791777885703382627] 
dist 141=[.02129897072007457846,.66137670896704470099] 
dist 142=[-.08847699687479300513,.73006540915898288411] 
dist 143=[-.20169013793485230001,.77191917597572050955] 
dist 144=[-.30826796959765911009,.80210624396163859965] 
dist 145=[-.3915705482391394746 ,.82423888976401987096] 
dist 146=[-.473670265497249983  ,.83987680661935878497] 
dist 147=[-.57544922386424615214,.84414660182314956478] 
dist 148=[-.67188729742833876148,.84413114405801019356] 
dist 149=[-.73267779687606306078,.84266792942912435168] 
dist 150=[-.77891956145694036606,-.04955839101948540654] 
dist 151=[-.8173103487858170164 ,-.09311159376160832883] 
dist 152=[-.847655415693666612  ,-.19154625489593669999] 
dist 153=[-.86179585755189819907,-.20741099176663688495] 
dist 154=[-.86805687997886643583,-.20071214637159928558] 
dist 155=[-.86779069143729422469,-.10051401697396454637] 
dist 156=[-.541753742824826783  ,.00188941075495284329] 
dist 157=[-.58203432848475194477,.07106570795758373981] 
dist 158=[-.61798010802604972039,.12904613308643249506] 
dist 159=[-.6395720800525886457 ,.18849009610337267714] 
dist 160=[-.65476716037495386093,.24590420637083586432] 
dist 161=[-.66518719398888841582,.28738743506703631212] 
dist 162=[-.67173029103684329204,.32508900815871470402] 
dist 163=[-.67243608669386695126,.36741697383113628847] 
dist 164=[-.66886177938511974784,.40628962794041757414] 
dist 165=[-.66615494271681923036,.4302056496479744243 ] 
dist 166=[-.38752481188920271333,.44771549955145997008] 
dist 167=[-.36896554688898877366,.46102824167497231417] 
dist 168=[-.336193095501993951  ,.47060307320220046783] 
dist 169=[-.33097763394507100597,.47319902195347056717] 
dist 170=[-.28958298706376310892,.47322382967004389724] 
dist 171=[-.28097684488975449864,.47254108600685823665] 
dist 172=[-.26766323551336008192,.36423006941626662432] 
dist 173=[-.2636859433041540917 ,.3640564950733718805 ] 
dist 174=[-.17972858073075577369,.38334700944878536658] 
dist 175=[-.16841820981261172479,.39520617146069176415] 
dist 176=[-.14247773121410823951,.40387739176837072786] 
dist 177=[-.16302141810118307881,.41044754501892262492] 
dist 178=[-.19165838519894574201,.41515061196703855603] 
dist 179=[-.22613762417185098797,.41637160889873305161] 
dist 180=[-.25828378357257179654,.41551834688781685392] 
dist 181=[-.27761255566743893184,.41438301061750225928] 
dist 182=[-.29122189592515612445,.14679910805096693213] 
dist 183=[-.30054981525498854971,.14973705517720372135] 
dist 184=[-.30733590109753308088,.15178793913692335836] 
dist 185=[-.31080458964165520246,.15317122836319995526] 
dist 186=[-.31250034203066937158,.15402531666163080024] 
dist 187=[-.31221385203623603079,.15396364625897040693] 
dist 188=[-.26742672312296956422,.15329662785821012482] 
dist 189=[-.29209184797094374754,.15277572120552250277] 
dist 190=[-.30998064652162483836,.14914400708156439329] 
dist 191=[-.3232732492519548452 ,.1479648220724373528 ] 
dist 192=[-.33342409019184371173,.14491028752471097636] 
dist 193=[-.33877688638134053026,.14362806884265523617] 
dist 194=[-.34163564267177564713,.13660013030106151515] 
dist 195=[-.34183424818058855462,.13482735243725360799] 
dist 196=[-.30926974407534724547,.13077690462158641989] 
dist 197=[-.30373139884574158941,.12932989640458030483] 
dist 198=[-.29547272730615199256,.10907971273495644514] 
dist 199=[-.29341813984462982237,.1056678812418283151 ] 
dist 200=[-.2901999352201667943 ,.09918018805386411204] 
dist 201=[-.28841492445144324721,.09740288612092332499] 
dist 202=[-.28416782828073890186,.09077014377178915981] 
dist 203=[-.28223722633073898049,.08905178988187126085] 
dist 204=[-.26304456060436203313,.08594629470177623613] 
dist 205=[-.26844651428101813923,.08503424735266222689] 
dist 206=[-.27232267533072806522,.08686313838058924598] 
dist 207=[-.27362053753575256356,.12654148876323207904] 
dist 208=[-.27337089475921148157,.16387384303113571114] 
dist 209=[-.27276936533553957768,.19302558752126494327] 
dist 210=[-.26704024723339433808,.22173260019719837805] 
dist 211=[-.26515670444199643876,.25729037162040121854] 
dist 212=[-.25935045192504306943,.29097061125331363212] 
dist 213=[-.25707032265648786105,.31218632754021811493] 
dist 214=[.04377939459375781566,.3283081460963847531 ] 
dist 215=[.06347317925700241545,.3416640044060411245 ] 
dist 216=[.06676687553415139304,.35219841039271276986] 
dist 217=[.05719025600288331469,.35706269153607914343] 
dist 218=[.02366609669865632837,.35894917604410539654] 
dist 219=[-.02942633438648326562,.35880586617904242953] 
dist 220=[-.08288190783483559430,.11205125729652698793] 
dist 221=[-.1178549802814592516 ,.11570559227876272507] 
dist 222=[-.14594151021483250366,.11931476585498965822] 
dist 223=[-.17192091825835055283,.12185208900438212692] 
dist 224=[-.19451595512827145226,.12408906862772240019] 
dist 225=[-.20909936916751282591,.1264994697774823449 ] 
dist 226=[-.2205877081504298249 ,.12883501706278160261] 
dist 227=[-.23083380981175635197,.13077312474116927754] 
dist 228=[-.23956711495996157475,.13278972886892735424] 
dist 229=[-.24501964543023641127,.13543827557730896094] 
dist 230=[-.24910559315916088119,.13791325975673375049] 
dist 231=[-.25238655673505993855,.13923719880617419084] 
dist 232=[-.25489327747855955953,.13996986475838786159] 
dist 233=[-.25589016593692178328,.14008542691884305097] 
dist 234=[-.25597038808348240895,.13979435509432118693] 
dist 235=[-.25517662945280401239,.1392749638579608708 ] 
dist 236=[-.15142789983743860045,.13774970174233190683] 
dist 237=[-.15164441198806984022,.13690372844266920969] 
dist 238=[-.15063038364745245967,.13167106543985932582] 
dist 239=[-.15026599165970833922,.13025941136587767504] 
dist 240=[-.14263995865658230896,.12672192974694585561] 
dist 241=[-.14059120026719971006,.12534606970726825759] 
dist 242=[-.13891850524250094094,.12614014504514655449] 
dist 243=[-.13793378974496589093,.13169102516012637846] 
dist 244=[-.10438958924781542272,.1363885753713572747 ] 
dist 245=[-.09976010220446721840,.13887532743094057104] 
dist 246=[-.09061183481098093951,.14021438409364884861] 
dist 247=[-.08815208318702936892,.14033279041325593494] 
dist 248=[-.07904671861729778847,.1397759688431863353 ] 
dist 249=[-.07690583210749021598,.13927228001912957045] 
dist 250=[-.07316086954779914639,.13700376298934813983] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 1, 1, 2, 0, 1] 
dist 0=[65.350211229228385370  ,65.350211229228385370  ] 
dist 1=[64.973843120891512931  ,65.532819826974563592  ] 
dist 2=[64.233649734600794668  ,65.499317253581896480  ] 
dist 3=[63.228479098771239614  ,65.356597560552741326  ] 
dist 4=[61.793972051614516311  ,65.215188529547473085  ] 
dist 5=[59.767128704151141648  ,64.808675435851667074  ] 
dist 6=[56.396509290472213493  ,64.599082336743569694  ] 
dist 7=[52.898833145344115179  ,61.033558428677981236  ] 
dist 8=[50.364576262218530628  ,60.386838325216912043  ] 
dist 9=[48.045546723764395126  ,59.536727888238379444  ] 
dist 10=[45.407295186652946171  ,59.221982011700053468  ] 
dist 11=[42.758910819396841344  ,58.879978185886173748  ] 
dist 12=[39.843684351365569908  ,58.683737010802314650  ] 
dist 13=[33.644048398284864199  ,58.359658794070053639  ] 
dist 14=[29.418840586264013763  ,57.263247780837896576  ] 
dist 15=[25.822379140942367228  ,31.598269941134004773  ] 
dist 16=[22.133312852158515008  ,30.406607996880176901  ] 
dist 17=[18.657314625059884805  ,27.998024912979512069  ] 
dist 18=[15.911469706134094241  ,27.373565627168160083  ] 
dist 19=[13.167816387095063176  ,25.130208430976057911  ] 
dist 20=[9.7000950229547071578 ,24.653041337307517456  ] 
dist 21=[6.3577890301819606792 ,23.906133497055184309  ] 
dist 22=[4.1147039593656395781 ,23.708747080907398477  ] 
dist 23=[1.1151577131738619591 ,6.8528601837729074942 ] 
dist 24=[-1.0903603735210302553 ,5.4370202633528184985 ] 
dist 25=[-2.8846847434144058409 ,2.3156388976592415511 ] 
dist 26=[-4.5960541376013773756 ,1.7474796573597541646 ] 
dist 27=[-6.6655372565689984940 ,.29207673552817862153] 
dist 28=[-8.3446831393752030460 ,.16834128378304526335] 
dist 29=[-9.9201440820112452122 ,-1.6247969580887872172 ] 
dist 30=[-11.773582182210623307  ,-2.1061789645787084629 ] 
dist 31=[-13.495753647609447972  ,-5.7431351987430490735 ] 
dist 32=[-14.546932817372725745  ,-6.0535313852668027852 ] 
dist 33=[-15.311915334849515758  ,-6.2062395321194708807 ] 
dist 34=[-15.890910747022712751  ,-5.9854527386067381234 ] 
dist 35=[-16.319845891655489378  ,-5.5791673121497257691 ] 
dist 36=[-16.485389973830394787  ,-4.9401025627554422729 ] 
dist 37=[-16.537204101210099430  ,-4.0110101528697775097 ] 
dist 38=[-16.511686946549371116  ,-2.4471237577819923639 ] 
dist 39=[-10.271204814924817758  ,-.11179799378179863115] 
dist 40=[-10.056747932954644008  ,1.5146179472053389740 ] 
dist 41=[-9.6088376536544243769 ,2.8835061991475402194 ] 
dist 42=[-9.4729459820509571367 ,4.2553333550263509328 ] 
dist 43=[-8.8864143560317913155 ,5.5215044322215231606 ] 
dist 44=[-8.7564375994761279849 ,6.4690664213603178374 ] 
dist 45=[-8.4114496478659230670 ,7.3636658320044373199 ] 
dist 46=[-8.3263885715731091854 ,8.4187758360455863917 ] 
dist 47=[-2.3621172810981711735 ,9.3933278635003899326 ] 
dist 48=[-1.8113209598037872147 ,9.9666085942084011146 ] 
dist 49=[-.62121882914188305488,10.355735466294738438  ] 
dist 50=[-.35608648489309887877,10.595579378351669895  ] 
dist 51=[.9195184261917346145 ,10.753500082341475583  ] 
dist 52=[1.1405955826958078318 ,10.815600614222658169  ] 
dist 53=[1.6216191468528422673 ,10.819413798193166386  ] 
dist 54=[1.7091741757432569197 ,10.793934610494034649  ] 
dist 55=[1.8590403218669965705 ,9.4500086193519530147 ] 
dist 56=[1.3071522320211830852 ,9.2550012021382572501 ] 
dist 57=[.8309889468779865800 ,8.7226261653181855065 ] 
dist 58=[.3358488431000883949 ,8.6198163721093214400 ] 
dist 59=[-.1316968335122054316 ,7.6021429241769540062 ] 
dist 60=[-.4978418192704076283 ,7.3869015990050107156 ] 
dist 61=[-.8587210501485046241 ,6.6670046443523886826 ] 
dist 62=[-1.3052899449287308201 ,5.5485758986473274875 ] 
dist 63=[-1.7273010522854724125 ,-.45282025055416307187] 
dist 64=[-2.1335619447619435016 ,-.55058614073831801747] 
dist 65=[-2.6544892702750996917 ,-.8996386640006914321 ] 
dist 66=[-3.1301455122667882633 ,-.9543700161164022693 ] 
dist 67=[-3.5400382158175611704 ,-1.1906408686748374071 ] 
dist 68=[-3.7985820183433661064 ,-1.2320097103626245513 ] 
dist 69=[-3.9957948783976262784 ,-1.2645735785066492400 ] 
dist 70=[-4.1610162213016051896 ,-1.2409178697092107287 ] 
dist 71=[-4.2980953373131141255 ,-1.2003939640554758342 ] 
dist 72=[-4.3830091173612080646 ,-1.1523245792145898253 ] 
dist 73=[-4.4461739309931574318 ,-1.0281959881303015256 ] 
dist 74=[-4.4964024437090982634 ,-.8714721765062746534 ] 
dist 75=[-4.5346427128804122448 ,-.7150308367606476655 ] 
dist 76=[-4.5499348238687491817 ,-.5787408459584539677 ] 
dist 77=[-4.5514122538671281828 ,-.4315322392432300294 ] 
dist 78=[-4.5357345452898677748 ,-.2314937571380700949 ] 
dist 79=[-1.8242321927739912499 ,-.0336781030095820574 ] 
dist 80=[-1.7891857482091549727 ,.11821370123796855791] 
dist 81=[-1.4073708046315651242 ,.37564070926172154264] 
dist 82=[-1.3330106506882636080 ,.57829843137982625781] 
dist 83=[-1.2484911228218155801 ,.77922737807085882284] 
dist 84=[-1.2539454204336456557 ,1.0297641371348975268 ] 
dist 85=[-1.2967505839410794417 ,1.2675532303769909263 ] 
dist 86=[-1.3625160809813931447 ,1.5718632272665463500 ] 
dist 87=[-1.4271300786483738034 ,1.9596143285837246272 ] 
dist 88=[-1.4653294579913672557 ,2.2038868533621888130 ] 
dist 89=[-1.4912041509221946938 ,2.3894883407238478154 ] 
dist 90=[-1.5066797851420905176 ,2.5431594180131249473 ] 
dist 91=[-1.5139942202101969327 ,2.6649735114399907492 ] 
dist 92=[-1.5134247039220819945 ,2.7234791865912237132 ] 
dist 93=[-1.4975165539497269455 ,2.7526229266145174135 ] 
dist 94=[-1.4924143534563804672 ,2.7572876508313493542 ] 
dist 95=[-1.4046020649121883101 ,2.3859243049357784796 ] 
dist 96=[-1.3866139591938189037 ,2.3580779683375101714 ] 
dist 97=[-1.3305403875430633754 ,2.3181704924835199839 ] 
dist 98=[-1.3197564675890046498 ,2.3014512335922055760 ] 
dist 99=[-1.1872145729192435854 ,2.2502449753656359482 ] 
dist 100=[-1.1572502068191608467 ,2.2302343808866867304 ] 
dist 101=[-1.1259483792958093963 ,2.1943473474215389649 ] 
dist 102=[-1.1122368807208824142 ,2.1811278633248284526 ] 
dist 103=[-.8202668437837218313 ,1.5635364803735909229 ] 
dist 104=[-1.0203515854371287375 ,1.5543443092900234445 ] 
dist 105=[-1.1771907488267037565 ,1.5213162444127567467 ] 
dist 106=[-1.3157526545845285231 ,1.5092324099306958567 ] 
dist 107=[-1.4317773383717468167 ,1.4810487288722037521 ] 
dist 108=[-1.4987002158285495949 ,1.4695204945610727076 ] 
dist 109=[-1.5424176440861971102 ,.58326634956818044501] 
dist 110=[-1.7218250647005148889 ,.71057698984090326097] 
dist 111=[-1.9503323194785018403 ,.8402215001757645038 ] 
dist 112=[-2.0889384075535286706 ,.92777646396003283571] 
dist 113=[-2.1881936942744798912 ,1.0010603816670515916 ] 
dist 114=[-2.2596723992236466026 ,1.0737778791335460308 ] 
dist 115=[-2.3118552079962256857 ,1.1403408397778259828 ] 
dist 116=[-2.3341045045994250610 ,1.1890723000941168870 ] 
dist 117=[-2.3398909517891481216 ,1.2339389437592041741 ] 
dist 118=[-2.3371509640893181303 ,1.2850790347459151124 ] 
dist 119=[-2.1444412204277615087 ,1.3311560691795222012 ] 
dist 120=[-2.1096777698211361550 ,1.3558246213026150032 ] 
dist 121=[-2.0424421563752703532 ,1.3694389182759072937 ] 
dist 122=[-2.0213888372668259502 ,1.3714220677532057572 ] 
dist 123=[-1.9296934226415874356 ,1.3666165317762713919 ] 
dist 124=[-1.9062406134997501933 ,1.3620486442182675346 ] 
dist 125=[-1.8452011901405445928 ,1.3391598179166837157 ] 
dist 126=[-1.8233336351820226615 ,1.3322477899978244093 ] 
dist 127=[.23942030670132320785,1.0032147058382516741 ] 
dist 128=[.2615408311861654713 ,1.1010294555509854883 ] 
dist 129=[.35603417221612170863,1.1754061765177896179 ] 
dist 130=[.3729258743145829495 ,1.2370801282667916041 ] 
dist 131=[.39429032992007420953,1.2857540309876027714 ] 
dist 132=[.39433451021855359757,1.3082653506684162292 ] 
dist 133=[.34832843180725372226,1.3184428039386916979 ] 
dist 134=[.20780937358377610029,1.3179107545585584172 ] 
dist 135=[.0634359339798567088 ,1.1242180252083616724 ] 
dist 136=[-.0349723046917646699 ,1.1456293418020522099 ] 
dist 137=[-.1183813188981935768 ,1.1594198793065013382 ] 
dist 138=[-.2111178986716951442 ,1.1616467443130681944 ] 
dist 139=[-.2968189717944126016 ,1.1556927698390894573 ] 
dist 140=[-.3598326189449261581 ,1.1524865221035164830 ] 
dist 141=[-.4181954753931769463 ,.74321300581992914451] 
dist 142=[-.4853453723060669839 ,.73444580709418778603] 
dist 143=[-.5474463016818928711 ,.70810854875760584372] 
dist 144=[-.5856667410444460912 ,.7020746996899418451 ] 
dist 145=[-.6136577709707954292 ,.64210598401438160955] 
dist 146=[-.6349466268784151389 ,.62847222273537929255] 
dist 147=[-.6504083862822863267 ,.61115763219078981987] 
dist 148=[-.67351167259147497137,.60420217077525137222] 
dist 149=[-.70357278619033985184,.43768102254259419328] 
dist 150=[-.72117403230725206888,.41491300158181215031] 
dist 151=[-.73298597785537516219,.3663458290282538324 ] 
dist 152=[-.73994933973819923621,.35269522508413185229] 
dist 153=[-.7432380370983651907 ,.29745713664665398243] 
dist 154=[-.74257556927195015319,.28651732250165875474] 
dist 155=[-.73571629861555813215,.25989718828703353229] 
dist 156=[-.73173775708382114227,.26788172583353919542] 
dist 157=[-.4304664756737911323 ,.30632152134501069329] 
dist 158=[-.42557188182289850516,.35215276248874677414] 
dist 159=[-.27865352861190257336,.39462929279767970939] 
dist 160=[-.28867551318578450628,.41968572166295455298] 
dist 161=[-.2967022358796680472 ,.4367298900810445275 ] 
dist 162=[-.30067433013217757868,.4472428793918619927 ] 
dist 163=[-.30244027268432906893,.4543679052781682859 ] 
dist 164=[-.30230174797753118738,.4578969015650840752 ] 
dist 165=[-.2994752256269381215 ,.4594572812759252513 ] 
dist 166=[-.29822076474049915282,.4587304160614772469 ] 
dist 167=[-.29202888223576585525,.3959394775880037683 ] 
dist 168=[-.29097947956019864474,.4375753120925702622 ] 
dist 169=[-.26981106794783691084,.4682872025435703050 ] 
dist 170=[-.26471939678521269762,.4920708618973213423 ] 
dist 171=[-.26089063730366864191,.51057599395993661948] 
dist 172=[-.25960762233413819347,.52022676657365161553] 
dist 173=[-.1836432545727117841 ,.52523032982342138437] 
dist 174=[-.1737345895407596080 ,.52554640382028818081] 
dist 175=[-.1529897888843542893 ,.48482186412044171285] 
dist 176=[-.1472293367421430321 ,.47919683689847849149] 
dist 177=[-.1243935639364223550 ,.47975283871496528484] 
dist 178=[-.1197081343702164532 ,.47866469800120087485] 
dist 179=[-.1090266461317536194 ,.47661064656979348278] 
dist 180=[-.1060346576738176723 ,.47428436668828783544] 
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dist 182=[-.0883790150731628537 ,.46647904825355859831] 
dist 183=[-.0867338142058697698 ,.45010253025075357061] 
dist 184=[-.0876412867654160654 ,.45018309100625904505] 
dist 185=[-.14013636804542678146,.44412458721227601569] 
dist 186=[-.2022239966906733477 ,.44139810007634489305] 
dist 187=[-.26055046981108695331,.4344490774441499188 ] 
dist 188=[-.30592973614724028305,.4312476166128224255 ] 
dist 189=[-.35045431483672562653,-.04626304546181905326] 
dist 190=[-.40537086580268941027,-.05198643450485624058] 
dist 191=[-.45726034649402327159,-.10833363213918426958] 
dist 192=[-.48970762876417155191,-.11683272475052762139] 
dist 193=[-.51408299569115460554,-.11885417526441803283] 
dist 194=[-.53376736600262218934,-.10837881833425884358] 
dist 195=[-.5488968630742144718 ,-.09327000581229725635] 
dist 196=[-.5550992835145339046 ,-.06791817805580704222] 
dist 197=[-.5571774657279028088 ,-.02860688234491592734] 
dist 198=[-.5560921842017313008 ,.05090125464264371540] 
dist 199=[-.20110679401714134422,.13096253411421929678] 
dist 200=[-.20662228306301767028,.18328108449485621197] 
dist 201=[-.21182224801408021911,.22522273183743727957] 
dist 202=[-.21590623511508816887,.2638834455766794081 ] 
dist 203=[-.21995286358539542784,.2974092881201271764 ] 
dist 204=[-.22500410847428690741,.3188644309052024010 ] 
dist 205=[-.22961535675654675583,.3355562194133953004 ] 
dist 206=[-.23190626603155492768,.3500778204109488665 ] 
dist 207=[-.23293583924514900133,.3623191259019782247 ] 
dist 208=[-.23254158142651802854,.3699131522502207223 ] 
dist 209=[-.23119240039172041702,.3755465057401828982 ] 
dist 210=[-.23025085502116007336,.3799650065552125595 ] 
dist 211=[-.22609438625528251346,.3833800462415365070 ] 
dist 212=[-.2248444713205803159 ,.3843897520557335882 ] 
dist 213=[-.2103027099004334386 ,.3792265930926526280 ] 
dist 214=[-.2073028136685467006 ,.3692743846166998672 ] 
dist 215=[-.1988099290461753547 ,.24131773454194070276] 
dist 216=[-.1967626490147485564 ,.24500012641123135857] 
dist 217=[-.1788058457077792563 ,.24662552643345840698] 
dist 218=[-.1747550402417049098 ,.24694707532020764846] 
dist 219=[-.17551199269612464393,.23949763571379091105] 
dist 220=[-.18541958958294946014,.23749977435335969422] 
dist 221=[-.19338701980002416466,.23624444709053881169] 
dist 222=[-.2007703930970754578 ,.23568014247494937076] 
dist 223=[-.2068836209133813538 ,.18196950770795927568] 
dist 224=[-.2097835549569653072 ,.17459546487362056912] 
dist 225=[-.2108881081541160068 ,.16078342735431864938] 
dist 226=[-.2108897147448936744 ,.15719859376577343974] 
dist 227=[-.2078586439572081714 ,.1449461695240297668 ] 
dist 228=[-.2065383933481731246 ,.14163005852834774042] 
dist 229=[-.2032035030671089060 ,.13834452225749634742] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 1, 1, 1, 2] 
dist 0=[56.514381183347831925  ,56.514381183347831925  ] 
dist 1=[56.132788279000970788  ,57.037563431739487325  ] 
dist 2=[55.638826948545410220  ,57.518123926010849654  ] 
dist 3=[54.599214857791635454  ,57.729558745755609311  ] 
dist 4=[52.926708520823608387  ,57.784142798296983775  ] 
dist 5=[50.971275385046082062  ,57.750373226501787243  ] 
dist 6=[48.801678346366522879  ,57.396348849181878051  ] 
dist 7=[46.054876535512134132  ,57.260263066005469508  ] 
dist 8=[41.794231538602133734  ,56.753714942508472748  ] 
dist 9=[37.474002885556239223  ,56.597298980433973625  ] 
dist 10=[34.489136612688687453  ,54.293233459531103471  ] 
dist 11=[31.904073270248848736  ,53.807244680576431099  ] 
dist 12=[29.180251180640272101  ,53.274190023097562327  ] 
dist 13=[26.567308521462231769  ,52.431004912832272688  ] 
dist 14=[24.424809340200512509  ,47.031527884694756148  ] 
dist 15=[22.210384908963273551  ,43.632333963669818420  ] 
dist 16=[19.309721630998306228  ,34.046179610529224618  ] 
dist 17=[16.462441060949172854  ,33.827280450248106355  ] 
dist 18=[14.460960714395626516  ,25.455987236967702159  ] 
dist 19=[12.688624666942492743  ,24.397950099639094547  ] 
dist 20=[10.756203936103741251  ,22.269137595978838255  ] 
dist 21=[8.8585226675020737561 ,21.720898270806519050  ] 
dist 22=[7.2244532029855098281 ,19.772324985684843301  ] 
dist 23=[5.4620073809181292065 ,19.355046860695831424  ] 
dist 24=[3.0504936184455832836 ,18.744577741733585494  ] 
dist 25=[.70094471569682262224,18.570946524591504188  ] 
dist 26=[-.81407060176213466073,7.5252880103608890388 ] 
dist 27=[-2.0169567956572849773 ,7.2985118018443481826 ] 
dist 28=[-3.3502463068475208097 ,6.7923618255607266382 ] 
dist 29=[-5.5029304356650580923 ,4.4177736153864069713 ] 
dist 30=[-7.4739459581959260618 ,4.0928530359519054293 ] 
dist 31=[-8.9403289474777339477 ,2.6503728191069001907 ] 
dist 32=[-10.322763435446435254  ,-4.8298071575860917174 ] 
dist 33=[-11.958488744506718403  ,-5.4481993904865315293 ] 
dist 34=[-13.482663248200401415  ,-5.9682312129492527946 ] 
dist 35=[-14.419528445796383058  ,-5.9822002064671617511 ] 
dist 36=[-15.108855050937527162  ,-5.8105565748120914259 ] 
dist 37=[-15.644251553161325059  ,-5.5426863896046095321 ] 
dist 38=[-16.045584758522638849  ,-5.1621591982379094134 ] 
dist 39=[-16.199410208249246239  ,-4.6281482513194121407 ] 
dist 40=[-16.253162283721210099  ,-3.7475899756246084418 ] 
dist 41=[-16.254643296062380685  ,-2.8452743950869344169 ] 
dist 42=[-11.747688082215035909  ,-1.3299822453881469313 ] 
dist 43=[-11.660603407129303747  ,-.19193524368314371478] 
dist 44=[-11.447864585601419285  ,.79278510505698624607] 
dist 45=[-11.364331332178925790  ,1.9390884532389475525 ] 
dist 46=[-11.305900557267361326  ,2.9808858253257548668 ] 
dist 47=[-11.267297840376090643  ,3.7350285037322483647 ] 
dist 48=[-3.2521575305602982492 ,4.4227183963497994236 ] 
dist 49=[-2.5982909068854830368 ,5.1995137655414839231 ] 
dist 50=[-1.0944269772403434866 ,5.9161118689797839463 ] 
dist 51=[-.84692823692582803889,6.3635963413162780187 ] 
dist 52=[.3706158353393839072 ,6.6998551681327033604 ] 
dist 53=[.83344200832363686673,6.9724682792110628478 ] 
dist 54=[.90997759862086444125,7.1834416091587625342 ] 
dist 55=[1.0287855614906824516 ,7.2736441741834970147 ] 
dist 56=[1.0552743154148098765 ,7.3048470793430117336 ] 
dist 57=[.21149646765326193277,7.2939999906404784455 ] 
dist 58=[-.91844092295838437668,6.6906095804236076758 ] 
dist 59=[-1.6789365408498784306 ,6.6835689141558135522 ] 
dist 60=[-2.3129232275610665656 ,6.9915923266490300814 ] 
dist 61=[-2.9382236415879871003 ,7.1515010310477387041 ] 
dist 62=[-3.5085787910033871413 ,7.2339242681243535392 ] 
dist 63=[-3.9233876754170609856 ,7.2493977923680345292 ] 
dist 64=[-4.3028797021679385646 ,5.6569919892912429372 ] 
dist 65=[-4.7323471227722054134 ,5.6053974646897537037 ] 
dist 66=[-5.1227937717869336699 ,4.0922624838275668463 ] 
dist 67=[-5.3466100831642911662 ,3.8887172866508415546 ] 
dist 68=[-5.4907137791771879513 ,3.4752202464607106860 ] 
dist 69=[-5.5631323487930376240 ,3.3639488337796325981 ] 
dist 70=[-5.6009252409335953575 ,2.9458960006637230469 ] 
dist 71=[-5.6069104891856621101 ,2.8546497796234715598 ] 
dist 72=[-5.5906487076558131752 ,2.6840660578770364605 ] 
dist 73=[-5.5722879124642272498 ,2.6397333998781726612 ] 
dist 74=[-3.8803454389023989376 ,-.21098401270330263738] 
dist 75=[-4.2634873764644335247 ,-.46162758713900747282] 
dist 76=[-4.5463947158101040926 ,-.51503996416718421953] 
dist 77=[-4.7666311917806065548 ,-.58252312300088803347] 
dist 78=[-4.9377415947183185035 ,-.50061236393949798556] 
dist 79=[-5.0245678645313217265 ,-.3375824104479499921 ] 
dist 80=[-5.0663631346238951553 ,-.16246393224478104331] 
dist 81=[-5.0703119479846693657 ,-.03231666047708765802] 
dist 82=[-4.7392866418799450783 ,.08914524590099873672] 
dist 83=[-4.6756270722980739308 ,.2297198129085346318 ] 
dist 84=[-4.5778504426589459428 ,.37115263359196148767] 
dist 85=[-4.5421950873229693470 ,.4960911594450759069 ] 
dist 86=[-4.4294008933991816265 ,.63250689795069510455] 
dist 87=[-4.3877863679139341238 ,.81977715839031060692] 
dist 88=[-4.3190399480452350483 ,1.0059292830739473535 ] 
dist 89=[-4.2929135421745403504 ,1.1379189039895216741 ] 
dist 90=[-2.5680946442649871730 ,1.2553082460501483786 ] 
dist 91=[-2.5312640455544941283 ,1.3832660222494435977 ] 
dist 92=[-2.3322888014535636761 ,1.5081482931109915603 ] 
dist 93=[-2.2880663570119355352 ,1.7561015650983362438 ] 
dist 94=[-2.1978374855141573801 ,2.2773123860811812354 ] 
dist 95=[-2.1703040450231837930 ,2.6753423453081534703 ] 
dist 96=[1.0499829773154853356 ,3.0590914563753846468 ] 
dist 97=[1.1580287135108577926 ,3.5233088269351996966 ] 
dist 98=[1.1693732387203150718 ,3.9579092701718344799 ] 
dist 99=[1.1521876142371596957 ,4.2234681311200468216 ] 
dist 100=[1.0989935278770024588 ,4.4158418246575131806 ] 
dist 101=[1.0268261671880495673 ,4.5583914086353280591 ] 
dist 102=[.93393004082613166701,4.6629991729975462912 ] 
dist 103=[.80816601719123969954,4.7039724741632478885 ] 
dist 104=[.57304224255099573797,4.7145291439142079944 ] 
dist 105=[.03821493538796734581,4.7048940734589972644 ] 
dist 106=[-.50568224931357666527,1.8613632904266125644 ] 
dist 107=[-.87039024657736544516,1.8341839524383702221 ] 
dist 108=[-1.1732627310480274557 ,1.7043371443105389549 ] 
dist 109=[-1.4704432072916231561 ,1.6752113462639289846 ] 
dist 110=[-1.7408158800996586646 ,1.6055041530364867940 ] 
dist 111=[-1.9367298721063155580 ,1.5816581710952014051 ] 
dist 112=[-2.1154168302773060568 ,.60775225057798905757] 
dist 113=[-2.3170605025356527266 ,.50897628776021167042] 
dist 114=[-2.4997936247540276604 ,.30261880983166915284] 
dist 115=[-2.6030245238462522262 ,.24857811658469880303] 
dist 116=[-2.6676797055214066178 ,.04953414025755435614] 
dist 117=[-2.6964802311145630956 ,.01037311786445223317] 
dist 118=[-2.7097033311312802586 ,-.05956883643845518944] 
dist 119=[-2.7122066602354683932 ,-.07472428169226409521] 
dist 120=[-2.7073410958969405145 ,-.10715654258583407486] 
dist 121=[-2.6973761345664749897 ,-.09650904932392253242] 
dist 122=[-2.0938082656693638874 ,-.06394633402249428021] 
dist 123=[-2.0232399832707392536 ,.00694359879316950663] 
dist 124=[-1.8382633256208441620 ,.0969192327623185235 ] 
dist 125=[-1.8093400447401143923 ,.20564351363045589074] 
dist 126=[-1.4884720758705726194 ,.34880516674496216156] 
dist 127=[-1.3196426420641634077 ,.57619817963406588101] 
dist 128=[-.53757779921481786468,.80401744796471656205] 
dist 129=[-.44032993382896426194,.94888371092905238063] 
dist 130=[-.42639149918731148719,1.0605892695059094856 ] 
dist 131=[-.40409299880331017687,1.1560964010223643320 ] 
dist 132=[-.39832132602771541098,1.2341292585599547706 ] 
dist 133=[-.37409978009710484872,1.2761097811633660924 ] 
dist 134=[-.36852142448550257335,1.2996936553674360383 ] 
dist 135=[-.35449201598970597847,1.3053391037611775058 ] 
dist 136=[-.35014159445061289649,1.2897571903862894502 ] 
dist 137=[-.07955011467784239835,1.2853743522644249275 ] 
dist 138=[-.05485393617449713712,1.2814653153948239997 ] 
dist 139=[-.00221729634818792036,1.2772175955628762238 ] 
dist 140=[.01000932078257962038,1.2731051991704679244 ] 
dist 141=[.06338251838651913639,1.2697325279515120200 ] 
dist 142=[.07298654788805735758,1.2662674741863738029 ] 
dist 143=[.09153327179320027228,1.2617825877144132335 ] 
dist 144=[.09574946914921629102,.46340295704572874729] 
dist 145=[.04791106582721600232,.50798724281038536963] 
dist 146=[-.09689787841725149574,.53529528265829627107] 
dist 147=[-.24655825259231942015,.55516999217282437663] 
dist 148=[-.38764652015539911867,.57008901933705042086] 
dist 149=[-.49825466833734955449,.58067685545615456849] 
dist 150=[-.60757766570053561789,.58326658622103491789] 
dist 151=[-.74353889969936290341,.58312300924259107903] 
dist 152=[-.87258190343370366622,.58280209861588131072] 
dist 153=[-.95430230851432540161,-.05162515767621543743] 
dist 154=[-1.0169041074186662345 ,-.08195923556763529584] 
dist 155=[-1.0696665597862738623 ,-.15039753422527577643] 
dist 156=[-1.1119834160866135369 ,-.16136184023489179664] 
dist 157=[-1.1329086474592737269 ,-.2124317281439525471 ] 
dist 158=[-1.1425644227679745006 ,-.21855993457824787919] 
dist 159=[-1.1435484387831771988 ,-.14480943849264855492] 
dist 160=[-.43638694125077509473,-.00717448574148495429] 
dist 161=[-.45893284464317693199,.08575886674041841709] 
dist 162=[-.47248351183411823112,.16360563495509325212] 
dist 163=[-.48203289617312535976,.24201112002887367951] 
dist 164=[-.48861115447536021835,.31699946253701283933] 
dist 165=[-.49277207833502113097,.37157856117222496526] 
dist 166=[-.49290280298617688335,.42158601877119953118] 
dist 167=[-.49077502775958930427,.47833714450839813238] 
dist 168=[-.48845165241471065844,.53051983377351230502] 
dist 169=[-.26814381557127118258,.56230072274576788118] 
dist 170=[-.25450386312156627488,.58518334475252873082] 
dist 171=[-.22080939112261358833,.60186273105613224679] 
dist 172=[-.21509803179614917251,.61353906676243901622] 
dist 173=[-.17674030364873122643,.61646113318773348093] 
dist 174=[-.1702813199705891731 ,.61616877854823356279] 
dist 175=[-.1595238283976755924 ,.61501887042270190044] 
dist 176=[-.15668448750972116346,.47375952792830064658] 
dist 177=[-.10105794045106907455,.45914818537872884348] 
dist 178=[-.09364802306800447630,.42046003845636822578] 
dist 179=[-.09886581413816342946,.41418010399060276945] 
dist 180=[-.15046994683611065332,.34552263833895507949] 
dist 181=[-.19029693478670915706,.33165080866125885753] 
dist 182=[-.22906191378986546714,.31589381945682928224] 
dist 183=[-.27642872157722058177,.31100911755895528952] 
dist 184=[-.32094427090876289105,.29110250590399425972] 
dist 185=[-.3483337898079535398 ,.14978496140761797451] 
dist 186=[-.36837910515295109092,.11712310088911432858] 
dist 187=[-.38359432504183885179,.11250762792980411238] 
dist 188=[-.39511489236477259536,.11113434020332259134] 
dist 189=[-.4004201988263556507 ,.10732421457918895992] 
dist 190=[-.40239267049983227317,.10605047888660859097] 
dist 191=[-.40221795930873374193,.10531871597589249936] 
dist 192=[-.33478626360893797239,.10513807829410734514] 
dist 193=[-.37024443139118576828,.10532492808325999356] 
dist 194=[-.3964148043923006307 ,.10605875791899174665] 
dist 195=[-.41671541936710175846,.10733134188480674875] 
dist 196=[-.43256147496949833255,.109666858817133153  ] 
dist 197=[-.44095763490042436154,.11249811058559539248] 
dist 198=[-.44549760100462576058,.11574775769884027482] 
dist 199=[-.44595644221905836297,.11991654184151109833] 
dist 200=[-.41127739630152299957,.126413399936658646  ] 
dist 201=[-.40494512754842545579,.13291132441700244167] 
dist 202=[-.40063303185998918192,.13708429545125114423] 
dist 203=[-.39877499711964717942,.14034093665409402739] 
dist 204=[-.39306803404479493993,.14318425407867475048] 
dist 205=[-.39047223516195860537,.14553310808798849711] 
dist 206=[-.38385970460276993137,.1468175676164407198 ] 
dist 207=[-.38090861405595594614,.14756326250080150063] 
dist 208=[-.29775410239382381634,.14776304152519193091] 
dist 209=[-.28891155474085455296,.14758967527695699987] 
dist 210=[-.28636040055362870861,.14701628238701799216] 
dist 211=[-.28156752505841661153,.14795707248211237787] 
dist 212=[-.27974897805262006434,.19590181920636124885] 
dist 213=[-.27055681692771430651,.23370797380024438736] 
dist 214=[-.26806839001883203812,.27095244510423891669] 
dist 215=[-.26014801242304905192,.3171078473670247477 ] 
dist 216=[-.25812800780675706956,.36084191503067975569] 
dist 217=[.05220078232836482874,.38842560866399926748] 
dist 218=[.07399377399061820934,.40942953708578600555] 
dist 219=[.09148920728281844971,.42691090000264446627] 
dist 220=[.08310013437197710812,.44076666129700471583] 
dist 221=[.06979221143833973654,.44730486170640258154] 
dist 222=[.05035210057705469340,.44995788258340834497] 
dist 223=[-.00534413623189991285,.44993070598174267284] 
dist 224=[-.07581801299054207069,.10622099445934697416] 
dist 225=[-.12233939491818546423,.1072934854694768151 ] 
dist 226=[-.16016388291326778897,.10877657421583467582] 
dist 227=[-.1959386608638302726 ,.11084439893160599378] 
dist 228=[-.2276006691902991715 ,.11424943434475688697] 
dist 229=[-.24901588876671395117,.11824945623390666321] 
dist 230=[-.26699831992273170496,.12269093244386853448] 
dist 231=[-.28496401281734622897,.12830122660967936432] 
dist 232=[-.30085680427348621231,.13696436859623079951] 
dist 233=[-.3105687209892930294 ,.14564349950175189842] 
dist 234=[-.31759996429908893629,.15131741973602065698] 
dist 235=[-.32279742959279288875,.15586884576259071604] 
dist 236=[-.32640984230666872236,.16006918781501857634] 
dist 237=[-.32711705197783057418,.16371442013648758342] 
dist 238=[-.32626325098319529578,.16605083651124483101] 
dist 239=[-.32513518050057824838,.16787151113125246212] 
dist 240=[-.20532079550394429187,.16945861114404930982] 
dist 241=[-.20461789464778226907,.17062695755882214728] 
dist 242=[-.20109454372383064081,.170776735371142665  ] 
dist 243=[-.20014756131080681854,.17020654155360409419] 
dist 244=[-.18756695130007535029,.16968085473657364476] 
dist 245=[-.18442816512726088052,.16897462480601704633] 
dist 246=[-.1811751958415467474 ,.1773704537273417246 ] 
dist 247=[-.17943397519989210675,.18512220523993405541] 
dist 248=[-.13398249747880580895,.19167738502961452481] 
dist 249=[-.12769563259584655706,.19529911534838129178] 
dist 250=[-.11486478155064123771,.19745932444080458105] 
dist 251=[-.11134161408780056382,.19818328738985818652] 
dist 252=[-.09773522604862845260,.19792502587816747422] 
dist 253=[-.09476739947305215418,.19746598384503777037] 
dist 254=[-.08866973317581394149,.19430350628308678004] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 1, 1, 0, 1] 
dist 0=[61.016914786909722293  ,61.016914786909722293  ] 
dist 1=[59.838828393185148684  ,61.569898259449227419  ] 
dist 2=[58.519707446457274443  ,61.839796510457465635  ] 
dist 3=[57.403500177111717864  ,61.887530122872855950  ] 
dist 4=[56.220077707590384378  ,61.777102566474685767  ] 
dist 5=[54.632458029287199704  ,61.034333877707043829  ] 
dist 6=[52.902557394651248507  ,60.893526213940798122  ] 
dist 7=[51.150889881890427692  ,60.800899245751820105  ] 
dist 8=[49.043982730191006856  ,60.553880862044269693  ] 
dist 9=[45.895368456592724051  ,53.867540780966201446  ] 
dist 10=[42.628536984406056267  ,52.921512212216461094  ] 
dist 11=[40.049461767980696791  ,51.795457772709703213  ] 
dist 12=[37.474473605446600623  ,50.856531395659975898  ] 
dist 13=[34.223824466991200313  ,49.969279160903774632  ] 
dist 14=[30.778184138701770675  ,49.524424736998651772  ] 
dist 15=[27.424339680910386609  ,49.304166869852339216  ] 
dist 16=[23.486969710356601144  ,48.908988008279435272  ] 
dist 17=[17.710682607089343114  ,36.825881237352345955  ] 
dist 18=[11.956472156136562393  ,19.291179133433629633  ] 
dist 19=[8.1072583684658983409 ,16.593958846550650474  ] 
dist 20=[4.9070489095581601191 ,13.455086671513748040  ] 
dist 21=[1.7449541666126650330 ,9.5904075702876871259 ] 
dist 22=[-1.1596504259859278805 ,7.5834530367833362617 ] 
dist 23=[-3.3314344481114026214 ,7.2308797948930058969 ] 
dist 24=[-5.3874181497420167555 ,3.8557032126739620760 ] 
dist 25=[-7.8294753101863564616 ,2.4430285727901601393 ] 
dist 26=[-10.105130661134984024  ,-1.0464898648186472644 ] 
dist 27=[-11.496540241770284852  ,-1.5331904213658873434 ] 
dist 28=[-12.509703469525308098  ,-2.1902488793139512177 ] 
dist 29=[-13.274784808542487668  ,-2.2928847021540109457 ] 
dist 30=[-13.860529186975460899  ,-2.1971310723340340418 ] 
dist 31=[-14.157618620251334840  ,-1.8200919321914988110 ] 
dist 32=[-14.301303573250532025  ,-1.1728497924490619691 ] 
dist 33=[-14.304698513523680744  ,0                     ] 
dist 34=[-6.9140274359762608309 ,-3.3911705804527714651 ] 
dist 35=[-6.4848763176566766508 ,-2.2591301472117672743 ] 
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dist 171=[-.04916656409141219324,.38046647166060214512] 
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dist 173=[-.04233415705122456123,.39801353703212902639] 
dist 174=[-.03996399221828140796,.39989493279136379912] 
dist 175=[-.03928701339262724755,.39964330603589097977] 
dist 176=[-.00220973974503230342,.39831291633153979352] 
dist 177=[.00116172199361693387,.29832814854599275185] 
dist 178=[.00811832541847612583,.28792926162637661124] 
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dist 182=[-.10485126133143094579,.20093313423860376435] 
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dist 186=[-.21244470164253242914,.09944035516825751870] 
dist 187=[-.22681194464394861412,.1020192138946443031 ] 
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dist 189=[-.24758751720668290618,.10475797082208729341] 
dist 190=[-.25160184212243724893,.10489782678782653284] 
dist 191=[-.25340721789144905564,.104727827709677481  ] 
dist 192=[-.25368504850398652074,.00975607090808853236] 
dist 193=[-.20264857867001554362,-.01574232717561334063] 
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dist 195=[-.2427480616652283715 ,-.02779115120593612427] 
dist 196=[-.25653153155146581492,-.03981758538168117117] 
dist 197=[-.26740176731616823108,-.04085937451492754029] 
dist 198=[-.27294862048539944303,-.04217980776604991385] 
dist 199=[-.27565453023294002372,-.04202866020264826402] 
dist 200=[-.27607740901538240483,-.04134111899956382334] 
dist 201=[-.26118439883294232383,-.03997046705806984921] 
dist 202=[-.25801318860114897251,-.03783829819957636103] 
dist 203=[-.25546624992219178902,-.03411178428428135132] 
dist 204=[-.25417115760387196356,-.02964901222592465551] 
dist 205=[-.2494703890473106029 ,-.02457873713609730642] 
dist 206=[-.24766088848627370105,-.01809577217753783814] 
dist 207=[-.24290689171749386016,-.00799560498616903425] 
dist 208=[-.24084315229886894208,.00217893737736979249] 
dist 209=[-.08017422044902740048,.00895870073012398118] 
dist 210=[-.06581777770287159063,.04345406317163411220] 
dist 211=[-.04213460950075198565,.07378024695932233106] 
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dist 213=[-.02340763785183721669,.13397931563141644681] 
dist 214=[-.01929367670065645918,.15692555561346019668] 
dist 215=[-.01808263251209717383,.17916763697449597889] 
dist 216=[-.00859970579912308256,.2062292522489976543 ] 
dist 217=[-.00754110676885283551,.2316252703056752631 ] 
dist 218=[-.00525335710619475793,.2472217383274518137 ] 
dist 219=[-.00472728460616722910,.2586092826597190098 ] 
dist 220=[-.00224427551600932516,.26721181535349829856] 
dist 221=[-.00180923584480843800,.27348492441387768124] 
dist 222=[-.00081608951568894354,.27557805446948463988] 
dist 223=[-.00065538073743033203,.27600365764442147385] 
dist 224=[-.00641021675412467098,.27562328096557531498] 
dist 225=[-.04000623192123048901,.03366245227517689024] 
dist 226=[-.06234376805408503292,.02804457313454464584] 
dist 227=[-.08458233524653841359,.02672999904449155978] 
dist 228=[-.10783434992400514569,.02308031576603615758] 
dist 229=[-.12868323716420292652,.02250733721922765199] 
dist 230=[-.14326078872552774802,.02290669811042222960] 
dist 231=[-.15601787162727544959,.02473667157356270333] 
dist 232=[-.16960345083613417729,.02712840776451573944] 
dist 233=[-.18184253973819045845,.02976905662735771180] 
dist 234=[-.1892273286323369721 ,.03309389844227653772] 
dist 235=[-.19446131305371936271,.03821541611315455859] 
dist 236=[-.19811892896196678546,.04409086295758155152] 
dist 237=[-.20047774651671183664,.05042368925900035217] 
dist 238=[-.2008520571926341298 ,.05829552809654761852] 
dist 239=[-.19984542716480444708,.07031121301688230030] 
dist 240=[-.19926709983339040941,.08229118723312984951] 
dist 241=[-.13050912363666047434,.09002055583626815308] 
dist 242=[-.12935524645887052168,.09610563878007426642] 
dist 243=[-.12558647568137022815,.10152538061179428279] 
dist 244=[-.12467227586574346167,.10609325850231641909] 
dist 245=[-.11507597989276021139,.10877963886172524461] 
dist 246=[-.11282555035470289057,.11059838921705030839] 
dist 247=[-.11008494819578701278,.11595985640703945183] 
dist 248=[-.10890450876406234138,.12127889256858337048] 
dist 249=[-.07982258058921155694,.12580766741380556803] 
dist 250=[-.07582264637140162639,.12841486953717575554] 
dist 251=[-.06738929816446067760,.13010940157485066444] 
dist 252=[-.06502840859322488947,.13099679386735034088] 
dist 253=[-.05556407118039524061,.13129454047478466474] 
dist 254=[-.05364004436987885924,.1310702230654769418 ] 
dist 255=[-.04912190929807748843,.12970231244294453032] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 0, 0, 0, 0, 1] 
dist 0=[47.946122374467429294  ,47.946122374467429294  ] 
dist 1=[47.259068464765483040  ,48.270418997355625535  ] 
dist 2=[46.488137188680428203  ,48.422150678464570378  ] 
dist 3=[45.828873737160091623  ,48.422108548643123060  ] 
dist 4=[45.123199202984139437  ,48.304658618888793286  ] 
dist 5=[44.167158861416763618  ,47.944789097729189303  ] 
dist 6=[43.120117065999752416  ,47.815482178521238508  ] 
dist 7=[42.047518807226897395  ,47.708395230208075241  ] 
dist 8=[40.747979584199580461  ,47.406025977591195401  ] 
dist 9=[38.793387180530776220  ,43.867021490558449616  ] 
dist 10=[36.756909533324290270  ,42.911325283149642192  ] 
dist 11=[35.130249651304530948  ,42.645975644471558895  ] 
dist 12=[33.486973336117494229  ,41.631268873942844319  ] 
dist 13=[31.384034116723489140  ,41.374993488481838067  ] 
dist 14=[29.137830308908424731  ,40.870712897201205425  ] 
dist 15=[26.922155281139166593  ,40.713880104310172320  ] 
dist 16=[24.296596322084144084  ,39.944544907954081588  ] 
dist 17=[20.412807568629436354  ,32.662486958760849994  ] 
dist 18=[16.531875017775332526  ,22.284749856823446600  ] 
dist 19=[13.917699028567738081  ,21.848909508365787819  ] 
dist 20=[11.721766528317990627  ,17.722309403563666104  ] 
dist 21=[9.5117323960448840391 ,16.972985366206213282  ] 
dist 22=[7.4524900323744556298 ,16.050330293898008352  ] 
dist 23=[5.8589432804453187338 ,15.858747355323363905  ] 
dist 24=[4.2956269942171883867 ,11.942053476863761876  ] 
dist 25=[1.7240851075003915606 ,11.351610698686836515  ] 
dist 26=[-.12487738099394354216,7.7727264829316455070 ] 
dist 27=[-1.7468845041161694725 ,7.4195790059991144055 ] 
dist 28=[-3.4926603070481698277 ,5.9911548397357266524 ] 
dist 29=[-5.1949251629762076867 ,5.7280022128549736945 ] 
dist 30=[-6.6437793204982153482 ,5.2628369629353121018 ] 
dist 31=[-8.1935021876861057553 ,5.1693059479919506923 ] 
dist 32=[-10.300027817367687692  ,-.73430422887483453982] 
dist 33=[-12.327221689736809931  ,-1.2389643118108796378 ] 
dist 34=[-13.560202146107730180  ,-2.2881151815200481895 ] 
dist 35=[-14.457237485558282857  ,-2.5093462399954381846 ] 
dist 36=[-15.141597704174015163  ,-2.5146146003424324552 ] 
dist 37=[-15.662580397151925932  ,-2.4069825920088620377 ] 
dist 38=[-15.906342286449713707  ,-2.2503273511584800853 ] 
dist 39=[-16.010931886661730926  ,-2.0421278722694992609 ] 
dist 40=[-16.010713578512961777  ,-1.7584612085032190967 ] 
dist 41=[-15.148964109500507910  ,-1.3003621478882104392 ] 
dist 42=[-14.976138089844423628  ,-.81634685319647197843] 
dist 43=[-14.641522514359343652  ,-.42903074717199307313] 
dist 44=[-14.531657208604195228  ,-.03951127125382972771] 
dist 45=[-14.036696936687618454  ,.45369256443455726334] 
dist 46=[-13.906713452202978425  ,.97521430105427897657] 
dist 47=[-13.560783749131448862  ,1.4779788993052269601 ] 
dist 48=[-13.436899265537501369  ,2.0633605386899294880 ] 
dist 49=[-6.1862026967539965630 ,3.3215931956630532486 ] 
dist 50=[-4.6713076213665635793 ,5.1319350810488761694 ] 
dist 51=[-3.0303988618504531198 ,6.3398653921104936058 ] 
dist 52=[-2.7122779158995094506 ,7.3369141952356808409 ] 
dist 53=[-.72793251025180587346,8.3058120956983833388 ] 
dist 54=[-.3814446319520096213 ,9.1816969016991599219 ] 
dist 55=[.2873582571609921793 ,9.8076200887004284178 ] 
dist 56=[.44460918690172218647,10.370010984543309076  ] 
dist 57=[2.0174860301196338594 ,10.992423315779508874  ] 
dist 58=[2.2532100221808387725 ,11.546372101191709574  ] 
dist 59=[2.5468988268822325674 ,11.835574377985412388  ] 
dist 60=[2.5795533468676347159 ,11.986998086080665805  ] 
dist 61=[2.2279356740939070632 ,12.017391487232586346  ] 
dist 62=[1.6993533428087646970 ,11.935852959816232367  ] 
dist 63=[.86257472480085223308,11.870328921676374460  ] 
dist 64=[.01630651972641050721,11.283769659015227830  ] 
dist 65=[-.55016540837347235737,4.8930659856415716493 ] 
dist 66=[-1.0193735238564137234 ,2.9322033258505139006 ] 
dist 67=[-1.4776041774782986878 ,2.8658165754677148082 ] 
dist 68=[-1.8929690477609795087 ,2.3591796190314206938 ] 
dist 69=[-2.1911627114468068693 ,2.2609996038175022416 ] 
dist 70=[-2.5346514317550406299 ,2.1016907301477893802 ] 
dist 71=[-2.9673339194971931953 ,2.0597957953674419055 ] 
dist 72=[-3.3807896851533730885 ,1.2679849735182116200 ] 
dist 73=[-3.8755825661245873048 ,1.1646997772906642649 ] 
dist 74=[-4.3359905525360087234 ,.91706264276155039643] 
dist 75=[-4.6122487134706384894 ,.8796859567123350027 ] 
dist 76=[-4.8062855163004744721 ,.53296079392925773457] 
dist 77=[-4.9386123154418055085 ,.47072749176969636347] 
dist 78=[-5.0313953384472127685 ,.38899701675384731287] 
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dist 240=[-.09468995642011404280,.05092324713671002451] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 0, 0, 0, 1, 1, 2] 
dist 0=[8.0686288852603089922 ,8.0686288852603089922 ] 
dist 1=[7.3222889964277283328 ,9.5197502170782733368 ] 
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dist 3=[3.4845477638449472592 ,12.384768625461723158  ] 
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dist 6=[12.389592619360795906  ,15.922797314370550362  ] 
dist 7=[12.929250956839157537  ,16.658206292774328163  ] 
dist 8=[15.729652073151153545  ,17.218445532741933779  ] 
dist 9=[16.099841702978307650  ,17.689008431506628716  ] 
dist 10=[16.766737443475253244  ,18.067919682593761424  ] 
dist 11=[16.892417903922075859  ,18.262005435743275662  ] 
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dist 21=[10.404445573224145658  ,13.663629841582177737  ] 
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dist 23=[8.0719259730100014677 ,12.895652029132588936  ] 
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dist 44=[-9.0431715048340861909 ,-5.6842314216792925064 ] 
dist 45=[-9.0537447470335860283 ,-4.4267068089439273134 ] 
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dist 47=[-9.0079020677316600422 ,-2.2630235259295769262 ] 
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dist 60=[2.3559135743750358348 ,4.1691925860037353317 ] 
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dist 99=[.96633651687811533375,1.5062759749975333923 ] 
dist 100=[1.2506653897006128219 ,1.6219376117325617382 ] 
dist 101=[1.2901950532451904123 ,1.7400183466129483678 ] 
dist 102=[1.3670084567361774257 ,1.8452072927080579813 ] 
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dist 104=[1.3686626786066519234 ,1.9559091958712473604 ] 
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dist 108=[.82683767533655813644,2.0149448427863683051 ] 
dist 109=[.53139540692535439454,2.0088727007343804444 ] 
dist 110=[.23222081652789510736,2.0012468569695440957 ] 
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dist 112=[-.13730440041990280591,1.1162962247848051554 ] 
dist 113=[-.30375730470520174119,1.0370462814342383542 ] 
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dist 201=[.08165346218994182375,.12354025833149544683] 
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dist 203=[.05083271734844777528,.11633644578601620514] 
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dist 208=[-.06104034275850840472,.02487968353876997142] 
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dist 210=[-.09299035972587952143,.00495168357908097042] 
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dist 212=[-.11796116563935446994,-.01238699945501072609] 
dist 213=[-.13293329001572274354,-.01490808614765931231] 
dist 214=[-.14700269289655316754,-.02007922959234599839] 
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dist 217=[-.16707111514511480617,-.02384002447002317748] 
dist 218=[-.17072643399672098177,-.01843558765067681486] 
dist 219=[-.1719025036658637529 ,-.01154040316847166618] 
dist 220=[-.17210846532147480728,-.00223936307324602391] 
dist 221=[-.17189245018046716687,.02003548650010807576] 
dist 222=[-.15388247590432037708,.04506578603323380377] 
dist 223=[-.15349751969800426593,.06144758061420939973] 
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dist 226=[.03602194874846885299,.10168896008161410883] 
dist 227=[.03878705306171576867,.11057682842518811532] 
dist 228=[.05052543075921945090,.11801260518829444382] 
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dist 230=[.05315251209935266743,.13191376373615075075] 
dist 231=[.05226858068107765804,.13585008402286604021] 
dist 232=[.04839490754508046816,.13865021446282895222] 
dist 233=[.04159389679444205846,.14062850407704724209] 
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dist 235=[.02458519834841669495,.1420050277041322766 ] 
dist 236=[.01320762467996305198,.14151697133012606259] 
dist 237=[-.00440707282574616362,.14091676381381350092] 
dist 238=[-.02208976285662900836,.1284957153601607807 ] 
dist 239=[-.03373865069755408283,.128022506237848613  ] 
dist 240=[-.04318680555680737026,.06816648710028074009] 
dist 241=[-.05208824031132800668,.06558562053474806431] 
dist 242=[-.05994589056297019356,.05772021792312416978] 
dist 243=[-.06522917489569646609,.05673063599125777473] 
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dist 246=[-.07781896918525062399,.04507307719290693032] 
dist 247=[-.08018153213270810809,.04436431705625259787] 
dist 248=[-.08191367701755449399,.02977467696781872815] 
dist 249=[-.08323529294492908636,.02781439076491231783] 
dist 250=[-.08418948562181113031,.02324888893255677802] 
dist 251=[-.08445546759106135427,.02233135758058808278] 
dist 252=[-.08429414390401231261,.01616219180273957017] 
dist 253=[-.08408448518398270108,.01553614323877478323] 
dist 254=[-.07472260404502266759,.01291934870721201054] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 2, 0, 2, 0, 1] 
dist 0=[56.041677811336193829  ,56.041677811336193829  ] 
dist 1=[55.642213290748231476  ,56.379953629072905902  ] 
dist 2=[54.385488044410032129  ,56.802822024746373744  ] 
dist 3=[52.824595257182082263  ,56.946202122784841639  ] 
dist 4=[51.016348547825022140  ,56.965948297624045121  ] 
dist 5=[48.676799263175647024  ,56.895149713318200674  ] 
dist 6=[44.994079906528906771  ,56.743768289106847790  ] 
dist 7=[41.240213791060949348  ,56.650104918749670253  ] 
dist 8=[38.616439750384471410  ,56.066274291748675702  ] 
dist 9=[36.312336918084796699  ,55.898551575524230446  ] 
dist 10=[33.834846327221054203  ,55.239854818225321367  ] 
dist 11=[31.428175194565572121  ,55.133650912121884421  ] 
dist 12=[29.406663499056908295  ,53.203576372504380341  ] 
dist 13=[27.274510771699073141  ,52.750768598585045247  ] 
dist 14=[24.425551102212575838  ,51.044303371758371920  ] 
dist 15=[21.603599633496449617  ,48.055637285839631913  ] 
dist 16=[19.579070859867963786  ,31.465052458097183560  ] 
dist 17=[17.744166855361180994  ,30.533928679125163979  ] 
dist 18=[15.679229206105930622  ,29.508316379426388333  ] 
dist 19=[13.614376648892742220  ,29.318980116294525584  ] 
dist 20=[11.779356895391051303  ,20.752531766440085395  ] 
dist 21=[9.7526912574459458524 ,19.692005718556808830  ] 
dist 22=[6.9213930050876138030 ,17.557440744722709181  ] 
dist 23=[4.1400612676366016175 ,17.014968016274595819  ] 
dist 24=[2.3129081980450376857 ,15.123236365906349160  ] 
dist 25=[.50588118321044544954,14.722092459930867573  ] 
dist 26=[-1.2814194756285103274 ,14.221281743066898368  ] 
dist 27=[-3.1022046002620747140 ,14.109146695360361591  ] 
dist 28=[-4.8159136897104468953 ,4.0523008338142927280 ] 
dist 29=[-6.1762469869730058914 ,3.6237666230084688978 ] 
dist 30=[-7.5471663807819056956 ,1.8094945104068646087 ] 
dist 31=[-9.3046468459935958276 ,-1.0787454080966919198 ] 
dist 32=[-10.965753859728875831  ,-4.3603284980162121940 ] 
dist 33=[-11.951896645468279595  ,-4.5367370520252490301 ] 
dist 34=[-12.641913602316711025  ,-4.4607482715396646402 ] 
dist 35=[-13.119215110182345538  ,-4.2769060954480139733 ] 
dist 36=[-13.469709285067910298  ,-3.9536616409036316162 ] 
dist 37=[-13.652423550700349643  ,-3.4690268556192993051 ] 
dist 38=[-14.235534689047395669  ,-2.6410732364108187238 ] 
dist 39=[-14.773950562666989849  ,-1.7859831035144990276 ] 
dist 40=[-15.205465249504535637  ,-1.1928764293772223978 ] 
dist 41=[-15.422658292966366128  ,-.68012125381480284851] 
dist 42=[-15.525305345320364165  ,-.14520912862713710111] 
dist 43=[-15.531877231099632076  ,.36140862708607536064] 
dist 44=[-11.294521978278956892  ,.76148063132164681943] 
dist 45=[-11.176744562158130058  ,1.5066844324446370487 ] 
dist 46=[-11.076117248366811326  ,2.6031090507133368311 ] 
dist 47=[-11.011090129637803267  ,3.6553904823925855864 ] 
dist 48=[-3.0228933682330841339 ,4.6270226961047798645 ] 
dist 49=[-2.6188314259534342655 ,5.3044861811673650301 ] 
dist 50=[-2.5287386421819023311 ,5.8941524686187058760 ] 
dist 51=[-2.0010003714982267083 ,6.5184700204417657450 ] 
dist 52=[-1.9017288592670075000 ,7.0826507999888463569 ] 
dist 53=[-1.7034435212695885093 ,7.4323361300318716040 ] 
dist 54=[-1.6514173505636294299 ,7.6922343355769065126 ] 
dist 55=[2.5138812354163201773 ,7.8979606404222449989 ] 
dist 56=[3.2012514280335466191 ,8.0533976413266172784 ] 
dist 57=[3.2735879984591018838 ,8.1515043339694206404 ] 
dist 58=[3.1976861228424689568 ,8.6234186820874095111 ] 
dist 59=[2.9012257047395798813 ,9.0009477037440684282 ] 
dist 60=[2.1500975880569118555 ,9.2913264202125633295 ] 
dist 61=[1.3356726412855583564 ,9.4154376066318578298 ] 
dist 62=[.63823623705400190205,9.4674172016555826117 ] 
dist 63=[-.0802176356532214425 ,9.4698383661401479067 ] 
dist 64=[-.7557592260681390439 ,2.5483037810434490642 ] 
dist 65=[-1.2820208382805677651 ,2.3459260495128083474 ] 
dist 66=[-1.7989009393180753612 ,2.2945797653511769513 ] 
dist 67=[-2.4370372046832416512 ,2.0570389486058805498 ] 
dist 68=[-3.0401839856802878840 ,2.0085644245623145712 ] 
dist 69=[-3.4174754894226002314 ,1.8958614794913256234 ] 
dist 70=[-3.7010230894257773780 ,1.8636355116414220366 ] 
dist 71=[-3.9301632768157786401 ,.52593505507110093012] 
dist 72=[-4.1121183609378787762 ,.39187160997571140732] 
dist 73=[-4.2074083916339622510 ,.11944702481964616793] 
dist 74=[-4.2572966083583211515 ,.05078252442059028678] 
dist 75=[-4.2648388059020992292 ,-.18592819003779853384] 
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dist 80=[-3.7366958476067944142 ,-.21805411707488016268] 
dist 81=[-3.7851877906226948854 ,-.14141289952714639903] 
dist 82=[-3.7955179126930555839 ,-.00564520202824763249] 
dist 83=[-3.7452013327760981821 ,.15747085789542726808] 
dist 84=[-3.7299986089599679457 ,.34326219111026510854] 
dist 85=[-3.7189569783583679226 ,.58104908408497593095] 
dist 86=[-3.7107476375243392909 ,.95166593205249028311] 
dist 87=[-3.1118245158465803471 ,1.3231388189355688873 ] 
dist 88=[-2.9352412946981840248 ,1.5643515653134849535 ] 
dist 89=[-2.8964534260300759736 ,1.8798584685891458711 ] 
dist 90=[-2.7756186998548556135 ,2.3041962707301150672 ] 
dist 91=[-2.7574230016962295266 ,2.6916615734452918054 ] 
dist 92=[-.88279643295458464666,2.9749756167783478392 ] 
dist 93=[-.70485737534599131385,3.2360128048360245826 ] 
dist 94=[-.3267750242798261159 ,3.5345963883188269868 ] 
dist 95=[-.23453977645999369966,3.8054137011327902103 ] 
dist 96=[.14790109049897346754,3.9556592310939302437 ] 
dist 97=[.21860728884264646552,4.0462472916939947932 ] 
dist 98=[.3558622358377788638 ,4.0790161461303328124 ] 
dist 99=[.3879318888555478756 ,4.0900384195066758930 ] 
dist 100=[.47654243502358718709,4.0938444745234644982 ] 
dist 101=[.4684184631709131219 ,4.0930879756226553737 ] 
dist 102=[.05826838645099780318,4.0858822201688388101 ] 
dist 103=[-.44164095462676391253,3.3901466767861967865 ] 
dist 104=[-.77510361486341225126,3.2991093612806448574 ] 
dist 105=[-1.0501003722669517184 ,3.0559938001998080198 ] 
dist 106=[-1.3167378514781107996 ,2.9731277313170996796 ] 
dist 107=[-1.5572083045804886825 ,2.7280316955018355333 ] 
dist 108=[-1.7278020862713512735 ,.54877902811484619337] 
dist 109=[-1.8796836862936036548 ,.44268271482718608333] 
dist 110=[-2.0454958265358605713 ,.41511799696567813027] 
dist 111=[-2.1950122337811921949 ,.12995202862998602029] 
dist 112=[-2.2818739259182143584 ,.08633257279180630789] 
dist 113=[-2.3393741148544237118 ,.01108627670502232373] 
dist 114=[-2.3717351513951009266 ,-.00556122522626124089] 
dist 115=[-2.3890660509097794887 ,-.03804060313158625630] 
dist 116=[-2.3883821846800214546 ,-.03277214462980984632] 
dist 117=[-2.3756647224900777800 ,-.00960005966583596658] 
dist 118=[-2.3636695277273536489 ,.04400834844005970644] 
dist 119=[-1.6285327483969332590 ,.10114998961342419619] 
dist 120=[-1.6526542063305866283 ,.13842034157089573837] 
dist 121=[-1.6574437968827791124 ,.16821377259396231453] 
dist 122=[-1.6544973067890551742 ,.19552685274974191587] 
dist 123=[-1.6477541247075593078 ,.21910534972607913328] 
dist 124=[-1.0080355823067591058 ,.23400019867868943135] 
dist 125=[-.94958195828515275267,.24536655157014059709] 
dist 126=[-.8031222550401192579 ,.254869094468163568  ] 
dist 127=[-.78148005339432570032,.26269848169291514795] 
dist 128=[-.55332361107328189209,.26738969993826761748] 
dist 129=[-.51024257531586014582,.29425352975014407052] 
dist 130=[-.46051323516225017662,.40359015721139794875] 
dist 131=[-.45007168885451972624,.53942926571483801236] 
dist 132=[-.06820129836943798633,.66829451360916905088] 
dist 133=[-.02210883472153575133,.74980651008189366882] 
dist 134=[.07609493179036057794,.81214008196507187333] 
dist 135=[.05362236222496938132,.8644855314935005582 ] 
dist 136=[.02014473109047155637,.90632404734810730846] 
dist 137=[-.00844798553902585948,.92673595360214826324] 
dist 138=[-.03777948619458756297,.9372775560008224714 ] 
dist 139=[-.06527802744211864650,.93973405401877973436] 
dist 140=[-.08655829837755204144,.7103463207261122235 ] 
dist 141=[-.10732136050103462609,.76178246991537372058] 
dist 142=[-.13275631444277530273,.79849044634322882424] 
dist 143=[-.15668362419445678763,.82470055438349070726] 
dist 144=[-.17143203074000639651,.84395282028158501631] 
dist 145=[-.18225415186015993364,.85289190283835398325] 
dist 146=[-.19051799937715499346,.8559974541764521927 ] 
dist 147=[-.19681859505733057796,.85531754039205079689] 
dist 148=[-.1998089883204144057 ,.77854139769821718574] 
dist 149=[-.2009807954566493488 ,.76522620702605403783] 
dist 150=[-.20098573802375235836,.7434420963198710562 ] 
dist 151=[-.04031538131788017760,.73742387508530854637] 
dist 152=[-.03211111876557544483,.71072202636172627627] 
dist 153=[-.01291658261884005960,.70338158987012666533] 
dist 154=[-.00989352305637383244,.6842392665437848059 ] 
dist 155=[.00292542652445331285,.67676734460697936728] 
dist 156=[-.10207197364205670603,.19950291911484477819] 
dist 157=[-.21331108006855949571,.15628147168757567474] 
dist 158=[-.30660144023016981183,.06212444923940716513] 
dist 159=[-.39967927442023838974,.06276104350722554480] 
dist 160=[-.48785614951274684345,.06989392434500723726] 
dist 161=[-.55559872970636891953,.07517353058387520255] 
dist 162=[-.62034588512413178437,.08048012493410221964] 
dist 163=[-.69786421510733918016,.08732842646339080231] 
dist 164=[-.77002696390498980797,.09266436399174167689] 
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dist 166=[-.84396966614054208687,.10441651735182799811] 
dist 167=[-.8650114152430718153 ,.11036566469628658648] 
dist 168=[-.87951771593828090291,.11340413149150045772] 
dist 169=[-.88400451683856555729,.11504078597457792329] 
dist 170=[-.88370079732880416527,.11539400354520528597] 
dist 171=[-.88102491311615400053,.11397214383417962237] 
dist 172=[-.07952186253421966153,.16836256786731384303] 
dist 173=[-.08308148840676182133,.23809317745154809533] 
dist 174=[-.08661789371992200725,.29512276383806388382] 
dist 175=[-.08960007611773493202,.36997815276756757068] 
dist 176=[-.09094870165143178169,.44017781688838099578] 
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dist 180=[-.08868539928320101454,.62091843073963292192] 
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dist 182=[-.08722009285666006559,.6635580387882499637 ] 
dist 183=[-.07610838116682712005,.67546538524039431597] 
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dist 193=[-.35132379956776282919,.3131152711244317801 ] 
dist 194=[-.37374997439063788927,.2996012915108965003 ] 
dist 195=[-.39548146853575182284,.29539134296155386716] 
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dist 204=[-.12241097780815786495,.08262570123303729222] 
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dist 209=[-.1661413197275344948 ,.11908598765058965534] 
dist 210=[-.1678550326734740683 ,.12063225236228130929] 
dist 211=[-.16817157289575602406,.12143771104921803485] 
dist 212=[-.16375361692969168674,.12179021455319310538] 
dist 213=[-.16240473403063641657,.12187784958141920916] 
dist 214=[-.16023049743391079476,.12162664320700014343] 
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dist 220=[-.06891878002803174085,.06724782062336722313] 
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dist 222=[-.08531471595516062498,.08713629920721796284] 
dist 223=[-.09335481686615611037,.09841044060191733783] 
dist 224=[-.09795546347694274825,.10631359693049250177] 
dist 225=[-.1009115693597111662 ,.11325248218106278648] 
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dist 237=[-.10708804378345961428,.05873105516809277229] 
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dist 239=[-.10184341076266935007,.06700840402792945488] 
dist 240=[-.10069420500182441885,.07110927099072338321] 
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dist 244=[-.08900213633356041322,.07758424948995457983] 
dist 245=[-.08598861578726902838,.07773317835330904890] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 0, 2] 
dist 0=[55.073485624721920599  ,55.073485624721920599  ] 
dist 1=[53.805814353885802456  ,56.073649288420572801  ] 
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dist 4=[46.418849691083619527  ,57.097296356701233531  ] 
dist 5=[42.757872001778979343  ,57.107274346626537777  ] 
dist 6=[40.168882795962762112  ,57.041614919777715443  ] 
dist 7=[37.865230147716468506  ,56.778045619283913808  ] 
dist 8=[35.343352534752655294  ,56.159720362245332814  ] 
dist 9=[32.868588701583842707  ,55.602996039466804996  ] 
dist 10=[30.752841306883073068  ,55.291670177040938378  ] 
dist 11=[28.490353590294803571  ,54.940830278855560260  ] 
dist 12=[25.429246118223293254  ,54.753740632689360170  ] 
dist 13=[22.383296965522006991  ,54.409339514035425313  ] 
dist 14=[20.181094906422673785  ,54.236041983277693881  ] 
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dist 16=[15.883698096659892419  ,51.054073807256992805  ] 
dist 17=[13.587780819161391923  ,33.709318071059975024  ] 
dist 18=[11.534667999005982907  ,32.027648776387240417  ] 
dist 19=[9.2582463558040392039 ,27.991535826424780726  ] 
dist 20=[6.0694962665396491498 ,27.409622506733391879  ] 
dist 21=[2.9374963923592760300 ,21.707674836758137957  ] 
dist 22=[.88760433916422005713,20.673942567535470870  ] 
dist 23=[-.77108083623418549639,19.437973860356236617  ] 
dist 24=[-2.3400507153952135784 ,19.218282848766004156  ] 
dist 25=[-3.7401967342008499138 ,11.032824024167085007  ] 
dist 26=[-4.7244860923103065965 ,10.054683663746798967  ] 
dist 27=[-6.3541369644277163224 ,8.0130808516319678457 ] 
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dist 30=[-13.272740719664112157  ,5.2975150852316611736 ] 
dist 31=[-14.463984813692355504  ,4.7777988011256454717 ] 
dist 32=[-15.411100586918259425  ,4.6660349162605299366 ] 
dist 33=[-16.157901837396382168  ,-2.6828696661006590286 ] 
dist 34=[-16.548469936842949359  ,-2.3259144574317680894 ] 
dist 35=[-16.756259499600335995  ,-1.2289153937676860702 ] 
dist 36=[-16.790607509819693585  ,.50296615919774183184] 
dist 37=[-15.988043731677313528  ,2.2508364328065396583 ] 
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dist 40=[-15.493627332429301256  ,5.2649726511794082771 ] 
dist 41=[-15.240277553292441682  ,6.0668328205385759666 ] 
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dist 43=[-15.001605254459537522  ,7.0639508115042794767 ] 
dist 44=[-14.922407572864031322  ,7.5153800816211275417 ] 
dist 45=[-10.678351000930609638  ,7.9087256983138280017 ] 
dist 46=[-10.765224194698486866  ,8.1316877527134876451 ] 
dist 47=[-10.800583416027266232  ,8.2716475961218675926 ] 
dist 48=[-10.790630568299067876  ,8.3339073061490647259 ] 
dist 49=[-1.7752822750309822117 ,8.3429426832363611352 ] 
dist 50=[-1.6732240384508428961 ,8.3279979687211832247 ] 
dist 51=[-1.4712780890419694461 ,8.1887743441216758174 ] 
dist 52=[-1.4193760837685052379 ,8.1595747967258430307 ] 
dist 53=[-.82016287599780801119,8.7898583453767393774 ] 
dist 54=[-.73367407237768682619,9.5893526424532024589 ] 
dist 55=[-.5450989932784502797 ,10.185347959557088399  ] 
dist 56=[-.50168701909360053374,10.659611714565220592  ] 
dist 57=[-.28838013484658624638,11.024049938846293869  ] 
dist 58=[-.2506088670534213355 ,11.181714122081719492  ] 
dist 59=[-.16384709362057570872,11.247996751098380161  ] 
dist 60=[-.14857179487683216109,11.247676330885629285  ] 
dist 61=[-.01223660103731159510,6.9960733088261859513 ] 
dist 62=[.01272804148712962494,7.0308089913187471042 ] 
dist 63=[.02995703758002055529,7.0493979452739947896 ] 
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dist 101=[-3.4815587643316850958 ,3.8571628508072153642 ] 
dist 102=[-3.4511892406419714646 ,3.8170345889252228516 ] 
dist 103=[-3.3572555936711346996 ,3.7745256341145640206 ] 
dist 104=[-3.3289362440861453185 ,3.7488114445867356212 ] 
dist 105=[-3.0964915212003749066 ,3.6995803818499581706 ] 
dist 106=[-3.0406310966688436329 ,3.6719925630649300004 ] 
dist 107=[-2.9574572971592260064 ,3.6454538989955800758 ] 
dist 108=[-2.9281343848732988633 ,3.6246527435570788627 ] 
dist 109=[-2.2200579046945505137 ,1.9234720963989750683 ] 
dist 110=[-2.1205236735200080116 ,1.9661727471737267745 ] 
dist 111=[-1.9010571361666271956 ,1.9879767835655723047 ] 
dist 112=[-1.8372138866986302242 ,1.9933620808018292899 ] 
dist 113=[-1.5639966703564900085 ,1.9496074244652168005 ] 
dist 114=[-1.5097658845189980973 ,1.9384274002866730995 ] 
dist 115=[-1.3755189764147573980 ,1.9318763755300920234 ] 
dist 116=[-1.3474827274475680163 ,1.9299344786059473502 ] 
dist 117=[-1.3793394945367346437 ,-.69246869684273997415] 
dist 118=[-1.4347536822216507912 ,-.74750828159639533714] 
dist 119=[-1.4693816136601734402 ,-.86652858346808456388] 
dist 120=[-1.4956099395140578156 ,-.88397993493950549779] 
dist 121=[-1.5132810137875520767 ,-.99829524709357504044] 
dist 122=[-1.5218277277083309089 ,-1.0150549746790672387 ] 
dist 123=[-1.5253600664324317173 ,-1.0316187956739391085 ] 
dist 124=[-1.5230148449077809784 ,-1.0209701995162782870 ] 
dist 125=[-1.5171129684310565800 ,-1.0003444075113539006 ] 
dist 126=[-1.5100774698206258183 ,-.89292677014510167558] 
dist 127=[-1.4929381290760345145 ,-.70626718555547820428] 
dist 128=[-1.4841164739547983651 ,-.41667368511949089761] 
dist 129=[-.99434707056338545623,-.12370342965763469141] 
dist 130=[-.9902439052666054493 ,.07643060866496478126] 
dist 131=[-.98659908504061785303,.2465913023185966393 ] 
dist 132=[-.9826389541286013418 ,.41998073492875947329] 
dist 133=[-.20244969553473265579,.58186425165418257177] 
dist 134=[-.13837736282388937764,.70612158454415149802] 
dist 135=[.00424533893236060765,.82643478245545375136] 
dist 136=[.03190560329082832176,.97258389518565243347] 
dist 137=[.19664387244221557978,1.1095466075386216261 ] 
dist 138=[.22440152122441451829,1.1932095157528355225 ] 
dist 139=[.28070070000576463485,1.2537329376278768508 ] 
dist 140=[.29371088881634028973,1.2983766178711718272 ] 
dist 141=[.33987999865876268936,1.3311854282866131046 ] 
dist 142=[.29082886248885515235,1.3444919531143503832 ] 
dist 143=[.21402698599043727965,1.3480509864228584165 ] 
dist 144=[.08483391393073674179,1.3455394114008989164 ] 
dist 145=[-.04760952367437184749,.9008380273610404877 ] 
dist 146=[-.1373802410176643443 ,.91715946326574988407] 
dist 147=[-.24742949776198794914,.9246074766093064275 ] 
dist 148=[-.35733938963029609048,.92529611776687784495] 
dist 149=[-.45742620565058285976,.00798216800733085832] 
dist 150=[-.53000098341991774274,-.03318597076742302901] 
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dist 152=[-.67088545834176010458,-.13584235928969221163] 
dist 153=[-.7392885049638659773 ,-.19115340372681256423] 
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dist 156=[-.82951302229028182325,-.11481188988334293671] 
dist 157=[-.84294116156997365093,-.06650431999247416837] 
dist 158=[-.84569501852474608046,-.01136554558575101870] 
dist 159=[-.84426203522553697258,.05923766554435686325] 
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dist 230=[-.09291709148987540992,.23414719449618935023] 
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dist 235=[-.17624979701804165982,.1536068522489361267 ] 
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dist 237=[-.19146792691674406798,.08396387394018274819] 
dist 238=[-.19592640061740108106,.07852232367439704595] 
dist 239=[-.20387651915330245528,.06576948698054406896] 
dist 240=[-.21007837421033433193,.06321205608757509321] 
dist 241=[-.21454632220879856751,.04569942041215933280] 
dist 242=[-.21674413151793757532,.04241670149883807706] 
dist 243=[-.21769654512127160823,.03650604957429933486] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 2, 1, 1, 0, 2] 
dist 0=[52.886196743441525935  ,52.886196743441525935  ] 
dist 1=[52.606653367755364262  ,53.067003145468163003  ] 
dist 2=[51.582889539839176842  ,53.696431564193478256  ] 
dist 3=[49.947485350652556678  ,54.366144238889933464  ] 
dist 4=[47.225593280471625249  ,54.707845319552274353  ] 
dist 5=[44.403606964744084878  ,54.875225028902701401  ] 
dist 6=[42.368482247456376724  ,54.867977320999584347  ] 
dist 7=[40.516319167661113960  ,52.715873608612517953  ] 
dist 8=[38.424771290220068639  ,52.335041528097334322  ] 
dist 9=[36.334264872026661180  ,51.761225971763587635  ] 
dist 10=[34.486107829739407803  ,51.558422806169732606  ] 
dist 11=[32.457315336150765805  ,50.986147745316158295  ] 
dist 12=[29.645199855285353667  ,50.762628266363688901  ] 
dist 13=[26.816358734292742944  ,50.504996431611748460  ] 
dist 14=[24.720592276170900968  ,50.362117009533978384  ] 
dist 15=[22.754927784483180587  ,31.672135255507332635  ] 
dist 16=[20.445349853011984112  ,30.100074091641985893  ] 
dist 17=[18.082782112452952961  ,26.357089999344921616  ] 
dist 18=[15.905115368647381860  ,25.797570796043066827  ] 
dist 19=[13.438162717465737433  ,22.902924634805333564  ] 
dist 20=[9.9194698017864404793 ,22.745888403229281558  ] 
dist 21=[6.4457758167417536594 ,18.462408286863323296  ] 
dist 22=[4.1584312773021958374 ,18.197187891945584646  ] 
dist 23=[2.2934345168619371894 ,12.723866882558888109  ] 
dist 24=[.50696600398378712049,12.329222932150222475  ] 
dist 25=[-1.1011124221986636358 ,11.925224948418824382  ] 
dist 26=[-2.2535910747342998153 ,11.236252428469711851  ] 
dist 27=[-4.1577917953267288401 ,8.4316633011750303480 ] 
dist 28=[-5.9538379994502296314 ,6.9915336756718017950 ] 
dist 29=[-7.8669044062020298984 ,5.1078441760767960929 ] 
dist 30=[-10.453545151015508754  ,4.9693791482526772963 ] 
dist 31=[-12.941403984592538823  ,-.64435453545437141417] 
dist 32=[-14.460104300254617844  ,-1.1458278943276414592 ] 
dist 33=[-15.569240551687821979  ,-2.1535407097624730664 ] 
dist 34=[-16.420515480982790236  ,-2.3876296386175397170 ] 
dist 35=[-17.081642895716672840  ,-2.1905698409409418352 ] 
dist 36=[-17.430681509555294335  ,-.94610255669519470522] 
dist 37=[-17.621301644811612578  ,.3250529136364752473 ] 
dist 38=[-17.648549555790696242  ,1.1810563301618141748 ] 
dist 39=[-16.440802782748449419  ,1.8924161920570834760 ] 
dist 40=[-16.222812308938925651  ,2.5872184313953267851 ] 
dist 41=[-15.911997217900094165  ,3.2141020637893624616 ] 
dist 42=[-15.791185882847855056  ,3.6547932236269178753 ] 
dist 43=[-15.492546120633628259  ,4.0413907813519905428 ] 
dist 44=[-15.368082991944717318  ,4.4526464633432901031 ] 
dist 45=[-15.272720219359914944  ,4.8228467809496933463 ] 
dist 46=[-15.192998937176499970  ,5.0457619523102736689 ] 
dist 47=[-3.9437970368818386980 ,5.2022949852283349889 ] 
dist 48=[-3.0176096701095561156 ,5.3078125322685393483 ] 
dist 49=[-.9434492911219368877 ,5.3714097148639644692 ] 
dist 50=[-.83283283362590262244,5.3787677474394858989 ] 
dist 51=[-.68512001976780645907,5.3290281601127201239 ] 
dist 52=[-.64981865151300617163,5.3088364758371782395 ] 
dist 53=[.30483810566438288876,6.2446635541435647400 ] 
dist 54=[.41183629172515787124,7.6917364348191433330 ] 
dist 55=[.65131460037496407923,9.0583406239842132999 ] 
dist 56=[.68621814979677682936,9.9175900098170256772 ] 
dist 57=[.95608152397263806457,10.569886927242581528  ] 
dist 58=[.99805798044458999348,11.110491325178997166  ] 
dist 59=[1.0649044071331647675 ,11.538113037827727711  ] 
dist 60=[1.0766661032795029713 ,11.739470612282307121  ] 
dist 61=[1.1893250157483827786 ,11.832424339583180826  ] 
dist 62=[1.1937197081242838354 ,11.831380407831536453  ] 
dist 63=[1.1753990250295281950 ,3.1447105786734945705 ] 
dist 64=[.59130745930555733633,2.8255072463860300573 ] 
dist 65=[-.2099529839539020183 ,2.0571924786202331879 ] 
dist 66=[-1.0111105258805737850 ,1.9401006388567014262 ] 
dist 67=[-1.7495039873993785796 ,1.3075465739255777609 ] 
dist 68=[-2.3004272951732407605 ,1.3034946463823389442 ] 
dist 69=[-2.8189156420344788781 ,.51549610713850221048] 
dist 70=[-3.4280014434685134402 ,.45034881488142110173] 
dist 71=[-3.9941544671381423664 ,.298385204353337374  ] 
dist 72=[-4.3413594856829856738 ,.27270751852810412771] 
dist 73=[-4.5944356533117753312 ,.07374392476593296499] 
dist 74=[-4.7849625176147637575 ,.03871809230507339749] 
dist 75=[-4.9770530759316073981 ,-.01762261212308991113] 
dist 76=[-5.0783434907168341153 ,-.03087813064154871531] 
dist 77=[-5.1255271799348008107 ,-.23447823115226070045] 
dist 78=[-5.1320939727882407707 ,-.26078955534086889713] 
dist 79=[-5.0693673795423802146 ,.38151675243580222517] 
dist 80=[-5.0453066102366323912 ,.88614649034305848722] 
dist 81=[-4.9373957356782454038 ,1.3126197654383726134 ] 
dist 82=[-4.9150196444302187721 ,1.7425698396645147025 ] 
dist 83=[-4.5651575349360882900 ,2.1406757602371726444 ] 
dist 84=[-4.4812667099445982049 ,2.4401339770005770320 ] 
dist 85=[-4.4039425059068662040 ,2.7240199959633845509 ] 
dist 86=[-4.3687344667344297865 ,3.0600144367848211760 ] 
dist 87=[-3.1799455042278568928 ,3.3700017984001160507 ] 
dist 88=[-3.0202201599491116760 ,3.5501474469647090786 ] 
dist 89=[-2.6978887479576787936 ,3.6692807010582531109 ] 
dist 90=[-2.6114718077702668869 ,3.7358896105412291108 ] 
dist 91=[-2.2896120756443057659 ,3.7764969893013283064 ] 
dist 92=[-2.2180638258568632813 ,3.7919045315656834547 ] 
dist 93=[-2.2034932206924390581 ,3.7917190474531079566 ] 
dist 94=[-2.2080116032754734806 ,3.7800507297665619765 ] 
dist 95=[-2.2114068394734562795 ,2.8964261850204088742 ] 
dist 96=[-2.2098609712174520912 ,3.3125615051854168536 ] 
dist 97=[-2.2041572573622171978 ,3.6331912953027783620 ] 
dist 98=[-2.1954543700699268238 ,3.9071638839556656899 ] 
dist 99=[-2.1737995736064013477 ,4.1301208264078424394 ] 
dist 100=[-2.1615723369672649909 ,4.2471757430863450331 ] 
dist 101=[-2.1288851859111255775 ,4.3111899634402931254 ] 
dist 102=[-2.1133856750144135569 ,4.3242024225654543133 ] 
dist 103=[-2.0231876148024615028 ,4.2948363246968459260 ] 
dist 104=[-1.9993834150147672360 ,4.2752907997933273967 ] 
dist 105=[-1.9425623659369675088 ,4.2505157538094549545 ] 
dist 106=[-1.9211425670215136055 ,4.2306638158392428097 ] 
dist 107=[-1.8105896284289621878 ,3.5994584074222940723 ] 
dist 108=[-1.7839249035444182820 ,3.5327286108086013676 ] 
dist 109=[-1.7187372662101283307 ,3.4487061533386584667 ] 
dist 110=[-1.6950993062519801726 ,3.4413309869694769621 ] 
dist 111=[-.14628111442517731498,.62962154973124052193] 
dist 112=[-.14622979276360537364,.40090140361580413868] 
dist 113=[-.33175984044952765504,.21234293231087816336] 
dist 114=[-.74911561565553332159,.20931884546369876255] 
dist 115=[-1.1425174738366667610 ,.20295268452348885731] 
dist 116=[-1.4510531476485328706 ,.20084824675558487989] 
dist 117=[-1.7562036536533875322 ,-.04356827616612385771] 
dist 118=[-2.1361013645878910134 ,-.06107505997464639517] 
dist 119=[-2.4970452216787909138 ,-.10092744878901848191] 
dist 120=[-2.7265680344294417256 ,-.10668245780413060261] 
dist 121=[-2.9035512280278374196 ,-.15377654981823074395] 
dist 122=[-3.0548540884822140162 ,-.16128149063165557292] 
dist 123=[-3.1778874537892454853 ,-.17263711969582607501] 
dist 124=[-3.2420709772280114942 ,-.17449511935656412437] 
dist 125=[-3.2753744793738734896 ,-.19238375256479475247] 
dist 126=[-3.2789279682659097377 ,-.18340533730413803612] 
dist 127=[-.22541994349726621898,.03534275243785635576] 
dist 128=[-.22465280836830750097,.31466998957040737397] 
dist 129=[-.22230033747086223518,.54703361785057716488] 
dist 130=[-.22400363035777595811,.78158714895131256671] 
dist 131=[-.22484636085828423136,.9945059273712827283 ] 
dist 132=[-.22473807614343793896,1.1479001138619589324 ] 
dist 133=[-.08675812756212415761,1.2868854976791138870 ] 
dist 134=[-.07550879436693030176,1.4423249597334094735 ] 
dist 135=[-.04886731483041964164,1.5845639977944314678 ] 
dist 136=[-.04461649307608856485,1.6708821899903436159 ] 
dist 137=[-.01013864072075183929,1.7326790759012375442 ] 
dist 138=[-.00505993815930328162,1.7770737274609895185 ] 
dist 139=[.00631919621230666280,1.8073302181455436866 ] 
dist 140=[.00832052337610907622,1.8139661926240168905 ] 
dist 141=[.02090866029170213173,1.8098700277543093073 ] 
dist 142=[.02249237205008068811,1.8072558097248473201 ] 
dist 143=[.02127866456319405016,1.2831798000947481431 ] 
dist 144=[.01593741242492513865,1.2311278582583912062 ] 
dist 145=[.00837168121550730208,1.0975506146549163546 ] 
dist 146=[-.15351135016559870936,1.0764073068563840959 ] 
dist 147=[-.3073293707414314645 ,.8549229689473746595 ] 
dist 148=[-.42756488895379699786,.81152235934472900893] 
dist 149=[-.54604976650798447678,.76051743392733112696] 
dist 150=[-.69288383755496047749,.74596056096047233781] 
dist 151=[-.83193917341422588728,.33135591508584560912] 
dist 152=[-.91938978307194638514,.27939905630296901782] 
dist 153=[-.98565736127678622979,.16850727480239422498] 
dist 154=[-1.0401998311754571416 ,.14137937633949566457] 
dist 155=[-1.0829981659982579107 ,.04824852796961381790] 
dist 156=[-1.1024099051550102624 ,.04753377641287891605] 
dist 157=[-1.1116097884040112764 ,.04345885147429104942] 
dist 158=[-1.1136674535514160671 ,.04250384266524978408] 
dist 159=[-.86644959426747499423,.04143166960781236824] 
dist 160=[-.95495121410096980771,.04097809719167648830] 
dist 161=[-1.0207150059235404969 ,.04077893562766654540] 
dist 162=[-1.0725822556708221445 ,.04098632778254596064] 
dist 163=[-1.1130244457480953219 ,.04152214795968283946] 
dist 164=[-1.1331973399583550580 ,.04263068251555746860] 
dist 165=[-1.1424018114708998723 ,.04417618610418720806] 
dist 166=[-1.1435553838837121942 ,.07229701824860740467] 
dist 167=[-1.0844260802483189384 ,.09534160391568917799] 
dist 168=[-1.0760535901544102655 ,.11743633835840478918] 
dist 169=[-1.0638783263216898449 ,.1371882500718803033 ] 
dist 170=[-1.0579549252271787512 ,.15088483056782633013] 
dist 171=[-1.0342782195105712352 ,.1627453868417424901 ] 
dist 172=[-1.0261003690336196605 ,.17517062740096600525] 
dist 173=[-1.0046015083637227944 ,.18630815542199164265] 
dist 174=[-.99552680529059904864,.19303107834801845991] 
dist 175=[-.32455338700752370782,.19779283663873274771] 
dist 176=[-.2643965911575897412 ,.20961872034078164506] 
dist 177=[-.13142541713261910968,.33980379365886169548] 
dist 178=[-.10344108901079205299,.47174932284430687939] 
dist 179=[-.09875294863626375258,.59455293725141587237] 
dist 180=[-.09824263108356536320,.68826170767448605591] 
dist 181=[.11354212380986628009,.77850476032761962803] 
dist 182=[.09326237399302079043,.88748053858624910169] 
dist 183=[.07205156227413965674,.98934878787896398415] 
dist 184=[.04405021240090801634,1.0512325313228914026 ] 
dist 185=[.01386267475901096229,1.0956127365886750057 ] 
dist 186=[-.01606953018158104889,1.1276407135239545937 ] 
dist 187=[-.05151269467432151307,1.1504454590109420170 ] 
dist 188=[-.10368691648334599878,1.1580244755486607195 ] 
dist 189=[-.15718961464799437063,1.1588048384073331197 ] 
dist 190=[-.19793230240234190603,1.1551851238323379009 ] 
dist 191=[-.23707770295489360644,.16459831317964952018] 
dist 192=[-.28420602867590958501,.18930647870368172835] 
dist 193=[-.35752606505457287735,.21671011860057921786] 
dist 194=[-.45762369621017058445,.24498780587694133679] 
dist 195=[-.54760744729968540529,.27929262600768167146] 
dist 196=[-.61093737403377974224,.33074571224795350871] 
dist 197=[-.6667966574740111771 ,.38175340570914172706] 
dist 198=[-.72697424201035495239,.4142812769888148232 ] 
dist 199=[-.78130285731993969896,.43946890067473803496] 
dist 200=[-.81382526790279232721,.46118831747900414395] 
dist 201=[-.83656584122902288521,.47899021125033144288] 
dist 202=[-.85186475338679079831,.4885466492564697496 ] 
dist 203=[-.86120798355324247773,.49388491259820868855] 
dist 204=[-.86285543598434694276,.49485619006250448472] 
dist 205=[-.85657659835908463018,.49333644876489841782] 
dist 206=[-.85559659512228334195,.49176829950179525238] 
dist 207=[-.55520809606842377466,.48389173781118913934] 
dist 208=[-.54900853544331834977,.48140092081795447426] 
dist 209=[-.53018357622668329982,.45268069235321809787] 
dist 210=[-.52574975698453022031,.44538617927189973718] 
dist 211=[-.48202694685905460531,.44075070519018432618] 
dist 212=[-.47199851329048781676,.47255080024124440521] 
dist 213=[-.45918935536594878291,.49824069222394538515] 
dist 214=[-.45403935150861916297,.52225785014621055352] 
dist 215=[-.33005204393120948598,.54284353192330226021] 
dist 216=[-.31304432141097996249,.55484217298143251206] 
dist 217=[-.27674956090884158846,.56282950819040939993] 
dist 218=[-.26652162936882837564,.56741064539132578446] 
dist 219=[-.22499962822485816642,.56943878676682119985] 
dist 220=[-.21676982407378665039,.56866279681932300271] 
dist 221=[-.19655208158350062714,.56360855683358339358] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 1, 2, 2, 0, 2] 
dist 0=[62.477750418697820190  ,62.477750418697820190  ] 
dist 1=[62.216285240308681437  ,62.802877666998487596  ] 
dist 2=[61.611887340815701066  ,63.087133133115605759  ] 
dist 3=[60.504591677628013098  ,63.185416553997164521  ] 
dist 4=[58.610956633449971774  ,63.166185629403307126  ] 
dist 5=[56.352913759796268058  ,63.077458494157913191  ] 
dist 6=[53.790504035211692456  ,62.703756279917272133  ] 
dist 7=[50.509919621731896873  ,62.543446413585128398  ] 
dist 8=[45.384161565430014070  ,61.946319494197494754  ] 
dist 9=[40.180181088206685285  ,61.754062332131858847  ] 
dist 10=[36.587163933139761175  ,59.967082804433800013  ] 
dist 11=[33.479935378068482266  ,59.496123602433929868  ] 
dist 12=[30.215478900837075826  ,59.116988788138400532  ] 
dist 13=[27.092080741556319888  ,58.124594377755998395  ] 
dist 14=[24.547851503445660933  ,51.939940877649901985  ] 
dist 15=[21.934848587437094285  ,47.958739894345373662  ] 
dist 16=[18.536332886588505432  ,30.889074464408034347  ] 
dist 17=[15.215462146675130784  ,30.401727489100293832  ] 
dist 18=[12.912227312629029393  ,23.654352726313281400  ] 
dist 19=[10.906648931578242806  ,22.814062564717874232  ] 
dist 20=[8.7740249995116453261 ,17.797229454149036759  ] 
dist 21=[6.7131840768662005194 ,17.184810349893501089  ] 
dist 22=[4.9937022963272834846 ,14.899707608906725968  ] 
dist 23=[3.1867449125611788385 ,14.457827928092365761  ] 
dist 24=[.77531923137329109612,13.639568096793713869  ] 
dist 25=[-1.5536827653663524762 ,13.454582909137187260  ] 
dist 26=[-3.0315868331556249655 ,4.4872542070455049213 ] 
dist 27=[-4.6208473702108692567 ,4.1891042011878620847 ] 
dist 28=[-6.5122703330453780181 ,3.4607371863862060220 ] 
dist 29=[-8.3344851430946074616 ,.84141442239419145415] 
dist 30=[-9.9813090581654773577 ,.49974004311867473985] 
dist 31=[-11.172149942655225736  ,-.9901159831136803881 ] 
dist 32=[-12.617086787035582240  ,-4.8676064419848653614 ] 
dist 33=[-13.605217887933731882  ,-5.0099069276606137685 ] 
dist 34=[-14.645041342481428357  ,-5.3333622446853961730 ] 
dist 35=[-15.314309737315333554  ,-5.2556338750377378880 ] 
dist 36=[-15.771515190675345640  ,-4.9957654137390486641 ] 
dist 37=[-16.063135210690379502  ,-4.4237877867272488115 ] 
dist 38=[-16.248086677865915024  ,-3.6984082777663639120 ] 
dist 39=[-16.279059300912200305  ,-2.8259228953526867616 ] 
dist 40=[-16.244121439757177010  ,-1.6803190156396897544 ] 
dist 41=[-16.181489632433080262  ,.14288291553382526899] 
dist 42=[-13.794030783378269197  ,3.0279561289094795259 ] 
dist 43=[-13.650162861457785255  ,4.9575396754767468555 ] 
dist 44=[-12.949515384867285376  ,6.5543885193732956393 ] 
dist 45=[-12.790870611284882318  ,8.1120592848480465591 ] 
dist 46=[-12.343815872063749821  ,9.5235108333504428035 ] 
dist 47=[-12.238753463384958570  ,10.537070268165149791  ] 
dist 48=[-5.3809335792902615171 ,11.452629279566362372  ] 
dist 49=[-4.7127643137344037031 ,12.473231434671304687  ] 
dist 50=[-3.2407740729512742962 ,13.389219229141506349  ] 
dist 51=[-2.9166212706951081776 ,13.887321629835070071  ] 
dist 52=[-1.2167513634109102071 ,14.174577100586451800  ] 
dist 53=[-.91765156777553658176,14.248985287868918842  ] 
dist 54=[-.26029725240160118005,14.248479532763069536  ] 
dist 55=[-.12438886960471808224,14.236833642026302552  ] 
dist 56=[.99269720287825186966,14.215058078955353647  ] 
dist 57=[.52238231750261327425,14.174454729169558270  ] 
dist 58=[.17420857417510598907,11.106475473456338002  ] 
dist 59=[-.14662712313918442957,10.726544911997441945  ] 
dist 60=[-.46422498054517452063,9.7805061034253598791 ] 
dist 61=[-.75439488526102238294,9.5900841784534720281 ] 
dist 62=[-.96586460771578117096,8.0741043018054111889 ] 
dist 63=[-1.4252557894320148032 ,7.3014775108033121912 ] 
dist 64=[-2.0095690593417925714 ,-.72816275692348695792] 
dist 65=[-2.7426930332268907183 ,-1.0124076713993790957 ] 
dist 66=[-3.4410199867934514368 ,-1.0528975874105889105 ] 
dist 67=[-3.8865289329137939084 ,-1.0596905015653915502 ] 
dist 68=[-4.2313695035462845343 ,-1.0117767544840874586 ] 
dist 69=[-4.5281042723759237417 ,-.93430192227088643581] 
dist 70=[-4.7705713342721712944 ,-.82056419290031237969] 
dist 71=[-4.8989214544712009471 ,-.65885414731734804959] 
dist 72=[-4.9680328517605673414 ,-.39006028252231230697] 
dist 73=[-4.9789851930826202846 ,-.11488385996578177333] 
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dist 75=[-3.6667953281475922533 ,.23025042703287018321] 
dist 76=[-3.6789506736059407579 ,.38898908095430939428] 
dist 77=[-3.6704333165662111594 ,.5354720441788701254 ] 
dist 78=[-3.6484945084633956410 ,.64456273982999302983] 
dist 79=[-3.6325483329884461443 ,.74680575436949044675] 
dist 80=[-1.3974836414330868970 ,.90203754489115027455] 
dist 81=[-1.2037598976002397769 ,1.1744468006549677851 ] 
dist 82=[-.76167548654727433585,1.4303545065709377455 ] 
dist 83=[-.67770596914559164527,1.5874735838773394732 ] 
dist 84=[-.32503207576112267144,1.7020796268284887963 ] 
dist 85=[-.2142839138811671675 ,1.7964483058883294814 ] 
dist 86=[-.1911777462325566843 ,1.8714744167439847250 ] 
dist 87=[-.15934026566549605128,1.9176645140741824332 ] 
dist 88=[-.15048946265270930896,2.2330099412500653207 ] 
dist 89=[.40960281405984675697,2.4253600970725404135 ] 
dist 90=[.15124376161877201978,2.5641219600221041391 ] 
dist 91=[-.02810210547215273944,2.6656861625018304310 ] 
dist 92=[-.18339536529230714366,2.7411222078531098547 ] 
dist 93=[-.34583213435637004479,2.7756513879874908592 ] 
dist 94=[-.4998547745380186035 ,2.7867812519215049654 ] 
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dist 96=[-.74264324850025107014,1.5050926623285155464 ] 
dist 97=[-.89392743849488440577,1.4875844691952944419 ] 
dist 98=[-1.0374622379033460016 ,1.0663270234496873939 ] 
dist 99=[-1.1276067643958534611 ,1.0092032257827165966 ] 
dist 100=[-1.1956448360858353905 ,.93896311022995521552] 
dist 101=[-1.2510137462433921549 ,.9355136180694605561 ] 
dist 102=[-1.2937972702645946273 ,.93168672466767287558] 
dist 103=[-1.3116404839369719784 ,.92686840291732222024] 
dist 104=[-1.3197969405302784278 ,.92230623906742239447] 
dist 105=[-1.4145820105197865613 ,.60362517283020500102] 
dist 106=[-1.4806262031892053575 ,.19021848601924367236] 
dist 107=[-1.5245282060825422875 ,.06375448943616894619] 
dist 108=[-1.5552463905612066036 ,.03929475928080597429] 
dist 109=[-1.5687015202778487669 ,-.00188311257921876282] 
dist 110=[-1.5999463863740075771 ,.12828829835443022254] 
dist 111=[-1.6541192531271194043 ,.33243421185901147138] 
dist 112=[-1.6844525009132413547 ,.53746117030935858356] 
dist 113=[-1.6918824620881157017 ,.67114435770461972373] 
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dist 116=[-1.7184604266857674406 ,.95888630540657107222] 
dist 117=[-1.7142105060834448634 ,1.0107581363796794893 ] 
dist 118=[-1.7061292640144168559 ,1.0491325285245098174 ] 
dist 119=[-1.6977763331108147429 ,1.0789351072854606626 ] 
dist 120=[-1.6772848054035873723 ,1.1021279687744438276 ] 
dist 121=[-1.6669919919201862799 ,1.1141370498135448163 ] 
dist 122=[-.77672879151475095981,1.1201813970955303818 ] 
dist 123=[-.75552004477834349386,1.1195884796369259533 ] 
dist 124=[-.67629535592031011747,1.1147257893102154760 ] 
dist 125=[-.65780750514072676093,1.1100955255293933790 ] 
dist 126=[-.62453049993600623504,1.0918611403311388200 ] 
dist 127=[-.61570931859419028812,1.0820912629364823773 ] 
dist 128=[.14632279618290639517,.97017126105168415792] 
dist 129=[.16734681093057650904,1.1409312743111850309 ] 
dist 130=[.24493254409964508162,1.3014171434805598960 ] 
dist 131=[.23916298287528778356,1.4002641310088273689 ] 
dist 132=[.22212738674640368946,1.4727524197344941419 ] 
dist 133=[.19919330717212949427,1.5280747432284636294 ] 
dist 134=[.16989248851560826885,1.5691033152218189505 ] 
dist 135=[.13036869906249875108,1.5845639977944314672 ] 
dist 136=[.06665159238487641533,1.5890216581289227236 ] 
dist 137=[.00186827854674121043,1.5861504974073229695 ] 
dist 138=[-.11708483309581638385,.32046241558005885664] 
dist 139=[-.23428292466493649475,.29740263105027155181] 
dist 140=[-.36341948443074869414,.29402662867280742755] 
dist 141=[-.49246211619226313424,.24963469258923674031] 
dist 142=[-.60916382711621053192,.24050710116538612849] 
dist 143=[-.69242207538088870468,.23174214104945136291] 
dist 144=[-.76700001738778751447,.22989890988607614999] 
dist 145=[-.84907343505752627524,.12688550546205940373] 
dist 146=[-.92372895816934082226,.1139386783061603597 ] 
dist 147=[-.96871301573336791544,.08776490920462385451] 
dist 148=[-1.0005113555900816927 ,.08102299348922844116] 
dist 149=[-1.0225601196610812274 ,.05722777889986559119] 
dist 150=[-1.0368236945940257251 ,.05208793258222457547] 
dist 151=[-1.0396208742381939369 ,.04565792420844386902] 
dist 152=[-1.0343271016468145851 ,.06149289895927876300] 
dist 153=[-1.0327315411959145162 ,.19079019136931605965] 
dist 154=[-.78136838712596234019,.32056837268971936392] 
dist 155=[-.78309841594935383608,.40553025636415157245] 
dist 156=[-.77918478337237768036,.47378718853367708217] 
dist 157=[-.77741170873404668061,.53692203446147877978] 
dist 158=[-.73927561266155637178,.591794437742479012  ] 
dist 159=[-.7288464343803619918 ,.6270883497922479575 ] 
dist 160=[-.72029045836139061784,.65473273057349000651] 
dist 161=[-.71499296587566172598,.67908626314804513242] 
dist 162=[-.5417437351452900213 ,.69915058095697876172] 
dist 163=[-.51775547137864972849,.70968306045057126733] 
dist 164=[-.47021087820626577147,.71522174679841759673] 
dist 165=[-.45738169024683049993,.71536417088950807823] 
dist 166=[-.4096218298641630063 ,.71201131656601804984] 
dist 167=[-.39845390407568344599,.70964488652106627034] 
dist 168=[-.37848285231744782777,.69552138414102040084] 
dist 169=[-.37320890087357524304,.69345683530689246774] 
dist 170=[-.06194070418032775564,.22238970795766443595] 
dist 171=[-.03220961563974105550,.25412095131314240844] 
dist 172=[-.02672853020537500106,.27887573351322820096] 
dist 173=[.01009148164275860820,.3005465312318934962 ] 
dist 174=[.01649303548632476555,.31855211420920816378] 
dist 175=[.02828730278795452913,.32868296649149202584] 
dist 176=[.03087994043471653084,.33497891152514332938] 
dist 177=[.06130343306534726894,.33768400483235344401] 
dist 178=[.05815747265753429691,.33860072342512914676] 
dist 179=[.04970273064278116705,.33776101864270690887] 
dist 180=[.03428805064383112888,.33576428276421586541] 
dist 181=[.01560613226902335843,.33433798485369282066] 
dist 182=[-.00588441324097165480,.33430070454118226689] 
dist 183=[-.03351916816003878874,.33310638698787761862] 
dist 184=[-.07671536965559593787,.33168198998657409708] 
dist 185=[-.11994891163325728975,.31104538011744404337] 
dist 186=[-.15719600919516274535,.145666161086097248  ] 
dist 187=[-.19398659799763174245,.12939527160096858026] 
dist 188=[-.22990369373913841688,.09351227354500049254] 
dist 189=[-.26244712450485649781,.08527432155692349564] 
dist 190=[-.28577791734511659422,.04356291772251797048] 
dist 191=[-.30679493589011653339,.03615227981770648675] 
dist 192=[-.33010716380812762875,.01935597895905495644] 
dist 193=[-.35088693223153239674,.01616795236256879172] 
dist 194=[-.3618001532702121858 ,-.00814618063378560746] 
dist 195=[-.36783699115497865616,-.00570363349038257829] 
dist 196=[-.36916164908523912428,-.00096425201775273514] 
dist 197=[-.36630850962445978459,.00488030709254533612] 
dist 198=[-.36360586201760247325,.01173211681374444970] 
dist 199=[-.3610321926669916749 ,.02062407810002134677] 
dist 200=[-.33778428490261226099,.03460810929646354352] 
dist 201=[-.28309065253352597656,.04870949142222420155] 
dist 202=[-.12573753215265514313,.05806960736972594097] 
dist 203=[-.12814406783802436562,.07165978238527132469] 
dist 204=[-.12875402905467167892,.08522693740341815333] 
dist 205=[-.12872481585929156201,.09927416290176719485] 
dist 206=[-.1285804268779261819 ,.11252913402281823876] 
dist 207=[-.12832559982556673862,.12293604560944756829] 
dist 208=[-.12785475526251548677,.13323546204677045097] 
dist 209=[-.10620623819116432383,.14606236715437203585] 
dist 210=[-.10303238489072564796,.15824645433880711202] 
dist 211=[-.09710543806155620983,.16598163051008912339] 
dist 212=[-.09550789170471383573,.17193092902166722009] 
dist 213=[-.08974840439647766180,.17775356123992297135] 
dist 214=[-.08817756507926539654,.18180157376895107478] 
dist 215=[-.08585148692622882625,.18397538729238946936] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 1, 0, 0, 1] 
dist 0=[64.293206180381487102  ,64.293206180381487102  ] 
dist 1=[63.783459118731872130  ,64.469853479310010025  ] 
dist 2=[62.944607384407592252  ,64.665553169394001900  ] 
dist 3=[61.690804526973064539  ,64.778917493683306111  ] 
dist 4=[59.889988412054813138  ,64.728659262704011931  ] 
dist 5=[56.866606805595415779  ,64.512009751084999778  ] 
dist 6=[53.715778786049288889  ,64.341349952487697725  ] 
dist 7=[51.405992409297589025  ,64.011123284381082714  ] 
dist 8=[49.264951282380772969  ,62.855966179274896217  ] 
dist 9=[46.787998713272172157  ,59.578214876164600295  ] 
dist 10=[44.278025132787004062  ,58.847386944315342599  ] 
dist 11=[39.481526893502497206  ,57.803097407161063078  ] 
dist 12=[33.486973336117494228  ,57.450979206033855729  ] 
dist 13=[29.402232224209883735  ,56.822594895857159582  ] 
dist 14=[25.925603826471830646  ,56.496260166828983160  ] 
dist 15=[22.359316426520074178  ,54.144917989466078496  ] 
dist 16=[18.998431129649130212  ,48.723232348644193655  ] 
dist 17=[16.341848969381293170  ,29.321497068670883850  ] 
dist 18=[13.685560934760568731  ,27.109644272611172814  ] 
dist 19=[10.325407254885461804  ,26.632507725975632985  ] 
dist 20=[7.0848880007173121729 ,25.877364902247713672  ] 
dist 21=[4.9061148384691744339 ,25.676546857701944716  ] 
dist 22=[3.0808443974314832408 ,11.142186041694398225  ] 
dist 23=[1.2517509741524651033 ,9.4608450680640769333 ] 
dist 24=[-1.3607125303658544407 ,9.0553996416490965055 ] 
dist 25=[-3.9798439557918113635 ,2.7037998465452873788 ] 
dist 26=[-6.3747033579555981743 ,.73062262680061367267] 
dist 27=[-8.1498811910701681140 ,.5034140158896417228 ] 
dist 28=[-9.8167174409397219521 ,-1.4355489577972113912 ] 
dist 29=[-11.778974852640644507  ,-2.6130192580255151559 ] 
dist 30=[-13.602165886732830769  ,-2.8473182902341446196 ] 
dist 31=[-14.713597876117364003  ,-3.6248278830903453943 ] 
dist 32=[-15.520472308282725626  ,-4.5667089546211027178 ] 
dist 33=[-16.127221282907300354  ,-6.0306057825939156978 ] 
dist 34=[-16.577830600115907883  ,-5.7027771116928164958 ] 
dist 35=[-16.761009205649622975  ,-5.1260497827417249760 ] 
dist 36=[-16.820703465799102804  ,-4.2595632831085771552 ] 
dist 37=[-16.787966248646974533  ,-2.7752449780971521747 ] 
dist 38=[-10.606831556818030481  ,-.56915858841199315627] 
dist 39=[-10.533502994229688830  ,1.0533403664017477555 ] 
dist 40=[-10.489538867554775618  ,2.4172872089089980042 ] 
dist 41=[-9.0245878678724999041 ,3.7812255785310769087 ] 
dist 42=[-8.8028068289699352947 ,5.0380154807723224453 ] 
dist 43=[-8.3182572385918415567 ,5.9747017706593231868 ] 
dist 44=[-8.1712486582558891825 ,6.8551486139983017179 ] 
dist 45=[-7.5269680113630327824 ,7.8878155949702766638 ] 
dist 46=[-7.3957234086919635888 ,8.8384984796358028186 ] 
dist 47=[-7.0276419732538025633 ,9.3919478160714402164 ] 
dist 48=[-6.9710272835152522641 ,9.7603697399741091119 ] 
dist 49=[-2.0583364991007835991 ,9.9728800170957725107 ] 
dist 50=[-1.5903516076394622063 ,10.110360840091446386  ] 
dist 51=[-.59420573902241640887,10.179267796796407628  ] 
dist 52=[-.35859251895995429717,10.211124675973199570  ] 
dist 53=[.65769425360214520411,10.200259838868154878  ] 
dist 54=[.84174617969591847805,8.6326424157506018354 ] 
dist 55=[1.1394593292984700165 ,8.4239683184845398757 ] 
dist 56=[.7109561319362622970 ,7.8578773833611732311 ] 
dist 57=[.2687393412242395762 ,7.7602424308559227906 ] 
dist 58=[-.1466075163830916095 ,6.7057359712899635159 ] 
dist 59=[-.4679825604948190641 ,6.4878497829383046821 ] 
dist 60=[-.7809972803268254961 ,6.2337978500833076400 ] 
dist 61=[-1.1630187969324565382 ,6.1308666974984297088 ] 
dist 62=[-1.5237662101800507503 ,3.8261222637287345062 ] 
dist 63=[-1.7519605540751847211 ,3.5255281190206693558 ] 
dist 64=[-1.9260698439971786881 ,2.5764636185328341236 ] 
dist 65=[-2.0711729535184847255 ,-.0296605239912301637 ] 
dist 66=[-2.5438088515238846006 ,-.1932589188435816586 ] 
dist 67=[-3.0082994952840359678 ,-.2172928632865445224 ] 
dist 68=[-3.4204226420452999501 ,-.40608337654047768962] 
dist 69=[-3.7671908208989284686 ,-.42913439835250154886] 
dist 70=[-3.9709299565680935905 ,-.41212556621410378836] 
dist 71=[-4.1090163066670096433 ,-.33616478167523872139] 
dist 72=[-4.1938730152142220333 ,-.22844288819799042169] 
dist 73=[-4.2532816304445213599 ,-.08473200538529799673] 
dist 74=[-4.2898185137928681280 ,.11249386702410109618] 
dist 75=[-4.3168763391519864080 ,.43368868560653406872] 
dist 76=[-4.3383873054227142378 ,.76096799856025402115] 
dist 77=[-4.3549189005427809208 ,.98246836389056109404] 
dist 78=[-4.3620676829569218760 ,1.1683903916758373042 ] 
dist 79=[-4.3638000752833218819 ,1.3537558878075440073 ] 
dist 80=[-4.3586751278675038789 ,1.5240443465620363002 ] 
dist 81=[-2.9436019475637125274 ,1.6498247998406194691 ] 
dist 82=[-2.9325563681020991459 ,1.7667835622932190016 ] 
dist 83=[-2.9204965095582876715 ,1.9018765114377904076 ] 
dist 84=[-2.3981135438037657085 ,2.0246902969686753825 ] 
dist 85=[-2.3232388226970824934 ,2.0926650639916581218 ] 
dist 86=[-2.1806182464090890462 ,2.1332859411124821549 ] 
dist 87=[-2.1422259387152350569 ,2.1831348570313532940 ] 
dist 88=[-2.0026250701321937420 ,2.3971515341725201348 ] 
dist 89=[-1.9664113024068651728 ,2.5747523411398730807 ] 
dist 90=[-1.9366781081053851522 ,2.7181473167816257808 ] 
dist 91=[-1.9254539108401265012 ,2.8891911678051687100 ] 
dist 92=[-1.8905144030258255487 ,3.0660731589811995365 ] 
dist 93=[-1.8739691006398322602 ,3.2099846683866934252 ] 
dist 94=[-1.6639008077747469467 ,3.2850705292248270659 ] 
dist 95=[-1.6279523435480675887 ,3.3240101396247746013 ] 
dist 96=[-1.5358343168016368522 ,3.3296410530857740016 ] 
dist 97=[-1.5126990574176065422 ,2.6822059524469687376 ] 
dist 98=[-1.3477987691972505198 ,2.6663976575233169384 ] 
dist 99=[-1.3118995353225513964 ,2.6568249347291668790 ] 
dist 100=[-1.2511399346356027021 ,2.6497090778869214732 ] 
dist 101=[-1.2339999298065087637 ,2.5832427773781019624 ] 
dist 102=[-.8651163616324465604 ,-.57546420580180557523] 
dist 103=[-1.0608296933538711987 ,-.67833417825850991455] 
dist 104=[-1.2136394999996537508 ,-.69894700353275806256] 
dist 105=[-1.3476021709178465800 ,-.91757978647901816116] 
dist 106=[-1.4590270238379945289 ,-.94867023603152535816] 
dist 107=[-1.5219168765883595259 ,-.95300204536979135163] 
dist 108=[-1.5612510444602771704 ,-.91506124199099530272] 
dist 109=[-1.5786982366861695142 ,-.85408263610445297086] 
dist 110=[-1.5875249157224180985 ,-.76479082041626183202] 
dist 111=[-1.5924636813096932369 ,-.63785871390479843348] 
dist 112=[-1.5955289873811157943 ,-.42673404669207505922] 
dist 113=[-1.5968724233037748455 ,-.2099402227423490961 ] 
dist 114=[-1.5970327668008158455 ,-.06039336439780354023] 
dist 115=[-1.5953731555087542136 ,.06821195871635092843] 
dist 116=[-1.5920749687073055149 ,.20147241626815109245] 
dist 117=[-1.5856926745639411834 ,.32717542360462919892] 
dist 118=[-.92103886954738756403,.42563483687277072094] 
dist 119=[-.88285703771336288342,.52278196195132506868] 
dist 120=[-.86860994379214488504,.64325008596757890868] 
dist 121=[-.5251645809872734758 ,.75723369543862448423] 
dist 122=[-.4805296633530124163 ,.82851417468020635533] 
dist 123=[-.3852949497796660704 ,.88200967982071893398] 
dist 124=[-.35968806607223108271,.92504946703189075244] 
dist 125=[-.25903869445576609828,.9581585624840007437 ] 
dist 126=[-.23968809047374402469,1.0191396785408170123 ] 
dist 127=[-.19795612521184366601,1.1186557945497843677 ] 
dist 128=[-.18734387405207525499,1.1946696006387490083 ] 
dist 129=[.54303821340413707643,1.2583243098095844474 ] 
dist 130=[.50341534579827857555,1.3090498669040147931 ] 
dist 131=[.44224602648174575714,1.3334804849553732603 ] 
dist 132=[.35369157425733751783,1.3447439166789541947 ] 
dist 133=[.20481584537563728063,1.3451869253368917462 ] 
dist 134=[.0521327709417156935 ,1.0946676003156454830 ] 
dist 135=[-.0516125295856758793 ,1.1083662878237701885 ] 
dist 136=[-.1397396804304009263 ,1.1109732602838359406 ] 
dist 137=[-.2351094177827631904 ,1.0800278692121502532 ] 
dist 138=[-.3223947165604603529 ,1.0783782243547977680 ] 
dist 139=[-.3864451067774680521 ,1.0746689126505498280 ] 
dist 140=[-.4456443362715905196 ,1.0700232752128708887 ] 
dist 141=[-.5135789459833756417 ,1.0579480639120987953 ] 
dist 142=[-.5763022924646460431 ,1.0514550877091036891 ] 
dist 143=[-.6147112655509464795 ,1.0354066191576189605 ] 
dist 144=[-.6426110188937373887 ,1.0280772520238352312 ] 
dist 145=[-.6634050613513949381 ,.34952369190803928097] 
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dist 159=[-1.0814500409398918669 ,.41502613434098118736] 
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dist 162=[-.1305247638936773933 ,.45888474173080951843] 
dist 163=[-.1216598677766977342 ,.46353259075071703048] 
dist 164=[-.1043737445992814964 ,.4651114919006225987 ] 
dist 165=[-.0999876621456767314 ,.47873594210025780454] 
dist 166=[.19665892618492756527,.53476187623220456611] 
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dist 173=[.09319765629955989757,.75554647071397845626] 
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dist 176=[-.10530923183884058497,.75087665064787502348] 
dist 177=[-.19814925229080356264,.51576519389852940895] 
dist 178=[-.25906966965474705994,.5140433650129837917 ] 
dist 179=[-.3081824429270571446 ,.50526085666495112158] 
dist 180=[-.35391425445184073112,.5028934369268208213 ] 
dist 181=[-.39388544266570519035,.47139068762207485126] 
dist 182=[-.42001515865947797068,.46338936384656702478] 
dist 183=[-.44096721757187117404,.45522286427470998189] 
dist 184=[-.46028066884424338942,.45084307355108177506] 
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dist 187=[-.49109956949375547645,.28840172442435790077] 
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dist 191=[-.4836319506447892243 ,.22254876777686762472] 
dist 192=[-.48179712780478714528,.21812836286417663461] 
dist 193=[-.4988097525212720398 ,-.11884875437336601791] 
dist 194=[-.5174652272466566737 ,-.1112656408603870472 ] 
dist 195=[-.5274901820201562762 ,-.09762833966543419857] 
dist 196=[-.5330991939386448985 ,-.05358584372997062600] 
dist 197=[-.5341356606509725134 ,.02757286278238649418] 
dist 198=[-.21748543609253815401,.10941070006307424608] 
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dist 201=[-.22695397290748761395,.2477160288650626107 ] 
dist 202=[-.22752763496652489853,.2836573799429848830 ] 
dist 203=[-.22697661772060400054,.3075455026102062134 ] 
dist 204=[-.22627739373286861596,.3271464442446485887 ] 
dist 205=[-.22059401274464238749,.3459833401318314336 ] 
dist 206=[-.21882676532034936336,.36239569657822160839] 
dist 207=[-.21380861133948760217,.37232332977227015351] 
dist 208=[-.21165319336961324112,.37938851856890449632] 
dist 209=[-.18589156926833187468,.38438011042541201089] 
dist 210=[-.1812508677896165172 ,.38764760842826109674] 
dist 211=[-.1719526759965708040 ,.38783382721189404014] 
dist 212=[-.1692050656001845828 ,.38635877833676329119] 
dist 213=[-.1577516696018940547 ,.3848280408045469581 ] 
dist 214=[-.1550630185595555279 ,.24938276881089011645] 
dist 215=[-.1484304916457076625 ,.25081520545416963221] 
dist 216=[-.15043601606031104411,.25090360454850822287] 
dist 217=[-.16997409479442363722,.2506765851955467844 ] 
dist 218=[-.18704590187817857154,.24015894287814019534] 
dist 219=[-.19819852088591229454,.2371684748333968816 ] 
dist 220=[-.20713360179805960633,.23513951916778245591] 
dist 221=[-.21535793291903331617,.23389909235119653933] 
dist 222=[-.22221391438132347036,.17860711558869978125] 
dist 223=[-.22568962497673693836,.17098047475286548202] 
dist 224=[-.2273478228461474929 ,.1562066147793653032 ] 
dist 225=[-.2273408473508285307 ,.152281312956088806  ] 
dist 226=[-.2255368264812862132 ,.13813268026076513963] 
dist 227=[-.2244977572446800271 ,.1346345165110560778 ] 
dist 228=[-.22274425131014749121,.12946194346164709745] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 1, 0, 2, 0, 2] 
dist 0=[61.689446765692003531  ,61.689446765692003531  ] 
dist 1=[61.449374805243655390  ,61.820926617951473961  ] 
dist 2=[61.101474802330852269  ,61.897840405848068509  ] 
dist 3=[60.377327703525145392  ,61.919916171330202060  ] 
dist 4=[58.767338435607388660  ,61.904868253445518487  ] 
dist 5=[56.781132184098476541  ,61.833576308848673072  ] 
dist 6=[54.470789497219221990  ,61.706922406256135882  ] 
dist 7=[51.476712983474163961  ,61.579223556323580459  ] 
dist 8=[46.760343096604288267  ,61.182448298760821478  ] 
dist 9=[41.958215458363868889  ,60.999811355331875348  ] 
dist 10=[38.621615617248085737  ,60.506059930633587186  ] 
dist 11=[35.714010810565683669  ,60.280696067402373598  ] 
dist 12=[32.624595060847138722  ,59.050786337053506362  ] 
dist 13=[29.647613213699200647  ,57.766134666963454090  ] 
dist 14=[27.188700015458176548  ,35.939793987181380276  ] 
dist 15=[24.632881832745147376  ,35.329520084393124210  ] 
dist 16=[21.268457981647790920  ,29.484240306588355795  ] 
dist 17=[17.962209657422556122  ,28.401347057812301026  ] 
dist 18=[15.638412862442917406  ,27.065874469787367795  ] 
dist 19=[13.130972679371260823  ,26.746480032694899505  ] 
dist 20=[10.227075961421595627  ,17.809759664998311830  ] 
dist 21=[6.5209928081169046167 ,16.705842211563720776  ] 
dist 22=[2.9330989640211516381 ,14.382505682312725471  ] 
dist 23=[.5008144690315626768 ,13.818275649246325288  ] 
dist 24=[-1.5578908016280620747 ,12.331342134127059826  ] 
dist 25=[-3.6544477363432076517 ,11.103224175544982341  ] 
dist 26=[-5.6251238650168589142 ,10.298425896192487209  ] 
dist 27=[-7.1818027436152397783 ,10.116026784939588927  ] 
dist 28=[-8.7418899940837379070 ,4.7262797492516505624 ] 
dist 29=[-10.727647246332673504  ,2.7040294917045676185 ] 
dist 30=[-12.609335317419950980  ,-2.5349111332434713706 ] 
dist 31=[-13.753925752118410396  ,-2.9323425548889262885 ] 
dist 32=[-14.586793955684093717  ,-4.5742024524229150771 ] 
dist 33=[-15.222455937096336064  ,-4.8683473603993165833 ] 
dist 34=[-15.697670459933786799  ,-5.2874585724361181474 ] 
dist 35=[-15.889067468412962913  ,-5.3583792490048774280 ] 
dist 36=[-15.960049827303050425  ,-5.3113429252421586060 ] 
dist 37=[-15.953495705033544186  ,-5.1001868718379045735 ] 
dist 38=[-15.539127326750824308  ,-4.7318290219927916041 ] 
dist 39=[-15.755774546639151243  ,-4.0565608046140925421 ] 
dist 40=[-15.878969071273347568  ,-3.2386490335186098829 ] 
dist 41=[-15.885209620235672223  ,-2.3006030835716228052 ] 
dist 42=[-15.817976960033005258  ,-1.0962537039886765091 ] 
dist 43=[-15.747358159753640525  ,.91592588992500660136] 
dist 44=[-13.260457826418711758  ,3.8607479225582682546 ] 
dist 45=[-13.135881655042993937  ,5.8237466265062347916 ] 
dist 46=[-6.1823084073530722155 ,7.4414347081883684283 ] 
dist 47=[-5.4963926895718166123 ,9.0085918560819037545 ] 
dist 48=[-3.9770505932534540253 ,10.421788725169340463  ] 
dist 49=[-3.6439401696592873682 ,11.425261850852288984  ] 
dist 50=[-1.8573664825255585359 ,12.320280512626341102  ] 
dist 51=[-1.5401970057050160953 ,13.300885305031426673  ] 
dist 52=[-.8564523129145987188 ,14.174577100586451808  ] 
dist 53=[-.6978083513657377090 ,14.642953138558116522  ] 
dist 54=[.5933312701684992021 ,14.904082970518306249  ] 
dist 55=[.8128950862512833568 ,14.964783811944645154  ] 
dist 56=[1.0294707593910458106 ,14.922639976088883030  ] 
dist 57=[.9499346269666739794 ,14.886999254278764096  ] 
dist 58=[.6475608001809397910 ,14.695860703261109692  ] 
dist 59=[.3680557974294370583 ,14.208675585269801571  ] 
dist 60=[.0839818187427474921 ,11.268301830533963127  ] 
dist 61=[-.4477185268678568340 ,10.414972431921318643  ] 
dist 62=[-1.1736078401896041936 ,.9718518739394951052 ] 
dist 63=[-1.6450312611102878030 ,.7828172002320793306 ] 
dist 64=[-2.0198671072806811697 ,.1176961879914756532 ] 
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dist 67=[-3.1101355301825470901 ,-.0112222367402772951 ] 
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dist 69=[-4.3476569371572592622 ,.1095112078955722262 ] 
dist 70=[-4.7206881230333816981 ,.2043164030420910613 ] 
dist 71=[-5.0417594456919972644 ,.33442492320157272024] 
dist 72=[-5.3042423248223432308 ,.54610247464072169835] 
dist 73=[-5.4435347709913045015 ,.76073363723031347604] 
dist 74=[-5.5190442741271464448 ,.90261560598627907933] 
dist 75=[-5.5304917994846853364 ,1.0178505613714329857 ] 
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dist 88=[-1.2983770807133856890 ,2.4226931424707498280 ] 
dist 89=[.71927164289943219105,2.5201374435956378277 ] 
dist 90=[.67099007753577697254,2.5925159065214858416 ] 
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dist 94=[-.1522647299336758860 ,1.8870467050815672865 ] 
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dist 98=[-.8863644906901280234 ,1.5900602643507681673 ] 
dist 99=[-1.0356721500310693245 ,1.5694259088712899109 ] 
dist 100=[-1.1751566552775351129 ,1.1238144048645370517 ] 
dist 101=[-1.3373162395748706628 ,1.0563667192652567027 ] 
dist 102=[-1.4861918849701836733 ,1.0400217971337730926 ] 
dist 103=[-1.5726870699906734752 ,1.0020108085459977703 ] 
dist 104=[-1.6298841813216317143 ,.98862399718792249276] 
dist 105=[-1.6618801178407017330 ,.6541191075029421255 ] 
dist 106=[-1.6816254380620630586 ,.5812960499592742485 ] 
dist 107=[-1.6899572272984053984 ,.5675192964840758276 ] 
dist 108=[-1.6915194546991778328 ,.18563891681032309324] 
dist 109=[-1.6859332474647825885 ,.06493915056964843897] 
dist 110=[-1.4990499723338060144 ,.16826586626671422963] 
dist 111=[-1.6288945933339003835 ,.30340027224968966576] 
dist 112=[-1.7347750012646054384 ,.41358138752943998266] 
dist 113=[-1.7906391250972493635 ,.5181287148767124354 ] 
dist 114=[-1.8216964527697134819 ,.6107274023472226927 ] 
dist 115=[-1.8285802185154497010 ,.6732457248422469136 ] 
dist 116=[-1.8395969036753384273 ,.7255288077232346249 ] 
dist 117=[-1.8446800963210151094 ,.7772951510122132881 ] 
dist 118=[-1.8446961004327606038 ,.8231639852382316352 ] 
dist 119=[-1.8380476588272802800 ,.8519238287604695853 ] 
dist 120=[-1.8271790086886427354 ,.8735596199286418641 ] 
dist 121=[-1.8176118209092590774 ,.8910202832030903190 ] 
dist 122=[-1.7940850954379864350 ,.9043845868967408294 ] 
dist 123=[-1.7826166688905729855 ,.9096850801867613976 ] 
dist 124=[-.62642665171196958711,.9100706502773231309 ] 
dist 125=[-.52485441030188649264,.9077295530187463939 ] 
dist 126=[-.29634952236451661378,.3475948098764449612 ] 
dist 127=[-.2510771740758073733 ,.5623176116838564144 ] 
dist 128=[.02392337336303169702,.7629769585709436021 ] 
dist 129=[.07172445435164645442,.9173385959336536896 ] 
dist 130=[.16666977761500965654,1.0671386756478908023 ] 
dist 131=[.18953323207865618241,1.2496001116660828542 ] 
dist 132=[.34132373199330866522,1.4208657707796420732 ] 
dist 133=[.34359795268858201734,1.5259979237963585517 ] 
dist 134=[.34229279135413307702,1.6026790335737751126 ] 
dist 135=[.33461487640520577382,1.6604318807443068010 ] 
dist 136=[.32099935769355194106,1.7030005270368970908 ] 
dist 137=[.29576471029506427017,1.7191006474180498709 ] 
dist 138=[.2386756359615547666 ,1.7234001763805490703 ] 
dist 139=[.0551242605811053728 ,1.7188863150985333442 ] 
dist 140=[-.1320405552864372412 ,.3761294654275131126 ] 
dist 141=[-.2575764017237826090 ,.37396712772136707446] 
dist 142=[-.3942247316682393643 ,.14258970746585868673] 
dist 143=[-.5353615885587553622 ,.12226305948143650461] 
dist 144=[-.6630790461743602077 ,.07620040156842412796] 
dist 145=[-.7543403739660159591 ,.06720841638266944413] 
dist 146=[-.8362386080736529372 ,.01065248042605459919] 
dist 147=[-.9266036360971176904 ,.00075108489308567591] 
dist 148=[-1.0088534271476782052 ,-.01840983579606250932] 
dist 149=[-1.0583753985707630979 ,-.02292159170717351149] 
dist 150=[-1.0933373000672417335 ,-.06774404404361744066] 
dist 151=[-1.1174965373131174788 ,-.07450893713978331261] 
dist 152=[-1.1331647603427773468 ,-.08162387680371219020] 
dist 153=[-1.1361779758528773750 ,-.0410939943539315134 ] 
dist 154=[-1.1308753822658890547 ,.05123450770660835174] 
dist 155=[-1.1287397894388690246 ,.19495762394417640335] 
dist 156=[-.8437765804917071028 ,.3392240803614499576 ] 
dist 157=[-.84399626486636530896,.43371974430034806173] 
dist 158=[-.83619821653515156031,.5096946256420086781 ] 
dist 159=[-.833578647353461797  ,.5800728418382461582 ] 
dist 160=[-.78866277949717125502,.6413174735703599058 ] 
dist 161=[-.77681117178957197101,.6808535733069302620 ] 
dist 162=[-.76607154437298931089,.7119864878593994540 ] 
dist 163=[-.75958976863605574816,.7397051895382468358 ] 
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dist 166=[-.49486386838494527279,.7819607114360015499 ] 
dist 167=[-.4807589138752242413 ,.7831492415210884896 ] 
dist 168=[-.42748739003615082175,.7805660269421769214 ] 
dist 169=[-.41536163804419834388,.7782192100140873555 ] 
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dist 171=[-.38618572608898108761,.7614084240583918793 ] 
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dist 207=[-.04493558585190983030,.1390217180491219028 ] 
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dist 210=[-.02699266784393396927,.18437446304051652451] 
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dist 214=[-.03435277316294305122,.21269501556044543186] 
dist 215=[-.03828203892873348146,.21466953072033401056] 
dist 216=[-.04308315424663920655,.21520084795733918308] 
dist 217=[-.05032051956800380188,.21490247179731438585] 
dist 218=[-.05855692525989687515,.20334745468124354629] 
dist 219=[-.06734366971535011798,.19265362131141849929] 
dist 220=[-.07820313425411126486,.14958745016151170066] 
dist 221=[-.09470866747583783788,.14657144710132075358] 
dist 222=[-.11103093137385643698,.1381003336611254259 ] 
dist 223=[-.12115910419298563644,.13661684874278806454] 
dist 224=[-.12867365944603412058,.11973135485126806118] 
dist 225=[-.13456847583979153267,.11614437585527681291] 
dist 226=[-.1390848359795685676 ,.11216805604764027762] 
dist 227=[-.14110005079846754813,.11068282800498226167] 
dist 228=[-.14191608706926978935,.06987286872540833230] 
dist 229=[-.14177570372968413688,.06451930083891406410] 
dist 230=[-.13380329176589781479,.05635639422617338813] 
dist 231=[-.13207755514478431937,.05743702939964537650] 
dist 232=[-.1287690660159353238 ,.05821862675408205292] 
dist 233=[-.1262951482074818385 ,.05879496496759742725] 
dist 234=[-.10447585743980948522,.05919368267767203867] 
dist 235=[-.09034215507920490656,.05926634878995668524] 
dist 236=[-.04285101491956745429,.05911293178372763887] 
dist 237=[-.05503200939695058132,.05893321617892981661] 
dist 238=[-.06467955297966115958,.05799351126245536523] 
dist 239=[-.07337868827158287521,.05757805115469137779] 
dist 240=[-.08079233082039976410,.05674565903492589213] 
dist 241=[-.08531061798570278918,.05639780334751451247] 
dist 242=[-.09064197829446624194,.05449496976347640748] 
dist 243=[-.09376699950330992065,.05401536928992530987] 
dist 244=[-.09564243154839629245,.05227478486685557125] 
dist 245=[-.09630110309587242221,.05201905552739964207] 
dist 246=[-.09647382537663943880,.04706803453160528454] 
dist 247=[-.09641019105440981976,.04614721461088452285] 
dist 248=[-.09616190576289449432,.04377341508824297301] 
dist 249=[-.09442788101882421522,.04316102461773901510] 
dist 250=[-.08157057646589333991,.03885501618360966916] 
dist 251=[-.07283462015920985958,.03791178665390328005] 
dist 252=[-.07154592299054433823,.03628901790044801529]