8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 1, 2, 2, 1, 2] 
dist 0=[110.78613535004552095   ,110.78613535004552095   ] 
dist 1=[107.25796045739744083   ,112.30932777242486933   ] 
dist 2=[103.20241119230403396   ,112.83163452405621414   ] 
dist 3=[99.574686033340224438  ,112.63270722044699956   ] 
dist 4=[95.604766381718892134  ,110.97238499701288578   ] 
dist 5=[90.176053835525165724  ,108.36674299913630046   ] 
dist 6=[84.262378923062622295  ,106.53065396650349034   ] 
dist 7=[78.352433762631243192  ,105.72788391972131646   ] 
dist 8=[71.329047893879667407  ,101.79390638334993115   ] 
dist 9=[60.966122846544376831  ,80.444095553872818546  ] 
dist 10=[50.460669012665397566  ,69.813706698522524392  ] 
dist 11=[42.869119132223987367  ,68.397740416858979157  ] 
dist 12=[35.973143253524886015  ,53.184592896031430858  ] 
dist 13=[28.251146869131605921  ,50.235231425017589860  ] 
dist 14=[20.022317456588684037  ,45.237254535550826706  ] 
dist 15=[11.304748653132474416  ,44.216674801903254203  ] 
dist 16=[-.25883254140846820967,19.932060352643918109  ] 
dist 17=[-11.217347021729017612  ,19.022848355037691218  ] 
dist 18=[-17.533927151717520005  ,6.5088887657465241603 ] 
dist 19=[-21.682195479533361178  ,4.7367160281791596028 ] 
dist 20=[-24.005868967728026877  ,1.3515025960362297291 ] 
dist 21=[-25.480390328400789747  ,.55897979463428126496] 
dist 22=[-26.583541464848041942  ,-1.7549217499605095442 ] 
dist 23=[-27.810049266334413578  ,-2.1407431711965706066 ] 
dist 24=[-28.360867070317661752  ,-1.9791591643714065010 ] 
dist 25=[-28.469316164372708369  ,-1.0469925819081086281 ] 
dist 26=[-17.125206250134315071  ,.01370755341327246985] 
dist 27=[-17.045916877677395347  ,.68850993072097824505] 
dist 28=[-14.092299030887968225  ,1.1969298939788418542 ] 
dist 29=[-13.376832873054291373  ,2.4673173318219348002 ] 
dist 30=[-12.854000920134166624  ,4.9502660750065766716 ] 
dist 31=[-12.715207323090679798  ,7.1537120933287050873 ] 
dist 32=[-2.3141360498338274286 ,9.4946726939387591102 ] 
dist 33=[-1.0940106872063684091 ,11.543347914277362465  ] 
dist 34=[.54952441097025836051,12.589092715015358515  ] 
dist 35=[.19986728946167499921,13.113110426471931170  ] 
dist 36=[-.12750765455842438206,13.193854780293382457  ] 
dist 37=[-.49464238954062434763,12.690229926646513725  ] 
dist 38=[-.84555536096300544603,12.413132865668819864  ] 
dist 39=[-1.1092906142646476064 ,11.986785504185302108  ] 
dist 40=[-1.3528172951932151227 ,11.770986281945490591  ] 
dist 41=[-1.6243672721110952833 ,8.0090186050567829408 ] 
dist 42=[-2.5406768133799602018 ,7.8073206249352087936 ] 
dist 43=[-4.5684655277907047065 ,7.6906335318752088920 ] 
dist 44=[-6.4626274538739455121 ,6.6288173353604848442 ] 
dist 45=[-8.0714299574082731102 ,6.3506899422265737894 ] 
dist 46=[-8.9668543925242641223 ,5.9211091885421891360 ] 
dist 47=[-9.4891916880999706031 ,5.7667414712642364872 ] 
dist 48=[-9.6202867601261764139 ,2.2287275681550338863 ] 
dist 49=[-3.0088841352911947053 ,1.7654857638058833228 ] 
dist 50=[-3.3553172316942160580 ,.8554606844024041859 ] 
dist 51=[-4.3781263695504869067 ,1.1351277668228527558 ] 
dist 52=[-5.2385523761597760797 ,1.3674664916521238922 ] 
dist 53=[-5.7102528302459371998 ,1.5877563942251034792 ] 
dist 54=[-5.9786542657227149351 ,1.7769313637723192327 ] 
dist 55=[-6.0319071673820255472 ,1.8957424663144760515 ] 
dist 56=[-2.8682016357251369143 ,1.9759145158743231097 ] 
dist 57=[-1.7133366879084146578 ,1.9879508900955013874 ] 
dist 58=[-1.6570803578769198478 ,.13048082856749353729] 
dist 59=[-1.6489481157080483751 ,.56107355804976862631] 
dist 60=[-1.3468722755432398729 ,1.0168239472433721159 ] 
dist 61=[-1.2740364328186195614 ,1.4194404212083063377 ] 
dist 62=[-1.2235246698522452104 ,1.6742812757429160804 ] 
dist 63=[-1.2120805592959392233 ,1.8646099745670532412 ] 
dist 64=[-.14739274236694390887,2.0114717198387306588 ] 
dist 65=[-.02318646445911956394,2.1146546657444654500 ] 
dist 66=[.05987774347170421566,2.1351736942040187415 ] 
dist 67=[.02710016725469896975,2.1185650773512898706 ] 
dist 68=[-.00202818696353689151,2.1018091246575597670 ] 
dist 69=[-.03271387085351814005,1.8107910721788079776 ] 
dist 70=[-.06111842256155488085,1.7318643330753019055 ] 
dist 71=[-.08122708085371484054,1.6467218336691055081 ] 
dist 72=[-.09866155149453920925,1.6006843849564082263 ] 
dist 73=[-.24576060103305532391,.83731564594070431246] 
dist 74=[-.52995463800289707483,.81148006129670544264] 
dist 75=[-.76447157759086207431,.79895853420832986967] 
dist 76=[-.98652612583364098289,.68259172691612775546] 
dist 77=[-1.2104908354029763388 ,.65270000608985958024] 
dist 78=[-1.3294787436649064632 ,.60764323670136648425] 
dist 79=[-1.3948178457930050995 ,.59122468626383086067] 
dist 80=[-1.4072348511080538755 ,.19787608541569786685] 
dist 81=[-.45123870487599427269,.14553031764252748604] 
dist 82=[-.45970327490581109029,.03274286856283111573] 
dist 83=[-.46305219374046110019,.05662330442877028669] 
dist 84=[-.55330003173004450166,.07632863974230022445] 
dist 85=[-.60324528672767463474,.09483487788267281158] 
dist 86=[-.63230458804587470003,.11112711432542395421] 
dist 87=[-.63962322445207326019,.12092706386327397256] 
dist 88=[-.36465309602131429438,.12637867693607263931] 
dist 89=[-.19366215242152351633,.12723094739281343344] 
dist 90=[-.18652407919436024479,.01591412862265883479] 
dist 91=[-.18511800575061281918,.07401150302000257330] 
dist 92=[-.15146326285884735172,.13134580495319987694] 
dist 93=[-.14334592753908332462,.18124307944575769648] 
dist 94=[-.13656675338588191832,.21161746133569140296] 
dist 95=[-.13411175739393181187,.23292831498110725264] 
dist 96=[-.07842783155294894088,.24686512359539734814] 
dist 97=[-.10579848590831660648,.25557361719957128439] 
dist 98=[-.13342149193455782586,.256591470553569159  ] 
dist 99=[-.1521448037334404517 ,.25355053331006007759] 
dist 100=[-.16754900340860336371,.24976681853081986813] 
dist 101=[-.1820001016597265122 ,.22047490617557193111] 
dist 102=[-.19437460714878054601,.21218332184838652265] 
dist 103=[-.20153762605473650796,.19804972030512746101] 
dist 104=[-.2061139157140721204 ,.19327220669446350934] 
dist 105=[-.2082225232230679599 ,.10573461825999288637] 
dist 106=[-.20852760940460946646,.10132995011808972065] 
dist 107=[-.20650384908215807839,.10031870513345023837] 
dist 108=[-.20154111221857586536,.08192333838717800414] 
dist 109=[-.19853446873363550449,.07750519371530448488] 
dist 110=[-.1795406672948527704 ,.07325411035478544949] 
dist 111=[-.17453750504018413067,.07137649481813205028] 
dist 112=[-.14994743397327794118,.01799748754113273751] 
dist 113=[-.05037486767320524651,.02175582081549160103] 
dist 114=[-.05084031368826050671,.02559811941697987543] 
dist 115=[-.05058810195718994341,.02826912182667226144] 
dist 116=[-.05388756223740672011,.03053611104784351459] 
dist 117=[-.05895985875364812632,.03277620527669533150] 
dist 118=[-.06201871117626180697,.03498538028635759787] 
dist 119=[-.06276399676000887284,.03721156676247877503] 
dist 120=[-.02432215483049036710,.03828034158280168676] 
dist 121=[-.02424117278197452215,.03842391328057730749] 
dist 122=[-.02322074935539717890,-.00309164160270749202] 
dist 123=[-.02307303053999549029,-.00292771277835534275] 
dist 124=[-.01857312902341349093,-.00271854796440298691] 
dist 125=[-.01750887091249449312,-.00239791815774167531] 
dist 126=[-.01673823704215369867,-.00203728584333466881] 
dist 127=[-.01656646981930812730,-.00166919056539195777] 
dist 128=[-.00181489724217084559,-.00123169190536689366] 
dist 129=[-.00178972057683198323,.00211506775423329786] 
dist 130=[3.54307724289360871010e-05,.00498532027570244618] 
dist 131=[.00024732022162203055,.00763803091758027849] 
dist 132=[.00072814193392208763,.00988750293690196530] 
dist 133=[.00080234256460378982,.01115669123613641167] 
dist 134=[.00132182819377830726,.01192790697186955572] 
dist 135=[.00139981080770232046,.01220019014926726893] 
dist 136=[.00150499713570821717,.01221985944443522525] 
dist 137=[.00148884507602584010,.01214517382012856886] 
dist 138=[.00143988804487905711,.01170327804450231297] 
dist 139=[.00136854879857114373,.01151278924337131058] 
dist 140=[.00126847548531678257,.00976062642032870708] 
dist 141=[.00110537128766843635,.00931831518833307983] 
dist 142=[.00091789700947892679,.00865071128170079507] 
dist 143=[.00072101508076132662,.00841062900007534232] 
dist 144=[-.00155770569849515088,.00273123021705924626] 
dist 145=[-.00362643703323833528,.00197927979752224493] 
dist 146=[-.00530555797501142626,.00030230814356214901] 
dist 147=[-.00684675670441147615,.00016109583903284723] 
dist 148=[-.00814615568063383761,-2.76872572078743598490e-05] 
dist 149=[-.00886514001937815946,-6.98525634161401973990e-05] 
dist 150=[-.00928344213709569498,-.00026127141185287261] 
dist 151=[-.00938888597446496490,-.00029566561277378564] 
dist 152=[-.00286150387511392476,-.00033874354527212473] 
dist 153=[-.00284855850982175250,-.00033727877056841845] 
dist 154=[-.00272163360974723756,-.00032523352602812882] 
dist 155=[-.00270281294584227413,-.00030950548534493282] 
dist 156=[-.00217035266541181666,-.00028835627409483870] 
dist 157=[-.00205387787350340762,-.00025477623917796213] 
dist 158=[-.00194917549584873193,-.00021652948209503082] 
dist 159=[-.00192735505472349410,-.00017684279179498458] 
dist 160=[-.00035503043366146503,5.97920583698669382860e-05] 
dist 161=[-.00019431069293555297,.00049309398444521714] 
dist 162=[-8.87189746975186511380e-06,.00084556573660945420] 
dist 163=[1.31596812825536959610e-05,.00117042343139496777] 
dist 164=[6.30712374832905983420e-05,.00144528948129333756] 
dist 165=[7.12236982739827228300e-05,.00159925871503188491] 
dist 166=[.00012525711380330270,.00169136081446141340] 
dist 167=[.00013355591830782925,.00172057123519014908] 
dist 168=[.00014517952380436880,.00171627958608981088] 
dist 169=[.00014426610527994529,.00170500332711563520] 
dist 170=[.00014004288068241220,.00163063104622104489] 
dist 171=[.00013352479402688658,.00161128129192353739] 
dist 172=[.00012419807729640221,.00132096664839068178] 
dist 173=[.00010881882354496076,.00125112010982915039] 
dist 174=[9.10748791180893728170e-05,.00117580324532167494] 
dist 175=[1.42415024517560000000e-05,.00113813031233168127] 
dist 176=[-.00029535460337185327,.00040738110072042246] 
dist 177=[-.00050285786398944656,.00035018829334020263] 
dist 178=[-.00067142066186540983,.00022863303457824285] 
dist 179=[-.00082639154762355470,.00019566632289594548] 
dist 180=[-.00095724358711685817,7.22764532519211311860e-05] 
dist 181=[-.00103003472798333819,4.62711409052576179600e-05] 
dist 182=[-.00107290796849867987,9.93139584609306952350e-06] 
dist 183=[-.00108496123068913450,0                     ] 
dist 184=[-.00036110377731536402,-3.93942902705624973890e-05] 
dist 185=[-.00035923043083711842,-3.93395546083969424280e-05] 
dist 186=[-.00034269461594624483,-3.81742250365905379100e-05] 
dist 187=[-.00034025296341718795,-3.65070414539085580520e-05] 
dist 188=[-.00027233136550293740,-3.41835852621209742730e-05] 
dist 189=[-.00025639623769508170,-3.04116498738515864030e-05] 
dist 190=[-.00024449790218652827,-2.60829816052975706500e-05] 
dist 191=[-.00024175116915190516,-2.03342043779165889660e-05] 
dist 192=[-2.88054792266850859360e-05,-1.25997106997801702300e-05] 
dist 193=[-2.79391635155004916960e-05,3.55862130444368264020e-05] 
dist 194=[-1.08382549971364503450e-05,7.80223822372161225930e-05] 
dist 195=[-8.41640092285505203550e-06,.00011710951265841818] 
dist 196=[-3.24625196209676935090e-06,.00015016695394770226] 
dist 197=[-1.88085793135509251150e-06,.00016866035803719922] 
dist 198=[3.07800978835254729460e-06,.00017969171632979836] 
dist 199=[4.08359010971424962860e-06,.00018311889605009862] 
dist 200=[5.17573923083301501880e-06,.00018278276581532443] 
dist 201=[5.10959289095393643050e-06,.00018148414596680327] 
dist 202=[4.72978369239080504240e-06,.00017434010342037421] 
dist 203=[4.18953697384825348560e-06,.00017154976229279515] 
dist 204=[3.43812335889422449980e-06,.00014441351687522182] 
dist 205=[2.21959098958870359830e-06,.00013765427601069108] 
dist 206=[8.21555919488637558350e-07,.00012786357996344179] 
dist 207=[-6.42824818687183336020e-07,.00012421430248672263] 
dist 208=[-2.27681177067749751460e-05,3.83113643518375980690e-05] 
dist 209=[-5.30854765089707309240e-05,2.72331533067445711610e-05] 
dist 210=[-7.76823811950052069670e-05,1.87660550628006440480e-05] 
dist 211=[-.00010024514324419418,1.71789328761598064170e-05] 
dist 212=[-.00011926152886435065,1.41443223923833036900e-05] 
dist 213=[-.00012977601291518603,1.33348520142498308830e-05] 
dist 214=[-.00013588425675082037,1.05230833208519885850e-05] 
dist 215=[-.00013740370054561544,9.74795871454544833370e-06] 
dist 216=[-4.62738367050738224310e-05,9.16681209074266638910e-06] 
dist 217=[-4.53821496157346420390e-05,9.09504141740608883970e-06] 
dist 218=[-4.06905237475051409240e-05,-4.27938016813492020940e-06] 
dist 219=[-4.02771109993308998020e-05,-4.09319689136266200170e-06] 
dist 220=[-3.27517125624099365750e-05,-3.81986454459118413640e-06] 
dist 221=[-3.09590354532469404340e-05,-3.36260537021879379060e-06] 
dist 222=[-2.92508722680946415860e-05,-2.83266183649650812070e-06] 
dist 223=[-2.85264263547326047780e-05,-2.17745655802449028310e-06] 
dist 224=[-1.28414795919867134710e-05,4.39626230253580282730e-07] 
dist 225=[-1.26506921557459461690e-05,6.89670620340837227970e-06] 
dist 226=[-1.22475267657978528720e-05,1.21890858778470757500e-05] 
dist 227=[-1.20528567694286260530e-05,1.70601060082173236180e-05] 
dist 228=[-1.18979126544428060610e-05,2.11774582979619041830e-05] 
dist 229=[-1.17603140508316824150e-05,2.34770782955650889200e-05] 
dist 230=[-1.16471149107274132180e-05,2.48439194744513491710e-05] 
dist 231=[-1.15891188925054328160e-05,2.52572858251863613250e-05] 
dist 232=[-1.15613638998003148390e-05,2.51616764068245955780e-05] 
dist 233=[-1.15683215142978532960e-05,2.45073766760817695640e-05] 
dist 234=[-1.15591002293807340560e-05,1.69259679142595189270e-05] 
dist 235=[-1.14671326787817821550e-05,1.67127345824032715270e-05] 
dist 236=[-1.12988871870314823100e-05,1.37597869096727076610e-05] 
dist 237=[-1.11575355692370374560e-05,1.30460780034285732870e-05] 
dist 238=[-1.06138827901005578520e-05,1.22355727286262893470e-05] 
dist 239=[-1.03986910735233248630e-05,1.18507620261022526070e-05] 
dist 240=[-9.80921625273897821180e-06,3.67008998310178170000e-06] 
dist 241=[-9.55446943511563043680e-06,3.60816421322769638090e-06] 
dist 242=[-8.17873813701617746290e-06,2.66292148732449001760e-06] 
dist 243=[-7.80618526279750409830e-06,2.47260625875855140600e-06] 
dist 244=[-7.26243916826958493890e-06,2.12113934543331870140e-06] 
dist 245=[-7.05970843672729802640e-06,2.02724897484197099640e-06] 
dist 246=[-6.57878346261526042980e-06,1.70709922125188234370e-06] 
dist 247=[-6.41159557619453053400e-06,1.61045381544745990300e-06] 
dist 248=[-6.29588501564214182440e-06,1.54858594735012528450e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[108.58489715743059684   ,108.58489715743059684   ] 
dist 1=[107.85206396108668832   ,109.21839260708524436   ] 
dist 2=[105.57876610998555976   ,109.47499257871986204   ] 
dist 3=[102.14643008121728931   ,109.35045232052965013   ] 
dist 4=[97.432166331243578863  ,107.36784867853254906   ] 
dist 5=[90.958874582932475992  ,106.42469048079992384   ] 
dist 6=[80.534447373426934456  ,105.08550610858563404   ] 
dist 7=[69.671330382606957238  ,104.39470313068282677   ] 
dist 8=[61.449268658624918982  ,83.197337239397517312  ] 
dist 9=[53.699997770477926384  ,80.143852416109700757  ] 
dist 10=[44.701425600811623005  ,76.719209350100519081  ] 
dist 11=[35.692170680392984293  ,75.883176122819415411  ] 
dist 12=[27.886477076214023398  ,59.797095225114289535  ] 
dist 13=[19.508000347271393295  ,57.404949570995949656  ] 
dist 14=[8.1957128668463443355 ,51.399561131571130939  ] 
dist 15=[-2.6275770465252876268 ,50.260615715737583781  ] 
dist 16=[-9.0657518673527938189 ,28.062908560059842479  ] 
dist 17=[-13.542131818434504912  ,25.045166153002013716  ] 
dist 18=[-16.551116408682919972  ,18.219496345538873979  ] 
dist 19=[-19.272432162187175384  ,16.806771978917204851  ] 
dist 20=[-25.850283971784166041  ,8.5403816992188019738 ] 
dist 21=[-30.208282106704176193  ,7.0953841145537526246 ] 
dist 22=[-33.949695955083443594  ,6.2097435872381495532 ] 
dist 23=[-37.297839797951394709  ,6.1441383403404371022 ] 
dist 24=[-39.762458491373055803  ,6.4070303185831102356 ] 
dist 25=[-40.572531169707996494  ,7.0969419816844312632 ] 
dist 26=[-40.718002700213986644  ,8.2097716612403255737 ] 
dist 27=[-38.586165224593492346  ,10.160333502302537336  ] 
dist 28=[-2.3424635181957005213 ,12.059444922045958753  ] 
dist 29=[-1.1807683129458351391 ,12.970814317008403725  ] 
dist 30=[-.95778228712339063689,13.420716006698494514  ] 
dist 31=[7.1326750151447752813 ,13.484821703484978439  ] 
dist 32=[7.7506606594946096431 ,12.543088582446227949  ] 
dist 33=[8.4310684808276760720 ,12.228827198694193455  ] 
dist 34=[8.1497642476320370474 ,11.984684314517671710  ] 
dist 35=[5.4099741983504975294 ,11.784588997448172333  ] 
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dist 164=[8.44810291521748654050e-05,.00222058388273697485] 
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dist 169=[-.00139024771657163304,1.83090696782018737060e-05] 
dist 170=[-.00148271658459172064,-5.28678391262068332660e-05] 
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dist 173=[-.00175281903234006555,-.00064492713393590206] 
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dist 183=[-5.33673142306124756100e-05,.00064569646683096503] 
dist 184=[-2.54720519284974299980e-06,.00077672974056372875] 
dist 185=[.00011533191864343238,.00084959862966840339] 
dist 186=[.00013298709823197993,.00089377650975953969] 
dist 187=[.00026943726596608883,.00090438597898302798] 
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dist 190=[.00032710428248398304,.00035121066914083343] 
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dist 193=[.00022116104028003786,.00034258794693065441] 
dist 194=[.00017101816306796493,.00033726070466995375] 
dist 195=[9.54805707884275553230e-05,.00028839739946899619] 
dist 196=[1.97527681821496490790e-05,.00027579176971040090] 
dist 197=[-3.11465997997341246330e-05,.00025669251109940752] 
dist 198=[-7.26420949162672193280e-05,.00024975243212968651] 
dist 199=[-.00011103141326838173,8.37978036438413596330e-05] 
dist 200=[-.00014360713607137924,6.17796496229100107100e-05] 
dist 201=[-.00016201952020091848,1.24769116902383496540e-05] 
dist 202=[-.00019915090451230751,1.75376760969748143410e-06] 
dist 203=[-.00023745188314941674,-5.20225825318554988460e-05] 
dist 204=[-.00025865294620818284,-6.13918317279268854980e-05] 
dist 205=[-.00027099721013201089,-7.69768569525549039100e-05] 
dist 206=[-.00027410570639330232,-8.00832669946931856220e-05] 
dist 207=[-.00016751210238496613,-8.14729693119529900080e-05] 
dist 208=[-.00014217524144901965,-7.98693311797907049810e-05] 
dist 209=[-.00013576096800907331,-7.62034757028111844890e-05] 
dist 210=[-.00012602871982315311,-6.67108610201728972740e-05] 
dist 211=[-.00012254208001291318,-2.17733480948269501080e-05] 
dist 212=[-6.15175667410134613460e-05,2.32108558147970570580e-05] 
dist 213=[-5.84566827556300572630e-05,5.33485244136124074480e-05] 
dist 214=[-5.78031805270283848480e-05,7.78135121116626971200e-05] 
dist 215=[-1.16717757915163536110e-05,.00010027302284229714] 
dist 216=[-6.09371535095480591080e-06,.00011921048076613947] 
dist 217=[6.77311815105410017690e-06,.00012969026669434200] 
dist 218=[8.93526077526213436190e-06,.00013579102516177269] 
dist 219=[2.38559046838371849770e-05,.00013732839931226619] 
dist 220=[2.61521191395497486010e-05,4.69335891022041297140e-05] 
dist 221=[3.04349355046013323210e-05,4.98169658096980194780e-05] 
dist 222=[3.11710196070914555580e-05,5.09090358980537127310e-05] 
dist 223=[3.18246394755137598020e-05,5.10032002110159049410e-05] 
dist 224=[2.83388954969562720030e-05,5.07388942478555394450e-05] 
dist 225=[2.31817680129982403160e-05,4.86811830108361463780e-05] 
dist 226=[1.67707854305636625240e-05,4.81224830222580092870e-05] 
dist 227=[7.13733233633598180160e-06,3.96218615122538420880e-05] 
dist 228=[-2.51263851472738895010e-06,3.75585541670069427870e-05] 
dist 229=[-8.98931358971091671730e-06,3.53406951003552577520e-05] 
dist 230=[-1.42598026312060583870e-05,3.42205087291372004290e-05] 
dist 231=[-1.91203614774789151940e-05,1.26211625756761722120e-05] 
dist 232=[-2.32345985365406496360e-05,1.09219447256428465280e-05] 
dist 233=[-2.55416615090431062140e-05,7.27827410274629075630e-06] 
dist 234=[-2.69246120404542031360e-05,6.27947760641033581540e-06] 
dist 235=[-2.83702621509816226540e-05,2.47784323123106632890e-06] 
dist 236=[-3.05757700063937706020e-05,1.68802105862194166040e-06] 
dist 237=[-3.19839204376073697720e-05,4.44142661414427685640e-07] 
dist 238=[-3.23285229219611775630e-05,1.28188411644782314360e-07] 
dist 239=[-2.56305209083426230260e-05,-5.46984277259870540370e-06] 
dist 240=[-2.12531133525272999950e-05,-5.11960615656055115410e-06] 
dist 241=[-2.01843473926078407560e-05,-4.40741450260868355830e-06] 
dist 242=[-1.88626763856971371930e-05,-2.07917188002660683300e-06] 
dist 243=[-1.82859715744431134740e-05,2.45496504615941702530e-06] 
dist 244=[-8.73524781464545121700e-06,6.99655077231390088120e-06] 
dist 245=[-8.25709703887604678840e-06,1.00447915936472494910e-05] 
dist 246=[-6.04608994092109503340e-06,1.25256000402499586490e-05] 
dist 247=[-2.89039672443099529240e-06,1.48140490233714085900e-05] 
dist 248=[-1.07624591948806486250e-06,1.67516516326683522880e-05] 
dist 249=[-6.94287886588578810030e-07,1.78393349639858390950e-05] 
dist 250=[-1.53319249591104869870e-07,1.85408105789049933810e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 2, 1, 0, 2] 
dist 0=[147.14852461560714824   ,147.14852461560714824   ] 
dist 1=[145.67008736083564331   ,147.54860771854374306   ] 
dist 2=[140.21323577270847270   ,147.82092012040046020   ] 
dist 3=[132.79229516564871255   ,147.47825914324627140   ] 
dist 4=[123.66878299879439992   ,136.57680705434208383   ] 
dist 5=[111.72785736589026843   ,134.21769668004147551   ] 
dist 6=[93.105329602840189022  ,128.51967017550513375   ] 
dist 7=[74.105376232805883827  ,126.52218718486614632   ] 
dist 8=[60.658033612875103411  ,102.15768259989899348   ] 
dist 9=[48.912222696254004114  ,97.272758130003551201  ] 
dist 10=[36.660025356115569081  ,93.129703722659001428  ] 
dist 11=[25.207188999175535121  ,92.296833082888661296  ] 
dist 12=[16.624651302322914253  ,32.523744599770696281  ] 
dist 13=[8.5688880399414849876 ,29.851032572281332669  ] 
dist 14=[-.81564010729312727413,26.121562987913260468  ] 
dist 15=[-9.4324087381126365698 ,25.240949044300906115  ] 
dist 16=[-16.341733706020664489  ,-12.081645650659291140  ] 
dist 17=[-22.588961282704389222  ,-15.583388318044677232  ] 
dist 18=[-27.314281789980535683  ,-17.617491340832478551  ] 
dist 19=[-31.150715770043971834  ,-17.809182755629658119  ] 
dist 20=[-34.067289270541044233  ,-16.182296563773454225  ] 
dist 21=[-35.138099538545847814  ,-13.219355467305360253  ] 
dist 22=[-35.405640995763625274  ,-7.8304327035168379494 ] 
dist 23=[-35.113404896968331809  ,-2.2074111575496820226 ] 
dist 24=[-31.728724340377335700  ,1.6900395187217121881 ] 
dist 25=[-30.666525144900529780  ,4.9443209741876495285 ] 
dist 26=[-29.122314546459917120  ,8.0261261287691762970 ] 
dist 27=[-28.466682073618813842  ,10.648188590509544176  ] 
dist 28=[-11.405583633071291364  ,12.083473859722309021  ] 
dist 29=[-9.1305279296459111828 ,12.881942373905247325  ] 
dist 30=[-3.9050444207956395558 ,13.024008962144872104  ] 
dist 31=[-2.8414456131091432446 ,17.183628914850662316  ] 
dist 32=[3.3007377002334083148 ,21.154043022468019901  ] 
dist 33=[4.2800154724500153950 ,23.355362393678084509  ] 
dist 34=[4.3835758035934070748 ,24.637636093942026059  ] 
dist 35=[4.3286944697866685721 ,24.960731159543193519  ] 
dist 36=[4.0045233899067735906 ,7.8721761704191402800 ] 
dist 37=[3.4440216513260395654 ,8.0349630277038832918 ] 
dist 38=[2.4392369763112435044 ,8.0540368536369118283 ] 
dist 39=[1.3858039288465019122 ,8.0430077307369929354 ] 
dist 40=[.63168821943215802528,6.9634714359216013655 ] 
dist 41=[-.02715669120746161092,6.6684269191162618454 ] 
dist 42=[-.70394257183881290571,6.4668454138564406318 ] 
dist 43=[-1.3203251348251401677 ,6.3732290385364770151 ] 
dist 44=[-1.9608436464387783206 ,1.5097403060846607587 ] 
dist 45=[-2.5168123963642933243 ,.92662012576663176638] 
dist 46=[-2.9607475515552949028 ,-.45354175572235802828] 
dist 47=[-3.3559758685245393492 ,-.6559074603575365602 ] 
dist 48=[-3.6671341869551213199 ,-2.0162071704962189209 ] 
dist 49=[-3.7776961855933456841 ,-2.0814405030412896738 ] 
dist 50=[-4.0659649147216611174 ,-1.9824473309994478217 ] 
dist 51=[-4.2860003880055505028 ,-1.8147716199301019357 ] 
dist 52=[-4.4099192097146126816 ,-1.5700419167986313184 ] 
dist 53=[-4.4253764612435058412 ,-1.2289011648443419406 ] 
dist 54=[-4.3194493029348005231 ,-.67861189342630322904] 
dist 55=[-4.2875104379157246863 ,-.11760853304819405977] 
dist 56=[-3.5837497420142248911 ,.2661529584305181319 ] 
dist 57=[-3.4063578655139988243 ,.63941805427666259337] 
dist 58=[-3.2441035659407317618 ,1.1443579258976327522 ] 
dist 59=[-3.1652111523924246010 ,1.6357876690807402014 ] 
dist 60=[-.90686913417698472918,2.0490397037931323430 ] 
dist 61=[-.66849440461215433738,2.2728400741747758969 ] 
dist 62=[-.12248285564546213685,2.3967261661146103415 ] 
dist 63=[-.01619227018723331921,2.4241824669151062578 ] 
dist 64=[.61587374203982260333,2.1901523826584323294 ] 
dist 65=[.71030356181729261295,2.4305755006121696970 ] 
dist 66=[.67786748242502497332,2.5662941619760018312 ] 
dist 67=[.62661434971724955724,2.5982901392839654908 ] 
dist 68=[.55479434474025102717,1.0260714683842441791 ] 
dist 69=[.45598485961560307012,1.0327378640319544859 ] 
dist 70=[.29759340329799802677,1.0112804247199629784 ] 
dist 71=[.1359551583341218898 ,1.0081459268925164516 ] 
dist 72=[.02423207636943237604,.83745047500886329471] 
dist 73=[-.06987557073712699355,.79485804350234637589] 
dist 74=[-.16165831492541253293,.76760520882257481825] 
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dist 159=[2.48592142626225895260e-05,.00644593649390114362] 
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dist 168=[7.19809606511752539050e-05,.00146353082905137230] 
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dist 190=[1.79432094339199006170e-05,.00062992356993058193] 
dist 191=[4.23286271550572392050e-05,.00063779767614593674] 
dist 192=[.00017816198660517393,.00051913959085904633] 
dist 193=[.00020076863150396166,.00056808107843232751] 
dist 194=[.00023872102630581326,.00059739215045339369] 
dist 195=[.00022122212442879445,.00060483897830340901] 
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dist 199=[6.72416721562719197410e-05,.00023345799657010623] 
dist 200=[9.21316087849653550370e-06,.00018933024887407752] 
dist 201=[-2.98318422795136811470e-05,.00017881801411795226] 
dist 202=[-6.17038667703021751730e-05,.00016987587371405118] 
dist 203=[-9.12529928454966205280e-05,.00016671531877051357] 
dist 204=[-.00011636697373738111,2.08899094167909230980e-05] 
dist 205=[-.00013062983427723084,3.48273786675511501020e-06] 
dist 206=[-.00013941344811527176,-3.68370987686647974140e-05] 
dist 207=[-.00014277290809284978,-4.30271252511261283760e-05] 
dist 208=[-.00014315797327732930,-8.98107815133130008980e-05] 
dist 209=[-.00014249022654463182,-9.67660115747312591980e-05] 
dist 210=[-.00013666109451622417,-.00010952189710274226] 
dist 211=[-.00013659584691567897,-9.92220032987929104120e-05] 
dist 212=[-.00013627785469529825,-8.49490720745972480140e-05] 
dist 213=[-.00013544038556227175,-6.91008105594164508970e-05] 
dist 214=[-.00012930161408944743,-4.93800406163577795710e-05] 
dist 215=[-.00012803829597904000,-1.97302212570797661880e-05] 
dist 216=[-.00010365422289956926,9.96734519330609727220e-06] 
dist 217=[-9.78660627543681945260e-05,2.98780043341157385550e-05] 
dist 218=[-9.25436624444255143310e-05,4.60539251161401957870e-05] 
dist 219=[-9.04319210283449955770e-05,6.09225088171212580940e-05] 
dist 220=[-1.94954465412185460100e-05,7.34701339504233154660e-05] 
dist 221=[-1.22283198142975890440e-05,8.04304993984557490570e-05] 
dist 222=[4.19970265594612240930e-06,8.45157582333876162540e-05] 
dist 223=[7.38732157621966579950e-06,8.55796929586252946430e-05] 
dist 224=[2.55457643499705316090e-05,6.71981276928063955060e-05] 
dist 225=[2.85381108411815498980e-05,7.36029791916098269290e-05] 
dist 226=[3.24430154524524138080e-05,7.74832311598295895390e-05] 
dist 227=[2.83217438527325739930e-05,7.84369532937319805700e-05] 
dist 228=[2.33689624426329830300e-05,3.44936385279713504940e-05] 
dist 229=[1.78900783402232326690e-05,3.42216422565464470150e-05] 
dist 230=[1.10850301751980029380e-05,3.32447295836054104630e-05] 
dist 231=[8.66191884243579071460e-07,3.26559151252896463150e-05] 
dist 232=[-9.36683326886645478710e-06,2.89409680537242231350e-05] 
dist 233=[-1.62282999989187945730e-05,2.79601515834688495580e-05] 
dist 234=[-2.18045262718887849180e-05,2.56341489946772772010e-05] 
dist 235=[-2.69342393369212457950e-05,2.47906202575796585920e-05] 
dist 236=[-3.12670025646953355560e-05,1.33954222853999186380e-05] 
dist 237=[-3.36787629843142102100e-05,1.16050609862172228650e-05] 
dist 238=[-3.51009005860486767760e-05,7.83965837984555392920e-06] 
dist 239=[-3.55041369222233345680e-05,6.82132149791703042700e-06] 
dist 240=[-3.53801323081123770940e-05,3.04253033028378374240e-06] 
dist 241=[-3.50565016820485336240e-05,2.22493303732802226560e-06] 
dist 242=[-3.38615845874786777640e-05,1.16188868475714408040e-06] 
dist 243=[-3.13506290757479515170e-05,9.01704510436438223830e-07] 
dist 244=[-9.64612123534539508520e-07,8.00441949903501000170e-07] 
dist 245=[-9.60118503989561596220e-07,7.59776618978086615560e-07] 
dist 246=[-9.34574589733288706020e-07,6.54023467475650177540e-07] 
dist 247=[-9.17570216726931982150e-07,6.23668191059646128560e-07] 
dist 248=[-6.66336824556955787390e-07,4.33121599181139508440e-07] 
dist 249=[-6.25345972685452595210e-07,3.92662596377261596230e-07] 
dist 250=[-5.15014320144225012170e-07,3.12549014355988705920e-07] 
dist 251=[-4.94942674710342525570e-07,2.90176129007831982290e-07] 
dist 252=[-3.01497349589965949570e-07,-4.14807463516442125870e-08] 
dist 253=[-2.63970215108366430240e-07,-9.07899193830474048580e-08] 
dist 254=[-2.09987609817904050430e-07,-1.17665322186237211780e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 1, 2, 0, 1] 
dist 0=[119.07778825025642420   ,119.07778825025642420   ] 
dist 1=[117.64268715711492759   ,120.09487089380549626   ] 
dist 2=[115.31689221947048961   ,120.75017900938865252   ] 
dist 3=[111.98030954112173330   ,120.99140977154651530   ] 
dist 4=[104.52575768415336035   ,120.53551824370791099   ] 
dist 5=[96.148837154162075631  ,119.25285253265720441   ] 
dist 6=[85.309554305203298308  ,118.43031086937906140   ] 
dist 7=[71.480921382589785887  ,98.163389554438456604  ] 
dist 8=[61.275426429519975601  ,95.060175584769058150  ] 
dist 9=[51.919393439018347315  ,86.170361884493987634  ] 
dist 10=[41.451075146602360414  ,84.794726866603701549  ] 
dist 11=[31.206112624563843834  ,66.883933671801426033  ] 
dist 12=[22.723052111811337019  ,65.716062923271309287  ] 
dist 13=[13.959054252895017711  ,59.383710783617911621  ] 
dist 14=[2.5700536577639586724 ,58.414666141604864139  ] 
dist 15=[-8.1871936780296581933 ,18.994466761443081369  ] 
dist 16=[-14.443996196806847059  ,17.180752541989303250  ] 
dist 17=[-18.623109787286610388  ,9.5127854087832781552 ] 
dist 18=[-21.105881161897724066  ,8.1296439454161519228 ] 
dist 19=[-22.756630383499689313  ,5.5054674832480014984 ] 
dist 20=[-23.615400510423331937  ,4.8970661456955104767 ] 
dist 21=[-24.094436717538572728  ,3.0818997695881922700 ] 
dist 22=[-25.628285050395412859  ,2.7825162088330678638 ] 
dist 23=[-27.690114870621648992  ,2.8694359617313427333 ] 
dist 24=[-28.781629639597056222  ,3.4517520849706817772 ] 
dist 25=[-29.240941150815853550  ,4.2593185378703529846 ] 
dist 26=[-29.330576090281262969  ,5.2484130316406199411 ] 
dist 27=[-26.877000783343896811  ,6.5326888010467067333 ] 
dist 28=[-24.263881751495078891  ,8.5206904491685598295 ] 
dist 29=[-21.109854127429381445  ,10.421191622125316451  ] 
dist 30=[-20.863779345026798475  ,11.360864314749126222  ] 
dist 31=[-4.4960805030108198572 ,11.847110138966991708  ] 
dist 32=[-2.5582733741279709248 ,11.944417909228796250  ] 
dist 33=[1.9731539227609089232 ,11.867900477257330295  ] 
dist 34=[2.6526285801172124962 ,11.958768161242392612  ] 
dist 35=[7.9861590569374600246 ,11.566439668532627098  ] 
dist 36=[5.2780966298874961964 ,11.325209555275328909  ] 
dist 37=[2.4907592564812490475 ,12.372565862524161324  ] 
dist 38=[.54096512486516027492,13.029006508231707149  ] 
dist 39=[-1.1229582294595564075 ,13.399491084816786123  ] 
dist 40=[-2.7776036196110692737 ,13.426883290350128058  ] 
dist 41=[-4.2551839493425627689 ,13.189112770217933074  ] 
dist 42=[-5.8254059211569396932 ,12.997200621051545381  ] 
dist 43=[-7.2935525967392078907 ,11.338456288662504228  ] 
dist 44=[-8.1101966269662931010 ,10.888077427918327326  ] 
dist 45=[-8.5869171345394152624 ,10.167342658205419998  ] 
dist 46=[-8.7071344092145628849 ,9.9125545078188011418 ] 
dist 47=[-7.3479884911301420787 ,4.2734069925365907499 ] 
dist 48=[-7.3106769724826516809 ,3.5624576021172477355 ] 
dist 49=[-6.8292766777102730132 ,1.9678557906547049490 ] 
dist 50=[-7.5500391155328244007 ,1.5814451202550575101 ] 
dist 51=[-9.0290031623989533776 ,-.2239093177552182854 ] 
dist 52=[-9.8393317877689630775 ,.14281050022204179048] 
dist 53=[-10.299418271110167860  ,2.1537192469758448918 ] 
dist 54=[-10.387926877584239225  ,3.5100198297724606100 ] 
dist 55=[-3.1385442784476004224 ,4.6177188221311915021 ] 
dist 56=[-2.9682961199386551689 ,5.6422269682815373848 ] 
dist 57=[-2.6877743976534441924 ,6.5086605889367471114 ] 
dist 58=[-2.6771443505149290086 ,6.9891130308815647026 ] 
dist 59=[-2.2156586038913495177 ,7.2690445329100318154 ] 
dist 60=[-2.1016604312106664232 ,7.3397644510688251670 ] 
dist 61=[-2.0242934309444072545 ,1.5308448738360477872 ] 
dist 62=[-2.0040178822466378348 ,1.6682151569290478619 ] 
dist 63=[-.28887446835198999616,1.7667091206010865611 ] 
dist 64=[-.08778555471976366995,1.7886537419429407908 ] 
dist 65=[.37985429507519931658,1.7798363374274463200 ] 
dist 66=[.44994387011082157065,1.7711970032984325950 ] 
dist 67=[.99575049927297842179,1.5161640631276236670 ] 
dist 68=[.97224222615278495141,1.4476290387097718947 ] 
dist 69=[.72870109389060465074,1.3886463695874998793 ] 
dist 70=[.34916969834683320843,1.3731275464174455408 ] 
dist 71=[-.03448659748768103142,1.3938032765073626669 ] 
dist 72=[-.29443393340781194783,1.3915033037868189272 ] 
dist 73=[-.50795286541179413981,1.3522663103583598509 ] 
dist 74=[-.70939106410922881562,1.3337004952681141193 ] 
dist 75=[-.89428133827149904788,1.1369102229776421151 ] 
dist 76=[-.9944577935239405653 ,1.0862938065963239444 ] 
dist 77=[-1.0508091890444232338 ,1.0162780573241015495 ] 
dist 78=[-1.0632178282319836342 ,.98823580633734398595] 
dist 79=[-.46558102085391867532,.32118183519088911128] 
dist 80=[-.47403938733632413437,.23567578276198932026] 
dist 81=[-.5572241858564704065 ,.04315858484372398686] 
dist 82=[-.73047334647261832351,.00260602268373093824] 
dist 83=[-.87723944951650780928,-.21028178724429306191] 
dist 84=[-.95915813585502219466,-.24669664358978810507] 
dist 85=[-1.0065772173880987876 ,-.22620932761552062606] 
dist 86=[-1.0179259776663223867 ,-.10338237809735532421] 
dist 87=[-.36867279988283726492,.02067789103763967810] 
dist 88=[-.36664554980743479777,.10496642947486955114] 
dist 89=[-.35801387178739282737,.1745367515906214968 ] 
dist 90=[-.35208621351484315707,.24018869274259808572] 
dist 91=[-.31327311851766875629,.29668670705981386307] 
dist 92=[-.30283083171806859966,.32992934783078971425] 
dist 93=[-.27792961050206765341,.35185967067062307929] 
dist 94=[-.26880329312439980122,.36346380427068110474] 
dist 95=[-.14392644449980314166,.368813653817378733  ] 
dist 96=[-.12432370152656679062,.36750807319534874478] 
dist 97=[-.08281726858664952823,.35959564609729335846] 
dist 98=[-.07151595431112594458,.35359398353410923964] 
dist 99=[-.02909662733055077767,.31331229970822000882] 
dist 100=[-.02003352908118618731,.3023458303195359049 ] 
dist 101=[-.00713976793929993767,.25997846681176568582] 
dist 102=[-.00339838406566887298,.20596855562514745747] 
dist 103=[-.02306511417294856635,.20602365611544214015] 
dist 104=[-.06393910414119247966,.20484909301664939529] 
dist 105=[-.09723307152154598607,.1960933367494493429 ] 
dist 106=[-.12792791248192905527,.19386571170259575345] 
dist 107=[-.15385352517458307799,.1583881020536529123 ] 
dist 108=[-.16821688472475131915,.14984077540579882998] 
dist 109=[-.17657968513319805232,.14091994548045855819] 
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dist 177=[-.00100651796796552348,-3.04786845074142337690e-05] 
dist 178=[-.00132222410750289424,-.00010448534758228082] 
dist 179=[-.00158870853464469353,-.00050787425932841886] 
dist 180=[-.00173671321494784403,-.00053270420571185925] 
dist 181=[-.00182493089032066504,-.00039914446313700572] 
dist 182=[-.00184716215114090583,-.00019703108615039734] 
dist 183=[-.00071510813537139499,5.85557692459953216000e-06] 
dist 184=[-.00071216014695371983,.00014249054253495466] 
dist 185=[-.00068113779152589959,.00025413820779798670] 
dist 186=[-.00067647952362234531,.00035782025466301966] 
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dist 188=[-.00051242342237722768,.00049632260536396097] 
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dist 190=[-.00048352932373620573,.00053991334155782479] 
dist 191=[-4.13570802986606271950e-05,.00054170504357922699] 
dist 192=[1.02488030573413396120e-05,.00053915160265169543] 
dist 193=[.00013028345160970190,.00051782972163706152] 
dist 194=[.00014767030394258887,.00051196209504576466] 
dist 195=[.00022426432552812678,.00042208852986809388] 
dist 196=[.00017218378317774428,.00040021273065428636] 
dist 197=[.00010712450057317495,.00037674772067576718] 
dist 198=[9.04162932562180000000e-06,.00036499797612146742] 
dist 199=[-8.92886036309009498100e-05,.00036495748277210754] 
dist 200=[-.00015533159818000768,.00036259812810441070] 
dist 201=[-.00020910939237923468,.00034860995009820840] 
dist 202=[-.00025874187646726603,.00034325779707455776] 
dist 203=[-.00030076388293534580,.00028859188337095098] 
dist 204=[-.00032432489354349762,.00027497966467816020] 
dist 205=[-.00033972475763575203,.00025590691061074482] 
dist 206=[-.00034339597107791273,.00024853715316678588] 
dist 207=[-.00012515154326983264,7.97386898389628683790e-05] 
dist 208=[-.00012464255108806258,5.75850602178784640950e-05] 
dist 209=[-.00015735277382542107,8.20984546043597399310e-06] 
dist 210=[-.00020277328522533087,-2.60555600558233036100e-06] 
dist 211=[-.00024106590745369246,-5.56249808323901585770e-05] 
dist 212=[-.00026225329176499180,-6.49282353700901778500e-05] 
dist 213=[-.00027457975577768317,-4.97051058079952742010e-05] 
dist 214=[-.00027768692332426839,-1.81073207939222741390e-05] 
dist 215=[-9.69555561036903641010e-05,1.35572593050064688700e-05] 
dist 216=[-9.61657529265510877810e-05,3.48170844084362165770e-05] 
dist 217=[-9.31701066493642843170e-05,5.21233142621493943000e-05] 
dist 218=[-9.14062137718803334470e-05,6.80898899319499438050e-05] 
dist 219=[-8.03595666324295993950e-05,8.16067276433820825800e-05] 
dist 220=[-7.74553491115347569630e-05,8.91860848356957910970e-05] 
dist 221=[-7.10243651160681785790e-05,9.37281063321610795100e-05] 
dist 222=[-6.87857328642235171240e-05,9.51849592904074594470e-05] 
dist 223=[-3.45155141943681080050e-05,9.51006506387498709420e-05] 
dist 224=[-2.93138609805620811480e-05,9.42852831981794545860e-05] 
dist 225=[-1.82638420745342076740e-05,9.13808198918387692920e-05] 
dist 226=[-1.52824504717194552950e-05,8.96848914958065157460e-05] 
dist 227=[-4.19980621966039977020e-06,7.90930363232998171940e-05] 
dist 228=[-1.86956289503301041100e-06,7.63140342457878003320e-05] 
dist 229=[1.20533144484069477400e-06,6.58913105217420805160e-05] 
dist 230=[-4.45914474793711730400e-08,5.11144383943566388120e-05] 
dist 231=[-9.37657606958468227600e-06,5.09522709561989232020e-05] 
dist 232=[-1.56463503494814245760e-05,5.06073335178754863640e-05] 
dist 233=[-2.07547086421034683190e-05,4.83723599729378770950e-05] 
dist 234=[-2.54752603830312407880e-05,4.77997146735170358930e-05] 
dist 235=[-2.94768981091194107600e-05,3.91399689755165949460e-05] 
dist 236=[-3.17307865999615737290e-05,3.70602304191879563140e-05] 
dist 237=[-3.30946584518275140360e-05,3.48318976850674699630e-05] 
dist 238=[-3.35624661689176150790e-05,3.37171080194880015170e-05] 
dist 239=[-3.36251345168820722910e-05,1.19483513945213421150e-05] 
dist 240=[-3.33803333418529442620e-05,1.02620259016114442810e-05] 
dist 241=[-3.28692054668576997430e-05,6.68237441582242335500e-06] 
dist 242=[-3.24796998447480284710e-05,5.71263076497846610420e-06] 
dist 243=[-3.06695914109154109260e-05,2.09035548318345079420e-06] 
dist 244=[-3.04882789522785637900e-05,1.32501238580465631480e-06] 
dist 245=[-3.17499678634239727510e-05,2.73868888766432705210e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 2, 2, 1, 2] 
dist 0=[129.64828335840729338   ,129.64828335840729338   ] 
dist 1=[127.81374275842174722   ,130.17415440134232535   ] 
dist 2=[122.66001177314191714   ,130.13935737777308067   ] 
dist 3=[115.90928041853881699   ,129.85979079132490905   ] 
dist 4=[107.72311934250712572   ,125.03834953326939644   ] 
dist 5=[97.065691904528079440  ,120.70284242511139350   ] 
dist 6=[80.487670488703465678  ,118.29952307427921009   ] 
dist 7=[63.558700090396863450  ,115.92520249070028936   ] 
dist 8=[51.500646793708310993  ,110.88738914964627412   ] 
dist 9=[40.876830588460780096  ,88.436536706161076887  ] 
dist 10=[29.636380339942989919  ,86.665682588606630938  ] 
dist 11=[19.018358442289797276  ,60.376304838969369521  ] 
dist 12=[10.856578416158133512  ,58.068084395011592142  ] 
dist 13=[2.9903363242433177099 ,44.077561867151526404  ] 
dist 14=[-6.4757828764507380136 ,41.728098439139056028  ] 
dist 15=[-15.191833914055594309  ,36.717596981356244606  ] 
dist 16=[-20.079993595855238944  ,35.799059145027756339  ] 
dist 17=[-23.245098809394050040  ,1.2616983645091571752 ] 
dist 18=[-28.318023338299796235  ,-.49434315044931972341] 
dist 19=[-32.540715031386951089  ,-7.9202971499213878056 ] 
dist 20=[-34.371227646060855652  ,-9.1009724681051469211 ] 
dist 21=[-35.159103449739702227  ,-11.344926727021093213  ] 
dist 22=[-35.218587959932103222  ,-10.777856691415136070  ] 
dist 23=[-31.983430811566851671  ,-8.5357534931538355461 ] 
dist 24=[-30.943941952995615244  ,-4.4326466733566034980 ] 
dist 25=[-30.165586128430784700  ,-.78692643118336361863] 
dist 26=[-29.581100933456686737  ,2.8656925910266504396 ] 
dist 27=[-9.7664991962231239376 ,6.2437638537727908579 ] 
dist 28=[-7.3179529843082420817 ,8.8973504718572211616 ] 
dist 29=[-1.4252843307277919987 ,12.193374673412291792  ] 
dist 30=[-.5636300922096628873 ,14.780524533969414290  ] 
dist 31=[7.0125640899750300747 ,17.298049268572978793  ] 
dist 32=[8.2028052160999293094 ,20.326394950957686837  ] 
dist 33=[10.136213765999424154  ,22.996557689924283617  ] 
dist 34=[10.450998601924612531  ,24.094200797670386451  ] 
dist 35=[9.9242197788280666765 ,24.549583715055035564  ] 
dist 36=[8.5152774184090863124 ,24.663204751798118744  ] 
dist 37=[6.5721680855848487401 ,21.892961974813153563  ] 
dist 38=[3.4581270193575203566 ,21.169080970750017542  ] 
dist 39=[.29014042491816632041,20.743950416999872015  ] 
dist 40=[-1.8676902370078258077 ,20.636176469918440746  ] 
dist 41=[-3.6479004492625494417 ,15.393756313964678205  ] 
dist 42=[-5.3188238038451527073 ,14.960858996289412939  ] 
dist 43=[-6.8318560726546533954 ,6.9993332654589337473 ] 
dist 44=[-7.6850585730075117448 ,6.2453651123884115274 ] 
dist 45=[-8.1664781409835087111 ,4.5372304241601199250 ] 
dist 46=[-9.8214083325308321724 ,4.0687806876775030584 ] 
dist 47=[-11.948610777853760296  ,1.9924981721842221361 ] 
dist 48=[-13.080047884152437736  ,1.6002848644470134749 ] 
dist 49=[-13.697659179116256711  ,.70836434875892613262] 
dist 50=[-13.817512402412485379  ,.52160349151527011398] 
dist 51=[-12.767166421108946391  ,-3.1454476548418239861 ] 
dist 52=[-12.620371561724895897  ,-2.7762656190748605568 ] 
dist 53=[-11.230665212004365327  ,-2.2721660685083764406 ] 
dist 54=[-10.822205976056003063  ,-1.4677887468086148811 ] 
dist 55=[-10.201581861423025157  ,-.64804778504813491589] 
dist 56=[-9.9586376217035722317 ,-.0828259445644108849 ] 
dist 57=[-3.7940175905171143517 ,1.0650470047068768539 ] 
dist 58=[-2.9671937166500905164 ,3.3623858073046588569 ] 
dist 59=[-1.0813009094266290963 ,5.2364194570253892429 ] 
dist 60=[-.68511764196790084013,6.9672418311510666611 ] 
dist 61=[1.4103067830078412778 ,8.4301920290327410212 ] 
dist 62=[1.4423963486981387452 ,9.2411618437514221554 ] 
dist 63=[1.8842291896252314104 ,9.7135353386333828230 ] 
dist 64=[1.8838452950397785961 ,9.8325081791226109256 ] 
dist 65=[1.8179095016469445845 ,3.0163778927477480529 ] 
dist 66=[1.6475783277058170015 ,3.0521383005887252999 ] 
dist 67=[1.4283311184176305072 ,3.0309843344232009992 ] 
dist 68=[1.1681868408504230395 ,3.0213997375125390679 ] 
dist 69=[.83408217197441837302,2.5801153630495566926 ] 
dist 70=[.32122674511713578881,2.4644750467230614310 ] 
dist 71=[-.19504602870715463896,2.3771763298825510120 ] 
dist 72=[-.54274434897264824997,2.3392260875425122009 ] 
dist 73=[-.8263571212777788754 ,.50765868513440196573] 
dist 74=[-1.0883012402732381930 ,.28740875411927452491] 
dist 75=[-1.3097322442631488376 ,-.18443238454075030142] 
dist 76=[-1.4327645619898400145 ,-.23912434925258629843] 
dist 77=[-1.5047225903672390204 ,-.34347593215383703606] 
dist 78=[-1.5228245953858011283 ,-.36470913792806319006] 
dist 79=[-1.6528225744224435701 ,-.40980640643616059327] 
dist 80=[-1.7271302656363673711 ,-.41107520308685589878] 
dist 81=[-1.7643289021547926358 ,-.39650886296025526829] 
dist 82=[-1.7664418887112642611 ,-.35703135235166368759] 
dist 83=[-1.7167028409262376380 ,-.30573973409421804656] 
dist 84=[-1.7021248451778408522 ,-.24426306663690676036] 
dist 85=[-1.4178955740869912776 ,-.16489972369529260247] 
dist 86=[-1.3468474294136246700 ,-.04259246011226722703] 
dist 87=[-1.2787556635922166606 ,.08082597849005122930] 
dist 88=[-1.2447543196065618651 ,.16460903654946204836] 
dist 89=[-.37247237499826275264,.23371453546434687415] 
dist 90=[-.28341753252241039089,.36585239464698161381] 
dist 91=[-.08077508483717792864,.56506815522078417612] 
dist 92=[-.03885645494919499718,.74954818445829132018] 
dist 93=[-.01382008767173519834,.90600294225660266936] 
dist 94=[-.00743176010249706266,1.0007626865834042578 ] 
dist 95=[.01393886861318106991,1.0549262995154293832 ] 
dist 96=[.01473237904820821553,1.0675311503678463734 ] 
dist 97=[.00841235104794674989,.41339974125971989692] 
dist 98=[-.00904935569648746962,.40695391100238761436] 
dist 99=[-.03182209972710396703,.3968929817179525894 ] 
dist 100=[-.05923232423052930858,.39543961856210917999] 
dist 101=[-.09469678547165972995,.3265889511954114124 ] 
dist 102=[-.14945000228785354785,.3152029763738737027 ] 
dist 103=[-.20477137938633954105,.29848633185223592657] 
dist 104=[-.24249572538702609839,.29587951570342267955] 
dist 105=[-.27380680298978224957,.03840007382488470232] 
dist 106=[-.30367465293800090435,.02405621442044411162] 
dist 107=[-.32962506433588376393,-.03201592750720081755] 
dist 108=[-.35235234281530680654,-.03845843850935751921] 
dist 109=[-.36505422929029741192,-.05019202559547592153] 
dist 110=[-.36731870020708584119,-.05236259539333577618] 
dist 111=[-.19776757169011410587,-.05558558042619010344] 
dist 112=[-.20545353808521610633,-.05531767804353846889] 
dist 113=[-.20877978453683525511,-.05355941466785365226] 
dist 114=[-.20846144534628882206,-.04936175001423350666] 
dist 115=[-.20304688411596954502,-.04403526854824462030] 
dist 116=[-.20000331332772931891,-.03779466713985015935] 
dist 117=[-.17214688765245355232,-.02982166901519375778] 
dist 118=[-.16483688238273809757,-.01761666311573685503] 
dist 119=[-.15371404737134632908,-.00532233456207723248] 
dist 120=[-.14964623893380694135,.00300591986083251356] 
dist 121=[-.05126452482705289647,.02420542438909083067] 
dist 122=[-.03812978389380508189,.06043038087288393083] 
dist 123=[-.00862459549880745212,.08987783148687006124] 
dist 124=[-.00226181327231430720,.11695802565717310356] 
dist 125=[.02556466707881677765,.13980718086299421527] 
dist 126=[.02598802087228190447,.1524567211019373063 ] 
dist 127=[.02870037115163362415,.15981814129177146213] 
dist 128=[.02812430170075178713,.16167229503308022009] 
dist 129=[.02672879053817759477,.04884738274265057871] 
dist 130=[.02388844531520752953,.04886884128140767986] 
dist 131=[.02041163542735904286,.04732890152044675797] 
dist 132=[.01648893636883265405,.04700710804492448076] 
dist 133=[.01156909435456908065,.03876727880859764078] 
dist 134=[.00413315139824498056,.03674811873508771702] 
dist 135=[-.00332406522440052073,.03509629243078441270] 
dist 136=[-.00832851618034220229,.03447158312296182131] 
dist 137=[-.01239722713117313564,.00533225034686310929] 
dist 138=[-.01613951794710808267,.00184824085008735798] 
dist 139=[-.01929733691803884222,-.00414205180392000024] 
dist 140=[-.02104563181424102868,-.00492016247076357585] 
dist 141=[-.02206308969298867128,-.00626395959269272039] 
dist 142=[-.02478030733292921621,-.00652023476813359449] 
dist 143=[-.02651223954295159315,-.00673942652365291501] 
dist 144=[-.02724027796729002112,-.00664710269274868221] 
dist 145=[-.02739850649096012468,-.00638233069592532482] 
dist 146=[-.02729836433850889296,-.00582039647335725116] 
dist 147=[-.02623421222014975250,-.00512538996811522812] 
dist 148=[-.02598115517653636191,-.00433220272291267674] 
dist 149=[-.02129885438798385695,-.00333150393537502807] 
dist 150=[-.02016536886709432300,-.00181253523936473746] 
dist 151=[-.01907976737549441364,-.00028636866210981213] 
dist 152=[-.01858967962745614715,.00074295689446327779] 
dist 153=[-.00465050439500710182,.00194679848122500586] 
dist 154=[-.00320909316957175646,.00570197109182865190] 
dist 155=[5.13827179824955149260e-05,.00875645552303472192] 
dist 156=[.00070470164863950653,.01156962294475585846] 
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dist 181=[-.00258737492200665625,-.00043539659240712447] 
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dist 204=[-.00033068978380570873,-6.93902353036844222510e-05] 
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dist 207=[-.00044933814598298748,-9.25367273105008483180e-05] 
dist 208=[-.00045796480590029683,-8.98325047007707200380e-05] 
dist 209=[-.00045765759535453816,-8.42929818101811730220e-05] 
dist 210=[-.00045491796010328474,-7.35793662485243664980e-05] 
dist 211=[-.00043566771054985823,-6.06300250539729723160e-05] 
dist 212=[-.00043056677302931715,-4.62124478261598394870e-05] 
dist 213=[-.00035364698270686348,-2.82453573520265758300e-05] 
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dist 218=[-9.52771741533738045210e-05,.00013345080162164722] 
dist 219=[-6.27745188544929644070e-05,.00017855098237038658] 
dist 220=[-5.39178914207586899400e-05,.00022006911824332553] 
dist 221=[-2.05236766275687996520e-05,.00025515789338433591] 
dist 222=[-1.35273739338044761730e-05,.00027472902769985005] 
dist 223=[-3.21621580365860053900e-06,.00028665836676713078] 
dist 224=[-2.84519918893233629510e-06,.00028973480106583573] 
dist 225=[-5.13330108543359180270e-06,9.17595208961911463930e-05] 
dist 226=[-9.62607096465814948770e-06,8.99420605414641918530e-05] 
dist 227=[-1.50784772892361903550e-05,8.08630780068632411080e-05] 
dist 228=[-2.11773863127995654550e-05,7.94751727077691958160e-05] 
dist 229=[-2.87964513196052889550e-05,7.04591004256023142950e-05] 
dist 230=[-4.02853678385651428840e-05,6.80389912020532495250e-05] 
dist 231=[-5.18088058564549312110e-05,6.26649567469250183590e-05] 
dist 232=[-5.95651664420676756970e-05,6.07688355422118083520e-05] 
dist 233=[-6.59010011393052097910e-05,8.80196672323624533860e-06] 
dist 234=[-7.17841661187095036500e-05,7.56560355124035219650e-06] 
dist 235=[-7.67920253533228912200e-05,2.89686339334619044530e-06] 
dist 236=[-7.96524350394043166700e-05,1.91997522576937018000e-06] 
dist 237=[-8.16327112867482558190e-05,4.64787098891903575500e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 0, 0, 2, 1, 2] 
dist 0=[126.61917291113030554   ,126.61917291113030554   ] 
dist 1=[122.63196520794959611   ,127.91533553473372363   ] 
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dist 3=[110.18105003997951815   ,127.59090715935020646   ] 
dist 4=[100.78119084185846519   ,125.80406610220464568   ] 
dist 5=[85.895822025936035694  ,119.10968013917678349   ] 
dist 6=[70.597565343425745062  ,117.39329909076371328   ] 
dist 7=[59.549951101063947467  ,112.69613526579120978   ] 
dist 8=[49.660238643278693014  ,103.93387658605508968   ] 
dist 9=[38.950982009660894646  ,87.327250617502853455  ] 
dist 10=[28.679811008924377185  ,83.700592208257892802  ] 
dist 11=[20.518555797027064203  ,79.524122560159736243  ] 
dist 12=[12.395011196333321063  ,77.783938625386053608  ] 
dist 13=[2.2495200029765581550 ,49.192800026010561940  ] 
dist 14=[-7.2347908776956859709 ,44.532750492995416819  ] 
dist 15=[-12.733644578069479075  ,43.721043832424388350  ] 
dist 16=[-16.386238575570482983  ,16.822290983569721812  ] 
dist 17=[-18.517550193312623217  ,1.8480475057160936220 ] 
dist 18=[-21.457055773331266818  ,-.67034531197960173179] 
dist 19=[-25.961039460754811060  ,-4.9721012871644443441 ] 
dist 20=[-30.069904245896551403  ,-5.7408780108921759594 ] 
dist 21=[-33.348255897597217673  ,-9.1236670979112302678 ] 
dist 22=[-34.552354605742856150  ,-7.7655080618067541244 ] 
dist 23=[-34.948681424253102466  ,-4.4933042474701465854 ] 
dist 24=[-35.000239389174714737  ,-.84854279107355874076] 
dist 25=[-30.766613201904793351  ,1.9955663681438153696 ] 
dist 26=[-29.596036575727469975  ,4.7038884011618094608 ] 
dist 27=[-28.852446091048792704  ,7.8231349130502047402 ] 
dist 28=[-28.533639836983818000  ,10.874125630048343922  ] 
dist 29=[-7.3942640580095873827 ,13.319235039071516905  ] 
dist 30=[-4.8691638149021415920 ,15.744031726751697025  ] 
dist 31=[1.0610055306427144607 ,18.723655715225823916  ] 
dist 32=[1.9750576358221109119 ,21.379375087859339691  ] 
dist 33=[9.1058961295776411859 ,22.520585091086472106  ] 
dist 34=[8.9952166915393382319 ,23.020030861793316483  ] 
dist 35=[7.6712544594987776939 ,23.121322933349781315  ] 
dist 36=[5.8296508264730945701 ,20.772281140142824785  ] 
dist 37=[2.8643828068172730039 ,20.125555249520841761  ] 
dist 38=[-.15407596721054956964,19.716933781080819898  ] 
dist 39=[-2.2073517363179051799 ,19.546410585519195551  ] 
dist 40=[-3.8971182821848155692 ,17.663475687917485946  ] 
dist 41=[-5.4746368036238633008 ,15.639024048052627245  ] 
dist 42=[-6.8137695277741848907 ,15.059711769058467204  ] 
dist 43=[-7.5583669392882668629 ,14.109480481712282168  ] 
dist 44=[-7.9929475901281580222 ,13.772330594009699668  ] 
dist 45=[-9.5991584976483010097 ,6.3788009521261373380 ] 
dist 46=[-10.848293875321011436  ,5.4660142186078913461 ] 
dist 47=[-11.821001413343009762  ,3.4149116019210398594 ] 
dist 48=[-12.543575777794892807  ,2.8943635920572091409 ] 
dist 49=[-12.800228224301969326  ,.53330798158661592112] 
dist 50=[-13.446350402122798892  ,.09665822168598203027] 
dist 51=[-14.079574976008807844  ,-.78669353575733305672] 
dist 52=[-14.198169436683456048  ,-.99678089636504383662] 
dist 53=[-11.456794597948951579  ,-1.1182343495888113805 ] 
dist 54=[-10.704367413763212118  ,-.46959979314570796486] 
dist 55=[-10.403768159868762904  ,-.02023836984729173401] 
dist 56=[-6.4007422242230441853 ,3.3313229843793912782 ] 
dist 57=[-5.8225875953347775582 ,5.7784611721197132337 ] 
dist 58=[-4.5634790451503081242 ,7.7756435335765570440 ] 
dist 59=[-3.5239442662882014531 ,9.6219817503558602355 ] 
dist 60=[-2.7386824016197421828 ,11.183998589584484574  ] 
dist 61=[-1.1318940749397865999 ,12.059531862297077914  ] 
dist 62=[-.43127273234681637339,12.579889052290853434  ] 
dist 63=[-.25756394084036332325,12.701202685838357343  ] 
dist 64=[.54257555687111456297,1.6218855296611993439 ] 
dist 65=[1.1838364425396825175 ,1.6133516049987099575 ] 
dist 66=[1.0465914147816151984 ,1.5846665557423539563 ] 
dist 67=[.87677463455084596961,1.7308142890573888341 ] 
dist 68=[.65455714946670958789,1.8137915048637759613 ] 
dist 69=[.30930876889759405584,1.8572668690682679928 ] 
dist 70=[-.03942731184296893740,1.8591794521793432807 ] 
dist 71=[-.27551633234905400554,1.8189094701860603988 ] 
dist 72=[-.46927301492498887764,1.7946186278977997508 ] 
dist 73=[-.65004935048381610468,1.5468251458046786336 ] 
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dist 75=[-.90816590982030168594,1.3878783305978752253 ] 
dist 76=[-.95947150604702077994,1.3510099886859114639 ] 
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dist 78=[-.4969715602563543988 ,.34379267685820172788] 
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dist 85=[-.47539180016195319034,-.06345828668462441845] 
dist 86=[-.47490444000605326202,.06134810211849198437] 
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dist 90=[-.38445880009237343551,.33474529182311840527] 
dist 91=[-.35619962746471192876,.36633380270201778904] 
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dist 93=[-.14133700579382066904,.39430626198396160949] 
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dist 100=[.00451727893948831524,.28370071439519400832] 
dist 101=[-.02653637067471758025,.26745445358677805095] 
dist 102=[-.05790707839871993238,.26648964216436524987] 
dist 103=[-.07923959482812490394,.25555408419538281533] 
dist 104=[-.09686986164045009563,.25341328226667765742] 
dist 105=[-.11621402540282710415,.20534654893260239629] 
dist 106=[-.13964223566975641362,.19384240199698429992] 
dist 107=[-.15262070624441179154,.18399644477852889287] 
dist 108=[-.16017670102169604472,.18041358413913310585] 
dist 109=[-.16208018596149784361,.03271431784490707021] 
dist 110=[-.14731255236566963285,.02065835525931360331] 
dist 111=[-.14813381732560181724,-.00701937621231785187] 
dist 112=[-.14827346000583398513,-.01198858595275176981] 
dist 113=[-.14752529773665085515,-.04370097232594269708] 
dist 114=[-.14629586586813032953,-.03883600881614916848] 
dist 115=[-.14452439720624967454,-.03310708870087561075] 
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dist 117=[-.06206103004698325250,-.01452288362362928473] 
dist 118=[-.06206564644866080701,-.00318892473968675173] 
dist 119=[-.05991559671939596094,.00449059464230032172] 
dist 120=[-.05960546952564622723,.01081138144438388348] 
dist 121=[-.04851868929807562480,.01675222636621674586] 
dist 122=[-.04584839833827489557,.02185270008382650109] 
dist 123=[-.04399922969564582834,.02483785663490417132] 
dist 124=[-.04358027270835214737,.02678912036408716611] 
dist 125=[-.00456188083151197951,.02778587055856800687] 
dist 126=[-9.41009720288194478240e-06,.02819134983127946517] 
dist 127=[.01054605787073391473,.02816634680583406239] 
dist 128=[.01212204802632285640,.02723706958179780985] 
dist 129=[.01939635181045886254,.02699724989463021959] 
dist 130=[.01673446770451905688,.02825761349225920597] 
dist 131=[.01370088317185434424,.03038611844023354821] 
dist 132=[.00987717259388876570,.03129154787713971357] 
dist 133=[.00407816913859656388,.03154233720747186331] 
dist 134=[-.00174365719551159525,.03141337506285843054] 
dist 135=[-.00565813171190031277,.03041730638271913404] 
dist 136=[-.00884832256889925172,.02993820085536930729] 
dist 137=[-.01179487429124918046,.02556241722791966212] 
dist 138=[-.01428945097478883203,.02443850483892872094] 
dist 139=[-.01573624383647968331,.02273066644670874743] 
dist 140=[-.01660111165593986071,.02211385504474393504] 
dist 141=[-.01680148950607686385,.00735517496832853651] 
dist 142=[-.00927443590611502997,.00538770824026223477] 
dist 143=[-.01367111562495018643,.00098475674303994490] 
dist 144=[-.01771012997908355217,2.94715593100418611420e-05] 
dist 145=[-.02111663526971464379,-.00476054595290218671] 
dist 146=[-.02300193245223022213,-.00507886826899748526] 
dist 147=[-.02409886510773352684,-.00433624711984258250] 
dist 148=[-.02437513227741432515,-.00339601948843465345] 
dist 149=[-.00734050731870800130,-.00196537336168288670] 
dist 150=[-.00732308999523627624,-.00052680919627235432] 
dist 151=[-.00704681792127007021,.00044490737047650732] 
dist 152=[-.00699239861227574616,.00124185954809298496] 
dist 153=[-.00571297866719461107,.00198663879609632929] 
dist 154=[-.00540461048027024707,.00262346847956472568] 
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dist 197=[7.71181500810750000000e-06,.00047784390546287414] 
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dist 210=[-.00034529318136765376,-7.90995851809782832890e-05] 
dist 211=[-.00036155052962130192,-6.23683086556585328070e-05] 
dist 212=[-.00036564903606429057,-4.15582872908280401880e-05] 
dist 213=[-.00012208888639507619,-1.02791201527852514850e-05] 
dist 214=[-.00012126517928997520,2.10512821742343372860e-05] 
dist 215=[-.00011701948607586230,4.20650466426408298310e-05] 
dist 216=[-.00011484746406834629,5.91478108350453804390e-05] 
dist 217=[-9.85238011061976547370e-05,7.48696808048868879670e-05] 
dist 218=[-9.43173006477302543560e-05,8.81526083574253000070e-05] 
dist 219=[-8.70011029438746023420e-05,9.55511952713781950390e-05] 
dist 220=[-8.47193458761697359380e-05,9.99198225833924071420e-05] 
dist 221=[-3.16343584360324638620e-05,.00010117180836030160] 
dist 222=[-2.43453526827914466690e-05,.00010096099993944727] 
dist 223=[-8.26843234614514442510e-06,9.99289901820112394430e-05] 
dist 224=[-4.42711013760425240700e-06,9.73409489341115551720e-05] 
dist 225=[1.12869004039141768120e-05,9.58634820434047459330e-05] 
dist 226=[7.48764815729043810250e-06,8.67045701234515952900e-05] 
dist 227=[3.25184213978537786090e-06,8.43120136165027676460e-05] 
dist 228=[-2.03042708800846112400e-06,7.25994880195759943470e-05] 
dist 229=[-9.98504167027985920320e-06,6.71692268438866602230e-05] 
dist 230=[-1.79582629259108572510e-05,6.67271211250288076300e-05] 
dist 231=[-2.33145267491933663550e-05,6.38105717841351143970e-05] 
dist 232=[-2.76779966871551564230e-05,6.30566304090464973460e-05] 
dist 233=[-3.17092853698751855510e-05,5.16740089053424327170e-05] 
dist 234=[-3.51260451526115680650e-05,4.89364796026565187590e-05] 
dist 235=[-3.70494983668376674650e-05,4.59976936938997102750e-05] 
dist 236=[-3.82121221607579229400e-05,4.45210990961046539720e-05] 
dist 237=[-3.86079785149532395690e-05,1.58693369638429093010e-05] 
dist 238=[-3.86581591843607702790e-05,1.36424681298939331800e-05] 
dist 239=[-3.84482157029589702930e-05,8.90964419739695025830e-06] 
dist 240=[-3.80124556710302755340e-05,7.62566583701089708200e-06] 
dist 241=[-3.75335872237745781430e-05,2.81854145346803838650e-06] 
dist 242=[-4.02392789549882352840e-05,1.80494810644482413170e-06] 
dist 243=[-4.19123495630255136970e-05,3.87965250742824390890e-07] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 1, 0, 2, 1, 2] 
dist 0=[122.47070243846785736   ,122.47070243846785736   ] 
dist 1=[121.33805039704530889   ,123.48527273661882559   ] 
dist 2=[117.85757175897939235   ,124.85544449031073825   ] 
dist 3=[111.51147150634051940   ,127.00110149495877120   ] 
dist 4=[99.740977599646954601  ,128.87757529069492626   ] 
dist 5=[87.239509107710604971  ,129.18259312785066788   ] 
dist 6=[77.984550306084756296  ,128.58107663730674236   ] 
dist 7=[69.477102395826933543  ,126.85324978857525522   ] 
dist 8=[59.930067008252894513  ,106.30078792507543094   ] 
dist 9=[50.573253564145465580  ,102.99342643385235135   ] 
dist 10=[40.943187842559335032  ,93.169737929975976699  ] 
dist 11=[32.650371558731061431  ,91.758989486198799718  ] 
dist 12=[24.152490031536429891  ,71.059192205816370000  ] 
dist 13=[13.199726794034834860  ,66.778189399564447823  ] 
dist 14=[2.8069370201866957441 ,62.728204870709105823  ] 
dist 15=[-3.4690619668047158386 ,61.957730175985096680  ] 
dist 16=[-7.9495988800069925421 ,14.000095907754086777  ] 
dist 17=[-11.188851503154352773  ,8.4393190532847651874 ] 
dist 18=[-13.613385123729814104  ,-3.1271927745080845504 ] 
dist 19=[-14.842917847876512402  ,-3.4273113754229781938 ] 
dist 20=[-21.140543554280524314  ,-2.5466036854814480992 ] 
dist 21=[-25.187806223895878369  ,-1.4030770566335962102 ] 
dist 22=[-27.845543034570760732  ,-.5042482724722303416 ] 
dist 23=[-29.277437924377413137  ,.30685244110213223719] 
dist 24=[-30.007816656305781466  ,1.1168086589870790429 ] 
dist 25=[-30.042224689558910501  ,1.7915060038126205220 ] 
dist 26=[-29.379832596835793669  ,2.0730241852081570374 ] 
dist 27=[-28.984159526880504643  ,2.1816836234635046481 ] 
dist 28=[-25.009214324756250720  ,2.1806605818747492017 ] 
dist 29=[-23.970955650418274330  ,3.0173397969216579779 ] 
dist 30=[-22.442245171560102854  ,4.6180281271775354874 ] 
dist 31=[-21.864457574757305091  ,5.4969706865962066561 ] 
dist 32=[-7.8720744857761135577 ,6.0087934442940137815 ] 
dist 33=[-6.0187819068627120876 ,7.2128950086255267191 ] 
dist 34=[-1.8428789412197763726 ,11.291509316308525375  ] 
dist 35=[-.96677488104299679171,15.035209254025042264  ] 
dist 36=[-.64369501891413775652,18.190336505338283812  ] 
dist 37=[-.88965188607864612979,19.932189754525857935  ] 
dist 38=[-1.0928892670233373355 ,20.939974991068370727  ] 
dist 39=[-1.2936304081738968412 ,21.180443323540800791  ] 
dist 40=[-1.5310327496535187614 ,6.5020992942356476277 ] 
dist 41=[-1.7627832877800749236 ,6.5317575949818910498 ] 
dist 42=[-1.9418356830716838201 ,6.3670320809527765650 ] 
dist 43=[-2.1109734241566344165 ,6.3429354891180662012 ] 
dist 44=[-2.4117042063265747625 ,5.2407054706827739198 ] 
dist 45=[-2.8712155035549337033 ,4.9703822306654810014 ] 
dist 46=[-3.2559919758541448408 ,4.7889580726932719128 ] 
dist 47=[-3.4323519509009935267 ,4.7464715173799392174 ] 
dist 48=[-3.5063614168850439542 ,2.4489269169584237888 ] 
dist 49=[-3.4989914841150189888 ,2.0377872515697348523 ] 
dist 50=[-3.2620626290939131968 ,1.9487819934226959007 ] 
dist 51=[-3.1720663545086952083 ,1.6997134497816956963 ] 
dist 52=[-3.0333372173193448079 ,1.6493224294862116991 ] 
dist 53=[-3.0702221973887694456 ,1.0245555301110278106 ] 
dist 54=[-3.2203704251627646287 ,.91009572733593099273] 
dist 55=[-3.3364530057869070065 ,.7882500875847961783 ] 
dist 56=[-3.3863410165566272903 ,1.3198900246933154462 ] 
dist 57=[-3.3812134490628681761 ,1.8142479887580106786 ] 
dist 58=[-3.3013864493996910246 ,2.2332389074991825911 ] 
dist 59=[-3.2421027716276031272 ,2.4659464939310192171 ] 
dist 60=[-2.8121014814286954770 ,2.6016535739008170754 ] 
dist 61=[-2.4789295713787570377 ,2.6358636135532339286 ] 
dist 62=[-2.3128782733332294454 ,.82076330700918951781] 
dist 63=[-2.2516291998409729876 ,.85673827721597232975] 
dist 64=[-.77567185327295237554,.87101228369483504918] 
dist 65=[-.57964556696917598752,.87480007118938274297] 
dist 66=[-.13961778552901503507,1.3125427376024248684 ] 
dist 67=[-.04493336907470811374,1.7149208294172844883 ] 
dist 68=[.27858171784826832088,2.0543722656302078405 ] 
dist 69=[.12380323731568603054,2.2422811402435799905 ] 
dist 70=[.01694320223365309091,2.3516887937988009721 ] 
dist 71=[-.07294841281904274484,2.3792239853077544891 ] 
dist 72=[-.16043355642718918691,.72331602724999674844] 
dist 73=[-.2436646148905557986 ,.72354163853147571061] 
dist 74=[-.34365068360185622056,.69994764688223682866] 
dist 75=[-.4058868356602133689 ,.69552614069861030569] 
dist 76=[-.45116612343849784985,.57381102935169059629] 
dist 77=[-.48390310278007365924,.54561723768418519281] 
dist 78=[-.50568940756685345083,.51805913527146025355] 
dist 79=[-.50990648301679143983,.50968545820083818338] 
dist 80=[-.50309402024634918518,.10799792209483571354] 
dist 81=[-.50003436832854984368,.05903165481702570649] 
dist 82=[-.42385167769980294426,-.05428295324820655575] 
dist 83=[-.40394276514930375283,-.07293984380791015191] 
dist 84=[-.3861975960951816456 ,-.06718581485436234956] 
dist 85=[-.3939086871930412251 ,.02960588784531182741] 
dist 86=[-.41960764985905743676,.09481435235250412897] 
dist 87=[-.43016638835661453136,.14801906982721050559] 
dist 88=[-.43215432848037569463,.19717450466864104031] 
dist 89=[-.43025250010424673321,.23873061053244410265] 
dist 90=[-.4137747978772698603 ,.26177627435499789048] 
dist 91=[-.40893131253618548403,.28449696921080808884] 
dist 92=[-.33854422183954899966,.30038378910114518985] 
dist 93=[-.32132182517086613365,.30398078079971135415] 
dist 94=[-.30214836238046115895,.12070682737325562486] 
dist 95=[-.29276779914499512977,.12226917908152355608] 
dist 96=[-.11227615724044688195,.12143125903131491173] 
dist 97=[-.09736387258429574777,.12485440177491141107] 
dist 98=[-.06527243830636278655,.16892959675257596098] 
dist 99=[-.05645385298793231925,.20959182850923303579] 
dist 100=[-.02272346666420897836,.24401084178578971975] 
dist 101=[-.01577055569537906619,.26329823959937885712] 
dist 102=[-.03011603878805400304,.27590055033639104385] 
dist 103=[-.04507438018391045183,.27879584703889779771] 
dist 104=[-.05909218475054997188,.10064546578922554077] 
dist 105=[-.07109455517829770309,.10005188804669823248] 
dist 106=[-.07805323444665333935,.09688513180324466233] 
dist 107=[-.08251658390641798334,.09497654210052158226] 
dist 108=[-.08461436068252577136,.08226167769737162961] 
dist 109=[-.08541696960038241824,.07890674027202092212] 
dist 110=[-.08487704060130255746,.07265628496599578789] 
dist 111=[-.08323497369172326760,.07071350330178855147] 
dist 112=[-.08206523578487231995,.02852134752867482875] 
dist 113=[-.07433205520025691466,.02259906768635563302] 
dist 114=[-.07224180931395542143,.00962161394052666483] 
dist 115=[-.06604824032998524277,.00633901869155519996] 
dist 116=[-.06410491308634152918,.00516091673384202526] 
dist 117=[-.04776067779515611638,.01225849126193735836] 
dist 118=[-.03635842392290904022,.01704870393662542924] 
dist 119=[-.02769292615829600452,.02096778671639102821] 
dist 120=[-.01614423023795114338,.02734927240031520941] 
dist 121=[-.01553048273093967274,.03583686419144326293] 
dist 122=[-.01518676961105497688,.04300394798262283290] 
dist 123=[-.01267980081308055745,.0469745436893307128 ] 
dist 124=[-.00689607093040843375,.04929059539306787860] 
dist 125=[.01318729872902150779,.04987181037258282958] 
dist 126=[.01309911855758410876,.01536338988035646119] 
dist 127=[.01266359503626870663,.01544348770257012748] 
dist 128=[.01165320937856482012,.01508409242969769534] 
dist 129=[.01037860331816423061,.01502901741499180808] 
dist 130=[.00889390983939048750,.01247160973904994266] 
dist 131=[.00700223321506137011,.01190106124723269936] 
dist 132=[.00411168333138925567,.01137985251126333410] 
dist 133=[.00120151068459835855,.01127206963393697430] 
dist 134=[-.00076820501826337164,.00268532983515718020] 
dist 135=[-.00238755590123673318,.00164428677894111163] 
dist 136=[-.00416818801420946162,-.00078455862571699190] 
dist 137=[-.00603643863311520669,-.00118132274230108633] 
dist 138=[-.00763759666382238455,-.00409119765483509648] 
dist 139=[-.00856981807153286008,-.00453709121480083188] 
dist 140=[-.00917309032256235118,-.00539331382164929702] 
dist 141=[-.00946852243897002888,-.00553385327878100428] 
dist 142=[-.00957466856678350499,-.00593270594511894505] 
dist 143=[-.00955335512696830130,-.00582984761899894371] 
dist 144=[-.00922699432434869380,-.00552774389459646001] 
dist 145=[-.00912918993989551272,-.00481665229428970884] 
dist 146=[-.00758104065342869968,-.00388744102133191075] 
dist 147=[-.00719828974372874950,-.00272339175726967166] 
dist 148=[-.00679129860333872141,-.00096539631145284513] 
dist 149=[-.00658065580375129242,.00079729187907430124] 
dist 150=[-.00257189454461227751,.00198000395116795243] 
dist 151=[-.00225147529257640891,.00294141779839014500] 
dist 152=[-.00155221311433937783,.00382552643433742702] 
dist 153=[-.00135672148045494823,.00457149599411337517] 
dist 154=[-.00058979470706784319,.00527510423336057741] 
dist 155=[-.00043476070839421524,.00572949203836836075] 
dist 156=[-.0001452001922101746 ,.00601883374580752691] 
dist 157=[-7.89652188552582980510e-05,.00608473954379713479] 
dist 158=[.00157232280605849822,.00203877815087722434] 
dist 159=[.00150829788839742753,.00204167670690114856] 
dist 160=[.00137414755483961908,.00197742846742790994] 
dist 161=[.00120872594849857066,.00196779227169158082] 
dist 162=[.00102052638461996342,.00161048489326675161] 
dist 163=[.00078345268244321276,.00152362939738187185] 
dist 164=[.00042396670258935276,.00146365393970785152] 
dist 165=[6.28865206043396631480e-05,.00144899114428904475] 
dist 166=[-.00018052721380686747,.00016665352868378907] 
dist 167=[-.00037966635167545304,1.66586895404469815310e-05] 
dist 168=[-.00056497406494374467,-.00024553500542870316] 
dist 169=[-.00072289803511233805,-.00038373236420345203] 
dist 170=[-.00082484858480445147,-.00060714996233764025] 
dist 171=[-.00093879371189306109,-.00069304424607038752] 
dist 172=[-.00101123163082691185,-.00070666684467933258] 
dist 173=[-.00104397225777274183,-.00073016922636175980] 
dist 174=[-.00105480592368021751,-.00071352359644349681] 
dist 175=[-.00105141682614771089,-.00067738043222891554] 
dist 176=[-.00101919919079581722,-.00060613700157532300] 
dist 177=[-.00100408625876812557,-.00051961397603890424] 
dist 178=[-.00085582197308468797,-.00042279832815323013] 
dist 179=[-.00081777111641657758,-.00030185794316951436] 
dist 180=[-.00076268002184512667,-.00011954322153643513] 
dist 181=[-.00074171463328628000,6.32019812471357470800e-05] 
dist 182=[-.00024134260056282438,.00018585435485569682] 
dist 183=[-.00017619978821174995,.00029835206352399537] 
dist 184=[-3.00119105994154756110e-05,.00044296502741018727] 
dist 185=[1.29141390818542456120e-06,.00057588670600987588] 
dist 186=[.00016152494173669115,.00068802460653055928] 
dist 187=[.00018920412529792098,.00075011813818872671] 
dist 188=[.00020367819256095295,.00078637252291270869] 
dist 189=[.00020773090458015925,.00079546636413356254] 
dist 190=[.00020395314599290811,.00026794707277109705] 
dist 191=[.00019527329262314745,.00026700470051935290] 
dist 192=[.00017786517170030913,.00025922777398463850] 
dist 193=[.00015662653648620142,.00025496293965207380] 
dist 194=[.00012400767093504402,.00021950267304072003] 
dist 195=[8.05596423653745957340e-05,.00021023935020327261] 
dist 196=[1.52507700257503854280e-05,.00019522564348536596] 
dist 197=[-5.01478595953315848130e-05,.00019011749975884513] 
dist 198=[-9.39528517333704111240e-05,6.84225135244379887100e-05] 
dist 199=[-.00012949229846552116,5.19707396797393625620e-05] 
dist 200=[-.00016207258370739337,2.43910495930908972740e-05] 
dist 201=[-.00018950234615510575,6.99232604444939010990e-06] 
dist 202=[-.00020459142157360813,-1.22477894748506982900e-05] 
dist 203=[-.00021324862328082752,-2.13837164510489386660e-05] 
dist 204=[-.00021514009302150725,-2.36216741001643482830e-05] 
dist 205=[-.00021400191297799267,-2.42179082023467775020e-05] 
dist 206=[-.00014852870937840273,-2.28512978206692925610e-05] 
dist 207=[-.00014782545419756152,-1.98786165612880721970e-05] 
dist 208=[-.00014136330827122175,-1.40150661943092512790e-05] 
dist 209=[-.00014019550985135566,-6.89152361624556534410e-06] 
dist 210=[-.00011310684491294839,1.08455104733453172130e-06] 
dist 211=[-.00010667947078193098,1.10527136288788553550e-05] 
dist 212=[-.00010133626761871202,2.60865347185841182040e-05] 
dist 213=[-9.95705977191020413320e-05,4.11629471447690710890e-05] 
dist 214=[-1.67361706208195614410e-05,5.13004916815079849310e-05] 
dist 215=[-9.19015445123180635110e-06,5.95688274403296615840e-05] 
dist 216=[9.18399903382264869460e-07,6.72236376822877072310e-05] 
dist 217=[9.79257830550156376090e-06,7.37223026745025781900e-05] 
dist 218=[1.94496615364519535040e-05,7.74002204594068008550e-05] 
dist 219=[2.39187825532411583150e-05,7.96487215497664608880e-05] 
dist 220=[2.48208229199654526670e-05,8.04719811061857495380e-05] 
dist 221=[2.49725507015587305960e-05,8.07205414859649462960e-05] 
dist 222=[2.43560218931544310870e-05,3.75490356732317122340e-05] 
dist 223=[2.31059647691438318710e-05,3.73712199356915608240e-05] 
dist 224=[2.06968048229781721080e-05,3.61160727335982769220e-05] 
dist 225=[1.77876147004441693330e-05,3.55544614544053942470e-05] 
dist 226=[1.38637584210115675650e-05,3.02318379648446928380e-05] 
dist 227=[8.39514551956590551730e-06,2.88772290638541133080e-05] 
dist 228=[1.91659067217769666800e-07,2.68738852577251432310e-05] 
dist 229=[-8.01877998942251319400e-06,2.61331251884444664510e-05] 
dist 230=[-1.35150432703243152510e-05,9.27200809081858400480e-06] 
dist 231=[-1.79715318817210859390e-05,6.07528516500637288220e-06] 
dist 232=[-2.20533594304731179240e-05,5.20945558007237592480e-06] 
dist 233=[-2.54880869935252828460e-05,1.98001840527699551450e-06] 
dist 234=[-2.73751270596794405670e-05,1.29425856995821501750e-06] 
dist 235=[-2.84548454665683034500e-05,3.68514847996823016600e-07] 
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dist 240=[-1.62173775323382978040e-05,9.63314218927582258640e-07] 
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dist 242=[-1.22519843748202872720e-05,2.26890787069496283410e-06] 
dist 243=[-1.16316898049403093390e-05,3.13242245310331172110e-06] 
dist 244=[-1.14414103861640645550e-05,4.43584553442673814590e-06] 
dist 245=[-6.80107869294721385260e-06,5.74365565780056457700e-06] 
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dist 247=[-1.80272077693287642900e-06,7.34495931957824834500e-06] 
dist 248=[-1.55405692155985420050e-06,8.01503037499767400670e-06] 
dist 249=[-6.09433964542794258930e-07,8.58622250235782717780e-06] 
dist 250=[-4.12917344088285362090e-07,8.91396767896254519820e-06] 
dist 251=[-1.06944925203079422220e-07,9.13225323203675910280e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 2, 0, 1] 
dist 0=[113.16375314678062825   ,113.16375314678062825   ] 
dist 1=[111.94683735822095151   ,113.91973134641851372   ] 
dist 2=[108.83595628129693765   ,115.18801519030823839   ] 
dist 3=[103.65453706345951658   ,116.32957568386903535   ] 
dist 4=[94.205934786280941912  ,116.58537994535145185   ] 
dist 5=[84.137666067196011531  ,116.22923374419013550   ] 
dist 6=[76.488933155636475474  ,115.74149392687354772   ] 
dist 7=[69.253011953483349887  ,94.729498037505534068  ] 
dist 8=[60.811422548722882960  ,91.692767230572543181  ] 
dist 9=[52.337769518554926731  ,83.314934599740885072  ] 
dist 10=[44.961052928764617787  ,81.820054528484546553  ] 
dist 11=[37.013106070647636221  ,65.679856580723387898  ] 
dist 12=[26.243845655222646552  ,62.335360431221472529  ] 
dist 13=[15.826459412224855508  ,58.961514422686851045  ] 
dist 14=[9.2741775292317486811 ,56.871376280053304821  ] 
dist 15=[4.2899399853845064957 ,22.096257513336684639  ] 
dist 16=[.12166274571457013287,17.812295396085487967  ] 
dist 17=[-4.9723624761505184763 ,7.8035777835665883564 ] 
dist 18=[-12.470991735281568984  ,6.2863257589717377182 ] 
dist 19=[-18.971839007002496556  ,-6.0516782920972614427 ] 
dist 20=[-23.004264376309725029  ,-6.3142103265924293996 ] 
dist 21=[-25.967682743052681993  ,-6.3561665864083951234 ] 
dist 22=[-28.223564303756470866  ,-3.9911042424907796610 ] 
dist 23=[-29.794001794743645793  ,-1.2033583786080293953 ] 
dist 24=[-30.152858771064036519  ,1.0598623409399722840 ] 
dist 25=[-29.867321947550173307  ,3.2823222703449448339 ] 
dist 26=[-29.818187832720665504  ,5.9231714438822457838 ] 
dist 27=[-25.208768497669543057  ,8.5413156578563788950 ] 
dist 28=[-24.031360288810502820  ,10.682012326518107055  ] 
dist 29=[-23.291798633627297125  ,12.840270916791855646  ] 
dist 30=[-23.094878449588248329  ,15.537863437890964640  ] 
dist 31=[-4.6035623709312308133 ,17.966365585652702793  ] 
dist 32=[-2.4314872328147211714 ,19.058962972447504998  ] 
dist 33=[2.6050686999606037168 ,19.560628101452387909  ] 
dist 34=[2.8136319692623043218 ,19.637347129564557712  ] 
dist 35=[2.3447934736020549660 ,17.893792231891957655  ] 
dist 36=[1.4535172135627307574 ,17.369990275092163098  ] 
dist 37=[.51462732774159194702,17.002616975489649965  ] 
dist 38=[-.14354032760007468096,16.770576921924087701  ] 
dist 39=[-.69950999143574276347,14.410383285534068289  ] 
dist 40=[-1.2348196587161695097 ,14.470632970601812464  ] 
dist 41=[-2.5198610003442864924 ,14.338804424473455343  ] 
dist 42=[-5.1219746094391499949 ,14.156054431042151837  ] 
dist 43=[-7.4182622834867336054 ,12.777966234943119059  ] 
dist 44=[-8.8694204174024155670 ,12.382765813512329753  ] 
dist 45=[-9.9513866855476882662 ,11.505403877776661840  ] 
dist 46=[-10.784000828414857212  ,11.185974612288010822  ] 
dist 47=[-11.383830768327613165  ,5.9685366148774793070 ] 
dist 48=[-11.542189146835338245  ,5.2091930315820608756 ] 
dist 49=[-11.510382573372434029  ,3.5574180681898641077 ] 
dist 50=[-11.370788143326755335  ,3.0987253527304372160 ] 
dist 51=[-12.006595654732881528  ,1.3149938318904594778 ] 
dist 52=[-12.958336244932590173  ,.95361145562632351337] 
dist 53=[-13.507264155589084946  ,.29777941384246543471] 
dist 54=[-13.633719692897279655  ,.15328389755889524329] 
dist 55=[-4.7721820369225103800 ,2.1946659598817856930 ] 
dist 56=[-4.2926828285953676601 ,4.0818888726988397133 ] 
dist 57=[-3.2339083132664017114 ,5.6259045860330949927 ] 
dist 58=[-2.9297730839945785602 ,7.0592336940419111547 ] 
dist 59=[-.14588621529661159842,8.2756889387009837852 ] 
dist 60=[.16533724774071295309,9.0072856849674916771 ] 
dist 61=[.46560770741616939701,9.4248132941079601085 ] 
dist 62=[.4898633735232815027 ,9.5012918133537656805 ] 
dist 63=[.5081377187797419965 ,2.0810781714479716755 ] 
dist 64=[.48368478529504940046,2.1154275333463130851 ] 
dist 65=[.44127813800447912578,2.1156941006624990325 ] 
dist 66=[.37840066039137260794,2.1153581465159645339 ] 
dist 67=[.29025010861241608168,1.8085491905316740578 ] 
dist 68=[.1475645406030094889 ,1.7286445144584163063 ] 
dist 69=[.00197759690682999378,1.6815503337428718436 ] 
dist 70=[-.09770741764511785865,1.6686325643236676183 ] 
dist 71=[-.18268421043406676206,.3075139900482411117 ] 
dist 72=[-.26999742663495225629,.1471948652314838174 ] 
dist 73=[-.34318446158356040512,-.01340672355932741060] 
dist 74=[-.5611660066404766244 ,-.03154192195102012727] 
dist 75=[-.78598111298426615453,-.06810380324653574739] 
dist 76=[-.92242587213094271311,-.07620857358041894675] 
dist 77=[-1.0176828060608853781 ,-.126708377551443994  ] 
dist 78=[-1.0790807387448482643 ,-.13371490140172706434] 
dist 79=[-1.1168907777181062636 ,-.13596587729660210015] 
dist 80=[-1.1215620141249894572 ,-.12652894960800833313] 
dist 81=[-1.1068794808921549680 ,-.11163512583792547116] 
dist 82=[-1.0918802036477715701 ,-.09075467097012460303] 
dist 83=[-.95706216592379969389,-.06201456832771014092] 
dist 84=[-.91967369043826322808,-.01592369006449501187] 
dist 85=[-.86170456245715207017,.03112322978096455279] 
dist 86=[-.84021911580338904434,.06366431276397583494] 
dist 87=[-.31667757245166773452,.12233918445496566779] 
dist 88=[-.24703660803311406358,.31971728931539699136] 
dist 89=[-.08951183516843143540,.48051083627115725788] 
dist 90=[-.05699234395748070758,.62900252564464481288] 
dist 91=[-.04547682219203847626,.75505541505084319693] 
dist 92=[-.04364482059947979159,.82475821566804444286] 
dist 93=[-.02319123009054758599,.86516961079057816068] 
dist 94=[-.02067462627366157335,.87494920289482266316] 
dist 95=[-.02244274449377067859,.25696031859577989982] 
dist 96=[-.03043126762769104298,.25874521520595503526] 
dist 97=[-.04154001559230484213,.25377861016564124752] 
dist 98=[-.05569663396977170862,.25294389536116264634] 
dist 99=[-.07446990471789514781,.22220955268394824009] 
dist 100=[-.10390642744790656952,.21567333714766652266] 
dist 101=[-.13376770059124374831,.20211327278918146459] 
dist 102=[-.15423005300037447354,.19719734875572979515] 
dist 103=[-.1713006214320884669 ,.07497091689360476254] 
dist 104=[-.18770491455749993849,.07016418128459246964] 
dist 105=[-.20357381186209463397,.05223780805971715913] 
dist 106=[-.21622427508874177774,.04783014721371263098] 
dist 107=[-.22245384491295175155,.04210288730425990327] 
dist 108=[-.22320912171291932099,.03999836244126532763] 
dist 109=[-.12872607051205455327,.03831800799675679953] 
dist 110=[-.13441511539748655796,.03846239897877363621] 
dist 111=[-.13724572202995643789,.03972292158980125403] 
dist 112=[-.13729001718250737657,.04279726114524646531] 
dist 113=[-.13402690419820462261,.04671447961778001671] 
dist 114=[-.1323058754862731652 ,.05132147112663089745] 
dist 115=[-.11349181822990122303,.05721646927863426091] 
dist 116=[-.10857250207879884899,.06624707888327311165] 
dist 117=[-.10191250318178835854,.07533927443612800854] 
dist 118=[-.09915302859627099266,.08147912059225605674] 
dist 119=[-.03201399959822595711,.08650827319581784869] 
dist 120=[-.02373816484280903684,.09119201282906380073] 
dist 121=[-.00509507166022162103,.09518125505698525443] 
dist 122=[-.00112584667017432160,.09745381037609433347] 
dist 123=[.00913043841493359263,.09885987805193431258] 
dist 124=[.00934782588330874329,.09940979465998497293] 
dist 125=[.01086495129986954196,.09929489038516218883] 
dist 126=[.01082227595576576021,.09806179476781301058] 
dist 127=[.01043161431286877938,.03158237011149657052] 
dist 128=[.00947615852919427436,.03162685088954866093] 
dist 129=[.00825829031263883044,.03062365537042610513] 
dist 130=[.00682579918175328180,.03047892052731146921] 
dist 131=[.00499292781094346077,.02491686232383500302] 
dist 132=[.00218559242810893530,.02356704621191427416] 
dist 133=[-.00064001781870914438,.02264890987789374406] 
dist 134=[-.00254555015577321480,.02243864049778126167] 
dist 135=[-.00410334441091510364,.00249621166255518959] 
dist 136=[-.00554879050980218186,.00016769250731308996] 
dist 137=[-.00680916548228448815,-.00186847598320229453] 
dist 138=[-.00956413699454187119,-.00218549945250934501] 
dist 139=[-.01261035057155629967,-.00279948406716985911] 
dist 140=[-.01436712778436453637,-.00292135687072552950] 
dist 141=[-.01548339111711544618,-.00316939947872178565] 
dist 142=[-.01598685697859587276,-.00317094845463921052] 
dist 143=[-.0161547691242300906 ,-.00308324036951426800] 
dist 144=[-.01610138261398271128,-.00285360259307016717] 
dist 145=[-.0156195221639495178 ,-.00255692970323831673] 
dist 146=[-.01537695625567934914,-.00220305327414972752] 
dist 147=[-.01316321463774287287,-.00174713158314195870] 
dist 148=[-.01259076812722336573,-.00104531051521982479] 
dist 149=[-.01171993983332697931,-.00033717145865653637] 
dist 150=[-.01140440697815077202,.00014387115731444125] 
dist 151=[-.00382926922498935984,.00195309435531937546] 
dist 152=[-.00281880355071740140,.00473630250945657735] 
dist 153=[-.00055480924624533490,.00699751370588768822] 
dist 154=[-6.43796759520065192860e-05,.00907548975701698310] 
dist 155=[.00143799057343067055,.01082830029702041294] 
dist 156=[.00146380220499278634,.01179847494375465513] 
dist 157=[.00165465132382006619,.01236299440744884346] 
dist 158=[.00162661861155867024,.01250517467656571380] 
dist 159=[.00154975418399426915,.00376769654490984347] 
dist 160=[.00138829718457918280,.00376212576722686190] 
dist 161=[.00118914585862110202,.00362769765368977229] 
dist 162=[.00096261716640760715,.00360073308810023172] 
dist 163=[.00067736977000602422,.00295086963747737638] 
dist 164=[.00024508891899776711,.00279339697756955796] 
dist 165=[-.00018871594396488041,.00266234448600631074] 
dist 166=[-.00048002303453230003,.00261396038756178218] 
dist 167=[-.00071700252378486710,.00037657480038917854] 
dist 168=[-.00093513737013599318,.00010916111449765046] 
dist 169=[-.00111926595853983994,-.00022839040331195335] 
dist 170=[-.00134423284094479743,-.00027382660292294939] 
dist 171=[-.00171108522703130231,-.00035441408061226162] 
dist 172=[-.00191958453763797635,-.00036936083362493189] 
dist 173=[-.00204818258853716542,-.00038679561191974687] 
dist 174=[-.00209780512653229798,-.00038257666214962269] 
dist 175=[-.00210383425361131135,-.00036767702874973513] 
dist 176=[-.00209417523345108683,-.00033472960830555536] 
dist 177=[-.00200831223386612552,-.00029359196262214059] 
dist 178=[-.00198834602053115068,-.00024617114178524845] 
dist 179=[-.00162551401442277613,-.00018605191685128625] 
dist 180=[-.00153814858298600683,-9.44950038871372391390e-05] 
dist 181=[-.00145401537612308361,-2.41499401453662793770e-06] 
dist 182=[-.00141645419950132252,5.97841724963379697410e-05] 
dist 183=[-.00034708353064286570,.00015701991788682779] 
dist 184=[-.00023682240345216565,.00044409476339246195] 
dist 185=[1.20864366808241799440e-05,.00067745374295011608] 
dist 186=[6.21877258235751685860e-05,.00089217120557951027] 
dist 187=[.00014172757363231494,.00107352279928835955] 
dist 188=[.00014496483673704125,.00117440103885333520] 
dist 189=[.00015289716104578890,.00123577854143119041] 
dist 190=[.00014970014196050752,.00125041044239678413] 
dist 191=[.00014151681066996893,.00048364853168298758] 
dist 192=[.00012461214461098021,.00048226394490232417] 
dist 193=[.00010383930038141723,.00046248133689655435] 
dist 194=[8.02965215730792875660e-05,.00045960588817853306] 
dist 195=[5.06985441887445913780e-05,.00037054824415663313] 
dist 196=[5.88321685214520000000e-06,.00034941775453174995] 
dist 197=[-3.90992088869371913780e-05,.00033420200394971027] 
dist 198=[-6.93616135733100875660e-05,.00033076544001741925] 
dist 199=[-9.40503748015770343640e-05,3.84610320523622414780e-05] 
dist 200=[-.00011690509418584581,3.34975084621080603010e-05] 
dist 201=[-.00013629649599919033,1.41945316889001247490e-05] 
dist 202=[-.00015456423757053895,1.02600446374544351310e-05] 
dist 203=[-.00019974487122556717,3.15799005374350000000e-06] 
dist 204=[-.00022530775504586950,1.60139089857630001290e-06] 
dist 205=[-.00024092814793861203,-4.49772447163055726600e-05] 
dist 206=[-.00024663225339228651,-4.40346702212736478290e-05] 
dist 207=[-.00024726789986250576,-4.16590660294447067650e-05] 
dist 208=[-.00024582097803701329,-3.67707310527602437870e-05] 
dist 209=[-.00023711521700685517,-3.07684769719372928370e-05] 
dist 210=[-.00023320968840214083,-2.39696265041625896740e-05] 
dist 211=[-.00019823789058640878,-1.54232578724368517190e-05] 
dist 212=[-.00018935933822767968,-2.48207439495610951630e-06] 
dist 213=[-.00017571067266065789,1.05120012015752327030e-05] 
dist 214=[-.00017088133932709513,1.92686867465772706690e-05] 
dist 215=[-5.80589251341320061040e-05,3.42451002117241243500e-05] 
dist 216=[-4.32663428371717157100e-05,7.59991896841899821040e-05] 
dist 217=[-1.03653437379031184750e-05,.00010989848241510934] 
dist 218=[-2.95310029222478186890e-06,.00014102561985811597] 
dist 219=[2.42746421926540937440e-07,.00016727562644653516] 
dist 220=[6.87543627915731265660e-07,.00018180913329724289] 
dist 221=[1.34929321877732010760e-06,.00019031288925553542] 
dist 222=[6.67252143460002239590e-07,.00019243472675989012] 
dist 223=[-8.51223841832936243190e-07,5.73741386104271067680e-05] 
dist 224=[-3.86813434179584445810e-06,5.71382365764406852610e-05] 
dist 225=[-7.54015084189598108080e-06,5.46478727998160419610e-05] 
dist 226=[-1.16600105269674682350e-05,5.42757735509539279980e-05] 
dist 227=[-1.68141039972288803420e-05,4.37617890027731970540e-05] 
dist 228=[-2.45928666028591401650e-05,4.22861034313073730960e-05] 
dist 229=[-3.23952123558442399720e-05,3.92322385631915558420e-05] 
dist 230=[-3.76430900171829220810e-05,3.87884930227936461420e-05] 
dist 231=[-4.19247537958125092360e-05,1.53410133970702713050e-05] 
dist 232=[-4.58908498430362738400e-05,1.41899609241807907070e-05] 
dist 233=[-4.92592501856691938490e-05,1.00091596376489659090e-05] 
dist 234=[-5.11678293407432721570e-05,8.98972889226998914110e-06] 
dist 235=[-5.24591753355079580160e-05,7.88139035008090649790e-06] 
dist 236=[-5.27721860224516990070e-05,7.58798249711808309420e-06] 
dist 237=[-3.42127817038392587510e-05,7.53118619571064351680e-06] 
dist 238=[-3.48257863634169494430e-05,7.66389416040527839950e-06] 
dist 239=[-3.47612498659609430540e-05,7.95757047270465822370e-06] 
dist 240=[-3.45395384790945766050e-05,8.53999340495562960500e-06] 
dist 241=[-3.30517584438479309470e-05,9.24859231167430777140e-06] 
dist 242=[-3.26586129018704521150e-05,1.00433068769479742840e-05] 
dist 243=[-2.68060461922753754080e-05,1.10373590593890430190e-05] 
dist 244=[-2.53950517164370548560e-05,1.25374939105147733940e-05] 
dist 245=[-2.38648349526469463770e-05,1.40422214020842037680e-05] 
dist 246=[-2.31029505075603176040e-05,1.50545357304136325090e-05] 
dist 247=[-8.31965122156063225930e-06,1.58807507856713290460e-05] 
dist 248=[-7.15952804767979514640e-06,1.66465829160942672450e-05] 
dist 249=[-4.69061201498931247940e-06,1.72973810990730086670e-05] 
dist 250=[-4.01975153812290359450e-06,1.76668616366386885380e-05] 
dist 251=[-1.50172597066548029140e-06,1.94717221130076961200e-05] 
dist 252=[-9.71967142082475170700e-07,2.09550904358934249560e-05] 
dist 253=[-2.17185804402452193000e-07,2.18387644847198202690e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 1, 1, 0, 1] 
dist 0=[107.20972906848043577   ,107.20972906848043577   ] 
dist 1=[101.04344043350756330   ,110.10068739149983362   ] 
dist 2=[94.245517698625918495  ,111.65403234173746988   ] 
dist 3=[88.840558131658855165  ,112.53223812559392914   ] 
dist 4=[83.499191036727987650  ,112.89211575491716404   ] 
dist 5=[76.939105967485629305  ,112.04021864473338667   ] 
dist 6=[70.168470099141721445  ,111.33848309209000418   ] 
dist 7=[63.976772044772413392  ,110.40329247601607345   ] 
dist 8=[57.049549354196069640  ,109.69147041745846046   ] 
dist 9=[47.330747513776364675  ,85.484595723931365571  ] 
dist 10=[37.704289328788726196  ,82.125587230544308719  ] 
dist 11=[31.141379886960567766  ,72.800358159422755627  ] 
dist 12=[25.565883813830354408  ,71.463008592794029914  ] 
dist 13=[19.880780626186370226  ,53.775352689117916460  ] 
dist 14=[14.561614544716745606  ,50.230491685698096771  ] 
dist 15=[10.446779523980616767  ,46.677727462572600222  ] 
dist 16=[.01255778796378682835,46.025158204321408339  ] 
dist 17=[-6.5352057099126160431 ,12.853666482589917281  ] 
dist 18=[-11.246194384267598297  ,6.3690182446795156056 ] 
dist 19=[-14.720274910379782472  ,5.4540482092280670907 ] 
dist 20=[-17.324665558449450121  ,3.4611165032671382087 ] 
dist 21=[-18.565134891346477150  ,3.0278421573270213294 ] 
dist 22=[-20.194788079553615733  ,.5836877443689359106 ] 
dist 23=[-21.974450591994610458  ,.10968942478106999121] 
dist 24=[-22.705278221667940250  ,-.78790915581038404737] 
dist 25=[-22.897103465007797303  ,-1.0187019877387131337 ] 
dist 26=[-22.806206909612908407  ,-3.0332519982631137959 ] 
dist 27=[-22.041729002883059624  ,-.28038158423142455117] 
dist 28=[-21.715211181889412186  ,2.3646931328734206047 ] 
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dist 227=[3.61738426200071857200e-06,5.68190002066768991310e-05] 
dist 228=[6.03354179421485979270e-06,5.33700071325661468240e-05] 
dist 229=[1.89733766033527564700e-05,5.22591029847989196310e-05] 
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dist 231=[6.58953977098756275070e-06,4.69145090877544426810e-05] 
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dist 237=[-3.32807630815210878520e-05,2.17583338568480838890e-05] 
dist 238=[-3.49715741789556285050e-05,2.13079944957460258390e-05] 
dist 239=[-3.55194457616660714040e-05,1.99772294330744889680e-05] 
dist 240=[-3.54347429621323221520e-05,1.94033443533842303300e-05] 
dist 241=[-3.51939273105695904040e-05,1.62432651979925654430e-05] 
dist 242=[-3.37014078489620867730e-05,1.54337182624190513250e-05] 
dist 243=[-3.32538428338813977850e-05,1.41378830661540175290e-05] 
dist 244=[-2.74817782495050637420e-05,1.37134278298234464110e-05] 
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dist 248=[-5.29563969201703848030e-06,1.17130536908839256080e-05] 
dist 249=[-3.98509471739818992270e-06,1.16050071001900699720e-05] 
dist 250=[-2.66435577903961659520e-06,1.14738918637401587990e-05] 
dist 251=[-2.30175946873375632320e-06,1.10359297600419899200e-05] 
dist 252=[-9.17945257313131484320e-07,1.08038884115353828120e-05] 
dist 253=[-6.31304989888768825700e-07,9.40287469645810238580e-06] 
dist 254=[-1.70592928582515620330e-07,9.04268220135714218570e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 2, 0, 1, 2] 
dist 0=[123.34356995753539696   ,123.34356995753539696   ] 
dist 1=[122.06823742412994166   ,123.97952585423962001   ] 
dist 2=[119.34993704838808939   ,123.93575825930171801   ] 
dist 3=[112.95673746603532434   ,123.62794652414064824   ] 
dist 4=[105.65700595809267683   ,120.65977201730951705   ] 
dist 5=[99.334388739993498632  ,119.38073720841886745   ] 
dist 6=[90.974580952523617027  ,118.25947513681441361   ] 
dist 7=[77.863286690583078112  ,117.28074320978881563   ] 
dist 8=[68.059910328941928988  ,87.520719866708201547  ] 
dist 9=[58.930765932167784798  ,83.376166943895631866  ] 
dist 10=[48.487078719882442926  ,74.624334162372855108  ] 
dist 11=[37.637198664206149790  ,72.170276127652294703  ] 
dist 12=[22.090362433455189276  ,62.526789661853353299  ] 
dist 13=[11.560718995058965989  ,60.476532488117039642  ] 
dist 14=[2.8144445871859974040 ,56.534251807727851010  ] 
dist 15=[-5.6420698970453225862 ,55.555896371064815531  ] 
dist 16=[-13.158606284937886274  ,9.3474340800216093705 ] 
dist 17=[-18.170694319524082209  ,7.1718677815804974363 ] 
dist 18=[-22.274155418600146678  ,3.8058431832141960868 ] 
dist 19=[-26.186768311320751557  ,3.0448689849226184246 ] 
dist 20=[-29.380305629078799810  ,-12.302398790692352970  ] 
dist 21=[-30.625930908048673904  ,-14.052658228159035174  ] 
dist 22=[-31.086757856249112980  ,-10.644574187173098089  ] 
dist 23=[-31.144129969587934096  ,-5.0052074921100455162 ] 
dist 24=[-27.619174540932801882  ,-.77041671210704242607] 
dist 25=[-26.616856660826177994  ,3.1181655770280333905 ] 
dist 26=[-25.958509148864493319  ,7.3984365151080201869 ] 
dist 27=[-25.631594995236136226  ,11.475970648205583733  ] 
dist 28=[-7.1457464423178449897 ,14.568450254670557388  ] 
dist 29=[-4.9236210606638863672 ,17.472591104994301340  ] 
dist 30=[.32413752634275303496,20.812785746227369688  ] 
dist 31=[1.1222405876936741101 ,23.740460031063648319  ] 
dist 32=[7.5265313718501770264 ,25.009627954197178743  ] 
dist 33=[8.4988727127616947066 ,25.563074433080050668  ] 
dist 34=[10.264290999004909434  ,25.642545570165990787  ] 
dist 35=[10.550078461494392484  ,23.163568715727837288  ] 
dist 36=[13.289422124654970701  ,22.435144203763333069  ] 
dist 37=[13.307226295607170775  ,21.935811479244849033  ] 
dist 38=[10.072492112205880350  ,21.641631134547950869  ] 
dist 39=[4.1317099275218219914 ,15.979869129749719129  ] 
dist 40=[.02760924016511194869,14.189640785136484644  ] 
dist 41=[-3.4263472163170319130 ,13.672276482070429585  ] 
dist 42=[-6.7893837452288325553 ,12.799572594276240466  ] 
dist 43=[-9.7504845244099847685 ,12.497643759163824622  ] 
dist 44=[-11.610727258074376245  ,6.1939894113317754159 ] 
dist 45=[-12.984997021583213797  ,5.4453961368437486335 ] 
dist 46=[-14.019194758587191495  ,3.7713391660208410940 ] 
dist 47=[-14.751403404590815700  ,3.3107721482429903143 ] 
dist 48=[-14.927421553226678085  ,1.3719628202544367762 ] 
dist 49=[-14.867939413772190108  ,.99934834271675287211] 
dist 50=[-14.678427619664666231  ,.22038007842071684668] 
dist 51=[-13.128540003386938204  ,.02181421424364481344] 
dist 52=[-12.668762674247215530  ,-.61581925911911967277] 
dist 53=[-11.867692625172900150  ,-.60440743479692496855] 
dist 54=[-11.595027944610455953  ,-.35179350287442662499] 
dist 55=[-6.0320635319187656627 ,2.6926038425542307878 ] 
dist 56=[-5.3859658407103985366 ,5.1476218933444025031 ] 
dist 57=[-3.9463377596606188923 ,7.1566396337499652163 ] 
dist 58=[-2.9448037287918331079 ,9.0227882888692540998 ] 
dist 59=[-2.3483248936454243038 ,10.656165266421779705  ] 
dist 60=[-.38492618126056260646,11.600907072299780763  ] 
dist 61=[-.15470772431779156961,12.132063410429354415  ] 
dist 62=[.37894582336344751149,12.223969037732640757  ] 
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dist 188=[-3.99159975790343905050e-05,.00166706021419051071] 
dist 189=[1.09507510802786725430e-05,.00175442869183100730] 
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dist 200=[-5.98694146088372569580e-05,.00028316037526439073] 
dist 201=[-.00014147642350524315,.00027031557450185315] 
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dist 206=[-.00034786194063347232,8.58015360619343113700e-06] 
dist 207=[-.00034884170458911498,-2.07713102870108405700e-06] 
dist 208=[-.00034684241530633896,-5.44319456583711048400e-05] 
dist 209=[-.00033454995557037018,-6.36126950208863054210e-05] 
dist 210=[-.00032912694441295307,-7.81570959342943938280e-05] 
dist 211=[-.00027946492150121243,-8.09732661407673597050e-05] 
dist 212=[-.00026687756263220842,-8.10271506264962358330e-05] 
dist 213=[-.00024782772410517107,-7.89392057275495992800e-05] 
dist 214=[-.00024097834969521666,-4.36837464290606675860e-05] 
dist 215=[-7.86671720525847395420e-05,4.47858989245219719630e-05] 
dist 216=[-6.29597658492307548640e-05,.00010406084016473045] 
dist 217=[-5.96625875598555943100e-05,.00015218127841210816] 
dist 218=[-5.64920169351775658090e-05,.00019635971206478568] 
dist 219=[-5.57966044630734014570e-05,.00023361066885301412] 
dist 220=[-1.02405069408691427400e-05,.00025422399653114474] 
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dist 222=[7.89419980071654317250e-06,.00026924113479928142] 
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dist 225=[2.66713613993047351610e-05,7.78183783996508965220e-05] 
dist 226=[3.06647705361198685360e-05,7.72754848836884833780e-05] 
dist 227=[3.13056170268741727540e-05,6.22697146516471468420e-05] 
dist 228=[3.13999536220412146950e-05,5.90374044277650327770e-05] 
dist 229=[3.03391657648441608360e-05,5.59296861609519153770e-05] 
dist 230=[1.68277852038725143280e-05,5.52469075125484252690e-05] 
dist 231=[-1.73339751001284270890e-06,4.70377410102077438520e-05] 
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dist 234=[-3.36961509368168603750e-05,3.43225108155987592500e-05] 
dist 235=[-4.16215170588373498540e-05,3.32228465348924259740e-05] 
dist 236=[-4.60716041896890805340e-05,1.18719458029774220080e-05] 
dist 237=[-4.87468982692434942180e-05,1.02042949573726913910e-05] 
dist 238=[-4.96251495131494051020e-05,6.66073130575727911760e-06] 
dist 239=[-4.95382766064232352710e-05,5.69964738190556972910e-06] 
dist 240=[-4.92243962854510348050e-05,2.10292500935031123380e-06] 
dist 241=[-4.71057781907682492530e-05,1.34429695956054204130e-06] 
dist 242=[-4.65482128822438535900e-05,2.87030247965811929990e-07] 
dist 243=[-3.82001641012011058520e-05,0                     ] 
dist 244=[-3.61877896826498853750e-05,-1.27331345486838368020e-07] 
dist 245=[-3.40132666529762500060e-05,3.85973940070504606130e-07] 
dist 246=[-3.29264868707393353590e-05,1.35772811727827879630e-06] 
dist 247=[-1.18600561312716540780e-05,8.59015992173572280940e-06] 
dist 248=[-1.02195522003650814010e-05,1.45820707122784968680e-05] 
dist 249=[-6.73324207439048505040e-06,1.94509084792110496800e-05] 
dist 250=[-5.72277650515630178030e-06,2.39290859526609625930e-05] 
dist 251=[-2.14299291893597956500e-06,2.77113133623839834710e-05] 
dist 252=[-1.39022223046208725500e-06,2.98166896003595306570e-05] 
dist 253=[-3.13195302866393091850e-07,3.10635523668786069330e-05] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 2, 2, 1, 0, 2] 
dist 0=[130.76796524359224678   ,130.76796524359224678   ] 
dist 1=[130.05905683433005624   ,130.51642485816814324   ] 
dist 2=[127.00452049067362308   ,130.76796524359224678   ] 
dist 3=[122.53299140970857990   ,129.85979079132491077   ] 
dist 4=[116.62442982627306168   ,121.31418136328820854   ] 
dist 5=[108.63828774745355051   ,118.92568580783431487   ] 
dist 6=[95.900919831030417679  ,117.64082054965866734   ] 
dist 7=[82.308925765666960589  ,114.08772152672736162   ] 
dist 8=[65.352350869333184850  ,91.267897191255019896  ] 
dist 9=[53.210935117604847380  ,87.520229030697325440  ] 
dist 10=[42.449972200688596642  ,83.413409502353743022  ] 
dist 11=[30.966779746484479816  ,81.789971606241255372  ] 
dist 12=[20.059903652050493660  ,48.819784566904418989  ] 
dist 13=[11.576683696725043559  ,43.957288927249529128  ] 
dist 14=[3.3052309794352612567 ,42.812338233150281621  ] 
dist 15=[-6.7843241838079704446 ,33.574456833520898734  ] 
dist 16=[-16.110214295186989770  ,4.990779153851032350  ] 
dist 17=[-21.349839854125398929  ,-.5732182673672792719 ] 
dist 18=[-24.891580796888182767  ,-2.848266905802308616  ] 
dist 19=[-29.276402728021416266  ,-5.9387604718722691081 ] 
dist 20=[-32.826318801429683584  ,-6.4116714158244007453 ] 
dist 21=[-34.245390863613328784  ,-5.3731500573929651531 ] 
dist 22=[-34.773890881505464566  ,-2.6141895355883620629 ] 
dist 23=[-34.767093355109340687  ,.5057467380140360685 ] 
dist 24=[-31.162139849980201529  ,2.9840011583499860363 ] 
dist 25=[-30.057162058795070046  ,5.3803716918308081194 ] 
dist 26=[-29.195982408606174064  ,8.1884234924920059897 ] 
dist 27=[-28.594087007241223046  ,10.959403877849234384  ] 
dist 28=[-9.1480860531656830657 ,13.216100837440964348  ] 
dist 29=[-6.7424438841360569392 ,15.486179682724381250  ] 
dist 30=[-.9898789316524431962 ,18.319142998295762760  ] 
dist 31=[-.1308104063382483187 ,20.847218249587305762  ] 
dist 32=[7.1648291225956738219 ,21.909175184076522239  ] 
dist 33=[8.3064398493341557361 ,22.364504432709098045  ] 
dist 34=[10.228289871507986481  ,22.478190372123276239  ] 
dist 35=[10.581425514787579011  ,20.025140118636750372  ] 
dist 36=[10.550504531215500873  ,19.931687114671227410  ] 
dist 37=[9.0580224830064466227 ,20.025493841255316695  ] 
dist 38=[6.9934710758642123265 ,19.652840261665972902  ] 
dist 39=[3.6792843424504340058 ,19.461947674664564289  ] 
dist 40=[.30667767131599095563,16.539823155836856566  ] 
dist 41=[-1.9904147435684198050 ,15.778891221715049423  ] 
dist 42=[-4.7857109300469502860 ,14.914406815931487189  ] 
dist 43=[-7.2939513844098207455 ,14.482953343136809601  ] 
dist 44=[-8.8730493454349273493 ,6.6522341708875679272 ] 
dist 45=[-10.043573371879516885  ,5.9240216372493067881 ] 
dist 46=[-10.931880180581775412  ,4.2812658162193931510 ] 
dist 47=[-11.567314802528862564  ,3.8281829265480721405 ] 
dist 48=[-11.734495808894446479  ,1.8569227526679055025 ] 
dist 49=[-12.680884151866546159  ,1.4820484350082301028 ] 
dist 50=[-13.280089633299861736  ,.6447439494125945509 ] 
dist 51=[-13.393756325696891101  ,.45692483795839743324] 
dist 52=[-9.9424426307271273475 ,-3.2959151373435129703 ] 
dist 53=[-9.3757366048530631836 ,-2.9141618139954416707 ] 
dist 54=[-9.1533995272683782858 ,-2.1613694117017062650 ] 
dist 55=[-3.5000864124720740880 ,.96954335559102323642] 
dist 56=[-2.7415643346088251721 ,3.0788065358522055225 ] 
dist 57=[-1.0104312920801066626 ,4.7996926088212587702 ] 
dist 58=[-.64693409607941407643,6.3893869413850780491 ] 
dist 59=[.34516073116627805786,7.7331599463506107151 ] 
dist 60=[1.1229500406034600732 ,8.4781202505735190169 ] 
dist 61=[1.2421800620022073829 ,8.9120624654578507329 ] 
dist 62=[1.4520891900444549272 ,9.0213504507906139656 ] 
dist 63=[1.4857367125301258482 ,2.7670816301820584394 ] 
dist 64=[1.9665047942483319362 ,2.8011161463941805578 ] 
dist 65=[1.9686545812046369059 ,2.7843647338936633745 ] 
dist 66=[1.9017474977428812036 ,2.7759408133707946212 ] 
dist 67=[1.7254893534038006703 ,2.3736918242514632074 ] 
dist 68=[1.4978127301081806995 ,2.2680211621827613048 ] 
dist 69=[1.2267629864914426620 ,2.1882422762924163362 ] 
dist 70=[.87812627499163670084,2.1533493216358738547 ] 
dist 71=[.2305589973502863551 ,1.5788539658548289032 ] 
dist 72=[-.2116342519512593696 ,.61999371710612443741] 
dist 73=[-.57739988860017701247,.4924616950667513915 ] 
dist 74=[-.92394779304041867975,.20227357390594333464] 
dist 75=[-1.2232193299554510887 ,.13950582336776232346] 
dist 76=[-1.4013761877691918722 ,-.19476266769682855966] 
dist 77=[-1.5215687960658557331 ,-.2521367664192593884 ] 
dist 78=[-1.5908212356290574184 ,-.362143187113458542  ] 
dist 79=[-1.6259121067508648142 ,-.38465355889965591036] 
dist 80=[-1.6281048251242262072 ,-.43351930203125982159] 
dist 81=[-1.5828915912048349746 ,-.43564207297889354928] 
dist 82=[-1.5694444784610445169 ,-.42129483794208123896] 
dist 83=[-1.3083244167560859598 ,-.38123299603741936017] 
dist 84=[-1.2429563123172812859 ,-.32891595816193488597] 
dist 85=[-1.1801053570486586304 ,-.26590711534947215062] 
dist 86=[-1.1484798571851395649 ,-.18438818917136303299] 
dist 87=[-.36491628005013529027,.11496713187250907276] 
dist 88=[-.26681845698649373998,.33963364348037982454] 
dist 89=[-.16834971009147178692,.52307554450006793552] 
dist 90=[-.11105093092045098547,.69300065494692258243] 
dist 91=[-.09657070763575020435,.8371424773711731293 ] 
dist 92=[-.02836854521645297144,.92490401815422192623] 
dist 93=[-.01589928524081514288,.97480944483313692381] 
dist 94=[.01079058034680009558,.98642710664021557324] 
dist 95=[.01682833934752632113,.42044175086323616434] 
dist 96=[.03967913371283401186,.42593933085151176368] 
dist 97=[.04034875186136806372,.42463522361631432694] 
dist 98=[.03360140157863704533,.41322363832525959431] 
dist 99=[.01519958244634776512,.40580416592285773922] 
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dist 168=[-.00047747724573152346,.00069152623072956082] 
dist 169=[-.00117331971217625908,.00047935714555764471] 
dist 170=[-.00181906176353115353,-9.08466871875404342410e-07] 
dist 171=[-.00236830535034456849,-9.70571538959410640060e-05] 
dist 172=[-.00268101821898525253,-.00063346314319319573] 
dist 173=[-.00287461770225658809,-.00072291986139685341] 
dist 174=[-.00295094646404081321,-.00087984734193297688] 
dist 175=[-.00296600529012206283,-.00090808879817999843] 
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dist 180=[-.00228147428359838772,-.00070364303004950157] 
dist 181=[-.00212029074081084517,-.00059720934004571499] 
dist 182=[-.00206211458912211867,-.00037966914749416603] 
dist 183=[-.00067937018114796223,.00037448344403603641] 
dist 184=[-.00049608958076275842,.00087990110461449100] 
dist 185=[-8.66231206313496286070e-05,.00129030734639008699] 
dist 186=[2.74532352027770046480e-06,.00166720803327477858] 
dist 187=[.00018311943405084833,.00198504840914524370] 
dist 188=[.00036632788150924813,.00216094824723260501] 
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dist 191=[.00044917304162340059,.00069720599658111282] 
dist 192=[.00046680881284014346,.00069494976265650301] 
dist 193=[.00045413699954033643,.00066599950228548303] 
dist 194=[.00042891689665083364,.00066166616511239481] 
dist 195=[.00038063134078661547,.00053390985560132850] 
dist 196=[.00032243370974427804,.00050596745945062370] 
dist 197=[.00025785403448439324,.00048048921529784781] 
dist 198=[.00014626068139813805,.00047513890476582773] 
dist 199=[-1.21138152708549369000e-05,.00033292945634154033] 
dist 200=[-.00011851162247255208,.00011362597290098174] 
dist 201=[-.00020519671440347252,8.48195782988352473430e-05] 
dist 202=[-.00028530058167075849,2.06262438379888482360e-05] 
dist 203=[-.00035320944903638090,6.26372521276443094470e-06] 
dist 204=[-.00039147348868127871,-6.29320257331113050970e-05] 
dist 205=[-.00041464945744685055,-7.51887292160663382870e-05] 
dist 206=[-.00042265034376899546,-9.49861823107810051320e-05] 
dist 207=[-.00042240494893986528,-9.91200423204061140810e-05] 
dist 208=[-.00041988852122065261,-9.99818155153974675160e-05] 
dist 209=[-.00040214723072694391,-9.71891571072245079580e-05] 
dist 210=[-.00039744204159226333,-9.14296248817301400350e-05] 
dist 211=[-.00032646893044174333,-8.02648778271461011150e-05] 
dist 212=[-.00030932489846309877,-6.67621149808779435410e-05] 
dist 213=[-.00029085735211691423,-5.17183421204368024140e-05] 
dist 214=[-.00028158303770328753,-4.42341429106210000000e-06] 
dist 215=[-.00010208953440060246,7.19222373942978745200e-05] 
dist 216=[-8.80275341561280715180e-05,.00012313011716282028] 
dist 217=[-5.80224032266861308940e-05,.00016476369543199933] 
dist 218=[-4.98445531935168859580e-05,.00020309286213448802] 
dist 219=[-1.89991045057468658870e-05,.00023548787613356326] 
dist 220=[-1.25387263385887772410e-05,.00025355876650998998] 
dist 221=[-2.99381862954073428730e-06,.00026459244888069286] 
dist 222=[-3.88755400548955712670e-07,.00026743243087844678] 
dist 223=[4.22851458951851582930e-06,9.68707659489856001930e-05] 
dist 224=[4.89631864522205528460e-06,9.67608446411027064280e-05] 
dist 225=[3.74243047474352911420e-06,9.60406145988497488580e-05] 
dist 226=[1.29349389593892282170e-06,9.25266207633604395770e-05] 
dist 227=[-3.49930629336924623690e-06,9.07750787843059249070e-05] 
dist 228=[-9.31075469134859868490e-06,7.76779747519757351930e-05] 
dist 229=[-1.58048179074129374080e-05,7.43199490437511934610e-05] 
dist 230=[-2.39132976835328367430e-05,6.84534778807297577790e-05] 
dist 231=[-3.61355332203540824110e-05,6.66390316858090198690e-05] 
dist 232=[-4.83924526418617882450e-05,2.46173748743357958470e-05] 
dist 233=[-5.66388727736084705890e-05,1.88396001884182944540e-05] 
dist 234=[-6.33709698949201863080e-05,9.37832494821713530780e-06] 
dist 235=[-7.09015829766906990940e-05,8.06281450838781806780e-06] 
dist 236=[-7.62537477193536665900e-05,3.09289586293182158480e-06] 
dist 237=[-7.94812597971371308190e-05,2.05342589837873261840e-06] 
dist 238=[-8.05635633122453710910e-05,4.99826875018578616190e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[110.46184193865194096   ,110.46184193865194096   ] 
dist 1=[107.18745813118599374   ,111.44110256121993705   ] 
dist 2=[103.23493286829135206   ,112.05487532773670749   ] 
dist 3=[99.671980962381266615  ,112.53169130245604072   ] 
dist 4=[95.750205196406276285  ,112.30288584429875518   ] 
dist 5=[90.358367747732209622  ,109.07582923748104614   ] 
dist 6=[84.470632665413612418  ,107.87454718712658218   ] 
dist 7=[78.414183963919544857  ,106.10221476678481028   ] 
dist 8=[66.246377865893824521  ,105.28784058374645093   ] 
dist 9=[57.116557245884515985  ,81.328117528173762398  ] 
dist 10=[48.597699145583367220  ,77.979692507365415873  ] 
dist 11=[38.841620796479186904  ,68.995617334687201330  ] 
dist 12=[29.159968659336426997  ,67.579391434972305897  ] 
dist 13=[20.921736157462570768  ,51.370572394833908347  ] 
dist 14=[12.211045625345875717  ,48.138583356703783969  ] 
dist 15=[.62353718645266738643,44.474724761100264492  ] 
dist 16=[-10.371656576196278730  ,43.469076039966882669  ] 
dist 17=[-16.732016396483260224  ,19.010311991310252736  ] 
dist 18=[-20.937057285839271496  ,7.7560094642653584592 ] 
dist 19=[-23.348967078252223931  ,4.5119755989696892149 ] 
dist 20=[-24.907562960952799884  ,1.0881435196778498375 ] 
dist 21=[-25.707372151114662538  ,.28686348598023689471] 
dist 22=[-26.366883762658183773  ,-2.0540520140358165330 ] 
dist 23=[-27.600815257281509114  ,-2.4400895556137780842 ] 
dist 24=[-28.160350298479002785  ,-2.2701612173289233808 ] 
dist 25=[-28.275382011879596949  ,-1.3159310418930568388 ] 
dist 26=[-17.564564218526847535  ,-.2246143481000583321 ] 
dist 27=[-17.033988593738104010  ,.49246770003446981884] 
dist 28=[-16.956541828932896270  ,2.3976868257000816974 ] 
dist 29=[-13.940798373824055891  ,4.8481655726596275108 ] 
dist 30=[-13.216617715962098660  ,7.0300250016263341308 ] 
dist 31=[-12.703306068668916920  ,9.3589187412681948240 ] 
dist 32=[-12.587914607167358303  ,11.401136152509423842  ] 
dist 33=[-2.1026950470911903112 ,12.447579743974534943  ] 
dist 34=[-.87931812364652828841,12.973151889965850006  ] 
dist 35=[-.31111581484328963522,13.057949665647190748  ] 
dist 36=[-.67394571677886671175,12.582695411206354846  ] 
dist 37=[-1.0751667243790323340 ,12.313434338298469675  ] 
dist 38=[-1.4557895159177148544 ,11.882454703543589291  ] 
dist 39=[-1.7376147133527933405 ,11.671066450999664766  ] 
dist 40=[-1.9938027118624349422 ,7.6578183959924780504 ] 
dist 41=[-2.6124447620192019131 ,7.7903801045175100153 ] 
dist 42=[-4.6308183839124255759 ,7.7813364910942672199 ] 
dist 43=[-6.5142111225221406288 ,7.5779208771793048211 ] 
dist 44=[-8.1110944666976679359 ,7.4686003103631377051 ] 
dist 45=[-8.9947822276406621050 ,6.4153873543101330267 ] 
dist 46=[-9.5047230656416045502 ,6.1417604170203476977 ] 
dist 47=[-9.6195366878380216798 ,5.7350469813662527886 ] 
dist 48=[-2.8611248348163281867 ,5.5834316100890641894 ] 
dist 49=[-3.0585152521521742011 ,1.9246846647422110658 ] 
dist 50=[-3.1544461764158850655 ,1.4392042324719524182 ] 
dist 51=[-3.1783419564648378167 ,1.4661028969681251807 ] 
dist 52=[-4.1306757500204659659 ,1.8114648088582874148 ] 
dist 53=[-4.9637440622550231141 ,2.2107435131070327495 ] 
dist 54=[-5.4249118704150807173 ,2.5328782065473982854 ] 
dist 55=[-5.6932547848288135806 ,2.6803865736685194477 ] 
dist 56=[-5.7607875101829155446 ,2.7481881291868767940 ] 
dist 57=[-1.7777290300905108971 ,2.7544316654679268129 ] 
dist 58=[-1.7790816300752428893 ,.19888759406284934788] 
dist 59=[-1.7225167663131959893 ,.61475424324106457359] 
dist 60=[-1.7119978438254243667 ,.98469795436045026579] 
dist 61=[-1.4099786076713267008 ,1.2233610190310311837 ] 
dist 62=[-1.3372097208823925358 ,1.4068350418434516467 ] 
dist 63=[-1.2774273901967472462 ,1.5580372033979979160 ] 
dist 64=[-1.2576776487451807086 ,1.6726493523393410777 ] 
dist 65=[-.20940078434263247231,1.7109689866358989423 ] 
dist 66=[-.08445006487783141050,1.7162124241067096756 ] 
dist 67=[.20682773989454511949,1.6993253703589602529 ] 
dist 68=[.25072827671663791755,1.5293649019840420631 ] 
dist 69=[.59485808440214656277,1.4766499270946624529 ] 
dist 70=[.64620106134984486801,1.3987898761135420480 ] 
dist 71=[.33688371876880450161,1.3664798141024604742 ] 
dist 72=[-.11909470188543231604,.9533940318310340534 ] 
dist 73=[-.42678008948684353946,.95931906545745466559] 
dist 74=[-.6781866472498129611 ,.95596402317026780791] 
dist 75=[-.91086536449900429159,.91858686397770880926] 
dist 76=[-1.1077054708878077521 ,.9100089018992923044 ] 
dist 77=[-1.2169036748895788373 ,.74489990564263833503] 
dist 78=[-1.2806454379622287614 ,.70504531891388555126] 
dist 79=[-1.2966768591865273221 ,.66763479619735115413] 
dist 80=[-.42827714940786676202,.65137633104677555386] 
dist 81=[-.4362274239471908479 ,.16296009483796679321] 
dist 82=[-.43664394826909726376,.11267896005128413737] 
dist 83=[-.43408856890351930248,-.00108439658484642606] 
dist 84=[-.39461907422781138337,-.02372651456839191332] 
dist 85=[-.47699240985796021716,-.15049613777582476004] 
dist 86=[-.52288779148519873437,-.17158710223150245178] 
dist 87=[-.55146169818559072553,-.11959756172074387851] 
dist 88=[-.55818034291621820949,-.01122973860223844207] 
dist 89=[-.27035716537036044697,.06260606300730514301] 
dist 90=[-.26786810117710584748,.12376693185355469237] 
dist 91=[-.26072765730002903796,.18183859289162853791] 
dist 92=[-.25649569916522930035,.23205382351526828862] 
dist 93=[-.22994621364135209925,.26203853484502978166] 
dist 94=[-.22296930171821900313,.28236895849811281722] 
dist 95=[-.20310304265494586068,.29427364799447540696] 
dist 96=[-.19661698430989852034,.30067064207151579849] 
dist 97=[-.12056682623292905385,.30049338574142331552] 
dist 98=[-.10745149607225769261,.29463541299440433196] 
dist 99=[-.08095848080053022134,.28958804243781490428] 
dist 100=[-.07381416473012259525,.25476641489070301986] 
dist 101=[-.04791079194861011916,.24515301775720262275] 
dist 102=[-.04168999935566546204,.22689292315574874314] 
dist 103=[-.03495868955786006545,.19099576770291681975] 
dist 104=[-.03335741603803410767,.10915982529405773441] 
dist 105=[-.04129986838788340916,.10969743259129540996] 
dist 106=[-.06457388379706369734,.10914196298485412028] 
dist 107=[-.08883770431424191327,.10543085944736677885] 
dist 108=[-.10945461301755288359,.10374531825034061104] 
dist 109=[-.12238070107507295305,.08827522794816099952] 
dist 110=[-.1300130025395766156 ,.08433811919570903866] 
dist 111=[-.13186428689584386903,.07837574146446125892] 
dist 112=[-.05931685061586766938,.07622757797729003148] 
dist 113=[-.05973564677609769648,.02505129217074163367] 
dist 114=[-.05857291523417119833,.01823772872234210149] 
dist 115=[-.05840476728504726280,.00301294273001724542] 
dist 116=[-.06127308200006905901,-.00029334523152035757] 
dist 117=[-.07302755266803977275,-.01677044882114288937] 
dist 118=[-.07953197261549496020,-.01964407421099265251] 
dist 119=[-.08331610392573738224,-.01934065701023352772] 
dist 120=[-.08426911460901611800,-.00615101948642903857] 
dist 121=[-.02540511806667739725,.00279877799417021668] 
dist 122=[-.02531583389556637680,.01017873916731251304] 
dist 123=[-.02429581087169577125,.01713752611564197430] 
dist 124=[-.02409924686198961203,.02312726068694412230] 
dist 125=[-.01961343609758387207,.02666095034537645270] 
dist 126=[-.01853983832723820545,.02900609791467575943] 
dist 127=[-.01763131652596442399,.03027845465925128812] 
dist 128=[-.01730628842189449000,.03090443683310005231] 
dist 129=[-.00231855355830707964,.03090020381134891926] 
dist 130=[-.00052878403154958276,.03019439323401705501] 
dist 131=[.00362157880754356956,.02975351308782703809] 
dist 132=[.00425694312795427062,.02572248439939258215] 
dist 133=[.00909023540142184835,.02465118895612354254] 
dist 134=[.00980769155595082386,.02301810046278182634] 
dist 135=[.00454555444089148410,.02241724939000183327] 
dist 136=[-.00349509300623353265,.01399585310115657341] 
dist 137=[-.00889300756523403336,.01399067788466918296] 
dist 138=[-.01328304917218752180,.01391189169148495760] 
dist 139=[-.01732254482709556600,.01330940144655651017] 
dist 140=[-.02073171914333019509,.01317305576393987602] 
dist 141=[-.02261940240137451171,.01073369070786280430] 
dist 142=[-.02371806632248292130,.01015009568587784498] 
dist 143=[-.02399480441786154085,.00958566746861504789] 
dist 144=[-.00725762761528732487,.00933791677925953258] 
dist 145=[-.00727223160253665448,.00223370668743350563] 
dist 146=[-.00706834927300744614,.00150231970941487502] 
dist 147=[-.00702387600454669072,-.00014492809143043533] 
dist 148=[-.00593617588032629743,-.00047759135549655218] 
dist 149=[-.00713238398032078033,-.00228752876498547146] 
dist 150=[-.00779649341136443174,-.00259156965375475995] 
dist 151=[-.00819039186127654282,-.00199002267334258006] 
dist 152=[-.00829099799349566899,-.00034178058511883924] 
dist 153=[-.00320280402562780457,.00077098181130830338] 
dist 154=[-.00318887711642984770,.00168294885536312719] 
dist 155=[-.00304746489316991426,.00253406941071993938] 
dist 156=[-.00302703015831909617,.00326100665393547067] 
dist 157=[-.00242776630131142632,.00367998778301627152] 
dist 158=[-.00228672401467285173,.00394583895467955471] 
dist 159=[-.00218358931758240152,.00406488160833161246] 
dist 160=[-.00216081222258121092,.00409853606240190940] 
dist 161=[-.00017260645322501690,.00408676745187913195] 
dist 162=[5.88658760434501051830e-05,.00393444064163704678] 
dist 163=[.00059610703349342868,.00389741692997884183] 
dist 164=[.00067446500595362162,.00320261134660013956] 
dist 165=[.00129702057179108296,.00303361244922374832] 
dist 166=[.00138789074553902727,.00287239685097424492] 
dist 167=[.00055855746903956775,.00279880664489524392] 
dist 168=[-.00028111297874363406,.00161212306720020889] 
dist 169=[-.00084496709854651408,.00161166595587659303] 
dist 170=[-.00130387736590531854,.00160083142634415204] 
dist 171=[-.00172690041503732617,.00154044826363245024] 
dist 172=[-.00208459662349391142,.00151505082608152186] 
dist 173=[-.00228463637680502502,.00128208842641230181] 
dist 174=[-.00241018930153195271,.00122352510766192648] 
dist 175=[-.00243898652201647510,.00113505302258532771] 
dist 176=[-.00094813706905230553,.00110335904048103838] 
dist 177=[-.00094764196056989692,.00035543067108295078] 
dist 178=[-.00091366095591133553,.00025641641536305125] 
dist 179=[-.00090870361315930515,3.58065332326486748240e-05] 
dist 180=[-.00090598466055194740,-1.25299024534666540800e-05] 
dist 181=[-.00107701504231482094,-.00024916618275862606] 
dist 182=[-.00117164277379628363,-.00029070390454400094] 
dist 183=[-.00122669335770356117,-.00027158694860728919] 
dist 184=[-.00124056727467133488,-6.50331797221306052770e-05] 
dist 185=[-.00037775242286344633,7.42443652011518373230e-05] 
dist 186=[-.00037579324594421775,.00018813586806991542] 
dist 187=[-.00035846625959978933,.00029404605695396752] 
dist 188=[-.00035592910532280604,.00038426956258468486] 
dist 189=[-.00028492797932961203,.00043588199039525355] 
dist 190=[-.00026937017439282783,.00046814484783039574] 
dist 191=[-.00025564679986075510,.00048154749628792836] 
dist 192=[-.00025283551788268185,.00048490336681770872] 
dist 193=[-4.53944417147665436620e-05,.00048279381342945725] 
dist 194=[-2.04636482622489269350e-05,.00046698376442251386] 
dist 195=[3.66645232868987861920e-05,.00045975127812852282] 
dist 196=[4.64168637624245906840e-05,.00039160580871051195] 
dist 197=[.00011130647776480485,.00037428515543290682] 
dist 198=[.00012138566988670910,.00034806642284942860] 
dist 199=[6.30028937174992492490e-05,.00033857396907669616] 
dist 200=[-6.04477672043333474460e-05,.00022729115074703374] 
dist 201=[-.00014320099027536474,.00022650320509751024] 
dist 202=[-.00021041210201390900,.00022494424901738692] 
dist 203=[-.00027215272123570488,.00021498167441879136] 
dist 204=[-.00032422440935329669,.00021240945942730621] 
dist 205=[-.00035304464501798286,.00017398165791288545] 
dist 206=[-.00036982000508796106,.00016475239261847787] 
dist 207=[-.00037404719019740749,.00015478772473288855] 
dist 208=[-.00011836589818368892,.00014981643953196650] 
dist 209=[-.00011797609701732508,5.32023346315005470870e-05] 
dist 210=[-.00011366070030980865,4.56662805062765731200e-05] 
dist 211=[-.00011247641516862943,2.96806181264636681790e-05] 
dist 212=[-.00010934086407095174,2.53542496111809073030e-05] 
dist 213=[-.00012655722785119484,9.21820584020455224340e-06] 
dist 214=[-.00013612259193986841,5.80517675903274884760e-06] 
dist 215=[-.00014174109252106736,1.16890599387736806280e-06] 
dist 216=[-.00014328487566069157,2.48591748450948888010e-06] 
dist 217=[-6.20521618536789934810e-05,2.11086530048569157200e-05] 
dist 218=[-6.14086435454911449930e-05,3.62852826381172959310e-05] 
dist 219=[-5.97983360288204954790e-05,5.03158979528808374730e-05] 
dist 220=[-5.88876301366486683930e-05,6.22140945344671374670e-05] 
dist 221=[-5.32597270696622367900e-05,6.89238833026255939250e-05] 
dist 222=[-5.17913981033985021400e-05,7.29948480200301616380e-05] 
dist 223=[-4.71691716373131994820e-05,7.44155257228878128040e-05] 
dist 224=[-4.60117678509726056740e-05,7.44615872788330648390e-05] 
dist 225=[-3.05082445762075636200e-05,7.39517643159130962340e-05] 
dist 226=[-2.77119497104333579060e-05,7.13411886586846433110e-05] 
dist 227=[-2.22105363322875944170e-05,7.00126093339440152250e-05] 
dist 228=[-2.07310064189677697010e-05,6.00155113210822962420e-05] 
dist 229=[-1.54593217065642459990e-05,5.74422667103960912210e-05] 
dist 230=[-1.41042353704757110620e-05,5.29105684338574586200e-05] 
dist 231=[-1.28416465474000492520e-05,4.63427931785397018610e-05] 
dist 232=[-1.25776605542098685920e-05,1.91592979668004240200e-05] 
dist 233=[-2.00995811406232186750e-05,1.45988067366969656140e-05] 
dist 234=[-2.69372348539230044050e-05,9.66927910220523902610e-06] 
dist 235=[-3.32366095545358087060e-05,8.32236428398090045050e-06] 
dist 236=[-3.85633601744525017560e-05,3.22179690000492220090e-06] 
dist 237=[-4.15390946844693672200e-05,2.15724802499606696510e-06] 
dist 238=[-4.33919346222186541750e-05,5.39229889705137349580e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 1, 2, 1, 2] 
dist 0=[116.81709926992505428   ,116.81709926992505428   ] 
dist 1=[110.93921539775246564   ,120.72071282978857596   ] 
dist 2=[100.99073497069098695   ,122.81428761292434259   ] 
dist 3=[90.551395790547612113  ,123.88764634450993423   ] 
dist 4=[82.714569904515388874  ,123.74273096381400147   ] 
dist 5=[75.401857399562819930  ,122.88813203696678940   ] 
dist 6=[67.030047299214388372  ,122.15171261150477924   ] 
dist 7=[58.724893622462561762  ,117.51319322628809111   ] 
dist 8=[51.663041970009798369  ,110.61183380433866142   ] 
dist 9=[44.198797124531835573  ,88.239839829223921009  ] 
dist 10=[34.268558439420973231  ,86.879743563364417752  ] 
dist 11=[24.628441579770705618  ,67.237263603200417007  ] 
dist 12=[18.314203421735221664  ,63.193891618910508349  ] 
dist 13=[13.220639366606674157  ,59.339009943306379282  ] 
dist 14=[8.4488724807852108305 ,58.612023695655762833  ] 
dist 15=[4.2282611412059665308 ,32.685684714329778856  ] 
dist 16=[1.3313268688855957499 ,25.143299219208680024  ] 
dist 17=[-4.9191368500930679174 ,4.4142779450101180001 ] 
dist 18=[-12.564559215365236625  ,4.0920341720212663789 ] 
dist 19=[-19.070219214357047143  ,3.5026475546491499429 ] 
dist 20=[-22.873976096869341595  ,3.3643714152934293627 ] 
dist 21=[-25.393087036112257079  ,3.2700605941604288498 ] 
dist 22=[-26.796600028611765422  ,3.2063748503021493603 ] 
dist 23=[-27.535521004562820734  ,2.9960637947707560994 ] 
dist 24=[-27.588099712379466257  ,2.8934875141364367203 ] 
dist 25=[-27.017406092507343039  ,2.5283027685742093170 ] 
dist 26=[-26.661780601909495528  ,2.3663509077190624213 ] 
dist 27=[-23.025540933364505601  ,.10011984071358134043] 
dist 28=[-22.072523104473352291  ,-.36917919161409864309] 
dist 29=[-20.680343107187023627  ,1.2130531795739119330 ] 
dist 30=[-20.148455645692117162  ,3.2232201276106703821 ] 
dist 31=[-7.2308969023575911065 ,5.0830050632783292615 ] 
dist 32=[-5.5221907405086728523 ,7.1767853386314649777 ] 
dist 33=[-4.2988160069866351081 ,10.200726931122665748  ] 
dist 34=[-4.1518211121729947804 ,13.643690923505777840  ] 
dist 35=[-.38771821479573979171,16.547624698032897425  ] 
dist 36=[.07257286335346390957,18.154785208678578812  ] 
dist 37=[1.0874244998319385436 ,19.089881480217589474  ] 
dist 38=[1.2726833852579630116 ,19.325384390262586819  ] 
dist 39=[2.2983225008939756871 ,9.7040701481884101300 ] 
dist 40=[2.4648465858393631650 ,9.6486309090198465980 ] 
dist 41=[2.6593471740418935367 ,5.9223724748865917962 ] 
dist 42=[1.0041403112665309297 ,5.8901649780174190935 ] 
dist 43=[-.43638186875527598586,4.9129819334995293688 ] 
dist 44=[-1.8759629904402639139 ,4.6702665263601914285 ] 
dist 45=[-3.1656726851612646932 ,4.4774640250052380447 ] 
dist 46=[-4.0125353708279223651 ,4.4047119390050443510 ] 
dist 47=[-4.6803510759816919845 ,2.7401548775746791497 ] 
dist 48=[-5.2608459142034093754 ,2.6034546094871753693 ] 
dist 49=[-5.7168386034397437384 ,2.3589257541360319293 ] 
dist 50=[-5.8908504829795150881 ,2.2899549120675798912 ] 
dist 51=[-5.9351498166389608002 ,1.3323344756210737833 ] 
dist 52=[-5.8880616459386690482 ,1.2422623746775488719 ] 
dist 53=[-5.3673646687154262708 ,1.0599266980812126222 ] 
dist 54=[-5.1978332795988920478 ,1.0065436744623985304 ] 
dist 55=[-4.9210583366287034768 ,.78858262280314914651] 
dist 56=[-4.8144403289130686266 ,.7370815773479237344 ] 
dist 57=[-3.0772286626936924585 ,.70179710802666465119] 
dist 58=[-3.0495762003272050126 ,1.7430741727516276057 ] 
dist 59=[-2.5113208797770016734 ,2.5938533642835713129 ] 
dist 60=[-2.3800727522474071389 ,3.3807183661314787052 ] 
dist 61=[-2.2561041147740214382 ,4.0456726876285142906 ] 
dist 62=[-2.1999501111085039953 ,4.4127628534699468753 ] 
dist 63=[-.58016769578065657711,4.6242639945950301983 ] 
dist 64=[-.41107549637052842798,4.6718604550327595394 ] 
dist 65=[-.26736016508829295435,1.2538290827119822871 ] 
dist 66=[-.25920439494537706978,1.3105212012992358685 ] 
dist 67=[-.00374650567433078521,1.5892244733919714261 ] 
dist 68=[.02709538187043565595,1.7462423640007478502 ] 
dist 69=[.09507255493568299685,1.8436299651184705071 ] 
dist 70=[.10737843766066923831,1.8660723780145875749 ] 
dist 71=[.17495929049446985375,1.0640841651572831013 ] 
dist 72=[.1859526418463798339 ,1.0575737923922424727 ] 
dist 73=[.1961903391457390427 ,.70486699033497667779] 
dist 74=[.01549732157558452190,.70128025170950345272] 
dist 75=[-.15237229080488407926,.5715636481750375164 ] 
dist 76=[-.31447622951690891389,.54032925929505342471] 
dist 77=[-.45640527586954620491,.51864149369337620999] 
dist 78=[-.54424722025267161402,.51373354196696413673] 
dist 79=[-.60760386038520258355,.17983175207159415373] 
dist 80=[-.65241005373653956846,.17083264211433855256] 
dist 81=[-.68261121308280089726,.154387709432409995  ] 
dist 82=[-.68800832203397120764,.14973326703791758555] 
dist 83=[-.68367960515769706306,.07495637886964162650] 
dist 84=[-.67521565975101086194,.06760569558408753352] 
dist 85=[-.59676118048726305731,.05363348114094520574] 
dist 86=[-.57432050217726235332,.05000931474099362757] 
dist 87=[-.54005195476862021212,.03784458892300304021] 
dist 88=[-.52690761346986632576,.03450964316241346985] 
dist 89=[-.36426184746812219194,.06371320621863942212] 
dist 90=[-.3581270985780385694 ,.18674851399308208345] 
dist 91=[-.30780276634418671033,.28704345710870628058] 
dist 92=[-.2947444382538034204 ,.37959576296356168357] 
dist 93=[-.27333363496951788099,.45779743157153408205] 
dist 94=[-.26617272680967638646,.50113474254725089561] 
dist 95=[-.10412678152578233022,.5263715545947027271 ] 
dist 96=[-.08425401094311482369,.53272976145012636691] 
dist 97=[-.03201807558836928463,.18212173579955300461] 
dist 98=[-.02334133322154410610,.2285767058239013706 ] 
dist 99=[-.02310898168277309459,.26766063831979319892] 
dist 100=[-.02303017872099316851,.28911529679899917817] 
dist 101=[-.02303467419508102247,.30136634211850148301] 
dist 102=[-.02313598998873522151,.30390643103056435443] 
dist 103=[-.02327434224510698017,.12625316369637800027] 
dist 104=[-.02342755020755099922,.12420268844741220383] 
dist 105=[-.02361133738876772756,.08092036080140774328] 
dist 106=[-.02387291139925126751,.08029800275411761986] 
dist 107=[-.03395813936744353447,.06560850330169282778] 
dist 108=[-.05399433181826723895,.06207116670960205121] 
dist 109=[-.07126208468911379256,.05910683526004690253] 
dist 110=[-.08148141441742276638,.05803392070501805220] 
dist 111=[-.08830171970118351198,.03931003306870523663] 
dist 112=[-.09207980987076033258,.03771537532078253384] 
dist 113=[-.09387663409632906821,.03421792913188333179] 
dist 114=[-.09393694620264003081,.03304307898906597477] 
dist 115=[-.09114476921945377046,.01581460369688603885] 
dist 116=[-.09038492204757882736,.01318928410465634588] 
dist 117=[-.07502713023225037836,.00778954489491929662] 
dist 118=[-.07121182657452882148,.00638154909949368321] 
dist 119=[-.06764517575551831322,.00145975728229621930] 
dist 120=[-.06594266667673855926,.00035362891169832894] 
dist 121=[-.04793006493060239022,.00529270293892551012] 
dist 122=[-.04491974117369081245,.01841802174589158524] 
dist 123=[-.03574470509546945916,.02912514066215957738] 
dist 124=[-.03381296996944155458,.03902857229852479140] 
dist 125=[-.03195110979450788916,.04742020631135984722] 
dist 126=[-.03112899453552041882,.05241058353021824794] 
dist 127=[-.00755522790804480171,.05529400476910788868] 
dist 128=[-.00512350601880737080,.05596702757923735529] 
dist 129=[.00035975024333488357,.02191024824789115743] 
dist 130=[.00146410790789328031,.02199694331553651153] 
dist 131=[.00751180329374439398,.02360742819944717329] 
dist 132=[.00852565379277078552,.02582097414798288478] 
dist 133=[.01023063732657742492,.02715037011896670329] 
dist 134=[.01055227565354769530,.02747818643211672504] 
dist 135=[.01063248972629495611,.01605717874731614266] 
dist 136=[.00678455489621764412,.01591422762940826661] 
dist 137=[.00195263380502202098,.01014922136727555981] 
dist 138=[-.00131681635145211526,.01008366085152161964] 
dist 139=[-.00400375905260929956,.00810947209995292038] 
dist 140=[-.00652338661476709933,.00764305539344921460] 
dist 141=[-.00868332312801266883,.00730431697068012813] 
dist 142=[-.00994245526648300756,.00722869278010688227] 
dist 143=[-.01075946015371202977,.00061464225408051159] 
dist 144=[-.01116437346925391400,-.00015537654040934263] 
dist 145=[-.01133337833684164442,-.00194244275923752463] 
dist 146=[-.01131252374739529738,-.00220400497111586564] 
dist 147=[-.01101008626443778860,-.00427460103550029635] 
dist 148=[-.01084458748544599177,-.00457723747272128972] 
dist 149=[-.00932198205416153729,-.00512260721724420657] 
dist 150=[-.00892367961087145896,-.00520209581010088391] 
dist 151=[-.00832017562263201788,-.00448874478954426542] 
dist 152=[-.00809889193170199791,-.00157986820231752520] 
dist 153=[-.00512622432507862559,.00133661706806208786] 
dist 154=[-.00504248138294441377,.00329341275180655880] 
dist 155=[-.00427315452011546013,.00488402095218905400] 
dist 156=[-.00407912396625274002,.00634669191799587002] 
dist 157=[-.00378613274058415573,.00758083216438146431] 
dist 158=[-.00368088469665282718,.00826412866054396286] 
dist 159=[-.00119267019638654184,.00866216816960480774] 
dist 160=[-.00086324849194192427,.00876230961324014656] 
dist 161=[-.00012875464395259701,.00268689702374399188] 
dist 162=[3.19445461469503268900e-05,.00300558123055562292] 
dist 163=[.00082165273523849336,.00357492121866835355] 
dist 164=[.00096009758836696447,.00388994490949227631] 
dist 165=[.00117925143394783277,.00407322265447428342] 
dist 166=[.00122149872877608948,.00411942145578578946] 
dist 167=[.00121995362888415245,.00190777804120138358] 
dist 168=[.00060685752778208984,.00188877992088401958] 
dist 169=[-8.83687133297848219160e-06,.00121957484633974157] 
dist 170=[-.00042374867142637713,.00120824425414381359] 
dist 171=[-.00076304655213142640,.00098165653814126436] 
dist 172=[-.00107854677161178961,.00092762746481406983] 
dist 173=[-.00134727288131418663,.00087877430421929051] 
dist 174=[-.00150087313172910373,.00085953916374631944] 
dist 175=[-.00159671748921824360,.00015454354030593868] 
dist 176=[-.00163614854523817294,7.15842003907574096820e-05] 
dist 177=[-.00164332241209744011,-.00011867751331962902] 
dist 178=[-.00163613355159600822,-.00015109016886212370] 
dist 179=[-.00157261728668084203,-.00036779125400107520] 
dist 180=[-.00155496481490811979,-.00040140906178110346] 
dist 181=[-.00128321601538721672,-.00046143057918801734] 
dist 182=[-.00121693746707693485,-.00047108317928932952] 
dist 183=[-.00114595707232030584,-.00032824740528318974] 
dist 184=[-.00110984198757988286,-3.04413764240720400000e-05] 
dist 185=[-.00071594491144325583,.00026819092045644654] 
dist 186=[-.00070744446627450231,.00046883379725992712] 
dist 187=[-.00057978439957244557,.00063227680471937856] 
dist 188=[-.00054908705786366728,.00078321363697906405] 
dist 189=[-.00051602134664083721,.00091106145837086427] 
dist 190=[-.00049946930992031727,.00098283314294931782] 
dist 191=[-.00017824286970386922,.00103050203037847031] 
dist 192=[-.00015316832276413960,.00104166312859049731] 
dist 193=[-9.99008836666708258120e-05,.00050605139726754251] 
dist 194=[-8.54605915753075775740e-05,.00050369715432736255] 
dist 195=[-3.14546247913124837880e-05,.00049664741801810237] 
dist 196=[-2.00615961168555162810e-05,.00049114453168499643] 
dist 197=[-4.24576671997502408600e-06,.00047101377307692998] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 2, 0, 2, 0, 1] 
dist 0=[124.77324044456272228   ,124.77324044456272228   ] 
dist 1=[120.43429102447494021   ,126.48235831365001728   ] 
dist 2=[113.04034162681600502   ,128.91703038966191095   ] 
dist 3=[100.86857975358831778   ,130.98030877459517315   ] 
dist 4=[88.214667641590004470  ,131.17824243206382957   ] 
dist 5=[78.896516885265910350  ,130.51285493284667398   ] 
dist 6=[70.380342652978368932  ,129.63136554168753598   ] 
dist 7=[60.897914943519345339  ,122.20495095638679091   ] 
dist 8=[51.648695623231656826  ,107.01929597856509183   ] 
dist 9=[44.044978490117945383  ,97.455181364638236336  ] 
dist 10=[36.237733628766374348  ,96.059552622014134397  ] 
dist 11=[26.153203757619954174  ,75.331583091771683147  ] 
dist 12=[16.481368993296495103  ,71.004975187010535270  ] 
dist 13=[10.311066792139021706  ,66.916107923935456629  ] 
dist 14=[5.5136025868330443415 ,66.074983334363512712  ] 
dist 15=[1.3148629629872560678 ,34.063052720587368362  ] 
dist 16=[-4.8372776266682448958 ,11.134630416041218483  ] 
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dist 220=[1.15192903893033351520e-05,.00016815570592656527] 
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dist 229=[-1.83447849994106785450e-05,4.23410296658780698140e-05] 
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dist 237=[-3.29454842516875191740e-05,1.70388398088021576700e-05] 
dist 238=[-3.48558402750172593580e-05,1.68692810413534042310e-05] 
dist 239=[-3.54739173685208093790e-05,1.66336228566431509080e-05] 
dist 240=[-3.54017438104578444760e-05,1.62698112499691621260e-05] 
dist 241=[-3.51728191523323982400e-05,1.59753215284536132620e-05] 
dist 242=[-3.36567145489734370330e-05,1.55231401963697585480e-05] 
dist 243=[-3.32506002353571708650e-05,1.52920474094305452320e-05] 
dist 244=[-2.73070955085637319090e-05,1.43210218379768356270e-05] 
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dist 246=[-2.43010319755611110480e-05,1.36035062454015820480e-05] 
dist 247=[-2.35271092519520260420e-05,1.33273569130140223380e-05] 
dist 248=[-8.52915425195935674810e-06,1.30775404210994599440e-05] 
dist 249=[-7.34009790994828559860e-06,1.29522353405044364880e-05] 
dist 250=[-4.80952038594710642130e-06,1.39944447266943111510e-05] 
dist 251=[-4.12188327996930264990e-06,1.72286855038201267660e-05] 
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dist 253=[-9.97692658173444481780e-07,2.14840038733361636260e-05] 
dist 254=[-2.23347672016152534860e-07,2.24037678529244294580e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 1, 2, 0, 1] 
dist 0=[124.71280737644418912   ,124.71280737644418912   ] 
dist 1=[122.75949702239614508   ,126.29534417184981800   ] 
dist 2=[118.86544738295094370   ,128.70453359806203919   ] 
dist 3=[112.42877810451972153   ,130.78546338460675164   ] 
dist 4=[100.37093040313525960   ,131.06795196883304622   ] 
dist 5=[87.558088864901092803  ,130.45137674692336304   ] 
dist 6=[78.117212147733072589  ,129.65388873741947491   ] 
dist 7=[69.483414295627167181  ,109.39186809533800856   ] 
dist 8=[59.862023336162696021  ,106.17399633702905525   ] 
dist 9=[50.472730894571415397  ,96.469369718210080347  ] 
dist 10=[42.746722182345734256  ,95.075465945201756936  ] 
dist 11=[34.807620586635042233  ,74.183738915314281484  ] 
dist 12=[24.544560298570001140  ,69.837121931394642579  ] 
dist 13=[14.716275836833464121  ,65.771502763947320836  ] 
dist 14=[8.5017707236050640258 ,64.992843431255425025  ] 
dist 15=[-1.6082566342032122616 ,15.666186338549011272  ] 
dist 16=[-7.7414814982892697636 ,9.9402227018863728202 ] 
dist 17=[-12.008138418720266087  ,-1.2271662135550816692 ] 
dist 18=[-14.885036283522713790  ,-2.0667472477419858376 ] 
dist 19=[-20.779775164665283141  ,-2.2085814338453202462 ] 
dist 20=[-25.055642952315597354  ,-1.2247748759847567538 ] 
dist 21=[-27.927624036550240738  ,.01080226659899275170] 
dist 22=[-29.607663377868752065  ,.95453188321789130155] 
dist 23=[-30.551104324911941138  ,1.7837706285869526303 ] 
dist 24=[-30.648452588904823039  ,2.5791530538018263315 ] 
dist 25=[-30.107150866959243205  ,3.2186888869536045489 ] 
dist 26=[-29.717743571338251520  ,3.4362945390892131271 ] 
dist 27=[-25.785194887483654579  ,3.4925484576838850931 ] 
dist 28=[-24.740503194462100940  ,3.5026312761762188146 ] 
dist 29=[-23.198861730123016891  ,2.9117479525852660014 ] 
dist 30=[-22.611338335621933700  ,4.8068261904201363426 ] 
dist 31=[-8.2759378521241244033 ,6.5051462504148070348 ] 
dist 32=[-6.3744803682098971223 ,7.3986183734236863112 ] 
dist 33=[-2.1116592409184716998 ,11.518978423720316640  ] 
dist 34=[-1.4062459052554034504 ,15.366748925749278914  ] 
dist 35=[-1.2286803860594844360 ,18.610925311241334208  ] 
dist 36=[-1.1821797277619057113 ,20.403035459828190726  ] 
dist 37=[-1.1724181350467602164 ,21.440994866327571672  ] 
dist 38=[-1.1991264720656726754 ,21.690947553940477802  ] 
dist 39=[-1.2512275346086816489 ,6.6258110843256350955 ] 
dist 40=[-1.3435183276957458418 ,6.6667974204873861604 ] 
dist 41=[-1.4470146567572410508 ,6.5216994736883797277 ] 
dist 42=[-1.5442819921585723328 ,6.5004143594076069693 ] 
dist 43=[-2.0286507110900388207 ,5.3959634834704581804 ] 
dist 44=[-2.7061032764121723073 ,5.1225353084951145047 ] 
dist 45=[-3.2567815188268380236 ,4.9430270360301118504 ] 
dist 46=[-3.7637719978304270474 ,4.9004100349976193583 ] 
dist 47=[-4.1760276022880578181 ,3.2194647725909055959 ] 
dist 48=[-4.3510618713554126264 ,3.1230716126788408374 ] 
dist 49=[-4.4137804007632837640 ,2.6350203560984985014 ] 
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dist 158=[-8.32889935426808846890e-05,.00734028093582335218] 
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dist 185=[-3.57802388553310087140e-05,.00053640959808068836] 
dist 186=[1.94555595808220331660e-06,.00069632119876929084] 
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dist 193=[.00013649011167391585,.00030238702704258063] 
dist 194=[.00010539747005530311,.00029833261538473389] 
dist 195=[6.31192381440331051450e-05,.00025188469197042599] 
dist 196=[-3.95599965124157070860e-07,.00024017043449516293] 
dist 197=[-6.39830308322834870020e-05,.00022490633410756005] 
dist 198=[-.00010654994554733718,.00021846879627403997] 
dist 199=[-.00014105737929906424,6.14660340533164365100e-05] 
dist 200=[-.00017264450703227502,4.47791408315191443740e-05] 
dist 201=[-.00019920429736466496,2.04558950168282617750e-05] 
dist 202=[-.00021375035154559131,1.52215612366343072600e-05] 
dist 203=[-.00022200938739716721,8.10664374654955646890e-06] 
dist 204=[-.00022360583420920297,6.13516352790012796750e-06] 
dist 205=[-.00022237701915731247,5.61359715606116437660e-06] 
dist 206=[-.00021941818608389900,6.62074219119897863290e-06] 
dist 207=[-.00017399270330657252,8.91500410331358963310e-06] 
dist 208=[-.00017317308483963862,1.35047217477108955820e-05] 
dist 209=[-.00016535238342672999,1.91007951960519402770e-05] 
dist 210=[-.00016417909913388293,2.53912457222616574920e-05] 
dist 211=[-.00013141989453339674,3.32683208943229794050e-05] 
dist 212=[-.00012371134254377267,4.51645837082983478940e-05] 
dist 213=[-.00011793592990016045,5.70995636585498463720e-05] 
dist 214=[-.00011655479001408384,6.51306096717921483140e-05] 
dist 215=[-2.12911885330752586920e-05,7.16867141681272366730e-05] 
dist 216=[-1.28226405026451324070e-05,7.77656449124149034840e-05] 
dist 217=[6.46947126122647300690e-06,8.29325314346259443810e-05] 
dist 218=[1.00365692452320758120e-05,8.58674933281917263930e-05] 
dist 219=[2.10443605456485179040e-05,8.76756383035482152210e-05] 
dist 220=[2.18251036407882370920e-05,8.83686805665358848550e-05] 
dist 221=[2.19906740809915439690e-05,8.86419965295168184680e-05] 
dist 222=[2.14456149587204574290e-05,8.88543840037707412720e-05] 
dist 223=[2.03326483564532243960e-05,4.29497563970782100090e-05] 
dist 224=[1.81824805850220152820e-05,4.27527336446091985150e-05] 
dist 225=[1.55843814091198156410e-05,4.12128094690042689920e-05] 
dist 226=[1.15633762944828352840e-05,4.06586177880862835390e-05] 
dist 227=[6.18927071765972297610e-06,3.41109957823549605830e-05] 
dist 228=[-1.86900167610635174990e-06,3.24803730286112549630e-05] 
dist 229=[-9.93272174058436144010e-06,3.04058624529380169600e-05] 
dist 230=[-1.53284913019376447320e-05,2.95157118566013200010e-05] 
dist 231=[-1.97009930509421649820e-05,8.70600099426250178970e-06] 
dist 232=[-2.37016304553585551620e-05,8.03520990828533664880e-06] 
dist 233=[-2.70649884777308913300e-05,5.58562100269491521120e-06] 
dist 234=[-2.89070244351764667910e-05,4.99560135757953481380e-06] 
dist 235=[-2.99532044133514076070e-05,4.32316466065015093150e-06] 
dist 236=[-3.01563993431153014800e-05,4.12917054561853542100e-06] 
dist 237=[-3.00004458546037987560e-05,4.06776598372208810400e-06] 
dist 238=[-2.96205503431569599510e-05,4.11057684256044831280e-06] 
dist 239=[-1.49552240510542476060e-05,4.23660722742859770700e-06] 
dist 240=[-1.48024022515108002150e-05,4.50569891995437311450e-06] 
dist 241=[-1.26671174227940326500e-05,4.83911379499714910210e-06] 
dist 242=[-1.25002453615404069570e-05,5.22058213863066064760e-06] 
dist 243=[-1.07047238763515067510e-05,5.70258005929919375030e-06] 
dist 244=[-1.04389266372955347910e-05,6.43519630149752861870e-06] 
dist 245=[-9.37016760262941258830e-06,7.17208524248309347640e-06] 
dist 246=[-9.09719147680814837200e-06,7.67107500452843662830e-06] 
dist 247=[-1.49412641703907501300e-06,8.08186075684528814540e-06] 
dist 248=[-1.29083909691355456920e-06,8.46856488816089414470e-06] 
dist 249=[-5.15000424824049083610e-07,8.80135678948637952710e-06] 
dist 250=[-3.54294050746772843230e-07,8.99810605283008895780e-06] 
dist 251=[-9.58295081487271047550e-08,9.12995080566678278520e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 1, 2, 0, 1] 
dist 0=[124.71294134348043250   ,124.71294134348043250   ] 
dist 1=[122.75961935859990468   ,126.29548675147399672   ] 
dist 2=[118.86551448780231401   ,128.70471942219705460   ] 
dist 3=[112.42876204312414972   ,130.78569755563340435   ] 
dist 4=[100.37079179871331611   ,131.06821500837344682   ] 
dist 5=[87.557827954313806751  ,130.45165623343158815   ] 
dist 6=[78.116869008467687728  ,129.65417446101676471   ] 
dist 7=[69.483004115115677915  ,109.39212557601172523   ] 
dist 8=[59.861551147711937758  ,106.17424030731696253   ] 
dist 9=[50.472206116396931990  ,96.469651446391449241  ] 
dist 10=[42.746167755913369567  ,95.075686574722000517  ] 
dist 11=[34.807048188057292538  ,74.184190456200458395  ] 
dist 12=[24.543981667693685193  ,69.837612290130097802  ] 
dist 13=[14.715697134399517959  ,65.771840335882570012  ] 
dist 14=[8.5011985094297258886 ,64.992980537569395921  ] 
dist 15=[-1.6079848319263890991 ,15.667261650801839025  ] 
dist 16=[-7.7412475576275289102 ,9.9413620726277782884 ] 
dist 17=[-12.007959307736560665  ,-1.2274904394416786928 ] 
dist 18=[-14.884948096154468478  ,-2.0670505535894392345 ] 
dist 19=[-20.781519895381254152  ,-2.2086679795210489692 ] 
dist 20=[-25.057445386796980275  ,-1.2246655377305797313 ] 
dist 21=[-27.929451863197033265  ,.01110707838620444383] 
dist 22=[-29.609478242468454253  ,.95496629362041730443] 
dist 23=[-30.552869405524531844  ,1.7843086748759857082 ] 
dist 24=[-30.650209852529002153  ,2.5797834909615525811 ] 
dist 25=[-30.108706016927126369  ,3.2193952074913648097 ] 
dist 26=[-29.719374801915646478  ,3.4370389515924004657 ] 
dist 27=[-25.785996540748799710  ,3.4933100000241746770 ] 
dist 28=[-24.741138756478441688  ,3.5033854959620211219 ] 
dist 29=[-23.199654502881403707  ,2.9107244168284732180 ] 
dist 30=[-22.612042977240676342  ,4.8058433838412277207 ] 
dist 31=[-8.2741495865402004097 ,6.5042763460990937120 ] 
dist 32=[-6.3724576782713110822 ,7.3980396205989640158 ] 
dist 33=[-2.1111809889693216049 ,11.517762307869964555  ] 
dist 34=[-1.4065393406686017787 ,15.365297817077099964  ] 
dist 35=[-1.2290594299278003185 ,18.609279144535402046  ] 
dist 36=[-1.1826303251678797505 ,20.401287251557686743  ] 
dist 37=[-1.1729400993347540444 ,21.439195165797204894  ] 
dist 38=[-1.1996958954492377712 ,21.689153526400072454  ] 
dist 39=[-1.2518351118563779996 ,6.6292561133501199448 ] 
dist 40=[-1.3441603180902798053 ,6.6701804563357738674 ] 
dist 41=[-1.4476852423234093476 ,6.5249393375357200282 ] 
dist 42=[-1.5449676263974106871 ,6.5035306742886753116 ] 
dist 43=[-2.0393150714566083182 ,5.3987768862011467514 ] 
dist 44=[-2.7170994859356252248 ,5.1252595910585770186 ] 
dist 45=[-3.2679616577684261956 ,4.9453958476534328725 ] 
dist 46=[-3.7749767149245845742 ,4.9024446118139862759 ] 
dist 47=[-4.1871186127451739277 ,3.2202556666280850580 ] 
dist 48=[-4.3617877294133455868 ,3.1238202782255888808 ] 
dist 49=[-4.4241557344442042494 ,2.6355110640831285117 ] 
dist 50=[-4.4006820971295689423 ,2.5243666328598013868 ] 
dist 51=[-4.0495050625030766891 ,2.2359611717582047048 ] 
dist 52=[-3.9276106648222803926 ,2.1515161821013963039 ] 
dist 53=[-3.7619000135098250034 ,1.2349385272575215895 ] 
dist 54=[-3.8910484408889695302 ,1.0772231518270947846 ] 
dist 55=[-3.9484415413143741991 ,.77919632312737350383] 
dist 56=[-3.9399979134721608894 ,1.0412178060219867791 ] 
dist 57=[-3.8511412376950730486 ,1.7030910646857105101 ] 
dist 58=[-3.7857416706090216675 ,2.3174103244339156832 ] 
dist 59=[-3.3401228327969841151 ,2.8377033821860584059 ] 
dist 60=[-2.9837807146656408629 ,3.1267607336441129892 ] 
dist 61=[-2.3869754682059678551 ,3.2953982946941820912 ] 
dist 62=[-2.3238245903970576864 ,3.3377114174179302031 ] 
dist 63=[-.79698840881017020441,1.0407897151834172105 ] 
dist 64=[-.59484049591928633185,1.0746416286786874620 ] 
dist 65=[-.14022778156965348784,1.3321328950492416569 ] 
dist 66=[-.04324210056657153755,1.7454426290683618983 ] 
dist 67=[.36516242707069436648,2.0941811112138200537 ] 
dist 68=[.24084256625688056171,2.2875507523043622049 ] 
dist 69=[.11372020637259856539,2.4000307520544204945 ] 
dist 70=[.02559312014265755734,2.4282040437524915636 ] 
dist 71=[-.04888450659483839961,.7611854915537068099 ] 
dist 72=[-.12188685825599576034,.7616221285101225196 ] 
dist 73=[-.23274275170762323555,.73740146261267230664] 
dist 74=[-.37571761009701039042,.73261131696734603999] 
dist 75=[-.50054239194535387854,.60297117010753376052] 
dist 76=[-.57712417242976000706,.57133392464310545773] 
dist 77=[-.63154638833030450756,.54603142313008344774] 
dist 78=[-.66847068336353176687,.53707405097839515853] 
dist 79=[-.69136924297498255534,.09126443125541050515] 
dist 80=[-.69466910334437676565,.03844237246380822000] 
dist 81=[-.68161504521294531389,-.08463534424252163123] 
dist 82=[-.6755804305620938403 ,-.10344376652797938131] 
dist 83=[-.57304857947487533446,-.1382234790063663806 ] 
dist 84=[-.54639896834827308274,-.05678981832074343563] 
dist 85=[-.51816806619462959061,.02527177215374668818] 
dist 86=[-.50300551231193943251,.08058873375493559113] 
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dist 161=[6.35930141255551594690e-05,.00200326261770451629] 
dist 162=[.00021093530828764998,.00263128771913167349] 
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dist 171=[-.00073990961966795224,.00107911486363853637] 
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dist 173=[-.00076476438423989616,.00097046091895710778] 
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dist 175=[-.00073343215199813825,7.95580289604265549400e-05] 
dist 176=[-.00072533672194135082,-2.30665990987353662450e-05] 
dist 177=[-.00059974658722059917,-.00026157849790718904] 
dist 178=[-.00056898762449651850,-.00024724583435887020] 
dist 179=[-.00058903047393706886,-.00015539452635609951] 
dist 180=[-.00066264729385903515,-1.65358947556580900000e-05] 
dist 181=[-.00070692473020753187,.00012277960624627419] 
dist 182=[-.00072151743855876461,.00021644777367586134] 
dist 183=[-.00072121527681456153,.00029281044393054281] 
dist 184=[-.00071643956319791993,.00036342008691631503] 
dist 185=[-.00068883460774813672,.00042328193840298091] 
dist 186=[-.00067802025532570296,.00045697371009141184] 
dist 187=[-.00057092130704990772,.00048007426222101505] 
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dist 189=[-.00050594907268111627,.00018321399913620486] 
dist 190=[-.00049149095374552392,.00018259653890397468] 
dist 191=[-.00015787531512565485,.00017770114514924391] 
dist 192=[-.00011391443122526615,.00021407334363756728] 
dist 193=[-1.59571370943274122450e-05,.00031224493116428892] 
dist 194=[5.50367692374351476150e-06,.00040233583620542881] 
dist 195=[6.78650539485174994470e-05,.00047828650217301717] 
dist 196=[1.91471543046687713610e-05,.00052030915593738588] 
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dist 198=[-6.25049608601901981520e-05,.00055091876769344042] 
dist 199=[-8.92330597228528761340e-05,.00018472654200070200] 
dist 200=[-.00011392004394862306,.00018333711950054591] 
dist 201=[-.00013483633374152390,.00017676330780735653] 
dist 202=[-.00014659296926737877,.00017330899726437413] 
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dist 205=[-.00015607814528740249,.00013126181508562535] 
dist 206=[-.00015463629986331356,.00012781611702970504] 
dist 207=[-.00015077609876485227,4.95252941689516823590e-05] 
dist 208=[-.00014848155976200966,3.86512635094880435550e-05] 
dist 209=[-.00013406895986946929,1.47984278145678724580e-05] 
dist 210=[-.00013027593242162975,8.89636591643838869400e-06] 
dist 211=[-.00011883759393265505,6.22528145250305425140e-08] 
dist 212=[-.00011557461774460462,1.27983111060757730740e-05] 
dist 213=[-9.95919465409642293440e-05,2.55754170669965856020e-05] 
dist 214=[-.00010121204160741689,3.41706916673027195750e-05] 
dist 215=[-.00010086783448118234,4.11843477162660364990e-05] 
dist 216=[-.00010017705523269835,4.76819162137952229210e-05] 
dist 217=[-9.57388370277592703850e-05,5.32003163397440462810e-05] 
dist 218=[-9.46008436951224914540e-05,5.63263515102055170260e-05] 
dist 219=[-7.74571518897972721270e-05,5.82409057407728064170e-05] 
dist 220=[-7.33411192071396683390e-05,5.89493412968562847940e-05] 
dist 221=[-6.89211738739102036400e-05,5.91024380447369610970e-05] 
dist 222=[-6.67067774961723940330e-05,5.88120122829872422100e-05] 
dist 223=[-2.36318915450036708420e-05,5.81484465053724390410e-05] 
dist 224=[-2.02881207404797628960e-05,5.74311020380094392380e-05] 
dist 225=[-1.31937492573531319240e-05,5.51993248595522835180e-05] 
dist 226=[-1.12731387023947011930e-05,5.41485234314960494080e-05] 
dist 227=[-4.10656835429479148310e-06,5.61807153237389693970e-05] 
dist 228=[-2.59115840362570905700e-06,6.04284528760247311800e-05] 
dist 229=[-5.25898928654320711830e-07,6.29245909475722306860e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 1, 2, 0, 2] 
dist 0=[128.46305499861838375   ,128.46305499861838375   ] 
dist 1=[126.48241175718991220   ,131.47451375860842055   ] 
dist 2=[121.64069074460923266   ,134.09257028547455268   ] 
dist 3=[113.45700152951014169   ,134.47698496687061260   ] 
dist 4=[100.14730965727949770   ,133.92373293135785954   ] 
dist 5=[86.367381934509749953  ,132.95476390098195174   ] 
dist 6=[76.307020990065606951  ,125.88325156603267299   ] 
dist 7=[67.199756245664031432  ,117.52748287078068977   ] 
dist 8=[57.191927814717415525  ,102.33529098085750800   ] 
dist 9=[47.510499372703716919  ,100.95129036860788061   ] 
dist 10=[39.686053085126109705  ,79.783542953780283659  ] 
dist 11=[31.774575282571544464  ,75.331583091771680597  ] 
dist 12=[21.720799439410683888  ,71.190004866837661620  ] 
dist 13=[12.142118297121898607  ,70.335725436028578305  ] 
dist 14=[6.1155061944779392337 ,42.083790793720204973  ] 
dist 15=[1.5241052228240676995 ,36.559221870813533132  ] 
dist 16=[-6.0322674172133212731 ,1.6483861137860671039 ] 
dist 17=[-12.836514457257459119  ,-2.6068229197004622641 ] 
dist 18=[-20.636702168651381207  ,-3.1721258070848756767 ] 
dist 19=[-25.303293094206885269  ,-2.8231284274871304407 ] 
dist 20=[-28.523259697620637348  ,-1.2542361148864670427 ] 
dist 21=[-30.579807339149912546  ,.55948130114443893711] 
dist 22=[-31.850189272951789561  ,1.8857022342206044500 ] 
dist 23=[-32.048474340035282841  ,3.0217335334449842673 ] 
dist 24=[-31.636757367516699671  ,4.0942808391272268077 ] 
dist 25=[-31.286394613291012193  ,4.9656374719118312475 ] 
dist 26=[-27.142375523184633413  ,5.3097630634902004956 ] 
dist 27=[-26.032296538788967728  ,5.4287717295575509605 ] 
dist 28=[-24.530429935364725531  ,5.4172838305139557899 ] 
dist 29=[-23.898191808221977253  ,4.1728768344886036816 ] 
dist 30=[-8.6477068741963512146 ,4.3533091220098666763 ] 
dist 31=[-6.6902092868646681279 ,6.9251989397441942807 ] 
dist 32=[-2.3319964999111964659 ,11.222404918006711089  ] 
dist 33=[-1.3335085035147709697 ,15.212795428915095310  ] 
dist 34=[-.90224052261569154006,18.599531871963967411  ] 
dist 35=[-.6254160036876175348 ,20.466776987058579959  ] 
dist 36=[-.58015506749430475958,21.542769011391658020  ] 
dist 37=[.81142662404863462386,21.788244166838879450  ] 
dist 38=[.97077942061819518285,8.8943145375227405794 ] 
dist 39=[1.2714417891736779214 ,8.7550089236998785264 ] 
dist 40=[.46531485768266211895,7.6797076036511502767 ] 
dist 41=[-1.2987708694025424979 ,7.5771053194419526592 ] 
dist 42=[-2.7895942448143795896 ,6.8411487200253678495 ] 
dist 43=[-4.2479929061961719252 ,6.6354792278354089839 ] 
dist 44=[-5.5339640961281009093 ,6.1035500044935759458 ] 
dist 45=[-6.3413752905155028749 ,5.8982838659212819222 ] 
dist 46=[-6.9360452540638749700 ,3.3669883320981555397 ] 
dist 47=[-7.3787133244953870826 ,2.9556217213978002054 ] 
dist 48=[-7.6846362796354702782 ,2.0847116878667966973 ] 
dist 49=[-7.7368927767977657999 ,1.8445963588770214780 ] 
dist 50=[-7.6731478309003262593 ,.92909705643469742279] 
dist 51=[-7.5702572327259334023 ,.73182551127600410221] 
dist 52=[-6.7737636081880386576 ,.41607810698146013417] 
dist 53=[-6.0804503106729434904 ,.33344839712412265343] 
dist 54=[-3.4516053627686046852 ,.19409694784118276849] 
dist 55=[-3.4532744248204300135 ,.1577897574657124547 ] 
dist 56=[-3.3772144959689123537 ,.15309567925101689672] 
dist 57=[-3.3293548338519483214 ,.1897299552804754487 ] 
dist 58=[-2.8781830149118020668 ,.52727848948614658797] 
dist 59=[-2.7585299946227927252 ,.88906769930594193689] 
dist 60=[-2.5785812063844784953 ,1.2135957811501341008 ] 
dist 61=[-2.5114759103278791946 ,1.4276557629806286954 ] 
dist 62=[-.87756241430132509128,1.5976209608675984632 ] 
dist 63=[-.65983300394922043549,1.7474838614081075683 ] 
dist 64=[-.16957299410994161441,1.8610266980983666219 ] 
dist 65=[-.06490794234015684486,1.8890021451031860870 ] 
dist 66=[-.02636138955061831276,2.2587074390726110782 ] 
dist 67=[-.01176060503198105359,2.4675622792933265708 ] 
dist 68=[-.00823950744063771809,2.5891126702625135553 ] 
dist 69=[.04475486385327071397,2.6197288083272369097 ] 
dist 70=[.05129724575539668037,1.4878388413963717867 ] 
dist 71=[.06185924607577985656,1.4771292316316315826 ] 
dist 72=[.06399393122285001952,.77972719436744445676] 
dist 73=[-.02971232123640622852,.77490552037502080034] 
dist 74=[-.26914918862573643761,.64248562422232436101] 
dist 75=[-.49751713068323301896,.60978333655480699331] 
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dist 77=[-.81550117130324327116,.57342904749685150488] 
dist 78=[-.89850256484350433776,.09625207102836657688] 
dist 79=[-.95080701796635826501,.04289756463507115671] 
dist 80=[-.9822391762367675841 ,.04093680315759060057] 
dist 81=[-.9858294050523003311 ,.02481557192448572816] 
dist 82=[-.97145799087924247312,.02189313057051568425] 
dist 83=[-.95840198228024837367,.01724452177231302913] 
dist 84=[-.83749519318623562236,.01609196850427737265] 
dist 85=[-.80428074580270645154,.00307913594428125532] 
dist 86=[-.75376315253212729414,.00471606895594048168] 
dist 87=[-.73474925293567638656,.00654557799586973207] 
dist 88=[-.4237905495743273987 ,.10016761722295662413] 
dist 89=[-.41982142703006381269,.27410991673291548928] 
dist 90=[-.34481774123537526384,.41572170444828376895] 
dist 91=[-.32660231004087354278,.54618806833617319216] 
dist 92=[-.30926880614003625612,.65634611087074720524] 
dist 93=[-.30143122730944743878,.71734406601923138101] 
dist 94=[-.07693511621243325960,.75282622847445925246] 
dist 95=[-.05361940663886569580,.76169643775335743138] 
dist 96=[-.00081674148521488087,.23196623242733453208] 
dist 97=[.00158255060723536548,.23329198927941330842] 
dist 98=[-.00838382799899475977,.22863001752260703084] 
dist 99=[-.02100157996114226555,.24426280581245548741] 
dist 100=[-.04017300462824457058,.25770066344742276709] 
dist 101=[-.05938082663060088169,.26079630119050198766] 
dist 102=[-.07214290150067656032,.17419565337567288148] 
dist 103=[-.08235649793817500466,.17123472069880243992] 
dist 104=[-.09144965281148949076,.09774943574928910518] 
dist 105=[-.09888726652890695023,.09721190431929568292] 
dist 106=[-.10252949820343646006,.08079963873314717066] 
dist 107=[-.10400604577794688637,.08125508002413133394] 
dist 108=[-.10374663365382038554,.08064786474537424474] 
dist 109=[-.11701923348492228926,.07966012668845566079] 
dist 110=[-.12605294975173724388,.07860349134152014883] 
dist 111=[-.13058196488893491331,.07731206179075022142] 
dist 112=[-.13235311992966173451,.07616508912096742007] 
dist 113=[-.13220174789742133241,.07325447940504160553] 
dist 114=[-.12779716005890555826,.07174635991366741686] 
dist 115=[-.12668072751417481907,.06873410060630940769] 
dist 116=[-.10481198789603024348,.06748626308618035139] 
dist 117=[-.09944030599564054188,.06126655658169823765] 
dist 118=[-.09439064253979834085,.05911730111810880632] 
dist 119=[-.09204599308604030518,.05698528994077735954] 
dist 120=[-.04939177544831455355,.05565021250544218034] 
dist 121=[-.04861047530976012365,.05395280960339606966] 
dist 122=[-.04140771637474182887,.05327566304696490889] 
dist 123=[-.03956846881472811933,.05486834956021465918] 
dist 124=[-.03679180247157558969,.06651017434324614149] 
dist 125=[-.03578570867697970548,.07351534791020098320] 
dist 126=[-.01184016094351932494,.07749778074589276843] 
dist 127=[-.00866733920661483418,.07843425988657558854] 
dist 128=[-.00157532681580610822,.03060291713236565952] 
dist 129=[-3.08768183251423661000e-05,.03065806286974996654] 
dist 130=[.00765773756101816671,.03418027398234239212] 
dist 131=[.00899994870249539715,.03722249646503959812] 
dist 132=[.01118786900725518922,.03899296520234888388] 
dist 133=[.01163357649352359854,.03943923812150949565] 
dist 134=[.01173608797909044640,.02202100840054321214] 
dist 135=[.00916836205226594042,.02181799619109440064] 
dist 136=[.00246636442776924033,.01152269254259211763] 
dist 137=[-.00205910733682220999,.0114494985648586185 ] 
dist 138=[-.00576910738798324285,.00924728182411790537] 
dist 139=[-.00923380896891430852,.00876407130764205460] 
dist 140=[-.01219485221567718363,.00832871343233689338] 
dist 141=[-.01390540942728094512,.00823812483656362408] 
dist 142=[-.01499596220781439143,.00159975234194011729] 
dist 143=[-.01549571370301460117,.00079984157074641709] 
dist 144=[-.01566978371549106185,-.00104055554807019554] 
dist 145=[-.01562161588035406624,-.00135139754467982297] 
dist 146=[-.01516205613810609901,-.00346836640776007154] 
dist 147=[-.01492773134901633133,-.00379517295026975802] 
dist 148=[-.01278747122417327813,-.00439397315508211380] 
dist 149=[-.01223301314269948508,-.00449315773689342944] 
dist 150=[-.01138979518567298847,-.00455047090030192440] 
dist 151=[-.01108380240822467491,-.00214510541394838205] 
dist 152=[-.00691617213455086041,.00188355245985424186] 
dist 153=[-.00683567466907168909,.00458528512485237316] 
dist 154=[-.00561662365209950626,.00678046523828919567] 
dist 155=[-.00532200451553997954,.00879794883402715678] 
dist 156=[-.00500514802694310757,.01049979763639659866] 
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dist 192=[-2.42950089455837099700e-06,.00049248622979902911] 
dist 193=[1.98134189115202584070e-05,.00049068560781997408] 
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dist 199=[9.99580417677456408860e-05,.00033684430280181498] 
dist 200=[-1.64521593888194840850e-05,.00022654386580674170] 
dist 201=[-9.46418337202298927330e-05,.00022390906046833938] 
dist 202=[-.00015832611047513631,.00020769767700287520] 
dist 203=[-.00021714179449698562,.00020302815983751876] 
dist 204=[-.00026697823430515567,.00018666831904973093] 
dist 205=[-.00029500984696917413,.00018304468100916649] 
dist 206=[-.00031192293975282071,.00013989765125728011] 
dist 207=[-.00031761264834975667,.00013080554634476187] 
dist 208=[-.00031735023377025678,.00011420236607719966] 
dist 209=[-.00031522332875939184,.00010971567259166929] 
dist 210=[-.00030280286222737865,9.42785241435996796320e-05] 
dist 211=[-.00029814896307169817,8.94848553741895440640e-05] 
dist 212=[-.00025003071307291397,8.60306897567452379470e-05] 
dist 213=[-.00021508498651491200,8.49195809907745200050e-05] 
dist 214=[-.00017018509933479587,8.45811399558174290830e-05] 
dist 215=[-.00016543699400994003,8.45293560569148965240e-05] 
dist 216=[-.00012000923448245137,8.46767557924431815310e-05] 
dist 217=[-.00011797528771795135,8.51298749189741153740e-05] 
dist 218=[-9.92382036032795529200e-05,.00010308735567314481] 
dist 219=[-9.45761370116636242560e-05,.00013315908278392407] 
dist 220=[-8.75620404125608492600e-05,.00015851605516031531] 
dist 221=[-8.50559206280174497570e-05,.00017254872206450960] 
dist 222=[-2.60354480263573396690e-05,.00018071467243532892] 
dist 223=[-1.81964657238304112990e-05,.00018277644080825719] 
dist 224=[-7.98045596657891393120e-07,9.65531533242337902300e-05] 
dist 225=[3.03024578619532491070e-06,9.56545874822378916530e-05] 
dist 226=[2.13986872449690474210e-05,9.38220043306200006080e-05] 
dist 227=[2.46435852967099341800e-05,9.26784698514547649780e-05] 
dist 228=[2.92245906400682357180e-05,8.54005377995564522800e-05] 
dist 229=[2.97538021605928789950e-05,8.03253027958976120530e-05] 
dist 230=[2.40095383484190758350e-05,4.11347092534530376190e-05] 
dist 231=[1.02424642791675835580e-05,3.99059796903882607750e-05] 
dist 232=[-3.90797185573390096190e-06,3.50992326788900007730e-05] 
dist 233=[-1.34009976902349223890e-05,3.45111471203901660720e-05] 
dist 234=[-2.11214533393882946320e-05,3.08397553572609374240e-05] 
dist 235=[-2.82335152437564770810e-05,2.98762553758996970280e-05] 
dist 236=[-3.42478902194814835200e-05,2.73077357415827977460e-05] 
dist 237=[-3.76097340926505654240e-05,2.63392512506887527670e-05] 
dist 238=[-3.96108289430798790730e-05,1.57287249391290684640e-05] 
dist 239=[-4.02220458756785927860e-05,1.39451328351421774650e-05] 
dist 240=[-4.01357620564444271090e-05,1.02932471164570494340e-05] 
dist 241=[-3.98046747018215764770e-05,9.30896404226691903950e-06] 
dist 242=[-3.84107975477499992080e-05,5.71945579039662616900e-06] 
dist 243=[-3.76082351400700155480e-05,4.88726162311488572580e-06] 
dist 244=[-3.26187597296777555270e-05,3.94989413245970937070e-06] 
dist 245=[-2.88863016662507461220e-05,3.74673650025095449910e-06] 
dist 246=[-2.40779001463829385990e-05,3.75801174553309082360e-06] 
dist 247=[-2.35181921818053214060e-05,3.94890318270660746170e-06] 
dist 248=[-7.73635534517277204840e-06,5.52734771385783191610e-06] 
dist 249=[-6.66316755580776551890e-06,9.43297326943889444020e-06] 
dist 250=[-4.37674620606370911500e-06,1.26077068189554123640e-05] 
dist 251=[-3.75468932348928114350e-06,1.55296010436712086860e-05] 
dist 252=[-1.41501646602621367990e-06,1.79987089132986286400e-05] 
dist 253=[-9.23737359760247643940e-07,1.93755394160199396160e-05] 
dist 254=[-2.12676314125266248590e-07,2.01968808848044409260e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 0, 1, 1, 2] 
dist 0=[106.54055738398189293   ,106.54055738398189293   ] 
dist 1=[103.08801748683103758   ,108.49911294986642364   ] 
dist 2=[96.396331162163711807  ,109.24969888396313516   ] 
dist 3=[89.119169911268857729  ,109.50689743192231918   ] 
dist 4=[83.335296213244803515  ,109.49308134256381352   ] 
dist 5=[77.612364700520625792  ,109.33920975910215627   ] 
dist 6=[70.563791479285087804  ,109.04370971801923627   ] 
dist 7=[63.272049280844879102  ,108.58413789728387891   ] 
dist 8=[56.569671328230076078  ,105.85450566343967958   ] 
dist 9=[49.043305121287078724  ,84.857000014015207887  ] 
dist 10=[38.452036378651116786  ,81.690290484904779511  ] 
dist 11=[28.038881952663764477  ,73.294556828255851521  ] 
dist 12=[21.217930373250232364  ,71.790274461802498885  ] 
dist 13=[15.720310480325252520  ,57.920738737848994617  ] 
dist 14=[10.583990567546468963  ,53.648884119008204904  ] 
dist 15=[6.0554648104172358317 ,49.743594255842729447  ] 
dist 16=[1.9747157759627472483 ,48.332365993865647365  ] 
dist 17=[-3.8482565531835534258 ,18.315009622663802173  ] 
dist 18=[-9.1414123347335035662 ,14.592788175975063349  ] 
dist 19=[-13.711173121319162023  ,5.8441002845608103002 ] 
dist 20=[-16.651127024771134638  ,4.5706321576483005117 ] 
dist 21=[-18.987810184609573923  ,-4.7552539581171119137 ] 
dist 22=[-22.380142604949522893  ,-4.9588039816035907879 ] 
dist 23=[-24.779357726847338369  ,-2.1682527456981073008 ] 
dist 24=[-26.434069101886726466  ,.09801478636098433702] 
dist 25=[-27.477696568509979635  ,2.3129764321123654743 ] 
dist 26=[-27.677255538549162735  ,4.9286427064138339488 ] 
dist 27=[-27.136029695521149065  ,7.5113588867259650295 ] 
dist 28=[-27.050922783084755727  ,9.6039113114426005737 ] 
dist 29=[-22.560884819133746635  ,11.695499428517796343  ] 
dist 30=[-21.446539554402410089  ,14.284073798055791820  ] 
dist 31=[-20.699408564895020590  ,16.606172747408239282  ] 
dist 32=[-20.509989247267688189  ,17.642518576474230609  ] 
dist 33=[-3.6522293853307851706 ,18.125789554377076008  ] 
dist 34=[-1.6764518749750272489 ,18.246708189138541822  ] 
dist 35=[-.59494418654363611451,16.464146095941545947  ] 
dist 36=[-.89140107121628464784,15.996180239069116334  ] 
dist 37=[-1.1666087950295491538 ,15.720637463922312449  ] 
dist 38=[-1.4688015226570404918 ,15.650906432389018153  ] 
dist 39=[-1.7512977074332934247 ,12.001410114314742683  ] 
dist 40=[-1.9491478465321642133 ,12.523504684319115857  ] 
dist 41=[-2.1162322754945211373 ,12.783082673712954812  ] 
dist 42=[-3.6357717424779549107 ,12.797196453528242598  ] 
dist 43=[-5.7090581104413269647 ,12.531184340557791852  ] 
dist 44=[-7.0288980382952894743 ,12.358502981834502562  ] 
dist 45=[-8.0239736671675872389 ,10.704684285360872121  ] 
dist 46=[-8.8099025484487676610 ,10.265206415458831002  ] 
dist 47=[-9.3892525419111638368 ,9.6088435844881325878 ] 
dist 48=[-9.5647489068471449756 ,9.3619006703956548917 ] 
dist 49=[-9.5686008369950086579 ,3.3357174584637251862 ] 
dist 50=[-9.4653599568979761133 ,2.5339395616436823926 ] 
dist 51=[-8.4827477532865688579 ,.72335149348865621773] 
dist 52=[-8.1848033970811748532 ,.34147648094881220519] 
dist 53=[-8.5846820559115088789 ,-.17451560740992686357] 
dist 54=[-9.2514159049723622592 ,-.10530425257954052058] 
dist 55=[-9.6600099045672089000 ,.7397595280650325418 ] 
dist 56=[-9.7397006902740500807 ,2.4681937577536049994 ] 
dist 57=[-2.9416711305514546929 ,3.8792285642384492638 ] 
dist 58=[-2.9563817306226899395 ,5.1836677025197199307 ] 
dist 59=[-2.8853207927999895360 ,6.2866431609836218885 ] 
dist 60=[-2.8750081552006676004 ,6.8981993013209738038 ] 
dist 61=[-2.3778134590739380867 ,7.2544482393547412904 ] 
dist 62=[-2.2549820314932616806 ,7.3442143241939085168 ] 
dist 63=[-2.1745603883851647212 ,2.2594368841657531170 ] 
dist 64=[-2.1556172952731016125 ,2.2916136657872031647 ] 
dist 65=[-.29682885867708005914,2.2875204422155249974 ] 
dist 66=[-.07947678955021088625,2.2818342163360756836 ] 
dist 67=[.01196520531555613064,1.9606188787207923504 ] 
dist 68=[-.04124941336953737450,1.8743245261006415230 ] 
dist 69=[-.08545752396903351807,1.8131770573451458020 ] 
dist 70=[-.12721005975424193138,1.7850677086324593763 ] 
dist 71=[-.1628204859707252665 ,1.4024828955354651981 ] 
dist 72=[-.18273434190300354389,1.4582342663302311034 ] 
dist 73=[-.44143711110505942063,1.4827053187701827920 ] 
dist 74=[-.72663339756202963598,1.4807360999880977113 ] 
dist 75=[-.97344133649503362631,1.4425442998409993557 ] 
dist 76=[-1.1212426717869572514 ,1.4212028344411507863 ] 
dist 77=[-1.2220209020113315471 ,1.2228541096369871324 ] 
dist 78=[-1.2822406512133680951 ,1.1708872546884621839 ] 
dist 79=[-1.3144736209532752860 ,1.0924367504245184774 ] 
dist 80=[-1.3175902976056961006 ,1.0635269134639663352 ] 
dist 81=[-1.2832354150276634215 ,.36453454674582445288] 
dist 82=[-1.2732198441896718436 ,.2714233969666498243 ] 
dist 83=[-1.0618360765942947137 ,.06221557672874401969] 
dist 84=[-1.0087747606120137853 ,.01726368334619274592] 
dist 85=[-.98129781159082033876,.01267488700769973095] 
dist 86=[-1.0706940797373251471 ,.02519630098495860986] 
dist 87=[-1.1227058802087122543 ,.06612203471448135293] 
dist 88=[-1.1357795117378183252 ,.25131533486190818616] 
dist 89=[-.34631654636625064321,.40253365408750199549] 
dist 90=[-.34648790510068331174,.54259397300418317001] 
dist 91=[-.33528100745296286438,.66189560137211126976] 
dist 92=[-.33322458397003704929,.73357769485023596988] 
dist 93=[-.27434928371888700485,.7740558304465197957 ] 
dist 94=[-.26011787413533301239,.7835696731837214761 ] 
dist 95=[-.24840206035864426392,.30786759359986781674] 
dist 96=[-.24426578096787232039,.3096616171043592977 ] 
dist 97=[-.03886295058268218596,.30281278178701132215] 
dist 98=[-.01432400267223664635,.30181422098821059233] 
dist 99=[-.00744997296607968860,.25021804791848042239] 
dist 100=[-.01917423621238866123,.23737308138664190154] 
dist 101=[-.02881783621056737584,.2291240680615785703 ] 
dist 102=[-.03785474294308433126,.22714236179443513416] 
dist 103=[-.04558047342049210921,.1862535221468225006 ] 
dist 104=[-.05002079926834956512,.19135522889556618353] 
dist 105=[-.05423839045796583778,.19243732124409517213] 
dist 106=[-.09004139534461323976,.1917321403317179326 ] 
dist 107=[-.12080218743550514435,.18417943208622175356] 
dist 108=[-.13885382900948836686,.18244803987012872362] 
dist 109=[-.15071670075714352715,.14927344794353025419] 
dist 110=[-.15691302888475783784,.14126423286830216583] 
dist 111=[-.15977138471553085501,.13374754618752421804] 
dist 112=[-.15963033603525624818,.13047437839881414826] 
dist 113=[-.15569803245660425443,.03229521353161861034] 
dist 114=[-.15340374486786424153,.02223420937264182308] 
dist 115=[-.13223842111213871228,-.00053417579859678573] 
dist 116=[-.12665823232465465607,-.00507305168501714633] 
dist 117=[-.11820668178013638859,-.03046473603393808114] 
dist 118=[-.11509082654245659047,-.02286633561099215446] 
dist 119=[-.11142886204856143943,.01838057777093729470] 
dist 120=[-.11278063985422154056,.04606380012255258609] 
dist 121=[-.04428071119004372770,.06857306507711195444] 
dist 122=[-.04421021994733656528,.08927937436656732672] 
dist 123=[-.04251744065318401108,.10675309280210691249] 
dist 124=[-.04227322398483101226,.1164287404968331368 ] 
dist 125=[-.03422256349551052908,.12206630094871812734] 
dist 126=[-.03230088765398258227,.12348407873980927665] 
dist 127=[-.03094171772991528814,.03787369342670690566] 
dist 128=[-.03063728342558556826,.03791895808582215705] 
dist 129=[-.00293035555509186992,.03670547025637295823] 
dist 130=[.00029955935340666819,.03652291434201738725] 
dist 131=[.00778998785620817292,.02991272361010194749] 
dist 132=[.00889939875713291086,.02845097572044529471] 
dist 133=[.01742134151964119139,.02712389034197305709] 
dist 134=[.00874927046370433186,.02684856806304909516] 
dist 135=[3.61319734921035721600e-05,.02169675602669528628] 
dist 136=[-.00584011771973620007,.02227045617666467899] 
dist 137=[-.01064988589046102530,.02238064790261569834] 
dist 138=[-.01512914622487825083,.02226736243785738201] 
dist 139=[-.01894872013137121283,.02151262086548825000] 
dist 140=[-.02113956319813192038,.02116745546451898147] 
dist 141=[-.02251634124239615904,.01801761516722237148] 
dist 142=[-.02310413489277102073,.01721492213780718899] 
dist 143=[-.02323490898301199759,.01599565236276945979] 
dist 144=[-.02314263954409154796,.01555742248637324912] 
dist 145=[-.02226434523463008765,.00511694019215459973] 
dist 146=[-.02201710932519180129,.00372622802331987270] 
dist 147=[-.01819058567925543765,.00061873618455149857] 
dist 148=[-.01725503596369789038,-5.73796299123441660370e-05] 
dist 149=[-.01625452229878261344,-.00342124992665544665] 
dist 150=[-.01631146974947003835,-.0004815973840458976 ] 
dist 151=[-.01708553615764355225,.00374827930261346232] 
dist 152=[-.01728048982326348393,.00659128465123702245] 
dist 153=[-.00519421275804267484,.00890815946118009284] 
dist 154=[-.00517624789341878714,.01104917720463654840] 
dist 155=[-.00496836750289351424,.01286352336848539585] 
dist 156=[-.00492828837506091157,.01388342828952169677] 
dist 157=[-.00401267192681053074,.01457236904968044656] 
dist 158=[-.00379440493061507979,.01473054772014350822] 
dist 159=[-.00360614639276989000,.00490670098882756297] 
dist 160=[-.00353962135761519511,.00490089235978927100] 
dist 161=[-.00049233687482385090,.00471899629171654145] 
dist 162=[-.00012751099967914374,.00469162637236819226] 
dist 163=[.00071803311227011940,.00380828076001863146] 
dist 164=[.00084873239025018128,.00359654514795216110] 
dist 165=[.00183283640511713937,.00344477992192746334] 
dist 166=[.00137951222290084307,.00340782409840545552] 
dist 167=[.00030889192375858775,.00284926367560547644] 
dist 168=[-.00041203097546248724,.00290811861729605855] 
dist 169=[-.00100107109688685414,.00290728346610219719] 
dist 170=[-.00154808031349300842,.00289085584419687239] 
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dist 172=[-.00227905598180652552,.00273747404903486814] 
dist 173=[-.00244394923055374979,.00223427221462286777] 
dist 174=[-.00251016180453026148,.00211362553591988877] 
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dist 179=[-.00203996053535289708,2.31612555988742406930e-05] 
dist 180=[-.00195030472031438153,-4.56022287242929686520e-05] 
dist 181=[-.00181084343739615578,-.00040184340409460450] 
dist 182=[-.00176181341481274861,-.00028772187921525227] 
dist 183=[-.00172584923501341733,.00035234995452335012] 
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dist 190=[-.00047020326269965389,.00197804523386568679] 
dist 191=[-.00044888386695623537,.00056290076474107031] 
dist 192=[-.00044394979593674344,.00056136456609862270] 
dist 193=[-.00018408255386588138,.00053848137012109934] 
dist 194=[-.00015045097836903633,.00053517325254825291] 
dist 195=[-7.65580911784543096820e-05,.00044451405783969721] 
dist 196=[-5.75775498221855199880e-05,.00043232043528855214] 
dist 197=[2.06954511706572661640e-05,.00045613148190873508] 
dist 198=[-2.10361218986860284850e-05,.00049433571511368806] 
dist 199=[-.00017669163069815278,.00051733590532766925] 
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dist 201=[-.00036638985287594154,.00052486796381354289] 
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dist 203=[-.00051167503880142030,.00050592648580284826] 
dist 204=[-.00054917003975720385,.00049751413560940903] 
dist 205=[-.00057180851618336229,.00044481361861564447] 
dist 206=[-.00057946099935289028,.00043095741075181063] 
dist 207=[-.00057869459348147765,.00039394109792193761] 
dist 208=[-.00057407254470977494,.00038000070059371981] 
dist 209=[-.00055429320593143613,.00022701537602637432] 
dist 210=[-.00054279165136489216,.00020128448761296934] 
dist 211=[-.00047105498944388144,.00014862496409573207] 
dist 212=[-.00045224440428763538,.00013443569089803137] 
dist 213=[-.00041526400636984985,8.27290441918382115620e-05] 
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dist 215=[-.00025822194035223867,5.73177513792297942310e-05] 
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dist 217=[-7.41357917628883208160e-05,.00013392078867597783] 
dist 218=[-7.37487959526543519560e-05,.00017095918431122468] 
dist 219=[-7.05321528104662655280e-05,.00020217958262690971] 
dist 220=[-6.98976886962266721240e-05,.00021943704252796376] 
dist 221=[-5.78530579846713496390e-05,.00022945306908029295] 
dist 222=[-5.57802334683929806140e-05,.00023191950803388208] 
dist 223=[-5.12984213508921266440e-05,5.51467313253616939020e-05] 
dist 224=[-4.97515140168383061150e-05,5.48441139393648182770e-05] 
dist 225=[-2.46936586844178211180e-05,5.36300425402888080880e-05] 
dist 226=[-2.09406428511880782890e-05,5.27897434078084652460e-05] 
dist 227=[-1.28712032578228198910e-05,4.72744460012842826710e-05] 
dist 228=[-1.06768034549696089100e-05,5.07725871657591674420e-05] 
dist 229=[-2.39105819569211795280e-06,5.90430427268020535340e-05] 
dist 230=[-6.94825353047916189020e-07,6.36608559610860820830e-05] 
dist 231=[-1.63025215023119860220e-05,6.64032817858458679530e-05] 
dist 232=[-2.71914603021671659740e-05,6.72269353004599876420e-05] 
dist 233=[-3.60582523073475513160e-05,6.70159314808265564570e-05] 
dist 234=[-4.42449589753499461380e-05,6.64575450364893986180e-05] 
dist 235=[-5.11812474201430110870e-05,6.40069933633472005010e-05] 
dist 236=[-5.50830390907208585660e-05,6.26967880559184735170e-05] 
dist 237=[-5.74380135168396035990e-05,5.39607056235348325810e-05] 
dist 238=[-5.82324210128485692300e-05,5.17009470065130718010e-05] 
dist 239=[-5.82327662548598629880e-05,4.74911904392912086030e-05] 
dist 240=[-5.77017689861759052220e-05,4.61965380071425892400e-05] 
dist 241=[-5.62121125724451199990e-05,1.84777723290085723980e-05] 
dist 242=[-5.53313993572176019590e-05,1.45848027752691209260e-05] 
dist 243=[-4.98085786835331793760e-05,6.79070764169031498040e-06] 
dist 244=[-4.83556158842387511760e-05,5.79450588947390936730e-06] 
dist 245=[-4.41643402794885379670e-05,2.08629686043012144990e-06] 
dist 246=[-4.28335144666588818720e-05,1.30016215493122736850e-06] 
dist 247=[-3.27306590537793503700e-05,2.50660724910886262030e-07] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 1, 0, 0, 0, 1] 
dist 0=[110.76383701925225763   ,110.76383701925225763   ] 
dist 1=[107.26133750861479395   ,112.26941061136851166   ] 
dist 2=[103.23106213016935428   ,112.78054053370816115   ] 
dist 3=[99.619359454640955762  ,112.57580078809607787   ] 
dist 4=[95.661403766238320664  ,110.92332481549381826   ] 
dist 5=[90.241854274127544091  ,108.28250732145379033   ] 
dist 6=[84.334574667971518718  ,106.44762061812948975   ] 
dist 7=[78.425605072367428216  ,105.64364846079004960   ] 
dist 8=[71.399360593643771525  ,101.72921918586944218   ] 
dist 9=[61.027606676595899678  ,80.525260509232753136  ] 
dist 10=[50.512981766195374679  ,69.712728606908863691  ] 
dist 11=[42.917215855804208809  ,68.301825520224041776  ] 
dist 12=[36.019888174322780502  ,53.207011024595768565  ] 
dist 13=[28.300097514385022425  ,50.278838801190455075  ] 
dist 14=[20.048687294273967232  ,45.152179657475769828  ] 
dist 15=[11.329013043306407281  ,44.147826046489254797  ] 
dist 16=[-.24093728911068619528,19.901322955577744667  ] 
dist 17=[-11.207506117676070582  ,18.998295473383823114  ] 
dist 18=[-17.532878106530641754  ,6.3399073934356172655 ] 
dist 19=[-21.691992418241351400  ,4.5553320981748434058 ] 
dist 20=[-24.031862139223359163  ,1.1422210615838778354 ] 
dist 21=[-25.520170470228594546  ,.34388443359193816841] 
dist 22=[-26.441931890993783317  ,-1.9838383670922134768 ] 
dist 23=[-27.672299533749584147  ,-2.3654179205649712348 ] 
dist 24=[-28.226349261014077704  ,-2.1915894733011625407 ] 
dist 25=[-28.324984817259346765  ,-1.2331999570450420130 ] 
dist 26=[-17.177047578109324933  ,-.13861415457654476414] 
dist 27=[-17.103840485330716913  ,.57882439733371372741] 
dist 28=[-14.099038494693264606  ,1.1435785221884202583 ] 
dist 29=[-13.373822710843315668  ,2.6199922044356962920 ] 
dist 30=[-12.864596117257793351  ,5.1092705167636436924 ] 
dist 31=[-12.748670183249759440  ,7.3169132514666018823 ] 
dist 32=[-2.1747037432836136061 ,9.6601370713827736419 ] 
dist 33=[-.94031871571247007423,11.709795212829780516  ] 
dist 34=[.06816176061495899821,12.754655899010119133  ] 
dist 35=[-.33900360835111901312,13.275686547034549778  ] 
dist 36=[-.71342959597621503086,13.354942526952671739  ] 
dist 37=[-1.1241767270238254032 ,12.841508695269570307  ] 
dist 38=[-1.5120017926912409247 ,12.561774528900748040  ] 
dist 39=[-1.7962051450558660955 ,12.114397165937384728  ] 
dist 40=[-2.0516406462156179481 ,11.897144489996678075  ] 
dist 41=[-2.3261421298454750870 ,7.8629780693627051057 ] 
dist 42=[-2.6943388910969799322 ,7.6648328384123508191 ] 
dist 43=[-4.7569920517012633690 ,7.5546508452940148161 ] 
dist 44=[-6.6798421455995634268 ,6.4994007031087824498 ] 
dist 45=[-8.3099204654183319789 ,6.2241283639381909770 ] 
dist 46=[-9.2118008122267491657 ,5.8130964208116576161 ] 
dist 47=[-9.7320838031646973088 ,5.6602316168542110428 ] 
dist 48=[-9.8489243760388338592 ,1.9714568268061533294 ] 
dist 49=[-2.9237526448487164681 ,1.4821720913965116846 ] 
dist 50=[-3.1879168253830878580 ,1.2127570227657622811 ] 
dist 51=[-4.1877661558262188744 ,1.5065244697181074764 ] 
dist 52=[-5.0311964594515883527 ,1.9011451317005919527 ] 
dist 53=[-5.4980606658227119320 ,2.3077367589273248823 ] 
dist 54=[-5.7698348424570358505 ,2.6348395135200921515 ] 
dist 55=[-5.8382535122839230735 ,2.7828510835717290728 ] 
dist 56=[-2.8114295155755566251 ,2.8502093325724042870 ] 
dist 57=[-1.7863619387601007223 ,2.8576587531696267698 ] 
dist 58=[-1.7320069307271800937 ,-.07851277606174053528] 
dist 59=[-1.7211354781280415740 ,.20074479236525663822] 
dist 60=[-1.4256170655673370808 ,.62299936936071442772] 
dist 61=[-1.3563541693687876945 ,.99844094514269623514] 
dist 62=[-1.2893765473145072653 ,1.2403561059476434935 ] 
dist 63=[-1.2676155105250117738 ,1.4260035575153587817 ] 
dist 64=[-.27681147115072632458,1.5784227728308657073 ] 
dist 65=[-.15600383162942430877,1.6938167626936960580 ] 
dist 66=[.02123733655460166370,1.7325820378674022985 ] 
dist 67=[.02378852835484716887,1.7378134523490327139 ] 
dist 68=[.02652602075206666743,1.7200152588961777963 ] 
dist 69=[.02607585911517261230,1.5511963170111550857 ] 
dist 70=[.02444895325664638648,1.4984652087718494630 ] 
dist 71=[.02142290669237302989,1.4176788121897028256 ] 
dist 72=[.01690294409587281382,1.3853351901878092246 ] 
dist 73=[-.12874872933788607833,1.0477483275350784923 ] 
dist 74=[-.44410373949371088138,1.0086621221309672423 ] 
dist 75=[-.70173098844960262501,.99692779897341570166] 
dist 76=[-.94010848954702523744,.82670699318683712863] 
dist 77=[-1.1417429569053997005 ,.78494173119469376457] 
dist 78=[-1.2535708653629593839 ,.73826096615330148857] 
dist 79=[-1.3187250206355379482 ,.71547474212365764528] 
dist 80=[-1.3351434341160086021 ,.27794136989175606291] 
dist 81=[-.41083852888475679526,.24134550912599262525] 
dist 82=[-.41868280007292338211,.16241957141846780332] 
dist 83=[-.50885411994879671787,.14069266915084842686] 
dist 84=[-.59321158997524657328,.05732080623566762123] 
dist 85=[-.64052911157694233617,.04021097822775731535] 
dist 86=[-.67188945896046099999,.01144032411633172069] 
dist 87=[-.67893419229759198975,.01170319221260582337] 
dist 88=[-.33129355351102244764,.01213854727005252062] 
dist 89=[-.21765510506762465285,.01221182428002035211] 
dist 90=[-.20964995841119801779,.02258285007353104284] 
dist 91=[-.20842217317594509127,.07796176633833925989] 
dist 92=[-.16945957332824926858,.13081881545434491568] 
dist 93=[-.16011980797724562158,.17670450554922316184] 
dist 94=[-.15335064899912001016,.20442280123667216433] 
dist 95=[-.15165318200377955468,.22360968421396488756] 
dist 96=[-.04246857981316150425,.235645358293134078  ] 
dist 97=[-.05128759316425292011,.24251232588696646934] 
dist 98=[-.06019830002585003447,.24338354554534983413] 
dist 99=[-.06625660523031329650,.23768418018047584662] 
dist 100=[-.07126119121004847126,.23591107282032090802] 
dist 101=[-.07599012189040717565,.19744632528651170846] 
dist 102=[-.08006287409929797045,.18770971198639827754] 
dist 103=[-.08246330383085814856,.17876590790768510563] 
dist 104=[-.08405106718547023667,.17432545498139644337] 
dist 105=[-.08489855376911341871,.10971448612818682437] 
dist 106=[-.08512940863246782612,.10606950321276241764] 
dist 107=[-.08433910422657335291,.10432574048256736372] 
dist 108=[-.09988722947461088272,.0889930696844113137 ] 
dist 109=[-.12246392827503739986,.08506587118936547772] 
dist 110=[-.13575491312136610402,.07893811184039278873] 
dist 111=[-.14324003896563386163,.07679237645224315236] 
dist 112=[-.14499728055788412788,.02581520913123667607] 
dist 113=[-.06520957937965044990,.01898406908965395634] 
dist 114=[-.05751498072893341263,.01168297743312397562] 
dist 115=[-.05645695640205089598,.01183820087634243213] 
dist 116=[-.05630225453152364304,.01197899929739117313] 
dist 117=[-.04692414194896345151,.01212866930784839190] 
dist 118=[-.04456420239920880409,.01226586172512821022] 
dist 119=[-.04308839022493030844,.01235770774548844786] 
dist 120=[-.04272776317239034269,.01243797724855114149] 
dist 121=[-.02418389607345932930,.01249673137526282844] 
dist 122=[-.00267439196794866656,.00264714758846161824] 
dist 123=[-.00261150786758546760,.00977078285223005358] 
dist 124=[-.00238289522993675930,.01649346316767397218] 
dist 125=[-.00234995387275434162,.02228350066844223239] 
dist 126=[-.00175228462394181033,.02570544079481524619] 
dist 127=[-.00162337282692746586,.02798388457690947861] 
dist 128=[-.00150961391619598246,.02923541261519721710] 
dist 129=[-.00148709801515588739,.02986248591433181031] 
dist 130=[7.22898458549716460730e-05,.02986592315050234861] 
dist 131=[.00025328364392537485,.02919755836315283626] 
dist 132=[.00066114849129946996,.02877540189369578522] 
dist 133=[.00072543062026311577,.02488406204531680204] 
dist 134=[.00115611866456327189,.02384861435310202495] 
dist 135=[.00122150205475465873,.02227819824238476306] 
dist 136=[.00129974688511195468,.02169672703191471762] 
dist 137=[-.00337565389021050496,.00758244737674947072] 
dist 138=[-.00857468709914013479,.00570623770112964537] 
dist 139=[-.01280347576891965521,.00148238124927497910] 
dist 140=[-.01669522589387127998,.00112407014159403472] 
dist 141=[-.01997999805729397101,.00110116166100631457] 
dist 142=[-.02179912399717746582,.00089058276458893337] 
dist 143=[-.02285942247522853606,.00084211960011845805] 
dist 144=[-.02312588361570963389,.00076973142704683586] 
dist 145=[-.00709892984258982311,.00074514076604080175] 
dist 146=[-.00711543058761984290,.00019416543145640587] 
dist 147=[-.00690529472679374797,.00012165726636101483] 
dist 148=[-.00687355055208990770,-3.66506648704270518220e-05] 
dist 149=[-.00565090818402923191,-7.22189026988100174520e-05] 
dist 150=[-.00537999578460733759,-.00023012205526944915] 
dist 151=[-.00513323452127966122,-.00025870108135065279] 
dist 152=[-.00508213668282525286,-.00029184174919166468] 
dist 153=[-.00113518293021514689,-3.50860571311211906740e-05] 
dist 154=[-.00065758883400693155,.00107205003678792364] 
dist 155=[-.00027071216342716091,.00197937739710568913] 
dist 156=[-.00024928995179165557,.00282610169466608211] 
dist 157=[-.00024600814824247310,.00354922363061070409] 
dist 158=[-.00018712301705971985,.00396587288810988644] 
dist 159=[-.00017440643365885786,.00423006891291126216] 
dist 160=[-.00016221458881299152,.00434798433827398159] 
dist 161=[-.00015933973257246358,.00437966912150958077] 
dist 162=[-3.68379335248629252800e-06,.00436452476802182578] 
dist 163=[1.47456177671126796040e-05,.00420379206018038916] 
dist 164=[5.62415988397554357940e-05,.00415771937431387048] 
dist 165=[6.31435678296718278940e-05,.00344039924797691433] 
dist 166=[.00010717197665340193,.00326443548528898749] 
dist 167=[.00011400455640809379,.00307651759179986916] 
dist 168=[.0001008639392395612 ,.00298022847305331471] 
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dist 177=[-.00092858951056814505,8.77897008384207353290e-05] 
dist 178=[-.00092825642552901672,1.53800329505211541680e-05] 
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dist 190=[-3.89154234450556059620e-05,.00042649914798627208] 
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dist 192=[-3.51194439755263313540e-05,.00047153616231941545] 
dist 193=[-3.40431640750924289310e-05,.00047501322624383864] 
dist 194=[-2.79461360210076416720e-05,.00047299328003423717] 
dist 195=[-2.64190350019653314040e-05,.00045771762084853345] 
dist 196=[-2.41323911077074641210e-05,.00045056810712041165] 
dist 197=[-2.33414682106634721890e-05,.00038406641612522303] 
dist 198=[-2.15216313276911123930e-05,.00036703917928273865] 
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dist 201=[-5.79313404999765749390e-05,.00010912665080554547] 
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dist 206=[-.00034434723453046909,6.01580144534560000520e-05] 
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dist 224=[-3.07776285587558356060e-05,6.31001425521046041550e-05] 
dist 225=[-3.16795589247534340980e-05,6.31790749240631481430e-05] 
dist 226=[-3.25836007852147275600e-05,6.28738593224680126470e-05] 
dist 227=[-3.31885534864664521120e-05,6.01495732798810730650e-05] 
dist 228=[-3.36782654686315043670e-05,5.96330641070406828850e-05] 
dist 229=[-3.41248192174707604000e-05,4.82586552850911222790e-05] 
dist 230=[-3.44986531009588081270e-05,4.42878809072028238710e-05] 
dist 231=[-3.46996685118953344990e-05,4.12776888089799942940e-05] 
dist 232=[-3.48086143766167183250e-05,3.39404602982314688700e-05] 
dist 233=[-3.48169203117310078300e-05,9.11764690278175798450e-06] 
dist 234=[-3.46954483494835534460e-05,8.80784708651424090850e-06] 
dist 235=[-3.42891222524055188560e-05,8.70686296540989204220e-06] 
dist 236=[-3.36046170640962795760e-05,8.58067030608229936100e-06] 
dist 237=[-3.31878453382499986380e-05,8.45597048669937881530e-06] 
dist 238=[-3.09286709306858135640e-05,8.17644950203180932410e-06] 
dist 239=[-3.02303564910809281010e-05,8.01510319630744495090e-06] 
dist 240=[-2.74200894340944722540e-05,7.71152622098119264940e-06] 
dist 241=[-1.49508635120298390080e-05,7.58544333692291875540e-06] 
dist 242=[-1.48888467608564084500e-05,6.96649777019599130610e-06] 
dist 243=[-1.42925530928022572580e-05,6.73923585339452576660e-06] 
dist 244=[-1.41573497585760567730e-05,6.53943925684462129440e-06] 
dist 245=[-1.15948913160575674180e-05,6.39454441833042020700e-06] 
dist 246=[-1.09774194842710608840e-05,6.24963597682942128830e-06] 
dist 247=[-1.02074237265161708990e-05,6.19248671542856860650e-06] 
dist 248=[-7.62722600883682886280e-06,6.22004851799910693540e-06] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[110.46121040574155211   ,110.46121040574155211   ] 
dist 1=[107.18644536937204807   ,111.44059982107165162   ] 
dist 2=[103.23355874454841923   ,112.05450055091668103   ] 
dist 3=[99.670411391359550539  ,112.53149609173113385   ] 
dist 4=[95.748532080365014596  ,112.30277430531365772   ] 
dist 5=[90.356697453102480372  ,109.07604149149664835   ] 
dist 6=[84.469037140802867660  ,107.87480946226256033   ] 
dist 7=[78.414860554550711383  ,106.10261611617294314   ] 
dist 8=[66.247123777752040740  ,105.28825279756555635   ] 
dist 9=[57.117348622230915920  ,81.328373667697881068  ] 
dist 10=[48.598526666077242161  ,77.979920114852169623  ] 
dist 11=[38.842480563537426182  ,68.995830018059583364  ] 
dist 12=[29.160855230544957076  ,67.579534242442376542  ] 
dist 13=[20.922637222290206074  ,51.370813323212314445  ] 
dist 14=[12.211954770094724364  ,48.138835175885462509  ] 
dist 15=[.62444761910926900572,44.474794141582171243  ] 
dist 16=[-10.370759679696444329  ,43.468939263529230050  ] 
dist 17=[-16.731170097094688113  ,19.012193353410771632  ] 
dist 18=[-20.936296568875297643  ,7.7565427823468579911 ] 
dist 19=[-23.348358233513311671  ,4.5149646112697868617 ] 
dist 20=[-24.907100449991528542  ,1.0909892119271841892 ] 
dist 21=[-25.706973449677802858  ,.28955315968930757398] 
dist 22=[-26.366150962124283675  ,-2.0526871097065667324 ] 
dist 23=[-27.600068181135117796  ,-2.4396333854809315008 ] 
dist 24=[-28.159616504236658827  ,-2.2709008285851453984 ] 
dist 25=[-28.274948283612200465  ,-1.3185449133363749135 ] 
dist 26=[-17.563184249681721615  ,-.22908883014388697763] 
dist 27=[-17.032484861456168139  ,.48685143385723674244] 
dist 28=[-16.955128963434285405  ,2.3971175315501268652 ] 
dist 29=[-13.939097779784637771  ,4.8475267713444748076 ] 
dist 30=[-13.214885921941693979  ,7.0293324321029842373 ] 
dist 31=[-12.701828701060752622  ,9.3581811406903273107 ] 
dist 32=[-12.586767938849091047  ,11.400379192664922479  ] 
dist 33=[-2.1007157684636180066 ,12.446871014242216521  ] 
dist 34=[-.87731754951523235359,12.972465717703112171  ] 
dist 35=[-.31693578578324869439,13.057327146969940716  ] 
dist 36=[-.67782452467739351229,12.582482547937389705  ] 
dist 37=[-1.0757911845943524241 ,12.313331546089024574  ] 
dist 38=[-1.4526032210122043970 ,11.882060645064843527  ] 
dist 39=[-1.7302834578767676664 ,11.670733079001208452  ] 
dist 40=[-1.9813546435692322342 ,7.6543801892515806035 ] 
dist 41=[-2.6141389614961843756 ,7.7870112190732234277 ] 
dist 42=[-4.6338372095604680541 ,7.7779733663585673834 ] 
dist 43=[-6.5172146769738231096 ,7.5749358787377539612 ] 
dist 44=[-8.1140070456801135848 ,7.4654615856313007309 ] 
dist 45=[-8.9974938643581451099 ,6.4138661744502489590 ] 
dist 46=[-9.5071169994013078683 ,6.1405640088573586624 ] 
dist 47=[-9.6213765076709605072 ,5.7335339997816386636 ] 
dist 48=[-2.8574846846711871039 ,5.5820917075879398966 ] 
dist 49=[-3.0547093054850982519 ,1.9263847883849203533 ] 
dist 50=[-3.1505998115605863365 ,1.4408670044619074382 ] 
dist 51=[-3.1851624757694190255 ,1.4616745939164024790 ] 
dist 52=[-4.1337459309043252317 ,1.8553866722466308027 ] 
dist 53=[-4.9671191060074266822 ,2.2514400914165112418 ] 
dist 54=[-5.4283705482845675734 ,2.5697510882492800049 ] 
dist 55=[-5.6967529546959622689 ,2.7130922997934819409 ] 
dist 56=[-5.7643471004993492833 ,2.7781068545580771367 ] 
dist 57=[-1.7713087623500641417 ,2.7859993988635984846 ] 
dist 58=[-1.7726469910689751702 ,.19005327079908402617] 
dist 59=[-1.7174981678135856721 ,.6048228704099172665 ] 
dist 60=[-1.7061405293416786191 ,.97384740012114915157] 
dist 61=[-1.4081986752424127325 ,1.2120142559940959758 ] 
dist 62=[-1.3354105836166605856 ,1.3952166695159636372 ] 
dist 63=[-1.2759472219045517814 ,1.5463914874349414956 ] 
dist 64=[-1.2540163906030349474 ,1.6612348602816784588 ] 
dist 65=[-.20730897806284581451,1.7003095383829321941 ] 
dist 66=[-.08236113948894043814,1.7061055726248466074 ] 
dist 67=[.02834545177728185370,1.6889348455411355767 ] 
dist 68=[.03239370852308674425,1.5243165637340642631 ] 
dist 69=[.03266451546613252137,1.4727272233181833030 ] 
dist 70=[.03165494681633646245,1.3936571421646221569 ] 
dist 71=[.02898746718632877816,1.3619484772823651024 ] 
dist 72=[-.1252814544367761482 ,.94948028750865801285] 
dist 73=[-.43502227247203862827,.95551733473577400961] 
dist 74=[-.68809104603151400013,.95218570302581972643] 
dist 75=[-.92227668416344766636,.91522877000874955168] 
dist 76=[-1.1203740172155740338 ,.90651256002130980879] 
dist 77=[-1.2302428416174906754 ,.74308784766950291562] 
dist 78=[-1.2942555859124042656 ,.70357272735896023505] 
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dist 80=[-.40325807399368423454,.64906807741379355318] 
dist 81=[-.41119441224428840009,.16429470793627834685] 
dist 82=[-.41200864065923541549,.11392680130769265263] 
dist 83=[-.41133327638865981304,1.31141238494522552620e-05] 
dist 84=[-.39724388982355237049,-.00110537155438115972] 
dist 85=[-.47991664019750321394,-.00057177705347289296] 
dist 86=[-.5259598219504836665 ,-6.43287070002527215770e-05] 
dist 87=[-.55449117248438697383,.00030920973346508267] 
dist 88=[-.56115560498311593572,.00055292366763907277] 
dist 89=[-.21855406789919808333,.02200787041217840357] 
dist 90=[-.21820861039405749773,.07647113439318667888] 
dist 91=[-.20985828587086460657,.12847644879381615234] 
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dist 93=[-.16897661525955476852,.20093854336821313681] 
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dist 96=[-.15127186401965798063,.23862920836950327481] 
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dist 98=[-.01458114965962650318,.23396488905061655626] 
dist 99=[-.01648937234625403733,.2322188451719297854 ] 
dist 100=[-.01812639225832262247,.19444319152123170512] 
dist 101=[-.01976537409570530518,.18487132128054904642] 
dist 102=[-.02123323191785832925,.1760593546195797226 ] 
dist 103=[-.02219220275771366613,.17166103111251968381] 
dist 104=[-.02294100938807737635,.10898683518548734192] 
dist 105=[-.04501064415557915184,.10951709640470443402] 
dist 106=[-.07265020357933316381,.1089618387096225325 ] 
dist 107=[-.09829811227556726240,.10524538400624508701] 
dist 108=[-.12073997665297071184,.10356953594914384845] 
dist 109=[-.13380768415222432969,.08808365557405548343] 
dist 110=[-.14116337157572406993,.08414584058169682431] 
dist 111=[-.14287621024952999072,.07821048192634072222] 
dist 112=[-.05610084394665765473,.07606218444110871633] 
dist 113=[-.05653289299536360437,.02512228938419704443] 
dist 114=[-.05565271023448883860,.02556482821586625421] 
dist 115=[-.05546835603625173070,.02596205814607477102] 
dist 116=[-.06104289059640175356,.02639135482338303200] 
dist 117=[-.07273019245209313746,.02696248701987479141] 
dist 118=[-.07919782572874543277,.02815150927923138407] 
dist 119=[-.08296116354931927206,.02962916601904236453] 
dist 120=[-.08391003931015631307,.03028857347586808603] 
dist 121=[-.02565082753131748421,.03028743662773970040] 
dist 122=[-.02556392452322572933,.00951039017106421166] 
dist 123=[-.02448868919745940087,.01611995466225014521] 
dist 124=[-.02432894757921004172,.02181387755607276255] 
dist 125=[-.01961621567113287335,.02518126407545555302] 
dist 126=[-.01858302519900625686,.02742614586316461687] 
dist 127=[-.01765322103928685635,.02866490093434499316] 
dist 128=[-.01745968592485343831,.02929056274557920119] 
dist 129=[-.00334597259091730346,.02929698067537184941] 
dist 130=[-.00164624483163277363,.02865083151997609833] 
dist 131=[.00226075031407314545,.02823560121614278961] 
dist 132=[.00292174399292870400,.02443597356213159848] 
dist 133=[.00740267837024703818,.02342301589191170346] 
dist 134=[.00809515187546802480,.02187910694781495808] 
dist 135=[.00434509054904366209,.02130985387846475280] 
dist 136=[-.00328503134959010116,.01539318826211235083] 
dist 137=[-.00840798860901200026,.01538010975683356153] 
dist 138=[-.01257488811542154497,.01528717938839184129] 
dist 139=[-.01640960754991683893,.01463759350595116419] 
dist 140=[-.01964614738992477653,.01446635465477272717] 
dist 141=[-.02143831865596811229,.01187766124677232627] 
dist 142=[-.02248142350729395288,.01125300567066488478] 
dist 143=[-.02274417503760559433,.01058100684910860228] 
dist 144=[-.00688861574602025240,.01024331595888925051] 
dist 145=[-.00690522221526984732,.00371291222116318622] 
dist 146=[-.00671674179497334311,.00319933519591145725] 
dist 147=[-.00667601453590855579,.00210424389096366121] 
dist 148=[-.00737445789393316188,.00180619427921982108] 
dist 149=[-.00855277027475587145,.00068407301182261378] 
dist 150=[-.00920961093524565648,.00044895529072852534] 
dist 151=[-.00960728439093921164,.00010518509301949219] 
dist 152=[-.00971160201809173509,1.03614406036980491270e-05] 
dist 153=[-.00324770571700017184,.00072317806217895289] 
dist 154=[-.00323322184934378978,.00159009934644554359] 
dist 155=[-.00309082736236758679,.00239973011872548550] 
dist 156=[-.00306868649330515223,.00309158018544727228] 
dist 157=[-.00246742991889349598,.00349093895894677241] 
dist 158=[-.00232556922788678643,.00374509468315807598] 
dist 159=[-.00221755201729549760,.00386052614243536873] 
dist 160=[-.00218978108425046070,.00389476308088176714] 
dist 161=[-.00019787236041184697,.00388433287365515995] 
dist 162=[3.52190004793926509270e-05,.00374098437618811537] 
dist 163=[.00057760432208835695,.00370614187400606806] 
dist 164=[.00065623399753456056,.00304639734986165306] 
dist 165=[.00128993800485209816,.00288579394201131062] 
dist 166=[.00132935149951808392,.00273322815593779366] 
dist 167=[.00053429933823585195,.00266375160278909598] 
dist 168=[-.00026308394346499622,.00167193686367939159] 
dist 169=[-.00079861249625669417,.00167014281812749292] 
dist 170=[-.00123453029614961622,.00165908007075243526] 
dist 171=[-.00163644330689652419,.00159261644106543679] 
dist 172=[-.00197633439165330994,.00156937513238564073] 
dist 173=[-.00216708430834312181,.00131121560476851017] 
dist 174=[-.00228631581497435216,.00124755452870091713] 
dist 175=[-.00231373308906164697,.00116340152005684600] 
dist 176=[-.00094782418281769869,.00112899523194772929] 
dist 177=[-.00094647002428979357,.00032832046129433295] 
dist 178=[-.00091702718891599186,.00022877822853298110] 
dist 179=[-.00090715084023112476,6.00962258942918189010e-06] 
dist 180=[-.00086407241831174520,-4.10326034443486929490e-05] 
dist 181=[-.00103149871803903016,-.00028215685902489415] 
dist 182=[-.00112425850719672349,-.00032365076698995242] 
dist 183=[-.00117896699653228952,-.00019727230740078105] 
dist 184=[-.00119243367076714490,2.98483429386469678570e-05] 
dist 185=[-.00048165033182606836,.00018271261918877052] 
dist 186=[-.00047646454857633472,.00030752982738826072] 
dist 187=[-.00046583765123494450,.00042329566494299600] 
dist 188=[-.00045975940897354180,.00052170579502946340] 
dist 189=[-.00042216960219789010,.00057761579590440226] 
dist 190=[-.00041219531035535734,.00061206862383321980] 
dist 191=[-.00037531590862633278,.00062528776135496102] 
dist 192=[-.00036954998901814200,.00062690067527487184] 
dist 193=[-.00026974411430755337,.00062326804644856742] 
dist 194=[-.00024994862859090764,.00060080635360553365] 
dist 195=[-.00021275371118350513,.00059115470052627696] 
dist 196=[-.00020271670299439370,.00050057314334633158] 
dist 197=[-.00016766942839518190,.00047769540637007887] 
dist 198=[-.00015754015353704186,.00044107726446502063] 
dist 199=[-.00014936948947368126,.00035388063336226632] 
dist 200=[-.00014702462106378438,.00026215113307523663] 
dist 201=[-.00014649761427388999,.00026078647004157607] 
dist 202=[-.00019807197493120604,.00025863937423423394] 
dist 203=[-.00025653785549421452,.00024768994727063863] 
dist 204=[-.00030585002651037873,.00024363866726377836] 
dist 205=[-.00033314525839005713,.00020377909795290386] 
dist 206=[-.00034903177088456598,.00019394396384975040] 
dist 207=[-.00035304509960230151,.00017982557455583890] 
dist 208=[-.00019383293749950622,.00017454634974249644] 
dist 209=[-.00019244971965159756,4.96332838730339155780e-05] 
dist 210=[-.00018909367918222901,3.32056387840943128640e-05] 
dist 211=[-.00018702598510903307,-3.36515592301473502910e-06] 
dist 212=[-.00017372452976084939,-1.11782717857629135470e-05] 
dist 213=[-.00016992596827493339,-4.99888721038237418840e-05] 
dist 214=[-.00015607377933194303,-4.74217635581477864000e-05] 
dist 215=[-.00015001099567956863,-2.00217085097142618300e-05] 
dist 216=[-.00011582643131129048,7.82383516767110717270e-06] 
dist 217=[-7.44415111739456701560e-05,2.65291775653324364010e-05] 
dist 218=[-7.37647616414950732480e-05,4.17662757482445995660e-05] 
dist 219=[-7.16180205399353203460e-05,5.58410435604575361900e-05] 
dist 220=[-7.03733080561493478710e-05,6.77682555190408237350e-05] 
dist 221=[-6.26170681285557843080e-05,7.44783956751606821390e-05] 
dist 222=[-6.05837483747428238140e-05,7.85285830466474189380e-05] 
dist 223=[-5.53892855984102509390e-05,7.98943514331666976190e-05] 
dist 224=[-5.34402887493355233400e-05,7.98883824988750352310e-05] 
dist 225=[-3.07392034085990987860e-05,7.92710574813028084280e-05] 
dist 226=[-2.70137964159306704490e-05,7.66674708459769384390e-05] 
dist 227=[-1.93226737283838041600e-05,7.51299232832139551030e-05] 
dist 228=[-1.72503505251694737790e-05,6.54920051506031575700e-05] 
dist 229=[-9.66470041011313282010e-06,6.29578279624114237110e-05] 
dist 230=[-7.94462562675464787520e-06,5.78045740485752810460e-05] 
dist 231=[-5.94653861113686757770e-06,4.93115848552731313260e-05] 
dist 232=[-1.05018678052477600840e-05,2.54406590850043965600e-05] 
dist 233=[-1.81107626515868459810e-05,1.33085246383930002910e-05] 
dist 234=[-2.43020759809647504260e-05,8.84382042978821493320e-06] 
dist 235=[-3.00097177062449456600e-05,7.62183049370306803560e-06] 
dist 236=[-3.48385273568421505030e-05,2.98168430746461224960e-06] 
dist 237=[-3.75403733546611355000e-05,2.01567708143273113490e-06] 
dist 238=[-3.92278579166205896020e-05,5.18586395643839476390e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 0, 2, 1, 0, 2] 
dist 0=[116.49953415306772115   ,116.49953415306772115   ] 
dist 1=[114.73479093619836176   ,117.65953917561650339   ] 
dist 2=[111.50853531606763439   ,118.44176882205108981   ] 
dist 3=[104.53521090144131387   ,118.69321476654966464   ] 
dist 4=[96.839742767001741911  ,118.57027024115857879   ] 
dist 5=[90.739201560794848296  ,117.96292715244911325   ] 
dist 6=[84.715236845234462227  ,116.70729733137090090   ] 
dist 7=[72.668473411641996352  ,115.99217499958192495   ] 
dist 8=[62.975752614267475906  ,94.317177329791198893  ] 
dist 9=[54.021421905151705446  ,91.121144943372807376  ] 
dist 10=[43.898763597141573315  ,82.078221224856861716  ] 
dist 11=[33.929689941769343838  ,80.716716861699984171  ] 
dist 12=[25.570935217843842432  ,62.898885035584758241  ] 
dist 13=[16.841396070937825144  ,59.256739256913930574  ] 
dist 14=[5.3710401733670977692 ,55.551669201450837568  ] 
dist 15=[-5.5094112176651222982 ,54.699541885480736313  ] 
dist 16=[-11.898045907649245245  ,15.455384460588994114  ] 
dist 17=[-16.239201251072650596  ,10.821214760468319178  ] 
dist 18=[-18.965001073423478302  ,6.7522854742409878403 ] 
dist 19=[-20.850581754101988107  ,6.0758596698336208317 ] 
dist 20=[-21.838707288216317412  ,3.4201186620482417550 ] 
dist 21=[-22.681901007839083695  ,2.8495026483034183598 ] 
dist 22=[-25.429767383301325914  ,2.7067833578610031158 ] 
dist 23=[-27.397053143818839416  ,3.0607582167098584403 ] 
dist 24=[-28.779264937706056177  ,3.6619636017287570751 ] 
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dist 152=[-8.79403900338662722140e-05,.00468409120211066551] 
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dist 184=[-6.66049517401264679970e-05,.00046880638347288660] 
dist 185=[6.29666574149240967590e-05,.00051318749555783143] 
dist 186=[8.46206212830411049490e-05,.00054071665553098760] 
dist 187=[.00020610582333987951,.00054713874045651335] 
dist 188=[.00021016380184412150,.00046958456806934735] 
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dist 193=[.00013342929712105384,.00049062921913605128] 
dist 194=[.00010282750518349381,.00048508539544627273] 
dist 195=[5.66028352982468000620e-05,.00040006757869540996] 
dist 196=[1.02238304102132046900e-05,.00037935880824710968] 
dist 197=[-2.09917193539698187990e-05,.00035715146750393021] 
dist 198=[-4.64823209182704072000e-05,.00034587858053057419] 
dist 199=[-8.43272485781491423160e-05,.00012910087323487164] 
dist 200=[-.00014691362798177898,.00011199522959987467] 
dist 201=[-.00019788395426836802,7.51853571317376973560e-05] 
dist 202=[-.00024493605347489152,6.50545331105022252540e-05] 
dist 203=[-.00028477971367460833,2.62509807328821669790e-05] 
dist 204=[-.00030712969625930204,1.82352092988926670990e-05] 
dist 205=[-.00032182492916772299,5.06336984452734012480e-06] 
dist 206=[-.00032530444032639666,1.87521761712179987520e-06] 
dist 207=[-.00010589078561976970,-8.16806222501222865340e-05] 
dist 208=[-.00010505152321915284,-6.83618542410830550790e-05] 
dist 209=[-.00010131622288357132,-5.35960033235837810780e-05] 
dist 210=[-.00010040095555515567,-3.52364761620836404230e-05] 
dist 211=[-8.28682459411438390620e-05,-7.64792946837754429260e-06] 
dist 212=[-7.85868785223421642930e-05,1.99811307821916718070e-05] 
dist 213=[-7.45478610919143416940e-05,3.85017718437841724380e-05] 
dist 214=[-7.27012726402393582910e-05,5.35455969450218867870e-05] 
dist 215=[-1.30801492111904310170e-05,6.73696044457384275670e-05] 
dist 216=[-5.78787879869035549330e-06,7.90334756493741422320e-05] 
dist 217=[7.20017253596219145380e-06,8.55002047105889165910e-05] 
dist 218=[1.12167380952330246990e-05,8.93201383918080320220e-05] 
dist 219=[1.21607095702551538920e-05,9.02686876434789247670e-05] 
dist 220=[1.23693467731611742560e-05,5.78755689927769055930e-05] 
dist 221=[1.13295653834260872790e-05,6.15393674623390180080e-05] 
dist 222=[9.26007446501351681560e-06,6.29401751601382754330e-05] 
dist 223=[5.29751322877528747250e-06,6.31705021744908926430e-05] 
dist 224=[5.20845984984615467860e-07,6.27728702549450354510e-05] 
dist 225=[-4.78142751071389879100e-06,6.08288291890844897860e-05] 
dist 226=[-1.13787875345262306400e-05,5.96224567272500729080e-05] 
dist 227=[-2.12980785984145045480e-05,5.19431578137272351110e-05] 
dist 228=[-3.12351815445111284410e-05,4.99060494153031972830e-05] 
dist 229=[-3.79033756272535802360e-05,4.59460186558580112860e-05] 
dist 230=[-4.33278608475929344960e-05,4.46737332152808329600e-05] 
dist 231=[-4.83266568627925463730e-05,1.93459671040244875820e-05] 
dist 232=[-5.25547247623977157670e-05,1.57269978364682137420e-05] 
dist 233=[-5.49189266139383061730e-05,7.85479093731067001730e-06] 
dist 234=[-5.63271362143254681730e-05,5.76406139038306904330e-06] 
dist 235=[-5.67593020230995376880e-05,-2.27789120793249363450e-06] 
dist 236=[-5.66064256334994859270e-05,-3.85978373233015256730e-06] 
dist 237=[-5.60486139843528473370e-05,-5.36859650893060484830e-06] 
dist 238=[-5.40627224951947886190e-05,-4.83658654534768827610e-06] 
dist 239=[-1.61140710490746593170e-05,-3.80869068528576629870e-06] 
dist 240=[-1.34973015159486781860e-05,-2.56654102539445995020e-06] 
dist 241=[-1.28488826804238851100e-05,-1.18372220896211219260e-06] 
dist 242=[-1.19575604241716203460e-05,5.39508774890265208740e-07] 
dist 243=[-1.16071038488603797350e-05,3.13341451827900884180e-06] 
dist 244=[-6.86495425769618630030e-06,5.73335431597056243110e-06] 
dist 245=[-6.73684419339785570480e-06,7.48058141592518983670e-06] 
dist 246=[-5.86562301873525940770e-06,8.90480118699431759110e-06] 
dist 247=[-1.82432138480807477890e-06,1.02221997873404939240e-05] 
dist 248=[-6.93921950403550836610e-07,1.13400389542780759010e-05] 
dist 249=[-4.57025012182270932580e-07,1.19718844624758174310e-05] 
dist 250=[-1.08397643603557409380e-07,1.24010383585394131530e-05] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 1, 0, 0, 2] 
dist 0=[113.86732661381317508   ,113.86732661381317508   ] 
dist 1=[111.53462215393721999   ,115.03406603554092026   ] 
dist 2=[105.94237812516782060   ,115.98762062484436190   ] 
dist 3=[99.640612983908158125  ,116.55530437301991317   ] 
dist 4=[94.483927549327162453  ,116.17620390567324956   ] 
dist 5=[89.241103296662767045  ,115.39903296976165483   ] 
dist 6=[82.583352393205112714  ,114.56053544309708454   ] 
dist 7=[70.216520437607004509  ,113.03625118903852951   ] 
dist 8=[60.658797585031457080  ,110.88738914964627547   ] 
dist 9=[51.803237780596947375  ,89.652777192327200151  ] 
dist 10=[41.754235027389222878  ,86.388986101646153510  ] 
dist 11=[31.835897678239380172  ,77.238517371412810338  ] 
dist 12=[23.484611596353907221  ,75.918784470152308230  ] 
dist 13=[14.731876111803615016  ,58.250902921870787751  ] 
dist 14=[3.1900809290828995254 ,54.684511918438210175  ] 
dist 15=[-7.7578857980420405521 ,51.136140344579378321  ] 
dist 16=[-14.154203939516746751  ,50.453234108299216464  ] 
dist 17=[-18.461514447289267409  ,12.658835115868403773  ] 
dist 18=[-21.089719643485688753  ,10.952074200790785543  ] 
dist 19=[-22.862871449833971137  ,4.7121392515755127670 ] 
dist 20=[-23.758136754049447926  ,3.6490444806039647970 ] 
dist 21=[-24.217999674131950019  ,2.2073489328675103974 ] 
dist 22=[-26.057433490132413333  ,1.7791399712626297485 ] 
dist 23=[-28.014684821893764609  ,1.6278945693934970567 ] 
dist 24=[-28.753781469304678465  ,1.9884917544334118553 ] 
dist 25=[-28.966339865722088827  ,2.7534422007498344285 ] 
dist 26=[-28.824552931956190408  ,4.2425920328625786620 ] 
dist 27=[-22.422824396833026747  ,5.7373679599724696319 ] 
dist 28=[-22.253366657101463378  ,6.5275316683344703237 ] 
dist 29=[-18.949447652185023572  ,6.9694370579258504603 ] 
dist 30=[-18.105710874125952032  ,9.1590455856265273198 ] 
dist 31=[-17.250773389141257064  ,11.109185310976788601  ] 
dist 32=[-16.782588415802179697  ,12.071498213971712367  ] 
dist 33=[-4.6994733065536757326 ,12.551453580614105699  ] 
dist 34=[-3.1908065706277089460 ,12.591316381820157056  ] 
dist 35=[.3169805707988031765 ,11.878973183387923255  ] 
dist 36=[.85007554840048021056,11.571058389901489484  ] 
dist 37=[-.15390105036947565232,11.282042349652527372  ] 
dist 38=[-1.1710829993798149223 ,11.492837814729615900  ] 
dist 39=[-2.0895432972941472293 ,12.311765123148843394  ] 
dist 40=[-2.7026525001632819951 ,12.669291958451521626  ] 
dist 41=[-3.3418991591580907314 ,12.757130098780052088  ] 
dist 42=[-4.9353787710089071033 ,12.711307489390083972  ] 
dist 43=[-6.2924846760322345606 ,12.200827848147784962  ] 
dist 44=[-7.0748575131651811075 ,12.077539949775307641  ] 
dist 45=[-7.5353130314033451242 ,9.8302351271661863923 ] 
dist 46=[-7.6346499775971116574 ,9.2894609662607994962 ] 
dist 47=[-4.6147861537500500302 ,8.7563019985789905582 ] 
dist 48=[-4.9117483210879475613 ,8.5135676633300482768 ] 
dist 49=[-5.1955093759559380467 ,3.5460921127431051536 ] 
dist 50=[-5.5299814395821918884 ,3.1312199827527128521 ] 
dist 51=[-5.8659288370200770400 ,2.2113248111981368832 ] 
dist 52=[-6.1556234572067386607 ,1.9528253791591883381 ] 
dist 53=[-6.8099763649942797550 ,1.6885596972409500979 ] 
dist 54=[-7.4547955077311129055 ,2.2752363817984481481 ] 
dist 55=[-7.8131292698284606062 ,2.7719758994473507737 ] 
dist 56=[-7.8871099492059121971 ,3.0477471045338061751 ] 
dist 57=[.08552033521537081652,3.2085046493180094506 ] 
dist 58=[.18240272095614376437,3.2489709649590102427 ] 
dist 59=[.83504447162768930108,1.0009615651176243582 ] 
dist 60=[.93678805098276095583,1.2400067725509690490 ] 
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dist 197=[-8.20505213888884305550e-05,.00032175755820678830] 
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dist 211=[-8.08841013467449673290e-05,2.88043742509213620330e-05] 
dist 212=[-7.70670097147064463250e-05,4.96404689845127243950e-05] 
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dist 220=[2.17383693154768721500e-05,6.77241431328068215960e-05] 
dist 221=[1.95544939623632241740e-05,7.14072429697510287210e-05] 
dist 222=[1.53216218838614705570e-05,7.27324085614019219570e-05] 
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dist 224=[4.49829612362871567110e-06,7.22942567955484377650e-05] 
dist 225=[-2.61285294404729895990e-06,6.94567559578001811600e-05] 
dist 226=[-1.33198490306892578180e-05,6.84454595483739919440e-05] 
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dist 228=[-3.12639147508216092280e-05,5.44512716901644534650e-05] 
dist 229=[-3.71415059346662639490e-05,5.07756739136730814080e-05] 
dist 230=[-4.25763380695311782220e-05,4.92725259971205731670e-05] 
dist 231=[-4.71862995963908698090e-05,1.56473158779637472390e-05] 
dist 232=[-4.97886721862295456080e-05,1.35184482891790684120e-05] 
dist 233=[-5.13712175187015645930e-05,8.96388736741442959480e-06] 
dist 234=[-5.19318856928647583480e-05,7.71868499219911928240e-06] 
dist 235=[-5.19745779197298151160e-05,2.99884716259692064360e-06] 
dist 236=[-5.15003775527862182090e-05,2.01458766407847945400e-06] 
dist 237=[-5.05674246733490338150e-05,5.08656729997673038970e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 1, 1, 2] 
dist 0=[144.38192138417360342   ,144.38192138417360342   ] 
dist 1=[139.38156505557422490   ,145.67054654910790328   ] 
dist 2=[132.50761535829854495   ,145.77124691575116904   ] 
dist 3=[123.88806339610473420   ,145.80551270985286817   ] 
dist 4=[112.50955294395659593   ,144.57496725365171572   ] 
dist 5=[94.665800394521228732  ,133.36403725215571787   ] 
dist 6=[76.424947479984904753  ,130.85497130308819355   ] 
dist 7=[63.461527785485909552  ,122.10786138286639611   ] 
dist 8=[52.083192140465450587  ,120.85169807251589323   ] 
dist 9=[40.126949152743708071  ,98.514765380436228764  ] 
dist 10=[28.894867301161629078  ,93.666385222675313995  ] 
dist 11=[20.380691260704789049  ,89.497531201635017323  ] 
dist 12=[12.292523088717698276  ,88.665775245490807220  ] 
dist 13=[2.7278794713902892346 ,32.587650109760490527  ] 
dist 14=[-6.1116590713635645371 ,29.248914764211208114  ] 
dist 15=[-11.321506869150636794  ,26.942276219502641406  ] 
dist 16=[-14.891901284608329210  ,3.1954025751109395555 ] 
dist 17=[-17.465341666767322885  ,-14.305481322900761108  ] 
dist 18=[-23.452633177377152656  ,-15.591360281613480054  ] 
dist 19=[-27.915745326516911378  ,-14.308022407900336543  ] 
dist 20=[-31.420802354182248920  ,-11.746414686580360150  ] 
dist 21=[-34.024471527971784854  ,-6.9352656255859286967 ] 
dist 22=[-34.906305219402562803  ,-1.8860877502811615101 ] 
dist 23=[-35.057714618537841129  ,1.6256958121184494594 ] 
dist 24=[-34.743106267713889832  ,4.5636166224197581121 ] 
dist 25=[-31.195854390438473087  ,7.3471019158053741272 ] 
dist 26=[-30.117720965463130208  ,9.7100716867346187843 ] 
dist 27=[-28.548749295275487088  ,10.984891036250557430  ] 
dist 28=[-27.893803137079654948  ,11.666226533251877961  ] 
dist 29=[-11.022728010737992276  ,11.790638363275617137  ] 
dist 30=[-8.7755386383003771195 ,11.429159728422978114  ] 
dist 31=[-3.6270498278650924205 ,12.490448714630168189  ] 
dist 32=[-2.5753808790811596007 ,17.113819442712390875  ] 
dist 33=[3.4153878570805955304 ,21.021727796106721051  ] 
dist 34=[3.5337176323912957028 ,23.187882511970830406  ] 
dist 35=[3.3193448844124807910 ,24.449487143499798949  ] 
dist 36=[2.8973877151362595236 ,24.767342287995047985  ] 
dist 37=[2.1028364563339745040 ,7.8029210923086951910 ] 
dist 38=[1.2606738322346962355 ,7.9357007549563460567 ] 
dist 39=[.64925524747049780904,7.9365254515709402536 ] 
dist 40=[.10749470622129333926,7.9215538167932833765 ] 
dist 41=[-.45968652838685444089,6.8240702052935175691 ] 
dist 42=[-.982093244260558442  ,6.5287803970809847801 ] 
dist 43=[-1.3470073743832561934 ,6.3221290642467245590 ] 
dist 44=[-1.9698784295094937481 ,6.2298172638267297688 ] 
dist 45=[-2.5462179302019736643 ,1.4383280286424254033 ] 
dist 46=[-3.0075544184555550833 ,.86447182493385400037] 
dist 47=[-3.4202260795612751119 ,-.49359257742152497452] 
dist 48=[-3.7469002917790170590 ,-.69149939313614816606] 
dist 49=[-3.8672273835879413751 ,-1.5774041215167874909 ] 
dist 50=[-3.9005946307543589302 ,-1.4693880043131657265 ] 
dist 51=[-4.0184695642743345570 ,-1.2915974138075239033 ] 
dist 52=[-4.2253384046630195099 ,-1.0341540627998370052 ] 
dist 53=[-4.3378610622352173220 ,-.61007399646761395884] 
dist 54=[-4.3500635329375328018 ,-.17553937391882984301] 
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dist 56=[-4.2072921231354935482 ,.43460718371963654067] 
dist 57=[-3.5097439394182610277 ,.72855954721442443176] 
dist 58=[-3.3347203519952796997 ,1.2459138970348443750 ] 
dist 59=[-3.1741238558438655443 ,1.7570370174051791550 ] 
dist 60=[-3.0968901681288306606 ,2.1870995325620453113 ] 
dist 61=[-.87765611889037906488,2.4204798986779164061 ] 
dist 62=[-.64382879708921245135,2.5493992890898693333 ] 
dist 63=[-.10887847482909531111,2.5778733615193339477 ] 
dist 64=[-.00453115819817777505,1.7596161138255863973 ] 
dist 65=[.5886548469152421604 ,2.1509411325033316325 ] 
dist 66=[.54772522238967312461,2.3866655691566175001 ] 
dist 67=[.4876341797578520884 ,2.5199426379166861764 ] 
dist 68=[.40358560077929924602,2.5512936484812918494 ] 
dist 69=[.26755875665364344496,1.0214728000059407052 ] 
dist 70=[.12837913940285555227,1.0266724117736925154 ] 
dist 71=[.03179183131342505185,1.0044902852639169100 ] 
dist 72=[-.0499359040897751931 ,.99922406555463585052] 
dist 73=[-.13020034678388650892,.83557550784718830796] 
dist 74=[-.20129196300364506086,.79441507065788288583] 
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dist 80=[-.55984700824376894265,-.13787612465231803565] 
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dist 82=[-.55514435821763085676,-.2548231784949509036 ] 
dist 83=[-.55162220027663419646,-.21017838862422417604] 
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dist 85=[-.56643335601651276699,-.06310107152814808500] 
dist 86=[-.56524552894850986096,.02686032547660942330] 
dist 87=[-.54448441355534135375,.08751682208186035434] 
dist 88=[-.5397785539905281499 ,.13704311003258600132] 
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dist 90=[-.41818081101911670751,.22156548608038379056] 
dist 91=[-.39665859553417440839,.24303953247255141046] 
dist 92=[-.38756138038841311105,.27989064533872820911] 
dist 93=[-.12696486566892867894,.3096772389910134325 ] 
dist 94=[-.09466982787673823298,.3277273673183956642 ] 
dist 95=[-.02208560378772521977,.33185528092269547134] 
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dist 97=[.07354051140647119257,.34129165793431042796] 
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dist 100=[.04529849374169899610,.39497532425225605105] 
dist 101=[.02675884849012026989,.1445465226645314679 ] 
dist 102=[.00799071267614152489,.14411890346120169424] 
dist 103=[-.00481759224609016141,.14164099441824664526] 
dist 104=[-.03389387110579436785,.1395729374024849607 ] 
dist 105=[-.06294877630227387673,.1253976333531709542 ] 
dist 106=[-.08672273290296493431,.12149209427171729628] 
dist 107=[-.10883103697449204339,.1119474122402616995 ] 
dist 108=[-.12764575193842556072,.10836429963941975726] 
dist 109=[-.13834592766925329923,.06025831284922015266] 
dist 110=[-.14494613124094115998,.05264488500584342916] 
dist 111=[-.14748589023888199674,.03642773430722499593] 
dist 112=[-.14776416101516352785,.03197225026524786218] 
dist 113=[-.14664307257619051917,.01502373870045001650] 
dist 114=[-.14207524516659882774,.01143204159063900464] 
dist 115=[-.13930738810196585128,.00582883244418778410] 
dist 116=[-.12075489750237479712,.00435610325022175388] 
dist 117=[-.06675698106882936621,.00229517524394237096] 
dist 118=[-.06652208781222978448,.00228698774288176785] 
dist 119=[-.06394578042021167808,.00889755156142677146] 
dist 120=[-.06333271488791131125,.01429880738294314652] 
dist 121=[-.05193304625648148787,.01930639150459786904] 
dist 122=[-.04917244012086985419,.02362742630711277104] 
dist 123=[-.04653281406974737964,.02618445696988636588] 
dist 124=[-.04534265974190057661,.02762453792658231333] 
dist 125=[-.01138864651386191854,.02796362110371150616] 
dist 126=[-.00787339509466750336,.01379854019958817132] 
dist 127=[-.00434999933492369979,.02124196372824260199] 
dist 128=[.00167100672452706396,.02809728262735564268] 
dist 129=[.00984801377682410656,.03389077905284669146] 
dist 130=[.00880987635527033958,.03711838717746956776] 
dist 131=[.00757985463706597776,.03912278701341610760] 
dist 132=[.00600009476871353315,.03958969982400815086] 
dist 133=[.00357335814486826607,.01537457673064570401] 
dist 134=[.00112631812744208661,.01535124502677959730] 
dist 135=[-.00053418275300104404,.01476598772844582699] 
dist 136=[-.00190350333096076414,.01468152787159875476] 
dist 137=[-.00319481001993711756,.01188806727882216059] 
dist 138=[-.00430637394476613181,.01122093362947570547] 
dist 139=[-.00496227238018535250,.01074959766094854002] 
dist 140=[-.00539769850745099624,.01064387939222229892] 
dist 141=[-.00563419269363581580,.00103004237259147196] 
dist 142=[-.00575060032794697735,-9.08437767187466304160e-05] 
dist 143=[-.00574986622420737489,-.00269161191594618097] 
dist 144=[-.00561818394540030487,-.00307622275677009546] 
dist 145=[-.00622683998537410514,-.00476969263070253088] 
dist 146=[-.00705026880727901312,-.00408165478089219453] 
dist 147=[-.00755975642705048296,-.00330141591723674301] 
dist 148=[-.00776007175053023368,-.00232039786102021410] 
dist 149=[-.00779903541691112620,-.00083519318565939132] 
dist 150=[-.00775984240576976258,.00065487789231166004] 
dist 151=[-.00749676875515045293,.00165524825547673702] 
dist 152=[-.00737706066394324292,.00246887464330871301] 
dist 153=[-.00627711602226470205,.00321759243463618894] 
dist 154=[-.00599693396889743054,.00384951513473847754] 
dist 155=[-.00557340130808636211,.00419946917348550086] 
dist 156=[-.00542041064782661364,.00440343840665997885] 
dist 157=[-.00178473734477530439,.00445469972674630853] 
dist 158=[-.00130297433976794795,.00230679564797692684] 
dist 159=[-.00022673791778324411,.00338485540870593308] 
dist 160=[8.04931613347810373990e-06,.00437485972388587123] 
dist 161=[.00114673223436627356,.00520971511975149904] 
dist 162=[.00100452805181304155,.00567173517046748911] 
dist 163=[.00084131626989478361,.00594059260265892400] 
dist 164=[.00063483785232536907,.00600837454793647103] 
dist 165=[.00032083925680391127,.00183721207084363105] 
dist 166=[5.18239067536178190500e-06,.00183118125226869268] 
dist 167=[-.00020789049331127118,.00175423714294154611] 
dist 168=[-.00038247933979443542,.00174312377311920057] 
dist 169=[-.00054536065073672973,.00140286637104413516] 
dist 170=[-.00068443515890963806,.00132853228453399892] 
dist 171=[-.00076451465043624279,.00126416944289165376] 
dist 172=[-.00081522559528358116,.00125125611395404649] 
dist 173=[-.00083771224421870093,.00023906699642308887] 
dist 174=[-.00084360036069812892,.00011746873011532026] 
dist 175=[-.00084061629096909599,-.00016212099158716974] 
dist 176=[-.00080950605474269988,-.00020945391782002642] 
dist 177=[-.00092580789287989050,-.00042550528672167859] 
dist 178=[-.00102612016708172474,-.00035410868120471862] 
dist 179=[-.00108682845242018826,-.00027343960485332664] 
dist 180=[-.00110768099056133315,-.00017217659693744731] 
dist 181=[-.00110690665096632284,-1.90093770128267020000e-05] 
dist 182=[-.00110027269946759456,.00013468421271800843] 
dist 183=[-.00105366839976127215,.00023804044240161895] 
dist 184=[-.00104134612050020816,.00032232083899948183] 
dist 185=[-.00085519792262764349,.00040028081157321531] 
dist 186=[-.00081025231989494866,.00046639162827436497] 
dist 187=[-.00076188564468912470,.00050372215637886165] 
dist 188=[-.00073757763763831396,.00052939737301933498] 
dist 189=[-.00026719383850089024,.00053515848701346843] 
dist 190=[-.00023032755147705687,.00041074691725478648] 
dist 191=[-.00015168733686199700,.00043129685543137447] 
dist 192=[-.00013026512302310320,.00053166630073504425] 
dist 193=[-4.95224826560610079680e-05,.00061648774443028512] 
dist 194=[-3.26061792113613442870e-05,.00066379034847793496] 
dist 195=[-7.72422926287052324550e-06,.00069256682213011348] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 2, 1, 2] 
dist 0=[135.57153401110966946   ,135.57153401110966946   ] 
dist 1=[130.07066314224870437   ,139.43749207572314015   ] 
dist 2=[122.77453395891395927   ,140.27792922551674337   ] 
dist 3=[112.91755009429429367   ,139.95819994590531941   ] 
dist 4=[97.233071916957056614  ,139.50019576280001512   ] 
dist 5=[81.117162466373929946  ,129.66968125174074971   ] 
dist 6=[69.538310238686002570  ,127.16197509505989804   ] 
dist 7=[59.245263991833742327  ,114.70075796582359330   ] 
dist 8=[48.224144993020232758  ,111.30748062601192039   ] 
dist 9=[37.739593417412676119  ,89.504827897980775417  ] 
dist 10=[29.564905881179129409  ,84.841822795026352873  ] 
dist 11=[21.575469927689239254  ,80.699449417383601153  ] 
dist 12=[11.801148945405135698  ,79.875451226969561096  ] 
dist 13=[2.6352668649633054889 ,40.478864302789768839  ] 
dist 14=[-2.9394636062050546724 ,38.120243646821099098  ] 
dist 15=[-6.9688190911938193303 ,32.277312741092257613  ] 
dist 16=[-10.127689038970067750  ,26.473606591531406657  ] 
dist 17=[-18.829542579350329790  ,-8.8388134317796996671 ] 
dist 18=[-24.177370002149934101  ,-8.9475859563234157810 ] 
dist 19=[-28.040314491193379293  ,-7.4538763002157364683 ] 
dist 20=[-30.848668580556409649  ,-4.2119133194206998259 ] 
dist 21=[-32.814616473268103865  ,-.73071737005216338823] 
dist 22=[-33.330292707115601771  ,1.7179442581502858594 ] 
dist 23=[-33.268455344776293068  ,3.7749309050528179168 ] 
dist 24=[-32.925907690056661004  ,5.7143272122826779399 ] 
dist 25=[-29.182925424466724444  ,7.3359492981751027947 ] 
dist 26=[-28.107464742755930691  ,8.1379002709587810926 ] 
dist 27=[-26.546975064213657828  ,8.5278398074578930900 ] 
dist 28=[-25.912639780983829171  ,8.5359602990696416919 ] 
dist 29=[-10.009081793412946986  ,7.6986216376048767190 ] 
dist 30=[-7.8959890846818973578 ,7.4140244135911523075 ] 
dist 31=[-3.0775642822946991816 ,12.122454174996219468  ] 
dist 32=[-2.0850076286215373305 ,16.461448335601008438  ] 
dist 33=[.87429296564124542108,20.124308325066039862  ] 
dist 34=[.68153594339197244828,22.149272073238962816  ] 
dist 35=[.3081540988914348647 ,23.322403898722136050  ] 
dist 36=[-.3902879681936606887 ,23.604039601631102146  ] 
dist 37=[-1.1272322902742801445 ,7.7649014422505227984 ] 
dist 38=[-1.6537243057103960867 ,7.6650762041178247509 ] 
dist 39=[-2.1106160050766365599 ,7.6047273586450197601 ] 
dist 40=[-2.5725740680585662137 ,7.5892172638742209334 ] 
dist 41=[-2.9862527072861744625 ,6.2350162121839023190 ] 
dist 42=[-3.2521981263438267082 ,5.9418880046856031525 ] 
dist 43=[-3.4536803703518664499 ,5.7692640720664003567 ] 
dist 44=[-3.6121967232079896659 ,5.7259229622998333496 ] 
dist 45=[-3.7349341707687847560 ,2.4643333968476591353 ] 
dist 46=[-3.7947557085616544310 ,2.3529442358199016803 ] 
dist 47=[-3.8189277044087944889 ,2.1173739155276440201 ] 
dist 48=[-3.8048503578892964283 ,2.0432132616909679491 ] 
dist 49=[-4.1925880595916951442 ,1.7144348758644533318 ] 
dist 50=[-4.3517564170416062032 ,1.6401023827274447980 ] 
dist 51=[-4.4042949446365707311 ,1.4423002030757990924 ] 
dist 52=[-4.3765929207944527047 ,1.3916655017835581673 ] 
dist 53=[-4.0111528715494190735 ,1.0242960870962006557 ] 
dist 54=[-3.8873278177264598927 ,.9418506708873193514 ] 
dist 55=[-3.6983810569277446765 ,.8355865631784843815 ] 
dist 56=[-3.6187274795021391175 ,.79530045216519023922] 
dist 57=[-3.0992811888105029168 ,.75560718346066459466] 
dist 58=[-2.9738752445030443811 ,1.0444175293228604938 ] 
dist 59=[-2.7850797258571493950 ,1.7026319406439365182 ] 
dist 60=[-2.7139360876612936807 ,2.3131058377958505658 ] 
dist 61=[-.96687573910606236452,2.8299734296764431060 ] 
dist 62=[-.73378539052742778896,3.1168361405933468642 ] 
dist 63=[-.20750096209500570787,3.2840577086545520684 ] 
dist 64=[-.09559237349869948903,3.3261925897080410427 ] 
dist 65=[.49311531945982036006,2.4053413655820609679 ] 
dist 66=[.59399846053927230575,2.6298436000640155632 ] 
dist 67=[.60454936665620545569,2.7605209091402920497 ] 
dist 68=[.38283874886541133861,2.7934380219490061109 ] 
dist 69=[.15751020418272929789,.94387540703010809534] 
dist 70=[.00276524935254743529,.90708719319054789491] 
dist 71=[-.1266220406804072038 ,.8827418014499513137 ] 
dist 72=[-.25136301241794846474,.87073826076311659992] 
dist 73=[-.36044846799492350588,.69554578593220895806] 
dist 74=[-.42773342976877885001,.66100225245457292328] 
dist 75=[-.47599158055031928464,.63371131355676241486] 
dist 76=[-.50960338136725514646,.62303285808633459408] 
dist 77=[-.53183770889518960987,.11041997116529631416] 
dist 78=[-.53554203540047955063,.04913530811488932057] 
dist 79=[-.5624702841896015737 ,-.09454292820535640497] 
dist 80=[-.59756515075199835786,-.11584485216741580737] 
dist 81=[-.61932850070474379991,-.28801404463836111035] 
dist 82=[-.62292092174373423288,-.31384666512352938781] 
dist 83=[-.61115999878822018557,-.22854468039788958605] 
dist 84=[-.60705311170896579535,-.09179196700515134574] 
dist 85=[-.51076444261969381298,.04578632454580107862] 
dist 86=[-.48606725736915400637,.13839619571151953583] 
dist 87=[-.46387692424163298275,.21390669066872119711] 
dist 88=[-.45342456622824548495,.28362024499090621022] 
dist 89=[-.37343055108461486441,.34254955770037096403] 
dist 90=[-.35389518397028269318,.37549953724892125671] 
dist 91=[-.33539912747700661167,.39468062791807633721] 
dist 92=[-.32693155218574362359,.39935068491818127012] 
dist 93=[-.08498999905164210610,.31125382631879111944] 
dist 94=[-.05981121055756335716,.34542297494493089921] 
dist 95=[-.00268296746286116164,.36467318417015759615] 
dist 96=[.00867329642933711390,.36911625660147788726] 
dist 97=[.07293123400267522248,.23965803408368275028] 
dist 98=[.07844758307765023176,.263193596055480827  ] 
dist 99=[.05178848971899952359,.27774397026200540545] 
dist 100=[.01122471853866685977,.28109497974616045221] 
dist 101=[-.02951220186455972929,.1410277670950326677 ] 
dist 102=[-.05686000103274847409,.13585259223026442811] 
dist 103=[-.07908677802145913650,.12715694769076457612] 
dist 104=[-.09949674255917668935,.1241483432299894036 ] 
dist 105=[-.11667913489523209187,.08590059358772344396] 
dist 106=[-.12609418666463505165,.08119630246404222724] 
dist 107=[-.13143739510526650859,.07793841288748114376] 
dist 108=[-.13245622601537702388,.07719225027287775024] 
dist 109=[-.13154085808780072627,.00841051904390960487] 
dist 110=[-.12989412766344949029,.00038269355086037830] 
dist 111=[-.12596617728566795436,-.01028665153814471320] 
dist 112=[-.1188063187220329639 ,-.00769033989667209854] 
dist 113=[-.0768732842312958339 ,-.00431047092624168905] 
dist 114=[-.07697733664581111837,-.00025002452767456744] 
dist 115=[-.07547176296382838717,.00499848797046892934] 
dist 116=[-.07440334746410979906,.01309557040048901646] 
dist 117=[-.06460636261218348974,.02127267211775996263] 
dist 118=[-.06196830093978898266,.02683944405398553538] 
dist 119=[-.05794667100510577140,.03144915810421307877] 
dist 120=[-.05645496774108011871,.03582781983531890296] 
dist 121=[-.04510635411010167456,.03961869873089176279] 
dist 122=[-.04312120399747850438,.04314238110928622767] 
dist 123=[-.04012294934773578004,.04580062423974649724] 
dist 124=[-.03903308387589035500,.04645438905478604288] 
dist 125=[-.01302098555411804914,.05153179850446627754] 
dist 126=[-.00957288522800661815,.05626164709893281110] 
dist 127=[-.00185763955159501391,.05901479840479342731] 
dist 128=[-.00018008481438990819,.05970831249348048570] 
dist 129=[.00821275473233656896,.03707352458352313291] 
dist 130=[.00967564652128257758,.04038462838196194702] 
dist 131=[.01208816348656820775,.04231198983077727784] 
dist 132=[.01257329109744446791,.04279760798306115229] 
dist 133=[.01274454811141998606,.01467433241140455771] 
dist 134=[.01189504462371321375,.01393957132310335459] 
dist 135=[.00920502611962599997,.01335543699761899997] 
dist 136=[.00510173155909209924,.01312607050357359434] 
dist 137=[.00097305513298727934,.01009617413862479564] 
dist 138=[-.00181791070427808664,.00957477014895491836] 
dist 139=[-.00410877359426992309,.00910493008763716401] 
dist 140=[-.00625224188353651097,.00900732484608669137] 
dist 141=[-.00808643383889287437,.00178794992814234580] 
dist 142=[-.00914959194723284306,.00091760044056438317] 
dist 143=[-.00983174422397240309,-.00108747978874542315] 
dist 144=[-.01015350653532847041,-.00142507890581757674] 
dist 145=[-.01026088223974588460,-.00374084613076484629] 
dist 146=[-.01023886693681289753,-.00409769411794849395] 
dist 147=[-.00987312245660871143,-.00475755299739108208] 
dist 148=[-.00978250622306825405,-.00486897497869773253] 
dist 149=[-.00805516421759801480,-.00495168157234410343] 
dist 150=[-.00786631246099314597,-.00480538269136404423] 
dist 151=[-.00754192159758554997,-.00353239712474153279] 
dist 152=[-.00745489355317515454,-.00143157891538245999] 
dist 153=[-.00613162706526182792,.00067600800110859558] 
dist 154=[-.00581115337658035669,.00209194388180448749] 
dist 155=[-.00546686559701826930,.00324490326676972253] 
dist 156=[-.00529314708442765303,.00430845896847100542] 
dist 157=[-.00194057090024469946,.00520817000247302938] 
dist 158=[-.00167656495950789104,.00571810771482411076] 
dist 159=[-.00111165070095187169,.00603251780352518359] 
dist 160=[-.00095723885892840163,.00610492260457750622] 
dist 161=[-.00037200663614463384,.00439547821130367769] 
dist 162=[-.00025005888598851576,.00473586231373632083] 
dist 163=[-6.32304352872606066160e-05,.00494864266738744100] 
dist 164=[-1.43117319623639333840e-05,.00500197018060163998] 
dist 165=[.00170173007687384994,.00189224396434534542] 
dist 166=[.00154582947355857235,.00179125230675105782] 
dist 167=[.00119473217102981849,.00171394918529078150] 
dist 168=[.00066247925903430013,.00168919420930260677] 
dist 169=[.00012788329588636577,.00131478884391058863] 
dist 170=[-.00023253239785383532,.00124331083908484338] 
dist 171=[-.00052743798988074532,.00117999173816336062] 
dist 172=[-.00080195325417391445,.00115525659532405572] 
dist 173=[-.00103597931979201921,.00016537757162239538] 
dist 174=[-.00117013942385702861,4.61943192346558245020e-05] 
dist 175=[-.00125436259519364266,-.00022950660124287626] 
dist 176=[-.00129013634291718471,-.00027275889067321685] 
dist 177=[-.00129882489465600318,-.00059221196157582878] 
dist 178=[-.00129410086187519919,-.00064009771163600622] 
dist 179=[-.00124650882872798062,-.00072799505405729878] 
dist 180=[-.00123260607683531494,-.00074201860976392665] 
dist 181=[-.00102200675646967079,-.00074706249784421263] 
dist 182=[-.00097028957555056630,-.00066343609825021090] 
dist 183=[-.00091420313346552539,-.00047117036147953281] 
dist 184=[-.00090563833417518253,-.00016115269848966253] 
dist 185=[-.00072173327941488878,.00014943878747840196] 
dist 186=[-.00067873282396317252,.00035767996557475704] 
dist 187=[-.00064645214721811506,.00052684150308184810] 
dist 188=[-.00063909512325575718,.00068227017379529797] 
dist 189=[-.00010988249533335632,.00081337054133339349] 
dist 190=[-6.00726050535574538900e-05,.00088593738785649337] 
dist 191=[5.34448893601386324020e-05,.00092818275781686322] 
dist 192=[7.39286806522679168380e-05,.00093883056231312563] 
dist 193=[.00020148154523659851,.00047882222258281975] 
dist 194=[.00022178984806033967,.00048101489719384074] 
dist 195=[.00025680597532191140,.00048524163028432519] 
dist 196=[.00023609025369528305,.00049223795784744031] 
dist 197=[.00020513242678779254,.00026789403695984652] 
dist 198=[.00017040039208825492,.00026166067734896929] 
dist 199=[.00012695061986077930,.00025353142322733503] 
dist 200=[4.82801408694962118320e-05,.00024865877944158342] 
dist 201=[-3.55678768249873711300e-05,.00021797043297361619] 
dist 202=[-9.18616604459433926560e-05,.00020987757347853375] 
dist 203=[-.00013768232760404552,.00019269269692908495] 
dist 204=[-.00017994653968824827,.00018685255523734088] 
dist 205=[-.00021571791371201826,8.96279987458161954060e-05] 
dist 206=[-.00023575847584469273,7.51719455685305890700e-05] 
dist 207=[-.00024774426622771636,4.42186323164643738070e-05] 
dist 208=[-.00025153374808061060,3.58635495124460892470e-05] 
dist 209=[-.00025127967759631717,4.67841678968135223160e-06] 
dist 210=[-.00024906168710209765,-1.74414372071694795210e-06] 
dist 211=[-.00024158539135387653,-1.04992165161017152380e-05] 
dist 212=[-.00022555803864867528,-1.23772462519544403320e-05] 
dist 213=[-.00013642654956832477,-1.23773776857646797340e-05] 
dist 214=[-.00012921944195506434,-1.06207202275849552580e-05] 
dist 215=[-.00012172236752680467,-7.27977022297617299910e-06] 
dist 216=[-.00011802438372318297,4.16020737622164223190e-06] 
dist 217=[-4.25826992387867014440e-05,3.00435958472889235120e-05] 
dist 218=[-3.68247640534002373000e-05,4.99572233821181226460e-05] 
dist 219=[-2.47122782365379738070e-05,6.70567267023348647980e-05] 
dist 220=[-2.11118186776450706140e-05,8.28199526323294573840e-05] 
dist 221=[-8.27829321855494814710e-06,9.61553631201417418590e-05] 
dist 222=[-5.60814083252024066840e-06,.00010361509500940488] 
dist 223=[-1.45182219145037103010e-06,.00010832991524682814] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[119.35090765739097393   ,119.35090765739097393   ] 
dist 1=[117.92136773711833192   ,120.38356060871000513   ] 
dist 2=[115.63132643060344285   ,121.08698196519292747   ] 
dist 3=[112.26813243821946680   ,121.37864867034890873   ] 
dist 4=[104.50228674603905038   ,120.93746335758239674   ] 
dist 5=[95.987908009818925335  ,119.67734331861186560   ] 
dist 6=[85.617982739009065245  ,118.85540584137625807   ] 
dist 7=[71.743986344897432867  ,98.548615250759448057  ] 
dist 8=[61.505714392973672045  ,95.435290743883666975  ] 
dist 9=[52.120399894182428310  ,86.520728994907576771  ] 
dist 10=[41.620598776771895335  ,85.131092190423033596  ] 
dist 11=[31.345778523541112789  ,67.172102456173514367  ] 
dist 12=[22.839888206529409047  ,65.329325646964545836  ] 
dist 13=[14.054198523251409574  ,59.619718854828533961  ] 
dist 14=[2.6398550933782301205 ,58.616182337318604140  ] 
dist 15=[-8.1567603327936224400 ,18.516742566506079976  ] 
dist 16=[-14.490912265370613196  ,16.700374862726106661  ] 
dist 17=[-18.788385499769038231  ,9.1831732750884567396 ] 
dist 18=[-21.473266396675485859  ,7.8170816213807306205 ] 
dist 19=[-23.294517238565751051  ,5.3053266648976496882 ] 
dist 20=[-24.146175719132749174  ,4.7452752921218685658 ] 
dist 21=[-24.487039329724232395  ,3.2142085140735514190 ] 
dist 22=[-26.028408461162839769  ,3.0092916405723564244 ] 
dist 23=[-27.615523049487698464  ,3.1710848572062797109 ] 
dist 24=[-28.689071063695549584  ,3.8189299061500375330 ] 
dist 25=[-29.138964260411445282  ,4.6793588862990277396 ] 
dist 26=[-29.244710381347524272  ,5.6930335223726898849 ] 
dist 27=[-26.708057949120586172  ,6.9853339690205695110 ] 
dist 28=[-24.052278216275119039  ,8.9604567407197839436 ] 
dist 29=[-21.303649686736524489  ,10.836470395708870126  ] 
dist 30=[-20.979858704041127182  ,11.738080049397942529  ] 
dist 31=[-4.7530299376402034212 ,13.099796076158003551  ] 
dist 32=[-2.8151862472528268713 ,13.980758630217761546  ] 
dist 33=[1.7559173751513404101 ,14.384596359333315000  ] 
dist 34=[2.4171355125102428000 ,14.378004422711939098  ] 
dist 35=[7.9842352558952938865 ,13.314953127094251719  ] 
dist 36=[5.6576616506936442041 ,12.905324218480042029  ] 
dist 37=[2.8723899548290010894 ,13.090227923573591571  ] 
dist 38=[.92716692344380611155,13.640217822604547742  ] 
dist 39=[-.7294315036923746415 ,13.879830532807646503  ] 
dist 40=[-2.6817510295252803280 ,13.877039755978406740  ] 
dist 41=[-4.3637424675844155678 ,13.427721546957824716  ] 
dist 42=[-6.0807387062225998908 ,13.306649630230825753  ] 
dist 43=[-7.6860031732645636169 ,10.973724628052083147  ] 
dist 44=[-8.5375044322682837187 ,10.400476882672602274  ] 
dist 45=[-9.0025195300542802256 ,9.8435596851372461443 ] 
dist 46=[-9.0878244096279388939 ,9.5771556713908629494 ] 
dist 47=[-6.7483525130896540166 ,2.8855955568528179815 ] 
dist 48=[-6.6808043591745197204 ,2.1289969437911880413 ] 
dist 49=[-6.0298520881282883632 ,.39812253719106123995] 
dist 50=[-5.9244869475131962854 ,.06289981497042370559] 
dist 51=[-7.2751185367328169718 ,-1.9349629577812554077 ] 
dist 52=[-7.9934791708799587532 ,-1.3086302252734011970 ] 
dist 53=[-8.3953563547152214927 ,.51091867803728029803] 
dist 54=[-8.4896466161678381457 ,1.7386656264143359799 ] 
dist 55=[-3.2276087892946434502 ,2.7417925606242021108 ] 
dist 56=[-3.2485289790225017346 ,3.6701092502344612193 ] 
dist 57=[-3.1812186171620501709 ,4.4553869380301585209 ] 
dist 58=[-3.1710378386843026862 ,4.8909318498388415635 ] 
dist 59=[-2.6361300790822761514 ,5.1447308553334856952 ] 
dist 60=[-2.5026901176340355141 ,5.2086770325555230220 ] 
dist 61=[-2.4161036020539910538 ,1.5982550298826066823 ] 
dist 62=[-2.3944588891846426515 ,1.6275904069186086635 ] 
dist 63=[-.35268195861079294468,1.6294370711329923340 ] 
dist 64=[-.1134850268324633296 ,1.6265210028845930868 ] 
dist 65=[.44158861918395942034,1.4069465612305923328 ] 
dist 66=[.5261304176222562072 ,1.3475201213520841603 ] 
dist 67=[.91138381009859277019,1.3043137568072748471 ] 
dist 68=[.53430428427144424203,1.4241156977450538009 ] 
dist 69=[.1524239949851980304 ,1.5481633288819482229 ] 
dist 70=[-.10829539878649599549,1.6136687251784123988 ] 
dist 71=[-.32477891418894754268,1.6445617487819589347 ] 
dist 72=[-.53114164845969447386,1.6435148447167771350 ] 
dist 73=[-.71011501642492243199,1.6041038377635057403 ] 
dist 74=[-.81792257340786476898,1.5803674331127994432 ] 
dist 75=[-.89217780770048995742,1.3644921697443665708 ] 
dist 76=[-.93802311047786289755,1.3074345755827138602 ] 
dist 77=[-.9636209853128556555 ,1.2199662660315726728 ] 
dist 78=[-.96645016834910336998,1.1880920430370785540 ] 
dist 79=[-.94304286963354286533,.42311270969709731958] 
dist 80=[-.935386381819005711  ,.32179396772412797957] 
dist 81=[-.78376578253778820876,.09437690634683643418] 
dist 82=[-.91939365932629960134,.04451991609309594733] 
dist 83=[-1.0986266839358273104 ,-.20619232769402952842] 
dist 84=[-1.1981368439677186938 ,-.12889591654124083263] 
dist 85=[-1.2561286649560542918 ,.06943760523602142275] 
dist 86=[-1.2705460254993522741 ,.20315040564438388077] 
dist 87=[-.37503175147422893047,.31243120656233362494] 
dist 88=[-.37564184365022800414,.41379316928720642875] 
dist 89=[-.36421981887859109446,.4998370838068845951 ] 
dist 90=[-.3622851098599936548 ,.55280316655869459552] 
dist 91=[-.30523872411903143228,.58261040500456227103] 
dist 92=[-.29405108210103651721,.58955103665326160578] 
dist 93=[-.27374834853860750543,.22135024686826122651] 
dist 94=[-.26731950274136817844,.22288251322538615504] 
dist 95=[-.11431676697698034376,.21847396844519720602] 
dist 96=[-.09308518435152358344,.21783647405731244626] 
dist 97=[-.04519217180776063223,.18116304356440287195] 
dist 98=[-.03419379602091850302,.21382782372931339672] 
dist 99=[.02052794540279264225,.25550593333707131295] 
dist 100=[-.01282882903229374827,.27936157094024880574] 
dist 101=[-.07344766362406028251,.2942920274136917252 ] 
dist 102=[-.1145088234694855563 ,.3005385477459986635 ] 
dist 103=[-.14829679690231252531,.30170986636278475463] 
dist 104=[-.18004583862835641088,.29998432387400223293] 
dist 105=[-.20730316900196314927,.28969416236140862439] 
dist 106=[-.22326198501701420455,.28460096930157008038] 
dist 107=[-.23370312840580132257,.24283175638644798966] 
dist 108=[-.23905917921697124766,.23210690065107557177] 
dist 109=[-.24141833789739903501,.21452936284470505103] 
dist 110=[-.23996200048972646954,.20868891436771909633] 
dist 111=[-.23596825260563265563,.07135795045042896565] 
dist 112=[-.23312315905457215939,.05274452909179352185] 
dist 113=[-.21411268973830253088,.01174278887432400114] 
dist 114=[-.20894118243774612786,.00212690323846361685] 
dist 115=[-.1908210704893934787 ,-.02965069814754453692] 
dist 116=[-.18714959663194100297,-.01689590989604294094] 
dist 117=[-.13642902945995368878,.01307871582771718029] 
dist 118=[-.13804296142891637099,.03320047340802142113] 
dist 119=[-.04533201624022419480,.04956439769852581765] 
dist 120=[-.04527772032173058718,.06462073822081336468] 
dist 121=[-.04358299262120281827,.07732737637335163533] 
dist 122=[-.04333859934276342425,.08436300151982055349] 
dist 123=[-.03513068457159295742,.08845780726920526898] 
dist 124=[-.03316748568067211186,.08948922651208087600] 
dist 125=[-.03178576591538154674,.02706215753451355490] 
dist 126=[-.03147574013172905244,.02711107042164297973] 
dist 127=[-.00308317997334043543,.02633861905432932441] 
dist 128=[.00022723123767447855,.02617112785898011166] 
dist 129=[.00790384013380756454,.02167991040445849408] 
dist 130=[.00904297365351497837,.02056993435247378426] 
dist 131=[.01350266052646108033,.01967304352753196109] 
dist 132=[.00739238879718677216,.02068050176996277921] 
dist 133=[.00125011602703597802,.02219149148610556432] 
dist 134=[-.00289580348046087049,.02279578809399841666] 
dist 135=[-.00629275082043822633,.02292490130283700650] 
dist 136=[-.00946172012283019610,.02281410335102091473] 
dist 137=[-.01216746741820795798,.02205231659443491879] 
dist 138=[-.01372549325270264742,.02170016369049572751] 
dist 139=[-.01471224055668305884,.01848378472323849944] 
dist 140=[-.01515011401227913610,.01766272887329251675] 
dist 141=[-.01526992684907389555,.01641595743525302938] 
dist 142=[-.01522428663046121301,.01596717230217520550] 
dist 143=[-.01465291835097666506,.00526269082883103461] 
dist 144=[-.01451451521219499549,.00383641129380226795] 
dist 145=[-.01192268612748086692,.00064817072737210454] 
dist 146=[-.01287289200476346445,-4.47194306951716250840e-05] 
dist 147=[-.01533847957099135190,-.00350025127945930410] 
dist 148=[-.01670290628718444115,-.00207326799776229833] 
dist 149=[-.01749672943812618574,.00105370486278454496] 
dist 150=[-.01769665209633102628,.00315333753974370349] 
dist 151=[-.00532518785281460184,.00486202497482093914] 
dist 152=[-.00530807945793167365,.00643686094888184957] 
dist 153=[-.00509793813552292812,.00776837161444607940] 
dist 154=[-.00505713251312461226,.00851099518938881698] 
dist 155=[-.00412011014140379404,.00897859021545342998] 
dist 156=[-.00389534314428534261,.00908580456658919481] 
dist 157=[-.00370555852222358396,.00352832150884646627] 
dist 158=[-.00363712928632223336,.00352585029073762776] 
dist 159=[-.00048938351103160119,.00339791160264776183] 
dist 160=[-.00011336348406468772,.00337935331884195674] 
dist 161=[.00075917803977890973,.00274411244366197460] 
dist 162=[.00089257374916183536,.00259165161721078164] 
dist 163=[.00177358317059855129,.00248490999685818981] 
dist 164=[.00100801252824157205,.00271481052425347595] 
dist 165=[.00023944045326966449,.00288973648983940707] 
dist 166=[-.00027834239487585014,.00295116236447279860] 
dist 167=[-.00070165116917145100,.00295155612923613793] 
dist 168=[-.00109514087290548761,.00293541217121258707] 
dist 169=[-.00143025033976145827,.00280941304705041244] 
dist 170=[-.00162177729917433414,.00278073334876931217] 
dist 171=[-.00174128180416382836,.00226715708870564357] 
dist 172=[-.00179044903849201103,.00214413479241267571] 
dist 173=[-.00180235467508691479,.00202515713962644164] 
dist 174=[-.00179422525928395760,.00197269376947891148] 
dist 175=[-.00173555724081879866,.00047338121903193969] 
dist 176=[-.00170806925867890560,.00031910057686559792] 
dist 177=[-.00145603573522427012,-2.85084659024687260650e-05] 
dist 178=[-.00139153453078502505,-9.87173315209712632600e-05] 
dist 179=[-.00150742300146807140,-.00048117976895899004] 
dist 180=[-.00164781272950180752,-.00023367304030343447] 
dist 181=[-.00173146755164183233,.00022555076815209774] 
dist 182=[-.00175256672513387934,.00053336992723818179] 
dist 183=[-.00067652779309448125,.00078336593638673587] 
dist 184=[-.00067375690196067743,.00101300156188251311] 
dist 185=[-.00064428332633295876,.00120667052868593792] 
dist 186=[-.00064000212980282522,.00131385886532863775] 
dist 187=[-.00051381924558918456,.00137624723771676636] 
dist 188=[-.00048406961788648760,.00139196897452859499] 
dist 189=[-.00046233631888741713,.00042415469070266523] 
dist 190=[-.00045747055741055877,.00042301737122154421] 
dist 191=[-3.81239067562007183400e-05,.00040591565410637272] 
dist 192=[1.07282018714161561890e-05,.00040334964576921473] 
dist 193=[.00012424411823760106,.00032610440968872900] 
dist 194=[.00014075257410594899,.00030922253027214782] 
dist 195=[.00018634478416239566,.00029376562728347518] 
dist 196=[9.00548046380918569610e-05,.00031504483636317021] 
dist 197=[-6.48779085420854260050e-06,.00033623430105232103] 
dist 198=[-7.13796756802045644280e-05,.00034335547084801772] 
dist 199=[-.00012428168077487071,.00034343327004894725] 
dist 200=[-.00017321853955798660,.00034116997913965689] 
dist 201=[-.00021473792069378903,.00032848297813429692] 
dist 202=[-.00023818887497408811,.00032302443497052561] 
dist 203=[-.00025246514509700001,.00027378404534677509] 
dist 204=[-.00025755662579262398,.00026136723416996751] 
dist 205=[-.00025761553542987218,.00024238901877566090] 
dist 206=[-.00025614747506931365,.00023566238408178541] 
dist 207=[-.00024546983490576536,7.82518636969804653910e-05] 
dist 208=[-.00024261620927997917,5.75643887669925110240e-05] 
dist 209=[-.00019944725357359875,1.15708720926099098890e-05] 
dist 210=[-.00019516530422517322,1.28036855144982800230e-06] 
dist 211=[-.00023152653253643618,-4.78726605153722773570e-05] 
dist 212=[-.00025164880473935973,-3.01292093580280000000e-06] 
dist 213=[-.00026336540858957661,4.35905480366722831640e-05] 
dist 214=[-.00026632374673585403,7.48583121301201308720e-05] 
dist 215=[-7.97607462725564319520e-05,.00010028840146079357] 
dist 216=[-7.93622418176327591080e-05,.00012371267005512645] 
dist 217=[-7.57538697275417446100e-05,.00014351787199479628] 
dist 218=[-7.52104341096584997610e-05,.00015457796948060950] 
dist 219=[-6.04262876917543299560e-05,.00016143366003144335] 
dist 220=[-5.77817154909740972060e-05,.00016316859989285717] 
dist 221=[-5.41249606379954090740e-05,4.44173336978758436730e-05] 
dist 222=[-5.34879368438391916180e-05,4.41574593683011609440e-05] 
dist 223=[-2.25840255752432313240e-05,4.34099364873907294400e-05] 
dist 224=[-1.84199275296417607440e-05,4.28527637914059348760e-05] 
dist 225=[-9.32062439713509491460e-06,3.91274877232845475270e-05] 
dist 226=[-6.94006034940357153150e-06,4.88855508654364609710e-05] 
dist 227=[2.52132628135207481830e-06,5.72964322189708495040e-05] 
dist 228=[-2.97265806270789014740e-06,6.19946332433735054740e-05] 
dist 229=[-1.68729203221425467010e-05,6.47873868902010509980e-05] 
dist 230=[-2.62070149337643038480e-05,6.56321274035500246310e-05] 
dist 231=[-3.38078947174925699630e-05,6.54201971853397123610e-05] 
dist 232=[-4.08261192301920815490e-05,6.48993181257381490860e-05] 
dist 233=[-4.67726401925117042070e-05,6.23800018370964970560e-05] 
dist 234=[-5.01181338806886881540e-05,6.12392046299198968530e-05] 
dist 235=[-5.21379534600151528860e-05,5.20403556448432519950e-05] 
dist 236=[-5.28206734536040156840e-05,4.97141343002111283580e-05] 
dist 237=[-5.28334756270596047190e-05,4.58649297191987116840e-05] 
dist 238=[-5.23257389229829548380e-05,4.46124077284266829780e-05] 
dist 239=[-5.11247397306975662250e-05,1.54536659508643660270e-05] 
dist 240=[-5.04115688350996405510e-05,1.14974461627806873850e-05] 
dist 241=[-4.59331150660233409390e-05,6.35488474301298553410e-06] 
dist 242=[-4.47539540236681234570e-05,5.43217287738825926920e-06] 
dist 243=[-4.07925812137800361650e-05,1.98618032392632588080e-06] 
dist 244=[-3.99504453809257426850e-05,1.25797267022282241640e-06] 
dist 245=[-3.02144787375871306080e-05,2.59194311292383349200e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 0, 0, 2] 
dist 0=[116.75520187887645667   ,116.75520187887645667   ] 
dist 1=[110.86282926951667990   ,120.67046493205387748   ] 
dist 2=[100.89258508075297693   ,122.77453395891396266   ] 
dist 3=[90.431486885547637598  ,123.85773654592989404   ] 
dist 4=[82.580192910416039791  ,123.72188993634423101   ] 
dist 5=[75.255874033960352824  ,122.87318741180295530   ] 
dist 6=[66.873668949050319481  ,122.14156449843366819   ] 
dist 7=[58.559963630847635694  ,117.52749208020577285   ] 
dist 8=[51.493826906722529448  ,110.64682940133432231   ] 
dist 9=[44.027706418573598834  ,88.223398407498463329  ] 
dist 10=[34.098487789147489006  ,86.854746662447321314  ] 
dist 11=[24.463372023605305658  ,67.258781300883367472  ] 
dist 12=[18.163065122417139860  ,63.224041157730167854  ] 
dist 13=[13.092383138840893257  ,59.348605951525387018  ] 
dist 14=[8.3611517612212341441 ,58.592318449599023149  ] 
dist 15=[4.1883453534812812109 ,32.854115154853788230  ] 
dist 16=[1.3431532391487621667 ,25.324266916808930264  ] 
dist 17=[-5.1282836594205485368 ,4.2124897400497922434 ] 
dist 18=[-12.789521872366056765  ,3.8840798680346162088 ] 
dist 19=[-19.308570915167474662  ,3.2543756700110288545 ] 
dist 20=[-23.119865916597839230  ,3.1137434769162516964 ] 
dist 21=[-25.643543342109175869  ,2.9985944506053404933 ] 
dist 22=[-27.048643685631785761  ,2.9366906934809808619 ] 
dist 23=[-27.787606671404250435  ,2.7097463289630726051 ] 
dist 24=[-27.837297637882134651  ,2.6042639510814233988 ] 
dist 25=[-27.263651116038907322  ,2.2614945521116532228 ] 
dist 26=[-26.897354075884281742  ,2.0873839133761966509 ] 
dist 27=[-23.258971813700230339  ,-.20396648956513018332] 
dist 28=[-22.303027645645478104  ,-.67173857831997413063] 
dist 29=[-20.880872554829228036  ,1.3313287989173257774 ] 
dist 30=[-20.347391693876928311  ,3.3402213303081647087 ] 
dist 31=[-7.5626696855905848184 ,5.2000399512810858711 ] 
dist 32=[-5.8966338770614230671 ,7.2956579488174412438 ] 
dist 33=[-4.2576997857343768337 ,10.610252326798615107  ] 
dist 34=[-4.1076069148733793598 ,14.058759948633728021  ] 
dist 35=[-1.6608542922354863733 ,16.966364441000127828  ] 
dist 36=[-1.3101239887700650704 ,18.573708302840640411  ] 
dist 37=[-.58826615325925290632,19.506479615262428387  ] 
dist 38=[-.40324272383613367947,19.735697402740173451  ] 
dist 39=[.23917332290308668403,9.7601358369263750255 ] 
dist 40=[.37630438359474842318,9.7332287335852307250 ] 
dist 41=[.49218398853800532727,5.7845893945674347663 ] 
dist 42=[.46414261038948349767,5.7636023712946750923 ] 
dist 43=[-.24659131330385406198,5.3309932249642228524 ] 
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dist 192=[-5.10657072031265360490e-05,.00119790189913284469] 
dist 193=[6.56381767189247623190e-05,.00050516461974251258] 
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dist 201=[-1.60349088520035013940e-05,.00022214183595563810] 
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dist 209=[-.00026189715176841383,7.16502921329373533850e-05] 
dist 210=[-.00025996559235200887,6.56742176401332008570e-05] 
dist 211=[-.00025101919075706503,4.40188653963293324200e-05] 
dist 212=[-.00024589525318781001,3.88232794502813996740e-05] 
dist 213=[-.00021258043405823797,3.32652875578250310400e-05] 
dist 214=[-.00018748957675236935,3.20220036832556457830e-05] 
dist 215=[-.00015432678319993664,3.21198733826829335580e-05] 
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dist 217=[-5.42090558301534801470e-05,3.71639165599356361400e-05] 
dist 218=[-4.68466977760113644190e-05,6.40198185282364649690e-05] 
dist 219=[-3.10892054271281260440e-05,8.58679087338423721760e-05] 
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dist 222=[-7.02548037883085642050e-06,.00013254997951996739] 
dist 223=[-1.78705559633730885320e-06,.00013851767200392680] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 2, 2, 0, 1, 2] 
dist 0=[128.80352864091710273   ,128.80352864091710273   ] 
dist 1=[127.62534916228357345   ,129.14110940537358388   ] 
dist 2=[123.28855988441023114   ,129.40921971329565706   ] 
dist 3=[117.34908484709294755   ,129.17669640585165280   ] 
dist 4=[109.85618294149188421   ,121.66257152106156064   ] 
dist 5=[99.930895997603367931  ,119.49118286393931572   ] 
dist 6=[84.317601019857314638  ,117.52226954579267281   ] 
dist 7=[68.309432883622386329  ,116.19349544713977475   ] 
dist 8=[56.808278552874141640  ,90.730660588073586095  ] 
dist 9=[46.572978316127763122  ,87.088805927923122436  ] 
dist 10=[35.583193973965811937  ,82.916131699396206886  ] 
dist 11=[25.100980069526707468  ,81.138675030002004580  ] 
dist 12=[16.870535866619528645  ,48.964109892522675426  ] 
dist 13=[8.7706420859424369710 ,46.757797582706457796  ] 
dist 14=[-1.2165303588368014147 ,41.790758655804341886  ] 
dist 15=[-10.508199301465761052  ,41.074534009721027052  ] 
dist 16=[-15.846946353839643689  ,3.9755078576985857651 ] 
dist 17=[-20.802291854213015108  ,1.0248451720092318244 ] 
dist 18=[-25.558506261614601734  ,-3.4070597586285900097 ] 
dist 19=[-29.988030288623831469  ,-4.2082402508704365517 ] 
dist 20=[-33.561311613320346359  ,-9.9586423205861401836 ] 
dist 21=[-34.915594616997643089  ,-9.6727591385612373236 ] 
dist 22=[-35.405621338043998484  ,-8.1382784187117190098 ] 
dist 23=[-35.526521031175865129  ,-4.6233027871157487043 ] 
dist 24=[-31.175414769049169454  ,-.74038916771310728393] 
dist 25=[-30.034572729746170896  ,2.2615947689347197102 ] 
dist 26=[-29.363382169304114059  ,5.0975984157549860540 ] 
dist 27=[-29.193584859271789852  ,8.3348015132323580068 ] 
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dist 30=[1.6388274815362990882 ,16.459861964618948575  ] 
dist 31=[2.8414243561862093788 ,19.466774578564274411  ] 
dist 32=[9.8698310942804673053 ,22.141088376325098982  ] 
dist 33=[10.239770422372102151  ,23.289926511517665487  ] 
dist 34=[9.5972592784979763528 ,23.783750299465210086  ] 
dist 35=[8.5527893040770184394 ,23.851008047284018970  ] 
dist 36=[7.0688708822933729451 ,21.516691598018295116  ] 
dist 37=[5.0206958862014201412 ,20.830010518476945140  ] 
dist 38=[1.7367615658911715895 ,20.358687829491889980  ] 
dist 39=[-1.6041262278068459641 ,20.079831301238047150  ] 
dist 40=[-3.8789652300193713550 ,14.941040176884366807  ] 
dist 41=[-5.7546741419951867627 ,14.382544203321132547  ] 
dist 42=[-7.5132311727761389283 ,13.544014941184339761  ] 
dist 43=[-9.0811209992685082545 ,13.216062162177829538  ] 
dist 44=[-9.9671557598664119205 ,4.9606062261187626599 ] 
dist 45=[-10.738427049236601935  ,3.8567206692916193496 ] 
dist 46=[-12.000219373578577932  ,1.3451638292399631656 ] 
dist 47=[-12.941226360414190658  ,.81844963100041411518] 
dist 48=[-13.602580225213500329  ,-.28439084936224275179] 
dist 49=[-13.754729611742417413  ,-.16155185625621874386] 
dist 50=[-13.692680333713803895  ,.3222000568402202947 ] 
dist 51=[-13.514139576680290943  ,.98438558948771153725] 
dist 52=[-12.068476341221646815  ,1.8156900186437485802 ] 
dist 53=[-11.641404860722992759  ,2.9105442177084781751 ] 
dist 54=[-10.897461480838278011  ,4.6189945239285149675 ] 
dist 55=[-10.644920554684245109  ,6.3480800841824172270 ] 
dist 56=[-4.3665970708186496489 ,7.5250251841956470789 ] 
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dist 58=[-3.1040615096028825566 ,9.4182496124993792555 ] 
dist 59=[-3.0546695955746050754 ,10.210881787095390635  ] 
dist 60=[-.62038998416381405652,10.677928793070802397  ] 
dist 61=[-.32904481525666637856,10.986742675973352683  ] 
dist 62=[.35920385654205987755,11.151541423069564345  ] 
dist 63=[.45905376252007623439,11.208868189340331627  ] 
dist 64=[1.2994842486683258131 ,2.5356930739170120959 ] 
dist 65=[1.3628640128451178760 ,2.5669421040797089892 ] 
dist 66=[1.2446267187526040903 ,2.5456292598409166366 ] 
dist 67=[1.0884166505874726120 ,2.5424241111268633288 ] 
dist 68=[.89850359669033918237,2.2574212697477183092 ] 
dist 69=[.65193252315336681382,2.2586025720924519131 ] 
dist 70=[.27082030610068142867,2.1905797655923425135 ] 
dist 71=[-.11346288222666421805,2.1723371103079989665 ] 
dist 72=[-.37264654923876328904,1.8018058433157023193 ] 
dist 73=[-.58434273431163815486,1.7099595929460775874 ] 
dist 74=[-.78018001548181431831,1.6242480675845772208 ] 
dist 75=[-.945805544421078078  ,1.5837568460164376359 ] 
dist 76=[-1.0376473117194292937 ,.4314631401871033362 ] 
dist 77=[-1.1204482077578000546 ,.31083651503486273351] 
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dist 88=[-.41913421761717035902,.14265075745236566834] 
dist 89=[-.39700316510461152159,.37689372263044725911] 
dist 90=[-.38226814406683340966,.56753987813600486014] 
dist 91=[-.37880836849074920175,.74312499198724336257] 
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dist 93=[-.00859782341828158920,.97354017426414970217] 
dist 94=[.08126919876609847508,1.0213838753250707164 ] 
dist 95=[.09484725825614399503,1.0333951209577260832 ] 
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dist 99=[.10126615927406966977,.30436353628036244012] 
dist 100=[.07987163762642187219,.26833240583016747221] 
dist 101=[.05246762571158080918,.26772816973929113184] 
dist 102=[.01045999021575689716,.26030005771506961485] 
dist 103=[-.03184252085221759490,.25636698607063123229] 
dist 104=[-.06041927912937551452,.22001963171636572942] 
dist 105=[-.08383753889965751560,.21055563390212695209] 
dist 106=[-.10566602583421132044,.19625320520537757733] 
dist 107=[-.12496802366889335913,.19100984656376526048] 
dist 108=[-.15681720351616843965,.06498966995782426528] 
dist 109=[-.17577587080970849054,.04826900870214318583] 
dist 110=[-.18796786982624019574,.01076124835538428958] 
dist 111=[-.19377901248987331839,.00263919072404106848] 
dist 112=[-.1957448798923789731 ,-.00568569456344683582] 
dist 113=[-.19520680303692204245,-.00266678077075860703] 
dist 114=[-.20425671877415758295,.00424608488890045764] 
dist 115=[-.20661840563463704834,.01294213485304172694] 
dist 116=[-.15543785630581664107,.02304180335275432153] 
dist 117=[-.14775526875701470527,.03589172216706881968] 
dist 118=[-.13894850309625213524,.05550784393118482834] 
dist 119=[-.13472659247858116707,.07525080118511248420] 
dist 120=[-.04948933625284456104,.08860517468249381620] 
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dist 190=[-9.76897156891476837810e-05,.00163043363957179794] 
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dist 202=[-.00040414804285444165,.00054143087583304924] 
dist 203=[-.00048542024237881373,.00052678915112189419] 
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dist 206=[-.00061684156267822232,3.73137552774963530010e-05] 
dist 207=[-.00062514053982352484,1.31586380840899336870e-05] 
dist 208=[-.00062560501706924428,-6.87949107533296258750e-05] 
dist 209=[-.00061971648327161933,-8.05814726368212429120e-05] 
dist 210=[-.00060551294241442419,-9.93472936140810332510e-05] 
dist 211=[-.00057580732571928815,-.00010308368364998826] 
dist 212=[-.00025165397583749270,-.00010320443588576497] 
dist 213=[-.00024047866161737527,-.00010031107118283051] 
dist 214=[-.00022288431883437103,-9.47205315809270455550e-05] 
dist 215=[-.00021681063323750700,-3.24372202986144812010e-05] 
dist 216=[-8.33179131068535331630e-05,4.66499228054906337590e-05] 
dist 217=[-7.96324460411183887670e-05,9.96356765678211689920e-05] 
dist 218=[-7.39779778422363299130e-05,.00014264902499983104] 
dist 219=[-7.19682757174021205340e-05,.00018213835962323129] 
dist 220=[-2.41594701873919796150e-05,.00021543680706711933] 
dist 221=[-1.77789942087741626570e-05,.00023386763273196230] 
dist 222=[-3.48896202544931884650e-06,.00024459838462213129] 
dist 223=[-3.93592872769192873710e-07,.00024731990490901572] 
dist 224=[1.52325972942006132970e-05,6.93309137167049937590e-05] 
dist 225=[1.79468323173138232980e-05,7.56277199766081042930e-05] 
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dist 227=[2.34448273371462265460e-05,8.06303625017038229420e-05] 
dist 228=[2.37056897086853961430e-05,8.05760003967434662890e-05] 
dist 229=[2.19879428248208863860e-05,7.98866808679807778960e-05] 
dist 230=[9.54423456202687962940e-06,7.74874196275207728450e-05] 
dist 231=[-1.07168615705609865430e-05,7.60826081636823328570e-05] 
dist 232=[-3.10083628374631042690e-05,6.73007069897405257410e-05] 
dist 233=[-4.46217891821132429240e-05,6.49944013799143428210e-05] 
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dist 236=[-7.45265363736613950310e-05,3.10023171833478548030e-05] 
dist 237=[-7.93548959403774703480e-05,2.68263965439360027110e-05] 
dist 238=[-8.22351238049420192590e-05,1.80799089387165964040e-05] 
dist 239=[-8.31294123456493693460e-05,1.57238700651155598150e-05] 
dist 240=[-8.29150832852066837410e-05,7.04361467260306235390e-06] 
dist 241=[-8.21843364307878302710e-05,5.14930928859970771910e-06] 
dist 242=[-7.94444968412770505310e-05,2.83342864682216884430e-06] 
dist 243=[-7.36068106312886023650e-05,2.37391680859253209640e-06] 
dist 244=[-2.93263582579747519060e-05,2.44666706216981222310e-06] 
dist 245=[-2.82142661960677478070e-05,2.99440973069942966600e-06] 
dist 246=[-2.59301967181407311550e-05,3.98336557239121005800e-06] 
dist 247=[-2.51703117071358513470e-05,5.80820016403932289730e-06] 
dist 248=[-1.24129012688222233350e-05,9.21783066484143066150e-06] 
dist 249=[-1.06568857730882658940e-05,1.55917653030604455960e-05] 
dist 250=[-6.93101412317812523930e-06,2.07658608490389423210e-05] 
dist 251=[-5.92209526297479866530e-06,2.55163220651484507780e-05] 
dist 252=[-2.15680074957467420280e-06,2.95227035450655827480e-05] 
dist 253=[-1.36030128730887048630e-06,3.17421726370586618160e-05] 
dist 254=[-2.75636307515914088760e-07,3.30466491628377990160e-05] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 0, 0, 0, 2] 
dist 0=[110.45071975277800057   ,110.45071975277800057   ] 
dist 1=[107.17267224121498694   ,111.43140613103233324   ] 
dist 2=[103.21668595936752886   ,112.04715214615449667   ] 
dist 3=[99.652388345789189006  ,112.52602244980256151   ] 
dist 4=[95.730635056544792134  ,112.29858141406582207   ] 
dist 5=[90.340764459286285598  ,109.07800288093084168   ] 
dist 6=[84.456110545745437777  ,107.87807104471669169   ] 
dist 7=[78.401373386691694980  ,106.10466308425330009   ] 
dist 8=[66.230417287240159982  ,105.29085706595886407   ] 
dist 9=[57.099209896757740275  ,81.345867395129793360  ] 
dist 10=[48.580046399022342124  ,77.997122715900468807  ] 
dist 11=[38.825109841465140678  ,69.024423136484725597  ] 
dist 12=[29.145452148200172767  ,67.598724623963424850  ] 
dist 13=[20.910299314363354677  ,51.436769255445795537  ] 
dist 14=[12.204038057686217565  ,48.212788259478356988  ] 
dist 15=[.62388325236280824671,44.525270192329223087  ] 
dist 16=[-10.362826263779339643  ,43.486518969000629730  ] 
dist 17=[-16.714272522702010264  ,19.089624768636746857  ] 
dist 18=[-20.908547206124134007  ,7.9538082346767617856 ] 
dist 19=[-23.304631258985505733  ,4.7425378864723136153 ] 
dist 20=[-24.850026019974717140  ,1.3429200872445784279 ] 
dist 21=[-25.649487892113630721  ,.54634555820389786655] 
dist 22=[-26.604519721921121120  ,-1.7850394671199319165 ] 
dist 23=[-27.837558309966699567  ,-2.1772857862400596342 ] 
dist 24=[-28.395093815671358534  ,-2.0214135012175594478 ] 
dist 25=[-28.522795572893812721  ,-1.0954353246695332256 ] 
dist 26=[-17.315259029618835203  ,-.04045521142337289433] 
dist 27=[-16.820681306838027581  ,.63050389129043036357] 
dist 28=[-16.727943843703289074  ,2.2203680870405238107 ] 
dist 29=[-13.858704881147127616  ,4.6628669508721973341 ] 
dist 30=[-13.163333345369645261  ,6.8394994602862768774 ] 
dist 31=[-12.616795795379795852  ,9.1657045722773168312 ] 
dist 32=[-12.442455883644345727  ,11.206846288209180757  ] 
dist 33=[-2.4643579101428478434 ,12.254464635648988124  ] 
dist 34=[-1.2853159091275986642 ,12.783554231959769057  ] 
dist 35=[.26579500498416605263,12.870209886226416135  ] 
dist 36=[-.04732880681730304968,12.407128287123197828  ] 
dist 37=[-.40104182747555504868,12.141133755198990331  ] 
dist 38=[-.74041163776754363477,11.733740065501812308  ] 
dist 39=[-.99735112231696504371,11.524149640469762811  ] 
dist 40=[-1.2363827672385630116 ,8.0841099109965110307 ] 
dist 41=[-2.4320084713283501157 ,8.2344110813459068207 ] 
dist 42=[-4.4153431469127939290 ,8.2237268491221510202 ] 
dist 43=[-6.2684880859984523241 ,8.0405459998201361105 ] 
dist 44=[-7.8421247554684065206 ,7.9012486775530563124 ] 
dist 45=[-8.7173174156389553407 ,6.9232076233445352951 ] 
dist 46=[-9.2281413155169454353 ,6.6578672997490160782 ] 
dist 47=[-9.3569516576986511717 ,6.1737550423429188832 ] 
dist 48=[-2.9517318231369904041 ,6.0229915001390816590 ] 
dist 49=[-3.1511862480662032636 ,2.8891082783735633856 ] 
dist 50=[-3.2468813117675682566 ,2.5075639192962375752 ] 
dist 51=[-4.1092565350094807643 ,1.6843751961177677583 ] 
dist 52=[-5.1242516682965285108 ,1.4582231162501448955 ] 
dist 53=[-5.9796924843460054681 ,1.4669632250404195159 ] 
dist 54=[-6.4518605067031904567 ,1.6509651226232207371 ] 
dist 55=[-6.7249228484043186560 ,1.7653804930910103969 ] 
dist 56=[-6.7898586973192506100 ,1.8416008578813881338 ] 
dist 57=[-1.3379802024918124326 ,1.8531080754907718311 ] 
dist 58=[-.05026671554002389015,.38249177857763153785] 
dist 59=[.03970966247265992864,.81980326621347300893] 
dist 60=[.19252773552700241594,1.2067599036645891244 ] 
dist 61=[.19713255752834874958,1.4527422946820847988 ] 
dist 62=[.19492457823131027088,1.6376630536758284541 ] 
dist 63=[.18029719486676180863,1.7825619030315219136 ] 
dist 64=[.15481079964318461563,1.8859933462803893367 ] 
dist 65=[.10887629359856840143,1.9088327426396698198 ] 
dist 66=[.06056805515234009528,1.8983984638593834787 ] 
dist 67=[.02564972438406114223,1.8888491958823822331 ] 
dist 68=[-.00521726733506038802,1.6165270640028609104 ] 
dist 69=[-.03750109886442154258,1.5434350638073179028 ] 
dist 70=[-.06725515378108215968,1.4798186125478379323 ] 
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dist 72=[-.10599297864441749008,.4676676760852713741 ] 
dist 73=[-.31865611513598782499,.36327939552539494677] 
dist 74=[-.54660688989092514923,.12025601251483440747] 
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dist 80=[-.45400661978431559868,-.03962061403467300082] 
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dist 83=[-.46223907906165173087,.05882292989367868665] 
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dist 88=[-.07732689702947401867,.13202132309663443524] 
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dist 90=[-.02282589775480896670,.07431277296124056525] 
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dist 92=[-.02539451331850009061,.18142038884461843048] 
dist 93=[-.03416942595269705400,.21176652637073041488] 
dist 94=[-.04565520244455222216,.23306422554941010839] 
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dist 97=[-.10520231559090888423,.25674111195668263932] 
dist 98=[-.13317983684583370177,.25371835952593741784] 
dist 99=[-.15214071276250481527,.2499150785478206535 ] 
dist 100=[-.16773785475090381419,.22069532326185164562] 
dist 101=[-.1823662809212151826 ,.2124145372687120283 ] 
dist 102=[-.19489048447027891983,.19823017099345452405] 
dist 103=[-.20213673159451830413,.19345807712446536449] 
dist 104=[-.20676198495139055044,.07669708518911604064] 
dist 105=[-.20888423195371339729,.06068452687008467046] 
dist 106=[-.20918529282976415313,.02472707302351025527] 
dist 107=[-.20715795521366998275,.01650941221090977448] 
dist 108=[-.20215757796416496331,.01111579505777934593] 
dist 109=[-.19912969016648784112,.01195152777159431602] 
dist 110=[-.18760321614254962183,.01325233946906998044] 
dist 111=[-.18984047422085460011,.01506018954999705036] 
dist 112=[-.05776695088627488256,.01754144492506150667] 
dist 113=[-.05817556880272592334,.02151543253680889418] 
dist 114=[-.05718618637919897616,.02557349720743365511] 
dist 115=[-.05691831835852487157,.02838904825008290543] 
dist 116=[-.04793210587535168629,.03077340792592580754] 
dist 117=[-.04563471885375059277,.03312134166800643805] 
dist 118=[-.04387123547998529657,.03543864941981979610] 
dist 119=[-.04313872784650592310,.03770669688535245525] 
dist 120=[-.00809525650013426377,.03879835434276168102] 
dist 121=[-.00389858736979764696,.03894784992063926913] 
dist 122=[-.00286670353461144730,.01253254661519548341] 
dist 123=[-.00280695958406062841,.01953220281701213693] 
dist 124=[-.00257841234570127933,.02554727267365439356] 
dist 125=[-.00254549893808509468,.02907728297389102603] 
dist 126=[-.00191941638962272422,.03139657264462806465] 
dist 127=[-.00178292423398616502,.03260619213159088070] 
dist 128=[-.00166517792165752909,.03312022194923337975] 
dist 129=[-.00164164877467681951,.03310295527796853496] 
dist 130=[4.46939361341046488800e-05,.03203679740819329409] 
dist 131=[.00024044564200573392,.03175828415896692640] 
dist 132=[.00068381052008573950,.02627595639494251244] 
dist 133=[.00075261517872162930,.02492350864876020232] 
dist 134=[.00122870382796768185,.02365023010054339429] 
dist 135=[.00130038192620597306,.02305101286429274397] 
dist 136=[-.00200472938002385009,.00615593337172683302] 
dist 137=[-.00661122769279397355,.00439506793872621022] 
dist 138=[-.01036631579410425149,.00133156407490235774] 
dist 139=[-.01383587720828433167,.00130830482942792298] 
dist 140=[-.01677389962489038543,.00122667621405037992] 
dist 141=[-.01848926929448086463,.00120238059484184507] 
dist 142=[-.01950549298292048280,.00097976993820089418] 
dist 143=[-.01974139145412598117,.00092791262113978292] 
dist 144=[-.00770752168183269207,.00085014855312772092] 
dist 145=[-.00772712434350092647,.00082359195264607434] 
dist 146=[-.00750148749195034875,.00022350296400572091] 
dist 147=[-.00746871656995301411,.00014430976254054297] 
dist 148=[-.00612914045895576691,-2.91526394692976470270e-05] 
dist 149=[-.00580182718170952702,-6.79632101212797199350e-05] 
dist 150=[-.00558214332821253966,-.00024307311154259339] 
dist 151=[-.00553082245246224335,-.00027460017841041134] 
dist 152=[-.00099588426432677654,-.00031331156592879921] 
dist 153=[-.00100662617934100690,.00050786495229209935] 
dist 154=[-.00029957500023582820,.00144714290035095803] 
dist 155=[-.00029418197439664383,.00232572694209030262] 
dist 156=[-.00027266600784179020,.00307747877421262222] 
dist 157=[-.00026910202105938634,.00351326374863540700] 
dist 158=[-.00020740210339169235,.00379297026344562593] 
dist 159=[-.00019371078174641175,.00392513518732172106] 
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dist 182=[-.00066271548673907660,-2.88852847609406202610e-05] 
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dist 184=[-.00013595541163064311,6.39618529753270340660e-06] 
dist 185=[-9.18550556668197425820e-05,.00015126989381661364] 
dist 186=[-3.66180914441379801920e-05,.00026964180309934235] 
dist 187=[-3.60280252818720551370e-05,.00037955620811843154] 
dist 188=[-3.37284347070052772470e-05,.00047307620935506326] 
dist 189=[-3.31800770192591129580e-05,.00052635887596048926] 
dist 190=[-2.64836404687021718690e-05,.00055938753566308493] 
dist 191=[-2.49453125831012584510e-05,.00057249525124906513] 
dist 192=[-2.30844215082920922340e-05,.00057434642058044870] 
dist 193=[-2.22899791601705746420e-05,.00057162353071871666] 
dist 194=[-3.71676149916602415560e-06,.00054898403993809868] 
dist 195=[-1.36803038934169274260e-06,.00054275872395818421] 
dist 196=[3.87242080198474200700e-06,.00044744466714934991] 
dist 197=[4.88257672527061361170e-06,.00042424848535320609] 
dist 198=[1.03920293503553097790e-05,.00039936375869447377] 
dist 199=[9.51918128470290000000e-06,.00038674508881112008] 
dist 200=[-9.47307965249891600450e-05,.00014393293257419389] 
dist 201=[-.00016474760050187655,.00012478595359091880] 
dist 202=[-.00022175920497618812,8.36193900024122699350e-05] 
dist 203=[-.00027437326352500407,7.23009970829212810770e-05] 
dist 204=[-.00031891789812689743,2.90168365809165041010e-05] 
dist 205=[-.00034389046238684210,2.12361776933914988580e-05] 
dist 206=[-.00036018934547386749,1.77089569600136262790e-05] 
dist 207=[-.00036408101681762742,1.68522040384622548070e-05] 
dist 208=[-.00012180946682542615,1.54359013575541998660e-05] 
dist 209=[-.00012152575829028314,1.49875967532364523300e-05] 
dist 210=[-.00011673936516054395,4.79902966379197801440e-06] 
dist 211=[-.00011599599299725905,3.42004925296304234280e-06] 
dist 212=[-9.39144454137404493160e-05,3.95448474112614428100e-07] 
dist 213=[-8.86460052483409966430e-05,-3.15094463410294789140e-07] 
dist 214=[-8.47529690916487697810e-05,-2.95501600997027808260e-06] 
dist 215=[-8.37512293450997169930e-05,-3.36303851383207673310e-06] 
dist 216=[-1.82325259659103597320e-05,-3.91006452546720609560e-06] 
dist 217=[-1.83520759313802958930e-05,1.12933265137374636840e-05] 
dist 218=[-1.80780662390223596680e-05,2.58978543884332216580e-05] 
dist 219=[-1.84597220737604101170e-05,3.94350462836630842280e-05] 
dist 220=[-1.92604193148212139840e-05,5.09393038032214407920e-05] 
dist 221=[-2.08214746491786532860e-05,5.74721756356376236850e-05] 
dist 222=[-2.27121223823227536210e-05,6.14947933426466203890e-05] 
dist 223=[-2.48215641463535311130e-05,6.30322797512047281090e-05] 
dist 224=[-2.74528965601599956870e-05,6.32628430822972181670e-05] 
dist 225=[-3.14158143090075140300e-05,6.29383851519942264800e-05] 
dist 226=[-3.53871631402988323380e-05,6.06526764693611233540e-05] 
dist 227=[-3.80520155376939967880e-05,5.97837799175061728350e-05] 
dist 228=[-4.02192536269835745350e-05,5.02965916790446924560e-05] 
dist 229=[-4.22148487863528946720e-05,4.71762069074519961180e-05] 
dist 230=[-4.39011797924448641430e-05,4.29176370220313561870e-05] 
dist 231=[-4.48404906333535981460e-05,4.17159895385667331910e-05] 
dist 232=[-4.53950017032455183620e-05,1.29609002651532484210e-05] 
dist 233=[-4.55534838099817600260e-05,9.86986082469773299060e-06] 
dist 234=[-4.54262001746743443870e-05,9.76863115528597381950e-06] 
dist 235=[-4.49130493597402070070e-05,9.63967377729448082190e-06] 
dist 236=[-4.38900147270021474060e-05,9.46114137730986534650e-06] 
dist 237=[-4.33169456376259631460e-05,9.33121809766458984130e-06] 
dist 238=[-3.98145690484451546060e-05,8.84163925287679989150e-06] 
dist 239=[-3.74324616525540104010e-05,8.65173010265020191120e-06] 
dist 240=[-1.52067596330381326950e-05,8.16193612894829798770e-06] 
dist 241=[-1.51389274332536371510e-05,7.95524667891852995290e-06] 
dist 242=[-1.45584487873378909240e-05,6.86113497576382788770e-06] 
dist 243=[-1.43929190202096671680e-05,6.55526097464412912870e-06] 
dist 244=[-1.19224274447313729450e-05,6.14237987632871349240e-06] 
dist 245=[-1.13186858870804187290e-05,5.97265249993462023890e-06] 
dist 246=[-1.06604297405868065090e-05,5.63204109642278803460e-06] 
dist 247=[-9.54802097725335576250e-06,5.51937317638391259340e-06] 
dist 248=[-2.74255240788272230880e-06,5.51745085563932402690e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 2, 0, 1] 
dist 0=[146.13704010658471600   ,146.13704010658471600   ] 
dist 1=[144.77146170004854828   ,146.22055880796722789   ] 
dist 2=[139.40810734365048600   ,146.48850700280172004   ] 
dist 3=[132.11598567678776365   ,146.68015554232938646   ] 
dist 4=[123.09011929797563266   ,140.87696781097588843   ] 
dist 5=[111.24188384683212707   ,134.90992746832918937   ] 
dist 6=[92.728188875756127626  ,132.46512962732046748   ] 
dist 7=[73.825914328859634916  ,124.01503985380994054   ] 
dist 8=[60.426747727841129899  ,122.64252655025616481   ] 
dist 9=[48.701114121347831388  ,101.04667802742092285   ] 
dist 10=[36.435064785012354275  ,96.314466488528900388  ] 
dist 11=[24.946761650809378878  ,91.832583187892281458  ] 
dist 12=[16.298275998964112988  ,90.529547003877740616  ] 
dist 13=[8.1413814692499158257 ,32.682085890178427814  ] 
dist 14=[-1.4188438346484908792 ,27.760822365821090019  ] 
dist 15=[-10.202748733532036102  ,9.9037434847695094618 ] 
dist 16=[-15.277836875754097095  ,7.4542343966180606364 ] 
dist 17=[-20.502330921178016394  ,-11.177543953945225644  ] 
dist 18=[-26.734756893150434810  ,-13.993703859618311005  ] 
dist 19=[-31.388760182273535380  ,-18.446362575947087907  ] 
dist 20=[-35.057491614978165348  ,-16.939232240338265484  ] 
dist 21=[-37.778863286867882025  ,-14.100701393330356867  ] 
dist 22=[-38.669139011418935234  ,-8.8728876660652488710 ] 
dist 23=[-38.775602097227959861  ,-3.4020168428203049879 ] 
dist 24=[-38.366090862894936996  ,.4067607857924414412 ] 
dist 25=[-34.484940839017379070  ,3.6034193270902479659 ] 
dist 26=[-33.300674205947344087  ,6.6566606766454809557 ] 
dist 27=[-31.421460896875174009  ,9.2757769709658316493 ] 
dist 28=[-30.705973231407458835  ,10.755551559576066280  ] 
dist 29=[-15.990912339792220857  ,11.618567553184303679  ] 
dist 30=[-14.263313605732996058  ,11.827544493311367987  ] 
dist 31=[-10.342832869081287470  ,15.802629079803749015  ] 
dist 32=[-9.2948744751547300435 ,20.545095806123486398  ] 
dist 33=[-4.5337401493871934846 ,24.889142178817615774  ] 
dist 34=[-3.6461109797016016222 ,27.248149823607273159  ] 
dist 35=[-1.6202454042464389739 ,28.556359356529710003  ] 
dist 36=[-1.2165306979762633250 ,28.799884490263504824  ] 
dist 37=[3.1625803110611735664 ,7.3969496933348430206 ] 
dist 38=[1.4144842770057654145 ,7.5278529241429606348 ] 
dist 39=[-.38099984626139052953,7.5219337141727446240 ] 
dist 40=[-1.6248154773197533085 ,7.4394361547505566272 ] 
dist 41=[-2.6720429958730461200 ,6.7114295766621335251 ] 
dist 42=[-3.6886592869907602279 ,6.4909423621427683858 ] 
dist 43=[-4.5786056320498072600 ,6.0757970720096641084 ] 
dist 44=[-5.1238299030293984224 ,5.9348892930958474335 ] 
dist 45=[-5.5088585194967580054 ,2.6456723732402728386 ] 
dist 46=[-5.7637889774939405837 ,2.1834277504619562138 ] 
dist 47=[-5.9248058476237264370 ,1.1391477964865718172 ] 
dist 48=[-5.9373948014711728761 ,.89319832968535378627] 
dist 49=[-5.8626800405603019648 ,-.3069966808160652794 ] 
dist 50=[-5.7919760290548913390 ,-.3926001638772133872 ] 
dist 51=[-5.2689255951460752221 ,-.3939284723181284993 ] 
dist 52=[-4.8494568090500148371 ,-.3231357398776317314 ] 
dist 53=[-2.5683130784352324682 ,-.1919016672423147805 ] 
dist 54=[-2.5160223403493402238 ,.0503939926840146819 ] 
dist 55=[-1.4469004431879795575 ,.30697014110509367968] 
dist 56=[-1.4729706534120615551 ,.66588331767970617841] 
dist 57=[-1.4782473625381991672 ,1.1156572428642360394 ] 
dist 58=[-1.4482664378273297564 ,1.5337789693301922377 ] 
dist 59=[-1.1661445795368298400 ,1.8881193867806083067 ] 
dist 60=[-.94757665446235293373,2.0849110243104917081 ] 
dist 61=[.02493930946952114682,2.1996943957775275272 ] 
dist 62=[.30311308301288668745,2.2286142392597792488 ] 
dist 63=[.69544710700400419821,1.4812094629209769035 ] 
dist 64=[.71611381939000995868,1.5100392044255053627 ] 
dist 65=[.72357556191862014071,1.5130084252280359270 ] 
dist 66=[.68656072839544144047,1.5135353495686294135 ] 
dist 67=[.629963657325544799  ,1.2990023603878756166 ] 
dist 68=[.55245449599594795356,1.2431758983053152244 ] 
dist 69=[.44673314671192093979,1.2103363905809017959 ] 
dist 70=[.27814308915695846691,1.2015087315161827837 ] 
dist 71=[.10638374636098497588,.22814946874308632534] 
dist 72=[-.01206860451548675301,.11349663665328243847] 
dist 73=[-.20559407925914550167,-.01630247070052338474] 
dist 74=[-.3909395860143178819 ,-.03592066778990496227] 
dist 75=[-.55228246616365681189,-.19450849787865564195] 
dist 76=[-.65057911277337656039,-.21878348287054979804] 
dist 77=[-.71965635020103700015,-.26274724819024117575] 
dist 78=[-.76507613795790133881,-.26991389531150470056] 
dist 79=[-.79356364533702071814,-.3428669684331814015 ] 
dist 80=[-.79751388250468030223,-.34546678616495459314] 
dist 81=[-.7876508681280171267 ,-.33598060393852476308] 
dist 82=[-.7777225569778965284 ,-.30788727684892872408] 
dist 83=[-.67998688096032612057,-.27086979459431585852] 
dist 84=[-.65301027980873036824,-.225953295811022361  ] 
dist 85=[-.613449463740370821  ,-.16767405954141772799] 
dist 86=[-.5979124205587279118 ,-.07761080585590736194] 
dist 87=[-.21439555344154784667,.07413099771429280928] 
dist 88=[-.16384437444740905069,.21339956076818071369] 
dist 89=[-.04914975186155457412,.32685698316045763872] 
dist 90=[-.02498839165185044497,.43148369567845848116] 
dist 91=[.05522079258679396885,.51989753240601917591] 
dist 92=[.06561659556330325019,.56910323602895006099] 
dist 93=[.08659581783262916092,.59770141633254346585] 
dist 94=[.09022042219463070046,.60478596777947577516] 
dist 95=[.10191499519252634043,.19847334144854448856] 
dist 96=[.10287461337010976982,.19940722958407356747] 
dist 97=[.10073223848623095364,.19621130825238870454] 
dist 98=[.09388067915601733824,.19420617257536459516] 
dist 99=[.08471978826510900843,.16725328133428946846] 
dist 100=[.06449490739405736122,.16008511352803849718] 
dist 101=[.03888319985181324014,.15141864574778927154] 
dist 102=[-6.70088607976153601000e-05,.14731863729514129122] 
dist 103=[-.03917132845430359080,.06089338072542370911] 
dist 104=[-.06539588677775153645,.05436822957187097795] 
dist 105=[-.08667806475851255946,.04051298819539608804] 
dist 106=[-.1061644505052811403 ,.03665783289599567001] 
dist 107=[-.1225268547139812866 ,.02182540578211612036] 
dist 108=[-.13140836749115079085,.01861134782609686249] 
dist 109=[-.13633375588415737964,.01335266485979802888] 
dist 110=[-.13699161871480758408,.01199669586652992896] 
dist 111=[-.11337746581517434053,.00957928812012772992] 
dist 112=[-.11326514075221888734,.00939499128343192129] 
dist 113=[-.10902404445932530129,.01011081517559348959] 
dist 114=[-.10838465508779948   ,.01221603692332968298] 
dist 115=[-.08759713407476787745,.01498919538347896009] 
dist 116=[-.08261625097293368100,.01835713907300291319] 
dist 117=[-.07903348994573656874,.02273120703228221328] 
dist 118=[-.07815942995319183383,.02949888822578769470] 
dist 119=[-.01728838829042767357,.03633667945084228298] 
dist 120=[-.01179458731739162929,.04098957304866048425] 
dist 121=[-.00314113609702653462,.04483863506905224541] 
dist 122=[-.00147797588416102944,.04848640533390765311] 
dist 123=[.00726968206216388645,.05163725075187892003] 
dist 124=[.00877074373488140413,.05410303401688004780] 
dist 125=[.01149856978247824083,.05747885312111295535] 
dist 126=[.01200277373997902281,.05831843603897124508] 
dist 127=[.01274325495903668598,.02642198065147913525] 
dist 128=[.01267113418047259985,.02648378054462759776] 
dist 129=[.01224655893816826445,.02569747033208548235] 
dist 130=[.01124291565392928262,.02558399552650076683] 
dist 131=[.00997194597931325639,.02097817006230093623] 
dist 132=[.00848588166074169473,.01985457746285217291] 
dist 133=[.00658914818303030194,.01909964066916638942] 
dist 134=[.00368762883216383334,.01892545321618236565] 
dist 135=[.00076571640770551321,.00220152958319969598] 
dist 136=[-.00172130190261232815,.00074941251066250656] 
dist 137=[-.00493279911747828725,-.00141561690423537316] 
dist 138=[-.00793502440907011527,-.00173479077469449059] 
dist 139=[-.01050278013284790073,-.00434596405438710380] 
dist 140=[-.01198953538714870849,-.00473881823052540296] 
dist 141=[-.01294167172563486381,-.00543190183249627628] 
dist 142=[-.01338714005179022226,-.00554293744227292063] 
dist 143=[-.01355077503224279510,-.00591212038038156037] 
dist 144=[-.01351331876723943775,-.00581144639280735864] 
dist 145=[-.01312525355639687871,-.00554321250432253999] 
dist 146=[-.01292354974465625673,-.00498365555640093183] 
dist 147=[-.01108182109208898343,-.00429456673373676904] 
dist 148=[-.01060342975919593624,-.00351200538865233352] 
dist 149=[-.00987550222156618106,-.00252729771229534215] 
dist 150=[-.00961104313003869020,-.00103559527128924078] 
dist 151=[-.00324766584812655566,.00161884216259171742] 
dist 152=[-.00239858146940463139,.00395867883843333193] 
dist 153=[-.00049462608888980932,.00586000801255984665] 
dist 154=[-8.27435377269986905500e-05,.00760764869064715176] 
dist 155=[.00110647213078205226,.00908194726374975959] 
dist 156=[.00127053921375785724,.00989801938151050581] 
dist 157=[.00156884899950997845,.01037289033791255536] 
dist 158=[.00162192368658550463,.01049249381939543650] 
dist 159=[.00168602209504756343,.00316384657961286992] 
dist 160=[.00166545818609196219,.00316108678752778329] 
dist 161=[.00160280061362971077,.00305236497646203766] 
dist 162=[.00146807722579255921,.00303029516945757656] 
dist 163=[.00130093561126861229,.00248839587710331131] 
dist 164=[.00110954897712103436,.00235662119189908450] 
dist 165=[.00086769319078261954,.00224755479469261898] 
dist 166=[.00050015499911427773,.00220698870276330414] 
dist 167=[.00011120075848270848,.00032535708697414438] 
dist 168=[-.00036837476027009900,.00010044030145148629] 
dist 169=[-.00076020442077753669,-.00027822788787565972] 
dist 170=[-.00112401964499520792,-.00032149044029544115] 
dist 171=[-.00143356699837915160,-.00065513447207769435] 
dist 172=[-.00160994172824329364,-.00070437738073000006] 
dist 173=[-.00171929363706638616,-.00079246712853025705] 
dist 174=[-.00176274772366301020,-.00080557268200619141] 
dist 175=[-.00176949542159337409,-.00085963245262778529] 
dist 176=[-.00176191195045258535,-.00083894355664869253] 
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dist 178=[-.00167418794446095494,-.00070778699504607112] 
dist 179=[-.00136990641586605048,-.00060240808369904071] 
dist 180=[-.00129651187724188941,-.00048466400397550726] 
dist 181=[-.00122597087078073390,-.00033769402990730292] 
dist 182=[-.00119437041006838951,-.00011626967136466787] 
dist 183=[-.00029451020918123460,.00012985243463465818] 
dist 184=[-.00020162799380565256,.00037167130484959124] 
dist 185=[-3.14130588493159763390e-05,.00056828497493777159] 
dist 186=[-5.19188113755231458300e-06,.00074925110723986740] 
dist 187=[.00012657891969165045,.00090212723730619589] 
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dist 194=[.00016863798341654099,.00038800056175920848] 
dist 195=[.00014679332270770355,.00031332806890096760] 
dist 196=[.00012219422867923370,.00029556624875424217] 
dist 197=[9.13635178967431660500e-05,.00028279853471085399] 
dist 198=[4.47744474419110098810e-05,.00027986531324815036] 
dist 199=[-1.97314302834124647300e-06,2.88544760901688433090e-05] 
dist 200=[-3.52923908072134337740e-05,1.52069636146352931510e-05] 
dist 201=[-8.38197306685261601130e-05,-1.62880570997422922550e-05] 
dist 202=[-.00012876956758113473,-2.15744812080778771990e-05] 
dist 203=[-.00016694802182306093,-5.81483399801888801250e-05] 
dist 204=[-.00018858992294204485,-6.37732353499407933500e-05] 
dist 205=[-.00020186674340014997,-7.42981606700903619330e-05] 
dist 206=[-.00020683224712288988,-7.61188011568283499290e-05] 
dist 207=[-.00020750801643737976,-7.78335169583118680350e-05] 
dist 208=[-.00020636507127053461,-7.56596178129434394130e-05] 
dist 209=[-.00019903774298718956,-7.10991370092151704530e-05] 
dist 210=[-.00019590745028396434,-6.22086028966692370930e-05] 
dist 211=[-.00016599290750702715,-5.14411647342037079510e-05] 
dist 212=[-.00015852974782642351,-3.94276753505372957760e-05] 
dist 213=[-.00014732666254774649,-2.44415087738769154610e-05] 
dist 214=[-.00014321086140266764,-1.87019034047960000000e-06] 
dist 215=[-4.68357370928322698480e-05,2.64319774352699465500e-05] 
dist 216=[-3.40717226855091560660e-05,6.16118264667491390040e-05] 
dist 217=[-1.79031606840039006100e-05,9.01732403149911860300e-05] 
dist 218=[-1.54555246484640558910e-05,.00011639700492325110] 
dist 219=[-6.12735914477047502110e-06,.00013850945786811808] 
dist 220=[-4.19172509133857222020e-06,.00015074608579468616] 
dist 221=[-1.11607021339430611330e-06,.00015786599929058699] 
dist 222=[-3.42713575381023886690e-07,.00015966140154591662] 
dist 223=[3.23291121966149295870e-05,5.11615220084989378930e-05] 
dist 224=[3.12258538651141590960e-05,5.09039058463265060280e-05] 
dist 225=[2.91384081637183922370e-05,4.89716040624501273330e-05] 
dist 226=[2.52153238623269298700e-05,4.83390425640820764620e-05] 
dist 227=[2.05104748491624763520e-05,4.03006478894968412310e-05] 
dist 228=[1.53187370969205808930e-05,3.83186996997318694840e-05] 
dist 229=[8.87906505609417029250e-06,3.59206329436224785280e-05] 
dist 230=[-7.81090640489701132110e-07,3.48419419426152901000e-05] 
dist 231=[-1.04496421789779815380e-05,1.36151596611187761000e-05] 
dist 232=[-1.69227011327595271630e-05,1.19678162738193505200e-05] 
dist 233=[-2.21720355280674056100e-05,8.53710946532943930810e-06] 
dist 234=[-2.69815522289660390880e-05,7.60763910406394669840e-06] 
dist 235=[-3.10297137183122862800e-05,4.16870438420110173130e-06] 
dist 236=[-3.32559136851677162190e-05,3.40326987777326767830e-06] 
dist 237=[-3.45325541744412186910e-05,2.43671980452100145480e-06] 
dist 238=[-3.48102400993263266620e-05,2.18536319593275629390e-06] 
dist 239=[-2.94193450465734081090e-05,2.14491155670830547280e-06] 
dist 240=[-2.92360115750790730030e-05,2.32251726011340559220e-06] 
dist 241=[-2.79816872507063904800e-05,2.68969438185288383450e-06] 
dist 242=[-2.76531438315405289540e-05,3.40204890465973821990e-06] 
dist 243=[-2.26899910931567827380e-05,4.26376608561479998650e-06] 
dist 244=[-2.14934991489867148640e-05,5.22405824691737430680e-06] 
dist 245=[-2.02075400454935962390e-05,6.42131461729978263010e-06] 
dist 246=[-1.95611071375505010870e-05,8.22398582282693153330e-06] 
dist 247=[-7.03646907405925261860e-06,1.00307902675351004170e-05] 
dist 248=[-6.05953895213761111940e-06,1.12444837270797387690e-05] 
dist 249=[-3.97855445502565759470e-06,1.22331355295790031120e-05] 
dist 250=[-3.41249496566092687280e-06,1.41394218548844791440e-05] 
dist 251=[-1.28413860077957331690e-06,1.63854648575647567940e-05] 
dist 252=[-8.37069942856320067790e-07,1.76369953619777922000e-05] 
dist 253=[-1.91755041387687066620e-07,1.83891696780873883450e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 1, 0, 1] 
dist 0=[114.79534189379339626   ,114.79534189379339626   ] 
dist 1=[110.10056953338102221   ,117.53725870609727580   ] 
dist 2=[100.97141803419242490   ,118.90494366883961566   ] 
dist 3=[91.150990646183967257  ,119.83812496508678233   ] 
dist 4=[83.705168247541974058  ,120.84120971589865122   ] 
dist 5=[76.684871464182534902  ,121.55882795880032939   ] 
dist 6=[68.539892329458987879  ,121.36221355930895665   ] 
dist 7=[60.396384256974442260  ,120.47533412278661609   ] 
dist 8=[53.367668874301345305  ,118.44778617110559145   ] 
dist 9=[45.846864142925927395  ,97.062383080759302010  ] 
dist 10=[35.721414199336382224  ,93.721808944248038713  ] 
dist 11=[25.862657455147324740  ,84.094648888419733410  ] 
dist 12=[19.398725983475827678  ,82.713635529465972522  ] 
dist 13=[14.177768259275141096  ,63.317269746203668210  ] 
dist 14=[9.2762959147532577461 ,59.357379721738026061  ] 
dist 15=[.49982743268910463874,55.522521685835108917  ] 
dist 16=[-5.8732898108460873056 ,54.805284772677117777  ] 
dist 17=[-10.383596284834587441  ,11.684358437611445760  ] 
dist 18=[-13.573179158355045440  ,6.6941351451238547252 ] 
dist 19=[-15.936124883007779011  ,2.6930768986790540334 ] 
dist 20=[-17.146989933136077333  ,2.4468541943759617678 ] 
dist 21=[-19.546656709697138980  ,2.0754880042608814940 ] 
dist 22=[-23.074275755437629038  ,1.9761623207277966814 ] 
dist 23=[-25.338222515992960866  ,1.5532278429298300037 ] 
dist 24=[-26.451402663624008210  ,1.4226027453450257771 ] 
dist 25=[-26.927014288479703419  ,1.0378497794898100040 ] 
dist 26=[-26.900069346777084460  ,.87486299763986685295] 
dist 27=[-26.176391566415540796  ,.40536543063407605149] 
dist 28=[-25.810272310688436446  ,2.2444325313980466218 ] 
dist 29=[-22.117297065691005539  ,3.9849840172862209244 ] 
dist 30=[-21.170892546129991706  ,6.0009018782421084021 ] 
dist 31=[-19.787193747575031639  ,7.8136127073613484544 ] 
dist 32=[-19.266711899234800435  ,8.7500464254045717696 ] 
dist 33=[-6.7660662715892585861 ,9.2610259823841166378 ] 
dist 34=[-5.1146694774353860913 ,9.3808215868216951480 ] 
dist 35=[-1.4026456068914635051 ,10.001113388756654510  ] 
dist 36=[-.62389654575780217253,13.315265235989061073  ] 
dist 37=[1.1258826808240742045 ,16.109351062161146942  ] 
dist 38=[1.3015455799637784283 ,17.655237801960680220  ] 
dist 39=[2.2406295731038348692 ,18.554502691034867867  ] 
dist 40=[1.0408535946785688330 ,18.780962541395590687  ] 
dist 41=[-.25087022828287539007,5.8604383230060656441 ] 
dist 42=[-1.5503538243935150242 ,5.8724284266523951327 ] 
dist 43=[-2.7194762244776982310 ,5.7045143965999659366 ] 
dist 44=[-3.4949688749193892655 ,5.6694113616736873552 ] 
dist 45=[-4.1150206305808836458 ,4.6971966305585894002 ] 
dist 46=[-4.6686053559838617479 ,4.4590114983009822596 ] 
dist 47=[-5.1105336486724738883 ,4.2658039053589476493 ] 
dist 48=[-5.2877805503632339565 ,4.1950449019163778247 ] 
dist 49=[-5.3410557071762268638 ,2.1507993094392499692 ] 
dist 50=[-5.3048311832490247658 ,2.0863160093201926195 ] 
dist 51=[-4.8590194529868916244 ,1.1959861581738979913 ] 
dist 52=[-4.7101110210765213425 ,1.1106870863524584842 ] 
dist 53=[-4.4659595524718439359 ,.93754788120425742416] 
dist 54=[-4.3709277358664872606 ,.88718064823390189818] 
dist 55=[-2.9521057623245866155 ,.68245760328458056722] 
dist 56=[-3.0442367585084719405 ,1.5617804784726990339 ] 
dist 57=[-3.0706818660021447256 ,2.3297140391759560456 ] 
dist 58=[-3.0622045870242297041 ,3.0401521794434077672 ] 
dist 59=[-2.9477696407063122791 ,3.6404626660839679696 ] 
dist 60=[-2.9204369955725234982 ,3.9714841899556907758 ] 
dist 61=[-2.3983473121801975345 ,4.1616244491386784492 ] 
dist 62=[-2.2717613894979976804 ,4.2029669665989129895 ] 
dist 63=[-2.1515747888537627294 ,1.1262985651478133852 ] 
dist 64=[-2.0978260580167321299 ,1.1643732020499378323 ] 
dist 65=[-.5437431030984168106 ,1.1769755340169100749 ] 
dist 66=[-.38178476305802409342,1.1801225375094037329 ] 
dist 67=[-.01521688874356618163,1.0319945393152502703 ] 
dist 68=[.03158082275574834847,1.2615142306455249758 ] 
dist 69=[.09352339716759035891,1.5275281737044253649 ] 
dist 70=[.10501977786785117559,1.6757781718616591906 ] 
dist 71=[.16474493026950837927,1.7685363543747617784 ] 
dist 72=[.02234946144185630861,1.7899755784223906757 ] 
dist 73=[-.13010208386171486906,.6986705478051254683 ] 
dist 74=[-.27778393041774459676,.69815970072512318701] 
dist 75=[-.40736904306172700776,.67269759703739193411] 
dist 76=[-.48804205381714018839,.66902217263225584499] 
dist 77=[-.54677686941639819427,.54332999129755827727] 
dist 78=[-.58934949770732664881,.51324829874649151181] 
dist 79=[-.61866309678967667212,.49206447401227008038] 
dist 80=[-.62478231199855396284,.48731086589402050388] 
dist 81=[-.62163399473375425638,.13889520925436807899] 
dist 82=[-.61410542830997482527,.13459763246895021276] 
dist 83=[-.54430422350809446483,.06731187583795335789] 
dist 84=[-.52411546847238643055,.06087738245388099932] 
dist 85=[-.49325346594975323585,.04894962854824376601] 
dist 86=[-.48135622291775764168,.04590798394695008702] 
dist 87=[-.34751344741353582473,.05646927770555393105] 
dist 88=[-.35695680199509614387,.16849364249365609872] 
dist 89=[-.35910416847713102616,.25984082246806553942] 
dist 90=[-.35734192875980487026,.34416834794116139257] 
dist 91=[-.34582249305394045763,.41543156416311948389] 
dist 92=[-.33996502396038520704,.45492819633144495184] 
dist 93=[-.29152517253429150136,.47793011846482103423] 
dist 94=[-.27903089142205785551,.48372543410849089688] 
dist 95=[-.25866394840851932749,.14788548969428244954] 
dist 96=[-.25183532542324894147,.14947821052189935396] 
dist 97=[-.09662530873459918727,.14812467935009036273] 
dist 98=[-.06870538163409488089,.16469140218594627554] 
dist 99=[-.02149967227477628743,.20043894361697698252] 
dist 100=[-.02178706702968461113,.22426633042827611653] 
dist 101=[-.02210548439684732184,.25405804965077475872] 
dist 102=[-.02252259417923463120,.27438223455113776585] 
dist 103=[-.02294634336479351436,.28595122290387535685] 
dist 104=[-.02329291284857811515,.28826337537778383769] 
dist 105=[-.03047802931436988930,.08025619704846952065] 
dist 106=[-.04880953214964944475,.08001364489998195594] 
dist 107=[-.06462636785919287614,.07687484364174800226] 
dist 108=[-.07401782452026670222,.07626641839918232380] 
dist 109=[-.08032319512973203067,.06217317324901338061] 
dist 110=[-.08389274427076792907,.05879254847378998735] 
dist 111=[-.08565250805012515851,.05594341973622612750] 
dist 112=[-.08574624211575139246,.05492125427510281976] 
dist 113=[-.08328108471124535013,.03163750294794863078] 
dist 114=[-.08259790113429651905,.03054483200424262873] 
dist 115=[-.06865240111732506890,.01452615245946273690] 
dist 116=[-.06517795495126217975,.01208751119963661185] 
dist 117=[-.06193809311069956938,.00708244207594804232] 
dist 118=[-.06038171840963913171,.00578092876898892015] 
dist 119=[-.04463471212061271256,.00470918627084790685] 
dist 120=[-.04571577089447254594,.01671032679689563032] 
dist 121=[-.04601056738343580774,.02650340048373894497] 
dist 122=[-.04548178985661835050,.03556551017088801474] 
dist 123=[-.04196470912749957324,.04324639482203467964] 
dist 124=[-.04153833130541167970,.04784972457672770796] 
dist 125=[-.03386875274049289370,.05048165813444113809] 
dist 126=[-.03203179781799341031,.05109736288746450885] 
dist 127=[-.03025823470414550741,.02002076556950660305] 
dist 128=[-.02947862194159457581,.02011168545830929997] 
dist 129=[-.00709954399117426252,.01961128316769261945] 
dist 130=[-.00479289851297268163,.01953871899279308563] 
dist 131=[.00040459147131837671,.01613444665633683907] 
dist 132=[.00145280488016230157,.01865392251812455678] 
dist 133=[.00717198874835105156,.02242749589035178885] 
dist 134=[.00625802318050961821,.02452322447040157576] 
dist 135=[.00183508378071983996,.02577240674962658629] 
dist 136=[-.00115929872946795608,.02608704801494251614] 
dist 137=[-.00362181767812262010,.01009273205164445052] 
dist 138=[-.00593353940296164655,.01005187540897868428] 
dist 139=[-.00791686115120493756,.00961292588876588829] 
dist 140=[-.00907580700701353257,.00954933410384072691] 
dist 141=[-.00983124808591611024,.00766781926546402347] 
dist 142=[-.01021289124172085537,.00722434228192943366] 
dist 143=[-.01037837605548996221,.00690059369903663165] 
dist 144=[-.01036272215681531001,.00682858617319772587] 
dist 145=[-.01009339416140645368,.00056266707822035822] 
dist 146=[-.00994264324339563757,-.00016664750583306254] 
dist 147=[-.00855558800516259051,-.00185932923415834202] 
dist 148=[-.00819169313163617450,-.00210651282070857885] 
dist 149=[-.00764017398099134427,-.00406791609179253107] 
dist 150=[-.00743763492724783087,-.00145837580916039479] 
dist 151=[-.00496418282478568632,.00121598880047290709] 
dist 152=[-.00507019417411336449,.00301055188928680237] 
dist 153=[-.00507158130018226260,.00446944909344776939] 
dist 154=[-.00503840330863167263,.00581119032239092275] 
dist 155=[-.00485029733738412557,.00694336048080792412] 
dist 156=[-.00477066295095658533,.00757022897055325376] 
dist 157=[-.00403916195490922224,.00793543676101567678] 
dist 158=[-.00385506626873043619,.00802729871695170682] 
dist 159=[-.00357712853164544487,.00246256566298987295] 
dist 160=[-.00347741423926071022,.00246406093831446079] 
dist 161=[-.00112270115651245182,.00238173461893343054] 
dist 162=[-.00081100804266933454,.00236966981621151391] 
dist 163=[-.00011634066569888839,.00220823984102544026] 
dist 164=[3.57443678819970716800e-05,.00284685513518727752] 
dist 165=[.00078155208454949441,.00338524186068090823] 
dist 166=[.00056025193415818378,.00368312677593436584] 
dist 167=[-4.70891932490871459620e-06,.00385642748610100256] 
dist 168=[-.00038555636156236903,.00390010646991186710] 
dist 169=[-.00069711975614980579,.00121146656583623496] 
dist 170=[-.00098701994805716747,.00120485207414890222] 
dist 171=[-.00123406123820945565,.00115189428792173979] 
dist 172=[-.00137547280609874948,.00114119807529252488] 
dist 173=[-.00146397245469021455,.00092557379741753649] 
dist 174=[-.00150095219004799964,.00087428369958461625] 
dist 175=[-.00150831159181932661,.00082821343705749563] 
dist 176=[-.00150196111002634899,.00081045097055481750] 
dist 177=[-.00144419116462189276,.00014432496594163301] 
dist 178=[-.00142804912107659735,6.58689143016376544070e-05] 
dist 179=[-.00117905342114278849,-.00011396404103309198] 
dist 180=[-.00111826135358792264,-.00014464078480064327] 
dist 181=[-.00105319049770901341,-.00030257598199650009] 
dist 182=[-.00102003966894943323,-2.91179655354880200000e-05] 
dist 183=[-.00070315964794268404,.00024513444323351182] 
dist 184=[-.00071476617064582509,.00042943013801522286] 
dist 185=[-.00071248371357566233,.00057958734506849731] 
dist 186=[-.00070764503878726764,.00071830021582914772] 
dist 187=[-.00067642350894074947,.00083582092348340754] 
dist 188=[-.00066836291991933554,.00090183870551567711] 
dist 189=[-.00054751575596560421,.00094605103169108818] 
dist 190=[-.00051848216677363850,.00095630594713972408] 
dist 191=[-.00048719325654435054,.00046912039030358543] 
dist 192=[-.00047154877771149692,.00046728670454487479] 
dist 193=[-.00016773306678791984,.00046117733982492983] 
dist 194=[-.00014403375170924326,.00045606679878365994] 
dist 195=[-9.37340179139935708550e-05,.00043115442395243359] 
dist 196=[-8.01130589141611841030e-05,.00042248224193488530] 
dist 197=[-2.92607215052785231180e-05,.00039749311642583332] 
dist 198=[-1.85162070556276066790e-05,.00042759312554403334] 
dist 199=[-3.80083798909378374730e-06,.00044528724689655167] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 1, 1, 2, 0, 2] 
dist 0=[126.71234644414065801   ,126.71234644414065801   ] 
dist 1=[122.72297567498273350   ,128.00554293749464074   ] 
dist 2=[117.29030753782125120   ,128.17202514688911078   ] 
dist 3=[110.26378555645093372   ,127.68257521781067816   ] 
dist 4=[100.85868971489733465   ,125.90070618146793986   ] 
dist 5=[85.965554859064645691  ,119.15640298575873072   ] 
dist 6=[70.659567979454903047  ,117.44451309626977484   ] 
dist 7=[59.606859663128562421  ,112.72597999763067072   ] 
dist 8=[49.713107928571847603  ,104.02517646483274686   ] 
dist 9=[39.000309396465586245  ,87.378466553223564937  ] 
dist 10=[28.726272897728514381  ,83.743617443664543665  ] 
dist 11=[20.563664353265521706  ,79.573920025832356855  ] 
dist 12=[12.439643104247744378  ,77.847206683299282729  ] 
dist 13=[2.2947678938771944937 ,49.089243764769686074  ] 
dist 14=[-7.1891057099917560720 ,44.442270487256920928  ] 
dist 15=[-12.689145513860667529  ,43.620629775914970037  ] 
dist 16=[-16.344311729699633912  ,16.702375546372824002  ] 
dist 17=[-18.480689959904352675  ,1.7153431197451886556 ] 
dist 18=[-21.386199868752701166  ,-.78742174260112935166] 
dist 19=[-25.890726745604144524  ,-5.0977217236465657661 ] 
dist 20=[-29.999715218547109628  ,-5.8708390303583424164 ] 
dist 21=[-33.279267662914808811  ,-9.1295083924409944623 ] 
dist 22=[-34.488185723711943490  ,-7.7274284689022837355 ] 
dist 23=[-34.887964785877399322  ,-4.3904319373327864172 ] 
dist 24=[-34.935295962557017088  ,-.68137844740945234499] 
dist 25=[-30.739325769731140044  ,2.2046599847248782405 ] 
dist 26=[-29.571602604281978749  ,4.9457167639259467152 ] 
dist 27=[-28.823489839713253210  ,8.0927480786063133669 ] 
dist 28=[-28.489012075746238920  ,11.165509299225642698  ] 
dist 29=[-7.4835145014644875114 ,13.619471328426051044  ] 
dist 30=[-4.9701966527902843005 ,16.045142566817049425  ] 
dist 31=[.94180357953941590198,19.014854001559271362  ] 
dist 32=[1.8482317850345588277 ,21.662004848108604550  ] 
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dist 229=[1.47780176819718586510e-05,7.96146641211798826940e-05] 
dist 230=[9.27761449914736030550e-06,7.90088949002681735740e-05] 
dist 231=[-6.16682136581442571230e-06,7.58875891391436097510e-05] 
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dist 238=[-6.09256330979899140080e-05,1.36333470757461704020e-05] 
dist 239=[-6.16944093099655702960e-05,8.90089304476268597740e-06] 
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dist 242=[-5.98157487167050449000e-05,1.79896633303806591910e-06] 
dist 243=[-5.90425684278883227340e-05,3.85072025482101971870e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 2, 0, 1, 0, 2] 
dist 0=[121.04669669386231719   ,121.04669669386231719   ] 
dist 1=[117.49843623609320203   ,122.75960055949440823   ] 
dist 2=[111.58347917442090772   ,124.05671174502258028   ] 
dist 3=[100.46494134415275952   ,125.94076017487413279   ] 
dist 4=[88.619101581945629643  ,127.53673839534950010   ] 
dist 5=[79.809913885001435823  ,127.69364961323132572   ] 
dist 6=[71.672674711476924250  ,127.00445952886919793   ] 
dist 7=[62.481158958476836621  ,126.32485383521202728   ] 
dist 8=[53.436714708609812831  ,104.58721022554597670   ] 
dist 9=[45.869288537205968607  ,101.27764383969782519   ] 
dist 10=[37.979420311002977196  ,91.501365868093244329  ] 
dist 11=[27.626523760266751189  ,90.096386067240596666  ] 
dist 12=[17.661339127625243269  ,69.657573839050389034  ] 
dist 13=[11.309064348362562033  ,65.439587272246967151  ] 
dist 14=[6.3764943013035584038 ,61.429538337782331192  ] 
dist 15=[1.0772140114337060388 ,60.665303661455701201  ] 
dist 16=[-5.1952349963304437165 ,13.646117157631288415  ] 
dist 17=[-9.6202928311727485058 ,8.1952209403157963095 ] 
dist 18=[-12.720879845560159847  ,-1.0076153462073480762 ] 
dist 19=[-15.010388491753158361  ,-.62165560023787889163] 
dist 20=[-20.849355826531839051  ,.01924919619031791126] 
dist 21=[-24.810666576879873194  ,.56618604558540547407] 
dist 22=[-27.408404119185117920  ,1.0740786631817093449 ] 
dist 23=[-28.801015960775445550  ,1.5745762802024331110 ] 
dist 24=[-29.492896655740281136  ,1.9689100567116991488 ] 
dist 25=[-29.517301865232769086  ,2.0655934347890178996 ] 
dist 26=[-28.847467114754317513  ,2.0534206327568333601 ] 
dist 27=[-28.455035237391923591  ,2.0336459637856466006 ] 
dist 28=[-24.536612527725151111  ,.87562254340500982139] 
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dist 32=[-7.7210899129499920749 ,6.9570534959761872972 ] 
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dist 34=[-1.8736128506163881974 ,11.156130018188359049  ] 
dist 35=[-1.4090559606531416529 ,14.819951978510370637  ] 
dist 36=[-1.1316703932768250694 ,17.907937819447364155  ] 
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dist 40=[-1.1108382964644112910 ,6.3446306214733810405 ] 
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dist 44=[-2.5303910720882812254 ,5.1045268269445119531 ] 
dist 45=[-3.0663454031723271758 ,4.8403155565763359743 ] 
dist 46=[-3.5665351434199310506 ,4.6627670057292644881 ] 
dist 47=[-3.9763323704810483793 ,4.6216845577638908937 ] 
dist 48=[-4.1538868284335791782 ,2.7310756789159160738 ] 
dist 49=[-4.2204642838341573183 ,2.6146746296436137309 ] 
dist 50=[-4.2013612365450180216 ,2.3236340480430391787 ] 
dist 51=[-3.8786491096976807204 ,2.2282367343863936873 ] 
dist 52=[-3.7643671231972767889 ,1.2373708230873129361 ] 
dist 53=[-3.5890228494480575342 ,1.0703623287980231987 ] 
dist 54=[-3.8107380689901634239 ,.74876644195075250357] 
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dist 56=[-3.9703757662931477887 ,.98185194470164383083] 
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dist 59=[-3.5952574462502790914 ,2.7058943198120084519 ] 
dist 60=[-2.5167386109285846538 ,2.9831534464839012103 ] 
dist 61=[-2.4091491431714786124 ,3.1447966780848158481 ] 
dist 62=[-2.2477151591727640673 ,3.1855403221274719531 ] 
dist 63=[-2.1880697637210425464 ,.98929839727531719123] 
dist 64=[-.74856682951864943719,1.0250764860724248737 ] 
dist 65=[-.55707452085555364351,1.0374435293257429111 ] 
dist 66=[-.12710049821627247832,1.2731624631404490959 ] 
dist 67=[-.03496836001361496726,1.6647230146743713339 ] 
dist 68=[.09973086217032791686,1.9950357431680001402 ] 
dist 69=[.02499162665950671495,2.1778835334116969763 ] 
dist 70=[-.03841453374114009100,2.2842818010755632785 ] 
dist 71=[-.1009267935116287367 ,2.3110718260569837502 ] 
dist 72=[-.15643274114077573635,.70622531180127935592] 
dist 73=[-.192063098932660059  ,.70630589985990534465] 
dist 74=[-.29950616179406054793,.68322842802143974976] 
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dist 76=[-.48910194864490954223,.55855268103248681612] 
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dist 78=[-.5770512411612491196 ,.50544808041376566721] 
dist 79=[-.6001850228809485659 ,.4969352290498428225 ] 
dist 80=[-.60431423493992073875,.07878829625874170787] 
dist 81=[-.59436733272622536469,.02887909419039576996] 
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dist 162=[6.43331743547319438400e-05,.00230253620622764113] 
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dist 177=[-.00123149109557363748,4.68104294400969180400e-05] 
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dist 182=[-.00088134078890480418,-.00018208022685829392] 
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dist 186=[-.00073492217007128569,.00061331518896197308] 
dist 187=[-.00072777841519222591,.00073708762463031546] 
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dist 200=[-8.12433155918602613050e-05,.00021805004275398761] 
dist 201=[-.00012486229436956188,.00021613991395051680] 
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dist 207=[-.00023408595928882878,.00015705851110711217] 
dist 208=[-.00023227477908675223,9.06673621419558436340e-05] 
dist 209=[-.00022462176601286712,7.97580201318958880910e-05] 
dist 210=[-.00022010300755996244,5.72078818979350141970e-05] 
dist 211=[-.00019177956215502769,5.11209184580547432490e-05] 
dist 212=[-.00018433333535498273,2.87737338841370403220e-05] 
dist 213=[-.00016921452587059253,2.37180968207393755450e-05] 
dist 214=[-.00014424390975292077,1.76904889161259856850e-05] 
dist 215=[-9.70682590172998420700e-05,1.62917078427102927450e-05] 
dist 216=[-9.66063610750781225450e-05,2.84990325855870498640e-05] 
dist 217=[-9.58109216010999178190e-05,4.14076640904450110450e-05] 
dist 218=[-9.18656707286950462710e-05,5.33587849174471134210e-05] 
dist 219=[-9.02895209606067105310e-05,6.35049126851504450210e-05] 
dist 220=[-7.59745393037958403800e-05,6.92469319785560365720e-05] 
dist 221=[-7.24120984322263496240e-05,7.27570197493020983120e-05] 
dist 222=[-6.69988119507374366420e-05,7.40414378518071493310e-05] 
dist 223=[-6.50854014704200937100e-05,7.42677601762277747370e-05] 
dist 224=[-2.09727948810823868520e-05,7.35929388036367086100e-05] 
dist 225=[-1.80024289449010072660e-05,7.21967390153495406440e-05] 
dist 226=[-1.17016325311604392600e-05,7.13152168057457821740e-05] 
dist 227=[-9.99632753949086310880e-06,6.56748809296714608530e-05] 
dist 228=[-3.63569902348956931660e-06,6.41743425443296849070e-05] 
dist 229=[-2.29034811174530668550e-06,5.84849904509779968140e-05] 
dist 230=[-4.61826533389831095760e-07,5.60003800456014736700e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 1, 1, 0, 1] 
dist 0=[110.78993477715222147   ,110.78993477715222147   ] 
dist 1=[107.26165833969632793   ,112.31320328920176789   ] 
dist 2=[103.20601255346587144   ,112.83550098937135514   ] 
dist 3=[99.578231283346782171  ,112.63660393606093412   ] 
dist 4=[95.608275497790866398  ,110.97560185734053219   ] 
dist 5=[90.179545796923658150  ,108.37080638857839428   ] 
dist 6=[84.265867833141320593  ,106.53407199116171005   ] 
dist 7=[78.355942575260841915  ,105.73131366505352403   ] 
dist 8=[71.332597067310152690  ,101.79563927566448578   ] 
dist 9=[60.969750263297219635  ,80.446127141554272468  ] 
dist 10=[50.464341581716789854  ,69.817935382115473687  ] 
dist 11=[42.872700679220558265  ,68.401894284541239584  ] 
dist 12=[35.976518924417052108  ,53.178969792477973544  ] 
dist 13=[28.254111614419775059  ,50.229528056365520551  ] 
dist 14=[20.014592793763327865  ,45.240456315776089384  ] 
dist 15=[11.296941359804816479  ,44.219674113991812838  ] 
dist 16=[-.26646106033567216167,19.934902009763212774  ] 
dist 17=[-11.224560621362581223  ,19.025605149998902605  ] 
dist 18=[-17.540285893458193014  ,6.5103301073052731753 ] 
dist 19=[-21.687230478312748321  ,4.7379571556853465422 ] 
dist 20=[-24.008627830770981412  ,1.3523108555489381726 ] 
dist 21=[-25.481128934446317734  ,.55966899678080356613] 
dist 22=[-26.586732888128619968  ,-1.7546890315140409039 ] 
dist 23=[-27.813419186826876646  ,-2.1406580822110552151 ] 
dist 24=[-28.364329378292840775  ,-1.9791737705693360334 ] 
dist 25=[-28.472870463591113613  ,-1.0470649096974983516 ] 
dist 26=[-17.125937466063827832  ,.01361362328867832914] 
dist 27=[-17.046634279150325143  ,.68845971185831809847] 
dist 28=[-14.092939050317783985  ,1.1969784885204466080 ] 
dist 29=[-13.377450696593010354  ,2.4484001839155307273 ] 
dist 30=[-12.854571850738646404  ,4.9308863361994110480 ] 
dist 31=[-12.715737598713234465  ,7.1340353633080783774 ] 
dist 32=[-2.3143971878190819639 ,9.4748554527396450430 ] 
dist 33=[-1.0942320173760290084 ,11.523479563635913477  ] 
dist 34=[.54718584305222374539,12.569282322400481670  ] 
dist 35=[.19722369349328434502,13.093620576585380007  ] 
dist 36=[-.13039010199882341516,13.174455735792472343  ] 
dist 37=[-.49772902151555862102,12.671425736236045726  ] 
dist 38=[-.84880326754026052044,12.394488945944993416  ] 
dist 39=[-1.1126069729174748407 ,11.970896014116711843  ] 
dist 40=[-1.3561457186424498263 ,11.755185311650929957  ] 
dist 41=[-1.6276330348529730119 ,8.0097008764998477652 ] 
dist 42=[-2.5114804684035872267 ,7.8079870210541670733 ] 
dist 43=[-4.5385447435236481920 ,7.6912812992048191595 ] 
dist 44=[-6.4318941845684919953 ,6.6294068129502295835 ] 
dist 45=[-8.0394420765893673471 ,6.3512616182883642041 ] 
dist 46=[-8.9333999867188427344 ,5.9216238452983657492 ] 
dist 47=[-9.4551468064339639203 ,5.7672463590179506704 ] 
dist 48=[-9.5867154669645542004 ,2.2292295895200901150 ] 
dist 49=[-3.0231282044462119505 ,1.7660094765172627514 ] 
dist 50=[-3.3558111235773675441 ,.85396344180476502249] 
dist 51=[-4.3787228920684294955 ,1.1329085345111424682 ] 
dist 52=[-5.2392347957473916785 ,1.3646689627252183521 ] 
dist 53=[-5.7109815335673499197 ,1.5844415742617463322 ] 
dist 54=[-5.9794082241445008994 ,1.7731903249520691437 ] 
dist 55=[-6.0326635242207973004 ,1.8918592628132087550 ] 
dist 56=[-2.8771350035953758153 ,1.9719683820302652933 ] 
dist 57=[-1.7132726237182367484 ,1.9840569896580359246 ] 
dist 58=[-1.6570305407377872318 ,.13707586575671032801] 
dist 59=[-1.6488905787386008821 ,.39546326046682209645] 
dist 60=[-1.3468731064782994647 ,.84092871175033487514] 
dist 61=[-1.2740482883090273281 ,1.2348607598892706089 ] 
dist 62=[-1.2235187378996550423 ,1.4848894277589783471 ] 
dist 63=[-1.2120461487090743850 ,1.6724138065247300289 ] 
dist 64=[-.14756110209897757011,1.8185618713515199665 ] 
dist 65=[-.02337150527153211113,1.9224386347071528003 ] 
dist 66=[.07423734543793346141,1.9452305516940077103 ] 
dist 67=[.04267081061681390207,1.9334905366574222382 ] 
dist 68=[.01453399028621254593,1.9236810252979124811 ] 
dist 69=[-.01522801476478491043,1.6450107811727089347 ] 
dist 70=[-.04284488865438857368,1.5703832636468774522 ] 
dist 71=[-.06250191167829937286,1.5054883883173699537 ] 
dist 72=[-.07965283807083751872,1.4694999783897983381 ] 
dist 73=[-.09736474869007094876,.83752361521398134148] 
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dist 78=[-1.0842498738542171441 ,.60780999632578808054] 
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dist 80=[-1.1590165447689116329 ,.19821811683965237034] 
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dist 88=[-.37183125691226045992,.09507055295344231880] 
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dist 90=[-.18638502631732696065,.02801994607386658882] 
dist 91=[-.18498966231388987829,.06640747431220208980] 
dist 92=[-.15153709415034045054,.1240688824318536833 ] 
dist 93=[-.14351977792118858106,.17423642937292916494] 
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dist 96=[-.02109679402406933825,.24005753766502066021] 
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dist 100=[-.01221885216509585664,.2434603713394355633 ] 
dist 101=[-.01694812393693429908,.21329558583975355514] 
dist 102=[-.02111535261498897888,.20493108712656221551] 
dist 103=[-.02373474395851552156,.19222769959150100395] 
dist 104=[-.02566901711852123238,.18741219556103328182] 
dist 105=[-.02711917485188458875,.10765658752008687296] 
dist 106=[-.0694535016498327783 ,.10320183150407008524] 
dist 107=[-.10538163623629054134,.10212066301543039896] 
dist 108=[-.13850350012554088936,.08359694958345045995] 
dist 109=[-.16647936406944322351,.07913465301554562964] 
dist 110=[-.18198319444390598166,.07467946273385905891] 
dist 111=[-.19102675637480558456,.07260031430044391799] 
dist 112=[-.19329525650201499838,.02018981246251609286] 
dist 113=[-.05968104912927973585,.01493280518507571120] 
dist 114=[-.06008856192417377258,.01246675244386434143] 
dist 115=[-.05889879906304387453,.01532594815694661180] 
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dist 117=[-.06123271912200694967,.01990276097737515452] 
dist 118=[-.06449641886239201212,.02180576967638557572] 
dist 119=[-.06524032873659871490,.02291416508278648011] 
dist 120=[-.04437761342870679906,.02386948932422818624] 
dist 121=[-.02415738938952374481,.02404259369812879896] 
dist 122=[-.02313893494766516585,.00812660490230062026] 
dist 123=[-.02299189157085617169,.01592618415896167979] 
dist 124=[-.01850469791129798980,.02325788948121564975] 
dist 125=[-.01744367257394411064,.02955289560789235716] 
dist 126=[-.01667621354584168731,.03323761727664985865] 
dist 127=[-.01650615786614664764,.03564663923376115579] 
dist 128=[-.00142806821531456630,.03687819583220698346] 
dist 129=[.00032798401644582156,.03736906131902026810] 
dist 130=[.00440151606273945711,.03731037979567339382] 
dist 131=[.00499924853501735699,.03608834953478315032] 
dist 132=[.00971199811024811244,.03571282101569741861] 
dist 133=[.01040156281651911705,.02971139277834146205] 
dist 134=[.01163704961119856375,.02822149313872842395] 
dist 135=[.00803204799309068163,.02664127041648269304] 
dist 136=[.0012040179930992308 ,.02581884872374259978] 
dist 137=[-.00565743408176693563,.01207810665824769955] 
dist 138=[-.01028058637640619211,.01163876842806548286] 
dist 139=[-.01405866405614977624,.01144893621933903452] 
dist 140=[-.01756543247779602681,.00970804941238842327] 
dist 141=[-.02054629538366481216,.00926848310382650030] 
dist 142=[-.02237630670612777852,.00860362667546426411] 
dist 143=[-.02350180155830932579,.00836504468680494625] 
dist 144=[-.02376006163337187941,.00270729278034507924] 
dist 145=[-.00796266454528349717,.00195512094181879131] 
dist 146=[-.00798147392774594316,.00027697465917272121] 
dist 147=[-.00774570689409010020,-8.85552553543537805330e-05] 
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dist 149=[-.00882570114607130782,-.00221151913013686229] 
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dist 230=[-2.82182062565862584290e-05,6.20726927819464097520e-05] 
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dist 233=[-2.78065810340777806010e-05,3.35672449728140761440e-05] 
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dist 235=[-2.73019581407011464080e-05,3.16071878735274333770e-05] 
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dist 241=[-2.37155991428655024330e-05,3.34631551755647657070e-06] 
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dist 246=[-2.11156828458082328460e-05,1.19313948674919978490e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 0, 1] 
dist 0=[130.77336143506607373   ,130.77336143506607373   ] 
dist 1=[129.69461108110435224   ,130.74096082037754706   ] 
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dist 4=[114.26869405565836525   ,122.81831092037614952   ] 
dist 5=[105.71610958320211830   ,117.27429927719072694   ] 
dist 6=[92.258486709224270933  ,115.30306673430772103   ] 
dist 7=[78.425947110130043121  ,113.67955091110040766   ] 
dist 8=[68.377232124648309815  ,105.66708376834239646   ] 
dist 9=[59.307956322168212051  ,88.591720931034938231  ] 
dist 10=[49.246146580382895173  ,86.904867234852444389  ] 
dist 11=[31.537432740201091242  ,45.691852316336754080  ] 
dist 12=[18.879464944606630051  ,43.203192071038032391  ] 
dist 13=[8.2719252451749131876 ,38.273689229108303379  ] 
dist 14=[-2.1089897150018899914 ,37.140619534094936517  ] 
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dist 16=[-17.657524877825733898  ,24.794507053409975487  ] 
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dist 18=[-27.894305865850063882  ,-1.3940586391417595921 ] 
dist 19=[-32.092310770197018410  ,-8.9517573683933807894 ] 
dist 20=[-33.920363013102181344  ,-8.6724327070234954214 ] 
dist 21=[-34.710941032427048758  ,-7.2056810870928218568 ] 
dist 22=[-34.766318137433831058  ,-3.8527757945964711180 ] 
dist 23=[-31.621160593194415955  ,-.14859292777906773278] 
dist 24=[-30.598498638881257972  ,2.7191830905714729243 ] 
dist 25=[-29.824150215245798418  ,5.4329804257311548504 ] 
dist 26=[-29.227003455429263247  ,8.5383443043666915589 ] 
dist 27=[-9.7843798788255945414 ,11.567236317579063289  ] 
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dist 30=[-.72158506569001993478,19.297539840638683314  ] 
dist 31=[5.3566403444361370069 ,21.890677408866917244  ] 
dist 32=[5.6404014254609624800 ,22.967591555604233108  ] 
dist 33=[9.8272407648742787175 ,23.421462554266494944  ] 
dist 34=[10.156715105888143144  ,23.534742296451829565  ] 
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dist 40=[.98322879351771321277,16.103046845573920667  ] 
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dist 43=[-7.6566305376287098086 ,6.8621010895060011901 ] 
dist 44=[-9.3013500292283509283 ,6.1274658432233311595 ] 
dist 45=[-10.517490536720294650  ,4.4604368307738807945 ] 
dist 46=[-11.434920447062444461  ,4.0049183127918978541 ] 
dist 47=[-12.088157569834677018  ,1.9686080518926401641 ] 
dist 48=[-12.751234182214731200  ,1.5852330900406244358 ] 
dist 49=[-13.361028119005857910  ,.70672387308729967247] 
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dist 53=[-9.7769735333701594961 ,-3.3932050128043974861 ] 
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dist 59=[.27564021094104869535,8.0746926823270613011 ] 
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dist 197=[.00031652529523354986,.00049989726230336866] 
dist 198=[.00015209883087113741,.00049432962327092351] 
dist 199=[-1.27031689509628014230e-05,.00034802728538837179] 
dist 200=[-.00012341543017578801,.00033853731642006169] 
dist 201=[-.00021361206743974224,.00011541458444029720] 
dist 202=[-.00029695534204995372,8.61169827056576059530e-05] 
dist 203=[-.00036760691806549932,2.08510606081718316890e-05] 
dist 204=[-.00040741027012093405,6.23270873511236298180e-06] 
dist 205=[-.00043151074772744205,-6.40475623145214887570e-05] 
dist 206=[-.00043981316027102695,-7.65061116389553755470e-05] 
dist 207=[-.00043953523984715944,-9.65653523173903136150e-05] 
dist 208=[-.00043690954807141997,-.00010077041005248646] 
dist 209=[-.00041843335940121478,-.00010151786322022782] 
dist 210=[-.00041353563404394657,-9.86257033325109762720e-05] 
dist 211=[-.00033967167624444433,-9.27165523442879594540e-05] 
dist 212=[-.00032183115707667848,-8.12982235748913006550e-05] 
dist 213=[-.00030261247592386575,-6.75003494235684222980e-05] 
dist 214=[-.00029296212086362499,-4.56852901742466000000e-06] 
dist 215=[-.00010617678317112376,7.48686228920796104580e-05] 
dist 216=[-9.15446786615805146770e-05,.00012814910786845853] 
dist 217=[-6.03263194357861092070e-05,.00017146686758796937] 
dist 218=[-5.18188477305567282890e-05,.00021134519172537553] 
dist 219=[-1.99167629508360319570e-05,.00024504871259406873] 
dist 220=[-1.66391969630820538950e-05,.00026384821323049877] 
dist 221=[-4.18099888915851045370e-06,.00027531569084409309] 
dist 222=[-1.64703630097646228820e-06,.00027827053443839956] 
dist 223=[2.31877053959680692800e-06,9.79344290398928538500e-05] 
dist 224=[3.30404111461236691880e-06,9.93537268663455036920e-05] 
dist 225=[3.94133563014527010630e-06,9.92207540054784804520e-05] 
dist 226=[2.75763628268744036910e-06,9.84732651650875432650e-05] 
dist 227=[2.59545117604002602990e-07,9.48676317365085921550e-05] 
dist 228=[-4.62047571615069998590e-06,9.30569015750198893090e-05] 
dist 229=[-1.05348921220818631610e-05,7.96781311258207013650e-05] 
dist 230=[-1.71406555950460474570e-05,7.62448562078930999410e-05] 
dist 231=[-2.53865279568343203540e-05,7.01953423324768604220e-05] 
dist 232=[-3.88362522120008897840e-05,6.83409058473988682640e-05] 
dist 233=[-5.14584404374984778800e-05,2.54622100008056071360e-05] 
dist 234=[-6.31092696989940613410e-05,1.95541895163185519840e-05] 
dist 235=[-7.29785433246064153350e-05,9.49803746444534665690e-06] 
dist 236=[-7.85267195500007690760e-05,8.16176411388189045200e-06] 
dist 237=[-8.18709304703174759140e-05,3.11847293037995759460e-06] 
dist 238=[-8.29889647592517002420e-05,2.06270956926292293860e-06] 
dist 239=[-8.29944975414804483620e-05,4.96123820434735425850e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 1, 1, 2] 
dist 0=[101.09897581135439950   ,101.09897581135439950   ] 
dist 1=[97.663702046130109742  ,103.07279047894656564   ] 
dist 2=[91.384827889694636429  ,103.54573170439461978   ] 
dist 3=[84.602344360276509885  ,103.47737480310119382   ] 
dist 4=[79.157381151181942952  ,103.30205253942240802   ] 
dist 5=[73.715708238459772855  ,103.12776295066024472   ] 
dist 6=[66.933601099944998081  ,103.05668289770907336   ] 
dist 7=[59.871301268355800194  ,103.03303881845605301   ] 
dist 8=[53.303632226089604076  ,100.25637745852405821   ] 
dist 9=[45.866232274234215274  ,82.558269639127847872  ] 
dist 10=[35.323430013892716760  ,79.871733045557226414  ] 
dist 11=[24.961063617391260801  ,74.579316064636407793  ] 
dist 12=[18.238418291855233662  ,73.207548406686859690  ] 
dist 13=[12.892078222424245812  ,68.527534861441441983  ] 
dist 14=[8.0165935197351668508 ,65.320233797836527461  ] 
dist 15=[3.7941542101070676764 ,53.683347350096158713  ] 
dist 16=[-2.0797125346843863856 ,46.235358681607896649  ] 
dist 17=[-8.9959901980005792951 ,15.828556489206623685  ] 
dist 18=[-15.488818367129227008  ,14.662855022598754686  ] 
dist 19=[-21.131497457714624517  ,5.1331330211594444875 ] 
dist 20=[-24.668011825367495303  ,3.4399448522307363476 ] 
dist 21=[-27.313539931788256227  ,.82586845392974217173] 
dist 22=[-29.417622491134079243  ,.17350735689007330119] 
dist 23=[-30.895337361870143687  ,-3.5334512986079566339 ] 
dist 24=[-31.217685985010076169  ,-3.0239719778937469017 ] 
dist 25=[-30.819811945340704311  ,-2.3020779018154557107 ] 
dist 26=[-30.749401838264008012  ,-1.1342860065983113293 ] 
dist 27=[-25.879728900046883827  ,.04029676162908984535] 
dist 28=[-24.645427988453686551  ,.79210809327878813724] 
dist 29=[-23.841979552040646416  ,1.3655376696391404744 ] 
dist 30=[-23.619700992682766511  ,1.8338865116297849300 ] 
dist 31=[-17.904254653644671748  ,2.1964350891100644091 ] 
dist 32=[-16.951519566318346378  ,2.3509869935420541411 ] 
dist 33=[.22017014606852109966,4.2271799791969818363 ] 
dist 34=[.22713759081163073453,7.7664502949794631145 ] 
dist 35=[-.51236344012599680479,10.810984600016586229  ] 
dist 36=[-1.0443513694778402172 ,12.608587239825088869  ] 
dist 37=[-1.5085148283388102812 ,13.806246458810637230  ] 
dist 38=[-1.9802294404803607345 ,14.470256105743267145  ] 
dist 39=[-2.4027476652261537079 ,14.807785116430957725  ] 
dist 40=[-2.6724202819341944179 ,14.818079628610296959  ] 
dist 41=[-2.8737084082091009945 ,14.476761665027005497  ] 
dist 42=[-3.0255977832880607865 ,14.279292817518224205  ] 
dist 43=[-3.1850490668481594430 ,12.271281975337140587  ] 
dist 44=[-3.4168008974692871343 ,11.773815924140308407  ] 
dist 45=[-3.7406863738220167435 ,11.037053203925046647  ] 
dist 46=[-4.2663273612249214461 ,10.755415432768934625  ] 
dist 47=[-4.8687508642152420114 ,3.8365745293657435464 ] 
dist 48=[-5.4977156402244588150 ,2.9168273771548007582 ] 
dist 49=[-6.2546983025862616316 ,.83512328825267635136] 
dist 50=[-8.0306915676794880088 ,.39932606318798622703] 
dist 51=[-9.6192856464753007820 ,-.3164989372195769823 ] 
dist 52=[-10.481182890563614235  ,-.20341910500938417629] 
dist 53=[-10.959258916595690622  ,-.10050029323461462989] 
dist 54=[-11.053605407530716720  ,.01128972362420982941] 
dist 55=[-3.4241867562716172930 ,.11657129351517699965] 
dist 56=[-3.4442749114753440151 ,.193826153555605979  ] 
dist 57=[-3.3679302016301076569 ,.26354975914726732236] 
dist 58=[-3.3568379531343583818 ,.33914117749677500852] 
dist 59=[-2.7834142359492570036 ,.4056943554154073281 ] 
dist 60=[-2.6409823749088236212 ,.43961766722783644876] 
dist 61=[-2.5489404525345911665 ,.45643477500355665488] 
dist 62=[-2.5270675372018904482 ,.45880006144153240709] 
dist 63=[-.35558086472372497542,.44032274412834665041] 
dist 64=[-.10154429316321894885,.4305272785798921236 ] 
dist 65=[.24058325332194185355,.57647948863714746979] 
dist 66=[.11616521665719756486,.97064334224037341752] 
dist 67=[-.01054703752174394081,1.3090778622586152535 ] 
dist 68=[-.09680203282207078546,1.5074442394867963776 ] 
dist 69=[-.16784067141934834431,1.6375853023884403218 ] 
dist 70=[-.23423267872203956288,1.7052322639683871938 ] 
dist 71=[-.29061911591008350477,1.7362526398734071260 ] 
dist 72=[-.32198788430750885449,1.7347064261378740732 ] 
dist 73=[-.34033000220716359393,1.6916803378383965578 ] 
dist 74=[-.34494573590837247573,1.6668587031331753968 ] 
dist 75=[-.1138382432142187473 ,1.4361942220585874780 ] 
dist 76=[-.12133509739957226547,1.3755174859336423641 ] 
dist 77=[-.12490463240398277713,1.2838850639262323046 ] 
dist 78=[-.12524751161945580003,1.2500440511596534796 ] 
dist 79=[-.19151877581267283721,.4303046255602966169 ] 
dist 80=[-.49197846855804213136,.32109371945758988266] 
dist 81=[-.73624915113331843176,.07555530564559788965] 
dist 82=[-.9609113548793582968 ,.02283544931901176237] 
dist 83=[-1.1505201530356433810 ,-.01666870107995087883] 
dist 84=[-1.2555104686646386336 ,.00450448322535610366] 
dist 85=[-1.3165986465537858884 ,.02243526830519461512] 
dist 86=[-1.3319568601046604816 ,.04006255310365782394] 
dist 87=[-.40661732041833167137,.05567810772343962253] 
dist 88=[-.40701405270253733226,.06563218447819780983] 
dist 89=[-.3942141501026865237 ,.07314217491071783683] 
dist 90=[-.39190686329182000682,.07906680952401192765] 
dist 91=[-.32288827400116574385,.08335129796351926058] 
dist 92=[-.30623915239254840639,.08435441113665746848] 
dist 93=[-.29257148436755617487,.08404099779168599970] 
dist 94=[-.28796433854757242487,.08309390301344164701] 
dist 95=[-.04647499214664417480,.07356484511709336234] 
dist 96=[-.01764537569145770642,.07080084118831011052] 
dist 97=[.02833773383225939289,.09446474345438792058] 
dist 98=[.01465511968063927818,.14147993738026481327] 
dist 99=[-.00769946141966680905,.18156326676280523994] 
dist 100=[-.02303017872099590557,.20454788416899198601] 
dist 101=[-.03559089065351908604,.21898759095271471411] 
dist 102=[-.0472870720620795036 ,.22514883655705673597] 
dist 103=[-.05724109603158442156,.2265765509568237121 ] 
dist 104=[-.06288725953153023422,.22579775869678274667] 
dist 105=[-.06634570368635904963,.21700280733192700981] 
dist 106=[-.06761639333265089017,.21498735241621264684] 
dist 107=[-.06836371473429138548,.17596693247815039321] 
dist 108=[-.06974555803160397422,.16653673507036320018] 
dist 109=[-.07182884586498576677,.15773026418801777538] 
dist 110=[-.07536238163065902594,.1539064168859553034 ] 
dist 111=[-.07947401538497713058,.03814618942411935783] 
dist 112=[-.08385344778780491504,.02630849543478667478] 
dist 113=[-.08918495296749548654,-.00049539097182065941] 
dist 114=[-.09707798766214732958,-.00583085869718839652] 
dist 115=[-.11326137256216678815,-.00273905533366308165] 
dist 116=[-.12411909238268318221,.00016230531787395724] 
dist 117=[-.13095977902418809536,.00258315190467617706] 
dist 118=[-.13255501864823255809,.00490972246813928512] 
dist 119=[-.05218403557191731453,.00693974891371702754] 
dist 120=[-.05211573255028103794,.00818401447913605455] 
dist 121=[-.05015251635426110807,.00906683518038605098] 
dist 122=[-.04986942487553075478,.00966280854818339707] 
dist 123=[-.04040893756605307967,.01004718556388309598] 
dist 124=[-.03814725307248466351,.01010384525404156989] 
dist 125=[-.03655383057959315257,.01000374521898306241] 
dist 126=[-.03619653271277810866,.00987342552978807533] 
dist 127=[-.00350988631453095950,.00868738549795133872] 
dist 128=[.00030104702795066176,.00835353031864634193] 
dist 129=[.00432747949218142170,.01034593978823350068] 
dist 130=[.00166049744327041526,.01612386423742428168] 
dist 131=[-.00102099535990453290,.02103923120648742118] 
dist 132=[-.00282484230791207394,.02383974424346064917] 
dist 133=[-.00429463692156934603,.02557624380011978964] 
dist 134=[-.00565024456829197398,.02626723966326338779] 
dist 135=[-.00679541571975157988,.02641113281966931693] 
dist 136=[-.00742994394793777009,.02628191076608770740] 
dist 137=[-.00779941598464713037,.02540110716154639630] 
dist 138=[-.00789249780723838845,.02499486114509663030] 
dist 139=[-.00239669737723182947,.02128691153872836109] 
dist 140=[-.00241661792148709275,.02034068531464479339] 
dist 141=[-.00238223074487581946,.01890342107277785503] 
dist 142=[-.00237193865714004183,.01838634834920831736] 
dist 143=[-.00328772349058433710,.00605580797342132655] 
dist 144=[-.00780472710978139995,.00441279691583850397] 
dist 145=[-.01147258092623402282,.00074038572330816178] 
dist 146=[-.01484093670553587603,-5.79632833577275600720e-05] 
dist 147=[-.01768142276416671379,-.00017103441057671442] 
dist 148=[-.01925330729679915666,.00020652226904783518] 
dist 149=[-.02016782690646799495,.00051801112967430696] 
dist 150=[-.02039814637883963346,.00081190734910820949] 
dist 151=[-.00613601711719879838,.00106492867290058702] 
dist 152=[-.00611594810249801112,.00121418444183397476] 
dist 153=[-.00587306131757991984,.00131317705427308782] 
dist 154=[-.00582592813843548403,.00136670494447098590] 
dist 155=[-.00474551377953579017,.00139105927469234544] 
dist 156=[-.00448640934097883379,.00139122375771957451] 
dist 157=[-.00426755473298121135,.00134840917722470931] 
dist 158=[-.00418865791453647723,.00133691583096975715] 
dist 159=[-.00056138329407287673,.00110837781967510982] 
dist 160=[-.00012808107560123321,.00105174231661261646] 
dist 161=[.00049309398444496699,.00151643632570451665] 
dist 162=[.00020588401902287540,.00221021834342234426] 
dist 163=[-8.26396745223730417850e-05,.00279853905663727126] 
dist 164=[-.00027678636200418429,.00313034928528710845] 
dist 165=[-.00043514077513512169,.00333174431167935934] 
dist 166=[-.00058158223137737686,.00340225015483804424] 
dist 167=[-.00070565670379813807,.00340242148591569082] 
dist 168=[-.00077922362941342195,.00338372210018502050] 
dist 169=[-.00082192419179796661,.00323828979622909844] 
dist 170=[-.00083187529385143581,.00320520719359085705] 
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dist 178=[-.00144659816325444431,-9.97906411316013986220e-05] 
dist 179=[-.00173797816744476431,-2.80867530957571398600e-05] 
dist 180=[-.00189980119081786078,2.04249129634410149580e-05] 
dist 181=[-.00199618336188918090,6.02883166782975288680e-05] 
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dist 193=[6.66705349437604352910e-05,.00016414498378745878] 
dist 194=[2.33096905839507772280e-05,.00024907317622978336] 
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dist 196=[-4.93313481733990089070e-05,.00036147130421024430] 
dist 197=[-7.30405764808692780570e-05,.00038586623571397465] 
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dist 240=[-1.95155498941676218090e-05,1.12441307504190511370e-05] 
dist 241=[-2.18388898820000809220e-05,7.32003418307778197550e-06] 
dist 242=[-2.68501392826564917760e-05,6.25710009509534876170e-06] 
dist 243=[-3.10804339911461286480e-05,2.28751251625410551160e-06] 
dist 244=[-3.34318826706397868970e-05,1.44860835358491234420e-06] 
dist 245=[-3.48144708280375460640e-05,2.98303977847446882990e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 0, 2, 2, 0, 1] 
dist 0=[112.89422909974388182   ,112.89422909974388182   ] 
dist 1=[111.47297460477629080   ,113.98748438937139475   ] 
dist 2=[106.92124022479980575   ,115.03676242091119108   ] 
dist 3=[101.66525769210138063   ,115.10402435917035013   ] 
dist 4=[97.222299283953976527  ,113.07810972556572416   ] 
dist 5=[92.575507484330732043  ,112.09257143594497265   ] 
dist 6=[86.496078380395470388  ,110.33180442228627146   ] 
dist 7=[80.009451312193619806  ,109.58845884720551593   ] 
dist 8=[67.547306724504219064  ,86.705937537794034754  ] 
dist 9=[57.985044404442638113  ,83.425732861400099293  ] 
dist 10=[49.122996352140167410  ,76.402755501277517069  ] 
dist 11=[39.063563377701911304  ,73.022215258958111020  ] 
dist 12=[29.133360249030249789  ,56.002108526059929887  ] 
dist 13=[20.769800776084374250  ,52.576695902635398625  ] 
dist 14=[12.002221421640765181  ,48.954779672741469395  ] 
dist 15=[.43822537757822015096,48.099302956677447784  ] 
dist 16=[-10.510207359065173988  ,19.540053313948047949  ] 
dist 17=[-16.835064088762214800  ,15.837004299067599621  ] 
dist 18=[-21.006290350586038737  ,14.904156503950681924  ] 
dist 19=[-23.378227823433473664  ,5.5982706720411232115 ] 
dist 20=[-24.902351634698692907  ,4.1740360932472889509 ] 
dist 21=[-25.690234909476255923  ,1.6813628875613764920 ] 
dist 22=[-26.127782022894490970  ,1.1402124602946518542 ] 
dist 23=[-27.528054171302542671  ,-.08904578544229725089] 
dist 24=[-28.513772194127278338  ,-.09581863860437272390] 
dist 25=[-28.893021863737139328  ,.37766948261194312963] 
dist 26=[-28.731877681562608506  ,1.6071938973763698084 ] 
dist 27=[-19.907222214846258500  ,2.9067657821753587023 ] 
dist 28=[-16.595709375093837812  ,3.6612494499846809337 ] 
dist 29=[-15.779639002194363021  ,4.7255393432252823587 ] 
dist 30=[-15.189878232457476161  ,6.9002372342743205050 ] 
dist 31=[-15.017560119269698761  ,9.2203966169855903300 ] 
dist 32=[-2.9137133334912457162 ,11.254660976205414925  ] 
dist 33=[-1.4886674121181067541 ,12.297031676365152914  ] 
dist 34=[1.8321226725673731525 ,12.822288586259507438  ] 
dist 35=[.96622032724318511774,12.906764780972856643  ] 
dist 36=[.1532621875806245354 ,12.433426197904585729  ] 
dist 37=[-.55989438637731363877,12.165226688080890370  ] 
dist 38=[-1.2966210517559009923 ,11.754570290301271916  ] 
dist 39=[-1.9695247191477142657 ,11.544010208569132551  ] 
dist 40=[-2.4302212274254255927 ,9.5754475869419912422 ] 
dist 41=[-2.8132991144450672402 ,9.5749441915874409062 ] 
dist 42=[-4.4361962060858562254 ,9.3575224482928219588 ] 
dist 43=[-6.2937881625955092754 ,9.2181432894214518848 ] 
dist 44=[-7.8711258292627824954 ,7.9799661144979671431 ] 
dist 45=[-8.7483435099015308406 ,7.6516692612084132871 ] 
dist 46=[-9.2603425285537623461 ,7.1362232312069058121 ] 
dist 47=[-9.3894553772198002355 ,6.9528782259721608511 ] 
dist 48=[-3.2736340222984623536 ,2.8248824127507079108 ] 
dist 49=[-3.1598650011334608635 ,2.2932109648057805784 ] 
dist 50=[-4.0746552606534727796 ,1.0978760892102838691 ] 
dist 51=[-5.3041317938089088034 ,1.1355068342091060152 ] 
dist 52=[-6.3424063122264100953 ,1.6789691545290263877 ] 
dist 53=[-6.9112973923187441305 ,2.1267693197353862800 ] 
dist 54=[-7.2344941083538126385 ,2.5466715319763587601 ] 
dist 55=[-7.2973020386937983748 ,2.9051296979688119275 ] 
dist 56=[-1.9997085088635470345 ,3.1276098823442039954 ] 
dist 57=[-2.0041205872946650859 ,3.2645841130544020310 ] 
dist 58=[-1.9437587715709985931 ,3.2865416144469922051 ] 
dist 59=[-1.9349978457347545983 ,.82200544104068517621] 
dist 60=[-1.5867830833460130389 ,1.2094064604782414199 ] 
dist 61=[-1.5022107995317081065 ,1.4555446172846505663 ] 
dist 62=[-1.4444571759609639771 ,1.6404386691291685152 ] 
dist 63=[-1.4311594106027270063 ,1.7850560785639485974 ] 
dist 64=[-.18213567398458855631,1.8881412497063534998 ] 
dist 65=[-.03630558579008526895,1.9108680550852861971 ] 
dist 66=[.2210035068069504464 ,1.9000650298812024721 ] 
dist 67=[.1099646584700809461 ,1.8905191954379723885 ] 
dist 68=[.03238516272080253654,1.6174055035452874568 ] 
dist 69=[-.03375221666629932453,1.5441656328340952619 ] 
dist 70=[-.09943707495387590148,1.4805537813949853098 ] 
dist 71=[-.15803701770444004668,1.4451789579549884758 ] 
dist 72=[-.19609065644190476046,.98929393535317862982] 
dist 73=[-.31762786039345380308,.9864329224337070464 ] 
dist 74=[-.54594579526765894035,.95760068771781879034] 
dist 75=[-.76090515022699804453,.94293809474884253966] 
dist 76=[-.95832189023164618329,.80774675437134160547] 
dist 77=[-1.0653291379145339361 ,.77278489187810142347] 
dist 78=[-1.1254944216446326798 ,.71977106248872380352] 
dist 79=[-1.1387972844398407170 ,.70049299636935244268] 
dist 80=[-.45508166372506315927,.23802925902286911166] 
dist 81=[-.46285603410303651389,.17647648197085821248] 
dist 82=[-.46310094989389156224,.03858496837396785452] 
dist 83=[-.5476743346190393068 ,.02328185794346149624] 
dist 84=[-.65439734341849210912,.07379193758031226942] 
dist 85=[-.71346524276305936409,.11507495098346302693] 
dist 86=[-.74783376016271100584,.1532969481183895346 ] 
dist 87=[-.7564884297939630001 ,.18563637629584323217] 
dist 88=[-.22698011114538071274,.20357769961023462589] 
dist 89=[-.22671916140015712012,.21404204333208229793] 
dist 90=[-.21890296575679640796,.21667881808767980451] 
dist 91=[-.21720776668781612332,.12176199263459261468] 
dist 92=[-.17905016421070436122,.17114376977739699879] 
dist 93=[-.17005111178873543435,.20119897914038821568] 
dist 94=[-.16133801802649421674,.22227945372042842314] 
dist 95=[-.15810222183036318261,.23605297260651902858] 
dist 96=[-.03170118142733316437,.24464932893959098446] 
dist 97=[-.01625242383188956050,.24578832587661144436] 
dist 98=[.01583900836954017794,.2427488774991630441 ] 
dist 99=[-.00102435758153539101,.23955727325868249541] 
dist 100=[-.01254636076201404647,.20993679651666005347] 
dist 101=[-.02212257975034737306,.2017150449322330433 ] 
dist 102=[-.03126532651746094452,.18922717264098935235] 
dist 103=[-.03920285531344039151,.18449112979218247992] 
dist 104=[-.04399688442112435674,.13617641801621881361] 
dist 105=[-.06828726225609880859,.13549242998112285418] 
dist 106=[-.10364435552187974145,.13018591053037593551] 
dist 107=[-.13624106343015447133,.12859475877510760396] 
dist 108=[-.16377380815862459754,.10652501516763778717] 
dist 109=[-.17903249016761199184,.10112735856976040219] 
dist 110=[-.18793293780946271119,.09495212520808413875] 
dist 111=[-.19016548074073585989,.09201880951633088769] 
dist 112=[-.05871940919546609696,.03520030055610066884] 
dist 113=[-.05912629526100742107,.03044868452375768931] 
dist 114=[-.05796850397681644192,.02026119362403845544] 
dist 115=[-.06742580503049216064,.01747226667257060423] 
dist 116=[-.07836468494774467435,.02130870205003395244] 
dist 117=[-.08447758689123186364,.02594097620973935443] 
dist 118=[-.08833407109269933584,.03026451263553816267] 
dist 119=[-.08923687413159616023,.03395291749369935095] 
dist 120=[-.02075324254991295119,.03610276482439235424] 
dist 121=[-.02008548978109227868,.03773450595058352483] 
dist 122=[-.01771075962382078558,.03806221779800397183] 
dist 123=[.00408967948872477306,.02287578811629646944] 
dist 124=[.00897076830470105011,.02907455099536199560] 
dist 125=[.00873868041334786946,.03270420162004049280] 
dist 126=[.00810270307581621706,.03507877762487809695] 
dist 127=[.00727437437725418607,.03629597182886299189] 
dist 128=[.00627855627118058568,.03678400025066500840] 
dist 129=[.00499097754340813022,.03672778748443869824] 
dist 130=[.00300430370572884042,.03552820249239912874] 
dist 131=[.00099838128286053811,.03515892550350846709] 
dist 132=[-.00036572777382594529,.02925415355752029977] 
dist 133=[-.00149351257217065721,.02778784021914992121] 
dist 134=[-.00256149637595588683,.02623283744714328084] 
dist 135=[-.00348359196435481135,.02542327394114773873] 
dist 136=[-.00556299776228311868,.01005911231813648790] 
dist 137=[-.01011463154367058560,.00882640502024553743] 
dist 138=[-.01383444976380430777,.00612572040625859156] 
dist 139=[-.01728741587899956013,.00536749031942730821] 
dist 140=[-.02022270581116927654,.00237404892784934166] 
dist 141=[-.02202799835885541316,.00177240120767265141] 
dist 142=[-.02313580942376873440,.00062152897700313351] 
dist 143=[-.02338988074869972660,.00035077606924291472] 
dist 144=[-.00783156213221306672,-.00274871278629770217] 
dist 145=[-.00785068363508915054,-.00193617743824276654] 
dist 146=[-.00761976477476986652,-.00070371362644358467] 
dist 147=[-.00758617617349686210,.00053336354627611707] 
dist 148=[-.00622377466960592526,.00136424152350682421] 
dist 149=[-.00589105901047566921,.00204027908969704286] 
dist 150=[-.00566730743323766438,.00266268256086517415] 
dist 151=[-.00561494818488624555,.00318808963476860969] 
dist 152=[-.00065767386223442748,.00347907080180291377] 
dist 153=[-7.83164334868533999870e-05,.00364850315868167821] 
dist 154=[.00104566087312362385,.00369117036908514730] 
dist 155=[.00109918900808941015,.00236179562184779870] 
dist 156=[.00108884115673918788,.00312492122168983702] 
dist 157=[.00104810926253551414,.00356712452731553616] 
dist 158=[.00095643257409073428,.00385073172063800194] 
dist 159=[.00084151696710717923,.00398427374612815773] 
dist 160=[.00070851047998741422,.00403408591664010058] 
dist 161=[.00053955684219502437,.00402324660180542605] 
dist 162=[.00028191396614610704,.00390876798128719634] 
dist 163=[2.26961816969234257330e-05,.00384855254649818101] 
dist 164=[-.00015251941441407350,.00330224150412228651] 
dist 165=[-.00029632507770236886,.00316010888299943386] 
dist 166=[-.00043085576466419681,.00294293054482352267] 
dist 167=[-.00054595625566590700,.00286430756527664524] 
dist 168=[-.00061263034269719932,.00097677648502909801] 
dist 169=[-.00118762615518944088,.00072534817872423876] 
dist 170=[-.00175359275650107122,.00016179632837938239] 
dist 171=[-.00227385948602526710,3.91697527432181413780e-05] 
dist 172=[-.00271277648506263981,-.00044608778551470027] 
dist 173=[-.00295575953836198791,-.00042228622301266582] 
dist 174=[-.00309729771374071297,-.00037319364023128028] 
dist 175=[-.00313287989272834037,-.00031289254277896955] 
dist 176=[-.00093696271514432714,-.00024458569612286663] 
dist 177=[-.00093634125904758571,-.00015873541121476664] 
dist 178=[-.00090428881606573088,-2.87780426412989298450e-05] 
dist 179=[-.00089802236598579818,.00010164175715419678] 
dist 180=[-.00074061508747911761,.00018933076159267147] 
dist 181=[-.00070429778321811528,.00026080884835604209] 
dist 182=[-.00066697698561047158,.00032687070610848523] 
dist 183=[-.00065466623382448569,.00038284376348240673] 
dist 184=[-.00014171592187938624,.00041426858128005633] 
dist 185=[-7.85965752300247292180e-05,.00043531056978635488] 
dist 186=[2.08228307092093862020e-05,.00043995062660432881] 
dist 187=[2.74910443218545586370e-05,.00038807671370422579] 
dist 188=[2.28897336297414656270e-05,.00048284169623626543] 
dist 189=[1.17114623968845948260e-05,.00053683530530292151] 
dist 190=[-1.10653798405707214400e-05,.00057030679143023183] 
dist 191=[-3.89647056620174629260e-05,.00058359501352370168] 
dist 192=[-7.04838388219838540060e-05,.00058554189516629202] 
dist 193=[-.00011005242535777311,.00058266304101477345] 
dist 194=[-.00016991413863060770,.00056017682398400504] 
dist 195=[-.00023000284805450361,.00055319326152029358] 
dist 196=[-.00027047406760230531,.00045907652350615470] 
dist 197=[-.00030355018696535909,.00043597134785289550] 
dist 198=[-.00033427847768913894,.00040904365957844735] 
dist 199=[-.00036043513719030557,.00039647113537542499] 
dist 200=[-.00037536073540885532,9.25671108422810689310e-05] 
dist 201=[-.00038464253522627525,6.47973931769517785250e-05] 
dist 202=[-.00038839203053253046,2.20083638575730419320e-06] 
dist 203=[-.00038914268341604057,-1.06370408391321751830e-05] 
dist 204=[-.00038651758443549299,-6.61008630314452625530e-05] 
dist 205=[-.00038097951228260487,-6.22116620386494312280e-05] 
dist 206=[-.00037634395544680844,-5.46168900679721692540e-05] 
dist 207=[-.00035705563504907324,-4.54153165331880937970e-05] 
dist 208=[-.00011705045115159837,-3.51458669699872112260e-05] 
dist 209=[-.00011677101994599865,-2.23343024907454103200e-05] 
dist 210=[-.00011240984292692686,-3.03884196698016562860e-06] 
dist 211=[-.00011151214935788837,1.62961943375121090750e-05] 
dist 212=[-9.12952008097119534630e-05,2.92651237217902400160e-05] 
dist 213=[-8.64097156152227302260e-05,3.98059961047614424920e-05] 
dist 214=[-8.22190497186321347190e-05,4.95006702488605181970e-05] 
dist 215=[-8.06102340832022660910e-05,5.76844597286999702460e-05] 
dist 216=[-1.18562086301715629160e-05,6.22264635487901966730e-05] 
dist 217=[-3.60563260586009343500e-06,6.49265668409200543120e-05] 
dist 218=[3.02963651905082960670e-06,6.55950598242179120270e-05] 
dist 219=[3.35316597545136038400e-06,4.27341624730918821030e-05] 
dist 220=[2.49032502490555917700e-06,5.41225748147259423510e-05] 
dist 221=[7.26601860857294726790e-07,6.05840603626082635370e-05] 
dist 222=[-2.68204430938771015610e-06,6.45554170342101250250e-05] 
dist 223=[-6.80113226800783533550e-06,6.60569849097989790770e-05] 
dist 224=[-1.13859624902275678420e-05,6.62833781238289862190e-05] 
dist 225=[-1.70985349008332776430e-05,6.58808737617181612490e-05] 
dist 226=[-2.56956892836172571070e-05,6.37368138453725364950e-05] 
dist 227=[-3.43105773480678675580e-05,6.25219356617890623580e-05] 
dist 228=[-4.00936668250163434910e-05,5.40006450395779933660e-05] 
dist 229=[-4.48001364611623421270e-05,5.17709527636375545700e-05] 
dist 230=[-4.91402423165255148480e-05,4.77186756513562115070e-05] 
dist 231=[-5.28129518977599324260e-05,4.64836391896556889350e-05] 
dist 232=[-5.48694772424640471490e-05,1.83198564821789926680e-05] 
dist 233=[-5.60980616855348436340e-05,1.44046558544441315910e-05] 
dist 234=[-5.64833700302626515720e-05,5.80250976126650430570e-06] 
dist 235=[-5.63462599131255083560e-05,3.67738207778098503950e-06] 
dist 236=[-5.57736557433755483950e-05,-1.93510003353313443570e-06] 
dist 237=[-5.42594922475749471210e-05,-1.52076864771530732060e-06] 
dist 238=[-5.33985326282833173020e-05,-7.05978528655264723600e-07] 
dist 239=[-4.79201758817977597720e-05,2.83139810307468357320e-07] 
dist 240=[-1.01877934429096203370e-05,1.38971745165870711490e-06] 
dist 241=[-1.01373875578541324810e-05,2.77208878628221017170e-06] 
dist 242=[-9.98021073648586146690e-06,4.85633543266292769140e-06] 
dist 243=[-9.86197879025216105890e-06,6.94623902578850317700e-06] 
dist 244=[-9.06101265265811976430e-06,8.35110586013170024440e-06] 
dist 245=[-8.84107058477677812220e-06,9.49649143056789699240e-06] 
dist 246=[-7.92446585472975922470e-06,1.05561346314930810690e-05] 
dist 247=[-5.87627177646860718110e-06,1.14552033595338113690e-05] 
dist 248=[-4.78746175565109935990e-07,1.19630344230332048410e-05] 
dist 249=[-8.84123187784417929110e-08,1.22998812834381118120e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 1, 0, 1] 
dist 0=[113.66273693289488518   ,113.66273693289488518   ] 
dist 1=[111.36333636474169154   ,114.80834278454825752   ] 
dist 2=[105.83399136839160632   ,115.74730578166945046   ] 
dist 3=[99.597754076145068161  ,116.29929081250110789   ] 
dist 4=[94.484807239920596781  ,115.89466414974138079   ] 
dist 5=[89.277249244939001934  ,115.09491295709427048   ] 
dist 6=[82.651394278423777046  ,114.24913346329822834   ] 
dist 7=[70.234288697424345790  ,112.72824814181469600   ] 
dist 8=[60.729325547489886809  ,110.57192212690486090   ] 
dist 9=[51.916394032676310927  ,89.345628838584767196  ] 
dist 10=[41.906114881613366059  ,86.086396320613828537  ] 
dist 11=[32.020074638573416600  ,76.960094313242228756  ] 
dist 12=[23.685901473774623101  ,75.641719412190301838  ] 
dist 13=[14.942078271756427032  ,58.053143785109899497  ] 
dist 14=[3.4000180549197778900 ,54.503981496996400130  ] 
dist 15=[-7.5481121595452684748 ,50.964128216394947041  ] 
dist 16=[-13.935112517309116106  ,50.277672773951585014  ] 
dist 17=[-18.224603432588081582  ,12.716028216598481033  ] 
dist 18=[-20.819207516794896276  ,10.962363604630881118  ] 
dist 19=[-22.567424706069288415  ,4.5920579268222327263 ] 
dist 20=[-23.479275926651834035  ,3.5140054115954172786 ] 
dist 21=[-23.988931396024790872  ,2.0302686631821901358 ] 
dist 22=[-25.965505462024105297  ,1.5980822255389483535 ] 
dist 23=[-27.921976331742117422  ,1.4124529135988113090 ] 
dist 24=[-28.667166630709999357  ,1.7658991314656037423 ] 
dist 25=[-28.883723345768220695  ,2.5296654880080298679 ] 
dist 26=[-28.732841162752218255  ,4.0255876567463537006 ] 
dist 27=[-22.262912742376197697  ,5.5355661033029650802 ] 
dist 28=[-22.175517755162823090  ,6.3580165805002810642 ] 
dist 29=[-18.546906049377400621  ,6.8245145954323994994 ] 
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dist 209=[-.00012293721567829962,4.87794957240244774080e-05] 
dist 210=[-.00012145187663607716,3.42738459120737065100e-05] 
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dist 221=[-5.99624476418545233840e-05,8.48714214730295260260e-05] 
dist 222=[-5.84478867037384930550e-05,8.64130686970041606020e-05] 
dist 223=[-5.31995140534607382000e-05,8.63914453690171043480e-05] 
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dist 225=[-3.64474196899217194860e-05,8.26157743906214636810e-05] 
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dist 229=[-2.07478714561075294500e-05,6.09627899467858297980e-05] 
dist 230=[-1.92679394587579062480e-05,5.63326786862628095340e-05] 
dist 231=[-1.79500469861445380360e-05,4.12742503991799327210e-05] 
dist 232=[-1.76074974678434759960e-05,4.18015815115451406770e-05] 
dist 233=[-1.75512876218304839310e-05,4.15662170651024386820e-05] 
dist 234=[-1.76386182240364013440e-05,4.12524772581824325270e-05] 
dist 235=[-2.13365085841719396320e-05,3.93398408688720136070e-05] 
dist 236=[-2.37215617671137851800e-05,3.88725475033542952840e-05] 
dist 237=[-2.51665620158754551040e-05,3.16614955492318669340e-05] 
dist 238=[-2.56662219159070125900e-05,2.99411689024657707220e-05] 
dist 239=[-2.57806968878805162440e-05,2.81276737029942081060e-05] 
dist 240=[-2.56962664523525739120e-05,2.72532464159837730790e-05] 
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dist 242=[-2.51417036306282474430e-05,5.17418629167748656830e-06] 
dist 243=[-2.42932357087958459380e-05,3.39945481504510420250e-06] 
dist 244=[-2.38469149549892447990e-05,2.91678411743462031490e-06] 
dist 245=[-2.27809905660207678230e-05,1.10149487153391675170e-06] 
dist 246=[-2.23122372581772279530e-05,7.20687108936930192660e-07] 
dist 247=[-1.98182436345160725550e-05,1.67203903899182918300e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 2, 0, 0, 1] 
dist 0=[97.584101830247007834  ,97.584101830247007834  ] 
dist 1=[95.318219564845066075  ,98.798209120937700382  ] 
dist 2=[90.953552471146114560  ,98.996571483761338213  ] 
dist 3=[86.119466535376675277  ,98.616561807666737768  ] 
dist 4=[81.983045397782229916  ,97.673338982962429523  ] 
dist 5=[77.607982817109345425  ,97.226708946592427936  ] 
dist 6=[71.813360749715541246  ,96.734833419151703070  ] 
dist 7=[65.590013566033272575  ,96.290602476352245197  ] 
dist 8=[59.498968778133633621  ,92.930064778490240721  ] 
dist 9=[52.355126618730195721  ,74.412010714726209202  ] 
dist 10=[41.924035945627954274  ,73.390913955981242138  ] 
dist 11=[31.560779911751589576  ,70.334084253206716968  ] 
dist 12=[24.684535089912727580  ,69.720104648199244158  ] 
dist 13=[19.046002600456437876  ,65.952924542997442994  ] 
dist 14=[13.619508502320162093  ,59.863109599062467697  ] 
dist 15=[8.7351928646272531324 ,43.578423250585548186  ] 
dist 16=[5.2580586322842490420 ,42.607124073407114141  ] 
dist 17=[2.1332926949366786513 ,24.074276154235822929  ] 
dist 18=[-2.487827001059643239  ,21.603852989663907538  ] 
dist 19=[-8.6799416676224732576 ,15.950802800983888807  ] 
dist 20=[-13.381109830986840785  ,14.882689712115147221  ] 
dist 21=[-18.361004686922773303  ,7.8256714755757909360 ] 
dist 22=[-23.259530194538167822  ,6.5872465735486137843 ] 
dist 23=[-28.239163279408882987  ,4.2794713413434009903 ] 
dist 24=[-31.139026407968606269  ,4.461109624453168891  ] 
dist 25=[-33.058949837429987841  ,6.179464765943639274  ] 
dist 26=[-34.130188987869785585  ,8.359421271955352125  ] 
dist 27=[-34.670552442178398780  ,10.589843501589775054  ] 
dist 28=[-34.477851375259670512  ,12.517063033453837481  ] 
dist 29=[-30.413156965283456898  ,14.552413806990895945  ] 
dist 30=[-26.689840316689690593  ,17.222011961107576328  ] 
dist 31=[-2.5819085747339130059 ,19.635440114192414060  ] 
dist 32=[-2.3173661344351176592 ,20.656442593826751932  ] 
dist 33=[-1.8004329875536355674 ,21.098827304771148090  ] 
dist 34=[-1.6746784429362764848 ,21.209361755395044231  ] 
dist 35=[-.20640089097721430428,18.923167937183441875  ] 
dist 36=[.00749062609134132740,18.325247770785869416  ] 
dist 37=[.42014183077299156469,17.973911747968834005  ] 
dist 38=[.52011703116493054341,17.884784245758908725  ] 
dist 39=[.77505533070602461086,4.2898371034924302642 ] 
dist 40=[.7990618048347765033 ,3.9337159808530746672 ] 
dist 41=[-1.8001659185733069546 ,3.9794094450088234061 ] 
dist 42=[-4.5087733516071748418 ,3.9692879078029541227 ] 
dist 43=[-6.9033822312880731646 ,2.9587332414200509060 ] 
dist 44=[-8.4255307530237566564 ,2.8192221363113493386 ] 
dist 45=[-9.5709645188836512099 ,2.8172725243316345136 ] 
dist 46=[-10.471971366919428674  ,3.0010828081344917532 ] 
dist 47=[-11.133104384059793417  ,3.2828325084682192673 ] 
dist 48=[-11.326683728283849125  ,3.6696010005767444264 ] 
dist 49=[-11.325381752218760050  ,4.1975172616340201055 ] 
dist 50=[-11.211624559707971498  ,5.0394199590678632469 ] 
dist 51=[-10.027780769851953459  ,5.8961914482363766207 ] 
dist 52=[-9.6729142013864448168 ,6.4832098510198593508 ] 
dist 53=[-9.1647904596184229117 ,6.9718293614805483825 ] 
dist 54=[-8.7415875248800967525 ,7.4383622981518465210 ] 
dist 55=[-3.2458527007681956928 ,7.8424641526437403608 ] 
dist 56=[-2.5320929415158585091 ,8.0834668151226386721 ] 
dist 57=[-.90648271345740065592,8.2460435479096690511 ] 
dist 58=[-.5621863726712391755 ,8.3390643803749035123 ] 
dist 59=[-.29118962991572703607,8.3693508566607467090 ] 
dist 60=[-.27006321612820927245,8.2871754599034260248 ] 
dist 61=[-.21641595301174715757,8.1117812175003769631 ] 
dist 62=[-.20767001066264292623,7.7310698518172333099 ] 
dist 63=[-.12467339391953603069,2.5830403514708138386 ] 
dist 64=[-.10941526105209214246,2.6113764358186936308 ] 
dist 65=[-.0879647036211555113 ,2.5820650577728816956 ] 
dist 66=[-.08173961130674907380,2.5777967395342700835 ] 
dist 67=[.02680944235821879303,2.1689691439614943086 ] 
dist 68=[.04004334507840676226,2.0640272235305411394 ] 
dist 69=[.06571329320782579607,2.0016823316595506313 ] 
dist 70=[.07138049510878265744,1.9861404724509337150 ] 
dist 71=[.08607499464110742676,.3150964360962013792 ] 
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dist 203=[-.00025794930127967582,-3.73651845061516237700e-07] 
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dist 206=[-.00031790452665112726,-8.75359171051407324100e-07] 
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dist 212=[-.00024281708478854298,2.39298903646421122140e-06] 
dist 213=[-.00022538732439350366,2.92083342605192545780e-06] 
dist 214=[-.00021913161015803192,3.45631679599992020720e-06] 
dist 215=[-7.11419075870309892020e-05,4.11937041146197295880e-05] 
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dist 227=[-4.56794237142646274220e-06,5.66917721138487142980e-05] 
dist 228=[-4.78010493718465381020e-06,5.36283649822379109590e-05] 
dist 229=[-4.96041884904811470550e-06,5.08864244988815468220e-05] 
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dist 231=[-5.29499606757511536250e-06,9.24433496427633259600e-06] 
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dist 235=[-3.79639014535158595850e-05,9.14365423606805132740e-06] 
dist 236=[-4.19963367365582859950e-05,9.34477319643283880010e-06] 
dist 237=[-4.44095001940631523680e-05,9.77081188448815920990e-06] 
dist 238=[-4.51766027487504536030e-05,1.06041115293654662280e-05] 
dist 239=[-4.50658243622767231490e-05,1.16143282439509751360e-05] 
dist 240=[-4.47703074186570549140e-05,1.27428999125467364320e-05] 
dist 241=[-4.28201556353776283860e-05,1.41517753584787754830e-05] 
dist 242=[-4.23114954137373713410e-05,1.62750420110291721670e-05] 
dist 243=[-3.46935010013056879590e-05,1.84039307496362538210e-05] 
dist 244=[-3.28599606503797792510e-05,1.98351621438458578760e-05] 
dist 245=[-3.08809810649871560220e-05,2.10022970888615681660e-05] 
dist 246=[-2.98918074148304400750e-05,2.20825831941935406900e-05] 
dist 247=[-1.06902519480958909080e-05,2.29995993959571529440e-05] 
dist 248=[-9.19147785502454732420e-06,2.35184670358016703710e-05] 
dist 249=[-6.00552645787394895680e-06,2.38355416501503922930e-05] 
dist 250=[-5.14099301035590316530e-06,2.39513371019614662910e-05] 
dist 251=[-1.90304954991295675670e-06,2.51768198879987387790e-05] 
dist 252=[-1.22049706599613237230e-06,2.70890321474360939200e-05] 
dist 253=[-2.63806926445635356310e-07,2.82158592578729815960e-05] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 2, 0, 2] 
dist 0=[144.50523491306489611   ,144.50523491306489611   ] 
dist 1=[139.28191143440219199   ,146.01690579499072645   ] 
dist 2=[132.23668308818574005   ,146.14665201082672907   ] 
dist 3=[123.47958960987439890   ,145.89729149794293802   ] 
dist 4=[111.96307323778490488   ,144.22106674688016864   ] 
dist 5=[93.946436406449673624  ,132.79772663213426851   ] 
dist 6=[75.544102972104009193  ,129.60352295122577771   ] 
dist 7=[62.488173654230347680  ,126.28279624774409510   ] 
dist 8=[51.051411621799798552  ,109.69188840063705425   ] 
dist 9=[39.069419330017982762  ,95.039399511166161206  ] 
dist 10=[27.835588281431407479  ,90.906349586574681138  ] 
dist 11=[19.358576793857719515  ,90.078797177482021808  ] 
dist 12=[11.343451701628037137  ,48.361337846012924464  ] 
dist 13=[1.9199904413477458940 ,33.630214660320137734  ] 
dist 14=[-6.7712502560189145930 ,31.019992088872321972  ] 
dist 15=[-11.879732186001884061  ,27.206194338201940279  ] 
dist 16=[-16.647928742008472403  ,23.266236004135437205  ] 
dist 17=[-22.734597591457238000  ,-12.625673570916045409  ] 
dist 18=[-27.310684384429666298  ,-15.413833614272342704  ] 
dist 19=[-30.976007235119033826  ,-14.431180494270491446  ] 
dist 20=[-33.736895637403362266  ,-11.767203952700916046  ] 
dist 21=[-34.719672492878737919  ,-6.8202184787354454114 ] 
dist 22=[-34.936570758471348140  ,-1.6397996105878509714 ] 
dist 23=[-34.637771597604262925  ,1.9560234427169039628 ] 
dist 24=[-31.215444422288096602  ,4.9587099794258904319 ] 
dist 25=[-30.156143037099760370  ,7.7966792657939136105 ] 
dist 26=[-28.615638364024942213  ,10.202655965614769594  ] 
dist 27=[-27.966201024598474480  ,11.496535711810700330  ] 
dist 28=[-11.138690969857023818  ,12.182784407976669350  ] 
dist 29=[-8.8959047778071070623 ,12.309076507675572357  ] 
dist 30=[-3.7501145057240864009 ,12.377104613046237919  ] 
dist 31=[-2.7011252510345978245 ,16.999825587637562911  ] 
dist 32=[1.9334776581889857036 ,20.907943147978945387  ] 
dist 33=[3.3857518351188948118 ,23.074516534874510605  ] 
dist 34=[3.4897890063746924303 ,24.336469320757928425  ] 
dist 35=[3.2736511648549282019 ,24.654426086155569369  ] 
dist 36=[2.8527625989751782540 ,7.7724203572467816384 ] 
dist 37=[2.0631962787315339547 ,7.9206595882908330114 ] 
dist 38=[1.2270157313488419170 ,7.9315900038784947645 ] 
dist 39=[.62063275592548841282,7.9189985793229013901 ] 
dist 40=[.08395812798203398666,6.8409524685110087003 ] 
dist 41=[-.47700878181130862451,6.5484137302868155308 ] 
dist 42=[-.99319054037514227271,6.3463889337647717354 ] 
dist 43=[-1.3529573855269474111 ,6.2542934166521169880 ] 
dist 44=[-1.6591550287294084660 ,1.4651525747144605597 ] 
dist 45=[-2.0864561468798537382 ,.89123664374910838191] 
dist 46=[-2.6775966439313373489 ,-.46708310467277027559] 
dist 47=[-3.1477854876742187622 ,-.66569951002019091171] 
dist 48=[-3.5633116335665121562 ,-1.6010079984545813846 ] 
dist 49=[-3.8899167861112594529 ,-1.5527655005014666225 ] 
dist 50=[-4.0095159086838508069 ,-1.4479190037069265480 ] 
dist 51=[-4.2218035862781315032 ,-1.2748245709687950836 ] 
dist 52=[-4.3395938162178089304 ,-1.0239591601588330940 ] 
dist 53=[-4.3534762332635504168 ,-.61051518528207699203] 
dist 54=[-4.2463821244555997041 ,-.18681937019837339621] 
dist 55=[-4.2146352728929961421 ,.14699363956227760728] 
dist 56=[-3.5196881208278742426 ,.46392359852137660081] 
dist 57=[-3.3448780959016565079 ,.75582667003958263713] 
dist 58=[-3.1847981393756109630 ,1.0022085817757526507 ] 
dist 59=[-3.1073676856459229863 ,1.3104529176991492407 ] 
dist 60=[-.88588759031563626703,1.8398462052689395615 ] 
dist 61=[-.65161872648132950906,2.2853503808582540487 ] 
dist 62=[-.11529587378568447083,2.5273575850430881086 ] 
dist 63=[-.01080260746433138505,2.6614089107459671347 ] 
dist 64=[.60905334021080035155,2.6906805616803477089 ] 
dist 65=[.59021494300678986443,2.3896489474549910492 ] 
dist 66=[.54394461957954774698,2.5230968047848854699 ] 
dist 67=[.4783883979035548194 ,2.5545303006580740128 ] 
dist 68=[.38783840944844405331,1.0180265177093386806 ] 
dist 69=[.2423562413065378436 ,1.0238307162253710474 ] 
dist 70=[.09381953893794594134,1.0023097191753930425 ] 
dist 71=[-.00887845891209372618,.99780821106774523802] 
dist 72=[-.09539707037501082973,.8328963011780614297 ] 
dist 73=[-.17977611866467492557,.79149044036044994711] 
dist 74=[-.25413848290309130348,.76117366941509700061] 
dist 75=[-.30093594573961929616,.75056852018661617894] 
dist 76=[-.33557931796598328464,.12507833574774571345] 
dist 77=[-.36174573500892739771,.05095323507896586597] 
dist 78=[-.41331306126799979602,-.12327255472597564582] 
dist 79=[-.46221717682010327071,-.14850658430601377361] 
dist 80=[-.49721122210317450197,-.28244755978246493905] 
dist 81=[-.52104341084767132125,-.26092508970402779466] 
dist 82=[-.52565304394762835202,-.231900293714664255  ] 
dist 83=[-.54263396037214863818,-.19594479939977723742] 
dist 84=[-.54966064506050476275,-.14887395272381121043] 
dist 85=[-.54870606826043987758,-.07572892805075069385] 
dist 86=[-.53060290983351455857,-.00185880693068052499] 
dist 87=[-.5249559068632942891 ,.04809573602270381587] 
dist 88=[-.43689168762472964751,.08902711762339763574] 
dist 89=[-.41504757558216831422,.12709744509359659511] 
dist 90=[-.3914715430070737661 ,.15943390925135697621] 
dist 91=[-.37943448325383713422,.21886687750871231987] 
dist 92=[-.12794059898891893579,.28967863143608873346] 
dist 93=[-.09551191979550475502,.34951497085174351344] 
dist 94=[-.02260388909048896496,.38267640228453933648] 
dist 95=[-.00693125481553041862,.40198809015049303888] 
dist 96=[.07356963876623445377,.40685357667674067895] 
dist 97=[.08513916929140441427,.37370076190639050341] 
dist 98=[.07052594669772038104,.39185851835716455179] 
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dist 100=[.03178025413264250318,.13597664564806900389] 
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dist 159=[5.31796173375140785120e-06,.00663842398169916585] 
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dist 193=[-3.30372177308904612080e-05,.00066789172875132628] 
dist 194=[-7.88034227381762940500e-06,.00069694570090522768] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 1, 1, 2] 
dist 0=[129.51697798754727603   ,129.51697798754727603   ] 
dist 1=[126.85248937323225909   ,130.05905683433005615   ] 
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dist 5=[97.678139448452571281  ,118.23466799287344955   ] 
dist 6=[85.117815858851008042  ,116.10787963972901999   ] 
dist 7=[75.852030274933037716  ,108.40684601482794544   ] 
dist 8=[66.502829709416947747  ,105.41694396639604850   ] 
dist 9=[54.545832768720843852  ,88.082665204791097451  ] 
dist 10=[43.905167166006511139  ,84.308774453583894689  ] 
dist 11=[32.483503066277768088  ,80.206922322355731236  ] 
dist 12=[21.593712484609836879  ,78.663892597782224740  ] 
dist 13=[13.053773234373771058  ,46.245018325314041958  ] 
dist 14=[4.6601514739217491823 ,36.989053015947840699  ] 
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dist 16=[-15.255578411040502044  ,14.660011006192899235  ] 
dist 17=[-20.669050556570052918  ,-.05513818099800690484] 
dist 18=[-24.089060541744883876  ,-2.8915939432115390551 ] 
dist 19=[-25.733549552336395182  ,-4.4934611386492492079 ] 
dist 20=[-29.241247064775182300  ,-3.8267308066430639939 ] 
dist 21=[-32.453753632999421229  ,-1.6089596193563766653 ] 
dist 22=[-33.676841995171989267  ,.97136631455318785783] 
dist 23=[-34.087142626343576889  ,3.0841365686852249995 ] 
dist 24=[-34.053169893978932064  ,5.1777477218004614565 ] 
dist 25=[-30.339396607068501822  ,7.6954995917660541197 ] 
dist 26=[-29.231796923856018044  ,10.211134864926230020  ] 
dist 27=[-28.340309554310512112  ,12.303950302046217677  ] 
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dist 30=[-6.3724828581878340000 ,19.622315441961668450  ] 
dist 31=[-.76228558002355669103,20.664691442522337395  ] 
dist 32=[.08252818276432055441,21.120465930030270293  ] 
dist 33=[7.1533059029940757075 ,21.234310117066382719  ] 
dist 34=[8.2574436702135347753 ,18.962933959113134220  ] 
dist 35=[10.144380336230942197  ,18.368578315094281806  ] 
dist 36=[10.474188813007912448  ,18.883820242449858223  ] 
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dist 40=[-1.7919388494749324251 ,18.972413251169677245  ] 
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dist 42=[-6.8714165687642041487 ,15.322049566361979058  ] 
dist 43=[-8.3729491047634144119 ,14.474786781515107574  ] 
dist 44=[-9.4893332392814925800 ,14.051631784858481500  ] 
dist 45=[-10.342636131317239222  ,6.4118856873585736053 ] 
dist 46=[-10.956379888726985288  ,5.7041176591663466784 ] 
dist 47=[-11.122264693728102058  ,4.1109675353054531980 ] 
dist 48=[-11.102294944328185489  ,3.6702087260199951720 ] 
dist 49=[-11.287341643756513358  ,1.7712113764161711429 ] 
dist 50=[-12.349515457476504907  ,1.4087797465235295987 ] 
dist 51=[-12.931591453407909501  ,.60696255384837861494] 
dist 52=[-13.040977896542821566  ,.42062484288992487197] 
dist 53=[-8.6930708577082380713 ,-2.0569163048273868748 ] 
dist 54=[-3.3324381351536477401 ,.91375959309669445849] 
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dist 57=[-.62564446025584055628,6.0573708184156755388 ] 
dist 58=[.21764975639652251438,7.3329011373841339373 ] 
dist 59=[.32751951495560895124,8.0400636052414877870 ] 
dist 60=[1.0964822364898448777 ,8.4519976732763698818 ] 
dist 61=[1.2145628300838625165 ,8.5557408306964665197 ] 
dist 62=[1.4220029571731723528 ,2.6242273277393514093 ] 
dist 63=[1.4554089819199286955 ,2.6573168158118820889 ] 
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dist 65=[1.9497592869378026138 ,2.6354373232926753278 ] 
dist 66=[1.8849583987234509485 ,2.2556006858203618139 ] 
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dist 68=[1.4482890350165334150 ,2.0802409227268174806 ] 
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dist 71=[-.19958816011663232495,1.5673764810304087594 ] 
dist 72=[-.54715550898994245702,.61713000092062907879] 
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dist 109=[-.34396214713107377023,-.04057613318173099128] 
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dist 111=[-.34511588120257137895,-.05512641602329224705] 
dist 112=[-.17798582661951531378,-.05877195684542737287] 
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dist 118=[-.04509029171232451058,.02113023822049786196] 
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dist 120=[-.00770325264842978549,.07871807680914492364] 
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dist 128=[.03040001936126529318,.04151422167359646571] 
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dist 130=[.02834278580839021520,.03403244693803256800] 
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dist 133=[.01146908308979101787,.03027445813410880368] 
dist 134=[.00178963033902146121,.02257558755423017358] 
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dist 136=[-.01007808285039805135,.00759094862337598247] 
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dist 147=[-.01770723013358776290,-.00618041146841060941] 
dist 148=[-.01675571411061952534,-.00544576767224706539] 
dist 149=[-.01632547550104172956,-.00321146707476718084] 
dist 150=[-.00517134674028127352,.00169996169100144951] 
dist 151=[-.0050799053612388727 ,.00499651983571885894] 
dist 152=[-.00080706758351988984,.00767818456371569587] 
dist 153=[-.00029603698010599066,.01014828970216398548] 
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dist 209=[-.00037849057678857156,-9.76691395559306747360e-05] 
dist 210=[-.00031092060345599137,-9.19609729037512718300e-05] 
dist 211=[-.00029459659901566271,-8.08784233979575644090e-05] 
dist 212=[-.00027701330518256558,-6.74695556254980323560e-05] 
dist 213=[-.00026818178074719549,-4.24991369546245000000e-06] 
dist 214=[-9.72733808789645746280e-05,6.84553445687722842880e-05] 
dist 215=[-8.38826772098898103630e-05,.00011722256635163293] 
dist 216=[-5.53063379873718239910e-05,.00015687282765901567] 
dist 217=[-4.75167440081870024080e-05,.00019337759605996964] 
dist 218=[-1.81287971337713195330e-05,.00022423156629352369] 
dist 219=[-1.39777729460830075800e-05,.00024144427758313622] 
dist 220=[-2.86747964068773150790e-06,.00025196629058754949] 
dist 221=[-3.86528867518548492130e-07,.00025467100345281084] 
dist 222=[5.36706485977139005940e-06,9.37837171055444740980e-05] 
dist 223=[6.32741801410691690230e-06,9.51965767537588408020e-05] 
dist 224=[7.00906344414296706050e-06,9.50996806609283648330e-05] 
dist 225=[5.85373891123291406130e-06,9.44003550845478446290e-05] 
dist 226=[3.40373122755439762130e-06,9.09310624448888789860e-05] 
dist 227=[-1.38989099674281514930e-06,8.92368253491505705990e-05] 
dist 228=[-7.20189502758868633790e-06,7.62445891803811925130e-05] 
dist 229=[-1.36959624317233864960e-05,7.29221746751740593220e-05] 
dist 230=[-2.32251777038958810920e-05,6.72217255996834116650e-05] 
dist 231=[-3.75620522727685047970e-05,6.54261323067687885270e-05] 
dist 232=[-4.92356676007127301840e-05,2.37201084006677902210e-05] 
dist 233=[-6.00127065542026975130e-05,1.80108874913920343240e-05] 
dist 234=[-6.91429576046872308140e-05,9.39187684749645295680e-06] 
dist 235=[-7.42776992793100433960e-05,8.07606700239656388950e-06] 
dist 236=[-7.73753152715197412370e-05,3.10297345703140737920e-06] 
dist 237=[-7.84168150155720647580e-05,2.06322218736401075270e-06] 
dist 238=[-7.84294410655826585780e-05,5.04617041025675934540e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 1, 1, 1, 0, 1] 
dist 0=[149.68582926576619340   ,149.68582926576619340   ] 
dist 1=[147.94540559886385801   ,149.79532507406667628   ] 
dist 2=[144.80598833929830356   ,149.68582926576619340   ] 
dist 3=[137.59041540895596397   ,146.78084057001441141   ] 
dist 4=[128.35563101337975955   ,144.57496725365171530   ] 
dist 5=[117.74620379053658260   ,135.61144244719235481   ] 
dist 6=[104.28814679113495558   ,125.88817057527245939   ] 
dist 7=[83.730029074238672084  ,123.22067509414908483   ] 
dist 8=[62.905594747237944926  ,120.98759530749928660   ] 
dist 9=[48.384398823911139428  ,105.47408659259433439   ] 
dist 10=[35.923501014353217820  ,55.704220932490753453  ] 
dist 11=[23.275359023471366438  ,39.741044758985277593  ] 
dist 12=[11.673938013156395788  ,36.636915440878368508  ] 
dist 13=[3.1331020835171090736 ,19.410348395094262865  ] 
dist 14=[-7.6737632290738619034 ,16.561528530249108889  ] 
dist 15=[-14.841933934644699017  ,12.059666478143089308  ] 
dist 16=[-20.649650125406901413  ,11.173096773149179585  ] 
dist 17=[-26.064787088073696977  ,-11.101372177007003053  ] 
dist 18=[-30.542982928670109083  ,-22.034051504196788077  ] 
dist 19=[-32.629033371282705249  ,-24.505692663647082753  ] 
dist 20=[-33.562117079196653249  ,-23.170979561699521262  ] 
dist 21=[-33.554387440683473749  ,-20.419608915218824781  ] 
dist 22=[-31.383614669594391700  ,-16.220985936986599905  ] 
dist 23=[-30.531246256379883719  ,-9.1372705300178974677 ] 
dist 24=[-29.304016726734932338  ,-1.8546123553876786106 ] 
dist 25=[-28.715422614692416871  ,3.1383128010580302687 ] 
dist 26=[-12.381217351039556372  ,7.2734817883723205698 ] 
dist 27=[-10.189232196596090616  ,11.160777127667552607  ] 
dist 28=[-5.9845374015777609340 ,14.468266716480620083  ] 
dist 29=[-4.0606942848393037325 ,16.306645225381069398  ] 
dist 30=[.75012016066166064374,19.652967406267342417  ] 
dist 31=[2.6504525996895414340 ,21.821609679650765052  ] 
dist 32=[3.0564093373613801801 ,23.086013196285749130  ] 
dist 33=[5.7245438312953924656 ,23.404712947898204303  ] 
dist 34=[6.2244991206737695570 ,7.4409181917595218433 ] 
dist 35=[6.2519047722669206620 ,7.7560788354091210420 ] 
dist 36=[5.9222233018003399585 ,7.8762196575866481510 ] 
dist 37=[5.3303277532000584141 ,7.8903849186585344785 ] 
dist 38=[4.4520942919394759664 ,7.0196317269581023881 ] 
dist 39=[2.9856241829667901935 ,6.7707982281077118931 ] 
dist 40=[1.4741133269773587268 ,6.6053219312116330552 ] 
dist 41=[.41656238662323256019,6.5185323375943601425 ] 
dist 42=[-.48555547639001190956,1.7565819316190208154 ] 
dist 43=[-1.3814110918058598182 ,1.1825187939844797779 ] 
dist 44=[-2.1802864094202400102 ,.16832666206112070908] 
dist 45=[-2.6982181448114229125 ,-.38367792478063600771] 
dist 46=[-3.0991901479845803039 ,-1.5348676544340414465 ] 
dist 47=[-3.5258614614747894686 ,-1.9117795796256940558 ] 
dist 48=[-3.9141987538147320592 ,-2.0452092064513600990 ] 
dist 49=[-4.1851074621215653057 ,-2.8452399744591377542 ] 
dist 50=[-4.3598586103514354650 ,-2.9925161502102167297 ] 
dist 51=[-4.3919352637989989006 ,-2.7830153201699826896 ] 
dist 52=[-4.3226399011368619732 ,-2.4865955706193253061 ] 
dist 53=[-4.2955332183329843035 ,-2.1046271098512202436 ] 
dist 54=[-3.6274731710714663656 ,-1.5963558231166480777 ] 
dist 55=[-3.4547300655013740081 ,-.79858277615983923492] 
dist 56=[-3.3006431645616457390 ,.00925258369220656993] 
dist 57=[-3.2217108724293794001 ,.55756244494184272105] 
dist 58=[-.97313107746341286137,1.0087065995541766399 ] 
dist 59=[-.73430464965665248786,1.4447577102898068503 ] 
dist 60=[-.19507854158419060738,1.8355259772541431978 ] 
dist 61=[-.07766868371167144710,2.0468012444746160148 ] 
dist 62=[.53030099192708223677,2.1859170385053774991 ] 
dist 63=[.67802655647389707146,2.4174993239945377845 ] 
dist 64=[.7712949835905729035 ,2.5536417329724336580 ] 
dist 65=[.9258247251946271807 ,2.5850851372871484901 ] 
dist 66=[.91942481377126446702,1.0411984851202409188 ] 
dist 67=[.86163767268233405565,1.0516871548298736679 ] 
dist 68=[.78092729521668723781,1.0400089383806995784 ] 
dist 69=[.67781181504861991288,1.0363846822316617724 ] 
dist 70=[.54096671537140954533,.87845434246839711445] 
dist 71=[.32634635812424102024,.83746586967932955823] 
dist 72=[.10868545101834951099,.8078074390219804179 ] 
dist 73=[-.04025539845431367870,.79576313846330185859] 
dist 74=[-.16425730974085000344,.15525099065014309355] 
dist 75=[-.28297799170728762024,.07882788004657349701] 
dist 76=[-.38627403000675880733,-.10161230766925113592] 
dist 77=[-.44908085352330031764,-.1277719500155671413 ] 
dist 78=[-.49305423186301434566,-.34347303717949278176] 
dist 79=[-.52163247439857788272,-.37216444519777302544] 
dist 80=[-.54993597540441469706,-.40211259401703349566] 
dist 81=[-.57340195006117724366,-.43752171088109695515] 
dist 82=[-.58437756727475618073,-.42259658506709719019] 
dist 83=[-.58466055237424746632,-.38508845209799943028] 
dist 84=[-.56708481368266708345,-.33704823804312656709] 
dist 85=[-.56225958035904365611,-.28030661166422122815] 
dist 86=[-.46653872716895070019,-.2075769874181191261 ] 
dist 87=[-.4427833523383035876 ,-.09606477885627658697] 
dist 88=[-.4203147110998772448 ,.01618727018026418432] 
dist 89=[-.40949339732729764165,.09185986046248833470] 
dist 90=[-.13856797068921010255,.15368232596014642355] 
dist 91=[-.10467524821733583913,.21096633406674798387] 
dist 92=[-.02822309705371239280,.27770859378033611026] 
dist 93=[-.01186856717548667239,.3344385079524165229 ] 
dist 94=[.07344683408428180990,.36587098371982195962] 
dist 95=[.08811788359019659435,.38854937353405814266] 
dist 96=[.10948954766812973761,.40762364311232036549] 
dist 97=[.11854376667773715587,.41242837442642775216] 
dist 98=[.11854906893018844449,.14848210445362706755] 
dist 99=[.11491378265258189704,.14843249477125538546] 
dist 100=[.09589377436704540144,.14648522967307777143] 
dist 101=[.07403701523660290214,.14444766553571040508] 
dist 102=[.04637829329046210515,.12989554422523098921] 
dist 103=[.00432266979238479941,.12580729551354989252] 
dist 104=[-.03792462563163319054,.11638294329667452784] 
dist 105=[-.06634570368635753487,.11291379527016334047] 
dist 106=[-.08951826774514330945,.06011608950374990892] 
dist 107=[-.11093120177266786597,.05202172335442370802] 
dist 108=[-.12906115459724633445,.03451230794693647057] 
dist 109=[-.13920135536261626216,.02968237679144002645] 
dist 110=[-.1452359513027675629 ,.01110476777392309032] 
dist 111=[-.14706764918057796395,.00730373882571704911] 
dist 112=[-.1467014529751730795 ,.00351034629076502450] 
dist 113=[-.14401059724157264671,.00277736556349338765] 
dist 114=[-.07059716844269055167,.00103117621241615559] 
dist 115=[-.07043986462022022115,.00074914943251283750] 
dist 116=[-.06790904433643725289,-.00155291188005370366] 
dist 117=[-.06728458713817938970,-.00193950657472025653] 
dist 118=[-.05538595334803368241,-.00257864153300984254] 
dist 119=[-.05248210803093802002,-.00271441253480987741] 
dist 120=[-.04972457068112267245,-.00434225521827825783] 
dist 121=[-.04845931459809626732,.00399525283779543230] 
dist 122=[-.01250659775604262471,.01346477628887088014] 
dist 123=[-.00877309762156450757,.02118559134416317260] 
dist 124=[-.00603426561385092387,.02832134031469069320] 
dist 125=[-.00585024329646403849,.03436490031728612426] 
dist 126=[-.00403704316772968668,.03791055478323174512] 
dist 127=[-.00290624141186791443,.03999705369370593909] 
dist 128=[.01506818526579465426,.04143635064050349363] 
dist 129=[.01581995447607345567,.04193394957139953992] 
dist 130=[.01567411573929868302,.01632732399843193323] 
dist 131=[.01512134457166897313,.01633049927090712288] 
dist 132=[.01388488701987497131,.01576915430697600008] 
dist 133=[.01233732677378734541,.01568817427551273396] 
dist 134=[.01054919913465705544,.01277489559110460069] 
dist 135=[.00827970394385849195,.01207266525243788302] 
dist 136=[.00482080851703183971,.01158729592940619736] 
dist 137=[.00134111013547685868,.01147716732939310065] 
dist 138=[-.00101112525285632112,.00121839601148488517] 
dist 139=[-.00294205403846100322,2.12569585322951307200e-05] 
dist 140=[-.00474929691992635964,-.00275594755262057412] 
dist 141=[-.00629635909818389624,-.00317006433657079396] 
dist 142=[-.00719445306787389573,-.00638557875014619993] 
dist 143=[-.00777251494464405417,-.00685895530774841515] 
dist 144=[-.00804916600570026606,-.00748527372552989327] 
dist 145=[-.00826456201736624427,-.00783293833988139811] 
dist 146=[-.00833236277494668839,-.00790713409662754945] 
dist 147=[-.00829889775929977226,-.00749987439046142639] 
dist 148=[-.00803642310843234184,-.00668906309095804684] 
dist 149=[-.00791050564356073894,-.00570196879410877657] 
dist 150=[-.00675296372669794371,-.00459473429661980140] 
dist 151=[-.00645567826540063450,-.00321000265630451556] 
dist 152=[-.00600598505651166928,-.00112108271523783185] 
dist 153=[-.00584277208650066179,.00097283393563752040] 
dist 154=[-.00194795415588645357,.00237743883443649035] 
dist 155=[-.00143152853923112918,.00351897129023283101] 
dist 156=[-.00027606392383991817,.00456843267319365518] 
dist 157=[-2.45917661976812119410e-05,.00545383538004127219] 
dist 158=[.00123230546560885395,.00594400990615292892] 
dist 159=[.00145149276244252273,.00622949655536576628] 
dist 160=[.00181279640932864909,.00635339057465327998] 
dist 161=[.00187707820362716255,.00642618838750800274] 
dist 162=[.00184452393927402079,.00196935406075372363] 
dist 163=[.00176331635600604708,.00196506151210438758] 
dist 164=[.00159669149567270357,.00188723655506646437] 
dist 165=[.00139226440193464653,.00187600458250910299] 
dist 166=[.00116094665798173152,.00151568269360514907] 
dist 167=[.00087033757010290569,.00143569221417205032] 
dist 168=[.00043047895518856125,.00136860626659022995] 
dist 169=[-1.10863631952371352070e-05,.00135462677966396314] 
dist 170=[-.00030848336083611827,.00026768854216493457] 
dist 171=[-.00055151545909224994,.00013711062217254354] 
dist 172=[-.00077724257761670759,-.00016372943381430160] 
dist 173=[-.00096934043138051236,-.00021441645240327015] 
dist 174=[-.00107885836087146884,-.00056196980727900368] 
dist 175=[-.00114683814314490135,-.00061553984970856573] 
dist 176=[-.00117402303715469245,-.00071376825610239823] 
dist 177=[-.00118961125593032676,-.00073138259684912766] 
dist 178=[-.00119071414607086135,-.00071484872520326169] 
dist 179=[-.00118419725414948498,-.00067260667082721977] 
dist 180=[-.00113538018231455483,-.00058931907235972720] 
dist 181=[-.00112227787928783348,-.00048815649202637634] 
dist 182=[-.00092308886151597444,-.00037493474536410235] 
dist 183=[-.00087484116837979809,-.00023347718392290399] 
dist 184=[-.00082301353570275304,-2.01969468257491400000e-05] 
dist 185=[-.00079685699180544379,.00019362616486685523] 
dist 186=[-.00029190843545930950,.00033724282123670387] 
dist 187=[-.00025223583605834317,.00045419054379419978] 
dist 188=[-.00016733380870670073,.00056212767858858750] 
dist 189=[-.00014411788861807053,.00065351654376445063] 
dist 190=[-5.60866320853875436360e-05,.00070476089889405585] 
dist 191=[-3.77417063764308188440e-05,.00073829290942175238] 
dist 192=[-9.57649805072085193010e-06,.00074628048714058831] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 0, 2, 0, 1] 
dist 0=[124.71822793028464044   ,124.71822793028464044   ] 
dist 1=[122.76746348979887052   ,126.30006741209054023   ] 
dist 2=[118.89776730874007580   ,128.69224354399647404   ] 
dist 3=[112.49731706520499222   ,130.75264231130201214   ] 
dist 4=[100.48912226623251679   ,131.02046539899854542   ] 
dist 5=[87.724990322677832130  ,130.39492516016251087   ] 
dist 6=[78.316584765476338968  ,129.59212704120250875   ] 
dist 7=[69.708938835912015944  ,109.34929135876756345   ] 
dist 8=[60.111166306654116725  ,106.13265257984077578   ] 
dist 9=[50.741472757109532676  ,96.432608570731499972  ] 
dist 10=[43.025654359257891723  ,95.039293587872178975  ] 
dist 11=[35.091583050220419104  ,74.159482920044601066  ] 
dist 12=[24.827628624299058715  ,69.815337462279802530  ] 
dist 13=[14.992382849559965603  ,65.751946127230648436  ] 
dist 14=[8.4744953334950648707 ,64.973620085805156382  ] 
dist 15=[-1.8356308186514484292 ,15.674147989601933774  ] 
dist 16=[-7.9645770604954007523 ,9.9509093605011056315 ] 
dist 17=[-12.225093228985064254  ,-.94824238049753160696] 
dist 18=[-15.091859203865559286  ,-1.7922435892355531379 ] 
dist 19=[-20.746048578268955317  ,-1.9272331282037800181 ] 
dist 20=[-25.019231003192372411  ,-.94078654520347344079] 
dist 21=[-27.889427811949011128  ,.29763347064060267334] 
dist 22=[-29.568481610917611084  ,1.2436691684238037280 ] 
dist 23=[-30.511009863039870056  ,2.0752402644451319037 ] 
dist 24=[-30.608739841603706806  ,2.8735720908775233536 ] 
dist 25=[-30.065081257317897980  ,3.5161990034539912204 ] 
dist 26=[-29.678774041723420872  ,3.7367023094815400309 ] 
dist 27=[-25.735145066241705685  ,3.7902634713810680728 ] 
dist 28=[-24.688752068205760047  ,3.7812253798007074337 ] 
dist 29=[-23.155054823730782508  ,2.8302725366077254811 ] 
dist 30=[-22.566652938047756818  ,4.7216168483427691776 ] 
dist 31=[-8.2244842726057370417 ,6.4162406221701749367 ] 
dist 32=[-6.3281607362830445011 ,7.3098655333574190023 ] 
dist 33=[-2.0466757895855993496 ,11.359853153276614460  ] 
dist 34=[-1.2985721157987659310 ,15.204446820568457028  ] 
dist 35=[-.96545860220570118654,18.447966276135589101  ] 
dist 36=[-.88311825955178425737,20.243504645514849769  ] 
dist 37=[.4185262234235382902 ,21.289088743178459830  ] 
dist 38=[.58366676691709332459,21.552089435012823328  ] 
dist 39=[.89121431066239340587,6.7005380057679012208 ] 
dist 40=[.95620705290516479152,6.7379957028003133684 ] 
dist 41=[.06812954750367370195,6.5950759099200391779 ] 
dist 42=[-1.0409061616105534783 ,6.5631782160857986007 ] 
dist 43=[-2.0441908350791531354 ,5.5090059618251880467 ] 
dist 44=[-2.7185311596341493498 ,5.2560016999584671366 ] 
dist 45=[-3.2673337709567390241 ,5.0186468369809224498 ] 
dist 46=[-3.7737044621738720271 ,4.9369288757615615389 ] 
dist 47=[-4.1860096493398467388 ,1.2795833680972999186 ] 
dist 48=[-4.3618233494921301042 ,1.2294218188971569618 ] 
dist 49=[-4.4250147676625456455 ,.89086734153010360831] 
dist 50=[-4.4027115933408230820 ,.82349597593106967268] 
dist 51=[-4.0587699311347425620 ,.69625887811465235645] 
dist 52=[-3.9387413218531950097 ,.66374128909514305003] 
dist 53=[-3.7501384694654255573 ,.59097415219252462126] 
dist 54=[-3.8448158741730384504 ,.64269467773062553594] 
dist 55=[-3.8910566325587201108 ,.68230879322639234955] 
dist 56=[-3.8829158388680007640 ,1.1642079519280746053 ] 
dist 57=[-3.7532302806892437463 ,1.8200707637554130095 ] 
dist 58=[-3.7118347068803466409 ,2.4260542351276247781 ] 
dist 59=[-3.0932060979357898154 ,2.9373307919407254119 ] 
dist 60=[-2.9398261771607841689 ,3.2174848872215496759 ] 
dist 61=[-2.7698881869745663396 ,3.3759460338587698241 ] 
dist 62=[-2.6855477380419414036 ,3.4044120851706410559 ] 
dist 63=[-1.0780404533541071172 ,.99781434937358694768] 
dist 64=[-.94148951867173207288,1.0769546345591734609 ] 
dist 65=[-.64426832264803120361,1.4800846219364443326 ] 
dist 66=[-.56169190546422111032,1.8530706129002745995 ] 
dist 67=[-.24009602648448020959,2.1694362982478467717 ] 
dist 68=[-.17512270427433387184,2.3545537903360998053 ] 
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dist 189=[-1.48118471938306369070e-05,.00085201669985826151] 
dist 190=[-6.34877983893062309470e-06,.00086125606600502411] 
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dist 200=[-7.81669152027503931770e-05,4.37844268425808173480e-06] 
dist 201=[-9.89366320336673593870e-05,-4.42076428247692597420e-05] 
dist 202=[-.00011071258380129744,-5.13631407776525024420e-05] 
dist 203=[-.00012690249923153943,-9.12510387552674218040e-05] 
dist 204=[-.00014280036529053035,-9.29014706648059406060e-05] 
dist 205=[-.00015261642120768963,-9.46660276152438299820e-05] 
dist 206=[-.00015642728322884465,-9.23728239182201103040e-05] 
dist 207=[-.00015697066762608583,-8.77054864767210775360e-05] 
dist 208=[-.00015624272080801148,-7.86990860429279485550e-05] 
dist 209=[-.00015009462123365520,-6.78206809379132658230e-05] 
dist 210=[-.00014840906972795800,-5.57198121883294013490e-05] 
dist 211=[-.00012242369325747615,-4.05844646423437758180e-05] 
dist 212=[-.00011609760120047862,-1.36624892184267315070e-05] 
dist 213=[-.00010934174504207601,1.32982301263187928030e-05] 
dist 214=[-.00010589848507433708,3.13676081507546729120e-05] 
dist 215=[-2.68601695719237041150e-05,4.60408935820464330670e-05] 
dist 216=[-1.79539261017708924480e-05,5.95171470619386520520e-05] 
dist 217=[2.16497831073089006170e-06,7.08820722076534657010e-05] 
dist 218=[6.17028088740878062400e-06,7.71720927038668493700e-05] 
dist 219=[2.33473579476799444120e-05,8.52882011255176906100e-05] 
dist 220=[2.42687921787389841510e-05,9.33213374224047421540e-05] 
dist 221=[2.44443212977848210590e-05,9.81270165949606344550e-05] 
dist 222=[2.38821371811418569620e-05,9.92943710286872189160e-05] 
dist 223=[2.27176367116575920100e-05,3.99968328676283455050e-05] 
dist 224=[2.04569158295630947240e-05,3.97980206414831218210e-05] 
dist 225=[1.77216733221218378430e-05,3.84796207683402902130e-05] 
dist 226=[1.46728549730409019760e-05,3.78499487954729103020e-05] 
dist 227=[1.02954253350627824220e-05,3.23174777782193434310e-05] 
dist 228=[1.08087323556355842380e-06,3.08995827997201770230e-05] 
dist 229=[-8.14265567911667556500e-06,2.86898164466322462100e-05] 
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dist 231=[-1.93290432030621095810e-05,9.48224281483390282860e-06] 
dist 232=[-2.39214302890569258180e-05,7.01291353534995592580e-06] 
dist 233=[-2.77883047741750397990e-05,1.49894922725167650760e-06] 
dist 234=[-2.99175347978967013100e-05,2.83810881863463276950e-07] 
dist 235=[-3.11422200146126049030e-05,-1.21055826196875132610e-06] 
dist 236=[-3.14173877992850017030e-05,-1.48781561924915682700e-06] 
dist 237=[-3.12667818321381472720e-05,-1.53770265073058576100e-06] 
dist 238=[-3.08008393089366965400e-05,-1.37454686833374629280e-06] 
dist 239=[-1.47045460743875671850e-05,-1.02798563205746803220e-06] 
dist 240=[-1.45453947803866285260e-05,-3.49536564436841080450e-07] 
dist 241=[-1.18813846927997861380e-05,4.73172976675048267360e-07] 
dist 242=[-1.12420170796450837610e-05,1.39259981167794482510e-06] 
dist 243=[-1.05979209488724237580e-05,2.54064187356751202370e-06] 
dist 244=[-1.02973554151546711150e-05,4.27116934827085646860e-06] 
dist 245=[-7.08942011639994731090e-06,6.00658767043089090810e-06] 
dist 246=[-6.90453003372974054920e-06,7.17407980109533811030e-06] 
dist 247=[-2.05077614899696903360e-06,8.12706520878442465400e-06] 
dist 248=[-1.76308792925741889600e-06,9.01077242755522399870e-06] 
dist 249=[-6.76259042384148861300e-07,9.76213512894105092200e-06] 
dist 250=[-4.48933540647936722060e-07,1.01896412803710791600e-05] 
dist 251=[-1.09242801287833131440e-07,1.04761452278979894090e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 0, 0, 0, 1] 
dist 0=[149.84612424952035906   ,149.84612424952035906   ] 
dist 1=[148.10322466385039521   ,149.95273464488830909   ] 
dist 2=[144.95895597970543396   ,149.84612424952035906   ] 
dist 3=[137.77442033254398781   ,146.91579963546197579   ] 
dist 4=[128.55359892817807641   ,144.69712621123946125   ] 
dist 5=[117.95903066136304699   ,135.75357300869342263   ] 
dist 6=[104.51904040006067000   ,125.91038348062068994   ] 
dist 7=[83.987621359204548429  ,123.27393572323268804   ] 
dist 8=[63.189737582108288248  ,121.02976648610528962   ] 
dist 9=[48.686019362730922032  ,105.56721622249304977   ] 
dist 10=[36.238964372622400978  ,55.389865770688078120  ] 
dist 11=[23.602938869890380123  ,39.379364587513661875  ] 
dist 12=[12.011308947631418533  ,36.252822690811211492  ] 
dist 13=[2.7049198103547623590 ,19.079769572798913456  ] 
dist 14=[-8.1334382085017213927 ,16.230534505151643115  ] 
dist 15=[-15.314059248056371012  ,11.844871695721064704  ] 
dist 16=[-21.122348574901102550  ,10.955285098782695002  ] 
dist 17=[-26.521815574695096471  ,-11.201211985849947517  ] 
dist 18=[-30.974788983262894478  ,-22.504590666956490850  ] 
dist 19=[-33.023502109276098757  ,-24.255696205554203048  ] 
dist 20=[-33.928886985253461551  ,-22.972593074939985826  ] 
dist 21=[-33.893284899076617218  ,-20.276624058981910237  ] 
dist 22=[-31.560547424078564712  ,-16.145652151253451122  ] 
dist 23=[-30.667758578270993281  ,-9.1621699080472593424 ] 
dist 24=[-29.465041211088049282  ,-1.9791591643714118092 ] 
dist 25=[-28.855565124607964173  ,2.9484454264101581981 ] 
dist 26=[-12.294079687354767536  ,7.0322385946130677745 ] 
dist 27=[-10.119952492379616420  ,10.875254838863362836  ] 
dist 28=[-5.3457042465805082390 ,14.147533747975909973  ] 
dist 29=[-4.0399351511178686378 ,15.970546404723632866  ] 
dist 30=[1.5617223601517185584 ,19.404645948807954718  ] 
dist 31=[2.7956520308699228404 ,21.568188272127734641  ] 
dist 32=[3.8624037193294269596 ,22.822164695897471278  ] 
dist 33=[5.6959057334682021356 ,23.120620640472566510  ] 
dist 34=[6.4188371799315339040 ,8.0335872679145938990 ] 
dist 35=[6.3284080497933899201 ,8.3417321680794142335 ] 
dist 36=[6.0303155958183652870 ,8.4402634441254813750 ] 
dist 37=[5.4706673249656292104 ,8.3985569721366459330 ] 
dist 38=[4.6306561998259520604 ,7.7801758154424246969 ] 
dist 39=[3.2194775081177934241 ,7.5673408062988019144 ] 
dist 40=[1.4206527587879081440 ,7.1437760243112808030 ] 
dist 41=[-.79662367264634472358,6.9855590853403888461 ] 
dist 42=[-2.3100373734323504459 ,3.5721606818013758774 ] 
dist 43=[-3.5624883899298087314 ,2.9062177608658834462 ] 
dist 44=[-4.7451219044369414952 ,2.3193749602066068995 ] 
dist 45=[-5.7597977725402941292 ,1.4665039917440841763 ] 
dist 46=[-6.3462052161115148401 ,.81980076493947977633] 
dist 47=[-6.7184525695181368641 ,.28986129301952229177] 
dist 48=[-6.8853826968191847983 ,.2013473322604269394 ] 
dist 49=[-6.9353454129954950839 ,-.42419007605781553924] 
dist 50=[-3.9783482218419328520 ,-.52932231008201492753] 
dist 51=[-4.0225748455455724292 ,-.6595951666136776044 ] 
dist 52=[-4.0052189080293191835 ,-.65819380400729255148] 
dist 53=[-3.9586626967714535496 ,-.60696870856210296653] 
dist 54=[-3.5079714364666589299 ,-.48928319189694996825] 
dist 55=[-3.3777311657592607147 ,-.30424189501455214682] 
dist 56=[-3.1824458253120624583 ,.21275347128582478001] 
dist 57=[-3.1056003656883788050 ,.84609334852730167902] 
dist 58=[-1.1672806659659859843 ,1.3641351507529147691 ] 
dist 59=[-.90850483238205680504,1.8442010486226699587 ] 
dist 60=[-.31899052592284364929,2.2505355424210625204 ] 
dist 61=[-.19538021354202964646,2.4762430048458066133 ] 
dist 62=[.48232161135532259   ,2.6224165468469944687 ] 
dist 63=[.59705426022831833226,2.8749427100242477362 ] 
dist 64=[.80736696042808043999,3.0220075255321915335 ] 
dist 65=[.82506258007570916727,3.0589519560884452408 ] 
dist 66=[.81506103854054000091,1.7730899307934762935 ] 
dist 67=[.76149603114198348727,1.7720072392505818118 ] 
dist 68=[.68653545286317210635,1.7718132332686744899 ] 
dist 69=[.59061860245792185167,1.5118804257280151761 ] 
dist 70=[.46325054742667390113,1.4445943278905339011 ] 
dist 71=[.26342648664264841647,1.4053076587543884265 ] 
dist 72=[.06076710406435847378,1.3953990710432298549 ] 
dist 73=[-.07788043089013621799,.73179915769740624305] 
dist 74=[-.19327487279175903639,.15268507907524998978] 
dist 75=[-.30368369012841731692,.08369432144923036646] 
dist 76=[-.46216977352651995856,-.07938735603171613990] 
dist 77=[-.64931363603079508473,-.10320502103920137001] 
dist 78=[-.76274848326292454704,-.26665655569041443414] 
dist 79=[-.84177549012663813334,-.27510747024110401523] 
dist 80=[-.89240265093677353064,-.33049526159568038394] 
dist 81=[-.92338546333500669385,-.33143594740662721037] 
dist 82=[-.92720370635502718483,-.3194158537515826317 ] 
dist 83=[-.91464579985074479768,-.2869939345799954311 ] 
dist 84=[-.90247164975165517711,-.24492090757603079382] 
dist 85=[-.78969804595419425773,-.19458092212341275264] 
dist 86=[-.75857664779096118752,-.12966282855495298749] 
dist 87=[-.71121983974539684639,-.02971358994098311578] 
dist 88=[-.69335678135236036171,.07105689808709854891] 
dist 89=[-.38327468809106073764,.13924172486194245341] 
dist 90=[-.19200484106086922194,.25660465254788632138] 
dist 91=[-.09361959244383617998,.39001212299226702939] 
dist 92=[-.04499889920567764680,.51295682480285339151] 
dist 93=[-.03559480726899497366,.61678227191617262873] 
dist 94=[-.01509048054923368407,.67429708165673922713] 
dist 95=[-.00997088821787440951,.70778144747451153421] 
dist 96=[.11598245123074279208,.71621668815188011646] 
dist 97=[.12027793810853179437,.31363831598378471935] 
dist 98=[.12710232543043036579,.21955889359797409541] 
dist 99=[.12615916560731220506,.21539689290333634674] 
dist 100=[.12189078626414881268,.21433219507450884004] 
dist 101=[.11209943832187271215,.17998429715921007652] 
dist 102=[.09978014851291991656,.17126115248637867335] 
dist 103=[.08547322790822884833,.16450695695796767337] 
dist 104=[.0644252471392427211 ,.16175122081914174998] 
dist 105=[.01433525587340254193,.09225537744447182098] 
dist 106=[-.01959436360879112174,.01397790818913705350] 
dist 107=[-.04751110598537649608,.00213606664012670837] 
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dist 163=[.00192537312856864399,.00335680231192277333] 
dist 164=[.00184293365791264683,.00333755105419308792] 
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dist 169=[-2.93565606442872568260e-05,.00135722620083292603] 
dist 170=[-.00056581199659522841,.00026227083637138021] 
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dist 173=[-.00175561299574588834,-.00038639801748543263] 
dist 174=[-.00195196827686487016,-.00077518691919558341] 
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dist 176=[-.00211991440757927605,-.00093505875354261863] 
dist 177=[-.00212507892503557061,-.00095027195903586180] 
dist 178=[-.00211446652887835279,-.00097604593056865489] 
dist 179=[-.00202953324882566105,-.00094931537089338768] 
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dist 182=[-.00156680878274000625,-.00067293610687007828] 
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dist 184=[-.00142790646753951888,-3.31084353274353500000e-05] 
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dist 187=[-.00030562203043062009,.00082171719572376321] 
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dist 190=[-7.17599935406261131810e-05,.00127246957284931999] 
dist 191=[-1.91750397266533969870e-05,.00133166402093377630] 
dist 192=[-5.99827367305184901380e-06,.00134603886091094109] 
dist 193=[.00022730548109552833,.00076864986474875545] 
dist 194=[.00022834890025490417,.00047626187471548966] 
dist 195=[.00022295192448287361,.00045937336923855113] 
dist 196=[.00021200396705266052,.00045347230629510902] 
dist 197=[.00019090212786994294,.00037999319696574686] 
dist 198=[.00016542007324935523,.00036171326853619722] 
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dist 200=[6.66427735626809383930e-05,.00032922879948701615] 
dist 201=[-3.12358211930938573130e-05,.00021177313711026313] 
dist 202=[-.00010984710550667780,.00013523977140528021] 
dist 203=[-.00017269184745764905,.00012188205413674286] 
dist 204=[-.00023119241190900224,9.49538281761447580440e-05] 
dist 205=[-.00028068393515778374,8.76603270745734882580e-05] 
dist 206=[-.00030837418703294581,6.11070182778331769400e-05] 
dist 207=[-.00032488793286763005,5.46779239769958730690e-05] 
dist 208=[-.00033000217169021500,4.75190518183442939200e-05] 
dist 209=[-.00032930302113449595,4.55437198350571071600e-05] 
dist 210=[-.00015212770489083237,4.50473038614244199090e-05] 
dist 211=[-.00014686668401542154,4.57426153431762056840e-05] 
dist 212=[-.00014488323055387151,4.74255374366657987850e-05] 
dist 213=[-.00013701608954843361,5.08514129826195270950e-05] 
dist 214=[-.00011627180003887696,5.50478576504734336610e-05] 
dist 215=[-.00010958709808996427,5.97909484816451472740e-05] 
dist 216=[-.00010571762138608546,6.57482314359937347520e-05] 
dist 217=[-9.88415485138161876260e-05,7.47664246744517603510e-05] 
dist 218=[-3.39789485201999989720e-05,8.38266272957579048430e-05] 
dist 219=[-2.92792599501240879900e-05,8.99510002276873777750e-05] 
dist 220=[-1.92599478679306371810e-05,9.49824922150862771950e-05] 
dist 221=[-1.65320729703632444720e-05,9.97034518710334553500e-05] 
dist 222=[-6.26003371459342615150e-06,.00010375680125509993] 
dist 223=[-4.10558014339467415990e-06,.00010673528322899397] 
dist 224=[-9.60126340809533582080e-07,.00010853756936284231] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 0, 0, 1, 2] 
dist 0=[120.90071811109514941   ,120.90071811109514941   ] 
dist 1=[119.65071704020997755   ,121.51334201188548944   ] 
dist 2=[115.27774192146036437   ,122.06059305576988184   ] 
dist 3=[109.94418270701812385   ,121.76901719427617323   ] 
dist 4=[104.83536815861644582   ,116.75960776718430897   ] 
dist 5=[98.954951377781027763  ,115.10136005681536375   ] 
dist 6=[90.559979930394430066  ,113.31427394866063008   ] 
dist 7=[81.311494575555253409  ,112.24379582318731448   ] 
dist 8=[67.990887571077709832  ,84.605417490669176227  ] 
dist 9=[57.427517574269673762  ,80.519740191481609922  ] 
dist 10=[45.189941898670313870  ,79.105042520988188471  ] 
dist 11=[29.301767588222823642  ,65.839219746312175841  ] 
dist 12=[18.420490005337925801  ,55.053581690003272851  ] 
dist 13=[9.2569927770024271072 ,52.929252859728037900  ] 
dist 14=[.19583164305427863383,48.174296872187720454  ] 
dist 15=[-7.9900129329623199688 ,46.981140273764655749  ] 
dist 16=[-13.678259519499192295  ,16.231243247612943371  ] 
dist 17=[-20.330671254121510742  ,12.661824308262659814  ] 
dist 18=[-25.228700061284069559  ,11.848986629961752124  ] 
dist 19=[-28.907536437582601367  ,-7.1312531372404308365 ] 
dist 20=[-31.573675257909914039  ,-9.2838009725505456277 ] 
dist 21=[-32.435816701198678369  ,-12.448307661774838071  ] 
dist 22=[-32.628853990320732550  ,-13.099141713027364117  ] 
dist 23=[-32.620576963781337491  ,-12.907361021595324536  ] 
dist 24=[-27.659963739343704698  ,-6.3647112660733221583 ] 
dist 25=[-27.092821075266543168  ,-1.2418246126714940815 ] 
dist 26=[-26.780583145928716087  ,3.3672803994559459676 ] 
dist 27=[-8.2728567185563413003 ,8.3163212599804036181 ] 
dist 28=[-6.0348490596867936182 ,12.969356423877328749  ] 
dist 29=[-.73833214248150551875,16.411370815756777422  ] 
dist 30=[.08958399767439519834,19.563198228460168638  ] 
dist 31=[6.5903689561956189649 ,23.073951603856734967  ] 
dist 32=[7.5833461223845125363 ,26.113102135175310805  ] 
dist 33=[9.4222495496918660386 ,27.395053852389705551  ] 
dist 34=[9.7350780705855464419 ,27.931554668697031092  ] 
dist 35=[13.303200835110090677  ,28.003841571963556487  ] 
dist 36=[13.444967687210490078  ,25.162757865381672564  ] 
dist 37=[13.031593786402776663  ,24.336723990479949689  ] 
dist 38=[11.773005517868535682  ,23.776955432079114145  ] 
dist 39=[10.110357546599800470  ,23.459498268906956091  ] 
dist 40=[4.4090024396074267788 ,14.247849489353574827  ] 
dist 41=[-.05307246280204755627,13.377016118120138286  ] 
dist 42=[-3.8023513133658479584 ,13.072076755677560955  ] 
dist 43=[-7.4441498087474661241 ,6.6616167129446660738 ] 
dist 44=[-10.645555564008692318  ,5.9051040173299016237 ] 
dist 45=[-12.648512076935789836  ,4.2055685946566111058 ] 
dist 46=[-14.118836860050118713  ,3.7330582569255024927 ] 
dist 47=[-15.208192625989417851  ,1.7300327831064644245 ] 
dist 48=[-15.969918887703659663  ,1.3450212300700021474 ] 
dist 49=[-16.140204440465871589  ,.51780927654055326162] 
dist 50=[-16.062996703067015608  ,.30661660139681538374] 
dist 51=[-15.851818636824577202  ,-.43820386751392758593] 
dist 52=[-14.151803342994786833  ,-.44585163397271195485] 
dist 53=[-13.650575042585430521  ,-.19311419732161753137] 
dist 54=[-12.782314000424856417  ,.47168988458212496857] 
dist 55=[-12.486315174192969487  ,1.3301755875854685518 ] 
dist 56=[-6.4493609756415133052 ,2.8208829134750130090 ] 
dist 57=[-5.7377599870110313918 ,5.4800276851967911279 ] 
dist 58=[-3.3007323889174544347 ,7.6565374610009874793 ] 
dist 59=[-1.3134115485149044756 ,9.6792907097666403893 ] 
dist 60=[-.2070255429891792804 ,11.492201644187197811  ] 
dist 61=[.34303437044369710933,12.506396431244751166  ] 
dist 62=[.42980349134968525924,13.073589969867646982  ] 
dist 63=[1.0652361410284559324 ,13.172954012911159583  ] 
dist 64=[1.1609102297272499019 ,3.0015231778266039531 ] 
dist 65=[1.3287903588674183172 ,3.0415322225113698768 ] 
dist 66=[1.3538188401859010823 ,3.0228127672008359113 ] 
dist 67=[1.6079646223984282763 ,3.0199699495149150987 ] 
dist 68=[1.5901422606575526928 ,2.5586910570339031361 ] 
dist 69=[1.5221806299409975328 ,2.4392931090974392301 ] 
dist 70=[1.3701693910565857918 ,2.3695200684583699397 ] 
dist 71=[1.0716763059115648963 ,2.3516845361742450693 ] 
dist 72=[.39304830722134098926,1.3229719168168134573 ] 
dist 73=[-.06968147287743045378,1.2397844299038478587 ] 
dist 74=[-.45341927833415946277,1.2084948133505223203 ] 
dist 75=[-.81859875669171437679,.43769967328211047886] 
dist 76=[-1.1350406997698343569 ,.33481002071073739038] 
dist 77=[-1.3253818963892089099 ,.10220409439786648671] 
dist 78=[-1.4562219238068948319 ,.05249087902578572150] 
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dist 80=[-1.5834151123258021167 ,-.25392751130088823902] 
dist 81=[-1.5879350703445607590 ,-.3357388372324084864 ] 
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dist 85=[-1.2898683590497903019 ,-.35918826725047395349] 
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dist 87=[-1.1771261261907626877 ,-.24798483053387365591] 
dist 88=[-.42406997186012773019,.16774299012188206579] 
dist 89=[-.32348726590050687338,.44710873991982063965] 
dist 90=[-.27915625593900330855,.6745172779962486979 ] 
dist 91=[-.06564980379274078134,.88400245351374064796] 
dist 92=[-.03950521898985446831,1.0608824515412516797 ] 
dist 93=[.02153866085512102920,1.1588617271266775834 ] 
dist 94=[.03137319654499492103,1.2159501681356917232 ] 
dist 95=[.10451561523330920458,1.2303073091107023721 ] 
dist 96=[.11569207406654746115,.37168701314275906189] 
dist 97=[.13693446371257175248,.37356332391956455024] 
dist 98=[.14052180467719087368,.36543509582839704852] 
dist 99=[.15040086352721036745,.36357685601826150452] 
dist 100=[.1477036115433695164 ,.30510743117052214862] 
dist 101=[.13999657804253370521,.29104707915669196361] 
dist 102=[.12366005077314907842,.27761135237527150756] 
dist 103=[.09530585387255738515,.27281913142080171419] 
dist 104=[.00795237144255417060,.17679678802779652421] 
dist 105=[-.05114807090812359465,.16652821706930351504] 
dist 106=[-.09970609006195433786,.16145853184708181475] 
dist 107=[-.14521243984665637058,.06417152961367169237] 
dist 108=[-.1841986519173898588 ,.05602656741980717891] 
dist 109=[-.20687554009260226931,.03827126606417500328] 
dist 110=[-.22152552195178569888,.03332276336035492617] 
dist 111=[-.22864990872372465967,.01398519151427960792] 
dist 112=[-.2311998372946095835 ,.01007612645136922213] 
dist 113=[-.2306522236469428846 ,.00287337463747316915] 
dist 114=[-.22290439284742616503,.00125851696502154823] 
dist 115=[-.22038813279816965218,-.00237367122529402476] 
dist 116=[-.18377295564570846932,-.00104181474197401212] 
dist 117=[-.17467216942721279402,.00280811167579529641] 
dist 118=[-.16447254868183442855,.01099186916371329593] 
dist 119=[-.15946370359211706694,.02111649749994520552] 
dist 120=[-.06379630960072587353,.03712699209927581906] 
dist 121=[-.05584727664441872524,.06647716437870910944] 
dist 122=[-.03472357050382209802,.09043124103696982771] 
dist 123=[-.00387735926713279094,.11261828312020606972] 
dist 124=[-.00027607094882585604,.13144958038126116515] 
dist 125=[.00807302683411863503,.14257817460161933645] 
dist 126=[.00932664832974993258,.14968391031794697779] 
dist 127=[.01897440885378963317,.15125057568940484012] 
dist 128=[.02039880624135565792,.04831329895099596957] 
dist 129=[.02292947229204898396,.04837153015669727811] 
dist 130=[.02329592819966388435,.04681588441247046251] 
dist 131=[.02486859161817159142,.04659146383885603811] 
dist 132=[.02426492016263808949,.03806414052028273926] 
dist 133=[.02298168122069678170,.03599695722557222164] 
dist 134=[.02046977140203256209,.03458734138073131034] 
dist 135=[.01432358201674412449,.03426501299738666071] 
dist 136=[.00375873230882911546,.01942194607178549868] 
dist 137=[-.00337122653135983826,.01807807346736263654] 
dist 138=[-.00921258185702666114,.01759095430150664242] 
dist 139=[-.01466176182513318203,.00590060869539683033] 
dist 140=[-.01931496991836828689,.00434159053696839928] 
dist 141=[-.02199637410002523554,.00084899295285740154] 
dist 142=[-.02369743463261767672,9.25901466509021852690e-05] 
dist 143=[-.02445878738483139494,-.00372027410177439127] 
dist 144=[-.02470717366271755931,-.00438307490624928466] 
dist 145=[-.02462281505502305366,-.00548758006996972863] 
dist 146=[-.02388000319685927694,-.00570679477373772072] 
dist 147=[-.02350831887310854364,-.00580768267876965440] 
dist 148=[-.02011733371799392250,-.00570042534229803976] 
dist 149=[-.01924121118766442865,-.00545170791806356766] 
dist 150=[-.01790832538007660336,-.00495163287280866572] 
dist 151=[-.01742567897977307169,-.00334970067322671115] 
dist 152=[-.00584374267911545746,.00299593109764744904] 
dist 153=[-.00429884799167262658,.00725099051337716350] 
dist 154=[-.00402745653490365674,.01070788916796645685] 
dist 155=[-.00057871895191416475,.01388453035003646417] 
dist 156=[-.00016658340704622742,.01656403999584116403] 
dist 157=[.00079222652276757089,.01804712142898408739] 
dist 158=[.00093773974852418704,.01891008087939054732] 
dist 159=[.00206426061308229244,.01912742581443782479] 
dist 160=[.00223168892904225889,.00576161170735093541] 
dist 161=[.00254135444991735323,.00575243501283104190] 
dist 162=[.00258909741645054718,.00554545215815726802] 
dist 163=[.00264256398720570707,.00550401796730179879] 
dist 164=[.00257560798319945451,.00450893431058865818] 
dist 165=[.00243988938316463479,.00426794618380822946] 
dist 166=[.00217839347990014324,.00406724178514267451] 
dist 167=[.00147870414655917283,.00399321909803512253] 
dist 168=[.00018433788342043100,.00236566626097977290] 
dist 169=[-.00068671387206791909,.00223617836296593906] 
dist 170=[-.00139784662435463683,.00217848448552360491] 
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dist 172=[-.00261781396078531875,.00036297007524423755] 
dist 173=[-.00293624742329443303,-2.01779567160575816080e-05] 
dist 174=[-.00313246880249652402,-9.72709868735033238660e-05] 
dist 175=[-.00320778045423000388,-.00052128624427608466] 
dist 176=[-.00321645710538319340,-.00059229234327257677] 
dist 177=[-.00320151782340990381,-.00071301402197397570] 
dist 178=[-.00306987329000227779,-.00073551930387853135] 
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dist 180=[-.00248425966186461939,-.00072859178532882528] 
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dist 183=[-.00216459091082031889,-.00041400299191317902] 
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dist 186=[-.00050827900247816177,.00103585780062066649] 
dist 187=[-4.43612038059885310050e-05,.00136406334941458106] 
dist 188=[9.70859972331174893180e-06,.00164125811929523573] 
dist 189=[.00013518178772980818,.00179543613861171929] 
dist 190=[.00015361727302777593,.00188913485872514435] 
dist 191=[.00029897259559735216,.00191149967539717356] 
dist 192=[.00032024921268388010,.00073948038693946031] 
dist 193=[.00035855744773136890,.00073731189186647798] 
dist 194=[.00036414456167134832,.00070695647548100544] 
dist 195=[.00037408659067387095,.00070254252948192797] 
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dist 197=[.00034263608566510055,.00053396229267910172] 
dist 198=[.00030390983096941606,.00051067044771728938] 
dist 199=[.00020279207132352121,.00050540674193061569] 
dist 200=[4.26685181990832816010e-05,.00028815318430398181] 
dist 201=[-6.49710898173564813660e-05,.00026754848867304599] 
dist 202=[-.00015273865038943605,.00026014283730489828] 
dist 203=[-.00023395979658706498,8.47559057557578332370e-05] 
dist 204=[-.00030289646992922825,6.15200016037405680580e-05] 
dist 205=[-.00034188830769816349,9.67954480203765303460e-06] 
dist 206=[-.00036569898607610541,-1.65951989601383838550e-06] 
dist 207=[-.00037435889896542253,-5.75207621785377526650e-05] 
dist 208=[-.00037528386590068810,-6.73076863968702607980e-05] 
dist 209=[-.00037309156858810799,-8.29185918162569287040e-05] 
dist 210=[-.00035977545163192787,-8.60314874786460909910e-05] 
dist 211=[-.00035393169467739896,-8.62024337861822172710e-05] 
dist 212=[-.00030041740740683096,-8.40521051963920923240e-05] 
dist 213=[-.00028686558694606129,-7.98383628847365935360e-05] 
dist 214=[-.00026635804632841019,-7.18151533758096648140e-05] 
dist 215=[-.00025898820440635161,-4.68561964812604916380e-05] 
dist 216=[-8.44231972124325136180e-05,4.82774655660756611830e-05] 
dist 217=[-6.12941700339530607840e-05,.00011201471781114454] 
dist 218=[-5.95892113293686573340e-05,.00016375580374627688] 
dist 219=[-1.10910525629058552600e-05,.00021125606486992890] 
dist 220=[-5.22788332908228089620e-06,.00025130721360177171] 
dist 221=[8.23209586204325004050e-06,.00027346980194208277] 
dist 222=[1.05200305806366895950e-05,.00028636462042566768] 
dist 223=[2.58975345025469765540e-05,.00028961567214074914] 
dist 224=[2.82799773884900249440e-05,8.78359335963123930860e-05] 
dist 225=[3.25750589843571084850e-05,8.74678206151401184590e-05] 
dist 226=[3.32616532437190195030e-05,8.36614521042088605100e-05] 
dist 227=[3.34420233827566818990e-05,8.30741389336528732100e-05] 
dist 228=[3.23368182471670222470e-05,6.69104077039429211170e-05] 
dist 229=[3.02532423416851551480e-05,6.34308724901445773120e-05] 
dist 230=[2.63426451028651554830e-05,6.00858156924339779300e-05] 
dist 231=[1.80679658134750836180e-05,5.93508332715864833600e-05] 
dist 232=[-1.88464067543281293360e-06,3.89760970614430327980e-05] 
dist 233=[-1.52777514090370649070e-05,3.66327146484551279560e-05] 
dist 234=[-2.61783823737058431240e-05,3.54607876327805206750e-05] 
dist 235=[-3.62341119932245255110e-05,1.27282986301905651610e-05] 
dist 236=[-4.47478244751492727690e-05,1.09509059146974412060e-05] 
dist 237=[-4.95255757300338930930e-05,7.16942308142213041670e-06] 
dist 238=[-5.23943792763610395330e-05,6.14229887206211946070e-06] 
dist 239=[-5.33282623751307146110e-05,2.28929805373720706080e-06] 
dist 240=[-5.32249581196342717040e-05,1.47833834180221609860e-06] 
dist 241=[-5.28846057107062359600e-05,3.27640064135043640760e-07] 
dist 242=[-5.06007811538140266260e-05,0                     ] 
dist 243=[-5.00014527061863626250e-05,-3.92920680271692376760e-08] 
dist 244=[-4.10229343323921713470e-05,5.05464509742138738900e-07] 
dist 245=[-3.88595459474270363050e-05,1.54215993312709893070e-06] 
dist 246=[-3.65233161706964791100e-05,3.49493839543784958190e-06] 
dist 247=[-3.53553063128814618310e-05,5.83869057358842102730e-06] 
dist 248=[-1.27083825679952620140e-05,9.19022619263812632750e-06] 
dist 249=[-1.09398086760298194660e-05,1.56303091253248010540e-05] 
dist 250=[-7.15470922421557220310e-06,2.08634274859055360810e-05] 
dist 251=[-6.13093001596816350730e-06,2.56769263795707256470e-05] 
dist 252=[-2.28887116889424111750e-06,2.97426180421090541780e-05] 
dist 253=[-1.48042445365120764620e-06,3.20063535216970302980e-05] 
dist 254=[-3.30001581229446583410e-07,3.33525863695320068090e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 1, 1, 1, 2] 
dist 0=[129.14855001328097468   ,129.14855001328097468   ] 
dist 1=[127.34442759217299220   ,129.66015368126082482   ] 
dist 2=[122.24619609455063013   ,129.63397393281184455   ] 
dist 3=[115.56141177855238398   ,129.36858268868614050   ] 
dist 4=[107.44714231579206716   ,124.59713856015753684   ] 
dist 5=[96.878244150073493494  ,120.30436783917601305   ] 
dist 6=[80.432214288080584919  ,117.92183206666111504   ] 
dist 7=[63.634797108742769371  ,115.57543715958582568   ] 
dist 8=[51.663528211077034163  ,110.57190618074942804   ] 
dist 9=[41.108585928576092818  ,88.109100628985229217  ] 
dist 10=[29.928577796513647235  ,86.340393337156222918  ] 
dist 11=[19.359442822674939934  ,60.422988644797722060  ] 
dist 12=[11.220654584186484166  ,58.121323113990500584  ] 
dist 13=[3.3623325143612247334 ,44.257226040852500767  ] 
dist 14=[-6.1147506423322574195 ,41.927880925433267360  ] 
dist 15=[-14.841009913771058511  ,36.938894908729296845  ] 
dist 16=[-19.718248250913320552  ,36.039463035156813127  ] 
dist 17=[-23.016137171874841840  ,1.3939922090522321774 ] 
dist 18=[-28.104991890284379464  ,-.18770367363771803204] 
dist 19=[-32.337979843340878048  ,-7.8178515230777177015 ] 
dist 20=[-34.143798349977988870  ,-9.0112957035474147161 ] 
dist 21=[-34.924948892959324262  ,-11.338550047923831770  ] 
dist 22=[-35.066020953700578527  ,-10.817854206808501138  ] 
dist 23=[-31.507079754524373652  ,-9.0441276357539962890 ] 
dist 24=[-30.495983846969651179  ,-5.2220731339190959353 ] 
dist 25=[-29.835083038797661608  ,-1.0438296868161342530 ] 
dist 26=[-29.517271221057808616  ,2.1505132664978942694 ] 
dist 27=[-8.3878514436171756290 ,5.1397410817674975421 ] 
dist 28=[-5.8506379092629833451 ,8.5161906455459515323 ] 
dist 29=[.12314443350805018056,11.787442233634938962  ] 
dist 30=[1.0587616513225847298 ,14.366266698141203169  ] 
dist 31=[8.2918618696995669773 ,16.886157316702837597  ] 
dist 32=[9.3878478968626969428 ,19.932196001569994655  ] 
dist 33=[11.438531341072420424  ,22.635099838433376888  ] 
dist 34=[11.787957208449960840  ,23.794845802169177223  ] 
dist 35=[10.703116725132384308  ,24.289208280988866018  ] 
dist 36=[9.0399522594053054681 ,24.343735050056265591  ] 
dist 37=[6.7845927133008539603 ,21.988778812100715198  ] 
dist 38=[3.2059350593492436521 ,21.279302330638422869  ] 
dist 39=[-.42467759852397946102,20.778974675842416056  ] 
dist 40=[-2.8868363302980088873 ,20.455866770209433630  ] 
dist 41=[-4.9075739967817040749 ,14.650460825704107841  ] 
dist 42=[-6.7878087127141630892 ,14.309700567257673782  ] 
dist 43=[-8.3817898085840035383 ,6.8719839819185361713 ] 
dist 44=[-9.2672369387154000538 ,5.9645183674489286507 ] 
dist 45=[-9.7836542665321085104 ,3.9217751509359418538 ] 
dist 46=[-11.332534866938639544  ,3.3906657805795670965 ] 
dist 47=[-12.677607405933531846  ,1.0116268814365242985 ] 
dist 48=[-13.832410481018134024  ,.56779465039547444336] 
dist 49=[-14.485880005857188557  ,-.35213086946530130879] 
dist 50=[-14.605369461030693537  ,-.5794096876325174034 ] 
dist 51=[-14.327948517173373943  ,-1.2845419041496445900 ] 
dist 52=[-14.140480127890851871  ,-1.2902086093844649860 ] 
dist 53=[-12.634679744786488360  ,-1.0442704129441494260 ] 
dist 54=[-12.191157705472251228  ,-.39976272974560861026] 
dist 55=[-11.400119865520173550  ,.43196186409890416238] 
dist 56=[-11.138382250072405582  ,1.4213309586145731784 ] 
dist 57=[-6.1142175582427449990 ,2.8561485169794611565 ] 
dist 58=[-4.8038916231396595430 ,5.1727762446586091814 ] 
dist 59=[-1.7490094495417108128 ,7.0703357984634398366 ] 
dist 60=[-1.2794489159783366505 ,8.8361711356313967329 ] 
dist 61=[.42615012516518376692,10.423249630470561971  ] 
dist 62=[.52557688159793728197,11.328171018801922892  ] 
dist 63=[1.2577959279372391021 ,11.830600742797620996  ] 
dist 64=[1.3677733801542899090 ,11.918409309834474925  ] 
dist 65=[1.5024359430348523680 ,2.5057280542423489120 ] 
dist 66=[1.3763034966038060067 ,2.5407455064390144991 ] 
dist 67=[1.2102657484884825835 ,2.5285823022088223716 ] 
dist 68=[1.0090116951473863549 ,2.5266793585742772577 ] 
dist 69=[.74801705242151144711,2.1446778805124200694 ] 
dist 70=[.34482431274043484473,2.0457411740359344244 ] 
dist 71=[-.06185713794046840212,1.9878855047070138355 ] 
dist 72=[-.336729039374020822  ,1.9730227950384261443 ] 
dist 73=[-.56194008638036586356,1.4203711400612432915 ] 
dist 74=[-.77156034518172505461,1.3843017425900262814 ] 
dist 75=[-.96051957002907229227,.49851144572292967751] 
dist 76=[-1.0665474730246456597 ,.37999529209525386978] 
dist 77=[-1.1262162876246262463 ,.11244838709508368488] 
dist 78=[-1.1398098292919112543 ,.05506692005831965819] 
dist 79=[-1.2458807343386393858 ,-.24446570910656660635] 
dist 80=[-1.3610821758197768999 ,-.29599727180615587458] 
dist 81=[-1.4281523811278614632 ,-.38916393542635812442] 
dist 82=[-1.4450440479967505652 ,-.40626850943453593317] 
dist 83=[-1.3073386964129258622 ,-.37512667831341434516] 
dist 84=[-1.2894878930379514295 ,-.32515744749768014811] 
dist 85=[-1.1256200295870017960 ,-.26000419137938065516] 
dist 86=[-1.0807683875349935582 ,-.15894029311773302472] 
dist 87=[-1.0122303864220707151 ,-.05674710384050997109] 
dist 88=[-.98662185664982725023,.01289783766461391986] 
dist 89=[-.35714728030623366449,.13986580702659939995] 
dist 90=[-.31658817811923015234,.37361805827287887351] 
dist 91=[-.08323462052089651507,.56391391235993151284] 
dist 92=[-.04247905436218888384,.7392318540095408708 ] 
dist 93=[.02811036656539828496,.88727006851072304821] 
dist 94=[.03937314125487663521,.96927755891500511554] 
dist 95=[.12325982500956379792,1.0170719199535811523 ] 
dist 96=[.13604308592567346702,1.0290875781101008142 ] 
dist 97=[.16031731739835670927,.31036988030140930959] 
dist 98=[.16434936981142723375,.31203778938110555614] 
dist 99=[.17307497884201906101,.30543450260194937098] 
dist 100=[.14059457665767086372,.30393749020188490932] 
dist 101=[.09951648752037035474,.25673053816778428814] 
dist 102=[.03708657466224842653,.25370757455861766845] 
dist 103=[-.02560689927146607741,.23240972090434616156] 
dist 104=[-.06773325152956741693,.22841633409968492343] 
dist 105=[-.10202282086692797915,.18968205519487090661] 
dist 106=[-.13360800201060267016,.18397559753988047643] 
dist 107=[-.16027687061283316706,.07416615445340819479] 
dist 108=[-.17505049476619071236,.06474298678283060485] 
dist 109=[-.18366619230265007651,.04426554013741559047] 
dist 110=[-.18582926129971082027,.03857135482633596075] 
dist 111=[-.19089983695748217555,.01640497523544959526] 
dist 112=[-.19695508478261327361,.01189861608696900128] 
dist 113=[-.19914161097325529592,.00371769882794956525] 
dist 114=[-.19864193534998044547,.00191206515383526193] 
dist 115=[-.19207201074623146109,-.01670436522042642485] 
dist 116=[-.18977392473266065772,-.01536945737858061364] 
dist 117=[-.15883534807281095725,-.01157189072224651904] 
dist 118=[-.15110393454149363599,-.00352808384339774869] 
dist 119=[-.14199984829993519016,.00641509608843037243] 
dist 120=[-.13774414078657590426,.01775508222055053446] 
dist 121=[-.06089802145843525057,.03804540867610514305] 
dist 122=[-.04738985713260833858,.06262340445033323061] 
dist 123=[-.00245725804479560150,.08269531206031217599] 
dist 124=[.00187782922308703168,.10130740575375066834] 
dist 125=[.02016356861922803668,.11711883145825803855] 
dist 126=[.02067041757976464702,.12650295404951967638] 
dist 127=[.02205432837489166460,.13264269279343624051] 
dist 128=[.02164896327903793159,.13397406858960915278] 
dist 129=[.02050943854886177953,.04020297655894970680] 
dist 130=[.01810209528210308536,.04025927852948989324] 
dist 131=[.01512838097345395066,.03898187213318520418] 
dist 132=[.01173993892188907532,.03879737587053245407] 
dist 133=[.00746889579128230534,.03171760799700406563] 
dist 134=[.0009907846435367758 ,.02999945100095584030] 
dist 135=[-.00551446612476377854,.02883019888512882434] 
dist 136=[-.00989344671463045322,.02856192242829827497] 
dist 137=[-.01346815355534007686,.00569459664777666144] 
dist 138=[-.01678052136722269596,.00497138109751288323] 
dist 139=[-.01959281609026683863,.00214277187709750880] 
dist 140=[-.02125121514882587809,.00156952909758533258] 
dist 141=[-.02232765841419577270,.0005109942723144926 ] 
dist 142=[-.02257189296174831912,.00027222348568567127] 
dist 143=[-.01971735532916031742,-.00754061877984508861] 
dist 144=[-.02035842234018704167,-.00744271853327234111] 
dist 145=[-.02057228957203998984,-.00715770687104124099] 
dist 146=[-.02050428852765797351,-.00655079919532753375] 
dist 147=[-.01989086694606775048,-.00579955626339694684] 
dist 148=[-.01958180638435568567,-.00494140199404258677] 
dist 149=[-.01676359682114323199,-.00385822385508849021] 
dist 150=[-.01603476323420364811,-.00221347754353259209] 
dist 151=[-.01492541357670516392,-.00056065312845303558] 
dist 152=[-.01452367278654358834,.00055465223451614838] 
dist 153=[-.00488257024300831084,.00249411715594745030] 
dist 154=[-.00359689398931698835,.00603794555908211801] 
dist 155=[-.00071653732836439602,.00891713017826357946] 
dist 156=[-9.20319231427824059490e-05,.01156301625397092551] 
dist 157=[.00305354228452396853,.01379487674438951193] 
dist 158=[.00360060245626620376,.01503021513962206667] 
dist 159=[.00382161856704644527,.01574906837703761554] 
dist 160=[.00372705891606571234,.01593011737802948077] 
dist 161=[.00352727187580946455,.00479388611561219867] 
dist 162=[.00313691960163407703,.00478687746868971032] 
dist 163=[.00266394830202281484,.00461579077776431153] 
dist 164=[.00213609796347682343,.00458166822859093357] 
dist 165=[.00147761175143045799,.00375653969281839463] 
dist 166=[.00048592886792216344,.00355822119973629942] 
dist 167=[-.00050771727478176476,.00338759530568749025] 
dist 168=[-.00117401146313800799,.00332629976903714904] 
dist 169=[-.00171533525107172231,.00051314437087649506] 
dist 170=[-.00221280148876799365,.00017559781294407870] 
dist 171=[-.00263244169010989189,-.00051016163931525756] 
dist 172=[-.00286476326711317781,-.00061150894484046968] 
dist 173=[-.00300017571132024971,-.00077907994022138022] 
dist 174=[-.00303426366433486792,-.00081310975969114078] 
dist 175=[-.00265275573975125176,-.00082831271816110301] 
dist 176=[-.00271614412476038663,-.00080872906417242204] 
dist 177=[-.00272371636928294259,-.00076479144712458894] 
dist 178=[-.00271092722117798137,-.00067729624184453908] 
dist 179=[-.00260056429129199021,-.00057074399939811694] 
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dist 181=[-.00210894273272342718,-.00030145414578538044] 
dist 182=[-.00199675603113317694,-7.55176660801997395900e-05] 
dist 183=[-.00188511595391631069,.00015111118149052411] 
dist 184=[-.00183278699162121793,.00030354238414725068] 
dist 185=[-.00049838005443075826,.00042790607596747623] 
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dist 187=[-6.75201152436117911820e-05,.00091918073026475634] 
dist 188=[-3.28796949677987894800e-06,.00119282137766863629] 
dist 189=[8.58171561376732922900e-05,.00142401003670545020] 
dist 190=[9.35657492338075907490e-05,.00155274247899238216] 
dist 191=[.00010283849133402656,.00163173432696716649] 
dist 192=[9.41763163490710915770e-05,.00165051999703816874] 
dist 193=[7.44592214986092433050e-05,.00071190709010270572] 
dist 194=[3.50229925493451400000e-05,.00069879609688647459] 
dist 195=[-1.30606098374754687200e-05,.00059765568395715899] 
dist 196=[-6.71168101258094870160e-05,.00058215654090509809] 
dist 197=[-.00013481550628844416,.00052734648105357663] 
dist 198=[-.00023707219184820884,.00051327902406875407] 
dist 199=[-.00033968262226992575,.00042384539278748562] 
dist 200=[-.00040878820120578361,.00041905777861475128] 
dist 201=[-.00046527221573550285,4.22220452423685079730e-05] 
dist 202=[-.00051776989621120990,1.86167262609729130090e-05] 
dist 203=[-.00056248438972806914,-6.28285010904661937640e-05] 
dist 204=[-.00058806614496386820,-7.41616720918655701110e-05] 
dist 205=[-.00060723371501878265,-9.26988273590556697850e-05] 
dist 206=[-.00061155347064589161,-9.64760227096209041930e-05] 
dist 207=[-.00030658058247095646,-9.75083612134992956400e-05] 
dist 208=[-.00031383915334315314,-9.51005586414484662380e-05] 
dist 209=[-.00031467323151896381,-9.00309248293241086040e-05] 
dist 210=[-.00031282015660508327,-8.01353608432860531860e-05] 
dist 211=[-.00030185473684933646,-6.81456463734212243590e-05] 
dist 212=[-.00029678061532242890,-5.47601291171580281860e-05] 
dist 213=[-.00025280911827663366,-3.80558267700844743760e-05] 
dist 214=[-.00024160537238711604,-1.28875666709166311030e-05] 
dist 215=[-.00022398203288010814,1.23452941653200120650e-05] 
dist 216=[-.00021788684352821653,2.93065120538091661050e-05] 
dist 217=[-7.64909939619035907610e-05,4.63392851849336979050e-05] 
dist 218=[-5.79717977577620703420e-05,9.95776917579460688540e-05] 
dist 219=[-1.69055022111208736610e-05,.00014280039431911866] 
dist 220=[-7.42824861463531605650e-06,.00018248766345362960] 
dist 221=[1.95242722793465438500e-05,.00021595593400524637] 
dist 222=[2.03857282333728339850e-05,.00023448465616351317] 
dist 223=[2.10284046114379690070e-05,.00024530535659717043] 
dist 224=[1.95070263480051240340e-05,.00024802526106502702] 
dist 225=[1.64605732228926823550e-05,7.53629648602359299730e-05] 
dist 226=[1.06147536885100590160e-05,7.40440323744294811410e-05] 
dist 227=[3.56354472601411131250e-06,6.57108666480006143090e-05] 
dist 228=[-4.26953712735276459370e-06,6.48380626712577880450e-05] 
dist 229=[-1.40200782377315182140e-05,5.81987547828734141410e-05] 
dist 230=[-2.86853879633193468630e-05,5.62550419913731630540e-05] 
dist 231=[-4.33802427600055814990e-05,4.93753563236212696280e-05] 
dist 232=[-5.32482865086444690810e-05,4.85053221476924639920e-05] 
dist 233=[-6.12841331620413350120e-05,1.83390822341004461150e-05] 
dist 234=[-6.87039784683776127300e-05,1.60614311261867782160e-05] 
dist 235=[-7.49905804710269758080e-05,7.65798714137619907680e-06] 
dist 236=[-7.85267195530029475130e-05,5.81556528479950256150e-06] 
dist 237=[-8.08167413395677701020e-05,3.54026592249353850830e-06] 
dist 238=[-8.13797510712880553690e-05,3.04993539772617505900e-06] 
dist 239=[-3.53105491015682176930e-05,3.07544974812794737810e-06] 
dist 240=[-3.60760189990770401940e-05,3.58200371907645396280e-06] 
dist 241=[-3.61395542057295637360e-05,4.52693085160944586970e-06] 
dist 242=[-3.58856248457842409500e-05,6.29324236861343210750e-06] 
dist 243=[-3.47544138817319951070e-05,8.40857786235809523870e-06] 
dist 244=[-3.40698761459929683800e-05,1.07394688046426632030e-05] 
dist 245=[-2.97455639846649697530e-05,1.36286917243896155790e-05] 
dist 246=[-2.86029731169307956860e-05,1.79611142870743801020e-05] 
dist 247=[-2.63079224185152433270e-05,2.22975005166542646530e-05] 
dist 248=[-2.55550817124963650960e-05,2.52024864206731769910e-05] 
dist 249=[-1.24089782019663744820e-05,2.75605750032861150510e-05] 
dist 250=[-1.06544460703101178060e-05,2.97253480521574381670e-05] 
dist 251=[-6.93118694886112382330e-06,3.15507577439946732900e-05] 
dist 252=[-5.92279540825348010800e-06,3.25613003826747761660e-05] 
dist 253=[-2.15859440468601950270e-06,3.31498991003087328340e-05] 
dist 254=[-1.36241686555721973340e-06,3.32998448840035491620e-05] 
dist 255=[-2.76859325384993070640e-07,3.31393991283827760640e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 2, 2, 1, 2] 
dist 0=[130.26214378269581870   ,130.26214378269581870   ] 
dist 1=[129.20639886885446719   ,130.22094869868525765   ] 
dist 2=[125.44574582713911905   ,130.26214378269581870   ] 
dist 3=[120.33916644905784014   ,129.14166487743335292   ] 
dist 4=[113.92817822684799033   ,122.39825601232252957   ] 
dist 5=[105.44349692492850925   ,116.90879114304609908   ] 
dist 6=[92.087244527354021817  ,114.96075007975996956   ] 
dist 7=[78.355813002452052462  ,113.35119464907408416   ] 
dist 8=[68.373956690050487546  ,105.40217188469022370   ] 
dist 9=[59.357927526260022641  ,88.259495204381400920  ] 
dist 10=[49.404241111080937912  ,86.577232476111710796  ] 
dist 11=[31.545917478134475987  ,45.877323690431702310  ] 
dist 12=[18.963412945229454394  ,43.408688755536333540  ] 
dist 13=[8.4149433358092213768 ,38.501253634523240539  ] 
dist 14=[-1.9155873095086151750 ,37.367393555069068121  ] 
dist 15=[-11.162303356040454103  ,29.387329762971635175  ] 
dist 16=[-17.407998609870762854  ,25.143299219208683346  ] 
dist 17=[-22.597775465382868028  ,-.20727515928196840621] 
dist 18=[-27.659296518405829430  ,-1.0960390924234378704 ] 
dist 19=[-31.867827572402236428  ,-8.9360537718079228310 ] 
dist 20=[-33.668817477377314231  ,-8.7031873276860161374 ] 
dist 21=[-34.451941281582859177  ,-7.2921184558925141417 ] 
dist 22=[-34.595641134449847104  ,-4.0205517224949754116 ] 
dist 23=[-31.100019039262886813  ,-.39675670289530874592] 
dist 24=[-30.108167201402546313  ,2.4191193364203846749 ] 
dist 25=[-29.461071641806611178  ,5.0929933579868584541 ] 
dist 26=[-29.152785983324985468  ,8.1655289016174280773 ] 
dist 27=[-8.2871312395104343744 ,11.169525950173788914  ] 
dist 28=[-5.7824691482618081685 ,13.578471663886201396  ] 
dist 29=[.1121114014697959466 ,15.969568863218511123  ] 
dist 30=[1.0373912394190151262 ,18.911294807840303572  ] 
dist 31=[5.6540100893266728639 ,21.536879845396132144  ] 
dist 32=[5.8826555036319603579 ,22.675020404943301101  ] 
dist 33=[11.271613257884853860  ,23.167306779450813639  ] 
dist 34=[11.611183483917850964  ,23.222438550306908732  ] 
dist 35=[14.031162458806348738  ,21.021641038725434218  ] 
dist 36=[13.104035389291023938  ,20.353699232464475980  ] 
dist 37=[11.726245156557580850  ,19.878993410134642519  ] 
dist 38=[8.9022662082029352902 ,19.565435584120434537  ] 
dist 39=[3.4741810322141441999 ,15.934464966703260693  ] 
dist 40=[-.27249817895377681082,15.368222115523076236  ] 
dist 41=[-3.4225324361469160066 ,14.427963398140787048  ] 
dist 42=[-6.4849258577165372893 ,14.092515859734096212  ] 
dist 43=[-9.1785058427829916916 ,6.7369480007333815809 ] 
dist 44=[-10.866117700510155987  ,5.8366799404763320648 ] 
dist 45=[-12.107675415113443288  ,3.8085379602141451415 ] 
dist 46=[-13.032579841656375405  ,3.2851289064257519041 ] 
dist 47=[-13.681478080336942958  ,.92131787005290210979] 
dist 48=[-13.827857367886394516  ,.482032562069526447  ] 
dist 49=[-14.233345490435175654  ,-.42794991120883670924] 
dist 50=[-14.351834311916896390  ,-.65200027381811922157] 
dist 51=[-12.143881947576929202  ,-1.3446761184679312222 ] 
dist 52=[-11.719356871158487414  ,-1.3527870374026749733 ] 
dist 53=[-10.957786474387781547  ,-1.1158952886205951373 ] 
dist 54=[-10.706980868767756899  ,-.49152069398548394242] 
dist 55=[-5.9325407431766453793 ,2.7828510835717290749 ] 
dist 56=[-5.4036423608831688239 ,5.0037074319467795390 ] 
dist 57=[-3.8603397364627573569 ,6.8231898121714745676 ] 
dist 58=[-2.7840006708977254353 ,8.5169281050562983668 ] 
dist 59=[-.47723666335512758319,10.043489814550356635  ] 
dist 60=[-.206513256533680152  ,10.913175397117069065  ] 
dist 61=[.42077990129935359811,11.395330771764745960  ] 
dist 62=[.51917197258570168718,11.479568858938844337  ] 
dist 63=[1.2432189517478704070 ,2.3798008363509841455 ] 
dist 64=[1.3173616239282146573 ,2.4138128465527740197 ] 
dist 65=[1.5425641897125968440 ,2.4048466282679680380 ] 
dist 66=[1.5703191045450631085 ,2.4025920985964404904 ] 
dist 67=[1.6159799522019222248 ,2.0696130979413364312 ] 
dist 68=[1.4774627142532634298 ,2.0562300156614168213 ] 
dist 69=[1.2957992798343956096 ,1.8957088639742736835 ] 
dist 70=[.85074496644657163477,1.8792162179701805730 ] 
dist 71=[.30815291715918437293,1.5837704569623297308 ] 
dist 72=[-.06207806284260112469,1.5440558675035029524 ] 
dist 73=[-.36935654538899637607,1.4037742370791448858 ] 
dist 74=[-.66215486769090809958,1.3680158472736273298 ] 
dist 75=[-.91611232705690715356,.48849909381374804387] 
dist 76=[-1.0692705266261610521 ,.37095076298969275482] 
dist 77=[-1.1750357998434926073 ,.10541009724703513712] 
dist 78=[-1.2409425761851296466 ,.04879784677384772193] 
dist 79=[-1.2800627360835339681 ,-.2488409363436225324 ] 
dist 80=[-1.3392326016045136129 ,-.2998916495596724393 ] 
dist 81=[-1.4054395477951272981 ,-.39228205780641406458] 
dist 82=[-1.4221172684529958652 ,-.4092215825917926881 ] 
dist 83=[-1.0915883934253219934 ,-.43309761575035852384] 
dist 84=[-1.0488279012913234074 ,-.40804810974385650536] 
dist 85=[-.98079368368339368743,-.35921868435322770058] 
dist 86=[-.95635846718525428129,-.17274981065450855459] 
dist 87=[-.38330168856322407651,.16066207746169962416] 
dist 88=[-.38037788036457484863,.38480510488821451384] 
dist 89=[-.32232138183308514877,.56735273278140058853] 
dist 90=[-.316859085511367902  ,.7356556377250441101 ] 
dist 91=[-.05609940386577584297,.87787445447457234519] 
dist 92=[-.03186884467539420553,.95772054555690341626] 
dist 93=[.04830506089818371587,1.0039819801982975113 ] 
dist 94=[.05913488738214112290,1.0151125053917996516 ] 
dist 95=[.09620399924978396624,.34102536189203981336] 
dist 96=[.10096045191019404095,.35422567287460202018] 
dist 97=[.1255361816821060735 ,.36145534079984257139] 
dist 98=[.1238478747194575784 ,.36076341103678506534] 
dist 99=[.1134122728122460458 ,.35509120538186010154] 
dist 100=[.08863435161003079100,.34994881690583851102] 
dist 101=[.04913558946089372200,.31411914031910524196] 
dist 102=[-.03919009349980904019,.30417208898088642366] 
dist 103=[-.12806933578908600071,.28046217273658901283] 
dist 104=[-.18812418963359533937,.2716381946527096017 ] 
dist 105=[-.23738038651787050287,.17251062015666814391] 
dist 106=[-.28339504095103874161,.1681382179275012991 ] 
dist 107=[-.32271335348196427889,.08583598043385373465] 
dist 108=[-.34538864617982395901,.07450791440079863987] 
dist 109=[-.3597897272391766569 ,.03182180726474570739] 
dist 110=[-.36626392686567756536,.02276977485228046131] 
dist 111=[-.36777992181586792267,.00974719638949185531] 
dist 112=[-.36249720091500687018,.00604382726858635855] 
dist 113=[-.14595442642345902671,.00429350858671454727] 
dist 114=[-.1448308458247666427 ,.00565657826543116828] 
dist 115=[-.12890290008993258747,.00931587890719496288] 
dist 116=[-.12473193704126164929,.01696282939879460545] 
dist 117=[-.11545123203881402484,.02638329312307504143] 
dist 118=[-.11210554389707736355,.03708462645646692023] 
dist 119=[-.05876687465629382187,.05055168256550217613] 
dist 120=[-.05104487030122046539,.07095331018250916262] 
dist 121=[-.04026724228055587361,.09142829445476454711] 
dist 122=[-.03988502596920026742,.10961508309173513255] 
dist 123=[-.01213113178084579101,.1273419985134948281 ] 
dist 124=[-.00849133325440792105,.13712089605132828678] 
dist 125=[-.00240474306413429934,.14276422362580845957] 
dist 126=[-.00096067926593152520,.14407239441767922625] 
dist 127=[.02195582814218509937,.03313782363226404088] 
dist 128=[.02359631552679798734,.03426590220031847393] 
dist 129=[.02653453385841775460,.03466849792238723682] 
dist 130=[.02696999057266533356,.03460686963453347595] 
dist 131=[.02641852505620895781,.03339823601988561230] 
dist 132=[.02373338579661356579,.03309531466066089661] 
dist 133=[.02043446283436412870,.02782483199550069577] 
dist 134=[.01669747195386624743,.02739169953853609375] 
dist 135=[.01200097035709373401,.02450932505781019463] 
dist 136=[.00489229927773532738,.02388535379760705744] 
dist 137=[-.00224068677224155634,.02082786995622786439] 
dist 138=[-.00703389424592341357,.02026361853736272400] 
dist 139=[-.01093777793081625678,.00678136809761106704] 
dist 140=[-.01454016152522758479,.00499347409158620590] 
dist 141=[-.01758821500849520999,.00099133724538874652] 
dist 142=[-.01932651477692268941,.00012115975391334762] 
dist 143=[-.02038931702570399064,-.00423883564176305716] 
dist 144=[-.02096341998425961060,-.00499854298521947641] 
dist 145=[-.02196421566183699875,-.00625733318552454225] 
dist 146=[-.02221631730479236073,-.00650921522556099743] 
dist 147=[-.00779176300316699993,-.00661102696411671615] 
dist 148=[-.00775236944039789219,-.00647743864349719676] 
dist 149=[-.00651781013673094230,-.00617643584110564796] 
dist 150=[-.00647895958056108747,-.00526313261143188861] 
dist 151=[-.00574899258018548295,-.00410896878308128266] 
dist 152=[-.00569114761583282236,-.00235344706809828183] 
dist 153=[-.00473775140614520100,-.00058948969609300801] 
dist 154=[-.00468783687229817318,.00060058452335101207] 
dist 155=[-.00093789211190547577,.00157520099829661061] 
dist 156=[-.00048582579764490497,.00248379254866616193] 
dist 157=[.00055628388454532328,.00325927323786490999] 
dist 158=[.00073156775999156167,.00370544108118232897] 
dist 159=[.00193754868940339452,.00398758923845873899] 
dist 160=[.00212326191155373596,.00411191941893256284] 
dist 161=[.00246813938600817814,.00415001934100611362] 
dist 162=[.00252688988907172092,.00413529068588444428] 
dist 163=[.00257479612601134113,.00411939665573481860] 
dist 164=[.00250019979246930076,.00409745989599992186] 
dist 165=[.00234744895153336712,.00392988519886888520] 
dist 166=[.00205209827845011627,.00388468619699308849] 
dist 167=[.00159977707051138354,.00319671972785512744] 
dist 168=[.00054852451830307909,.00302992735343679456] 
dist 169=[-.00050477115296949563,.00285076577007946516] 
dist 170=[-.00121103041937732152,.00276028328622805499] 
dist 171=[-.00178479337078270827,.00101480364805233406] 
dist 172=[-.00231202699540409392,.00087742193051673875] 
dist 173=[-.00275675243461988868,.00058315854001570842] 
dist 174=[-.00300292219457188751,.00050261817506557653] 
dist 175=[-.00314624527850429477,.00019675330748736238] 
dist 176=[-.00318234493444170173,.00013311029193821931] 
dist 177=[-.00257951053163142437,3.43170643285548001710e-05] 
dist 178=[-.00260731553311394363,8.82165776899709982860e-06] 
dist 179=[-.00102748800036886376,-.00088512394400982489] 
dist 180=[-.00101004989591507820,-.00079967778551203881] 
dist 181=[-.00095472465357726448,-.00069552801466178809] 
dist 182=[-.00093569403906876116,-.00057849910510851926] 
dist 183=[-.00081262592578404562,-.00040120859232182904] 
dist 184=[-.00078004948198366714,-.00012357062713735893] 
dist 185=[-.00071857187507284602,.00015464366210797174] 
dist 186=[-.00069925572254453420,.00034134852899938039] 
dist 187=[-.00029107200778913257,.00049321822589259735] 
dist 188=[-.00023346940270949742,.00063311993158587701] 
dist 189=[-.00010750111305252282,.00075139287503381130] 
dist 190=[-7.51736557634743715060e-05,.00081738528323820793] 
dist 191=[5.52082195483018094690e-05,.00085649665422948782] 
dist 192=[8.02724385520225076790e-05,.00086803757105727282] 
dist 193=[.00011788943096495182,.00086640130032706485] 
dist 194=[.00012632933843117330,.00085319134590605837] 
dist 195=[.00012702639590989822,.00056548248693480849] 
dist 196=[.00011999471152218896,.00055902537902798322] 
dist 197=[.00010611585452154537,.00045997363114179190] 
dist 198=[7.30280595358404048770e-05,.00043595516003341349] 
dist 199=[2.14298422930415509840e-05,.00041027892061910611] 
dist 200=[-5.63209493447732745110e-05,.00039724340788118940] 
dist 201=[-.00013425523675489856,.00016623375894703292] 
dist 202=[-.00018658324577131882,.00014724710387232943] 
dist 203=[-.00022917652359564044,8.40475977312554685040e-05] 
dist 204=[-.00028292870757708619,7.24872535879336409610e-05] 
dist 205=[-.00032854150630455026,2.85213347812750843650e-05] 
dist 206=[-.00035406208009769716,1.93816811325300063760e-05] 
dist 207=[-.00037028279908040176,5.06283658030959917390e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 1, 0, 0, 2] 
dist 0=[121.95970602511023023   ,121.95970602511023023   ] 
dist 1=[120.84478627554756259   ,122.95667874154770031   ] 
dist 2=[117.41710571728184488   ,124.29387785702083255   ] 
dist 3=[111.15897357291006824   ,126.37785792622932443   ] 
dist 4=[99.545193082199379980  ,128.19698883876955877   ] 
dist 5=[87.205774112812647355  ,128.48623410549678351   ] 
dist 6=[78.059971987229940311  ,127.87994502552358004   ] 
dist 7=[69.641744257848027058  ,126.13845466035556779   ] 
dist 8=[60.177612271302788439  ,105.62533527913728972   ] 
dist 9=[50.891392601124568931  ,102.31539235487859966   ] 
dist 10=[41.192260188728125732  ,92.637893990177066421  ] 
dist 11=[32.937587087607122138  ,91.138884197627235589  ] 
dist 12=[24.463772030260780033  ,71.071545600493600108  ] 
dist 13=[13.521526010724853415  ,66.910477670823497760  ] 
dist 14=[3.1320107414180374266 ,62.656313303853833496  ] 
dist 15=[-3.1486786261413163114 ,61.566172552462595192  ] 
dist 16=[-7.6404935736490563600 ,15.872451666885188871  ] 
dist 17=[-10.902637137411865670  ,10.489863540354286275  ] 
dist 18=[-13.351183468264069696  ,-1.8888424488107034114 ] 
dist 19=[-16.363306520214493680  ,-3.2486509742168637459 ] 
dist 20=[-23.416325796625844309  ,-2.4589822413793293586 ] 
dist 21=[-27.520301982145830540  ,-1.4066258954453668149 ] 
dist 22=[-30.211037927030670712  ,-.56887138789821521578] 
dist 23=[-31.651243112905187928  ,.19267211226325363536] 
dist 24=[-32.359634560571119450  ,.95718608981277978675] 
dist 25=[-32.360834309744996429  ,1.5936170983255104835 ] 
dist 26=[-31.626612447055562345  ,1.8540703430959297704 ] 
dist 27=[-31.144061583286720462  ,1.9508392159891756916 ] 
dist 28=[-27.005018513131539035  ,1.9479763869713546698 ] 
dist 29=[-25.912509040434035593  ,2.9275117953423672994 ] 
dist 30=[-24.131805450422592856  ,4.5273798815292948541 ] 
dist 31=[-23.525670744906626970  ,5.4080190734421879470 ] 
dist 32=[-11.366620395966270334  ,5.9236597696943953987 ] 
dist 33=[-9.9358869861437686413 ,9.9959111940735692842 ] 
dist 34=[-6.8122747088597525413 ,14.090664621937598847  ] 
dist 35=[-5.9465757602272177280 ,17.867747004568805686  ] 
dist 36=[-2.5727883557176449390 ,21.104853906810082951  ] 
dist 37=[-1.9008499042483850107 ,22.999831138561641509  ] 
dist 38=[-.83398379946882564201,24.072266677899036603  ] 
dist 39=[-.99173944133800673299,24.270529141281954883  ] 
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dist 193=[.00015073574510455606,.00023106520801107019] 
dist 194=[.00012804255437584737,.00018770562081657069] 
dist 195=[9.94082811022443394100e-05,.00017815931852738876] 
dist 196=[5.60704102119549743200e-05,.00016955472684918766] 
dist 197=[1.25703154057713791600e-05,.00016777968447643144] 
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dist 201=[-9.78897834557925765950e-05,-2.53464679071470965500e-05] 
dist 202=[-.00012182278752052801,-6.85782419136277770720e-05] 
dist 203=[-.00013542679514907789,-7.52251256646025726690e-05] 
dist 204=[-.00014381915652855187,-8.76809755833701543170e-05] 
dist 205=[-.00014706049942580156,-8.98420665700434121820e-05] 
dist 206=[-.00014741552165645737,-9.19304364730022073910e-05] 
dist 207=[-.00014667825325285965,-8.93821048940271241220e-05] 
dist 208=[-.00014078606839003565,-8.18366482892132772320e-05] 
dist 209=[-.00013917874642980270,-6.96283298676432128820e-05] 
dist 210=[-.00011464958339800537,-5.60462036291089381450e-05] 
dist 211=[-.00010868953279580886,-3.88909028825637406060e-05] 
dist 212=[-.00010229006124679106,-1.31003889229323557020e-05] 
dist 213=[-9.90516574752367968150e-05,1.27298541085877292750e-05] 
dist 214=[-3.66622662570196662320e-05,3.00431490900964268220e-05] 
dist 215=[-3.17504493680105657700e-05,4.41035945562277267220e-05] 
dist 216=[-2.12065134486400798670e-05,5.70441926465293075870e-05] 
dist 217=[-1.83126954818081242720e-05,7.05205961289234671330e-05] 
dist 218=[-7.27692767497021594730e-06,8.19261825862580819530e-05] 
dist 219=[-4.98822497506312981460e-06,8.83139769929813241220e-05] 
dist 220=[-1.33573311093513307970e-06,9.24291332730599886810e-05] 
dist 221=[-4.21813259937886920420e-07,9.34263857785804891430e-05] 
dist 222=[2.27519380084187167320e-05,3.41533954373384033590e-05] 
dist 223=[2.16613969684086116900e-05,3.39926173144835906360e-05] 
dist 224=[1.95303807488701514990e-05,3.28630019632685110630e-05] 
dist 225=[1.69476716054902792310e-05,3.23447389697274738420e-05] 
dist 226=[1.36800280992652866070e-05,2.75445718715791910780e-05] 
dist 227=[8.55243246839291400000e-06,2.63194017690471568680e-05] 
dist 228=[8.54808945089355233570e-07,2.44783228848071539940e-05] 
dist 229=[-6.85109944553376356200e-06,2.38080531038293989850e-05] 
dist 230=[-1.20116422863637161540e-05,8.11143450660156343880e-06] 
dist 231=[-1.61979555990125241880e-05,5.65401293584427661740e-06] 
dist 232=[-2.00355588775032134650e-05,4.03490405365986977060e-06] 
dist 233=[-2.32669138979486262310e-05,7.72818622613779753000e-07] 
dist 234=[-2.50460189271498561280e-05,1.02438376551258469230e-07] 
dist 235=[-2.60690124416539901610e-05,-8.49352440941369356830e-07] 
dist 236=[-2.62980777487670789320e-05,-1.08708886882399240820e-06] 
dist 237=[-2.61742975583276329550e-05,-1.13381492952333525930e-06] 
dist 238=[-1.44463674422790458950e-05,-9.93946560388843314100e-07] 
dist 239=[-1.38406874242898499480e-05,-6.93980065100133028210e-07] 
dist 240=[-1.36809060685695524620e-05,-1.04932348750378255920e-07] 
dist 241=[-1.12373706413647366440e-05,6.09915163206178256980e-07] 
dist 242=[-1.06468403724616678790e-05,1.40943460305482221570e-06] 
dist 243=[-1.00158566092316616290e-05,2.40812962208819621650e-06] 
dist 244=[-9.69611611863814653450e-06,3.91388395481612864890e-06] 
dist 245=[-6.23801491184634437230e-06,5.42390902813351109120e-06] 
dist 246=[-3.03621420980140147380e-06,6.43958788012604511480e-06] 
dist 247=[-2.00760140774914730770e-06,7.26840997600942906960e-06] 
dist 248=[-1.72679330738898935460e-06,8.03651732442197560320e-06] 
dist 249=[-6.64890859419723899450e-07,8.68922581652527032340e-06] 
dist 250=[-4.42973306778370041670e-07,9.05985606192186072550e-06] 
dist 251=[-1.09020762034042459780e-07,9.29619588118415862480e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 0, 1, 2] 
dist 0=[124.35545679537362445   ,124.35545679537362445   ] 
dist 1=[122.43001698964231402   ,125.91318482516084751   ] 
dist 2=[118.63018387368338133   ,128.24033437745394624   ] 
dist 3=[112.33626661061300756   ,130.23429716268363454   ] 
dist 4=[100.49899776299093372   ,130.47240588220677302   ] 
dist 5=[87.908270577220326707  ,129.83193142437773048   ] 
dist 6=[78.616241696889187843  ,129.03154514320441726   ] 
dist 7=[70.103260232100071323  ,108.82230405236595291   ] 
dist 8=[60.592691852322552781  ,105.59737304193043276   ] 
dist 9=[51.296731130137705674  ,96.054344085424041254  ] 
dist 10=[43.622093638230617218  ,94.549228592171299412  ] 
dist 11=[35.712498355017682284  ,74.376873153632291420  ] 
dist 12=[25.455955655134007566  ,70.164469473759485715  ] 
dist 13=[15.618409235371903721  ,65.837277319489060545  ] 
dist 14=[8.4034072246234714901 ,64.663440169427349359  ] 
dist 15=[-1.8953286387490087813 ,17.940926201387609169  ] 
dist 16=[-8.0062773075992898209 ,12.414992320696341155  ] 
dist 17=[-12.240803772237048452  ,-.32772665876796560862] 
dist 18=[-16.286367870532769970  ,-1.3948340327633444865 ] 
dist 19=[-23.678184593516618083  ,-1.7075695709969968463 ] 
dist 20=[-28.021806296760118709  ,-.88383898128562703398] 
dist 21=[-30.922598326428816024  ,.19203113189926886858] 
dist 22=[-32.584740236255665002  ,1.0297933740620058316 ] 
dist 23=[-33.481003098715035422  ,1.7741816015690264055 ] 
dist 24=[-33.539637293014463043  ,2.4937111538398250763 ] 
dist 25=[-32.857326952250164014  ,3.0707998157565859414 ] 
dist 26=[-32.401361191941023422  ,3.2567922655290965554 ] 
dist 27=[-28.039340600621100312  ,3.2921947626855119099 ] 
dist 28=[-26.887068285302169368  ,3.2825335720076964592 ] 
dist 29=[-25.133332033000180839  ,3.4084772145061169089 ] 
dist 30=[-24.489434480890551296  ,5.2869398577890604680 ] 
dist 31=[-11.713239824315490102  ,6.9735235713420435084 ] 
dist 32=[-10.274920483722579886  ,9.8397628072264741096 ] 
dist 33=[-7.1159981443336420507 ,13.971445867957438058  ] 
dist 34=[-6.2348900541826892861 ,17.790021512759863109  ] 
dist 35=[-2.7680539067903386461 ,21.100860635565406698  ] 
dist 36=[-2.0834774782016818231 ,23.041876356959772625  ] 
dist 37=[-.75368837265072017386,24.132396323966566038  ] 
dist 38=[-.43634891797829937862,24.335403829692350793  ] 
dist 39=[.72353749490664183002,6.7014015939406569498 ] 
dist 40=[-.85795734425336706606,6.6773834343182371499 ] 
dist 41=[-2.2024959143941652044 ,6.5679526511531246885 ] 
dist 42=[-3.5299515724913477967 ,6.4755134809075809654 ] 
dist 43=[-4.7079132207291591955 ,5.8416477770280280595 ] 
dist 44=[-5.4600949406748531296 ,5.6683085011089558279 ] 
dist 45=[-6.0286563481601243567 ,5.1904760680630229394 ] 
dist 46=[-6.4789396895726951222 ,5.0106359542826046347 ] 
dist 47=[-6.8053215534778786696 ,2.9896434359582489069 ] 
dist 48=[-6.8824663165262459370 ,2.6485486948260002884 ] 
dist 49=[-6.8467757443356307318 ,1.9392127163316467290 ] 
dist 50=[-6.7605388004375795110 ,1.7443076230277075577 ] 
dist 51=[-6.0581398997729497754 ,1.0095943491308347646 ] 
dist 52=[-5.8505008518328824546 ,.84462750277963693509] 
dist 53=[-4.9990108636297674357 ,.59905237531507330569] 
dist 54=[-3.5073159923983661158 ,.52681038787152583762] 
dist 55=[-.93677507212673376937,.42804922416160842972] 
dist 56=[-.78114942886798907129,.39771273660513148971] 
dist 57=[-.65488566520455441589,.38928112226424515143] 
dist 58=[-.69515235796952569946,.72241361028180574046] 
dist 59=[-.71839855115301049403,1.0329736548792821185 ] 
dist 60=[-.72421540920318997743,1.2374121397284161922 ] 
dist 61=[-.20900501515658331176,1.3992328444466623841 ] 
dist 62=[-.19181572227334225798,1.5409862044334136233 ] 
dist 63=[-.1477591830240127815 ,1.6488772455926920377 ] 
dist 64=[-.14140800007935404464,1.6763693370886370798 ] 
dist 65=[-.07351369720862089978,1.6767564268376312907 ] 
dist 66=[-.06161328718277739660,1.6768207744076715284 ] 
dist 67=[-.04525748703175918967,1.4327019861636099895 ] 
dist 68=[-.04242264804561531880,1.3694997639696853850 ] 
dist 69=[.04187535763236814078,1.3325928312763970093 ] 
dist 70=[.05194658885654016642,1.3232791288973986687 ] 
dist 71=[.07099556359435791417,.24025421810386864859] 
dist 72=[-.01783685468567793372,.11311318121582455351] 
dist 73=[-.23147575696647810584,.12383830883077063972] 
dist 74=[-.4357044837960763512 ,.1287314284962308737 ] 
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dist 189=[1.85322053091006558000e-06,.00107449990566056525] 
dist 190=[2.54943824596886344900e-06,.00108724511441211363] 
dist 191=[3.94274852390819859260e-06,.00042106661590926618] 
dist 192=[4.18266680394095277240e-06,.00042003322439297131] 
dist 193=[4.93310781762979228570e-06,.00040316740329184664] 
dist 194=[4.85178946103748323490e-06,.00040072769509363947] 
dist 195=[4.27977694985387595150e-06,.00032347106570330882] 
dist 196=[3.02016330567640137070e-06,.00030510609484281732] 
dist 197=[1.66910180737250680340e-06,.00029197637009420629] 
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dist 201=[-8.62277218073623489240e-05,2.40856766419670553850e-06] 
dist 202=[-.00013261450103557269,2.17269022522867716370e-06] 
dist 203=[-.00017201444819004484,1.85572061361982012530e-06] 
dist 204=[-.00019435074369703175,1.77744850141807880450e-06] 
dist 205=[-.00020805614352710365,3.09406615852037025270e-08] 
dist 206=[-.00021318773376508578,-1.78524280692479778940e-07] 
dist 207=[-.00021390727620849430,-5.37114560716922468670e-07] 
dist 208=[-.00021271962042704801,-6.05348140082105948210e-07] 
dist 209=[-.00020526520736997953,-6.45556403495592373310e-07] 
dist 210=[-.00020194980482217915,-5.34735218180780667780e-07] 
dist 211=[-.00017157316894822277,-3.18892452071650856050e-07] 
dist 212=[-.00016386350514110044,8.47761174220374965660e-08] 
dist 213=[-.00015219728241471477,1.67699130433140757440e-06] 
dist 214=[-.00014799819775893561,2.92270162132163749910e-06] 
dist 215=[-4.84197675200099208750e-05,2.73405812006056690300e-05] 
dist 216=[-3.52248235497136054410e-05,6.37106389485664318370e-05] 
dist 217=[-5.77101334243589614500e-06,9.32382633568515801800e-05] 
dist 218=[-2.05732756012410821360e-06,.00012034906049899104] 
dist 219=[-1.87627938551069505190e-06,.00014320944207287336] 
dist 220=[-1.81228246726748151270e-06,.00015585993589160961] 
dist 221=[6.90170783447197432110e-06,.00016322063766777703] 
dist 222=[6.41862242800826127340e-06,.00016507672003408902] 
dist 223=[5.49587411755514515780e-06,5.02870126410829617510e-05] 
dist 224=[3.75558740863879323510e-06,5.00939694968281794160e-05] 
dist 225=[1.66690693793354796110e-06,4.79350314501606330770e-05] 
dist 226=[-6.39167909872970812030e-07,4.76170636742993383320e-05] 
dist 227=[-3.49981869652788539530e-06,3.82757672243961785240e-05] 
dist 228=[-7.79044892582535395180e-06,3.62743074873447637640e-05] 
dist 229=[-1.20825600787868225070e-05,3.44507609771606864780e-05] 
dist 230=[-1.49490884310492370980e-05,3.40768199486543364130e-05] 
dist 231=[-1.72652542678442659160e-05,1.42136809580977999020e-05] 
dist 232=[-1.93721374228255211540e-05,1.47813229950845157900e-05] 
dist 233=[-2.11339549513181330690e-05,1.52521366603244340640e-05] 
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dist 235=[-2.54971923713004369570e-05,1.56254949358901865650e-05] 
dist 236=[-2.82334078370984808960e-05,1.56162456954720379390e-05] 
dist 237=[-2.98814405949453397860e-05,1.55508246000942229510e-05] 
dist 238=[-3.04294749211831161870e-05,1.54539593567518257140e-05] 
dist 239=[-3.03849807868356948040e-05,1.53172393915155949150e-05] 
dist 240=[-3.01954005874190427780e-05,1.51019229818930988910e-05] 
dist 241=[-2.89009527842695331240e-05,1.48360911136374111260e-05] 
dist 242=[-2.85604487581933869980e-05,1.45737299004366232800e-05] 
dist 243=[-2.34401312065556200420e-05,1.42380077321038992380e-05] 
dist 244=[-2.22054031489540809780e-05,1.40265230132177631190e-05] 
dist 245=[-2.08743861160155501560e-05,1.32754339165925394660e-05] 
dist 246=[-2.02072966919132086580e-05,1.29561357311392592770e-05] 
dist 247=[-7.27920026565235397090e-06,1.26992777958950576510e-05] 
dist 248=[-6.26840003102703164630e-06,1.24670206652183364810e-05] 
dist 249=[-4.11534623958979321620e-06,1.22733701172149138470e-05] 
dist 250=[-3.52970652659098838850e-06,1.46304553594467894750e-05] 
dist 251=[-1.32787585094486457220e-06,1.69542657715687683380e-05] 
dist 252=[-8.65343921578115802390e-07,1.82490888510540992000e-05] 
dist 253=[-1.98045960276487503550e-07,1.90271957741172054380e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 0, 2, 0, 2] 
dist 0=[129.03042341517224166   ,129.03042341517224166   ] 
dist 1=[126.27252455489902405   ,129.61766354661862831   ] 
dist 2=[122.16070988133625068   ,129.18781766659542416   ] 
dist 3=[116.60041442437159767   ,128.62451985192555230   ] 
dist 4=[109.01597898268188616   ,127.34309101137733130   ] 
dist 5=[96.850456929311339976  ,118.04845887791490497   ] 
dist 6=[84.261935259636145527  ,115.88659526138427344   ] 
dist 7=[74.989489173578474217  ,113.43662802340238550   ] 
dist 8=[66.492082778894424080  ,98.159859417205212862  ] 
dist 9=[56.972628466457090958  ,85.266486369804875547  ] 
dist 10=[47.636574491577894446  ,81.215696824421694011  ] 
dist 11=[39.856302537075461789  ,79.673924941513782107  ] 
dist 12=[26.509351717362524719  ,46.383659947309970734  ] 
dist 13=[14.376484515016957553  ,45.284115662466570111  ] 
dist 14=[4.2841713041804239810 ,35.799426204546096500  ] 
dist 15=[-5.4732326145315962722 ,34.136888075741377025  ] 
dist 16=[-14.124687617795472898  ,27.030982658625723252  ] 
dist 17=[-19.824879487601047051  ,-.39103951940546989805] 
dist 18=[-24.405258474955432895  ,-4.3629101829482563750 ] 
dist 19=[-28.615371026440005050  ,-4.7726360788433783005 ] 
dist 20=[-31.999755484295263262  ,-4.1055177689886082129 ] 
dist 21=[-33.299300964004354802  ,-1.8983263649718457931 ] 
dist 22=[-33.768991879427812765  ,.66923596037581027064] 
dist 23=[-33.838423970783523765  ,2.7736674676445332937 ] 
dist 24=[-29.902498855065052148  ,4.8615610892569130156 ] 
dist 25=[-28.960438687666681916  ,7.3767835567593852196 ] 
dist 26=[-28.106579755402522622  ,9.8929268693259128365 ] 
dist 27=[-27.797024216982528678  ,11.991999334825410584  ] 
dist 28=[-7.4650230739427614327 ,14.147533747975912844  ] 
dist 29=[-4.9593998534867056194 ,16.896630824443727556  ] 
dist 30=[.77499683430818900828,19.379372226389189738  ] 
dist 31=[1.6616695669220889256 ,20.479800645101345186  ] 
dist 32=[4.7625377323212084111 ,20.970967647695714840  ] 
dist 33=[9.6137802329879939479 ,21.029186153588464844  ] 
dist 34=[11.549008807678688761  ,19.130356092080427292  ] 
dist 35=[11.872542738456953030  ,18.545244525835676966  ] 
dist 36=[12.725899570982427792  ,18.122958780279701143  ] 
dist 37=[8.1175091588588168066 ,17.831961328622637074  ] 
dist 38=[3.1813382233788267420 ,17.384468610435110123  ] 
dist 39=[-.22977745817293589814,17.151705417632928761  ] 
dist 40=[-3.1013691286965205439 ,15.218233811366305254  ] 
dist 41=[-5.8984666044738338572 ,14.660429986041647644  ] 
dist 42=[-8.3618123050697463575 ,13.740988548102728471  ] 
dist 43=[-9.9100855753440628639 ,13.415029969517646661  ] 
dist 44=[-11.054690252162434883  ,6.2842283712659092663 ] 
dist 45=[-11.917512801836725628  ,5.4076943847030282894 ] 
dist 46=[-12.528484377282595642  ,3.4375457676949427873 ] 
dist 47=[-12.673790010914634044  ,2.9333021384774025800 ] 
dist 48=[-12.619900868872891780  ,.65872971560001650886] 
dist 49=[-13.066171060638206085  ,.23666014951854946629] 
dist 50=[-13.681563504583332175  ,-.62309958982399081381] 
dist 51=[-13.795726360563895803  ,-.82998212788440799483] 
dist 52=[-10.071239876042717916  ,-1.4424731546675946004 ] 
dist 53=[-9.8422419711806284231 ,-.36673466776971458186] 
dist 54=[-5.5127074907734318511 ,2.6347405093173929188 ] 
dist 55=[-5.0421139868747954042 ,4.6630430124406940062 ] 
dist 56=[-4.0055482782136202948 ,6.3246780319915042161 ] 
dist 57=[-3.6552556364313700837 ,7.8711611541371610467 ] 
dist 58=[-2.6723182982482482444 ,9.2421092997543871388 ] 
dist 59=[-2.6514933966164953064 ,10.043489814550358175  ] 
dist 60=[-.43035560342090173943,10.489129226859378571  ] 
dist 61=[-.16996870080543825092,10.566276511664163418  ] 
dist 62=[.43342559945070065913,2.1519333430927915803 ] 
dist 63=[.52722731619756518425,2.1847463944598774517 ] 
dist 64=[1.0667577877692055412 ,2.1811992374285691429 ] 
dist 65=[1.3280690516178155604 ,2.2208018625998770214 ] 
dist 66=[1.4180475789050174449 ,2.2364311944566435961 ] 
dist 67=[1.3792111304873936595 ,2.2064645613412163669 ] 
dist 68=[1.2504378279435591757 ,2.1873591321799702275 ] 
dist 69=[.77739325676742748529,1.8718752454674756883 ] 
dist 70=[.28470200737110440081,1.7880577710525384905 ] 
dist 71=[-.05174935020423362109,1.7165789055052095991 ] 
dist 72=[-.33125180573076716722,1.6483475085496560777 ] 
dist 73=[-.59797876977307703763,1.4290964737752068706 ] 
dist 74=[-.82956559263634920671,1.3368429579042818407 ] 
dist 75=[-.96963666142553622555,1.3024263666613818871 ] 
dist 76=[-1.0668468451788909761 ,.45997017520700068243] 
dist 77=[-1.2666305461433799157 ,.3474570356672622655 ] 
dist 78=[-1.3909491850133305378 ,.17792991458218532865] 
dist 79=[-1.4593057473550330604 ,.08053409798947010184] 
dist 80=[-1.4730190448496155751 ,.06180376131559839077] 
dist 81=[-1.2848929626224450078 ,-.29221775034996094888] 
dist 82=[-1.3481075441940772986 ,-.37918321844397915243] 
dist 83=[-1.3640309112190823216 ,-.39510658343281220751] 
dist 84=[-.89577418859534955804,-.39966654504638605892] 
dist 85=[-.87350644409502271223,-.15719866493451440656] 
dist 86=[-.40620504873496889338,.14588523417999191007] 
dist 87=[-.403843137277997558  ,.34968447741226122796] 
dist 88=[-.36016911360387710349,.51570092357804938657] 
dist 89=[-.31931264321393019015,.66881215188931941212] 
dist 90=[-.30589152729453611092,.798321197963737187  ] 
dist 91=[-.30065200514103084157,.87109931360692137388] 
dist 92=[-.05158687632049799623,.91323085675101686498] 
dist 93=[-.02180145005647205809,.92328154697480319031] 
dist 94=[.04798460440484876570,.30015658363744789421] 
dist 95=[.05835757202347704800,.32231175844458531183] 
dist 96=[.10555166287866981865,.33575193012834432816] 
dist 97=[.13123406419709798224,.3434485604619874936 ] 
dist 98=[.12988016355924865649,.34305987923536878888] 
dist 99=[.0927566420679797282 ,.33824934804938115161] 
dist 100=[.03895580095747915936,.33350016429684738168] 
dist 101=[-.04323882223638365822,.29990285108875815996] 
dist 102=[-.12596281171589282738,.29050835130771659392] 
dist 103=[-.18186925295210115309,.26809620248451360238] 
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dist 188=[-5.86179991310805513600e-05,.00110119243436950595] 
dist 189=[-2.33440090151802372790e-07,.00111418473524029614] 
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dist 197=[9.65400390966346166890e-05,.00042837564817964555] 
dist 198=[8.69980315482953952750e-07,.00041320915042990209] 
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dist 200=[-.00011590703022886840,.00034679711482316585] 
dist 201=[-.00016446437634028241,.00033168100298846745] 
dist 202=[-.00020568675125734121,.00030666207502053906] 
dist 203=[-.00022901893329120323,.00029845837136668236] 
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dist 205=[-.00024852324999344799,9.54515408298835916930e-05] 
dist 206=[-.00024912809394620449,4.61921893285219014790e-05] 
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dist 208=[-.00030608700541443311,-1.74815180127213005970e-05] 
dist 209=[-.00033090334247525539,-2.73380580394885356190e-05] 
dist 210=[-.00034551242050382538,-4.21709791091444169480e-05] 
dist 211=[-.00034917229527992812,-4.56458179664045532260e-05] 
dist 212=[-.00018017377020595010,-3.66169622845432940670e-05] 
dist 213=[-.00017525681786995799,1.99269642954527761580e-05] 
dist 214=[-9.68433278884356276050e-05,7.65487353653471761250e-05] 
dist 215=[-8.93636174280147031010e-05,.00011451045301155098] 
dist 216=[-7.47174128669188552820e-05,.00014535595210533221] 
dist 217=[-6.75969323224317254400e-05,.00017372148013699006] 
dist 218=[-5.91656297212730538170e-05,.00019767263180960037] 
dist 219=[-5.73934845312168653490e-05,.00021098997463867213] 
dist 220=[-1.40987268907918993600e-05,.00021894112054354570] 
dist 221=[-8.58185029806084065000e-06,.00022099938941792745] 
dist 222=[3.98606616508342103610e-06,4.95934602016397466300e-05] 
dist 223=[6.31495772312242212510e-06,4.93796329745597645860e-05] 
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dist 225=[2.02568696839464587990e-05,5.31675390632712355700e-05] 
dist 226=[1.42398026943621351910e-05,5.60773246237961796420e-05] 
dist 227=[7.57437140536023863050e-06,5.70327858595591913770e-05] 
dist 228=[-7.10586212874320200150e-07,5.70240956958416700610e-05] 
dist 229=[-1.31586906326860566040e-05,5.65532891243754007260e-05] 
dist 230=[-2.56273643988543920310e-05,5.48427754072326622030e-05] 
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dist 233=[-4.70744922046060419180e-05,4.58485800261107265570e-05] 
dist 234=[-5.23824099498066914030e-05,4.20218671283779211820e-05] 
dist 235=[-5.53539626179955876780e-05,4.06593947505193569030e-05] 
dist 236=[-5.71288020063573727700e-05,2.12792607896621989130e-05] 
dist 237=[-5.76849288095721296250e-05,1.82792274809196983150e-05] 
dist 238=[-5.75316845019673613310e-05,1.19549844501420055910e-05] 
dist 239=[-5.70156143002217521170e-05,1.02500118704928874970e-05] 
dist 240=[-5.51429107655208050860e-05,3.94232388661483285760e-06] 
dist 241=[-5.40739208113428519810e-05,2.58869810708521992680e-06] 
dist 242=[-4.74471862757519438550e-05,8.74861792462459444370e-07] 
dist 243=[-4.25684640832778283470e-05,5.21473043424397522740e-07] 
dist 244=[-2.07687170136367572560e-05,5.37801754312617698880e-07] 
dist 245=[-2.01266815830825542370e-05,8.60426701507004646150e-07] 
dist 246=[-7.57873340921907645400e-06,5.47413552935711709570e-06] 
dist 247=[-6.52174108322756994810e-06,9.31822657698234608390e-06] 
dist 248=[-4.27237766209753033360e-06,1.24417765946006012520e-05] 
dist 249=[-3.66119125426833102600e-06,1.53146472125124576990e-05] 
dist 250=[-1.36729281747964071890e-06,1.77410113179307886110e-05] 
dist 251=[-8.84639599874483929470e-07,1.90915822685816753220e-05] 
dist 252=[-1.97420703252400278840e-07,1.98994379351014945100e-05] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 1, 0, 0, 2] 
dist 0=[128.22885192958393233   ,128.22885192958393233   ] 
dist 1=[126.23360302082492706   ,131.26345968315533706   ] 
dist 2=[121.35703428373783930   ,133.91583821602653237   ] 
dist 3=[113.12789600309206644   ,134.33418194779494455   ] 
dist 4=[99.751073520433767878  ,133.80389040786960491   ] 
dist 5=[85.904404114611969724  ,132.85419078151184992   ] 
dist 6=[75.800142399542712455  ,125.88329998195570835   ] 
dist 7=[66.658150513142374490  ,117.61535942351950859   ] 
dist 8=[56.620011621114662750  ,102.19126122670109067   ] 
dist 9=[46.914170835082080294  ,100.82732794822790688   ] 
dist 10=[39.078422734751563039  ,79.600436742012698516  ] 
dist 11=[31.163332874425839457  ,75.139462712575895177  ] 
dist 12=[21.115689085796382399  ,71.048866163937130562  ] 
dist 13=[11.551783825681637950  ,70.258651244750917467  ] 
dist 14=[5.5558786162012153216 ,42.413893748234224586  ] 
dist 15=[1.0121519720551255629 ,37.066498182648272566  ] 
dist 16=[-5.2916053534621653419 ,1.1068012053398035724 ] 
dist 17=[-12.312693123899993140  ,-3.0811198658214537992 ] 
dist 18=[-20.081194083918132244  ,-3.6013575080372505230 ] 
dist 19=[-24.738293037670554636  ,-3.1980403818024554561 ] 
dist 20=[-27.963513403517082820  ,-1.5494066380660629195 ] 
dist 21=[-30.046926676988738557  ,.3433726707702683097 ] 
dist 22=[-31.356779838768006291  ,1.7212074010278384545 ] 
dist 23=[-31.565064880670143068  ,2.8976202142391236985 ] 
dist 24=[-31.237986662082505052  ,4.0046195933707948314 ] 
dist 25=[-30.863890877016131444  ,4.9031112367082464199 ] 
dist 26=[-27.015310243150188539  ,5.2585546005111196434 ] 
dist 27=[-25.962713178292210593  ,5.3874896969181348085 ] 
dist 28=[-24.411628542678494864  ,5.3976434047662740833 ] 
dist 29=[-23.808935477408868820  ,4.0945818253940494389 ] 
dist 30=[-8.9095391293450106364 ,3.7233623093183576275 ] 
dist 31=[-6.9305712858549078333 ,7.3996654756974647674 ] 
dist 32=[-2.4577436793529372240 ,11.774531131437017461  ] 
dist 33=[-1.5190354012763775343 ,15.798584548374869886  ] 
dist 34=[-1.1543545149584194892 ,19.193130375925542925  ] 
dist 35=[-1.1025375721421154774 ,21.069146285531841784  ] 
dist 36=[-1.1675327381836043906 ,22.156197642765428283  ] 
dist 37=[-1.2680271601182280269 ,22.418589260011671071  ] 
dist 38=[-1.3664952822281946176 ,8.1919539491495813481 ] 
dist 39=[-1.4745703038347001763 ,8.1744735640362604050 ] 
dist 40=[-1.6144277747133699865 ,6.8206792677638849278 ] 
dist 41=[-1.7553758475769303793 ,6.8038452982962905145 ] 
dist 42=[-1.8684465361582708128 ,5.6911429109082798834 ] 
dist 43=[-1.9783109611680486236 ,5.4111882647207797776 ] 
dist 44=[-2.3070735154612993609 ,5.2334081953445159211 ] 
dist 45=[-3.0248781336090289968 ,5.1894509221653834545 ] 
dist 46=[-3.6009936702630054266 ,3.4307628498492929746 ] 
dist 47=[-4.1191531149123161927 ,3.1743540034777889364 ] 
dist 48=[-4.5348392828330557474 ,3.0802163086516354310 ] 
dist 49=[-4.7045807317862643181 ,2.6053131632425917965 ] 
dist 50=[-4.7599109335481743008 ,2.4975416734001958170 ] 
dist 51=[-4.7292054124446104714 ,2.2085780796898828842 ] 
dist 52=[-4.3310779357641990748 ,2.1313510779441975375 ] 
dist 53=[-4.1966429770397693122 ,1.2563811314591739415 ] 
dist 54=[-3.9925177762038439559 ,1.1031298201766979306 ] 
dist 55=[-3.9726848952918231635 ,.81761867458647502868] 
dist 56=[-3.8922591772613475066 ,.74651770661138097563] 
dist 57=[-3.8300338022002554072 ,1.1284073663970045608 ] 
dist 58=[-3.3798833354489761785 ,1.8385706414935910228 ] 
dist 59=[-3.2571309843023340084 ,2.4971970729307017502 ] 
dist 60=[-2.5997053956660596250 ,3.0548265220544780023 ] 
dist 61=[-2.4638566761963347398 ,3.3643092862783663323 ] 
dist 62=[-.86034456508979871755,3.5447666521364938034 ] 
dist 63=[-.64826379054874768891,3.5902249147652528844 ] 
dist 64=[-.17073712525803317632,1.4000592977803541877 ] 
dist 65=[-.06863991444622753955,1.8362552182086909603 ] 
dist 66=[.46104737036669547877,2.2043864646887806668 ] 
dist 67=[.40714519558516651011,2.4084604035453673312 ] 
dist 68=[.26633110648226954278,2.5273766938575124763 ] 
dist 69=[.12256423887096130891,2.5571272969587747227 ] 
dist 70=[.02313176857250186745,.95437259233880324942] 
dist 71=[-.06067910585365860294,.94513331437467734244] 
dist 72=[-.14249933442655494416,.77662189220430373779] 
dist 73=[-.2146715284770393748 ,.77167512757313817108] 
dist 74=[-.26022291655192923247,.63870714899154883803] 
dist 75=[-.34752072218713518109,.60594429992562412335] 
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dist 80=[-.67412090007977536992,-.04595338902049964574] 
dist 81=[-.67793696632643025134,-.06644650634598507094] 
dist 82=[-.66461267110050094299,-.21144363408186819317] 
dist 83=[-.66035036341880920998,-.1540623058399254303 ] 
dist 84=[-.55408060397426211581,-.06269123043308293281] 
dist 85=[-.5269523698600427634 ,.02934265068847155213] 
dist 86=[-.50333768108975512905,.09135573086197722558] 
dist 87=[-.49197534203745978699,.14195943470834525205] 
dist 88=[-.46178934390174126661,.18871676431358559469] 
dist 89=[-.4569320966286744972 ,.22824477604652746538] 
dist 90=[-.37644287873097844124,.25015842949821738976] 
dist 91=[-.35683248105731867301,.26877080044335020833] 
dist 92=[-.33667724343916764909,.33213243975140349907] 
dist 93=[-.3266368890040638743 ,.36905150845514669138] 
dist 94=[-.12279422464119552019,.389916809756635821  ] 
dist 95=[-.10691076042735829115,.39471124919854568257] 
dist 96=[-.07252786434703698482,.2533471271012815225 ] 
dist 97=[-.06301612951748210015,.25593772890097196437] 
dist 98=[-.02625512529537793554,.25906548764910760725] 
dist 99=[-.01874759373069832104,.28003385814722622155] 
dist 100=[-.00557806985799074126,.29449719607417126596] 
dist 101=[-.00262867206815785951,.2978143059308842367 ] 
dist 102=[-.00554787675957833321,.1224848072464870276 ] 
dist 103=[-.01634936788598269578,.12151488049716846113] 
dist 104=[-.02660636942290543491,.01852677381765472591] 
dist 105=[-.03547806400785455273,.00645153345013129346] 
dist 106=[-.04078225226248857088,-.02152294548773738514] 
dist 107=[-.04494900733842090925,-.02587994601866806998] 
dist 108=[-.06137305522538281086,-.03426501777034484526] 
dist 109=[-.07115295020714958511,-.03864730102286024641] 
dist 110=[-.07775491180670945035,-.03833266415420599579] 
dist 111=[-.08156691826490444999,-.03682614243501413712] 
dist 112=[-.08362240080832689710,-.03334511064715443564] 
dist 113=[-.08372715448412503093,-.02895946559842855508] 
dist 114=[-.08207108677822552227,-.02386123881141724095] 
dist 115=[-.08090669978847861738,-.01737401436458585115] 
dist 116=[-.07023299309286837165,-.00747386676675090559] 
dist 117=[-.06736140209137081944,.00248127392572250857] 
dist 118=[-.06298346738602470187,.00918719990109621888] 
dist 119=[-.061360610033346022  ,.01466278085984800728] 
dist 120=[-.02165247500534141457,.01973435451242274212] 
dist 121=[-.01634217706629036941,.02405600727332705382] 
dist 122=[-.00436552521576426204,.03577499119649188062] 
dist 123=[-.00179878981642479771,.04677607965663862778] 
dist 124=[.01044783042575033079,.05606256180272270270] 
dist 125=[.01116750049961390731,.06120535109479322842] 
dist 126=[.01112406908474797529,.06419884427039237340] 
dist 127=[.01077833033781541379,.06495289439544706445] 
dist 128=[.00994032487517214894,.01968721176280112194] 
dist 129=[.00887365488866064197,.01975516838623955670] 
dist 130=[.00761994340665964762,.01926335466733377414] 
dist 131=[.00601577852394890554,.01915113330010710396] 
dist 132=[.00355764490963828047,.01594801890210869684] 
dist 133=[.00108076279694336924,.01514835541531921576] 
dist 134=[-.00059796233042150902,.01451207903929543724] 
dist 135=[-.00198032035100421196,.01426133545141315416] 
dist 136=[-.00328083028210480328,.00242786016776676507] 
dist 137=[-.00439836177396206478,.00101194543018211228] 
dist 138=[-.00505442280591183099,-.00230769026864942336] 
dist 139=[-.00680446660587491213,-.00280054744849543042] 
dist 140=[-.00879768028142918340,-.00521158026433958405] 
dist 141=[-.00995255810414606194,-.00576740148132156264] 
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