8 phat 5 dirichlet min maxes function [0, 1, 0, 0, 1, 2, 0, 0, 1] 
dist 0=[341.90729122642360225   ,341.90729122642360225   ] 
dist 1=[317.94516188412491087   ,348.33605979082033458   ] 
dist 2=[283.36406925609400678   ,348.97605267380838192   ] 
dist 3=[247.53395736062753789   ,343.67584591929579625   ] 
dist 4=[181.96250222025086586   ,333.18599893063334902   ] 
dist 5=[125.13486208317100074   ,247.90418919839846229   ] 
dist 6=[70.254503176842058052  ,228.23272197339216038   ] 
dist 7=[9.3523868511606729150 ,161.46503829266844913   ] 
dist 8=[-42.682715170414784671  ,151.67633454140460228   ] 
dist 9=[-63.498033643136429666  ,32.614327086327098466  ] 
dist 10=[-71.491356100888774730  ,9.3460398915042178727 ] 
dist 11=[-77.812546474588111539  ,5.1192052654414998046 ] 
dist 12=[-85.847369953805163107  ,5.8455960119684895387 ] 
dist 13=[-86.045293195858518457  ,12.609104019009601744  ] 
dist 14=[-67.578217906669302124  ,19.464471177954546266  ] 
dist 15=[-53.814931963982838938  ,28.002701527688457655  ] 
dist 16=[-50.865139286126840014  ,36.691846291193993627  ] 
dist 17=[-2.1510953191623966406 ,38.220456925080798488  ] 
dist 18=[2.5657647451658360080 ,34.931170965706176364  ] 
dist 19=[-3.4688975344697890636 ,33.187612366180980870  ] 
dist 20=[-8.0451045384039921968 ,34.848959576266748627  ] 
dist 21=[-14.440397041660101872  ,34.412509169438191453  ] 
dist 22=[-20.799086267085507888  ,33.310143404553941828  ] 
dist 23=[-22.468225068549247883  ,25.010777087955938317  ] 
dist 24=[-15.512112512658204738  ,23.529110241804888752  ] 
dist 25=[-16.857978787601178966  ,2.7356024011363288512 ] 
dist 26=[-17.948054364146955168  ,3.1393547314739925503 ] 
dist 27=[-18.854543249336889777  ,6.7799860786045051434 ] 
dist 28=[-19.708802488343465671  ,9.0865895640091350176 ] 
dist 29=[-8.1464065434121097235 ,9.6874174245823948157 ] 
dist 30=[-8.0068097424387697399 ,3.7646158786120588455 ] 
dist 31=[-6.2708715073267028354 ,4.7690849164824820675 ] 
dist 32=[-6.0092812794034253335 ,5.2202632983446339178 ] 
dist 33=[.36163133667272907767,5.1783322009441671341 ] 
dist 34=[-.13170851647992956964,4.4512732002556426417 ] 
dist 35=[-.94214109491039451463,4.0467086449228282036 ] 
dist 36=[-1.5000247926842739713 ,4.0597176270384709444 ] 
dist 37=[-2.8306755189137406874 ,4.0895506228925185108 ] 
dist 38=[-3.7721826938241781840 ,3.9590883218350286615 ] 
dist 39=[-4.0172531996272704878 ,3.2071587880834514982 ] 
dist 40=[-1.4071956762395051118 ,2.8849729713376748725 ] 
dist 41=[-1.3178280310413889565 ,.51380886415997172363] 
dist 42=[-2.2693368684155511067 ,.33697053748360083492] 
dist 43=[-2.9656937955552453494 ,.74526098247488614945] 
dist 44=[-3.1464762615881906979 ,1.0183640366225106193 ] 
dist 45=[-.96554546481117047047,1.0846445572630132909 ] 
dist 46=[-.94106560484978029451,.62457602240178714328] 
dist 47=[-.72714003086301983074,.717910693601849066  ] 
dist 48=[-.68908000963251594927,.73318648467994252909] 
dist 49=[.02234116346307440768,.71701921155850247649] 
dist 50=[-.01751965841960794365,.56371298726968370701] 
dist 51=[-.12284038968038717795,.52896522704550375529] 
dist 52=[-.19334588915586869528,.54085937349702193536] 
dist 53=[-.29577968686539277424,.53273760804245005356] 
dist 54=[-.40238727587338527188,.51542175144310244868] 
dist 55=[-.4293604749186281192 ,.39295768554388295151] 
dist 56=[-.29401891468771635981,.36834561015532199629] 
dist 57=[-.29282084822312474146,.03281809811636483507] 
dist 58=[-.28555107440745719617,.06490489081233060776] 
dist 59=[-.28611088492027326285,.12683510490845147055] 
dist 60=[-.30556318699349103427,.16577498055572106871] 
dist 61=[-.1229443886819765983 ,.17589976204401140288] 
dist 62=[-.11952647627147117507,.07804095648557095303] 
dist 63=[-.09092145860041767012,.08866311147136775393] 
dist 64=[-.08665128497022464749,.08987751096768454041] 
dist 65=[.00985572861695793357,.08716130911141505711] 
dist 66=[-.00803957500924446065,.07107717296546123382] 
dist 67=[-.02146911581471754830,.06388193493378292575] 
dist 68=[-.03022305012060203084,.06294340565328934384] 
dist 69=[-.05074518229101051333,.06219989313184071678] 
dist 70=[-.06626529313580917104,.05983860354280451424] 
dist 71=[-.07029534769785290040,.04780676705756256226] 
dist 72=[-.02474693100215195505,.04278834314360973423] 
dist 73=[-.02283913742649655023,.00693758722581537312] 
dist 74=[-.03553963380043188006,.00940953558777752789] 
dist 75=[-.04609788817671569949,.01587400903337121049] 
dist 76=[-.04883732312584844123,.020028503251668399  ] 
dist 77=[-.01439180839540290489,.02121510944312907607] 
dist 78=[-.01393570724543704579,.01078205695274574243] 
dist 79=[-.01064360505501323572,.01191217825561499396] 
dist 80=[-.01001085338135244250,.01179844081521035888] 
dist 81=[.00068860355823897119,.01142400284545061408] 
dist 82=[-.00058837708250956186,.00880854133853888385] 
dist 83=[-.00224787592255943006,.00820506343626894367] 
dist 84=[-.00332185369778724466,.00818085764688851226] 
dist 85=[-.00506110389386510420,.00799095648923127728] 
dist 86=[-.00669666315759281715,.00770224197657789567] 
dist 87=[-.00714297688716085919,.00587881140035291505] 
dist 88=[-.00283215264367812103,.00546082572835709790] 
dist 89=[-.00266233324044182179,.00054668625169911753] 
dist 90=[-.00351347713556111186,.00118737843935650662] 
dist 91=[-.00459700944063168766,.00216518338484459746] 
dist 92=[-.00488595214696086484,.00277890439508324117] 
dist 93=[-.00181916224467910033,.00293879399423868128] 
dist 94=[-.00176051128432035107,.00127439480478449773] 
dist 95=[-.00132330427582621825,.00140838638839176514] 
dist 96=[-.00125741135304947378,.00139646467747362685] 
dist 97=[-.00025397156351058242,.00134501226515716253] 
dist 98=[-.00069261813043436753,.00107708610235435388] 
dist 99=[-.00096892736768924971,.00113945592524859748] 
dist 100=[-.00114474933988429008,.00122181091323566301] 
dist 101=[-.00119616286323524992,.00120148782345442020] 
dist 102=[-.00117453342745850888,.00114594481613711501] 
dist 103=[-.00111798382604653944,.00094897156171792736] 
dist 104=[-.00093120320395962307,.00085000802357676265] 
dist 105=[-.00083796173271769706,.00031135609227891149] 
dist 106=[-.00053452934762098815,.00018982539473191728] 
dist 107=[-.00069012863516515636,.00030363760349294648] 
dist 108=[-.00073053269071088261,.00037503292173867549] 
dist 109=[-.00021008288646690302,.00039362661926492154] 
dist 110=[-.00020289890242047746,.00017128698623837317] 
dist 111=[-.00015495727692797154,.00018637564697703754] 
dist 112=[-.00014428604553187708,.00018229536759958334] 
dist 113=[-2.66475421840598527050e-05,.00017592341364473333] 
dist 114=[-6.65217960676800610900e-05,.00013374400429606485] 
dist 115=[-9.16579483816762146860e-05,.00014290816473978138] 
dist 116=[-.00010768149392827487,.00015238429828144405] 
dist 117=[-.00011243775209402048,.00014848027565445694] 
dist 118=[-.00011138019551787010,.00014230568190019582] 
dist 119=[-.00010705216584287856,.00011157301889128440] 
dist 120=[-9.43849204960641767650e-05,.00010017705839370186] 
dist 121=[-8.80339992401397176060e-05,1.10383444216089189920e-05] 
dist 122=[-5.96177530387707222560e-05,-3.19447431945808098860e-06] 
dist 123=[-7.14107620911185189070e-05,-1.16197581119219383370e-05] 
dist 124=[-7.57152634391408253420e-05,3.85237317140776547470e-06] 
dist 125=[-2.55741294275831882250e-05,1.35992834966354764260e-05] 
dist 126=[-2.46935229952533390760e-05,1.98063816384929028850e-05] 
dist 127=[-1.84334484900463994740e-05,2.16362389593968171730e-05] 
dist 128=[-1.75004189931172546810e-05,2.12479912756683247940e-05] 
dist 129=[2.56273129576709134200e-06,2.03999134835137395520e-05] 
dist 130=[5.71756016269050566230e-06,1.62164994054099745980e-05] 
dist 131=[2.70499712034847734110e-06,1.44941180641308586560e-05] 
dist 132=[-6.48989202368873856040e-06,1.32207835941102173990e-05] 
dist 133=[-1.22317808094848638370e-05,1.29016190992317399660e-05] 
dist 134=[-1.58305601889658540800e-05,1.23612522480843718570e-05] 
dist 135=[-1.67641126469610520900e-05,9.77327970777206407160e-06] 
dist 136=[-4.91266247144498846870e-06,8.72522230421564666740e-06] 
dist 137=[-4.74601582617976263180e-06,1.30072749717851460900e-06] 
dist 138=[-7.45354809264613817940e-06,-1.66407977237542960440e-07] 
dist 139=[-9.62972173051990682120e-06,-1.20821358359224586330e-06] 
dist 140=[-1.01941193313462086080e-05,6.62363146979906553870e-07] 
dist 141=[-2.97422890083494942030e-06,1.83704515991050748580e-06] 
dist 142=[-2.86625943995642014530e-06,2.58105385334161406320e-06] 
dist 143=[-2.16004607643509150110e-06,2.79180249953606991320e-06] 
dist 144=[-2.02646806569562158280e-06,2.71746717145064659600e-06] 
dist 145=[1.91554020908300375530e-07,2.61665876658979587260e-06] 
dist 146=[5.52360013201483689710e-07,1.99018915029067635800e-06] 
dist 147=[3.37761505480127500820e-07,1.84925382849090373450e-06] 
dist 148=[-6.02004380327857637990e-07,1.68969336997739699620e-06] 
dist 149=[-1.18928341665465352340e-06,1.63835651116133630680e-06] 
dist 150=[-1.55805418268944868110e-06,1.57556891348940782370e-06] 
dist 151=[-1.65544751502390119960e-06,1.19477844530183057140e-06] 
dist 152=[-6.21873296861424674380e-07,1.10936310348297773320e-06] 
dist 153=[-6.00894978025182025040e-07,8.64355070021900124770e-08] 
dist 154=[-7.20926358805685694900e-07,-6.90126186143488523030e-08] 
dist 155=[-9.42579930294136269400e-07,-1.66994837033186000840e-07] 
dist 156=[-1.00056015923986485480e-06,6.22478815530798006740e-08] 
dist 157=[-3.75041433358832193440e-07,2.06029697683676564010e-07] 
dist 158=[-3.61670478630379125770e-07,2.96954751280641029330e-07] 
dist 159=[-2.69281459049035391240e-07,3.22433969533083008370e-07] 
dist 160=[-2.55291926689923955160e-07,3.15086996788035280470e-07] 
dist 161=[3.80314341307794659810e-08,3.02024175214128412240e-07] 
dist 162=[8.41370845984227656190e-08,2.39090486543657274820e-07] 
dist 163=[3.78803861657773158640e-08,2.13491806232260436100e-07] 
dist 164=[-9.76891539532127783270e-08,1.95341694122921118350e-07] 
dist 165=[-1.82285059390147085760e-07,1.90142278204010646760e-07] 
dist 166=[-2.35282856380087117200e-07,1.82098159446445625870e-07] 
dist 167=[-2.49025919665211367080e-07,1.43319284060988435200e-07] 
dist 168=[-7.47897246114571918020e-08,1.28229553624804351720e-07] 
dist 169=[-7.21813842322824289180e-08,1.83007280289848135950e-08] 
dist 170=[-1.08563017626453030150e-07,-3.10270284797455069860e-09] 
dist 171=[-1.40235610878194481960e-07,-1.49083334141564101160e-08] 
dist 172=[-1.48449810234622140320e-07,1.39500356611881154060e-08] 
dist 173=[-4.60438944155078341760e-08,3.20129303011219576890e-08] 
dist 174=[-4.43669719453430024910e-08,4.33962319659340168980e-08] 
dist 175=[-3.30843435674057807700e-08,4.65020587686588208030e-08] 
dist 176=[-3.12647084643917827180e-08,4.51350134723425286470e-08] 
dist 177=[2.90866917202251812330e-09,4.33808208251029987670e-08] 
dist 178=[8.21426022903432929910e-09,3.31023793880344617390e-08] 
dist 179=[1.87365615900000000000e-10,3.05491652422121432700e-08] 
dist 180=[-1.34674624164159380420e-08,2.49073844822832652250e-08] 
dist 181=[-2.19989744868146639260e-08,2.41109802177878117060e-08] 
dist 182=[-2.73581685220543086240e-08,2.31817894971368344740e-08] 
dist 183=[-2.87818146435028202330e-08,1.75205377820965859960e-08] 
dist 184=[-9.03130870502975398700e-09,1.62998478160697230990e-08] 
dist 185=[-8.70894577135890823410e-09,1.10156022300721657070e-09] 
dist 186=[-1.04703670525489451140e-08,-1.19202370078958458600e-09] 
dist 187=[-1.37121836562819937350e-08,-2.28055946472647111200e-09] 
dist 188=[-1.45577140648313909620e-08,1.09895860993153693160e-09] 
dist 189=[-5.70514703827295170070e-09,3.21345458200900970320e-09] 
dist 190=[-5.48912476993362532520e-09,4.54539013474641204480e-09] 
dist 191=[-4.14695393661561948370e-09,4.90768118101725781360e-09] 
dist 192=[-3.86532069695294887280e-09,4.78640589778815194760e-09] 
dist 193=[2.72354277351196426130e-10,4.57971665237601232500e-09] 
dist 194=[9.58832785509486566270e-10,3.64454493469832650280e-09] 
dist 195=[2.61009428579306184240e-10,3.22758918055059553890e-09] 
dist 196=[-1.73274143582545997330e-09,3.39806513176091437340e-09] 
dist 197=[-2.97636061297358342890e-09,3.28842614153502819350e-09] 
dist 198=[-3.75530252061258992150e-09,3.16112117348913292650e-09] 
dist 199=[-3.95731931183432980910e-09,2.39039554422861520080e-09] 
dist 200=[-9.59062045194689791150e-10,2.22230692604930273800e-09] 
dist 201=[-9.32265153058566015640e-10,2.83683012228007820620e-10] 
dist 202=[-1.46405669413027326820e-09,9.08700361099367697070e-12] 
dist 203=[-1.87954310625646567790e-09,3.33765750922955153390e-10] 
dist 204=[-1.98727714108788400470e-09,9.26192427525881467870e-10] 
dist 205=[-1.44309876093940616840e-09,1.30686586190766568980e-09] 
dist 206=[-1.37746047358923322320e-09,1.54587985807131265680e-09] 
dist 207=[-1.18708800835142883350e-09,1.60925198094914656120e-09] 
dist 208=[-1.10646424829916632170e-09,1.59126295111147225950e-09] 
dist 209=[-7.75474980140673558890e-10,1.51654300147513307300e-09] 
dist 210=[-7.70116543565360641110e-10,1.56647912296788219590e-09] 
dist 211=[-7.95847773920487034050e-10,1.87827774458983988100e-09] 
dist 212=[-1.45903578419937847850e-09,1.95956927538210239210e-09] 
dist 213=[-1.98666554243010655390e-09,1.90045154382334117100e-09] 
dist 214=[-2.31704558298082209120e-09,1.81954086481119194480e-09] 
dist 215=[-2.40270598888261133960e-09,1.41954139350388200780e-09] 
dist 216=[-9.86027044997834613160e-10,1.27725801003109455990e-09] 
dist 217=[-1.19499805800354106260e-09,1.30932681985099955360e-09] 
dist 218=[-1.32526522197731201340e-09,1.68023620843489075490e-09] 
dist 219=[-1.40681318182823411980e-09,1.91248274584713457760e-09] 
dist 220=[-1.42790822768773540950e-09,1.97274604000355838320e-09] 
dist 221=[-7.24938004725387152340e-10,4.89425296446303748600e-10] 
dist 222=[-6.90260091611282992570e-10,5.98275247008520174730e-10] 
dist 223=[-5.85289753672778521090e-10,6.26652978743574014630e-10] 
dist 224=[-5.44817059452736982300e-10,6.11437114590104907990e-10] 
dist 225=[-4.41914029901198244020e-10,5.81888724196401199640e-10] 
dist 226=[-3.97199949365821096600e-10,8.30190670365243050940e-10] 
dist 227=[-3.69182927876822210080e-10,9.86358399294935226410e-10] 
dist 228=[-3.61874584074779982690e-10,1.02689737442697676500e-09] 
dist 229=[-4.66535416164046423930e-10,1.01732919163860052310e-09] 
dist 230=[-5.80743356471023949010e-10,9.80262859258825984030e-10] 
dist 231=[-6.10399699537534086060e-10,9.21033903374127361660e-10] 
dist 232=[-5.89243761413072733850e-10,8.56938467450462753580e-10] 
dist 233=[-9.45780530543492609990e-10,7.30955879511364356840e-10] 
dist 234=[-1.34059178900121618480e-09,6.71707814286665734480e-10] 
dist 235=[-1.58779858364182711020e-09,6.34610317166891195500e-10] 
dist 236=[-1.65191286896092959870e-09,6.24990347267387580640e-10] 
dist 237=[-1.59578012348603533860e-09,2.24859651342088038710e-10] 
dist 238=[-1.53334983653653874420e-09,3.12085429122179020330e-10] 
dist 239=[-1.15645361684948586160e-09,3.34712366114462407070e-10] 
dist 240=[-1.07605839504509143320e-09,3.36076721875466791770e-10] 
dist 241=[-1.26384273019678437980e-10,3.83906916908386591930e-10] 
dist 242=[-5.65267521825841954960e-11,7.07049197121398873260e-10] 
dist 243=[-1.95655511183530541550e-10,9.09378184123133628540e-10] 
dist 244=[-4.18556513036495861940e-10,9.61846851956069439730e-10] 
dist 245=[-5.57508318404459378650e-10,9.30885761003715327540e-10] 
dist 246=[-6.44511475084667025190e-10,8.92806710941031754760e-10] 
dist 247=[-6.67076182067013971080e-10,6.84945131949048189020e-10] 
dist 248=[-6.44378272661173492810e-10,6.26540771455839300330e-10] 
dist 249=[-6.19196982160374869120e-10,3.58044541886965942110e-10] 
dist 250=[-4.66799083763568988560e-10,3.73320578067656845540e-10] 
dist 251=[-5.91635285207780492500e-10,3.82885895674222445250e-10] 

8 phat 5 dirichlet min maxes function [2, 1, 2, 0, 2, 1, 0, 2] 
dist 0=[341.56449991942045230   ,341.56449991942045230   ] 
dist 1=[323.71828752354016719   ,347.26453005059515872   ] 
dist 2=[272.22070137890847046   ,351.50020387686719787   ] 
dist 3=[211.99229476278656736   ,352.37133169267173845   ] 
dist 4=[159.98751857406503966   ,308.28871941087343165   ] 
dist 5=[108.62606108376329149   ,261.22356153326486384   ] 
dist 6=[49.828990405213640945  ,241.48625932019767135   ] 
dist 7=[-2.1362745931405039446 ,176.38305133083771019   ] 
dist 8=[-27.280424437433785089  ,164.13331932569174449   ] 
dist 9=[-39.882832765244990632  ,27.208546844425804380  ] 
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dist 65=[.01043345523991035477,.07163067399097413584] 
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dist 68=[-.03590638171763102629,.06683384447317926523] 
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dist 70=[-.05314783285053065816,.06354913986899244798] 
dist 71=[-.05255576733405929271,.05077595726961003252] 
dist 72=[-.05086176132874599935,.04544818827314930408] 
dist 73=[-.03916878469058255521,.00736661471717841060] 
dist 74=[-.03772717422997694744,-.00017527258017533006] 
dist 75=[-.04894031547070527813,.01108667554347616614] 
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dist 77=[-.01528755284597368994,.02984691915446108647] 
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dist 79=[-.01130600123108164839,.01215478865349238216] 
dist 80=[-.01063590151643911763,.01182902385951585721] 
dist 81=[.00076943494027788895,.00902279854929542676] 
dist 82=[.0002419834816010761 ,.00860265446176452989] 
dist 83=[-.00266290159341909401,.00795381983354801372] 
dist 84=[-.00449950395792079434,.00864132690814450848] 
dist 85=[-.00575429515788754422,.00844099548233598263] 
dist 86=[-.00634144397169226627,.00813710868917618359] 
dist 87=[-.00627886509762954563,.00620623550391208928] 
dist 88=[-.00604245798568752625,.00576997395313552374] 
dist 89=[-.00484374793975539648,.00050810626297094600] 
dist 90=[-.00432767648814514752,-.00026294794913565563] 
dist 91=[-.00482328157879393607,.00197963616095447131] 
dist 92=[-.00512938503758379218,.00366110151060980350] 
dist 93=[-.00193496456258464758,.00471648917239667652] 
dist 94=[-.00187267234079214918,.00499213256632012262] 
dist 95=[-.00140723096135576090,.00149059178898813005] 
dist 96=[-.00133758510615891608,.00142254573904020983] 
dist 97=[-.00010160851280467310,.00121092640425733845] 
dist 98=[-.00058145901005898620,.00110122233959977893] 
dist 99=[-.00106579850766574172,.00091635836078879100] 
dist 100=[-.00137189305886653778,.00099865903971284914] 
dist 101=[-.00156766065593904370,.00097868404688583459] 
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dist 103=[-.00081938887506501171,.00074468638008707013] 
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dist 105=[-.00060281908075576791,.00020680162966002302] 
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dist 107=[-.00072596196028021638,.00039121827562745866] 
dist 108=[-.00076875446664322751,.00044989500667361361] 
dist 109=[-.00022860901388721396,.00048756687180534676] 
dist 110=[-.00022090343753679964,.00049930348897407268] 
dist 111=[-.00016566923410685588,.00018506602862369933] 
dist 112=[-.00015700767034051460,.00017921755652191006] 
dist 113=[1.23629793615166745270e-05,.00013486400053539435] 
dist 114=[3.97901184152416127940e-05,.00012825044798830294] 
dist 115=[-1.72081323038849692330e-05,.00012035461083920715] 
dist 116=[-6.01995942765848971910e-05,.00012990506088203190] 
dist 117=[-8.75448452549810740550e-05,.00012620374619929080] 
dist 118=[-9.55387995472304431260e-05,.00012152648754438106] 
dist 119=[-9.37455204794640835590e-05,9.18958068824585980320e-05] 
dist 120=[-8.99793309601556326560e-05,8.57643295293491379530e-05] 
dist 121=[-7.14760359133687908180e-05,6.30476701240821498000e-06] 
dist 122=[-6.38749327678951803640e-05,-5.39795753902233919010e-06] 
dist 123=[-6.99177588431581696400e-05,2.86665193633199765090e-05] 
dist 124=[-7.43018318614120483710e-05,5.39874979027890730160e-05] 
dist 125=[-2.88563054112012996350e-05,6.98564623311313067680e-05] 
dist 126=[-2.78645259221446110100e-05,7.39728817110067657460e-05] 
dist 127=[-2.08043833863422221090e-05,2.16621432969184264650e-05] 
dist 128=[-1.97520836181126000030e-05,2.09204394554221048440e-05] 
dist 129=[2.88652885194778256120e-06,1.58612393903487679020e-05] 
dist 130=[5.31122349651991681820e-06,1.48972914013652827610e-05] 
dist 131=[-2.93474696358176084070e-06,1.37556071358614603750e-05] 
dist 132=[-8.10964489781730649250e-06,1.49171835872147089940e-05] 
dist 133=[-1.13845616016965396310e-05,1.45588916394433038090e-05] 
dist 134=[-1.23066722331459712370e-05,1.39496621084684488420e-05] 
dist 135=[-1.19727486452721585260e-05,1.10304249766569620870e-05] 
dist 136=[-1.15265855586923489460e-05,9.84768497699898092860e-06] 
dist 137=[-8.76359446940108755210e-06,1.46994802661322488180e-06] 
dist 138=[-8.41103195418729432970e-06,-1.85685896370694634260e-07] 
dist 139=[-1.08669958709644304560e-05,2.65675073317021374360e-06] 
dist 140=[-1.15039606397463057690e-05,5.24423288254144340440e-06] 
dist 141=[-3.35584508262846468260e-06,6.86864635915133452050e-06] 
dist 142=[-3.23416574286304845490e-06,7.29708702074485342280e-06] 
dist 143=[-2.43775313215885379490e-06,2.73850873027196579240e-06] 
dist 144=[-2.28695951240309837950e-06,2.64539267392549897850e-06] 
dist 145=[2.14891339137073348990e-07,1.97757698534279511210e-06] 
dist 146=[6.21917260965090203780e-07,1.87764598211939286000e-06] 
dist 147=[-2.74195672853394050190e-07,1.77119319006202214830e-06] 
dist 148=[-9.07174537831453543620e-07,1.90724893794877281450e-06] 
dist 149=[-1.30716288224254927950e-06,1.84942870562270835570e-06] 
dist 150=[-1.41863345580833658600e-06,1.77860948738372165140e-06] 
dist 151=[-1.38551598376805609540e-06,1.34875008190067080130e-06] 
dist 152=[-1.32794565985373813060e-06,1.25241608003240650740e-06] 
dist 153=[-1.05014548330049358740e-06,9.82324946564040094830e-08] 
dist 154=[-9.38180109859962474160e-07,-7.70403785386148359740e-08] 
dist 155=[-1.06370115728793058330e-06,4.25561842694636227290e-07] 
dist 156=[-1.12912374936891629190e-06,7.97710053485623305850e-07] 
dist 157=[-4.22488611126510634680e-07,1.03085146992928651920e-06] 
dist 158=[-4.07470202673802548010e-07,1.09132502972945333310e-06] 
dist 159=[-3.03224286018509701460e-07,3.23032105854704199710e-07] 
dist 160=[-2.87659864437202908930e-07,3.11734728924403972840e-07] 
dist 161=[4.25829699060963482580e-08,2.32771058871420876640e-07] 
dist 162=[7.57902098632423861120e-08,2.20606861893000866170e-07] 
dist 163=[-4.59438125052019698210e-08,2.03468537432232165480e-07] 
dist 164=[-1.22228480980370514100e-07,2.19972190049798162930e-07] 
dist 165=[-1.70292030513452799730e-07,2.14165609110484480660e-07] 
dist 166=[-1.83383278848082598290e-07,2.05080109976610904190e-07] 
dist 167=[-1.77822233128343214460e-07,1.61630415538360248720e-07] 
dist 168=[-1.71108189611558000180e-07,1.44424772822482160490e-07] 
dist 169=[-1.29286160133322938260e-07,2.17012137099789597920e-08] 
dist 170=[-1.23156425844291264550e-07,-2.25991501987555044230e-09] 
dist 171=[-1.58831970693891342820e-07,3.83141634298342993890e-08] 
dist 172=[-1.68084823788443658070e-07,7.57795893094561602930e-08] 
dist 173=[-5.06688460017897860930e-08,9.92781675524512234330e-08] 
dist 174=[-4.88274935679310737770e-08,1.05441113565741637660e-07] 
dist 175=[-3.64406074108205565200e-08,4.08743944163171043730e-08] 
dist 176=[-3.44147599271856936790e-08,3.94245131790112162100e-08] 
dist 177=[1.02107809124387359980e-09,2.94013680971230927800e-08] 
dist 178=[6.70198204530859592410e-09,2.78543040821434959760e-08] 
dist 179=[-4.42951860681756003760e-09,2.80145864934243260760e-08] 
dist 180=[-1.38846943141270311170e-08,2.99748291008077499810e-08] 
dist 181=[-1.98373510130441822430e-08,2.90583984263374806250e-08] 
dist 182=[-2.14497652914800704030e-08,2.78946264563674799810e-08] 
dist 183=[-2.08857088340491980160e-08,2.13794143050299079040e-08] 
dist 184=[-2.00090672792733089440e-08,1.96103941516408016640e-08] 
dist 185=[-1.57297355809709367080e-08,5.17529032910852890030e-09] 
dist 186=[-1.47908549709741104630e-08,3.18420077377115238090e-09] 
dist 187=[-1.83707745525018402180e-08,6.31550213496099838550e-09] 
dist 188=[-1.93103099670149948610e-08,1.17915055693435880380e-08] 
dist 189=[-6.76322069277942039860e-09,1.52213039527366168230e-08] 
dist 190=[-6.51556749950287375870e-09,1.61107921236146325880e-08] 
dist 191=[-4.85336360690817851420e-09,5.38940365758134712360e-09] 
dist 192=[-4.58769455039747778660e-09,5.19453582451471906180e-09] 
dist 193=[6.43579837593789562970e-10,3.86945296471146984600e-09] 
dist 194=[1.16536178318503257030e-09,3.66204171519613673820e-09] 
dist 195=[-6.59105201200436776920e-10,3.33953485408362905930e-09] 
dist 196=[-1.88041705101441602100e-09,3.60037840936364143240e-09] 
dist 197=[-2.64805165644794893290e-09,3.48748162388887070680e-09] 
dist 198=[-2.85333428282857339150e-09,3.34998647578693283070e-09] 
dist 199=[-2.76872860444281818690e-09,2.55204589402458779800e-09] 
dist 200=[-2.65751420317755564870e-09,2.35544054318197948220e-09] 
dist 201=[-2.07077690759561783780e-09,-6.24000123827286715460e-11] 
dist 202=[-1.87016272992559068920e-09,-2.18138421162649368710e-10] 
dist 203=[-2.08362765277320173850e-09,8.08961742592208856600e-10] 
dist 204=[-2.22509333966397262630e-09,1.50906433228313735680e-09] 
dist 205=[-2.15450257900950391750e-09,1.95358184135091429070e-09] 
dist 206=[-2.06759866538503458290e-09,2.06829610501941507210e-09] 
dist 207=[-1.58280038130704112420e-09,9.50491454432842971820e-10] 
dist 208=[-1.45234203846580151890e-09,9.10497148146045707410e-10] 
dist 209=[-5.82153289072755199320e-11,7.12635401151172023120e-10] 
dist 210=[-4.94511197145457978650e-10,1.00280948031188103780e-09] 
dist 211=[-9.31108984533640437170e-10,1.34058233794029952600e-09] 
dist 212=[-1.20357592541940823670e-09,1.42867775035676886040e-09] 
dist 213=[-1.37448663102979339400e-09,1.38910140976668511660e-09] 
dist 214=[-1.41946582779421469030e-09,1.32685441606446588210e-09] 
dist 215=[-1.37711678890971569570e-09,1.05754262573509634020e-09] 
dist 216=[-1.31849568873127038200e-09,9.31552990799443479750e-10] 
dist 217=[-1.02948140931342279790e-09,5.54703123711934693550e-10] 
dist 218=[-9.49639390917730660500e-10,5.06542363795166974330e-10] 
dist 219=[-1.13221437609442250600e-09,5.79553817509284380720e-10] 
dist 220=[-1.17956269718280809520e-09,6.97612644022027199750e-10] 
dist 221=[-9.21277581455723780780e-10,7.71542367524282446910e-10] 
dist 222=[-9.58791785952885711350e-10,8.02602270400237723670e-10] 
dist 223=[-9.40920906517991062620e-10,7.83994027223258703150e-10] 
dist 224=[-8.89718733082646992120e-10,7.45231142919558670820e-10] 
dist 225=[-7.70967904720328522860e-10,6.19124637555661054200e-10] 
dist 226=[-7.12583695842471719020e-10,5.57038351296354574680e-10] 
dist 227=[-4.14511104482214262610e-10,6.15460364012432718520e-10] 
dist 228=[-6.31103751250897962380e-10,9.30402354447475996570e-10] 
dist 229=[-7.80874331673103953890e-10,1.12757121968468598160e-09] 
dist 230=[-8.19761075205803986220e-10,1.17864802043003005230e-09] 
dist 231=[-8.13646910759845172370e-10,1.15565538568574601390e-09] 
dist 232=[-7.89875582811416266520e-10,1.09396940982684995570e-09] 
dist 233=[-7.51875930642996994800e-10,9.39983721966385166090e-10] 
dist 234=[-6.99202213511584654580e-10,8.64233507659373777000e-10] 
dist 235=[-1.02556978653139598240e-09,1.02195031520263260640e-09] 
dist 236=[-1.23419210123212101790e-09,1.22308940569552632080e-09] 
dist 237=[-1.36481355079117756720e-09,1.34902888053930340610e-09] 

8 phat 5 dirichlet min maxes function [2, 1, 1, 2, 2, 0, 1, 1, 2] 
dist 0=[340.98956043613263478   ,340.98956043613263478   ] 
dist 1=[317.50285725692682086   ,347.24345145247396450   ] 
dist 2=[283.45474719487690530   ,347.68577086237082147   ] 
dist 3=[247.95416079730666881   ,342.24677292361362491   ] 
dist 4=[182.18723382899319376   ,331.71771371269511503   ] 
dist 5=[125.71704206903001053   ,246.54173981654091464   ] 
dist 6=[71.056054214202613484  ,226.92699150383167493   ] 
dist 7=[10.198321478947662476  ,160.70386244962524834   ] 
dist 8=[-41.807104284764040773  ,150.83426621155166266   ] 
dist 9=[-62.459550290164137145  ,32.886770795589295356  ] 
dist 10=[-70.439706021056807050  ,9.0545136484942475054 ] 
dist 11=[-77.895789236085695490  ,4.6596225560484058259 ] 
dist 12=[-86.000707171885413510  ,5.2971675746328146161 ] 
dist 13=[-86.197712493989538361  ,12.076222295409297247  ] 
dist 14=[-66.528984497480161933  ,19.073576249837915662  ] 
dist 15=[-52.745457341161324739  ,24.510362577688311252  ] 
dist 16=[-50.374390677381785475  ,33.561965017781087640  ] 
dist 17=[-.54519263252592709482,35.129649745156444425  ] 
dist 18=[.3743409651694412657 ,33.634849348515829028  ] 
dist 19=[-6.0138066567282660329 ,31.185616772047991493  ] 
dist 20=[-10.814091939007521136  ,31.796484738486775701  ] 
dist 21=[-17.176033491698775320  ,32.300738516593741572  ] 
dist 22=[-23.968444447901212174  ,31.322632396224236771  ] 
dist 23=[-25.743394952997519362  ,25.614658104859445041  ] 
dist 24=[-13.222889390513198130  ,22.964137225463569222  ] 
dist 25=[-11.931713358087997413  ,6.5742223776396761051 ] 
dist 26=[-18.160288580868079830  ,6.4674250439149371483 ] 
dist 27=[-23.637958991587370068  ,10.192344089559961135  ] 
dist 28=[-24.946966916990761706  ,12.662159589658585289  ] 
dist 29=[-6.6288553640683153442 ,13.312252235765125523  ] 
dist 30=[-6.4861017788365404304 ,4.0131738574081055692 ] 
dist 31=[-5.0353438667321218732 ,4.9534132935662866627 ] 
dist 32=[-4.8054851652561249211 ,5.3185690079317878907 ] 
dist 33=[.31160460965254928884,5.2759491813768373265 ] 
dist 34=[.07271983867995950378,4.2992138351060058956 ] 
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dist 97=[.00015188739128795736,.00153251867003454923] 
dist 98=[-5.25966631647116467030e-05,.00118393204277294991] 
dist 99=[-.00020643818822690615,.00109155263062966698] 
dist 100=[-.00046459880336600683,.00090437421296906889] 
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dist 113=[-8.08757340970842246280e-05,.00024869145656310516] 
dist 114=[-5.58069265917071913780e-05,.00020335973732354204] 
dist 115=[-2.85183504345611940400e-05,.00018063556771109045] 
dist 116=[-4.04327594395012674400e-05,.00012624458749367047] 
dist 117=[-6.52366358355623696010e-05,.00012278178119231247] 
dist 118=[-8.43159820558143952300e-05,.00011769119269122587] 
dist 119=[-8.99052856841566464410e-05,9.16575923110907891350e-05] 
dist 120=[-8.93451617655149679810e-05,8.26982427415714852390e-05] 
dist 121=[-8.47235383224728683590e-05,6.66271182630314696820e-06] 
dist 122=[-7.69036923909023171080e-05,9.39278585772976480950e-06] 
dist 123=[-7.17354483737630150500e-05,1.87336776815814725670e-05] 
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dist 125=[-2.57315907703904598000e-05,2.61803114774996166910e-05] 
dist 126=[-2.48456411801649107470e-05,9.88805476616826932970e-06] 
dist 127=[-1.85471413870857401350e-05,9.57705628955667747440e-06] 
dist 128=[-1.76084026182075851230e-05,7.20987896034345515060e-06] 
dist 129=[2.57841370618650064590e-06,6.85685409765735596510e-06] 
dist 130=[-9.25252655768851558650e-07,8.52170755073262559280e-06] 
dist 131=[-3.22421992228553383820e-06,1.22680260926542980760e-05] 
dist 132=[-4.68722036799071790320e-06,1.33021516109912471950e-05] 
dist 133=[-5.11629531253247525710e-06,1.29810862392968566950e-05] 
dist 134=[-5.02158683988988289700e-06,1.24374300594779057840e-05] 
dist 135=[-4.82050241076580564920e-06,9.83345862106412072270e-06] 
dist 136=[-3.82888425599595718600e-06,8.77904756624719300030e-06] 
dist 137=[-4.00350979390698115260e-06,1.30824121811997895980e-06] 
dist 138=[-7.49887724477192521110e-06,1.53546614657182804230e-06] 
dist 139=[-9.68842849920134036530e-06,2.88764533949030445830e-06] 
dist 140=[-1.02562957585569489270e-05,3.73513422967510811270e-06] 
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dist 143=[-2.17404989339449993170e-06,1.13959659599550467760e-06] 
dist 144=[-2.03940299059305904830e-06,8.54294034331226641310e-07] 
dist 145=[1.91568694935739563830e-07,8.11467274521171406540e-07] 
dist 146=[-2.11886908048790945910e-07,1.13287230253809894480e-06] 
dist 147=[-4.97417166377027961960e-07,1.58080156461844205870e-06] 
dist 148=[-6.78112508974778443150e-07,1.70204737612718243090e-06] 
dist 149=[-7.28972416192697205030e-07,1.65029469232577587970e-06] 
dist 150=[-7.09495736456601765960e-07,1.58708870416208040150e-06] 
dist 151=[-6.82281026371411552600e-07,1.20324147689137700540e-06] 
dist 152=[-5.22902434473386682460e-07,1.11747430136711323220e-06] 
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dist 154=[-7.25039414629983187540e-07,2.13731339040009723130e-07] 
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dist 157=[-3.76858906238239824010e-07,4.59708005741923009180e-07] 
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dist 160=[-2.56551487176992184890e-07,1.07113525547105215550e-07] 
dist 161=[3.86705842552466086730e-08,1.01692228506186172720e-07] 
dist 162=[-1.48772795935989010680e-08,1.26093631302830214910e-07] 
dist 163=[-4.91698636412889331750e-08,1.80627349280022400750e-07] 
dist 164=[-7.08478960040093414020e-08,1.95314142319570944830e-07] 
dist 165=[-7.69054890129447302580e-08,1.90128384062245908750e-07] 
dist 166=[-7.51774752703453801130e-08,1.82079045840167972320e-07] 
dist 167=[-7.20125375595954263900e-08,1.43360244391491384460e-07] 
dist 168=[-5.72889205987329043460e-08,1.28220172903212004120e-07] 
dist 169=[-5.76695199888699756100e-08,1.77603560823861930630e-08] 
dist 170=[-1.08387550908365708340e-07,2.46285353724552884430e-08] 
dist 171=[-1.40152066602217082530e-07,4.50853290071322165190e-08] 
dist 172=[-1.48389312261470590530e-07,5.79010655146716886150e-08] 
dist 173=[-4.57941536680261537580e-08,6.12249958381374650720e-08] 
dist 174=[-4.40698930173816511950e-08,1.55810981876816289430e-08] 
dist 175=[-3.32688215829465941650e-08,1.50010928346482561890e-08] 
dist 176=[-3.10591911004834923980e-08,1.15081085568699472830e-08] 
dist 177=[2.40969066263933631180e-09,1.06326637680263036510e-08] 
dist 178=[-3.06526913485449090890e-09,1.81877881158390518100e-08] 
dist 179=[-6.86321720449806393450e-09,2.50892826671712060150e-08] 
dist 180=[-9.28822839567388045120e-09,2.69232749965957086420e-08] 
dist 181=[-9.95653125688625320910e-09,2.60076913956612006950e-08] 
dist 182=[-9.65118309933085039540e-09,2.50534358977436556820e-08] 
dist 183=[-9.29253670800788182570e-09,1.85933062321633815010e-08] 
dist 184=[-6.98690042845194026300e-09,1.76135348107453518790e-08] 
dist 185=[-6.54721629886300124520e-09,3.43603868989502948260e-10] 
dist 186=[-9.56671462557099828350e-09,1.71271572234465374190e-09] 
dist 187=[-1.27158004573715200150e-08,3.70826006831642474630e-09] 
dist 188=[-1.35831938993177014070e-08,5.14087679221239236230e-09] 
dist 189=[-6.87268166422766198200e-09,5.51243543346355489350e-09] 
dist 190=[-6.61796300421035011970e-09,1.65854567298233520600e-09] 
dist 191=[-4.94314487105619871920e-09,1.58481555219524320790e-09] 
dist 192=[-4.65776078188565898720e-09,1.29749778468181432060e-09] 
dist 193=[8.20557455669262211230e-11,1.15319700817863583240e-09] 
dist 194=[-6.91482877122318041220e-10,2.47864112593053378180e-09] 
dist 195=[-1.17561991920533881580e-09,3.48689898165377983580e-09] 
dist 196=[-1.48077016176383719700e-09,3.75358601916109169600e-09] 
dist 197=[-1.56420850085392919560e-09,3.64171541436381166020e-09] 
dist 198=[-1.55980215664633504940e-09,3.49174935074520672070e-09] 
dist 199=[-1.52624601814647921260e-09,2.70324863397646098520e-09] 
dist 200=[-1.46967792566546868800e-09,2.45492235143015967640e-09] 
dist 201=[-1.37652488290911147310e-09,1.29833675149218525090e-09] 
dist 202=[-1.95678601949371631770e-09,1.98033551127007229930e-09] 
dist 203=[-2.44256278402676611510e-09,2.40552154849708254660e-09] 
dist 204=[-2.58488578698679794240e-09,2.67163414401872509310e-09] 
dist 205=[-2.60283113162015060230e-09,2.74024031547822294490e-09] 
dist 206=[-2.52091774296965109570e-09,-6.03997137933144941390e-10] 
dist 207=[-2.41444743553347868070e-09,-3.75655279282223119290e-10] 
dist 208=[-1.87206150891774384350e-09,1.61703851966926789430e-10] 
dist 209=[-1.69336173695330491220e-09,1.14933460453998830150e-09] 
dist 210=[-5.61177060439163804980e-10,1.76518368722087535120e-09] 
dist 211=[-3.65432791803067944550e-10,2.15097377024856158830e-09] 
dist 212=[-3.26634595583853579030e-10,2.25141526313913007540e-09] 
dist 213=[-3.36095110072492209090e-10,2.22357741306855434040e-09] 
dist 214=[-3.74278426603295440690e-10,2.11467544585602539750e-09] 
dist 215=[-4.75777287783065652210e-10,1.94047484726254663220e-09] 
dist 216=[-9.15353382049949570450e-10,1.80715914096119975800e-09] 
dist 217=[-2.02639340710598282140e-09,1.69418645453082651050e-09] 
dist 218=[-2.75019999129796999500e-09,1.71498074669387271760e-09] 
dist 219=[-3.20339976540562449500e-09,1.72801114422505748850e-09] 
dist 220=[-3.32091820918131588210e-09,1.73142989564571354810e-09] 
dist 221=[-2.21980008025680715810e-09,5.25036007422486875900e-10] 
dist 222=[-2.13517040662632775430e-09,-4.76138595551543223190e-10] 
dist 223=[-1.62534576023361126260e-09,-1.37434374461128737520e-10] 
dist 224=[-1.49850412153535593340e-09,4.05981037655587355010e-10] 
dist 225=[-1.14051059345626842690e-09,9.49416428372303447330e-10] 
dist 226=[-8.04363293475833344190e-10,1.28819834046271793340e-09] 
dist 227=[-8.10704737177307845120e-10,1.50033933389762401590e-09] 
dist 228=[-8.12304293711174710100e-10,1.55539430801954652800e-09] 
dist 229=[-7.87459993836379373360e-10,1.52358526524855248790e-09] 
dist 230=[-7.53929694621518467940e-10,1.44380793544183463900e-09] 
dist 231=[-5.87474016613872541490e-10,1.22995367859250877550e-09] 
dist 232=[-5.29043455253663383830e-10,1.12472516290338322730e-09] 
dist 233=[-9.00304047394914629860e-10,1.00557515419779067980e-09] 
dist 234=[-1.39178126269937019590e-09,9.35374750841852320520e-10] 
dist 235=[-1.69951315885549691030e-09,8.91614434680876256220e-10] 
dist 236=[-1.93548440738348152210e-09,8.64214161386814033970e-10] 
dist 237=[-2.01121102227517907570e-09,8.57105732882879321290e-10] 
dist 238=[-1.94661982533173239630e-09,5.96936544669899962430e-10] 
dist 239=[-1.86682501730531639750e-09,6.07823979789204099510e-10] 
dist 240=[-1.43330163320162420990e-09,6.25295826925714729740e-10] 
dist 241=[-1.31005966099771463750e-09,1.12657638293563466490e-09] 
dist 242=[-1.03693028938814622910e-09,1.70812974782652890500e-09] 
dist 243=[-1.20662015322026610830e-09,2.07225595978374938680e-09] 
dist 244=[-1.25061765749142945930e-09,2.16667888837514592020e-09] 
dist 245=[-1.23602923912152611150e-09,2.12410567173766536780e-09] 
dist 246=[-1.17978636799191165910e-09,2.01115013761339797780e-09] 
dist 247=[-1.08996231046428314060e-09,1.72534433665281621200e-09] 
dist 248=[-1.01477173617562290740e-09,1.58472534761916026090e-09] 
dist 249=[-1.70627158577572752500e-09,1.56768448107825010240e-09] 
dist 250=[-2.18027770981841145380e-09,1.74888286038138867100e-09] 
dist 251=[-2.47706477958317996970e-09,1.86233612188389409710e-09] 

8 phat 5 dirichlet min maxes function [2, 1, 0, 0, 1, 0, 0, 1] 
dist 0=[360.07717619703774655   ,360.07717619703774655   ] 
dist 1=[331.10830550197136035   ,370.88216823023874781   ] 
dist 2=[269.87170009655158638   ,367.39655026612337396   ] 
dist 3=[201.96293064330281168   ,349.05102985191644671   ] 
dist 4=[146.61384397032301053   ,286.89396611666343470   ] 
dist 5=[94.827733341670981157  ,224.19526198447549507   ] 
dist 6=[39.765146428151927310  ,209.78101340314455956   ] 
dist 7=[-7.6105711250243171270 ,153.60308821149832557   ] 
dist 8=[-29.842249153752943372  ,128.16373093991301335   ] 
dist 9=[-67.898565206617483532  ,-3.1725046680675682353 ] 
dist 10=[-89.958169666052866775  ,-20.566518616138933336  ] 
dist 11=[-100.26074873925905118   ,-15.318544588214447089  ] 
dist 12=[-100.84803016338040364   ,-3.6042891868525859280 ] 
dist 13=[-83.753933085517982119  ,7.0972429584600445077 ] 
dist 14=[-80.608490962029784683  ,22.596031298396955102  ] 
dist 15=[-7.3597430725961569605 ,39.164643964786511273  ] 
dist 16=[10.033942248571743376  ,55.186036070202986242  ] 
dist 17=[12.591031444832654165  ,66.397488151300623522  ] 
dist 18=[2.8623426499438429530 ,68.132186948236055185  ] 
dist 19=[-7.6620295613079705960 ,59.481454295121355454  ] 
dist 20=[-14.601688648109910302  ,57.567426381371744510  ] 
dist 21=[-19.467119643308932279  ,39.411210871282157350  ] 
dist 22=[-20.557171412748744350  ,35.665651941429419507  ] 
dist 23=[-29.363007804767322113  ,7.4826729435773844639 ] 
dist 24=[-35.707040671446732864  ,3.3700281428373646754 ] 
dist 25=[-38.129730978297732421  ,7.0119112946136076006 ] 
dist 26=[-37.497294645214524629  ,13.984428121582617142  ] 
dist 27=[-31.859736474984999990  ,21.241032103151812390  ] 
dist 28=[-28.610925581297321101  ,25.987119254848215594  ] 
dist 29=[-8.8632492097590373698 ,29.158171029578406439  ] 
dist 30=[-8.4177961923697416835 ,30.370292786705360011  ] 
dist 31=[.00238886235011542888,30.205280103233749751  ] 
dist 32=[1.3775652830259063128 ,28.082850292450933998  ] 
dist 33=[1.7769614023439414677 ,7.5999301049209670085 ] 
dist 34=[.57733230757053015609,7.5533205859851704387 ] 
dist 35=[-.66444221799860602786,6.1978534807229742015 ] 
dist 36=[-1.4556155634127552991 ,6.0235170151786180602 ] 
dist 37=[-1.9571988365042525082 ,4.6838014311737494321 ] 
dist 38=[-2.0879818537833488100 ,4.3718086140628776451 ] 
dist 39=[-3.3269743836424095033 ,.5197478761844834061 ] 
dist 40=[-3.8424639340580377577 ,-.07633803659854427294] 
dist 41=[-3.9426819689760532429 ,-.47349251337149086151] 
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dist 142=[-3.29608217776212230800e-06,1.55730534424283316220e-06] 
dist 143=[4.89806231360723419760e-07,1.51844196026918153480e-06] 
dist 144=[1.03769004657196952500e-06,1.60388695850706561440e-06] 
dist 145=[7.15347654087552732440e-07,2.30512566666900811360e-06] 
dist 146=[1.91181614956971930950e-07,2.49694709823945138710e-06] 
dist 147=[-3.34728855680003671520e-07,2.43467896560580987910e-06] 
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dist 151=[-7.53335464988137680790e-07,2.44807176460147703020e-07] 
dist 152=[-1.40884058247468902130e-06,-3.19058809448420872050e-08] 
dist 153=[-1.81943133253826889450e-06,-2.22101985895545671670e-07] 
dist 154=[-1.92591663557016304570e-06,-9.38362139565743974530e-08] 
dist 155=[-5.60905033012073311640e-07,3.50292401559168769900e-08] 
dist 156=[-5.40356708448773133940e-07,1.15965291174512423060e-07] 
dist 157=[-4.06941033152665443010e-07,1.67260196452502995790e-07] 
dist 158=[-3.81618572697600138130e-07,1.81868013279729764090e-07] 
dist 159=[3.60579427340639976060e-08,1.77945690131499618850e-07] 
dist 160=[1.03946103689511985070e-07,2.12946214909014444440e-07] 
dist 161=[9.68026974589739542430e-08,2.96793466968716369470e-07] 
dist 162=[2.13026814565809409630e-08,3.19350888918912546100e-07] 
dist 163=[-5.43456240324420723460e-08,3.09482981155006104630e-07] 
dist 164=[-1.01563101576868688280e-07,2.97582252979246638820e-07] 
dist 165=[-1.31149630306600290500e-07,2.25509379166434935890e-07] 
dist 166=[-1.38825696901956913580e-07,2.09426554734224857000e-07] 
dist 167=[-6.97890038949185344520e-08,1.67854672048053677320e-08] 
dist 168=[-1.36256092797530900530e-07,-1.23511575145682883690e-08] 
dist 169=[-1.77921347419555096660e-07,-2.38214305306881624000e-08] 
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dist 171=[-7.02154689913827761160e-08,7.13306158227300579490e-09] 
dist 172=[-6.76713278189167963160e-08,1.68480677483278264900e-08] 
dist 173=[-5.05243588850959030140e-08,2.29815906775190157550e-08] 
dist 174=[-4.77285836775914301750e-08,2.46780171069667247670e-08] 
dist 175=[6.37232264607845561730e-09,2.39974485151642183940e-08] 
dist 176=[1.24171613488911932110e-08,2.46302937545875981400e-08] 
dist 177=[7.72443145016059602060e-09,3.48998564731898939230e-08] 
dist 178=[1.27786559580000000000e-10,3.76495244961988737140e-08] 
dist 179=[-7.48610150163059602060e-09,3.66152809007434237280e-08] 
dist 180=[-1.22458016636811932110e-08,3.50714252072991616690e-08] 
dist 181=[-1.52379430274999539500e-08,2.75080770093039892480e-08] 
dist 182=[-1.60371793718551566690e-08,2.46814540430290406950e-08] 
dist 183=[-1.14136356675373197910e-08,4.13320093181726716990e-09] 
dist 184=[-2.08618998063870647580e-08,2.90215460673403933380e-10] 
dist 185=[-2.67790697115203534210e-08,-3.25560795693764418210e-09] 
dist 186=[-2.83134461537307089090e-08,-9.34480940321199218430e-11] 
dist 187=[-9.38785745660239590810e-09,3.07286388288230433950e-09] 
dist 188=[-9.00462069733575880960e-09,5.04936456679968816580e-09] 
dist 189=[-6.96900147324600684320e-09,6.28901436798136546200e-09] 
dist 190=[-6.33550943513849609950e-09,6.61418406838491951130e-09] 
dist 191=[-3.17202819273476745440e-10,6.53290322329328327890e-09] 
dist 192=[-2.45207525225207292210e-10,6.20535939604677341330e-09] 
dist 193=[-7.32914116235203962760e-10,5.67991384760870864880e-09] 
dist 194=[-1.52112016913273863970e-09,5.41930613091030238350e-09] 
dist 195=[-2.31088665855927331650e-09,5.24056836641487859500e-09] 
dist 196=[-2.80465349352726999690e-09,5.04036081229019020270e-09] 
dist 197=[-3.11524046218471856790e-09,3.78933801488593318270e-09] 
dist 198=[-3.19873062641093202900e-09,3.54206549318741361470e-09] 
dist 199=[-3.15161612805789244720e-09,8.13096271252549755730e-10] 
dist 200=[-2.97301899954243696690e-09,4.99787094126036969990e-10] 
dist 201=[-2.89160187128305033330e-09,7.84763481846509950740e-11] 

8 phat 5 dirichlet min maxes function [0, 1, 1, 1, 0, 0, 2] 
dist 0=[299.50254089741753982   ,299.50254089741753982   ] 
dist 1=[288.70542103094099301   ,302.67784657440095718   ] 
dist 2=[269.54912672735759649   ,301.11290572269672918   ] 
dist 3=[241.75326931618266337   ,279.41486716724045777   ] 
dist 4=[196.58458017183608726   ,276.02081261664026190   ] 
dist 5=[148.57292620632951666   ,194.41833336638012964   ] 
dist 6=[109.61193810070477492   ,182.28911928646933308   ] 
dist 7=[71.773466071261269118  ,118.58557173525447031   ] 
dist 8=[28.579135417807930960  ,89.871490189225135579  ] 
dist 9=[-13.802443943836816977  ,22.154167642854527722  ] 
dist 10=[-41.478338490634014755  ,11.885842069509687268  ] 
dist 11=[-55.603655657436815739  ,-10.606089508278861368  ] 
dist 12=[-58.018713039047598690  ,-15.008308313149074017  ] 
dist 13=[-54.247410662227994269  ,-9.8896896388269163531 ] 
dist 14=[-52.681314038805976637  ,6.2373351074975967248 ] 
dist 15=[-40.948497964379195025  ,20.940239484963516097  ] 
dist 16=[-38.496294058362715300  ,34.361815032820375068  ] 
dist 17=[-7.9110546960883010293 ,43.847659177721564283  ] 
dist 18=[-3.5476706798244304133 ,45.704121389367194105  ] 
dist 19=[3.0171512216693152245 ,40.700936657203324887  ] 
dist 20=[4.1646419150224208456 ,39.927746655057555522  ] 
dist 21=[3.4935610655628050605 ,28.085074377486995502  ] 
dist 22=[-8.4687174432531805222 ,27.035505880697324021  ] 
dist 23=[-17.143163044362401194  ,21.967374298334114903  ] 
dist 24=[-21.868229716289804906  ,19.461071980175122845  ] 
dist 25=[-24.010495584515271142  ,4.6528522466747302835 ] 
dist 26=[-23.835739612574957447  ,1.5302774213812510403 ] 
dist 27=[-22.595073349222902111  ,-3.6269834380607132602 ] 
dist 28=[-23.230811669842796817  ,-4.0379081241530316566 ] 
dist 29=[-4.6485356465446581095 ,6.0935489419205541442 ] 
dist 30=[-4.5363105023830875291 ,12.949084599976911040  ] 
dist 31=[-3.4893415528694142060 ,17.280829075822476246  ] 
dist 32=[-3.3319267502581945142 ,18.407997664382353511  ] 
dist 33=[-.37169978251703899365,5.7754130542878944420 ] 
dist 34=[.06309756637858820895,5.7686069052592785661 ] 
dist 35=[.78864991984036748541,4.7630694561632744391 ] 
dist 36=[.90023624555594998281,4.5497849975074393552 ] 
dist 37=[-.31879024806274779297,2.3018107373629418435 ] 
dist 38=[-1.8042273390919550188 ,2.2197167611199109904 ] 
dist 39=[-2.8110015583618142336 ,1.7835248213212626119 ] 
dist 40=[-3.2319742589171756528 ,1.5992944284960330566 ] 
dist 41=[-3.3005852153277823831 ,.27825926507567416414] 
dist 42=[-3.2262350626148464630 ,.01694270568563997208] 
dist 43=[-2.5436159955417234515 ,-.32881887696339262094] 
dist 44=[-2.3794033897901853483 ,-.35778421937638679222] 
dist 45=[-.52738529349589415093,.62823383011412687159] 
dist 46=[-.51218597399540937674,1.3676026520171243268 ] 
dist 47=[-.39500209414446241152,1.8549675717178077101 ] 
dist 48=[-.37135439263034748138,1.9750877571617827043 ] 
dist 49=[-.06583108053626409296,.77833177183091964577] 
dist 50=[-.02828012582376405095,.76701542936895647941] 
dist 51=[.02907727155328322410,.60436271413805779945] 
dist 52=[.03956640274577233108,.57991239002597604963] 
dist 53=[-.03770513007385236248,.32920730949497417623] 
dist 54=[-.22577313010507114528,.31693251726275497661] 
dist 55=[-.35048006969399234456,.24669237778536508899] 
dist 56=[-.39747168629997647847,.22520641527241394025] 
dist 57=[-.40228058734701027502,.02082917067503114573] 
dist 58=[-.3899757021540747076 ,-.00714703067836111993] 
dist 59=[-.31737999533470709946,-.04815604264371241699] 
dist 60=[-.28540562657599561497,-.05182377770588737180] 
dist 61=[-.06508196991668502518,.11588417635544983299] 
dist 62=[-.06311246428120972278,.2259150360644309299 ] 
dist 63=[-.04768444552002800740,.29505136285073768303] 
dist 64=[-.04538279303339098538,.31301156021660310323] 
dist 65=[-.00477664291945537749,.09524913287986426300] 
dist 66=[.00090150248990375186,.09309355135983077865] 
dist 67=[.01041624031303151161,.07204222926777187241] 
dist 68=[.01191263174974617666,.06862786927003415423] 
dist 69=[-.01067047283113840991,.03277945957940764323] 
dist 70=[-.03385087267844600453,.03148856485768304342] 
dist 71=[-.04889050739933570004,.02506016409046947071] 
dist 72=[-.05388953225818166947,.02241209695163148623] 
dist 73=[-.05326539211255849751,.00352789035927638508] 
dist 74=[-.05157597257482670160,-.00020748065998022388] 
dist 75=[-.03952680474342128685,-.00489581671065918483] 
dist 76=[-.03698346376938047747,-.00529932265078790048] 
dist 77=[-.00756912960938445826,.01066304394973185986] 
dist 78=[-.00731662227068137577,.02199255986368297340] 
dist 79=[-.00556123487849265782,.02915344584457518822] 
dist 80=[-.00522657082026359671,.03112389904831891874] 
dist 81=[-.00030744261810589430,.01233306451188758951] 
dist 82=[.00028187073699421591,.01200508448444583252] 
dist 83=[.00130817278177565300,.00916088141535159551] 
dist 84=[.00146772491856031068,.00873638228813588566] 
dist 85=[-.00097939324274433856,.00416872207167627491] 
dist 86=[-.00387747362246326578,.00401514598860103949] 
dist 87=[-.00574517379258763649,.00305578651507315391] 
dist 88=[-.00634173370817914710,.00283986591458633993] 
dist 89=[-.00628179431892246916,.00024055973792152566] 
dist 90=[-.00604783210640822028,-.00015520615556325059] 
dist 91=[-.00484195560699125269,-.00067415584032042801] 
dist 92=[-.00433470673752325401,-.00072592337779921222] 
dist 93=[-.00095361965759024782,.00188922931559146135] 
dist 94=[-.00092175607014118007,.00359412051970066614] 
dist 95=[-.00069027091420996218,.00466343844154648729] 
dist 96=[-.00065564439801945780,.00494090418670810212] 
dist 97=[-6.83608914391669931250e-05,.00145733490331306136] 
dist 98=[1.13868694479897342060e-05,.00141245233644510490] 
dist 99=[.00014488666846880253,.00108133610246550997] 
dist 100=[.00016603229205308876,.00101765860579128685] 
dist 101=[-.00018448625994407412,.00048222761041032577] 
dist 102=[-.00053535802607505101,.00046234589961158682] 
dist 103=[-.00075928084177761806,.00036602261833956181] 
dist 104=[-.00082621387179027845,.00032702433115289494] 
dist 105=[-.00080821431982803690,5.03889204196259009570e-05] 
dist 106=[-.00077947285296647682,-4.07505919632793816120e-06] 
dist 107=[-.00059521980866502960,-5.84736952966089571150e-05] 
dist 108=[-.00055345830916325997,-6.39110706449755444490e-05] 
dist 109=[-.00011229606534228917,.00017621453838728584] 
dist 110=[-.00010841786194182721,.00035162125063094933] 
dist 111=[-8.11218333199000426320e-05,.00046196640600833133] 
dist 112=[-7.68330889834009527250e-05,.00049144140282085265] 
dist 113=[-1.67580109249430772660e-05,.00018563709041729556] 
dist 114=[-1.01917367624654794850e-05,.00017979231450912040] 
dist 115=[-1.49693558076378369870e-06,.00013534196982171355] 
dist 116=[0                     ,.00012871350163211307] 
dist 117=[-1.73800108687722891070e-05,6.99110774097413829020e-05] 
dist 118=[-6.05343695492147492470e-05,6.71424415210430178270e-05] 
dist 119=[-8.79914024410248589850e-05,5.16475714596274783270e-05] 
dist 120=[-9.60351722911375646410e-05,4.72994808937726475480e-05] 
dist 121=[-9.42459086098445468130e-05,3.01835908286517710900e-06] 
dist 122=[-9.04698262422304912480e-05,-2.72293201882949832210e-06] 
dist 123=[-7.18444390352212702940e-05,-1.28933206710884135830e-05] 
dist 124=[-6.42352975317699883340e-05,-1.18084758218693196140e-05] 
dist 125=[-1.41422825707833150050e-05,2.87956577562491297290e-05] 
dist 126=[-1.36469750902562972590e-05,5.41496109595471318420e-05] 
dist 127=[-1.01701071254115413580e-05,7.00401249408504537710e-05] 
dist 128=[-9.65195087594104539550e-06,7.41634668564386605360e-05] 
dist 129=[1.44021682662334147780e-06,2.20867809998694663930e-05] 
dist 130=[3.18334035834183716880e-06,2.13565329110139880150e-05] 
dist 131=[6.71974778908115649300e-06,1.60034377362230340300e-05] 
dist 132=[4.55585693700303216490e-06,1.52048816372670609490e-05] 
dist 133=[-3.96095953278813578800e-06,7.12850094258180228470e-06] 
dist 134=[-9.30532072088622104580e-06,6.82736713712456923850e-06] 
dist 135=[-1.26868993085416269290e-05,5.39270534503505264050e-06] 
dist 136=[-1.36377066878618309490e-05,4.81332406798389633260e-06] 
dist 137=[-1.32724593860992663380e-05,7.11957258373831690920e-07] 
dist 138=[-1.27628162736843869820e-05,-9.83094366495134077910e-08] 
dist 139=[-9.78223206747192429330e-06,-1.46696069898335783370e-06] 
dist 140=[-9.00741968567967852540e-06,-9.00680979849800000000e-08] 
dist 141=[-2.39059763635478154190e-06,4.00234006966111124520e-06] 
dist 142=[-1.58179384618389339030e-06,6.56267536325766770460e-06] 
dist 143=[-1.19068492077019395950e-06,8.17400382277117497260e-06] 
dist 144=[-1.11664127882255425730e-06,8.60790250582984332910e-06] 
dist 145=[1.07073004577375409540e-07,2.78716113368690677100e-06] 
dist 146=[3.06184223826295032740e-07,2.69256177567263406590e-06] 
dist 147=[7.01467089905953105470e-07,2.01275490505276621530e-06] 
dist 148=[7.50110322306823762370e-07,1.91142566301427679270e-06] 
dist 149=[-2.77001246741021136420e-07,9.04889118228499154700e-07] 
dist 150=[-9.20963336248259906830e-07,8.70026063644800101370e-07] 
dist 151=[-1.32794606988978635050e-06,6.59254205676442605750e-07] 
dist 152=[-1.44148079860212406170e-06,6.12168312412171614570e-07] 
dist 153=[-1.40805904568788132960e-06,4.73869119358748898730e-08] 
dist 154=[-1.34951441820199594950e-06,-3.82368902258605666270e-08] 
dist 155=[-1.06787828065054407810e-06,-1.88454574202148928730e-07] 
dist 156=[-9.53524620056879385570e-07,-1.74216852732254254600e-07] 
dist 157=[-2.06219345520220344510e-07,4.33827052493306973680e-07] 
dist 158=[-1.98809138629629577730e-07,8.13228110082218627230e-07] 
dist 159=[-1.47807748127577213760e-07,1.05091229837163002200e-06] 
dist 160=[-1.40170262443141450750e-07,1.11255864017593100100e-06] 
dist 161=[2.14190375149616909890e-08,3.24937879863613611330e-07] 
dist 162=[4.67870844547891980550e-08,3.13261010967745481630e-07] 
dist 163=[9.83237758485823628870e-08,2.36359862298510151960e-07] 
dist 164=[7.79928323472969906160e-08,2.21765763516976399700e-07] 
dist 165=[-4.55763441735245188690e-08,1.04096166314216310050e-07] 
dist 166=[-1.22914882790843884350e-07,9.96427846512816000120e-08] 
dist 167=[-1.71650018060978294580e-07,7.85811800150556298940e-08] 
dist 168=[-1.84940722292118532350e-07,7.01191320765850469420e-08] 
dist 169=[-1.79421576367035071500e-07,1.04049258611789657820e-08] 
dist 170=[-1.72591131881993682440e-07,-1.36431213029218787720e-09] 
dist 171=[-1.30868898070228209690e-07,-2.11432071188309248580e-08] 
dist 172=[-1.21594149119632085990e-07,-2.18464758915123032550e-08] 
dist 173=[-2.39760715118808796650e-08,3.99701231583553301230e-08] 
dist 174=[-2.31066618170167005410e-08,7.85582627168318050350e-08] 
dist 175=[-1.71758516725940301680e-08,1.02758350433821598400e-07] 
dist 176=[-1.62725350287368170350e-08,1.09099026249432375220e-07] 
dist 177=[1.11973609479097521770e-09,4.12817620459063921820e-08] 
dist 178=[3.96207209575692282960e-09,3.98205325150845343540e-08] 
dist 179=[9.49651634697765196820e-09,2.96833929281850422920e-08] 
dist 180=[1.03566922142319295660e-08,2.81362901696666079420e-08] 
dist 181=[-4.40140869897998460720e-09,1.36121050847815922470e-08] 
dist 182=[-1.39377849717515451950e-08,1.30864433906991072920e-08] 
dist 183=[-1.99419574139799178220e-08,9.88089420842872790530e-09] 
dist 184=[-2.15691599568317757180e-08,9.19737080473558764860e-09] 
dist 185=[-2.10021697647682461240e-08,1.12383165045091661890e-09] 
dist 186=[-2.01219366602476756750e-08,-1.49964529911919012660e-11] 
dist 187=[-1.58126789533616918840e-08,-1.90845691028034082680e-09] 
dist 188=[-1.41778090477194843100e-08,-2.22023794082207569090e-09] 
dist 189=[-2.86629158598465840980e-09,6.38403552354880509610e-09] 
dist 190=[-2.76113930562240978770e-09,1.19423065635613054070e-08] 
dist 191=[-2.05567776726209852520e-09,1.54235397867891269650e-08] 
dist 192=[-1.94351860901712391500e-09,1.63261358308490758120e-08] 
dist 193=[-1.14811434616558494060e-09,5.27961452606580970730e-09] 
dist 194=[-9.41939471316870159130e-10,5.08984945510401359950e-09] 
dist 195=[-7.83085058376827551840e-10,3.78546079623692121710e-09] 
dist 196=[-7.37564554530890240690e-10,3.58867799987243494630e-09] 
dist 197=[-1.79741977178783716760e-09,2.92985893940303387150e-09] 
dist 198=[-3.16464671166520393970e-09,2.77623547647251633470e-09] 
dist 199=[-4.02344885738168469990e-09,2.52899338435013122760e-09] 
dist 200=[-4.25188073050311360380e-09,2.35600475088087523530e-09] 
dist 201=[-4.12570745820832894130e-09,1.73239572655438390010e-09] 
dist 202=[-3.95463286899477295150e-09,1.48361799120299879680e-09] 
dist 203=[-3.06662248885306678620e-09,1.32748870188528126890e-09] 
dist 204=[-1.99207381350128103560e-09,1.28624717126167002880e-09] 
dist 205=[-1.19964692124910927310e-10,1.27573576165821353590e-09] 
dist 206=[-1.46597190160799033190e-11,1.37958587665551485270e-09] 
dist 207=[-3.06854134632543387300e-11,1.81226594455708183030e-09] 
dist 208=[-5.60800604682424677700e-11,1.92463788841823215520e-09] 
dist 209=[-8.13877807082305971260e-11,8.88255098128178107220e-10] 
dist 210=[-9.70753529034050324730e-11,8.51582728612816980530e-10] 
dist 211=[-1.06806316862899951830e-10,6.62198680363427914550e-10] 
dist 212=[-1.09135024152721003470e-10,5.99334136060145546290e-10] 
dist 213=[-2.32148088489257443330e-10,1.11252805592315515430e-10] 
dist 214=[-4.62842391578222701450e-10,1.12782194075731176990e-10] 
dist 215=[-6.07586112363605241790e-10,1.15105857713407381260e-10] 
dist 216=[-6.45755045523966368520e-10,1.18743571259680424660e-10] 
dist 217=[-6.25486387555473036310e-10,1.80138447367255947570e-10] 
dist 218=[-6.00315744548432838390e-10,2.18413225900828496630e-10] 
dist 219=[-4.59704707225756288660e-10,2.42384968940555893260e-10] 
dist 220=[-4.21797490499956653370e-10,2.48623933849448853830e-10] 
dist 221=[-1.80397137230305184190e-10,1.34828748075650718650e-10] 
dist 222=[-1.72203144392902892430e-10,2.91440616333650790190e-10] 
dist 223=[-1.38088105264418066870e-10,3.89584987595542033790e-10] 
dist 224=[-1.21283446656834187430e-10,4.15212963930613732070e-10] 
dist 225=[-2.89024561905709274070e-11,4.06136178232600270060e-10] 
dist 226=[-1.00931220968976964740e-11,3.85668362998995169430e-10] 
dist 227=[-1.63965016652388935560e-11,3.23460301277008359000e-10] 
dist 228=[-6.70670979454544602110e-11,2.92809067626052982450e-10] 
dist 229=[-2.16377214071363193850e-10,1.61183214969528253570e-10] 
dist 230=[-3.42886949653949921820e-10,1.72866770347528415630e-10] 
dist 231=[-4.22122780284163081060e-10,1.91510147828418305740e-10] 
dist 232=[-4.42721309771964649610e-10,2.21404491466884090810e-10] 
dist 233=[-4.28400674120970923280e-10,2.51295489810349875800e-10] 
dist 234=[-4.11013640824539942460e-10,2.69925861827239766020e-10] 
dist 235=[-2.94201671387528829160e-10,2.81588194658239928180e-10] 
dist 236=[-1.46584836533870522080e-10,2.84607081571179420860e-10] 
dist 237=[-1.27128633160842844820e-10,2.75155563221969231030e-10] 
dist 238=[-1.17639057079366692050e-10,2.64166836434808947240e-10] 
dist 239=[-1.11698283438204268990e-10,2.00757388059154580960e-10] 
dist 240=[-1.10161925937948405020e-10,8.72213499009626230400e-11] 
dist 241=[-9.05484714238296513000e-11,8.46642016809310899750e-11] 
dist 242=[-1.15127929572437633690e-10,9.59963236950689136950e-11] 
dist 243=[-1.33788360895391519560e-10,1.03092732214141137150e-10] 
dist 244=[-1.38620495714875368420e-10,1.04935269150668040820e-10] 
dist 245=[-1.35877740455138760570e-10,1.13603818483101972240e-10] 
dist 246=[-1.28659205573967803860e-10,1.41201819119787374620e-10] 
dist 247=[-1.02078785029552035920e-10,1.58479141608401534920e-10] 
dist 248=[-9.15687597680243646500e-11,1.62954142654576037270e-10] 
dist 249=[-1.55451555108657363640e-10,1.60843384110088642940e-10] 
dist 250=[-2.01566255323161617040e-10,1.52723052312178258410e-10] 
dist 251=[-2.30439211313612669990e-10,1.32319031263743512190e-10] 

8 phat 5 dirichlet min maxes function [2, 2, 1, 0, 2, 0, 0, 1] 
dist 0=[374.21730469448157864   ,374.21730469448157864   ] 
dist 1=[352.55275398640215975   ,378.64082247901744420   ] 
dist 2=[302.62475360592218791   ,374.21730469448157864   ] 
dist 3=[245.73750503761623105   ,345.42710209239222194   ] 
dist 4=[196.56355680221972766   ,292.95379533848472034   ] 
dist 5=[147.71155470656893727   ,225.95359171539705757   ] 
dist 6=[91.149198853945210443  ,213.05560173956051297   ] 
dist 7=[30.914754356624376582  ,123.43148826117948644   ] 
dist 8=[-23.615019789386609792  ,79.418875123045759763  ] 
dist 9=[-61.946827127742776684  ,1.9803939211223544067 ] 
dist 10=[-83.369244555811890460  ,2.5969619473918816139 ] 
dist 11=[-93.276921812276595602  ,8.6113657106756816987 ] 
dist 12=[-93.916696187678067878  ,17.142981665706676609  ] 
dist 13=[-77.862301248667481122  ,27.235021327502125540  ] 
dist 14=[-75.256178819717919298  ,39.829577744011882760  ] 
dist 15=[-2.7590023605455432936 ,49.678608800430705540  ] 
dist 16=[9.0102888229081286465 ,51.351597782561311244  ] 
dist 17=[32.296300183571861995  ,46.098590105920894340  ] 
dist 18=[20.136344328644149601  ,44.311428217058904046  ] 
dist 19=[-.49484345324543144405,44.847617899930213972  ] 
dist 20=[-14.601579302465252583  ,43.935939986599303873  ] 
dist 21=[-24.662436146841802421  ,36.600681724998680260  ] 
dist 22=[-29.826053450020961535  ,33.135272282091814731  ] 
dist 23=[-31.964393228371620971  ,6.9850799283612025010 ] 
dist 24=[-33.940662494636723848  ,1.7855714814044075002 ] 
dist 25=[-31.767059607642047828  ,-4.1526481079717553226 ] 
dist 26=[-33.787014080827814480  ,-1.3813575680070082912 ] 
dist 27=[-13.030188053381603478  ,11.152858626529461572  ] 
dist 28=[-10.299782089748652571  ,19.938933226454714339  ] 
dist 29=[-8.2328615571738770883 ,25.540830887354638098  ] 
dist 30=[-7.8268865504371750335 ,26.508513268257944477  ] 
dist 31=[-.01740294573802136457,5.2637626490786303268 ] 
dist 32=[1.2576831254881879457 ,5.2476501930652776829 ] 
dist 33=[3.7924250452903649173 ,5.1059487721132144614 ] 
dist 34=[1.8779104448004417839 ,5.7370588922727021724 ] 
dist 35=[-.10673195434857634121,5.7526090106536099768 ] 
dist 36=[-1.4115138391477887982 ,5.5920036251851355647 ] 
dist 37=[-2.2966665514600835825 ,4.3470752480470743627 ] 
dist 38=[-2.6695235550964827987 ,4.0601457039394511192 ] 
dist 39=[-3.5621757853823600962 ,.48143114352837254155] 
dist 40=[-3.7959548652663106364 ,-.07037446638911754219] 
dist 41=[-3.2119688235653221573 ,-1.1009170715210763401 ] 
dist 42=[-3.4254959268018697465 ,-.4393190852594159141 ] 
dist 43=[-1.4829260480273781700 ,.77335415824450102607] 
dist 44=[-1.4315235880800975806 ,1.5357472363960133259 ] 
dist 45=[-1.1754602706055839822 ,2.0154269480512943707 ] 
dist 46=[-1.0384811151281207173 ,2.1400434011735987706 ] 
dist 47=[-.25895846846456787165,1.1415514511679367388 ] 
dist 48=[-.09129380242193017070,1.2302808961159503092 ] 
dist 49=[.16458068964350083017,1.2271549476951956017 ] 
dist 50=[.12999333915614513093,1.1419889010406741403 ] 
dist 51=[-.06110145797342920039,.67729515585455080672] 
dist 52=[-.22187897079766211459,.65391221634509410553] 
dist 53=[-.32748393557935701609,.527091388136506752  ] 
dist 54=[-.36518891968502682803,.47277944377047592662] 
dist 55=[-.41781742706143934858,.08158629855595965438] 
dist 56=[-.44968282534010782576,.01343927434500737479] 
dist 57=[-.49901927448006718405,-.13163079619014421453] 
dist 58=[-.52903329282859631938,-.05283343617469488823] 
dist 59=[-.15731306873518565656,.07462028660393401206] 
dist 60=[-.15293039927358888172,.15487695170735813067] 
dist 61=[-.11803128591400941826,.20616652645999777938] 
dist 62=[-.11127796794260542499,.21982039844781661199] 
dist 63=[.00620285164772245208,.08474340345932328678] 
dist 64=[.02535155586787906246,.08277345610599765921] 
dist 65=[.05641601116695572069,.08096675542355249515] 
dist 66=[.02542895487853731234,.08860458621035919985] 
dist 67=[-.00602760251774682516,.08706253523681349273] 
dist 68=[-.02610294949166003217,.08408688371746600717] 
dist 69=[-.03914781262456190604,.06443076380540730646] 
dist 70=[-.04353360785374256897,.05995462433111250146] 
dist 71=[-.04338152764531286743,.00573859785496054388] 
dist 72=[-.04184965081981802883,-.00255694460980650151] 
dist 73=[-.04954072307704936754,-.01751539304200261421] 
dist 74=[-.05275848606278587646,-.00595573279368945330] 
dist 75=[-.02002796841390932341,.01285207912838727765] 
dist 76=[-.01943470753471751170,.02462205994623703212] 
dist 77=[-.01471032435314890630,.03200828376916285685] 
dist 78=[-.01400313348789014896,.03392594882473930879] 
dist 79=[.00166847730875010654,.01020500106812443716] 
dist 80=[.00414497620252593100,.00992145290277193200] 
dist 81=[.00638487289292202892,.00945546389776411255] 
dist 82=[.00252553526420473162,.01036095498082540856] 
dist 83=[-.00137226359172650194,.01020350350336000638] 
dist 84=[-.00383890541402836782,.00980471251735735976] 
dist 85=[-.00542029051098690865,.00781371572237287398] 
dist 86=[-.00590768480138808082,.00698594572525707390] 
dist 87=[-.00579347281192552303,.00119233540055007754] 
dist 88=[-.00588159740850379691,4.91908092566210078600e-05] 
dist 89=[-.00759929804150787934,-.00189225161133756737] 
dist 90=[-.00804564916377112599,-.00059397231804603581] 
dist 91=[-.00237333353268857482,.00132064588076284926] 
dist 92=[-.00229770384169410806,.00252102960748528852] 
dist 93=[-.00173308053783354951,.00327790035886443913] 
dist 94=[-.00164289139970178152,.00348341123336058463] 
dist 95=[-.00035324840447693687,.00130679350223691173] 
dist 96=[-.00010552221587740859,.00136538966852236936] 
dist 97=[.00031237585123857440,.00175860457561539517] 
dist 98=[-.00016807364870493730,.00187078525311167959] 
dist 99=[-.00076177806584862964,.00182709195823428228] 
dist 100=[-.00113610712422012974,.00175038428581116869] 
dist 101=[-.00137481358355188304,.00138406389465096200] 
dist 102=[-.00144587035880622606,.00123344711519909391] 
dist 103=[-.00143178083686462313,.00018415293208621986] 
dist 104=[-.00135467929303533696,-2.44843368642440255740e-05] 
dist 105=[-.00119453769516907337,-.00027037311495482260] 
dist 106=[-.00094893477355292149,-8.54297133604239777360e-05] 
dist 107=[-.00030060501314758118,.00020165308752170567] 
dist 108=[-.00029066194007165463,.00038097914080194032] 
dist 109=[-.00021782125488751530,.00049339230048617596] 
dist 110=[-.00020696239214699752,.00052255507196374241] 
dist 111=[2.89473932622796341640e-05,.00015338079924608712] 
dist 112=[6.60937681802601099850e-05,.00014829336831056061] 
dist 113=[9.61921406872394419090e-05,.00014269219329905732] 
dist 114=[3.80808798306633099250e-05,.00015519937528259082] 
dist 115=[-2.03466472604233221130e-05,.00015184942677942923] 
dist 116=[-5.70748578378728363840e-05,.00014561362087922558] 
dist 117=[-8.03794952332715522350e-05,.00011538505593610268] 
dist 118=[-8.70685972497694364790e-05,.00010306324705608566] 
dist 119=[-8.48509539009628277900e-05,1.56510550584873030740e-05] 
dist 120=[-8.75629367992902456110e-05,-1.63299885109970160120e-06] 
dist 121=[-.00011321581348953877,-3.09857746506024043800e-05] 
dist 122=[-.00011986953543325443,-1.06492298012860961680e-05] 
dist 123=[-3.50369048899924114090e-05,1.87229554659980536810e-05] 
dist 124=[-3.37992661009660824260e-05,3.70850764472780122350e-05] 
dist 125=[-2.55459199493438416770e-05,4.86201314401086705550e-05] 
dist 126=[-2.39785791868269677120e-05,5.16746956752692261090e-05] 
dist 127=[2.14752153546124046890e-06,1.94339287642980894400e-05] 
dist 128=[6.39948052133475973250e-06,1.87883960352475909020e-05] 
dist 129=[1.24025233028823454710e-05,1.84493250812285353970e-05] 
dist 130=[5.26631610791784545900e-06,1.99023383406633205000e-05] 
dist 131=[-1.90108189816435453010e-06,1.93281256401347178690e-05] 
dist 132=[-6.40044732968132780130e-06,1.85972298529541848780e-05] 
dist 133=[-9.24979379087718313590e-06,1.41190832961099127350e-05] 
dist 134=[-1.00567289010542621100e-05,1.31143761112523243510e-05] 
dist 135=[-9.83669361999824574820e-06,1.05316972015171271830e-06] 
dist 136=[-9.43271865432065586850e-06,-7.79298774862663549630e-07] 
dist 137=[-1.10984354667627702640e-05,-4.01012623767501498650e-06] 
dist 138=[-1.17856112314706427390e-05,-1.22903860964797146960e-06] 
dist 139=[-4.41564326220577038180e-06,3.00806560850909364300e-06] 
dist 140=[-4.26181700428055387290e-06,5.65246686797980840420e-06] 
dist 141=[-3.17814176324140352000e-06,7.30933325472002535510e-06] 
dist 142=[-3.01621230844193006160e-06,7.73913060496114796270e-06] 
dist 143=[4.46002181566757896100e-07,2.29753986596538356900e-06] 
dist 144=[9.90215099416188256210e-07,2.21852158710422732500e-06] 
dist 145=[1.40873933222333036210e-06,2.11093003949251691660e-06] 
dist 146=[5.42486867093863971230e-07,2.28662453575574830870e-06] 
dist 147=[-3.26487956859237770650e-07,2.22955750889766925130e-06] 
dist 148=[-8.70992901256894582170e-07,2.13579760198805506380e-06] 
dist 149=[-1.21453948696060004440e-06,1.68643920815649537340e-06] 
dist 150=[-1.30910973282064456930e-06,1.50633536020144102760e-06] 
dist 151=[-1.27040477719294751900e-06,2.20790447814598551190e-07] 
dist 152=[-1.28365210461051728020e-06,-3.22044806671949495280e-08] 
dist 153=[-1.65848525022752542070e-06,-4.60238996940365308840e-07] 
dist 154=[-1.75570384051293774480e-06,-1.54977658832380778090e-07] 
dist 155=[-5.20526605765422072570e-07,2.71126995978061243920e-07] 
dist 156=[-5.02016265612059570540e-07,5.37217273148462163380e-07] 
dist 157=[-3.75300640451007331270e-07,7.04175398915948830660e-07] 
dist 158=[-3.54503206429512278250e-07,7.48073276646926397410e-07] 
dist 159=[3.07857174483690881190e-08,2.89955033756669523100e-07] 
dist 160=[9.31777434321332377220e-08,2.79829119204896128750e-07] 
dist 161=[1.83264028293220923230e-07,2.75991747714772212940e-07] 
dist 162=[7.69185069223072837270e-08,2.96829017368178115570e-07] 
dist 163=[-3.00168088510981784340e-08,2.87487562069377521020e-07] 
dist 164=[-9.69526331542146283260e-08,2.76582268526108620650e-07] 
dist 165=[-1.39145313104857880200e-07,2.08521399463766019100e-07] 
dist 166=[-1.50684065401441275230e-07,1.94634849991197876140e-07] 
dist 167=[-1.46931608252430456560e-07,1.33461849007889377570e-08] 
dist 168=[-1.40727471662058804210e-07,-1.32010153172604707560e-08] 
dist 169=[-1.59052107146774878140e-07,-6.00958032149635679840e-08] 
dist 170=[-1.68888061960075265110e-07,-1.71405080839642054970e-08] 
dist 171=[-6.69945794270386055250e-08,4.60773867770104115880e-08] 
dist 172=[-6.45894653741896319680e-08,8.55127746349259440580e-08] 
dist 173=[-4.80523683817906785470e-08,1.10214092038623578810e-07] 
dist 174=[-4.55509490182320169000e-08,1.16620299751436154670e-07] 
dist 175=[6.73274826536702628310e-09,3.34497396751117321980e-08] 
dist 176=[1.47943990214203958310e-08,3.22100658464031352830e-08] 
dist 177=[1.97498901189336247660e-08,3.22963038956181469150e-08] 
dist 178=[7.37376913345147199980e-09,3.48950125080171204590e-08] 
dist 179=[-5.41016490657265531460e-09,3.39437159556554082670e-08] 
dist 180=[-1.34481150008715497060e-08,3.25082437543466099050e-08] 
dist 181=[-1.85042522450236751950e-08,2.55345292760034437700e-08] 
dist 182=[-1.98643842393576905610e-08,2.28798051029209649830e-08] 
dist 183=[-1.92310041177492990580e-08,3.04034393674056107850e-09] 
dist 184=[-1.91180510396923900550e-08,-7.84752411573434136830e-10] 
dist 185=[-2.47385510371268709040e-08,-7.28777550127615110500e-09] 
dist 186=[-2.61961197427091322590e-08,-1.82843082090342098900e-09] 
dist 187=[-8.49780065859006773440e-09,4.22843650661021087060e-09] 
dist 188=[-8.16260444942994356430e-09,8.06597669410170036450e-09] 
dist 189=[-6.25093427662988325660e-09,1.04823262868037417560e-08] 
dist 190=[-5.74818366786942659800e-09,1.11138332930001669020e-08] 
dist 191=[2.62171336117952794830e-11,4.14991491376265886120e-09] 
dist 192=[1.03128163783837299020e-09,3.99526537833513459580e-09] 
dist 193=[1.64710238205267051660e-09,5.21602370429671879070e-09] 
dist 194=[-9.12101156069790592550e-11,5.56784329800684294780e-09] 
dist 195=[-1.83193520246662863490e-09,5.39148360767331127650e-09] 
dist 196=[-2.91949488092148280090e-09,5.17773985938151029000e-09] 
dist 197=[-3.61840782732079015460e-09,3.94554822544272346090e-09] 
dist 198=[-3.80803220675249265170e-09,3.63847232149194035440e-09] 
dist 199=[-3.67959399251384406460e-09,2.96520250483309700770e-10] 
dist 200=[-3.54230962471546671650e-09,4.31253611395983686190e-10] 
dist 201=[-3.31124304702542984780e-09,7.07683130533202131870e-10] 
dist 202=[-3.51165535826495960940e-09,1.15386537826320161360e-09] 
dist 203=[-2.13170291582513300400e-09,1.60064425837320109630e-09] 
dist 204=[-2.05207971792272980510e-09,1.87939198366041953790e-09] 
dist 205=[-2.25851593882694720490e-09,2.05400688996858290970e-09] 
dist 206=[-2.31731021586564322760e-09,2.09928677896244510630e-09] 
dist 207=[-2.25635565229166423710e-09,1.76320564054456510810e-09] 
dist 208=[-2.14887778469662898860e-09,1.83122749118897899130e-09] 
dist 209=[-1.74995487948208034520e-09,2.18652307440317831110e-09] 
dist 210=[-1.55403496769892599530e-09,2.27938775320881966980e-09] 
dist 211=[-1.00684781145240178210e-09,2.21011184194948986250e-09] 
dist 212=[-1.49729015714893851750e-09,2.11682146725962886290e-09] 
dist 213=[-1.83071587253565564250e-09,2.04759783281509526980e-09] 
dist 214=[-1.91760968809708588670e-09,2.15400896103713051820e-09] 
dist 215=[-1.87761886542016060670e-09,2.10562869740614174200e-09] 
dist 216=[-1.78056793394357099210e-09,1.99877131112579901270e-09] 
dist 217=[-1.89842468480356832450e-09,1.67709643405700199780e-09] 
dist 218=[-1.97348440642414492760e-09,1.54851060198828880730e-09] 
dist 219=[-1.92330583890840700530e-09,1.62135878421289677040e-09] 
dist 220=[-2.01937064275982296360e-09,1.91362266871086761750e-09] 
dist 221=[-2.24700903766404307140e-09,2.09663470943821309420e-09] 
dist 222=[-2.30602744957508954280e-09,2.14411791571492783390e-09] 
dist 223=[-6.43646351146961161910e-10,8.90858931221677763520e-10] 
dist 224=[-1.08222923894103531680e-09,1.39726217982063270600e-09] 
dist 225=[-1.35680853053910853570e-09,1.74929214596046614920e-09] 
dist 226=[-1.42794943926003300440e-09,1.84063602752369784570e-09] 
dist 227=[-1.40077240028074566510e-09,1.80053405900396036210e-09] 
dist 228=[-1.32536197734158131880e-09,1.70859402105780487490e-09] 
dist 229=[-1.14335114384163175040e-09,1.43896539830768595450e-09] 
dist 230=[-1.05381469631235513620e-09,1.30629198062594921760e-09] 
dist 231=[-1.21176037123950957590e-09,1.23705106703774102680e-09] 
dist 232=[-1.64033375964309316040e-09,1.50867878803670745270e-09] 
dist 233=[-1.92796639915921397390e-09,1.67874831919766221770e-09] 

8 phat 5 dirichlet min maxes function [1, 1, 2, 1, 1, 2, 0, 1, 2] 
dist 0=[357.30685407158886731   ,357.30685407158886731   ] 
dist 1=[346.04592236661437860   ,362.35411229459449166   ] 
dist 2=[313.52362055871887634   ,361.24293845011290218   ] 
dist 3=[256.04565199955412809   ,352.76899540832817054   ] 
dist 4=[183.92740375972260584   ,273.97728604817980768   ] 
dist 5=[124.44515582724890796   ,254.52620978573819165   ] 
dist 6=[68.256215139896022321  ,194.31006061407768787   ] 
dist 7=[7.7980171813169184161 ,175.34200940637089314   ] 
dist 8=[-43.246480879460107245  ,51.343284361867137322  ] 
dist 9=[-63.249120695289291846  ,21.314207808723730958  ] 
dist 10=[-70.792351415068063103  ,14.183999015386895048  ] 
dist 11=[-76.766081008251748675  ,8.6936002161702842386 ] 
dist 12=[-86.580082541544911763  ,10.798261653830774047  ] 
dist 13=[-88.222263450182024918  ,16.234158470399776034  ] 
dist 14=[-72.824441107615770309  ,26.028472551127249426  ] 
dist 15=[-62.516279784424768909  ,34.537199998364206608  ] 
dist 16=[-2.0490279293887216329 ,36.209854227647148638  ] 
dist 17=[7.7545778363248108773 ,35.568654021984110741  ] 
dist 18=[14.884451131761770621  ,33.969510287477489756  ] 
dist 19=[.06399393974927559270,39.240936912005884785  ] 
dist 20=[-10.225457329488932457  ,40.246148273056254247  ] 
dist 21=[-17.695330131635998244  ,39.132926888981186477  ] 
dist 22=[-24.409504772070885327  ,32.264010147296546638  ] 
dist 23=[-26.199359099916029937  ,28.925759059141336699  ] 
dist 24=[-23.214884294356223545  ,9.0949354343240078115 ] 
dist 25=[-22.854786204493592191  ,5.1251039238255006465 ] 
dist 26=[-29.751877166595772059  ,.08014956701748498371] 
dist 27=[-31.395167081247577121  ,9.2900969385940168430 ] 
dist 28=[-8.1465823733484285866 ,15.175219700036773512  ] 
dist 29=[-7.9495044449036262754 ,19.085677925022841158  ] 
dist 30=[-6.2133655874171341800 ,20.074509781072885621  ] 
dist 31=[-5.9533293524903246195 ,5.5224967582349554626 ] 
dist 32=[.373209036805692224  ,5.8694182383485296699 ] 
dist 33=[1.3827347146247500256 ,5.7917068267002541669 ] 
dist 34=[1.4430885910631044014 ,4.7422825039925244902 ] 
dist 35=[-.02951179991055096437,4.3925446446429611352 ] 
dist 36=[-1.4536261894239351255 ,4.0360015156679023371 ] 
dist 37=[-2.7223821702084745138 ,3.9051507065999736943 ] 
dist 38=[-3.6682738429106735555 ,3.1627923858371413117 ] 
dist 39=[-3.8790617393455286489 ,2.8420518438597283695 ] 
dist 40=[-2.0641194845994438213 ,.50820387252990616427] 
dist 41=[-2.2519257530438247808 ,.04556218636902389722] 
dist 42=[-2.9407560852251281640 ,-.27406600554778064129] 
dist 43=[-3.1195612728419694591 ,.64332558959334107129] 
dist 44=[-.93514929118294619526,1.2225962350093192745 ] 
dist 45=[-.91109208591170559605,1.5926630139583292633 ] 
dist 46=[-.70725061130446253485,1.6870534745452224868 ] 
dist 47=[-.66770009842165831402,.81732118412604652711] 
dist 48=[.02980686314615547284,.84360179782003512704] 
dist 49=[.09882135679298041281,.81747170494206233548] 
dist 50=[-.17799806005240722623,.69781649619728196126] 
dist 51=[-.46102700423926504864,.62880666874594521435] 
dist 52=[-.64271241326509404292,.51403436584036648599] 
dist 53=[-.76140054973892016352,.49697493158960558265] 
dist 54=[-.80210501897288531553,.38169234580545733716] 
dist 55=[-.79421969477499033314,.35539566955656806895] 
dist 56=[-.2722831135558604056 ,.03547423314236563217] 
dist 57=[-.22523589710752178792,-.01359428383815695236] 
dist 58=[-.29104229020050312404,.01519088370434539704] 
dist 59=[-.31020112472040504962,.11528328786501226523] 
dist 60=[-.11827756928010111846,.1829988328257875242 ] 
dist 61=[-.11492398148747403218,.22983799840054879068] 
dist 62=[-.08730507875304555219,.24029033848373052197] 
dist 63=[-.08316808402040431828,.04376587923134644337] 
dist 64=[.00956908477359744031,.04292875535126364321] 
dist 65=[.02423908020902780335,.03739933774368774292] 
dist 66=[.01365445514903655337,.05510567745404065035] 
dist 67=[-.00264336130168930791,.06058588609915900111] 
dist 68=[-.01311557828411887093,.05979974831553169206] 
dist 69=[-.01999010141099695388,.05751384472997685939] 
dist 70=[-.02244127405715250847,.04587471620605127419] 
dist 71=[-.02253578150286609245,.04108019906917468465] 
dist 72=[-.02179070108412112249,.00654766552501276001] 
dist 73=[-.03402181171270471071,-.00026077051963785864] 
dist 74=[-.04413236945937430097,-.00320223221661090505] 
dist 75=[-.04675606763962923607,.00663418509512758747] 
dist 76=[-.01399302314057111811,.01279644913310940595] 
dist 77=[-.01355678974529004585,.01666583484780805773] 
dist 78=[-.01024287501604688878,.01767030128341152650] 
dist 79=[-.00971946957665962839,.00525946085612728596] 
dist 80=[.00064445734915074747,.00512269911632725675] 
dist 81=[.00232414867545433059,.00518570032878202929] 
dist 82=[.00140433319841754361,.00730522866733144371] 
dist 83=[-.00061284751163661826,.00792331074652512912] 
dist 84=[-.00189500569529251742,.00772829207499413140] 
dist 85=[-.00272254813356683835,.00745138422227873768] 
dist 86=[-.00298885224892737921,.00565259156291093096] 
dist 87=[-.00294574835845107246,.00527835360290311728] 
dist 88=[-.00284757921188412061,.00042315574111221632] 
dist 89=[-.00324590408476728781,-.00029353774163429753] 
dist 90=[-.00426822228502539158,-.00038259986310214098] 
dist 91=[-.00454058659261823568,.00063883081833899193] 
dist 92=[-.00177021322970193895,.00127973775975488901] 
dist 93=[-.00171260279753686897,.00168404503882664378] 
dist 94=[-.00128542148851393635,.00179388518636910574] 
dist 95=[-.00122172985627289389,.00067707829527256144] 
dist 96=[.00014289769306966215,.00065800075194827322] 
dist 97=[.00035865130898023191,.00060229585321533137] 
dist 98=[.00014594379501946064,.00086382606204986036] 
dist 99=[-.00011504010543499783,.00093883321240225700] 
dist 100=[-.00028021306330690584,.00091991907533189025] 
dist 101=[-.00038616574337616915,.00088175687218101288] 
dist 102=[-.00041898630067785335,.00070331654492408109] 
dist 103=[-.00041419074912009235,.00062452959050674385] 
dist 104=[-.00039656152794390336,.00014581579667069889] 
dist 105=[-.00055868843240283764,5.04734289093693784440e-05] 
dist 106=[-.00071087380940851887,5.94905983696174341930e-05] 
dist 107=[-.00075076539489684002,.00021393478241433022] 
dist 108=[-.00020620872900744998,.00031066334415913303] 
dist 109=[-.00019899968338903847,.00037156636665725508] 
dist 110=[-.00015056463355249587,.00038794037150887238] 
dist 111=[-.00014136035911326013,7.94474297695198697370e-05] 
dist 112=[2.31553058956140261070e-06,7.69407125767592202000e-05] 
dist 113=[-1.49656966452188166330e-06,7.98733268597224992740e-05] 
dist 114=[-3.63972459453970030430e-05,.00010914854861867864] 
dist 115=[-7.14977187969780043920e-05,.00011736961113315894] 
dist 116=[-9.35599743597561153400e-05,.00011513201002515046] 
dist 117=[-.00010755066798337290,.00010983142025204459] 
dist 118=[-.00011154252805961010,9.03019455596975085900e-05] 
dist 119=[-.00010940942600412296,8.05401804043804697530e-05] 
dist 120=[-.00010400712776531202,2.72749631484309814230e-05] 
dist 121=[-8.70891790527648761630e-05,1.48805418066123427490e-05] 
dist 122=[-7.86826192572827646390e-05,2.50532042284197943460e-06] 
dist 123=[-6.92899785961722695170e-05,1.78491197914119725320e-05] 
dist 124=[-2.59797845643666973510e-05,2.74538408640340417830e-05] 
dist 125=[-2.50813694266935398020e-05,3.34992646328330485030e-05] 
dist 126=[-1.87187842576418380160e-05,3.51239743465310189670e-05] 
dist 127=[-1.77672083898631015600e-05,9.92644683087594506700e-06] 
dist 128=[2.60004990367598312640e-06,9.60785977437429984630e-06] 
dist 129=[5.80276557878093830620e-06,8.62612374544834360150e-06] 
dist 130=[2.72534484729884997580e-06,1.24072783999691445860e-05] 
dist 131=[-9.37136618383980704140e-07,1.34479018963116420780e-05] 
dist 132=[-3.24074153993291109140e-06,1.31186888578631318520e-05] 
dist 133=[-4.70407404458234265540e-06,1.25690616379164498040e-05] 
dist 134=[-5.12786364336849780890e-06,9.92855096473499526930e-06] 
dist 135=[-5.02693072872333024170e-06,8.86934550098187501110e-06] 
dist 136=[-4.82352663091831533190e-06,1.30604476076630936440e-06] 
dist 137=[-7.54800197511643492770e-06,-1.82251972616101287020e-07] 
dist 138=[-9.75353095883039667940e-06,-6.34104001902073978720e-07] 
dist 139=[-1.03255795988747522090e-05,1.53975430011219510730e-06] 
dist 140=[-3.06032025241799172430e-06,2.89689895693743883060e-06] 
dist 141=[-2.95199822495583004460e-06,3.74737344115768142370e-06] 
dist 142=[-2.20278590227312108180e-06,3.96798063455258523670e-06] 
dist 143=[-2.08592148028825571140e-06,1.16170840656768130010e-06] 
dist 144=[1.80873051331588552230e-07,1.12153268813725356860e-06] 
dist 145=[5.47711672417976256160e-07,1.16393903872336552630e-06] 
dist 146=[2.83626917476544104460e-07,1.61876782083302582710e-06] 
dist 147=[-1.58534839219662992160e-07,1.74155234231659879220e-06] 
dist 148=[-4.35872359424043309780e-07,1.68734106792052788300e-06] 
dist 149=[-6.11237700428272836500e-07,1.62339158433272942090e-06] 
dist 150=[-6.60308094977385568670e-07,1.22487297676092945630e-06] 
dist 151=[-6.42035637679961110630e-07,1.14272419442065150760e-06] 
dist 152=[-6.18007407381717583700e-07,7.93109893824733690990e-08] 
dist 153=[-7.15057400622507579610e-07,-7.70468214650390334500e-08] 
dist 154=[-9.36660560540033195530e-07,-7.93683267269956928770e-08] 
dist 155=[-9.94657132264470431190e-07,1.42568541765826751290e-07] 
dist 156=[-3.85822509988806081040e-07,2.81211741312178336350e-07] 
dist 157=[-3.72056770234137807200e-07,3.68234177176368552020e-07] 
dist 158=[-2.76782635557904369870e-07,3.91157558910576823720e-07] 
dist 159=[-2.62543492997648977200e-07,1.47202591656285726590e-07] 
dist 160=[3.98857831401378993980e-08,1.42159054876274944380e-07] 
dist 161=[8.73800494838763553580e-08,1.29103970266439761440e-07] 
dist 162=[3.92908122928564393620e-08,1.84953702668448948490e-07] 
dist 163=[-1.49208816462146854530e-08,1.99963561735937222260e-07] 
dist 164=[-4.88925160766315422470e-08,1.94655271807339805710e-07] 
dist 165=[-7.03449417626272052700e-08,1.86368534922736522830e-07] 
dist 166=[-7.62923246817785057900e-08,1.46969508552037321500e-07] 
dist 167=[-7.44626323028888984920e-08,1.31215676835367791060e-07] 
dist 168=[-7.13690336134602356290e-08,1.91709847339231724900e-08] 
dist 169=[-1.12378039684798927020e-07,-2.89002568606622464880e-09] 
dist 170=[-1.45082954394861471110e-07,-9.27969421164774407290e-09] 
dist 171=[-1.53564421575479957360e-07,2.25895451841051421780e-08] 
dist 172=[-4.53799165881216209150e-08,4.24733528441935147040e-08] 
dist 173=[-4.36921550041106656230e-08,5.49293295255776980330e-08] 
dist 174=[-3.28254386434749462150e-08,5.81596068372973912470e-08] 
dist 175=[-3.07898007988795132900e-08,1.82837062023104494750e-08] 
dist 176=[2.93633465208527229130e-09,1.76396794699317524190e-08] 
dist 177=[8.35652926687781873950e-09,1.72646857481756631250e-08] 
dist 178=[4.16428776639900852990e-09,2.40079986637418880020e-08] 
dist 179=[-2.68117966876942739340e-09,2.57998473665006975420e-08] 
dist 180=[-6.96328636706724571920e-09,2.49594643595186896850e-08] 
dist 181=[-9.65934293375263077680e-09,2.40091576181687429200e-08] 
dist 182=[-1.03896901057030976660e-08,1.80583602183970866070e-08] 
dist 183=[-1.00525907864962413520e-08,1.68802885057676887470e-08] 
dist 184=[-9.68809613289224863840e-09,7.80238532040231553710e-10] 
dist 185=[-1.03396739535193487040e-08,-1.59063531580513933740e-09] 
dist 186=[-1.36256264151237415390e-08,-1.46247368073896624150e-09] 
dist 187=[-1.44820428403105432140e-08,1.70768576471333972020e-09] 
dist 188=[-6.72439377324655850880e-09,3.86693129363135437870e-09] 
dist 189=[-6.47119585153406570360e-09,5.27746356382881206610e-09] 
dist 190=[-4.85971371244868376570e-09,5.64419982965348038240e-09] 
dist 191=[-4.55403376935103299530e-09,3.46128378372722940270e-09] 
dist 192=[4.51806585032905962140e-10,3.33284073197657656650e-09] 
dist 193=[1.26674216668585135280e-09,2.57022678506850782800e-09] 
dist 194=[5.45628766206253092220e-10,3.57109018554237389590e-09] 
dist 195=[-5.59266042996703412350e-10,3.83529447535486670230e-09] 
dist 196=[-1.29347343789132736070e-09,3.70623614012661545710e-09] 
dist 197=[-1.80682766156014922290e-09,3.56670643146283241190e-09] 
dist 198=[-1.94338110301080205800e-09,2.66689799074970958200e-09] 
dist 199=[-1.88226346120772542310e-09,2.50678087452426689470e-09] 
dist 200=[-1.80882296536374394560e-09,1.13328002757014747980e-10] 
dist 201=[-1.52574830777274624590e-09,-2.35714932840459963410e-10] 
dist 202=[-2.00918977492761652080e-09,-1.91980672409732656080e-10] 
dist 203=[-2.13455688170804519470e-09,3.48851601509255621560e-10] 
dist 204=[-1.88114338631321982800e-09,8.09722339778902734810e-10] 
dist 205=[-1.80457866031696267260e-09,1.09873748424806752460e-09] 
dist 206=[-1.38599116385084544920e-09,1.17461847429224624410e-09] 
dist 207=[-1.26750968364242356760e-09,1.13590042224468939710e-09] 
dist 208=[-3.26431693686945264380e-10,1.09166567160016268950e-09] 
dist 209=[-1.36934792251920384930e-10,1.19276146220832112530e-09] 
dist 210=[-8.90620022005440468110e-11,1.50368611243939767620e-09] 
dist 211=[-5.56165721855685600420e-10,1.58469321008496947170e-09] 
dist 212=[-8.90401532281217525170e-10,1.55201193104376067200e-09] 
dist 213=[-1.09981011798319124650e-09,1.47148156964097353660e-09] 
dist 214=[-1.15439479308408057330e-09,1.24936321332838295400e-09] 
dist 215=[-1.12486973133584022610e-09,1.13998886376198443410e-09] 
dist 216=[-1.07193005799460626500e-09,7.12186965518046717400e-10] 
dist 217=[-1.43006476977976291930e-09,5.99229916484421397750e-10] 
dist 218=[-1.71267398327194113200e-09,5.29364157908807020110e-10] 
dist 219=[-1.78595947460696848830e-09,1.10494739801709798150e-09] 
dist 220=[-1.01622752566901995910e-09,1.46385804644565559220e-09] 
dist 221=[-1.05044391651806993970e-09,1.68862550359924218070e-09] 
dist 222=[-1.05928770119761404070e-09,1.74700271245386046780e-09] 
dist 223=[-1.53551185932003090870e-10,1.68868524050468982910e-09] 
dist 224=[-1.68855035479147801460e-10,1.62173297838746016440e-09] 
dist 225=[-2.11917224805928093640e-10,1.22958693852661140780e-09] 
dist 226=[-2.81048052723534351440e-10,1.13815601472023700890e-09] 
dist 227=[-3.50193008241140609070e-10,3.78625520634829026590e-10] 
dist 228=[-7.27041739712258027190e-10,4.81362583865322183300e-10] 
dist 229=[-9.85400177332161671780e-10,5.45672769667282229180e-10] 
dist 230=[-1.05242538699939133580e-09,5.62314646697068702670e-10] 
dist 231=[-1.03239886412438925180e-09,5.43783060336163739930e-10] 
dist 232=[-9.76923248992722273810e-10,5.21899652169236652660e-10] 
dist 233=[-8.42265578253350053760e-10,3.97744710642804221280e-10] 
dist 234=[-7.76005658331920912240e-10,4.34990764737689443700e-10] 
dist 235=[-7.46362401351417182150e-10,8.30166761763487638400e-10] 
dist 236=[-8.15524439313397489300e-10,1.07651254712511698740e-09] 
dist 237=[-8.58827934064717936200e-10,1.23075978135215034770e-09] 
dist 238=[-8.70056638055378887380e-10,1.27076552751187925740e-09] 
dist 239=[-1.10208509881071443350e-10,1.23010841796966235250e-09] 
dist 240=[-1.83282351425586600410e-10,1.17955753385544176820e-09] 
dist 241=[-2.28831786930950657420e-10,9.06572025139103464460e-10] 
dist 242=[-2.57348469723977656240e-10,8.27776882790054601420e-10] 
dist 243=[-2.85098593737290410070e-10,2.20380990842142886740e-10] 
dist 244=[-5.96472863001412448060e-10,2.22147643445723023820e-10] 
dist 245=[-7.91433194189362651510e-10,2.28946068090082227310e-10] 
dist 246=[-8.41990278363583235590e-10,2.39801415137739814350e-10] 
dist 247=[-8.26004658272100500350e-10,2.57213345868061368250e-10] 
dist 248=[-7.81552797793677690550e-10,2.74624713398382922130e-10] 
dist 249=[-6.74225558354583668180e-10,2.85477893846040509130e-10] 
dist 250=[-6.21419221755072804740e-10,2.92272779320399712640e-10] 
dist 251=[-4.42876988059659238370e-10,5.77928604486571232470e-10] 
dist 252=[-4.02345108360088558430e-10,8.22750223213508920670e-10] 
dist 253=[-3.76966951244630959930e-10,9.76039142101768595080e-10] 

8 phat 5 dirichlet min maxes function [2, 2, 0, 2, 0, 1, 1, 2] 
dist 0=[376.11148204304961459   ,376.11148204304961459   ] 
dist 1=[354.07784750113716227   ,380.66148042282881896   ] 
dist 2=[303.55883224619723117   ,376.11148204304961459   ] 
dist 3=[246.08729662192384061   ,346.74676790484093820   ] 
dist 4=[196.57045550272652057   ,294.95284035484370628   ] 
dist 5=[147.53216103067794674   ,227.43680219812773440   ] 
dist 6=[90.988863611851585876  ,214.41093338211976017   ] 
dist 7=[30.370986641166276372  ,121.84841920915876135   ] 
dist 8=[-24.650511544834296290  ,77.509758799243323327  ] 
dist 9=[-63.237244374481990618  ,2.2858392991439531043 ] 
dist 10=[-84.601244027686696493  ,3.1796183839204861641 ] 
dist 11=[-94.440224069192226641  ,9.4477368582189673280 ] 
dist 12=[-94.856513182215715310  ,18.088905585325403208  ] 
dist 13=[-79.095726123457304818  ,28.188608263758812714  ] 
dist 14=[-75.718504500554420653  ,40.643963711824721686  ] 
dist 15=[-5.8280965749244814297 ,50.167058748099400842  ] 
dist 16=[5.6837210631319253521 ,51.879345895977458770  ] 
dist 17=[30.442091874362547724  ,45.459328853924884344  ] 
dist 18=[22.550031606731571970  ,47.820674630673427243  ] 
dist 19=[2.8328621808957126317 ,48.885206189957688130  ] 
dist 20=[-10.695632638815652016  ,47.773881981217463532  ] 
dist 21=[-20.389430753581027688  ,37.399541481275081426  ] 
dist 22=[-25.451292250740615386  ,34.988190980282848607  ] 
dist 23=[-27.571746009292957605  ,5.3344744075451316316 ] 
dist 24=[-27.266441163897586871  ,.57394218550394028201] 
dist 25=[-27.531772381227913422  ,-8.7404880706341507049 ] 
dist 26=[-29.336569984433315886  ,-5.1354875061830410133 ] 
dist 27=[-11.556296685527420618  ,7.2427172359887123990 ] 
dist 28=[-11.428722475321517464  ,15.072639410724461195  ] 
dist 29=[-9.0933251403854654114 ,20.017158016589309326  ] 
dist 30=[-8.7350274103486392634 ,21.303475221922170704  ] 
dist 31=[.33397655641153472326,6.5649363148966662054 ] 
dist 32=[1.7922094384461389052 ,6.5350490333015389075 ] 
dist 33=[4.4818971671320736635 ,6.0397030906047848839 ] 
dist 34=[1.9328948257794062830 ,5.9601314845612299496 ] 
dist 35=[-.70269803520623499487,5.9102495887509270702 ] 
dist 36=[-2.4263047354877343125 ,5.7378203281033247884 ] 
dist 37=[-3.5854854178933448504 ,4.6940085559375415095 ] 
dist 38=[-4.0526188633190640020 ,4.2196124354181800269 ] 
dist 39=[-4.3843089122137610662 ,.86348332102526192684] 
dist 40=[-4.6649871527789758950 ,.19464386358754410523] 
dist 41=[-4.3423167099867531440 ,-.98967627656958987488] 
dist 42=[-4.6060762077379676071 ,-.184297543469598015  ] 
dist 43=[-1.3461622156140066072 ,1.1503978143549487764 ] 
dist 44=[-1.3181719160350079982 ,2.0006931156997770149 ] 
dist 45=[-1.0573137673646918968 ,2.5800277664447827706 ] 
dist 46=[-.97884275760058251515,2.7220229422884934119 ] 
dist 47=[-.29729551033048588242,.7225131478724107847 ] 
dist 48=[-.15546290812045274591,.81393618143506688001] 
dist 49=[.10155188557579352265,1.0383137214153131486 ] 
dist 50=[-.02930822130390654983,1.1184926327538175483 ] 
dist 51=[-.42356744098749191489,1.1057710435904895656 ] 
dist 52=[-.67719849876090467795,1.0617945315763860324 ] 
dist 53=[-.84398361990557166162,.85205517079577681029] 
dist 54=[-.90405060688170000082,.75356556644046425517] 
dist 55=[-.90646577023792268424,.14494255750149913945] 
dist 56=[-.86231153201180484061,.01839956600276876203] 
dist 57=[-.75816480929284645009,-.13598311559018342156] 
dist 58=[-.58282910911848225718,-.1624335356003518061 ] 
dist 59=[-.16221812014223230977,-.13299792300728467369] 
dist 60=[-.15804037065656169897,-.06206388923860026506] 
dist 61=[-.12088773594085411866,.01046779355115761285] 
dist 62=[-.11534029105773314178,.05726063166726017428] 
dist 63=[.01214491591662391251,.08816214021647597689] 
dist 64=[.03236154371748668433,.09955152743352569566] 
dist 65=[.07308439860309439167,.10042555738134436673] 
dist 66=[.07918384769403347293,.09725374596178048790] 
dist 67=[.05800461049908769513,.08233390180367654812] 
dist 68=[.01462485852404246217,.07930421665699341110] 
dist 69=[-.02913564647991995533,.06355432233094062153] 
dist 70=[-.05656906408780999051,.05692153689804686066] 
dist 71=[-.07380224350835508494,.00942559401716219176] 
dist 72=[-.07827855429367791290,1.08955474420016489410e-05] 
dist 73=[-.06095272832628264650,-.01628069019322141372] 
dist 74=[-.06458834938118124140,-.01929331369945040849] 
dist 75=[-.01909419655558233981,-.01526533579639279978] 
dist 76=[-.01851493906885628033,-.00633254443731550264] 
dist 77=[-.01418910490525748504,.00272875138160667323] 
dist 78=[-.01336002417337886586,.00850020785690388511] 
dist 79=[.00089298882728786342,.01223679514356327868] 
dist 80=[.00321483271705474869,.01346246832645094597] 
dist 81=[.00794930250377507741,.01328680484949778047] 
dist 82=[.00869154690633922875,.01285932589857499559] 
dist 83=[.00627844703103838953,.01056494162101700103] 
dist 84=[.00181901309391269646,.01019138377811578558] 
dist 85=[-.00267532175929191653,.00778498012691043457] 
dist 86=[-.00549839428316113587,.00724050979750461570] 
dist 87=[-.00728184397342364101,.00065456899755849721] 
dist 88=[-.00777112736932823721,-.00035024734670480918] 
dist 89=[-.00602634602472536302,-.00214982752166836220] 
dist 90=[-.00641200113188417065,-.00247151127504862435] 
dist 91=[-.00247321223432715947,-.00200571161262806056] 
dist 92=[-.00239193937457493170,-.00084022881319193966] 
dist 93=[-.00182387380548324398,.00033739017835016259] 
dist 94=[-.00171213607884385728,.00108342348412571905] 
dist 95=[.00012147832055001544,.00156262644937044401] 
dist 96=[.00042152223189796138,.00171230841232868679] 
dist 97=[.00102534778251714515,.00168415952328601704] 
dist 98=[.00112131219779852801,.00162570131387460335] 
dist 99=[.00085865319675297828,.00137735910550524540] 
dist 100=[.00020745166594690482,.00132843980642030753] 
dist 101=[-.00047199846037423428,.00099686315584718510] 
dist 102=[-.00089675627728692833,.00093861972463679379] 
dist 103=[-.00116314461367447277,.00012758239251009644] 
dist 104=[-.00123226462847569635,-1.19830078658280127060e-05] 
dist 105=[-.00090805182765808823,-.00025064066590619334] 
dist 106=[-.00096174904925127396,-.00029200597855791143] 
dist 107=[-.00037252841788048934,-.00022969954896828175] 
dist 108=[-.00035602288884647122,-5.27616403383071766400e-05] 
dist 109=[-.00029242048585951340,.00013742135045196107] 
dist 110=[-.00026031325272748432,.00025665721743251787] 
dist 111=[-8.38237017151329434440e-05,.00033190006567221188] 
dist 112=[-4.34127151567780344520e-05,.00035252638725659012] 
dist 113=[1.61286669562139017200e-05,.00034590443982117799] 
dist 114=[2.73871323419734438760e-05,.00031611842259780816] 
dist 115=[2.52169500510658895720e-05,.00016919667136176084] 
dist 116=[-1.11139368785948817560e-05,.00016235124874524508] 
dist 117=[-6.21222937505468558450e-05,.00012607241884887274] 
dist 118=[-9.42431526151971751440e-05,.00011430843945722386] 
dist 119=[-.00011516478240560382,7.10086252453981096330e-06] 
dist 120=[-.00012249593713304312,-7.45860207466928444500e-06] 
dist 121=[-.00011981097066119151,-3.35852703453716594460e-05] 
dist 122=[-.00011393839469413934,-3.80034241373644607220e-05] 
dist 123=[-3.70120078143346583980e-05,-2.96947102716404805590e-05] 
dist 124=[-3.57580147478244632680e-05,-1.27280594109966349480e-05] 
dist 125=[-2.67350952787429367430e-05,4.34007344305931062120e-06] 
dist 126=[-2.53901912009712673680e-05,1.50819538112436156500e-05] 
dist 127=[3.65321333092876550930e-06,2.19121474111973671580e-05] 
dist 128=[8.22275925945514085770e-06,2.39039386933355172310e-05] 
dist 129=[1.74844217760422987830e-05,2.34475207840292532850e-05] 
dist 130=[1.88663374900375233500e-05,2.25053209741322491300e-05] 
dist 131=[1.30603636334039090190e-05,1.86875816807067047750e-05] 
dist 132=[2.97406716672930288290e-06,1.79111008886975858950e-05] 
dist 133=[-7.13716293297950325830e-06,1.41747044282295347730e-05] 
dist 134=[-1.34503301734836169370e-05,1.26568079740075261170e-05] 
dist 135=[-1.74068694837523780660e-05,1.90279964422955588290e-06] 
dist 136=[-1.84333469686289642040e-05,-2.23159352161029931300e-07] 
dist 137=[-1.39462803767041101810e-05,-3.82544067572785722510e-06] 
dist 138=[-1.47644621087901321280e-05,-4.42875144123348734620e-06] 
dist 139=[-4.30803093098591707600e-06,-3.37726414057568072450e-06] 
dist 140=[-4.15335792281094843510e-06,-1.31118568139631031850e-06] 
dist 141=[-3.13408237190350381080e-06,7.63610593872960086470e-07] 
dist 142=[-2.94064626661735691930e-06,2.06545902256322604530e-06] 
dist 143=[2.70884220919863584720e-07,2.88909115361703711600e-06] 
dist 144=[7.93557660205652745870e-07,3.12038277022896296560e-06] 
dist 145=[1.83517461351817737970e-06,3.03332214476781837080e-06] 
dist 146=[2.00111264574464601970e-06,2.92146507115438880340e-06] 
dist 147=[1.39191194126203314050e-06,2.37650539711977391040e-06] 
dist 148=[3.75137473752422092710e-07,2.28597995690005107230e-06] 
dist 149=[-6.44157076273484079370e-07,1.73402879811000693570e-06] 
dist 150=[-1.28107075533385655320e-06,1.61059329488478794490e-06] 
dist 151=[-1.68099433552380891910e-06,1.26970928254991751660e-07] 
dist 152=[-1.78664212777549017420e-06,-9.81203122293325687360e-08] 
dist 153=[-1.36440381104218070800e-06,-4.94291128975016656110e-07] 
dist 154=[-1.44855863842008356320e-06,-5.59392066545970549920e-07] 
dist 155=[-5.42698823388922374990e-07,-4.40445175528090224400e-07] 
dist 156=[-5.23547379153583335090e-07,-1.85865998995309508490e-07] 
dist 157=[-3.90008997649941784580e-07,6.95926979748712070610e-08] 
dist 158=[-3.69968800939956152900e-07,2.29773173986105424270e-07] 
dist 159=[5.51245518933801851690e-08,3.31022831659233089390e-07] 
dist 160=[1.21923774820383556810e-07,3.59201076382204027740e-07] 
dist 161=[2.57857991142143703070e-07,3.50816387359667511280e-07] 
dist 162=[2.78209673647440876520e-07,3.36183002792618972920e-07] 
dist 163=[1.93522767780719127340e-07,2.74446656906973078960e-07] 
dist 164=[4.23736638698782693710e-08,2.62825119666654992760e-07] 
dist 165=[-1.09098696545937517760e-07,2.07430171552926325860e-07] 
dist 166=[-2.03609862000402320980e-07,1.85200073404372041190e-07] 
dist 167=[-2.62817389636442843980e-07,2.77391727852731941780e-08] 
dist 168=[-2.78173487403997265890e-07,-3.23436731057875913760e-09] 
dist 169=[-2.04573531132500941160e-07,-5.53918907034877641760e-08] 
dist 170=[-2.16515319178114774300e-07,-6.39660149364141064590e-08] 
dist 171=[-6.39569202205891215310e-08,-4.86665426101282508470e-08] 
dist 172=[-6.16619492905318407700e-08,-1.83974885961213094990e-08] 
dist 173=[-4.59077914974489290320e-08,1.19992817442753911910e-08] 
dist 174=[-4.34955793390298684880e-08,3.13917088983667345500e-08] 
dist 175=[4.04979260394406715070e-09,4.36088771921326044760e-08] 
dist 176=[1.15714813361696719130e-08,4.69342617170145421370e-08] 
dist 177=[2.64894061000130567260e-08,4.55049061258672156030e-08] 
dist 178=[2.86084065449456192200e-08,4.37882574066691753970e-08] 
dist 179=[1.94431465278171677360e-08,3.44535149485870469610e-08] 
dist 180=[4.64981149063782192090e-09,3.31501310555072300570e-08] 
dist 181=[-1.01647960464115238860e-08,2.49245103170868380190e-08] 
dist 182=[-1.94126985194019752880e-08,2.33182974059624580720e-08] 
dist 183=[-2.53244605292670201980e-08,1.24048799909447763920e-09] 
dist 184=[-2.68759728354316314890e-08,-2.01376198070353400420e-09] 
dist 185=[-1.89240144883387279680e-08,-7.83349663407686025360e-09] 
dist 186=[-2.01097631173060102390e-08,-7.41269773411403496230e-09] 
dist 187=[-9.01102012356615293320e-09,-5.34819225613314573030e-09] 
dist 188=[-8.66956262350869241580e-09,-1.65774898106773089390e-09] 
dist 189=[-6.54737656677599065520e-09,2.34804010437149954370e-09] 
dist 190=[-6.10681915129639448980e-09,4.85295984973534004850e-09] 
dist 191=[4.52889354729633290330e-10,6.42937853951565073690e-09] 
dist 192=[1.53836995268894649400e-09,6.85513394881366691910e-09] 
dist 193=[3.01382919327649106570e-09,6.66622888452962145810e-09] 
dist 194=[2.26370668163504010000e-09,6.38747426566594427340e-09] 
dist 195=[1.05421609235260045320e-09,5.16129384717699639040e-09] 
dist 196=[-8.94804539706915933560e-10,4.96304666936704416790e-09] 
dist 197=[-2.84573881330643232190e-09,3.74451104338311218670e-09] 
dist 198=[-4.06266373127887197210e-09,3.48968534951356627560e-09] 
dist 199=[-4.82488534108532295840e-09,1.85916091427846440690e-09] 
dist 200=[-5.02255021359929368020e-09,1.82010420428555792600e-09] 
dist 201=[-2.89421697194230911710e-09,1.76620127519288554490e-09] 
dist 202=[-3.06345809208951102410e-09,1.68277491983912619770e-09] 
dist 203=[-2.22079500576595327060e-09,1.35373670603254634650e-09] 
dist 204=[-2.11547530224717898040e-09,1.19297702931444266220e-09] 
dist 205=[-1.73198024994318713440e-09,6.78138872777421235720e-10] 
dist 206=[-1.54273810588681397990e-09,1.18572783749758660890e-09] 
dist 207=[-1.52109930362445972370e-09,1.50420393684540197110e-09] 
dist 208=[-1.60111147972521906920e-09,1.64154234884535356520e-09] 
dist 209=[-1.56211733177473529100e-09,2.05163844608527029390e-09] 
dist 210=[-1.48420756374864670780e-09,2.15873844893404458350e-09] 
dist 211=[-1.23235339668419144340e-09,2.08854977428448011630e-09] 
dist 212=[-1.10877053150975651660e-09,2.00487378634828671870e-09] 
dist 213=[-1.10278807813023154170e-09,1.52827075663806332790e-09] 
dist 214=[-1.28114560801996819370e-09,1.42167482775219537330e-09] 
dist 215=[-1.39286041274452023810e-09,1.59217604447799972770e-09] 
dist 216=[-1.42187270064235239390e-09,1.63637197284127529630e-09] 
dist 217=[-1.31356222335641936660e-09,1.20326840088752710440e-09] 
dist 218=[-1.34863765122562919100e-09,1.22981298931134428610e-09] 
dist 219=[-7.97878217489370508920e-10,6.72680683673099315700e-11] 
dist 220=[-7.52749133765479857460e-10,2.70990605238972020050e-10] 
dist 221=[-6.67987724047106050560e-10,5.96516466128704964250e-10] 
dist 222=[-1.11215874418528590390e-09,1.11884242519329823780e-09] 
dist 223=[-1.64470193437973220540e-09,1.64120241285789151160e-09] 
dist 224=[-1.97663888876765329320e-09,1.96686054174762445590e-09] 
dist 225=[-2.18443726314060606420e-09,2.17079863191928654430e-09] 
dist 226=[-2.23824537498659647600e-09,2.22375644727057180740e-09] 
dist 227=[-2.17028461469685406390e-09,2.18495076716303854440e-09] 
dist 228=[-2.07746746454333038950e-09,2.06423546232201086920e-09] 
dist 229=[-1.62179600452830041980e-09,1.80319972491508679420e-09] 
dist 230=[-1.45782799682576275830e-09,1.67475042974600284230e-09] 
dist 231=[-1.53960627675862473870e-09,1.40750657025843277440e-09] 
dist 232=[-2.23585106310555706020e-09,1.45071867476641425760e-09] 
dist 233=[-2.70150807228960533890e-09,1.54696280642401159430e-09] 
dist 234=[-2.82227656932031798410e-09,1.63972623639115609850e-09] 
dist 235=[-2.74442565204212931480e-09,1.60780272633981633640e-09] 
dist 236=[-2.61971309645511092730e-09,1.52199057136023033160e-09] 
dist 237=[-2.09696462421423591290e-09,1.30784078545097333840e-09] 
dist 238=[-1.83976381177292554740e-09,1.20248275268905031910e-09] 
dist 239=[-1.89216068079168384880e-09,1.01614627794536113040e-09] 
dist 240=[-1.97409085202394865960e-09,1.78432769399130098460e-09] 
dist 241=[-1.93191562400690849530e-09,2.26530806477247951760e-09] 
dist 242=[-1.94626492857589123360e-09,2.39003591116549790420e-09] 
dist 243=[-1.90702378937012292070e-09,2.33991430039433926430e-09] 
dist 244=[-1.80654666565443815570e-09,2.21847951546096482950e-09] 
dist 245=[-1.54316893790822200830e-09,1.88197500585603484260e-09] 
dist 246=[-1.41358669735860385310e-09,1.71641100203049090790e-09] 
dist 247=[-1.86340963096987809490e-09,1.77296244690298437090e-09] 
dist 248=[-2.32283541857338834110e-09,2.04126939109744242530e-09] 
dist 249=[-2.61049334616652256030e-09,2.20926274762237646240e-09] 

8 phat 5 dirichlet min maxes function [0, 1, 1, 1, 1, 0, 2, 1, 2] 
dist 0=[340.98822149649692858   ,340.98822149649692858   ] 
dist 1=[317.50197131401063132   ,347.24193274993570279   ] 
dist 2=[283.45440495008765543   ,347.68401250795456218   ] 
dist 3=[247.95415752665372510   ,342.24489915527771847   ] 
dist 4=[182.18798674244940588   ,331.71579286735138319   ] 
dist 5=[125.71835145958835358   ,246.53989634005786309   ] 
dist 6=[71.057709271529000746  ,226.92518348566135601   ] 
dist 7=[10.200058720307159923  ,160.70286150509132570   ] 
dist 8=[-41.805332531596517975  ,150.83303599757789214   ] 
dist 9=[-62.457616567108555861  ,32.887089143153596779  ] 
dist 10=[-70.437821653223814643  ,9.0550288874504685732 ] 
dist 11=[-77.896558606020963548  ,4.6601914086267113919 ] 
dist 12=[-86.001540595777985794  ,5.2977711380125128753 ] 
dist 13=[-86.198564697303984816  ,12.076837466185296660  ] 
dist 14=[-66.526536828203727888  ,19.074126710049042703  ] 
dist 15=[-52.742049091326538729  ,24.505109494308103671  ] 
dist 16=[-50.372798782669966062  ,33.557171911891712961  ] 
dist 17=[-.53845579805426532179,35.124856177410848931  ] 
dist 18=[.37565026513971306832,33.632787499327205342  ] 
dist 19=[-6.0123627061612264690 ,31.182338730140786723  ] 
dist 20=[-10.812566917501194791  ,31.785003205813958173  ] 
dist 21=[-17.181053095124813322  ,32.290459666257161447  ] 
dist 22=[-23.974328212372689170  ,31.312478572816304119  ] 
dist 23=[-25.749455376857947268  ,25.610375435770504076  ] 
dist 24=[-13.221904793260010006  ,22.957515071456106542  ] 
dist 25=[-11.930937806103840008  ,6.5782939633959050941 ] 
dist 26=[-18.170960888658575167  ,6.4665954985477209303 ] 
dist 27=[-23.648826437395517278  ,10.191753469410367679  ] 
dist 28=[-24.958190757230718675  ,12.661721531751334702  ] 
dist 29=[-6.6073817108354310873 ,13.311801857601034499  ] 
dist 30=[-6.4674135698593771116 ,4.0069696471220774264 ] 
dist 31=[-5.0120901879725332794 ,4.9470484300831115718 ] 
dist 32=[-4.7938790793828511809 ,5.3126868982959791094 ] 
dist 33=[.35202252820646914122,5.2701209221110094915 ] 
dist 34=[.06961087746432321670,4.2962861128065485853 ] 
dist 35=[-.52861502761137546133,4.0423041500476547348 ] 
dist 36=[-.95402495144705785109,3.2693090205980585179 ] 
dist 37=[-2.1166376063011435748 ,3.2700262120336359231 ] 
dist 38=[-2.9663615567376278959 ,3.1582274302787719393 ] 
dist 39=[-3.1666903632025263942 ,2.5462445728225443396 ] 
dist 40=[-1.2929183137456974235 ,2.2858206632016056184 ] 
dist 41=[-1.2955969038044429043 ,.4002668485388404454 ] 
dist 42=[-1.8287859385177758056 ,.34259182447507961048] 
dist 43=[-2.3842475585782544464 ,.69817832490857304991] 
dist 44=[-2.5284171635525517853 ,.92260838833348641219] 
dist 45=[-.75359177125837592653,.98102894373184211431] 
dist 46=[-.7328279154923075922 ,.5596437605275432798 ] 
dist 47=[-.56706040152831144496,.65889027648912898122] 
dist 48=[-.53379370396339845892,.68609387595371071302] 
dist 49=[.01211824030093545027,.6708831125526206203 ] 
dist 50=[-.05131226048908341362,.55772584719551002004] 
dist 51=[-.13236606729712137083,.50371424156263309148] 
dist 52=[-.18940047007701752516,.4370226259468012216 ] 
dist 53=[-.38003011742143905629,.42952196138742604611] 
dist 54=[-.5000842316776988185 ,.41448609722134097733] 
dist 55=[-.53130053922952634995,.3192383546973950999 ] 
dist 56=[-.16453800513479898907,.29523320071808386155] 
dist 57=[-.16228626091064752914,.05552529639653171370] 
dist 58=[-.19720403889731304593,.08099555602990259293] 
dist 59=[-.25457840758578721216,.12003751646006762639] 
dist 60=[-.27046582438589208914,.14527032258789319028] 
dist 61=[-.09417439510540934517,.15298949545786539044] 
dist 62=[-.09138577338021150824,.08305049991477815293] 
dist 63=[-.06917137393678862205,.09309705102924008559] 
dist 64=[-.06585676421101121587,.09326612730166039948] 
dist 65=[.00796390833234518322,.09069087609085019770] 
dist 66=[-.00203508561620254043,.07020814709419162780] 
dist 67=[-.01159367444892225181,.06581249556190858437] 
dist 68=[-.01792629673958784494,.04816654967112762662] 
dist 69=[-.03790165571286135719,.04743283109836121545] 
dist 70=[-.05085137114181507174,.04558173722413325064] 
dist 71=[-.05425263518215927026,.03630940333625219289] 
dist 72=[-.02181114319871069729,.03248050860293053787] 
dist 73=[-.02135548583015670951,.00514855099694262814] 
dist 74=[-.02712584536197809084,.00598776565981907968] 
dist 75=[-.03515649224360865250,.01162496154242909487] 
dist 76=[-.03723983079897110368,.01516670558414156707] 
dist 77=[-.01095574323416052737,.01608631992011646259] 
dist 78=[-.01059449290136235944,.01000697035615476562] 
dist 79=[-.00806140877620601962,.01119111412330917630] 
dist 80=[-.00757807355567697422,.01120401875934356156] 
dist 81=[.00058930906613816140,.01082322878733475247] 
dist 82=[-.00052637476753291793,.00874054597341147791] 
dist 83=[-.00170518772747824968,.00783921359699220787] 
dist 84=[-.00331379305503372721,.00618969243346164625] 
dist 85=[-.00637256805083117428,.00603341000441930926] 
dist 86=[-.00829275051232727487,.00581223720866991379] 
dist 87=[-.00879116767684003485,.00442549948257778607] 
dist 88=[-.00261200920449521065,.00411320061446046784] 
dist 89=[-.00254145491851712906,.00035145330755078871] 
dist 90=[-.00263087825155176014,.00056856859923247341] 
dist 91=[-.00345085925815184318,.00115907381008079000] 
dist 92=[-.00366800834892292209,.00153209717283371955] 
dist 93=[-.00138045242701655967,.00163424812760154889] 
dist 94=[-.00133465699257479679,.00134991997322059819] 
dist 95=[-.00100026003690230696,.00147961671156758041] 
dist 96=[-.00095015127915550604,.00145609223928466526] 
dist 97=[.00013120322616446578,.00140700703672722867] 
dist 98=[-5.06524830204589400650e-05,.00107951094848428401] 
dist 99=[-.00019773168604325653,.00100462789046050870] 
dist 100=[-.00031174047201254099,.00071335535182185910] 
dist 101=[-.00062924988097941167,.00069778066404588392] 
dist 102=[-.00082943242631015061,.00066911828369965287] 
dist 103=[-.00088362697594228999,.00052986586331819407] 
dist 104=[-.00033593956753614937,.00047350059999365731] 
dist 105=[-.00032626789170634529,7.25675876941105444560e-05] 
dist 106=[-.00040121359936932427,9.68765787816969951310e-05] 
dist 107=[-.00051855927446853563,.00018334267070561011] 
dist 108=[-.00054900209253460168,.00023758092271003684] 
dist 109=[-.00016236724797244886,.00025166222312011718] 
dist 110=[-.00015677311023758015,.00015804726186190021] 
dist 111=[-.00011749356067768789,.00017356009498392851] 
dist 112=[-.00011116478256528378,.00017120789460706255] 
dist 113=[1.88779998139317767100e-06,.00016462226025334469] 
dist 114=[-1.64111746849594963040e-05,.00013129860990514575] 
dist 115=[-3.52237041230586868500e-05,.00011750265020758416] 
dist 116=[-5.18731372001215585710e-05,.00010056022347580836] 
dist 117=[-9.80610099560298520040e-05,9.76892326455417920590e-05] 
dist 118=[-.00012702237358530168,9.38827893579081725760e-05] 
dist 119=[-.00013453970932898601,7.18595835992636575020e-05] 
dist 120=[-4.02199124670872979620e-05,6.61484498120843218110e-05] 
dist 121=[-3.89657645381506577960e-05,1.73653059520971808030e-05] 
dist 122=[-4.84353530947450134180e-05,1.91662640730026562170e-05] 
dist 123=[-6.02636189694320573580e-05,2.79789064972749952340e-05] 
dist 124=[-6.34135391864590795110e-05,3.35440347684069776340e-05] 
dist 125=[-1.05359786865549428730e-05,3.50781660692206296880e-05] 
dist 126=[9.57946739873498514690e-06,2.30276136810797491500e-05] 
dist 127=[8.30492456526997882300e-06,2.48343890171123268760e-05] 
dist 128=[6.16567155639199335980e-06,2.42363502389460348820e-05] 
dist 129=[2.65172566471052031980e-06,2.33262137519944305860e-05] 
dist 130=[-8.84965162026388733580e-07,1.79171101491695591900e-05] 
dist 131=[-3.11254579909626017890e-06,1.65038865860691086390e-05] 
dist 132=[-7.24767548877585318360e-06,4.45721525899089166010e-06] 
dist 133=[-1.19356288583616904210e-05,2.83121484716777559160e-06] 
dist 134=[-1.48925408252587548720e-05,5.29750938214030829250e-07] 
dist 135=[-1.57014602717713545080e-05,0                     ] 
dist 136=[-5.10026998806498970540e-06,-2.71403563399878348410e-06] 
dist 137=[-4.93447856888928478820e-06,-6.17322595049750556840e-07] 
dist 138=[-3.70376073015493588750e-06,1.48498222830110937120e-06] 
dist 139=[-3.52026936318741262190e-06,2.79776134481990915900e-06] 
dist 140=[4.84770989789248476250e-07,3.62054415439442386520e-06] 
dist 141=[1.11582058272833429130e-06,3.83397938882835954490e-06] 
dist 142=[1.12004843778972440350e-06,2.42003341346967300100e-06] 
dist 143=[9.62392692510742440090e-07,2.63559297420721193010e-06] 
dist 144=[7.01477628721651144960e-07,2.58168880918243540220e-06] 
dist 145=[2.75709671121194746320e-07,2.47659659447293508200e-06] 
dist 146=[-1.52022390543396651610e-07,1.96443578610458779560e-06] 
dist 147=[-4.20565102239230945020e-07,1.75498241914285434660e-06] 
dist 148=[-7.91810655297737527510e-07,2.68472845076631840310e-07] 
dist 149=[-1.48850594820236277420e-06,-2.55566286731842777010e-08] 
dist 150=[-1.92507126906401508510e-06,-5.04059244493015950020e-07] 
dist 151=[-2.03831040614885648510e-06,-4.23234518008937795170e-07] 
dist 152=[-5.96500498613591027530e-07,-2.91162702455018532170e-07] 
dist 153=[-5.75698526036212216150e-07,-7.69837647243195102330e-08] 
dist 154=[-4.35687935665413789670e-07,1.37738120353672511940e-07] 
dist 155=[-4.09053487400724995730e-07,2.71918516625022775820e-07] 
dist 156=[3.57005010506108485780e-08,3.56171857093993931250e-07] 
dist 157=[1.08105826954252537220e-07,3.78418658600457476890e-07] 
dist 158=[1.41739686713560461110e-07,3.14232505408652665070e-07] 
dist 159=[1.22253255338304349440e-07,3.39259113262898491820e-07] 
dist 160=[9.02359670434171951890e-08,3.29707778198908092680e-07] 
dist 161=[3.81646932498713125850e-08,3.17328570426866358710e-07] 
dist 162=[-1.42416529854586100920e-08,2.40987711879138953290e-07] 
dist 163=[-4.71242437165366749780e-08,2.23934481239985568590e-07] 
dist 164=[-7.31647680360686119030e-08,1.80471091814983550960e-08] 
dist 165=[-1.44227357641166149910e-07,-1.31761836378713145280e-08] 
dist 166=[-1.88823605339143444020e-07,-6.83417734909869415080e-08] 
dist 167=[-2.00558342483281271440e-07,-5.87744295781529817500e-08] 
dist 168=[-7.58801217532705141140e-08,-3.96091845647714547920e-08] 
dist 169=[-7.32573617192817674040e-08,-8.62908560399774772620e-09] 
dist 170=[-5.47279717572578991500e-08,2.24164082981228649110e-08] 
dist 171=[-5.19091162094218842380e-08,4.17890683405691701310e-08] 
dist 172=[7.41987749863543220900e-09,5.39260789509077497820e-08] 
dist 173=[1.64961287321141336580e-08,5.70744499083909887450e-08] 
dist 174=[1.59931371601153650680e-08,3.65174822662823823540e-08] 
dist 175=[1.36041955207634749750e-08,3.95735087670881291860e-08] 
dist 176=[9.70878737581139382090e-09,3.85993374862169509600e-08] 
dist 177=[3.39661981154788571790e-09,3.69963479597981393760e-08] 
dist 178=[-2.93273533986632238950e-09,2.91449668407081391060e-08] 
dist 179=[-6.89489543140300357230e-09,2.61111078787981307140e-08] 
dist 180=[-1.16574459225787190530e-08,3.77615152513508272710e-09] 
dist 181=[-2.18572780358869303190e-08,-5.36666677263966020720e-10] 
dist 182=[-2.82464848568989727400e-08,-6.27078661166969245950e-09] 
dist 183=[-2.99031044471899795210e-08,-5.14325453568738751450e-09] 
dist 184=[-9.52042967645118187510e-09,-3.31504321826796349170e-09] 
dist 185=[-9.18289356893080721030e-09,-3.60940938774922187330e-10] 
dist 186=[-6.84834299676683611570e-09,2.59834697751799321410e-09] 
dist 187=[-6.48793225090179826400e-09,4.44669837793081725210e-09] 
dist 188=[-2.28433558524028800290e-10,5.60698410600672220310e-09] 
dist 189=[6.42505176103210715970e-10,5.91337620804840111720e-09] 
dist 190=[5.54580613434411398550e-10,5.91914915093296244850e-09] 
dist 191=[1.51604350567070281620e-10,6.31594779163832467730e-09] 
dist 192=[-5.03386066482908137060e-10,6.12160598453451808420e-09] 
dist 193=[-1.56313755817040546300e-09,5.88342867794846529730e-09] 
dist 194=[-2.62539183804323278940e-09,4.47208897273009859370e-09] 
dist 195=[-3.29010311428772121240e-09,4.13844308333384678180e-09] 
dist 196=[-3.70889037827133633470e-09,2.35926557057820121900e-11] 
dist 197=[-3.82296983313288121620e-09,-5.31113037431244098930e-10] 
dist 198=[-3.79745866187333348980e-09,-9.14429410848969349780e-10] 
dist 199=[-3.67802079494968672340e-09,-7.07648067835562234440e-10] 
dist 200=[-1.45688636379592641570e-09,-3.74797700705434828230e-10] 
dist 201=[-1.39809622968795726260e-09,1.61146086342899492940e-10] 
dist 202=[-1.08389846853420784390e-09,6.97524580704633814660e-10] 
dist 203=[-9.85608821757507747740e-10,1.03206328522216122160e-09] 
dist 204=[-3.45758498315749346360e-10,1.24159038561376833830e-09] 
dist 205=[-3.29133436173611214910e-10,1.29592973075447283710e-09] 
dist 206=[-3.16274887414652037920e-10,9.67554362834935850070e-10] 
dist 207=[-3.03974246880995207500e-10,1.03023110580190500320e-09] 
dist 208=[-2.25177928213266197090e-10,9.96715646904947730640e-10] 
dist 209=[-2.12378944821107419890e-10,9.58650726779073920960e-10] 
dist 210=[-1.19300874871692052710e-10,7.21864633623241700180e-10] 
dist 211=[-1.06119409211559729910e-10,6.74086505147659854330e-10] 
dist 212=[-2.03749074749829162460e-10,2.72979177741307874730e-10] 
dist 213=[-3.95179954976745894910e-10,2.83821743875303713780e-10] 
dist 214=[-5.44763015380215213940e-10,2.77604565101166957840e-10] 
dist 215=[-5.84009618254490024240e-10,2.62944450756630967280e-10] 
dist 216=[-5.73603672147195764150e-10,2.32219441044397011250e-10] 
dist 217=[-5.42757145898098679490e-10,2.89065291480778283160e-10] 
dist 218=[-4.69622052941155012110e-10,3.51191616920364966650e-10] 
dist 219=[-4.93122594713945951480e-10,3.89932535232331363770e-10] 
dist 220=[-5.61087911097767455270e-10,4.14192735031776716700e-10] 
dist 221=[-5.78757574230556566850e-10,5.60745155331274895380e-10] 
dist 222=[-2.21549462841438261440e-10,6.80483504583950321400e-10] 
dist 223=[-2.26136916572061218240e-10,7.11668274912528081740e-10] 
dist 224=[-2.19377034630102248180e-10,6.88035757944396105890e-10] 
dist 225=[-2.09687487815887793330e-10,6.60772218922246496740e-10] 
dist 226=[-1.67755641169267393610e-10,5.01159857009050721170e-10] 
dist 227=[-2.04432801709098867790e-10,4.63794600165714108670e-10] 
dist 228=[-2.65569097016121488320e-10,1.96859050632514842920e-10] 
dist 229=[-3.50196556120051996020e-10,1.85618264340141258500e-10] 
dist 230=[-4.13188957843578436450e-10,1.78582503830282540270e-10] 
dist 231=[-4.29532857935824602160e-10,1.76768862882646527030e-10] 
dist 232=[-5.07379634921752594500e-11,5.08202499703215035290e-11] 
dist 233=[-4.70949631821617365010e-11,5.69882266819858732200e-11] 
dist 234=[-3.67063390850379141390e-11,6.68699925813792931280e-11] 
dist 235=[-5.82415768333198134670e-11,8.27466475400271591650e-11] 
dist 236=[-1.09023012787285384590e-10,9.86303361936750252240e-11] 
dist 237=[-1.40671908090918768140e-10,1.08539414428068445110e-10] 
dist 238=[-1.60481193593444020640e-10,1.14751818960732814820e-10] 
dist 239=[-1.65603396520054165350e-10,1.16380073496639626960e-10] 
dist 240=[-1.65431472801090127240e-10,1.14636982459768623700e-10] 
dist 241=[-1.64824011043339850150e-10,1.08051455670215704950e-10] 
dist 242=[-1.63863530726167925630e-10,1.25951020660238566200e-10] 
dist 243=[-1.62330050614148134860e-10,1.63377685625062183270e-10] 
dist 244=[-1.60797887649128344080e-10,1.95466644012680193220e-10] 
dist 245=[-1.59842522453956419570e-10,2.67717178484168455720e-10] 
dist 246=[-1.59243373193206142490e-10,3.12953127085133053260e-10] 
dist 247=[-1.38900461635805205400e-10,3.24679204327446669690e-10] 
dist 248=[-1.47903726586153772280e-10,3.13752098762089612000e-10] 
dist 249=[-1.62344353295148134840e-10,3.01366666044934028030e-10] 
dist 250=[-1.76784397193142497380e-10,2.28042571758690216760e-10] 
dist 251=[-1.85785391481491064290e-10,2.11483703840755109990e-10] 
dist 252=[-1.91420663324219513400e-10,4.61383692270150346330e-12] 

8 phat 5 dirichlet min maxes function [1, 1, 2, 2, 1, 0, 2, 0, 1] 
dist 0=[358.61772705996653350   ,358.61772705996653350   ] 
dist 1=[347.26566034145897114   ,363.90415550036370230   ] 
dist 2=[314.07122648588010645   ,362.95597366569622752   ] 
dist 3=[256.42507992893755751   ,354.53141346624575488   ] 
dist 4=[183.60090882651190963   ,275.67615599500266291   ] 
dist 5=[123.68438042347069082   ,256.12007655578411840   ] 
dist 6=[67.233098049468974284  ,193.43461045287058170   ] 
dist 7=[6.7314793800779530512 ,176.38431533332341241   ] 
dist 8=[-44.338306256960675820  ,50.696813357681330888  ] 
dist 9=[-64.533590554142805348  ,21.022974943405871657  ] 
dist 10=[-72.086543866699655700  ,13.915146604155224823  ] 
dist 11=[-78.387909851395500313  ,9.1025953369733676031 ] 
dist 12=[-86.501750131089879877  ,11.405932077024324603  ] 
dist 13=[-88.140502266090724821  ,16.944416713924808322  ] 
dist 14=[-72.516299656042534231  ,26.714145688794347159  ] 
dist 15=[-63.128562230420999728  ,35.040712035748072914  ] 
dist 16=[-2.9864755342844460238 ,37.890631888918498860  ] 
dist 17=[6.8629886098112941055 ,39.333355496651099975  ] 
dist 18=[16.919742154649177197  ,36.853660800425303399  ] 
dist 19=[2.7946543223523860447 ,41.642196727680640442  ] 
dist 20=[-7.0571218012830879182 ,41.724584362622743001  ] 
dist 21=[-14.249570812065763984  ,40.530438857783502038  ] 
dist 22=[-20.341086862825193743  ,31.137342568566807145  ] 
dist 23=[-21.973767477628149437  ,29.098510338354416999  ] 
dist 24=[-19.945111618632448160  ,3.9988920286513420391 ] 
dist 25=[-18.727240404170855454  ,-5.68062550445008276010e-05] 
dist 26=[-23.468049644677590298  ,-3.9209083602220229747 ] 
dist 27=[-24.972846744670078938  ,5.1807510790921783907 ] 
dist 28=[-9.8464557826078870927 ,10.949816687751095257  ] 
dist 29=[-9.6974435303586406113 ,14.596368172415121810  ] 
dist 30=[-7.6325790201157274403 ,15.545375981228344859  ] 
dist 31=[-7.3215909881516637236 ,4.9224786787753810108 ] 
dist 32=[.3962850609541088319 ,5.3644423579277547444 ] 
dist 33=[1.6315937389603161595 ,5.3146464130167827941 ] 
dist 34=[1.6338787418307303378 ,4.5560754520647731770 ] 
dist 35=[-.27607594839497212642,4.9128922732189979660 ] 
dist 36=[-1.5333537160742102031 ,4.9656554637436532621 ] 
dist 37=[-2.9191704226861050565 ,4.8121197410800570341 ] 
dist 38=[-3.8829727489453038587 ,3.9091078073136005868 ] 
dist 39=[-4.1340016142257655415 ,3.5175077363641902176 ] 
dist 40=[-2.7414919890416608312 ,.63773156269353672196] 
dist 41=[-2.7566528957558153956 ,.06860014882563347478] 
dist 42=[-3.6049405064457718360 ,-.45590583576830918571] 
dist 43=[-3.8251955824365710960 ,.53593872992345600943] 
dist 44=[-1.1706326857137988575 ,1.1647264450687642700 ] 
dist 45=[-1.1427480568970684192 ,1.5795679887634787998 ] 
dist 46=[-.88289146995937335992,1.6816346730092726606 ] 
dist 47=[-.83998115503244069052,.8086320586102071117 ] 
dist 48=[.02558664735416503301,.8216451081030693861 ] 
dist 49=[.16629155355882383045,.80062184313539788081] 
dist 50=[.21545483777620400126,.63402618091594148875] 
dist 51=[-.03228396094280202700,.65615920015568017249] 
dist 52=[-.22042229100505605676,.64753119481009309287] 
dist 53=[-.38616713985292141191,.62675653535144486028] 
dist 54=[-.50081662778306842911,.47912218866241105327] 
dist 55=[-.52973960161567092284,.4486859308886658925 ] 
dist 56=[-.33296779237270866822,.04172204401096558919] 
dist 57=[-.32337331554155597085,-.01846494572419686141] 
dist 58=[-.35084802488371818029,-.05078448057567717396] 
dist 59=[-.37470904372008498084,.09909497600668343052] 
dist 60=[-.14956999535951927312,.19310204992483507068] 
dist 61=[-.14550869733672606508,.25217291305769230172] 
dist 62=[-.11088074349577117477,.26751870517795850101] 
dist 63=[-.10571064951152759312,.08138316045024934246] 
dist 64=[.01174741685900351300,.07955156014697107087] 
dist 65=[.03034850576460561387,.06158213407241818127] 
dist 66=[.02193116374399431027,.06946132474145920990] 
dist 67=[-.00914181352011663247,.07658163628624589114] 
dist 68=[-.02896640517788308474,.07576824930518612821] 
dist 69=[-.04183331149367569216,.07291985532873783101] 
dist 70=[-.04611791679120052438,.05831631392768700484] 
dist 71=[-.04559240989700623176,.05220493962377712376] 
dist 72=[-.04414870020070385707,.00852769986464194434] 
dist 73=[-.04327234714540645918,-.00012554716855109403] 
dist 74=[-.05614464333992481179,-.00628448254465227813] 
dist 75=[-.05948461668026210729,.00914443597160157085] 
dist 76=[-.01754122569032944720,.01884125226816397693] 
dist 77=[-.01699290747281002677,.02497088406159777914] 
dist 78=[-.0129946178983808848 ,.02665864128994084932] 
dist 79=[-.01222467286503801494,.01055805173881768896] 
dist 80=[.00080895799419512780,.01027830032225886490] 
dist 81=[.00293705940070531496,.00784511922516798428] 
dist 82=[.00301243613206315653,.00918718766064528388] 
dist 83=[-.00090946842963128745,.00998418297922072731] 
dist 84=[-.00339940217526220740,.00975911611353744845] 
dist 85=[-.00500444792441570300,.00940833559193911960] 
dist 86=[-.00551779277929288025,.00718614976717154864] 
dist 87=[-.00546707410630206403,.00667458835084832675] 
dist 88=[-.00526128104146773864,.00069163494902417963] 
dist 89=[-.00429807255676050291,-.00021668982468851457] 
dist 90=[-.00562092370086936040,-.00058547390186811834] 
dist 91=[-.00597429228468221523,.00175856275814152080] 
dist 92=[-.00221947353339292561,.00322449061905845126] 
dist 93=[-.00214857494252663840,.00414430028443086623] 
dist 94=[-.00161662606763468937,.00438378281518927635] 
dist 95=[-.00153619588229112853,.00124889189044956294] 
dist 96=[-.00019172695333395011,.00121051989287711166] 
dist 97=[4.70940549789560179160e-05,.00111400267736401680] 
dist 98=[-.00025335044567820473,.00146685503942449048] 
dist 99=[-.00087746498029384623,.00156931972912479386] 
dist 100=[-.00127029712670656585,.00154466865574867852] 
dist 101=[-.00151997493660161474,.00147200880059317317] 
dist 102=[-.00159240784323417169,.00122802422196887504] 
dist 103=[-.00156218441807919944,.00110531911958528795] 
dist 104=[-.00148826849336912561,.00044110953989373286] 
dist 105=[-.00123045245890521184,.00027788222311228689] 
dist 106=[-.00110183258357366181,6.17992687244407204110e-05] 
dist 107=[-.00089375516918926046,.00025410810681434340] 
dist 108=[-.00025577885823785660,.00042423869104321391] 
dist 109=[-.00024712758073685371,.00053093201418607686] 
dist 110=[-.00018920900086917955,.00055868739789676067] 
dist 111=[-.00017588117255403882,.00015916398005744828] 
dist 112=[-3.01095790130631704140e-05,.00015415996572003479] 
dist 113=[-2.26730598421129748430e-06,.00014343969376644686] 
dist 114=[-2.47649123463553536730e-05,.00018588506026926583] 
dist 115=[-8.42095230786832324090e-05,.00019771081327195156] 
dist 116=[-.00012163423064758637,.00019279876193980359] 
dist 117=[-.00014544315119511030,.00018462984365557351] 
dist 118=[-.00015241150356210416,.00014580039389519819] 
dist 119=[-.00015074350619571693,.00012996428953206023] 
dist 120=[-.00014256648300013104,1.91116216681929866910e-05] 
dist 121=[-.00012568217727014772,-2.88041118044829753890e-06] 
dist 122=[-.00011718041114516644,-1.02743174819849640130e-05] 
dist 123=[-9.40651825348304770340e-05,2.45546680339697418800e-05] 
dist 124=[-3.08300208596968104330e-05,4.63027707228052712640e-05] 
dist 125=[-2.97745421264573819960e-05,5.99332538260774843160e-05] 
dist 126=[-2.22389325857492121800e-05,6.34696138597375885910e-05] 
dist 127=[-2.11157759328175636000e-05,1.88862537293018538730e-05] 
dist 128=[3.07287061499699761940e-06,1.82604486664423807240e-05] 
dist 129=[6.87719332751182465130e-06,1.37170314527660482710e-05] 
dist 130=[4.52906305943458793490e-06,1.46910943026492852830e-05] 
dist 131=[-2.61831808711070185320e-06,1.59365402296742075790e-05] 
dist 132=[-7.10441682978156368180e-06,1.55578430260160482860e-05] 
dist 133=[-9.94395998045597142840e-06,1.49080726979462254250e-05] 
dist 134=[-1.07444272096905426510e-05,1.17909911537809064580e-05] 
dist 135=[-1.04481163757127418400e-05,1.05271450541196516730e-05] 
dist 136=[-1.00639428731792026690e-05,1.57436148227706942700e-06] 
dist 137=[-8.98711134656236036400e-06,-1.95091507703727265680e-07] 
dist 138=[-1.16121078202806140390e-05,-1.29741019127001920100e-06] 
dist 139=[-1.22929179170083684330e-05,2.21455293370464563150e-06] 
dist 140=[-3.58619407700004489360e-06,4.40931899030532954610e-06] 
dist 141=[-3.45650417370473675410e-06,5.78762213561758408130e-06] 
dist 142=[-2.60620586631784776270e-06,6.15205027530535449180e-06] 
dist 143=[-2.44502915343061908980e-06,2.39120893713776205630e-06] 
dist 144=[2.28412099232754338500e-07,2.31013919000463562970e-06] 
dist 145=[6.63447958359389417330e-07,1.72707873146440807170e-06] 
dist 146=[6.43691587436784177680e-07,1.89296029512249892700e-06] 
dist 147=[-2.37550752944549560070e-07,2.03874008633094906850e-06] 
dist 148=[-7.90099396613298862160e-07,1.97723965339915466190e-06] 
dist 149=[-1.13934943635224172990e-06,1.90163912139486443940e-06] 
dist 150=[-1.23685971208777000760e-06,1.44212944589130970900e-06] 
dist 151=[-1.20827360203445391880e-06,1.33925602740199357430e-06] 
dist 152=[-1.15806581230574782540e-06,1.05148109812098839360e-07] 
dist 153=[-9.16435789826834024910e-07,-8.21554370974182742780e-08] 
dist 154=[-1.13630144394629072690e-06,-1.49454548803508776250e-07] 
dist 155=[-1.20624468237391645320e-06,3.72272265833640185230e-07] 
dist 156=[-4.51200081037736129240e-07,6.97818299898585704060e-07] 
dist 157=[-4.35187749656555663240e-07,9.01765368716288629930e-07] 
dist 158=[-3.23988194694168758020e-07,9.54661725066650812820e-07] 
dist 159=[-3.07312475372801239660e-07,2.79263294035159749900e-07] 
dist 160=[4.62136644932945948480e-08,2.69245455181130958890e-07] 
dist 161=[1.01763410423751334160e-07,2.03092036627266368200e-07] 
dist 162=[6.68998092261557086080e-08,2.16466611022466183940e-07] 
dist 163=[-3.90920536643660134350e-08,2.34126685742606649070e-07] 
dist 164=[-1.05433086998356323820e-07,2.27995292008844577680e-07] 
dist 165=[-1.47241645269744911060e-07,2.18324446100657424730e-07] 
dist 166=[-1.58650477161740069030e-07,1.72167329311671012680e-07] 
dist 167=[-1.53938254612303400330e-07,1.53778899246521494720e-07] 
dist 168=[-1.48066543341266853640e-07,2.25480785474212633410e-08] 
dist 169=[-1.31500536287622865070e-07,-3.26636251289131345780e-09] 
dist 170=[-1.69781500726682063750e-07,-1.84233911726733581880e-08] 
dist 171=[-1.79709668132701730730e-07,3.47417725319150317820e-08] 
dist 172=[-5.33908379531309363650e-08,6.79298962566511996870e-08] 
dist 173=[-5.14665493578669231690e-08,8.87857942538942127950e-08] 
dist 174=[-3.83012979894414687120e-08,9.42577893505324542010e-08] 
dist 175=[-3.62843186655361268650e-08,3.53937911406142122800e-08] 
dist 176=[2.96536047709415017300e-09,3.41428884107577563660e-08] 
dist 177=[9.28419356941882472440e-09,2.54461582339748562430e-08] 
dist 178=[9.04069883970403070500e-09,2.83376722718593307020e-08] 
dist 179=[-3.77724067906747709290e-09,3.04324574400436459150e-08] 
dist 180=[-1.19112163515759852300e-08,2.94629815878902999820e-08] 
dist 181=[-1.70560678546953400000e-08,2.83282789552675590250e-08] 
dist 182=[-1.84512503313717959930e-08,2.14141255638790191600e-08] 
dist 183=[-1.79699263488980837880e-08,1.99206322046073711540e-08] 
dist 184=[-1.72146191162842671420e-08,1.91924820264620522080e-09] 
dist 185=[-1.35492918222198433110e-08,-7.11853038520722098300e-10] 
dist 186=[-1.67305142623950180860e-08,-2.03364071448004356880e-09] 
dist 187=[-1.77318981003959873760e-08,5.58231606131184230560e-09] 
dist 188=[-7.36036955049349489920e-09,1.03326649806012028650e-08] 
dist 189=[-7.07667179217960712300e-09,1.33079842387259364650e-08] 
dist 190=[-5.37184781995625400200e-09,1.40796061087082391770e-08] 
dist 191=[-4.98322216815714040990e-09,4.47573147495816016690e-09] 
dist 192=[2.39413028063024649410e-10,4.30150814839990135580e-09] 
dist 193=[1.11989557052799968650e-09,3.29499776033296445170e-09] 
dist 194=[8.74179973858978020830e-10,4.23534891937549207260e-09] 
dist 195=[-9.10605164393150289250e-10,4.53377692280937984600e-09] 
dist 196=[-2.02556124406354306590e-09,4.40220713961081637200e-09] 
dist 197=[-2.72604686942991414090e-09,4.21732444127825431600e-09] 
dist 198=[-2.91267637918817295310e-09,3.28934030891278997480e-09] 
dist 199=[-2.81980970712170004050e-09,2.96464748728632561400e-09] 
dist 200=[-2.71061570141962415680e-09,9.63432468403433525740e-10] 
dist 201=[-2.53657504257412512190e-09,6.51955564577072788560e-10] 
dist 202=[-3.12424079531957635670e-09,2.69175506718223546330e-10] 
dist 203=[-3.27663697497490064820e-09,8.06110889488423968070e-10] 
dist 204=[-1.22437067531256475630e-09,1.31306698842714704160e-09] 
dist 205=[-1.17281496120991429280e-09,1.63105144012617014160e-09] 
dist 206=[-9.15827615803529215690e-10,1.71461472251795604790e-09] 
dist 207=[-8.24562856323801276070e-10,2.04749658615148270380e-10] 
dist 208=[-3.50845445286799758180e-10,4.67460764946244694450e-10] 
dist 209=[-3.05419917420711447880e-10,6.76670849705077372640e-10] 
dist 210=[-2.76732448457031789410e-10,8.65235416029917911920e-10] 
dist 211=[-2.68777392578825922380e-10,9.18060621962568375310e-10] 
dist 212=[-2.76274382345795128970e-10,8.85958384678315099230e-10] 
dist 213=[-3.07165626161696257020e-10,8.52891014529181892820e-10] 
dist 214=[-3.56848954804185405430e-10,6.33699962591355629010e-10] 
dist 215=[-4.36811981709081463100e-10,5.98904097639405138970e-10] 
dist 216=[-5.99786969615530305900e-10,6.19785383061295916160e-10] 
dist 217=[-7.01387551166478451650e-10,7.62232926419711623150e-10] 
dist 218=[-7.64988830154371316230e-10,8.51414416329236766840e-10] 
dist 219=[-7.81430502157911772810e-10,8.74538944109049253210e-10] 
dist 220=[-6.88120185896738268550e-10,3.01784695537724631350e-10] 
dist 221=[-6.58327417848127120580e-10,3.33230629924232275900e-10] 
dist 222=[-5.17205023823683605580e-10,3.41380908340803082670e-10] 
dist 223=[-4.62165925375753166330e-10,2.66313598951944338780e-10] 
dist 224=[-3.65603429483963478120e-10,3.43722878927752792610e-10] 
dist 225=[-4.59277768569665487660e-10,3.93663713189966865730e-10] 
dist 226=[-5.17903102716442389350e-10,5.08876358134922149360e-10] 
dist 227=[-5.33048850793888677520e-10,5.38812252933533297340e-10] 
dist 228=[-5.33059678779395278880e-10,5.25009830350863372580e-10] 
dist 229=[-5.33317136962372377600e-10,5.51653734541805636810e-10] 
dist 230=[-5.33766180340938966730e-10,5.73520398911104902790e-10] 
dist 231=[-5.34515443897083087900e-10,5.57937500918165930320e-10] 
dist 232=[-5.35270968253227209160e-10,6.46893016683162448130e-10] 
dist 233=[-5.35744347041793798320e-10,8.82995401948214118820e-10] 
dist 234=[-5.36041480694770897230e-10,1.03081762161451563030e-09] 
dist 235=[-5.36118194030277498750e-10,1.06913375086300549750e-09] 
dist 236=[-4.88017414684136643100e-10,1.04048550953354450430e-09] 
dist 237=[-4.62383712168843573960e-10,9.92365338289358483260e-10] 
dist 238=[-3.86714163638157693930e-10,8.00162309899024486810e-10] 
dist 239=[-3.00103692734843906820e-10,7.05600844461294288580e-10] 
dist 240=[-4.11702177302094583090e-10,3.64303745861882758740e-10] 
dist 241=[-7.08046480403178153300e-10,4.96180597283014423080e-10] 
dist 242=[-8.93592785178280441230e-10,5.78754122776825833600e-10] 
dist 243=[-9.41701623182466462240e-10,6.00170543789687813570e-10] 
dist 244=[-9.14125766907073412940e-10,5.81638051374987043450e-10] 
dist 245=[-8.74096335974716092160e-10,5.57094556546685352890e-10] 
dist 246=[-6.89016331028100596340e-10,4.32656036545908821110e-10] 
dist 247=[-6.13404914824989350420e-10,3.90951558278912640410e-10] 
dist 248=[-3.93964720382910385260e-10,4.57907542235585200340e-10] 
dist 249=[-4.71800773551338657030e-10,6.10691148616321995190e-10] 
dist 250=[-5.23804296624981648490e-10,7.06352610416505948410e-10] 

8 phat 5 dirichlet min maxes function [2, 1, 0, 0, 1, 0, 1, 2] 
dist 0=[340.57088356984693473   ,340.57088356984693473   ] 
dist 1=[323.08996540608209207   ,346.05806887135595677   ] 
dist 2=[272.36479950788213161   ,350.10834092397008703   ] 
dist 3=[212.93764181377736909   ,350.92198645573236640   ] 
dist 4=[161.40859681643625670   ,306.73113663472606857   ] 
dist 5=[110.31318543327559239   ,259.73283933402461302   ] 
dist 6=[51.509207563713728667  ,240.05983786302157979   ] 
dist 7=[-.57955724275896181147,175.35057076771214624   ] 
dist 8=[-25.906181701086219810  ,163.17250169703806154   ] 
dist 9=[-38.729360847243085985  ,27.437582004954753613  ] 
dist 10=[-51.597553809176529128  ,5.1909161976559349266 ] 
dist 11=[-72.099539417077192434  ,5.3910960898921399439 ] 
dist 12=[-80.520741186940042428  ,12.756949713963614253  ] 
dist 13=[-84.194891312516838500  ,21.913583514388020083  ] 
dist 14=[-83.170007948747484395  ,33.686196045818435176  ] 
dist 15=[-66.062051223099044060  ,43.043019909585288275  ] 
dist 16=[-63.483812614668231141  ,44.795869594613391330  ] 
dist 17=[.5199833504460145335 ,40.431157008042867759  ] 
dist 18=[4.2010693668787218019 ,39.185441319401135530  ] 
dist 19=[-5.5266973272091003854 ,33.200114377012790786  ] 
dist 20=[-11.983064581402176641  ,38.322511777689154625  ] 
dist 21=[-19.831507210365435132  ,39.164247507741640096  ] 
dist 22=[-24.499119152373228201  ,38.081215815844264070  ] 
dist 23=[-26.491215482729009886  ,31.168363492607920303  ] 
dist 24=[-26.128351615906751053  ,28.118840789274957875  ] 
dist 25=[-22.418280940322515226  ,5.4367415046727757607 ] 
dist 26=[-21.105204138730284987  ,8.4908118754894140420 ] 
dist 27=[-27.777103107863645842  ,14.052905157370350220  ] 
dist 28=[-29.509470639320483773  ,17.754170159299333845  ] 
dist 29=[-9.0000283272569938315 ,20.588256585713504615  ] 
dist 30=[-8.8136698213560206634 ,21.412813126538204677  ] 
dist 31=[-6.9332371971904658510 ,4.9854347578756729015 ] 
dist 32=[-6.5649770247566446190 ,4.9715843175608101623 ] 
dist 33=[.13374151701044709702,4.0315235269829939906 ] 
dist 34=[.60708778032588829828,3.8894109456876328167 ] 
dist 35=[-.64407869475178763501,4.4354240800955485784 ] 
dist 36=[-1.4430003802091181469 ,4.9255148603015025811 ] 
dist 37=[-2.1781706749863848405 ,4.8930131423112831813 ] 
dist 38=[-2.5327265142482204472 ,4.7421943805303869273 ] 
dist 39=[-2.6125453923224934366 ,3.6629209112537002479 ] 
dist 40=[-2.5470265323850871107 ,3.4149953230368969173 ] 
dist 41=[-2.1040751716640563363 ,.3741884893830419913 ] 
dist 42=[-2.0672639420643177860 ,-.09448149696604114621] 
dist 43=[-2.7466024692612849174 ,.7382562866456923534 ] 
dist 44=[-2.9307821721467165704 ,1.4611632848107403417 ] 
dist 45=[-1.1276392518319883536 ,1.9163285171094907453 ] 
dist 46=[-1.0991348369927954913 ,2.0344884154682161386 ] 
dist 47=[-.84216330487391110842,.61181426135850185199] 
dist 48=[-.80363521088825764265,.60120019430775805874] 
dist 49=[.07996208723003372988,.48024633276405282966] 
dist 50=[.03303485360579458521,.45201904611338590638] 
dist 51=[-.10987446648664359151,.51774093361026686474] 
dist 52=[-.24618896286290684023,.57331382888095186313] 
dist 53=[-.34907468488277152979,.5690822560810623673 ] 
dist 54=[-.3855888286259399609 ,.54832943502322574649] 
dist 55=[-.38413362434791496027,.43933045014394653243] 
dist 56=[-.37166230604633177041,.39389127820481789125] 
dist 57=[-.29158504936843947904,.0649668903597235114 ] 
dist 58=[-.32167123977879396729,.10543877436996726432] 
dist 59=[-.41810134304594723304,.17328150652935379282] 
dist 60=[-.44313053104475883586,.21722343819070324665] 
dist 61=[-.1332967598569814037 ,.2464019510463103806 ] 
dist 62=[-.12940042203863931418,.25836860433617467271] 
dist 63=[-.09832016610669190246,.07873225099035090652] 
dist 64=[-.09338467408863786436,.07690717801090829729] 
dist 65=[.00536809615195083098,.05923375076544782673] 
dist 66=[.00792319851585082401,.05659196476245336115] 
dist 67=[-.01414137098322044855,.06905388624307638596] 
dist 68=[-.02801538989232761824,.07518189529724689440] 
dist 69=[-.03674553386238253377,.07355396346631254868] 
dist 70=[-.04038561570705469478,.07098845677681099972] 
dist 71=[-.0402530973786026341 ,.0539743958923898536 ] 
dist 72=[-.03883043707093728337,.05042899760808059748] 
dist 73=[-.03124542312659834233,.00419814512189756238] 
dist 74=[-.03071163279673578476,-.00264233287383895025] 
dist 75=[-.04047833651731264438,.01198614070129091061] 
dist 76=[-.04309935641554941906,.02294266197341538773] 
dist 77=[-.01688256359058301028,.02981814824095376856] 
dist 78=[-.01635603164178404187,.03160259660610925273] 
dist 79=[-.01232394551251432980,.00935172593584371252] 
dist 80=[-.01172259831925205736,.00908424079911937737] 
dist 81=[.00148240151408321145,.00699991859088041402] 
dist 82=[.00097342760194877878,.00659264910214764021] 
dist 83=[-.00136539317989519033,.00799356155495005802] 
dist 84=[-.00348738521827618760,.00872871693502935982] 
dist 85=[-.00494606028890125925,.00857144190166037792] 
dist 86=[-.00539688648157568399,.00822784184196643835] 
dist 87=[-.00529726927352694840,.00654600945546686489] 
dist 88=[-.00511226866190948057,.00584481310445318490] 
dist 89=[-.00392448539500973500,.00099698044798176468] 
dist 90=[-.00497479698835751518,3.68762002228864576750e-05] 
dist 91=[-.00641915833422708276,.00124812629380339230] 
dist 92=[-.00679441825559336283,.00238002475987663643] 
dist 93=[-.00196884806339274631,.00309324512533336911] 
dist 94=[-.00190188450834846433,.00328585842692453314] 
dist 95=[-.00144288845451212816,.00118967347238861136] 
dist 96=[-.00135546738598258542,.00115379341302678752] 
dist 97=[-.00031675633907857508,.00087389866524448465] 
dist 98=[-.00011890732065437374,.00117197365316491898] 
dist 99=[-.00065811188519364189,.00150088002677378706] 
dist 100=[-.00099799059524738408,.00159310008765575953] 
dist 101=[-.00121463363715504659,.00155509717414633596] 
dist 102=[-.00127892079282570984,.00148804465441751242] 
dist 103=[-.00126495193564376930,.00118340447171496555] 
dist 104=[-.00119837253393329545,.00104722641942579195] 
dist 105=[-.00104655076041779706,.00019173921680446083] 
dist 106=[-.00096987280987208236,1.59533132502510643740e-05] 
dist 107=[-.00069441184207459546,.00019897773796149482] 
dist 108=[-.00073532438879438544,.00036335806383140369] 
dist 109=[-.00024833107005485141,.00046642430400843681] 
dist 110=[-.00023991647547614193,.00049321087921869601] 
dist 111=[-.00017941573684190546,.00013224611154855814] 
dist 112=[-.00017036633769919807,.00012803402514118868] 
dist 113=[-2.18815342576982753640e-05,.00010311041605440908] 
dist 114=[-2.43977971839667401030e-05,.00012034031712878998] 
dist 115=[-9.27066815395551243450e-05,.00015681365446855866] 
dist 116=[-.00013557984511611828,.00016698494070208265] 
dist 117=[-.00016271243943275613,.00016387369258290566] 
dist 118=[-.00017034800409108334,.00015598987819207972] 
dist 119=[-.00016685016007720097,.00012999759852917906] 
dist 120=[-.00015892348185480195,.00011703681401940385] 
dist 121=[-.00013115634236342840,4.72023510926956158610e-05] 
dist 122=[-.00011735543817012992,2.99564410152352487880e-05] 
dist 123=[-9.32047510399500362950e-05,3.12762179816557863540e-05] 
dist 124=[-9.86791996891828966490e-05,5.12242624545737477750e-05] 
dist 125=[-2.92655931587008325650e-05,6.37943720972063206720e-05] 
dist 126=[-2.82443240599910473960e-05,6.70544798108666388140e-05] 
dist 127=[-2.11081381087927848400e-05,1.23532466791629148250e-05] 
dist 128=[-1.99924452288668976040e-05,1.18742953828010613920e-05] 
dist 129=[1.68568049239392999870e-06,9.46860808499141720200e-06] 
dist 130=[1.60275063899931903270e-06,1.10993659466858115790e-05] 
dist 131=[-3.75117889144111002940e-06,1.54596239830133221520e-05] 
dist 132=[-7.09635562257424636290e-06,1.66482226005930874760e-05] 
dist 133=[-9.19363772404422384530e-06,1.61430651911308179150e-05] 
dist 134=[-9.73775596383646573020e-06,1.55351477053695280620e-05] 
dist 135=[-2.86126399920456806250e-06,1.17296387444453118070e-05] 
dist 136=[-2.76816626435505621810e-06,1.09437176007285026420e-05] 
dist 137=[-3.45279971628792520950e-06,7.76412673764595612360e-07] 
dist 138=[-6.83588494717072850710e-06,-7.15052057043823574830e-07] 
dist 139=[-8.95779547049832120580e-06,3.75567782964448243170e-07] 
dist 140=[-9.51436918382371696160e-06,1.06188275027271308100e-06] 
dist 141=[-3.68548834940441131740e-06,1.49809793958111560190e-06] 
dist 142=[-3.55547133484319072950e-06,1.62477737843347444670e-06] 
dist 143=[-2.64766403291531499430e-06,1.58507885635374921650e-06] 
dist 144=[-2.51235874697460497930e-06,1.52736609934156717430e-06] 
dist 145=[3.78234103548792433530e-07,1.16389280479216189020e-06] 
dist 146=[2.00270007905708581240e-07,1.22810368956598925380e-06] 
dist 147=[-3.48891617153871562320e-07,1.76242266488318005870e-06] 
dist 148=[-6.92355961721715859510e-07,1.90725477578260278280e-06] 
dist 149=[-9.08215364274514793240e-07,1.85816874416514357070e-06] 
dist 150=[-9.65533470345397407190e-07,1.77937849370434535140e-06] 
dist 151=[-3.63726651853347355320e-07,1.40497596357748267160e-06] 
dist 152=[-3.51793601157090053780e-07,1.25380791190178663200e-06] 
dist 153=[-5.75766547168728158910e-07,1.85618449967920855250e-07] 
dist 154=[-1.07582129543891155140e-06,-2.54919615734229008020e-08] 
dist 155=[-1.38901964042625614320e-06,3.63707852270911207910e-08] 
dist 156=[-1.47024430921846727920e-06,1.20948062997291112840e-07] 
dist 157=[-4.27856183104306334710e-07,1.74587762348620514410e-07] 
dist 158=[-4.12044109471757124630e-07,1.89940419678667815980e-07] 
dist 159=[-3.10051306749196674030e-07,1.85933668672048163930e-07] 
dist 160=[-2.90680625839878145440e-07,1.78381656442044116590e-07] 
dist 161=[2.77718628648932012810e-08,1.41150907999441791500e-07] 
dist 162=[2.22653664297494060860e-08,1.62824296452908217320e-07] 
dist 163=[-5.67786906733277970420e-08,2.26695072683048477250e-07] 
dist 164=[-1.06119357345880568700e-07,2.43770395896351686500e-07] 
dist 165=[-1.37037637171803981770e-07,2.36108937880820027940e-07] 
dist 166=[-1.45059463304841631420e-07,2.26999031283790252290e-07] 
dist 167=[-4.46829923584302904800e-08,1.71898185045814837920e-07] 
dist 168=[-4.31329212121689287590e-08,1.59673779891366049690e-07] 
dist 169=[-5.31946032354181483360e-08,1.26164762547442566860e-08] 
dist 170=[-1.03798616921924835080e-07,-8.77575000559277947750e-09] 
dist 171=[-1.35513554791009047540e-07,7.37688280888402223420e-09] 
dist 172=[-1.43788858401973760550e-07,1.75018682342282662810e-08] 
dist 173=[-5.35935609000074171580e-08,2.38974032544979443100e-08] 
dist 174=[-5.16294039359053768730e-08,2.56728517388032526270e-08] 
dist 175=[-3.85815947378230210420e-08,2.49745582733620754180e-08] 
dist 176=[-3.63824068286136967540e-08,2.39947166603533884300e-08] 
dist 177=[4.61455960579356210800e-09,1.84702138498360145590e-08] 
dist 178=[1.40880466890000000000e-10,1.91663055134098481790e-08] 
dist 179=[-7.82557756667976490030e-09,2.70286141654479363810e-08] 
dist 180=[-1.28064677251410253380e-08,2.91214997307679766730e-08] 
dist 181=[-1.59383548891914278480e-08,2.82972145841467413800e-08] 
dist 182=[-1.67762668902255590410e-08,2.71087043088337241740e-08] 
dist 183=[-6.57439627515327964470e-09,2.11879194725379015590e-08] 
dist 184=[-6.28708156708571393190e-09,1.90670025617144398360e-08] 
dist 185=[-8.74695574596685815290e-09,3.23891339577165833730e-09] 
dist 186=[-1.59180665079466049810e-08,3.56024171803938993680e-10] 
dist 187=[-2.04089398344304344540e-08,2.47634812657478490390e-09] 
dist 188=[-2.15734621862149242340e-08,4.33810894415409377380e-09] 
dist 189=[-7.65493249418286585460e-09,5.50774739555281881630e-09] 
dist 190=[-7.33032259869399467210e-09,5.81889835340959973350e-09] 
dist 191=[-5.73893982749369032960e-09,5.73746884264231077250e-09] 
dist 192=[-5.15217302438859210450e-09,5.41144727265443958280e-09] 
dist 193=[-5.72917369250332329620e-10,4.83873048201177704010e-09] 
dist 194=[-1.01752194506342417970e-09,4.51055133829990585690e-09] 
dist 195=[-1.95107079250358901180e-09,4.16505553088252345590e-09] 
dist 196=[-2.53466913877249840250e-09,4.43679194056701519810e-09] 
dist 197=[-2.90170041142245722120e-09,4.28318580024401776830e-09] 
dist 198=[-3.00023743164402000520e-09,4.12465343591639832020e-09] 
dist 199=[-2.94095603832611196250e-09,3.06124397873220728450e-09] 
dist 200=[-2.78951696092525421360e-09,2.89763527236616755140e-09] 
dist 201=[-2.36751366957148047730e-09,6.19950357175994329150e-10] 
dist 202=[-2.15905309660061189840e-09,3.68147570519038732560e-10] 
dist 203=[-2.13733855019404866740e-09,5.73802014407471530140e-11] 

8 phat 5 dirichlet min maxes function [0, 2, 2, 2, 1, 2, 1, 0, 2] 
dist 0=[340.27031544386276572   ,340.27031544386276572   ] 
dist 1=[327.29418496188258242   ,346.37638792314111298   ] 
dist 2=[283.46514333443298502   ,350.49674183537896513   ] 
dist 3=[230.31370726245911165   ,345.42563752725114495   ] 
dist 4=[183.25891264484622776   ,265.22185238982279268   ] 
dist 5=[135.66679530960279678   ,246.06776589058081203   ] 
dist 6=[79.442239103885319376  ,184.27572667256732176   ] 
dist 7=[28.346067831112244299  ,170.74284452636241606   ] 
dist 8=[.40799918867990100394,41.495596286756743882  ] 
dist 9=[-39.018221347966641857  ,19.749620182435742223  ] 
dist 10=[-70.795069074828421064  ,-17.313488981793039282  ] 
dist 11=[-86.411406853464857611  ,-12.566579125290035802  ] 
dist 12=[-91.658619554940010318  ,3.0635371919586666576 ] 
dist 13=[-90.926455302506740358  ,17.967763398232857013  ] 
dist 14=[-72.896421435558917287  ,32.461221619524615413  ] 
dist 15=[-70.175041564826972175  ,47.130190783548191810  ] 
dist 16=[-.04184900134514666298,57.676977277501400813  ] 
dist 17=[5.2307081195508849995 ,59.464542118056405381  ] 
dist 18=[1.1203043764153727950 ,52.224112328845211038  ] 
dist 19=[-3.7461841540481104991 ,50.766504387910889334  ] 
dist 20=[-7.1401559796749852205 ,43.138090482769255559  ] 
dist 21=[-13.447688032699272568  ,42.013825862611059198  ] 
dist 22=[-24.556386870491710484  ,34.525344013028666385  ] 
dist 23=[-30.264480332878005789  ,31.168363483426538385  ] 
dist 24=[-32.569319572456112591  ,6.1474757794871873394 ] 
dist 25=[-32.112066655952120237  ,7.4477473624067342798 ] 
dist 26=[-30.632984476968708772  ,12.763264187491227964  ] 
dist 27=[-32.550233701719441079  ,18.340492903181367871  ] 
dist 28=[-9.9482705586620440544 ,22.021043428007920170  ] 
dist 29=[-9.7571579437789782626 ,24.506504010637786099  ] 
dist 30=[-7.7048710053680911009 ,25.501630708408644184  ] 
dist 31=[-7.3008157765437668425 ,25.396854628622590974  ] 
dist 32=[.11493782606392139539,6.8982164345964657774 ] 
dist 33=[.98617936750312290081,6.8598648665706853102 ] 
dist 34=[.37572108372359970358,5.5256008256895846416 ] 
dist 35=[-.27307586692780990545,5.4545234791060691668 ] 
dist 36=[-.69313342302778381004,5.4300372859245871554 ] 
dist 37=[-1.8708335386258909547 ,5.2661673358418559398 ] 
dist 38=[-3.0163016612095626209 ,4.0742282570030092786 ] 
dist 39=[-3.4878713280671431302 ,3.7994772654592186175 ] 
dist 40=[-3.5820814975722281751 ,.4247366457082209351 ] 
dist 41=[-3.4877546228853755406 ,-.09588042809703677162] 
dist 42=[-3.0484863195572407257 ,-.13135418974351451765] 
dist 43=[-3.2523875896296329143 ,.02066917829242252270] 
dist 44=[-1.2536588134089101661 ,1.0120092046394781795 ] 
dist 45=[-1.2230132035879648223 ,2.0007126471429565475 ] 
dist 46=[-.93915462355818437209,2.6228744526326288729 ] 
dist 47=[-.89658738251779102561,2.7843536619687774650 ] 
dist 48=[.08645076979907888619,.83946463717447062749] 
dist 49=[.06933418030134337489,.82361010953964407099] 
dist 50=[-.00772615581502295260,.65336829157438243591] 
dist 51=[-.08806296995320973982,.63764919942936465934] 
dist 52=[-.14034923043328270751,.6338987853386712923 ] 
dist 53=[-.3098237202949161187 ,.61107411516784362449] 
dist 54=[-.44755855445847058914,.49020994315791345917] 
dist 55=[-.49586181045586541139,.43961259787442049807] 
dist 56=[-.49347475504023748239,.07313017151824667795] 
dist 57=[-.47795292433583196064,.10693069610639522259] 
dist 58=[-.4656758976027445626 ,.16919068918633991205] 
dist 59=[-.49358929640976982431,.23301794206075860641] 
dist 60=[-.14860715733060941837,.27433496306635099642] 
dist 61=[-.1443402784727895706 ,.30174354919292711619] 
dist 62=[-.10983152434102802464,.31207136281528516062] 
dist 63=[-.10434294295078599255,.31272937489107220789] 
dist 64=[.00579179820027746657,.10838765265112933456] 
dist 65=[.01747942999142600564,.10578132090866427162] 
dist 66=[.00494812595513510522,.08128186643024473578] 
dist 67=[-.00782055307568962769,.08383357208084588858] 
dist 68=[-.01587656524791866165,.08208439821346377346] 
dist 69=[-.03344635017278313801,.07924203570260972753] 
dist 70=[-.05005009240173515309,.06028704694392022119] 
dist 71=[-.05556443461829656032,.05633426538279976091] 
dist 72=[-.05529338548926400837,.00473280549686547451] 
dist 73=[-.05331257369825451560,-.00290589810844848968] 
dist 74=[-.04514855143154609612,-.00214907173973320176] 
dist 75=[-.04808249975518720131,.00051646342757600963] 
dist 76=[-.01885534788406225792,.01647939409218709665] 
dist 77=[-.01827415424455314079,.03151693860872466823] 
dist 78=[-.01378316077024548956,.04095202844737331971] 
dist 79=[-.01311333385872623393,.04340058095035554844] 
dist 80=[.00168400784985176339,.01284741854548579685] 
dist 81=[.00196886665022390263,.01247222251960696102] 
dist 82=[.00060824046715616279,.00959071640054039511] 
dist 83=[-.00077376900405714354,.00969700717522516224] 
dist 84=[-.00164805230762708074,.00952819956442710489] 
dist 85=[-.00467432546227945025,.00914965058838254517] 
dist 86=[-.00666216273835178900,.00727588197551412600] 
dist 87=[-.00727150432649534396,.00650474806823627406] 
dist 88=[-.00713067625930890317,.00101636970144754414] 
dist 89=[-.00688254844777383996,-6.95543548867906887390e-05] 
dist 90=[-.00708427287091641538,-.00029273241337906188] 
dist 91=[-.00750266872414080368,5.23816892046055459790e-05] 
dist 92=[-.00220127611338071941,.00154165657247770827] 
dist 93=[-.00212697215058564508,.00309207480841403909] 
dist 94=[-.00161482611111151292,.00406825203485772188] 
dist 95=[-.00151721146450220864,.00433037685382547972] 
dist 96=[.00012446031876436440,.00163973718352458952] 
dist 97=[.00027516654626341912,.00158983339642814264] 
dist 98=[6.79421042418304506860e-05,.00120071677623749340] 
dist 99=[-.00014110522307065867,.00124758739536854791] 
dist 100=[-.00027216347280733043,.00121462135655227498] 
dist 101=[-.00053073340506702137,.00116963750255367540] 
dist 102=[-.00077457372205383008,.00088975383182090322] 
dist 103=[-.00084744008310578688,.00082677535379110490] 
dist 104=[-.00083332704037271772,6.92119359621435656950e-05] 
dist 105=[-.00080046051914018706,-4.60665799808627974330e-05] 
dist 106=[-.00069592794011457281,-2.38801065732599326280e-05] 
dist 107=[-.00073948271640260242,2.10968334963647348080e-05] 
dist 108=[-.00027792106509583252,.00025363601568918079] 
dist 109=[-.00026856100711684478,.00047803604018931467] 
dist 110=[-.00020091515379291869,.00061870206436213129] 
dist 111=[-.00019083123049435959,.00065520663050189845] 
dist 112=[2.69418917623336944410e-05,.00019437114798508048] 
dist 113=[1.75291027665172655950e-05,.00018804954723155532] 
dist 114=[-3.83201189651918578700e-06,.00014183975482441909] 
dist 115=[-2.53847098857151672320e-05,.00014385163781179687] 
dist 116=[-3.89574609351487952040e-05,.00014057305722423240] 
dist 117=[-8.19993558687966402690e-05,.00013475511993069573] 
dist 118=[-.00011201477097175916,.00010662484498433744] 
dist 119=[-.00012056265616393159,9.52598347453600614340e-05] 
dist 120=[-.00011745820580080007,1.64085565447175596070e-05] 
dist 121=[-.00011298452535814196,2.52096666985736002300e-05] 
dist 122=[-.00010458177564657671,3.96876360881616535450e-05] 
dist 123=[-.00011071276100238317,5.42649871426980266950e-05] 
dist 124=[-3.28723258455217399160e-05,6.34520772946171572610e-05] 
dist 125=[-3.17337634595684390080e-05,6.93064837442621392580e-05] 
dist 126=[-2.36742856166742171650e-05,7.23160650115558323360e-05] 
dist 127=[-2.24721841901390177300e-05,7.61876258910544934380e-05] 
dist 128=[4.16167721402182195720e-07,7.24673277007259212390e-06] 
dist 129=[4.22741733067845294650e-06,1.39327241261567668820e-05] 
dist 130=[1.00013392869778489890e-06,1.89248836150765850440e-05] 
dist 131=[-2.26893428012077236590e-06,2.02878951459940502060e-05] 
dist 132=[-4.31292750814259877940e-06,1.96984332722148069430e-05] 
dist 133=[-5.59494916184055189010e-06,1.89279570112911188960e-05] 
dist 134=[-5.92760900746201855230e-06,1.44810784188997833180e-05] 
dist 135=[-1.74741502109802496220e-06,1.33301239357948756790e-05] 
dist 136=[-5.98065180090002860490e-06,3.48497853425513227020e-06] 
dist 137=[-9.77204103708349251120e-06,2.16435341060126783770e-06] 
dist 138=[-1.21535222137843712510e-05,3.60472068009500932230e-07] 
dist 139=[-1.27859624655352031460e-05,2.22037506466601665660e-07] 
dist 140=[-4.12911890015035942180e-06,6.43120436478056122050e-07] 
dist 141=[-3.98389547154764998420e-06,9.11940275337478063450e-07] 
dist 142=[-2.96760820625437469820e-06,9.92445052913456730360e-07] 
dist 143=[-2.81613883168458264130e-06,9.70980261363071456820e-07] 
dist 144=[4.22782487108770106030e-07,9.36510325623641552780e-07] 
dist 145=[4.59926392873631985810e-07,1.37486912629348423540e-06] 
dist 146=[1.24878727670753619750e-07,1.97386272442863232360e-06] 
dist 147=[-2.11633414501364746590e-07,2.13660807408018175320e-06] 
dist 148=[-4.22292038828219121840e-07,2.08205291150324861550e-06] 
dist 149=[-5.54834867718046445440e-07,1.99391151126597908790e-06] 
dist 150=[-5.90274396444126838910e-07,1.57455599317214070830e-06] 
dist 151=[-2.23224468240968714180e-07,1.40528577897186914920e-06] 
dist 152=[-6.44116990898418310350e-07,2.07504123051358043010e-07] 
dist 153=[-1.20436518678051790860e-06,-2.91199712026803165190e-08] 
dist 154=[-1.55527091483130673450e-06,-6.15490662176567746870e-08] 
dist 155=[-1.64627524061120303410e-06,2.08723732250479415860e-08] 
dist 156=[-4.79647365079832108210e-07,7.27849127428387279270e-08] 
dist 157=[-4.61973220721584962560e-07,1.05833465914466750170e-07] 
dist 158=[-3.47608472860241479620e-07,1.15552182947853691040e-07] 
dist 159=[-3.25994946280234112320e-07,1.13438482360608592780e-07] 
dist 160=[3.15583501898357814840e-08,1.08909743118855976510e-07] 
dist 161=[6.29841290988676515420e-08,1.81950902251821446150e-07] 
dist 162=[1.42690192216695869920e-08,2.53530514179462247620e-07] 
dist 163=[-3.45766124936684775910e-08,2.72698072229789393180e-07] 
dist 164=[-6.51276510415737653060e-08,2.64175889718635223770e-07] 
dist 165=[-8.42821201547812378370e-08,2.53982387846561716610e-07] 
dist 166=[-8.92517010772485293950e-08,1.92436443185439078400e-07] 
dist 167=[-2.65722381910498878300e-08,1.78677640722190163090e-07] 
dist 168=[-5.93314098900536263120e-08,1.36721475553106115460e-08] 
dist 169=[-1.16260275663320016140e-07,-1.13538083980548626090e-08] 
dist 170=[-1.51940941041217413870e-07,-6.25261464163968197970e-09] 
dist 171=[-1.61253935109690390900e-07,3.69130490814223881170e-09] 
dist 172=[-6.04575831482408312220e-08,9.93450912125351249120e-09] 
dist 173=[-5.82800816988757009620e-08,1.38881258389778580920e-08] 
dist 174=[-4.33170871037894761200e-08,1.50064762555198097770e-08] 
dist 175=[-4.10775320705293018230e-08,1.45918881302016860380e-08] 
dist 176=[6.26591879288710826390e-09,1.40611006948592144640e-08] 
dist 177=[6.64537660806615689430e-09,2.02960721559136291230e-08] 
dist 178=[1.83464724789372343800e-09,2.90351536268228619000e-08] 
dist 179=[-2.98895408886871002070e-09,3.13665904673279921590e-08] 
dist 180=[-6.00389453417449376340e-09,3.05149626336603828620e-08] 
dist 181=[-7.89766213937808912400e-09,2.92089823937458394470e-08] 
dist 182=[-8.39905932582191705890e-09,2.30244040820649264900e-08] 
dist 183=[-4.50851597327174510070e-09,2.05509263357445400390e-08] 
dist 184=[-9.45485740080030833170e-09,3.00531368943919427390e-09] 
dist 185=[-1.76358127916666929730e-08,-4.48602654329461779620e-10] 
dist 186=[-2.27591509017146646500e-08,2.17288097027268187570e-10] 
dist 187=[-2.40877187507881856120e-08,2.51544555818964319740e-09] 
dist 188=[-7.71211271052755961690e-09,3.95080325009871881430e-09] 
dist 189=[-7.40451073227160759370e-09,4.85183315358723990580e-09] 
dist 190=[-5.67299133191327902750e-09,5.08980149674609336810e-09] 
dist 191=[-5.20779514645442044160e-09,5.04114043851615034040e-09] 
dist 192=[-6.96930099815729884800e-10,4.83702455660330074700e-09] 
dist 193=[-9.74421297370129632390e-10,4.50824198812716459730e-09] 
dist 194=[-1.42476125412523763590e-09,4.19533701679121257370e-09] 
dist 195=[-1.87649062466634563910e-09,4.08339275615121917730e-09] 
dist 196=[-2.15937648709374538250e-09,3.95007935924776200760e-09] 
dist 197=[-2.33776818896807001780e-09,3.79654103185611529310e-09] 
dist 198=[-2.38665073301751160630e-09,2.86917536134166203630e-09] 
dist 199=[-2.37312737631774931400e-09,2.66692029611385919260e-09] 
dist 200=[-2.31091104760640363980e-09,1.34286599037505074710e-10] 
dist 201=[-2.20974816698381462670e-09,-2.41941334247202951790e-10] 
dist 202=[-2.18210523384621355880e-09,-3.71667209630205712430e-11] 
dist 203=[-2.31845858369366064950e-09,2.22990308555482442640e-10] 
dist 204=[-9.87226492720524650440e-10,3.85564077015437668690e-10] 
dist 205=[-9.50434604813851130660e-10,4.98825440016254804860e-10] 
dist 206=[-7.10078215806329267120e-10,5.32351675732415456670e-10] 
dist 207=[-6.68586631610696998110e-10,5.15925153348736446690e-10] 
dist 208=[4.10583640370653760340e-11,4.95330553503932135480e-10] 
dist 209=[5.22554591744954469150e-12,3.79045599966563497210e-10] 
dist 210=[-5.27430498270362735010e-11,5.03860665252036913670e-10] 
dist 211=[-1.13770342463960352360e-10,5.42039712108710433250e-10] 
dist 212=[-2.40055969024299746820e-10,5.25220584150155786560e-10] 
dist 213=[-3.19139874155696932720e-10,5.03978618429655852130e-10] 
dist 214=[-3.39646834327799940080e-10,3.86854277155010481940e-10] 
dist 215=[-1.01088694086282225280e-10,3.54154468751069070750e-10] 
dist 216=[-1.33388031951283580650e-10,1.12881252026406483770e-10] 
dist 217=[-2.56527235587032448430e-10,1.20533568044938063690e-10] 
dist 218=[-3.33634164764679412150e-10,1.32959625190801137090e-10] 
dist 219=[-3.53622265760798285210e-10,1.61155917331723066100e-10] 
dist 220=[-2.23364934025852085530e-10,2.13461568617960208190e-10] 
dist 221=[-2.57749971865141801060e-10,2.46231861360390350730e-10] 
dist 222=[-2.66574777735602274320e-10,2.54767518064760955560e-10] 
dist 223=[-2.62830625220730903970e-10,2.45662385143888826740e-10] 
dist 224=[-2.48742553943250215120e-10,2.36522993415610743360e-10] 
dist 225=[-2.26303968945513570210e-10,1.89885774443779838000e-10] 
dist 226=[-2.10805940194551257050e-10,2.29500000026009758030e-10] 
dist 227=[-1.54418223420107253870e-10,2.39826210754862271190e-10] 
dist 228=[-1.32020189802370608860e-10,3.05708385560138568350e-10] 
dist 229=[-1.18331377395768526480e-10,3.65417926934658510830e-10] 
dist 230=[-1.14362878194018549710e-10,3.80875798044095968670e-10] 
dist 231=[-1.41254093957170148800e-10,3.68034032210736888630e-10] 
dist 232=[-1.84000530025171670850e-10,3.53498411314567568060e-10] 
dist 233=[-2.10645222050950950760e-10,2.67473839961945504490e-10] 
dist 234=[-2.27323513202325173480e-10,2.48049629693008371870e-10] 
dist 235=[-2.31635927697390174930e-10,3.41343147347447167920e-11] 
dist 236=[-1.55712148906522449090e-10,5.00334164941057822770e-11] 
dist 237=[-2.11725152339328645740e-10,5.99896263567675855910e-11] 
dist 238=[-2.26242739605497966310e-10,6.25737304681791915780e-11] 
dist 239=[-2.19107433918394345900e-10,6.08811725753182591480e-11] 
dist 240=[-2.09992545358043260520e-10,5.80841681490107488920e-11] 
dist 241=[-1.62144011619134223780e-10,4.67055560148700581190e-11] 
dist 242=[-1.47360726591183866530e-10,3.00635728331377035520e-11] 
dist 243=[-5.43364280667070951680e-11,7.31094011090364859880e-11] 
dist 244=[-5.34440210721564216610e-11,1.18676465411257289450e-10] 
dist 245=[-5.04278654009530071050e-11,1.47206026341057157610e-10] 

8 phat 5 dirichlet min maxes function [2, 0, 2, 1, 0, 1, 1, 2] 
dist 0=[374.21747979655222253   ,374.21747979655222253   ] 
dist 1=[352.55292760980357805   ,378.64098564892508307   ] 
dist 2=[302.62492604257159586   ,374.21747979655222253   ] 
dist 3=[245.73767674201068262   ,345.42717678708888749   ] 
dist 4=[196.56372879376239192   ,292.95396469232605080   ] 
dist 5=[147.71172776570946388   ,225.95371809204387512   ] 
dist 6=[91.149374205983161529  ,213.05572208498048830   ] 
dist 7=[30.914738081118071773  ,123.43127718326757899   ] 
dist 8=[-23.615076251643349557  ,79.418575745375879072  ] 
dist 9=[-61.946908785005551447  ,1.9805042094499770841 ] 
dist 10=[-83.369332749637156505  ,2.5970100545058079549 ] 
dist 11=[-93.277010104146778833  ,8.6113514019310667284 ] 
dist 12=[-93.916777942707966028  ,17.142928338107440419  ] 
dist 13=[-77.862385404730596330  ,27.234943511785202253  ] 
dist 14=[-75.256235756520152874  ,39.829493518308854061  ] 
dist 15=[-2.7590869311942567932 ,49.678531335808490629  ] 
dist 16=[9.0102039309539976509 ,51.351519619035430409  ] 
dist 17=[32.296280997695381554  ,46.098557710990370232  ] 
dist 18=[20.136245848481923085  ,44.311373714844601462  ] 
dist 19=[-.49494857580288263741,44.847781957953902026  ] 
dist 20=[-14.601688494384825187  ,43.936103168217655129  ] 
dist 21=[-24.662547795700804627  ,36.600756430687617454  ] 
dist 22=[-29.826165523847853712  ,33.135383374312149577  ] 
dist 23=[-31.962946277396801963  ,6.9849937195526073543 ] 
dist 24=[-33.939185533953134731  ,1.7854922577502040291 ] 
dist 25=[-31.766886568449796707  ,-4.1529889236976130480 ] 
dist 26=[-33.786838749480847355  ,-1.3811872921699601481 ] 
dist 27=[-13.030403206367010083  ,11.153019611193086963  ] 
dist 28=[-10.300095090174598295  ,19.939061201694877929  ] 
dist 29=[-8.2329443047926357958 ,25.540982475048442774  ] 
dist 30=[-7.8270955894331627509 ,26.508666489280572317  ] 
dist 31=[-.01750817148532957582,5.2637184891168741113 ] 
dist 32=[1.2575831662542232766 ,5.2476074203098035258 ] 
dist 33=[3.7923965289711319718 ,5.1061398133734748501 ] 
dist 34=[1.8778980158717822542 ,5.7372543938723428577 ] 
dist 35=[-.10672819792780626079,5.7527888876174528200 ] 
dist 36=[-1.4114998948268253293 ,5.5921817490169735690 ] 
dist 37=[-2.2966461276305712126 ,4.3471629250537477381 ] 
dist 38=[-2.6695012385613424611 ,4.0602672262886195090 ] 
dist 39=[-3.5498167711963457454 ,.48136983321896860069] 
dist 40=[-3.7833865204626124503 ,-.07042546725265792959] 
dist 41=[-3.2118151180868584301 ,-1.1009626910019799722 ] 
dist 42=[-3.4253405736264215566 ,-.43931530577033454358] 
dist 43=[-1.4853941234827354643 ,.77334847888275773528] 
dist 44=[-1.4340755697514710028 ,1.5357356524366108488 ] 
dist 45=[-1.1757627137876520153 ,2.0154116653203481786 ] 
dist 46=[-1.0399240763242069974 ,2.1400271629456356546 ] 
dist 47=[-.25169618936216901788,1.1340565776864221523 ] 
dist 48=[-.08340033553546929861,1.2227557382457988097 ] 
dist 49=[.17598426314945345191,1.2200986461900871922 ] 
dist 50=[.13787334770602429836,1.1366489649859886942 ] 
dist 51=[-.06110546739096515809,.67731739029543856659] 
dist 52=[-.22188231635243687948,.65393355738517764567] 
dist 53=[-.32748685781244825651,.52710834058419949202] 
dist 54=[-.3651917156648557725 ,.47279459317749476703] 
dist 55=[-.41815332172891550317,.08158864501179569018] 
dist 56=[-.44250990832112005659,.00396366908303652539] 
dist 57=[-.49903584498526320586,-.13163530357315340545] 
dist 58=[-.52905083968605586998,-.05282540294685545003] 
dist 59=[-.15731820621892954546,.07462744638704027385] 
dist 60=[-.15293536083071148447,.15488358698892532858] 
dist 61=[-.11803504678510699782,.2061726812309445316 ] 
dist 62=[-.11128150101548205906,.21982670713447678629] 
dist 63=[.00620315241549897372,.08473828392118930523] 
dist 64=[.02535248057342495158,.09409030982008488643] 
dist 65=[.05639408157359800291,.09502523702817152231] 
dist 66=[.02540151756031901590,.09204748077209692965] 
dist 67=[-.00606057325062599768,.08706537317875199178] 
dist 68=[-.02613939463064728614,.08408961595532204269] 
dist 69=[-.03918645843712949873,.06443284082960252070] 
dist 70=[-.05373476877238399247,.05995655431897265233] 
dist 71=[-.07010257361680096964,.00573875470482276712] 
dist 72=[-.07435224844741186120,-.00255705742452012754] 
dist 73=[-.04954234937015595059,-.01751598359850621035] 
dist 74=[-.05276021393269382455,-.00589608499149331142] 
dist 75=[-.02002861766401484598,.01291469131235900963] 
dist 76=[-.01943533475717971244,.02468672752942974219] 
dist 77=[-.01471079294072696442,.03207448393649731660] 
dist 78=[-.01400357868918933926,.03399310238802504152] 
dist 79=[.00166855036004801953,.01140357346450228289] 
dist 80=[.00414513087317032879,.01256834692291113121] 
dist 81=[.00619312633010591902,.01242370538199745704] 
dist 82=[.00226642265575762327,.01202189690678681259] 
dist 83=[-.00169895328941742670,.01020382191169368990] 
dist 84=[-.00420780612958359799,.00980501797584910595] 
dist 85=[-.00581565166527115433,.00781395551801908294] 
dist 86=[-.00630991100893414248,.00698616158531546577] 
dist 87=[-.00705630189083240883,.00119234760299582436] 
dist 88=[-.00752515830594677347,4.91632103375324454680e-05] 
dist 89=[-.00759952365765979233,-.00189235114240905802] 
dist 90=[-.00804588895178895940,-9.27094103756801000000e-05] 
dist 91=[-.00237340674738230079,.00182277867176960222] 
dist 92=[-.00229777447442509266,.00302627542444437907] 
dist 93=[-.00173313594552921838,.00378816416867947343] 
dist 94=[-.00164294140353381791,.00400194654879348485] 
dist 95=[-.00035313829304708095,.00134276462971481537] 
dist 96=[-.00010539468270117141,.00148100307733747019] 
dist 97=[.00031255774569281075,.00175852607256861093] 
dist 98=[-.00016817017917252321,.00187070774158373360] 
dist 99=[-.00076176797108022680,.00182701520207981571] 
dist 100=[-.00113603028691830477,.00175031259291328898] 
dist 101=[-.00137469467458939076,.00138399620032841690] 
dist 102=[-.00144573994246077176,.00123339708442898227] 
dist 103=[-.00143165414065880858,.00018409357351228854] 
dist 104=[-.00135455737020446882,-2.45373580590728790040e-05] 
dist 105=[-.00119444502556901250,-.00027038180635205587] 
dist 106=[-.00094889531768166493,-.00029358124930691510] 
dist 107=[-.00030061453099456630,-.00021509943880760658] 
dist 108=[-.00029067112476548910,-8.55368038907195917610e-05] 
dist 109=[-.00021782807786181481,4.50195405770632472680e-05] 
dist 110=[-.00020696888249690828,.00012736128316743959] 
dist 111=[2.89484443594643641500e-05,.00017987712522787971] 
dist 112=[6.60960011344766464800e-05,.00019550179999381945] 
dist 113=[.00014133928840541870,.00019104143859639866] 
dist 114=[.00012782810434538474,.00018430793587687162] 
dist 115=[8.86129521477924876630e-05,.00015185416390775573] 
dist 116=[2.45411684961088862200e-05,.00014561812298004699] 
dist 117=[-3.98051266422641152630e-05,.00011538885199259736] 
dist 118=[-8.00868533038892193130e-05,.00010306641983260577] 
dist 119=[-.00010543514622830656,1.56525288979802428670e-05] 
dist 120=[-.00011222442797807781,-1.63204070746669974140e-06] 
dist 121=[-.00011322078579421578,-3.09854781888781810080e-05] 
dist 122=[-.00011987475416528638,-3.59556148733541099410e-05] 
dist 123=[-3.50365659847976099830e-05,-2.82107646877810127910e-05] 
dist 124=[-3.37989168549277097630e-05,-1.21121351701512864630e-05] 
dist 125=[-2.55458366254776578220e-05,4.08491736743582036550e-06] 
dist 126=[-2.39783380987703038940e-05,1.42806870893873068880e-05] 
dist 127=[2.14698494568128534300e-06,2.07657212340392238450e-05] 
dist 128=[6.39890897023833202120e-06,2.26612030814222218520e-05] 
dist 129=[1.48944060658568485530e-05,2.22354367332010557130e-05] 
dist 130=[1.62445446419882287640e-05,2.13420380307290803500e-05] 
dist 131=[1.24129692478219895080e-05,1.93287125884736442550e-05] 
dist 132=[2.81855275984821771120e-06,1.85978358891320957830e-05] 
dist 133=[-6.79999455491337409990e-06,1.41192507909545865670e-05] 
dist 134=[-1.28056702109235687700e-05,1.31148023952500991670e-05] 
dist 135=[-1.65695007389460038110e-05,1.05247756863115391740e-06] 
dist 136=[-1.75458408478474175470e-05,-7.79933551199661257220e-07] 
dist 137=[-1.10970569755110760330e-05,-4.01079729049031791680e-06] 
dist 138=[-1.17841805148292291560e-05,-4.40181369783599763980e-06] 
dist 139=[-4.41601795149068251280e-06,-3.20712655682203975740e-06] 
dist 140=[-4.26214657883057794640e-06,-1.25953663828208546510e-06] 
dist 141=[-3.17860461205308856050e-06,6.96778983339249849260e-07] 
dist 142=[-3.01644399359679324150e-06,1.92469805298983149940e-06] 
dist 143=[4.45451167734370858640e-07,2.70178816040860234250e-06] 
dist 144=[9.89716006342432074150e-07,2.92059651864331326650e-06] 
dist 145=[2.09539013713259114870e-06,2.84132580888651747480e-06] 
dist 146=[1.93681685771073841220e-06,2.73547218331212126720e-06] 
dist 147=[1.33226945737134874980e-06,2.23100723518622407160e-06] 
dist 148=[3.52518552981681237050e-07,2.13719357759612748220e-06] 
dist 149=[-6.29835884570877096800e-07,1.68747177977469018200e-06] 
dist 150=[-1.24363535766460308810e-06,1.50731512438951439120e-06] 
dist 151=[-1.62897973824949818090e-06,2.21612572839091209900e-07] 
dist 152=[-1.73061935381920332620e-06,-3.13045000030609263420e-08] 
dist 153=[-1.65934717206482937900e-06,-4.59026619030554870770e-07] 
dist 154=[-1.75657764581127156810e-06,-5.29689485732586369480e-07] 
dist 155=[-5.20727344774165797300e-07,-4.13546005714693452880e-07] 
dist 156=[-5.02189854706248898990e-07,-1.74425815418067126010e-07] 
dist 157=[-3.74326160766251005700e-07,6.55382104294392008110e-08] 
dist 158=[-3.54625059642835979370e-07,2.15976713575874512100e-07] 
dist 159=[3.10751073391722619180e-08,3.11042649474163239270e-07] 
dist 160=[9.33460849339141416890e-08,3.37539123847015633040e-07] 
dist 161=[2.16600749060386306970e-07,3.29616368425985146650e-07] 
dist 162=[2.36017962768979219920e-07,3.15963477199295624490e-07] 
dist 163=[1.82037313957805283630e-07,2.86365605443323396570e-07] 
dist 164=[4.09038037106462352090e-08,2.75494200577980407020e-07] 
dist 165=[-1.00850170936893109220e-07,2.07762969872727433590e-07] 
dist 166=[-1.89298683710591986300e-07,1.93871293758657353370e-07] 
dist 167=[-2.44707779203775602560e-07,1.30616636112973534730e-08] 
dist 168=[-2.59076093391856025550e-07,-1.34947202865906697230e-08] 
dist 169=[-1.58659871015660295570e-07,-6.04647615278831678710e-08] 
dist 170=[-1.68485595415659129370e-07,-6.46622661864422296680e-08] 
dist 171=[-6.61494582221423217710e-08,-4.58379174508741119110e-08] 
dist 172=[-6.37637506624537531070e-08,-1.53680554056872806380e-08] 
dist 173=[-4.75250566049185199680e-08,1.51756750688195506410e-08] 
dist 174=[-4.49714975016548299640e-08,3.42869993553376684040e-08] 
dist 175=[6.37611533261978748540e-09,4.63245960642622630160e-08] 
dist 176=[1.44897389684361533810e-08,4.95956435402401708610e-08] 
dist 177=[2.83511932538176862230e-08,4.80982503986191380720e-08] 
dist 178=[2.29726671978629890830e-08,4.62460787920659653990e-08] 
dist 179=[1.42585221404276853070e-08,3.51243976800472035050e-08] 
dist 180=[1.82679521700000000000e-10,3.25812003115323666440e-08] 
dist 181=[-1.39174580089276853070e-08,2.55939314328012664060e-08] 
dist 182=[-2.27259871435629890830e-08,2.29310046986570422970e-08] 
dist 183=[-2.82581212851176862230e-08,3.55175149345291474840e-09] 
dist 184=[-2.97256362284145612590e-08,0                     ] 
dist 185=[-2.48327769613422249580e-08,-6.29486946536916148590e-09] 
dist 186=[-2.62689217272402944500e-08,-7.30207131080661767080e-09] 
dist 187=[-8.48480955404209824330e-09,-6.66827343729710188270e-09] 
dist 188=[-8.15781639104528655840e-09,-2.64310311460721452890e-09] 
dist 189=[-6.19357416930578912740e-09,1.38954500458037283390e-09] 
dist 190=[-5.74482320804971166170e-09,3.91093205185304824020e-09] 
dist 191=[2.72162887265319277180e-10,5.49737282487257328130e-09] 
dist 192=[1.28704153427155064430e-09,5.92511026052373761190e-09] 
dist 193=[3.13685677425517522620e-09,5.78076440414350693190e-09] 
dist 194=[3.40622540323578094260e-09,5.52330910730747785250e-09] 
dist 195=[2.49946031416194459270e-09,5.06579020545244409420e-09] 
dist 196=[7.63755888153844734890e-11,4.86720984642623848610e-09] 
dist 197=[-2.34856952887117564740e-09,3.69794039299088962670e-09] 
dist 198=[-3.86097717050623187890e-09,3.42185799435532981330e-09] 
dist 199=[-4.80822950137772644410e-09,1.08858436564762798570e-09] 
dist 200=[-5.05394552679134309250e-09,7.06018779758008151790e-10] 
dist 201=[-3.69563229338365656140e-09,2.19288256350986865650e-10] 
dist 202=[-3.87764862623539019700e-09,1.32508098559306339610e-10] 
dist 203=[-2.00729176205778786910e-09,2.64203341139873975620e-10] 
dist 204=[-1.92327086863931020490e-09,6.20169926343949596880e-10] 
dist 205=[-1.49640032705258110280e-09,9.76787215332025218540e-10] 
dist 206=[-1.35167876343406391970e-09,1.23794680949547732870e-09] 
dist 207=[-1.43166086106362792280e-09,1.59509331458935566190e-09] 
dist 208=[-1.55643175755634412170e-09,2.07605444728078584450e-09] 
dist 209=[-1.63420797672025802370e-09,2.37754157984910146550e-09] 
dist 210=[-1.65364191657025584820e-09,2.45645219708711066110e-09] 
dist 211=[-1.60547274347037673190e-09,2.40627424049898275610e-09] 
dist 212=[-1.53388132473125100350e-09,2.28117360913009444710e-09] 
dist 213=[-1.62927082208766793010e-09,1.93909134835772893590e-09] 
dist 214=[-2.23160426621185037510e-09,1.77060998261835023040e-09] 
dist 215=[-2.60867786426333306930e-09,1.32928146845654300140e-09] 
dist 216=[-2.70626054088657975230e-09,1.32823169851678087920e-09] 
dist 217=[-2.65654050244866841750e-09,1.25686270723968405200e-09] 
dist 218=[-2.78215912307814741010e-09,1.32793139137436590180e-09] 
dist 219=[-2.71015168795323315060e-09,1.29808817046246826200e-09] 
dist 220=[-2.58273470932190801120e-09,1.23231285258143743850e-09] 
dist 221=[-2.09793896468769788310e-09,1.03342514776984161400e-09] 
dist 222=[-1.85936746574354548180e-09,9.35620896255444312530e-10] 
dist 223=[-6.94534576652050713330e-10,1.14115115449392392190e-09] 
dist 224=[-1.09915576906580479780e-09,1.92643294725278885140e-09] 
dist 225=[-1.35247049790817453140e-09,2.41814581376257216040e-09] 
dist 226=[-1.41809676635920535580e-09,2.54571029817589730050e-09] 
dist 227=[-1.38626150173008124230e-09,2.46570586241014280800e-09] 
dist 228=[-1.31621625709348522720e-09,2.36305522255557059740e-09] 
dist 229=[-1.10293943818838373820e-09,1.82556776184036112400e-09] 
dist 230=[-9.98019766606112913290e-10,1.65834907856157083180e-09] 
dist 231=[-1.22271243077684113740e-09,1.17327088944058054510e-09] 
dist 232=[-1.51479083873138838530e-09,1.36069027899840136770e-09] 
dist 233=[-1.69766986393568971210e-09,1.47803565263135229860e-09] 

8 phat 5 dirichlet min maxes function [2, 0, 2, 0, 2, 0, 2] 
dist 0=[300.31145416451105577   ,300.31145416451105577   ] 
dist 1=[289.21881027629178570   ,303.77420328203392748   ] 
dist 2=[269.87059157005666759   ,302.23910084137364178   ] 
dist 3=[241.94661338935693877   ,280.30784844542051680   ] 
dist 4=[196.72752586781943800   ,277.08984546763377846   ] 
dist 5=[148.67605386454745379   ,193.78141532147425032   ] 
dist 6=[109.62736330622936022   ,181.37813411070243756   ] 
dist 7=[71.659936238972263019  ,117.24322380529954736   ] 
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dist 16=[-38.957302265517135071  ,35.357284411859277343  ] 
dist 17=[-3.1985339437733568599 ,44.905378987061015725  ] 
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dist 49=[-.2110523768546313366 ,.78944974859482003455] 
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dist 51=[-.05216510039435519777,.62588823244951255075] 
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dist 54=[-.52481827221938142577,.58653424282628174226] 
dist 55=[-.67361815841004025892,.50551595383013208343] 
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dist 57=[-.71851704828123139296,.24802088657630510609] 
dist 58=[-.68985759413271988382,.18546725498319231581] 
dist 59=[-.55999250700830257496,.11980100735827455918] 
dist 60=[-.32315895070061948649,.10571225921657659059] 
dist 61=[-.07955133239127801435,.11347890795553614963] 
dist 62=[-.07693837913079391586,.22321432535040669438] 
dist 63=[-.05856583587057596713,.29239319866842530678] 
dist 64=[-.05506340605684685186,.30962650040225591539] 
dist 65=[-.00600437398332348156,.09510058019363596320] 
dist 66=[.00085803905520955589,.09294559411434717460] 
dist 67=[.01238470790292709837,.07168649169699833279] 
dist 68=[.01424023527834157912,.0685106287149758475 ] 
dist 69=[-.00653423813514105314,.04366287641230519980] 
dist 70=[-.02907393462974188497,.04206518521996798699] 
dist 71=[-.04374079442275483279,.03203254865191611543] 
dist 72=[-.04871508280187244815,.02977479641327766062] 
dist 73=[-.04860305277097393265,.00255809324288281263] 
dist 74=[-.04690049394992605932,-.00158921878357110682] 
dist 75=[-.03776642768653519920,-.00498449979111940933] 
dist 76=[-.03385576691935436952,-.00546422311373919904] 
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dist 78=[-.00965524264815158789,.02765739730413699402] 
dist 79=[-.00723795871071005976,.03596356411588705731] 
dist 80=[-.00687629891734128944,.03811932063073243076] 
dist 81=[-.00144881411737616703,.01130797296612896234] 
dist 82=[-.00088667914644821521,.01098836186914203805] 
dist 83=[-.00013527294542156411,.00846970207540759040] 
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dist 85=[-.00135733117195646233,.00503310853752883891] 
dist 86=[-.00409436326485149852,.00482680642338403241] 
dist 87=[-.00585140905162817198,.00382183880071373869] 
dist 88=[-.00639782121797996962,.00341642320624925716] 
dist 89=[-.00628296845627931688,.00051378242998581545] 
dist 90=[-.00606721220185938372,-5.75509980768097210360e-05] 
dist 91=[-.00464687472499263270,-.00077941173599452106] 
dist 92=[-.00432376780959756983,-.00083046654308030088] 
dist 93=[-.00117406338376135035,.00135085396779897396] 
dist 94=[-.00113374193862343425,.00271787962891157228] 
dist 95=[-.00084870748068905156,.00357904974312504843] 
dist 96=[-.00080410110842749499,.00381104522097048583] 
dist 97=[-3.89476008764891286870e-05,.00147308790801771448] 
dist 98=[5.57299217895590862850e-05,.00142721502417800891] 
dist 99=[.00022356085252331329,.00109191346365670907] 
dist 100=[.00024993761633084014,.00102726350518968943] 
dist 101=[-.00018825925290516833,.00064668870253070529] 
dist 102=[-.00054300539089386057,.00062251336184882246] 
dist 103=[-.00076950133921921843,.00047033753770659856] 
dist 104=[-.00083748591388349684,.00043889613830488354] 
dist 105=[-.00081879071532060708,.00043971768974586653] 
dist 106=[-.00079064663893193297,.00045258508063867769] 
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dist 108=[-.00050395426457157912,.00046271551194869284] 
dist 109=[-.00019654336796645985,.00045674130198096382] 
dist 110=[-.00018601512797483786,.00043390306948527472] 
dist 111=[-.00015669379923176784,.00054293734105740780] 
dist 112=[-.00014245326800149418,.00057511545234166098] 
dist 113=[-6.80716929386403991820e-05,.00021907033855056225] 
dist 114=[-4.79406260619999478840e-05,.00020977021300181421] 
dist 115=[-2.59812260024528592110e-05,.00017159613837529158] 
dist 116=[-2.25708757347376586770e-05,.00012100644034778858] 
dist 117=[-2.56807577104910897190e-05,7.44075508399750655560e-05] 
dist 118=[-6.81074491545767315870e-05,7.12712559301616674690e-05] 
dist 119=[-9.50213746417571336150e-05,6.03324832488424231100e-05] 
dist 120=[-.00010273209409524234,5.61502532330967465070e-05] 
dist 121=[-.00010029575327516849,4.28828575032177131970e-05] 
dist 122=[-9.63959014706366153660e-05,3.74393934442277446930e-05] 
dist 123=[-7.48077954144849531630e-05,3.40260553178803625870e-05] 
dist 124=[-6.60295701863138830770e-05,3.31286691693704200530e-05] 
dist 125=[-1.71398560626527501280e-05,3.33993094983120946830e-05] 
dist 126=[-1.65119011845272884230e-05,3.90153703966092387850e-05] 
dist 127=[-1.24326665126499793530e-05,5.13945179004624007470e-05] 
dist 128=[-1.16609093371015962950e-05,5.46850057519449001180e-05] 
dist 129=[1.11337015068548804630e-06,2.21925709282392505250e-05] 
dist 130=[3.19161369217942272610e-06,2.14572869749809882340e-05] 
dist 131=[7.31974733528586612780e-06,1.60770680630464500000e-05] 
dist 132=[6.02668953065820585480e-06,1.52750251870712681040e-05] 
dist 133=[-2.15500278754766748070e-06,9.43790597181488848190e-06] 
dist 134=[-7.29170522838383443530e-06,9.07472079145966996190e-06] 
dist 135=[-1.05453025052915824290e-05,6.87766654838763400230e-06] 
dist 136=[-1.14680982074378446730e-05,6.38621415295344468710e-06] 
dist 137=[-1.12197160272731309760e-05,4.95024679691748002570e-07] 
dist 138=[-1.07586563409507060980e-05,-3.98929119267904683330e-07] 
dist 139=[-8.52493254752993539010e-06,-1.96809613684146446270e-06] 
dist 140=[-7.61412712084063222070e-06,-1.40001173838857925650e-06] 
dist 141=[-2.15307701126688373600e-06,3.44803799979897444000e-06] 
dist 142=[-2.07591800497391208830e-06,6.47376425633335391760e-06] 
dist 143=[-1.54341478625462725410e-06,8.36954598538372470680e-06] 
dist 144=[-1.46403513580876983830e-06,8.86126526706715331000e-06] 
dist 145=[2.21877161680601701670e-07,2.58905037142889563440e-06] 
dist 146=[4.86575560999493777660e-07,2.49753482480624889920e-06] 
dist 147=[1.02537266742954624080e-06,1.88762075084741812970e-06] 
dist 148=[6.26541132671173111570e-07,1.77170095828090118870e-06] 
dist 149=[-3.58274329978711409080e-07,1.08728947279228307970e-06] 
dist 150=[-9.75216439913428991560e-07,1.04088319681656399250e-06] 
dist 151=[-1.36456056593036843580e-06,8.20544855978572655690e-07] 
dist 152=[-1.47194287692724517110e-06,7.32588404679234025700e-07] 
dist 153=[-1.42943452801172066490e-06,1.08209583737868727930e-07] 
dist 154=[-1.37538512476569746050e-06,-1.44683279565153274250e-08] 
dist 155=[-1.04409566450908636160e-06,-2.20850743970263560180e-07] 
dist 156=[-9.69873841445486833040e-07,-1.75069772231141905210e-07] 
dist 157=[-2.54069749531375312150e-07,3.18682668146442302080e-07] 
dist 158=[-2.44830138737657350660e-07,6.26997009107713545250e-07] 
dist 159=[-1.82140958033525078300e-07,8.20422538299440188370e-07] 
dist 160=[-1.72442342744281159180e-07,8.71218465285962422730e-07] 
dist 161=[4.68332052033652371570e-09,3.26668829100014888110e-07] 
dist 162=[3.40607731040018568370e-08,3.15284680707109942530e-07] 
dist 163=[8.99010017059796533550e-08,2.35140668024445767330e-07] 
dist 164=[8.68560590789497260530e-08,2.23132627657018947370e-07] 
dist 165=[-3.35105585276211050970e-08,1.51371613567550641810e-07] 
dist 166=[-1.08878443333111005180e-07,1.45332130193246725870e-07] 
dist 167=[-1.56392542177706972220e-07,1.11070381854542793090e-07] 
dist 168=[-1.69400016745471917750e-07,1.02135235753993171320e-07] 
dist 169=[-1.65171147650607397510e-07,2.64225864685519959250e-08] 
dist 170=[-1.58227604058657906350e-07,1.62292661035731583570e-08] 
dist 171=[-1.24923458430303332610e-07,2.53691234847342511520e-09] 
dist 172=[-1.11594939893857999830e-07,0                     ] 
dist 173=[-3.15201311011216523310e-08,5.09198111236060902240e-08] 
dist 174=[-3.03727061457757815560e-08,9.52135349254171574030e-08] 
dist 175=[-2.25496147105367181020e-08,1.22958447263574473580e-07] 
dist 176=[-2.13787130342935512770e-08,1.30154525999847647810e-07] 
dist 177=[3.31945815945292229360e-09,3.86246360381254431580e-08] 
dist 178=[7.19627855849413624400e-09,3.72498362156301329610e-08] 
dist 179=[1.50821520465925632710e-08,2.77653855585779051090e-08] 
dist 180=[8.97241081070424427220e-09,2.63043608070833985310e-08] 
dist 181=[-5.50988006876802878160e-09,1.58938251507613806430e-08] 
dist 182=[-1.45641724286585233480e-08,1.52166053261175818400e-08] 
dist 183=[-2.02599283185065284910e-08,1.19392039004308399240e-08] 
dist 184=[-2.17927217919381269200e-08,1.06975467013817169050e-08] 
dist 185=[-2.11050357764777418830e-08,1.33791350313130866150e-09] 
dist 186=[-2.03073946312956843900e-08,-4.70470774182144007310e-10] 
dist 187=[-1.52916697599084446090e-08,-3.55742694438337701990e-09] 
dist 188=[-1.42911765765655851350e-08,-2.62835303907435726860e-09] 
dist 189=[-3.97511214178323519890e-09,4.47746609762689764500e-09] 
dist 190=[-3.82520022890740601530e-09,8.91182063524997267280e-09] 
dist 191=[-2.86745507626056922480e-09,1.16918933748931188580e-08] 
dist 192=[-2.69013834565314967510e-09,1.24189995682183215900e-08] 
dist 193=[2.57065485450349838150e-10,5.10987370615790844580e-09] 
dist 194=[7.31707108822415776170e-10,4.92170258867923871050e-09] 
dist 195=[1.66713763106552915930e-09,3.69320049191894490160e-09] 
dist 196=[1.21675650532826820400e-09,3.47061158496418304060e-09] 
dist 197=[-6.92138939851871278820e-10,2.18962622186781506270e-09] 
dist 198=[-1.89790333255758441900e-09,2.08901569226569773800e-09] 
dist 199=[-2.65576468731873797310e-09,1.69560641137200793440e-09] 
dist 200=[-2.85842936842740770780e-09,1.50224170398523209010e-09] 
dist 201=[-2.77303356776826715690e-09,6.23438779811088149070e-10] 
dist 202=[-2.66208297802757865060e-09,4.36022908046035597230e-10] 
dist 203=[-2.04483268355404425610e-09,2.16271826233593564650e-10] 
dist 204=[-2.04592625904984349350e-09,1.75626546468291151990e-10] 
dist 205=[-2.55775026592302019750e-10,7.25637525255713243350e-10] 
dist 206=[-2.44225050160755909170e-10,1.36030951053907844500e-09] 
dist 207=[-2.31909645138641324610e-10,1.75779460523139452240e-09] 
dist 208=[-2.58076766416790960380e-10,1.86087558725092370710e-09] 
dist 209=[-2.84068212224940595900e-10,9.74226830637812793870e-10] 
dist 210=[-2.99988111000519193890e-10,9.34235246006124704370e-10] 
dist 211=[-3.09619446237722467160e-10,7.23734945838393636220e-10] 
dist 212=[-3.11352566323604101750e-10,6.57111438265944866940e-10] 
dist 213=[-3.10712899691022824790e-10,4.96586975098076895450e-10] 
dist 214=[-5.03423185074406406860e-10,4.76659012930852789140e-10] 
dist 215=[-6.61370353421285608920e-10,3.63619468235979049560e-10] 
dist 216=[-7.02885062116919516450e-10,3.34598339429676201130e-10] 
dist 217=[-6.78919757629394566830e-10,1.09974502644615521390e-10] 
dist 218=[-6.53235862163610395060e-10,1.25264482425710082130e-10] 
dist 219=[-5.01884630254487509230e-10,1.34804222540886207360e-10] 
dist 220=[-4.58884785985080223220e-10,1.37206128179767676080e-10] 
dist 221=[-2.24002031845194983240e-10,2.89077333868002232590e-10] 
dist 222=[-2.05760033527178759160e-10,4.09964643787244206490e-10] 
dist 223=[-8.33304661929380403070e-11,4.85649487522615197610e-10] 
dist 224=[-7.79863306715812285120e-11,5.05242265198756997390e-10] 
dist 225=[-6.42860513029043189760e-11,3.18056702956217741260e-10] 
dist 226=[-1.04566315574344866450e-10,3.02042196241325780280e-10] 
dist 227=[-1.29778202677623289220e-10,3.03203279317961211240e-10] 
dist 228=[-3.49338061829541214170e-10,4.30355611121960688340e-10] 
dist 229=[-5.90879957267555682680e-10,5.57482883425960165440e-10] 
dist 230=[-7.41475361289439610930e-10,6.36704823306055099450e-10] 
dist 231=[-8.35792942097476867900e-10,6.86281557300129137600e-10] 
dist 232=[-8.60305362543921376650e-10,6.99081917719082428430e-10] 
dist 233=[-8.47649763837222751000e-10,6.74424681050383254360e-10] 
dist 234=[-7.98632435763410259310e-10,6.48819835764731338030e-10] 
dist 235=[-7.20308352073083794910e-10,4.83694371396832905510e-10] 
dist 236=[-6.71272396847940112180e-10,4.55272797858546004810e-10] 
dist 237=[-4.68952710067039626000e-10,6.48902466593107351850e-10] 
dist 238=[-3.90618965525381970720e-10,9.50968546904043678010e-10] 
dist 239=[-3.44654155337228467750e-10,1.14010682226097973840e-09] 
dist 240=[-3.70219582631580746030e-10,1.18916667850211495090e-09] 
dist 241=[-3.61286178466512846190e-10,1.15430799823359854390e-09] 
dist 242=[-3.43621633160275725390e-10,1.10382582337553468120e-09] 
dist 243=[-3.30344855278195865500e-10,8.69717054656790588580e-10] 
dist 244=[-3.44142946799637197170e-10,7.74637219040675052490e-10] 
dist 245=[-3.64644416291039694390e-10,2.52053009570623481220e-10] 
dist 246=[-6.75611984668671214010e-10,3.50769391575693312000e-10] 
dist 247=[-8.70318608484596357970e-10,4.12575870438628825160e-10] 
dist 248=[-9.20811867328660220910e-10,4.28597867382439977230e-10] 
dist 249=[-8.91915538701123201390e-10,4.15951553464108081140e-10] 
dist 250=[-8.54719024570057371860e-10,3.97824582661993999820e-10] 
dist 251=[-6.60709889476764038780e-10,3.12966311590095293910e-10] 
dist 252=[-5.99813344571141568710e-10,2.79174542241203637520e-10] 
dist 253=[-3.39831935786732040130e-10,3.95984188402667706760e-10] 
dist 254=[-3.54131427071454043480e-10,5.28940647837987527240e-10] 
dist 255=[-3.63084503237020185650e-10,6.12188119793497494890e-10] 

8 phat 5 dirichlet min maxes function [1, 1, 0, 2, 1, 1, 2] 
dist 0=[300.31138240218086765   ,300.31138240218086765   ] 
dist 1=[289.21923058381631545   ,303.77363949052264064   ] 
dist 2=[269.87131686595102798   ,302.23840180668287398   ] 
dist 3=[241.94752712949840298   ,280.30681884266365481   ] 
dist 4=[196.72848244087044485   ,277.08887798094553321   ] 
dist 5=[148.67698176114314943   ,193.78123314142225639   ] 
dist 6=[109.62820410421525591   ,181.37821315951919421   ] 
dist 7=[71.660642893355502358  ,117.24334362335661242   ] 
dist 8=[28.267227053372291496  ,90.555725219642455737  ] 
dist 9=[-15.254014865790836399  ,22.584054842580302447  ] 
dist 10=[-42.752689178730029708  ,12.320346312408315984  ] 
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dist 109=[-.00014733773576390321,.00024921290813980804] 
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dist 111=[-.00010602387734188237,.00060951423474323261] 
dist 112=[-.00010063218498898570,.00064552927905309539] 
dist 113=[1.49049693249572901240e-05,.00018943544214808673] 
dist 114=[3.30638794745353036580e-05,.00018312394390812472] 
dist 115=[6.99000781869432189010e-05,.00013920341468546312] 
dist 116=[4.69611356701664028730e-05,.00013081599320081977] 
dist 117=[-2.51866643399517352470e-05,7.42255655658537241590e-05] 
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dist 123=[-7.68028109917007394810e-05,-1.52626039639170682890e-05] 
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dist 130=[3.18372047046932116760e-06,2.31882385896730107170e-05] 
dist 131=[7.30185437995934938960e-06,1.73674936850448593130e-05] 
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dist 145=[2.22914914685126912750e-07,2.83430782838489400950e-06] 
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dist 147=[1.02448624846307384910e-06,2.04790749306538915400e-06] 
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dist 155=[-1.13852034875491082300e-06,-2.24395429792381471850e-07] 
dist 156=[-1.06240473351477993040e-06,-1.91498434640049866960e-07] 
dist 157=[-2.52490778899656992780e-07,3.34152770767426183520e-07] 
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dist 162=[4.59460677408658897760e-08,3.45386471037422439090e-07] 
dist 163=[1.05637830201805687860e-07,2.57452613185440865200e-07] 
dist 164=[9.48293765446964522080e-08,2.44336723402183324930e-07] 
dist 165=[-3.71024804946509946510e-08,1.39127877474207481530e-07] 
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dist 169=[-1.81238120686280736700e-07,6.44246145121933748330e-09] 
dist 170=[-1.73607959952847320390e-07,-6.49428332429161865320e-09] 
dist 171=[-1.37025332013512406090e-07,-2.92094195568578254380e-08] 
dist 172=[-1.22412846023568219510e-07,-2.17775896354483311810e-08] 
dist 173=[-3.18145793787735987190e-08,5.58936965216648203710e-08] 
dist 174=[-3.06485312601467122020e-08,1.04382862859865657030e-07] 
dist 175=[-2.28071862027515737640e-08,1.34824569439689771840e-07] 
dist 176=[-2.15722561180284427080e-08,1.42719492654478808490e-07] 
dist 177=[3.10715153587482607800e-09,4.25148978199779010750e-08] 
dist 178=[7.00763012831596939420e-09,4.09514421739748238470e-08] 
dist 179=[1.49118130793824219140e-08,3.08461790556901756180e-08] 
dist 180=[9.76115418960849497620e-09,2.89117023232149230030e-08] 
dist 181=[-6.11572806991825190370e-09,1.63648341497947216890e-08] 
dist 182=[-1.62306020913872786530e-08,1.56628688911056043280e-08] 
dist 183=[-2.25917636272595154990e-08,1.23198662402539468040e-08] 
dist 184=[-2.42999970523225926470e-08,1.10107055368390738460e-08] 
dist 185=[-2.35404902449315542390e-08,1.83212466665136611370e-09] 
dist 186=[-2.26389213498271180700e-08,6.56138373470367314060e-11] 
dist 187=[-1.71203215269470049170e-08,-2.84262645725892264920e-09] 
dist 188=[-1.59299720842803084370e-08,-2.80246718447123941790e-09] 
dist 189=[-3.96140911112364927230e-09,5.18108090592614732340e-09] 
dist 190=[-3.81134838766925218060e-09,1.01899222962797372800e-08] 
dist 191=[-2.86171356752139822860e-09,1.33296037817713983120e-08] 
dist 192=[-2.68039132924837017380e-09,1.41496489586334371440e-08] 
dist 193=[3.52083705847471293590e-11,5.71570416219497391540e-09] 
dist 194=[4.87582418405523913030e-10,5.50714318805880202880e-09] 
dist 195=[1.25777367402399942280e-09,4.11369774383316064160e-09] 
dist 196=[1.32183708661553930860e-09,3.88200952598027810820e-09] 
dist 197=[-7.06851950729770545600e-10,2.39050656320144299550e-09] 
dist 198=[-2.02859087035881198450e-09,2.30067445428686597000e-09] 
dist 199=[-2.86614791395366561990e-09,1.71531207510097221610e-09] 
dist 200=[-3.08967813512983750570e-09,1.61593516344365826490e-09] 
dist 201=[-2.99355658753113630100e-09,1.70195791183062170660e-10] 
dist 202=[-2.87701865032399290630e-09,9.34894659335120812560e-12] 
dist 203=[-2.18995414771728623860e-09,-2.54859803744784311800e-10] 
dist 204=[-2.02413453377915591760e-09,-2.97554257486951955620e-10] 
dist 205=[-8.46287820374417239480e-10,8.62289928684365525800e-10] 
dist 206=[-8.11852469660725621140e-10,1.58558814411228859450e-09] 
dist 207=[-6.23718864050646556820e-10,2.03856355487582326500e-09] 
dist 208=[-5.70304408354296649470e-10,2.15602440208061135450e-09] 
dist 209=[-1.60281422517317659440e-10,1.19379380898398851830e-09] 
dist 210=[-9.77703986487628195990e-11,1.14222160988926559370e-09] 
dist 211=[-1.44197361189777925620e-11,9.01241189183410980390e-10] 
dist 212=[-1.58664309889197800120e-11,8.03089140273004433650e-10] 
dist 213=[-4.30513693528473549860e-10,6.06311256735464016360e-10] 
dist 214=[-7.11287424140471272960e-10,5.81363374148112615740e-10] 
dist 215=[-8.99061286655760868380e-10,4.47710358973211811110e-10] 
dist 216=[-9.51912574430483792310e-10,4.08150811360147043280e-10] 
dist 217=[-9.19229311654235299090e-10,2.97256741208318106120e-10] 
dist 218=[-8.84320849246574048850e-10,3.06086405408696306570e-10] 
dist 219=[-6.86008806404324053020e-10,3.11611571549103411470e-10] 
dist 220=[-6.20974442071137807140e-10,3.13044129064993292900e-10] 
dist 221=[-5.50902848202736862710e-10,3.91556914050337811780e-10] 
dist 222=[-5.25231466852095471530e-10,5.85236025712752387000e-10] 
dist 223=[-4.25085186345727069790e-10,7.06511153023001458830e-10] 
dist 224=[-3.75798660769443659430e-10,7.37957870832429520980e-10] 
dist 225=[-1.17359979606564190500e-10,3.88315388007321946710e-10] 
dist 226=[-1.52791532788218602350e-10,3.83102049313371539610e-10] 
dist 227=[-1.83106589972033918400e-10,4.82198826765116912970e-10] 
dist 228=[-1.90950256704046272610e-10,5.07912918195758304070e-10] 
dist 229=[-1.84092731743442113500e-10,4.92181999293938663480e-10] 
dist 230=[-2.34009345968209675700e-10,4.71478144135407560200e-10] 
dist 231=[-3.00256472257757907700e-10,3.65752675201590502990e-10] 
dist 232=[-3.17493982041925501980e-10,3.30879053995567033590e-10] 
dist 233=[-3.09473274157602029660e-10,1.59234566582829468020e-10] 
dist 234=[-2.94787233077656135900e-10,1.53459488889628573130e-10] 
dist 235=[-3.43758506199423977660e-10,1.57143720608952804020e-10] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 0, 2, 0, 0, 2] 
dist 0=[315.43456766236573342   ,315.43456766236573342   ] 
dist 1=[294.46286972472483723   ,323.52761178313637857   ] 
dist 2=[247.60788003506676358   ,320.59186287116417283   ] 
dist 3=[194.48025773149975363   ,314.08024858369176941   ] 
dist 4=[148.69660068152076235   ,269.27390712011344890   ] 
dist 5=[103.24821445074367378   ,229.14910425100964113   ] 
dist 6=[50.564278217935821613  ,211.92122269929988683   ] 
dist 7=[3.6109970516302305821 ,180.66179806162375549   ] 
dist 8=[-25.010015066030540165  ,161.45815451309179651   ] 
dist 9=[-65.133626985947317227  ,38.689393910159851240  ] 
dist 10=[-97.249064139529821536  ,31.827535584964458309  ] 
dist 11=[-119.87008059894785220   ,.03671381436633155336] 
dist 12=[-123.48690589453412094   ,7.7688418750584101391 ] 
dist 13=[-118.72471435778635313   ,21.266771295431711796  ] 
dist 14=[-112.11012053403804442   ,35.239720510906363719  ] 
dist 15=[-14.257802893009603062  ,49.763245189454194381  ] 
dist 16=[11.092856962567443711  ,65.985167865260864436  ] 
dist 17=[8.7023952627969630658 ,77.619056333863563442  ] 
dist 18=[1.4042758275545531558 ,79.220859062856879602  ] 
dist 19=[-6.6697275114764195034 ,68.150207772743665429  ] 
dist 20=[-12.078652801382156467  ,65.985222585176521661  ] 
dist 21=[-16.000664694019766368  ,9.1962711288792762256 ] 
dist 22=[-19.321855082657389248  ,8.1504509071503027066 ] 
dist 23=[-33.713542326733632002  ,4.5697068124891422806 ] 
dist 24=[-40.725387970631862299  ,6.0537170744052624973 ] 
dist 25=[-43.239652437997281771  ,9.8736507994548643561 ] 
dist 26=[-42.468402249577762254  ,17.130597800466473765  ] 
dist 27=[-35.889233224023131155  ,24.669768438845854054  ] 
dist 28=[-32.278069350830754880  ,29.586642865489027090  ] 
dist 29=[-7.8101574892196196053 ,32.857526520686208560  ] 
dist 30=[-2.7466274258677657324 ,34.078653030146439615  ] 
dist 31=[1.9193610277005788320 ,33.836146625111452415  ] 
dist 32=[1.7953184995037365525 ,31.480330774319903454  ] 
dist 33=[1.3583397071370622640 ,9.0379172919812736942 ] 
dist 34=[.47367600024003488137,8.9599321440537651116 ] 
dist 35=[-.45111888213582063588,7.1634718336183395071 ] 
dist 36=[-1.0438938296747730775 ,6.8933562798811290915 ] 
dist 37=[-1.4209694847819991636 ,-.22871478590255031264] 
dist 38=[-2.5003309719567119093 ,-.32786597030259785369] 
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dist 46=[-.11032409682972646111,2.6156898299599991299 ] 
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dist 60=[-.4455724761109163616 ,.35827920372955155258] 
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dist 77=[-.00827582630243681094,.02139341955601727645] 
dist 78=[-8.40061566882494446810e-05,.04083898834280946020] 
dist 79=[.00408118637192035021,.05303798014310414576] 
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dist 92=[-.00632170716851216206,.00035758268721198790] 
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dist 96=[.00050322935502867586,.00559789719882975166] 
dist 97=[.00034548657410749557,.00211768078517523663] 
dist 98=[8.36135622009524655670e-05,.00205228290211283717] 
dist 99=[-.00018018859414782344,.00154784332699254016] 
dist 100=[-.00034542206532486283,.00147234475084812283] 
dist 101=[-.00044916951029526581,-.00011386019694840875] 
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dist 107=[-.00082044170737612698,2.75596517456271394660e-05] 
dist 108=[-.00073378641189642446,6.35172140764945586920e-05] 
dist 109=[-.00011488279356014404,.00032694211983349187] 
dist 110=[7.13025776696861433770e-06,.00061637120571756868] 
dist 111=[4.70522343250377790350e-05,.00079778854735753352] 
dist 112=[3.75746107623964618190e-05,.00084486967972070920] 
dist 113=[2.13673337074802354870e-05,.00025124481439519519] 
dist 114=[-5.46654541778786829770e-06,.00024301303436631544] 
dist 115=[-3.25059650391094421180e-05,.00018275860386258324] 
dist 116=[-4.95114608668855886740e-05,.00017326581600947438] 
dist 117=[-6.02869308754610520560e-05,1.57329988176849077900e-05] 
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dist 121=[-.00014627162552878584,3.29922379974377192470e-05] 
dist 122=[-.00014077061035992714,5.14558782273294800790e-05] 
dist 123=[-.00010739274773121931,7.00303004647054808120e-05] 
dist 124=[-9.94123267751429248510e-05,8.17205521553706822040e-05] 
dist 125=[-7.14583222502839249440e-06,8.91541223668368282710e-05] 
dist 126=[5.75040755672934580090e-06,9.13225298269624601290e-05] 
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dist 128=[7.78095450469423549090e-06,8.79940266035764913980e-05] 
dist 129=[5.29405755909961279820e-06,3.18164576424701330480e-05] 
dist 130=[1.23104225956184014580e-06,3.07457447871598930500e-05] 
dist 131=[-2.84803932676997250560e-06,2.30022993107202869040e-05] 
dist 132=[-5.39732587360244316810e-06,2.18480659432425155020e-05] 
dist 133=[-6.99585180115398012090e-06,-1.88033307348956247460e-06] 
dist 134=[-1.04895533238265459420e-05,-2.21331160783359064600e-06] 
dist 135=[-1.51415632113628199560e-05,-2.17409121988425885710e-06] 
dist 136=[-1.64469259444246063620e-05,-1.87619334813637450740e-06] 
dist 137=[-1.60744000138903406430e-05,-1.37429415565793205450e-06] 
dist 138=[-1.54087810709066542420e-05,-5.48495525972526492400e-07] 
dist 139=[-1.21988855611663979140e-05,2.82927294399219072110e-07] 
dist 140=[-1.08936118318336566440e-05,8.06667112351851518390e-07] 
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dist 142=[1.87634894779847427330e-07,9.28016297264800473500e-06] 
dist 143=[9.81561347812963450250e-07,1.19944476586574404350e-05] 
dist 144=[8.26626442649366519700e-07,1.26984429481715105600e-05] 
dist 145=[5.70651619702953367940e-07,3.70853786706014299080e-06] 
dist 146=[1.53418080693943291270e-07,3.57604115850547490020e-06] 
dist 147=[-2.65366047381396785540e-07,2.69964634582369076210e-06] 
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dist 149=[-6.92087318850436872560e-07,-2.32116406712480239850e-07] 
dist 150=[-1.39914263928474585430e-06,-2.82726369085946155850e-07] 
dist 151=[-1.95572590408673457090e-06,-2.76769612968145114480e-07] 
dist 152=[-2.10810318229495455280e-06,-2.39496340425603450180e-07] 
dist 153=[-2.04597200969212406090e-06,-1.77416785111243053650e-07] 
dist 154=[-1.96818803283603974100e-06,-7.58080398243699150420e-08] 
dist 155=[-1.49352418039858661730e-06,2.63605678354832234840e-08] 
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dist 158=[8.38320236137577886310e-08,8.98878166653659336380e-07] 
dist 159=[1.38108684986853324730e-07,1.17573416827177374970e-06] 
dist 160=[1.15245739244362021140e-07,1.24832719734880323930e-06] 
dist 161=[7.79065981617168743160e-08,4.67345726261760063520e-07] 
dist 162=[1.73751751941713635610e-08,4.50923537869999362040e-07] 
dist 163=[-4.32944533226341472250e-08,3.35995412367173947810e-07] 
dist 164=[-8.11703156834392939450e-08,3.18798102261567849600e-07] 
dist 165=[-1.04905939544794598010e-07,-2.79449097871541697840e-08] 
dist 166=[-1.55966427461462606420e-07,-3.25926554645389448540e-08] 
dist 167=[-2.23827243018941169050e-07,-3.17500933824111863110e-08] 
dist 168=[-2.42285932005087871130e-07,-2.72315087696074882390e-08] 
dist 169=[-2.36103351732377562840e-07,-1.97887489605656414860e-08] 
dist 170=[-2.26133486316399951470e-07,-7.64022425733285871730e-09] 
dist 171=[-1.78460306883525045990e-07,4.75595919180588374570e-09] 
dist 172=[-1.59391008875621774610e-07,1.25304514457263971390e-08] 
dist 173=[-2.33060141018870173070e-08,7.26635538681442155210e-08] 
dist 174=[3.45805436205927219620e-09,1.35983382226745316660e-07] 
dist 175=[1.40320351349581151430e-08,1.75643929267551772050e-07] 
dist 176=[1.17430310711563844130e-08,1.85930230834686165830e-07] 
dist 177=[8.01288383935186583770e-09,5.51254860630455015530e-08] 
dist 178=[1.97143058617667987540e-09,5.31482902099428997120e-08] 
dist 179=[-4.08365303628659747510e-09,3.96456920832254327070e-08] 
dist 180=[-7.87721675559567603000e-09,3.75032793888575546690e-08] 
dist 181=[-1.02597075606994817960e-08,-3.24886847881453079640e-09] 
dist 182=[-2.10482715865874178920e-08,-3.72951888782357050260e-09] 
dist 183=[-2.92352241898469883040e-08,-3.63089461308118267500e-09] 
dist 184=[-3.14283002715611213660e-08,-3.12412917964080648510e-09] 
dist 185=[-3.04280058916322063770e-08,-2.29222600593702082120e-09] 
dist 186=[-2.92715304744475325570e-08,-9.12310002963754207590e-10] 
dist 187=[-2.20550523275722098260e-08,4.77299464011069618430e-10] 
dist 188=[-2.05921697018811692640e-08,1.34855213832471991970e-09] 
dist 189=[-1.32532903404136175520e-09,6.45099373500395476270e-09] 
dist 190=[1.49547646579151029250e-09,1.28012387564869679680e-08] 
dist 191=[1.66673956109121300290e-09,1.67818229063894196120e-08] 
dist 192=[1.31812391438464508500e-09,1.78218257513466376550e-08] 
dist 193=[7.12616881730477423770e-10,7.17572802632245074480e-09] 
dist 194=[-2.84437620651111240060e-10,6.91684984320242446520e-09] 
dist 195=[-1.28271846370969990510e-09,5.14351671946052040010e-09] 
dist 196=[-1.90551358922148989130e-09,4.87503960032345492920e-09] 
dist 197=[-2.29564062144455603110e-09,6.21168301504821582460e-10] 
dist 198=[-2.42418237842418686200e-09,5.88122703888752239160e-10] 
dist 199=[-3.46297417778819242210e-09,5.66159017774154377080e-10] 
dist 200=[-3.74006639884721870240e-09,5.41604272563400933340e-10] 
dist 201=[-3.62544965529308884690e-09,4.15280268494097637050e-10] 
dist 202=[-3.48270680952419003110e-09,3.77451347824377621920e-10] 
dist 203=[-2.65798648830601721830e-09,1.70074171953572522100e-10] 
dist 204=[-2.45030985356414290300e-09,1.28520196272683717770e-10] 
dist 205=[-4.89570375491284495410e-10,8.74294578243397236070e-10] 
dist 206=[-5.10850350177533371110e-10,1.78434737732139385920e-09] 
dist 207=[-5.07937587973230585140e-10,2.35428107067652916960e-09] 
dist 208=[-5.00469726241837551050e-10,2.50208171055175537600e-09] 
dist 209=[-4.89207707522391864340e-10,1.37361021021130843430e-09] 
dist 210=[-4.71656458091995458810e-10,1.31725810078818198790e-09] 
dist 211=[-4.54226344401599053380e-10,1.01884004643103650100e-09] 
dist 212=[-4.43434783262153367040e-10,9.26283483882775135010e-10] 
dist 213=[-4.36732020113760332640e-10,9.10774564037553345160e-10] 
dist 214=[-7.14631896637618239750e-10,9.45222271487028655800e-10] 
dist 215=[-9.11960962866028602250e-10,9.14750106673329566930e-10] 
dist 216=[-9.69286101930362086290e-10,8.76942520835418558570e-10] 
dist 217=[-9.36842413125672548920e-10,6.74488563366017612410e-10] 
dist 218=[-9.00611988697343623530e-10,6.15143263211483829370e-10] 
dist 219=[-6.78258427148223337410e-10,1.50448361106277591130e-10] 
dist 220=[-6.32481829400099794610e-10,1.60152083923239639710e-10] 
dist 221=[-5.93050845172960597050e-10,2.45554145235449648740e-10] 
dist 222=[-6.30630270654871605320e-10,3.97614511346727433890e-10] 
dist 223=[-6.26663507355978598300e-10,5.24098347310836515950e-10] 
dist 224=[-6.11736563303477832100e-10,5.56897546973821844570e-10] 
dist 225=[-5.87961621618351532800e-10,1.23167430320044664680e-10] 
dist 226=[-5.49872355699039605400e-10,2.34794663524603802570e-10] 
dist 227=[-5.11794066779727677970e-10,6.43889514459697010520e-10] 
dist 228=[-4.88061751954601378650e-10,8.98894134730036305250e-10] 
dist 229=[-4.73204143492100612450e-10,1.05854614745281155170e-09] 
dist 230=[-4.69352067129207605240e-10,1.09991878991611468110e-09] 
dist 231=[-3.88783808546681644190e-10,1.06396584641928531150e-09] 
dist 232=[-3.93432433671890380210e-10,1.02092451590443690020e-09] 
dist 233=[-3.82329385618552792670e-10,7.79764915654764995170e-10] 
dist 234=[-3.65290431877541901660e-10,7.16423869447387173270e-10] 
dist 235=[-3.34767168610070298680e-10,4.69404985366829642880e-10] 
dist 236=[-5.57292035191498487570e-10,4.28124930911036075910e-10] 
dist 237=[-6.96616134629644969590e-10,2.39606980985172574360e-10] 
dist 238=[-7.32734814196682599290e-10,2.36734471372707428130e-10] 
dist 239=[-7.19643448950524123180e-10,3.02561305436254729420e-10] 
dist 240=[-6.80123380872585907870e-10,3.19649852975905578700e-10] 
dist 241=[-6.50734057585203303040e-10,3.12515239119591529530e-10] 
dist 242=[-6.21898771670681713260e-10,2.96732244533581425910e-10] 
dist 243=[-4.92550379016744217700e-10,5.63515662334435231050e-10] 
dist 244=[-4.82647196992802461220e-10,7.62155062536472693870e-10] 
dist 245=[-4.88243341895169021030e-10,8.86527945850614830020e-10] 
dist 246=[-4.89695460202285411020e-10,9.18778646744183359620e-10] 
dist 247=[-3.24433440084644381610e-10,5.05980000062010848580e-10] 
dist 248=[-3.40230668179654485210e-10,5.34801215772532438340e-10] 
dist 249=[-3.32587943264426420450e-10,5.21069717136950392850e-10] 
dist 250=[-3.15815791210308368940e-10,4.96403106584702702420e-10] 
dist 251=[-2.64470090811595183640e-10,4.04266445999601836870e-10] 
dist 252=[-2.39206314515543499180e-10,3.58935950233371027830e-10] 
dist 253=[-3.29627476177471160530e-10,3.01327460035282897890e-10] 
dist 254=[-4.22649932065228107790e-10,3.34575630570398574390e-10] 
dist 255=[-4.80893442254888114040e-10,3.55393377482009103220e-10] 

8 phat 5 dirichlet min maxes function [1, 2, 1, 0, 2, 0, 0, 0, 1] 
dist 0=[390.82526552895113047   ,390.82526552895113047   ] 
dist 1=[376.30366122419823688   ,388.98819927443592475   ] 
dist 2=[341.61061038997168548   ,390.82526552895113047   ] 
dist 3=[275.84222736469398066   ,343.45439783335656762   ] 
dist 4=[204.44945918860715318   ,316.54883687959350739   ] 
dist 5=[147.52423114514212178   ,259.66730274721323258   ] 
dist 6=[56.097563468470766818  ,123.80900596779526739   ] 
dist 7=[-6.6615019828445195296 ,111.26368549354262761   ] 
dist 8=[-53.189803688267970246  ,75.970277504921164463  ] 
dist 9=[-83.898304405165075130  ,-3.6130104985120745912 ] 
dist 10=[-101.72113131006038222   ,-26.905002919838800288  ] 
dist 11=[-104.54548043216199103   ,-12.595865283607828164  ] 
dist 12=[-90.125985759422299264  ,6.9922926644229759868 ] 
dist 13=[-87.898013069826395580  ,24.413647033591639339  ] 
dist 14=[-11.057194763737141701  ,40.783860983132172533  ] 
dist 15=[6.6964155999742922183 ,56.855803173745525153  ] 
dist 16=[15.832207679684580285  ,68.184830082159791721  ] 
dist 17=[36.987166586144871963  ,69.844492362462305372  ] 
dist 18=[35.376972576374376439  ,61.207083523398484782  ] 
dist 19=[25.783410939770027317  ,58.881049286828915112  ] 
dist 20=[-.52608614359274125148,42.561313505966251124  ] 
dist 21=[-19.149917270430829327  ,38.647015943492868999  ] 
dist 22=[-32.285631580819422881  ,12.129824601871640325  ] 
dist 23=[-38.782778658218708515  ,3.0260929597274818910 ] 
dist 24=[-41.169641005714332535  ,.8983699091473541836 ] 
dist 25=[-40.387863772273105947  ,-2.7141693938043236190 ] 
dist 26=[-34.306629054387715291  ,-.7144417811357833081 ] 
dist 27=[-30.640878888307830377  ,4.0778502515146569266 ] 
dist 28=[-13.917150995592925149  ,13.995080176444407532  ] 
dist 29=[-9.2203881574765897201 ,25.063885257808879808  ] 
dist 30=[-.19128068588850346882,32.313595131392595108  ] 
dist 31=[1.2856129382243373165 ,33.744017936623740971  ] 
dist 32=[3.6958149390615218446 ,7.3230585305398137592 ] 
dist 33=[4.9457932833600688846 ,7.2832805844036937960 ] 
dist 34=[4.3893299491162557468 ,6.6986443127347365179 ] 
dist 35=[2.5705289296478207161 ,6.5287937158615622226 ] 
dist 36=[-.18051406668943885418,5.1077806728578056966 ] 
dist 37=[-1.9827209675489912252 ,4.7754003094285551032 ] 
dist 38=[-3.1994738939989894846 ,.6082021855472656322 ] 
dist 39=[-3.7012179738510492566 ,-.03710601290013557152] 
dist 40=[-3.8329876142653402975 ,-1.1268088922549326144 ] 
dist 41=[-3.9870352229934949615 ,-1.2580289921404970537 ] 
dist 42=[-3.0484871145757442003 ,-1.1324459779473230035 ] 
dist 43=[-2.7466028183092731517 ,-.60015703636985951905] 
dist 44=[-1.3661629883392587875 ,1.0712801588372509933 ] 
dist 45=[-1.2242365425416504950 ,2.1215298380653269798 ] 
dist 46=[-.26625070803923266102,2.7821185481675367905 ] 
dist 47=[-.05405992672442864165,2.9537131673020272444 ] 
dist 48=[.06046277999393605387,1.3455879253425281036 ] 
dist 49=[.08513691490223308015,1.3304291744226266734 ] 
dist 50=[.05138329735328770865,.7985859361175527238 ] 
dist 51=[-.02297071643576570955,.77239826353238795219] 
dist 52=[-.15820619156275152868,.62545243601655677333] 
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dist 55=[-.50257295393944008163,.00807374735761180912] 
dist 56=[-.58790230309875526242,-.15335030827999079515] 
dist 57=[-.62343907307974774197,-.18538600608877277892] 
dist 58=[-.3759396884595174825 ,-.16703743628645127526] 
dist 59=[-.3504896560602284533 ,-.07202690241154499799] 
dist 60=[-.14059423015624453699,.10293055394738905162] 
dist 61=[-.13268729868735081812,.21304145705469977285] 
dist 62=[.00638876342313316594,.28322972737042995038] 
dist 63=[.02906998639461851206,.30203001220623028533] 
dist 64=[.07589845129880226206,.11625370121690700772] 
dist 65=[.08342550569813868891,.11347152479074517704] 
dist 66=[.07715390727318804925,.10330708653065797474] 
dist 67=[.03463487538171965115,.09987206678524566315] 
dist 68=[-.00849540584163914874,.07670738573438386707] 
dist 69=[-.03598884941236374186,.07140776901071311926] 
dist 70=[-.05468025899153598197,.00709516761012976954] 
dist 71=[-.07126593392689570103,-.00276067826753907587] 
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dist 73=[-.06255900084504594181,-.02247976358773704148] 
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dist 78=[.00189445309075957104,.04393584347020342180] 
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dist 80=[.01012017591734991727,.01395613115601504347] 
dist 81=[.01021514715451178462,.01356215246190238195] 
dist 82=[.00846107516773605053,.01217173114292709806] 
dist 83=[.00308707997575136339,.01170506663709820892] 
dist 84=[-.00233733703581953251,.00934868050143543100] 
dist 85=[-.00576695111668063797,.00836070202585551132] 
dist 86=[-.00796260324754382991,.00146345714765396024] 
dist 87=[-.00863299129433898769,.00010153274238051238] 
dist 88=[-.00906819101483895739,-.00221599045146250448] 
dist 89=[-.00960135763488500423,-.00263841886444187303] 
dist 90=[-.00628552459272658921,-.00253556737253891308] 
dist 91=[-.00579289796859020398,-.0001221249533016266 ] 
dist 92=[-.00207559821451576771,.00249630396630886107] 
dist 93=[-.00196824451052799001,.00414087084169315381] 
dist 94=[-.00050885990722379266,.00518147993024052525] 
dist 95=[-.00021943015414956874,.00547252019567975938] 
dist 96=[.00025522330288945339,.00218482173766186361] 
dist 97=[.00035960697235432983,.00232274109734157701] 
dist 98=[.00033695556526865300,.00227129480669794217] 
dist 99=[-.00013826309536038570,.00217535764383589258] 
dist 100=[-.00093048503312500672,.00172852648891612945] 
dist 101=[-.00142989897446822574,.00153383746510264116] 
dist 102=[-.00174829278176803164,.00026404168201865381] 
dist 103=[-.00184291314862919112,6.09008508406373098840e-06] 
dist 104=[-.00182392981256028395,-.00032199274581424813] 
dist 105=[-.00170443358618084353,-.00034262495855517688] 
dist 106=[-.00035965911905798118,-.00029564539699922379] 
dist 107=[-.00034800185653707290,-.00021631743550342658] 
dist 108=[-.00026128271648120424,-8.56723675672021777580e-05] 
dist 109=[-.00024835354248714662,4.58916173133226060920e-05] 
dist 110=[3.39879516660597688680e-05,.00012878973087606612] 
dist 111=[7.84760427663647363720e-05,.00018158249972901816] 
dist 112=[.00015527328693540560,.00019713066586651915] 
dist 113=[.00015257047613633287,.00019245000308935497] 
dist 114=[.00012867153159446970,.00018560995744591214] 
dist 115=[8.91099732745579582820e-05,.00017447538780126025] 
dist 116=[2.45692169763405356600e-05,.00013840734886619084] 
dist 117=[-4.02255352395372308820e-05,.00012365576738228734] 
dist 118=[-8.07741147327427572830e-05,1.89435423628997900910e-05] 
dist 119=[-.00010628009750409004,-1.76830078488333747650e-06] 
dist 120=[-.00013555161730342709,-3.70062417045040077290e-05] 
dist 121=[-.00014352796293195502,-4.30273794027291824220e-05] 
dist 122=[-4.27617533127812090810e-05,-3.82410027921987678620e-05] 
dist 123=[-4.05270240479678210230e-05,-2.83428501240707060110e-05] 
dist 124=[-3.06735519775830920940e-05,-1.21350912703897137800e-05] 
dist 125=[-2.87996115668620118460e-05,4.16367939121032744550e-06] 
dist 126=[2.51697716274278363140e-06,1.44155334766766379180e-05] 
dist 127=[7.61440461967970064130e-06,2.09282385139395142240e-05] 
dist 128=[1.78212849139673196280e-05,2.28152451502076784070e-05] 
dist 129=[1.94403718554659666730e-05,2.38505059142322163460e-05] 
dist 130=[1.84244955729463984680e-05,2.31805745785721844730e-05] 
dist 131=[1.24728435691508020310e-05,2.23096681226206423110e-05] 
dist 132=[2.82286538147864293140e-06,1.69483625673100229760e-05] 
dist 133=[-6.84945724271874616560e-06,1.57441206547065918580e-05] 
dist 134=[-1.28879289836698725940e-05,1.28094720294172395190e-06] 
dist 135=[-1.66720310658571261540e-05,-9.17412385475001705140e-07] 
dist 136=[-1.76536014429791659990e-05,-4.79950781505569976280e-06] 
dist 137=[-1.41310984919070359700e-05,-5.15435214997513608930e-06] 
dist 138=[-5.29782019469115129920e-06,-4.42400672084603903710e-06] 
dist 139=[-5.11521217172950552640e-06,-3.22106954370691008440e-06] 
dist 140=[-3.81869189246548752380e-06,-1.26211507838685816830e-06] 
dist 141=[-3.62483430708098035500e-06,7.04865400706251823620e-07] 
dist 142=[5.29677683125429441070e-07,1.93863610574399176930e-06] 
dist 143=[1.18302433416749866810e-06,2.71878585624813060700e-06] 
dist 144=[2.39113876937831883780e-06,2.93712885750145060120e-06] 
dist 145=[2.31967294596235260690e-06,2.85590651118964478300e-06] 
dist 146=[1.94628016704631795200e-06,2.74903338735663098360e-06] 
dist 147=[1.33796785227288087960e-06,2.56502946594925422820e-06] 
dist 148=[3.52906461887305868640e-07,2.02674422427447169300e-06] 
dist 149=[-6.34486194317331445170e-07,1.81043391201447254300e-06] 
dist 150=[-1.25134352479549353150e-06,2.67520834121773634130e-07] 
dist 151=[-1.63852738409156923960e-06,-3.62562802303535850540e-08] 
dist 152=[-1.99166243009810608470e-06,-5.50574623948993894100e-07] 
dist 153=[-2.10846063731838341110e-06,-6.36000758619705111830e-07] 
dist 154=[-6.31891537148036866740e-07,-5.62858372883824422140e-07] 
dist 155=[-6.01814724401255458930e-07,-4.15003889886569872020e-07] 
dist 156=[-4.49520547256841573060e-07,-1.74769489717926882730e-07] 
dist 157=[-4.25381784694252212380e-07,6.62469311428161059630e-08] 
dist 158=[3.63122316887337257450e-08,2.17278880255454357930e-07] 
dist 159=[1.11122341919646657710e-07,3.12652505662601879250e-07] 
dist 160=[2.59272304394827801420e-07,3.39094218728297750540e-07] 
dist 161=[2.82769914793447118490e-07,3.55955565960740271290e-07] 
dist 162=[2.70279446225514136920e-07,3.44947649114693801110e-07] 
dist 163=[1.82353223902505212300e-07,3.31871452249505886380e-07] 
dist 164=[4.04176184924379375370e-08,2.50559698083867529230e-07] 
dist 165=[-1.01711473444829337320e-07,2.33641672110631992270e-07] 
dist 166=[-1.90389452229348262080e-07,1.73897558323904671760e-08] 
dist 167=[-2.45942235501401723020e-07,-1.43869341745389525380e-08] 
dist 168=[-2.60352783199677888460e-07,-7.03160648103076072080e-08] 
dist 169=[-2.04100356255493107420e-07,-7.52661096042744630490e-08] 
dist 170=[-7.88439006495693419840e-08,-6.38814367727929442150e-08] 
dist 171=[-7.60285357410745752170e-08,-4.53789029055390630060e-08] 
dist 172=[-5.66315492622376516810e-08,-1.54450706474833378260e-08] 
dist 173=[-5.36640808284187052240e-08,1.45572541082723874150e-08] 
dist 174=[7.86222878628543452850e-09,3.33259002407262685870e-08] 
dist 175=[1.73345348164712925430e-08,4.51437620471377872730e-08] 
dist 176=[2.97995950640666757770e-08,4.83470537253092001720e-08] 
dist 177=[2.85606860865489549210e-08,4.69028692643555080000e-08] 
dist 178=[2.31332463085987766410e-08,4.50719440946653713150e-08] 
dist 179=[1.43499297741301771720e-08,3.84416425653857712220e-08] 
dist 180=[1.70135123100000000000e-10,3.17254417337357268840e-08] 
dist 181=[-1.40321917244301771720e-08,2.70690950317116425090e-08] 
dist 182=[-2.29030511398987766410e-08,5.03354797564131789990e-09] 
dist 183=[-2.84729934432489549210e-08,8.27634404408860410220e-10] 
dist 184=[-3.05035518165586050210e-08,0                     ] 
dist 185=[-3.22495497714376878690e-08,-8.22262456932953587850e-09] 
dist 186=[-9.55572285429723272250e-09,-7.94226122440041146610e-09] 
dist 187=[-8.45340440599046393450e-09,-6.24994109492018091000e-09] 
dist 188=[-6.74734956600692111090e-09,-2.59850421443004602280e-09] 
dist 189=[-5.95980529842565873570e-09,1.05987388286008887040e-09] 
dist 190=[2.16068337780893256250e-10,3.34742232107056710030e-09] 
dist 191=[1.16971749524182461120e-09,4.78691586631545010730e-09] 
dist 192=[2.99939529297513089250e-09,5.17542799713261186020e-09] 
dist 193=[3.28832575252204564160e-09,5.33936677514646195450e-09] 
dist 194=[3.15410266621612955250e-09,5.17030463106776933820e-09] 
dist 195=[2.59709800313475947830e-09,4.96933244994512314150e-09] 
dist 196=[5.43941278664961214130e-10,3.76765920936941310590e-09] 
dist 197=[-1.62018553832190893160e-09,3.49413887699182686880e-09] 
dist 198=[-2.96990248941837757250e-09,1.13888937321820404600e-09] 
dist 199=[-3.81520859261825363870e-09,7.75591612857037265040e-10] 
dist 200=[-4.03434457521016957560e-09,3.30250550889027369900e-10] 
dist 201=[-3.84000625377410798310e-09,2.46208291813323967680e-10] 
dist 202=[-1.07436708762271893470e-09,2.34895741112043234420e-10] 
dist 203=[-8.28592389717355954610e-10,2.24052526093974034360e-10] 
dist 204=[-7.57634178742035538610e-10,1.70091480678176435580e-10] 
dist 205=[-5.57235836033900957090e-10,5.32594826233134107350e-10] 
dist 206=[-5.49277900327261365800e-10,8.53576210431312460920e-10] 
dist 207=[-5.43911706790099160480e-10,1.05477105207083360320e-09] 
dist 208=[-5.40134239711166664110e-10,1.10731607081480191690e-09] 
dist 209=[-5.38268448840814899840e-10,1.06829343179410852050e-09] 
dist 210=[-5.25367417317891744950e-10,8.82637487847758156140e-10] 
dist 211=[-4.98283866237473267580e-10,8.43292763555604885170e-10] 
dist 212=[-4.98994223127664929730e-10,6.72910973645347783430e-10] 
dist 213=[-8.11871377513848103650e-10,7.16758960426494840200e-10] 
dist 214=[-1.06819886851523865110e-09,7.66270007341670660500e-10] 
dist 215=[-1.22880266481334839520e-09,9.79364051436365215580e-10] 
dist 216=[-1.27065803529589411060e-09,1.12410026144017953100e-09] 
dist 217=[-8.27496703779387366550e-10,1.16139402279410796660e-09] 
dist 218=[-1.56200861287539941380e-10,1.12878490941763487950e-09] 
dist 219=[-1.53591159090221792830e-10,1.07768602110000108420e-09] 
dist 220=[-1.49236429459890100530e-10,8.60479818082104764690e-10] 
dist 221=[-2.40442266350396744370e-10,7.56094998285969575810e-10] 
dist 222=[-4.49325607950497129770e-10,2.43513903698443796300e-10] 
dist 223=[-7.23182101048801871220e-10,2.32200154901876626660e-10] 
dist 224=[-9.19829326212855041770e-10,2.72925514386040285060e-10] 
dist 225=[-9.70738186758488837330e-10,2.83570137048824613500e-10] 
dist 226=[-9.62095798612063556430e-10,3.04971568445887746090e-10] 
dist 227=[-9.29087002994119370170e-10,3.87181545607846996170e-10] 
dist 228=[-8.76427464125193914310e-10,5.18424345982851327340e-10] 
dist 229=[-8.15281707832411960250e-10,1.00516469565385327050e-09] 
dist 230=[-1.10683829169662611330e-09,1.32907866823133769440e-09] 
dist 231=[-1.30300995782567206020e-09,1.53187120725357732610e-09] 
dist 232=[-1.42583382740619496930e-09,1.58441939161134389740e-09] 

8 phat 5 dirichlet min maxes function [1, 0, 1, 2, 0, 2, 0, 2] 
dist 0=[360.07869744716233554   ,360.07869744716233554   ] 
dist 1=[331.10907156688065602   ,370.88413100074606333   ] 
dist 2=[269.87125433734405747   ,367.39863415947424722   ] 
dist 3=[201.96127631611678962   ,349.05278435388587805   ] 
dist 4=[146.61144714705202953   ,286.89591240024662723   ] 
dist 5=[94.824886237419277282  ,224.19682344031172370   ] 
dist 6=[39.762217376747383879  ,209.78235971242137772   ] 
dist 7=[-7.6136142928367344061 ,153.60291687150224823   ] 
dist 8=[-29.845866679238694925  ,128.16409825149645629   ] 
dist 9=[-67.900369860887184739  ,-3.1716875787749127261 ] 
dist 10=[-89.960008846905781355  ,-20.565721416874637067  ] 
dist 11=[-100.26257432373081223   ,-15.310089691851308497  ] 
dist 12=[-100.84965004849874834   ,-3.5936312187830193037 ] 
dist 13=[-83.753931047226249397  ,7.1092174172056745095 ] 
dist 14=[-80.609542447939341248  ,22.595587045102510872  ] 
dist 15=[-7.3602041758625838821 ,39.164056089670121874  ] 
dist 16=[10.030790335520031227  ,55.185401262419850567  ] 
dist 17=[12.587408366924913318  ,66.396912696153327992  ] 
dist 18=[2.8638092949982949844 ,68.131583333250758291  ] 
dist 19=[-7.6554903403909203000 ,59.481318516903281839  ] 
dist 20=[-14.592035674308990527  ,57.566993316013513110  ] 
dist 21=[-19.455413333800027971  ,39.412952775499076600  ] 
dist 22=[-20.545293838018643019  ,35.668687760477187140  ] 
dist 23=[-29.364630614441613523  ,7.4796691636637189202 ] 
dist 24=[-35.708663105698846431  ,3.3676558749613097424 ] 
dist 25=[-38.131259864404148049  ,7.0099768590491917280 ] 
dist 26=[-37.498765825940514196  ,13.983221261411933589  ] 
dist 27=[-31.860730353228644464  ,21.240561334758071041  ] 
dist 28=[-28.611922229245904296  ,25.987119435355161376  ] 
dist 29=[-8.8659836782044435411 ,29.158480035814302008  ] 
dist 30=[-8.4235116749826284469 ,30.370713121190373509  ] 
dist 31=[-.00137418310120174099,30.205756673462780756  ] 
dist 32=[1.3739604391153317649 ,28.083423116422305831  ] 
dist 33=[1.7677188073082409903 ,7.6008384508267929604 ] 
dist 34=[.60521444577881672028,7.5542802419710592093 ] 
dist 35=[-.59955001571466869571,6.2038930185435742848 ] 
dist 36=[-1.3680479843668930767 ,6.0294477439077336640 ] 
dist 37=[-1.8559672283488410536 ,4.6865159533134480375 ] 
dist 38=[-2.0645076475481231800 ,4.3756621651662585943 ] 
dist 39=[-3.3229149150144968476 ,.51790137225866377213] 
dist 40=[-3.8383079364857349078 ,-.07778586348127824509] 
dist 41=[-3.9385412130557828901 ,-.43040610970115353673] 
dist 42=[-3.8338987924831473915 ,.02219741502219887091] 
dist 43=[-3.1538040392730576139 ,.48560850966541478403] 
dist 44=[-2.8410699185532094154 ,.78147756783323628932] 
dist 45=[-1.1772623872480790786 ,1.1107895812966564380 ] 
dist 46=[-1.0768511536478105795 ,2.1977679604190834423 ] 
dist 47=[-.16732010462306374621,2.8813919207798205576 ] 
dist 48=[-.16694135834791732875,3.0589635297523544564 ] 
dist 49=[-.18345801864828683549,.92501229058035440937] 
dist 50=[-.22335332158640081045,.90716654225344197918] 
dist 51=[-.26662654603808145448,.73030719154601687792] 
dist 52=[-.29626533664427957138,.70500860998523702021] 
dist 53=[-.31723653083978599799,.56811121815763038797] 
dist 54=[-.3289208965569535183 ,.5095330676061673754 ] 
dist 55=[-.46758477319013109065,.08775028635296027806] 
dist 56=[-.51999837139085824332,.00406161396187619357] 
dist 57=[-.53822252664508447697,-.08072388718039703743] 
dist 58=[-.57058023937096842704,-.03857202783759642187] 
dist 59=[-.38851551372162637585,.00477054604085452447] 
dist 60=[-.36218872104919957574,.03296458750156995950] 
dist 61=[-.12719908823336588711,.10658749595602870428] 
dist 62=[-.1199122966985768347 ,.22039823966414473496] 
dist 63=[.00674941492718833624,.29287873193804317934] 
dist 64=[.02739434101862687590,.31233557589041147792] 
dist 65=[.03526699163467983164,.12015765915499238352] 
dist 66=[.00908726515982391516,.11725322818998286708] 
dist 67=[-.01737546632003949673,.09387386523329917238] 
dist 68=[-.03398614485903552321,.09065975351807933251] 
dist 69=[-.04442794902643022855,.06945713226176237225] 
dist 70=[-.04713972438213231007,.06462952535237989224] 
dist 71=[-.05565494022961200662,.00617419103547714300] 
dist 72=[-.06175778069718262416,-.00276876495903666803] 
dist 73=[-.06143703958872340592,-.00933249625441669749] 
dist 74=[-.05923402132727110283,-.00397928065663419715] 
dist 75=[-.04756692117997886457,.00146948183305979453] 
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dist 86=[-.00595885006139906820,.00754099664836987215] 
dist 87=[-.00822452328550290559,.00131706265981336391] 
dist 88=[-.00891455181256629341,8.87855463761814296450e-05] 
dist 89=[-.00873601795239019176,-.00122060465434724943] 
dist 90=[-.00870338559155147210,-.00054445007793229215] 
dist 91=[-.00648738635617062951,.00014072797813524444] 
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dist 93=[-.00186775068847916794,.00257867266686910074] 
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dist 99=[-.00028179184030442930,.00213978710076691717] 
dist 100=[-.00053810247909425774,.00204742754262493969] 
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dist 103=[-.00168735473095759029,.00028139849767184263] 
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dist 107=[-.00032394925371098445,2.84219921295610579950e-05] 
dist 108=[-.00031322184116253909,8.18029891866577390090e-05] 
dist 109=[-.00023470226702565511,.00011595666123932059] 
dist 110=[-.00022299685555001568,.00012633831879309883] 
dist 111=[3.12321455374549367990e-05,.00012370952766432117] 
dist 112=[7.12616011599539467120e-05,.00011942791080522287] 
dist 113=[5.75924284779739044300e-05,.00015379526933274866] 
dist 114=[1.60967968500673135890e-05,.00016726123876895761] 
dist 115=[-2.56080839358553873160e-05,.00016363920565264469] 
dist 116=[-5.17354067665662949250e-05,.00015691557168387932] 
dist 117=[-6.81909954179368453830e-05,.00012433325796408518] 
dist 118=[-7.26223939141635764980e-05,.00011105428591126338] 
dist 119=[-5.02470846536717716370e-05,1.68562331066993664770e-05] 
dist 120=[-9.43673197561064114640e-05,-1.76929933044045755340e-06] 
dist 121=[-.00012201084140023215,-1.83741850997921218090e-05] 
dist 122=[-.00012918087130486072,-7.93513246080371242990e-06] 
dist 123=[-3.77566767934732627100e-05,2.57884904305091722580e-06] 
dist 124=[-3.64219457215385172260e-05,9.20852172754728050620e-06] 
dist 125=[-2.75261364258902061600e-05,1.34365225592070713860e-05] 
dist 126=[-2.58368069954343403900e-05,1.46953685754618811700e-05] 
dist 127=[2.31674544531256754690e-06,1.44462301383298244480e-05] 
dist 128=[6.89864701650046059450e-06,1.42080937903269985920e-05] 
dist 129=[8.08415284885214218710e-06,1.98835187718440549450e-05] 
dist 130=[1.84826254522393650380e-06,2.14483466268295075250e-05] 
dist 131=[-4.40600975525641917740e-06,2.08286020287354404940e-05] 
dist 132=[-8.31217915765477146760e-06,2.00407209988581617950e-05] 
dist 133=[-1.07606678277214442020e-05,1.52142279317075422420e-05] 
dist 134=[-1.13958508123466922640e-05,1.41317153270837851330e-05] 
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dist 136=[-9.13947640469566081380e-06,-8.41094431237374460360e-07] 
dist 137=[-1.19590489372948288750e-05,-2.09168845067155639550e-06] 
dist 138=[-1.26993987191222245080e-05,-8.25569976836974005180e-07] 
dist 139=[-4.75892962561867217680e-06,4.47187988187737932430e-07] 
dist 140=[-4.59302453088917080810e-06,1.24683738850983122730e-06] 
dist 141=[-3.42509756871413061830e-06,1.75379947768248848370e-06] 
dist 142=[-3.25038792281880614880e-06,1.89840306698177495860e-06] 
dist 143=[4.80624969852924501670e-07,1.84900586622823528010e-06] 
dist 144=[1.06713327043263585190e-06,1.78076139542293501770e-06] 
dist 145=[8.68981345850988801360e-07,2.27615418463881398750e-06] 
dist 146=[2.30868919541897501270e-07,2.46544948079772435380e-06] 
dist 147=[-4.09243722672406926730e-07,2.40379769511777944090e-06] 
dist 148=[-8.09347029210564707640e-07,2.30270243231006659990e-06] 
dist 149=[-1.06064466011191688740e-06,1.81800515405465195060e-06] 
dist 150=[-1.12711206079883964280e-06,1.62398005505728901790e-06] 
dist 151=[-7.39031621055490360510e-07,2.38444601754009268010e-07] 
dist 152=[-1.38393779110210253180e-06,-3.41305558871509245370e-08] 
dist 153=[-1.78789393962811058580e-06,-2.69779643754895707200e-07] 
dist 154=[-1.89266583129160206770e-06,-1.14362583729903018940e-07] 
dist 155=[-5.61574974767344697490e-07,4.17048656202718390960e-08] 
dist 156=[-5.41590847645030340420e-07,1.39902626735700087230e-07] 
dist 157=[-4.03562959531625329540e-07,2.02049681791784542660e-07] 
dist 158=[-3.82427332832290536140e-07,2.19565234505163855050e-07] 
dist 159=[3.33771878855445363880e-08,2.14641694955652588900e-07] 
dist 160=[1.00515809122121856610e-07,2.13776934802179525670e-07] 
dist 161=[1.18815961770576365430e-07,2.97105196805508993690e-07] 
dist 162=[2.64631848410799998080e-08,3.19514136947296680540e-07] 
dist 163=[-6.60484450720663658900e-08,3.09473821050765910900e-07] 
dist 164=[-1.23782317591626636250e-07,2.97712223014006768920e-07] 
dist 165=[-1.59958029775886353490e-07,2.24582020808998991040e-07] 
dist 166=[-1.69339218216339362880e-07,2.09500337851666677660e-07] 
dist 167=[-6.68819667248252170960e-08,1.50525240728956504510e-08] 
dist 168=[-1.31646166082437467950e-07,-1.35165955933146541100e-08] 
dist 169=[-1.72248129743229471620e-07,-2.96055591577443672820e-08] 
dist 170=[-1.82865246492934631830e-07,-1.01913573420413824380e-08] 
dist 171=[-7.05201496827368676810e-08,9.27905371803160245160e-09] 
dist 172=[-6.79922963963080867770e-08,2.14705581402765315700e-08] 
dist 173=[-5.05713079292305801840e-08,2.91583305487553440210e-08] 
dist 174=[-4.79544572408848037910e-08,3.12654490900872345190e-08] 
dist 175=[7.22943256059596223430e-09,3.03639324933278013640e-08] 
dist 176=[1.51798370661489890080e-08,2.91810441273512416980e-08] 
dist 177=[9.43185475947888610480e-09,3.38981519389682606250e-08] 
dist 178=[1.37450106650000000000e-10,3.66329986778633502170e-08] 
dist 179=[-9.17543803935888610480e-09,3.56695932185731106020e-08] 
dist 180=[-1.49952122543289890080e-08,3.41296413408605599260e-08] 
dist 181=[-1.86519600783303074150e-08,2.70339758513118953430e-08] 
dist 182=[-1.96252348446827648650e-08,2.40222498293961855510e-08] 
dist 183=[-1.16824586402939339250e-08,4.26209697054715897730e-09] 
dist 184=[-2.12840177569239447860e-08,3.10216763153613377410e-10] 
dist 185=[-2.73321704456700089700e-08,-4.08482681303363185300e-09] 
dist 186=[-2.89006509376519811160e-08,-1.66261145216690875550e-09] 
dist 187=[-7.53983397354548302990e-09,7.65289309199814347420e-10] 
dist 188=[-7.26065775566256275820e-09,2.28450952931846177790e-09] 
dist 189=[-5.44628428676168034070e-09,3.24160284114249196670e-09] 
dist 190=[-5.11656838313508072810e-09,3.50218812441848121070e-09] 
dist 191=[8.03489255187125048060e-11,3.42601797573179270370e-09] 
dist 192=[9.50810642034801359200e-10,3.27531323288497991070e-09] 
dist 193=[1.54814062257153515610e-09,4.41753072854546102330e-09] 
dist 194=[1.16452265663056246770e-11,4.72093131117232627870e-09] 
dist 195=[-1.52626709669892390720e-09,4.58175955708565429720e-09] 
dist 196=[-2.48554708213870849190e-09,4.39227160698555675170e-09] 
dist 197=[-3.08640950159590554060e-09,3.40642144753171538670e-09] 
dist 198=[-3.24230184293120627080e-09,3.08758581271352150790e-09] 
dist 199=[-1.66596283094217828850e-09,1.08103085314454676630e-09] 
dist 200=[-2.57484455957297980730e-09,7.99442077918513455590e-10] 
dist 201=[-3.14435523280620425400e-09,4.94855610314409868420e-10] 
dist 202=[-3.29277157385139752580e-09,4.33772122667900339420e-10] 
dist 203=[-7.86350402302434702810e-10,4.17130800417280536310e-10] 
dist 204=[-7.55665683529692948180e-10,3.99165775187080011370e-10] 
dist 205=[-5.77433690131477077110e-10,3.48925975706242483350e-10] 
dist 206=[-5.32436484691685135140e-10,3.58834543881887072950e-10] 
dist 207=[-3.45352429329579970530e-10,3.55647778432599069660e-10] 
dist 208=[-3.27944224392409538760e-10,3.63543233953157043420e-10] 
dist 209=[-2.70808889714486753270e-10,4.73504150956466529800e-10] 
dist 210=[-2.83044303654426051830e-10,5.06036186266320513400e-10] 
dist 211=[-2.83700041014287471640e-10,4.99068936321427761310e-10] 
dist 212=[-3.24508325052107810520e-10,4.70840705848821168540e-10] 
dist 213=[-3.50165856485263194860e-10,4.20926224051377184380e-10] 
dist 214=[-3.57031756921214289190e-10,3.92482131598770593510e-10] 
dist 215=[-4.93463318680295003740e-10,4.81701427232016708970e-10] 
dist 216=[-6.04903232190405568300e-10,5.65334756753584451320e-10] 
dist 217=[-6.74691122434244281490e-10,6.17597494935628685350e-10] 
dist 218=[-6.92788348064158435930e-10,6.30937563866469632780e-10] 
dist 219=[-1.31390546714845978740e-10,6.10034139054337220420e-10] 
dist 220=[-2.28807002267514919900e-10,5.85337870476710064550e-10] 
dist 221=[-2.89776259797093641420e-10,4.46532321888856403950e-10] 
dist 222=[-3.05538554480569617640e-10,4.10580016197782883740e-10] 
dist 223=[-2.98894746093378795470e-10,1.81508111562459390170e-10] 
dist 224=[-2.98374002037702298110e-10,1.82412596700023674580e-10] 
dist 225=[-3.73620492670854095060e-10,1.83015616031740527060e-10] 
dist 226=[-3.98158513530481250880e-10,1.83250558156736095940e-10] 
dist 227=[-3.91528259714751946130e-10,1.78956260206058678480e-10] 
dist 228=[-3.69485338193081694140e-10,1.70211285294703843220e-10] 
dist 229=[-3.26739226750336909740e-10,1.40821165747006934500e-10] 
dist 230=[-3.23971445887127991280e-10,2.03771120929210676840e-10] 
dist 231=[-3.63421075969946141550e-10,4.13848997623830062080e-10] 
dist 232=[-3.88015220011033096090e-10,5.44806457219306978230e-10] 
dist 233=[-4.03414641434711877440e-10,6.26801293705821957970e-10] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 2, 2, 2, 2, 1, 2] 
dist 0=[445.41791998626787777   ,445.41791998626787777   ] 
dist 1=[418.92780291744242309   ,445.27430538968527139   ] 
dist 2=[365.03189196054337969   ,445.41791998626787777   ] 
dist 3=[268.69792779072298225   ,388.33784587538769217   ] 
dist 4=[167.37170006118742195   ,355.36075083887336169   ] 
dist 5=[93.717892246732324575  ,293.74933196275501688   ] 
dist 6=[33.538774594265291915  ,129.92145906788485433   ] 
dist 7=[-16.565689362258166983  ,68.243090267858372357  ] 
dist 8=[-59.135460300147961752  ,54.994279126956372462  ] 
dist 9=[-88.086599735809391260  ,-52.306718908699279012  ] 
dist 10=[-103.13792151817814869   ,-53.872645649827180879  ] 
dist 11=[-104.03819258439208183   ,-24.999357546796827226  ] 
dist 12=[-91.640375871369461532  ,7.1689398825674478405 ] 
dist 13=[-84.179120612661234695  ,28.378703797288155634  ] 
dist 14=[-22.352135321899798244  ,41.953794424098789399  ] 
dist 15=[-10.020791476512738176  ,50.165354770236609194  ] 
dist 16=[7.1590035396622350228 ,68.680183970439566520  ] 
dist 17=[15.324003332023834411  ,73.499733969701674700  ] 
dist 18=[13.570298456755021138  ,23.926631438548016675  ] 
dist 19=[8.0275150243935362790 ,24.100577854628999930  ] 
dist 20=[1.7784827745868335794 ,20.240069052821711688  ] 
dist 21=[-2.7310234694649530034 ,19.412368120266486019  ] 
dist 22=[-6.1468938699860370335 ,2.0643569835656640090 ] 
dist 23=[-9.1967120562208800684 ,-1.6553100042103889721 ] 
dist 24=[-11.666900459126380487  ,-4.8150565091931716686 ] 
dist 25=[-12.818425457483406110  ,-6.9748188627148296552 ] 
dist 26=[-13.213797857219696296  ,-5.3857767599618757496 ] 
dist 27=[-12.952256211746170032  ,-2.1624638731254641195 ] 
dist 28=[-10.268134884434456885  ,1.2160440753169610266 ] 
dist 29=[-9.6218850284629838224 ,3.4869366785275261799 ] 
dist 30=[-3.1604663628167643268 ,6.2059119147749471600 ] 
dist 31=[-1.1106762876007592091 ,8.3325808402202736530 ] 
dist 32=[-.60674981089063888644,8.7902069006596133746 ] 
dist 33=[2.2224841542316947902 ,7.8017128324171520703 ] 
dist 34=[1.7714875483512096614 ,3.1381516267789556133 ] 
dist 35=[.87421804626973292961,3.0942132098382573116 ] 
dist 36=[-.06962579092201173780,2.4665008640342868025 ] 
dist 37=[-.70173157467176544921,2.3488355715215659615 ] 
dist 38=[-1.1409721235073891655 ,-.03945431881723577448] 
dist 39=[-1.3453687153823084060 ,-.42650521914907522493] 
dist 40=[-1.5081163790155279470 ,-1.1155071342959501806 ] 
dist 41=[-1.6946110086201919690 ,-.99308681428121809403] 
dist 42=[-1.6984534169487389583 ,-.73348627255062460322] 
dist 43=[-1.6493151995669723216 ,-.26779148404258999022] 
dist 44=[-1.2868056495929715927 ,.20906032158531068325] 
dist 45=[-1.1946729707402798115 ,.51203589107114277403] 
dist 46=[-.21018492575358462741,.70841384335094514615] 
dist 47=[-.02769421310083267703,.88593051254573248415] 
dist 48=[.29719773695119744141,1.1585913019317340056 ] 
dist 49=[.31845555866702833693,1.2293910436224009879 ] 
dist 50=[.21155052209839637585,.43979672338311348712] 
dist 51=[.02755177542714969102,.42525786457675210377] 
dist 52=[-.15940289887898200796,.35219413741551201539] 
dist 53=[-.27779240905560491915,.31244311683576560359] 
dist 54=[-.35329706540887640611,.08505526101624432302] 
dist 55=[-.37521040241224892436,.03567462222721581478] 
dist 56=[-.37003866802324458229,-.01780423753370935264] 
dist 57=[-.3412762823652594336 ,-.01324136325393354206] 
dist 58=[-.20535580654953291115,-.00061543565963393363] 
dist 59=[-.19882604655732343763,.02390741320073861518] 
dist 60=[-.15325466774820403176,.04969368018773669581] 
dist 61=[-.14277284694094499822,.06723052932760257095] 
dist 62=[-.01496777591597421186,.07979607665316533102] 
dist 63=[.00467320594849638368,.08783405083501593800] 
dist 64=[.04059124452772756909,.11623213289805735834] 
dist 65=[.04762469725558996871,.12400421977857572558] 
dist 66=[.04746837010799744327,.06585241113800973923] 
dist 67=[.02644340426258589417,.06294217316472046241] 
dist 68=[-.00595200632415729947,.03529668178581321053] 
dist 69=[-.02665230574190401663,.03366041208157125808] 
dist 70=[-.04012928400338990141,-.00363032798504821912] 
dist 71=[-.04471410828079598403,-.00954164124711421488] 
dist 72=[-.04462855637442574076,-.02146979149524780049] 
dist 73=[-.04307044762253970052,-.02326912021768050076] 
dist 74=[-.03469333416910894265,-.02374999366508442329] 
dist 75=[-.03110269250731986831,-.00618585492977040165] 
dist 76=[-.01859583721272389836,.01323585826415192321] 
dist 77=[-.01666153385577944907,.02539208979550823159] 
dist 78=[-.00271540657492754989,.03302121477572627369] 
dist 79=[3.76389524793411960890e-05,.03500128046247870731] 
dist 80=[.00479849824954904091,.01781676932131332473] 
dist 81=[.00567283293952973792,.01887916068627723458] 
dist 82=[.00559081336412038430,.00778224312546348232] 
dist 83=[.00272631383733151326,.00733555267083459580] 
dist 84=[-.00124288440418194013,.00416573568057506494] 
dist 85=[-.00375727937443220990,.00395550242537800690] 
dist 86=[-.00537191246746281001,-.00024307175108526509] 
dist 87=[-.00587506627121272436,-.00092374057086848398] 
dist 88=[-.00577083741948359781,-.00230495499555679929] 
dist 89=[-.00557301344739005552,-.00252287679391838239] 
dist 90=[-.00426926169727422514,-.00248734956196817211] 
dist 91=[-.00397235058249854226,-.00076363323292112082] 
dist 92=[-.00229898389720937644,.00124058806725735457] 
dist 93=[-.00214758598675904322,.00249671043541906197] 
dist 94=[-.00017513077573784447,.00328807566687174204] 
dist 95=[.00011643116349612943,.00350136253174028688] 
dist 96=[.00064097941353229113,.00172919147570318564] 
dist 97=[.00073420299242415561,.00184066020867821540] 
dist 98=[.00072013461028701948,.00098807426807706223] 
dist 99=[.00036036687020067140,.00093554553217869636] 
dist 100=[-.00014214947174458727,.00054845144589119380] 
dist 101=[-.00045930206620879174,.00051193182244204305] 
dist 102=[-.00066184143879956379,-2.35798549256195387900e-05] 
dist 103=[-.00072271238921837369,-.00011286341480599155] 
dist 104=[-.00070894180474197260,-.00028956029393660625] 
dist 105=[-.00068277411261680858,-.00031874152659479037] 
dist 106=[-.00053057481896613407,-.00031133186073143305] 
dist 107=[-.00048564050000224564,-8.76674415973486882410e-05] 
dist 108=[-.00031257739415213225,.00020356482946486031] 
dist 109=[-.00029272881098473519,.00038550611057204103] 
dist 110=[-3.84451619087879762050e-05,.00049956957463816238] 
dist 111=[3.06961067151079815690e-06,.00052916949277004030] 
dist 112=[7.38603881835816161850e-05,.00027131867269626242] 
dist 113=[8.60904460862824081650e-05,.00028731230556388892] 
dist 114=[8.39573108189427051110e-05,.00013449779680358780] 
dist 115=[2.95209719817059680760e-05,.00012210048993860508] 
dist 116=[-4.46336129344801815570e-05,9.80251738697730385720e-05] 
dist 117=[-9.10958652902100991090e-05,8.84126039990478028750e-05] 
dist 118=[-.00012039785743354889,3.64443284410035909360e-05] 
dist 119=[-.00012840741103862008,2.35293757827369605370e-05] 
dist 120=[-.00012569242732228854,6.60405773451294978410e-06] 
dist 121=[-.00011365239119415386,3.29892541974060242680e-06] 
dist 122=[-6.42684590668883379740e-05,4.10638038070450096680e-06] 
dist 123=[-6.01505860910226179440e-05,8.38358877664991693860e-06] 
dist 124=[-3.40185229437320563420e-05,2.29389343845941456520e-05] 
dist 125=[-3.16059594834316770980e-05,3.87703467917748924200e-05] 
dist 126=[-2.61097759859682552700e-06,4.87328904022046833990e-05] 
dist 127=[1.79907101107730050490e-06,5.14080878835122837760e-05] 
dist 128=[9.60182999741797336390e-06,2.66573588325975873570e-05] 
dist 129=[1.09193052234200351240e-05,2.83200903192586223970e-05] 
dist 130=[1.06298663043459080840e-05,1.46519405504583870240e-05] 
dist 131=[5.49600531635891301870e-06,1.39217617640838803380e-05] 
dist 132=[-1.95820567370536881130e-06,7.67599788227860175770e-06] 
dist 133=[-6.63894194560835114220e-06,7.28795110991986049210e-06] 
dist 134=[-9.60450477994849358710e-06,-1.04786719863718369220e-06] 
dist 135=[-1.04472188310974443770e-05,-2.35946148295820135500e-06] 
dist 136=[-1.02227423673370485800e-05,-5.02224238783496740880e-06] 
dist 137=[-9.80330360829962905660e-06,-5.42223772647571889140e-06] 
dist 138=[-7.76865816776025227700e-06,-5.28750300895876366570e-06] 
dist 139=[-6.93932091988127488460e-06,-1.27837962872265641210e-06] 
dist 140=[-4.07310390357874409790e-06,3.13852036603158597800e-06] 
dist 141=[-3.63932751296666828640e-06,5.89523685549282753450e-06] 
dist 142=[-5.40818979349676187960e-07,7.62249684136820519280e-06] 
dist 143=[6.89313442621234544060e-08,8.07050846273392470300e-06] 
dist 144=[1.10251246483943792650e-06,3.99503557818417506520e-06] 
dist 145=[1.27524747307052747300e-06,4.22953297158762503980e-06] 
dist 146=[1.23680132834351930140e-06,1.72232930677616946680e-06] 
dist 147=[5.72835571241130889050e-07,1.61689004013308202600e-06] 
dist 148=[-3.25290532326774752850e-07,9.04292948973480328980e-07] 
dist 149=[-8.87986306552517257060e-07,8.57024884178732879110e-07] 
dist 150=[-1.24315666246155688560e-06,-7.31423699421345288710e-08] 
dist 151=[-1.34123865325567304510e-06,-2.23370219072056346270e-07] 
dist 152=[-1.30274652654932574220e-06,-5.21577223042380619910e-07] 
dist 153=[-1.25344134398362594680e-06,-5.69203698242824691050e-07] 
dist 154=[-9.52250848774492692310e-07,-5.48782431530731278490e-07] 
dist 155=[-8.83978378684187988750e-07,-1.59133094646805624880e-07] 
dist 156=[-5.01918530659001875360e-07,2.92480936153759130190e-07] 
dist 157=[-4.68081809081207957380e-07,5.74491756378972319430e-07] 
dist 158=[-3.35717888274512432470e-08,7.51421895375618672220e-07] 
dist 159=[3.05254206981826568100e-08,7.97896672276905528610e-07] 
dist 160=[1.43834467184260513520e-07,3.84701267463967547090e-07] 
dist 161=[1.62403276620191648740e-07,4.08564744608030957390e-07] 
dist 162=[1.57458787805607249060e-07,2.13727154250467648330e-07] 
dist 163=[7.85438224590686015270e-08,2.02856373902589324450e-07] 
dist 164=[-3.09550827785671429990e-08,1.13788683018775005990e-07] 
dist 165=[-9.95081857975554197550e-08,1.07924216100627851640e-07] 
dist 166=[-1.42733194612868363260e-07,-1.58847028586032191060e-08] 
dist 167=[-1.54581438367134048670e-07,-3.52541026397306401750e-08] 
dist 168=[-1.50707379815574416160e-07,-7.47431494721960757370e-08] 
dist 169=[-1.44405094053708991660e-07,-8.06517361620817837930e-08] 
dist 170=[-1.13819500394687440180e-07,-7.79088000151399021560e-08] 
dist 171=[-1.01856642414798051580e-07,-1.82768440160487661620e-08] 
dist 172=[-6.05267020212777753600e-08,4.58363333588387134270e-08] 
dist 173=[-5.40726644468772319310e-08,8.58318693859512671850e-08] 
dist 174=[-7.94878387203712574900e-09,1.10884794769313618500e-07] 
dist 175=[1.09310582824363883240e-09,1.17382711359659671400e-07] 
dist 176=[1.63432398427577795060e-08,5.95165192664275565300e-08] 
dist 177=[1.88450597126303116970e-08,6.29957714961929654010e-08] 
dist 178=[1.82421437955659502980e-08,2.62882833428317638200e-08] 
dist 179=[8.25903692943181162770e-09,2.48236640866016999560e-08] 
dist 180=[-4.95136172079387638450e-09,1.42055353860751639590e-08] 
dist 181=[-1.33943870534024512220e-08,1.34488181561185892770e-08] 
dist 182=[-1.87055884189529246080e-08,-1.71064945912842022840e-09] 
dist 183=[-2.01348327957191487540e-08,-3.94772966004802403810e-09] 
dist 184=[-1.95119933472739569100e-08,-8.48523292593959266410e-09] 
dist 185=[-1.87630926364752046940e-08,-9.17187780798572656420e-09] 
dist 186=[-1.42100753909374839490e-08,-8.77285956761958317710e-09] 
dist 187=[-1.32046838082312438630e-08,-2.08460304822223082530e-09] 
dist 188=[-7.81478952369376891970e-09,4.61079885063512152590e-09] 
dist 189=[-6.88408741896862494650e-09,8.78898238147834663720e-09] 
dist 190=[-1.93683392121104435130e-09,1.14084115841038360770e-08] 
dist 191=[-8.63550000888937356460e-10,1.20934331031691615380e-08] 
dist 192=[7.40592054528338843160e-10,8.61761284943820631120e-09] 
dist 193=[1.01547995238368176110e-09,9.08000686867106604580e-09] 
dist 194=[9.55069257537147145350e-10,3.50907852681991913360e-09] 
dist 195=[6.95125083177764510480e-10,3.21973146256937094400e-09] 
dist 196=[-1.02192344012740278510e-09,1.84135042239791032670e-09] 
dist 197=[-2.21654319390256020890e-09,1.71370800355713982020e-09] 
dist 198=[-2.96722726189626468090e-09,1.52955359173536138240e-09] 
dist 199=[-3.16760812067865104530e-09,1.43098170534214316630e-09] 
dist 200=[-3.22357192557250120530e-09,1.36817184223032898070e-09] 
dist 201=[-3.35473479322327171240e-09,1.34957054259868861930e-09] 
dist 202=[-3.26231090540733695560e-09,1.32942776231149322700e-09] 
dist 203=[-3.11724579638937105680e-09,1.26062895500101091900e-09] 
dist 204=[-2.48027201512654814350e-09,1.15230812885000769600e-09] 
dist 205=[-2.18944387589383458190e-09,1.58897171084106311010e-09] 
dist 206=[-1.09302996827010349910e-09,2.08820688742131486990e-09] 
dist 207=[-1.58042393746783827480e-09,2.21922332838999380280e-09] 
dist 208=[-1.88528913077140291870e-09,2.59389536981629711750e-09] 
dist 209=[-1.96371102885568401850e-09,2.74059503589478506290e-09] 
dist 210=[-1.91558423052832404020e-09,2.66269917990877979450e-09] 
dist 211=[-1.82182804225030391750e-09,2.54477722466426597010e-09] 
dist 212=[-1.50327810986834291700e-09,2.01739443884012223960e-09] 
dist 213=[-1.60640358311271521350e-09,1.78638700305932952460e-09] 
dist 214=[-2.00657273028458133310e-09,9.15919433649803656290e-10] 
dist 215=[-2.11081152965548625210e-09,1.49181075295664346470e-09] 
dist 216=[-2.07815739328366911430e-09,1.85230030050662330660e-09] 
dist 217=[-2.19654740138218293840e-09,1.94558829041464342910e-09] 
dist 218=[-2.16831873457907427410e-09,1.91591907657730219720e-09] 
dist 219=[-2.05872337992615035400e-09,1.80565896917997645740e-09] 
dist 220=[-1.88355709799163209940e-09,1.62077690665735867680e-09] 
dist 221=[-1.75432952516919633500e-09,1.61723361173302486840e-09] 
dist 222=[-2.10247631789921586710e-09,2.21621911876234657440e-09] 
dist 223=[-2.41416359425897545730e-09,2.76881349096209893560e-09] 
dist 224=[-2.60931320039467052460e-09,3.11480985643029798460e-09] 
dist 225=[-2.65991095616303161810e-09,3.20452986192570314560e-09] 
dist 226=[-1.24766266489324885480e-09,8.54092629711227534210e-10] 
dist 227=[-1.65266330828720003620e-09,1.64120867798044700880e-09] 
dist 228=[-2.42304000885942828030e-09,2.42830147785966648290e-09] 
dist 229=[-2.90329340011825734280e-09,2.91892820008010960900e-09] 
dist 230=[-3.20401606206459008140e-09,3.22609776396925362670e-09] 
dist 231=[-3.28204658959989401710e-09,3.30569836129440007320e-09] 
dist 232=[-3.18994518143876573800e-09,3.24016962403507797090e-09] 
dist 233=[-3.04652297474313970040e-09,3.06833075921780324470e-09] 
dist 234=[-2.42789338210555524820e-09,2.62880736293588456630e-09] 
dist 235=[-2.13797833656133020490e-09,2.41257096656482863940e-09] 
dist 236=[-1.98245360632322000240e-09,1.29064551627975284670e-09] 
dist 237=[-3.04071924886058110260e-09,2.01597611229085871190e-09] 
dist 238=[-3.70331883958758148590e-09,2.56916046566781184140e-09] 
dist 239=[-3.87512161518384882170e-09,2.71261922889700070310e-09] 
dist 240=[-3.77466496757939390010e-09,2.64956225964047767660e-09] 
dist 241=[-3.59693101312362886180e-09,2.51791839844431408270e-09] 
dist 242=[-2.92267868059784838690e-09,2.09452391521164475280e-09] 
dist 243=[-2.59094538049545215260e-09,1.88620743250116905700e-09] 
dist 244=[-1.33906856165158264760e-09,1.59480255977012538510e-09] 
dist 245=[-2.14992592241670097060e-09,2.68946801937693805230e-09] 
dist 246=[-2.65762581710293609750e-09,3.37486286140869703570e-09] 
dist 247=[-2.78928022720909969200e-09,3.55258562749146207320e-09] 
dist 248=[-2.72437737024605842640e-09,3.45886144153000681810e-09] 
dist 249=[-2.58906170807973270450e-09,3.29756118797839430860e-09] 
dist 250=[-2.15334697053007404180e-09,2.66843844012915072700e-09] 
dist 251=[-1.93897135195489987900e-09,2.35890690928055226310e-09] 
dist 252=[-2.26302929845311625650e-09,2.19553237647866347240e-09] 
dist 253=[-2.78046472279743629590e-09,2.57037160155868554660e-09] 
dist 254=[-3.10444385377384586030e-09,2.80506789959561130730e-09] 

8 phat 5 dirichlet min maxes function [2, 1, 2, 0, 0, 0, 1, 0, 2] 
dist 0=[374.18049704751931620   ,374.18049704751931620   ] 
dist 1=[356.71483456005981811   ,386.10736851901749360   ] 
dist 2=[301.47722812585988964   ,393.09560820860956962   ] 
dist 3=[234.94660401093700982   ,386.74567462385826109   ] 
dist 4=[180.32214911242735694   ,305.96791554261827430   ] 
dist 5=[129.06038763819678851   ,285.15017191668861679   ] 
dist 6=[74.464758740020221903  ,206.50738835936599429   ] 
dist 7=[25.405406995509454307  ,194.94249995264487297   ] 
dist 8=[-23.911499236871169742  ,13.084491297832481390  ] 
dist 9=[-45.291391020618239717  ,-5.6125996550775907016 ] 
dist 10=[-74.966180112465007720  ,-2.8246832746306749380 ] 
dist 11=[-88.612319999779806181  ,3.7363714063941706305 ] 
dist 12=[-91.269344089988105636  ,8.6308808670969426685 ] 
dist 13=[-88.949740615639385639  ,11.223280374819971127  ] 
dist 14=[-72.896640938605137609  ,11.357394669616007759  ] 
dist 15=[-66.062320293280830454  ,14.169058466397104685  ] 
dist 16=[-13.512144630513012178  ,21.933706394017187147  ] 
dist 17=[-3.5385856730176332816 ,45.463572220324481936  ] 
dist 18=[-2.5673810915390209868 ,60.576672768228872104  ] 
dist 19=[2.1115609560738537092 ,64.499319351334112618  ] 
dist 20=[2.9412610663641526015 ,20.104202418718988957  ] 
dist 21=[-3.1238475234628391081 ,19.749131586888885996  ] 
dist 22=[-8.1573047753476698519 ,15.652405833455824540  ] 
dist 23=[-11.322992544321226472  ,14.852210690549731146  ] 
dist 24=[-13.087310461529651963  ,3.6862329904572446652 ] 
dist 25=[-13.170263897976956586  ,2.3372173860643713360 ] 
dist 26=[-11.711289828305900164  ,1.9064989045514594034 ] 
dist 27=[-10.697828040572758245  ,1.9282611786544273918 ] 
dist 28=[-10.573047226276436084  ,3.4929877680742657685 ] 
dist 29=[-10.262542085747461460  ,7.2790785074713269098 ] 
dist 30=[-7.9515676548404819878 ,9.6537155835829903687 ] 
dist 31=[-7.4211888818020810657 ,10.214585095653018884  ] 
dist 32=[-.86222820157884259339,3.1060921772422070589 ] 
dist 33=[.14568193341558888607,4.3916607306298355126 ] 
dist 34=[.14807968680796958312,5.8678931958188373309 ] 
dist 35=[.11534602182296465712,6.2626572825793840232 ] 
dist 36=[.06205013877771485898,2.4267907569314580558 ] 
dist 37=[-.72667489652072698142,2.3682694781948742560 ] 
dist 38=[-1.2940603928663958565 ,1.8228354431361024103 ] 
dist 39=[-1.5725982011323518272 ,1.7404138106120575724 ] 
dist 40=[-1.6745589997184831047 ,.02821944484885108129] 
dist 41=[-1.6480627979486898649 ,-.00762561607974271560] 
dist 42=[-1.3922855858668447869 ,.00370380480998033262] 
dist 43=[-1.2606997015914837127 ,.12149894591289911809] 
dist 44=[-1.2123876187472029913 ,.44882185559485247431] 
dist 45=[-1.1687810488921668989 ,.92082560142209715563] 
dist 46=[-.93887296881281980806,1.2185118256088316924 ] 
dist 47=[-.84191178186441663985,1.2959189196611572530 ] 
dist 48=[-.14229264390012608252,.4001006399964610731 ] 
dist 49=[-.00380075484277570250,.68333299159831509824] 
dist 50=[-.02828012585521067637,.88921156136954672988] 
dist 51=[-.09088330901612114900,.94263695397040817875] 
dist 52=[-.13163158913587793235,.28560537788398511864] 
dist 53=[-.15861971648483961939,.27668229714117904606] 
dist 54=[-.19832190691089657559,.21461982793262963993] 
dist 55=[-.22534049359758725946,.19943296679652197937] 
dist 56=[-.22814659418914443609,.07167107936309708957] 
dist 57=[-.22242161612369935503,.06314488194274128814] 
dist 58=[-.17432162900929769833,.05782901037551136368] 
dist 59=[-.16286622717311703503,.04421552268681726351] 
dist 60=[-.15386612349465551576,.04471528462831294837] 
dist 61=[-.14849957902749918087,.09553282035296229997] 
dist 62=[-.11357053682589837139,.12873335570780304667] 
dist 63=[-.10565794941795991504,.13710224065546495326] 
dist 64=[-.00982483338702272722,.05362445848377676826] 
dist 65=[.00482682794680491341,.06645314556478411545] 
dist 66=[.01259341569795747521,.08748621011295009402] 
dist 67=[-.00229624400692850025,.09312404314292855163] 
dist 68=[-.01188108693773879679,.03530729565839563679] 
dist 69=[-.01819018905506606259,.03422377045325919418] 
dist 70=[-.02441137773839386191,.02582826629209964056] 
dist 71=[-.02751822040252739824,.02457286591869935967] 
dist 72=[-.0277263002893130127 ,-.00309396479165733390] 
dist 73=[-.02683949854304667485,-.00745941170709048739] 
dist 74=[-.02177458245147352966,-.00295669716506069651] 
dist 75=[-.01955965307080559083,.00604373787103343055] 
dist 76=[-.01781444607915398627,.01168393481848791106] 
dist 77=[-.01710924552459756115,.01566845315094627463] 
dist 78=[-.01359736248198425736,.02041902861798712001] 
dist 79=[-.01216614783959394890,.02165351588406757627] 
dist 80=[-.00188494969007808015,.00656128809424945920] 
dist 81=[.00014015787637599964,.01016910803381643028] 
dist 82=[.00130088035523965319,.01317356076587114614] 
dist 83=[-.00054459460532954268,.01395307447483645519] 
dist 84=[-.00171893059651932649,.00421473848096112619] 
dist 85=[-.00266003407339642584,.00407279941361701683] 
dist 86=[-.00371131883976070796,.00307871056107569274] 
dist 87=[-.00405322163256789209,.00290169222979400664] 
dist 88=[-.00399723057714322174,-.00021118664233606546] 
dist 89=[-.00385981464870360646,-.00071046205356757384] 
dist 90=[-.00298847082794084933,-.00036510103558791084] 
dist 91=[-.00275647092115774524,.00057094640084385306] 
dist 92=[-.00229524820833969548,.00115847185615560844] 
dist 93=[-.00221129260668556786,.00193909797759325531] 
dist 94=[-.00167389311162022930,.00243561065766426285] 
dist 95=[-.00156279285269579154,.00257884080384087345] 
dist 96=[-.00011796684358930476,.00139955456792886785] 
dist 97=[9.49163211368493091810e-05,.00136489728128044161] 
dist 98=[.00017843449750068623,.00129761524939692945] 
dist 99=[-5.15975865883291012540e-05,.00134821369934376079] 
dist 100=[-.00019736959029595738,.00052512289403306425] 
dist 101=[-.00029106588861250767,.00050743391010047334] 
dist 102=[-.00032047760474882730,.00037962406214513500] 
dist 103=[-.00031679608295150135,.00036057181964103059] 
dist 104=[-.00030482542289453478,-5.13051321214703566260e-05] 
dist 105=[-.00024349277535450580,-.00011611581691839878] 
dist 106=[-.00024946214093198918,-4.18386285792107509540e-05] 
dist 107=[-.00027095649900209373,9.51698320659941538260e-05] 
dist 108=[-.00026478974460813659,.00018081196370043715] 
dist 109=[-.00025381781803532165,.00023452073900945730] 
dist 110=[-.00020091515379291878,.00024845971627071767] 
dist 111=[-.00017942702552043664,7.43268435365781954830e-05] 
dist 112=[-2.70230010314416929070e-05,8.13840270369839486960e-05] 
dist 113=[3.09860313938881200290e-06,.00015271451849846320] 
dist 114=[1.83661444291905814760e-05,.00019740187749452707] 
dist 115=[-9.82211271601828722600e-06,.00020899217082911735] 
dist 116=[-2.75869957277118226290e-05,6.10484497102272596920e-05] 
dist 117=[-3.89037139342668103880e-05,5.88639775295522024010e-05] 
dist 118=[-4.22431117636216391840e-05,4.44318377340932554690e-05] 
dist 119=[-4.12474662522104223500e-05,4.16950252474923191560e-05] 
dist 120=[-3.97837246275672353990e-05,-3.81231938569164533580e-06] 
dist 121=[-3.02045871143693351540e-05,-1.12173914968795194050e-05] 
dist 122=[-3.21597450468562622960e-05,-5.26906990166006624430e-06] 
dist 123=[-3.46624693561630294090e-05,8.61929588839000803770e-06] 
dist 124=[-3.36369693090871859190e-05,1.73113315343888494870e-05] 
dist 125=[-3.23571064811721326660e-05,2.27793323603660288520e-05] 
dist 126=[-2.45501753976725106280e-05,2.42410379803736308210e-05] 
dist 127=[-2.28010992953272331530e-05,9.47125707734562122810e-06] 
dist 128=[-1.80909079318832067210e-06,9.16845986838045563280e-06] 
dist 129=[1.37880884017176591640e-06,1.47687430154414861620e-05] 
dist 130=[2.60313282909698686920e-06,1.93181908689998643180e-05] 
dist 131=[-8.91372120024772782240e-07,2.05106021286745780990e-05] 
dist 132=[-3.08979872402651064650e-06,7.67763601536365292800e-06] 
dist 133=[-4.48679804467161523530e-06,7.40742022095184482760e-06] 
dist 134=[-4.89237469455480855400e-06,5.51803456366218965600e-06] 
dist 135=[-4.79721458168520196720e-06,5.23593902828132190320e-06] 
dist 136=[-4.60348579035752011330e-06,-7.82619028248235373660e-07] 
dist 137=[-3.65458501526190156990e-06,-1.72836498696350351780e-06] 
dist 138=[-3.67295428046296349160e-06,-6.05590026122926833460e-07] 
dist 139=[-3.97540896379422085680e-06,1.46862606553770275480e-06] 
dist 140=[-3.87345771524405777910e-06,2.76387418459858349640e-06] 
dist 141=[-3.70966567913336614330e-06,3.57557703189222622190e-06] 
dist 142=[-2.92760232576146873210e-06,3.78612880524149135470e-06] 
dist 143=[-2.61440146420868239570e-06,1.10955221556727004530e-06] 
dist 144=[-3.82227749341987233020e-07,1.19257178688521973110e-06] 
dist 145=[5.71663513271497784070e-08,2.23199072033944433810e-06] 
dist 146=[2.71284780131721879300e-07,2.88302001549957404100e-06] 
dist 147=[-1.50789294690276754450e-07,3.05186807462120832890e-06] 
dist 148=[-4.15656816259942552930e-07,9.01346559641432423500e-07] 
dist 149=[-5.83174787521728203820e-07,8.69079434623958028850e-07] 
dist 150=[-6.30127267913531099820e-07,6.50460615167258997630e-07] 
dist 151=[-6.12826480456048295400e-07,6.13146715591293555550e-07] 
dist 152=[-5.89875362199558752330e-07,-5.31121061359046351410e-08] 
dist 153=[-4.48605217939124629210e-07,-1.61251404298836672750e-07] 
dist 154=[-4.80035747953519307130e-07,-7.53374162901899384200e-08] 
dist 155=[-5.15935184233318768600e-07,1.37176474532526617370e-07] 
dist 156=[-4.99490076057184338940e-07,2.69938841553161229690e-07] 
dist 157=[-4.80458430136682362950e-07,3.53274142054086416970e-07] 
dist 158=[-3.62184674424110014780e-07,3.75233039932027508390e-07] 
dist 159=[-3.37961474060603605800e-07,1.41566706081321088930e-07] 
dist 160=[-2.34557949389173633120e-08,1.36650492173341791390e-07] 
dist 161=[2.23809189262410967440e-08,2.11379217410690632890e-07] 
dist 162=[3.51809594858097177640e-08,2.76739909597510753160e-07] 
dist 163=[-1.78739357420774841110e-08,2.93810021675978591370e-07] 
dist 164=[-5.11202421516151592530e-08,1.13712510454594325840e-07] 
dist 165=[-7.21141740362517171850e-08,1.09602080885105959880e-07] 
dist 166=[-7.79334360622293020700e-08,8.15425031807189374700e-08] 
dist 167=[-7.59544762541290599320e-08,7.72451145841102989450e-08] 
dist 168=[-7.28789672204720056720e-08,-1.14736451032198890650e-08] 
dist 169=[-5.69070827252347699190e-08,-2.54383942117141636780e-08] 
dist 170=[-5.51153427704655093080e-08,-6.45546448166984141710e-09] 
dist 171=[-5.95091911531638752210e-08,2.31022541156047208110e-08] 
dist 172=[-5.79078105074799300480e-08,4.19153587297782205070e-08] 
dist 173=[-5.54105466204962407450e-08,5.37010335469563327830e-08] 
dist 174=[-4.37991879878414657080e-08,5.67580364931142966070e-08] 
dist 175=[-3.89830457994065986270e-08,2.19141628254518793070e-08] 
dist 176=[-6.76535091707658769620e-09,2.10728672201251194100e-08] 
dist 177=[-3.78920476497679947820e-10,3.42588080651270232040e-08] 
dist 178=[2.99820923294160865950e-09,4.39512059304872641590e-08] 
dist 179=[-4.28985746855054068230e-09,4.64647087723716849490e-08] 
dist 180=[-9.72391362750579723080e-09,1.34068380140315400910e-08] 
dist 181=[-1.31408435665529890460e-08,1.28690302429713754550e-08] 
dist 182=[-1.40573232103567489470e-08,9.90942205173136687930e-09] 
dist 183=[-1.36233197881852247150e-08,9.06033585143362030740e-09] 
dist 184=[-1.30915185299788989420e-08,6.66964645770440281130e-10] 
dist 185=[-9.96035518116874555500e-09,-7.35290362866821123040e-10] 
dist 186=[-9.20981835618276708280e-09,-3.00704280375145415010e-11] 
dist 187=[-9.42232508382754190840e-09,4.03291353959819525800e-09] 
dist 188=[-9.13565257630842477900e-09,6.57143215506918241040e-09] 
dist 189=[-8.75996545503536088360e-09,8.16163210989553540770e-09] 
dist 190=[-6.76488853975137899660e-09,8.57463988323077109430e-09] 
dist 191=[-6.15462895389011168820e-09,2.77145504192564113180e-09] 
dist 192=[-8.95987513130729062840e-10,2.65812866808289997790e-09] 
dist 193=[2.52995735101409500070e-11,4.85335481913900412490e-09] 
dist 194=[4.23323822689665745990e-10,6.23840587876970520420e-09] 
dist 195=[-7.34823645096754658280e-10,6.59756715919820091740e-09] 
dist 196=[-1.45832206016491994730e-09,1.94339666366376165920e-09] 
dist 197=[-1.91290456095659647490e-09,1.85468510647171359330e-09] 
dist 198=[-2.03412724737532841210e-09,1.83387379494342994570e-09] 
dist 199=[-2.02955462937384192710e-09,2.30430054532413522040e-09] 
dist 200=[-3.04109482878284144040e-09,2.77425935396484049650e-09] 
dist 201=[-3.91230706900322661200e-09,3.06674309672562476110e-09] 
dist 202=[-4.45816756895865426050e-09,3.24938470159271071040e-09] 
dist 203=[-4.60048052280827044190e-09,3.29570259927362009420e-09] 
dist 204=[-4.44124533916655969730e-09,3.26565408353740527510e-09] 
dist 205=[-4.27128343151412869610e-09,3.58422188452725140160e-09] 
dist 206=[-3.19688032273411570390e-09,3.72322310590002278560e-09] 
dist 207=[-2.99780842451118745390e-09,3.64115248313932118780e-09] 
dist 208=[-3.09753662914880143230e-09,3.45728105809563926480e-09] 
dist 209=[-4.37634517317746949050e-09,2.89982718896310811850e-09] 
dist 210=[-5.17690019338591730750e-09,2.62533343163972723210e-09] 
dist 211=[-5.38420015308810013520e-09,2.20129592362664212440e-09] 
dist 212=[-5.24906872247918753720e-09,1.20823465694921747150e-09] 
dist 213=[-4.99729494488911199740e-09,1.15112592855757469950e-09] 
dist 214=[-4.09224345498638715920e-09,1.05971526430557695420e-09] 
dist 215=[-3.90725099062351350840e-09,9.86806799202069062200e-10] 
dist 216=[-3.68941889922413477730e-09,2.36185464450709788640e-09] 
dist 217=[-3.23740361022957304420e-09,3.91184972497863558790e-09] 
dist 218=[-3.01493444431514876910e-09,4.88228710441874212700e-09] 
dist 219=[-1.90162064088589016580e-09,5.13381406131941766710e-09] 
dist 220=[-1.79589462606225609670e-09,4.98310007850099521670e-09] 
dist 221=[-1.69417719734707728080e-09,4.76510635126161648510e-09] 
dist 222=[-1.50282388105313695630e-09,3.47482330258651905070e-09] 
dist 223=[-1.40108216093795814170e-09,2.06798349824471468770e-09] 
dist 224=[-1.62791051950245342040e-09,1.69838771520084075630e-09] 
dist 225=[-1.88614479865999801510e-09,2.10583367165230056890e-09] 
dist 226=[-2.04782925992572987120e-09,2.36094936613431710830e-09] 

8 phat 5 dirichlet min maxes function [0, 0, 1, 2, 2, 0, 0, 1, 2] 
dist 0=[388.63104227952635174   ,388.63104227952635174   ] 
dist 1=[370.65026941590203680   ,388.46340424332100738   ] 
dist 2=[329.93342414494620103   ,388.63104227952635174   ] 
dist 3=[252.08098956283022395   ,350.80070405662155764   ] 
dist 4=[168.13695988499308497   ,319.42080071373201480   ] 
dist 5=[103.33291689940242407   ,254.42102842274239319   ] 
dist 6=[46.189039411171292768  ,240.06141099693190329   ] 
dist 7=[-9.0384038607124532894 ,130.27474544920180312   ] 
dist 8=[-53.437375167166758278  ,50.697529909285022291  ] 
dist 9=[-68.885605377935678825  ,-7.8825906135087174275 ] 
dist 10=[-89.232760926179354940  ,-19.275643047440979982  ] 
dist 11=[-103.37502718498995295   ,-10.100554756032959638  ] 
dist 12=[-104.92649248749576951   ,7.6684107756693536234 ] 
dist 13=[-89.158124401288902332  ,23.994235576134472736  ] 
dist 14=[-85.973945430114318901  ,39.642200029185589417  ] 
dist 15=[-7.7032945384632228555 ,55.367971804747557667  ] 
dist 16=[5.2444331756291572876 ,66.567092181767662486  ] 
dist 17=[32.438133448026483427  ,68.219390517421924200  ] 
dist 18=[26.558729840735872367  ,59.877377657553427416  ] 
dist 19=[9.6906219940991236071 ,57.567586562388720753  ] 
dist 20=[-8.0085144281604927241 ,53.311605838171233560  ] 
dist 21=[-19.372490752550892897  ,44.853230532861705510  ] 
dist 22=[-31.930038398613075182  ,40.299412949097171404  ] 
dist 23=[-38.332678118605734737  ,14.496473127973560253  ] 
dist 24=[-40.701987271627266338  ,9.2938598316847092149 ] 
dist 25=[-40.692469868320672562  ,-.03667327989571088549] 
dist 26=[-42.955433816134712355  ,-2.3571258137833614454 ] 
dist 27=[-30.342385946873634885  ,-1.3561239723574546893 ] 
dist 28=[-14.598002158529383473  ,14.834196294551254845  ] 
dist 29=[-11.358433479730455784  ,25.153413582522317232  ] 
dist 30=[-8.1958331012824685718 ,32.115337239634060942  ] 
dist 31=[.22597487260635673664,33.754207484638685453  ] 
dist 32=[1.5835795011185127861 ,7.1044832628261192447 ] 
dist 33=[4.0517712164982337989 ,7.0873487056891445429 ] 
dist 34=[2.9865734954680416306 ,5.7518057566146522569 ] 
dist 35=[1.0391730338055040439 ,5.5511888555142893188 ] 
dist 36=[-.9635150064391589583 ,5.3757579005088735544 ] 
dist 37=[-2.2436904165167733866 ,4.3745567722361340190 ] 
dist 38=[-3.1191864934468050015 ,3.9597448440996497358 ] 
dist 39=[-3.5914536243662863309 ,.72064931478336988498] 
dist 40=[-3.7087985210560283197 ,.09751582374460168100] 
dist 41=[-3.8924340066006820046 ,-1.0261785045018450525 ] 
dist 42=[-4.1335256452643243908 ,-.91044175521661583374] 
dist 43=[-2.6957961105951873041 ,-.23694717277668440278] 
dist 44=[-1.3772492611569173479 ,1.0374164828095826535 ] 
dist 45=[-1.1507004629417409768 ,2.0649378172642017457 ] 
dist 46=[-1.0269927641323861753 ,2.7114947309806970058 ] 
dist 47=[-.32307068782632441185,2.8794707400799647375 ] 
dist 48=[-.16463381408711980965,1.2629026452732306626 ] 
dist 49=[.08990273935672622572,1.2014445626007808133 ] 
dist 50=[.13429577776838572322,.99341082947461121871] 
dist 51=[-.03614411102568467325,.86371823192170118207] 
dist 52=[-.21170816398885212837,.8361653960319057523 ] 
dist 53=[-.39537541028885951231,.62563374017006509778] 
dist 54=[-.51876641407853608917,.59393304926793560379] 
dist 55=[-.55082310153458199181,.14659550975714154643] 
dist 56=[-.49084143708672162001,.10021249019256930537] 
dist 57=[-.47648330619263684653,.02512669632106953531] 
dist 58=[-.45878835498930652935,.00332400049107533742] 
dist 59=[-.34472684772218973278,-.04871817798842750501] 
dist 60=[-.03942343021213207296,.10017875018300540367] 
dist 61=[.00769074966458854984,.20836391883944391772] 
dist 62=[.06585452011277774573,.27760191462506149268] 
dist 63=[.07273704985358172256,.29596738002220300983] 
dist 64=[.07635690560702675730,.11421638918641352795] 
dist 65=[.06552245749361853820,.11160477831358235081] 
dist 66=[.04620457154177982219,.08604611944213915561] 
dist 67=[.01365919682475101445,.08221320415295931890] 
dist 68=[-.01924962631719669752,.00756448423006904176] 
dist 69=[-.03997973961004298437,-.00145745246454892709] 
dist 70=[-.05325451638361463054,-.01820838818295391308] 
dist 71=[-.05863827371824499302,-.02157252152176158330] 
dist 72=[-.05847639220020832974,-.02187076639419973923] 
dist 73=[-.05642478987010346641,-.01928344250891868901] 
dist 74=[-.04539380796731527168,-.01457109667320779447] 
dist 75=[-.04071443819647828153,-.00655290633342088113] 
dist 76=[-.00691891276843594711,.01729415743272278649] 
dist 77=[-.00023534580955975285,.03316506387693278529] 
dist 78=[.00969621692285382871,.04312543165526043015] 
dist 79=[.01055089572304700407,.04571155560545319693] 
dist 80=[.01095260900083434122,.01375990783580701564] 
dist 81=[.00922969418908866974,.01338118663208644276] 
dist 82=[.00629523646955328070,.0102157166207532446 ] 
dist 83=[.00144774091992309842,.00970958301153391561] 
dist 84=[-.00343041725985364669,.00146268944479615054] 
dist 85=[-.00648400930065096718,.00019455325818905273] 
dist 86=[-.00840085439996524435,-.00199303917383163144] 
dist 87=[-.00889941686089623145,-.0024183258319857673 ] 
dist 88=[-.00778720732778879844,-.00239207774159153200] 
dist 89=[-.00751917335558355722,-.00200503893146886101] 
dist 90=[-.00574396120846275354,-.00133609379807546018] 
dist 91=[-.00535308060512732918,-.00022294877291720887] 
dist 92=[-.00067368990980070761,.00174218493675686601] 
dist 93=[-.00026981604536241277,.00336180281475364415] 
dist 94=[.00017401536437266766,.00438351513370362679] 
dist 95=[.00028188986732407130,.00466197368089492082] 
dist 96=[.00027191966518596347,.00216569752811653532] 
dist 97=[.00010159993785557101,.00207634419839250349] 
dist 98=[-.00019394491253627409,.00165728641022804358] 
dist 99=[-.00068678095875538371,.00146904137983281295] 
dist 100=[-.00118499681281111853,.00026890297885626429] 
dist 101=[-.00150144624641867895,2.28114919537793681720e-05] 
dist 102=[-.00170580506179846251,-.00029778095833458513] 
dist 103=[-.00177218337770532292,-.00034365600994441317] 
dist 104=[-.00089444577929640173,-.00033899147955441264] 
dist 105=[-.00085942979138338583,-.00029485173328032535] 
dist 106=[-.00068457796716237161,-.00021969961567906469] 
dist 107=[-.00061216527369906900,-9.54570156934016454470e-05] 
dist 108=[-9.68400015148984745370e-05,.00027186952769364226] 
dist 109=[5.21085853056135451140e-06,.00051385355883136994] 
dist 110=[.00015669319659260254,.00066554956810910952] 
dist 111=[.00016940703276630348,.00070490376492660467] 
dist 112=[.00016982830034010273,.00020696351300623926] 
dist 113=[.00014219583539118280,.00020012826670213326] 
dist 114=[9.65755136838599266300e-05,.00015225569125561428] 
dist 115=[2.22518520786242801680e-05,.00014310515090364150] 
dist 116=[-5.23205979004028402010e-05,1.86867687498179152910e-05] 
dist 117=[-9.89074694644385251820e-05,-9.57725215773802262990e-07] 
dist 118=[-.00012811304158389563,-3.46243266021908790840e-05] 
dist 119=[-.00013568988565579812,-4.05854030225009952910e-05] 
dist 120=[-.00011450812134390525,-3.97446743638512671140e-05] 
dist 121=[-.00011031024359171140,-3.42300224104035301080e-05] 
dist 122=[-8.39974301387224214140e-05,-2.50182496342057948210e-05] 
dist 123=[-7.80636219227466948700e-05,-9.92170448713376434910e-06] 
dist 124=[-6.64630660112933925120e-06,2.52446434800533668990e-05] 
dist 125=[4.22708674352989656600e-06,5.00278294931954130360e-05] 
dist 126=[1.67984675265787302680e-05,6.55979699147338859740e-05] 
dist 127=[1.83386785960974834530e-05,6.97233590684283928970e-05] 
dist 128=[1.79218932949677888020e-05,2.62318054151591670580e-05] 
dist 129=[1.50723514903742380620e-05,2.53633114662387775250e-05] 
dist 130=[1.03897488221270104550e-05,1.90084682574419842410e-05] 
dist 131=[2.77627830620864370570e-06,1.80579791184023388590e-05] 
dist 132=[-4.86105390753284004730e-06,1.28503679152677031350e-06] 
dist 133=[-9.63635813151497665420e-06,-8.09808963890064093580e-07] 
dist 134=[-1.26367759966922926160e-05,-4.53307871834733405700e-06] 
dist 135=[-1.35736077533677909050e-05,-5.17577302443880026660e-06] 
dist 136=[-1.32794556489276439670e-05,-5.05453668214122733720e-06] 
dist 137=[-1.27349482179243976350e-05,-4.36670206488322528590e-06] 
dist 138=[-1.00847770985605463440e-05,-3.22888951643258925740e-06] 
dist 139=[-9.01330438478200297180e-06,-1.37235210458557866860e-06] 
dist 140=[-1.35553438422474629950e-06,4.06018199057958655120e-06] 
dist 141=[1.52743788759723590730e-07,7.63053186060211452870e-06] 
dist 142=[2.37571584126758439030e-06,9.86771911635185887200e-06] 
dist 143=[2.56666854385561392660e-06,1.04480596135730154660e-05] 
dist 144=[2.51815270494262144210e-06,3.10069897777482457310e-06] 
dist 145=[2.10034933944266917000e-06,2.99429697459912054180e-06] 
dist 146=[1.42041349706271281860e-06,2.24233103691748768190e-06] 
dist 147=[3.19973720149996246410e-07,2.12364934640991408190e-06] 
dist 148=[-7.82583399876381925530e-07,2.62124257148864791720e-07] 
dist 149=[-1.47076495315734326520e-06,-2.85163947613242037670e-08] 
dist 150=[-1.90202014210978802160e-06,-5.22602582935456934150e-07] 
dist 151=[-2.01389193879602403120e-06,-6.06420670674830840450e-07] 
dist 152=[-1.71401340394154848020e-06,-5.89533997099965126960e-07] 
dist 153=[-1.64999770976473485630e-06,-5.04942785938241663990e-07] 
dist 154=[-1.24659456027729548190e-06,-3.66377171572572719990e-07] 
dist 155=[-1.16338055611924578270e-06,-1.41357989431739962690e-07] 
dist 156=[-8.38924406256925056840e-08,3.65343881468908185450e-07] 
dist 157=[7.48318981382187430530e-08,7.24541485939780254480e-07] 
dist 158=[2.47679812141663986210e-07,9.49932516584405422310e-07] 
dist 159=[2.70559323019183950410e-07,1.00921593651485159250e-06] 
dist 160=[2.61627371737728194820e-07,3.91710506452281744720e-07] 
dist 161=[2.19503364486530935050e-07,3.78072542698852611400e-07] 
dist 162=[1.51089462231450025780e-07,2.81925111373213626980e-07] 
dist 163=[4.04610485073454299790e-08,2.67580622342104280890e-07] 
dist 164=[-7.03753806925288986580e-08,1.62250283140357140320e-08] 
dist 165=[-1.39597394360248308430e-07,-1.43592593555382829680e-08] 
dist 166=[-1.87354739023984955510e-07,-6.86115554224635360530e-08] 
dist 167=[-2.02945544312686443500e-07,-7.76237170826604571070e-08] 
dist 168=[-1.97911123440848961990e-07,-7.53936338068173952520e-08] 
dist 169=[-1.89569641913081758420e-07,-6.48616632784584717040e-08] 
dist 170=[-1.49901279886971278870e-07,-4.76967942670062679260e-08] 
dist 171=[-1.33705272112676200740e-07,-1.98887476266825244420e-08] 
dist 172=[-2.08575873779397786470e-08,6.21318709779032969430e-08] 
dist 173=[1.56574120696387078630e-09,1.15544773739202800890e-07] 
dist 174=[3.55302093575143070520e-08,1.49001561290411121050e-07] 
dist 175=[3.83633424989038037820e-08,1.57678503888047264100e-07] 
dist 176=[3.71211491614215721700e-08,4.53282211477418163420e-08] 
dist 177=[3.08963510905134618460e-08,4.36706335309566369070e-08] 
dist 178=[2.08429864788221657950e-08,3.28891427297082384380e-08] 
dist 179=[4.63001628311989036220e-09,3.08471261858958047950e-08] 
dist 180=[-1.16016166940212850910e-08,3.75405819241012746300e-09] 
dist 181=[-2.17274831033238811760e-08,-5.25024166855125164970e-10] 
dist 182=[-2.80702686624331914960e-08,-7.76497166084011557960e-09] 
dist 183=[-2.97152700719486407350e-08,-8.96352493561140142510e-09] 
dist 184=[-2.50060018695721610450e-08,-8.67769137926793002210e-09] 
dist 185=[-2.40345963039564823310e-08,-7.40286721359027462380e-09] 
dist 186=[-1.82889093974293276070e-08,-5.33608741104364753030e-09] 
dist 187=[-1.69161404083420361230e-08,-1.99624932934027384910e-09] 
dist 188=[-1.64034489867127210560e-09,5.94048546062077864700e-09] 
dist 189=[7.12804003257294339800e-10,1.13908761537249833450e-08] 
dist 190=[3.55810924220474501690e-09,1.48075798554998588040e-08] 
dist 191=[3.88365473372134769750e-09,1.57003889279480782970e-08] 
dist 192=[3.69328486923032212630e-09,6.74206355399961138010e-09] 
dist 193=[2.90705796164015095220e-09,6.42899129614891141700e-09] 
dist 194=[1.64222792501166204360e-09,5.26887504413246462820e-09] 
dist 195=[-3.93715832958422474990e-10,4.69258317089876706520e-09] 
dist 196=[-2.95223341167230971780e-09,1.79936834442580694330e-09] 
dist 197=[-4.93648070861488213530e-09,1.35596542178572708920e-09] 
dist 198=[-6.18233838354505611720e-09,9.00850459969074499410e-10] 
dist 199=[-6.51274623294675609000e-09,8.11080626016648064670e-10] 
dist 200=[-6.30880393551582779380e-09,-3.38093589470135729050e-11] 
dist 201=[-6.05580808091325591510e-09,6.88419980698376237400e-11] 
dist 202=[-4.63418924771517147420e-09,3.15811037850668557520e-10] 
dist 203=[-4.25570118777808123340e-09,9.68934363701138900530e-10] 
dist 204=[-1.54992289529049606050e-09,1.62288847721160924460e-09] 
dist 205=[-1.77610490955591617210e-09,2.91842066797248304960e-09] 
dist 206=[-1.91674753100224926570e-09,3.90645469844715135650e-09] 
dist 207=[-1.95119265251308652320e-09,4.16464701760836465980e-09] 
dist 208=[-1.90250176726017734620e-09,4.05563496959295806900e-09] 
dist 209=[-1.80817622325709264050e-09,3.86858773081550778000e-09] 
dist 210=[-1.49580248441561322190e-09,3.12258540267039457400e-09] 
dist 211=[-1.34261330126290839240e-09,2.75505799106527323070e-09] 
dist 212=[-1.61053107322816505060e-09,1.06610590959466389460e-09] 
dist 213=[-2.76755038854779362600e-09,1.64737369809048885830e-09] 
dist 214=[-3.49227492636793469050e-09,2.01111814448347384530e-09] 
dist 215=[-3.68080119834568498150e-09,2.10501975391522210560e-09] 
dist 216=[-3.56419770441103896270e-09,2.04306067722883221620e-09] 
dist 217=[-3.41743319375864956000e-09,1.95329889501265836720e-09] 
dist 218=[-2.63039723035984714840e-09,1.54038055017574806550e-09] 
dist 219=[-2.39867485440105661080e-09,1.37036602112999597500e-09] 
dist 220=[-1.58290979291226551760e-09,1.68380708036442427940e-09] 
dist 221=[-1.80221175986761958100e-09,2.11825091886424050210e-09] 
dist 222=[-1.93949665331379913250e-09,2.39028225010965735370e-09] 
dist 223=[-1.97505828863491465510e-09,2.46083515262696162370e-09] 
dist 224=[-1.59959306219468316930e-09,1.93260262199133983000e-09] 
dist 225=[-1.52244583695229590100e-09,1.84810668350633930800e-09] 
dist 226=[-1.24962536646695727420e-09,1.46546314999427751010e-09] 
dist 227=[-1.11542271846950002610e-09,1.29702257042103968260e-09] 
dist 228=[-1.17601497121601658760e-09,1.17137129911647050560e-09] 
dist 229=[-1.41603129033276118690e-09,1.40112237277466572540e-09] 
dist 230=[-1.56631648522637687610e-09,1.54496385734577758170e-09] 

8 phat 5 dirichlet min maxes function [1, 2, 0, 0, 0, 2, 2, 0, 2] 
dist 0=[387.44578473706748801   ,387.44578473706748801   ] 
dist 1=[366.73870687848136168   ,388.90205527517602960   ] 
dist 2=[322.34151897128967320   ,387.44578473706748801   ] 
dist 3=[241.29669159475451878   ,352.78006600392718845   ] 
dist 4=[154.99058989364337151   ,331.71579286330412408   ] 
dist 5=[89.785711391913185236  ,259.02126614155573147   ] 
dist 6=[33.661924531551851629  ,174.36391979461843024   ] 
dist 7=[-18.344295937318892272  ,119.51781461921536016   ] 
dist 8=[-59.154787160824978152  ,108.11830837376708499   ] 
dist 9=[-84.315277760875919823  ,-1.6101735653336243603 ] 
dist 10=[-102.43170952016028481   ,-28.525432104191082619  ] 
dist 11=[-105.19833692462788175   ,-32.453651719955778643  ] 
dist 12=[-91.488336550435920633  ,-15.666303536898198027  ] 
dist 13=[-88.551999820671588902  ,6.4514606436375746162 ] 
dist 14=[-9.9398993717473749432 ,25.548495898450634496  ] 
dist 15=[3.1754710431011033721 ,43.098726021817889932  ] 
dist 16=[30.754655805531519090  ,59.796514469869407240  ] 
dist 17=[35.363485862231279781  ,71.384469389380123885  ] 
dist 18=[27.119886495859105079  ,73.031136998291435698  ] 
dist 19=[9.6178277739899350727 ,63.837875664485260383  ] 
dist 20=[-8.6604934907947691926 ,61.367552765679067485  ] 
dist 21=[-20.363415004774032113  ,41.517828237460917335  ] 
dist 22=[-27.801702345416203052  ,15.449591180660086386  ] 
dist 23=[-33.997684010282768540  ,10.171609994144625297  ] 
dist 24=[-41.495951705364616160  ,.60268509504572569828] 
dist 25=[-43.814811381846851316  ,-1.7734204391000240753 ] 
dist 26=[-42.367862533533681463  ,-3.8709242498760119782 ] 
dist 27=[-35.994510281292100878  ,-1.1995461788472574792 ] 
dist 28=[-32.150313614859150086  ,4.2638020905124643916 ] 
dist 29=[-14.411855666194372004  ,15.518480742902474683  ] 
dist 30=[-3.8384181458342798513 ,26.508666352381901616  ] 
dist 31=[1.5745515839152783030 ,33.984664179345245981  ] 
dist 32=[4.3471075754780984034 ,35.696727378023406995  ] 
dist 33=[4.1290832733169600687 ,7.6066990968945517162 ] 
dist 34=[3.0272065079471950583 ,7.5799671809939061316 ] 
dist 35=[1.0346434080182260833 ,6.1371904162243586445 ] 
dist 36=[-1.0100171299813797664 ,5.9190188879122176526 ] 
dist 37=[-2.3145105782170681200 ,4.0411708645379273404 ] 
dist 38=[-3.1994733666457264875 ,.80346623370244153933] 
dist 39=[-3.4113104593405759065 ,.15791972003358807721] 
dist 40=[-4.0723260595331717397 ,-1.0058820741334661564 ] 
dist 41=[-4.3239744934713481556 ,-1.2481169647191783860 ] 
dist 42=[-3.8685376745081255829 ,-.97595122287119673425] 
dist 43=[-3.1939786213446442327 ,-.4774317210588446289 ] 
dist 44=[-2.8781913587247151675 ,.03794976327069800494] 
dist 45=[-.95897690340140592086,1.1210045768190137191 ] 
dist 46=[-.1276535906588683026 ,2.2178459429395868434 ] 
dist 47=[.13145210467145673939,2.9079835521961693524 ] 
dist 48=[.45638634880454523497,3.0874148944967413860 ] 
dist 49=[.51105262568004190626,.92797661273039593359] 
dist 50=[.42303293723673613607,.91174478654282857588] 
dist 51=[.11257335134637017665,.75194830595099843284] 
dist 52=[-.20181692933572176406,.68520170867495572648] 
dist 53=[-.39939051839236894148,.5413747135903296328 ] 
dist 54=[-.52367736683234267093,.13784478869726265909] 
dist 55=[-.55598297091145349759,.07845671063757389761] 
dist 56=[-.59186626834496354992,-.02040634693055749924] 
dist 57=[-.58949661639632677599,-.04640436176914174827] 
dist 58=[-.57024989818524767315,-.04862337486140093936] 
dist 59=[-.44830912633442991595,-.01276847901321134554] 
dist 60=[-.41040474160943870151,.05164013620676847639] 
dist 61=[-.14370466409233363376,.18913098065365432882] 
dist 62=[.00558894519531501253,.30518880416752090234] 
dist 63=[.03264930348780748169,.38076391186579257612] 
dist 64=[.07465067142288950568,.4019708837662616313 ] 
dist 65=[.06528558259017567443,.11910053579386277838] 
dist 66=[.04608607466990000831,.11635560952153768447] 
dist 67=[.01380951837206122064,.08965140878089528138] 
dist 68=[-.01881408859584299041,.08565980182918948188] 
dist 69=[-.03936227767136860788,.05902106278496292834] 
dist 70=[-.05248669202759802252,.00995035664309598813] 
dist 71=[-.05602142961821407050,.00021534685643975947] 
dist 72=[-.06289784446897985409,-.01669873713461463753] 
dist 73=[-.06666043600615751182,-.01965685065312695062] 
dist 74=[-.05872712371279156479,-.01482750211748330934] 
dist 75=[-.04726620997094045240,-.00664184304368839138] 
dist 76=[-.04236371146261841238,.00166444025455222733] 
dist 77=[-.01387909412796078702,.01810797107637747597] 
dist 78=[-.00027631948616943340,.03467803846561618448] 
dist 79=[.00326952696825178692,.04507641189762621197] 
dist 80=[.00818530602202142360,.04777528262021494859] 
dist 81=[.00896093550993150759,.01414374200407504715] 
dist 82=[.00640977168603179981,.01374075621993364168] 
dist 83=[.00145814412817496805,.01059197569873180756] 
dist 84=[-.00352279914647574717,.00997588830186453529] 
dist 85=[-.00663986960941112370,.00751375010449659613] 
dist 86=[-.00859619373238458456,.00069692149967404573] 
dist 87=[-.00910480864834634396,-.00034472445205443980] 
dist 88=[-.00814595998637448815,-.00221610361372480054] 
dist 89=[-.00799705667080197606,-.00203248603426617313] 
dist 90=[-.00771846777317713089,-.00135387504145620326] 
dist 91=[-.00592447170631202627,-.00022684151578003475] 
dist 92=[-.00549673325608981898,.00091053048454963039] 
dist 93=[-.00175150574807205013,.00186516906144130321] 
dist 94=[-1.00173225530663734200e-05,.00357743632157245544] 
dist 95=[.00029568566463847742,.00465687104543832346] 
dist 96=[.00028308367451893146,.00494950933807325214] 
dist 97=[.00010557938706760757,.00209650255323049169] 
dist 98=[-.00020091114413424673,.00174593211758002782] 
dist 99=[-.00071089160097199557,.00148279267674317572] 
dist 100=[-.00122615389957085193,.00125679322165167253] 
dist 101=[-.00155316994737741324,.00087144503459621082] 
dist 102=[-.00176410274641310606,.00013542644240097213] 
dist 103=[-.00183211942932383203,-9.66619182923767917790e-06] 
dist 104=[-.00094512961521538040,-.00025799382128851505] 
dist 105=[-.00100101876996275715,-.00024048846104512577] 
dist 106=[-.00089007711534034747,-.00016434572329757046] 
dist 107=[-.00071108294562136895,-3.87004369533621088940e-05] 
dist 108=[-.00063382423688926202,8.79094702846426051960e-05] 
dist 109=[-.00020598083853168384,.00029865093309848155] 
dist 110=[-2.22952610133527419200e-05,.00054730524060307858] 
dist 111=[5.09790498669023413640e-05,.00070324886790706680] 
dist 112=[5.85937019079733918400e-05,.00074385841702364111] 
dist 113=[3.19102324678151009170e-05,.00022024917579929394] 
dist 114=[-1.27533088814810072760e-05,.00019445171618755916] 
dist 115=[-8.60180067108762424280e-05,.00016717227822001656] 
dist 116=[-.00015972384581191803,.00014548090957892653] 
dist 117=[-.00020610158334009958,.00011238969178214338] 
dist 118=[-.00023557644608361812,1.52237819880595549570e-05] 
dist 119=[-.00024413717465121404,9.12641042874873678260e-06] 
dist 120=[-.00010818276939076767,1.07225953367802431160e-05] 
dist 121=[-.00010660450133198978,1.88564196403108598300e-05] 
dist 122=[-.00010197040565501182,3.21953055320094342270e-05] 
dist 123=[-8.37024686265228972410e-05,5.38606009003261554470e-05] 
dist 124=[-7.44464499157243837430e-05,7.55850855756482463660e-05] 
dist 125=[-2.76536170617718714770e-05,8.91539133970951049900e-05] 
dist 126=[-1.72885628869456944770e-05,9.76619379151979670180e-05] 
dist 127=[-2.98323876396041481140e-06,9.98776494088077707180e-05] 
dist 128=[0                     ,9.74651267647861056480e-05] 
dist 129=[1.49556978917058816760e-05,2.16041388259193438090e-05] 
dist 130=[1.03301745054681404090e-05,1.90862504142767243390e-05] 
dist 131=[2.81309344064231970860e-06,1.82978429818251188840e-05] 
dist 132=[-4.72686694367069100700e-06,1.44900498817122238990e-05] 
dist 133=[-9.44128139020811225840e-06,1.29405027688270784110e-05] 
dist 134=[-1.24037370757647705180e-05,1.95481775062852892520e-06] 
dist 135=[-1.31901141364187011580e-05,-2.17144160598558143010e-07] 
dist 136=[-1.42383881167311300490e-05,-3.90164501473751845690e-06] 
dist 137=[-1.50744039499544082290e-05,-4.43609471019585267850e-06] 
dist 138=[-4.40315290114371638910e-06,-3.27919598139260404640e-06] 
dist 139=[-4.24636260787596815440e-06,-1.39352675194072078130e-06] 
dist 140=[-3.20681878374327163450e-06,5.00501516424584013150e-07] 
dist 141=[-3.00953202407925395600e-06,1.68953067952231231430e-06] 
dist 142=[2.73617397484718107040e-07,2.44252070574502722450e-06] 
dist 143=[8.07891185613918651750e-07,2.65576677896289807350e-06] 
dist 144=[1.87408497085785957040e-06,2.59786729431106579870e-06] 
dist 145=[2.04371701079084852320e-06,2.50244211168237125440e-06] 
dist 146=[1.44416376313385006100e-06,2.42914543457367675750e-06] 
dist 147=[3.23810752922039159560e-07,2.33694008000434329390e-06] 
dist 148=[-7.98589698124849631060e-07,1.77359398624282509340e-06] 
dist 149=[-1.49909751882468362250e-06,1.64724397680860989020e-06] 
dist 150=[-1.93799957803713936610e-06,1.31477191391019407820e-07] 
dist 151=[-2.05183960009451793140e-06,-9.87297565693456449850e-08] 
dist 152=[-1.39567595812941650980e-06,-5.04188404864856996320e-07] 
dist 153=[-1.48191332065797686960e-06,-5.12411104450203514730e-07] 
dist 154=[-5.54649106772131507530e-07,-3.72331128762846108680e-07] 
dist 155=[-5.35217263831012580560e-07,-1.44992478892221616900e-07] 
dist 156=[-3.98857882544232112490e-07,8.30896154127559070520e-08] 
dist 157=[-3.78510553915661143570e-07,2.26014134435716875280e-07] 
dist 158=[5.61226822090977977100e-08,3.16201893357881059320e-07] 
dist 159=[1.24411600567903821460e-07,3.41053547676604097740e-07] 
dist 160=[2.63280976761868777910e-07,3.31183609778859679290e-07] 
dist 161=[2.25285649938600536530e-07,3.18648620499046403750e-07] 
dist 162=[1.54579979244365538830e-07,2.80276290490811079120e-07] 
dist 163=[4.03123574333577156420e-08,2.68443987936362392510e-07] 
dist 164=[-7.41531243490501076310e-08,2.11964450189879288590e-07] 
dist 165=[-1.45627495855195105460e-07,1.89247259280680177790e-07] 
dist 166=[-1.90466944290500457250e-07,2.83138363957588393430e-08] 
dist 167=[-2.02240478320917799290e-07,-3.37849780967863903770e-09] 
dist 168=[-2.08986412850067811600e-07,-5.68182845713921841820e-08] 
dist 169=[-2.21199780877094920820e-07,-6.47136596678544926760e-08] 
dist 170=[-6.56664848591222379420e-08,-4.75911686637427331180e-08] 
dist 171=[-6.33237072595182723370e-08,-1.98643458184488037070e-08] 
dist 172=[-4.71439663450177939640e-08,7.93428341338512573780e-09] 
dist 173=[-4.46920429091880082580e-08,2.53745105442764987240e-08] 
dist 174=[9.16359903828264139670e-10,3.63806998952991040330e-08] 
dist 175=[8.50286598627392469810e-09,3.93911551052084496280e-08] 
dist 176=[2.29328479466942598390e-08,3.83947747059271798370e-08] 
dist 177=[2.52442853725148793700e-08,4.06206566058492881330e-08] 
dist 178=[2.07139646526847707530e-08,3.93781052181363832900e-08] 
dist 179=[4.39426367465701436770e-09,3.78264359795174305820e-08] 
dist 180=[-1.19431531401517420270e-08,2.88670993290818669660e-08] 
dist 181=[-2.21345130113156389460e-08,2.66047251742283774100e-08] 
dist 182=[-2.85180716270790084190e-08,6.82141625505111067550e-09] 
dist 183=[-3.01733997786495785320e-08,4.20859535779526894490e-09] 
dist 184=[-2.40935196530715456110e-08,6.75406437781666863980e-10] 
dist 185=[-2.53319218551748793700e-08,0                     ] 
dist 186=[-9.66820489406239101280e-09,-5.21062938101249723510e-09] 
dist 187=[-9.23616778794465033850e-09,-8.45453162394680136730e-10] 
dist 188=[-7.41998060010049125630e-09,3.54749062084935797830e-09] 
dist 189=[-6.52035694888537904790e-09,6.28928552120545921340e-09] 
dist 190=[-1.56327264445342575390e-09,8.00865227498425993790e-09] 
dist 191=[-4.92704341794064589900e-10,8.45925232583654547400e-09] 
dist 192=[1.18328084576584553840e-09,8.29664125143229650520e-09] 
dist 193=[1.08559064865596058220e-09,7.65150723096872689430e-09] 
dist 194=[3.94673656755467554840e-10,4.05914841256271059900e-09] 
dist 195=[-7.20467393189668631100e-10,3.73747819677394251120e-09] 
dist 196=[-1.83730106311480482750e-09,1.52644076474452199540e-09] 
dist 197=[-2.74196503895088478800e-09,9.73133252699838712030e-10] 
dist 198=[-3.40707267322275220760e-09,9.59914328422549584340e-11] 

8 phat 5 dirichlet min maxes function [2, 0, 0, 1, 1, 2, 0, 2] 
dist 0=[374.29282360854480045   ,374.29282360854480045   ] 
dist 1=[352.70931120918168364   ,378.64730313771454266   ] 
dist 2=[302.92903724521014808   ,374.29282360854480045   ] 
dist 3=[246.19691903761063781   ,345.27805613266769394   ] 
dist 4=[197.13277004682844903   ,293.05034530064303725   ] 
dist 5=[148.36537688746253630   ,225.91751991212588493   ] 
dist 6=[91.861130354438264153  ,213.15366219580344689   ] 
dist 7=[31.552827207024383740  ,123.00028897210307404   ] 
dist 8=[-22.893137447980830251  ,78.783582376543619003  ] 
dist 9=[-61.191934439863961309  ,2.6180367648501386340 ] 
dist 10=[-82.650680087633803414  ,3.0923986454016350082 ] 
dist 11=[-92.716835122582685030  ,8.9521603953270651966 ] 
dist 12=[-93.323478956644467975  ,17.362034652792081274  ] 
dist 13=[-78.430670459557550138  ,27.346434123315752407  ] 
dist 14=[-74.912565348423090985  ,39.840923640787313222  ] 
dist 15=[-5.1929329712578056827 ,49.591142303736123322  ] 
dist 16=[6.2530787399399239623 ,51.244640462685697440  ] 
dist 17=[30.180380156743121150  ,45.850793782969217074  ] 
dist 18=[20.140193587152826587  ,45.499252179202381222  ] 
dist 19=[-.4137728703274064932 ,47.510958022506061156  ] 
dist 20=[-14.468984681622799008  ,46.439107987768957238  ] 
dist 21=[-24.496346419547826267  ,38.796717859829905017  ] 
dist 22=[-29.651130019987391372  ,34.844592562153646081  ] 
dist 23=[-31.703485304192062697  ,11.829686477849817508  ] 
dist 24=[-31.159661108455985032  ,7.2039217208575863890 ] 
dist 25=[-35.312444643277427560  ,-1.0834992936514667628 ] 
dist 26=[-37.279239627483404438  ,-.53837467192049066532] 
dist 27=[-12.190926481038000076  ,11.961307152750672073  ] 
dist 28=[-9.7939968251584097071 ,19.939473574402483860  ] 
dist 29=[-7.4607534845563599673 ,25.313445014011157410  ] 
dist 30=[-7.1568777896447056333 ,26.601019218859348139  ] 
dist 31=[.26480793506565433209,5.3565681215625021265 ] 
dist 32=[1.4578152303610853222 ,5.6771484387966301022 ] 
dist 33=[3.8764496837096003391 ,6.0037020308985874044 ] 
dist 34=[1.9754931527084203002 ,5.9298052038648073129 ] 
dist 35=[-.05291043909551641237,4.8594541624581763095 ] 
dist 36=[-1.3953796254871092560 ,4.7175859376970758278 ] 
dist 37=[-2.3145103721177860745 ,3.8165747592546741045 ] 
dist 38=[-2.7177424197209201643 ,3.4572256675684741978 ] 
dist 39=[-3.3423337860420352884 ,.59204698852390960595] 
dist 40=[-3.5665756909911026047 ,.04587920981938046308] 
dist 41=[-3.3890818181408730821 ,-.93698678444824285882] 
dist 42=[-3.5987733448333845537 ,-.46313581951280324329] 
dist 43=[-1.3282041676528778708 ,.785085517878407704  ] 
dist 44=[-1.2339090706281056662 ,1.5706419638023603640 ] 
dist 45=[-1.0415991932075612753 ,2.0651884264241529560 ] 
dist 46=[-.93803300850880066716,2.1936963078456365192 ] 
dist 47=[-.35896338479844464443,1.1380766471325748146 ] 
dist 48=[-.21983734592760754431,1.2406286607935572140 ] 
dist 49=[-.01634624592304451355,1.2395206907500542785 ] 
dist 50=[.03239814748724966466,1.1366489649859886954 ] 
dist 51=[-.05923310039274779500,.71073924618272015716] 
dist 52=[-.22578666623015679803,.68581866783405014146] 
dist 53=[-.33576319945897230195,.52435147448022836623] 
dist 54=[-.4240202101200204462 ,.48595160514061034918] 
dist 55=[-.55657653377298152568,.01368581950337874906] 
dist 56=[-.59101568648999392094,-.03953320249378249064] 
dist 57=[-.4375151452632917758 ,-.14482252051659657783] 
dist 58=[-.43060226389313775359,-.05567855065307019109] 
dist 59=[-.16587348875602308567,.07632103624832348679] 
dist 60=[-.16159629951098471016,.15953620458678935198] 
dist 61=[-.12359625530091930015,.21302763565899716422] 
dist 62=[-.11792269965029358728,.22706606211289821141] 
dist 63=[.01243948445843772382,.09051584623415698506] 
dist 64=[.03311176528449305229,.10111255150409281389] 
dist 65=[.05886931339748746279,.10102745826995710519] 
dist 66=[.02675783519637920055,.09809044683811671698] 
dist 67=[-.00589553992006062660,.08419377749817319860] 
dist 68=[-.02678880140894606079,.0810940895992407648 ] 
dist 69=[-.04041843759289634485,.06498678919418279571] 
dist 70=[-.04510807073341800176,.05820301087275469385] 
dist 71=[-.05719014727392470942,.00963630380572921094] 
dist 72=[-.06096444802497178588,8.64671233877782251830e-06] 
dist 73=[-.06233857799034779701,-.01664998147951083065] 
dist 74=[-.06605647597428213994,-.00629178171456958204] 
dist 75=[-.01952177200364187034,.01328151852493575363] 
dist 76=[-.01892879400843012089,.02553573840708658694] 
dist 77=[-.01450790012269324478,.03322771472219712786] 
dist 78=[-.01365797351685205137,.03522492893875771820] 
dist 79=[.00091552766356155757,.01085846206014849723] 
dist 80=[.00328981068131411381,.01209754522654382330] 
dist 81=[.00673538097825953432,.01207406202045681976] 
dist 82=[.00273923913052095142,.01165350664904956591] 
dist 83=[-.00130124739025915116,.01080233577406286212] 
dist 84=[-.00386249494407286522,.01042021080132530067] 
dist 85=[-.00550875863412317447,.00796034264962264680] 
dist 86=[-.00684729652276203778,.00740293820358511485] 
dist 87=[-.00890605234062632316,.00067074393939344063] 
dist 88=[-.00944057993727648553,-.00035688847058453916] 
dist 89=[-.00616601871055088778,-.00219691382154615190] 
dist 90=[-.00656046478832933231,-.00078628993455605410] 
dist 91=[-.00248569160909930873,.00121119724335197688] 
dist 92=[-.00240755107361961757,.00246384163057644221] 
dist 93=[-.00181590954134062873,.00325369740109441658] 
dist 94=[-.00172477242280880706,.00346792395709905419] 
dist 95=[.00021573558579318475,.00147690841027571475] 
dist 96=[.00052229830745218935,.00161394793232147254] 
dist 97=[.00088568684874350952,.00158420496470475087] 
dist 98=[.00038576791426478425,.00153056727205305115] 
dist 99=[-.00011844793879556102,.00127116541606564835] 
dist 100=[-.00043707066159721557,.00122112497729911702] 
dist 101=[-.00064097208834271835,.00096340049044301518] 
dist 102=[-.00070314869578399387,.00086691939871236595] 
dist 103=[-.00087150943624061272,.00013450720570242267] 
dist 104=[-.00092874392501680414,-7.97690864333065861150e-06] 
dist 105=[-.00093358943458747466,-.00025078936934364320] 
dist 106=[-.00098860029317096344,-8.99377465367286924530e-05] 
dist 107=[-.00033545416721667711,.00021031003228031258] 
dist 108=[-.00032040645408812041,.00039789938306412535] 
dist 109=[-.00026364352791708334,.00051550690353058228] 
dist 110=[-.00023503707361552350,.00054601866082864652] 
dist 111=[-7.81831814705598566540e-05,.00030183724689904357] 
dist 112=[-4.19237910685934325750e-05,.00032121222901325273] 
dist 113=[1.07377476746039983980e-05,.00031540076615768767] 
dist 114=[2.06992296811456742040e-05,.00028801997074130651] 
dist 115=[-2.10745985343734523350e-05,.00017724429817719737] 
dist 116=[-5.95408982951162178730e-05,.00017045570814355722] 
dist 117=[-8.39808210720246648500e-05,.00013058342997791194] 
dist 118=[-.00010653448711209147,.00012031218880930915] 
dist 119=[-.00013800159103590739,3.18458759896748618400e-05] 
dist 120=[-.00014616521099493018,2.00020841606224829510e-05] 
dist 121=[-.00011478005341835993,3.53761975564150631720e-06] 
dist 122=[-.00011446681134832191,0                     ] 
dist 123=[-3.16075829709290393950e-05,1.95486824914887007670e-05] 
dist 124=[-2.97114891057390954860e-05,3.87821702348910011480e-05] 
dist 125=[2.32922370448930571610e-06,5.08686324641666777360e-05] 
dist 126=[7.54737785912299308640e-06,5.40758179196017971830e-05] 
dist 127=[1.80903777757834296570e-05,2.24845104081742207580e-05] 
dist 128=[1.75872215905246859190e-05,2.43729631967018720580e-05] 
dist 129=[1.30077419048692736630e-05,2.37665889011142591620e-05] 
dist 130=[5.53130939808212092180e-06,2.28980998062325462780e-05] 
dist 131=[-1.98109519515543181250e-06,1.74413618441599037270e-05] 
dist 132=[-6.70034185836244409110e-06,1.62101578544767732380e-05] 
dist 133=[-9.69226968053173398110e-06,1.38752614672830104760e-06] 
dist 134=[-1.05465142543656100580e-05,-8.69561983735464308120e-07] 
dist 135=[-1.36128581092398212020e-05,-4.88242026574940289080e-06] 
dist 136=[-1.44703197009613597080e-05,-5.57606974329964687230e-06] 
dist 137=[-7.84663616066008520630e-06,-5.44658019021609838680e-06] 
dist 138=[-7.01244013335619675810e-06,-1.27481594915183039000e-06] 
dist 139=[-3.94982341605124143540e-06,3.16810416566005250640e-06] 
dist 140=[-3.75266313285464520550e-06,5.94130511215937663760e-06] 
dist 141=[5.21021512915490557610e-07,7.67901688674945859910e-06] 
dist 142=[1.19422902966949877130e-06,8.12985937093318091310e-06] 
dist 143=[2.33962476221893186320e-06,2.59110329749283756100e-06] 
dist 144=[1.99113297898919732720e-06,2.81903476778930597070e-06] 
dist 145=[1.41995021667771000230e-06,2.75896779643874699590e-06] 
dist 146=[4.92149274858265057120e-07,2.64615379691238010520e-06] 
dist 147=[-4.38775918759979888090e-07,2.09617651591273220440e-06] 
dist 148=[-1.02209744867986721350e-06,1.87356154940839986600e-06] 
dist 149=[-1.39034990377387174930e-06,2.82801499256963615230e-07] 
dist 150=[-1.58533373640165211440e-06,-3.05463715448407981150e-08] 
dist 151=[-2.05021932204888977150e-06,-5.63349113931221260370e-07] 
dist 152=[-2.17081589868258636110e-06,-6.53815992166661955690e-07] 
dist 153=[-1.06733327782349393450e-06,-4.53728774004321277790e-07] 
dist 154=[-9.82568171810449654920e-07,-7.70352466160000000000e-09] 
dist 155=[-4.65671387330228523860e-07,4.39344626902521277790e-07] 
dist 156=[-4.41529539000912343770e-07,7.18815868869144536200e-07] 
dist 157=[-2.75572469975931957500e-08,8.94508438282943719520e-07] 
dist 158=[0                     ,9.41449805102830113550e-07] 
dist 159=[2.67172409385332508490e-07,3.39685125164124051420e-07] 
dist 160=[2.62494150252277903080e-07,3.66311891143615372660e-07] 
dist 161=[1.93356854859814849990e-07,3.55610094228429010130e-07] 
dist 162=[8.13126809372224526600e-08,3.42359963151979048650e-07] 
dist 163=[-3.10458445535019448300e-08,2.58679187567342705430e-07] 
dist 164=[-1.01404475227991897820e-07,2.41447066996408394390e-07] 
dist 165=[-1.45783302461409662940e-07,1.70437411831496862230e-08] 
dist 166=[-1.57979705230237138930e-07,-1.59758053936407407130e-08] 
dist 167=[-1.96830521259274993070e-07,-7.46586786741515331590e-08] 
dist 168=[-2.09155683202158479800e-07,-8.44075633974372332930e-08] 
dist 169=[-1.16456204684792502530e-07,-8.19790076622817588740e-08] 
dist 170=[-1.04159644387948228840e-07,-1.94254064003522698900e-08] 
dist 171=[-5.92550303169458091690e-08,4.66625071518672526270e-08] 
dist 172=[-5.61358232553324349720e-08,8.78912059575194065530e-08] 
dist 173=[7.72534958655653858610e-09,1.13716929784052648500e-07] 
dist 174=[1.77949447420569031520e-08,1.20414986738903466670e-07] 
dist 175=[3.64353407278456779490e-08,3.99593490042451919400e-08] 
dist 176=[3.11784313530506720210e-08,4.32525317880413218670e-08] 
dist 177=[2.26544960059283149760e-08,4.21663453939088294440e-08] 
dist 178=[8.87947241114330147040e-09,4.04079433655596853650e-08] 
dist 179=[-4.92306797049171200480e-09,3.18212368239318777800e-08] 
dist 180=[-1.35539113879240690740e-08,2.85034006248655652000e-08] 
dist 181=[-1.89848413152570750050e-08,4.49225228948331574200e-09] 
dist 182=[-2.39974724542273716990e-08,-1.07569435696625852400e-10] 
dist 183=[-3.09177794678637192170e-08,-7.80043600559021840000e-09] 
dist 184=[-3.27125619044787092290e-08,-9.08256328035635335370e-09] 
dist 185=[-1.48589897406168791720e-08,-8.76858226365406391620e-09] 
dist 186=[-1.34174482872892642280e-08,-1.42308141952227167820e-09] 
dist 187=[-7.53589704623684363140e-09,6.16459659846902010570e-09] 
dist 188=[-7.06972784008378185500e-09,1.08997595257655383200e-08] 
dist 189=[-4.93537109666630924200e-10,1.38686604466238349550e-08] 
dist 190=[5.32071813025511188650e-10,1.46457995556500595600e-08] 
dist 191=[2.36870733846674341480e-09,6.05754203761163311720e-09] 
dist 192=[1.81324854283448704250e-09,6.44914488950726681850e-09] 
dist 193=[6.16892758559085219730e-10,6.28673782935659118340e-09] 
dist 194=[-1.31494642213621540190e-09,6.00684621336168680190e-09] 
dist 195=[-3.25028306899151602470e-09,4.81034862602107603770e-09] 
dist 196=[-4.46022675591691784930e-09,4.22449879559643070310e-09] 
dist 197=[-5.22139167729279911770e-09,9.52114562890735567770e-10] 
dist 198=[-5.42634783414697415990e-09,2.52543944928765002370e-10] 
dist 199=[-5.32961075787274543130e-09,-8.01200151124618235390e-10] 
dist 200=[-4.92745440272377573110e-09,-9.44347318054112414270e-10] 
dist 201=[-2.03133361036962437140e-09,-1.00683571692019642130e-09] 
dist 202=[-1.94293377137469316100e-09,-2.67363038645434027690e-10] 
dist 203=[-1.77843272612459045960e-09,4.72827565253428367290e-10] 
dist 204=[-1.65628641539271344120e-09,9.34566006803914697580e-10] 
dist 205=[-1.33830404405728051000e-09,1.75051368980981177220e-09] 
dist 206=[-1.20015152421107814000e-09,2.50681842407540071890e-09] 
dist 207=[-1.11288942107793201310e-09,2.98112010434999395000e-09] 
dist 208=[-1.08865089828745416020e-09,3.10571879738187096940e-09] 
dist 209=[-1.06134389057626406210e-09,3.03266110143166189910e-09] 
dist 210=[-1.00818588823953284560e-09,2.88509366974159478510e-09] 
dist 211=[-8.36404504636704097870e-10,2.38315402223992849270e-09] 
dist 212=[-7.65625716968595511430e-10,2.13581146150063981280e-09] 
dist 213=[-1.45087837862346804390e-09,8.03163324991889117520e-10] 
dist 214=[-2.36377037660242627770e-09,8.55794686029206312600e-10] 
dist 215=[-2.93556510155752893010e-09,1.05807554348699786590e-09] 
dist 216=[-3.08427105167835707690e-09,1.11008497780222422520e-09] 
dist 217=[-2.99231863905773370700e-09,1.08804428408661521250e-09] 
dist 218=[-2.86350490081167088420e-09,1.02975231011845674580e-09] 
dist 219=[-2.24312553079468223030e-09,8.84967898201947733960e-10] 
dist 220=[-2.00988659348340325910e-09,9.50115912249648946390e-10] 
dist 221=[-6.79820184136153808780e-10,1.08944302878141198230e-09] 
dist 222=[-1.03774730683485258770e-09,1.67871361986282604690e-09] 
dist 223=[-1.26179119705811483160e-09,2.17621806506591817530e-09] 
dist 224=[-1.31975517426627329870e-09,2.30535572143998099840e-09] 
dist 225=[-1.29306020262784918670e-09,2.25043105945873734250e-09] 
dist 226=[-1.22483231115707023420e-09,2.14005558010771769090e-09] 
dist 227=[-1.04657746193877855680e-09,1.77041475195802384890e-09] 
dist 228=[-9.58905758692625488300e-10,1.58851751509190924340e-09] 
dist 229=[-1.49506990603710451330e-09,1.33215115685853293360e-09] 
dist 230=[-1.95029596217099001640e-09,1.44272375854529568770e-09] 
dist 231=[-2.23532764203861339500e-09,1.51195046378366020290e-09] 

8 phat 5 dirichlet min maxes function [1, 0, 1, 1, 0, 2, 0, 1] 
dist 0=[341.56577199406499668   ,341.56577199406499668   ] 
dist 1=[323.71953785426897379   ,347.26577758243912333   ] 
dist 2=[272.22147948218239971   ,351.50174519879688121   ] 
dist 3=[211.99251662602731804   ,352.37313936167974837   ] 
dist 4=[159.98739485402549484   ,308.29065318146146909   ] 
dist 5=[108.62572293237318696   ,261.22542735295822271   ] 
dist 6=[49.828601613991335260  ,241.48803750200163696   ] 
dist 7=[-2.1366380322548554925 ,176.38444207290879832   ] 
dist 8=[-27.280709367607679269  ,164.13454724846488136   ] 
dist 9=[-39.883051146152833418  ,27.208689850461329131  ] 
dist 10=[-51.719112135460125804  ,4.7794991784235785751 ] 
dist 11=[-72.432932338118850114  ,5.9524002283077601036 ] 
dist 12=[-81.251124668632828808  ,13.320390710823301930  ] 
dist 13=[-84.845821522785071600  ,22.427125037081057980  ] 
dist 14=[-83.676723842963454735  ,34.068461522291419994  ] 
dist 15=[-66.790809047860553791  ,43.194716393801965164  ] 
dist 16=[-63.675984299914448504  ,44.959920157524543868  ] 
dist 17=[-1.1666604438300614147 ,39.903413669446861236  ] 
dist 18=[7.3405184372011928816 ,39.124614762282731625  ] 
dist 19=[-.45641218548103968984,36.282606611199172931  ] 
dist 20=[-8.8272996289870302377 ,41.005583150398785773  ] 
dist 21=[-17.384274972530371081  ,41.125988957981785120  ] 
dist 22=[-21.986776989421310933  ,39.872936080188535487  ] 
dist 23=[-24.022627699703071770  ,31.178834766591482894  ] 
dist 24=[-23.814830034589101695  ,28.681043719359397293  ] 
dist 25=[-20.436791747768167779  ,4.6034873339968766038 ] 
dist 26=[-21.489016801608427031  ,.37253681537370760254] 
dist 27=[-25.785189470279045134  ,6.2026737799484242092 ] 
dist 28=[-27.213754678863303109  ,13.060996654496123382  ] 
dist 29=[-9.6244300325260919269 ,17.393461698381465139  ] 
dist 30=[-9.4652503159718284703 ,18.520718132255447016  ] 
dist 31=[-7.4232062432657971368 ,5.7857267319019121028 ] 
dist 32=[-7.1161936298190435197 ,5.7711413906235733011 ] 
dist 33=[.42085117536418921582,4.7499754955873284994 ] 
dist 34=[.73711132233657342994,4.5342671425367008947 ] 
dist 35=[-.88924582358555517766,4.2469281652506412984 ] 
dist 36=[-1.9230974246249611924 ,4.7999607563183899991 ] 
dist 37=[-2.8350843686794483994 ,4.8403939108932815690 ] 
dist 38=[-3.2503881461380222182 ,4.6872485864334144013 ] 
dist 39=[-3.3126981509185278436 ,3.8016918048270073438 ] 
dist 40=[-3.2360913461438989509 ,3.4188936331712329879 ] 
dist 41=[-2.5478672511680144711 ,.61467601811042726746] 
dist 42=[-2.6936725137664201389 ,.06005954190950171747] 
dist 43=[-3.5201003079011087818 ,.63613770880408966264] 
dist 44=[-3.7346007348436665096 ,1.3773318616594570477 ] 
dist 45=[-1.1347772053816940605 ,1.8646806108364255850 ] 
dist 46=[-1.1075257227884124690 ,1.9855857665120108938 ] 
dist 47=[-.85573893572794603512,.78074835547257232222] 
dist 48=[-.81252785515718324637,.76882793095574533732] 
dist 49=[.02875187643630863824,.60463781539108973735] 
dist 50=[.08811620072832702971,.57996415575743914432] 
dist 51=[-.09053985699471221380,.57850981732363284928] 
dist 52=[-.22843183621135498677,.63613113495289170426] 
dist 53=[-.35320622439511441481,.627280267851313322  ] 
dist 54=[-.39981295412178011866,.6068796597077573386 ] 
dist 55=[-.40411094699369261818,.46429964261575604012] 
dist 56=[-.39157198042699032734,.43411837089557608232] 
dist 57=[-.31842561661798060102,.04094493837070283153] 
dist 58=[-.2943910114105250281 ,-.01775560038943185709] 
dist 59=[-.34399113520247370375,.11740085663632125644] 
dist 60=[-.36718758849359190227,.22777653276955679279] 
dist 61=[-.14473792643863064072,.29712654637380536955] 
dist 62=[-.14074394979898722218,.31515001521919344852] 
dist 63=[-.10712122517434891531,.09551737461350221604] 
dist 64=[-.10210134604989296927,.09331725407336087039] 
dist 65=[.01153293276861542194,.07214067181208887294] 
dist 66=[.00984805783064009963,.06869869736230988182] 
dist 67=[-.01862653263464296097,.06729225884914174718] 
dist 68=[-.03859869724559559270,.07411697855332576985] 
dist 69=[-.05398689563848440906,.07326980593830365611] 
dist 70=[-.05904874136069814034,.07049685971674820456] 
dist 71=[-.05830192562835997009,.05634065658856917305] 
dist 72=[-.05631829769478962055,.05042899757274174005] 
dist 73=[-.04364341232654879977,.00819973353278073524] 
dist 74=[-.04186445246085566630,-.00016493211275999579] 
dist 75=[-.05430537906656655224,.01683144989487198447] 
dist 76=[-.05753334903508901113,.02823890897887030015] 
dist 77=[-.01695498152180174026,.03549516777627910569] 
dist 78=[-.01642008498964328719,.03759701649399096929] 
dist 79=[-.01254682968436984957,.01233534841287667674] 
dist 80=[-.01180104178221544552,.01200197077492415308] 
dist 81=[.00078393324598935592,.00916841585735075935] 
dist 82=[.00121251285136176314,.00872711220390646338] 
dist 83=[-.00178183378740552844,.00889832527560903616] 
dist 84=[-.00397258509339001366,.00966409910302365463] 
dist 85=[-.00584738557212430077,.00944200302725452951] 
dist 86=[-.00644327291691538410,.00910102271865803334] 
dist 87=[-.00637944871813544487,.00695025647005094804] 
dist 88=[-.00613843098338446149,.00645366866201444999] 
dist 89=[-.00492446639503969438,.00068485205975970282] 
dist 90=[-.00439608603357133465,-.00018984442735554451] 
dist 91=[-.00544884740615437902,.00203079419717554797] 
dist 92=[-.00578989614434445219,.00374421788653657375] 
dist 93=[-.00214283833643607612,.00481916916087026939] 
dist 94=[-.00207391277485160726,.00509884413206394026] 
dist 95=[-.00155979518144256575,.00139960102032307666] 
dist 96=[-.00148178327593268514,.00135791928220815212] 
dist 97=[-.00026452831510844452,.00107823361145818411] 
dist 98=[-.00018082641635171151,.00115607065591630385] 
dist 99=[-.00088049218345226817,.00150155498918052996] 
dist 100=[-.00132088024478601483,.00160147555819020352] 
dist 101=[-.00160080366782442991,.00157673364062405668] 
dist 102=[-.00168207401405685281,.00150088927902623614] 
dist 103=[-.00164942803645930281,.00126083043517444415] 
dist 104=[-.00157295771610375877,.00114021296339057252] 
dist 105=[-.00129176184502792797,.00049184559491553797] 
dist 106=[-.00115139840390929999,.00032718098094884654] 
dist 107=[-.00081736042939268703,.00026982000476122104] 
dist 108=[-.00086502499183807860,.00046846073407585309] 
dist 109=[-.00024598416349523860,.00059295573612497047] 
dist 110=[-.00023767035244637685,.00062517674938281128] 
dist 111=[-.00018235744023199210,.00013363214054320584] 
dist 112=[-.00016907368965639422,.00012902794885292288] 
dist 113=[-4.04861608264637856320e-05,.00010729441408597172] 
dist 114=[-1.50527422607181108350e-05,.00015036833715721262] 
dist 115=[-8.43559751175723097280e-05,.00019215196730744655] 
dist 116=[-.00012797402308330164,.00020374822030368220] 
dist 117=[-.00015570985164120106,.00019875544824826519] 
dist 118=[-.00016380071787687163,.00019014401279718217] 
dist 119=[-.00016184802763241530,.00015118755660750596] 
dist 120=[-.00015329126943589543,.00013376057004993281] 
dist 121=[-.00013374961666070594,2.46240497149233061780e-05] 
dist 122=[-.00012391495322039090,2.18283526502897054430e-06] 
dist 123=[-8.73407085747401932320e-05,2.76826114787723273230e-06] 
dist 124=[-9.25339020013896848730e-05,9.93700442393222489650e-06] 
dist 125=[-2.92671336846918077060e-05,1.45117380128933425090e-05] 
dist 126=[-2.82617738003727449460e-05,1.58798856355175917720e-05] 
dist 127=[-2.11020494231878298250e-05,1.56177546704690122430e-05] 
dist 128=[-2.00349361999954212090e-05,1.50015098773202616580e-05] 
dist 129=[2.92636204083590189290e-06,1.19397802588556472350e-05] 
dist 130=[2.00337566920545966380e-06,1.06745535598175584330e-05] 
dist 131=[-4.75910884469687728630e-06,1.39507319144528418220e-05] 
dist 132=[-8.98297582772064001920e-06,1.51294280633733546700e-05] 
dist 133=[-1.16306584579511682620e-05,1.47665921346864182350e-05] 
dist 134=[-1.23175224156387411570e-05,1.41488209163873497950e-05] 
dist 135=[-3.61473340488329351690e-06,1.11883790775510386850e-05] 
dist 136=[-3.49410785685598781230e-06,9.98865780070300860750e-06] 
dist 137=[-4.55467037486547541830e-06,1.49172903379005191360e-06] 
dist 138=[-8.53146520075224358220e-06,-1.87570904133769899310e-07] 
dist 139=[-1.10226234638957356260e-05,4.82199964594614168920e-07] 
dist 140=[-1.16687168446923920320e-05,1.34765126135150956510e-06] 
dist 141=[-3.40307051113668423420e-06,1.89656443919398390840e-06] 
dist 142=[-3.27972516443801325910e-06,2.05361455032652361400e-06] 
dist 143=[-2.47221633569720432280e-06,2.00071074401491916170e-06] 
dist 144=[-2.31929191055748573420e-06,1.92705444076145008430e-06] 
dist 145=[2.17785634376799385690e-07,1.46668738408525619450e-06] 
dist 146=[2.50427692235349209540e-07,1.36304958591183422360e-06] 
dist 147=[-4.41844068335818053250e-07,1.79627604978124676960e-06] 
dist 148=[-8.74590839763209804150e-07,1.93430994685519993640e-06] 
dist 149=[-1.14642112419169739830e-06,1.87572928017037927140e-06] 
dist 150=[-1.21836863535485999700e-06,1.80390123949693856510e-06] 
dist 151=[-4.58998970547833240120e-07,1.36804906319011277390e-06] 
dist 152=[-4.43701039584671499790e-07,1.27025396626984079800e-06] 
dist 153=[-4.21072115459479119240e-07,1.00118364967013846170e-07] 
dist 154=[-8.25578033694638650620e-07,-7.75943907176300108740e-08] 
dist 155=[-1.07920223669812716820e-06,4.50521160497336409800e-08] 
dist 156=[-1.14556225815489966960e-06,1.51263000975791615810e-07] 
dist 157=[-4.27660050559519300600e-07,2.18528582259958998760e-07] 
dist 158=[-4.12464245970380709710e-07,2.37538438463867738960e-07] 
dist 159=[-3.06953178991554407330e-07,2.32275807300788488510e-07] 
dist 160=[-2.91200584514608084680e-07,2.22741287201145852140e-07] 
dist 161=[4.37788759933188592060e-08,1.76218383587195710280e-07] 
dist 162=[2.88110127976552322240e-08,1.57580265445380816290e-07] 
dist 163=[-7.12009712107364052840e-08,2.05073462420976660980e-07] 
dist 164=[-1.33618116889959390300e-07,2.21768118278671718460e-07] 
dist 165=[-1.72726019556436963900e-07,2.15952665446864818650e-07] 
dist 166=[-1.82871860701977794770e-07,2.06766024915227553570e-07] 
dist 167=[-5.50630937072461329150e-08,1.63162814857236353420e-07] 
dist 168=[-5.31626509539891873680e-08,1.45618627823795237840e-07] 
dist 169=[-6.71321053701830128780e-08,2.18783048521201807930e-08] 
dist 170=[-1.25028320437318286620e-07,-2.50066821158003436550e-09] 
dist 171=[-1.61289158505213967440e-07,1.02176544399400694420e-08] 
dist 172=[-1.70693349663397125020e-07,2.35068942574507974200e-08] 
dist 173=[-5.01118382560951842100e-08,3.18884813570442288090e-08] 
dist 174=[-4.83006334602122996180e-08,3.41890642153502110630e-08] 
dist 175=[-3.61104194863570709990e-08,3.31993007413720302450e-08] 
dist 176=[-3.40481950783605561810e-08,3.19138712264870886650e-08] 
dist 177=[3.23192721527353092560e-09,2.43602780520608688210e-08] 
dist 178=[1.53588618000000000000e-10,2.24835766869903648650e-08] 
dist 179=[-9.88921351830361438950e-09,2.64970952311953658780e-08] 
dist 180=[-1.61657171043412205080e-08,2.84787219244345857570e-08] 
dist 181=[-2.01099690252324515770e-08,2.75762133324911811420e-08] 
dist 182=[-2.11607842682902531290e-08,2.65078401850617507640e-08] 
dist 183=[-7.18461406101013462540e-09,2.00783461998999987820e-08] 
dist 184=[-6.93161185965618456370e-09,1.86395814190304858630e-08] 
dist 185=[-6.27262215703384935220e-09,1.53075698574537301240e-09] 
dist 186=[-1.21807697262833841180e-08,-1.01084232844429672630e-09] 
dist 187=[-1.58833524337142440370e-08,7.81486557366088094030e-10] 
dist 188=[-1.68492335763400593040e-08,2.44632399949102302140e-09] 
dist 189=[-6.07501612074019292090e-09,3.49532745408646333750e-09] 
dist 190=[-5.85328527997633582090e-09,3.78130518694041339740e-09] 
dist 191=[-4.36202904605098977140e-09,3.68837556732070645250e-09] 
dist 192=[-4.12322584490334576330e-09,3.52995732467822760090e-09] 
dist 193=[5.74167506525527007820e-10,2.80616416413444994070e-09] 
dist 194=[3.31926883123511414240e-10,2.48851721021141163390e-09] 
dist 195=[-1.25556348628114266570e-09,3.00078274964313248200e-09] 
dist 196=[-2.24579531387947160210e-09,3.23597105903698958080e-09] 
dist 197=[-2.86603315369016962520e-09,3.14186044229663474540e-09] 
dist 198=[-3.02688351719441275460e-09,3.01190386605195148570e-09] 
dist 199=[-7.40769513833474365760e-10,2.33923911900459184490e-09] 
dist 200=[-7.14439731693065627610e-10,2.11829033769800460150e-09] 
dist 201=[-8.63502110528980401960e-10,2.32012927383884198900e-10] 
dist 202=[-1.65081193432064620230e-09,-1.08138639903775773000e-10] 
dist 203=[-2.14385937270226794730e-09,8.20606808271370313960e-11] 
dist 204=[-2.27171933468877019840e-09,2.53729378484093209670e-10] 
dist 205=[-9.36867159012021369800e-10,3.61762530696102986200e-10] 
dist 206=[-9.00415890431192950690e-10,3.90921740416511724200e-10] 
dist 207=[-6.82949782800946322150e-10,3.82922983162825572800e-10] 
dist 208=[-6.33272281043068104820e-10,3.64482623448220525670e-10] 
dist 209=[3.08478354604207546080e-11,3.02595501825853333940e-10] 
dist 210=[-7.67516016707395843150e-12,3.97113567585491540710e-10] 
dist 211=[-1.90533892621385935450e-10,5.40338602775394064670e-10] 
dist 212=[-3.04618995932931145720e-10,5.77949552706222483930e-10] 
dist 213=[-3.76121917266914250000e-10,5.60980248762296640160e-10] 
dist 214=[-3.94784027743636836760e-10,5.37130883710763661830e-10] 
dist 215=[-1.21331544595487115460e-11,4.19844381588161902380e-10] 
dist 216=[-9.94450954176709619180e-11,3.77282523969180937320e-10] 
dist 217=[-3.22891194327731838930e-10,2.45883821190343670630e-10] 
dist 218=[-4.62222731669549587100e-10,2.20340916194968140550e-10] 
dist 219=[-5.49494378280909269490e-10,2.04273850476645707090e-10] 
dist 220=[-5.72182597074500702290e-10,1.99951986149504097760e-10] 
dist 221=[-1.95480023330495531970e-10,1.95966804471389317120e-10] 
dist 222=[-2.00544955782343858610e-10,1.85372084364358058380e-10] 
dist 223=[-1.95136344654016198110e-10,1.79283719773707073490e-10] 
dist 224=[-1.85976170037679003670e-10,1.70088611614411211490e-10] 
dist 225=[-2.25448771904604755380e-10,2.45675556120655565650e-10] 
dist 226=[-2.50840405489014018010e-10,3.14568198012816113550e-10] 
dist 227=[-2.66714537704198991230e-10,3.57727794341714719170e-10] 
dist 228=[-2.70779438630837533540e-10,3.68970765531500125540e-10] 
dist 229=[-2.69461211571713135240e-10,3.56589053032590320880e-10] 
dist 230=[-2.64574691060284675410e-10,3.42558647575290770530e-10] 
dist 231=[-2.56804892672333240510e-10,2.59073988933546444350e-10] 
dist 232=[-2.44367149428525753130e-10,2.40436695822308585830e-10] 
dist 233=[-2.90515126845741509220e-10,3.15709077099977462860e-10] 
dist 234=[-3.24654423241518019370e-10,4.02885565389114148830e-10] 
dist 235=[-3.46030641960032587080e-10,4.70673022353113413620e-10] 
dist 236=[-3.51573530278185934490e-10,4.88830277419580305200e-10] 
dist 237=[-2.10957381503451874860e-10,4.75417591830335075070e-10] 
dist 238=[-2.11136684318848041560e-10,4.53720549288299719410e-10] 
dist 239=[-2.13568332918585917150e-10,4.01853221996552894530e-10] 
dist 240=[-2.22990251680498609180e-10,3.84447722961919829260e-10] 
dist 241=[-2.57331202175566634690e-10,3.01718878528709131060e-10] 
dist 242=[-3.12409028963826005050e-10,2.75039612494411503690e-10] 
dist 243=[-3.96059814046420274240e-10,3.30570841016354081380e-10] 
dist 244=[-4.17747999618455629870e-10,4.38973344662315102170e-10] 
dist 245=[-4.10301774230151556340e-10,5.06845183336019190650e-10] 
dist 246=[-3.87756452961101349670e-10,5.24441374011422917680e-10] 
dist 247=[-3.37792696300911225990e-10,5.09335784285302289670e-10] 
dist 248=[-3.13210887354740955300e-10,4.86790298876252082980e-10] 
dist 249=[-2.63858853952908078370e-10,3.85413207536924445630e-10] 
dist 250=[-3.02755182716997845010e-10,3.48036164491085462570e-10] 
dist 251=[-3.27109183387224248190e-10,3.91630500539248279360e-10] 

8 phat 5 dirichlet min maxes function [0, 2, 0, 0, 0, 0, 0, 2] 
dist 0=[406.63003978379371237   ,406.63003978379371237   ] 
dist 1=[368.44282734584457757   ,420.49819115309929211   ] 
dist 2=[292.14900158152262398   ,418.24336287078624696   ] 
dist 3=[209.39384178934043679   ,381.15100328505814932   ] 
dist 4=[145.64943948229834815   ,333.72503662759127591   ] 
dist 5=[89.785715827166504349  ,251.61069169648181343   ] 
dist 6=[36.499367875594036336  ,239.50682027618677818   ] 
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dist 67=[-.00045932471229989967,.04218158620144964180] 
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dist 80=[.00011437712467044392,.02193828298120929169] 
dist 81=[.00164393813689403151,.01576861497290909266] 
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dist 97=[.00021667719206533488,.00150671115161626353] 
dist 98=[9.83229247654210469240e-05,.00160381768298746792] 
dist 99=[-2.20264346345777357140e-05,.00064994209436697613] 
dist 100=[-9.90457723031284895510e-05,.00062761655301628903] 
dist 101=[-.00014930155503040643,.00047711501830090195] 
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dist 106=[-.00044956011666015234,-2.31763837820221709020e-05] 
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dist 109=[-.00026189250008261449,.00012289959779187713] 
dist 110=[-.00024713378305086824,.00021439285044459196] 
dist 111=[-7.09625590158280885700e-06,.00028215343400839950] 
dist 112=[2.66985850399995243410e-05,.00029993506415991523] 
dist 113=[2.49155422328347428560e-05,.00018399291261326544] 
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dist 118=[-7.27111957527961301690e-05,6.96927533054169918040e-05] 
dist 119=[-9.35169588076918241820e-05,2.67958011554001606690e-05] 
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dist 121=[-9.72698819901506939190e-05,2.27655570340566751610e-06] 
dist 122=[-8.82468434981992105070e-05,-4.64508830373472519430e-07] 
dist 123=[-1.79382607185380029140e-05,4.48698614060109222630e-06] 
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dist 125=[-6.92975444247696063420e-06,1.20599608801503784300e-05] 
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dist 127=[5.05976357973049381880e-06,2.13235104097224110000e-05] 
dist 128=[4.40706654739472743670e-06,2.26969146718655948200e-05] 
dist 129=[3.28865831662437884220e-06,2.21555503824807249290e-05] 
dist 130=[1.43425125855688412780e-06,2.14216065197462624340e-05] 
dist 131=[-4.36835387691448583110e-07,1.60506104740552734460e-05] 
dist 132=[-1.62000735812773118190e-06,1.52499052195854514860e-05] 
dist 133=[-2.37799211450697000800e-06,-2.14195816778839250290e-06] 
dist 134=[-7.27945361022873193170e-06,-2.52152210979122782900e-06] 
dist 135=[-1.05277293294068078910e-05,-2.53886977524889049650e-06] 
dist 136=[-1.14491156563599551400e-05,-2.12769204946411944030e-06] 
dist 137=[-1.12011849734140974160e-05,-1.44648641107947462920e-06] 
dist 138=[-1.07409940382623392780e-05,-3.34735090853298043960e-07] 
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dist 140=[-7.60170837147769075570e-06,1.47835923657015751090e-06] 
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dist 142=[1.23103200613376753040e-07,6.46036623193838547770e-06] 
dist 143=[5.94690312924115301480e-07,8.35271750526063340420e-06] 
dist 144=[5.12839211107969223130e-07,8.84354719837764676690e-06] 
dist 145=[3.75444500293448887000e-07,2.58776702003102300050e-06] 
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dist 150=[-9.73322433658208406260e-07,-2.74826792943588203950e-07] 
dist 151=[-1.36233136625875097210e-06,-2.69303948038505489570e-07] 
dist 152=[-1.46962432870836600570e-06,-2.26685298064975632490e-07] 
dist 153=[-1.42728560562245037620e-06,-1.56371634146865985490e-07] 
dist 154=[-1.37322956491665013970e-06,-4.11530450250235277720e-08] 
dist 155=[-1.04309616473984759740e-06,7.44623812381489300790e-08] 
dist 156=[-9.68359374530726032370e-07,1.46774094049202638500e-07] 
dist 157=[-7.90770584458519185290e-08,3.20300946861066030780e-07] 
dist 158=[5.64355107878952015330e-08,6.29144391457080549680e-07] 
dist 159=[7.44661504557553316240e-08,8.22901060943549025360e-07] 
dist 160=[6.43026515115630270370e-08,8.73782611022533431810e-07] 
dist 161=[4.74172026808981089020e-08,3.25283893308586330070e-07] 
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dist 163=[-8.95728581872878724050e-09,2.34368514694980925250e-07] 
dist 164=[-2.68612062425925719860e-08,2.22171657504548617420e-07] 
dist 165=[-3.82194105205642254750e-08,-3.17353664095700980760e-08] 
dist 166=[-1.09728689062465093080e-07,-3.65561377469041288520e-08] 
dist 167=[-1.57177385784638238090e-07,-3.55628691014540404930e-08] 
dist 168=[-1.70167635251989234980e-07,-2.95365263257808696850e-08] 
dist 169=[-1.65882703606094898890e-07,-1.97002881380907422840e-08] 
dist 170=[-1.58939737373599974340e-07,-3.75883643660356866370e-09] 
dist 171=[-1.25261154814366659060e-07,1.22970043905945343600e-08] 
dist 172=[-1.12094471184297255020e-07,2.25462167366653405180e-08] 
dist 173=[-1.68958530917541065390e-08,5.07909794296400097700e-08] 
dist 174=[1.53587702128226761940e-09,9.46222149330410787210e-08] 
dist 175=[6.78731896652627123270e-09,1.22077547615450397660e-07] 
dist 176=[5.77494257301657929530e-09,1.29198535958417058460e-07] 
dist 177=[4.09993185818758432510e-09,4.01540722085285515920e-08] 
dist 178=[1.36678958967868057120e-09,3.87003361959654286230e-08] 
dist 179=[-2.23120390617809201580e-09,2.89925225496346518950e-08] 
dist 180=[-5.05799874912346845890e-09,2.73222056027516703310e-08] 
dist 181=[-6.84004993816874658980e-09,-2.26970670853613884980e-09] 
dist 182=[-1.46492164066196917190e-08,-2.53091909223736113840e-09] 
dist 183=[-2.03957633216162521500e-08,-2.40478484539607536270e-09] 
dist 184=[-2.19870993786553750510e-08,-1.82100291856246109400e-09] 
dist 185=[-2.12729567617085877120e-08,-8.71554665713641803760e-10] 
dist 186=[-2.04881886015817544850e-08,6.64493829913066714780e-10] 
dist 187=[-1.54336527336165792530e-08,3.07063646442560870790e-09] 
dist 188=[-1.44196537405118410110e-08,4.57351733822346914080e-09] 
dist 189=[-1.44696348051580108660e-09,5.51504049300536351870e-09] 
dist 190=[-1.37261593101501255490e-09,9.14806459426939271980e-09] 
dist 191=[5.93963945433561476960e-10,1.19602257185068148870e-08] 
dist 192=[4.81646687437623322500e-10,1.26956544936848186670e-08] 
dist 193=[2.96461613726960529600e-10,4.78316413164097706090e-09] 
dist 194=[-5.21024325940067668500e-12,4.60156225431037625010e-09] 
dist 195=[-3.08158038645761882930e-10,3.49513251419212299200e-09] 
dist 196=[-4.98298061756424676040e-10,3.24594138257133983620e-09] 
dist 197=[-8.34778190875960690520e-10,4.81925785543122901290e-11] 
dist 198=[-2.00006265273280255010e-09,3.05401892188013516200e-11] 
dist 199=[-2.73257705006745556530e-09,7.62795171602238840100e-11] 
dist 200=[-2.92866583992805636680e-09,2.63369553805976804590e-10] 
dist 201=[-2.83751097339264670710e-09,5.64078939915609682060e-10] 
dist 202=[-2.72727285872736829630e-09,1.04797234027344138960e-09] 
dist 203=[-2.07140724625721344250e-09,1.85529997898918434450e-09] 
dist 204=[-1.93512337931977949410e-09,2.35894808975061806310e-09] 
dist 205=[-2.06822267137097118800e-09,2.67466259539612483800e-09] 
dist 206=[-2.10272713362688277940e-09,2.75729062613031578490e-09] 
dist 207=[1.88129483890821406600e-10,2.68015540838402425790e-09] 
dist 208=[2.52025627415718406780e-10,2.56047070056437235850e-09] 
dist 209=[8.08996265352384539190e-10,2.09204532881725906780e-09] 
dist 210=[2.33130336728156348990e-10,2.00098928893835517630e-09] 
dist 211=[-9.33301785087176506440e-10,1.57908596517335289240e-09] 
dist 212=[-1.67237638489850101900e-09,1.40570331418730214810e-09] 
dist 213=[-2.13524877666933797400e-09,7.07943306522113856940e-10] 
dist 214=[-2.25552743958398987420e-09,5.36106788499213207830e-10] 
dist 215=[-2.22187145439058919560e-09,3.61766568352670127030e-10] 
dist 216=[-2.09398285108762754270e-09,3.26603092294750269860e-10] 
dist 217=[-2.02179282405608926160e-09,4.62689389414707672640e-10] 
dist 218=[-1.94389931435017181100e-09,1.29489615596488811650e-09] 
dist 219=[-2.04001780152336788360e-09,2.14498322062971073360e-09] 
dist 220=[-2.34762037564051549770e-09,2.67490357590536069450e-09] 
dist 221=[-2.54022053379875604570e-09,3.00669194053150086150e-09] 
dist 222=[-2.59017760388139065840e-09,3.09270002184275208300e-09] 
dist 223=[-1.42175650285279814940e-09,1.86589325470705095130e-09] 
dist 224=[-1.25120101267443264380e-09,1.92342696022845526390e-09] 
dist 225=[-1.28854092312237393760e-09,3.75342157206039401650e-11] 
dist 226=[-1.43318116453892819090e-09,4.70799090700946164100e-10] 
dist 227=[-1.66430396883996667390e-09,1.08908126897491781770e-09] 
dist 228=[-2.03515766298707803110e-09,1.47448978472253321660e-09] 
dist 229=[-2.40603639683418938930e-09,2.66816962385703884130e-09] 
dist 230=[-2.63725650283522787200e-09,3.45243055695728202640e-09] 
dist 231=[-2.78205517026178212590e-09,3.94344977246094946580e-09] 
dist 232=[-2.81965760627728398710e-09,4.07071954861415606240e-09] 
dist 233=[-2.75589258087377972410e-09,3.96961280392895186720e-09] 
dist 234=[-2.61733179731807366650e-09,3.77842968535724100650e-09] 
dist 235=[-2.18889126719894028840e-09,3.10010682778963945950e-09] 
dist 236=[-1.97808242757325753640e-09,2.76638048795055377470e-09] 
dist 237=[-1.81274359891626742750e-09,1.95325857930357380660e-09] 
dist 238=[-2.99014393263750792120e-09,2.29885217811107182630e-09] 
dist 239=[-3.72733619449799418050e-09,2.83329559198402895070e-09] 
dist 240=[-3.91848033438921481050e-09,2.97189575204196305660e-09] 
dist 241=[-3.83026311254501357470e-09,2.90752438313423016670e-09] 
dist 242=[-3.63717589869148751540e-09,2.75858465351682715690e-09] 
dist 243=[-3.04509259923406960530e-09,2.32635924979724163800e-09] 
dist 244=[-2.75378726708672914700e-09,2.11369763519499715980e-09] 
dist 245=[-1.61211053500458588750e-09,2.02395610345891515840e-09] 
dist 246=[-2.52949936524694944890e-09,3.21318308712340810500e-09] 
dist 247=[-3.10390139360649969770e-09,3.95778527273792306410e-09] 
dist 248=[-3.25285242718390270680e-09,4.15086105321244912340e-09] 
dist 249=[-3.18174592769626675610e-09,4.03120872692505914770e-09] 
dist 250=[-3.01935744201460153000e-09,3.85289051580708847190e-09] 
dist 251=[-2.54199639073417386120e-09,3.04971467173091788930e-09] 
dist 252=[-2.30713043405335359440e-09,2.70381179222211324310e-09] 
dist 253=[-2.49247160985210053940e-09,2.54109585612521032720e-09] 
dist 254=[-2.94477020750245556030e-09,3.09614550288465093460e-09] 
dist 255=[-3.22796547652519023990e-09,3.44367601573379119600e-09] 

8 phat 5 dirichlet min maxes function [2, 1, 2, 1, 1, 0, 2, 0, 1] 
dist 0=[357.31893715502379637   ,357.31893715502379637   ] 
dist 1=[346.05453155419730353   ,362.36757783087820140   ] 
dist 2=[313.53531657733967795   ,361.25591847133284548   ] 
dist 3=[256.03933809689848272   ,352.78218813163979637   ] 
dist 4=[183.91172554553858348   ,273.99152529044160579   ] 
dist 5=[124.42396927162655128   ,254.54007776552168883   ] 
dist 6=[68.231998417894087835  ,194.31016813347825533   ] 
dist 7=[7.7739897460890869231 ,175.35194757620549500   ] 
dist 8=[-43.267019067528945276  ,51.353437271907590957  ] 
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dist 50=[-.05073585544700789324,.87998657374364549551] 
dist 51=[-.04004418137164633099,.61342296882319141676] 
dist 52=[-.19166010748513163188,.59964086274724896303] 
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dist 54=[-.50426492372198003033,.44096512998664648277] 
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dist 56=[-.37911138734636007516,.00691967557909965356] 
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dist 60=[-.13977939455850701749,.11704860343182745232] 
dist 61=[-.13597609387842198022,.1568944316230328276 ] 
dist 62=[-.10360049111350895056,.16716582414247275252] 
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dist 65=[.02836978285385260162,.08970855268039205696] 
dist 66=[.02011272071415208035,.06980757986934626704] 
dist 67=[-.00408559691131772172,.07153827786953860705] 
dist 68=[-.01961980760599334910,.07077010660760005875] 
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dist 70=[-.05222128178745225245,.05446091435494465800] 
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dist 73=[-.04040627157038965037,-.00013490183559830094] 
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dist 76=[-.01638673590022828050,.01899427130964351193] 
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dist 80=[.00080459583500434370,.01108561626126805899] 
dist 81=[.00279580231330009657,.01070846512809582174] 
dist 82=[.00180135137318039964,.00863940354767159436] 
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dist 84=[-.00326210087602844905,.00905973803245471833] 
dist 85=[-.00627835847742557165,.00873496701118286521] 
dist 86=[-.00817189433791287387,.00666575908989960981] 
dist 87=[-.00866358264555854042,.00619699519115195325] 
dist 88=[-.00464430204835106038,.00055932594814194562] 
dist 89=[-.00394543843025425182,-.00030019226543083842] 
dist 90=[-.00517992826715097242,-8.69959909927790000000e-05] 
dist 91=[-.00550894900043319494,.00140437576752360858] 
dist 92=[-.00207586867124162955,.00234313511181928032] 
dist 93=[-.00200956852071713973,.00293893348911600574] 
dist 94=[-.00151103295201889382,.00310896700162729872] 
dist 95=[-.00143656444585500589,.00148375497911532568] 
dist 96=[.00015464104783086045,.00145854627689252582] 
dist 97=[.00040704707239001536,.00140982161625226307] 
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dist 99=[-.00015296462587251324,.00111208126562441365] 
dist 100=[-.00039856015886675156,.00109090936599984333] 
dist 101=[-.00060679843928686875,.00104592989681087365] 
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dist 105=[-.00066762019710793916,7.84359823725726637420e-05] 
dist 106=[-.00084637252852224378,5.55699856679343450370e-05] 
dist 107=[-.00089336234239641980,.00028708937227646030] 
dist 108=[-.00024381151809945576,.00043204272828363535] 
dist 109=[-.00023555287718990560,.00052325932133989906] 
dist 110=[-.00017758045646709535,.00054767480798590763] 
dist 111=[-.00016756172609756649,.00017349118537771482] 
dist 112=[-2.08750541365196363370e-05,.00017111655704790731] 
dist 113=[4.24811165200969809930e-06,.00016451628933719288] 
dist 114=[-2.62387244896300094030e-05,.00015831126680731053] 
dist 115=[-7.03839321798954637060e-05,.00016863701330769453] 
dist 116=[-9.82193423808381759650e-05,.00016422967888086712] 
dist 117=[-.00011597180880585493,.00015746848610474380] 
dist 118=[-.00012729220866692766,.00012293322243141052] 
dist 119=[-.00013483167552981064,.00011083128375045131] 
dist 120=[-.00011379889638627036,9.83048077992387767430e-06] 
dist 121=[-.00010300434878775387,-5.49151711925604087510e-06] 
dist 122=[-9.60532818709549449440e-05,-2.49468436589132907030e-05] 
dist 123=[-8.06196374841111712290e-05,-9.93175992654885041140e-06] 
dist 124=[-3.07726060719822578690e-05,5.17863574586658988060e-06] 
dist 125=[-2.97190919020510338840e-05,1.46903479198426568520e-05] 
dist 126=[-2.21975523460859296670e-05,2.07386660502890771940e-05] 
dist 127=[-2.10764599075836551470e-05,2.25012595045293894230e-05] 
dist 128=[3.06700108691997452410e-06,2.19585081543829334090e-05] 
dist 129=[6.86422237033724859010e-06,2.11613248012990352590e-05] 
dist 130=[1.03597509686551577180e-05,1.61288154093048776460e-05] 
dist 131=[2.77986689403085523120e-06,1.59070083815661977880e-05] 
dist 132=[-4.82621468250994727240e-06,1.55289814507119756830e-05] 
dist 133=[-9.58344968525332074880e-06,1.48804480806724909970e-05] 
dist 134=[-1.25735738680959342850e-05,1.17689244533571779680e-05] 
dist 135=[-1.33680695174593905110e-05,1.05076392723154266920e-05] 
dist 136=[-5.03582749397040330040e-06,1.57061328317922848050e-06] 
dist 137=[-8.96928936889225583710e-06,-1.95555157725388447830e-07] 
dist 138=[-1.15892624689685342840e-05,-3.18555025922208857740e-06] 
dist 139=[-1.22687697259217962420e-05,-1.37090226229088979700e-06] 
dist 140=[-3.58085802332808456310e-06,4.88164224317486799530e-07] 
dist 141=[-3.45135777477863201380e-06,1.65655489954137520410e-06] 
dist 142=[-2.60232202285927631600e-06,2.39783434666614791530e-06] 
dist 143=[-2.44138182841448863020e-06,2.61058948492763078770e-06] 
dist 144=[2.27885410916436195810e-07,2.55673099639963318430e-06] 
dist 145=[6.62212201298702807090e-07,2.45272212560137040350e-06] 
dist 146=[1.41249191888407432420e-06,1.94416263452330314630e-06] 
dist 147=[3.15459208782208309190e-07,2.03572210508409860080e-06] 
dist 148=[-7.83900240926357706190e-07,1.97431701970507275830e-06] 
dist 149=[-1.47015795698226743350e-06,1.89882057989423043240e-06] 
dist 150=[-1.90019344595417771530e-06,1.44003774916402206650e-06] 
dist 151=[-2.01176821866876298610e-06,1.33726923568374259870e-06] 
dist 152=[-5.98552110730016108900e-07,1.05379338758685872250e-07] 
dist 153=[-8.68056373228182362110e-07,-8.15793219065070108710e-08] 
dist 154=[-1.13490740989150657070e-06,-3.50935039910322305660e-07] 
dist 155=[-1.20475296507249327590e-06,-1.21944275846906890710e-07] 
dist 156=[-4.50068009298982597670e-07,1.07867263038908523840e-07] 
dist 157=[-4.34094234462567121250e-07,2.51916095156268068880e-07] 
dist 158=[-3.23190012762709806380e-07,3.42901860581100068050e-07] 
dist 159=[-3.06541513846690928360e-07,3.68153212350302828050e-07] 
dist 160=[4.60321309954170883400e-08,3.57930648732061023100e-07] 
dist 161=[1.01434918086605020350e-07,3.44059805226294403610e-07] 
dist 162=[1.12292065299780742630e-07,2.63580238342273976150e-07] 
dist 163=[2.00753080360000000000e-09,2.42590717234984567740e-07] 
dist 164=[-1.08546063307180742630e-07,2.27516287015489390150e-07] 
dist 165=[-1.77671089629201943110e-07,2.17863701187764785730e-07] 
dist 166=[-2.21138477852552826370e-07,1.71821600544783178930e-07] 
dist 167=[-2.32773609885013782730e-07,1.53455489992568881950e-07] 
dist 168=[-7.61276604934814337070e-08,2.25449024420984494060e-08] 
dist 169=[-1.31185393254938207950e-07,-3.16225050587998208270e-09] 
dist 170=[-1.69375258047369488410e-07,-4.65066968529373104270e-08] 
dist 171=[-1.79278782377589855900e-07,-2.02643145862807033490e-08] 
dist 172=[-5.32602790505949923980e-08,7.82362199019156962040e-09] 
dist 173=[-5.12656200670434923650e-08,2.54164546890557908950e-08] 
dist 174=[-3.86833738328463678180e-08,3.65174337443529896720e-08] 
dist 175=[-3.61455477802279729140e-08,3.95771030701505605310e-08] 
dist 176=[2.63185886291899658620e-09,3.85741659111096101650e-08] 
dist 177=[8.94378691709803992230e-09,3.69966315133586522320e-08] 
dist 178=[2.12905106994255831930e-08,2.89868917471815327510e-08] 
dist 179=[5.43542853874452119300e-09,3.11217430089130327840e-08] 
dist 180=[-1.07353539012668453180e-08,3.01094878317881609250e-08] 
dist 181=[-2.08240159469305580100e-08,2.89679341436426140410e-08] 
dist 182=[-2.71437693507597437150e-08,2.17673765900131024870e-08] 
dist 183=[-2.87828210544207888470e-08,2.03694450601811336010e-08] 
dist 184=[-1.05877107216791244760e-08,1.99637299080883177310e-09] 
dist 185=[-1.27915067893631323000e-08,-5.82297745965221889690e-10] 
dist 186=[-1.65732884164593454530e-08,-4.98420555067356538780e-09] 
dist 187=[-1.75602397968449352660e-08,-2.41210832710751719360e-09] 
dist 188=[-6.46003318335369660470e-09,1.49154428536022148960e-09] 
dist 189=[-6.21544364208331066520e-09,3.93247127306222322360e-09] 
dist 190=[-4.69486173929158040530e-09,5.48619487265001706700e-09] 
dist 191=[-4.37874209586065731130e-09,5.91027585207288810990e-09] 
dist 192=[3.22335396336650040420e-10,5.76962576900089593970e-09] 
dist 193=[1.10045648086814845660e-09,5.50963580173521778660e-09] 
dist 194=[2.21302105302623393070e-09,4.44843511006937447350e-09] 
dist 195=[-5.05645139015825431890e-11,3.92228791756104399140e-09] 
dist 196=[-2.47617222592288590820e-09,3.72952245596345655110e-09] 
dist 197=[-3.98842494420621297810e-09,3.55965648915343194780e-09] 
dist 198=[-4.93490294876159433490e-09,2.87156671091604150470e-09] 
dist 199=[-5.17888098649847319180e-09,2.53154167625312829240e-09] 
dist 200=[-1.71340321848892570150e-09,1.12474892715202906190e-09] 
dist 201=[-2.63097297290771490060e-09,8.45170561124471055210e-10] 
dist 202=[-3.20564354455543426700e-09,5.54478880355555550210e-10] 
dist 203=[-3.35480095531212734810e-09,4.95711542178418104320e-10] 
dist 204=[-4.66190914966093372090e-10,5.62106145797515838670e-10] 
dist 205=[-4.41787873947660948480e-10,8.88827378426451461930e-10] 
dist 206=[-3.80026227319850769830e-10,1.09413292226430660290e-09] 
dist 207=[-4.14861866725961805270e-10,1.14892973187223042980e-09] 
dist 208=[-6.95622581324421405010e-10,1.13670981516248472900e-09] 
dist 209=[-9.32949168887647823190e-10,1.08359667556912006510e-09] 
dist 210=[-1.08127923752152991850e-09,9.97701890650910875750e-10] 
dist 211=[-1.11917730405786539990e-09,9.29291466593483305120e-10] 
dist 212=[-1.09106399588407338970e-09,8.12879603700045182090e-10] 
dist 213=[-1.38041217050563517210e-09,7.66968043578689688690e-10] 
dist 214=[-1.64521562922524669930e-09,7.47777105669819013060e-10] 
dist 215=[-1.71431681067159441110e-09,8.57478166241837135800e-10] 
dist 216=[-1.65880932736439128690e-09,9.67156964703855258620e-10] 
dist 217=[-1.59186531144056483140e-09,1.03556892884745483160e-09] 
dist 218=[-1.14168086560119658050e-09,1.07847409336179114660e-09] 
dist 219=[-1.10014748769497610770e-09,1.08978030996433461760e-09] 
dist 220=[-3.09782382293394652190e-10,6.16362474922019907030e-10] 
dist 221=[-2.99045709769381580460e-10,6.55463211289604203960e-10] 
dist 222=[-2.92260016785785607570e-10,7.18027875113589207670e-10] 
dist 223=[-5.15780863227378858630e-10,8.18484666841218085510e-10] 
dist 224=[-1.04619075612149407050e-09,9.18966939168846963320e-10] 
dist 225=[-1.37680652415573571730e-09,9.81630672692831967590e-10] 
dist 226=[-1.58378648353147348020e-09,1.02089296606041626400e-09] 
dist 227=[-1.63740093578243617160e-09,1.03113140528475771710e-09] 
dist 228=[-1.59406912447577437000e-09,1.01061162227611537460e-09] 
dist 229=[-1.51978057678616933650e-09,9.57195942315112120340e-10] 
dist 230=[-1.22930711092332119120e-09,9.46536049369635324060e-10] 
dist 231=[-1.08640570421137648080e-09,9.71951325869178314320e-10] 
dist 232=[-6.13356597044744857940e-10,6.48423203288743321350e-10] 
dist 233=[-9.42496997288767744240e-10,1.10584116618017373680e-09] 
dist 234=[-1.14858741150110701440e-09,1.39223454680447858680e-09] 
dist 235=[-1.20204359124888514980e-09,1.46648317565033601150e-09] 
dist 236=[-1.18056286927873072830e-09,1.43866836464284971430e-09] 
dist 237=[-1.11577891153874610300e-09,1.36119171353153535400e-09] 
dist 238=[-9.71470881438660904200e-10,1.17458317038213588450e-09] 
dist 239=[-9.00466537372629139970e-10,1.08277420701260652050e-09] 
dist 240=[-9.17846845198789156760e-10,7.91932526113224777840e-10] 
dist 241=[-1.39500384057049995870e-09,1.19098849683369718810e-09] 
dist 242=[-1.69376137857653799720e-09,1.44084904502307627260e-09] 
dist 243=[-1.77122649886185235820e-09,1.50564307471306089770e-09] 
dist 244=[-1.72245630321924538390e-09,1.47688389899193950910e-09] 
dist 245=[-1.64407451707845754260e-09,1.39756723060647118660e-09] 
dist 246=[-1.31672106803374231790e-09,1.20448618557685160600e-09] 
dist 247=[-1.15566206604384911670e-09,1.10948818028114836770e-09] 
dist 248=[-1.25201872225142600180e-09,1.18824367316139498790e-09] 
dist 249=[-1.56357218964767598860e-09,1.36505073824215846390e-09] 
dist 250=[-1.75864372831045759200e-09,1.47575426435453540250e-09] 

8 phat 5 dirichlet min maxes function [2, 1, 2, 1, 2, 2, 0, 0, 1] 
dist 0=[344.23133905084502475   ,344.23133905084502475   ] 
dist 1=[302.63382806061845487   ,356.59667421046328477   ] 
dist 2=[250.72398197741713310   ,362.42042255992256821   ] 
dist 3=[205.15940842447921897   ,364.03936615467971967   ] 
dist 4=[159.60098336304945223   ,355.30487329654161712   ] 
dist 5=[106.65529324440497384   ,268.74700345700032668   ] 
dist 6=[57.738669828529139977  ,248.07454463389877087   ] 
dist 7=[27.554599433379880196  ,175.18883046298900809   ] 
dist 8=[-17.112351282819740877  ,164.36001997839254921   ] 
dist 9=[-40.347076368912561239  ,11.502905648194935188  ] 
dist 10=[-51.173577471833275373  ,6.2275647613008950839 ] 
dist 11=[-69.898844502049523923  ,4.8264150359895236173 ] 
dist 12=[-80.046720865136483232  ,3.0566009090802192868 ] 
dist 13=[-80.657935421262426379  ,1.8169947305695111182 ] 
dist 14=[-78.077956110466587296  ,7.0628737169102429617 ] 
dist 15=[-63.105118646879004082  ,18.338383679888837673  ] 
dist 16=[-56.943343159919900126  ,26.568555314833930166  ] 
dist 17=[-11.936681364574183077  ,28.469236795440505651  ] 
dist 18=[-3.1912039667065690633 ,41.112632925643811409  ] 
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dist 90=[-.00324940250667635040,.00020423742343882196] 
dist 91=[-.00291262424946506836,.00042752247338173726] 
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dist 113=[-4.31349996497446333060e-06,.00012252638215572577] 
dist 114=[-1.99139585753254696830e-05,.00011941624865487852] 
dist 115=[-3.13776019847772894870e-05,.00011861014136844502] 
dist 116=[-3.86370341750031092690e-05,.00011794437949864122] 
dist 117=[-4.08537583918381342730e-05,5.70249311239911453880e-05] 
dist 118=[-5.96240149749038128100e-05,5.47367731991974997790e-05] 
dist 119=[-6.52147287158796986660e-05,4.26090489443556018240e-05] 
dist 120=[-6.41115797608872766140e-05,3.86301042686075876520e-05] 
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dist 122=[-4.89893808779192915700e-05,1.06768556725190606560e-05] 
dist 123=[-4.37951390603348179540e-05,1.19523077779086778290e-05] 
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dist 125=[-1.72308128057994774040e-05,3.68764373522317749350e-05] 
dist 126=[4.44983324076193237380e-06,4.77416309232995276050e-05] 
dist 127=[3.86879576880985683990e-06,5.05602440235448214530e-05] 
dist 128=[2.88123413705210618320e-06,1.48292602153835583560e-05] 
dist 129=[1.24972879597727656610e-06,1.43319887550035188350e-05] 
dist 130=[-3.94859966187653051220e-07,1.08878791853877400930e-05] 
dist 131=[-1.43321931680120370880e-06,1.02304821296966643240e-05] 
dist 132=[-2.09680146079607924820e-06,-8.35728318191230892990e-07] 
dist 133=[-5.53062544194595349890e-06,-2.22754074258801041920e-06] 
dist 134=[-7.78022773965993903760e-06,-2.23073150207369747650e-06] 
dist 135=[-8.42186919028962856230e-06,-1.86730535828186778750e-06] 
dist 136=[-8.20271827698996608450e-06,-1.26771543033142696710e-06] 
dist 137=[-7.89995682835827075150e-06,-2.91151652819262300280e-07] 
dist 138=[-6.01182842458563279050e-06,6.88625435340002366730e-07] 
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dist 140=[-4.69776342268806759860e-07,1.81368536761791565590e-06] 
dist 141=[3.08942478860261895250e-07,3.58817614426383252900e-06] 
dist 142=[5.21600673079479004290e-07,4.70268745173954529620e-06] 
dist 143=[4.49129837047523873510e-07,4.99745236389792214320e-06] 
dist 144=[3.28155508895631367640e-07,1.87881548590276528260e-06] 
dist 145=[1.29936211688503272740e-07,1.81590056679746816450e-06] 
dist 146=[-6.95986370779366526370e-08,1.36017425997108635980e-06] 
dist 147=[-1.95076854450404487010e-07,1.29126266131296644300e-06] 
dist 148=[-2.74740446992370912920e-07,-1.79692817049092201940e-07] 
dist 149=[-6.23742472484370679730e-07,-2.40718242155571860960e-07] 
dist 150=[-8.99282621938907728620e-07,-2.35139342417767893400e-07] 
dist 151=[-9.76921292050406747910e-07,-1.97627105809709559740e-07] 
dist 152=[-9.55029873076171791740e-07,-1.36005622748025248040e-07] 
dist 153=[-9.15694765448855736740e-07,-3.58284574160948587900e-08] 
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dist 156=[-9.97403434010389084480e-08,2.93444967487676132750e-07] 
dist 157=[7.61543049248490784650e-09,5.48640356491200284380e-07] 
dist 158=[6.52662103121987345790e-08,7.08530613495330650040e-07] 
dist 159=[5.63369147564828823040e-08,7.50010474717294713660e-07] 
dist 160=[4.15634804247523939480e-08,2.24649986903066210370e-07] 
dist 161=[1.74577762511319541680e-08,2.16800992435363181450e-07] 
dist 162=[-6.76053830518848562350e-09,1.62552193038208584120e-07] 
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dist 164=[-3.96404787857504522850e-08,-3.25459002491946424160e-09] 
dist 165=[-9.26364954219302960510e-08,-2.88199169336854093290e-08] 
dist 166=[-1.26058113408505182630e-07,-3.19940059985219597470e-08] 
dist 167=[-1.35225513623010367140e-07,-2.65816527267938831910e-08] 
dist 168=[-1.31378058194098640420e-07,-1.77717647490504367800e-08] 
dist 169=[-1.26223640826672683480e-07,-3.51188587334328645730e-09] 
dist 170=[-9.68140151902048838130e-08,1.07757545737238638840e-08] 
dist 171=[-8.89241347862366963560e-08,1.96934429720203102760e-08] 
dist 172=[-2.36547077070940402140e-08,4.04873279971124014170e-08] 
dist 173=[-1.47135141998883941810e-08,6.61698004185719000910e-08] 
dist 174=[-2.47205255724672920820e-09,8.23066734663070236300e-08] 
dist 175=[0                     ,8.66012547351004818460e-08] 
dist 176=[4.06808424806156336560e-09,2.80708274193734608260e-08] 
dist 177=[1.61736142929352852700e-09,2.70858006017017174700e-08] 
dist 178=[-1.67111211407370467310e-09,2.02033858914340592890e-08] 
dist 179=[-3.74652264270545470150e-09,1.91573135027199533760e-08] 
dist 180=[-5.05551693970843379160e-09,-2.78960767576965439230e-09] 
dist 181=[-9.43930782666307360910e-09,-3.08125717249705704160e-09] 
dist 182=[-1.35260779707870530580e-08,-2.96305973347618767040e-09] 
dist 183=[-1.46406654340102132090e-08,-2.42247259735751716910e-09] 
dist 184=[-1.42376677313428645670e-08,-1.54410158439332697790e-09] 
dist 185=[-1.36686224435215359680e-08,-1.23412567947986041250e-10] 
dist 186=[-1.05706087579765332840e-08,1.30002629129735489600e-09] 
dist 187=[-9.63663011431236931930e-09,2.52762310407098915930e-09] 
dist 188=[-4.92143644701877825450e-10,3.43511397117033390870e-09] 
dist 189=[2.03919706673550773600e-10,7.03643511341833247790e-09] 
dist 190=[1.90997603973978920330e-10,9.29221659544713626330e-09] 
dist 191=[1.15696510496798028190e-10,9.87724587692042437530e-09] 
dist 192=[-9.10863807363799631180e-12,4.67356388929238944890e-09] 
dist 193=[-2.12918315656365237590e-10,4.47638010593189672790e-09] 
dist 194=[-4.17722391659092478520e-10,3.52674210282861202950e-09] 
dist 195=[-5.46389071009528503100e-10,3.15466092931853642320e-09] 
dist 196=[-1.40875673357458227490e-09,4.38683576315264169000e-10] 
dist 197=[-2.66073156483321794700e-09,4.41487470172730474760e-10] 
dist 198=[-3.44696666807349792300e-09,4.26480756558639033500e-10] 
dist 199=[-3.65580329780399064430e-09,4.06651130164804709860e-10] 
dist 200=[-3.58266820629610434040e-09,3.21545898216612291850e-10] 
dist 201=[-3.40054482520588115740e-09,2.83593030484791287800e-10] 
dist 202=[-2.87408337188085392620e-09,5.53553229097499714670e-10] 
dist 203=[-2.61383877467336506480e-09,1.42884476242021524230e-09] 
dist 204=[-2.41801392664756701830e-09,2.65586581424439926410e-09] 
dist 205=[-2.66830651735014071750e-09,3.42081493400327561200e-09] 
dist 206=[-2.82494868023808325440e-09,3.89965279467609882460e-09] 
dist 207=[-2.86556493090506477370e-09,4.02337850649770523620e-09] 
dist 208=[-5.27757119024819018600e-10,7.09766429390773955230e-10] 
dist 209=[-6.27459233982643139960e-10,6.85024897636674981970e-10] 
dist 210=[-8.15409948171740434820e-10,8.64902819226858112060e-10] 
dist 211=[-1.12464221042935504630e-09,1.08392183362643796090e-09] 
dist 212=[-1.31919794951364935880e-09,1.22096149255013126050e-09] 
dist 213=[-1.36982843093334996480e-09,1.25629912083528628000e-09] 
dist 214=[-1.33954062364734973480e-09,1.21352474333679755050e-09] 
dist 215=[-1.27178823792204931910e-09,1.16583188678397887690e-09] 
dist 216=[-1.06716936646622511140e-09,8.80108294298852034070e-10] 
dist 217=[-9.66440834565177945160e-10,8.17972661589600577370e-10] 
dist 218=[-8.86020712327099410290e-10,9.98122129897349710630e-10] 
dist 219=[-9.55888804564179503100e-10,1.30532729437800796990e-09] 
dist 220=[-9.99639641801377573730e-10,1.49767905912626981480e-09] 
dist 221=[-1.05270676481253344350e-09,1.54755753586606615530e-09] 
dist 222=[-1.15291991875680360510e-09,1.23799294726752883320e-09] 
dist 223=[-1.17890374380738458020e-09,1.27077211001022877200e-09] 
dist 224=[-9.21917417662669805100e-10,1.23413812456945112880e-09] 
dist 225=[-1.09052099075987037370e-09,1.17974646522572491290e-09] 
dist 226=[-1.25913360035707094260e-09,1.41285847108872312130e-09] 
dist 227=[-1.36425098409346731950e-09,1.84247652811054829730e-09] 
dist 228=[-1.43007721242170504600e-09,2.11146154865711926430e-09] 
dist 229=[-1.44716690116717791190e-09,2.18119115141974074750e-09] 
dist 230=[-1.40176757909849166500e-09,2.13977210349033264510e-09] 
dist 231=[-1.34331366743361069670e-09,2.02458854125902491480e-09] 
dist 232=[-1.03840748295136214630e-09,1.74669183522975042770e-09] 
dist 233=[-9.42704813820564276860e-10,1.60996955921737845700e-09] 
dist 234=[-1.36358514405958846440e-09,9.07127384951989938670e-10] 
dist 235=[-2.07297492341833003020e-09,7.12118980923782544030e-10] 
dist 236=[-2.51713884557936839570e-09,9.37576951781361565210e-10] 
dist 237=[-2.63230835283943407570e-09,9.96045199887946763470e-10] 
dist 238=[-2.56548134819807654790e-09,9.82522058656401334900e-10] 
dist 239=[-2.44334411078646876780e-09,9.50962366319100320320e-10] 
dist 240=[-1.99478133514000909320e-09,9.28232482042579803810e-10] 
dist 241=[-1.77408669382027412350e-09,8.82718489337399505620e-10] 
dist 242=[-7.88091565642360121360e-10,1.12661593302834846550e-09] 
dist 243=[-1.14514701605799803480e-09,1.87887127122586141590e-09] 
dist 244=[-1.36870872290044187980e-09,2.34987607240506722590e-09] 
dist 245=[-1.42668064947167637090e-09,2.47200902062167500620e-09] 
dist 246=[-1.40284800260131780770e-09,2.40198386301418810200e-09] 
dist 247=[-1.32426938616904858760e-09,2.29455650450505902340e-09] 
dist 248=[-1.16427823525961338820e-09,1.82450055412699965720e-09] 
dist 249=[-1.08556129491865614260e-09,1.61023255691217702990e-09] 
dist 250=[-1.44354766185489058390e-09,1.41000836707815136790e-09] 
dist 251=[-1.76451785619055777750e-09,1.66010943406000147560e-09] 
dist 252=[-1.96548548607699045200e-09,1.81670396836458070770e-09] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 1, 2, 1, 0, 0, 2] 
dist 0=[340.86134565089209142   ,340.86134565089209142   ] 
dist 1=[317.42282889040033439   ,347.09215022375235269   ] 
dist 2=[283.43138106315135901   ,347.49418148173782837   ] 
dist 3=[247.95053108826257012   ,342.03759397832384322   ] 
dist 4=[182.38207952393611669   ,331.49495403144375959   ] 
dist 5=[125.97727865661482785   ,246.25899178386926275   ] 
dist 6=[71.339772170624290212  ,226.66275579851489462   ] 
dist 7=[10.447780767425849018  ,160.39863451682703082   ] 
dist 8=[-41.649760518017554593  ,150.63650984319426514   ] 
dist 9=[-62.501228485484192343  ,32.569978781633672654  ] 
dist 10=[-70.598922751941518887  ,8.4493592865821829478 ] 
dist 11=[-77.360764290929312288  ,4.0164578680753653752 ] 
dist 12=[-85.418320234464179335  ,4.6825716182066863893 ] 
dist 13=[-85.585749687667419791  ,11.590073301130417732  ] 
dist 14=[-66.878328409084233982  ,18.765143055471842187  ] 
dist 15=[-52.715234560989328538  ,25.756412901369007627  ] 
dist 16=[-50.580346951011673037  ,34.795722122272684497  ] 
dist 17=[.65686866777429499062,36.289313897256216900  ] 
dist 18=[.41299764019751296125,34.664522896658101938  ] 
dist 19=[-5.9625556603334384162 ,31.978518374670511041  ] 
dist 20=[-10.788778501441230045  ,30.529967425970675867  ] 
dist 21=[-18.646092907539838616  ,31.056923743764529302  ] 
dist 22=[-25.657250626477878412  ,30.156542775036775645  ] 
dist 23=[-27.381901435093629722  ,24.589248913957801230  ] 
dist 24=[-13.764429830927192750  ,22.176228677851793196  ] 
dist 25=[-12.644464058441870231  ,4.2067977154929060167 ] 
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dist 97=[8.07165018658943378710e-05,.00130575999212331272] 
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dist 122=[-5.63102921620790931650e-05,-1.20194816378947559840e-06] 
dist 123=[-7.27687911210193215580e-05,-1.12512656813854027020e-05] 
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dist 125=[-2.24878520308748257780e-05,1.31506958450821173300e-05] 
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dist 128=[-1.53394844727471219290e-05,2.05590801345801570480e-05] 
dist 129=[1.42451978195870873240e-06,1.97393691335655277450e-05] 
dist 130=[4.15223439439079059400e-06,1.56933929858225374440e-05] 
dist 131=[2.61937416137850163770e-06,1.40268125617049756790e-05] 
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dist 145=[2.89876648543164431760e-07,2.53048375690018501260e-06] 
dist 146=[6.38043155284658593850e-07,1.92520874145967116640e-06] 
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dist 156=[-1.12400993440301655670e-06,5.97977150763324362590e-08] 
dist 157=[-3.32558386013760241050e-07,1.98749994365155061400e-07] 
dist 158=[-3.20595031941660987830e-07,2.86630967553457308040e-07] 
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dist 160=[-2.26067282093227456010e-07,3.04217361109948720350e-07] 
dist 161=[2.01211949005308546120e-08,2.91604714508600429630e-07] 
dist 162=[5.99895292577823525130e-08,2.30911673155136557890e-07] 
dist 163=[3.68522489517802702460e-08,2.06141647954126281920e-07] 
dist 164=[-9.43256225531037527820e-08,1.89637033914728611760e-07] 
dist 165=[-1.76183417900419479770e-07,1.83572631477604233660e-07] 
dist 166=[-2.27467910558147628300e-07,1.76544693050030605660e-07] 
dist 167=[-2.40770752829669040410e-07,1.33204409912258876580e-07] 
dist 168=[-7.02737150621290725640e-08,1.24157442365247625540e-07] 
dist 169=[-6.78251633329947817800e-08,9.08516909039263643010e-09] 
dist 170=[-7.84869484543089171670e-08,-7.84657442281188551330e-09] 
dist 171=[-1.02587339436264874770e-07,-1.64754206893250303640e-08] 
dist 172=[-1.08877507551122571480e-07,9.85593527841997769950e-09] 
dist 173=[-4.13383014302201197570e-08,2.63417767064438925430e-08] 
dist 174=[-3.98356410299201640140e-08,3.67359850257962784640e-08] 
dist 175=[-2.96596414184654450480e-08,3.95820088090746816570e-08] 
dist 176=[-2.80656997560842425600e-08,3.84414231600225434190e-08] 
dist 177=[4.04170225660846559240e-09,3.69540011137769022140e-08] 
dist 178=[9.11220323287751889130e-09,2.82194126001568067170e-08] 
dist 179=[3.83362055482833151340e-09,2.60414322529181060150e-08] 
dist 180=[-9.56576867024225304730e-09,2.18269396918164256830e-08] 
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dist 182=[-2.31792835139782567350e-08,2.03181608472389262190e-08] 
dist 183=[-2.45567905993625215710e-08,1.59998678897441359850e-08] 
dist 184=[-7.25658869463138419870e-09,1.42913654488812797390e-08] 
dist 185=[-7.00160836888173115080e-09,2.47396630959392985130e-09] 
dist 186=[-1.24745626427022917640e-08,1.54051895596163578260e-10] 
dist 187=[-1.59988478291485507890e-08,-1.83526961623207955720e-09] 
dist 188=[-1.69127848129499069650e-08,8.52338324892893864780e-10] 
dist 189=[-5.00848326225646011940e-09,2.54900581216844636320e-09] 
dist 190=[-4.81317339276914234420e-09,3.61915580202852506830e-09] 
dist 191=[-3.66280325212040058110e-09,3.91319900270817810040e-09] 
dist 192=[-3.38754570381283671530e-09,3.85049898402628323500e-09] 
dist 193=[9.97086808772100198890e-12,3.65609772033603393960e-09] 
dist 194=[5.06166956708898419560e-10,3.11674687950508289120e-09] 
dist 195=[-3.99517765693625202500e-10,2.94685460702633035030e-09] 
dist 196=[-2.30606238804934060790e-09,3.15032638684664813520e-09] 
dist 197=[-3.49530170365970448430e-09,3.05041197850236782410e-09] 
dist 198=[-4.24018732171986023230e-09,2.92889214084572885930e-09] 
dist 199=[-4.43336865539761841390e-09,2.23442870199163908580e-09] 
dist 200=[-1.08850941133007557360e-10,2.05781039908080466030e-09] 
dist 201=[-9.10663420651004941230e-10,7.62633549243317447790e-10] 
dist 202=[-1.42244199230595949100e-09,6.65246518529454513530e-10] 
dist 203=[-1.85935889286816503240e-09,6.19122595824780129890e-10] 
dist 204=[-1.97265988921101749250e-09,4.37399041868348737380e-10] 
dist 205=[-8.93912854180743513910e-10,3.67283283508098081950e-10] 
dist 206=[-1.06887170563032886700e-09,3.24090100964788703250e-10] 
dist 207=[-1.11287667278400325050e-09,3.14388688403732147600e-10] 
dist 208=[-1.15443560612073591440e-09,5.72451354051181348280e-10] 
dist 209=[-1.31993192862302645660e-09,1.24578424315431946070e-09] 
dist 210=[-1.58516656268526083330e-09,1.66568450823627050340e-09] 
dist 211=[-2.01134682177570374930e-09,1.92876413341199016920e-09] 
dist 212=[-2.65374803105665964160e-09,2.79219924232980312280e-09] 
dist 213=[-3.05422006724464677480e-09,3.48154996645030770180e-09] 
dist 214=[-3.30493041516369779120e-09,3.91314699772907933600e-09] 
dist 215=[-3.36980793549982387820e-09,4.02506088658955672130e-09] 
dist 216=[-8.86209700216232097800e-10,3.13022517281353856890e-09] 
dist 217=[-6.47345720868581890860e-10,2.99726613059794008230e-09] 
dist 218=[-1.17684028103994303230e-09,2.33228025457325550460e-09] 
dist 219=[-1.50841765097136726370e-09,2.10296807753230989960e-09] 
dist 220=[-1.59449746106213864850e-09,1.55048495182437807640e-09] 
dist 221=[-1.71653503878678704620e-09,1.51342147996032851450e-09] 
dist 222=[-2.18785141634394815440e-09,1.43904317600493000470e-09] 
dist 223=[-2.32046185101954664060e-09,1.19093977545776202830e-09] 
dist 224=[-2.28535538809694892280e-09,1.06889510843994614350e-09] 
dist 225=[-2.15367840990810169810e-09,7.51256276095888214170e-10] 
dist 226=[-1.93531271265492994640e-09,1.12534158302824993820e-09] 
dist 227=[-1.80367636342608272080e-09,1.40936376216031810320e-09] 
dist 228=[-1.55656487030643264560e-09,1.73073914253998382390e-09] 
dist 229=[-1.51471071271734405040e-09,2.54139843553032431050e-09] 
dist 230=[-1.44478633955630457970e-09,3.04895288942935734340e-09] 
dist 231=[-1.16403959210110752130e-09,3.18052517788714509800e-09] 
dist 232=[-1.02591738786599186910e-09,3.07492627579815947730e-09] 
dist 233=[-1.00835149034647109920e-09,2.95215717033710783670e-09] 
dist 234=[-1.21139528050602970810e-09,2.24357295659907133720e-09] 
dist 235=[-1.33852726945061741690e-09,2.07167846117261419340e-09] 
dist 236=[-1.37149531917400542700e-09,1.71727410296139992980e-09] 
dist 237=[-1.58780186989585575140e-09,1.65616053774606619310e-09] 
dist 238=[-2.07010484976101243700e-09,1.59399419620483299920e-09] 
dist 239=[-2.19515708463742374690e-09,1.18378885932556189120e-09] 
dist 240=[-2.16369149886483468900e-09,1.11860371264949836100e-09] 
dist 241=[-2.04239377357919299310e-09,4.10727908564334826720e-10] 
dist 242=[-1.84867438620689589590e-09,4.81261345343987034650e-10] 
dist 243=[-1.72254947659290297110e-09,1.12533520222206993360e-09] 
dist 244=[-1.87492346375609647270e-09,2.04761970562304695660e-09] 
dist 245=[-2.08500080885640335400e-09,2.66762960410461589640e-09] 
dist 246=[-2.21653545348157359380e-09,3.09544686500718926520e-09] 

8 phat 5 dirichlet min maxes function [0, 2, 2, 1, 2, 2, 2, 0, 2] 
dist 0=[445.84812751401051611   ,445.84812751401051611   ] 
dist 1=[419.18729351051344443   ,445.75889442934556978   ] 
dist 2=[365.01518266434343618   ,445.84812751401051611   ] 
dist 3=[268.23758659421855159   ,388.75879142833656942   ] 
dist 4=[166.47173234449744000   ,355.89627363991688858   ] 
dist 5=[92.557383363203920286  ,294.02495626035622740   ] 
dist 6=[32.233437025767832633  ,130.65023220874389143   ] 
dist 7=[-17.864665081072606991  ,68.488453404989300828  ] 
dist 8=[-60.335628467552785562  ,55.247869610773632896  ] 
dist 9=[-89.236003961227122693  ,-52.601795345719905086  ] 
dist 10=[-104.11699155753715717   ,-55.047419094978771614  ] 
dist 11=[-104.97223837470877078   ,-26.149471908836126664  ] 
dist 12=[-92.005962893479060413  ,6.0333569871795491563 ] 
dist 13=[-84.697320707135600566  ,27.234943553631326348  ] 
dist 14=[-22.277142277555643242  ,40.783861038215839310  ] 
dist 15=[-10.030544582085466632  ,49.679046385937569752  ] 
dist 16=[7.5190360675513896659 ,68.185452266405619344  ] 
dist 17=[15.776710868146268555  ,72.914721978626728999  ] 
dist 18=[11.875045744299337154  ,25.142826909815441403  ] 
dist 19=[3.0186460568893417300 ,24.968338940271586786  ] 
dist 20=[-6.4499607023244669190 ,21.645831009961667644  ] 
dist 21=[-12.739620536639271795  ,19.558477121989055066  ] 
dist 22=[-16.972361942379476803  ,5.4427306433140579282 ] 
dist 23=[-18.577815961182463390  ,3.0260930150245406458 ] 
dist 24=[-18.761581395871723261  ,.5999809217193754544 ] 
dist 25=[-17.546481750582962158  ,.09945319033723538375] 
dist 26=[-12.129264659260728703  ,.19024883923427545823] 
dist 27=[-11.886936702666620566  ,1.0394397023976835375 ] 
dist 28=[-9.9231787356001770217 ,2.0888221598005531997 ] 
dist 29=[-8.9775252020868284540 ,2.9589826043789680628 ] 
dist 30=[-1.9010021293486135930 ,5.8227792493781404229 ] 
dist 31=[-.48807431187652416976,7.8420963201217235731 ] 
dist 32=[2.1156625799790297058 ,8.7086322944533829164 ] 
dist 33=[2.6664440031692532984 ,9.2594137176436061918 ] 
dist 34=[2.4876277231164544362 ,3.9545499481031736490 ] 
dist 35=[1.7687593316892322414 ,3.8190820645663307726 ] 
dist 36=[-.05880691963660333778,2.2522392763562430543 ] 
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dist 39=[-2.4501105967305061466 ,-.34757940959440654392] 
dist 40=[-2.5403708853980526486 ,-1.0446707252869938964 ] 
dist 41=[-2.4818792904732457297 ,-1.2069828534261367424 ] 
dist 42=[-2.0506328357166870014 ,-1.1063676521729719637 ] 
dist 43=[-1.8562956169869276282 ,-.42055982330819380696] 
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dist 47=[.01796893660632342800,1.9287136062249937110 ] 
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dist 54=[-.42650389886738926002,.1037543482462173424 ] 
dist 55=[-.45791754104316989614,.03377161564431703253] 
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dist 57=[-.34748617278144287348,.00977865578281503725] 
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dist 67=[.02544664132744480504,.06047514381163712213] 
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dist 76=[-.01809689365085734560,.01269544757808435651] 
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dist 80=[.00495801645451724302,.01526837230753091657] 
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dist 83=[.00262337022635992152,.00704912163325601819] 
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dist 85=[-.00360386119872367781,.00395788637946418232] 
dist 86=[-.00515566047836097635,-.00048504157587324496] 
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dist 91=[-.00381654535501734487,-.00073457128018960925] 
dist 92=[-.00219575838604124497,.00119090335888507463] 
dist 93=[-.00196392604684245966,.00239779179415846657] 
dist 94=[-.00031217203794212021,.00315822424878796589] 
dist 95=[1.48981956566960418330e-05,.00336331203419113196] 
dist 96=[.00057574120341664115,.00234587944401369551] 
dist 97=[.00067525339720694688,.00225653571639721686] 
dist 98=[.00060283382740234700,.00093908276406082494] 
dist 99=[.00035884384918265765,.00089356813005040757] 
dist 100=[-.00011403617257375403,.00049506503046347277] 
dist 101=[-.00041271544161992474,.00045911068387543719] 
dist 102=[-.00060371124024217395,-3.57474277090847044950e-05] 
dist 103=[-.00066166165772244386,-.00011633126937619680] 
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dist 105=[-.00062626625514158729,-.00030475246121286431] 
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dist 107=[-.00044626371531936567,-8.30737776911712786560e-05] 
dist 108=[-.00026904015052139023,.00019704273917160496] 
dist 109=[-.00025005250482534168,.00037204774921210435] 
dist 110=[-2.14386594609132004890e-05,.00048176681777225265] 
dist 111=[1.33797915858629982750e-05,.00051024353291298634] 
dist 112=[7.52716603689870740070e-05,.00022984596351405133] 
dist 113=[8.59627847119444829060e-05,.00022311826500437701] 
dist 114=[7.82407413600230072450e-05,.00012183137646242317] 
dist 115=[2.72484585229470957540e-05,.00011074463165386630] 
dist 116=[-3.97766539505925880770e-05,7.99718784774476531520e-05] 
dist 117=[-8.17276723678225501770e-05,5.78648853236585093140e-05] 
dist 118=[-.00010812500298573441,2.16216072551946857980e-05] 
dist 119=[-.00011519977591575542,6.17608676026307572410e-06] 
dist 120=[-.00011259531147669259,2.99813308681581149890e-06] 
dist 121=[-8.83136995755002214120e-05,3.57088149698005324960e-06] 
dist 122=[-6.77744086187249748720e-05,7.47979144041590200600e-06] 
dist 123=[-6.24369062012365955460e-05,1.40247995629000527880e-05] 
dist 124=[-3.23223474394942397550e-05,2.74615267355410943830e-05] 
dist 125=[-2.88844555612358254360e-05,4.51730066603325377460e-05] 
dist 126=[-4.43874446360365206090e-06,5.63367858956791014980e-05] 
dist 127=[0                     ,5.93762898962984008680e-05] 
dist 128=[8.54290583718799278720e-06,3.60438555731894137700e-05] 
dist 129=[9.93043531452382770940e-06,3.34966718698305993730e-05] 
dist 130=[9.07010268840124819650e-06,1.02175444918794078480e-05] 
dist 131=[6.61951138413015976310e-06,9.61921383633575534620e-06] 
dist 132=[2.61373030225886839250e-06,7.29321952262685265800e-06] 
dist 133=[-1.41242839296815444600e-06,6.82411582040073019650e-06] 
dist 134=[-3.94190012842151509110e-06,-1.09921109506167831720e-07] 
dist 135=[-5.54545120260484565550e-06,-1.26465831462923613380e-06] 
dist 136=[-6.00271737891006260300e-06,-3.48143729757968083280e-06] 
dist 137=[-6.14612856624617275570e-06,-3.85068619857647395190e-06] 
dist 138=[-5.97225073819931793100e-06,-3.70002175851667737350e-06] 
dist 139=[-5.74009162063669308900e-06,-2.74964928133041098320e-06] 
dist 140=[-4.39424870137485905970e-06,-7.30863435931282819550e-07] 
dist 141=[-4.04539186293034594800e-06,1.29350736188510534540e-06] 
dist 142=[-1.06301298588808070730e-06,2.55881676899437027980e-06] 
dist 143=[-6.62590702665342377530e-07,3.35351585006067678440e-06] 
dist 144=[-1.12577209363698284930e-07,3.68259601190147737350e-06] 
dist 145=[0                     ,3.87551914235637395190e-06] 
dist 146=[1.15562233376398004350e-06,1.29433552220052383170e-06] 
dist 147=[8.53614066498923274250e-07,1.20945843607977852830e-06] 
dist 148=[3.61857624076727852510e-07,9.20354292688198148740e-07] 
dist 149=[-1.31912826490667568190e-07,8.56166625486300931190e-07] 
dist 150=[-4.41764430491206260570e-07,-1.26807767325390191220e-07] 
dist 151=[-6.37858867581048073690e-07,-2.81332704425643155990e-07] 
dist 152=[-6.93105457477470944210e-07,-5.94828367422739455200e-07] 
dist 153=[-6.77585973275965303780e-07,-6.41649721666871469150e-07] 
dist 154=[-6.49676509164487283220e-07,-5.56242404133736465350e-07] 
dist 155=[-6.05755907898963912760e-07,-3.76192373876870995730e-07] 
dist 156=[-4.78579652938573996880e-07,-8.50497686524637526160e-08] 
dist 157=[-4.27292097264493769580e-07,2.06634170427949987410e-07] 
dist 158=[-6.30750904280053027340e-08,3.88663038065993735020e-07] 
dist 159=[8.80375596817960277960e-09,5.02709734356121102770e-07] 
dist 160=[1.30378238892030651650e-07,5.32293233407148332810e-07] 
dist 161=[1.50483193524191478640e-07,4.99239825307044786800e-07] 
dist 162=[1.34795999208080577690e-07,1.53789565174605000290e-07] 
dist 163=[9.77154633323821745390e-08,1.41050624030529889290e-07] 
dist 164=[3.75347702211357106490e-08,1.08968344394929357340e-07] 
dist 165=[-2.28205099337907531060e-08,9.96381674438624410750e-08] 
dist 166=[-6.06132332211763131660e-08,-1.00741500624883684290e-08] 
dist 167=[-8.44461368647144758900e-08,-2.78564545545799750130e-08] 
dist 168=[-9.09820515075422489480e-08,-6.32872503653948661170e-08] 
dist 169=[-8.82806256463902543500e-08,-6.88543706534446159900e-08] 
dist 170=[-8.49546848904867752720e-08,-5.83921621622710768850e-08] 
dist 171=[-7.68837713726435514770e-08,-4.00155658039470596040e-08] 
dist 172=[-5.98741763100161904270e-08,-1.03292207305240316190e-08] 
dist 173=[-5.41151411077561050400e-08,1.94060370876189963880e-08] 
dist 174=[-4.26647355797704778950e-09,3.79726663839030136540e-08] 
dist 175=[3.46540780689156666720e-09,4.96206500434675795070e-08] 
dist 176=[1.70450563519177054390e-08,5.26804362015833579080e-08] 
dist 177=[1.92507138909949788760e-08,4.97951034438255545870e-08] 
dist 178=[1.64822440480098440050e-08,1.89047613864435333990e-08] 
dist 179=[1.19425558493699994750e-08,1.82155432927837118790e-08] 
dist 180=[4.59593927872164300480e-09,1.36204414959247719890e-08] 
dist 181=[-2.83139634606742304230e-09,1.28463071153983819320e-08] 
dist 182=[-7.51189712809209692610e-09,-1.62028903136992807600e-09] 
dist 183=[-1.04599693771749055250e-08,-3.92311903621141441810e-09] 
dist 184=[-1.12612360746939757870e-08,-8.52827996726229749230e-09] 
dist 185=[-1.09048171420796594650e-08,-8.55486411142554455350e-09] 
dist 186=[-1.05053707148937459710e-08,-7.04791503390150993850e-09] 
dist 187=[-9.55558030616922538460e-09,-4.61484055335852671190e-09] 
dist 188=[-7.40038142646864063890e-09,-6.91597622303952942080e-10] 
dist 189=[-6.71938153420781914680e-09,3.23604049205982083210e-09] 
dist 190=[-8.49504921867756635020e-10,5.68619065802060406140e-09] 
dist 191=[1.74313455509722084240e-10,7.22093290269763866510e-09] 
dist 192=[1.31313109287733065610e-09,7.61896615146538015840e-09] 
dist 193=[1.23611010026948642020e-09,7.06517671085965148730e-09] 
dist 194=[8.98407314623776789400e-10,4.29078124151413879180e-09] 
dist 195=[3.51818865470272532390e-10,4.10258401108595111410e-09] 
dist 196=[-5.30723442326208181490e-10,3.25664325572740934440e-09] 
dist 197=[-1.77241436262153097980e-09,2.88409535320765393920e-09] 
dist 198=[-2.75823966303053749020e-09,1.12167599393203627900e-09] 
dist 199=[-3.37619074623450023420e-09,1.09646272148259159090e-09] 
dist 200=[-3.53768651015264268260e-09,1.08640496299241636850e-09] 
dist 201=[-3.47523029246064355160e-09,1.05625401100981825290e-09] 
dist 202=[-2.65855820624222251040e-09,1.00333277700134734480e-09] 
dist 203=[-2.12918257803659246760e-09,8.26125095706547662810e-10] 
dist 204=[-1.86801255213470763850e-09,7.39786979248277801360e-10] 
dist 205=[-1.41792258059146381660e-09,1.14408702267969680120e-09] 
dist 206=[-8.26726618182148536540e-10,1.85666681446157170570e-09] 
dist 207=[-1.02481572295026989800e-09,2.30288373628798023750e-09] 
dist 208=[-1.07513372306185090870e-09,2.41859672490896740530e-09] 
dist 209=[-1.06453109102389395840e-09,1.58245706168579123760e-09] 
dist 210=[-1.02766368735408628500e-09,3.99233251237109119770e-10] 
dist 211=[-9.69497699312763111080e-10,6.63414780651121161900e-10] 
dist 212=[-9.88999690949295953030e-10,1.08664015878824268710e-09] 
dist 213=[-1.54737484038883188440e-09,1.50970749845536421210e-09] 
dist 214=[-1.89560941936269589100e-09,1.77327504345937625430e-09] 
dist 215=[-2.11381198989803929970e-09,1.93813714839566128630e-09] 
dist 216=[-2.17074107616848537380e-09,1.98053993114859190660e-09] 
dist 217=[-2.09808287973082002820e-09,1.96359859462137263460e-09] 
dist 218=[-2.01541767438666260550e-09,1.89959738802344042900e-09] 
dist 219=[-1.52518415577577672240e-09,1.79761364987019665290e-09] 
dist 220=[-1.41462768808969075660e-09,1.67198091614310860980e-09] 
dist 221=[-1.88572436724503238080e-09,1.47081052099054935330e-09] 
dist 222=[-2.65924958844567669580e-09,1.36897872706730557690e-09] 
dist 223=[-3.14352765559665796290e-09,1.30522482349937337110e-09] 
dist 224=[-3.26901079757588461030e-09,1.28869304299215409900e-09] 
dist 225=[-3.16142008049619529050e-09,8.90517481270478063720e-10] 
dist 226=[-3.03421340901178919150e-09,8.63240700703406430350e-10] 
dist 227=[-2.31264038594281496800e-09,8.26676699553938957600e-10] 
dist 228=[-2.12921591539075886410e-09,6.45909104103850770710e-10] 
dist 229=[-5.34567188295272619290e-10,6.45113561204343821100e-10] 
dist 230=[-8.18174556560370630320e-10,1.42837357251050533830e-09] 
dist 231=[-9.95761793314403671600e-10,1.91877939250677319660e-09] 
dist 232=[-1.04183998826765375790e-09,2.04591874276017929550e-09] 
dist 233=[-1.02075784443859600150e-09,2.00598962491856365480e-09] 
dist 234=[-9.67093208695076767720e-10,1.89901846050691781270e-09] 
dist 235=[-8.25367266905564527890e-10,1.63116767920009602160e-09] 
dist 236=[-7.55630466537597338590e-10,1.49938941896355374470e-09] 
dist 237=[-1.46296624456068718570e-09,1.20700329651867804260e-09] 
dist 238=[-2.00048532950770335110e-09,1.20381456122608905290e-09] 
dist 239=[-2.33703767000975249330e-09,1.20181945315288111450e-09] 

8 phat 5 dirichlet min maxes function [2, 2, 1, 0, 2, 0, 2, 0, 2] 
dist 0=[321.96962121960827786   ,321.96962121960827786   ] 
dist 1=[289.21923058392912866   ,331.10905151733891847   ] 
dist 2=[248.99348512703084245   ,330.32116173107211099   ] 
dist 3=[210.30024997110330454   ,324.91185675334211131   ] 
dist 4=[168.39130708624968261   ,307.81771350962349203   ] 
dist 5=[114.77099805364792746   ,223.97030989086574186   ] 
dist 6=[63.875868674733740632  ,193.43563021539444392   ] 
dist 7=[32.344067869775391938  ,169.54586823651203089   ] 
dist 8=[3.9939806145056638912 ,106.90411552352672075   ] 
dist 9=[-38.497248407498702070  ,21.322208403578015252  ] 
dist 10=[-67.195298904054926430  ,-12.550383836131158712  ] 
dist 11=[-81.135613214844083146  ,-15.310340649788127445  ] 
dist 12=[-85.587514828706207868  ,-14.336394302630046225  ] 
dist 13=[-84.763967714831886915  ,-.00260859190303507905] 
dist 14=[-72.452485087769305392  ,16.780573159641257749  ] 
dist 15=[-65.120820444730237123  ,32.462560429108162173  ] 
dist 16=[-3.9213615278349000523 ,47.481336591650271928  ] 
dist 17=[-2.1544620406849495836 ,58.026550379978925724  ] 
dist 18=[-.71956595179482768758,59.845747258439796380  ] 
dist 19=[-.48730528731792272658,52.297571195571870260  ] 
dist 20=[-.81825275373778362033,51.053582929857686837  ] 
dist 21=[-.81887050720371279139,39.094902444530987007  ] 
dist 22=[-12.311221495444357407  ,32.065198107446643904  ] 
dist 23=[-23.355605367774722161  ,28.936650013486263963  ] 
dist 24=[-29.064836146309119499  ,9.5792355856190782969 ] 
dist 25=[-31.531372706088713271  ,13.823594740162540729  ] 
dist 26=[-31.277094376774004710  ,18.290428796054924099  ] 
dist 27=[-30.317510454691456279  ,21.241016310855490817  ] 
dist 28=[-23.935642146624755203  ,23.230508744729285884  ] 
dist 29=[-9.0690165760366383770 ,24.013523389054985283  ] 
dist 30=[-7.1474842030364929777 ,23.857669962901947551  ] 
dist 31=[-6.7699388264722431250 ,22.486476264962766504  ] 
dist 32=[.07269269882639733378,19.493050196533449613  ] 
dist 33=[.10339934774162728677,7.2362438330017462404 ] 
dist 34=[.11371697808535996865,7.1944728761736920230 ] 
dist 35=[.06608952317075844376,5.7916129894334468568 ] 
dist 36=[.00752730637017179218,5.5810607265693562178 ] 
dist 37=[-.18177786000811036832,4.8910867835440113857 ] 
dist 38=[-1.9602083782456345714 ,3.7804675332775030397 ] 
dist 39=[-3.1599270334617049061 ,3.5251584079999163583 ] 
dist 40=[-3.6528792960892426540 ,.38965301953935830233] 
dist 41=[-3.7504207395967620614 ,.18478329356183909231] 
dist 42=[-3.6514153763016334601 ,.3678549411275362805 ] 
dist 43=[-3.0214796546656768595 ,.48688839895172948583] 
dist 44=[-2.7072297361903241953 ,.56509571705228154834] 
dist 45=[-1.1347338536438042824 ,1.0565734343594403397 ] 
dist 46=[-.87023835374046367764,2.0918948857116055136 ] 
dist 47=[-.83072878941495441235,2.7430578769874257395 ] 
dist 48=[-.34061994918394373341,2.9122004193230005925 ] 
dist 49=[-.31450052440875942511,.88097929568054630544] 
dist 50=[-.20473940671121070379,.86413517773685573065] 
dist 51=[-.1650314575359969557 ,.68265540107833195833] 
dist 52=[-.1419456093766332904 ,.64657437143893135385] 
dist 53=[-.13958455384614909435,.5659383617451977345 ] 
dist 54=[-.30264748391717623427,.45403548402871009662] 
dist 55=[-.44510196004985118398,.40685522552622752265] 
dist 56=[-.49515729727952314453,.06799875709289235418] 
dist 57=[-.49303433697233454174,.00085976528198782634] 
dist 58=[-.47818517990656682521,-.11555303107397673224] 
dist 59=[-.45913602669234462149,-.13725125287972437266] 
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dist 65=[.02261569895114443340,.11446938888940922052] 
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dist 69=[-.00834815387168232396,.07241233206403320889] 
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dist 88=[-.00789395091748902097,.00105294058463398125] 
dist 89=[-.00773478969524373541,7.89465322455926851680e-05] 
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dist 99=[1.51821100768858541940e-05,.00185750720809878636] 
dist 100=[-1.56019233706407665850e-06,.00181406950872140660] 
dist 101=[-.00071121236675312117,.00173371205745939024] 
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dist 108=[-.00060845164410296130,-.00011433228180204674] 
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dist 110=[-.00018561174787523284,.00051180291274019133] 
dist 111=[-.00017628653959944911,.00066269261641982108] 
dist 112=[2.52225358121486343000e-05,.00070183616857458475] 
dist 113=[5.69294355614703355330e-05,.00020590575892235554] 
dist 114=[.00012118958749619402,.00019901922275701636] 
dist 115=[.00012898131006870469,.00015123142671947631] 
dist 116=[5.09694758229219951950e-05,.00014210871804782227] 
dist 117=[-2.74437859292396023580e-05,.00012423525281918216] 
dist 118=[-7.67129908979139352180e-05,9.83315040723212825590e-05] 
dist 119=[-.00010795320306633735,8.78089694340227481700e-05] 
dist 120=[-.00011687546683364050,1.32114535092071404790e-05] 
dist 121=[-.00011384765887812583,-1.53374143946483198530e-06] 
dist 122=[-.00010964992150964982,-2.65270718006543960330e-05] 
dist 123=[-.00010235073951471245,-3.07182010780557460380e-05] 
dist 124=[-7.75464176626869887000e-05,-1.42495446171086028150e-05] 
dist 125=[-2.88157371868784146820e-05,2.51511371625714093670e-05] 
dist 126=[-2.17475620147345468920e-05,4.97788185437813223700e-05] 
dist 127=[-2.04071525481406307190e-05,6.52471766818811114020e-05] 
dist 128=[1.87414753331986339670e-06,6.93388925554310829710e-05] 
dist 129=[5.49991794650538714500e-06,2.60659532844744890290e-05] 
dist 130=[1.27280491499314818570e-05,2.51946544568279378570e-05] 
dist 131=[1.38789903840205688180e-05,1.88651271083209446280e-05] 
dist 132=[7.04793255168655645710e-06,1.79183553414698393820e-05] 
dist 133=[-2.56390367442143357060e-06,1.58486744967928551700e-05] 
dist 134=[-8.59553139119382039270e-06,1.20243304669145439100e-05] 
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dist 136=[-1.34894780721083102910e-05,8.84751212781563717350e-07] 
dist 137=[-1.31889472407686403240e-05,-6.76708686702115298320e-07] 
dist 138=[-1.26456285262345112590e-05,-3.42504791969304229470e-06] 
dist 139=[-1.00492504778289944560e-05,-3.87712111142278937870e-06] 
dist 140=[-8.94432653084634416850e-06,-1.64413534650787090060e-06] 
dist 141=[-3.62901087819893924560e-06,4.03571481636594409110e-06] 
dist 142=[-2.70328161124708452260e-06,7.58031894674427648780e-06] 
dist 143=[-2.56489711595170160130e-06,9.80113120122297187290e-06] 
dist 144=[3.83963055760677471900e-07,1.03772068212034510920e-05] 
dist 145=[8.47285770528231256810e-07,3.07972667866693467420e-06] 
dist 146=[1.78851552691358030000e-06,2.97332256695141633120e-06] 
dist 147=[1.88691984839838637350e-06,2.22462643279438452970e-06] 
dist 148=[7.26102498179677285220e-07,2.10708993840384905530e-06] 
dist 149=[-4.38173687126218768080e-07,1.81826329143088875840e-06] 
dist 150=[-1.16735559783246122280e-06,1.43474119431818687850e-06] 
dist 151=[-1.62724149191144352530e-06,1.28136414320516872080e-06] 
dist 152=[-1.75346819225588954260e-06,1.86965367872721163080e-07] 
dist 153=[-1.70122019767196894760e-06,-2.83525378854007665580e-08] 
dist 154=[-1.63746871512884882180e-06,-3.92196399808706096680e-07] 
dist 155=[-1.49535326280267853330e-06,-4.51956548076956485090e-07] 
dist 156=[-1.15413503484077341060e-06,-2.07663578030224972850e-07] 
dist 157=[-4.26947505889579647600e-07,3.63327799251625922830e-07] 
dist 158=[-3.18413227492374563410e-07,7.19862646205715404550e-07] 
dist 159=[-3.01196584881862634710e-07,9.43545593236771663670e-07] 
dist 160=[2.67752142227826454450e-08,1.00231659073976463940e-06] 
dist 161=[7.98396678657748516340e-08,3.88632083505535352100e-07] 
dist 162=[1.84717812090344491330e-07,3.75026512298904910390e-07] 
dist 163=[2.01126836308225897480e-07,2.79533362513650022200e-07] 
dist 164=[1.03255152389851430270e-07,2.65256513141825316340e-07] 
dist 165=[-3.99257770037691204050e-08,2.34839996829643704160e-07] 
dist 166=[-1.29530398747769646810e-07,1.77078402133364706390e-07] 
dist 167=[-1.85993020272398548290e-07,1.65188222061553760190e-07] 
dist 168=[-2.01394280978208990800e-07,1.14674628501038383790e-08] 
dist 169=[-1.96328080452565449970e-07,-1.11241526449254917210e-08] 
dist 170=[-1.88030879115630604330e-07,-5.09464654637662751700e-08] 
dist 171=[-1.48580529549616974170e-07,-5.73705184180554174290e-08] 
dist 172=[-1.32569861173987494650e-07,-2.35976064020748603700e-08] 
dist 173=[-5.45991048846334359560e-08,6.10758151335354717180e-08] 
dist 174=[-4.05779194501854547840e-08,1.13893273025189420550e-07] 
dist 175=[-3.84765933731218273220e-08,1.46976084412496236440e-07] 
dist 176=[5.82419937108799063520e-09,1.55555936534543137470e-07] 
dist 177=[1.26595512567477121990e-08,4.49474086359516680490e-08] 
dist 178=[2.65389837723767438690e-08,4.32932484662196169420e-08] 
dist 179=[2.73826737952198724880e-08,3.26215132528673563450e-08] 
dist 180=[1.04535871547049042750e-08,3.05657319563204711720e-08] 
dist 181=[-6.64768023407544119290e-09,2.73768569677860631190e-08] 
dist 182=[-1.73445950613863554210e-08,2.15262837781085377860e-08] 
dist 183=[-2.40719018688108468510e-08,1.92599100660078215990e-08] 
dist 184=[-2.58786819920519367610e-08,2.58974315049519600590e-09] 
dist 185=[-2.50705266166208646690e-08,-6.53650748994600023230e-10] 
dist 186=[-2.41093895336574057780e-08,-6.15983013871345846790e-09] 
dist 187=[-2.22536827056531008700e-08,-7.05067700496709436980e-09] 
dist 188=[-1.69645188655891672510e-08,-2.75732951966279640080e-09] 
dist 189=[-6.69066526280272244600e-09,5.68044207010878301120e-09] 
dist 190=[-5.03739557498975427780e-09,1.09484610244896089830e-08] 
dist 191=[-4.70959323486414743600e-09,1.42790933149632335410e-08] 
dist 192=[2.99491279769400917230e-10,1.51490171530997958210e-08] 
dist 193=[1.12492468370277500020e-09,5.63417615996396028940e-09] 
dist 194=[2.72490440776036787660e-09,5.42994378387491321140e-09] 
dist 195=[2.97279113432389402440e-09,4.13348963808156531560e-09] 
dist 196=[1.13908321600478964210e-09,3.99091427316378299880e-09] 
dist 197=[-1.00608946987820674790e-09,3.84363939394822029960e-09] 
dist 198=[-2.34642781242640190560e-09,2.85190150668878828730e-09] 
dist 199=[-3.18883042677771322900e-09,2.70085690457559165640e-09] 
dist 200=[-3.41401398170629157650e-09,1.33539037252773547030e-10] 
dist 201=[-3.31212987811382398100e-09,-2.01174325107719713060e-10] 
dist 202=[-3.17864473991650539680e-09,-7.96643524834051967160e-10] 
dist 203=[-2.44643851891100285170e-09,-8.91233714163504722110e-10] 
dist 204=[-2.23613199890374170270e-09,5.55710535652701328200e-11] 
dist 205=[-1.42015091276980920800e-09,1.14326228157194170560e-09] 
dist 206=[-1.06106449000901178480e-09,1.82160006954423770690e-09] 
dist 207=[-9.98045004161676100340e-10,2.24643082791124097660e-09] 
dist 208=[-2.15160201290800447730e-10,2.35659367835575170760e-09] 
dist 209=[-1.20545028675121455090e-10,1.24177210718328143370e-09] 
dist 210=[-1.16658752249704341080e-10,1.18879300294578168450e-09] 
dist 211=[-1.11694775825520313200e-10,1.11733570404832967500e-09] 
dist 212=[-1.04713132893209029390e-10,1.08078487926608021280e-09] 
dist 213=[-3.91811207799356444650e-10,1.03788772351835868660e-09] 
dist 214=[-7.00458190801225764250e-10,7.88754267691134832720e-10] 
dist 215=[-9.07876641932851868710e-10,7.28780443917134423440e-10] 
dist 216=[-9.62213094770351616860e-10,4.48567588907172953470e-10] 
dist 217=[-9.44913954517096404140e-10,5.26240300933309033200e-10] 
dist 218=[-9.07282403427644094780e-10,5.74804529134715793340e-10] 
dist 219=[-9.49724826967717978320e-10,5.87255092609948715630e-10] 
dist 220=[-9.22068960283834178040e-10,5.67525846282116750170e-10] 
dist 221=[-8.81757779136980903380e-10,6.48120584790955858460e-10] 
dist 222=[-6.95087542279011725050e-10,9.43298380561244557240e-10] 
dist 223=[-7.28919417566967331960e-10,1.12812570944814330300e-09] 
dist 224=[-7.44484302988936690050e-10,1.17605393928867862020e-09] 
dist 225=[-3.04204669298471403310e-10,6.02755843191872484950e-10] 
dist 226=[-3.89241187716976477900e-10,6.96581701435583228400e-10] 
dist 227=[-4.11248805461408054430e-10,7.36998855803436502910e-10] 
dist 228=[-4.01039399370567708730e-10,7.18416656550367552160e-10] 
dist 229=[-3.81666834223302213310e-10,6.84155713525276953960e-10] 
dist 230=[-3.13439631013931520770e-10,5.59107901949508885610e-10] 
dist 231=[-3.58774339847456525100e-10,4.97573288764725688690e-10] 
dist 232=[-4.97843895260219543460e-10,3.93164340346026367400e-10] 
dist 233=[-6.97651470797944657310e-10,3.71670799799635696430e-10] 
dist 234=[-8.22756646685949595510e-10,3.86636612276997704950e-10] 

8 phat 5 dirichlet min maxes function [1, 1, 0, 1, 0, 2, 0, 0, 2] 
dist 0=[322.19868717041843091   ,322.19868717041843091   ] 
dist 1=[288.70068577915339057   ,331.81022399861871070   ] 
dist 2=[247.73766071297706475   ,331.31180260410717712   ] 
dist 3=[208.61261709885025789   ,325.94717383073653588   ] 
dist 4=[166.46983091577679187   ,308.80364268534878144   ] 
dist 5=[112.87537985559690120   ,224.98538765190701516   ] 
dist 6=[62.139543245059695959  ,194.18972150330564602   ] 
dist 7=[30.887266967825982287  ,169.78658182274314851   ] 
dist 8=[4.0273871147205617533 ,107.65210902575184273   ] 
dist 9=[-38.653456976315186713  ,20.823183725891388931  ] 
dist 10=[-67.443821545986763171  ,-11.624040907559079416  ] 
dist 11=[-81.346508670536160189  ,-13.915415813139934973  ] 
dist 12=[-85.727961554634159035  ,-12.707238213375467933  ] 
dist 13=[-84.859571601810538899  ,.23997201602521960284] 
dist 14=[-72.824676570422608583  ,16.842801807890257456  ] 
dist 15=[-65.093621859218035811  ,32.378375634949751851  ] 
dist 16=[-4.1217842973409284272 ,47.282807653011689890  ] 
dist 17=[-1.5867687444658839068 ,57.733185439272159675  ] 
dist 18=[-3.0885836221265173597 ,59.539610793028346405  ] 
dist 19=[-4.9619030188699128039 ,51.907330971109375879  ] 
dist 20=[-6.4504983777529702156 ,50.730735839344908213  ] 
dist 21=[-7.3573009695533556238 ,38.970471934297683371  ] 
dist 22=[-12.083938916800349084  ,32.011170596351479585  ] 
dist 23=[-23.058696630953841670  ,28.913617786028343739  ] 
dist 24=[-28.744954319854337764  ,5.7905042834488408974 ] 
dist 25=[-31.096696876309763751  ,1.2172269154416223088 ] 
dist 26=[-30.741140336085936939  ,-.66813931272927322824] 
dist 27=[-30.554450344179285552  ,-.2637030105219929096 ] 
dist 28=[-23.790339268225700220  ,.1257760780359970779 ] 
dist 29=[-9.0820339904662995380 ,8.1041447933788138326 ] 
dist 30=[-7.1396307415312537745 ,16.906931174749913783  ] 
dist 31=[-6.8397155825602224816 ,22.464853518226198868  ] 
dist 32=[.3630399665148130984 ,23.910722241490941512  ] 
dist 33=[.27206337601940546984,7.3839265573492728492 ] 
dist 34=[-.14796832193819739565,7.3486396172840512912 ] 
dist 35=[-.42302048562772777778,6.0489066180902048814 ] 
dist 36=[-.60003698499936951018,5.7382478896086268947 ] 
dist 37=[-.78536270423389439928,4.5411912166968273721 ] 
dist 38=[-2.7187022747765871181 ,3.6930940674936018307 ] 
dist 39=[-4.0181011619940741119 ,3.3140160281339161078 ] 
dist 40=[-4.5404996852885669569 ,.67743374252582638252] 
dist 41=[-4.6000957273620657909 ,.15271278338447022211] 
dist 42=[-4.4758357178297114480 ,-.01884568994773657177] 
dist 43=[-3.6675817512197756686 ,.05124653521588097124] 
dist 44=[-3.2702167556668027477 ,.10423124547295720565] 
dist 45=[-1.0805112663378752130 ,1.2840581915529588863 ] 
dist 46=[-.82752894363458643632,2.2344845412965639365 ] 
dist 47=[-.75804286470062597037,2.8815362322541589190 ] 
dist 48=[-.33488842140575037047,3.0406579980759065928 ] 
dist 49=[-.2317627409278859434 ,.85689695703663446364] 
dist 50=[-.06417382205722208542,.93413136603168865646] 
dist 51=[-.06110560765847620935,.99668605602658235467] 
dist 52=[-.08610572950789673995,.98228278311012180897] 
dist 53=[-.34858879009418460823,.94039245293913906382] 
dist 54=[-.6172219119381132585 ,.76088329548450086235] 
dist 55=[-.79395401916419393665,.66995954022437075006] 
dist 56=[-.85778921584756817822,.16648486643926377895] 
dist 57=[-.86076615343339703135,.05601326813838597250] 
dist 58=[-.82139671789408813551,-.00094482532327817693] 
dist 59=[-.69887093364067500483,.00917755045411414179] 
dist 60=[-.12242918492581237415,.01635390553339447417] 
dist 61=[-.11905915908831153975,.01996233012153622287] 
dist 62=[-.09063322740168784252,.02134828377054084304] 
dist 63=[-.08639033747053067062,.02103820640032404810] 
dist 64=[.00972184387459401467,.01783470677588203313] 
dist 65=[.00381286321553187334,.03847221978401042297] 
dist 66=[-.00573999782390279733,.05687537879001533924] 
dist 67=[-.01177706411532890699,.06265337573620100700] 
dist 68=[-.01558792525994240134,.06194337249866984316] 
dist 69=[-.01657911198571266101,.05960131008518568104] 
dist 70=[-.00520563991305050758,.04763502589554937574] 
dist 71=[-.00517948663620711923,.04263952262850634552] 
dist 72=[-.01860029866989891102,.00692521361051703874] 
dist 73=[-.03537280502488084063,-.00014830165333261203] 
dist 74=[-.04589046597681848674,.00038453866339749687] 
dist 75=[-.04861936992993736470,.00171213703295513935] 
dist 76=[-.01433971196226479992,.00260731048693054120] 
dist 77=[-.01388762773622033225,.00297186646534978453] 
dist 78=[-.01060943363144129325,.00301717006708115707] 
dist 79=[-.00998181333430685312,.00294594598354980744] 
dist 80=[.00071664301321889077,.00230311953795990054] 
dist 81=[.00047776072969346242,.00526732881737801178] 
dist 82=[-.00055517137640068894,.00745907703985218735] 
dist 83=[-.00121030135644511373,.00810563038573628966] 
dist 84=[-.00164431826892631546,.00791919024701153442] 
dist 85=[-.00175559565250422958,.00763457926616395327] 
dist 86=[-.00074293778861362528,.00582364139886617311] 
dist 87=[-.00072912378107840765,.00541458839181021710] 
dist 88=[-.00172818196065066340,.00047770795676005345] 
dist 89=[-.00344449833652272589,-.00019526343503935915] 
dist 90=[-.00452361044785547715,.00010165531982255365] 
dist 91=[-.00481093973144732718,.00029292405133463465] 
dist 92=[-.00182685157301566308,.00041888430812009315] 
dist 93=[-.00176719539094031436,.00046448321294595513] 
dist 94=[-.00133315983021032960,.00046368971298602611] 
dist 95=[-.00126194804359877203,.00044958177965072093] 
dist 96=[.00014659000121031667,.00035172766215493499] 
dist 97=[5.45558260084282163530e-05,.00062611460931674580] 
dist 98=[-.00010851324541023744,.00089742924767549619] 
dist 99=[-.00021079845776912489,.00097464445962079684] 
dist 100=[-.00028276937396195870,.00095158837433205046] 
dist 101=[-.00030367974089276942,.00091430673387728801] 
dist 102=[-.00031421929663302368,.00071050082679786414] 
dist 103=[-.00034916737838212082,.00064625623016412725] 
dist 104=[-.00040393697625085773,9.48301143792629136410e-05] 
dist 105=[-.00052579991280620430,5.23771848500041111510e-06] 
dist 106=[-.00068050886318450465,7.73368313991650633140e-05] 
dist 107=[-.00072065349601552305,.00012259559222075271] 
dist 108=[-.00023508662635301421,.00015118240125365005] 
dist 109=[-.00022618226937156816,.00015903777125033525] 
dist 110=[-.00017537019142634429,.00015764150076909018] 
dist 111=[-.00016041092952161393,.00015057806481203344] 
dist 112=[-2.79575436785503571520e-05,.00013901521225675978] 
dist 113=[-3.98689551199846321700e-05,.00012933791039345129] 
dist 114=[-5.19547034509407571700e-05,.00011369694643567724] 
dist 115=[-5.96565064177936449580e-05,.00012268874369669914] 
dist 116=[-6.46463801208711697570e-05,.00011916283224921175] 
dist 117=[-6.62890460948442279660e-05,.00011476911701720198] 
dist 118=[-6.63323435853598073330e-05,8.66035495270822921930e-05] 
dist 119=[-6.51612316668199453290e-05,8.09843068091447687920e-05] 
dist 120=[-6.30516141460187475830e-05,5.68406271792622455820e-06] 
dist 121=[-5.94769516573632764100e-05,-3.32914313710043268540e-06] 
dist 122=[-6.50112976173834443960e-05,8.93519474470608663790e-07] 
dist 123=[-6.91131728518034608770e-05,3.57872807030457100990e-06] 
dist 124=[-2.72597166223434491000e-05,5.31385402986782639010e-06] 
dist 125=[-2.63246469269908443400e-05,5.87705263653434090470e-06] 
dist 126=[-1.96584902021370902540e-05,5.83158268899127579360e-06] 
dist 127=[-1.86648661597216735230e-05,5.61801645278936339540e-06] 
dist 128=[2.72169809980803285430e-06,4.50192919486116888080e-06] 
dist 129=[7.83387625905689204470e-07,9.02088421283348386510e-06] 
dist 130=[-1.74341323452372830580e-06,1.29924192667765166030e-05] 
dist 131=[-3.32381044713983863590e-06,1.40917018930277213060e-05] 
dist 132=[-4.31526689320114102870e-06,1.37550639900433284320e-05] 
dist 133=[-4.57262769771532701940e-06,1.31800201055767458420e-05] 
dist 134=[-1.37226618597904516130e-06,1.04231417567021158990e-05] 
dist 135=[-1.33228817351836853850e-06,9.30563942625908636280e-06] 
dist 136=[-4.24221916882801401220e-06,1.39101008613680829740e-06] 
dist 137=[-7.94669133017037335390e-06,-1.73216738819504690560e-07] 
dist 138=[-1.02672794691461156630e-05,1.77199951559998814750e-07] 
dist 139=[-1.08691366239815674980e-05,5.06563894786266120520e-07] 
dist 140=[-3.17010054488072499410e-06,7.17147293056125924870e-07] 
dist 141=[-3.05529566084354259160e-06,7.80841757065438206540e-07] 
dist 142=[-2.30341074437765622710e-06,7.64198165124817818840e-07] 
dist 143=[-2.16085593753403883210e-06,7.37654345048298300150e-07] 
dist 144=[2.02143694613161485840e-07,5.60930661469887024250e-07] 
dist 145=[9.93924850951802166760e-08,1.19913900523881641460e-06] 
dist 146=[-1.57933709797661307170e-07,1.67376403755794757660e-06] 
dist 147=[-3.19184149844005425120e-07,1.80247906150737997970e-06] 
dist 148=[-4.20732746804838509120e-07,1.74798714544684731730e-06] 
dist 149=[-4.48062169669881380930e-07,1.68108610321934401090e-06] 
dist 150=[-1.76782958931098081240e-07,1.27493985350502086190e-06] 
dist 151=[-1.71327534882149383030e-07,1.18383650515383427500e-06] 
dist 152=[-3.92472219864183326690e-07,9.37566122207621284330e-08] 
dist 153=[-7.69271490521592954850e-07,-4.89002252458674253810e-08] 
dist 154=[-1.00552917330910621060e-06,1.64348097008296395030e-08] 
dist 155=[-1.06735435212440595050e-06,5.76213420680404263290e-08] 
dist 156=[-3.97661258826022641380e-07,8.38772459060179108130e-08] 
dist 157=[-3.83541280010021055900e-07,9.16716503426855794630e-08] 
dist 158=[-2.85471878758050658110e-07,9.00530937801143208550e-08] 
dist 159=[-2.70810330015787742390e-07,8.65092830564409505820e-08] 
dist 160=[4.07951161262048051960e-08,6.85848688462801974890e-08] 
dist 161=[1.17664430249430456680e-08,1.32957901656977815170e-07] 
dist 162=[-2.68148361651449654690e-08,1.90562657560902633420e-07] 
dist 163=[-5.09525881050713399390e-08,2.06107319255904218170e-07] 
dist 164=[-6.60822915099186140750e-08,2.00732578803436977900e-07] 
dist 165=[-7.00071754113159815200e-08,1.92180579764281577450e-07] 
dist 166=[-2.22047613956053595570e-08,1.51778825495509862640e-07] 
dist 167=[-2.14419746381076728840e-08,1.35355485847191339430e-07] 
dist 168=[-6.27614615081928433660e-08,2.06460107720756998040e-08] 
dist 169=[-1.16774861938427893720e-07,-2.03497318050551205990e-09] 
dist 170=[-1.50604014144204766580e-07,3.29236503734470672380e-09] 
dist 171=[-1.59377572555876111000e-07,8.65987204574937446930e-09] 
dist 172=[-4.56713025375243354890e-08,1.20592083962318769610e-08] 
dist 173=[-4.40281363623802700520e-08,1.30213339457995635890e-08] 
dist 174=[-3.27514051574277597640e-08,1.26439548016176919200e-08] 
dist 175=[-3.10417596614752218620e-08,1.22009582233556505760e-08] 
dist 176=[2.58474022316388577670e-09,9.09079629847394354580e-09] 
dist 177=[1.79264075484229824550e-09,1.75557080537227221340e-08] 
dist 178=[-2.14176399224710053640e-09,2.43065524629411066120e-08] 
dist 179=[-4.60102304197113160860e-09,2.61062100763219633430e-08] 
dist 180=[-6.14568357576684473340e-09,2.52802788213335066840e-08] 
dist 181=[-6.56209464901249003070e-09,2.43017169476315557180e-08] 
dist 182=[-4.01152284425486166760e-09,1.84060832875272751140e-08] 
dist 183=[-3.86964297757599352050e-09,1.70894113174341267280e-08] 
dist 184=[-5.94646970679792933540e-09,1.76717065861697562950e-09] 
dist 185=[-1.12449566012039802670e-08,-4.95115900602627271670e-10] 
dist 186=[-1.45656371202259961380e-08,5.42675467133012393100e-10] 
dist 187=[-1.54321789659183962100e-08,1.42647610610708989490e-09] 
dist 188=[-5.03228227071606063110e-09,2.01936174917228795590e-09] 
dist 189=[-4.84817634923991883970e-09,2.18179178239115610310e-09] 
dist 190=[-3.62298641411266045870e-09,2.13040772812988815740e-09] 
dist 191=[-3.41704183516960847240e-09,2.03767492369974449230e-09] 
dist 192=[2.66151554568040160720e-10,1.63055331496883347740e-09] 
dist 193=[1.95849960883313653160e-10,1.90194833759434550950e-09] 
dist 194=[-7.53209537252639094610e-10,2.62873921538287713610e-09] 
dist 195=[-1.34598570753421764070e-09,2.82261026765946340450e-09] 
dist 196=[-1.71827617637438513720e-09,2.74577498252316190140e-09] 
dist 197=[-1.81716333426096151430e-09,2.62777575377601398650e-09] 
dist 198=[-1.75980425085583366410e-09,2.10042818771487037010e-09] 
dist 199=[-1.69013918633550941740e-09,1.88117483789332713320e-09] 
dist 200=[-1.32695490942197721170e-09,8.15929514341220050010e-10] 
dist 201=[-2.09123273930212514410e-09,5.66491549881640630540e-10] 
dist 202=[-2.56985407031877777380e-09,3.52330279950515289860e-10] 
dist 203=[-2.69397213640966303440e-09,7.83754337092713295170e-10] 
dist 204=[-6.29303043748239350040e-10,1.05643079110995421230e-09] 
dist 205=[-6.00406896422058654770e-10,1.12784878438027845810e-09] 
dist 206=[-4.87687892016266032230e-10,1.10702811631387576450e-09] 
dist 207=[-4.31867976974011128620e-10,1.04789998341832510470e-09] 
dist 208=[-1.26401763817335652280e-10,9.03047576710020058480e-10] 
dist 209=[-2.31234690161164165800e-10,8.31608485676765398080e-10] 
dist 210=[-7.49986347474126389940e-10,5.55569997743279264230e-10] 
dist 211=[-1.08703922318304346460e-09,5.84220519727527476380e-10] 
dist 212=[-1.29808728568483161440e-09,5.76202939689040118770e-10] 
dist 213=[-1.35281257456177329220e-09,5.43399586456312414250e-10] 
dist 214=[-6.17923513759247393260e-10,4.90674198074685600540e-10] 
dist 215=[-5.93217149843890490470e-10,4.57328709070085953730e-10] 
dist 216=[-6.22237870582666845380e-10,6.38627292273327947370e-10] 
dist 217=[-7.32083651831500303370e-10,7.81073614122971470380e-10] 
dist 218=[-8.00887633113584896060e-10,8.70192708149965301620e-10] 
dist 219=[-8.18774144181321386890e-10,8.93154677136947990530e-10] 
dist 220=[2.16556409027957296150e-10,8.66796084353773530820e-10] 
dist 221=[1.81156444111952783270e-10,8.28825845459143822420e-10] 
dist 222=[1.24718609265584710890e-10,6.52937825123439921020e-10] 
dist 223=[3.42612628864487856580e-11,5.81506428723071567280e-10] 
dist 224=[-2.74071800720797572080e-10,3.79563161063947903110e-10] 
dist 225=[-5.07569759775014583290e-10,3.63577374942822388400e-10] 
dist 226=[-6.53745596938596507890e-10,4.21088616827846975390e-10] 
dist 227=[-6.91601138027649651650e-10,4.56944956801938534090e-10] 
dist 228=[-7.03781718102791630090e-10,4.79390776558855252280e-10] 
dist 229=[-7.26959973905644776760e-10,4.85202877230010330840e-10] 
dist 230=[-5.93694631510034831030e-10,4.72064481471365203310e-10] 
dist 231=[-5.52927263214772520160e-10,4.62727427134860958060e-10] 
dist 232=[-7.22749197473671322700e-10,7.55646562766344361780e-10] 
dist 233=[-8.36019045393853475810e-10,9.38237175235942251370e-10] 
dist 234=[-9.06940938205372750080e-10,1.05255532506752620780e-09] 
dist 235=[-9.25331660662488132430e-10,1.08218563919173850080e-09] 
dist 236=[-2.49236852125360751730e-10,1.04689475720478384140e-09] 
dist 237=[-2.63419715100888542450e-10,1.00448331522655600850e-09] 
dist 238=[-2.64724546302138313800e-10,7.67674619945698411090e-10] 
dist 239=[-2.69782708172324929780e-10,7.04897559651868821820e-10] 
dist 240=[-3.40543216088091000370e-10,1.28743745217216583100e-10] 
dist 241=[-6.11220002192012058020e-10,1.59149715575828678470e-10] 
dist 242=[-7.80695592122887601340e-10,3.58948874410858654440e-10] 
dist 243=[-8.24637951270896358630e-10,4.83496699060696527710e-10] 
dist 244=[-8.00418381542294933570e-10,5.61478152664812784400e-10] 
dist 245=[-7.65437094912674362230e-10,5.81697151208684062380e-10] 
dist 246=[-6.16927969197607902370e-10,5.65565595606298946280e-10] 
dist 247=[-5.70746207448279445880e-10,5.39937982255829898270e-10] 
dist 248=[-4.81014910440966356340e-10,5.76828630043326747510e-10] 
dist 249=[-4.85651902316457360030e-10,7.83893857399503893440e-10] 
dist 250=[-4.88555528363101515410e-10,9.13542373127262845730e-10] 

8 phat 5 dirichlet min maxes function [2, 2, 2, 0, 1, 2, 0, 2] 
dist 0=[375.46399490035913589   ,375.46399490035913589   ] 
dist 1=[353.60851780697447912   ,379.92999648503700610   ] 
dist 2=[303.38401251358468833   ,375.46399490035913589   ] 
dist 3=[246.20873826254134935   ,346.18317012666278910   ] 
dist 4=[196.87687889707681987   ,294.27509276626280236   ] 
dist 5=[147.95406779869347098   ,226.79397955435721374   ] 
dist 6=[91.439288469702091029  ,213.96625569937097147   ] 
dist 7=[31.274686999377996606  ,122.17534010264804333   ] 
dist 8=[-23.445645467152321931  ,77.843591667350686841  ] 
dist 9=[-61.869583909609241106  ,2.6616651847200307805 ] 
dist 10=[-83.252043851947261399  ,3.4917325822751460093 ] 
dist 11=[-93.344927925734007510  ,9.6968571037123835262 ] 
dist 12=[-93.704272590318425964  ,18.300417055268016584  ] 
dist 13=[-79.208976857813882613  ,28.378703799497956571  ] 
dist 14=[-75.009960022368442403  ,40.833508389697705855  ] 
dist 15=[-10.101995537523953040  ,50.354806476348118653  ] 
dist 16=[1.0267075453722046095 ,52.062549931995592595  ] 
dist 17=[25.125707684356605143  ,45.710739921106785615  ] 
dist 18=[22.616983312175595110  ,52.359969782807406084  ] 
dist 19=[2.8360912777009569329 ,53.344159237785022313  ] 
dist 20=[-10.732813816124576796  ,51.970417613555895838  ] 
dist 21=[-20.452607732080733139  ,41.057481332437519377  ] 
dist 22=[-25.522672142508645681  ,37.864704391961355975  ] 
dist 23=[-27.641581785396674969  ,13.423376580723561310  ] 
dist 24=[-27.334817139988499983  ,9.6586548041305705294 ] 
dist 25=[-33.319347051826921234  ,2.8139046197454997573 ] 
dist 26=[-35.204487969609813578  ,1.0432192274946143692 ] 
dist 27=[-9.6651661132129698795 ,7.2198771943602205643 ] 
dist 28=[-9.4234636569246574930 ,15.069536903162806947  ] 
dist 29=[-.56454042927685278749,20.025508565824298058  ] 
dist 30=[.90453455231237089437,21.314765474364997299  ] 
dist 31=[3.7978400551117014790 ,6.6228233004250770576 ] 
dist 32=[4.2575727362298224918 ,6.5916910684445317415 ] 
dist 33=[4.6245592840320654798 ,5.9865010942178960669 ] 
dist 34=[2.1113958921073639724 ,5.9078627440036071918 ] 
dist 35=[-.48805777847050106564,5.0277947003242818392 ] 
dist 36=[-2.1890151595893484922 ,4.5539905649912617594 ] 
dist 37=[-3.3339707531336433769 ,1.1172680756312781407 ] 
dist 38=[-3.7974111599109725967 ,.42294080427915945887] 
dist 39=[-4.3776835260639108561 ,-.88198640613337383946] 
dist 40=[-4.6554412831180704183 ,-1.1590029291575462723 ] 
dist 41=[-2.9602036563317133132 ,-1.3144689948840113276 ] 
dist 42=[-2.7581148496675707169 ,-.51110341918567621234] 
dist 43=[-1.1652934633075781083 ,.82226358847667840178] 
dist 44=[-1.0893183000545208414 ,1.6673945808877206250 ] 
dist 45=[-.3607083233113001287 ,2.2257492150943756203 ] 
dist 46=[-.20984412108000866527,2.3646773603153721692 ] 
dist 47=[.08855415797862266538,1.0549692444256048076 ] 
dist 48=[.15195368329654032262,1.1603875877672574048 ] 
dist 49=[.22574469915461330398,1.1665944838549196479 ] 
dist 50=[-.03635655135881848413,1.1264442538731447325 ] 
dist 51=[-.44368161141784244292,.91363902080893958186] 
dist 52=[-.70627518519874268969,.81202434769469123254] 
dist 53=[-.87948310101910878649,.15761855810425502076] 
dist 54=[-.94289689352309488661,.02240096750901199177] 
dist 55=[-.9466175146941828889 ,-.13778453287898915245] 
dist 56=[-.88997789391766169079,-.16941987241257123707] 
dist 57=[-.35899697097419401624,-.17790022241010611207] 
dist 58=[-.32243363011417211085,-.06644202180103020824] 
dist 59=[-.13767501749842978986,.13299696905853650905] 
dist 60=[-.13206770540359621764,.25801720113723048202] 
dist 61=[.00862537376517729898,.3365467698762899694 ] 
dist 62=[.03116509571323504628,.35693512877393822281] 
dist 63=[.07621363237549933763,.10665242509071250597] 
dist 64=[.08299244467915998368,.10403725069882686473] 
dist 65=[.06939012797629391496,.09192124646756547544] 
dist 66=[.02907796732770635814,.08906702644340862671] 
dist 67=[-.01181401806013724361,.07247305122062873279] 
dist 68=[-.03786047195962596453,.06510946334383550659] 
dist 69=[-.05472572528337375734,.01193076289027797774] 
dist 70=[-.06026422357434479144,.00133697671859996746] 
dist 71=[-.06779233793179344836,-.01744303040702927498] 
dist 72=[-.07190565621681611492,-.02129120522201566340] 
dist 73=[-.04431030744839577612,-.02145328486929978990] 
dist 74=[-.04126016809773135455,-.00814755784594350317] 
dist 75=[-.01638794574114847269,.01258353857117334332] 
dist 76=[-.01548258918024265065,.02559926319942438184] 
dist 77=[.00062705616301000473,.03381526061818698853] 
dist 78=[.00325645580780605885,.03605541910700878780] 
dist 79=[.00872154777294096975,.01375987025974674662] 
dist 80=[.00961119577417305495,.01338448429800621961] 
dist 81=[.00900740556585345277,.01202857444801781127] 
dist 82=[.00396775047358218493,.01164138518793011851] 
dist 83=[-.00112636857376135896,.00896601150539745393] 
dist 84=[-.00435631457412052902,.00834998517396780426] 
dist 85=[-.00643423026532702766,.00086401612661708855] 
dist 86=[-.00709042274978535929,-.00028511696804631777] 
dist 87=[-.00701371173190281923,-.00238323771847900988] 
dist 88=[-.00728535185160625207,-.00279203525598993743] 
dist 89=[-.00539500076266021843,-.00277993258869687332] 
dist 90=[-.00483163113682129157,-.00092783244333760722] 
dist 91=[-.00206690042628083599,.00210501837479333586] 
dist 92=[-.00197074517950127291,.00400097787859105318] 
dist 93=[.00021065222606626374,.00519005479303459352] 
dist 94=[.00055643096238100637,.00549867840838073642] 
dist 95=[.00125886433721336136,.00164512977586219091] 
dist 96=[.00136603171687098713,.00159522911497056696] 
dist 97=[.00101897708744310265,.00142839023653790318] 
dist 98=[.00039676520520057046,.00137499529292138693] 
dist 99=[-.00023001151846398844,.00110110407722696617] 
dist 100=[-.00062511557724500454,.00098521760597016696] 
dist 101=[-.00087690431862977311,.00017537170652776568] 
dist 102=[-.00095141130653663467,1.53043934550223443020e-05] 
dist 103=[-.00106421283257021394,-.00025822424319210205] 
dist 104=[-.00112692367964298005,-.00030904907429831997] 
dist 105=[-.00068238577989410472,-.00030304180725775129] 
dist 106=[-.00063544843098531324,-9.54796028082765145560e-05] 
dist 107=[-.00024518049084641419,.00021188960870543951] 
dist 108=[-.00023261930347376359,.00040435077243282535] 
dist 109=[-6.03639094743488184500e-05,.00052552886628684072] 
dist 110=[-2.62662663112918756810e-05,.00055815178912126990] 
dist 111=[2.98836054351453086080e-05,.00025654391156267606] 
dist 112=[4.22954024240612032430e-05,.00027315318548777688] 
dist 113=[3.97093513275977879560e-05,.00026745532476628430] 
dist 114=[-1.72928025809784675920e-05,.00025628564244204335] 
dist 115=[-.00011033208368347925,.00020384840243836404] 
dist 116=[-.00016888007537926798,.00018100508790154431] 
dist 117=[-.00020610130501082012,3.12563024563492168310e-05] 
dist 118=[-.00021694309454690315,8.68775895449888020530e-07] 
dist 119=[-.00021445142614218811,-3.78018463176691075210e-05] 
dist 120=[-.00020027426842573035,-4.33133475894544932600e-05] 
dist 121=[-8.08628765341558254360e-05,-4.24905761706702188520e-05] 
dist 122=[-7.22574800068598845310e-05,-1.34228186806662129140e-05] 
dist 123=[-3.09763284117277249940e-05,3.24727754476121038560e-05] 
dist 124=[-2.94589983002015928040e-05,6.11272833325789887600e-05] 
dist 125=[3.91699624523539224460e-06,7.90846853501658057470e-05] 
dist 126=[9.18113760839162930140e-06,8.37427742332652975610e-05] 
dist 127=[1.98294806462630249120e-05,2.45158461712295016010e-05] 
dist 128=[2.09951755851507679810e-05,2.36721286079252066800e-05] 
dist 129=[1.52912409846031446640e-05,2.15300482664699462120e-05] 
dist 130=[5.99914931337825200890e-06,2.06664621178660467350e-05] 
dist 131=[-3.33162110554005896990e-06,1.64197554642161884570e-05] 
dist 132=[-9.18564469291449579440e-06,1.46739680516982760810e-05] 
dist 133=[-1.28886950359125595160e-05,2.27607338381497360360e-06] 
dist 134=[-1.39279555054446644230e-05,-1.77674724043587036970e-07] 
dist 135=[-1.60443503468996516340e-05,-4.36278467569174550650e-06] 
dist 136=[-1.69899285284687615830e-05,-5.08706425624291367930e-06] 
dist 137=[-9.91213368104368631580e-06,-4.96235975279662375640e-06] 
dist 138=[-9.20867909739265047730e-06,-1.67680138779071645680e-06] 
dist 139=[-3.64402594673943106350e-06,3.00841617641320595440e-06] 
dist 140=[-3.42268446411846742710e-06,5.93547954913207734840e-06] 
dist 141=[2.88876696717574607460e-07,7.77287673007175444940e-06] 
dist 142=[8.93162158661704581680e-07,8.25715511724915346190e-06] 
dist 143=[2.10689053039041629220e-06,3.09861746945344719680e-06] 
dist 144=[2.29892322549139863280e-06,2.99283769232810522460e-06] 
dist 145=[1.96956921283951711040e-06,2.75055731873335916210e-06] 
dist 146=[8.31130709405049047450e-07,2.64819454901142648180e-06] 
dist 147=[-3.11150830432519013110e-07,2.01353855956914961730e-06] 
dist 148=[-1.02709324721323320120e-06,1.87085728366824806920e-06] 
dist 149=[-1.47933582979663282370e-06,1.54686149341582614730e-07] 
dist 150=[-1.60501105275619480270e-06,-1.06244967467846188820e-07] 
dist 151=[-1.57727414618588968710e-06,-5.68151874117292349410e-07] 
dist 152=[-1.67573147018926662040e-06,-6.46314212631160656860e-07] 
dist 153=[-1.18750236826679440810e-06,-6.29372702209991631710e-07] 
dist 154=[-1.06077640488749841240e-06,-1.93063894220960459370e-07] 
dist 155=[-4.54739145171655126270e-07,4.81718797820502550760e-07] 
dist 156=[-4.31804589019884636180e-07,9.02818525467742699230e-07] 
dist 157=[6.19757767251208779770e-08,1.16663417008797104450e-06] 
dist 158=[1.39659777693643783300e-07,1.23506331657476938550e-06] 
dist 159=[2.97347672534181969210e-07,3.64612751389825556400e-07] 
dist 160=[3.07561677959741726630e-07,3.51837315101406636910e-07] 
dist 161=[2.22715076186977658710e-07,3.18473478244483864620e-07] 
dist 162=[8.53775738498489263710e-08,3.05244180593080744230e-07] 
dist 163=[-5.22936837875798059360e-08,2.41491872820097347540e-07] 
dist 164=[-1.38437103302023874750e-07,2.15684147994907462870e-07] 
dist 165=[-1.92698792950090225210e-07,3.25646566614450789460e-08] 
dist 166=[-2.07450460909823065070e-07,-3.55111676736523898230e-09] 
dist 167=[-2.37381587172806741880e-07,-6.46935027251560766420e-08] 
dist 168=[-2.51295463290311504390e-07,-7.49371616846603050560e-08] 
dist 169=[-1.46212013554376150400e-07,-7.27051528259214591220e-08] 
dist 170=[-1.36297613570014793370e-07,-2.40687665243984808410e-08] 
dist 171=[-5.36133560420553716290e-08,4.38255768500007755150e-08] 
dist 172=[-5.06393206401459991200e-08,8.62073738158068500070e-08] 
dist 173=[4.34411737340761723940e-09,1.12787644735839814860e-07] 
dist 174=[1.31867344947281782460e-08,1.19755607527609740650e-07] 
dist 175=[3.07493632992751486050e-08,4.60128639975293569690e-08] 
dist 176=[3.35613242626117173800e-08,4.43804130058617435750e-08] 
dist 177=[2.85291339874764993210e-08,4.09896608585618646290e-08] 
dist 178=[1.18482307980595649750e-08,3.94505636506937687850e-08] 
dist 179=[-4.90249169542242008930e-09,2.97577129688120796970e-08] 
dist 180=[-1.55266281566715682900e-08,2.77913152647136409010e-08] 
dist 181=[-2.22139578433461201240e-08,1.92072550948047235790e-09] 
dist 182=[-2.40227265866537335120e-08,-1.86291359448503189150e-09] 
dist 183=[-2.34151668395857591500e-08,-8.56810290272766976830e-09] 
dist 184=[-2.40105140810383595170e-08,-9.66841474522349799840e-09] 
dist 185=[-1.77925124465154420590e-08,-9.36053617907007701660e-09] 
dist 186=[-1.57841386021282382730e-08,-2.31997369516084297910e-09] 
dist 187=[-7.00986644458846114030e-09,7.83542330236634056400e-09] 
dist 188=[-6.57703384189031771590e-09,1.41694004641225545780e-08] 
dist 189=[4.61558494593227743450e-10,1.81364913691158240350e-08] 
dist 190=[1.59427792630316971710e-09,1.91653086126354630660e-08] 
dist 191=[3.81738293965706938680e-09,5.68036832119389638680e-09] 
dist 192=[3.72233250427382232320e-09,5.54032416479407681580e-09] 
dist 193=[2.68998590645725361240e-09,5.38526256739982975130e-09] 
dist 194=[1.02290957786117584870e-09,5.16596127947972664580e-09] 
dist 195=[-8.01847028434320460990e-10,4.04057974761008135500e-09] 
dist 196=[-2.14837559304554161780e-09,3.63844378200311560620e-09] 
dist 197=[-2.99466138489637873110e-09,1.00691081264728703170e-09] 
dist 198=[-3.22462938563727295250e-09,5.31528635764202602770e-10] 
dist 199=[-4.03660458135211113050e-09,-1.50957105563050453670e-10] 
dist 200=[-4.24718188556645975390e-09,-2.71325836848100920660e-10] 
dist 201=[-2.39267611243385972800e-09,-2.61396739497888725020e-10] 
dist 202=[-2.11055478090291893700e-09,2.51515367698881437730e-10] 
dist 203=[-1.25848601438671238430e-09,1.41941486098145062760e-09] 
dist 204=[-1.12125297441734593750e-09,2.14795426275791258770e-09] 
dist 205=[-5.59393404777373199720e-10,2.60448105838906225150e-09] 
dist 206=[-5.16341825335943471870e-10,2.72348233840239211110e-09] 
dist 207=[-4.96801727404776944130e-10,1.25576370003940443140e-09] 
dist 208=[-4.76323250913653674200e-10,1.33040832556568945730e-09] 
dist 209=[-3.59638811585426773840e-10,1.28674866179789528960e-09] 
dist 210=[-3.62002068372678477340e-10,1.23703048595622541460e-09] 
dist 211=[-8.47182420838799337400e-10,9.33427760789839735080e-10] 
dist 212=[-1.14993681110814615850e-09,8.69333038971413415680e-10] 
dist 213=[-1.33981424738116509410e-09,7.28112746836471839050e-10] 
dist 214=[-1.38971847830135977800e-09,7.28901904865356954660e-10] 
dist 215=[-1.35269024102068060330e-09,7.15235331607956329570e-10] 
dist 216=[-1.29092002244008529530e-09,6.75617155327392039320e-10] 
dist 217=[-1.03757666159194516350e-09,5.88657387608961614820e-10] 
dist 218=[-9.12770426886034116400e-10,5.46032335001119457270e-10] 
dist 219=[-5.68674318255167736430e-10,5.17570340571973785060e-10] 
dist 220=[-8.20077696285674431070e-10,8.99682563154677663890e-10] 
dist 221=[-1.07141494261618112570e-09,1.13901982233861212450e-09] 
dist 222=[-1.22802396802187377830e-09,1.41484881828319706060e-09] 
dist 223=[-1.32601187515741699660e-09,1.59280032408213756770e-09] 
dist 224=[-1.35127501521054047190e-09,1.63908999777134886170e-09] 
dist 225=[-1.32123595020578850450e-09,1.59757575397376605960e-09] 
dist 226=[-1.25406580431208222670e-09,1.52163971555680279870e-09] 
dist 227=[-1.05346100191366057930e-09,1.24191828771159176520e-09] 
dist 228=[-9.94621712260761724140e-10,1.20306663371305799240e-09] 
dist 229=[-1.06516940279601312040e-09,1.36197714939452144470e-09] 
dist 230=[-1.16738763126845153640e-09,1.40312884571460255110e-09] 
dist 231=[-1.46047509995847885070e-09,1.38678381828874094440e-09] 
dist 232=[-1.53651408204427971220e-09,1.45385007545702762190e-09] 
dist 233=[-1.49663390322571619200e-09,1.41607163456388650380e-09] 
dist 234=[-1.42627481265509839140e-09,1.34942909456278663400e-09] 
dist 235=[-1.15828303762560192850e-09,1.09611421233850629200e-09] 
dist 236=[-1.38415091014863903800e-09,1.16363632791533990200e-09] 
dist 237=[-1.64229840784268382420e-09,1.29621884162983384200e-09] 
dist 238=[-1.70923780103444171940e-09,1.33059895380861007760e-09] 
dist 239=[-1.26411044728504963780e-09,1.33412506487477409020e-09] 
dist 240=[-1.33072364853614950730e-09,1.40451330104439189080e-09] 
dist 241=[-1.29592444105959597790e-09,1.36936798032320260100e-09] 
dist 242=[-1.23518313221251048590e-09,1.30370901025188220930e-09] 
dist 243=[-1.00166423299520170530e-09,1.06769911975111775270e-09] 
dist 244=[-8.86774075830258578190e-10,9.51577831727642093270e-10] 
dist 245=[-9.51757478169402177270e-10,9.24140129103591808700e-10] 
dist 246=[-1.16865873123740385600e-09,1.09973416272936743820e-09] 
dist 247=[-1.30446622966947350330e-09,1.21004000690950537510e-09] 

8 phat 5 dirichlet min maxes function [2, 0, 0, 0, 1, 0, 2] 
dist 0=[322.75511372886429172   ,322.75511372886429172   ] 
dist 1=[317.38833633296562125   ,319.07620082613017293   ] 
dist 2=[297.60598711151856838   ,322.75511372886429172   ] 
dist 3=[266.05128323230879725   ,286.84058545620037055   ] 
dist 4=[215.19383911134466397   ,278.88734297564562291   ] 
dist 5=[159.75615518158344523   ,178.39052942327892084   ] 
dist 6=[110.09313420003811853   ,158.50305772757028559   ] 
dist 7=[59.514090895071841071  ,105.43088686089795680   ] 
dist 8=[-.60231301401536935566,93.209336694692323794  ] 
dist 9=[-52.642794784485585290  ,11.513383504474803680  ] 
dist 10=[-72.226242187714029605  ,-2.8226534978610581981 ] 
dist 11=[-79.011878471112689525  ,-25.044951327882238303  ] 
dist 12=[-81.254554253343957419  ,-27.374077219375871079  ] 
dist 13=[-26.092874100524659206  ,-23.817611430164855015  ] 
dist 14=[-24.525684128208983552  ,-2.2702899369440210982 ] 
dist 15=[-18.188638996903559724  ,15.627321309710497295  ] 
dist 16=[-16.284408905307278882  ,29.333760119693641975  ] 
dist 17=[-1.5948449520768653419 ,38.597301728572174758  ] 
dist 18=[1.1214293953017706500 ,40.106794207709854489  ] 
dist 19=[5.5407078248246623161 ,37.523801133436892678  ] 
dist 20=[6.0884651646474481591 ,34.950757892792950268  ] 
dist 21=[-7.1010517068059769822 ,13.757696405716572789  ] 
dist 22=[-18.623646413591921769  ,12.802358138747722820  ] 
dist 23=[-25.975903360427263566  ,9.5210455896959754979 ] 
dist 24=[-27.889838382741399402  ,8.1020295290699657537 ] 
dist 25=[-11.830381928343850314  ,.8757547466550648255 ] 
dist 26=[-12.183052286103091287  ,.08024534528903685050] 
dist 27=[-11.594588965919635829  ,-1.3033360749787737193 ] 
dist 28=[-9.1042086432709743518 ,-1.5382103042374055465 ] 
dist 29=[-3.3352049848603242423 ,-.66204159795638857755] 
dist 30=[-3.2504347035157027197 ,1.9732140795589841767 ] 
dist 31=[-2.4936897350002806350 ,3.8823682587970969401 ] 
dist 32=[-2.3788554978009173331 ,4.9180795520107843340 ] 
dist 33=[.13267040323448698429,5.3826211307615802315 ] 
dist 34=[.38215093766037557292,5.3389719559800512233 ] 
dist 35=[.863099919930596806  ,4.5899491217539986745 ] 
dist 36=[.92900240401466505239,4.1718327081884468654 ] 
dist 37=[-1.3833496885077992872 ,1.6363601086940408796 ] 
dist 38=[-2.9207538665287783240 ,1.5773733711970045616 ] 
dist 39=[-3.8921824185770665311 ,1.2609555672727874938 ] 
dist 40=[-4.1449798207505031795 ,1.1337870432663020706 ] 
dist 41=[-1.3034801168390408211 ,.18386418615022449162] 
dist 42=[-1.3026081187189292149 ,-.00088774284854911309] 
dist 43=[-1.1728583511398602947 ,-.22472831071907579897] 
dist 44=[-1.2438326608591042129 ,-.25054457207408878821] 
dist 45=[-.39465101023133236324,.0743176994098585271 ] 
dist 46=[-.38123975072736113841,.41010650654978461259] 
dist 47=[-.29855603909886232627,.63808386115676118639] 
dist 48=[-.27395745231915363034,.73408309609497354609] 
dist 49=[-.01382049675237450975,.7502057394149614547 ] 
dist 50=[.03260162585830910690,.73359669195941130802] 
dist 51=[.11213242051741693021,.57812740546180882949] 
dist 52=[.12032924065469665766,.54144813889412024299] 
dist 53=[-.14084333260661703589,.25224589397853660787] 
dist 54=[-.30786696970124220844,.23986177526914085472] 
dist 55=[-.4183052961775568495 ,.19105352212533434151] 
dist 56=[-.4457230107891366878 ,.16732583011668463512] 
dist 57=[-.22501178612897569309,.03861566157811646707] 
dist 58=[-.21695925582769133293,.0100903133642280486 ] 
dist 59=[-.1920778079050380223 ,-.02430180506326514935] 
dist 60=[-.14185658402312884909,-.02766776242133919442] 
dist 61=[-.04940634297108697362,.00825531205124359319] 
dist 62=[-.04789292945295050894,.05120675326589461872] 
dist 63=[-.03615000408574118194,.07975194419781288407] 
dist 64=[-.03439813048250568513,.09063043634706852909] 
dist 65=[.00175612169606321783,.09188870669803483768] 
dist 66=[.00494814784309723200,.08911696598820846760] 
dist 67=[.01116151596704041225,.07268147638466583412] 
dist 68=[.01206011687867341366,.06532693027490054012] 
dist 69=[-.02661087310313767428,.02483452448642916347] 
dist 70=[-.05186164894465666542,.02385117546163820689] 
dist 71=[-.06772907379025099902,.01896993616418362867] 
dist 72=[-.07184933129248831472,.01696421989178871341] 
dist 73=[-.02153291903541498113,.00265851378811314114] 
dist 74=[-.02104258769196366911,-.00017014743215939573] 
dist 75=[-.01841179279138074244,-.00305487338603768089] 
dist 76=[-.01950105205234123650,-.00341000579409420816] 
dist 77=[-.00573067353926547641,.00230011556430541758] 
dist 78=[-.00553799726678617688,.00758329966627198121] 
dist 79=[-.00420618467520137342,.01101844659722119571] 
dist 80=[-.00395258732159279547,.01217494389002683196] 
dist 81=[.00031791811606253924,.01205986917067497503] 
dist 82=[.00075600873378385327,.01167749576488620118] 
dist 83=[.00156567102810990340,.00900463288387620321] 
dist 84=[.00167638098812585251,.00838787561880220188] 
dist 85=[-.00252919553030260545,.00315231689662135346] 
dist 86=[-.00517208110059409044,.00303576932659504877] 
dist 87=[-.00684421897665172095,.00230957946194351667] 
dist 88=[-.00730034094286221174,.00214629713785335251] 
dist 89=[-.00279429995057027984,.00018068377460751811] 
dist 90=[-.00272161895510819159,-3.08387659519709742300e-05] 
dist 91=[-.00208043532799776659,-.00033959355480441115] 
dist 92=[-.00198445286639157357,-.00038787240337532798] 
dist 93=[-.00072139201940507688,.00021952372493314221] 
dist 94=[-.00069711279613175760,.00087755154195460864] 
dist 95=[-.00052191273299888775,.00130232209656522135] 
dist 96=[-.00049550868276544325,.00143939139279553459] 
dist 97=[2.66235761093214679270e-05,.00142731490758759221] 
dist 98=[7.17546015890449170810e-05,.00137476020943942654] 
dist 99=[.00016030142153396031,.00110097054013587965] 
dist 100=[.00017333548660701814,.00098645769697649880] 
dist 101=[-.00042642963072037197,.00036479815734926288] 
dist 102=[-.00081290125225873024,.00034980591410770333] 
dist 103=[-.00105533310497178371,.00027615683249187304] 
dist 104=[-.00111825984185933517,.00024729077898472330] 
dist 105=[-.00033558064774146215,3.75780251675915202000e-05] 
dist 106=[-.00032571137011098049,-3.58732857024542407240e-06] 
dist 107=[-.00027052889964853027,-4.29271918136433978310e-05] 
dist 108=[-.00028639860320709232,-4.81088037948960236800e-05] 
dist 109=[-8.90936546127985322400e-05,4.33687441952240577500e-05] 
dist 110=[-8.56294136321932588160e-05,.00012372531071647967] 
dist 111=[-6.62103309076684066440e-05,.00017505298122647256] 
dist 112=[-6.05414351024468465890e-05,.00019048315423652877] 
dist 113=[-1.89622211155562192250e-06,.00018632024817236245] 
dist 114=[8.56950509383858687710e-06,.00017981033137658962] 
dist 115=[2.21714425683129278600e-05,.00013670084325369214] 
dist 116=[2.38562604569321300890e-05,.00012770921484049176] 
dist 117=[-3.86883812853620448920e-05,5.89277086348433920660e-05] 
dist 118=[-7.80012400042826728300e-05,5.61204667665767792670e-05] 
dist 119=[-.00010275011130689766,4.54213416780190265580e-05] 
dist 120=[-.00010939609090901985,4.01694929835354580100e-05] 
dist 121=[-5.41597206531275512280e-05,1.16023596300479064200e-05] 
dist 122=[-5.16101548289534384840e-05,5.59825797287337602420e-06] 
dist 123=[-4.40089280989719048730e-05,9.33687830590197443980e-07] 
dist 124=[-3.30216534102309110660e-05,0                     ] 
dist 125=[-5.41147178752839191020e-06,3.93421745888071917010e-06] 
dist 126=[-5.20731030507662174110e-06,1.38966744216117794120e-05] 
dist 127=[-3.85081200686396012190e-06,2.02413361760592544660e-05] 
dist 128=[-3.64843975337403548180e-06,2.21123950942009554340e-05] 
dist 129=[1.19618761625111152720e-07,2.17163914739112686760e-05] 
dist 130=[7.45865652803067967240e-07,2.08498417208495255930e-05] 
dist 131=[1.92561537207192296030e-06,1.65747739222753371410e-05] 
dist 132=[2.10307425466886459880e-06,1.48143442733902662820e-05] 
dist 133=[-6.63253583330297858880e-06,3.22407363398591370980e-06] 
dist 134=[-1.25013523239692368030e-05,3.09340619005757786040e-06] 
dist 135=[-1.61796939821012247010e-05,2.35793825631682589300e-06] 
dist 136=[-1.71338864708033490210e-05,2.16932718226668980670e-06] 
dist 137=[-5.02011093863606543160e-06,5.49834518909973237680e-07] 
dist 138=[-4.84989655438218689110e-06,3.33812461825025314130e-07] 
dist 139=[-3.68062768760788369370e-06,4.85089218768157870290e-08] 
dist 140=[-3.45755110768890373440e-06,0                     ] 
dist 141=[-6.73345832156513159400e-07,6.76369076236031800910e-07] 
dist 142=[-6.48007924459671804510e-07,1.87671453803816020670e-06] 
dist 143=[-4.79310336864416885560e-07,2.63700392554091125220e-06] 
dist 144=[-4.54156371640724804940e-07,2.85241837355324979250e-06] 
dist 145=[7.33015986865789156870e-08,2.77652850523696336790e-06] 
dist 146=[1.56012498406794421360e-07,2.67355279228008373800e-06] 
dist 147=[3.23771903980012753250e-07,2.03347146438408903550e-06] 
dist 148=[3.45549125663941320640e-07,1.88950357611585376890e-06] 
dist 149=[-6.14748344079507203820e-07,3.38243860365724830420e-07] 
dist 150=[-1.21486422819786160550e-06,3.23407112210254363670e-07] 
dist 151=[-1.59169884191976208700e-06,2.54354375422806533490e-07] 
dist 152=[-1.69122675840861421280e-06,2.26773479517684221450e-07] 
dist 153=[-6.35481674875230607810e-07,3.25947453374945024260e-08] 
dist 154=[-6.14035057817441785450e-07,-5.73421097830076971330e-09] 
dist 155=[-4.59402791815633158390e-07,-6.99283381669017961820e-08] 
dist 156=[-4.36224304453026869040e-07,-8.00956051384349978130e-08] 
dist 157=[-7.75061269979265753460e-08,6.33400225717886005620e-08] 
dist 158=[-7.44909465530037984530e-08,2.10351595206651543460e-07] 
dist 159=[-5.58491076965671700690e-08,3.03319763025200544840e-07] 
dist 160=[-5.22222931108365830680e-08,3.29372826307107289750e-07] 
dist 161=[5.02896279067719615460e-09,3.21847766495099329700e-07] 
dist 162=[1.43657504741061661660e-08,3.08527582583709098320e-07] 
dist 163=[3.26483022901932180380e-08,2.44083274993099971880e-07] 
dist 164=[3.53831652517003160010e-08,2.18088607764544507590e-07] 
dist 165=[-9.88613242585679240140e-08,4.31529072720699047740e-08] 
dist 166=[-1.85278742242627288480e-07,4.14679962033145934910e-08] 
dist 167=[-2.39419594894408384000e-07,3.11911119867752896880e-08] 
dist 168=[-2.53463318599441417200e-07,2.90869235995964659870e-08] 
dist 169=[-7.50662600802636991890e-08,1.96478873796350841190e-09] 
dist 170=[-7.24513422804149464840e-08,-1.99635778306707370800e-09] 
dist 171=[-5.41589603868310799220e-08,-8.91787712519155221100e-09] 
dist 172=[-5.13064194495189083160e-08,-9.99715584640662817080e-09] 
dist 173=[-9.67413741031056486070e-09,1.05120303441975920400e-08] 
dist 174=[-9.31161161776278437680e-09,2.81119196414649841340e-08] 
dist 175=[-6.97360479404135970920e-09,3.92070547871120594520e-08] 
dist 176=[-6.52928952002252603310e-09,4.22419523251379825130e-08] 
dist 177=[5.21825696443030329200e-10,4.09720927003096011510e-08] 
dist 178=[1.68316154810143785810e-09,3.94330784241908553530e-08] 
dist 179=[3.93638630104645221180e-09,2.97797816116629489810e-08] 
dist 180=[4.27492866461881578900e-09,2.77862813080179357020e-08] 
dist 181=[-8.67815716513944773980e-09,5.51655435562252549400e-09] 
dist 182=[-1.73253255556559834990e-08,5.29121755287992185330e-09] 
dist 183=[-2.27541438850847592690e-08,4.04304702644588392240e-09] 
dist 184=[-2.41794093173958931920e-08,3.70903606720293997850e-09] 
dist 185=[-9.73972717693385095540e-09,7.42637439735330465880e-10] 
dist 186=[-9.39206901693647168530e-09,2.12590209908581226470e-10] 
dist 187=[-7.02907142736967036970e-09,-4.98726395950121143460e-10] 
dist 188=[-6.63825750562265773940e-09,-6.14948419755923461360e-10] 
dist 189=[-2.06408001873502112240e-09,1.18455007107841871580e-09] 
dist 190=[-2.17039718797137221320e-09,3.44661088094753702190e-09] 
dist 191=[-2.34378462738425998330e-09,4.87113642904636086010e-09] 
dist 192=[-2.62470502499577730250e-09,5.25785294837341752360e-09] 
dist 193=[-2.90625089853729461900e-09,5.11645971181986454300e-09] 
dist 194=[-3.08206339505018237710e-09,4.90535150430665199110e-09] 
dist 195=[-3.19230711490653347150e-09,3.83215055305745595580e-09] 
dist 196=[-3.22107008071215687250e-09,3.45644924849415947690e-09] 
dist 197=[-3.18264696339302209680e-09,1.00778745560757075640e-09] 
dist 198=[-3.03385651860352630180e-09,9.68410509147100828490e-10] 
dist 199=[-3.59205327904564900730e-09,9.06644559729937397610e-10] 
dist 200=[-3.79741049821915269220e-09,8.43079314681860383810e-10] 
dist 201=[-1.57271362177560830520e-09,7.10736294344070011210e-10] 
dist 202=[-1.51116388397753129050e-09,6.50367926096906579350e-10] 
dist 203=[-1.15587953071704907650e-09,6.13260667256436651670e-10] 
dist 204=[-9.67727779628740397370e-10,6.05204154946758738650e-10] 
dist 205=[-2.14597995867731935910e-10,4.49304531064690696580e-10] 
dist 206=[-2.14847436582029623870e-10,8.36803829726379877430e-10] 
dist 207=[-2.15285978540124129860e-10,1.08016803999361128560e-09] 
dist 208=[-2.16022860353340787860e-10,1.14484347530476646950e-09] 
dist 209=[-2.16769195456557445730e-10,1.11055959765400654810e-09] 
dist 210=[-2.17244015454651951850e-10,1.06493054386319433740e-09] 
dist 211=[-2.17550671288949639940e-10,8.23550832980279624610e-10] 
dist 212=[-2.24767690435185893490e-10,7.48643290635131141480e-10] 
dist 213=[-4.89059660912718348900e-10,4.21080575816006624460e-10] 
dist 214=[-6.53830578032080808270e-10,4.38396665108471553260e-10] 
dist 215=[-7.56961009919474898940e-10,4.49215136764297812100e-10] 
dist 216=[-7.83563867009870163660e-10,4.52018125437114484360e-10] 
dist 217=[-3.55969356719519511390e-10,2.58883877875984256190e-10] 
dist 218=[-3.37069261772188676890e-10,3.54262874691890251250e-10] 
dist 219=[-3.01765736652154266780e-10,4.13984610597195292790e-10] 
dist 220=[-4.66646730466749431020e-10,4.29475950171114677810e-10] 
dist 221=[-6.31457130681344595260e-10,6.55060885345619218980e-10] 
dist 222=[-7.34123480712134272330e-10,8.09860240134390041370e-10] 
dist 223=[-7.98332078715677129400e-10,9.06857174402058101420e-10] 
dist 224=[-8.14826672047438842550e-10,9.32164025133498862010e-10] 
dist 225=[-7.86602205807567943330e-10,9.18586389890167287210e-10] 
dist 226=[-7.56112246281474655460e-10,8.65630909106182812410e-10] 
dist 227=[-5.67755389687892670700e-10,7.80949798361228885870e-10] 
dist 228=[-5.30485441956720881410e-10,7.27793495808917226210e-10] 
dist 229=[-7.03937860690137271630e-10,5.09083995229491942890e-10] 
dist 230=[-1.03146067100051466700e-09,4.24335047044538016340e-10] 
dist 231=[-1.23655112947540916910e-09,4.26836962975123587920e-10] 
dist 232=[-1.28977458565089007060e-09,4.57216180760364715570e-10] 
dist 233=[-1.25336328569178642530e-09,4.47584396243688085070e-10] 
dist 234=[-1.19725122315442908400e-09,4.24333123169901199070e-10] 
dist 235=[-9.52526186432720850110e-10,3.59982387221505258440e-10] 
dist 236=[-8.40223924173624555270e-10,3.28331987945916838340e-10] 
dist 237=[-2.64558564358558568080e-10,4.37557848670345341740e-10] 
dist 238=[-4.01084323405116924500e-10,7.83268835591495171990e-10] 
dist 239=[-4.90678359959982780860e-10,9.99733231264978382440e-10] 
dist 240=[-5.27941354928667861880e-10,1.05587697639733572390e-09] 
dist 241=[-6.58738517589853685400e-10,1.02461305044491078750e-09] 
dist 242=[-7.40273566152412256780e-10,9.80100883611555443800e-10] 
dist 243=[-7.91324658308777155730e-10,6.81272901583900786820e-10] 
dist 244=[-8.04562492560707563150e-10,4.02294864834853781590e-10] 
dist 245=[-7.79712604699775157840e-10,4.81889083622265271560e-10] 
dist 246=[-7.46807241825421811980e-10,5.31504912633717835840e-10] 
dist 247=[-5.25918100104721576750e-10,5.62570086081901517660e-10] 

8 phat 5 dirichlet min maxes function [1, 1, 1, 0, 2, 0, 2, 1, 2] 
dist 0=[319.16715382493793092   ,319.16715382493793092   ] 
dist 1=[289.43197989728393893   ,327.05119286215198248   ] 
dist 2=[250.96409117991516682   ,327.54182487095300956   ] 
dist 3=[213.07003105297078598   ,325.93326972585162768   ] 
dist 4=[171.31740452201207714   ,316.29000855454017935   ] 
dist 5=[116.94453549758476428   ,233.26291635116359524   ] 
dist 6=[65.112552107060231580  ,214.16031736576861668   ] 
dist 7=[33.018512030547244901  ,156.72810505255904333   ] 
dist 8=[5.5451480274652152125 ,143.93585436513191828   ] 
dist 9=[-27.707728558528423458  ,33.100540490602827524  ] 
dist 10=[-50.044359044136816288  ,14.457223022450880952  ] 
dist 11=[-67.012901742741829623  ,-15.620048061059252377  ] 
dist 12=[-79.217546517070126265  ,-.49323439430004910672] 
dist 13=[-82.332629871712480361  ,13.987981347064236097  ] 
dist 14=[-81.184018350564514981  ,28.059723184151480835  ] 
dist 15=[-64.209284871741533001  ,42.233292060364440425  ] 
dist 16=[-61.653125944450000950  ,52.544161655690700067  ] 
dist 17=[-1.6744122232411723380 ,54.361064173076400394  ] 
dist 18=[.08447239564916956938,48.317545764505769394  ] 
dist 19=[.40758546340151704016,46.867018498613455428  ] 
dist 20=[.16625321610281928869,37.612248095793438801  ] 
dist 21=[-13.035987080562172872  ,38.322169212957366739  ] 
dist 22=[-23.585564028470481492  ,37.228031735045577554  ] 
dist 23=[-29.301436786651215882  ,30.403936642214148813  ] 
dist 24=[-31.855079789821104107  ,27.415242477171996878  ] 
dist 25=[-31.502058466613792975  ,14.243085429243456571  ] 
dist 26=[-27.307189626256264984  ,19.397037462541948730  ] 
dist 27=[-27.219310650703515761  ,22.721831980379267571  ] 
dist 28=[-28.911590520646785965  ,24.876169321967146208  ] 
dist 29=[-8.8013704554028428192 ,25.539148233874090673  ] 
dist 30=[-8.6113649553283323018 ,24.966232547610906461  ] 
dist 31=[-6.7586028866610570399 ,22.372121242281578064  ] 
dist 32=[-6.3964966417023140483 ,.19567246379665556744] 
dist 33=[.14982632628072289245,.82425869435138774464] 
dist 34=[.13181770425055979457,2.9596548247215821239 ] 
dist 35=[.07373547256893889673,4.3486948844569387894 ] 
dist 36=[.00731987802819324577,4.8210311115520707546 ] 
dist 37=[-.06966309361463357773,4.7828296642766536211 ] 
dist 38=[-.14578992732928634057,4.6334997927564681090 ] 
dist 39=[-.2105353353228387132 ,3.5750648220537423610 ] 
dist 40=[-.27268973116925035173,3.3326615287134767554 ] 
dist 41=[-.9764385671763559399 ,.36011996805257064734] 
dist 42=[-2.0226355630000321465 ,.34136580341308659708] 
dist 43=[-2.6848898644051479120 ,.45832536336957291668] 
dist 44=[-2.8650364621673629238 ,.53619016120527801722] 
dist 45=[-1.1012755660862582874 ,.56460625310441818133] 
dist 46=[-1.0729169613039542082 ,.57260084012446190019] 
dist 47=[-.82086735243951072607,.57216544541089842382] 
dist 48=[-.78322329531545323676,.56594737058041620804] 
dist 49=[-.28975865194350972703,.55197691223397783351] 
dist 50=[-.19579179048549601102,.5379501610621362739 ] 
dist 51=[-.16131382559877508909,.5315849960991787473 ] 
dist 52=[-.14117374292622870007,.55938990621808873931] 
dist 53=[-.13872394489115123377,.55483609763977112327] 
dist 54=[-.02760920011975921098,.53441940751070796279] 
dist 55=[-.02860153294137915219,.42818132854440255016] 
dist 56=[-.02529451264731765803,.38358551267975546934] 
dist 57=[-.16486811415443837024,.06352182947314271551] 
dist 58=[-.31514819307935791013,.00013384505754161870] 
dist 59=[-.40940571376052279928,.00560890632314371487] 
dist 60=[-.43386360177542068605,.01115380429341594710] 
dist 61=[-.12840785424905548751,.01427764072416794630] 
dist 62=[-.12450086267347742588,.01576354043501923775] 
dist 63=[-.09541263247021067321,.01567329660285316139] 
dist 64=[-.08982744486811826515,.01358120264342258423] 
dist 65=[.00308784728828042603,.01584847375703826067] 
dist 66=[-.00408320294700701038,.04670035126463782404] 
dist 67=[-.00863237704376215436,.06639769533940089616] 
dist 68=[-.01150935234796107567,.07231219910926366950] 
dist 69=[-.01225823808760834965,.07076999688390670388] 
dist 70=[-.00385183346561270815,.06826395111537651513] 
dist 71=[-.00386668206882183237,.05214114341114340208] 
dist 72=[-.00323590038293092376,.04849216275348821721] 
dist 73=[-.01532961750939162468,.00439505281327742918] 
dist 74=[-.03068635340456055971,.00018191742896448598] 
dist 75=[-.04034696407093135470,.00119281039423980274] 
dist 76=[-.04292823337842217260,.00188772120605827838] 
dist 77=[-.01623303369279723409,.00219630937244048922] 
dist 78=[-.01572369316067237788,.00226507186431777094] 
dist 79=[-.01184344421544549425,.00222060536880241289] 
dist 80=[-.01126277761483067948,.00176404935878333527] 
dist 81=[.00038238549789816288,.00165150655429901611] 
dist 82=[-.00042216094823709064,.00525867688325716692] 
dist 83=[-.00093412361000122245,.00765665582381638793] 
dist 84=[-.00127889610593137514,.00836008108891909883] 
dist 85=[-.00136195973505510437,.00820534538566482991] 
dist 86=[-.00054497589382823229,.00787728104472158555] 
dist 87=[-.00053955763210037161,.00625437057330781704] 
dist 88=[-.00043239637219041309,.00559415798327170652] 
dist 89=[-.00248658257958200001,.00085982066980286723] 
dist 90=[-.00469441355620704708,2.79764834580749942630e-05] 
dist 91=[-.00607811262102804677,.00016325584432305736] 
dist 92=[-.00643709938360940759,.00025412423560224963] 
dist 93=[-.00191736112430836994,.00029060814116726028] 
dist 94=[-.00185378805551226698,.00029602424229713868] 
dist 95=[-.00139235500664268206,.00028830343212717044] 
dist 96=[-.00132007700731041230,.00023217290841593971] 
dist 97=[4.37693073200598105750e-05,.00026425554470053346] 
dist 98=[-8.11563383161890076160e-05,.00071913623097387044] 
dist 99=[-.00015963730959960989,.00100698910756158536] 
dist 100=[-.00020899853681281226,.00108805275310951950] 
dist 101=[-.00022182923144462972,.00105795732490754281] 
dist 102=[-9.74570666474668643640e-05,.00101903179617742422] 
dist 103=[-9.58401443331886623970e-05,.00077108386424601318] 
dist 104=[-9.10085632302848083650e-05,.00071974074361172009] 
dist 105=[-.00022385066213781490,5.37801729283833035030e-05] 
dist 106=[-.00044603329572803603,8.64840343295509059950e-05] 
dist 107=[-.00058554786196660885,.00012460455132141054] 
dist 108=[-.00062241573370248435,.00014871952394378748] 
dist 109=[-.00025085761629060279,.00015542081203147748] 
dist 110=[-.00024151090152542163,.00015461502792646190] 
dist 111=[-.00018449564420402887,.00014980430813201282] 
dist 112=[-.00017085963150224003,.00014182966826205405] 
dist 113=[-5.02752628172144891600e-05,.00013185564232822137] 
dist 114=[-4.78969482506342341270e-05,.00011585684345366767] 
dist 115=[-4.65108956920539558550e-05,.00011515527063997116] 
dist 116=[-4.57252620958071908620e-05,.00012499357443760626] 
dist 117=[-4.56775991473348716830e-05,.00012208332871051081] 
dist 118=[-9.02180933479029977270e-06,.00011700369200088771] 
dist 119=[-8.81097912731005904840e-06,9.25768407385363027920e-05] 
dist 120=[-6.78274559845369394740e-06,8.26640398621227344880e-05] 
dist 121=[-3.75856612399132681590e-05,1.24042253759657704390e-05] 
dist 122=[-7.04708178431371731260e-05,6.46627775243329052550e-07] 
dist 123=[-9.10720167590946117270e-05,2.78617317982431294030e-06] 
dist 124=[-9.64151477098252368540e-05,4.17743399156209827680e-06] 
dist 125=[-2.81442109847486863330e-05,4.64677762244132897870e-06] 
dist 126=[-2.71315957219142620690e-05,4.63270206507146541280e-06] 
dist 127=[-2.04678798144719598060e-05,4.46932792721700422910e-06] 
dist 128=[-1.92046056227052121250e-05,3.59754505243104187760e-06] 
dist 129=[6.35386496255931846910e-07,3.93040585605585328600e-06] 
dist 130=[-1.38202867928027336880e-06,1.06241043194976505810e-05] 
dist 131=[-2.64464874615540072630e-06,1.48413673589015776930e-05] 
dist 132=[-3.43702543178795759640e-06,1.59901542470467039690e-05] 
dist 133=[-3.64267619566247073470e-06,1.55123422137614377170e-05] 
dist 134=[-1.08023079903377333990e-06,1.49205784703647530020e-05] 
dist 135=[-1.04962114162638327310e-06,1.13181349308228373300e-05] 
dist 136=[-8.09055938417348375730e-07,1.05109681410041688580e-05] 
dist 137=[-3.47142836489671960790e-06,8.30214800791955084990e-07] 
dist 138=[-6.81629182723181835100e-06,1.30756957952797560820e-07] 
dist 139=[-8.91384427418945542800e-06,3.92597813057155117440e-07] 
dist 140=[-9.46322732037239338100e-06,5.60750535140849778850e-07] 
dist 141=[-3.53977058396442740970e-06,6.13129326279371986640e-07] 
dist 142=[-3.41467066896010266800e-06,6.02192023331898956500e-07] 
dist 143=[-2.54282422568983690830e-06,5.81557161591399216060e-07] 
dist 144=[-2.41245975373651875390e-06,4.45371925657263973880e-07] 
dist 145=[8.01013066162267280720e-08,4.14502676370764452550e-07] 
dist 146=[-1.28969531920706743170e-07,1.18180121388085000390e-06] 
dist 147=[-2.60021527303571056320e-07,1.69507752397542053980e-06] 
dist 148=[-3.42601264864709083000e-07,1.83405220338918227500e-06] 
dist 149=[-3.64884933997188260320e-07,1.78656558743988903690e-06] 
dist 150=[-1.40896025973549598110e-07,1.71085303689290379370e-06] 
dist 151=[-1.36719762990848233620e-07,1.34999832635411559570e-06] 
dist 152=[-1.03453128043913634600e-07,1.20539014192507309070e-06] 
dist 153=[-5.51426850372248950980e-07,1.77029932814166292660e-07] 
dist 154=[-1.03082675460772119440e-06,1.24161069354272907510e-08] 
dist 155=[-1.33108790613663475840e-06,4.53220844676441889480e-08] 
dist 156=[-1.40896147000542218820e-06,6.63688701705787565950e-08] 
dist 157=[-4.15033680843580082200e-07,7.27606047761101210960e-08] 
dist 158=[-4.00122619759404561110e-07,7.16141392596728206980e-08] 
dist 159=[-2.98121790380900387830e-07,6.88809055072568740670e-08] 
dist 160=[-2.82196696356890099330e-07,5.44972518373859059520e-08] 
dist 161=[1.04968888785620007570e-08,6.06799857420787336020e-08] 
dist 162=[-1.99666766629947904370e-08,1.58621587176479523340e-07] 
dist 163=[-3.90020786704344985880e-08,2.20179037799643062970e-07] 
dist 164=[-5.09375218798280487850e-08,2.36618010933813450490e-07] 
dist 165=[-5.40334424931339956770e-08,2.29081799811188789160e-07] 
dist 166=[-1.91312303614488733480e-08,2.20307236822433279060e-07] 
dist 167=[-1.84997116188091708030e-08,1.66346636490548295040e-07] 
dist 168=[-1.39821312238306619270e-08,1.54946736486506631170e-07] 
dist 169=[-5.10053072110551491270e-08,1.25050576410464710220e-08] 
dist 170=[-9.91229292632542680680e-08,2.67899005621603308910e-09] 
dist 171=[-1.29281144952481738530e-07,7.25239812345212925670e-09] 
dist 172=[-1.37154242135904488420e-07,1.01522298952160252710e-08] 
dist 173=[-5.06312354743285709720e-08,1.09799283234830918220e-08] 
dist 174=[-4.87937704204717311270e-08,1.06923314554469661550e-08] 
dist 175=[-3.63382397902621376150e-08,1.02989726321763359440e-08] 
dist 176=[-3.43848368438325776470e-08,7.85688583379024983830e-09] 
dist 177=[1.40795240105191960400e-09,7.28193893747930810390e-09] 
dist 178=[-2.84899221283896944910e-09,1.74254352182243057240e-08] 
dist 179=[-5.50613623425464667650e-09,2.47848219164048526620e-08] 
dist 180=[-7.17110377391747324120e-09,2.67454634413946924910e-08] 
dist 181=[-7.60296789555385726570e-09,2.60545403692188310270e-08] 
dist 182=[-4.36754485257430042400e-09,2.49008274955856323550e-08] 
dist 183=[-4.21263718278358083570e-09,1.98883272309617038980e-08] 
dist 184=[-3.15125810140134970470e-09,1.75170323587331449640e-08] 
dist 185=[-9.51963878536974542570e-09,4.21794927633230061810e-09] 
dist 186=[-1.65924365845763235440e-08,1.45371534918992670790e-09] 
dist 187=[-2.10217403579809755250e-08,1.52254606536493219850e-09] 
dist 188=[-2.21703751935299538970e-08,2.16366686184243989020e-09] 
dist 189=[-4.45863106267795251030e-09,2.33822592194315947840e-09] 
dist 190=[-4.29486096779421429510e-09,2.28491750057436167500e-09] 
dist 191=[-3.21289961070123229920e-09,2.18233591445160316810e-09] 
dist 192=[-3.02672661061901676310e-09,1.76500586227025435120e-09] 
dist 193=[1.12254617362227241540e-10,1.55767918614389426160e-09] 
dist 194=[-8.96378661936155028660e-10,1.74894826979401354640e-09] 
dist 195=[-1.54888602705546768080e-09,2.38460074638963299400e-09] 
dist 196=[-1.95853386019185275690e-09,2.55373739066798844420e-09] 
dist 197=[-2.06702335615464926170e-09,2.52653135305106245250e-09] 
dist 198=[-1.99614168543215026130e-09,2.40509059173024664410e-09] 
dist 199=[-1.92194376530789205800e-09,2.20823799797725440590e-09] 
dist 200=[-1.42992483553768599650e-09,2.05704964403415106470e-09] 
dist 201=[-2.31722017623738522390e-09,1.96229710122104742820e-09] 
dist 202=[-3.13005309233085262890e-09,2.00552373246154952560e-09] 
dist 203=[-3.63924586401625625420e-09,2.03191483078640162950e-09] 
dist 204=[-3.77171810783408572420e-09,2.03734009455957120010e-09] 
dist 205=[4.21899234818949463740e-10,1.96370331572972739350e-09] 
dist 206=[3.14081882908615464740e-10,1.88902234957155040150e-09] 
dist 207=[1.42849894281336487020e-10,1.40485707983618487740e-09] 
dist 208=[-1.31075576776594296760e-10,1.32436821369904256030e-09] 
dist 209=[-6.12402524491959704310e-10,1.26343123647753350730e-09] 
dist 210=[-1.51655717555382263240e-09,1.24590324028066624170e-09] 
dist 211=[-2.08044241378993846830e-09,1.23491985558969444560e-09] 
dist 212=[-2.43361283745833424520e-09,1.22800117130568672630e-09] 
dist 213=[-2.52541776598107058670e-09,1.22613725805391940820e-09] 
dist 214=[-2.43570492826656296340e-09,3.00827565741476818110e-10] 
dist 215=[-2.34446284777336879210e-09,3.53447218143350807470e-10] 
dist 216=[-1.74061981168362528250e-09,7.37578194475121148170e-10] 
dist 217=[-1.64545806088058495920e-09,1.47372801984180635880e-09] 
dist 218=[-1.39788159515823356520e-09,1.93256090110913944370e-09] 
dist 219=[-1.45830481977201221100e-09,2.21978654098553602750e-09] 
dist 220=[-1.47397359094024229500e-09,2.29413938888406142550e-09] 
dist 221=[5.85548981503788967070e-10,2.22070376770143957490e-09] 
dist 222=[4.71900898242341560450e-10,2.12927323075687593530e-09] 
dist 223=[2.90477498633707208010e-10,1.63721640446261850730e-09] 
dist 224=[-8.67034683059352437880e-11,1.49413220013030412200e-09] 
dist 225=[-7.66303643366249299550e-10,1.25946496502041749210e-09] 
dist 226=[-1.59492924748421814220e-09,1.38870405639534020200e-09] 
dist 227=[-2.11147963922277529890e-09,1.46926454620213791830e-09] 
dist 228=[-2.43491437945249045830e-09,1.51970438316608642490e-09] 
dist 229=[-2.51880341786141522430e-09,1.53278405703077926880e-09] 
dist 230=[-2.43651425169474283990e-09,4.69692903362276253790e-11] 
dist 231=[-2.33802409664773375760e-09,1.05608646683364293860e-10] 
dist 232=[-1.78548386954784733500e-09,6.60418840073179025060e-10] 
dist 233=[-1.64075675558435493110e-09,1.48289429904594236490e-09] 
dist 234=[-1.29266910863818739370e-09,1.99560051122108237430e-09] 
dist 235=[-1.31497627022525170800e-09,2.31661792225573541700e-09] 
dist 236=[-1.32076046231635804980e-09,2.39985989092140388160e-09] 
dist 237=[-2.67927030214687276810e-10,1.68153759060961689590e-09] 
dist 238=[-2.64638197383992656890e-10,1.66588946778602573150e-09] 
dist 239=[-2.51964366575765322120e-10,1.60552137249894799690e-09] 
dist 240=[-2.31724226257698747510e-10,1.50910199680932667540e-09] 
dist 241=[-7.07874658050644983370e-10,1.40404990048914117690e-09] 
dist 242=[-1.65400798218043796780e-09,1.38342599492466631280e-09] 
dist 243=[-2.24379953467733854100e-09,1.40150424491071315970e-09] 
dist 244=[-2.61308273350272446490e-09,1.41282341802193154610e-09] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 1, 2, 2, 0, 0, 1] 
dist 0=[344.23366436658988872   ,344.23366436658988872   ] 
dist 1=[302.64504758703151868   ,356.59605095833340214   ] 
dist 2=[250.74346933727870622   ,362.41739947025087368   ] 
dist 3=[205.18291264646935887   ,364.03256657424346907   ] 
dist 4=[159.62552490023935757   ,355.29714120893849433   ] 
dist 5=[106.67664870298587898   ,268.74043259288040134   ] 
dist 6=[57.754295752311279098  ,248.06768103175118843   ] 
dist 7=[27.561535114020388339  ,175.18850452184397035   ] 
dist 8=[-17.127144968886733560  ,164.35581103035520981   ] 
dist 9=[-40.357973022920344721  ,11.511978053234844625  ] 
dist 10=[-51.181222623621289857  ,6.2349770615084897236 ] 
dist 11=[-69.917409531090507078  ,4.8317754631164936557 ] 
dist 12=[-80.065110104062968479  ,3.0636068444758763811 ] 
dist 13=[-80.675286168388266729  ,1.8252841228339340245 ] 
dist 14=[-78.094207379332227486  ,7.0620949648942200556 ] 
dist 15=[-63.117201460004649862  ,18.336729969921447612  ] 
dist 16=[-56.953394153981872468  ,26.565997527832040909  ] 
dist 17=[-11.968552311190079270  ,28.466130973347310069  ] 
dist 18=[-3.2269537883769538954 ,41.118271943401108248  ] 
dist 19=[-.94267333744363605141,54.146487954207263999  ] 
dist 20=[1.0435404249738631287 ,57.496426878999175266  ] 
dist 21=[-4.1288057932196590888 ,17.019191525773831995  ] 
dist 22=[-9.9450637006704424675 ,16.655182174650300482  ] 
dist 23=[-13.460767920920320813  ,13.608861514054709013  ] 
dist 24=[-15.322860901769520655  ,12.350003627326367084  ] 
dist 25=[-15.361329221929370636  ,9.4428923707608246414 ] 
dist 26=[-13.507307409384807166  ,3.0817017144861126411 ] 
dist 27=[-13.405425386956152150  ,1.5623576993090389248 ] 
dist 28=[-14.441397142938608597  ,3.7080741141203438623 ] 
dist 29=[-14.417070910880369043  ,8.1641024696489247691 ] 
dist 30=[-7.8671096687983295005 ,10.986369151026271457  ] 
dist 31=[-6.3299657775068591925 ,11.721524848348833677  ] 
dist 32=[-5.6969531770606385783 ,3.7647626449372529817 ] 
dist 33=[-.97774373721432185744,3.7947999121517285302 ] 
dist 34=[-.05493840412896554927,4.4361315085279757800 ] 
dist 35=[1.3365893379846054685 ,5.8028699994439073021 ] 
dist 36=[-.14685568503830828286,6.1574110689593978568 ] 
dist 37=[-1.1335507846089952017 ,1.9178335413584144194 ] 
dist 38=[-1.8126340050784724711 ,1.8618535332461589879 ] 
dist 39=[-2.1160799815565278669 ,1.4427971736182388221 ] 
dist 40=[-2.1856413072432965175 ,1.3512157730446783396 ] 
dist 41=[-2.1443437875906262296 ,-.03369895649816642002] 
dist 42=[-1.7008862250561281959 ,-.26433156412108958603] 
dist 43=[-1.5964829324046247253 ,-.37438484395765453228] 
dist 44=[-1.1006181760260743714 ,.39247356777692222638] 
dist 45=[-1.0713103917371944955 ,.88024672255551661335] 
dist 46=[-1.0269927629118548428 ,1.2066871458738086504 ] 
dist 47=[-.7918620168491475321 ,1.2874006328047682976 ] 
dist 48=[-.71574852819209159983,.75342341240908344739] 
dist 49=[-.05643338653725018917,.73593850302686849865] 
dist 50=[.03756304276357702253,.68549698032557527926] 
dist 51=[.17526774928820792636,.64302736639821657744] 
dist 52=[-.01949825376354063384,.57735817793968526511] 
dist 53=[-.1463516153810044809 ,.23877087569664233518] 
dist 54=[-.23129173453880802382,.23175735477604991225] 
dist 55=[-.26491675037192996253,.17555949244846895974] 
dist 56=[-.27021435989822642147,.16717243248543789911] 
dist 57=[-.26255052138084824272,-.01974502427319713092] 
dist 58=[-.21509885386818763019,-.04927120798534502631] 
dist 59=[-.1935305487745644586 ,-.04118805769995386294] 
dist 60=[-.12160880178567957459,.07743203468062146681] 
dist 61=[-.11980477943226521437,.15190345497535845327] 
dist 62=[-.1151459893032533723 ,.19872230830375122295] 
dist 63=[-.09174409390864097200,.2108817856618209861 ] 
dist 64=[-.08208798912118825615,.0634578643791149505 ] 
dist 65=[-.01304870262305702395,.06213336311126819095] 
dist 66=[.00060344194073170367,.06834513255410527798] 
dist 67=[.01793481004507233786,.08861416007500472363] 
dist 68=[-.00647522147061673293,.09387241784399615530] 
dist 69=[-.02210934790580522978,.02764897180354537276] 
dist 70=[-.03231612246770826695,.02674091277361193783] 
dist 71=[-.03583574830857461538,.02035483705089963998] 
dist 72=[-.03559781856223335460,.01913705377295169068] 
dist 73=[-.03449997789439477843,-.00146487595679075154] 
dist 74=[-.02666035709527624658,-.00481838457758892861] 
dist 75=[-.02484453882923701866,-.00503216686605365010] 
dist 76=[-.01558550956378934572,.00739721790043168874] 
dist 77=[-.01519475678116682888,.01521468061925911603] 
dist 78=[-.01463864298975817707,.02018193330255604488] 
dist 79=[-.01114720288719453031,.02152293001575202817] 
dist 80=[-.01036131331904515100,.00826255985888785655] 
dist 81=[-.00088859497318720523,.00805716954572678202] 
dist 82=[.00055465158883793716,.00661764229802314105] 
dist 83=[.00244060323268637140,.00868268090015145614] 
dist 84=[-.00062341481460117028,.00922969615429849093] 
dist 85=[-.00257406403536697800,.00347761154264490870] 
dist 86=[-.00383683749967004370,.00336245133409750563] 
dist 87=[-.00425167667523571689,.00252055312356392837] 
dist 88=[-.00422488157756102753,.00239435461874415995] 
dist 89=[-.00407205743968677125,-.00032958279773298251] 
dist 90=[-.00326662530334929177,-.00075853851318510130] 
dist 91=[-.00292801469253607623,-.00057322022652507885] 
dist 92=[-.00179402362960841827,.00125732964405896151] 
dist 93=[-.00175468396414706396,.00240244465676541183] 
dist 94=[-.00168292755651124889,.00312089468770221756] 
dist 95=[-.00133098471633902992,.00330739533772578198] 
dist 96=[-.00119098996294369465,.00099460370731525623] 
dist 97=[-.00017875513957961613,.00096609296492062053] 
dist 98=[2.02286425159440338340e-05,.00100484124037314402] 
dist 99=[.00025064807536826412,.00129980546284374002] 
dist 100=[-.00012660968597854324,.00137631978995395078] 
dist 101=[-.00036504395815465297,.00041966803943546134] 
dist 102=[-.00051760445374935509,.00040437142442445369] 
dist 103=[-.00056400329205510996,.00030743995822020962] 
dist 104=[-.00055229767063574519,.00028643438823114883] 
dist 105=[-.00053319407445685389,-1.62932906354388115170e-05] 
dist 106=[-.00040571062240202907,-6.67727041104771018420e-05] 
dist 107=[-.00037909322970972392,-7.19532233023936421350e-05] 
dist 108=[-.00025071971165115777,.00011420818215576063] 
dist 109=[-.00024346804227018896,.00023083363444107530] 
dist 110=[-.00023309225240361395,.00030428602308737378] 
dist 111=[-.00018187333222823400,.00032406503193488245] 
dist 112=[-.00016329563832876148,.00018161123344894120] 
dist 113=[-1.58837716078598236820e-05,.00017203318375962500] 
dist 114=[9.88835935462175574450e-06,.00015542760404082124] 
dist 115=[3.54316389326769260140e-05,.00014513470613346806] 
dist 116=[-1.14935871851914178150e-05,.00013256742428919868] 
dist 117=[-4.10805493248907970410e-05,5.14906558854001478540e-05] 
dist 118=[-5.99483501847423391240e-05,4.96938242608463090990e-05] 
dist 119=[-6.55648457226270451430e-05,3.70474785817812668210e-05] 
dist 120=[-6.44519375273777984320e-05,3.51627364381229707390e-05] 
dist 121=[-6.18992905915792781050e-05,-5.21685957172377169650e-06] 
dist 122=[-4.92460623086756473190e-05,-1.15631232502604539190e-05] 
dist 123=[-4.40240939252664877610e-05,-8.25296511922839927970e-06] 
dist 124=[-2.66097289363579795390e-05,1.96479990025843735390e-05] 
dist 125=[-2.59436041994117608040e-05,3.70736594666650033690e-05] 
dist 126=[-2.48495838279880551060e-05,4.79962375244962732720e-05] 
dist 127=[-1.96315134335032447630e-05,5.08297314934057795460e-05] 
dist 128=[-1.75234850730542411360e-05,1.49073843660709980230e-05] 
dist 129=[-2.59660092761032408150e-06,1.44071655859596683970e-05] 
dist 130=[3.52330551207411569160e-07,1.49926795014576480210e-05] 
dist 131=[3.68424751393572750620e-06,1.93656339661268451280e-05] 
dist 132=[-1.99332871584787569990e-06,2.04997364346797306710e-05] 
dist 133=[-5.56024937992545686410e-06,5.97568678305556379210e-06] 
dist 134=[-7.82144054779171883880e-06,5.75662750075761976480e-06] 
dist 135=[-8.46612697497855622530e-06,4.33408577326478293850e-06] 
dist 136=[-8.24558617823358424520e-06,4.06504953759317698070e-06] 
dist 137=[-7.94109411734770222280e-06,-3.89194249080002640900e-07] 
dist 138=[-6.04335022275271267320e-06,-1.11378348751166324910e-06] 
dist 139=[-5.61525318614786447570e-06,-1.02955317289357525100e-06] 
dist 140=[-3.39526323103606367440e-06,1.82489034294338542040e-06] 
dist 141=[-3.29020382443235133460e-06,3.60902191997862409880e-06] 
dist 142=[-3.16350536774794964750e-06,4.72957212045236826570e-06] 
dist 143=[-2.39785441575472804160e-06,5.02590745320390391210e-06] 
dist 144=[-2.22619171118544283640e-06,1.88683277557937696270e-06] 
dist 145=[-1.73343415640905999150e-07,1.82365951950233341700e-06] 
dist 146=[1.38378654846755335960e-07,1.44918463635121715880e-06] 
dist 147=[5.09805280357900452810e-07,1.89379104387607205610e-06] 
dist 148=[-1.86026705217644835680e-07,2.00991898092615972760e-06] 
dist 149=[-6.22649244266727830670e-07,7.49450974910235756110e-07] 
dist 150=[-8.98958947823475952760e-07,7.22565195644080432210e-07] 
dist 151=[-9.76801068657913401260e-07,5.37294225679619531570e-07] 
dist 152=[-9.54953334558545856140e-07,5.09554567915084167920e-07] 
dist 153=[-9.15589047995366251980e-07,-7.76198705196817476230e-08] 
dist 154=[-7.24592721347908362940e-07,-1.69828904501404890950e-07] 
dist 155=[-6.47540012714184993040e-07,-1.18991399382433145330e-07] 
dist 156=[-3.88671653801219661040e-07,2.92447428015641437560e-07] 
dist 157=[-3.78232259997944507370e-07,5.49210474706199128310e-07] 
dist 158=[-3.62067254706458787870e-07,7.10080344238546354440e-07] 
dist 159=[-2.85614091071661052070e-07,7.51809698309610029410e-07] 
dist 160=[-2.54818951978287379970e-07,2.23098681405964938150e-07] 
dist 161=[-3.81239237893345505060e-08,2.15391256531959374570e-07] 
dist 162=[4.64204254803355686200e-09,2.19369743686762720080e-07] 
dist 163=[5.24999674860296614930e-08,2.82956332464113937180e-07] 
dist 164=[-3.19326297581884354720e-08,2.99446871146615868320e-07] 
dist 165=[-8.48035970136619664590e-08,8.72636388465735391210e-08] 
dist 166=[-1.18146854628194700090e-07,8.40818379948823630700e-08] 
dist 167=[-1.27294303128952247340e-07,6.26108266435078690670e-08] 
dist 168=[-1.23511504177103339150e-07,5.92217256737405668330e-08] 
dist 169=[-1.18866141576437984470e-07,-5.52713897992614018980e-09] 
dist 170=[-8.98875472657561913440e-08,-1.59212626723420182000e-08] 
dist 171=[-8.37766452660669759040e-08,-1.45760661113825665040e-08] 
dist 172=[-4.91409305482357944000e-08,2.69482922341518521830e-08] 
dist 173=[-4.75913907863484586110e-08,5.28764084256926672480e-08] 
dist 174=[-4.57168911544373719700e-08,6.91430002849485504030e-08] 
dist 175=[-3.47919976623508397610e-08,7.34165383030961895060e-08] 
dist 176=[-3.21351045423743418880e-08,2.75951674288089670620e-08] 
dist 177=[-3.52773338327884216380e-09,2.66195459779809342790e-08] 
dist 178=[8.62307733996927240340e-10,2.20044606089865750830e-08] 
dist 179=[7.10342574034883481660e-09,2.84676218687403971060e-08] 
dist 180=[-3.16762910784986769360e-09,3.01516844180602609990e-08] 
dist 181=[-9.59562269342945224510e-09,9.35969355559868449540e-09] 
dist 182=[-1.36463017452311325130e-08,9.01398181600058703090e-09] 
dist 183=[-1.47515663635474652430e-08,6.73826738089276663520e-09] 
dist 184=[-1.43782542491747063470e-08,6.34772980260040295030e-09] 
dist 185=[-1.37716141960389676080e-08,-7.82743760991432273530e-10] 
dist 186=[-1.08726193788578045580e-08,-1.92441822620533548080e-09] 
dist 187=[-9.70893578410811825890e-09,-1.30105430249180890550e-09] 
dist 188=[-5.12335922487414290050e-09,4.70968881250736962810e-09] 
dist 189=[-5.01390167875913348570e-09,8.50018639742286005040e-09] 
dist 190=[-4.76714677307143118170e-09,1.08744170585094907360e-08] 
dist 191=[-3.97485544684459679210e-09,1.14901623909332834440e-08] 
dist 192=[-3.58309245506177854360e-09,3.35511358414237892130e-09] 
dist 193=[-1.74760741347730915810e-09,3.22345252192813436040e-09] 
dist 194=[-1.29885159260245222170e-09,4.14781309694381391980e-09] 
dist 195=[-8.21461687621318446260e-10,5.05983868541347430240e-09] 
dist 196=[-7.41924246943342082450e-10,5.29634632055656235190e-09] 
dist 197=[-1.59014100669670648160e-09,-8.74497218162282591460e-11] 
dist 198=[-2.12338465420600359880e-09,-3.33493799704537695380e-11] 
dist 199=[-2.26617460505124816540e-09,5.15696519207760841840e-11] 
dist 200=[-2.20049266594039615570e-09,2.56422882174858089720e-10] 
dist 201=[-2.10990272157669350410e-09,5.90784466449514870120e-10] 
dist 202=[-1.63669273514864343930e-09,8.53060564819214048210e-10] 
dist 203=[-1.48394372682338572030e-09,1.01696438404863859550e-09] 
dist 204=[-5.62822999965802974560e-10,1.05880306750182417880e-09] 
dist 205=[-5.57003635950318666760e-10,1.18292053989555229630e-09] 
dist 206=[-7.45586185722427679060e-10,1.49852052231558413930e-09] 
dist 207=[-1.10352989307356762160e-09,1.58036528070185805530e-09] 
dist 208=[-1.76206645211037987890e-09,1.99539290184467514080e-09] 
dist 209=[-2.81636078465664305730e-09,2.71738369532690463550e-09] 
dist 210=[-3.47370582462960601060e-09,3.16745990065449703190e-09] 
dist 211=[-3.88527513944494350070e-09,3.44924686158634550730e-09] 
dist 212=[-3.99199688002242764910e-09,3.52225205441875975730e-09] 
dist 213=[-3.06040154338726902660e-09,1.39029380040532973490e-09] 
dist 214=[-2.92731609432105997360e-09,1.48134867274127591100e-09] 
dist 215=[-2.30027269310596388160e-09,1.50446932673689735840e-09] 
dist 216=[-2.05408423490338009340e-09,1.47633256811390554370e-09] 
dist 217=[-1.87284146654436605430e-09,1.39576740718241000380e-09] 
dist 218=[-1.49258929964043018480e-09,1.78749930133305645000e-09] 
dist 219=[-1.31468950890406661090e-09,2.27187180685082212610e-09] 
dist 220=[-9.70493519863884837100e-10,2.40478767992603117920e-09] 
dist 221=[-1.46549397816482048500e-09,2.36762861783300740000e-09] 
dist 222=[-1.77536193440727164210e-09,2.23205923610893518880e-09] 
dist 223=[-1.85558022053163887220e-09,1.99622656527281888650e-09] 
dist 224=[-1.81020679116047823760e-09,1.86067706192574667560e-09] 
dist 225=[-1.76691255495569106590e-09,1.54643122017730814150e-09] 
dist 226=[-2.60173406129573937680e-09,1.25989522872714238390e-09] 
dist 227=[-3.12442710586617241770e-09,1.11888411827225153210e-09] 
dist 228=[-3.25994556764691656880e-09,8.55194165731713449270e-10] 
dist 229=[-3.15420666136793587100e-09,1.39393563591628060630e-09] 
dist 230=[-3.02590665202832398570e-09,1.73315168421766770170e-09] 
dist 231=[-2.31623502636704058120e-09,1.82107340416937802210e-09] 
dist 232=[-2.12345190419305731350e-09,1.76889503929703912050e-09] 
dist 233=[-1.43641881753158229160e-09,1.69029435145424632550e-09] 
dist 234=[-1.16883240397085914700e-09,1.62441338320229617440e-09] 
dist 235=[-1.03716870043279109740e-09,2.10732581559293461180e-09] 
dist 236=[-1.06856889275362368200e-09,2.23254275049390267100e-09] 
dist 237=[-1.42816323335065288200e-09,2.20251075663559569080e-09] 
dist 238=[-1.68058763643957223920e-09,2.08671603508007041420e-09] 
dist 239=[-1.74603152247985835670e-09,1.90178119158446788200e-09] 
dist 240=[-1.68585583936715242390e-09,1.77154651348093818940e-09] 
dist 241=[-2.14281890707551852420e-09,1.96714686769483881020e-09] 
dist 242=[-2.76030303385854251800e-09,2.19282455490066742490e-09] 
dist 243=[-3.19522221227853892140e-09,2.33412692535153132390e-09] 

8 phat 5 dirichlet min maxes function [1, 1, 1, 0, 0, 0, 2, 0, 1] 
dist 0=[374.12432687131495448   ,374.12432687131495448   ] 
dist 1=[356.65189564574137741   ,386.05003415114362003   ] 
dist 2=[301.38707571186010801   ,393.05176067134511749   ] 
dist 3=[234.83522478157917773   ,386.70287991493661566   ] 
dist 4=[180.19713819804519307   ,305.91429768278649254   ] 
dist 5=[128.92644215629847386   ,285.09748067318363856   ] 
dist 6=[74.327662625027007873  ,206.46616047093361115   ] 
dist 7=[25.586820727165337090  ,194.90299366535610156   ] 
dist 8=[-23.756981984999617812  ,13.087325074246322927  ] 
dist 9=[-45.201298720795399141  ,-5.6490429104887817141 ] 
dist 10=[-74.941802396514316628  ,-2.7701446466522188350 ] 
dist 11=[-88.584836028252382474  ,3.8809313748385381051 ] 
dist 12=[-91.241651815001455450  ,8.8285812399255269458 ] 
dist 13=[-88.922932953633469117  ,11.450314856127875480  ] 
dist 14=[-72.874896301648610174  ,11.585535833551608980  ] 
dist 15=[-66.042782895775466022  ,13.793021591088648492  ] 
dist 16=[-13.508648243128780791  ,21.644748953333952584  ] 
dist 17=[-3.5693804438503581833 ,45.447965052923260481  ] 
dist 18=[-2.6259351558480398373 ,60.556309744143951377  ] 
dist 19=[2.2682760455479504431 ,64.477722180548111204  ] 
dist 20=[2.6327638480169394228 ,20.097654450459752669  ] 
dist 21=[-4.0626221200850305019 ,19.742738743773210169  ] 
dist 22=[-9.1272363290230841621 ,15.647476683675585862  ] 
dist 23=[-12.243287684321263036  ,14.847563228453632561  ] 
dist 24=[-13.929890166400769688  ,3.5608575103078474549 ] 
dist 25=[-13.917678699086252775  ,2.2269924474613258517 ] 
dist 26=[-12.355965243055600293  ,1.8034603733028160107 ] 
dist 27=[-11.157361222312269036  ,1.6502602889742076315 ] 
dist 28=[-10.569384490346692402  ,4.5246263019515840015 ] 
dist 29=[-10.258997705788664297  ,8.7252982290843205055 ] 
dist 30=[-7.9488552532004003063 ,11.304061413482073270  ] 
dist 31=[-7.4186517724910461719 ,11.787182354321168321  ] 
dist 32=[-.86199209742317465021,2.0737039093415414731 ] 
dist 33=[.10910676792853133844,4.3901440587919795819 ] 
dist 34=[.13107575969857146521,5.8658870848634163852 ] 
dist 35=[.11833881928744734231,6.2605144551845254683 ] 
dist 36=[.07793015463022435230,2.4251089631098557516 ] 
dist 37=[.02093186965218502969,2.3669449001857424170 ] 
dist 38=[-.05870789618518201001,1.8213742250489575152 ] 
dist 39=[-.13317469582275800248,1.7398154338075450339 ] 
dist 40=[-.17179097352123729222,.05495484907703511144] 
dist 41=[-.73894770056153455002,.01250392134398328388] 
dist 42=[-1.1049052604288475892 ,.01557906110500691821] 
dist 43=[-1.2216215808440751310 ,.12495592948773687191] 
dist 44=[-1.2115869536258872228 ,.19952115715056799954] 
dist 45=[-1.1683651150024657992 ,.25152703950784305641] 
dist 46=[-.93854055726714713362,.27475102213704747557] 
dist 47=[-.84161408258115801094,.30169480022260969406] 
dist 48=[-.14224457801239611491,.36844571213132842073] 
dist 49=[-.00380198182996843595,.6846860087936801271 ] 
dist 50=[-.03001944477568067465,.88889171213928788222] 
dist 51=[-.09012515231456875976,.94229808117743053949] 
dist 52=[-.12928340400357781609,.2839869587694319784 ] 
dist 53=[-.15524278832499467811,.27519509440501517619] 
dist 54=[-.16466236536316149389,.21304209942188696972] 
dist 55=[-.1664427759202859949 ,.19840135287412030064] 
dist 56=[-.16306692350556364146,.07450862678889371717] 
dist 57=[-.15588928047585562756,.06522470079660653585] 
dist 58=[-.14479787183621130378,.05979124792010489694] 
dist 59=[-.15689216299860332508,.04445181832541291155] 
dist 60=[-.15380991029424448716,.03914021091665298091] 
dist 61=[-.1484453531952203057 ,.03676456538909007894] 
dist 62=[-.11352936157882233909,.03818368347278317447] 
dist 63=[-.10561948518627834395,.03910379351374360711] 
dist 64=[-.00982184508170153942,.03840776106484076730] 
dist 65=[.00482456781893176881,.06642961895028404291] 
dist 66=[.01234883242144721298,.08745521591856872813] 
dist 67=[-.00222736467512565518,.09309105134667794142] 
dist 68=[-.01161345652926397753,.03528255244015003530] 
dist 69=[-.01779469864946354814,.03419979778850810650] 
dist 70=[-.02003808518126591818,.02581178118455740511] 
dist 71=[-.02017167984601196547,.02455616479573088644] 
dist 72=[-.01951974749687680111,-.00309315441786730457] 
dist 73=[-.01583185540306547803,-.00745702529870078033] 
dist 74=[-.01656940790091280814,-.00289971847709204767] 
dist 75=[-.01812055271919465730,.00591324930411957988] 
dist 76=[-.0178072625024562517 ,.01143625580651130173] 
dist 77=[-.01710232408716901185,.01490492688948417211] 
dist 78=[-.01359210172695285804,.01580543575299715570] 
dist 79=[-.01216124994354124645,.00471437328927542773] 
dist 80=[-.00188465064827228938,.00537411596296398866] 
dist 81=[.00013975229746153666,.01016603666250004045] 
dist 82=[.00127537414111776681,.01316950411154164098] 
dist 83=[-.00053207635277448715,.01394875733275411148] 
dist 84=[-.00168243501877665430,.00416045393105210228] 
dist 85=[-.00242638681060456017,.00402427534053534721] 
dist 86=[-.00266877477160765422,.00302667095594031801] 
dist 87=[-.00263377963915608362,.00286998210420050124] 
dist 88=[-.00254730680716436401,-.00021156225924096134] 
dist 89=[-.00195856391922498888,-.00071063358778655761] 
dist 90=[-.00217984811797178445,-.00035810705442708922] 
dist 91=[-.00235732010844780667,.00055853007759455189] 
dist 92=[-.00229362465294750383,.00113390931545183911] 
dist 93=[-.00220970594217506621,.00149703057036877775] 
dist 94=[-.00167289096829329835,.00159591225704367851] 
dist 95=[-.00156168426350283735,.00061676305354348071] 
dist 96=[-.00011819275200935054,.00059910070704646851] 
dist 97=[9.46574012835426287460e-05,.00096561672800098110] 
dist 98=[.00016492949852556741,.00126828954526804460] 
dist 99=[-6.87964066298400091040e-05,.00134839864315659141] 
dist 100=[-.00021679737949546350,.00053440533478144729] 
dist 101=[-.00031180208933336175,.00051564384067617328] 
dist 102=[-.00034135520144360701,.00039015855949247620] 
dist 103=[-.00033548144483004511,.00036612563248982115] 
dist 104=[-.00032389013306206139,-3.16203388516983730280e-05] 
dist 105=[-.00024926692003313524,-9.64436980262379702620e-05] 
dist 106=[-.00028166139801752421,-4.11318331116732106120e-05] 
dist 107=[-.00030365176985300931,9.29224142158458159070e-05] 
dist 108=[-.00029436942890192513,.00017672046894958140] 
dist 109=[-.00028343978129754547,.00022927400595544233] 
dist 110=[-.00021281424862236122,.00024291438400123205] 
dist 111=[-.00019949896561629302,.00013760832302391287] 
dist 112=[-2.70042975297941884770e-05,.00014105937111605676] 
dist 113=[3.09545413642727497280e-06,.00015260461610308658] 
dist 114=[1.01695114124335120450e-05,.00019725969456705370] 
dist 115=[-2.82280913399814972930e-05,.00020884161559114794] 
dist 116=[-5.23145381975973712110e-05,7.88504286693471057320e-05] 
dist 117=[-6.75342006040377967560e-05,7.53223540921046436070e-05] 
dist 118=[-7.17559294549369241980e-05,6.11691803221259654070e-05] 
dist 119=[-7.05465413366230063030e-05,5.41037551390399900790e-05] 
dist 120=[-6.69637830974824642080e-05,1.52501788666390020230e-05] 
dist 121=[-5.68838498621268539890e-05,6.60453993933553891330e-06] 
dist 122=[-5.18615173980672579100e-05,3.99124956655004309610e-06] 
dist 123=[-3.46361907317682625300e-05,1.46079543733133764870e-05] 
dist 124=[-3.36114729172989941430e-05,2.12581998185130099690e-05] 
dist 125=[-3.23325915261285584540e-05,2.54464316554919727580e-05] 
dist 126=[-2.45315305696816222650e-05,2.65747266970957546080e-05] 
dist 127=[-2.27838325295488883320e-05,9.39295556927949577800e-06] 
dist 128=[-1.80698524534924734790e-06,9.09260648837235973240e-06] 
dist 129=[1.37864861333630162470e-06,1.47571573118435615940e-05] 
dist 130=[2.58218947732512571220e-06,1.93032058630641184260e-05] 
dist 131=[-8.83698270083234515760e-07,2.04947269670274967090e-05] 
dist 132=[-3.06409574380692091170e-06,7.67297822165632945550e-06] 
dist 133=[-4.44961242142725266100e-06,7.40287351083764397470e-06] 
dist 134=[-4.85180195636800868860e-06,5.51498826108354523080e-06] 
dist 135=[-4.75741619517061813610e-06,5.23272286350311028620e-06] 
dist 136=[-4.56523641305419498860e-06,-7.81648685372468902080e-07] 
dist 137=[-3.62441617533323692440e-06,-1.72678276597670464760e-06] 
dist 138=[-3.67154200107939287350e-06,-6.00445503820499005350e-07] 
dist 139=[-3.97383628805241524660e-06,1.45727243830515692830e-06] 
dist 140=[-3.87188819118983151660e-06,2.74195367629922850430e-06] 
dist 141=[-3.70819245252524064340e-06,3.54703352395004793960e-06] 
dist 142=[-2.92621716270876097840e-06,3.75586722309795341670e-06] 
dist 143=[-2.61336003191611476600e-06,1.09861890170815831400e-06] 
dist 144=[-3.81774011660102608480e-07,1.19149565263118357560e-06] 
dist 145=[5.72872027155290109030e-08,2.23014000214074139370e-06] 
dist 146=[2.68556074458332635760e-07,2.88068415388840019390e-06] 
dist 147=[-1.49571935351507953690e-07,3.04940639024910821860e-06] 
dist 148=[-4.11872291708976320820e-07,9.02347286366066265750e-07] 
dist 149=[-5.77766858092664963760e-07,8.70002554627381556360e-07] 
dist 150=[-6.24264834164592746660e-07,6.48407027177400300220e-07] 
dist 151=[-6.07093360350569521340e-07,6.13792290924123319160e-07] 
dist 152=[-5.84386198301968372930e-07,-5.44848611634425971320e-08] 
dist 153=[-4.44224040253975519440e-07,-1.62645841369017875470e-07] 
dist 154=[-4.78029685571832771130e-07,-7.49282339396565111580e-08] 
dist 155=[-5.13838808765913524350e-07,1.35139740294012306900e-07] 
dist 156=[-4.97501508349015823670e-07,2.66374639087047087250e-07] 
dist 157=[-4.78511459799450423060e-07,3.48751548776897691850e-07] 
dist 158=[-3.60966862687122513260e-07,3.70458592999022249110e-07] 
dist 159=[-3.36594613990943716370e-07,1.39985079891460390140e-07] 
dist 160=[-2.37354131774245395680e-08,1.35196643094575139770e-07] 
dist 161=[2.22886577600450283890e-08,2.11771571953022685980e-07] 
dist 162=[3.71678315886765024180e-08,2.77097049275797293250e-07] 
dist 163=[-1.40845053988067240720e-08,2.94157943737570345840e-07] 
dist 164=[-4.64242895279534682520e-08,1.13891086325923707570e-07] 
dist 165=[-6.68488994484102219490e-08,1.09778798086899583010e-07] 
dist 166=[-7.25168894582454723410e-08,8.16390871320213780780e-08] 
dist 167=[-7.07890230532531698360e-08,7.73688983506176525970e-08] 
dist 168=[-6.78460161788448546770e-08,-1.16500107102124259100e-08] 
dist 169=[-5.35857672589557876500e-08,-2.56451610726077478880e-08] 
dist 170=[-5.49969098715434490840e-08,-8.80793399551616809670e-09] 
dist 171=[-5.93924193726375736060e-08,2.15241112359098173020e-08] 
dist 172=[-5.77645416002602779090e-08,4.04978574779882237170e-08] 
dist 173=[-5.53020376757436301170e-08,5.23840519705442923740e-08] 
dist 174=[-4.35134031187993117890e-08,5.54671099444272402020e-08] 
dist 175=[-3.89068317499885350630e-08,1.67912682441380291690e-08] 
dist 176=[-5.63535195806524799930e-09,1.77163639099079425390e-08] 
dist 177=[8.33965201920529380220e-10,3.30414530148194495380e-08] 
dist 178=[3.84872878290049221620e-09,4.26388129563043176510e-08] 
dist 179=[-2.53655541579253149130e-09,4.51276702886511464990e-08] 
dist 180=[-6.53130799961269017070e-09,1.38733520777299169770e-08] 
dist 181=[-9.04695251923315843860e-09,1.33481877781084834380e-08] 
dist 182=[-9.72948611222657611640e-09,1.00548808184407924060e-08] 
dist 183=[-9.41636144051707337610e-09,9.39657192725115738470e-09] 
dist 184=[-9.07382415694651069940e-09,-6.81424211923542611330e-10] 
dist 185=[-6.75581229832639292890e-09,-2.25615033735700894340e-09] 
dist 186=[-7.53341984850233593870e-09,-1.14053793335139368780e-09] 
dist 187=[-8.08285855547376945430e-09,2.03244320887182912280e-09] 
dist 188=[-7.80671099192375415720e-09,4.01298736148173331200e-09] 
dist 189=[-7.51664121730741244710e-09,5.25501159349438555370e-09] 
dist 190=[-5.59226453067558210870e-09,5.58043447348810389260e-09] 
dist 191=[-5.28210543255406196400e-09,2.43181112864621449920e-09] 
dist 192=[-4.98530878025024196080e-10,2.33881702333407405350e-09] 
dist 193=[1.85440651662164413580e-10,3.36282524762945257090e-09] 
dist 194=[5.04682420636268980140e-10,4.36063404492619692710e-09] 
dist 195=[-4.52304074015338576570e-10,4.62036704595217314810e-09] 
dist 196=[-1.05039399764531536860e-09,2.28032641281747341510e-09] 
dist 197=[-1.42644420068789514790e-09,2.19570267227659838770e-09] 
dist 198=[-1.52727993355003559350e-09,1.63493259081014384770e-09] 
dist 199=[-1.48257433316075837990e-09,1.54378790722204080650e-09] 
dist 200=[-1.42242723148211375580e-09,2.46748550860432060090e-10] 
dist 201=[-1.14380190542657670150e-09,4.08235755882879247640e-11] 
dist 202=[-1.46219475982561155760e-09,1.13626560553523348580e-10] 
dist 203=[-1.54582435720089873620e-09,6.41666705287024754740e-10] 
dist 204=[-1.49582133958185453750e-09,9.70983215675631634620e-10] 
dist 205=[-1.43639606630530551580e-09,1.17723156522690307340e-09] 
dist 206=[-1.09308602687310267180e-09,1.23071921865055131550e-09] 
dist 207=[-1.00887788434729087960e-09,4.89845623278250038730e-10] 
dist 208=[-5.37755754574267724830e-10,6.08842322330901899230e-10] 
dist 209=[-5.75268860401704345330e-10,8.00680100687470137810e-10] 
dist 210=[-5.98615475569040390250e-10,9.20812653565881470840e-10] 
dist 211=[-6.20118880507005503500e-10,9.51967568332124450350e-10] 
dist 212=[-6.98129681358147933330e-10,8.50853045657257785610e-10] 
dist 213=[-7.47116365464545097590e-10,9.63612039210179340400e-10] 
dist 214=[-7.60119949510615414780e-10,9.92579003647662110420e-10] 
dist 215=[-7.48713879272532139370e-10,9.62082787892192298590e-10] 
dist 216=[-7.05991034210992009920e-10,9.20942618206626252670e-10] 
dist 217=[-7.16584735528731348010e-10,7.18172359389591468870e-10] 
dist 218=[-8.53605037437313850330e-10,6.46086675744385979380e-10] 
dist 219=[-8.89223613375084307360e-10,6.20252033540876115410e-10] 
dist 220=[-8.59864670025084638240e-10,8.21440472836086954970e-10] 
dist 221=[-8.25517522633312310730e-10,9.86711892533736416930e-10] 
dist 222=[-7.23108992726225758440e-10,1.02965823044886629910e-09] 
dist 223=[-6.87278224881753160530e-10,9.97569069208997948920e-10] 
dist 224=[-6.47773082868348428980e-10,9.55877223780279563320e-10] 
dist 225=[-5.80748874944931702660e-10,7.39820775173544024060e-10] 
dist 226=[-6.14130850964913206010e-10,7.38371880911037400900e-10] 
dist 227=[-6.36395203549014736670e-10,7.61551631934220606480e-10] 
dist 228=[-5.11333521486785059730e-10,7.60076726037650571540e-10] 
dist 229=[-6.72270829172510494490e-10,9.12269591052813267160e-10] 
dist 230=[-7.14032085101228879980e-10,9.51704327741832527760e-10] 
dist 231=[-6.95014364394715815340e-10,9.20203953597668805790e-10] 
dist 232=[-6.62818062920070706460e-10,8.83344440877151550900e-10] 
dist 233=[-5.34946437997836205030e-10,6.72100978937161240750e-10] 
dist 234=[-4.72025553510287971010e-10,6.19873765131154587330e-10] 
dist 235=[-5.00171180190491438910e-10,5.53236790772329713400e-10] 
dist 236=[-5.49467230981176955650e-10,7.14758425867088765910e-10] 
dist 237=[-5.80332357119262635100e-10,8.15895021311680286120e-10] 
dist 238=[-5.88336197930626130470e-10,8.42128528511633537640e-10] 
dist 239=[-3.63280107750683161880e-10,8.13143452422947730310e-10] 
dist 240=[-3.63038107189018646090e-10,7.81689372839665036700e-10] 
dist 241=[-3.62657114587767661640e-10,5.87058639356051483240e-10] 
dist 242=[-3.62050283620819504360e-10,5.48568107042396316940e-10] 
dist 243=[-3.80109486918147235200e-10,4.37490715024045350490e-10] 
dist 244=[-4.72622813128617567270e-10,5.97755016047290443280e-10] 
dist 245=[-5.30548943052300363480e-10,6.98099435650860012040e-10] 
dist 246=[-5.45572244328515577910e-10,7.24117352641639008710e-10] 
dist 247=[-5.29913724735313443780e-10,7.00695251448305841060e-10] 
dist 248=[-5.06412819208250955230e-10,6.72134701817112207220e-10] 
dist 249=[-4.71721956378313131610e-10,5.14920242487348163010e-10] 
dist 250=[-4.71002047960815954470e-10,4.71677902961637585530e-10] 
dist 251=[-5.18941539425818437600e-10,5.96277110933129639650e-10] 
dist 252=[-5.48825457296615890660e-10,7.89577733264364840500e-10] 
dist 253=[-5.67536468065816595780e-10,9.10608316305555555620e-10] 

8 phat 5 dirichlet min maxes function [2, 2, 1, 1, 0, 0, 1] 
dist 0=[300.31217212435597014   ,300.31217212435597014   ] 
dist 1=[289.21973359090664758   ,303.77471411414574729   ] 
dist 2=[269.87163924090496946   ,302.23950208533684031   ] 
dist 3=[241.94773434208133959   ,280.30810503222531944   ] 
dist 4=[196.72865520665658792   ,277.08992672012854520   ] 
dist 5=[148.67710766167729847   ,193.78051380667495441   ] 
dist 6=[109.62816688441844322   ,181.37722046421604384   ] 
dist 7=[71.660348170456230192  ,117.24191838342115720   ] 
dist 8=[28.266521540548855731  ,90.556580605343082324  ] 
dist 9=[-15.255492903515351356  ,22.585117854923734135  ] 
dist 10=[-42.753898894165796798  ,12.321435218763847449  ] 
dist 11=[-56.582940138407685312  ,-10.100341128983687430  ] 
dist 12=[-58.940329905417662691  ,-14.608685293338437594  ] 
dist 13=[-54.857233330939061672  ,-9.5749446740468687115 ] 
dist 14=[-53.353244820515876890  ,6.9256858282724756064 ] 
dist 15=[-40.835458208543147760  ,21.866912376313430073  ] 
dist 16=[-38.958161050969006387  ,35.358339844983063454  ] 
dist 17=[-3.1973006477602021156 ,44.906275555289077826  ] 
dist 18=[1.4074823351219282301 ,46.639370195211603810  ] 
dist 19=[9.2600197215824612642 ,41.994985263978565477  ] 
dist 20=[10.435509537536530266  ,40.583833643285813678  ] 
dist 21=[.5858609220913252358 ,24.803696938070745425  ] 
dist 22=[-12.177451917423364098  ,23.939838188638946927  ] 
dist 23=[-21.364788343273361239  ,19.240349501448065323  ] 
dist 24=[-26.240967522829362474  ,17.295522442509697963  ] 
dist 25=[-28.079907549874780837  ,13.824152560808923885  ] 
dist 26=[-27.912378166319852472  ,13.983951827196856743  ] 
dist 27=[-22.238575372186795137  ,14.107888682884932831  ] 
dist 28=[-18.702746179332118938  ,14.156928379588941275  ] 
dist 29=[-5.6330675002290138605 ,13.946604310953085930  ] 
dist 30=[-5.4760926674271359238 ,13.079315798125767948  ] 
dist 31=[-4.2274393865376248080 ,11.693069411701489328  ] 
dist 32=[-3.9882686290171806303 ,9.4936569879861737572 ] 
dist 33=[-.44482503875043665554,6.6229761025738015774 ] 
dist 34=[.06712749886309056031,6.5927654182972698533 ] 
dist 35=[.92926287479882334872,5.3250385663855108255 ] 
dist 36=[1.0670518067770077993 ,5.1327155345721908801 ] 
dist 37=[-.15368633000534436245,3.0226463648241892628 ] 
dist 38=[-1.7874467805683823492 ,2.9197277013114335172 ] 
dist 39=[-2.8922702739302012644 ,2.2370407453209447344 ] 
dist 40=[-3.3514660608138403817 ,2.0826347750903461659 ] 
dist 41=[-3.4473428346555773655 ,.20383244756914116725] 
dist 42=[-3.3584943312912938904 ,-.08428732924681218927] 
dist 43=[-2.7663236442267171700 ,-.42236966208988587736] 
dist 44=[-2.4942836182284582051 ,-.45926992192512013821] 
dist 45=[-.69119630531441942582,.96695502400466943408] 
dist 46=[-.67080014739708859069,1.9152079857320330935 ] 
dist 47=[-.50811513695330056366,2.5117514768389416760 ] 
dist 48=[-.48374752812117521717,2.6668152963597102527 ] 
dist 49=[-.02636430737033210343,.81838595928111514203] 
dist 50=[.02473929280315041956,.80371504795390142562] 
dist 51=[.11457274655034825466,.6309674417793947411 ] 
dist 52=[.12885717629103172979,.60203748013855500034] 
dist 53=[-.11637608839284739218,.34623474437522588193] 
dist 54=[-.32235193360800928835,.3327846164941334174 ] 
dist 55=[-.45725397190524167058,.2649364989362087192 ] 
dist 56=[-.50465476055467519859,.23722146027292841701] 
dist 57=[-.50187188849628734682,.21573553926528617662] 
dist 58=[-.48592734608709901669,.2151406794714653431 ] 
dist 59=[-.37844665247413485053,.21524104590039671977] 
dist 60=[-.34965565078085958694,.21621414469473484221] 
dist 61=[-.10404611586361928221,.21658890538030407059] 
dist 62=[-.07820908908500047703,.2397162738838327944 ] 
dist 63=[-.05897239984789055074,.30325086386993849014] 
dist 64=[-.05594166987327819797,.32124594965185837856] 
dist 65=[-.00602374112629957242,.01886092853963645806] 
dist 66=[.00094957601935570761,.03533713412950539416] 
dist 67=[.01268233805000895857,.04565290646977574124] 
dist 68=[.01457216614992155396,.04832783167184012489] 
dist 69=[.01405489707804638189,.04438693795056317172] 
dist 70=[.01197841151344289031,.04278086299074197978] 
dist 71=[.00865119348902537878,.03242111902718658282] 
dist 72=[.00330863975448978038,.03027242547076795773] 
dist 73=[-.00929789511909943348,.00236973997191223361] 
dist 74=[-.01862930311515455415,-.00174936905710262789] 
dist 75=[-.02449284482938280054,-.00592815942171986441] 
dist 76=[-.02604987686571297500,-.00643989324323880595] 
dist 77=[-.01015279341917351963,-.00618020186942940735] 
dist 78=[-.00981687106316618760,-.00514981147551494287] 
dist 79=[-.00735747577582887811,-.00350006405298300753] 
dist 80=[-.00699079438838270859,-.00085133563575404425] 
dist 81=[-.00048595069077904716,.00179784550826610880] 
dist 82=[.00022870852771381161,.00344958041833198136] 
dist 83=[.00145886533391974337,.00486784850524938476] 
dist 84=[.00165634098943718395,.00529022310247156769] 
dist 85=[.00158915183718702612,.00517677333337790600] 
dist 86=[.00131804375826043574,.00496251067893081893] 
dist 87=[.00088319497385759013,.00394187681750075907] 
dist 88=[.00018441137940440546,.00351199276285945482] 
dist 89=[-.00167397037597243263,.00065624056280203564] 
dist 90=[-.00305437000354863591,9.07584593989483839130e-05] 
dist 91=[-.00391925606558081988,-.00029982959295800317] 
dist 92=[-.00414364274909435724,-.00035237185118594485] 
dist 93=[-.00126775347373430111,-.00031599241438204238] 
dist 94=[-.00120439084196545646,-.00016073731916241134] 
dist 95=[-.00100654301731829241,8.98242552214013593610e-05] 
dist 96=[-.00090901446705776161,.00049381714342199286] 
dist 97=[-.00038875873783316203,.00089851745476666924] 
dist 98=[-.00025700248397718600,.00115185347670826346] 
dist 99=[-9.25831752857496837390e-05,.00131173233645492813] 
dist 100=[-6.28012238732065957060e-05,.00135606704886842546] 
dist 101=[-7.30961953205832697990e-05,.00064860186968452372] 
dist 102=[-.00011355648782242886,.00062406216990943270] 
dist 103=[-.00017828533472775797,.00047374417438550487] 
dist 104=[-.00028217583227476892,.00044004901414985628] 
dist 105=[-.00038605370513668606,8.78640735432862664030e-05] 
dist 106=[-.00045073814464286657,2.24001027001587645270e-05] 
dist 107=[-.00049114540611237361,-2.38689320417451631030e-05] 
dist 108=[-.00050140568964554475,-2.96090745317727167340e-05] 
dist 109=[-.00015809592457975947,-2.61979309754551109020e-05] 
dist 110=[-.00015107464002771158,-1.16466286539856680380e-05] 
dist 111=[-.00011980784391238553,1.18394158353863255880e-05] 
dist 112=[-.00010597670386078481,4.97126218570654398840e-05] 
dist 113=[-1.93546862525463026050e-05,8.76567736553160042610e-05] 
dist 114=[-1.57908318646119625370e-06,.00011142037029292822] 
dist 115=[2.11273974700431473500e-05,.00012643139163783566] 
dist 116=[2.40635660466842916990e-05,.00013062584759293375] 
dist 117=[2.32137836629422447770e-05,7.46921207546728547840e-05] 
dist 118=[1.98901607641918032460e-05,7.15488644556577329840e-05] 
dist 119=[1.45752091488962882400e-05,5.64890048482401846260e-05] 
dist 120=[6.04520784844781299650e-06,5.04574271679335187870e-05] 
dist 121=[-2.29412786348358374190e-05,7.40265739164676061730e-06] 
dist 122=[-4.29786431228992306710e-05,-1.06842227585236049390e-06] 
dist 123=[-5.55294202654076481260e-05,-1.11329286024525921140e-05] 
dist 124=[-5.87846166264765580850e-05,-1.19963516011407521770e-05] 
dist 125=[-1.74094570585326144210e-05,-1.15007893565489067490e-05] 
dist 126=[-1.67893553922985887850e-05,-9.54389951934179665880e-06] 
dist 127=[-1.25205527870037223320e-05,-6.41623789515337715740e-06] 
dist 128=[-1.18546434487004886600e-05,-1.39757920381874729660e-06] 
dist 129=[-1.12466487103333990970e-06,3.62132116867385257230e-06] 
dist 130=[1.97927431586338973700e-07,6.75001772616051006430e-06] 
dist 131=[2.41935586486980685920e-06,9.21047015759933341480e-06] 
dist 132=[2.77436954508563567080e-06,9.90498531607146636870e-06] 
dist 133=[2.67276494395513487400e-06,9.59324083019971011350e-06] 
dist 134=[2.27669887734897206590e-06,9.22847528893249815250e-06] 
dist 135=[1.64348457757767151740e-06,6.96133183702525385160e-06] 
dist 136=[6.27247794986689187430e-07,6.49377459235441126270e-06] 
dist 137=[-2.05976534839355925680e-06,4.50492036205085564500e-07] 
dist 138=[-4.06832596977904924590e-06,-4.37855416171769505430e-07] 
dist 139=[-5.32748920709033980130e-06,-1.15082309326023205950e-06] 
dist 140=[-5.65667982341121508680e-06,-1.24751673575417537550e-06] 
dist 141=[-2.18810966490539611090e-06,-1.19654980682778790240e-06] 
dist 142=[-2.10967816024468146390e-06,-9.98582136186744474280e-07] 
dist 143=[-1.56850202787308042380e-06,-6.82188913994932217820e-07] 
dist 144=[-1.48780976283076575270e-06,-1.74504089975720423860e-07] 
dist 145=[-7.35563182536854467800e-08,3.33208179028531371670e-07] 
dist 146=[6.57239147281444800010e-08,7.31857532948728415460e-07] 
dist 147=[3.08828164735222483620e-07,1.04816729224282221080e-06] 
dist 148=[3.47124523082492027900e-07,1.13284134117057986410e-06] 
dist 149=[3.34792424218491759970e-07,1.10246232601259473050e-06] 
dist 150=[2.86808024376017371550e-07,1.05533863296770035920e-06] 
dist 151=[2.10105410627038857590e-07,8.32417950984786946180e-07] 
dist 152=[8.68353233735362971460e-08,7.42760566370853688120e-07] 
dist 153=[-3.41837080394638592130e-07,1.08782875988322070910e-07] 
dist 154=[-6.38192617584791080230e-07,-1.63884983546334833940e-08] 
dist 155=[-8.23790522320616101770e-07,-1.60514641627059635970e-07] 
dist 156=[-8.71921580699903617500e-07,-1.73004173247373787330e-07] 
dist 157=[-2.53915425152517660720e-07,-1.65730206259474339360e-07] 
dist 158=[-2.44424578824450348350e-07,-1.37485819276083821250e-07] 
dist 159=[-1.83689144440385019130e-07,-9.23542063079085996260e-08] 
dist 160=[-1.72175139215241705290e-07,-1.99409773699274383180e-08] 
dist 161=[-1.63875719337208287540e-08,5.24749657431337230510e-08] 
dist 162=[2.66686911060577595280e-09,9.76177765420729451590e-08] 
dist 163=[3.46189923252413662680e-08,1.34668529464842388140e-07] 
dist 164=[3.97223892125765162210e-08,1.44684108886147162640e-07] 
dist 165=[3.82505258402404197330e-08,1.40034678448728821670e-07] 
dist 166=[3.25356701047076259680e-08,1.34606083316508633220e-07] 
dist 167=[2.34022767807767415830e-08,1.01841007512068791750e-07] 
dist 168=[8.74664387536013147940e-09,9.46201182566573745170e-08] 
dist 169=[-3.14292391624780514080e-08,7.21341721358480107980e-09] 
dist 170=[-6.13758091844635131480e-08,-5.94633528425537144280e-09] 
dist 171=[-8.01389667650216175600e-08,-1.60668844703219550400e-08] 
dist 172=[-8.50261895902980510260e-08,-1.74388696469442628890e-08] 
dist 173=[-3.20895745300103307080e-08,-1.67241702335769117510e-08] 
dist 174=[-3.09112082513781712790e-08,-1.39550206640036768720e-08] 
dist 175=[-2.30168259774422218740e-08,-9.53030793705890695050e-09] 
dist 176=[-2.17567619636803714060e-08,-2.24184760399003503720e-09] 
dist 177=[-1.44297533978628279800e-09,5.18716376773920126830e-09] 
dist 178=[5.44268829068475931840e-10,1.12601851114453888920e-08] 
dist 179=[3.93102565376013492100e-09,1.59328972076475287330e-08] 
dist 180=[4.46867527390500209990e-09,1.71680285452158976200e-08] 
dist 181=[4.30317082762695469430e-09,1.66873175004035572160e-08] 
dist 182=[3.66098083898900209670e-09,1.59694111054065446970e-08] 
dist 183=[2.63469783453549554780e-09,1.25744799006880066570e-08] 
dist 184=[9.87927658263673857360e-10,1.12258773918709129590e-08] 
dist 185=[-5.43852491880033009220e-09,2.11583359071673702030e-09] 
dist 186=[-9.74894161016502747010e-09,3.69922117909179397120e-10] 
dist 187=[-1.24481697066154430170e-08,-1.81605960320349101720e-09] 
dist 188=[-1.31481185794534715130e-08,-1.97056612492734772110e-09] 
dist 189=[-4.05569844723647789260e-09,-1.86805600895880252140e-09] 
dist 190=[-3.88973150057052040900e-09,-1.47142890429034089430e-09] 
dist 191=[-3.00649993801488555410e-09,-8.37758845246119918280e-10] 
dist 192=[-2.73550231959200495600e-09,1.78901680446644954160e-10] 
dist 193=[-7.84196710740282515750e-10,1.19558996437140982730e-09] 
dist 194=[-5.92475309302608692160e-10,2.02548920033573194160e-09] 
dist 195=[-3.97784208614342716370e-10,2.67645272022870136490e-09] 
dist 196=[-3.59104178886685907360e-10,2.84717034132465884140e-09] 
dist 197=[-3.49849831013848452320e-10,2.74910685204085394120e-09] 
dist 198=[-3.33189318148850326750e-10,2.64548898740820107910e-09] 
dist 199=[-2.71730908727632591050e-10,1.97348829421966233940e-09] 
dist 200=[-2.41511306772946331100e-10,1.85782612250780826160e-09] 
dist 201=[-6.31348672845609147830e-10,3.56261143125833550110e-10] 
dist 202=[-1.11049118584354327310e-09,2.55265057961335820950e-10] 
dist 203=[-1.42647611894266215530e-09,3.19370968612156668130e-10] 
dist 204=[-1.50853188435885098890e-09,3.35963098735154794500e-10] 
dist 205=[-4.90915652990101564610e-10,3.38737931082893431600e-10] 
dist 206=[-4.72383373995484538240e-10,3.49558050086361726780e-10] 
dist 207=[-3.53745685092078244810e-10,3.66858250986446848010e-10] 
dist 208=[-3.32082354350459771690e-10,4.07632702949982081260e-10] 
dist 209=[-5.40498994772154024110e-10,4.92773739282568657250e-10] 
dist 210=[-6.94205718974219987460e-10,5.45849682656819221610e-10] 
dist 211=[-7.90441362604640327030e-10,5.81585557067239695850e-10] 
dist 212=[-8.15386568530615062650e-10,5.96965909636237027390e-10] 
dist 213=[-7.89883086113860433660e-10,2.78143340599193239540e-10] 
dist 214=[-7.56841292931871662920e-10,2.86423494471128189060e-10] 
dist 215=[-5.85706897414318734640e-10,2.99503694514303848330e-10] 
dist 216=[-5.31113440758935513620e-10,3.20373788344732529350e-10] 
dist 217=[-4.10010735879748215910e-10,4.53871761638150744260e-10] 
dist 218=[-5.38713977187809616600e-10,6.55046976824352666740e-10] 
dist 219=[-6.19301513744989265030e-10,7.81006381646136287590e-10] 
dist 220=[-6.40198328657263386410e-10,8.13665251621541185960e-10] 
dist 221=[-2.57560930059270501960e-10,7.92610329065480962750e-10] 
dist 222=[-2.43429791941397192930e-10,7.55252663178918303550e-10] 
dist 223=[-2.16433878344463851540e-10,6.13937296989950920720e-10] 
dist 224=[-2.01630387390642459320e-10,5.44409833960345235870e-10] 
dist 225=[-3.91499731342093445670e-10,2.73180500295713346240e-10] 
dist 226=[-5.82994527640842356160e-10,2.59729503831708675990e-10] 
dist 227=[-7.10198360074562305630e-10,3.14230161102371174890e-10] 
dist 228=[-7.47553867606073264840e-10,3.28363427909300383870e-10] 
dist 229=[-7.24013233092187714770e-10,3.16615852134027455190e-10] 
dist 230=[-6.93890563409659869850e-10,3.04793611235655626610e-10] 
dist 231=[-5.45046149254678045440e-10,2.25927515267010200370e-10] 
dist 232=[-4.86946003266769403710e-10,2.98691544333449669980e-10] 
dist 233=[-4.74027779902802450340e-10,5.01176287473700038860e-10] 
dist 234=[-5.42971632595636406310e-10,6.27397862983141657370e-10] 
dist 235=[-5.86141850474181320590e-10,7.06427367514243034380e-10] 
dist 236=[-5.97342014014110740010e-10,7.26918766241596993960e-10] 
dist 237=[-5.81547559140851390150e-10,5.96309838200259008120e-10] 
dist 238=[-5.54471142117109341530e-10,5.69935625511780995100e-10] 
dist 239=[-4.48403419491571415330e-10,5.27812596288016952930e-10] 
dist 240=[-3.96215956658598110240e-10,4.91355546011756671870e-10] 
dist 241=[-5.35992420053486911060e-10,4.23370454926408723290e-10] 
dist 242=[-7.50969120573475523250e-10,4.00387115729253197880e-10] 
dist 243=[-8.85571377065823361810e-10,3.85996450179927360550e-10] 

8 phat 5 dirichlet min maxes function [0, 1, 0, 1, 2, 0, 2, 0, 2] 
dist 0=[322.20451297243562154   ,322.20451297243562154   ] 
dist 1=[288.70573945984330117   ,331.81652446058267019   ] 
dist 2=[247.74193982245522291   ,331.31799201853935810   ] 
dist 3=[208.61641203065207518   ,325.95187784866907996   ] 
dist 4=[166.47332184275453634   ,308.80585062905223094   ] 
dist 5=[112.87879073741524483   ,224.99151378339839135   ] 
dist 6=[62.142638164958047767  ,194.18291437095350516   ] 
dist 7=[30.889148716532852074  ,169.77924706934858253   ] 
dist 8=[4.0294575898457973267 ,107.64229297750450414   ] 
dist 9=[-38.652264663445121623  ,20.818522585439084263  ] 
dist 10=[-67.443150079930239660  ,-11.618658366461785776  ] 
dist 11=[-81.345904646599896540  ,-13.909645921158428872  ] 
dist 12=[-85.727107891299095175  ,-12.701234279058485968  ] 
dist 13=[-84.858906607799791653  ,.25044491426062644028] 
dist 14=[-72.831445011037601791  ,16.857161584785602926  ] 
dist 15=[-65.093073312448118118  ,32.395001553534566011  ] 
dist 16=[-4.1105397511484045005 ,47.299630007114635817  ] 
dist 17=[-1.5890501524307544284 ,57.747962471501500655  ] 
dist 18=[-3.0867618291061574884 ,59.554585650673834981  ] 
dist 19=[-4.9608890144305973294 ,51.911403681463595979  ] 
dist 20=[-6.4499606513399563776 ,50.740623940780054988  ] 
dist 21=[-7.3568179479543744723 ,38.977183889970245409  ] 
dist 22=[-12.055104197161884445  ,32.014091783552078124  ] 
dist 23=[-23.028368917352038974  ,28.918101046096993221  ] 
dist 24=[-28.714035557982584756  ,5.7808647854103552437 ] 
dist 25=[-31.065248175965021339  ,1.2063336112183943573 ] 
dist 26=[-30.712191840463538556  ,-.63492182514682574896] 
dist 27=[-30.546851657006401681  ,-.22667751308016194321] 
dist 28=[-23.770038559051463027  ,.16524320186570169021] 
dist 29=[-9.0950323174346629944 ,8.0404486625472003500 ] 
dist 30=[-7.1409121667362971889 ,16.838784555963245858  ] 
dist 31=[-6.8481958277398584418 ,22.392849205292814888  ] 
dist 32=[.39904073813762958129,23.837403752679113035  ] 
dist 33=[.21439965564830791996,7.4244616847655704582 ] 
dist 34=[-.20881308676276987553,7.3877514444468343949 ] 
dist 35=[-.48632768628034818717,6.0472613042161860929 ] 
dist 36=[-.66615364904117875651,5.7649807727965950287 ] 
dist 37=[-.71367416486201599292,4.5040819734493099022 ] 
dist 38=[-2.3777375249781959979 ,3.6579852570414020997 ] 
dist 39=[-3.6525590341708190959 ,3.2881645389838478684 ] 
dist 40=[-4.1684900374908285839 ,.59772045610865692649] 
dist 41=[-4.2340350533334032731 ,.13660906475426565676] 
dist 42=[-4.1314313393989266815 ,.30275294042284778411] 
dist 43=[-3.6011513475412488216 ,.41582727987678776211] 
dist 44=[-3.0326082527192162268 ,.49579669785455363903] 
dist 45=[-1.0541664829936822753 ,.83102651079230128629] 
dist 46=[-.82091113715976631159,1.7729064362642259955 ] 
dist 47=[-.77543848079687845464,2.3933546135987302743 ] 
dist 48=[-.37830114106306051833,2.5467954551011203518 ] 
dist 49=[-.43014339927817115628,.99008625581362229423] 
dist 50=[-.4883395497129212261 ,.9737733251854524386 ] 
dist 51=[-.5323500713803365175 ,.77481553221133971217] 
dist 52=[-.58894286556462723623,.73183786265751044791] 
dist 53=[-.60188224746451494986,.57725353626035676455] 
dist 54=[-.29014842497230193836,.44400983878365274952] 
dist 55=[-.44724821990882891457,.41350665334322935039] 
dist 56=[-.50506212026452503688,.04216566644835032973] 
dist 57=[-.50947009385125380609,-.01142782094416995943] 
dist 58=[-.49332469511791428702,-.00221941082939946798] 
dist 59=[-.40069755864849503361,.00429551891529315180] 
dist 60=[-.35989202328049581148,.00915199645005279873] 
dist 61=[-.1337873839299495531 ,.14836910280814162922] 
dist 62=[-.10186639864739706233,.28789100621949970391] 
dist 63=[-.09708459424608337305,.37552746673479531649] 
dist 64=[.00876494088847211857,.3982799989412499899 ] 
dist 65=[.00276801324911521267,.11902238070713476695] 
dist 66=[-.00341507499545630755,.11609603916982560492] 
dist 67=[-.00734526792322883913,.09040490637369451932] 
dist 68=[-.00983355826469846034,.08537656140226052505] 
dist 69=[-.01317686140932262169,.06717774864462902718] 
dist 70=[-.042231492643114538  ,.05366802083181263805] 
dist 71=[-.06104102366244188042,.04805929096282677844] 
dist 72=[-.06721185488828868923,.00788499049501679389] 
dist 73=[-.06638318804400689935,-4.14739778625770647390e-05] 
dist 74=[-.06421939659790262057,.00012184848710039848] 
dist 75=[-.05467183954417129659,.00100437062634637039] 
dist 76=[-.04600625538549537505,.00161640557554654491] 
dist 77=[-.01583276197327813383,.01403011475562288947] 
dist 78=[-.01198422720293214505,.02854298485182582207] 
dist 79=[-.01137351229187233377,.03770356380726082656] 
dist 80=[-6.10338155259399638740e-06,.04020058819141985297] 
dist 81=[.00034308529045113592,.01534136718296189841] 
dist 82=[-.00035809717684570850,.01492205082425580420] 
dist 83=[-.00080520770500062982,.01136598836543148374] 
dist 84=[-.00110925000609440868,.01083330146122679074] 
dist 85=[-.00125485243777970287,.00947686370019390513] 
dist 86=[-.00485492147120616034,.00728452047656420511] 
dist 87=[-.00717058736216612217,.00671097768158578708] 
dist 88=[-.00790119062993727435,.00182421446397420226] 
dist 89=[-.00781491099359025379,.00116266976337173377] 
dist 90=[-.00752103331603461747,.00022092663965946747] 
dist 91=[-.00637042736919236505,.00022710272082082999] 
dist 92=[-.00538293826305231610,.00031901001152271346] 
dist 93=[-.00201166950088907927,.00234281555611913648] 
dist 94=[-.00151525913358386664,.00445548943312262148] 
dist 95=[-.00143670065532095681,.00578045833624711289] 
dist 96=[.00011173108515875529,.00612433150472347368] 
dist 97=[3.95991176117863097790e-05,.00183334799313282499] 
dist 98=[-.00012155213735634967,.00177766021435204630] 
dist 99=[-.00022320968961854892,.00134613202696406443] 
dist 100=[-.00028742902510409728,.00127776371719134789] 
dist 101=[-.00030495232644551770,.00102745978960340098] 
dist 102=[-.00067917456400620922,.00080486344532337729] 
dist 103=[-.00095843617354155954,.00072675870248121097] 
dist 104=[-.00104106230128229729,9.33779513036675708370e-05] 
dist 105=[-.00101678215169145825,2.21883950248489719550e-05] 
dist 106=[-.00098078012023328984,9.04714145123073721480e-05] 
dist 107=[-.00079149067638903534,.00013327576335640106] 
dist 108=[-.00069561935990984537,.00016024096399195666] 
dist 109=[-.00024689701857560161,.00021215705805784571] 
dist 110=[-.00019050465723313313,.00042645791756234365] 
dist 111=[-.00017522661712762621,.00056127954338797856] 
dist 112=[-4.74040508799318618350e-05,.00059733580282310984] 
dist 113=[-4.69136880745271013850e-05,.00023345643537597627] 
dist 114=[-4.65694963215859050350e-05,.00022601482292529541] 
dist 115=[-4.64796088059232432970e-05,.00016994910855671682] 
dist 116=[-4.65411195521687232510e-05,.00016158947338377194] 
dist 117=[-4.67956920852067733250e-05,8.06462504394654597400e-05] 
dist 118=[-7.60622401175103568430e-05,-8.38039859458215844600e-06] 
dist 119=[-.00011050661032433141,-7.39107489726428451520e-06] 
dist 120=[-.00012052205828495620,-5.58994339723577818450e-06] 
dist 121=[-.00011819693653575414,-2.52479352206466246730e-06] 
dist 122=[-.00011342897549358046,5.89033052559509245470e-07] 
dist 123=[-9.00623459689075399610e-05,2.57904878253780458220e-06] 
dist 124=[-8.04774994297764325350e-05,3.87485428748043750640e-06] 
dist 125=[-1.24167889770114609700e-05,3.61695942664402048690e-05] 
dist 126=[1.04991024031297358370e-06,6.80844279072671728800e-05] 
dist 127=[3.58592135853822365200e-06,8.80849061594204624670e-05] 
dist 128=[2.45765835499567162600e-06,9.32729492883769118130e-05] 
dist 129=[5.93133853423808016340e-07,2.73060244668632278160e-05] 
dist 130=[-1.28332476460783259450e-06,2.63656263844827755800e-05] 
dist 131=[-2.45789914181769531910e-06,1.99780477151675082560e-05] 
dist 132=[-3.19508398099688137050e-06,1.87618769382495438680e-05] 
dist 133=[-3.71215700044339507630e-06,-1.00704174206852479930e-06] 
dist 134=[-1.02317829141159809470e-05,-1.00135598060681524170e-06] 
dist 135=[-1.43556018122965404910e-05,-8.71121272401519006180e-07] 
dist 136=[-1.55124149600191945390e-05,-6.43789481421444169500e-07] 
dist 137=[-1.50865875107040825610e-05,-2.63774495677857498990e-07] 
dist 138=[-1.45228664750880412380e-05,1.20485660214077313680e-07] 
dist 139=[-1.10386848631637419110e-05,3.64073449893332585250e-07] 
dist 140=[-1.02553273004413631320e-05,5.20647979442633851730e-07] 
dist 141=[-8.42881644349965237980e-07,3.35061917893613498350e-06] 
dist 142=[4.55332128362882899400e-07,6.61012560036030221570e-06] 
dist 143=[3.85624435761560686710e-07,8.65617120139499008220e-06] 
dist 144=[2.67983254625929534100e-07,9.19538743181622105800e-06] 
dist 145=[7.43669424387349570630e-08,3.45149810757599977260e-06] 
dist 146=[-1.20400877227834620130e-07,3.33364950870357986150e-06] 
dist 147=[-2.42511121063445773660e-07,2.49061407453782120850e-06] 
dist 148=[-3.19473544822379986770e-07,2.36488737720299087000e-06] 
dist 149=[-3.48695676746898419370e-07,-1.31302687707028002430e-07] 
dist 150=[-1.14620853076558597520e-06,-1.29687932009680039930e-07] 
dist 151=[-1.64994622554269193130e-06,-1.12893160327513518640e-07] 
dist 152=[-1.78986946044692057180e-06,-8.41784972537606946330e-08] 
dist 153=[-1.74754851436418328640e-06,-3.64668790340153501520e-08] 
dist 154=[-1.67476152427763454080e-06,1.16604707385269943860e-08] 
dist 155=[-1.32408541827642910930e-06,4.20810383887943535620e-08] 
dist 156=[-1.18281820082350280020e-06,6.15558549997682636190e-08] 
dist 157=[-1.78914578060697048100e-07,5.38474453812145237340e-07] 
dist 158=[1.85738714072147302350e-08,1.00705634790108497940e-06] 
dist 159=[5.43095672050473234860e-08,1.30060607952881957870e-06] 
dist 160=[3.70219150252821814910e-08,1.37675441653999993230e-06] 
dist 161=[8.82010071682001305770e-09,4.08763830993082294410e-07] 
dist 162=[-1.95839724659743350770e-08,3.94476845507429604390e-07] 
dist 163=[-3.73533398673311329320e-08,2.94030422455682023850e-07] 
dist 164=[-4.84945218582441665350e-08,2.79039797011673383070e-07] 
dist 165=[-7.50882407748655768280e-08,-5.62760114884558064730e-09] 
dist 166=[-1.73414511441646053510e-07,-1.57549412783256479620e-08] 
dist 167=[-2.35338942510149723460e-07,-1.35785155573286267870e-08] 
dist 168=[-2.52149877587095596630e-07,-9.93514512619134196100e-09] 
dist 169=[-2.44717261332291163360e-07,-3.90985486361927190200e-09] 
dist 170=[-2.35110183673870616820e-07,2.15848391468822874170e-09] 
dist 171=[-1.79827836222453279260e-07,5.97626030934001589060e-09] 
dist 172=[-1.65510583641187574370e-07,8.40167797589998306060e-09] 
dist 173=[-4.31571401894845018110e-08,7.44788190974218396470e-08] 
dist 174=[-2.67490516055710652270e-08,1.21579583635666119170e-07] 
dist 175=[-4.40646291078421962050e-09,1.51155434036935404250e-07] 
dist 176=[0                     ,1.58990557371711843310e-07] 
dist 177=[1.29962480528433094300e-09,5.10811934218094454450e-08] 
dist 178=[-1.61233514706512310690e-09,4.92690952266076637190e-08] 
dist 179=[-3.43389627880407485770e-09,3.67089261544056186330e-08] 
dist 180=[-4.57916502118936615620e-09,3.48004612684955492730e-08] 
dist 181=[-5.42657018376419033190e-09,-2.44423792444862826570e-09] 
dist 182=[-1.72174506888817228770e-08,-2.38306702663299543700e-09] 
dist 183=[-2.46390367780059183080e-08,-2.05367552502421186630e-09] 
dist 184=[-2.66461137560297001260e-08,-1.51090687228113739610e-09] 
dist 185=[-2.59621068995725881420e-08,-5.59608358812883132810e-10] 
dist 186=[-2.48521976685056294730e-08,4.72920630270865456130e-10] 
dist 187=[-1.96691530495620004810e-08,1.12029171178732703610e-09] 
dist 188=[-1.75073923372384575400e-08,1.52943058028563710360e-09] 
dist 189=[-2.99740682024855853190e-09,8.37703583754798725160e-09] 
dist 190=[-1.10947682455068818770e-10,1.53486603870044128370e-08] 
dist 191=[8.82785376179209055280e-10,1.97151301070319378190e-08] 
dist 192=[6.39452474034306359070e-10,2.08475280024033076490e-08] 
dist 193=[1.45147440557521392210e-10,5.67045439648227308790e-09] 
dist 194=[-4.26278773753805606010e-10,5.46395752066292725020e-09] 
dist 195=[-8.45501611960745958350e-10,4.08975914191291565490e-09] 
dist 196=[-1.10904590262359924790e-09,3.85445943373838786660e-09] 
dist 197=[-1.17957051634253105180e-09,-2.70925844194042784910e-10] 
dist 198=[-2.04137446554083731690e-09,-5.76393812880728046810e-10] 
dist 199=[-2.87608883975931125870e-09,-4.82124234223611295680e-10] 
dist 200=[-3.09934247116965708530e-09,-3.29934627740226970760e-10] 
dist 201=[-3.02942332554584380170e-09,4.34015440193402825220e-11] 
dist 202=[-2.88651065329908469890e-09,6.24212477942164737780e-10] 
dist 203=[-2.36846982798986091230e-09,9.86608484023931602920e-10] 
dist 204=[-2.11196421418278817740e-09,1.21385741638183721250e-09] 
dist 205=[-8.76938447620459828920e-10,1.44531546904784523510e-09] 
dist 206=[-5.96336114448019470740e-10,2.29306111931853613380e-09] 
dist 207=[-2.52066766537148989400e-10,2.82426231896899154060e-09] 
dist 208=[-1.87268833256865632990e-10,2.96268670935252409360e-09] 
dist 209=[-1.85835997828312556440e-10,9.17588459181490925920e-10] 
dist 210=[-7.22956006546925423340e-10,4.57452298667497809350e-10] 
dist 211=[-1.12296092638299571760e-09,3.83457904266939597080e-10] 
dist 212=[-1.37351797172998873520e-09,3.62366728522603583190e-10] 
dist 213=[-1.43870646167775188990e-09,3.56831117182433443870e-10] 
dist 214=[-1.39154778360267504660e-09,3.50503759907130000780e-10] 
dist 215=[-1.33575132958951307450e-09,4.05552435575013605260e-10] 
dist 216=[-1.01762565247712520100e-09,4.19088056743549549280e-10] 
dist 217=[-9.37588795360637185630e-10,4.28948487287310856180e-10] 
dist 218=[-2.81136960147240372270e-10,4.69809802689384161790e-10] 
dist 219=[-3.39884966925666919840e-10,6.70342698830947724480e-10] 
dist 220=[-4.33727134259664646850e-10,8.40309671413417830240e-10] 
dist 221=[-8.36098332733171973920e-10,8.96274904250379802420e-10] 
dist 222=[-1.08683520514345016020e-09,8.77023501275466527870e-10] 
dist 223=[-1.24373044721512190650e-09,8.54858568124967988110e-10] 
dist 224=[-1.28421270038845978460e-09,8.65586362163929293670e-10] 
dist 225=[-1.24036858532840762360e-09,7.21400990841772937590e-10] 
dist 226=[-1.19173313350200366390e-09,5.82091797220895881970e-10] 
dist 227=[-1.09667954863823304140e-09,5.21966345926999096460e-10] 
dist 228=[-1.30334014686166881920e-09,4.84319238225058049910e-10] 
dist 229=[-1.35694812189901349480e-09,4.74557238062176598560e-10] 
dist 230=[-1.30875727068904022790e-09,5.09793685505490037870e-10] 
dist 231=[-1.25956971261559636500e-09,6.97004830827879548730e-10] 
dist 232=[-9.35932016129090796140e-10,7.45483356748083508150e-10] 
dist 233=[-8.83936081737665855380e-10,7.38251173430511821320e-10] 
dist 234=[-1.28678799861363136010e-10,7.10616429506411027700e-10] 
dist 235=[-6.34775738463716470500e-11,6.66525262142379177380e-10] 
dist 236=[-2.23252517130891903880e-10,6.49787813125831925540e-10] 
dist 237=[-6.81230999934912561220e-10,6.98989951586275788570e-10] 
dist 238=[-9.66711508960451362520e-10,6.85750693917466088850e-10] 
dist 239=[-1.14544821586650230460e-09,6.48822438995876829130e-10] 
dist 240=[-1.19177552157245543570e-09,5.59906566106894444970e-10] 
dist 241=[-1.15270346202025130150e-09,5.95904528462433657950e-10] 
dist 242=[-1.10619538993070898050e-09,6.69535698276089467230e-10] 
dist 243=[-8.44055785311796904650e-10,7.15432244693758984770e-10] 
dist 244=[-8.21987648998616830360e-10,7.44165913004231985810e-10] 

8 phat 5 dirichlet min maxes function [2, 0, 0, 1, 1, 1, 0, 0, 2] 
dist 0=[344.38735158957959998   ,344.38735158957959998   ] 
dist 1=[302.91593188010099634   ,356.71607316380052849   ] 
dist 2=[251.11742574511295205   ,362.52490009852640770   ] 
dist 3=[205.62174388112678660   ,364.08770370941819879   ] 
dist 4=[160.10515799288934996   ,355.34439022471756999   ] 
dist 5=[107.16640015744268119   ,268.79731785176703780   ] 
dist 6=[58.198202848911666373  ,248.14191726821746291   ] 
dist 7=[27.830461761621591133  ,175.13459963876585007   ] 
dist 8=[-17.623062655965357632  ,164.41653663239370069   ] 
dist 9=[-40.722381241715296369  ,12.051165653397069519  ] 
dist 10=[-51.443406309076636906  ,6.9900859962273906435 ] 
dist 11=[-69.225662550056480752  ,5.5612359042254157777 ] 
dist 12=[-79.357047860086340072  ,3.8531024007808419261 ] 
dist 13=[-79.972228623843973446  ,2.6249104204799778274 ] 
dist 14=[-77.433320537952031671  ,6.7360442866632677769 ] 
dist 15=[-62.499681205386291675  ,18.005560999457146564  ] 
dist 16=[-56.481643828771532753  ,26.253213266918105407  ] 
dist 17=[-11.451127241549475804  ,28.145059157140334653  ] 
dist 18=[-1.8690647823685153474 ,39.941540144003883612  ] 
dist 19=[3.8937896645295390730 ,52.960929834893146722  ] 
dist 20=[3.1110188415518085259 ,56.338019259240362170  ] 
dist 21=[-4.6654166967210695833 ,17.416283168642612669  ] 
dist 22=[-10.500966647118184114  ,17.014754618698293272  ] 
dist 23=[-14.022183702809318557  ,13.299310584837069882  ] 
dist 24=[-15.878427807915749672  ,12.589314848446171921  ] 
dist 25=[-15.885062688995869886  ,6.0027093115872061277 ] 
dist 26=[-13.987849840624860388  ,3.1469459368618537384 ] 
dist 27=[-12.712118812781792201  ,2.5744684844808619274 ] 
dist 28=[-9.1316979625968271539 ,4.6786887880861032618 ] 
dist 29=[-9.0466069387466386776 ,9.1098206852916062315 ] 
dist 30=[-8.7602294034346822706 ,11.901383513326316654  ] 
dist 31=[-6.7480075088112290809 ,12.595345993956560664  ] 
dist 32=[-6.2925202832804387484 ,3.5235622765930903621 ] 
dist 33=[-.71196795694418906503,3.5672876699211830265 ] 
dist 34=[.18325138944980447362,3.7743144369099884924 ] 
dist 35=[.39637991404250177412,5.0168212239328592490 ] 
dist 36=[-.00719066719578789232,5.3560966211199329459 ] 
dist 37=[-.92764085907415088392,2.1190506835162061381 ] 
dist 38=[-1.5703509993844717140 ,2.0563482503764303206 ] 
dist 39=[-1.8758958666042520182 ,1.5958290986872909430 ] 
dist 40=[-1.9719492063737553874 ,1.4916884603041859660 ] 
dist 41=[-1.9399521952624801638 ,.3332494842611442446 ] 
dist 42=[-1.5911248087537677884 ,.01497577228145325774] 
dist 43=[-1.4700713800488390037 ,-.04586562074013685855] 
dist 44=[-1.2370880111511192353 ,.42660789939331726443] 
dist 45=[-1.2017641807282491075 ,.92258052268926136188] 
dist 46=[-1.1564632665725162728 ,1.2359756729155739144 ] 
dist 47=[-.86753476399290095188,1.3188177738671490992 ] 
dist 48=[-.80854891763707832815,.69298307809690987855] 
dist 49=[-.11611719838355727002,.69899231521836223572] 
dist 50=[.00070515162763178471,.68765269345450690646] 
dist 51=[.03206277534528602213,.75223052437962556081] 
dist 52=[-.11856897820745874711,.79722514044446190068] 
dist 53=[-.25905881584920285446,.34137113837541306831] 
dist 54=[-.35126847184087605788,.3248613196194832628 ] 
dist 55=[-.38384626496486612239,.27934418211098097756] 
dist 56=[-.38308489595504570941,.25583559567834661854] 
dist 57=[-.36817475094956572005,.13043248842284080524] 
dist 58=[-.3011699210721702871 ,.09543966875998122486] 
dist 59=[-.26617481630014705013,.05490364680992906313] 
dist 60=[-.13225647755994892499,.04482847276922081818] 
dist 61=[-.12930007359713866679,.05472940329446279104] 
dist 62=[-.1246798449992712711 ,.07875969501819745883] 
dist 63=[-.09514452657991396788,.08848564339837285415] 
dist 64=[-.08848170811536480240,.08924128332407421670] 
dist 65=[-.00793223088762936635,.08722295821161242679] 
dist 66=[.00220893174010636953,.06728001711751859751] 
dist 67=[.00379165924176910351,.07360769213096572368] 
dist 68=[-.00612516014813624799,.07830170387807014086] 
dist 69=[-.02727938249771248528,.02959517662407943171] 
dist 70=[-.04104615059138697167,.02865101239028992819] 
dist 71=[-.04571792773119085934,.02155077081307764993] 
dist 72=[-.04561616339915898228,.02048830604655797931] 
dist 73=[-.04401918609451037483,.00391313542702905970] 
dist 74=[-.03544871215366377555,.00033031786434885650] 
dist 75=[-.03177803473813065603,-.00036297331511325693] 
dist 76=[-.01520102956315640856,.01353648899646392190] 
dist 77=[-.01490383262912522617,.02595990549775371400] 
dist 78=[-.01430318978122213422,.03375651399342729050] 
dist 79=[-.01134533969900813238,.03578002703081907746] 
dist 80=[-.01014692708241478617,.01061206882580908438] 
dist 81=[-.00154884459444257564,.01031221226004226942] 
dist 82=[.00014385398615263525,.00851790227217871077] 
dist 83=[.00033035763194045933,.01102765802462391977] 
dist 84=[-.00127316030175369203,.01167874761246664285] 
dist 85=[-.00384220080270184603,.00347828885104380311] 
dist 86=[-.00549149912644403943,.00336155376562133767] 
dist 87=[-.00600458712266897061,.00252195652694454280] 
dist 88=[-.00589705391428851935,.00239060455455465765] 
dist 89=[-.00569457681023501967,.00048341540848927760] 
dist 90=[-.00436188272444120869,1.06973379047306917080e-05] 
dist 91=[-.00405834898430101220,-5.75636142560135566750e-05] 
dist 92=[-.00197045524459673974,.00126878580206341776] 
dist 93=[-.00191466660808811790,.00255230123699723127] 
dist 94=[-.00184381966101005961,.00336087303018958435] 
dist 95=[-.00139441212411341967,.00357871328655053545] 
dist 96=[-.00130146725612226042,.00136436430349404274] 
dist 97=[-.00010388536552651780,.00132327038218114865] 
dist 98=[2.43093362083001438420e-05,.00100400365590227807] 
dist 99=[4.43730006901549672690e-05,.00105958093913858078] 
dist 100=[-.00013434102472796875,.00112610656526894978] 
dist 101=[-.00045530505779992825,.00045903881269226760] 
dist 102=[-.00066036831067032580,.00044165163930209731] 
dist 103=[-.00072220383813075413,.00033963476899437278] 
dist 104=[-.00070956378868524522,.00031265954122225300] 
dist 105=[-.00068279182097533901,5.18462254360375414970e-05] 
dist 106=[-.00053594714434680559,5.63835576119253984650e-06] 
dist 107=[-.00048607590412183659,-3.39979089489491259190e-06] 
dist 108=[-.00029886603277927125,.00020948442538763033] 
dist 109=[-.00029007291767205135,.00039545866988702793] 
dist 110=[-.00027774089962218174,.00051205089339967710] 
dist 111=[-.00021631951006071597,.00054231114728599349] 
dist 112=[-.00019456112005889830,.00021430520546971717] 
dist 113=[-2.22689927338732635760e-05,.00020316116568276464] 
dist 114=[1.87397706617472576700e-06,.00018396195925625328] 
dist 115=[4.06508156871495550530e-06,.00017173539888728858] 
dist 116=[-3.28451148232547712810e-05,.00017401023244934433] 
dist 117=[-7.61819002674408899310e-05,9.03157055263391425860e-05] 
dist 118=[-.00010361237048520325,8.55040177198126944950e-05] 
dist 119=[-.00011133669672559370,7.40807175438109891460e-05] 
dist 120=[-.00010887318392114152,6.83936044743925434290e-05] 
dist 121=[-.00010419233032249507,3.91081856237684841630e-05] 
dist 122=[-8.32864859065623412100e-05,3.02056732840033028570e-05] 
dist 123=[-7.28566908430171988960e-05,2.16579584249666729160e-05] 
dist 124=[-2.88365039338450477850e-05,2.90996485847918293890e-05] 
dist 125=[-2.79625517412358571070e-05,4.78537746647809476550e-05] 
dist 126=[-2.68921535271212850830e-05,5.96731519019637331950e-05] 
dist 127=[-2.03911812485657539000e-05,6.28881661125532472030e-05] 
dist 128=[-1.89366085944366444650e-05,-1.32081185454263450050e-06] 
dist 129=[-1.48293334830484427810e-06,6.25968875888982969700e-06] 
dist 130=[2.89976223448241579350e-07,1.22860159784759741910e-05] 
dist 131=[5.58451456807094707100e-07,1.60644014972171078760e-05] 
dist 132=[1.08020172416400683790e-06,1.70529027923147434660e-05] 
dist 133=[1.13934389593151576280e-06,6.37975423738486036280e-06] 
dist 134=[1.07089136480498268490e-06,6.15292256133566692000e-06] 
dist 135=[8.77333169708452777470e-07,4.57923501933402074490e-06] 
dist 136=[5.80673340639090194610e-07,4.34388983182231692470e-06] 
dist 137=[-6.63505001633945269370e-07,7.14079142765473952210e-07] 
dist 138=[-2.13202050333406078760e-06,8.85383448046705171840e-08] 
dist 139=[-3.05588355865673222410e-06,-3.35631678741896772940e-08] 
dist 140=[-3.30483381702886337710e-06,-2.32271553898264404710e-07] 
dist 141=[-3.21784644889453390560e-06,-2.58922824767225430290e-07] 
dist 142=[-3.08110276838773166350e-06,-2.43365301209452058210e-07] 
dist 143=[-2.42997622893560973200e-06,-2.02507349553961047480e-07] 
dist 144=[-2.16985039790526934450e-06,-1.40679532686459637100e-07] 
dist 145=[-3.15903997571384650590e-07,9.91687424679116955370e-07] 
dist 146=[1.11451032049925571600e-08,1.85446127877722760090e-06] 
dist 147=[4.01273576203757364390e-08,2.39481747821220683580e-06] 
dist 148=[9.28264846520874961070e-08,2.53495721172233851680e-06] 
dist 149=[9.90601765294407496720e-08,7.49495090119441416470e-07] 
dist 150=[9.23497894465564224270e-08,7.22425947612222189840e-07] 
dist 151=[7.33322609881959123480e-08,5.37622150540746741260e-07] 
dist 152=[4.41816205540981179330e-08,5.09220447657917721560e-07] 
dist 153=[-1.09072717585018359000e-07,9.82103829552584127760e-08] 
dist 154=[-2.85572677895683058540e-07,2.32535118783113158540e-08] 
dist 155=[-3.96442064094179205430e-07,1.33021318276283469110e-08] 
dist 156=[-4.25954762038725951280e-07,1.16353576619216346560e-09] 
dist 157=[-4.12221687857408115200e-07,0                     ] 
dist 158=[-3.96451075265539979980e-07,-3.09618925238254772860e-08] 
dist 159=[-2.98839128853207622900e-07,-2.61734562100149029820e-08] 
dist 160=[-2.78761021209329570870e-07,-1.88603954016206019410e-08] 
dist 161=[-2.03627465552832117990e-08,8.84978028734923413680e-08] 
dist 162=[3.67988869730551415030e-09,1.74818723689820378770e-07] 
dist 163=[7.46528658980869194300e-09,2.28914567348527438310e-07] 
dist 164=[1.49261410877578885580e-08,2.43025740118798487820e-07] 
dist 165=[1.58776041435388646570e-08,9.50229222752655939840e-08] 
dist 166=[1.50537123326250250640e-08,9.15636364115583746690e-08] 
dist 167=[1.24875566716796535050e-08,6.81099527790874323620e-08] 
dist 168=[8.49720544753335219430e-09,6.44840732775178983770e-08] 
dist 169=[-1.05545006534632810780e-08,1.03312590377154442640e-08] 
dist 170=[-3.24891353755191833710e-08,5.96743013448543198610e-10] 
dist 171=[-4.62617768866188110840e-08,-1.15387452543501896840e-09] 
dist 172=[-4.99159995254460303850e-08,-4.19315696763009739200e-09] 
dist 173=[-4.85225566113989382870e-08,-4.62500196390110113550e-09] 
dist 174=[-4.64521044445023463970e-08,-4.40547773320502808670e-09] 
dist 175=[-3.65047741520642762620e-08,-3.72397592880682427490e-09] 
dist 176=[-3.26659485430139395010e-08,-2.66508437693518857160e-09] 
dist 177=[-4.91127935062037170520e-09,1.49379128839738000260e-08] 
dist 178=[-2.07536328143736412490e-10,2.76741298146204390820e-08] 
dist 179=[3.51223074338248148750e-10,3.56499180655229856070e-08] 
dist 180=[1.31795238683467515660e-09,3.77182282624831128280e-08] 
dist 181=[1.45630098362017455880e-09,1.19810804583292333520e-08] 
dist 182=[1.33168473931683551740e-09,1.15373896276170381500e-08] 
dist 183=[9.00827880449722233920e-10,8.60276777257488233870e-09] 
dist 184=[2.21453328453153482720e-10,8.11673268956872415980e-09] 
dist 185=[-1.51401927388155457410e-09,2.32561047457129277760e-09] 
dist 186=[-4.28064892544940758210e-09,1.79112603138173650090e-09] 
dist 187=[-6.01640862430365860230e-09,1.74090133336108922260e-09] 
dist 188=[-6.47398621046066854350e-09,1.70975826714555675360e-09] 
dist 189=[-6.28186543185493759080e-09,1.70190311459813934620e-09] 
dist 190=[-6.02007811353423113980e-09,1.34445465810428189060e-09] 
dist 191=[-4.67682177802759625300e-09,1.60290067647361842290e-09] 
dist 192=[-4.23097135510831472770e-09,2.01425807607548556820e-09] 
dist 193=[-6.34644003379362699360e-10,2.67300484824441501710e-09] 
dist 194=[-1.75287479999101045480e-10,3.36493525828137246640e-09] 
dist 195=[-1.39217632178775729820e-10,4.32114584336194056210e-09] 
dist 196=[-1.10899356830446372640e-10,4.56843443607621956900e-09] 
dist 197=[-1.05915134761905672620e-10,2.05541590270992736230e-09] 
dist 198=[-1.10691928002079188000e-10,1.96667391192400590790e-09] 
dist 199=[-1.23963984112799560950e-10,1.73560504989791102440e-09] 
dist 200=[-5.79829655850993684230e-10,1.61527739996225390910e-09] 
dist 201=[-1.77106974361329884960e-09,1.37074364676031715830e-09] 
dist 202=[-2.51398763946885182550e-09,1.25658380456557160080e-09] 
dist 203=[-2.97949240691257106630e-09,1.18475916536299073970e-09] 
dist 204=[-3.10093753396822818230e-09,1.16539599344198736870e-09] 
dist 205=[-3.03065198453670324170e-09,1.13359474559885856150e-09] 
dist 206=[-2.87940054504791732110e-09,1.08067658951833699150e-09] 
dist 207=[-2.40231307547147898480e-09,8.72483909157152318320e-10] 
dist 208=[-2.16740870620763931340e-09,7.70226326456669200760e-10] 
dist 209=[-9.13047248237304460600e-10,1.56088918945900376720e-09] 
dist 210=[-7.80521968789563508290e-10,2.49429543694186779490e-09] 
dist 211=[-9.83358265245964284210e-10,3.07881984849894377400e-09] 
dist 212=[-1.03575185298160894310e-09,3.23059071182061352130e-09] 
dist 213=[-1.01703197030476114210e-09,3.13416840760524183600e-09] 
dist 214=[-9.61105328358571520430e-10,2.99897833202568279080e-09] 
dist 215=[-8.36895397336452906160e-10,2.35028086788579065380e-09] 
dist 216=[-7.75833014814013413750e-10,2.10475086719091247110e-09] 
dist 217=[-9.31954024067063785620e-10,6.83600626509257837570e-10] 
dist 218=[-1.76511340733557587060e-09,1.02756105919521196530e-09] 
dist 219=[-2.28680423913470619250e-09,1.24289480684893511470e-09] 
dist 220=[-2.42214406672026523710e-09,1.29867260649512473660e-09] 
dist 221=[-2.36301682799278222000e-09,1.27382832147915329250e-09] 
dist 222=[-2.24836197146963500830e-09,1.20536529950447020440e-09] 
dist 223=[-1.85100709566999325780e-09,1.03901606276667844060e-09] 
dist 224=[-1.65549124594062963470e-09,9.57184928349725076480e-10] 
dist 225=[-1.36328626211274402960e-09,1.53241758629051501710e-09] 
dist 226=[-1.47426655182368600690e-09,2.00094181635358411310e-09] 
dist 227=[-1.54375150439110426800e-09,2.29429747835915205110e-09] 

8 phat 5 dirichlet min maxes function [1, 1, 0, 1, 1, 0, 0, 0, 1] 
dist 0=[387.43408933983796630   ,387.43408933983796630   ] 
dist 1=[366.73070464787947417   ,388.88949194885314331   ] 
dist 2=[322.33921051500681090   ,387.43408933983796630   ] 
dist 3=[241.30331539637571201   ,352.76899540767321218   ] 
dist 4=[155.00602002048955866   ,331.70488658414287774   ] 
dist 5=[89.806345931275337315  ,259.01236129897436769   ] 
dist 6=[33.685455345146265168  ,174.35387352621425650   ] 
dist 7=[-18.320857684454749106  ,119.51386046161794159   ] 
dist 8=[-59.134763324274910033  ,108.11724467846182429   ] 
dist 9=[-84.313175901902066002  ,-1.6015437776960103171 ] 
dist 10=[-102.42959795858308822   ,-28.536314066514848267  ] 
dist 11=[-105.19627668068175453   ,-32.462383774996162260  ] 
dist 12=[-91.486741367751843928  ,-15.672200439511661154  ] 
dist 13=[-88.550482752196231009  ,6.4484465174082517231 ] 
dist 14=[-9.9400014683145463743 ,25.547335214407272494  ] 
dist 15=[3.1751086768898487987 ,43.098787307997168618  ] 
dist 16=[30.753756756059440107  ,59.797026733796314231  ] 
dist 17=[35.362501777727473552  ,71.384900845187401888  ] 
dist 18=[27.046087889250520743  ,73.031818942503545158  ] 
dist 19=[9.5367270787565846971 ,63.837053789975189811  ] 
dist 20=[-8.7494937559698851909 ,61.368193727742499524  ] 
dist 21=[-20.458264467091734982  ,41.517029060352887112  ] 
dist 22=[-27.904050091189038646  ,15.447822893558847421  ] 
dist 23=[-33.989126624489238374  ,10.169893277177181725  ] 
dist 24=[-41.493081305460672634  ,.60078138395739015879] 
dist 25=[-43.811848708625627542  ,-1.7752258981727584302 ] 
dist 26=[-42.360449945573047062  ,-3.8723891901007737192 ] 
dist 27=[-35.991866157336247675  ,-1.1997473876165562642 ] 
dist 28=[-32.145525084682121629  ,4.2655722128247668150 ] 
dist 29=[-14.415233497089974906  ,15.524455096583081893  ] 
dist 30=[-3.8528433557443955943 ,26.517591457162920723  ] 
dist 31=[1.5795819619005753647 ,33.995205470934339966  ] 
dist 32=[3.9859848468636986934 ,35.707612530069573919  ] 
dist 33=[3.5028957013512078377 ,7.5911151987375046591 ] 
dist 34=[2.4145293183221590623 ,7.5638968214761396549 ] 
dist 35=[.4230911017671647742 ,6.1361867195851894956 ] 
dist 36=[-1.6282847279624112275 ,5.9089290207213363277 ] 
dist 37=[-2.9497424010359854833 ,4.0379827480428743406 ] 
dist 38=[-3.9108496284561640731 ,.79380929866511064004] 
dist 39=[-4.1321257011961649720 ,.16306196378259993399] 
dist 40=[-4.0642852184567836495 ,-1.0203315204672475751 ] 
dist 41=[-4.3157624710220580733 ,-1.0927457044053352094 ] 
dist 42=[-3.9149423493499814263 ,-.7976398389992316107 ] 
dist 43=[-3.2378998028553279095 ,-.26030096912126871581] 
dist 44=[-2.9103998273951475871 ,.29444536944562125883] 
dist 45=[-.96113532507693195744,1.1934225331421841144 ] 
dist 46=[-.2415745988101870566 ,2.2937671864865603846 ] 
dist 47=[.17970189258331589685,2.9898934348835180232 ] 
dist 48=[.28614692112712309462,3.1698553437162828193 ] 
dist 49=[.19022140125798064708,.97993145523950838523] 
dist 50=[.00237623753620820748,.8804202152403792012 ] 
dist 51=[-.32622827372206809728,.76763534039296805452] 
dist 52=[-.66219903280480367992,.71148607127740141868] 
dist 53=[-.8786836037880009781 ,.5100678795564902437 ] 
dist 54=[-1.0375990553785317757 ,.08950248781253640266] 
dist 55=[-1.0731180445238304409 ,.05454063199520076077] 
dist 56=[-.48123563568584114597,.05258907605345232468] 
dist 57=[-.48533199549553451221,.07919983487020278157] 
dist 58=[-.46945193324927765649,.12773677213791218509] 
dist 59=[-.38300595995905247394,.21029731484319808166] 
dist 60=[-.34181942771884124291,.29402452340030805589] 
dist 61=[-.12098125932700689398,.34709542322092874395] 
dist 62=[-.01538022846127814881,.38109090851198022573] 
dist 63=[.03295709016250035471,.39138088053033727551] 
dist 64=[.07546961734220663608,.38577629283096522821] 
dist 65=[.08188969548225429857,.09995960863478418357] 
dist 66=[.08470241764671994622,.09764615053621659442] 
dist 67=[.06660181685955670740,.08300387144994366955] 
dist 68=[.03008092455640709395,.07186321045871634978] 
dist 69=[-.00699577027113553047,.05974888978916828377] 
dist 70=[-.03066031147938115164,.00997594719768391975] 
dist 71=[-.04879954380287226226,.00014251918317995095] 
dist 72=[-.06343281873909812563,-.01695459654976867047] 
dist 73=[-.06723149577288386246,-.02017089249717390344] 
dist 74=[-.04925258333676859680,-.01996851626025068920] 
dist 75=[-.03963218408258631198,-.01730973148409769801] 
dist 76=[-.03552208507023093050,-.00703129047976895385] 
dist 77=[-.01421599110672041917,.01517580228112097950] 
dist 78=[-.00020194956102133238,.02907285236752719583] 
dist 79=[.00321069381037809698,.03779357092278793785] 
dist 80=[.00817247602555617482,.04005686368622878324] 
dist 81=[.00895529259776543792,.01186996450194342500] 
dist 82=[.00888442816279065797,.01153046687605156364] 
dist 83=[.00751425952988631197,.01083794920130299069] 
dist 84=[.00309244530327928351,.00836876605670779873] 
dist 85=[-.00144618259255925571,.00770811263297365620] 
dist 86=[-.00431925642252415696,.00066470480815489634] 
dist 87=[-.00616221298744030603,-.00037711789367409245] 
dist 88=[-.00673244853141263786,-.00225696687060182462] 
dist 89=[-.00660834539533428258,-.00259841294762932986] 
dist 90=[-.00638000087713631849,-.00255549925542258450] 
dist 91=[-.00488650967802951241,-.00221262549784142834] 
dist 92=[-.00454436405091453667,-.00084907553743736290] 
dist 93=[-.00179590217545861716,.00144060216682882406] 
dist 94=[.00017393183404067767,.00287534254068282400] 
dist 95=[.00048926555033065737,.00377905451764864285] 
dist 96=[.00113208300000696401,.00402235589690029881] 
dist 97=[.00123217630086775287,.00151632161730516425] 
dist 98=[.00120774008989523639,.00147084627232793617] 
dist 99=[.00092710271823199545,.00130930030418253792] 
dist 100=[.00035590140059192392,.00105837566594034257] 
dist 101=[-.00021971930603625936,.00093068750851584023] 
dist 102=[-.00058297293811285991,.00025723339679409995] 
dist 103=[-.00084938818144993918,.00012251140749279044] 
dist 104=[-.00107319158380575696,-8.50482358013522883990e-05] 
dist 105=[-.00113199742853413385,-.00012618538937761292] 
dist 106=[-.00083488310737600779,-.00011190483502607097] 
dist 107=[-.00067870002798792230,-3.19126643421190407290e-05] 
dist 108=[-.00059951258392678055,.00010024732709548852] 
dist 109=[-.00025873298991857127,.00039332400070612941] 
dist 110=[-6.36832024537938874230e-05,.00060630308872646583] 
dist 111=[1.30566636386138560450e-05,.00074033020699531174] 
dist 112=[6.86812508267038156040e-05,.00077628079934384404] 
dist 113=[7.93207585547486206580e-05,.00018827075384930545] 
dist 114=[7.49371910198402700820e-05,.00018540625527185647] 
dist 115=[3.68559226918728089180e-05,.00017659020925386737] 
dist 116=[-3.70745355882123104170e-05,.00014806482086605314] 
dist 117=[-.00011135945773879935,.00013371232446442195] 
dist 118=[-.00015798547010715068,5.63205317858840504960e-05] 
dist 119=[-.00018748915921675197,3.69020346679388098770e-05] 
dist 120=[-.00019577720636536198,1.18755898578985293540e-05] 
dist 121=[-.00019160867975070639,7.02850207008027147590e-06] 
dist 122=[-.00010061047183685535,8.05637137029673727680e-06] 
dist 123=[-7.72772979459051480600e-05,1.34805893108979550770e-05] 
dist 124=[-7.11433668599393274180e-05,2.24028828166030487300e-05] 
dist 125=[-2.62496374631547842960e-05,3.69200576122687250610e-05] 
dist 126=[3.36472082057159639090e-06,5.14930161520731413840e-05] 
dist 127=[8.42842043973087368320e-06,6.44292209973461387350e-05] 
dist 128=[1.79975326031400326070e-05,6.80258778752977803370e-05] 
dist 129=[1.94360709717632837580e-05,2.23114826722718768640e-05] 
dist 130=[1.90147540421945868250e-05,2.15720993911146349070e-05] 
dist 131=[1.42476242678615383510e-05,1.85238784073831185610e-05] 
dist 132=[6.05840950431499406670e-06,1.53563900799347955470e-05] 
dist 133=[-2.16714107991275021350e-06,1.30996616644597865070e-05] 
dist 134=[-7.33131800829710233730e-06,1.95898430155606282160e-06] 
dist 135=[-1.11049338020943676290e-05,-2.34690800717872451440e-07] 
dist 136=[-1.43577525915750452540e-05,-3.95899563297132766570e-06] 
dist 137=[-1.52015206662241642630e-05,-4.58590646253358806550e-06] 
dist 138=[-1.08163840588390968850e-05,-4.45269200399939897590e-06] 
dist 139=[-8.57069881437612108060e-06,-3.81061432084289779000e-06] 
dist 140=[-7.65487440846463587050e-06,-1.40683150763880000220e-06] 
dist 141=[-3.08443433946406746990e-06,3.46731166421411203090e-06] 
dist 142=[1.21187026714373414010e-07,6.50931710889809206300e-06] 
dist 143=[7.97387473578270067060e-07,8.41529645730614513230e-06] 
dist 144=[1.87247086012512479270e-06,8.90966053457984814400e-06] 
dist 145=[2.04517967308147867350e-06,2.60221020354838175850e-06] 
dist 146=[1.97396944483809894000e-06,2.51021644656552758190e-06] 
dist 147=[1.61611879573540481260e-06,2.39628153659107261370e-06] 
dist 148=[6.29647674006322300820e-07,1.81002699261872522220e-06] 
dist 149=[-3.60191781287447031030e-07,1.68878611922118612740e-06] 
dist 150=[-9.80277036507830825490e-07,1.21389913667993016530e-07] 
dist 151=[-1.37160058154935676030e-06,-1.09281736042818166290e-07] 
dist 152=[-1.47952009312321093720e-06,-5.17759574797327522990e-07] 
dist 153=[-1.46813518415596517040e-06,-5.85127760979298643100e-07] 
dist 154=[-1.38245233541690637080e-06,-5.67842226149369827700e-07] 
dist 155=[-1.04975371931124511880e-06,-4.88509311351925874680e-07] 
dist 156=[-9.74850782684668601100e-07,-1.74946891076452234190e-07] 
dist 157=[-3.87602293256999557800e-07,3.21743353550310021510e-07] 
dist 158=[5.65522758764136111450e-08,6.31891003600511591370e-07] 
dist 159=[1.27640197332912163270e-07,8.26465852777136585570e-07] 
dist 160=[2.69889139483532023480e-07,8.77562215474850135100e-07] 
dist 161=[2.91184535223384556110e-07,3.26995250041036314850e-07] 
dist 162=[2.80814644268337020980e-07,3.15606988588053830370e-07] 
dist 163=[2.06799523235463028690e-07,2.74923532573320188070e-07] 
dist 164=[8.69298744902893039200e-08,2.23365856588645625600e-07] 
dist 165=[-3.33755835766921286620e-08,1.93809738705729513270e-07] 
dist 166=[-1.08788531951387318120e-07,2.97222534865949884650e-08] 
dist 167=[-1.66842823483516573570e-07,-2.74024016072400948340e-09] 
dist 168=[-2.15205699707632956650e-07,-5.73231864840659749990e-08] 
dist 169=[-2.27748301007629000960e-07,-6.63307482530721689300e-08] 
dist 170=[-1.58184686648211941410e-07,-6.41996170568724051700e-08] 
dist 171=[-1.25177075481043220690e-07,-5.48534224431061381720e-08] 
dist 172=[-1.11566920528974760810e-07,-1.95241772917824788430e-08] 
dist 173=[-4.45337937058501463770e-08,5.19621556257964575760e-08] 
dist 174=[1.18643071665264879590e-09,9.65561607312141322040e-08] 
dist 175=[1.19773556099134114250e-08,1.24489130431425240450e-07] 
dist 176=[2.74692993403857049340e-08,1.31733980314834071420e-07] 
dist 177=[2.99000253598409469800e-08,3.76853701057292161490e-08] 
dist 178=[2.87580199819796819160e-08,3.63467936877945658730e-08] 
dist 179=[2.25971180445069854850e-08,3.45495443039183918520e-08] 
dist 180=[8.60388721499974470460e-09,2.63098668453787038140e-08] 
dist 181=[-5.41675121226749607850e-09,2.43102076628707924620e-08] 
dist 182=[-1.42317280423119394010e-08,2.45178650083997748500e-09] 
dist 183=[-1.98494881841390348840e-08,-9.14910923363097547270e-10] 
dist 184=[-2.14615347720716071250e-08,-6.64218605625456267140e-09] 
dist 185=[-2.27550106530515031800e-08,-7.57783866660066241030e-09] 
dist 186=[-1.99081410128483367020e-08,-7.33417396199540237940e-09] 
dist 187=[-1.51854227251644062150e-08,-6.28292158271382886410e-09] 
dist 188=[-1.40111478140381145510e-08,-2.16876403803131524980e-09] 
dist 189=[-5.63467146566866628360e-09,5.07749096859634699390e-09] 
dist 190=[4.41372077611950119710e-10,9.63361065772433370100e-09] 
dist 191=[1.48770531353114929140e-09,1.24899365865320716850e-08] 
dist 192=[3.30670987261320560330e-09,1.32368376739081361620e-08] 
dist 193=[3.58931743718817515960e-09,4.30953328944549542210e-09] 
dist 194=[3.42449538124445277800e-09,4.18539196881681160540e-09] 
dist 195=[2.51615838884081897970e-09,4.01393850878754487870e-09] 
dist 196=[9.57613684843053668630e-10,3.12425467361532362020e-09] 
dist 197=[-6.13833678365428528250e-10,2.82459899584823308800e-09] 
dist 198=[-1.80533692526976478710e-09,1.06751174808154415080e-09] 
dist 199=[-2.88987280373105857210e-09,7.01006906587295743170e-10] 
dist 200=[-3.56909065819584730040e-09,2.35905908885513696390e-10] 
dist 201=[-3.74524636907256967800e-09,1.50039049515327229370e-10] 
dist 202=[-2.24807922008046844110e-09,1.51560631829281123040e-10] 
dist 203=[-1.70148424558154503520e-09,1.67531953752109443500e-10] 
dist 204=[-1.58262869710003603770e-09,1.94838658627996558580e-10] 
dist 205=[-8.72135449078993207740e-10,5.99954391635554609480e-10] 
dist 206=[-3.22041240651128725410e-10,1.09738919449328637470e-09] 
dist 207=[-4.14860736484753146750e-10,1.40894699267794317450e-09] 
dist 208=[-4.72604173323865758400e-10,1.48974622180678039510e-09] 
dist 209=[-4.86795098120236390050e-10,1.06517740529339084250e-09] 
dist 210=[-4.82414568100741715630e-10,1.03126952293696669470e-09] 
dist 211=[-4.68520706571980286550e-10,9.89829254693569678030e-10] 
dist 212=[-4.46852924889401184170e-10,7.56610947084888129750e-10] 
dist 213=[-5.98838511265901017080e-10,6.95214054545296684200e-10] 
dist 214=[-8.94561018032132430940e-10,6.83340460169045828620e-10] 
dist 215=[-1.07996250336502325030e-09,8.38636699169500223280e-10] 
dist 216=[-1.12854678395230259620e-09,9.35858586676158577870e-10] 
dist 217=[-1.09201861113626241480e-09,9.61067401387256112220e-10] 
dist 218=[-1.04825610716875586710e-09,2.72261211903207228990e-10] 
dist 219=[-7.99411869016849076200e-10,2.96955978847613526040e-10] 
dist 220=[-7.35996968894690431040e-10,3.36863914286758269500e-10] 
dist 221=[-5.00145464061392230150e-10,5.62558769412907194540e-10] 
dist 222=[-5.78351698570444937030e-10,8.13691279722611627620e-10] 
dist 223=[-6.52848723168488319400e-10,9.71011620175234650710e-10] 
dist 224=[-6.74841024036774950570e-10,1.01197371204311854080e-09] 
dist 225=[-6.57971739166093134240e-10,9.91771454255072564400e-10] 
dist 226=[-6.26153752703687303070e-10,9.39575499904852409010e-10] 
dist 227=[-5.14113550030787915260e-10,8.02759415931541459580e-10] 
dist 228=[-4.59030393166180884460e-10,7.35403576822408090680e-10] 
dist 229=[-5.96006111003238940710e-10,3.84554570471976014400e-10] 
dist 230=[-9.17912701012138758310e-10,4.98399164601806145810e-10] 
dist 231=[-1.11949255775038410530e-09,6.20813809483958185090e-10] 
dist 232=[-1.17181905949103645250e-09,6.52501943366364016250e-10] 
dist 233=[-1.13609538900587965070e-09,6.29247113888172534430e-10] 
dist 234=[-1.08778147587269204390e-09,6.05584179898975758090e-10] 
dist 235=[-8.47576402091272421920e-10,4.49870220491983480900e-10] 
dist 236=[-7.63409842776970871410e-10,5.03822851396107512970e-10] 
dist 237=[-7.00089074149460427930e-10,6.66595406716609513390e-10] 
dist 238=[-8.72122338010324265550e-10,7.68065411388458742710e-10] 
dist 239=[-9.79829373471987705290e-10,8.31599111133415877940e-10] 
dist 240=[-1.00774353414098544020e-09,8.48073704804406636560e-10] 
dist 241=[-9.75194680108027118660e-10,3.21571895623904240760e-10] 
dist 242=[-9.35382148746264837510e-10,3.13002390832701798910e-10] 
dist 243=[-7.16993523882778875400e-10,2.99305566591397504550e-10] 
dist 244=[-6.56402882727980825350e-10,2.78288432222492296570e-10] 
dist 245=[-3.23070351990199953550e-10,3.77317134662391706820e-10] 
dist 246=[-4.52531229317190393230e-10,5.16213215604407918840e-10] 
dist 247=[-5.33591982960131414790e-10,6.16097108075456547230e-10] 
dist 248=[-5.54615970989036622790e-10,6.55897983437218827980e-10] 
dist 249=[-5.39881739987282732280e-10,6.44725104304504764050e-10] 
dist 250=[-5.14809827549446995280e-10,6.08808137927882173580e-10] 
dist 251=[-4.15869680684636668830e-10,5.33841484102346389310e-10] 
dist 252=[-3.67189405871472683600e-10,4.96958551425372681200e-10] 
dist 253=[-5.29603987473618561360e-10,4.63463655783110870600e-10] 
dist 254=[-7.06000734517538202800e-10,5.20017332948349894270e-10] 
dist 255=[-8.16447167256860356520e-10,5.55426683317197784340e-10] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 2, 2, 0, 1, 1, 2] 
dist 0=[340.79938265398471578   ,340.79938265398471578   ] 
dist 1=[317.44609710912372234   ,347.00566422656383846   ] 
dist 2=[283.54241844005145383   ,347.39796880326776743   ] 
dist 3=[248.13232164240810408   ,341.91544649119867243   ] 
dist 4=[182.16054689332135266   ,331.37430530670549632   ] 
dist 5=[125.75847503510802481   ,246.23090755914995136   ] 
dist 6=[71.141034973658855606  ,226.61697867806925012   ] 
dist 7=[10.296501537638333209  ,160.58267625327779796   ] 
dist 8=[-41.710247805505206586  ,150.62870984527054129   ] 
dist 9=[-62.375116029063927888  ,33.100540490599136918  ] 
dist 10=[-70.368327093313083151  ,9.2463315427525044354 ] 
dist 11=[-78.247196368253351707  ,4.8394691939183326600 ] 
dist 12=[-86.399129901291484887  ,5.4695453654661270607 ] 
dist 13=[-86.610208330141474712  ,12.246744565199109412  ] 
dist 14=[-65.861388279137541059  ,19.229396979125942477  ] 
dist 15=[-52.257112258883214810  ,24.458511196784039025  ] 
dist 16=[-49.943767483817242261  ,33.511302992228428132  ] 
dist 17=[-.61084788083199394311,35.080730201529441420  ] 
dist 18=[.61313363526775595377,33.597888828411983923  ] 
dist 19=[-5.7617264010111551225 ,31.150869069371021792  ] 
dist 20=[-10.554057428567534739  ,31.453253537203456755  ] 
dist 21=[-17.156605171918604458  ,32.193389587949760916  ] 
dist 22=[-23.941951079816854981  ,31.191328285789176827  ] 
dist 23=[-25.715036076015318815  ,26.249424524337361964  ] 
dist 24=[-13.013616722743998619  ,23.505725462666270748  ] 
dist 25=[-12.443239181110628969  ,9.2949225455031276122 ] 
dist 26=[-21.277789272570651193  ,6.1886141615436999708 ] 
dist 27=[-26.814056233071548972  ,9.8608688837648306461 ] 
dist 28=[-28.224497254035514266  ,12.335078411258459013  ] 
dist 29=[-3.7861253470354520997 ,12.978968754231832011  ] 
dist 30=[2.3301963404293266708 ,4.0182359008033086398 ] 
dist 31=[2.2246188535457007695 ,4.9581390450907231838 ] 
dist 32=[1.8071544945967582300 ,5.3236310362459507926 ] 
dist 33=[.9400480830495074851 ,5.2802987455315873013 ] 
dist 34=[.01936504379829737446,4.3058213535028442716 ] 
dist 35=[-.60599259622411441557,4.0492116771379955320 ] 
dist 36=[-1.0488063508596769811 ,.76594329476026194695] 
dist 37=[-2.1326475945275541006 ,.2435383223541789575 ] 
dist 38=[-2.9847242860868416304 ,-.82924568813730346409] 
dist 39=[-3.1851438707145474749 ,-1.0293625977680026500 ] 
dist 40=[-1.2905244437631840068 ,-.73156187540550808428] 
dist 41=[-1.2933075304944898523 ,-.15679660923565525432] 
dist 42=[-1.0612636293070540468 ,.4307947381194107757 ] 
dist 43=[-1.0263810337219134410 ,.8031268196215340253 ] 
dist 44=[-.09915287726219981849,1.0432696597635216919 ] 
dist 45=[.05508785486044996786,1.1038446039578891550 ] 
dist 46=[.15848939110525271076,.66346932336433981396] 
dist 47=[.09965669060613078502,.76517284472122000629] 
dist 48=[-.01975521581970271006,.79244385908417062504] 
dist 49=[-.23127716373216811961,.77014478609569582001] 
dist 50=[-.44790263827282195606,.65240655639847548049] 
dist 51=[-.58712834919459392163,.58417388905756752092] 
dist 52=[-.67815005100331718696,.1875794786602277686 ] 
dist 53=[-.7093934497783085808 ,.09838031748318803682] 
dist 54=[-.70217660451991713603,-.04742882459921941975] 
dist 55=[-.64518562880033542068,-.07219772757860471575] 
dist 56=[-.16318102381528258608,-.03440953953413470478] 
dist 57=[-.1597961457632148299 ,.03194224552483900457] 
dist 58=[-.12784952924362288597,.09980158641597165433] 
dist 59=[-.12137337162462946501,.14344398834479380019] 
dist 60=[.00062925298338014937,.17543962792824524772] 
dist 61=[.02001983735609914399,.1821262556725528156 ] 
dist 62=[.02087334177446252404,.08148828450566803163] 
dist 63=[.01879760889576047255,.09150152067331820772] 
dist 64=[.01452361659923056679,.09180220477359693261] 
dist 65=[.00690587227679518574,.08924776804951930086] 
dist 66=[-.00092123391906560589,.06948549211657427161] 
dist 67=[-.00600772762267689219,.06483961265894208889] 
dist 68=[-.01851519327709079996,.00776401619980426994] 
dist 69=[-.03882883273212036807,-.00106436244465671546] 
dist 70=[-.05193477981996065386,-.01075031090604525081] 
dist 71=[-.05534339087243576080,-.00917682975376914559] 
dist 72=[-.02145517305128883949,-.00636635806778975736] 
dist 73=[-.02100945772263850527,-.00162903829620316444] 
dist 74=[-.01628854507789938289,.00315829121549362633] 
dist 75=[-.01558023383255604550,.00616286125443786847] 
dist 76=[.00133667684587891310,.00805144232094713845] 
dist 77=[.00251849272726176645,.00854190074751187731] 
dist 78=[.00255438743992296165,.00985523088982920116] 
dist 79=[.00224988048575439813,.01102315509891766364] 
dist 80=[.00168454435296066345,.01103703295832791537] 
dist 81=[.00071507675795906342,.01066335167430286544] 
dist 82=[-.00027136756333105947,.00860678678142787351] 
dist 83=[-.00090260090088537666,.00772463477760502345] 
dist 84=[-.00324530660615031772,.00133828260861860836] 
dist 85=[-.00624920356777243308,7.37687289919452721490e-05] 
dist 86=[-.00813506697634595255,-.00116754983643068143] 
dist 87=[-.00862477700613984343,-.00099634703851073077] 
dist 88=[-.00260388426800469611,-.00069772861522532467] 
dist 89=[-.00253596456071347990,-.00019915621394590616] 
dist 90=[-.00194390583152567189,.00030399686588304914] 
dist 91=[-.00184881595417997074,.00062039708223150813] 
dist 92=[8.33955318922635101500e-05,.00082116074329244584] 
dist 93=[.00032939230100914020,.00094610038368466415] 
dist 94=[.00032936552547214494,.00135126199525593028] 
dist 95=[.00028771251336765146,.00147963888519546553] 
dist 96=[.00021377326542935576,.00145493234920167468] 
dist 97=[8.92771056470851761210e-05,.00140641446591772600] 
dist 98=[-3.68436066346608870440e-05,.00107383364023536104] 
dist 99=[-.00011708970153480644,.00100372108800767482] 
dist 100=[-.00029898474770346802,9.26177846757249171830e-05] 
dist 101=[-.00060683785885794166,-4.23265845484044661330e-05] 
dist 102=[-.00080106594917079996,-.00015050941449102916] 
dist 103=[-.00085393846231462426,-.00012360354651399242] 
dist 104=[-.00033533972240123631,-7.81375559044067517720e-05] 
dist 105=[-.00032569005487454083,-3.27509899676566835010e-06] 
dist 106=[-.00024703395686997088,7.20275095671005253870e-05] 
dist 107=[-.00023529984883852733,.00011920242274448815] 
dist 108=[-5.58058867111062246430e-06,.00014888515618089630] 
dist 109=[1.16348458730481767650e-07,.00015678612626711968] 
dist 110=[-1.86501498801357120450e-06,.00017031259611440606] 
dist 111=[-1.55865339343441203070e-05,.00018602637109224613] 
dist 112=[-3.85794608170498522030e-05,.00018365939333257641] 
dist 113=[-7.63064459025968644670e-05,.00017622284592537169] 
dist 114=[-.00011424395853714565,.00014258383217877236] 
dist 115=[-.00013805441193839102,.00012561051919975683] 
dist 116=[-.00015310492399953001,2.95511926701160340140e-05] 
dist 117=[-.00015728263055332390,9.00902614112592975220e-06] 
dist 118=[-.00015450434024331514,1.98948328100017630400e-06] 
dist 119=[-.00014274389604988232,4.23003031490364357990e-06] 
dist 120=[-3.95041621905837986500e-05,8.13362985030397707930e-06] 
dist 121=[-3.82311462618465438490e-05,1.46568931934078384930e-05] 
dist 122=[-2.91519864817245315340e-05,2.12583254769264899040e-05] 
dist 123=[-2.74123778999126090610e-05,2.54655128034422434090e-05] 
dist 124=[2.08102033038777857230e-06,2.81997481367309607700e-05] 
dist 125=[5.17537622138521578130e-06,2.91264579713462228830e-05] 
dist 126=[5.09026451162993074050e-06,2.06654225379707487150e-05] 
dist 127=[4.41889785675599374590e-06,2.24260088881315234060e-05] 
dist 128=[3.28543987751690940100e-06,2.18884898376278976060e-05] 
dist 129=[1.41860800955053570330e-06,2.10949157856478285110e-05] 
dist 130=[-4.61661392346683995780e-07,1.60801755964329575600e-05] 
dist 131=[-1.64729512178754304100e-06,1.49467945375283092990e-05] 
dist 132=[-4.80805714527818620250e-06,1.29780867671642649450e-06] 
dist 133=[-9.55084769533268412840e-06,-7.81947159895052030870e-07] 
dist 134=[-1.25320710435053871210e-05,-2.54923115295177366870e-06] 
dist 135=[-1.33244943143399359990e-05,-2.13192718143673340860e-06] 
dist 136=[-5.02046071851009273880e-06,-1.44575935002892025330e-06] 
dist 137=[-4.85732458489007242620e-06,-3.29906265099539732520e-07] 
dist 138=[-3.64684482758011273370e-06,7.89247685909190790790e-07] 
dist 139=[-3.46559868841021700290e-06,1.48823252956056595380e-06] 
dist 140=[4.73864080937104495840e-07,1.92636819808542522040e-06] 
dist 141=[6.08802365237346691100e-07,2.04002822345511289090e-06] 
dist 142=[5.95029622564963954740e-07,2.38596167100656378630e-06] 
dist 143=[5.11748218449737141370e-07,2.59839447870530410080e-06] 
dist 144=[3.73362877546179516880e-07,2.54513876235971810350e-06] 
dist 145=[1.47114703766869547100e-07,2.44176746691206177730e-06] 
dist 146=[-8.02916660532804221990e-08,1.93544135044043927050e-06] 
dist 147=[-2.23174324157764047540e-07,1.73035970347039294190e-06] 
dist 148=[-7.76269243567714810720e-07,2.62215299031937960290e-07] 
dist 149=[-1.46065319235989042660e-06,-2.68422247401085334490e-08] 
dist 150=[-1.88951320661645759270e-06,-2.67687046057685213970e-07] 
dist 151=[-2.00076882466481189990e-06,-2.24960710695870836380e-07] 
dist 152=[-5.95901037664333553380e-07,-1.54963859140418916740e-07] 
dist 153=[-5.75706107577996515630e-07,-4.13142939560684311860e-08] 
dist 154=[-4.31216666448610305480e-07,7.26551712399520545310e-08] 
dist 155=[-4.08935607516612580650e-07,1.43894234297083973920e-07] 
dist 156=[3.28532222562736095640e-08,1.88639832216368352120e-07] 
dist 157=[7.76627026381394632030e-08,2.24259150434398451320e-07] 
dist 158=[7.57403611490272235060e-08,3.13347762683676925220e-07] 
dist 159=[6.53734079237959197400e-08,3.38127679340729813830e-07] 
dist 160=[4.82894427458338704470e-08,3.28418355221316085450e-07] 
dist 161=[2.03251590024982587780e-08,3.16231354242895938910e-07] 
dist 162=[-7.79546938942770166670e-09,2.39049198774517403170e-07] 
dist 163=[-2.54419395309095217390e-08,2.23127408478328831460e-07] 
dist 164=[-6.96902347647270650090e-08,1.60074326420795585650e-08] 
dist 165=[-1.38685232981863395280e-07,-1.45165873751008281100e-08] 
dist 166=[-1.81992915142362397060e-07,-3.74521520315288383100e-08] 
dist 167=[-1.93408237468294705830e-07,-3.11520268444639644650e-08] 
dist 168=[-7.62083844559075198490e-08,-2.09195679843706622500e-08] 
dist 169=[-7.35788878745909608100e-08,-4.37404966102909948560e-09] 
dist 170=[-5.49271903309677103900e-08,1.23008801023855389910e-08] 
dist 171=[-5.21346045949855720750e-08,2.27206712942216822880e-08] 
dist 172=[7.08243842268393988000e-09,2.92488684907698659750e-08] 
dist 173=[8.30293024165170506570e-09,3.09419111863051370430e-08] 
dist 174=[8.07366546882776640710e-09,3.64431568814040718580e-08] 
dist 175=[6.92895758636254507320e-09,3.95059228940206307550e-08] 
dist 176=[5.05430154702310342470e-09,3.85250419972395777120e-08] 
dist 177=[1.93426922847923340290e-09,3.69337382293153031690e-08] 
dist 178=[-1.42442969652012413460e-09,2.90368351608783770720e-08] 
dist 179=[-3.59943236571962030980e-09,2.60673413470110868220e-08] 
dist 180=[-1.11906943374025983360e-08,3.20013138089813270570e-09] 
dist 181=[-2.14029017974061232730e-08,-1.19724344124007443450e-09] 
dist 182=[-2.78000486807635020440e-08,-3.57883363952009578130e-09] 
dist 183=[-2.94591765052990080290e-08,-2.98421260864745564300e-09] 
dist 184=[-1.04184689037518483020e-08,-2.01911170192930646960e-09] 
dist 185=[-1.00446726183789325080e-08,-4.58959625143427529060e-10] 
dist 186=[-7.50805155668769101270e-09,1.10402115994245141310e-09] 
dist 187=[-7.09335591602322682610e-09,2.08010709093060058510e-09] 
dist 188=[7.54860460086125021310e-10,2.69258812362324072110e-09] 
dist 189=[8.73697097854887307490e-10,3.65200605840243429950e-09] 
dist 190=[8.44915570839419600700e-10,5.17863221492579931880e-09] 
dist 191=[7.07666030325481171900e-10,5.58955291547871511120e-09] 
dist 192=[4.83780631745178841970e-10,5.41991749271035663580e-09] 
dist 193=[1.20914892889211352460e-10,5.20965837429632339130e-09] 
dist 194=[-2.42980309916756136930e-10,3.96323213067590029030e-09] 
dist 195=[-4.70863601297058467350e-10,3.66691834378193403670e-09] 
dist 196=[-1.11705423573981733940e-09,5.45872809719635399190e-11] 
dist 197=[-2.38952044328674815580e-09,-2.25585743318422706950e-10] 
dist 198=[-3.18714848400572237930e-09,-2.05661858764024427470e-10] 
dist 199=[-3.39549367425027969850e-09,-1.20183825407672639320e-10] 
dist 200=[-2.23408894511702432950e-09,1.78572573691107671930e-11] 
dist 201=[-2.12989632115816430340e-09,4.43813368705619915410e-10] 
dist 202=[-1.74041415404329071460e-09,8.99331566535697858400e-10] 
dist 203=[-1.54756371004695457290e-09,1.18339135647167254750e-09] 
dist 204=[-8.83434225045304100360e-10,1.36128561762609573510e-09] 
dist 205=[-8.91628236266001165990e-10,1.62015787540634292070e-09] 
dist 206=[-8.69678606830923755130e-10,2.03051464832581520940e-09] 
dist 207=[-8.26728971988528687670e-10,2.13855363456467523390e-09] 
dist 208=[-6.83778428088562364870e-10,2.09256171606608317790e-09] 
dist 209=[-6.13597815873529738760e-10,1.98738630482506508410e-09] 
dist 210=[-2.94426897583293726990e-10,1.66698055762170908660e-09] 
dist 211=[-2.56697688307646119780e-10,1.50894853760564022340e-09] 
dist 212=[-1.11356394418707058700e-09,8.52079390346976000090e-10] 
dist 213=[-1.76540918394451008280e-09,8.94571738829371067540e-10] 
dist 214=[-2.17375883272098888860e-09,8.62482591158672612190e-10] 
dist 215=[-2.28008786761937714080e-09,8.30093727254897007250e-10] 
dist 216=[-2.20828451788072258440e-09,6.16008622547754181810e-10] 
dist 217=[-2.11705672952856284920e-09,5.82394759002228834380e-10] 
dist 218=[-1.63189576601063174970e-09,3.37755455229124883760e-10] 
dist 219=[-1.48606103771157926320e-09,4.06174190084340742420e-10] 
dist 220=[-5.71911470874496749430e-10,5.31702463259305567320e-10] 
dist 221=[-5.92143545666828525350e-10,1.09469361770342273250e-09] 
dist 222=[-1.75761597611065110820e-10,1.44725947919079857050e-09] 
dist 223=[-1.81093306995732185250e-10,1.53881446400295830450e-09] 
dist 224=[-2.33207592956672068330e-10,1.48381095514122655070e-09] 
dist 225=[-5.86448917585659305900e-10,1.42854061164992323340e-09] 
dist 226=[-1.02782797889920280990e-09,1.05836400238371934990e-09] 
dist 227=[-1.30297969507696105140e-09,1.07708525216387595970e-09] 
dist 228=[-1.47526831938364723090e-09,1.15329651219495678780e-09] 
dist 229=[-1.51996361130629634290e-09,1.17303871376131861120e-09] 
dist 230=[-1.48791595829553033720e-09,1.14064823016307368090e-09] 
dist 231=[-1.41088333697463629490e-09,1.08880510112594585080e-09] 
dist 232=[-1.19561122305325377710e-09,8.71514678210805290260e-10] 
dist 233=[-1.08969116114209159590e-09,7.64611098911935240790e-10] 
dist 234=[-5.32984224705584831290e-10,8.51024860239221396680e-10] 
dist 235=[-7.41595887854761565420e-10,1.32553377654929750210e-09] 
dist 236=[-9.41491667171916654560e-10,1.62263819471267642740e-09] 
dist 237=[-9.93320461202606637570e-10,1.69968492489080498950e-09] 
dist 238=[-9.72064460902284950030e-10,1.65488314389109954550e-09] 
dist 239=[-9.22008203903033755690e-10,1.57768354421054838980e-09] 
dist 240=[-7.79359443408688944630e-10,1.27689602790565207090e-09] 
dist 241=[-7.09176667382039785580e-10,1.12890515714880546720e-09] 
dist 242=[-6.76310549363735001340e-10,5.60925225929390271510e-10] 
dist 243=[-1.15181285353435747460e-09,8.55483954250311867300e-10] 
dist 244=[-1.44953760710935744170e-09,1.04851300683237712620e-09] 
dist 245=[-1.52674188191090859760e-09,1.09856508206162832070e-09] 
dist 246=[-1.48662394227677623150e-09,1.07479532264962474430e-09] 
dist 247=[-1.41715002491727721100e-09,1.01970372880988546650e-09] 
dist 248=[-1.14782818460625884900e-09,8.60152718306810754630e-10] 
dist 249=[-1.01531950164287632860e-09,7.81652933848118612450e-10] 
dist 250=[-9.32099404694825908820e-10,9.68287191853233682560e-10] 
dist 251=[-1.08402511044812673370e-09,1.19667830992203063680e-09] 
dist 252=[-1.17914947948418406190e-09,1.33967960232445524080e-09] 

8 phat 5 dirichlet min maxes function [0, 2, 1, 2, 1, 2, 0, 1, 2] 
dist 0=[357.23263214192388969   ,357.23263214192388969   ] 
dist 1=[346.05742083499776331   ,362.27872358787208660   ] 
dist 2=[313.32192050476311572   ,361.20805084843015769   ] 
dist 3=[256.33886799326399766   ,352.73343684590168709   ] 
dist 4=[184.36243949097296145   ,273.89044842977515207   ] 
dist 5=[124.95191727862309974   ,254.41821877542507797   ] 
dist 6=[68.787052167929735625  ,194.18443344879572331   ] 
dist 7=[8.2869376714496535279 ,175.24404331927815185   ] 
dist 8=[-42.889518043537420651  ,50.839652851417964534  ] 
dist 9=[-63.214511319084626168  ,20.818522608967763625  ] 
dist 10=[-70.953367716095432530  ,13.712415689039689588  ] 
dist 11=[-77.314625854437869166  ,8.3440318983426523701 ] 
dist 12=[-85.972236057371019608  ,10.529991996976396428  ] 
dist 13=[-87.648812597900169902  ,16.055682761937369661  ] 
dist 14=[-72.452492868482790037  ,25.962845419657592993  ] 
dist 15=[-62.776597144935136390  ,34.600782824730488112  ] 
dist 16=[-.22553702801016929485,36.294810740950100980  ] 
dist 17=[9.8196735162781768386 ,37.408650783536328214  ] 
dist 18=[14.769245104514260937  ,35.512390935910108404  ] 
dist 19=[-.17486896756025124736,37.236991967844023367  ] 
dist 20=[-10.545532004782391997  ,38.276262191141870801  ] 
dist 21=[-19.798151123441145210  ,37.282863461351742326  ] 
dist 22=[-27.011251412544057459  ,30.640308241076948749  ] 
dist 23=[-28.747275991364783741  ,27.666642741778967159  ] 
dist 24=[-23.550211667677530023  ,5.4710395853709958170 ] 
dist 25=[-20.567782304663474739  ,1.0758819506649557668 ] 
dist 26=[-27.111011300573200303  ,-.65822494372137982116] 
dist 27=[-28.810302579690642904  ,8.5038633249594479716 ] 
dist 28=[-8.8112927588409495910 ,15.375006630058591588  ] 
dist 29=[-8.6428439249251235392 ,19.574584351115601693  ] 
dist 30=[-6.8276677032042426892 ,20.300516172267195907  ] 
dist 31=[-6.4688770149898958888 ,4.1002451311049730831 ] 
dist 32=[.07400534879773301439,4.5412546625653370335 ] 
dist 33=[1.1430810789098827940 ,4.5191527838915449137 ] 
dist 34=[1.3158980988922211877 ,4.3538966147082426236 ] 
dist 35=[-.08270654802094758436,4.8463923487969561208 ] 
dist 36=[-1.1515479045467343788 ,4.8248844142815306993 ] 
dist 37=[-2.4582570673884445012 ,4.6787899465693905039 ] 
dist 38=[-3.2845683560975536841 ,3.6222774835326497043 ] 
dist 39=[-3.4996500365361993902 ,3.3753692152853860582 ] 
dist 40=[-1.9363111767313168339 ,.41684030572851619235] 
dist 41=[-2.0534287589379085965 ,-.03825708523429083128] 
dist 42=[-2.7241807198352119505 ,-.25175415829353920711] 
dist 43=[-2.9048827648926514230 ,.60983850912483092182] 
dist 44=[-1.1068120679091466556 ,1.1522926937414560222 ] 
dist 45=[-1.0798080255554339940 ,1.4941464587652022557 ] 
dist 46=[-.82914692282316125532,1.5838672143582312317 ] 
dist 47=[-.79169949880338386968,.62091934570418423943] 
dist 48=[-.07654194049045294454,.63766120065818798686] 
dist 49=[.04691686679440357109,.62435271816028941995] 
dist 50=[-.14415291180222697798,.65979512763080765255] 
dist 51=[-.39562101718974824219,.71858854537328527431] 
dist 52=[-.55634343528560469062,.71497855763379738535] 
dist 53=[-.66084228075909278762,.68458237796892914679] 
dist 54=[-.69590622530831055382,.57058551825390337583] 
dist 55=[-.68848876150896010166,.51150505554776490274] 
dist 56=[-.65637325742883439298,.18545810747617559509] 
dist 57=[-.54968809338865368921,.10819444875920490245] 
dist 58=[-.49536838609860236326,.00372220265159995066] 
dist 59=[-.43648583305451221361,.10332299181068646434] 
dist 60=[-.12940122933234878624,.16589218438480887386] 
dist 61=[-.12557285143367057149,.20532246376106735623] 
dist 62=[-.09645821411305699748,.21582787775286673344] 
dist 63=[-.0908546692462385467 ,.07738606459375402050] 
dist 64=[.00569114141907878341,.07869847838962866099] 
dist 65=[.02141929242896780099,.07640386544634074283] 
dist 66=[.01376198459638136737,.06678416564517726961] 
dist 67=[-.00262814006871361042,.07284861399990585766] 
dist 68=[-.02255247209202883156,.07138835165966683694] 
dist 69=[-.04414730064247372243,.06888930414758782142] 
dist 70=[-.05772178447265934346,.0526730493392768373 ] 
dist 71=[-.06124894735192397408,.04899620383633698490] 
dist 72=[-.02192258260026821186,.00452025016023720655] 
dist 73=[-.03090827049428981994,-.00227581540483005408] 
dist 74=[-.04066774852729931253,-.00322760547776910516] 
dist 75=[-.04328279563609737458,.00666870831293874222] 
dist 76=[-.01638968668147906848,.01286894591548056461] 
dist 77=[-.01588480324666799913,.01676234166171867048] 
dist 78=[-.01198408305264529600,.01777306857369076764] 
dist 79=[-.01140019560510836777,.01059271229603026353] 
dist 80=[.00145330333201086675,.01049829851772951530] 
dist 81=[.00341710122361757754,.01017390623041154580] 
dist 82=[.00141276154782933798,.00781372421799162661] 
dist 83=[-.00061781076041681684,.00843787889291713349] 
dist 84=[-.00208911827671387296,.00829066182495774367] 
dist 85=[-.00432608130344082355,.00796197241123998925] 
dist 86=[-.00574524271181614798,.00632734930210976346] 
dist 87=[-.00613387820832851975,.00566056654301536906] 
dist 88=[-.00287001881142307497,.00087623870842715064] 
dist 89=[-.00473994257607853842,-6.65021343894192188480e-05] 
dist 90=[-.00613896891835941866,-.00038054029874745938] 
dist 91=[-.00650194980415986791,.00064756514860604343] 
dist 92=[-.00193799436200744927,.00129277482963619538] 
dist 93=[-.00187448215811961059,.00169990374173595869] 
dist 94=[-.00140967036943368943,.00181072532714838059] 
dist 95=[-.00133658504728290764,.00127944377434776783] 
dist 96=[9.92781351623961036740e-05,.00127053706132698822] 
dist 97=[.00033185392824177030,.00122337628705922220] 
dist 98=[.00012863596871576670,.00101703588733267320] 
dist 99=[-.00013834097189761141,.00109972187575728841] 
dist 100=[-.00041577067877845465,.00106996664577823690] 
dist 101=[-.00075553343934682016,.00103080577476826595] 
dist 102=[-.00096886679396936716,.00078037814775549802] 
dist 103=[-.00102465304444698520,.00072848203003005030] 
dist 104=[-.00042522851041669276,5.50312614349110482830e-05] 
dist 105=[-.00045074055359533648,-4.42529879082736781720e-05] 
dist 106=[-.00059194663446620069,9.79059777215649313530e-05] 
dist 107=[-.00062932297795852913,.00025573908910750602] 
dist 108=[-.00024486591674323830,.00035511091053660811] 
dist 109=[-.00023661770211563278,.00041829017604325466] 
dist 110=[-.00017701507238342109,.00043665088630048620] 
dist 111=[-.00016813051789551046,.00016388966664770478] 
dist 112=[-1.21020194039457218040e-07,.00016055707479682489] 
dist 113=[-2.28868274493043410620e-05,.00015492091867103477] 
dist 114=[-6.01674490935856053360e-05,.00012074025651957930] 
dist 115=[-9.76370344586465974690e-05,.00012644880549077459] 
dist 116=[-.00012113690442906639,.00012357375688917883] 
dist 117=[-.00013597518739328157,.00011845380971126041] 
dist 118=[-.00014006233943340674,9.37685718880735013590e-05] 
dist 119=[-.00013733601902333538,8.37374589885220548930e-05] 
dist 120=[-5.22717340831102313310e-05,1.26125378943902268930e-05] 
dist 121=[-7.13028320995946633680e-05,-1.44648070384378712590e-06] 
dist 122=[-9.21624785507070494170e-05,7.76793251122394260030e-06] 
dist 123=[-9.75727408562204249590e-05,2.34522849150327930010e-05] 
dist 124=[-2.84991619535164152590e-05,3.33225830111929141750e-05] 
dist 125=[-2.74798098855301383080e-05,3.95971570769574305180e-05] 
dist 126=[-2.07429370563225151760e-05,4.14230992240076121480e-05] 
dist 127=[-1.94653300454012671960e-05,1.90792812872180325900e-05] 
dist 128=[1.78168331388956355300e-06,1.87491175118585076960e-05] 
dist 129=[5.23898999135986387020e-06,1.80063536622215195580e-05] 
dist 130=[1.04682178147810588280e-05,1.50201954004795695220e-05] 
dist 131=[2.40088422315737116510e-06,1.61893857061862531470e-05] 
dist 132=[-5.68979213360783649570e-06,1.57109321962809792220e-05] 
dist 133=[-1.07427649853843898860e-05,1.51133096150463879020e-05] 
dist 134=[-1.39100310320151032650e-05,1.14671930935123485190e-05] 
dist 135=[-1.47318110639652278780e-05,1.06502256458241138290e-05] 
dist 136=[-4.38782937932016598590e-06,8.45487892455510934460e-07] 
dist 137=[-6.89998256984239595170e-06,-6.43487035157499417200e-07] 
dist 138=[-9.02515323124263905030e-06,-2.71091661286845903080e-06] 
dist 139=[-9.58223666796612671320e-06,-1.05790666599107369200e-06] 
dist 140=[-3.58957155565613240730e-06,6.03422960644870391910e-07] 
dist 141=[-3.46331942405538046900e-06,1.64701411400695656970e-06] 
dist 142=[-2.57996109037017503020e-06,2.30834531901307616870e-06] 
dist 143=[-2.44818103487566550660e-06,2.49638421535966213870e-06] 
dist 144=[3.63923730425236693890e-07,2.42937760265979412550e-06] 
dist 145=[8.05540697680423733010e-07,2.34060829734218553960e-06] 
dist 146=[1.11747474009638361200e-06,1.77243710767492785160e-06] 
dist 147=[3.02910107305380113810e-07,1.86002015392115054210e-06] 
dist 148=[-5.14035579132118486300e-07,1.81243758445619934840e-06] 
dist 149=[-1.02472170377350639070e-06,1.73578736463338595120e-06] 
dist 150=[-1.34553633479982314640e-06,1.37015248393396935750e-06] 
dist 151=[-1.43054085079249110140e-06,1.22335406483161060930e-06] 
dist 152=[-5.60541902030193247410e-07,1.82413357316951534030e-07] 
dist 153=[-1.04640706731035433970e-06,-2.24628882871916638110e-08] 
dist 154=[-1.35072808950123448180e-06,-3.54077484331886446400e-07] 
dist 155=[-1.42966051224275716330e-06,-1.49868693803395559310e-07] 
dist 156=[-4.26198112681668099960e-07,5.51620394911053276820e-08] 
dist 157=[-4.10977241424045652180e-07,1.83801936693461802750e-07] 
dist 158=[-3.05660819995575756700e-07,2.65195972224529781650e-07] 
dist 159=[-2.89949223066844202230e-07,2.88097097770079195820e-07] 
dist 160=[7.02059033135922456890e-09,2.81627168902283066160e-07] 
dist 161=[5.61288512422364885960e-08,2.69998339225274471480e-07] 
dist 162=[1.49679354224818001460e-07,2.44261105331826470790e-07] 
dist 163=[3.45364465719275504410e-08,2.61376963128449129450e-07] 
dist 164=[-8.66731766885783591700e-08,2.53395419330576927640e-07] 
dist 165=[-1.62313713497126286190e-07,2.43350401400577984290e-07] 
dist 166=[-2.09703803255298733280e-07,1.86030992207831300010e-07] 
dist 167=[-2.21995351005532018850e-07,1.71134421781844401230e-07] 
dist 168=[-7.75677722340041116120e-08,4.43974143394890306260e-08] 
dist 169=[-1.26404298911405825150e-07,2.73678090350506628620e-08] 
dist 170=[-1.57040722718631715960e-07,4.36953865634522827000e-09] 
dist 171=[-1.65100115005152172860e-07,0                     ] 
dist 172=[-5.31122909193856083490e-08,9.74471675019751923670e-09] 
dist 173=[-5.11943514508307207060e-08,2.52456182601953697870e-08] 
dist 174=[-3.80830157762050289660e-08,3.50733287571548313810e-08] 
dist 175=[-3.60825631663313938020e-08,3.77684714124906209920e-08] 
dist 176=[5.39006239209427141420e-09,3.66403546890738062400e-08] 
dist 177=[1.19151667117010560610e-08,3.52653307955759965360e-08] 
dist 178=[1.57220610042886550490e-08,2.66431225042851676120e-08] 
dist 179=[3.78611516912868034170e-09,2.77566413280592595830e-08] 
dist 180=[-8.16968803314629437200e-09,2.69825582865490175100e-08] 
dist 181=[-1.56346374532659084310e-08,2.58443228657909730070e-08] 
dist 182=[-2.04375672839733672570e-08,2.02478076591446279740e-08] 
dist 183=[-2.17006051819226196710e-08,1.81809152830955899020e-08] 
dist 184=[-8.60401703912097242610e-09,2.29318285192669068470e-09] 
dist 185=[-1.49813638122933243140e-08,-7.32001583710624664750e-10] 
dist 186=[-1.94079470906477674080e-08,-4.24838614091080927830e-09] 
dist 187=[-2.05571691061124129920e-08,-8.30715851909644499040e-10] 
dist 188=[-7.06979016368325258010e-09,2.99027932790166117520e-09] 
dist 189=[-6.72558549222140702950e-09,5.37774665137586256440e-09] 
dist 190=[-5.57781805156733576030e-09,6.87787201691887092280e-09] 
dist 191=[-5.01032038635144399940e-09,7.27752461123015546180e-09] 
dist 192=[-1.95594196850286589390e-09,7.11379616385790396330e-09] 
dist 193=[-1.21088171879872265110e-09,6.76936368434605841250e-09] 
dist 194=[-2.25488157192902879190e-10,5.59422419294764551020e-09] 
dist 195=[-6.53280483706460433050e-10,3.74613425099823967410e-09] 
dist 196=[-2.25960284253038816110e-09,3.62314197228762193860e-09] 
dist 197=[-3.26165164837441594300e-09,3.48136797768874578280e-09] 
dist 198=[-3.88931059964286943980e-09,2.63415203277372272870e-09] 
dist 199=[-4.05206938085025570940e-09,2.44433190459033393760e-09] 
dist 200=[-1.62426571563553706950e-09,1.29419037472878760330e-09] 
dist 201=[-1.61221889205056689380e-09,1.23280557104972236660e-09] 
dist 202=[-2.09300762610816736910e-09,9.90453304284792681990e-10] 
dist 203=[-2.22006562056058088850e-09,8.72267722211377083310e-10] 
dist 204=[-7.52127858171511478830e-10,6.02488845566427504400e-10] 
dist 205=[-8.82003253225066536690e-10,1.05903227734763609930e-09] 
dist 206=[-1.11143679039372624850e-09,1.34550330348174754700e-09] 
dist 207=[-1.16964049102379148330e-09,1.42107963819349072360e-09] 
dist 208=[-1.14414972007653580560e-09,1.38253618539966484250e-09] 
dist 209=[-1.08384551898679426470e-09,1.32088859207973883690e-09] 
dist 210=[-9.21956114899336415550e-10,1.05291226985099442780e-09] 
dist 211=[-8.42613825110796473290e-10,9.27840744001259924920e-10] 
dist 212=[-9.04974355892843745100e-10,9.40265917122554400030e-10] 
dist 213=[-1.05443699261420190550e-09,1.16010434131272677940e-09] 
dist 214=[-1.14807400133510162570e-09,1.29771785039402972660e-09] 

8 phat 5 dirichlet min maxes function [0, 2, 2, 0, 2, 1, 0, 1, 2] 
dist 0=[358.61667134777686252   ,358.61667134777686252   ] 
dist 1=[347.26453008117441057   ,363.90282662263019600   ] 
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dist 115=[-7.99114094460563645380e-05,.00019952539922107657] 
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dist 123=[-7.79862162872316064980e-05,-1.16731271469347361790e-05] 
dist 124=[-3.02126112562067669580e-05,3.93739679271429402460e-06] 
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dist 127=[-2.06920188267692114090e-05,2.18713897349066163210e-05] 
dist 128=[3.01192422847118567470e-06,2.14731434876401834030e-05] 
dist 129=[6.73997659917198900250e-06,2.06156653684762630240e-05] 
dist 130=[1.19242990427192699700e-05,1.63774709570693714340e-05] 
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dist 145=[6.51388815976788346250e-07,2.91114111840867545460e-06] 
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dist 156=[-4.42402061721814436100e-07,6.31302364766134207240e-08] 
dist 157=[-4.26708298627087388560e-07,2.10169667328119847730e-07] 
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dist 159=[-3.01316980128866595210e-07,3.29146141712859247540e-07] 
dist 160=[4.56079760051893015300e-08,3.21591608664446947890e-07] 
dist 161=[1.00107911428056271110e-07,3.08257399028968916570e-07] 
dist 162=[1.78392616109019316770e-07,2.43914271385529605000e-07] 
dist 163=[3.98910705526566337340e-08,2.29150270358954183550e-07] 
dist 164=[-9.88255144670060493620e-08,2.23129349165778508450e-07] 
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dist 166=[-2.39612381422373045280e-07,1.68384066291170504140e-07] 
dist 167=[-2.53677247730533626120e-07,1.50507313648098455650e-07] 
dist 168=[-7.46353260795249279350e-08,2.10874177559213721360e-08] 
dist 169=[-1.27795268392202212580e-07,-4.28688413153304197460e-09] 
dist 170=[-1.65228716605677233920e-07,-4.61581187230720836430e-08] 
dist 171=[-1.74937077887131974620e-07,-1.80616403192051867040e-08] 
dist 172=[-5.29730090794753389610e-08,1.01107438283617102740e-08] 
dist 173=[-5.10690361032230514040e-08,2.77718654145848122980e-08] 
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dist 175=[-3.60014142855800888170e-08,4.19755389903504522360e-08] 
dist 176=[3.24866076590414000160e-09,4.07512164115198572150e-08] 
dist 177=[9.63571492901608511290e-09,3.91831813839393998310e-08] 
dist 178=[1.92746794463923258580e-08,2.98504481166729070620e-08] 
dist 179=[4.92153994445774695750e-09,3.03733477163024896430e-08] 
dist 180=[-9.45266548237683195740e-09,2.94048179414739875610e-08] 
dist 181=[-1.84601771615359371640e-08,2.82715157903166170680e-08] 
dist 182=[-2.41198161792871599190e-08,2.13733498953627987110e-08] 
dist 183=[-2.56029646921424383460e-08,1.98798708958928878080e-08] 
dist 184=[-9.41969869269352852020e-09,1.69850463548385127730e-09] 
dist 185=[-1.28911087755461561260e-08,-1.00762339640232522880e-09] 
dist 186=[-1.67881626643756424330e-08,-5.70576152699336181760e-09] 
dist 187=[-1.78048661502526023520e-08,-2.41446401720151071870e-09] 
dist 188=[-6.33416247160074658570e-09,1.09261806507478600310e-09] 
dist 189=[-6.08921049542563168090e-09,3.28639549464542029990e-09] 
dist 190=[-4.63328248380114924440e-09,4.66768148154371795990e-09] 
dist 191=[-4.28913833653967298680e-09,5.04210638644971026150e-09] 
dist 192=[1.00658793355211673300e-10,4.89224038361180249800e-09] 
dist 193=[8.46328914969880680160e-10,4.70342442616692883490e-09] 
dist 194=[2.25949285937362394180e-09,3.73919900147531348870e-09] 
dist 195=[8.30804896125110506860e-10,3.99758296094128359660e-09] 
dist 196=[-1.05029668699776923230e-09,3.88052623410520782730e-09] 
dist 197=[-2.22368088863322652090e-09,3.71940576810918194970e-09] 
dist 198=[-2.95863602636329691010e-09,2.88991386296699048670e-09] 
dist 199=[-3.14922604456528563660e-09,2.61510550988173160250e-09] 
dist 200=[-1.98922607099301090510e-09,9.05942927549851567570e-10] 
dist 201=[-2.20000759724247139040e-09,6.59770762770421391820e-10] 
dist 202=[-2.69054253481699129230e-09,3.86232064887235826850e-10] 
dist 203=[-2.81775147492688564190e-09,3.32549250104955857220e-10] 
dist 204=[-1.14925484176489129130e-09,5.29096117325455908720e-10] 
dist 205=[-1.10090757099827230210e-09,9.67057499738067289300e-10] 
dist 206=[-8.59574320099740717320e-10,1.24192923995665755750e-09] 
dist 207=[-7.74064598753321803990e-10,1.31457282928735361110e-09] 
dist 208=[-5.05149225228710531290e-10,1.27103889480424866110e-09] 
dist 209=[-6.18066600775742854530e-10,1.22214230181935903850e-09] 
dist 210=[-7.16502031617446914690e-10,9.20125689251254114970e-10] 
dist 211=[-7.41474606011994296530e-10,8.60794854821052166740e-10] 
dist 212=[-7.15802611193439030130e-10,8.37285014916363578040e-10] 
dist 213=[-6.87450756770621086180e-10,7.99718197767320853720e-10] 
dist 214=[-7.20694057602317638700e-10,6.38296408254466577230e-10] 
dist 215=[-7.46835871849908742540e-10,5.61580196624477233780e-10] 
dist 216=[-4.18773457603506570680e-10,4.11124106675689884090e-10] 
dist 217=[-5.84929157441957475780e-10,4.11121965238075088990e-10] 
dist 218=[-6.88971749069159191210e-10,4.11432957768733000120e-10] 
dist 219=[-7.15951922453448028090e-10,4.35564514362711209680e-10] 
dist 220=[-4.99969816588097714650e-10,4.40293104168252533350e-10] 
dist 221=[-6.82100813755919920170e-10,4.59150148491112709890e-10] 
dist 222=[-7.96067554674366817860e-10,4.89377646180846717180e-10] 
dist 223=[-8.25472316698071318110e-10,6.79141567890134447160e-10] 
dist 224=[-1.04801289748808383360e-09,1.08519647346903926270e-09] 
dist 225=[-1.22177604674482557570e-09,1.33834422289641600890e-09] 
dist 226=[-1.33054751229835421520e-09,1.49687230158858085130e-09] 
dist 227=[-1.35869762048026889430e-09,1.53803499498255542360e-09] 
dist 228=[-1.34184294750945762220e-09,1.48557724601747744410e-09] 
dist 229=[-1.27705545224652014710e-09,1.42770885880269159930e-09] 
dist 230=[-1.17361875795595454230e-09,1.07517165325225756540e-09] 
dist 231=[-1.09287711944896188230e-09,1.00195816422483327470e-09] 
dist 232=[-8.41818745521089806730e-10,1.12621381631347241740e-09] 
dist 233=[-1.10136397003580310190e-09,1.62347551508376704250e-09] 
dist 234=[-1.28329360503432890950e-09,1.93481636447605168930e-09] 
dist 235=[-1.33048410570861041180e-09,2.01553472775123778440e-09] 
dist 236=[-1.29354505148461923890e-09,1.95034250002287757320e-09] 
dist 237=[-1.23499819067810400590e-09,1.87083143086087030140e-09] 
dist 238=[-9.86924882708861586020e-10,1.43330843562805915140e-09] 
dist 239=[-8.66686472497638563880e-10,1.31286768974423848360e-09] 
dist 240=[-4.31414831904603052080e-10,1.09491265645802939660e-09] 
dist 241=[-9.21104675687010456220e-10,1.03636320212151416340e-09] 
dist 242=[-1.22771012165865331120e-09,8.91398497918465731190e-10] 
dist 243=[-1.30721210186166058250e-09,7.15335784634992455860e-10] 
dist 244=[-1.27474708648027084420e-09,6.94254763716827885900e-10] 
dist 245=[-1.21337184601581281560e-09,6.63992272092645581960e-10] 
dist 246=[-9.95459589821127661070e-10,5.22448124125844400020e-10] 
dist 247=[-8.88245880926608045240e-10,4.65967751787848226710e-10] 
dist 248=[-5.91323966882228349640e-10,7.39549673043125686480e-10] 
dist 249=[-5.67914398620643352020e-10,1.02930146858436576680e-09] 
dist 250=[-5.53257440659913689250e-10,1.21072156316797117530e-09] 

8 phat 5 dirichlet min maxes function [0, 0, 0, 1, 1, 0, 0, 0, 2] 
dist 0=[390.20027130391927864   ,390.20027130391927864   ] 
dist 1=[375.83528277432547350   ,388.30759292299712630   ] 
dist 2=[341.43117871093756162   ,390.20027130391927864   ] 
dist 3=[276.15756747833592253   ,342.93307344924494851   ] 
dist 4=[205.26940495166047235   ,315.80319145987952028   ] 
dist 5=[148.15654565708343796   ,259.40870641261288508   ] 
dist 6=[57.789424879828049574  ,124.71062781995347251   ] 
dist 7=[-4.5869534780997358146 ,112.03383144594643538   ] 
dist 8=[-50.929930165274495965  ,75.656073007721944721  ] 
dist 9=[-81.716954290920642374  ,-4.1402496803273982083 ] 
dist 10=[-99.794957933986706392  ,-25.708789010881312948  ] 
dist 11=[-102.72851565363152188   ,-11.693757277640376299  ] 
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dist 45=[-.26023576779134549284,2.2499976937077595467 ] 
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dist 47=[.23216880420747930579,3.1056006946624334208 ] 
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dist 52=[-.5700128368271308244 ,.80921349312043488584] 
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dist 56=[-1.1031302010577620719 ,.03320653752240408924] 
dist 57=[-.46450171325616337463,.03112502161723255893] 
dist 58=[-.37938626839000474929,.05939317587481105967] 
dist 59=[-.33793238209164668907,.11095919600475874135] 
dist 60=[-.13351668580959536985,.19868003195222968984] 
dist 61=[-.01792450239829200512,.29022722833574301801] 
dist 62=[.02535291008664606619,.37143206861870001062] 
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dist 64=[.07986097502317343768,.10262250099399196928] 
dist 65=[.08302357154090372201,.10219574465902120623] 
dist 66=[.06330350451204396718,.09912166766124335327] 
dist 67=[.02859979744250998721,.07674074646129442872] 
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dist 71=[-.05788441508998687866,-.01994257847528881473] 
dist 72=[-.06172136635364318145,-.02359131840555176259] 
dist 73=[-.04681470540758425852,-.02375119219327927696] 
dist 74=[-.03767442784750422838,-.02090235538157407468] 
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dist 76=[-.01702315873890071147,.01442194336430063590] 
dist 77=[-.00019389165705494120,.02763237764419441937] 
dist 78=[.00464517950845058535,.03592232678010726383] 
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dist 80=[.01125490182747322126,.01221230764201472513] 
dist 81=[.00977905419092993517,.01215684384872468065] 
dist 82=[.00721792251293825572,.01172368851852555307] 
dist 83=[.00294875663530820762,.00941827800830079159] 
dist 84=[-.00136391652151674234,.00844464614972231204] 
dist 85=[-.00409418429354008875,.00141742986661935913] 
dist 86=[-.00690468417692506161,2.80548310858986527620e-05] 
dist 87=[-.00897392542241842200,-.00238982709495270211] 
dist 88=[-.00951111935309688676,-.00284718467706028235] 
dist 89=[-.00605454044122533556,-.00282124139412357228] 
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dist 91=[-.00431297863967970313,-.00082323107487040688] 
dist 92=[-.00201287324628299093,.00135374852346148236] 
dist 93=[.00010197480667333232,.00271786987524637436] 
dist 94=[.00044574232095038341,.00357708177706969684] 
dist 95=[.00114698505849525937,.00380834289455696856] 
dist 96=[.00125792049077755051,.00163157187071897052] 
dist 97=[.00124768140777214983,.001599219064521782  ] 
dist 98=[.00092605389271690527,.00154416805099169429] 
dist 99=[.00039494938626736684,.00117677636677900169] 
dist 100=[-.00014033324325109410,.00109872028706603743] 
dist 101=[-.00047820097151452754,.00010684030407817032] 
dist 102=[-.00069403280469905657,-3.93298088827469464720e-05] 
dist 103=[-.00088708329040552786,-.00030121226320874276] 
dist 104=[-.00094433483063447495,-.00034956083860458536] 
dist 105=[-.00071758845772002782,-.00034337120398705326] 
dist 106=[-.00057314341598476930,-.00029236965273273913] 
dist 107=[-.00051085709711817288,-7.30128975305051540040e-05] 
dist 108=[-.00025530166156594960,.00024441290364494313] 
dist 109=[-2.66430408883019753140e-05,.00044276562438251706] 
dist 110=[2.04027310715209381860e-05,.00056718843445543350] 
dist 111=[9.64091324252465063080e-05,.00059965011725427046] 
dist 112=[.00011094873285155559,.00024473112293267361] 
dist 113=[9.09060386903115959830e-05,.00024142195531690472] 
dist 114=[3.63459098313361574920e-05,.00023041412780582518] 
dist 115=[-5.27879696694125163630e-05,.00019181999679507010] 
dist 116=[-.00014234199782109969,.00017227002185666357] 
dist 117=[-.00019853501013922447,6.57214251616193847010e-05] 
dist 118=[-.00023407096123026808,4.00309092061170511040e-05] 
dist 119=[-.00024400385919836174,4.86566597348916809130e-06] 
dist 120=[-.00023896802044391348,-1.87294365511758155100e-06] 
dist 121=[-9.75320397390231779040e-05,-9.50317383243553308020e-07] 
dist 122=[-7.48651875214227168120e-05,4.96672324903193245900e-06] 
dist 123=[-6.89119873490769985450e-05,1.48368161374638806280e-05] 
dist 124=[-2.96888609104814079670e-05,3.10025325877148172600e-05] 
dist 125=[2.39011951127910912090e-06,5.02793786394500849440e-05] 
dist 126=[7.61375966919370042320e-06,6.25015241138241465110e-05] 
dist 127=[1.81458808582503442770e-05,6.58723174210365219840e-05] 
dist 128=[1.98066171416725901140e-05,2.44075584151708655420e-05] 
dist 129=[1.87250683486942492490e-05,2.37820795591258298660e-05] 
dist 130=[1.38435596018617041780e-05,2.29072946972871555980e-05] 
dist 131=[5.88568938905052563100e-06,1.74379339262114063520e-05] 
dist 132=[-2.10729404745168289230e-06,1.62048519485762916420e-05] 
dist 133=[-7.12526458533035799490e-06,1.37157237626978430260e-06] 
dist 134=[-1.03972487549123821830e-05,-8.86418017833096535520e-07] 
dist 135=[-1.36298504709172591350e-05,-4.89451296492357205600e-06] 
dist 136=[-1.44856022219076881400e-05,-5.58215257945038194680e-06] 
dist 137=[-1.05102858236054949840e-05,-5.44656653365457969280e-06] 
dist 138=[-8.32786286628906535780e-06,-4.70260519072404759220e-06] 
dist 139=[-7.43788882441068896600e-06,-1.36681359045939237450e-06] 
dist 140=[-3.74679667901074512980e-06,3.36957936387727596390e-06] 
dist 141=[1.18355814699172219280e-07,6.32559445615203887610e-06] 
dist 142=[1.19924208318329744490e-06,8.17768944879057211460e-06] 
dist 143=[2.56420358587593516180e-06,8.65807657642687639740e-06] 
dist 144=[2.52204369592760461880e-06,2.81958273302244547500e-06] 
dist 145=[2.16098769570924091260e-06,2.75755204207155655090e-06] 
dist 146=[1.57019835538108898640e-06,2.64421835363377717340e-06] 
dist 147=[6.11311098620467070410e-07,2.09322864317565049180e-06] 
dist 148=[-3.50610103962174848070e-07,1.87083224101651050940e-06] 
dist 149=[-9.53189801937376766910e-07,2.80318027833923326380e-07] 
dist 150=[-1.58430003673373835420e-06,-3.28051308296987902180e-08] 
dist 151=[-2.04862916392479114680e-06,-5.64839911329521518710e-07] 
dist 152=[-2.16907738815643680830e-06,-6.54712259236928214180e-07] 
dist 153=[-1.34386776525915358940e-06,-6.36056571602255716080e-07] 
dist 154=[-1.02028022814388344340e-06,-5.44569169387360411960e-07] 
dist 155=[-9.47615380443072267960e-07,-1.69868491667445939970e-07] 
dist 156=[-4.41363184857735785090e-07,3.12440883366046093970e-07] 
dist 157=[3.62466804105282637250e-08,6.13606364537711922800e-07] 
dist 158=[1.13589772624671538410e-07,8.02544421005561078390e-07] 
dist 159=[2.67423509393441465610e-07,8.52157604397012272040e-07] 
dist 160=[2.92129874280385998090e-07,3.67239058168598550040e-07] 
dist 161=[2.72667568303437575860e-07,3.56347083223853910650e-07] 
dist 162=[2.00719927604919906130e-07,3.43026938865963604570e-07] 
dist 163=[8.41650489053626411690e-08,2.59047878041541761910e-07] 
dist 164=[-3.26937228162346237810e-08,2.41816741252035163620e-07] 
dist 165=[-1.05847096404025792410e-07,1.70590850889254892220e-08] 
dist 166=[-1.51965170775016636060e-07,-1.59368845522256083970e-08] 
dist 167=[-1.97044303510308104880e-07,-7.44884863671987746040e-08] 
dist 168=[-2.09345518251125997850e-07,-8.41728526656629134650e-08] 
dist 169=[-1.53734749333706474350e-07,-8.17187929493405608140e-08] 
dist 170=[-1.21664158294926139930e-07,-7.03153236791409316340e-08] 
dist 171=[-1.08426306752672138060e-07,-1.82915808315093506760e-08] 
dist 172=[-5.60220186882911733410e-08,5.11322320546167383460e-08] 
dist 173=[2.43619358182629933180e-10,9.44391363332913231200e-08] 
dist 174=[1.83332222292326685890e-08,1.21565415760119276130e-07] 
dist 175=[3.53778485171543811680e-08,1.28600059644635362090e-07] 
dist 176=[3.42979173010525100530e-08,4.25824272611474572330e-08] 
dist 177=[2.94443356765842622030e-08,4.14767033046049262640e-08] 
dist 178=[2.15700978136024463330e-08,3.97644803457108628840e-08] 
dist 179=[8.13031486659358629090e-09,3.11787184273644266810e-08] 
dist 180=[-5.67766709824781577740e-09,2.80398702063931947240e-08] 
dist 181=[-1.43165614945993008750e-08,3.78560130526935811590e-09] 
dist 182=[-2.34066808649014878090e-08,-9.07716324290121472940e-10] 
dist 183=[-3.03050886729379876280e-08,-8.90866750547514863670e-09] 
dist 184=[-3.20941679358300473870e-08,-1.02247609735456654770e-08] 
dist 185=[-1.97687157168873304270e-08,-9.87347905338628860540e-09] 
dist 186=[-1.50467659031348412930e-08,-8.29644259628395351920e-09] 
dist 187=[-1.39119547512248803630e-08,-1.42263502521294485250e-09] 
dist 188=[-7.56916358201109885580e-09,5.45861605164806382070e-09] 
dist 189=[-5.12460911582499742620e-10,9.75283923450605003480e-09] 
dist 190=[1.12228756174145071430e-09,1.24450646872816172250e-08] 
dist 191=[2.72568984933421012450e-09,1.31492056197212829080e-08] 
dist 192=[2.64758192555527782460e-09,6.84400387298356709580e-09] 
dist 193=[2.27687882066510743850e-09,6.61803734404688118250e-09] 
dist 194=[1.67245536963304288970e-09,6.37205010691659106050e-09] 
dist 195=[6.21684402403506878740e-10,4.75762048458161772430e-09] 
dist 196=[-4.97146869602425574710e-10,4.48160909801375336250e-09] 
dist 197=[-1.60133366329895263290e-09,8.56841956647385624800e-10] 
dist 198=[-2.66364933248607207480e-09,4.71585016820910135230e-10] 
dist 199=[-3.41446139254556596240e-09,-7.47792683050725485170e-11] 
dist 200=[-3.61548869227997148990e-09,-1.72620325009259138040e-10] 
dist 201=[-1.87628951322009072530e-09,-1.34613956419382286990e-10] 
dist 202=[-2.01352736464176306620e-09,2.78827904352323732050e-10] 
dist 203=[-2.23048229165003583940e-09,1.61605690796552895630e-09] 
dist 204=[-2.71110940091027159360e-09,2.95395789332273418100e-09] 
dist 205=[-3.00992315027998617220e-09,3.78823709897037430090e-09] 
dist 206=[-3.19623320726536129670e-09,4.31069812791498616820e-09] 
dist 207=[-3.24291768926434285200e-09,4.44618568167023179620e-09] 
dist 208=[-3.13864680320146974830e-09,1.66639098909714823930e-09] 
dist 209=[-3.00775862267957916730e-09,1.62273978945695916650e-09] 
dist 210=[-2.31943874447411546720e-09,1.54889768588240783290e-09] 
dist 211=[-2.10928241946521704910e-09,1.24529785568511023590e-09] 
dist 212=[-1.09525946576754750150e-09,1.09557126887786777130e-09] 
dist 213=[-6.82224825958784979300e-10,1.57231561960245482670e-09] 
dist 214=[-1.07844567614221157360e-09,2.07426732383929101080e-09] 
dist 215=[-1.36570476862975737080e-09,2.20388547577318159220e-09] 
dist 216=[-1.44059667739279195690e-09,2.16234109132447335750e-09] 
dist 217=[-1.39090075285538774330e-09,2.04490006822498859770e-09] 
dist 218=[-1.33777357325039510730e-09,1.76989338950981563380e-09] 
dist 219=[-1.00128461900913003600e-09,1.63471876200965676220e-09] 
dist 220=[-1.54250413593178699340e-09,1.21928749164409239220e-09] 
dist 221=[-2.24640237243348103320e-09,9.58601529331126541590e-10] 
dist 222=[-2.68705306599979515890e-09,1.08592295918425414520e-09] 
dist 223=[-2.80115461594454969850e-09,1.32704026462145022600e-09] 
dist 224=[-2.70622949395340165230e-09,1.38968461839112426650e-09] 
dist 225=[-2.59984093065248655050e-09,1.36057610306235159250e-09] 
dist 226=[-1.98680021097251924400e-09,1.29009828532842016810e-09] 
dist 227=[-1.82432628852712637780e-09,1.09383205317741894020e-09] 
dist 228=[-1.15496533249274077280e-09,9.97239467142348762850e-10] 
dist 229=[-1.21298488168453947650e-09,1.61471778371093992100e-09] 
dist 230=[-1.55607137847650174060e-09,2.06477036505149321250e-09] 
dist 231=[-1.77776403314310496280e-09,2.18141858540340334050e-09] 
dist 232=[-1.83525448328006626510e-09,2.15282102345496640570e-09] 
dist 233=[-1.64593016322145228400e-09,2.04274196369579523550e-09] 
dist 234=[-1.58296103307008379070e-09,1.86696796287622336780e-09] 
dist 235=[-1.18403213413433424430e-09,1.84145550524463703280e-09] 
dist 236=[-2.27930247948487195330e-09,1.93547415600903224810e-09] 
dist 237=[-3.06417268310479147750e-09,1.99408497413496898430e-09] 
dist 238=[-3.55559232685724810900e-09,2.03078348080298054000e-09] 
dist 239=[-3.68300634872266825840e-09,2.04029961145082309690e-09] 
dist 240=[-3.56408476600798842240e-09,9.26915031330644351490e-10] 
dist 241=[-3.41860573782737959590e-09,9.22104331310468417390e-10] 
dist 242=[-2.62040503529999624640e-09,9.03499085379088784090e-10] 
dist 243=[-2.39903754544445477790e-09,8.73774934518859405640e-10] 
dist 244=[-4.27906438376868537910e-10,9.07602550406629203000e-10] 
dist 245=[-9.72346625680914029480e-10,1.70764464474610141800e-09] 
dist 246=[-1.35244703552674776710e-09,2.25121865461891072930e-09] 
dist 247=[-1.59043914938677203970e-09,2.39668661698951955630e-09] 
dist 248=[-1.65215598183460299970e-09,2.36244433007532174050e-09] 
dist 249=[-1.59297969150145125760e-09,2.23040891041199861670e-09] 
dist 250=[-1.53356415517849671260e-09,2.01953482944686148160e-09] 
dist 251=[-1.13629432361915709870e-09,1.88172902542112728580e-09] 
dist 252=[-2.03063779905713175660e-09,1.67687483139962562140e-09] 
dist 253=[-2.77533907590852550090e-09,1.67414356507128199940e-09] 
dist 254=[-3.24161491384603012430e-09,1.67243355505199567500e-09] 

8 phat 5 dirichlet min maxes function [0, 0, 1, 1, 1, 1, 2, 0, 2] 
dist 0=[344.38618763840270598   ,344.38618763840270598   ] 
dist 1=[302.91482964648068986   ,356.71486202140488119   ] 
dist 2=[251.11647188801658940   ,362.52356903363919561   ] 
dist 3=[205.62088580647128715   ,364.08640696667149713   ] 
dist 4=[160.10436330350587848   ,355.34308630502557897   ] 
dist 5=[107.16562916367350591   ,268.79595508971292922   ] 
dist 6=[58.197438941196900738  ,248.14068336301656297   ] 
dist 7=[27.829697290542561123  ,175.13323892523927034   ] 
dist 8=[-17.620928826996218356  ,164.41570479595759802   ] 
dist 9=[-40.720304486194681678  ,12.051035042476476226  ] 
dist 10=[-51.441514091329779229  ,6.9910744685432188181 ] 
dist 11=[-69.222168503993490877  ,5.5623532618007095626 ] 
dist 12=[-79.353528237584713498  ,3.8545915246913788279 ] 
dist 13=[-79.969070756388939828  ,2.6264517703987200116 ] 
dist 14=[-77.430186066339408489  ,6.7324192041778137308 ] 
dist 15=[-62.498394562437053185  ,18.001834529770903368  ] 
dist 16=[-56.479575928444523413  ,26.249324532938004205  ] 
dist 17=[-11.451671076249393878  ,28.141658269464472819  ] 
dist 18=[-1.8706909591081413431 ,39.944787493454949359  ] 
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dist 32=[-6.2899783487170174628 ,3.4917192539382618406 ] 
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dist 40=[-1.8759188603310169036 ,1.4623171079732473847 ] 
dist 41=[-1.8437267882045217128 ,.3349587130215324414 ] 
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dist 46=[-.98760609964144070916,1.3694239131170910344 ] 
dist 47=[-.78945788583232608931,1.4558559031141351674 ] 
dist 48=[-.70779340168915936998,.44377566064464372335] 
dist 49=[-.11517631452127579235,.43966639172422540048] 
dist 50=[-.00414519609054804406,.57694328789095636789] 
dist 51=[.00831618943172100503,.7500022171888939923 ] 
dist 52=[-.05223822465157253387,.79491377715719570154] 
dist 53=[-.16775512406640382711,.23922869056312524128] 
dist 54=[-.24488319334377810573,.23201601290924587245] 
dist 55=[-.27487655580495002617,.17584936674303465052] 
dist 56=[-.2771264025440154277 ,.16696156867865263714] 
dist 57=[-.2692252630668617848 ,.05346152788792420503] 
dist 58=[-.21288020052361109546,.04005586145186252984] 
dist 59=[-.19588399568005690812,.04325984829491509771] 
dist 60=[-.13413837471107780693,.07864838142819701010] 
dist 61=[-.13103880434489806117,.13579923363725886368] 
dist 62=[-.12640800220321382501,.17446096758819317945] 
dist 63=[-.09599191981291028136,.18400886061127554373] 
dist 64=[-.08967483615994369606,-.00678220363951840296] 
dist 65=[-.00731086797448837750,.02707598907465826029] 
dist 66=[.00212414351072744665,.05468058980473839912] 
dist 67=[.00359343640283056395,.07204295624089911413] 
dist 68=[.00620002803434235296,.07668221963726221784] 
dist 69=[.00629332597540677155,.03000526665760329510] 
dist 70=[.00570675021135354693,.02904748302924885517] 
dist 71=[.00456127992895160810,.02184380336987383149] 
dist 72=[.00293075185703440897,.02076946140470088124] 
dist 73=[-.00276127949166247773,.00360045531757345309] 
dist 74=[-.00970698067940428036,.00031626013955336929] 
dist 75=[-.01411869694739159389,-.00032073882056945142] 
dist 76=[-.01539830312845696618,-.00129438196585282792] 
dist 77=[-.01509779216664584925,-.00137333386666488878] 
dist 78=[-.01448792397067898955,-.00123275705621776487] 
dist 79=[-.01149990134632911966,-.00098147629427789053] 
dist 80=[-.01027758963779759363,-.00063249908910718893] 
dist 81=[-.00159298443281030945,.00460358766305866873] 
dist 82=[9.71027931393850787250e-06,.00867201854761057080] 
dist 83=[.00015051177801823558,.01122136253725989308] 
dist 84=[.00036903281500975586,.01188245487686771220] 
dist 85=[.00037988387546980238,.00348066682187564606] 
dist 86=[.00032938964012908226,.00336035673384329318] 
dist 87=[.00022375670194608299,.00254536942062450022] 
dist 88=[7.09306909683898768950e-05,.00239049250732126023] 
dist 89=[-.00051698278498229796,.00054832259623061394] 
dist 90=[-.00135194317643720117,.00028850961437103059] 
dist 91=[-.00187971271113677450,.00028386783220623310] 
dist 92=[-.00202720906726597376,.00028294105059574534] 
dist 93=[-.00197170334551174893,.00028634445359778481] 
dist 94=[-.00189690786094857110,.00031338758760063477] 
dist 95=[-.00144817864774400688,.00040377262109891476] 
dist 96=[-.00133952599673175216,.00054557381973255398] 
dist 97=[-.00017027321773368708,.00077095033752072956] 
dist 98=[6.34422382751103328010e-06,.00099573340410073508] 
dist 99=[2.22687063705085303890e-05,.00117760068426175769] 
dist 100=[4.88923392106079940550e-05,.00124325300742933383] 
dist 101=[5.08063038449083435620e-05,.00043744882115315415] 
dist 102=[4.51664735925359750940e-05,.00042243253506387866] 
dist 103=[3.17284471025392424590e-05,.00031551829809920113] 
dist 104=[1.17403803148005689210e-05,.00029952745711239730] 
dist 105=[-4.77211970285530796120e-05,5.73680050538592635770e-05] 
dist 106=[-.00014857788148400177,3.71761259810192293180e-05] 
dist 107=[-.00021224153923671247,3.57031020868451965860e-05] 
dist 108=[-.00022985435495506386,3.49495381944007293330e-05] 
dist 109=[-.00022444562116473754,3.50592736161243514530e-05] 
dist 110=[-.00021495253069477257,3.89282615721976543190e-05] 
dist 111=[-.00017073868860198911,5.26852206175884219730e-05] 
dist 112=[-.00015178424254814026,7.44419578254472616700e-05] 
dist 113=[-2.80360697902081307980e-05,.00010916421111664365] 
dist 114=[-1.53651973521674569270e-05,.00014382897244056326] 
dist 115=[-1.77522831801470647050e-05,.00017264463570802579] 
dist 116=[-1.92960523951590934170e-05,.00018206072776501396] 
dist 117=[-1.97865159007022908470e-05,5.14376961944721420700e-05] 
dist 118=[-2.00911357022384063670e-05,4.96255503434695889890e-05] 
dist 119=[-2.09229191906404820670e-05,3.70498826991486584630e-05] 
dist 120=[-2.21923542274599475350e-05,3.50875664693543662990e-05] 
dist 121=[-2.41881004445420183230e-05,1.74343023177258953870e-05] 
dist 122=[-2.61858721218909590560e-05,9.46878519535242751960e-06] 
dist 123=[-2.74636182000549645600e-05,7.13084129453963425200e-06] 
dist 124=[-2.92430192630594863390e-05,4.89909589458008408720e-06] 
dist 125=[-2.83401996395164896810e-05,4.53631072731969369030e-06] 
dist 126=[-2.72681403085031523660e-05,4.47158935467074851560e-06] 
dist 127=[-2.05792184431148625650e-05,4.33774096902366563000e-06] 
dist 128=[-1.91990696377448212770e-05,3.27950579893857250480e-06] 
dist 129=[-1.34789625181852982710e-06,6.06884353699923922930e-06] 
dist 130=[-3.96950726180319977530e-07,1.20053554073526714510e-05] 
dist 131=[-1.44029833245051562410e-06,1.57278562059935024080e-05] 
dist 132=[-2.10702462545287706390e-06,1.67026979316948812170e-05] 
dist 133=[-2.30828453769720994180e-06,6.46756311639581221540e-06] 
dist 134=[-2.27237160719838197570e-06,6.23765625117234062370e-06] 
dist 135=[-2.18338665179151237270e-06,4.64143845550133050380e-06] 
dist 136=[-1.73919091369323532870e-06,4.40356856030620205070e-06] 
dist 137=[-1.55515130394964966370e-06,-2.92901719486212839430e-07] 
dist 138=[-2.15752790353472130690e-06,6.91503619523414880600e-07] 
dist 139=[-3.09367386149361695640e-06,1.30645699124433676070e-06] 
dist 140=[-3.34589360036389084220e-06,1.69196649915489920890e-06] 
dist 141=[-3.25799656436736342480e-06,1.79197899861784413880e-06] 
dist 142=[-3.11933821638098549180e-06,5.26282641387792724490e-07] 
dist 143=[-2.46154299823255514110e-06,5.08931982308186494050e-07] 
dist 144=[-2.19675774691325819870e-06,3.87084400854247372360e-07] 
dist 145=[-3.22211481714710492300e-07,1.00839239743002640830e-06] 
dist 146=[-6.91724614646750426400e-08,1.88458995505188283290e-06] 
dist 147=[-1.95174403273829894830e-07,2.43334947721305578390e-06] 
dist 148=[-2.75172938050398398290e-07,2.57566166279052117730e-06] 
dist 149=[-2.98217305105074629260e-07,7.51199216247045108680e-07] 
dist 150=[-2.90739508766409496730e-07,7.23298861508870331560e-07] 
dist 151=[-2.80070402238345251060e-07,5.43795829442810840020e-07] 
dist 152=[-2.13423741486263605710e-07,5.09887602936380171940e-07] 
dist 153=[-1.98217725736895972590e-07,-3.68364064051107131770e-08] 
dist 154=[-2.85893818405373507930e-07,6.43615102862345187150e-08] 
dist 155=[-3.97804373128843064660e-07,1.27634243070944984370e-07] 
dist 156=[-4.27594979084967276090e-07,1.67393761911223152850e-07] 
dist 157=[-4.14033347909575063420e-07,1.77932435035314251580e-07] 
dist 158=[-3.97993815638192803320e-07,6.72773104856173484650e-08] 
dist 159=[-3.01438928039038919850e-07,6.50423131306903498140e-08] 
dist 160=[-2.79860203269950126280e-07,4.89001248661590258540e-08] 
dist 161=[-2.21015922998546957780e-08,9.38252313607143171870e-08] 
dist 162=[-7.40150406738038662840e-09,1.82968759088708160220e-07] 
dist 163=[-2.31430498810932029520e-08,2.38829159885316217780e-07] 
dist 164=[-3.31155797088682604910e-08,2.53391157285832072640e-07] 
dist 165=[-3.59470607749005110750e-08,9.44463248505858324110e-08] 
dist 166=[-3.51395291313112459190e-08,9.10084669524116099900e-08] 
dist 167=[-3.37197628124882936510e-08,6.76984948024306404280e-08] 
dist 168=[-2.65411363240077928010e-08,6.40942879318064640930e-08] 
dist 169=[-2.38619158475042535690e-08,-3.74372485393953384690e-09] 
dist 170=[-3.33300095874151627690e-08,1.06328085535767329530e-08] 
dist 171=[-4.69626739112340190740e-08,1.96060521146776874220e-08] 
dist 172=[-5.05806142180743851270e-08,2.52285801080328617290e-08] 
dist 173=[-4.91292138294152309850e-08,2.66871275700718471810e-08] 
dist 174=[-4.70690497725586680760e-08,9.19473668851917881020e-09] 
dist 175=[-3.67325488385724272520e-08,8.84795486593508576400e-09] 
dist 176=[-3.30989807305092043600e-08,6.80552570146923865230e-09] 
dist 177=[-5.45100346761716746160e-09,1.48826598910548933890e-08] 
dist 178=[-1.86076718500848303540e-09,2.74946718251366546660e-08] 
dist 179=[-4.16193221912265937880e-09,3.54206189246829096990e-08] 
dist 180=[-5.61228282208860226300e-09,3.74760036246159190480e-08] 
dist 181=[-6.00831542519869531140e-09,1.35874392168781948780e-08] 
dist 182=[-5.81791215371780309330e-09,1.30257685630838508910e-08] 
dist 183=[-5.60539173182999433310e-09,1.01113696102847576720e-08] 
dist 184=[-4.18457440630100937450e-09,9.16155032548072207650e-09] 
dist 185=[-3.94858184830377468030e-09,6.15047174788227386500e-10] 
dist 186=[-7.01505211409763829130e-09,1.38208703167052348110e-09] 
dist 187=[-9.21953368078951965830e-09,2.36502793509340315750e-09] 
dist 188=[-9.79791613320386364160e-09,2.98088133980440745240e-09] 
dist 189=[-9.46990917482794842330e-09,3.14078785568760827460e-09] 
dist 190=[-9.10407545218857734730e-09,1.15450022733773192310e-09] 
dist 191=[-6.85398843968240668340e-09,1.11178147425524104300e-09] 
dist 192=[-6.39354389788606201760e-09,8.43981270491053809080e-10] 
dist 193=[-1.15979495952189207520e-09,2.45811754850443541280e-09] 
dist 194=[-6.88888698342922547720e-10,4.20319766224568705770e-09] 
dist 195=[-4.69465345610848408120e-10,5.29611635064251825340e-09] 
dist 196=[-6.45722494484445099970e-10,5.57993276261104044710e-09] 
dist 197=[-6.93619604994857436670e-10,1.13278478673932499740e-09] 
dist 198=[-7.05288952369017740610e-10,1.08482304715391260030e-09] 
dist 199=[-7.41878778084331242200e-10,8.51292710047380955850e-10] 
dist 200=[-7.98835876095124521880e-10,7.63328783183471343900e-10] 
dist 201=[-8.89068329888138309180e-10,5.36900259675709589810e-10] 
dist 202=[-9.79052536971152096120e-10,1.12126589253995135890e-09] 
dist 203=[-1.03504560769194537530e-09,1.48583514945631498100e-09] 
dist 204=[-1.07006813779925887730e-09,1.71438934024008986530e-09] 
dist 205=[-1.07914674355248152910e-09,1.77425122928291790390e-09] 
dist 206=[-9.60133793896887816340e-10,1.72956853066104263780e-09] 
dist 207=[-1.07119107931986391930e-09,1.64775728619174281050e-09] 
dist 208=[-1.24896077731712976640e-09,1.34354442549250907780e-09] 
dist 209=[-1.69906888665330415510e-09,1.75976768070581607070e-09] 
dist 210=[-1.97955494729190427150e-09,2.17140738736972529030e-09] 
dist 211=[-2.15507693212716158030e-09,2.42915793038205288050e-09] 
dist 212=[-2.20038788637910256830e-09,2.49599741913425953510e-09] 
dist 213=[-2.12953300020277122900e-09,-1.21399799165411904800e-10] 
dist 214=[-2.04214018893095463650e-09,-8.56172724196151880220e-11] 
dist 215=[-1.56795363218990378930e-09,5.30703651113333404610e-11] 
dist 216=[-1.43291673517811243010e-09,2.74694013190760438670e-10] 
dist 217=[-1.07733072759847406020e-09,6.30319168552828922850e-10] 
dist 218=[-1.03079408840599831170e-09,1.11167745997494426040e-09] 
dist 219=[-1.15948531961164562890e-09,1.41174430048355728070e-09] 
dist 220=[-1.24005985333743922070e-09,1.59961896429813909110e-09] 
dist 221=[-1.26095490192110701500e-09,1.64831863258175573060e-09] 
dist 222=[-4.51866198519975231140e-10,1.35009606297268624630e-09] 
dist 223=[-4.41052602662801760710e-10,1.22471183589264028690e-09] 
dist 224=[-6.48180789818515160560e-10,1.14104587591906659130e-09] 
dist 225=[-1.30976338135540643090e-09,1.15252129620041297040e-09] 
dist 226=[-1.72218583587056788920e-09,1.23286694578297777950e-09] 
dist 227=[-1.98041580434575740190e-09,1.28317205708584726680e-09] 
dist 228=[-2.04738366722590514490e-09,1.29621132363911342320e-09] 
dist 229=[-1.06311014217239600970e-09,1.08615251200497650980e-09] 
dist 230=[-1.04076384492651012330e-09,1.05707190380351537480e-09] 
dist 231=[-9.86824181945779221850e-10,1.00815721759955223310e-09] 
dist 232=[-8.36677836785729670910e-10,8.13079567734796856730e-10] 
dist 233=[-7.62800152622678688350e-10,7.17104618987797508790e-10] 
dist 234=[-7.93983350284515544370e-10,5.97152076727863929760e-10] 
dist 235=[-1.00892799800960767870e-09,9.29425932111628626090e-10] 
dist 236=[-1.20064755517580130190e-09,1.13747339205359168810e-09] 
dist 237=[-1.25035634817101226480e-09,1.19142688840455788920e-09] 
dist 238=[-1.22198639111529862410e-09,1.16523045344034138620e-09] 
dist 239=[-1.16059327240300064150e-09,1.10590974903874667370e-09] 
dist 240=[-9.70188411377124377670e-10,9.30018461183455248560e-10] 
dist 241=[-8.76509274799753777570e-10,8.43477431861515595510e-10] 
dist 242=[-7.27585407498558693260e-10,7.14831781226025213620e-10] 
dist 243=[-9.99696565947851785570e-10,1.01718620777008757800e-09] 
dist 244=[-1.22847190002417387610e-09,1.25393515304528917610e-09] 
dist 245=[-1.28779642510576858870e-09,1.31532383273758715940e-09] 
dist 246=[-1.24560096698961131490e-09,1.28540339008922666850e-09] 
dist 247=[-1.19535582626656036590e-09,1.22090231560577468360e-09] 
dist 248=[-9.12092798028956742100e-10,1.02006455206111419080e-09] 
dist 249=[-8.38857223088552499030e-10,9.21251463246636353330e-10] 
dist 250=[-8.27535862430015438570e-10,6.77528964956281477350e-10] 
dist 251=[-1.13660310007828847190e-09,7.28911748309354754400e-10] 
dist 252=[-1.33011767473330853880e-09,7.94955939058796396250e-10] 

8 phat 5 dirichlet min maxes function [2, 1, 2, 1, 0, 1, 1, 2] 
dist 0=[374.21747980024783477   ,374.21747980024783477   ] 
dist 1=[352.55292761187469238   ,378.64098565354437684   ] 
dist 2=[302.62492604203383799   ,374.21747980024783477   ] 
dist 3=[245.73767673886390260   ,345.42717679108655647   ] 
dist 4=[196.56372878899053211   ,292.95396469692600432   ] 
dist 5=[147.71172775992209253   ,225.95371809576871845   ] 
dist 6=[91.149374199937396061  ,213.05572208819737548   ] 
dist 7=[30.914738079071114781  ,123.43127718256164925   ] 
dist 8=[-23.615076255083788780  ,79.418575745627632912  ] 
dist 9=[-61.946908789310834903  ,1.9805042067238442742 ] 
dist 10=[-83.369332754148909324  ,2.5970100547460853754 ] 
dist 11=[-93.277010108128079859  ,8.6113514051350343252 ] 
dist 12=[-93.916777946867144343  ,17.142928343152468424  ] 
dist 13=[-77.862385403998540440  ,27.234943517974743867  ] 
dist 14=[-75.256235759412298585  ,39.829493524775953976  ] 
dist 15=[-2.7590869206919306367 ,49.678531342617036282  ] 
dist 16=[9.0102039431313148459 ,51.351519625007080459  ] 
dist 17=[32.296281006347305601  ,46.098557719392283273  ] 
dist 18=[20.136245837578257758  ,44.311373719005691896  ] 
dist 19=[-.49494859488815834246,44.847781945881536036  ] 
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dist 42=[-3.4253404229187911115 ,-.43931535956344344566] 
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dist 48=[-.08340034650497311587,1.2227557532387070739 ] 
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dist 51=[-.06110560719757827363,.67731664696294191501] 
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dist 58=[-.52904953127547175499,-.05282545967162251454] 
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dist 60=[-.15293588358195143571,.15488339466106806975] 
dist 61=[-.11803516354941810462,.20617244970283520859] 
dist 62=[-.11128186650772067874,.21982647475885954806] 
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dist 70=[-.05373603503715697669,.05995153632927295946] 
dist 71=[-.07010386854877426995,.00572634455638592620] 
dist 72=[-.07435355627855630931,-.00257113422568383912] 
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dist 75=[-.02002921033348367137,.01291455844582957192] 
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dist 77=[-.01471134590654870191,.03207426879726267471] 
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dist 80=[.00419783619382626196,.01257608475916089138] 
dist 81=[.00619312806442176266,.01243131345657328557] 
dist 82=[.00226633529419777348,.01202907463930655748] 
dist 83=[-.00169912968372534433,.01015247190747083734] 
dist 84=[-.00420803783372845802,.00975701020768506201] 
dist 85=[-.00581591774807867863,.00776849314817157822] 
dist 86=[-.00631018540929004823,.00695256701023969598] 
dist 87=[-.00706627843137664986,.00109191664126481100] 
dist 88=[-.00753521598373584704,-6.35921757714069474960e-05] 
dist 89=[-.00751361952389202682,-.00199579157637605695] 
dist 90=[-.00795883557050280892,-9.27101746547992000000e-05] 
dist 91=[-.00237588067795842360,.00182269575069321015] 
dist 92=[-.00229994069784218074,.00302614152943756698] 
dist 93=[-.00173368906805055888,.00378799866792042061] 
dist 94=[-.00164443285249201783,.00400177358054711300] 
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dist 96=[.00040170269948753558,.00153266494457605106] 
dist 97=[.00078421087179190398,.00151739889919297956] 
dist 98=[.00028922616275386048,.00145929812978356802] 
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dist 100=[-.00052435739902743199,.00126591390462235563] 
dist 101=[-.00072536798173770735,.00095934903913471608] 
dist 102=[-.00091974042166870496,.00089572000287560245] 
dist 103=[-.00117042825860725925,6.91637389956214823870e-05] 
dist 104=[-.00123613600633567504,-5.27771242252500815400e-05] 
dist 105=[-.00072606928010892745,-.00017712955848881111] 
dist 106=[-.00077218240610269476,8.48445328975432713480e-05] 
dist 107=[-.00030090542155687947,.00038170723439677722] 
dist 108=[-.00029095186860070264,.00056787761651488076] 
dist 109=[-.00021803737539233398,.00068546027987892128] 
dist 110=[-.00020716753062754278,.00071796294222885052] 
dist 111=[2.89776397538166347510e-05,.00021540845291774389] 
dist 112=[4.85127720666438129870e-05,.00023105190447727087] 
dist 113=[1.42213427697067731410e-05,.00022604176575354180] 
dist 114=[-4.19878521100676174240e-05,.00021718072651672512] 
dist 115=[-9.85287262923463975530e-05,.00016964600577916397] 
dist 116=[-.00013410911974603436,.00015365915199071112] 
dist 117=[-.00015672967711011619,.00011550004886127795] 
dist 118=[-.00016332077878804232,.00010316585533313720] 
dist 119=[-.00016186918607929042,1.56668317332132332020e-05] 
dist 120=[-.00015348637137485032,-1.63436918318691347330e-06] 
dist 121=[-.00011332968102008848,-3.10159822500585963510e-05] 
dist 122=[-.00011999005039112683,-3.59907678930394111410e-05] 
dist 123=[-3.50716997878329311030e-05,-2.80262699750417740240e-05] 
dist 124=[-3.38327920204473747520e-05,-1.20346937914916878360e-05] 
dist 125=[-2.55711240294865190920e-05,4.05492521178727833830e-06] 
dist 126=[-2.40022548951610382100e-05,1.41833901458609932860e-05] 
dist 127=[2.14964005597787679160e-06,2.06260006139253339130e-05] 
dist 128=[6.40571392167635235720e-06,2.25098838534355629870e-05] 
dist 129=[1.49095422823121181040e-05,2.20879009111655630720e-05] 
dist 130=[1.62609777080693361170e-05,2.12007210526423040700e-05] 
dist 131=[1.23319413682476843530e-05,1.93469698008217022860e-05] 
dist 132=[2.80095260278690110100e-06,1.86153433417665050540e-05] 
dist 133=[-6.75409962386636215390e-06,1.41328537906944448660e-05] 
dist 134=[-1.27201671082005187350e-05,1.31271239055600407660e-05] 
dist 135=[-1.64591881455973942180e-05,1.05445470342408096020e-06] 
dist 136=[-1.74290940205919333760e-05,-7.79760458777418726640e-07] 
dist 137=[-1.11095263854011745940e-05,-4.01359308293925630540e-06] 
dist 138=[-1.17973688535686740300e-05,-4.37356826129212679140e-06] 
dist 139=[-4.42023666725254556790e-06,-3.18664822349147834640e-06] 
dist 140=[-4.26629268373560351520e-06,-1.25161083165610965800e-06] 
dist 141=[-3.18162264683120332800e-06,6.91860688997279027120e-07] 
dist 142=[-3.01936453045497259310e-06,1.91154780822124747400e-06] 
dist 143=[4.42459143899033149840e-07,2.68351148763813504580e-06] 
dist 144=[9.86693996340127917710e-07,2.90094421349021457480e-06] 
dist 145=[2.09436236252508753350e-06,2.82231579886245541460e-06] 
dist 146=[1.92418388134824719850e-06,2.71716110006856170360e-06] 
dist 147=[1.32333605526612695690e-06,2.23703821000409610390e-06] 
dist 148=[3.49548055745161514080e-07,2.14294991645582151660e-06] 
dist 149=[-6.26567503387203930110e-07,1.69209967504312643990e-06] 
dist 150=[-1.23645796240415417350e-06,1.51135789643971678950e-06] 
dist 151=[-1.61940464202906761840e-06,2.27065110329697271530e-07] 
dist 152=[-1.72041826118998800010e-06,-2.52416885917291668530e-08] 
dist 153=[-1.66450981392665142580e-06,-4.50749037009290788550e-07] 
dist 154=[-1.76179365623175788070e-06,-5.21155177780236432980e-07] 
dist 155=[-5.22693405017746422040e-07,-4.10240466939741120660e-07] 
dist 156=[-5.04160005527173335850e-07,-1.73195668482340437490e-07] 
dist 157=[-3.75780735137875643100e-07,6.47688658175220390420e-08] 
dist 158=[-3.56007256127864728400e-07,2.13958503690077650270e-07] 
dist 159=[8.22684622930374359350e-09,3.08239988954227406320e-07] 
dist 160=[6.85491973882091550650e-08,3.34527746466966069190e-07] 
dist 161=[1.83619981161152689890e-07,3.26725539851817880850e-07] 
dist 162=[2.02113425162465039080e-07,3.20994003161999392040e-07] 
dist 163=[1.80439806071904286590e-07,3.11312634611481730890e-07] 
dist 164=[4.01819473640413263880e-08,2.99007339586014788840e-07] 
dist 165=[-1.00527012763953232560e-07,2.28654431904166552780e-07] 
dist 166=[-1.88329089753685112010e-07,2.10348723635652647540e-07] 
dist 167=[-2.43333925296742238150e-07,5.47226969242739225800e-08] 
dist 168=[-2.57598766039100759120e-07,3.37950862160182171500e-08] 
dist 169=[-1.92915784166084223590e-07,5.45382769286540799580e-09] 
dist 170=[-2.02849700916535039080e-07,0                     ] 
dist 171=[-6.63501797969433685460e-08,-4.60833010365638793370e-08] 
dist 172=[-6.39682770465952842410e-08,-1.72825006458114493330e-08] 
dist 173=[-4.75984091997261817950e-08,1.15914527052309806700e-08] 
dist 174=[-4.51151690505832600940e-08,2.98437650910041283110e-08] 
dist 175=[6.75756652835713744970e-09,4.14078771997376228630e-08] 
dist 176=[1.49124850789767817840e-08,4.45557177513128010170e-08] 
dist 177=[3.15345366797328763920e-08,4.31894077986840372230e-08] 
dist 178=[2.68557648743192717400e-08,4.15684870995124401210e-08] 
dist 179=[1.82389427444686100420e-08,3.36229801748519997270e-08] 
dist 180=[4.32918043028084385580e-09,3.22315428361164999770e-08] 
dist 181=[-9.60110661282692233310e-09,2.51060590602627553280e-08] 
dist 182=[-1.82976659937475839840e-08,2.26856744329744593520e-08] 
dist 183=[-2.37524454129350479500e-08,2.08075398534690965690e-09] 
dist 184=[-2.51834662260012107070e-08,-1.74261734191558180110e-09] 
dist 185=[-2.32429679110065129330e-08,-8.08329319499957756400e-09] 
dist 186=[-2.46547632160209462290e-08,-6.93284289422510051240e-09] 
dist 187=[-9.67084557181853553900e-09,-5.06141489566244671640e-09] 
dist 188=[-9.30642596132400428840e-09,-2.03236126586040369250e-09] 
dist 189=[-6.99717881024406059090e-09,1.34438826671005276670e-09] 
dist 190=[-6.55088498786711611530e-09,3.54590721798439399070e-09] 
dist 191=[3.87393219557346988420e-10,4.93204730829371088300e-09] 
dist 192=[1.49383648733712207100e-09,5.30779594536854553410e-09] 
dist 193=[3.63545752576206044790e-09,5.19290432537232013710e-09] 
dist 194=[2.98572038494396270340e-09,5.56325695745842103650e-09] 
dist 195=[1.73727853799161082520e-09,5.42312151745006245620e-09] 
dist 196=[-2.73924313480705214560e-10,5.17440359729452486260e-09] 
dist 197=[-2.33849351089562102240e-09,4.20545161173957607280e-09] 
dist 198=[-3.66164022985352918330e-09,3.72873092896824674630e-09] 
dist 199=[-4.49039084037498764090e-09,1.64904309326233923720e-09] 
dist 200=[-4.70537856347396100840e-09,1.20953952855252457790e-09] 
dist 201=[-4.86455644786081319230e-09,7.32102923324458340380e-10] 
dist 202=[-5.09255647656414648220e-09,6.40565674316230285980e-10] 
dist 203=[-9.38976593926507108040e-10,5.88391282208604143440e-10] 
dist 204=[-8.91007822539905574860e-10,6.24161402766563612960e-10] 
dist 205=[-8.10191928962110334670e-10,7.05107803150166081380e-10] 
dist 206=[-1.06228819954385774050e-09,7.56186573165471046460e-10] 
dist 207=[-1.21943162702839620460e-09,7.88786412298972791470e-10] 
dist 208=[-1.25869715647612722410e-09,8.35588627918445481600e-10] 
dist 209=[-1.22088482881919637370e-09,1.02364994192217297240e-09] 
dist 210=[-1.16619710335033530380e-09,1.07301427113477450540e-09] 
dist 211=[-9.22985108696468627140e-10,1.06559546392738518450e-09] 
dist 212=[-8.17138445849756631010e-10,1.03467903494783044160e-09] 
dist 213=[-1.13549596599605637160e-09,9.84862873396989998520e-10] 
dist 214=[-1.50986332365297785990e-09,9.82333612875855829220e-10] 
dist 215=[-1.74436995080620199370e-09,1.00127901305349553050e-09] 
dist 216=[-1.80537881591602571200e-09,1.00638302453529569890e-09] 
dist 217=[-1.37813409611176056600e-10,9.20118751818525647050e-10] 
dist 218=[-1.47559456942103361570e-10,8.80536920264590451050e-10] 
dist 219=[-1.49772005929792846250e-10,8.37059914266861325100e-10] 
dist 220=[-5.57360902057872131510e-10,9.25698322511929595300e-10] 
dist 221=[-1.16990329955598957190e-09,1.01440342669699786530e-09] 
dist 222=[-1.55167644994205919120e-09,1.06976708997427795490e-09] 
dist 223=[-1.79064488773008334230e-09,1.10450090063973371210e-09] 
dist 224=[-1.85246474813385919060e-09,1.11365410992874426310e-09] 
dist 225=[-1.80586668906931491140e-09,1.08927948746050214380e-09] 
dist 226=[-1.71927769689029694360e-09,1.03392277369994731400e-09] 
dist 227=[-1.40751825013917056050e-09,8.69250975043900279670e-10] 
dist 228=[-1.25416548166916791900e-09,7.88196275584246720220e-10] 
dist 229=[-6.32565490022089541370e-10,8.23004076607224347070e-10] 
dist 230=[-9.32720321276084613560e-10,1.34404855404108622630e-09] 
dist 231=[-1.14644719466937570230e-09,1.67772654683365495380e-09] 
dist 232=[-1.20190853920874211710e-09,1.76421185358944330150e-09] 
dist 233=[-1.18855573351495936870e-09,1.72726046608656586390e-09] 
dist 234=[-1.21202243541581308340e-09,1.63751252169418126630e-09] 
dist 235=[-9.73674755303791395740e-10,1.38974698058230014790e-09] 
dist 236=[-9.03792096775138962340e-10,1.26785443646787185730e-09] 
dist 237=[-9.97558712365681635200e-10,8.02199895502973995750e-10] 
dist 238=[-1.55023593488062389390e-09,1.20329986910489086830e-09] 
dist 239=[-1.89627510831883192990e-09,1.45444435006607911710e-09] 
dist 240=[-1.98599351326121652730e-09,1.51958018812271954870e-09] 
dist 241=[-1.92959205116279826290e-09,1.49083355595076370170e-09] 
dist 242=[-1.84341480020755438930e-09,1.41051665493866579470e-09] 
dist 243=[-1.46488497605827456140e-09,1.21745630261332990760e-09] 
dist 244=[-1.29363134927243240570e-09,1.12246641858132274480e-09] 
dist 245=[-1.29448077014301349730e-09,1.24808029274417185170e-09] 
dist 246=[-1.59793739882139289890e-09,1.45345654990563963610e-09] 
dist 247=[-1.78793962460137174920e-09,1.58204729195999862560e-09] 

8 phat 5 dirichlet min maxes function [0, 1, 2, 1, 2, 2, 2, 0, 1] 
dist 0=[441.18180484306912316   ,441.18180484306912316   ] 
dist 1=[420.72529315208219538   ,442.28310484332614555   ] 
dist 2=[371.16567634088139765   ,441.18180484306912316   ] 
dist 3=[279.02209021160742255   ,388.81265810664695568   ] 
dist 4=[181.03703632059198080   ,370.18215825431414405   ] 
dist 5=[108.36676170461278187   ,285.58731647308917645   ] 
dist 6=[47.499358046484690328  ,272.89045006908935300   ] 
dist 7=[-5.8165167769591784707 ,81.984863446374821182  ] 
dist 8=[-47.391955748651521582  ,12.605545244552016125  ] 
dist 9=[-71.158860597941924726  ,-55.677199538322150048  ] 
dist 10=[-95.961009289274115292  ,-51.587448702705117842  ] 
dist 11=[-106.96200695270366664   ,-26.849318234150140831  ] 
dist 12=[-106.59622445116583829   ,1.5346000157573189517 ] 
dist 13=[-91.265943927461658096  ,20.627437841763945235  ] 
dist 14=[-83.676723532436594510  ,33.143418874697674227  ] 
dist 15=[-20.451414104941777413  ,36.417719537112969344  ] 
dist 16=[-8.1358386444622559051 ,51.352075276903327001  ] 
dist 17=[15.678892909564525851  ,69.845155610497926941  ] 
dist 18=[12.683300331961289609  ,74.557859397480220912  ] 
dist 19=[3.7288173558367685040 ,25.401142608739530204  ] 
dist 20=[-5.9286137118684434981 ,25.013020753722060046  ] 
dist 21=[-12.442055779439050971  ,21.360044598637659189  ] 
dist 22=[-16.929934822978870524  ,19.147826333459297630  ] 
dist 23=[-18.851352197810523980  ,5.2612458039424775245 ] 
dist 24=[-19.310732023748328430  ,2.3144882287115084578 ] 
dist 25=[-18.401598154290449464  ,-.33138844096429920388] 
dist 26=[-15.922453498296279167  ,-.20208951007065463803] 
dist 27=[-12.065349346603120280  ,.77665157457681052362] 
dist 28=[-11.783991719822202598  ,2.0516707941764133328 ] 
dist 29=[-9.7571579510794820090 ,4.7051229499476524669 ] 
dist 30=[-8.8136698387865453004 ,6.3897411687983638565 ] 
dist 31=[-1.7925072409376856143 ,6.8289640328608723592 ] 
dist 32=[-.39445210359192558223,6.5766064009162366587 ] 
dist 33=[2.0966589519913524950 ,8.6681035926805463813 ] 
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dist 36=[-.06098863935549337904,2.7706845551524420205 ] 
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dist 46=[-1.0950679051011107876 ,1.8423177312046228055 ] 
dist 47=[-.12607076522665698634,1.9574791428506526781 ] 
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dist 70=[-.03855558034677107524,.03040156642552859942] 
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dist 73=[-.04144666197434784947,-.01519419219027279105] 
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dist 75=[-.02994823008825135719,-.00315193612379575091] 
dist 76=[-.02307565217601350112,.01271784574491920653] 
dist 77=[-.01757447125252543342,.02441536127807389127] 
dist 78=[-.01642509911309148331,.03175698817238710708] 
dist 79=[-.00140573925976522693,.03366249381829223533] 
dist 80=[.00081883456350740875,.00999990269128303458] 
dist 81=[.00447579179757004572,.01313654913071311718] 
dist 82=[.00338215886927452459,.01399489642850109806] 
dist 83=[.00152458062769602990,.00707111013027986145] 
dist 84=[-.00119338476214296690,.00534769120557602679] 
dist 85=[-.00361521042052753303,.00404930493633342004] 
dist 86=[-.00517119032314003007,.00384453584149723794] 
dist 87=[-.00565766832749535646,-.00044439093282391832] 
dist 88=[-.00555897478094180435,-.00112338361370488348] 
dist 89=[-.00536913833646803210,-.00216134708152244233] 
dist 90=[-.00411303495970336166,-.00148116723051419021] 
dist 91=[-.00382819073801542752,-.00035852728814386155] 
dist 92=[-.00273476274229671242,.00119037791999088268] 
dist 93=[-.00215270979225596506,.00239885280618314328] 
dist 94=[-.00194467187565209775,.00316030987444488931] 
dist 95=[-.00029938814551477197,.00336572140639142025] 
dist 96=[1.78027294372214677000e-05,.00159684557476760349] 
dist 97=[.00052560540477368333,.00206813192820490373] 
dist 98=[.00038724170527886452,.00219039292972234215] 
dist 99=[.00015656455209243551,.00094676878096158953] 
dist 100=[-.00031346491696523892,.00076041625348342924] 
dist 101=[-.00066758550204495900,.00065701904964774775] 
dist 102=[-.00089211379059287135,.00060454522165325488] 
dist 103=[-.00095599297345378202,.00032933490826483714] 
dist 104=[-.00093575208858782083,.00024922683880964132] 
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dist 106=[-.00067308280950676299,.00014563183733844916] 
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dist 108=[-.00041317578238469352,.00019462878569990955] 
dist 109=[-.00032034546863464708,.00036895227060968502] 
dist 110=[-.00029069851776507616,.00047825451691207318] 
dist 111=[-2.04562416813903634930e-05,.00050664502878797040] 
dist 112=[1.32665170526667457640e-05,.00030321508553310073] 
dist 113=[6.83825265516741016730e-05,.00028901298779652113] 
dist 114=[5.09366082149237000160e-05,.00026478376841679390] 
dist 115=[2.21113643913095569750e-05,.00012007297161857545] 
dist 116=[-4.45096451942214888300e-05,.00011446941137891656] 
dist 117=[-8.76330572669090165770e-05,9.52567023960527280920e-05] 
dist 118=[-.00011483869505689771,8.55973139026322919170e-05] 
dist 119=[-.00012229483080902340,3.31839304348744779580e-05] 
dist 120=[-.00011979647849556045,2.04594572815583134410e-05] 
dist 121=[-.00011402262972387720,3.25349141542130188510e-06] 
dist 122=[-9.05302187108231879860e-05,-4.16334786639590122760e-08] 
dist 123=[-6.63251317863147027290e-05,6.99360875147953450250e-07] 
dist 124=[-3.94229740269524347920e-05,2.57490041337275865060e-05] 
dist 125=[-3.12032909723870865610e-05,4.24211313958809252430e-05] 
dist 126=[-2.78867100595013245770e-05,5.29455855125462620310e-05] 
dist 127=[-4.17647984721818052960e-06,5.58460099999997274230e-05] 
dist 128=[4.91833441322029861200e-07,2.36194808072903725210e-05] 
dist 129=[7.93862505406256822110e-06,3.05415310387443240180e-05] 
dist 130=[5.80093595312406898450e-06,3.23371004317273210880e-05] 
dist 131=[2.29849764658178295150e-06,9.59953798590277914040e-06] 
dist 132=[-1.22384178013649144650e-06,9.26806725234472031960e-06] 
dist 133=[-3.43877900040690318820e-06,6.93230388165027836760e-06] 
dist 134=[-4.84492699603458756030e-06,6.56857284211164336840e-06] 
dist 135=[-5.25000371209263537950e-06,-5.43080286431989674420e-07] 
dist 136=[-5.11793814083543919430e-06,-1.69423021353859234860e-06] 
dist 137=[-5.06670525531000548880e-06,-3.49465328739042061560e-06] 
dist 138=[-5.46006841728170461370e-06,-2.40844161184542864070e-06] 
dist 139=[-5.29755368840682295110e-06,-6.42704587051842505020e-07] 
dist 140=[-5.09905263339946601690e-06,1.12848899958705362980e-06] 
dist 141=[-3.85179895102391460050e-06,2.23589793649093560050e-06] 
dist 142=[-3.59405974401463150520e-06,2.93171170803187369010e-06] 
dist 143=[-2.57756757686307072620e-07,3.11616268049813729650e-06] 
dist 144=[2.33180167743825883830e-07,2.24172465855629278330e-06] 
dist 145=[1.01160413177799066380e-06,2.93859366855760352850e-06] 
dist 146=[7.47894014807267952630e-07,3.12169002563515481560e-06] 
dist 147=[3.17744760606488546210e-07,1.21023931420971458590e-06] 
dist 148=[-1.14372407631310861730e-07,1.16789360681788959720e-06] 
dist 149=[-3.85856020325973796290e-07,8.70420887090051465890e-07] 
dist 150=[-5.57986947145508677660e-07,8.26078877616742993910e-07] 
dist 151=[-6.06911213540656443600e-07,-1.23217609515759059320e-07] 
dist 152=[-5.93808053788609083060e-07,-2.72401570297772879020e-07] 
dist 153=[-5.78392551890317266490e-07,-4.86307905735249826450e-07] 
dist 154=[-6.26330287775334756360e-07,-3.28499556643591169210e-07] 
dist 155=[-6.10559937675197129930e-07,-7.31263291958061357710e-08] 
dist 156=[-5.84775541763453596670e-07,1.82730662910381897580e-07] 
dist 157=[-4.61962920620004391740e-07,3.42418292953017554390e-07] 
dist 158=[-4.12296454106601993950e-07,4.42470908942205725960e-07] 
dist 159=[-6.13385659790376485080e-08,4.68416123080526815210e-07] 
dist 160=[8.01179060780351473410e-09,3.53339220977868634260e-07] 
dist 161=[1.16292326655796426160e-07,4.56256768753882782050e-07] 
dist 162=[8.27356566726949104660e-08,4.82947835515165837070e-07] 
dist 163=[2.82493357946078272660e-08,1.41313504380281711680e-07] 
dist 164=[-2.64085935819692560520e-08,1.36131952413365451910e-07] 
dist 165=[-6.06461965588993457490e-08,1.02417948387261586910e-07] 
dist 166=[-8.22491739496436969030e-08,9.61055354450121400460e-08] 
dist 167=[-8.81979970887754636400e-08,-9.50488370236066724370e-09] 
dist 168=[-8.56554407481299992340e-08,-2.66561386512155049820e-08] 
dist 169=[-8.23552863371825402940e-08,-4.19344250624712483780e-08] 
dist 170=[-8.00262670033666407560e-08,-2.60797181973034239470e-08] 
dist 171=[-7.75528134897127750410e-08,-4.21490168410000000000e-10] 
dist 172=[-7.45558688024160819150e-08,2.52930624745834239470e-08] 
dist 173=[-5.65683768828743259570e-08,4.13665723144912483770e-08] 
dist 174=[-5.24615679499781969970e-08,5.14696842579393524750e-08] 
dist 175=[-4.94088800755176857320e-09,5.41657651422856545400e-08] 
dist 176=[2.51415487376997548080e-09,3.57823177227690545220e-08] 
dist 177=[1.44825300110756555080e-08,4.65616015244198732630e-08] 
dist 178=[1.04927079082333479240e-08,4.93761441292529552380e-08] 
dist 179=[4.03015911314133723780e-09,1.81047329925082194450e-08] 
dist 180=[-2.44945005797067344120e-09,1.74376911740859528210e-08] 
dist 181=[-6.50554532852298103700e-09,1.30781159827656335070e-08] 
dist 182=[-9.06232274386403753410e-09,1.22940561616908181450e-08] 
dist 183=[-9.76141279940106121780e-09,-1.34003615611531057000e-09] 
dist 184=[-9.51684007961474291010e-09,-3.41714884090147931280e-09] 
dist 185=[-9.38041583318939219020e-09,-6.05702510337385709080e-09] 
dist 186=[-1.00965578089874686930e-08,-3.78812337324970470500e-09] 
dist 187=[-9.80004452217983289790e-09,-1.28707320326165249980e-10] 
dist 188=[-9.40174077711434730920e-09,3.53516739994737420400e-09] 
dist 189=[-7.26223970301013328770e-09,5.82139006564852659170e-09] 
dist 190=[-6.61470364826138291090e-09,7.25419168273063854400e-09] 
dist 191=[-1.08800871634558936680e-09,7.62748028953034389330e-09] 
dist 192=[-1.62638961275897566240e-10,5.10541363695922162630e-09] 
dist 193=[2.01369594308264435470e-11,6.53954770694584387840e-09] 
dist 194=[-2.10632209438555315880e-10,6.91694582329985117250e-09] 
dist 195=[-5.86251858751206261780e-10,3.26963595959978738050e-09] 
dist 196=[-9.63192392353857207290e-10,3.14307156076150433080e-09] 
dist 197=[-1.19909216803323896850e-09,2.37891265231250809300e-09] 
dist 198=[-1.34756083474070468760e-09,2.21006102395450253290e-09] 
dist 199=[-1.38747616433474304140e-09,1.19326761987541252030e-09] 
dist 200=[-1.50919811493299554980e-09,1.18004793631342777460e-09] 
dist 201=[-1.96611319306132990650e-09,1.14217871216101591870e-09] 
dist 202=[-2.08629112792254239030e-09,1.08402930073988948480e-09] 
dist 203=[-2.01648169307290522500e-09,1.00750224231338532370e-09] 
dist 204=[-1.93894148543502414790e-09,9.01650755287697371540e-10] 
dist 205=[-1.45818501016288062860e-09,8.45447891726570935860e-10] 
dist 206=[-1.36194206509305020310e-09,8.10746046984159080550e-10] 
dist 207=[-5.08281058250107268440e-10,8.02769548298517324090e-10] 
dist 208=[-4.57070914974818006620e-10,1.08576525564017195190e-09] 
dist 209=[-4.24935362101206839360e-10,1.31234450791909257750e-09] 

8 phat 5 dirichlet min maxes function [2, 2, 1, 0, 1, 0, 1] 
dist 0=[300.31141013970551017   ,300.31141013970551017   ] 
dist 1=[289.21876528232420544   ,303.77416022329118810   ] 
dist 2=[269.87054596893246253   ,302.23906125957766327   ] 
dist 3=[241.94656740504341150   ,280.30780950658545176   ] 
dist 4=[196.72747977777810430   ,277.08981878871976580   ] 
dist 5=[148.67600781628856778   ,193.78146691409032629   ] 
dist 6=[109.62731744351048124   ,181.37819256368222639   ] 
dist 7=[71.659890676873269661  ,117.24330629639752891   ] 
dist 8=[28.266685081343144760  ,90.556391190572204110  ] 
dist 9=[-15.254044957477312841  ,22.584650555971255845  ] 
dist 10=[-42.752616126073867383  ,12.321082049276950271  ] 
dist 11=[-56.581919440286182823  ,-10.100554755683742523  ] 
dist 12=[-58.939375276445799125  ,-14.608715463299026011  ] 
dist 13=[-54.856039836502915882  ,-9.5754789381217947560 ] 
dist 14=[-53.351993832465080872  ,6.9247515903839323203 ] 
dist 15=[-40.835381749257181712  ,21.865732849949797406  ] 
dist 16=[-38.957330767915628546  ,35.357108907104206636  ] 
dist 17=[-3.1985645123020240366 ,44.905228913173811228  ] 
dist 18=[1.4061346053420638080 ,46.638247331166772071  ] 
dist 19=[9.2582947963114961617 ,41.995011476726853379  ] 
dist 20=[10.433769286931036756  ,40.583064148785647605  ] 
dist 21=[.58217218470842927585,24.807915771776990084  ] 
dist 22=[-12.181639318564973973  ,23.943783494675754095  ] 
dist 23=[-21.369288804240528765  ,19.244074989117235129  ] 
dist 24=[-26.245550697431676278  ,17.298277544592306006  ] 
dist 25=[-28.084418687494530653  ,13.828302739420429506  ] 
dist 26=[-27.916631957547790973  ,13.989220062664924122  ] 
dist 27=[-22.241099263416803539  ,14.113842120545348759  ] 
dist 28=[-18.709800007048649980  ,14.163024188465990898  ] 
dist 29=[-5.6301835088409159764 ,13.952223809345783179  ] 
dist 30=[-5.4734482595505307469 ,13.083235205399696181  ] 
dist 31=[-4.2276242437396726463 ,11.694299810926260700  ] 
dist 32=[-3.9864316677486785479 ,9.4905990125314633201 ] 
dist 33=[-.44801169687337258588,6.6120824799248638037 ] 
dist 34=[.06427676718839346750,6.5819442351130722342 ] 
dist 35=[.9263689485634006182 ,5.3198818996392145408 ] 
dist 36=[1.0641870785310923375 ,5.1253098876889971829 ] 
dist 37=[-.16438130122715481173,3.0635013077206796207 ] 
dist 38=[-1.7980143012914743051 ,2.9582349299422179961 ] 
dist 39=[-2.9028136915926223708 ,2.2707247576956527042 ] 
dist 40=[-3.3621326398915599676 ,2.1093245056011291332 ] 
dist 41=[-3.4589055540059020030 ,.27287767585620679524] 
dist 42=[-3.3685893180692552468 ,-.00630316919232899324] 
dist 43=[-2.7815014003400660940 ,-.42649136905574958136] 
dist 44=[-2.5015036725951808268 ,-.46341239550389925154] 
dist 45=[-.68947146530675019609,1.0106827595865326895 ] 
dist 46=[-.66913964273737309915,1.9634006584891523694 ] 
dist 47=[-.50678900148587424908,2.5628098871840935924 ] 
dist 48=[-.48255738601463673653,2.7187768237547234547 ] 
dist 49=[-.21421250351567616055,.7799572461053236077 ] 
dist 50=[-.15234699242818014417,.7660295159858560264 ] 
dist 51=[-.05591007846176699997,.62326117930377104982] 
dist 52=[-.02576517752207083331,.62911634810638013437] 
dist 53=[-.29250221196543958942,.62253189234605253124] 
dist 54=[-.51932739014865150653,.59120661476894856335] 
dist 55=[-.66733655588920615795,.50736177295395345373] 
dist 56=[-.71823343643374068964,.46482080574796104999] 
dist 57=[-.71266706273995369851,.2404612169784120899 ] 
dist 58=[-.68407172831081069349,.17699819768634859534] 
dist 59=[-.55722105873355400745,.10849561196002356849] 
dist 60=[-.326123570511508341  ,.09436084897385799712] 
dist 61=[-.11344587511292310381,.15946719233380281932] 
dist 62=[-.07694017191683289952,.26885967857847941859] 
dist 63=[-.05856747149713245858,.34033410250007058181] 
dist 64=[-.05506468337026808336,.35834044104610408851] 
dist 65=[-.00588662967220912338,.01855345202437292130] 
dist 66=[.00099050837384627684,.03478808476897166917] 
dist 67=[.01256842991226325474,.04495246585985698133] 
dist 68=[.01443044223321530757,.04758817269799211784] 
dist 69=[.01391347478498007357,.04367404402192057736] 
dist 70=[.01184795541591385975,.04207575136031993045] 
dist 71=[.00853999299332244245,.03204168188826943753] 
dist 72=[.00322970234413333680,.02978221311139319338] 
dist 73=[-.00957319224628012515,.00257391283151600332] 
dist 74=[-.01901901953111301306,-.00157138784008609779] 
dist 75=[-.02495284076406753289,-.00578463792970596494] 
dist 76=[-.02652489638381830257,-.00628825597267561436] 
dist 77=[-.00998510904506245114,-.00603495246261877640] 
dist 78=[-.00965485717146384007,-.00503238399440309081] 
dist 79=[-.00723748881113997292,-.00342763325096862170] 
dist 80=[-.00687603045795504402,-.00085152021641824937] 
dist 81=[-.00044376007896732160,.00172494772060636150] 
dist 82=[.00025519516739186330,.00333130699955345501] 
dist 83=[.00146448325319012161,.00479617187599817033] 
dist 84=[.00165805901396421049,.00521203650047608710] 
dist 85=[.00159092857548305938,.00509998679949186418] 
dist 86=[.00132093093550155426,.00488934263477338360] 
dist 87=[.00088801382778146161,.00388103658542311854] 
dist 88=[.00019245425751234996,.00346029062309207727] 
dist 89=[-.00164118362050862927,.00064259160915141864] 
dist 90=[-.00299599052425899955,8.73586632119021200630e-05] 
dist 91=[-.00384485396231958459,-.00031604670034936169] 
dist 92=[-.00406510400397463963,-.00036889166609177079] 
dist 93=[-.00125337487773579015,-.00033198110238922051] 
dist 94=[-.00119034590269081784,-.00017508423716282161] 
dist 95=[-.00099744187741494520,7.80263443204215846520e-05] 
dist 96=[-.00090235671475318331,.00048604917789134766] 
dist 97=[-.00039638605614778194,.00089476122514737417] 
dist 98=[-.00026668992701722619,.00115057549627421631] 
dist 99=[-.00010757352342614171,.00131198090627264125] 
dist 100=[-7.84603398955059854760e-05,.00135665578876447214] 
dist 101=[-8.60252862571991268920e-05,.00065988225106457092] 
dist 102=[-.00011620010400386165,.00063478262821221671] 
dist 103=[-.00016455097007327269,.00048251744392663117] 
dist 104=[-.00024222059950442724,.00044755358047039535] 
dist 105=[-.00031991741524851474,3.22399306981812791560e-05] 
dist 106=[-.00036837921752201622,-2.77944943393135964240e-05] 
dist 107=[-.00039875664145920733,-8.60531102332444675050e-05] 
dist 108=[-.00040671796555694085,-9.33356790159802833360e-05] 
dist 109=[-.00014733775854939151,-8.95599795543545896010e-05] 
dist 110=[-.00014220104711501016,-7.47685165690179073560e-05] 
dist 111=[-.00010602388723021370,-5.11097092246659224560e-05] 
dist 112=[-.00010063224613912678,-1.31348835862160251260e-05] 
dist 113=[-5.53539898562374347350e-06,2.48444912798948721560e-05] 
dist 114=[4.88715561467227997410e-06,4.88816275520244839010e-05] 
dist 115=[2.30936684234429391020e-05,7.02756632124356461240e-05] 
dist 116=[2.59712326365126538300e-05,7.61260310496482802120e-05] 
dist 117=[2.50592781345579498660e-05,7.42253163671131892670e-05] 
dist 118=[2.14730739434550994940e-05,7.10969394648103937270e-05] 
dist 119=[1.57347280690272417180e-05,5.61704629953476989100e-05] 
dist 120=[6.52238340597137810350e-06,5.01400569709934278800e-05] 
dist 121=[-2.29127901767073444770e-05,7.43256737053822743210e-06] 
dist 122=[-4.28868318845622332950e-05,-1.00450522937196337340e-06] 
dist 123=[-5.53978589164416480740e-05,-1.20029021651973752980e-05] 
dist 124=[-5.86425323997781115730e-05,-1.29363925853049271010e-05] 
dist 125=[-1.70972946572622588250e-05,-1.24020485201291714730e-05] 
dist 126=[-1.64709553813423136130e-05,-1.02939777668071674040e-05] 
dist 127=[-1.24021030592367690390e-05,-6.92355887954528075250e-06] 
dist 128=[-1.16321619739100668290e-05,-1.51448638813968433620e-06] 
dist 129=[-1.20494169379902416370e-06,3.89508504684997517200e-06] 
dist 130=[2.21776227634376027950e-07,7.26740104842204969400e-06] 
dist 131=[2.62059796372091230280e-06,9.37894202912728807330e-06] 
dist 132=[3.00428907780381921930e-06,9.92648835980295863220e-06] 
dist 133=[2.89430242032514602330e-06,9.41488485972675457890e-06] 
dist 134=[2.46388121863728749930e-06,9.05261425099566826290e-06] 
dist 135=[1.77545429170845201020e-06,6.86088489371933146280e-06] 
dist 136=[6.70425451945418513780e-07,6.37069771519430492950e-06] 
dist 137=[-2.11318895013272369340e-06,4.93804989911608502980e-07] 
dist 138=[-4.14141025437851313580e-06,-3.97921802284665453970e-07] 
dist 139=[-5.41276806419062880410e-06,-1.22805968712959739470e-06] 
dist 140=[-5.74487887821992806100e-06,-1.33251736144740702020e-06] 
dist 141=[-2.14712496541124428000e-06,-1.27847739816405393370e-06] 
dist 142=[-2.07015280993018443180e-06,-1.06798420708822711150e-06] 
dist 143=[-1.53938647972295959540e-06,-7.31461200811848362810e-07] 
dist 144=[-1.45998901942345609510e-06,-1.91351852496811716820e-07] 
dist 145=[-7.16596739072606317440e-08,3.48806461050224930550e-07] 
dist 146=[7.74425142676241781110e-08,7.19312606716883507940e-07] 
dist 147=[3.39224865944834726070e-07,1.02983587634510427670e-06] 
dist 148=[3.80424631069840606770e-07,1.11297736520208413070e-06] 
dist 149=[3.66954087654076677090e-07,1.08307187807803116040e-06] 
dist 150=[3.14372770217799836960e-07,1.03685395105093472510e-06] 
dist 151=[2.30291904887258884680e-07,8.17341818667977449760e-07] 
dist 152=[9.53402304768249113040e-08,7.29760777979932755870e-07] 
dist 153=[-3.34253245015240813070e-07,1.05894461284349431650e-07] 
dist 154=[-6.24546608620432516900e-07,-1.68096278414309891750e-08] 
dist 155=[-8.06349154825218161680e-07,-1.76156737863146326270e-07] 
dist 156=[-8.53497904596535045510e-07,-1.89826529367908540040e-07] 
dist 157=[-2.52204376068867064610e-07,-1.81904348635128642270e-07] 
dist 158=[-2.43047421808139581980e-07,-1.50924416369165033590e-07] 
dist 159=[-1.80728707239208258860e-07,-1.01411948152053953450e-07] 
dist 160=[-1.71191273003488181850e-07,-2.19620528700403380420e-08] 
dist 161=[-1.79023398694438799300e-08,5.74925003695432774590e-08] 
dist 162=[3.01638363905143880350e-09,1.07027170283996538080e-07] 
dist 163=[3.81198704265883597330e-08,1.38051614974478906100e-07] 
dist 164=[4.37292461286108618360e-08,1.46096523727924391780e-07] 
dist 165=[4.21286280720077768790e-08,1.38631138332840592960e-07] 
dist 166=[3.58987084009749789300e-08,1.33315463836993126550e-07] 
dist 167=[2.59394282825489556620e-08,1.00554860570803236930e-07] 
dist 168=[9.95637105545848431350e-09,9.37092305973109910950e-08] 
dist 169=[-3.02968920796349941330e-08,6.64676947936840997020e-09] 
dist 170=[-5.94748077516944748240e-08,-6.22754366308900681250e-09] 
dist 171=[-7.77574328358383983570e-08,-1.83181472693764160280e-08] 
dist 172=[-8.25218971479105871710e-08,-1.98457008214469686230e-08] 
dist 173=[-3.19251661764109997910e-08,-1.90317571805465125740e-08] 
dist 174=[-3.07618313653798910770e-08,-1.58737266834377775300e-08] 
dist 175=[-2.28434622207738726980e-08,-1.08223036907657268120e-08] 
dist 176=[-2.16517677661841057390e-08,-2.64322373174674405750e-09] 
dist 177=[-1.37933134609283330140e-09,5.53633709752223870660e-09] 
dist 178=[8.37451592933537148920e-10,1.07758938435981159250e-08] 
dist 179=[4.66318510463920416780e-09,1.53841111570672242180e-08] 
dist 180=[5.26808937855347811920e-09,1.66024597476383329370e-08] 
dist 181=[5.07572088424016818850e-09,1.61366839236883664740e-08] 
dist 182=[4.32812052973656385390e-09,1.54443553020034510490e-08] 
dist 183=[3.04736897542219416810e-09,1.21501031708447534520e-08] 
dist 184=[8.99721797159383057350e-10,1.08573609494719115060e-08] 
dist 185=[-4.95311398114515162450e-09,1.55629931370732582320e-09] 
dist 186=[-9.25300006149361933500e-09,-2.23618213329026129960e-10] 
dist 187=[-1.19456413499588955570e-08,-1.61925456559355089730e-09] 
dist 188=[-1.26438995106700378120e-08,-1.79292828898576611250e-09] 
dist 189=[-3.83679365276398333910e-09,-1.70461523119301944560e-09] 
dist 190=[-3.69472434772327756200e-09,-1.36213743626862944540e-09] 
dist 191=[-2.75198946601481828530e-09,-8.14845685734819099840e-10] 
dist 192=[-2.59854941206332098510e-09,6.33280050957513022880e-11] 
dist 193=[-5.67560344970930237750e-10,9.41546873486321704840e-10] 
dist 194=[-3.86906114482633582640e-10,1.48901908690013205590e-09] 
dist 195=[-1.68278513836357395630e-10,1.93697840506804351360e-09] 
dist 196=[-1.28266364316830509690e-10,2.08395457883436106940e-09] 
dist 197=[-1.29189309872416437950e-10,2.02376919234015512150e-09] 
dist 198=[-1.33274248097606126100e-10,1.93742902672688071320e-09] 
dist 199=[-1.39885616959012727970e-10,1.51821818205012173620e-09] 
dist 200=[-1.50554657087202383440e-10,1.36140366976480779310e-09] 
dist 201=[-6.81959878799507591090e-10,2.84162909183727694600e-10] 
dist 202=[-1.20327872591621313770e-09,2.51828300239897005040e-10] 
dist 203=[-1.52980460768580303310e-09,2.91455401847453832330e-10] 
dist 204=[-1.61467031963860129400e-09,3.01690518054404765840e-10] 
dist 205=[-1.39345587917613160640e-09,2.98572160669059065160e-10] 
dist 206=[-1.34089104277899878820e-09,2.86701845518270018090e-10] 
dist 207=[-9.97771366370167749520e-10,2.67768860426040842760e-10] 
dist 208=[-9.41019358847435632240e-10,2.49185109146570851370e-10] 
dist 209=[-4.62822053615890426990e-10,5.59204783417116316370e-10] 
dist 210=[-4.61672489489479538850e-10,7.64888414234169080450e-10] 
dist 211=[-4.70209687412689102850e-10,8.93770561341191716990e-10] 
dist 212=[-4.74918485181979021530e-10,9.27400561307357708730e-10] 
dist 213=[-4.62514565095955677110e-10,8.96588906624120824500e-10] 
dist 214=[-4.71355840140235938350e-10,8.61130517274006269080e-10] 
dist 215=[-4.85617768403536118530e-10,6.52792909094158403970e-10] 
dist 216=[-5.08604167486311488050e-10,6.04480446892033420570e-10] 
dist 217=[-5.31614021538086857680e-10,6.28268249861199749930e-10] 
dist 218=[-5.45967226881387037950e-10,8.46015300366730916950e-10] 
dist 219=[-5.54957705814667299990e-10,9.82324094255888965490e-10] 
dist 220=[-5.57289787575196407490e-10,1.01761124967195917710e-09] 
dist 221=[-4.51792850350770677120e-10,9.88073033758370131830e-10] 
dist 222=[-4.85043046985186591470e-10,9.44477601701625845940e-10] 
dist 223=[-5.38143769528118149250e-10,7.46611243727543329060e-10] 
dist 224=[-6.23325053469335496530e-10,6.62745374866029487020e-10] 
dist 225=[-7.08507556645552843820e-10,8.01250204970435198850e-10] 
dist 226=[-7.61612978799484401660e-10,1.05029392628258241200e-09] 
dist 227=[-7.94870691671900315980e-10,1.20622717559544025820e-09] 
dist 228=[-8.03511635323779318990e-10,1.24666353101292396330e-09] 
dist 229=[-6.89167542763771406230e-10,1.20610406906518272340e-09] 
dist 230=[-6.54580322612042998950e-10,1.15717701991720702720e-09] 
dist 231=[-5.46888856614887880190e-10,8.84893900490826187880e-10] 
dist 232=[-6.23314713246335496610e-10,8.12069068042075420400e-10] 
dist 233=[-7.05974468124560682960e-10,5.33082552692469829190e-10] 
dist 234=[-7.57502952514218739710e-10,6.48790360062127678470e-10] 
dist 235=[-7.89766595433481237610e-10,7.21237155158169753620e-10] 

8 phat 5 dirichlet min maxes function [1, 1, 1, 0, 2, 1, 1, 0, 1] 
dist 0=[392.32008430595716291   ,392.32008430595716291   ] 
dist 1=[377.67501800786606865   ,390.41807213408523421   ] 
dist 2=[342.80608216741417699   ,392.32008430595716291   ] 
dist 3=[276.77546012779643269   ,344.36522771386063070   ] 
dist 4=[205.13169637375318255   ,317.00125130551191897   ] 
dist 5=[147.73843974117354116   ,260.71460170507225551   ] 
dist 6=[56.638394834075084940  ,123.72451543948831141   ] 
dist 7=[-6.3269691448575993949 ,110.93955179994720860   ] 
dist 8=[-52.972574633396109454  ,74.383521159902994573  ] 
dist 9=[-83.682917597486243698  ,-4.9210303633401113765 ] 
dist 10=[-101.76108903925143007   ,-26.017298121098856126  ] 
dist 11=[-104.29895441224180700   ,-11.558327383359232838  ] 
dist 12=[-91.795495916644998500  ,8.1575492726027769285 ] 
dist 13=[-87.681010366245700311  ,25.615032914273210932  ] 
dist 14=[-14.693121440139255132  ,41.953794425988143822  ] 
dist 15=[-2.1647551973020457099 ,57.892619523309925410  ] 
dist 16=[16.921204276468725010  ,68.902774668223679584  ] 
dist 17=[30.470145317414615070  ,70.604226890645281770  ] 
dist 18=[36.327712905139336787  ,60.729837055193938716  ] 
dist 19=[28.112975227621326008  ,59.260849753714304816  ] 
dist 20=[2.9496863782435136292 ,47.830243267440800207  ] 
dist 21=[-15.119702225923726366  ,44.114023396496137500  ] 
dist 22=[-27.904050091189038647  ,16.405076876704701700  ] 
dist 23=[-34.304761344801759554  ,12.014754938324840958  ] 
dist 24=[-38.253702546329736397  ,3.6671881484296667319 ] 
dist 25=[-40.382287874401800971  ,1.5855684740100238550 ] 
dist 26=[-30.720787622754309299  ,-11.064511434084154824  ] 
dist 27=[-27.854636558717151865  ,-6.7483963500608405429 ] 
dist 28=[-9.7457411381041998949 ,9.6564937775377983397 ] 
dist 29=[-1.9931490561803498687 ,20.018530787586782431  ] 
dist 30=[1.1677891289008743778 ,26.555441233630649987  ] 
dist 31=[4.2262784285956084063 ,28.255482685501627356  ] 
dist 32=[4.7149388100904211998 ,8.7510034046450036912 ] 
dist 33=[6.0980469370792713772 ,8.6864439866994747012 ] 
dist 34=[5.3276037045025009678 ,7.0706683711990336322 ] 
dist 35=[2.7487975322039888868 ,6.7307161131759375423 ] 
dist 36=[-.66741426344291287447,4.7199550590074541595 ] 
dist 37=[-2.8945406697672354613 ,1.1314194556311260314 ] 
dist 38=[-4.3861634086771687642 ,.40838796018806118463] 
dist 39=[-4.9759646369990847298 ,-.92948879866681256571] 
dist 40=[-5.0349351507801150707 ,-1.2179576419462634703 ] 
dist 41=[-4.9058319234190609581 ,-1.3439792283603210598 ] 
dist 42=[-3.8503039671428551103 ,-1.1712503531414246352 ] 
dist 43=[-3.5884524008468246890 ,-.68311794570097388034] 
dist 44=[-1.1161567870516485539 ,1.0620799703435135365 ] 
dist 45=[-.44762839006912830168,2.1665656320541257607 ] 
dist 46=[-.29749308931524548174,2.8903764853837424564 ] 
dist 47=[-.01950522391538855334,3.0736165968030538253 ] 
dist 48=[.04794876915977020780,1.3034553546388953398 ] 
dist 49=[.11576596012226769189,1.3036717532462668780 ] 
dist 50=[.03721048708948796284,1.2552526577105545297 ] 
dist 51=[-.1255948979933400324 ,1.0211791647776283098 ] 
dist 52=[-.4784878576308723753 ,.89954169890813484441] 
dist 53=[-.80706362430466402433,.20574000576750336475] 
dist 54=[-1.0230817540315457657 ,.05665428078616473202] 
dist 55=[-1.1007882320182476295 ,-.14126077734042552751] 
dist 56=[-1.1038962261595498622 ,-.17450210930561571757] 
dist 57=[-.57582323929715647019,-.18017700698914859263] 
dist 58=[-.46686214938875868194,-.16060640439396385671] 
dist 59=[-.41915975251206176903,-.08582006581957363943] 
dist 60=[-.13263560015294324885,.17392648237796534265] 
dist 61=[-.00662889723975092655,.33669172117877956454] 
dist 62=[.03243688265974912506,.43890877529614359703] 
dist 63=[.07798419053667557354,.46544488675956283197] 
dist 64=[.08483162550813405142,.13888446950756361364] 
dist 65=[.09149912330727767220,.13536165504273669849] 
dist 66=[.07767310047848177932,.10518559795721250328] 
dist 67=[.03756184385585141618,.09929378177688274418] 
dist 68=[-.01563569331347663359,.06540510674940513438] 
dist 69=[-.04947538295275707988,.01176379873362941982] 
dist 70=[-.07134365637724155996,.00108800311049422871] 
dist 71=[-.07843957472406809312,-.01774947090336820090] 
dist 72=[-.07737894237744292025,-.02153763112815523566] 
dist 73=[-.07482806058629509296,-.02161386922287276108] 
dist 74=[-.05751536464549930435,-.01891293172995152002] 
dist 75=[-.05354700185153193875,-.01051666401157077577] 
dist 76=[-.01551365912508784765,.01641422008133076652] 
dist 77=[.00070580706811871942,.03331511561133264448] 
dist 78=[.00335223919857831114,.04397847063976256086] 
dist 79=[.00883258374353292265,.0468777932060612482 ] 
dist 80=[.00971844419731338756,.01786693128599496995] 
dist 81=[.00982338702371615130,.01736925034125703121] 
dist 82=[.00834883186423182530,.01321096933172099552] 
dist 83=[.00512378385013216794,.01258815314959239058] 
dist 84=[-.00148722424940913506,.00837512295114949953] 
dist 85=[-.00567481339539155869,.00084700945366227343] 
dist 86=[-.00836471159323887933,-.00030732453443206995] 
dist 87=[-.00920587390797889569,-.00240697273929704426] 
dist 88=[-.00909637552815644372,-.00280973307208527063] 
dist 89=[-.00875149373234590311,-.00278992590205230664] 
dist 90=[-.00698816640931534160,-.00243597363006348244] 
dist 91=[-.00625736391725708477,-.00119810310081116401] 
dist 92=[-.00197101154071941639,.00273352517564894110] 
dist 93=[2.92793913805751660450e-05,.00519094006143564350] 
dist 94=[.00056229164768252515,.00673199027612825234] 
dist 95=[.00126774763418248661,.00713194166358427097] 
dist 96=[.00137489101611199635,.00213254020261853773] 
dist 97=[.00138631292545913840,.00206701972911612460] 
dist 98=[.00116126932206079674,.00156369557088247320] 
dist 99=[.00051533151513125904,.00148400061694874617] 
dist 100=[-.00029595460526540712,.00098713648756692394] 
dist 101=[-.00080705146951356943,.00017848272625222472] 
dist 102=[-.00113244925395495985,1.86860486653450833630e-05] 
dist 103=[-.00122811006070506397,-.00025279087855376963] 
dist 104=[-.00119891336943129489,-.00030287699253962246] 
dist 105=[-.00115590298545017711,-.00029588622417850154] 
dist 106=[-.00087922486528709045,-.00024389670999989756] 
dist 107=[-.00081923037087873772,-.00012937546555590348] 
dist 108=[-.00023235001768685418,.00026865093485526530] 
dist 109=[-8.17163420798077161090e-05,.00051779211165977730] 
dist 110=[-4.93324417005281352540e-05,.00067458133542076585] 
dist 111=[-7.80870722935585858180e-07,.00071664432785420320] 
dist 112=[1.07502582928441202020e-05,.00029812670435287362] 
dist 113=[8.21979840615131870860e-06,.00029182829543686078] 
dist 114=[-1.39091829745107430670e-05,.00027923129113947550] 
dist 115=[-5.14612488312088431020e-05,.00022387355840769707] 
dist 116=[-.00011649277653524408,.00019693346202584955] 
dist 117=[-.00018931930665984458,4.29882737686239808200e-05] 
dist 118=[-.00023557644608361656,1.02704720260402051610e-05] 
dist 119=[-.00024896466594785964,-3.79102151864734997710e-05] 
dist 120=[-.00024576323917069672,-4.33638931015165002260e-05] 
dist 121=[-.00013175217157314480,-4.24823034031840225350e-05] 
dist 122=[-.00010456616945504319,-3.67821698939011070420e-05] 
dist 123=[-9.34291149705727604360e-05,-1.73200629476833179870e-05] 
dist 124=[-2.93951966898285629880e-05,4.20534282374241333180e-05] 
dist 125=[1.27591872191381769100e-06,7.91195646684073427970e-05] 
dist 126=[9.22777458864184617470e-06,.00010234727273678656] 
dist 127=[1.98710810197676012940e-05,.00010837234593674743] 
dist 128=[2.14606416819923413000e-05,3.17152469585926933760e-05] 
dist 129=[2.12234143173881256180e-05,3.06169939945371234050e-05] 
dist 130=[1.77225069701403710670e-05,2.31869520161241910840e-05] 
dist 131=[7.74224833970013986010e-06,2.17729660646212501650e-05] 
dist 132=[-4.32636702570629172360e-06,1.46442116915848491080e-05] 
dist 133=[-1.18954242615061711920e-05,2.25715522207572389180e-06] 
dist 134=[-1.66807441824040137670e-05,-1.93727766771765229310e-07] 
dist 135=[-1.80184015325002917450e-05,-4.36913692542641993000e-06] 
dist 136=[-1.75184210421325234890e-05,-5.08739999158285432460e-06] 
dist 137=[-1.68621630954067930180e-05,-4.95772200798407531810e-06] 
dist 138=[-1.28135973635544049340e-05,-4.25585436931436659160e-06] 
dist 139=[-1.19037460560939428390e-05,-2.16368228047045748460e-06] 
dist 140=[-3.41441039843422058030e-06,3.89413641995363438450e-06] 
dist 141=[2.92886615436606752980e-07,7.67827561911336991550e-06] 
dist 142=[8.96448599781374503590e-07,1.00533591081105992250e-05] 
dist 143=[2.10692271439744051520e-06,1.06788230396975968670e-05] 
dist 144=[2.29870258218089947350e-06,4.00631816118555993110e-06] 
dist 145=[2.23083125375021275210e-06,3.86890061928675431400e-06] 
dist 146=[1.87196284314539158660e-06,2.88968499055320614170e-06] 
dist 147=[1.07281158612631189530e-06,2.74323665838505755680e-06] 
dist 148=[-4.03855019178632187460e-07,1.86716318773664087240e-06] 
dist 149=[-1.32911038196728321720e-06,1.52914454223967102100e-07] 
dist 150=[-1.91329995124849409470e-06,-1.07555474161196595030e-07] 
dist 151=[-2.07507974387095870370e-06,-5.68174256272170257890e-07] 
dist 152=[-2.02543438031727853530e-06,-6.45699931176276306930e-07] 
dist 153=[-1.94092969887335306470e-06,-6.28297009619409553850e-07] 
dist 154=[-1.53396388172215229980e-06,-5.41468829712817673470e-07] 
dist 155=[-1.37041395510795717950e-06,-2.50113253026863753490e-07] 
dist 156=[-4.31039383060598891270e-07,6.21622962929073447140e-07] 
dist 157=[2.72821881724929077610e-08,1.16550856890186644670e-06] 
dist 158=[1.39779530736963215320e-07,1.50622140024187186030e-06] 
dist 159=[2.97214651143427189900e-07,1.59459497447570630090e-06] 
dist 160=[3.20850149560132011640e-07,4.73149115568100726300e-07] 
dist 161=[3.12634250881700115950e-07,4.56496999973810258910e-07] 
dist 162=[2.60412471722849438470e-07,3.41193684674981569880e-07] 
dist 163=[1.10467531571863726420e-07,3.22802660494766654570e-07] 
dist 164=[-6.85903073318737088900e-08,2.15598177783027263820e-07] 
dist 165=[-1.80605241072728113480e-07,3.17322965288583187620e-08] 
dist 166=[-2.51138683988480154380e-07,-4.34275505055797459580e-09] 
dist 167=[-2.70262951631825591420e-07,-6.55090272294215067750e-08] 
dist 168=[-2.61959088554913035400e-07,-7.57100596857786720930e-08] 
dist 169=[-2.52043435084333300320e-07,-7.34065844503712642990e-08] 
dist 170=[-1.90332998165054908980e-07,-6.27711556427925165940e-08] 
dist 171=[-1.77475376201467238370e-07,-3.08831701400416191670e-08] 
dist 172=[-5.12442844738523710100e-08,5.69035732124414208810e-08] 
dist 173=[4.43403166593443073420e-09,1.11698787295364767880e-07] 
dist 174=[1.33534363517283579420e-08,1.46061269592681334610e-07] 
dist 175=[3.10647214236864753700e-08,1.55064204951504215570e-07] 
dist 176=[3.38863873780547489170e-08,6.09537174597915666010e-08] 
dist 177=[3.26752452107049018670e-08,5.87711828844630161740e-08] 
dist 178=[2.74236589791298897990e-08,4.38565997843539644600e-08] 
dist 179=[1.52452903648070363090e-08,4.14929492143023992950e-08] 
dist 180=[-6.88437324531820937400e-09,2.77238436566039035990e-08] 
dist 181=[-2.10245019065293117650e-08,1.65296350485803834730e-09] 
dist 182=[-2.99212067375444069150e-08,-2.20893274228736731370e-09] 
dist 183=[-3.23196906379329573160e-08,-9.05540876310893042990e-09] 
dist 184=[-3.14182183554037970420e-08,-1.01704603973307822650e-08] 
dist 185=[-3.01313075214878481960e-08,-9.85137164115052478230e-09] 
dist 186=[-2.34247424201276000890e-08,-8.44607060108843223920e-09] 
dist 187=[-2.12193086720931795600e-08,-4.13441500742990279480e-09] 
dist 188=[-6.75462738086666366750e-09,8.53083561160984378520e-09] 
dist 189=[8.04141810133081043080e-10,1.64468257316115498460e-08] 
dist 190=[2.01529047794196685470e-09,2.14047290760239408090e-08] 
dist 191=[4.45139984216024856970e-09,2.26904979172073309470e-08] 
dist 192=[4.82856594816878232500e-09,9.39109738527128491820e-09] 
dist 193=[4.64298152551707624130e-09,9.02814653373525462640e-09] 
dist 194=[3.85781084363662991140e-09,6.86210877707868002460e-09] 
dist 195=[1.60123337180578610600e-09,6.35784014503181064060e-09] 
dist 196=[-1.71507344936340928690e-09,3.57210467060339475290e-09] 
dist 197=[-4.01271026214945515030e-09,4.88607200271954061050e-10] 
dist 198=[-5.45490813722744113100e-09,-4.53771198943162199450e-11] 
dist 199=[-5.83641453500347141010e-09,-9.41854945979871429370e-10] 
dist 200=[-5.65781963892393371450e-09,-1.08907690845137031170e-09] 
dist 201=[-5.42813648288575225270e-09,-1.05325346994840429090e-09] 
dist 202=[-4.17537258619309020670e-09,-8.99437407993007401830e-10] 
dist 203=[-3.81475774247523830600e-09,-5.59318490732580523480e-10] 
dist 204=[-1.56526570485273972230e-09,1.51325481923531192490e-09] 
dist 205=[-3.25607790128631562410e-10,2.82730387217860280970e-09] 
dist 206=[-6.57255456031798857160e-11,3.65018653497664719690e-09] 
dist 207=[3.51440717282109202350e-10,3.86357818843977545910e-09] 
dist 208=[4.20499449936635466490e-10,1.97385248218765295550e-09] 
dist 209=[4.02827792822375931710e-10,1.92705518278738622430e-09] 
dist 210=[3.29466797592555180400e-10,1.83391133317120474520e-09] 
dist 211=[1.57078320431539619410e-10,1.51094287281343665250e-09] 
dist 212=[-3.66884268662026653640e-10,1.35174821597077887700e-09] 
dist 213=[-1.10152963568302672050e-09,8.46287169475839417790e-10] 
dist 214=[-1.56775422922590275810e-09,7.69920087611468372070e-10] 
dist 215=[-1.85968932719582342450e-09,7.22136949423686621370e-10] 
dist 216=[-1.93539214742831012810e-09,7.09868207088009108950e-10] 
dist 217=[-1.38602011631694246060e-09,-3.52211532440195532320e-10] 
dist 218=[-1.33161046970818288150e-09,-2.54610801830866907270e-10] 
dist 219=[-1.00694443366883400750e-09,1.69648068907967776220e-10] 
dist 220=[-9.34838985632454130060e-10,7.25536376394398466760e-10] 
dist 221=[-4.23681449942653520610e-10,1.07216993532816469130e-09] 
dist 222=[-3.57238270366087561250e-10,1.28931376757922136490e-09] 
dist 223=[-3.41327025435935554160e-10,1.34584464354748361800e-09] 
dist 224=[1.23838642424417765400e-10,1.30378896053010301730e-09] 
dist 225=[1.06386396521760101260e-10,1.24956148982570572100e-09] 
dist 226=[3.04380883666724762600e-11,9.84683635008027135430e-10] 
dist 227=[-1.11173312335858735970e-10,8.94602473921146913950e-10] 
dist 228=[-6.81274164089692478570e-10,5.63091861243036708250e-10] 
dist 229=[-1.06943673072618546990e-09,5.62254854992749208120e-10] 
dist 230=[-1.31250703504386756200e-09,6.26503217412899968100e-10] 
dist 231=[-1.37560431646687893250e-09,6.66728430891972961680e-10] 
dist 232=[-1.34318895983643702140e-09,6.77158720398396754320e-10] 
dist 233=[-1.27695456682465151420e-09,1.09260904424675294450e-10] 
dist 234=[-1.05887215563907299080e-09,1.56629143304789184270e-10] 
dist 235=[-9.51558017157223465510e-10,3.19474718244044298290e-10] 
dist 236=[-6.69489292609616599840e-10,8.27256591528738507900e-10] 
dist 237=[-6.52486143273459773810e-10,1.14379752427721905440e-09] 
dist 238=[-6.41838819842509090360e-10,1.34199273474067105090e-09] 
dist 239=[-6.39077466648088596370e-10,1.39338623749410865220e-09] 
dist 240=[-2.10848154607001579250e-10,7.18090076230617666050e-10] 
dist 241=[-2.18167655340992305990e-10,7.02314158219148560400e-10] 
dist 242=[-2.46469586250598344100e-10,6.66558836744044176530e-10] 
dist 243=[-2.91684695929045518500e-10,5.71783338212998894950e-10] 
dist 244=[-3.64228702925178813160e-10,5.26034938328545200120e-10] 
dist 245=[-4.68875881559755236720e-10,3.42183503487695948680e-10] 
dist 246=[-6.83893898453630904140e-10,2.89479500604577994830e-10] 
dist 247=[-8.18522187396589669230e-10,2.56479889125686411700e-10] 

8 phat 5 dirichlet min maxes function [0, 1, 2, 2, 0, 0, 2] 
dist 0=[300.31222699946737064   ,300.31222699946737064   ] 
dist 1=[289.21979216785461018   ,303.77476527577216133   ] 
dist 2=[269.87170009820677818   ,302.23954821731693027   ] 
dist 3=[241.94779659233553811   ,280.30814862166863436   ] 
dist 4=[196.72871773680125223   ,277.08995533581554773   ] 
dist 5=[148.67716918503433468   ,193.78044863866026983   ] 
dist 6=[109.62822484018598015   ,181.37714804713635069   ] 
dist 7=[71.660400489962788093  ,117.24181597195896646   ] 
dist 8=[28.266564878856852833  ,90.556610959286900384  ] 
dist 9=[-15.255600634443337143  ,22.585068901401740689  ] 
dist 10=[-42.754004007559645490  ,12.321377026793339281  ] 
dist 11=[-56.583041606863508992  ,-10.100423013144758125  ] 
dist 12=[-58.940423913246273060  ,-14.608760606657093061  ] 
dist 13=[-54.857208985956749993  ,-9.5748258463280847031 ] 
dist 14=[-53.353221287912992929  ,6.9258488893031600130 ] 
dist 15=[-40.835440588710701958  ,21.867102033480962002  ] 
dist 16=[-38.958144312313505044  ,35.358533834047794936  ] 
dist 17=[-3.1972508632881263109 ,44.906441476004371718  ] 
dist 18=[1.4075283145976097519 ,46.639546065378140226  ] 
dist 19=[9.2600689643592334866 ,41.994991271090860296  ] 
dist 20=[10.435558726200361023  ,40.583953001244440477  ] 
dist 21=[.58638476297157660787,24.803684635295608583  ] 
dist 22=[-12.176860739443798489  ,23.939826393201359321  ] 
dist 23=[-21.364154958879624416  ,19.240340158776144753  ] 
dist 24=[-26.240323183257057871  ,17.295514098664275688  ] 
dist 25=[-28.079274096191250825  ,13.823572247554609791  ] 
dist 26=[-27.911780736847740000  ,13.983221165614092468  ] 
dist 27=[-22.238219659192407869  ,14.107067981123330751  ] 
dist 28=[-18.702736461855192036  ,14.156093897903856923  ] 
dist 29=[-5.6330646613933940056 ,13.945841791866330900  ] 
dist 30=[-5.4760899294286868258 ,13.078793727379772343  ] 
dist 31=[-4.2274373167133355603 ,11.692924112031828703  ] 
dist 32=[-3.9882666879265572150 ,9.4941089783648271373 ] 
dist 33=[-.4447769354715659821 ,6.6243992121173775626 ] 
dist 34=[.06717172779137352808,6.5942412163835534772 ] 
dist 35=[.9293099237542054009 ,5.3252582815342988929 ] 
dist 36=[1.0670987737474087923 ,5.1337042579703534945 ] 
dist 37=[-.15014533186534271407,3.0226447968939269433 ] 
dist 38=[-1.7835070358336512367 ,2.9197261928216957333 ] 
dist 39=[-2.8880766429543763072 ,2.2370396003638718595 ] 
dist 40=[-3.3471977408738358213 ,2.0826337116514797440 ] 
dist 41=[-3.4430964077733427647 ,.20383236266349238326] 
dist 42=[-3.3545249327744263909 ,-.08428726553878868698] 
dist 43=[-2.7625645368598711775 ,-.42230740933408550871] 
dist 44=[-2.4915120926818411593 ,-.45920738921612607811] 
dist 45=[-.69119594681835600547,.96036209928038385981] 
dist 46=[-.67079980145016057186,1.9083753108060815651 ] 
dist 47=[-.50811487900756281683,2.5047275178125609816 ] 
dist 48=[-.48374728340709184621,2.6596483729614318708 ] 
dist 49=[-.02632991672237045554,.82107902496395888733] 
dist 50=[.02476796537432768239,.80644045980321054976] 
dist 51=[.11459831319191113499,.63199168978605609894] 
dist 52=[.1288821285771942035 ,.60393134751770216107] 
dist 53=[-.08173816322818435443,.34623456380852057187] 
dist 54=[-.28317017365269979205,.33278444353972789423] 
dist 55=[-.41522201210158633292,.26493636236648167839] 
dist 56=[-.46188320559686022861,.23722133832426806109] 
dist 57=[-.45983992868565045424,.21167949346363133705] 
dist 58=[-.44630930678451333695,.20999944985414892116] 
dist 59=[-.34378941766721553426,.20946407217192772174] 
dist 60=[-.32218935791658767843,.21037436834297973873] 
dist 61=[-.08078717776523079545,.21132933944035141982] 
dist 62=[-.07820904775217409053,.2109915193931508124 ] 
dist 63=[-.05897236956519179562,.24948864986949577626] 
dist 64=[-.05594164069804688040,.26649559458512505718] 
dist 65=[-.00602501388819182325,.10682985720620122411] 
dist 66=[.00094970453913282773,.10428067649272930421] 
dist 67=[.01268484251269282391,.08016907292774366675] 
dist 68=[.01457507155096755124,.07656816432877075316] 
dist 69=[-.00767138370365070236,.04438691429573399656] 
dist 70=[-.03291745912681462817,.04278084023365502104] 
dist 71=[-.04929575070804931052,.03242110187681868999] 
dist 72=[-.05475035523997059400,.03027240945747993357] 
dist 73=[-.05450180929727825315,.00236973880880171942] 
dist 74=[-.05255507122670217151,-.00174936806756391884] 
dist 75=[-.04224310128354621589,-.00592937784162438545] 
dist 76=[-.03785379259123102047,-.00644122258813680440] 
dist 77=[-.01015278809350114446,.01623177626825873306] 
dist 78=[-.00981686592969132150,.03105608732218587322] 
dist 79=[-.00735747195159280924,.04035763383720611639] 
dist 80=[-.00699079076858061743,.04277155431884135052] 
dist 81=[-.00048604603995033871,.01266482527197632812] 
dist 82=[.00022876239989073642,.01229647137520158110] 
dist 83=[.00145918005830856598,.00945867292365273805] 
dist 84=[.00165669898814159752,.00891050635964168065] 
dist 85=[-.00154434630845613794,.00517680074253151965] 
dist 86=[-.00460425062883894407,.00496253741317351795] 
dist 87=[-.00656482008744927501,.00394189416118017656] 
dist 88=[-.00716692364441870364,.00351201150340209971] 
dist 89=[-.00702943201933795011,.00065625633945235869] 
dist 90=[-.00678523658353595564,9.07787954545001788380e-05] 
dist 91=[-.00519206953818187380,-.00030001067103956371] 
dist 92=[-.00482977980752384860,-.00035256710321403037] 
dist 93=[-.00126791480523602950,.00151859457543402061] 
dist 94=[-.00120454457630268368,.00304723221628460075] 
dist 95=[-.00100667026156439879,.00400975869843089237] 
dist 96=[-.00090912850332570635,.00426832159802485515] 
dist 97=[-.00038880116308289566,.00161686755576043133] 
dist 98=[-.00025702777573596422,.00156780546634850650] 
dist 99=[-9.25850507037920005520e-05,.00131188627828000542] 
dist 100=[-6.27988338967291382130e-05,.00135622959613104393] 
dist 101=[-.00014529953078818119,.00064860140360081877] 
dist 102=[-.00052207048737553847,.00062406173258799344] 
dist 103=[-.00076251877918600930,.00047374376939517102] 
dist 104=[-.00083448136482274504,.00044004870687315840] 
dist 105=[-.00082070146603038402,8.76644321534370931540e-05] 
dist 106=[-.00078839749545562486,2.21709608182749865860e-05] 
dist 107=[-.00062708426027426798,-2.47819308203309056190e-05] 
dist 108=[-.00056103601801947700,-3.05302864081830757910e-05] 
dist 109=[-.00015669711303126386,.00024847140076196320] 
dist 110=[-.00014968175579334078,.00046968925591519212] 
dist 111=[-.00011910061868866390,.00060835952110125009] 
dist 112=[-.00010500018334594862,.00064433996362194674] 
dist 113=[-2.27312738270896101150e-05,.00019206851314348846] 
dist 114=[-1.38758438506867609050e-05,.00018584486916596363] 
dist 115=[-2.08682468110905446540e-06,.00013990650742725898] 
dist 116=[0                     ,.00013267320824789327] 
dist 117=[-2.62311600377108281760e-05,7.46920730695625323360e-05] 
dist 118=[-7.19224042583054980150e-05,7.15488164840408818180e-05] 
dist 119=[-.00010089455221281778,5.64889835232154901160e-05] 
dist 120=[-.00010916962434867028,5.04573934583164895050e-05] 
dist 121=[-.00010628134423235250,7.40265194943045246570e-06] 
dist 122=[-.00010241182812151202,-1.06844040543145675830e-06] 
dist 123=[-7.75710769545161528450e-05,-1.53957621090540960680e-05] 
dist 124=[-7.24173364886139993670e-05,-1.33164202562934263640e-05] 
dist 125=[-1.74095078668213769790e-05,2.24243114197493447600e-05] 
dist 126=[-1.67893982435668266120e-05,4.47685730083619273140e-05] 
dist 127=[-1.25204242306304361880e-05,5.88071749829468650280e-05] 
dist 128=[-1.18546735053620989570e-05,6.25301401229939026120e-05] 
dist 129=[1.03872982011493479280e-06,2.43447136414640104650e-05] 
dist 130=[3.12532083191577855160e-06,2.35323136894233257640e-05] 
dist 131=[7.25374395429901149620e-06,1.76198311684079394530e-05] 
dist 132=[6.59391181216168825570e-06,1.67384525582576195310e-05] 
dist 133=[-2.37977232032143889850e-06,9.59283561065064394590e-06] 
dist 134=[-8.01136760207448707400e-06,9.22809055574867159170e-06] 
dist 135=[-1.15760601586660890050e-05,6.96100929494390428020e-06] 
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