8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 1, 2, 2, 1, 2] 
dist 0=[110.78613535004551862   ,110.78613535004551862   ] 
dist 1=[107.25796045739743980   ,112.30932777242486610   ] 
dist 2=[103.20241119230403424   ,112.83163452405621038   ] 
dist 3=[99.574686033340225598  ,112.63270722044699550   ] 
dist 4=[95.604766381718894038  ,110.97238499701288209   ] 
dist 5=[90.176053835525168276  ,108.36674299913629516   ] 
dist 6=[84.262378923062625399  ,106.53065396650348515   ] 
dist 7=[78.352433762631246602  ,105.72788391972131119   ] 
dist 8=[71.329047893879670987  ,101.79390638334992690   ] 
dist 9=[60.966122846544380455  ,80.444095553872821995  ] 
dist 10=[50.460669012665401172  ,69.813706698522519189  ] 
dist 11=[42.869119132223990912  ,68.397740416858973905  ] 
dist 12=[35.973143253524889434  ,53.184592896031431667  ] 
dist 13=[28.251146869131609133  ,50.235231425017591740  ] 
dist 14=[20.022317456588685897  ,45.237254535550823301  ] 
dist 15=[11.304748653132476423  ,44.216674801903250533  ] 
dist 16=[-.2588325414084661698 ,19.932060352643920100  ] 
dist 17=[-11.217347021729015597  ,19.022848355037693253  ] 
dist 18=[-17.533927151717518089  ,6.5088887657465230001 ] 
dist 19=[-21.682195479533359441  ,4.7367160281791581090 ] 
dist 20=[-24.005868967728025453  ,1.3515025960362274120 ] 
dist 21=[-25.480390328400788610  ,.55897979463427872864] 
dist 22=[-26.583541464848041638  ,-1.7549217499605129484 ] 
dist 23=[-27.810049266334413464  ,-2.1407431711965742557 ] 
dist 24=[-28.360867070317661760  ,-1.9791591643714102937 ] 
dist 25=[-28.469316164372708336  ,-1.0469925819081124565 ] 
dist 26=[-17.125206250134309963  ,.01370755341326865026] 
dist 27=[-17.045916877677390147  ,.68850993072097446324] 
dist 28=[-14.092299030887964749  ,1.1969298939788381369 ] 
dist 29=[-13.376832873054288260  ,2.4673173318219360415 ] 
dist 30=[-12.854000920134163375  ,4.9502660750065778829 ] 
dist 31=[-12.715207323090676138  ,7.1537120933287062858 ] 
dist 32=[-2.3141360498338296829 ,9.4946726939387603090 ] 
dist 33=[-1.0940106872063712496 ,11.543347914277363648  ] 
dist 34=[.54952441097026058324,12.589092715015359639  ] 
dist 35=[.19986728946167811736,13.113110426471932244  ] 
dist 36=[-.12750765455842053751,13.193854780293383472  ] 
dist 37=[-.49464238954061983856,12.690229926646514379  ] 
dist 38=[-.84555536096300037314,12.413132865668820426  ] 
dist 39=[-1.1092906142646422216 ,11.986785504185302741  ] 
dist 40=[-1.3528172951932095537 ,11.770986281945491176  ] 
dist 41=[-1.6243672721110896651 ,8.0090186050567840885 ] 
dist 42=[-2.5406768133799604643 ,7.8073206249352098788 ] 
dist 43=[-4.5684655277907046563 ,7.6906335318752099636 ] 
dist 44=[-6.4626274538739451755 ,6.6288173353604857012 ] 
dist 45=[-8.0714299574082722666 ,6.3506899422265745970 ] 
dist 46=[-8.9668543925242632904 ,5.9211091885421898913 ] 
dist 47=[-9.4891916880999697803 ,5.7667414712642372153 ] 
dist 48=[-9.6202867601261755980 ,2.2287275681550362732 ] 
dist 49=[-3.0088841352911966632 ,1.7654857638058863457 ] 
dist 50=[-3.3553172316942164612 ,.85546068440239993397] 
dist 51=[-4.3781263695504874435 ,1.1351277668228481470 ] 
dist 52=[-5.2385523761597767256 ,1.3674664916521189944 ] 
dist 53=[-5.7102528302459379056 ,1.5877563942250983173 ] 
dist 54=[-5.9786542657227156728 ,1.7769313637723138474 ] 
dist 55=[-6.0319071673820262887 ,1.8957424663144707247 ] 
dist 56=[-2.8682016357251382039 ,1.9759145158743175672 ] 
dist 57=[-1.7133366879084151740 ,1.9879508900954958176 ] 
dist 58=[-1.6570803578769203233 ,.1304808285674935471 ] 
dist 59=[-1.6489481157080488641 ,.56107355804976549603] 
dist 60=[-1.3468722755432401857 ,1.0168239472433685063 ] 
dist 61=[-1.2740364328186198386 ,1.4194404212083023238 ] 
dist 62=[-1.2235246698522455134 ,1.6742812757429118438 ] 
dist 63=[-1.2120805592959395800 ,1.8646099745670488759 ] 
dist 64=[-.14739274236694365014,2.0114717198387262633 ] 
dist 65=[-.02318646445911924736,2.1146546657444611088 ] 
dist 66=[.05987774347170535948,2.1351736942040144119 ] 
dist 67=[.02710016725470028584,2.1185650773512859038 ] 
dist 68=[-.00202818696353544325,2.1018091246575556922 ] 
dist 69=[-.03271387085351656851,1.8107910721788054413 ] 
dist 70=[-.06111842256155320787,1.7318643330752996890 ] 
dist 71=[-.08122708085371311296,1.6467218336691030985 ] 
dist 72=[-.09866155149453745063,1.6006843849564059875 ] 
dist 73=[-.24576060103305588212,.83731564594070403142] 
dist 74=[-.52995463800289800636,.81148006129670505674] 
dist 75=[-.76447157759086330955,.79895853420832960988] 
dist 76=[-.98652612583364322942,.68259172691612694353] 
dist 77=[-1.2104908354029784419 ,.65270000608985867321] 
dist 78=[-1.3294787436649084879 ,.60764323670136588792] 
dist 79=[-1.3948178457930070370 ,.59122468626383021334] 
dist 80=[-1.4072348511080558014 ,.19787608541569524358] 
dist 81=[-.45123870487599478625,.14553031764252465251] 
dist 82=[-.459703274905811581  ,.03274286856283037644] 
dist 83=[-.46305219374045761334,.05662330442876969765] 
dist 84=[-.55330003173004083169,.07632863974229975444] 
dist 85=[-.60324528672767086464,.09483487788267245125] 
dist 86=[-.63230458804587087123,.11112711432542387622] 
dist 87=[-.63962322445206941843,.12092706386327383216] 
dist 88=[-.36465309602131464201,.126378676936072464  ] 
dist 89=[-.19366215242152698774,.12723094739281324204] 
dist 90=[-.18652407919436344159,.01591412862265721041] 
dist 91=[-.18511800575061608807,.07401150302000228952] 
dist 92=[-.15146326285884986564,.13134580495319961499] 
dist 93=[-.14334592753908549391,.18124307944575745351] 
dist 94=[-.13656675338588390417,.21161746133569116942] 
dist 95=[-.13411175739393410241,.23292831498110702985] 
dist 96=[-.07842783155294864599,.24686512359539713085] 
dist 97=[-.10579848590831695504,.2555736171995710881 ] 
dist 98=[-.13342149193455881736,.2565914705535689526 ] 
dist 99=[-.15214480373344187359,.25355053331005997716] 
dist 100=[-.16754900340860513495,.24976681853081967825] 
dist 101=[-.18200010165972860211,.22047490617557224249] 
dist 102=[-.19437460714878290543,.21218332184838692577] 
dist 103=[-.20153762605473901508,.19804972030512764906] 
dist 104=[-.20611391571407471261,.19327220669446374605] 
dist 105=[-.20822252322307057115,.10573461825999037147] 
dist 106=[-.20852760940461204889,.10132995011808754304] 
dist 107=[-.20650384908216064903,.10031870513344786147] 
dist 108=[-.20154111221857825083,.08192333838717717876] 
dist 109=[-.19853446873363778812,.07750519371530396293] 
dist 110=[-.1795406672948544276 ,.07325411035478448219] 
dist 111=[-.17453750504018562537,.07137649481813036237] 
dist 112=[-.14994743397327858105,.01799748754113121627] 
dist 113=[-.05037486767320239421,.02175582081549019880] 
dist 114=[-.05084031368825774329,.02559811941697859078] 
dist 115=[-.05058810195718726570,.02826912182667105587] 
dist 116=[-.05388756223741124057,.03053611104784237291] 
dist 117=[-.05895985875365305484,.03277620527669424726] 
dist 118=[-.06201871117626703544,.03498538028635684965] 
dist 119=[-.06276399676001410685,.03721156676247788199] 
dist 120=[-.02432215483048837622,.03828034158280070319] 
dist 121=[-.02424117278197254845,.03842391328057630419] 
dist 122=[-.02322074935539528684,-.00309164160270990573] 
dist 123=[-.02307303053999362955,-.00292771277835771154] 
dist 124=[-.01857312902341192539,-.00271854796440527891] 
dist 125=[-.01750887091249300072,-.00239791815774382778] 
dist 126=[-.01673823704215231305,-.00203728584333665556] 
dist 127=[-.01656646981930681309,-.00166919056539376482] 
dist 128=[-.00181489724217229635,-.00123169190536847805] 
dist 129=[-.00178972057683356332,.00211506775423099710] 
dist 130=[3.54307724296704242840e-05,.00498532027570009763] 
dist 131=[.00024732022162298597,.00763803091757788542] 
dist 132=[.00072814193392358652,.00988750293689953380] 
dist 133=[.00080234256460531741,.01115669123613395770] 
dist 134=[.00132182819378052386,.01192790697186708770] 
dist 135=[.00139981080770461626,.01220019014926479338] 
dist 136=[.00150499713571068855,.01221985944443276730] 
dist 137=[.00148884507602833365,.01214517382012612277] 
dist 138=[.00143988804488155068,.01170327804450001780] 
dist 139=[.00136854879857364224,.01151278924336900312] 
dist 140=[.00126847548531929055,.00976062642032701775] 
dist 141=[.00110537128767096297,.00931831518833152614] 
dist 142=[.00091789700948147567,.00865071128169925021] 
dist 143=[.00072101508076389919,.00841062900007387005] 
dist 144=[-.00155770569849337657,.00273123021705781732] 
dist 145=[-.00362643703323694215,.00197927979752041172] 
dist 146=[-.00530555797501034281,.00030230814355932135] 
dist 147=[-.00684675670441067687,.00016109583902998010] 
dist 148=[-.00814615568063327830,-2.76872572116058804380e-05] 
dist 149=[-.00886514001937773371,-6.98525634198405045290e-05] 
dist 150=[-.00928344213709534776,-.00026127141185776793] 
dist 151=[-.00938888597446464115,-.00029566561277878638] 
dist 152=[-.00286150387511630441,-.00033874354527742695] 
dist 153=[-.00284855850982412073,-.00033727877057375844] 
dist 154=[-.00272163360974944797,-.00032523352603344681] 
dist 155=[-.00270281294584450652,-.00030950548535016309] 
dist 156=[-.00217035266541450634,-.00028835627409991857] 
dist 157=[-.00205387787350699092,-.00025477623918276944] 
dist 158=[-.00194917549585019276,-.00021652948209951465] 
dist 159=[-.00192735505472507085,-.00017684279179911595] 
dist 160=[-.00035503043366282157,5.97920583708924560660e-05] 
dist 161=[-.00019431069293731405,.00049309398444708172] 
dist 162=[-8.87189746778457379780e-06,.00084556573661199960] 
dist 163=[1.31596812850297236490e-05,.00117042343139813669] 
dist 164=[6.30712374870242992330e-05,.00144528948129703199] 
dist 165=[7.12236982777670236660e-05,.00159925871503586990] 
dist 166=[.00012525711380870970,.00169136081446556632] 
dist 167=[.00013355591831341589,.00172057123519434226] 
dist 168=[.00014517952381037444,.00171627958609396380] 
dist 169=[.00014426610528601061,.00170500332711976483] 
dist 170=[.00014004288068844485,.00163063104622490859] 
dist 171=[.00013352479403276966,.00161128129192742490] 
dist 172=[.00012419807730202576,.00132096664839349500] 
dist 173=[.00010881882355011294,.00125112010983172870] 
dist 174=[9.10748791226809872350e-05,.00117580324532424454] 
dist 175=[1.42415024517550000000e-05,.00113813031233412465] 
dist 176=[-.00029535460337199076,.00040738110072059434] 
dist 177=[-.00050285786398967495,.00035018829334034868] 
dist 178=[-.00067142066186571332,.00022863303457833599] 
dist 179=[-.00082639154762392547,.00019566632289602419] 
dist 180=[-.00095724358711728672,7.22764532519478049420e-05] 
dist 181=[-.00103003472798379888,4.62711409052732191100e-05] 
dist 182=[-.00107290796849915926,9.93139584609532009700e-06] 
dist 183=[-.00108496123068961934,0                     ] 
dist 184=[-.00036110377731507051,-3.93942902746036283390e-05] 
dist 185=[-.00035923043083683034,-3.93395546124871997950e-05] 
dist 186=[-.00034269461594594805,-3.81742250406365695090e-05] 
dist 187=[-.00034025296341691619,-3.65070414577770532700e-05] 
dist 188=[-.00027233136550260556,-3.41835852656852716890e-05] 
dist 189=[-.00025639623769474207,-3.04116498768650942990e-05] 
dist 190=[-.00024449790218625458,-2.60829816076581036990e-05] 
dist 191=[-.00024175116915171263,-2.03342043799582676160e-05] 
dist 192=[-2.88054792269974679600e-05,-1.25997107020005338500e-05] 
dist 193=[-2.79391635159369163200e-05,3.55862130439025096960e-05] 
dist 194=[-1.08382549945066275710e-05,7.80223822365951142730e-05] 
dist 195=[-8.41640091995579214610e-06,.00011710951265771770] 
dist 196=[-3.24625195847892781780e-06,.00015016695394693429] 
dist 197=[-1.88085792754424711210e-06,.00016866035803639357] 
dist 198=[3.07800979294673955230e-06,.00017969171632897019] 
dist 199=[4.08359011438874305920e-06,.00018311889604926280] 
dist 200=[5.17573923576781636310e-06,.00018278276581451558] 
dist 201=[5.10959289592174496120e-06,.00018148414596597672] 
dist 202=[4.72978369732175186300e-06,.00017434010341974830] 
dist 203=[4.18953697862511340510e-06,.00017154976229201477] 
dist 204=[3.43812336340480047530e-06,.00014441351687539518] 
dist 205=[2.21959099361751749290e-06,.00013765427601104336] 
dist 206=[8.21555922945707855260e-07,.00012786357996343013] 
dist 207=[-6.42824815854630463220e-07,.00012421430248680669] 
dist 208=[-2.27681177093819976360e-05,3.83113643545101452030e-05] 
dist 209=[-5.30854765120463478330e-05,2.72331533039448454460e-05] 
dist 210=[-7.76823811984607314510e-05,1.87660550604127174850e-05] 
dist 211=[-.00010024514324799843,1.71789328738839126740e-05] 
dist 212=[-.00011926152886844937,1.41443223902879562640e-05] 
dist 213=[-.00012977601291944812,1.33348520122034299950e-05] 
dist 214=[-.00013588425675517841,1.05230833189604046830e-05] 
dist 215=[-.00013740370055000002,9.74795871271845067060e-06] 
dist 216=[-4.62738366999084459400e-05,9.16681208893961625420e-06] 
dist 217=[-4.53821496107031407860e-05,9.09504141561392239080e-06] 
dist 218=[-4.06905237439985913340e-05,-4.27938016566081418650e-06] 
dist 219=[-4.02771109957551873130e-05,-4.09319688897043250740e-06] 
dist 220=[-3.27517125600539421650e-05,-3.81986454233915595900e-06] 
dist 221=[-3.09590354511480517060e-05,-3.36260536821987649990e-06] 
dist 222=[-2.92508722658866548690e-05,-2.83266183479782654290e-06] 
dist 223=[-2.85264263522202357870e-05,-2.17745656043887647740e-06] 
dist 224=[-1.28414795932243129050e-05,4.39626228593606833410e-07] 
dist 225=[-1.26506921569637609960e-05,6.89670620516348932020e-06] 
dist 226=[-1.22475267655252944620e-05,1.21890858793832063510e-05] 
dist 227=[-1.20528567686507426350e-05,1.70601060095531415280e-05] 
dist 228=[-1.18979126532554855720e-05,2.11774582991284671250e-05] 
dist 229=[-1.17603140492701026250e-05,2.34770782966382854560e-05] 
dist 230=[-1.16471149088508304710e-05,2.48439194754710243880e-05] 
dist 231=[-1.15891188904555510010e-05,2.52572858261925323710e-05] 
dist 232=[-1.15613638976518734840e-05,2.51616764078367902400e-05] 
dist 233=[-1.15683215121284336810e-05,2.45073766771165534200e-05] 
dist 234=[-1.15591002272138074180e-05,1.69259679097321245370e-05] 
dist 235=[-1.14671326766089827050e-05,1.67127345779024701640e-05] 
dist 236=[-1.12988871848459730040e-05,1.37597869061311731010e-05] 
dist 237=[-1.11575355670843469400e-05,1.30460780001075214670e-05] 
dist 238=[-1.06138827878592336640e-05,1.22355727254475736100e-05] 
dist 239=[-1.03986910713093725520e-05,1.18507620230418570440e-05] 
dist 240=[-9.80921625047617577050e-06,3.67008998262554930020e-06] 
dist 241=[-9.55446943283132765570e-06,3.60816421299904310900e-06] 
dist 242=[-8.17873813456813689700e-06,2.66292148532816241280e-06] 
dist 243=[-7.80618526036383904680e-06,2.47260625657493413090e-06] 
dist 244=[-7.26243916574442693430e-06,2.12113934274660737490e-06] 
dist 245=[-7.05970843423102151170e-06,2.02724897202042138750e-06] 
dist 246=[-6.57878346002959755080e-06,1.70709921788317198380e-06] 
dist 247=[-6.41159557359479783560e-06,1.61045381202460877790e-06] 
dist 248=[-6.29588501306184891150e-06,1.54858594375105324300e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[108.58489715743059986   ,108.58489715743059986   ] 
dist 1=[107.85206396108669125   ,109.21839260708524758   ] 
dist 2=[105.57876610998556262   ,109.47499257871986546   ] 
dist 3=[102.14643008121729195   ,109.35045232052965352   ] 
dist 4=[97.432166331243581086  ,107.36784867853255311   ] 
dist 5=[90.958874582932477590  ,106.42469048079992798   ] 
dist 6=[80.534447373426934989  ,105.08550610858563797   ] 
dist 7=[69.671330382606956679  ,104.39470313068283073   ] 
dist 8=[61.449268658624917691  ,83.197337239397521679  ] 
dist 9=[53.699997770477924499  ,80.143852416109705080  ] 
dist 10=[44.701425600811620574  ,76.719209350100517685  ] 
dist 11=[35.692170680392981405  ,75.883176122819413957  ] 
dist 12=[27.886477076214020257  ,59.797095225114287071  ] 
dist 13=[19.508000347271390009  ,57.404949570995947080  ] 
dist 14=[8.1957128668463410115 ,51.399561131571134075  ] 
dist 15=[-2.6275770465252909325 ,50.260615715737586849  ] 
dist 16=[-9.0657518673527970438 ,28.062908560059844047  ] 
dist 17=[-13.542131818434507998  ,25.045166153002015057  ] 
dist 18=[-16.551116408682922808  ,18.219496345538874835  ] 
dist 19=[-19.272432162187178750  ,16.806771978917205560  ] 
dist 20=[-25.850283971784169928  ,8.5403816992188022015 ] 
dist 21=[-30.208282106704180369  ,7.0953841145537527713 ] 
dist 22=[-33.949695955083447362  ,6.2097435872381537461 ] 
dist 23=[-37.297839797951398713  ,6.1441383403404417509 ] 
dist 24=[-39.762458491373059959  ,6.4070303185831152681 ] 
dist 25=[-40.572531169708000573  ,7.0969419816844365058 ] 
dist 26=[-40.718002700213990644  ,8.2097716612403309392 ] 
dist 27=[-38.586165224593495598  ,10.160333502302542732  ] 
dist 28=[-2.3424635181956994899 ,12.059444922045964114  ] 
dist 29=[-1.1807683129458337845 ,12.970814317008408941  ] 
dist 30=[-.95778228712338918433,13.420716006698499580  ] 
dist 31=[7.1326750151447761380 ,13.484821703484983445  ] 
dist 32=[7.7506606594946104900 ,12.543088582446232026  ] 
dist 33=[8.4310684808276769012 ,12.228827198694197261  ] 
dist 34=[8.1497642476320378527 ,11.984684314517675331  ] 
dist 35=[5.4099741983504985558 ,11.784588997448175841  ] 
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dist 164=[8.44810291522487889780e-05,.00222058388273907065] 
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dist 183=[-5.33673142296333996110e-05,.00064569646682703157] 
dist 184=[-2.54720519168999964180e-06,.00077672974055949975] 
dist 185=[.00011533191864490264,.00084959862966401039] 
dist 186=[.00013298709823355691,.00089377650975505147] 
dist 187=[.00026943726596762319,.00090438597897851441] 
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dist 189=[.00032557848605827837,.00034865310232774900] 
dist 190=[.00032710428248782839,.00035121066913995073] 
dist 191=[.00029736684780903376,.00035462463527740443] 
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dist 193=[.00022116104028293034,.00034258794692984744] 
dist 194=[.00017101816307042053,.00033726070466913785] 
dist 195=[9.54805707902304604900e-05,.00028839739946843035] 
dist 196=[1.97527681832997763360e-05,.00027579176970988908] 
dist 197=[-3.11465997990214915890e-05,.00025669251109888791] 
dist 198=[-7.26420949159094008580e-05,.00024975243212919617] 
dist 199=[-.00011103141326834976,8.37978036431468550350e-05] 
dist 200=[-.00014360713607162253,6.17796496220027263790e-05] 
dist 201=[-.00016201952020131467,1.24769116888110996250e-05] 
dist 202=[-.00019915090451205892,1.75376760823990845740e-06] 
dist 203=[-.00023745188314930638,-5.20225825339714823180e-05] 
dist 204=[-.00025865294620814742,-6.13918317301188141120e-05] 
dist 205=[-.00027099721013202273,-7.69768569549157672230e-05] 
dist 206=[-.00027410570639331495,-8.00832669970656091040e-05] 
dist 207=[-.00016751210238544840,-8.14729693143170004720e-05] 
dist 208=[-.00014217524144892897,-7.98693311820753026890e-05] 
dist 209=[-.00013576096800887452,-7.62034757049599081730e-05] 
dist 210=[-.00012602871982317311,-6.67108610234044153540e-05] 
dist 211=[-.00012254208001287470,-2.17733480979257671960e-05] 
dist 212=[-6.15175667427893959480e-05,2.32108558118307309910e-05] 
dist 213=[-5.84566827530848851320e-05,5.33485244107346225130e-05] 
dist 214=[-5.78031805245093017160e-05,7.78135121088568721670e-05] 
dist 215=[-1.16717757920173635290e-05,.00010027302283955745] 
dist 216=[-6.09371535131021163360e-06,.00011921048076345536] 
dist 217=[6.77311815102271960450e-06,.00012969026669168796] 
dist 218=[8.93526077530004544400e-06,.00013579102515914875] 
dist 219=[2.38559046842241897550e-05,.00013732839930963315] 
dist 220=[2.61521191399969143180e-05,4.69335891038660062170e-05] 
dist 221=[3.04349355051490694480e-05,4.98169658114425882590e-05] 
dist 222=[3.11710196076541025740e-05,5.09090358998243377110e-05] 
dist 223=[3.18246394760711651090e-05,5.10032002127785296140e-05] 
dist 224=[2.83388955010760917530e-05,5.07388942496087919210e-05] 
dist 225=[2.31817680162685681250e-05,4.86811830124950020800e-05] 
dist 226=[1.67707854327865708480e-05,4.81224830239144814080e-05] 
dist 227=[7.13733233699473460010e-06,3.96218615135265962570e-05] 
dist 228=[-2.51263851563313163270e-06,3.75585541681926041300e-05] 
dist 229=[-8.98931359166379892870e-06,3.53406951015079343010e-05] 
dist 230=[-1.42598026340077025250e-05,3.42205087302428460300e-05] 
dist 231=[-1.91203614810587803630e-05,1.26211625758807138690e-05] 
dist 232=[-2.32345985407763821870e-05,1.09219447258172421600e-05] 
dist 233=[-2.55416615136411135280e-05,7.27827410285790066980e-06] 
dist 234=[-2.69246120452626252400e-05,6.27947760650506544150e-06] 
dist 235=[-2.83702621514826403780e-05,2.47784323126355300530e-06] 
dist 236=[-3.05757700069306621960e-05,1.68802105864112718050e-06] 
dist 237=[-3.19839204381529690330e-05,4.44142661417195682590e-07] 
dist 238=[-3.23285229225209771350e-05,1.28188411642134317410e-07] 
dist 239=[-2.56305209128502396190e-05,-5.46984276886725579110e-06] 
dist 240=[-2.12531133552971009110e-05,-5.11960615294712015160e-06] 
dist 241=[-2.01843473950166862890e-05,-4.40741449919854729010e-06] 
dist 242=[-1.88626763883393850730e-05,-2.07917188175053113530e-06] 
dist 243=[-1.82859715768922786240e-05,2.45496504428190748280e-06] 
dist 244=[-8.73524781271031431390e-06,6.99655077028282607730e-06] 
dist 245=[-8.25709703672837634730e-06,1.00447915915135972960e-05] 
dist 246=[-6.04608993846225565290e-06,1.25256000380327182160e-05] 
dist 247=[-2.89039672428642490630e-06,1.48140490210776558840e-05] 
dist 248=[-1.07624591943860715010e-06,1.67516516303101659820e-05] 
dist 249=[-6.94287886559475985520e-07,1.78393349615923104430e-05] 
dist 250=[-1.53319249586980017660e-07,1.85408105764744040580e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 2, 1, 0, 2] 
dist 0=[147.14852461560714649   ,147.14852461560714649   ] 
dist 1=[145.67008736083564163   ,147.54860771854374125   ] 
dist 2=[140.21323577270847117   ,147.82092012040045834   ] 
dist 3=[132.79229516564871124   ,147.47825914324626962   ] 
dist 4=[123.66878299879439883   ,136.57680705434208196   ] 
dist 5=[111.72785736589026759   ,134.21769668004147364   ] 
dist 6=[93.105329602840188606  ,128.51967017550513250   ] 
dist 7=[74.105376232805883828  ,126.52218718486614511   ] 
dist 8=[60.658033612875103683  ,102.15768259989899197   ] 
dist 9=[48.912222696254004620  ,97.272758130003549761  ] 
dist 10=[36.660025356115569793  ,93.129703722659000113  ] 
dist 11=[25.207188999175535998  ,92.296833082888660076  ] 
dist 12=[16.624651302322915227  ,32.523744599770697023  ] 
dist 13=[8.5688880399414860224 ,29.851032572281333470  ] 
dist 14=[-.81564010729312622662,26.121562987913261396  ] 
dist 15=[-9.4324087381126355650 ,25.240949044300907052  ] 
dist 16=[-16.341733706020663009  ,-12.081645650659290110  ] 
dist 17=[-22.588961282704387625  ,-15.583388318044676389  ] 
dist 18=[-27.314281789980534014  ,-17.617491340832477257  ] 
dist 19=[-31.150715770043970142  ,-17.809182755629656127  ] 
dist 20=[-34.067289270541042557  ,-16.182296563773451841  ] 
dist 21=[-35.138099538545846215  ,-13.219355467305357385  ] 
dist 22=[-35.405640995763623732  ,-7.8304327035168343617 ] 
dist 23=[-35.113404896968330229  ,-2.2074111575496777142 ] 
dist 24=[-31.728724340377334678  ,1.6900395187217169782 ] 
dist 25=[-30.666525144900528881  ,4.9443209741876547113 ] 
dist 26=[-29.122314546459916149  ,8.0261261287691818357 ] 
dist 27=[-28.466682073618812936  ,10.648188590509550021  ] 
dist 28=[-11.405583633071291967  ,12.083473859722315026  ] 
dist 29=[-9.1305279296459118370 ,12.881942373905253428  ] 
dist 30=[-3.9050444207956403442 ,13.024008962144878174  ] 
dist 31=[-2.8414456131091440195 ,17.183628914850662924  ] 
dist 32=[3.3007377002334073417 ,21.154043022468020548  ] 
dist 33=[4.2800154724500089153 ,23.355362393678085173  ] 
dist 34=[4.3835758035934006404 ,24.637636093942026777  ] 
dist 35=[4.3286944697866636625 ,24.960731159543194213  ] 
dist 36=[4.0045233899067696101 ,7.8721761704191380112 ] 
dist 37=[3.4440216513260367309 ,8.0349630277038810906 ] 
dist 38=[2.4392369763112423812 ,8.0540368536369096947 ] 
dist 39=[1.3858039288465025017 ,8.0430077307369908175 ] 
dist 40=[.63168821943215976082,6.9634714359216009150 ] 
dist 41=[-.02715669120745894722,6.6684269191162614974 ] 
dist 42=[-.70394257183880939066,6.4668454138564401511 ] 
dist 43=[-1.3203251348251359357 ,6.3732290385364755439 ] 
dist 44=[-1.9608436464387718155 ,1.5097403060846619393 ] 
dist 45=[-2.5168123963642863467 ,.92662012576663311347] 
dist 46=[-2.9607475515552876523 ,-.45354175572235642931] 
dist 47=[-3.3559758685245320294 ,-.65590746035753484606] 
dist 48=[-3.6671341869551140787 ,-2.0162071704962166952 ] 
dist 49=[-3.7776961855933387547 ,-2.0814405030412873135 ] 
dist 50=[-4.0659649147216627079 ,-1.9824473309994453548 ] 
dist 51=[-4.2860003880055520856 ,-1.8147716199300993453 ] 
dist 52=[-4.4099192097146142439 ,-1.5700419167986285917 ] 
dist 53=[-4.4253764612435073884 ,-1.2289011648443390466 ] 
dist 54=[-4.3194493029348019871 ,-.67861189342630008443] 
dist 55=[-4.2875104379157261349 ,-.11760853304819066565] 
dist 56=[-3.5837497420142260450 ,.26615295843052169244] 
dist 57=[-3.4063578655139999093 ,.6394180542766637128 ] 
dist 58=[-3.2441035659407327855 ,1.1443579258976354127 ] 
dist 59=[-3.1652111523924256047 ,1.6357876690807424612 ] 
dist 60=[-.90686913417698593694,2.0490397037931342629 ] 
dist 61=[-.66849440461215580387,2.2728400741747776329 ] 
dist 62=[-.12248285564546424673,2.3967261661146119196 ] 
dist 63=[-.01619227018723544027,2.4241824669151078098 ] 
dist 64=[.61587374203981963473,2.1901523826584330845 ] 
dist 65=[.71030356181728680054,2.4305755006121705346 ] 
dist 66=[.67786748242501960989,2.5662941619760027194 ] 
dist 67=[.62661434971724472517,2.5982901392839663903 ] 
dist 68=[.55479434474024677722,1.0260714683842447166 ] 
dist 69=[.45598485961559953411,1.0327378640319549994 ] 
dist 70=[.29759340329799556191,1.0112804247199635962 ] 
dist 71=[.13595515833412049432,1.0081459268925169306 ] 
dist 72=[.02423207636943169450,.83745047500886432275] 
dist 73=[-.06987557073712709404,.79485804350234749647] 
dist 74=[-.16165831492541210179,.76760520882257559231] 
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dist 90=[-.38949685831670763275,.21104328463373704712] 
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dist 152=[-.00653505588983914596,.00096649687128344284] 
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dist 159=[2.48592142627565017460e-05,.00644593649389600001] 
dist 160=[.00124584540981204672,.00540967421423999881] 
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dist 168=[7.19809606514325580460e-05,.00146353082905080250] 
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dist 171=[-.00069986182376654799,.00130299254515929265] 
dist 172=[-.00089400079342502482,.00017983445300035135] 
dist 173=[-.00100516085769965364,4.68080518064132401610e-05] 
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dist 176=[-.00111003497991089229,-.00066844441661455006] 
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dist 189=[-.00010501293403953409,.00059734415486415021] 
dist 190=[1.79432094288550425540e-05,.00062992356993401842] 
dist 191=[4.23286271500586594910e-05,.00063779767614936669] 
dist 192=[.00017816198659866528,.00051913959086337868] 
dist 193=[.00020076863149732894,.00056808107843671832] 
dist 194=[.00023872102629880199,.00059739215045778490] 
dist 195=[.00022122212442747878,.00060483897830780856] 
dist 196=[.00019398908168614754,.00024696445328145530] 
dist 197=[.00016339113635684313,.00024586224222040783] 
dist 198=[.00012508451743170208,.00023543628113686682] 
dist 199=[6.72416721569142618900e-05,.00023345799656355517] 
dist 200=[9.21316087986166393730e-06,.00018933024886759765] 
dist 201=[-2.98318422776656543870e-05,.00017881801411155713] 
dist 202=[-6.17038667680619202750e-05,.00016987587370852199] 
dist 203=[-9.12529928428976902690e-05,.00016671531876591464] 
dist 204=[-.00011636697373447981,2.08899094115728567940e-05] 
dist 205=[-.00013062983427416205,3.48273786174807490650e-06] 
dist 206=[-.00013941344811210612,-3.68370987733553813260e-05] 
dist 207=[-.00014277290808966099,-4.30271252554762884690e-05] 
dist 208=[-.00014315797327419172,-8.98107815176659084320e-05] 
dist 209=[-.00014249022654149066,-9.67660115789563931370e-05] 
dist 210=[-.00013666109451343009,-.00010952189710687151] 
dist 211=[-.00013659584690444148,-9.92220032994481948480e-05] 
dist 212=[-.00013627785468414910,-8.49490720748831402010e-05] 
dist 213=[-.00013544038555119629,-6.91008105592989240360e-05] 
dist 214=[-.00012930161407898685,-4.93800406157427823140e-05] 
dist 215=[-.00012803829596860854,-1.97302212557218565580e-05] 
dist 216=[-.00010365422289154922,9.96734519540704921140e-06] 
dist 217=[-9.78660627468936544150e-05,2.98780043367140109340e-05] 
dist 218=[-9.25436624372011530360e-05,4.60539251191417469540e-05] 
dist 219=[-9.04319210210252013680e-05,6.09225088204927814540e-05] 
dist 220=[-1.94954465374222850370e-05,7.34701339541062606890e-05] 
dist 221=[-1.22283198099686698900e-05,8.04304994023108438170e-05] 
dist 222=[4.19970266164847104640e-06,8.45157582373632923040e-05] 
dist 223=[7.38732158188414777390e-06,8.55796929626053489690e-05] 
dist 224=[2.55457643575201272380e-05,6.71981276887272664210e-05] 
dist 225=[2.85381108489026234040e-05,7.36029791875342770210e-05] 
dist 226=[3.24430154497381435450e-05,7.74832311558308332120e-05] 
dist 227=[2.83217438500144578060e-05,7.84369532896446549400e-05] 
dist 228=[2.33689624399107550760e-05,3.44936385361610288150e-05] 
dist 229=[1.78900783374963052070e-05,3.42216422646829307730e-05] 
dist 230=[1.10850301724652759490e-05,3.32447295912825025670e-05] 
dist 231=[8.66191881502410980230e-07,3.26559151327117772770e-05] 
dist 232=[-9.36683327161620397610e-06,2.89409680595792429410e-05] 
dist 233=[-1.62283000016740532810e-05,2.79601515889164089000e-05] 
dist 234=[-2.18045262746487931710e-05,2.56341489997562006980e-05] 
dist 235=[-2.69342393396856258070e-05,2.47906202626428325770e-05] 
dist 236=[-3.12670025674636316190e-05,1.33954222848371911810e-05] 
dist 237=[-3.36787629870847509370e-05,1.16050609850139140920e-05] 
dist 238=[-3.51009005888208486200e-05,7.83965837712553692460e-06] 
dist 239=[-3.55041369249961913890e-05,6.82132149478955290320e-06] 
dist 240=[-3.53801323108983939090e-05,3.04253032557646401020e-06] 
dist 241=[-3.50565016847816557760e-05,2.22493303237899311810e-06] 
dist 242=[-3.38615845903026657920e-05,1.16188867933613249530e-06] 
dist 243=[-3.13506290788369023930e-05,9.01704504949491916070e-07] 
dist 244=[-9.64612119036994998040e-07,8.00441944443169668600e-07] 
dist 245=[-9.60118499654850343340e-07,7.59776613570565004390e-07] 
dist 246=[-9.34574585765195830270e-07,6.54023462251837708310e-07] 
dist 247=[-9.17570212887172745150e-07,6.23668185967195604940e-07] 
dist 248=[-6.66336822590217783440e-07,4.33121594685094997840e-07] 
dist 249=[-6.25345971005713157660e-07,3.92662592043850343250e-07] 
dist 250=[-5.15014319070214670080e-07,3.12549010389495830080e-07] 
dist 251=[-4.94942673828398708890e-07,2.90176125169672745120e-07] 
dist 252=[-3.01497349304338025550e-07,-4.14807483172822166180e-08] 
dist 253=[-2.63970214924557251010e-07,-9.07899210610868422820e-08] 
dist 254=[-2.09987610102781974450e-07,-1.17665322159732306040e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 1, 2, 0, 1] 
dist 0=[119.07778825025642325   ,119.07778825025642325   ] 
dist 1=[117.64268715711492670   ,120.09487089380549525   ] 
dist 2=[115.31689221947048877   ,120.75017900938865140   ] 
dist 3=[111.98030954112173258   ,120.99140977154651411   ] 
dist 4=[104.52575768415335977   ,120.53551824370790980   ] 
dist 5=[96.148837154162075258  ,119.25285253265720325   ] 
dist 6=[85.309554305203298253  ,118.43031086937906028   ] 
dist 7=[71.480921382589786174  ,98.163389554438455347  ] 
dist 8=[61.275426429519976118  ,95.060175584769056899  ] 
dist 9=[51.919393439018348017  ,86.170361884493986460  ] 
dist 10=[41.451075146602361287  ,84.794726866603700370  ] 
dist 11=[31.206112624563844846  ,66.883933671801425152  ] 
dist 12=[22.723052111811338111  ,65.716062923271309598  ] 
dist 13=[13.959054252895018850  ,59.383710783617910823  ] 
dist 14=[2.5700536577639598234 ,58.414666141604863311  ] 
dist 15=[-8.1871936780296570500 ,18.994466761443081444  ] 
dist 16=[-14.443996196806845948  ,17.180752541989303357  ] 
dist 17=[-18.623109787286609341  ,9.5127854087832780389 ] 
dist 18=[-21.105881161897723133  ,8.1296439454161517985 ] 
dist 19=[-22.756630383499688488  ,5.5054674832480012473 ] 
dist 20=[-23.615400510423331170  ,4.8970661456955101681 ] 
dist 21=[-24.094436717538571983  ,3.0818997695881916167 ] 
dist 22=[-25.628285050395412589  ,2.7825162088330670967 ] 
dist 23=[-27.690114870621648025  ,2.8694359617313418755 ] 
dist 24=[-28.781629639597055288  ,3.4517520849706808290 ] 
dist 25=[-29.240941150815852650  ,4.2593185378703519714 ] 
dist 26=[-29.330576090281262060  ,5.2484130316406188850 ] 
dist 27=[-26.877000783343896188  ,6.5326888010467056541 ] 
dist 28=[-24.263881751495078453  ,8.5206904491685587452 ] 
dist 29=[-21.109854127429381199  ,10.421191622125315378  ] 
dist 30=[-20.863779345026798302  ,11.360864314749125194  ] 
dist 31=[-4.4960805030108194637 ,11.847110138966990717  ] 
dist 32=[-2.5582733741279705219 ,11.944417909228795245  ] 
dist 33=[1.9731539227609093072 ,11.867900477257330004  ] 
dist 34=[2.6526285801172129011 ,11.958768161242392395  ] 
dist 35=[7.9861590569374592758 ,11.566439668532627321  ] 
dist 36=[5.2780966298874955790 ,11.325209555275329246  ] 
dist 37=[2.4907592564812485622 ,12.372565862524160570  ] 
dist 38=[.5409651248651598786 ,13.029006508231706394  ] 
dist 39=[-1.1229582294595567329 ,13.399491084816785371  ] 
dist 40=[-2.7776036196110695324 ,13.426883290350127314  ] 
dist 41=[-4.2551839493425629723 ,13.189112770217932356  ] 
dist 42=[-5.8254059211569424349 ,12.997200621051544684  ] 
dist 43=[-7.2935525967392107686 ,11.338456288662503593  ] 
dist 44=[-8.1101966269662960537 ,10.888077427918326709  ] 
dist 45=[-8.5869171345394182548 ,10.167342658205419450  ] 
dist 46=[-8.7071344092145658918 ,9.9125545078188005989 ] 
dist 47=[-7.3479884911301422219 ,4.2734069925365900214 ] 
dist 48=[-7.3106769724826518240 ,3.5624576021172469313 ] 
dist 49=[-6.8292766777102731376 ,1.9678557906547039378 ] 
dist 50=[-7.5500391155328236660 ,1.5814451202550565133 ] 
dist 51=[-9.0290031623989525442 ,-.22390931775521957797] 
dist 52=[-9.8393317877689621906 ,.14281050022204248579] 
dist 53=[-10.299418271110166945  ,2.1537192469758454313 ] 
dist 54=[-10.387926877584238302  ,3.5100198297724610467 ] 
dist 55=[-3.1385442784476012864 ,4.6177188221311918552 ] 
dist 56=[-2.9682961199386561118 ,5.6422269682815376616 ] 
dist 57=[-2.6877743976534443315 ,6.5086605889367473231 ] 
dist 58=[-2.6771443505149291359 ,6.9891130308815648795 ] 
dist 59=[-2.2156586038913496707 ,7.2690445329100319720 ] 
dist 60=[-2.1016604312106665793 ,7.3397644510688253183 ] 
dist 61=[-2.0242934309444073780 ,1.5308448738360471333 ] 
dist 62=[-2.0040178822466379183 ,1.6682151569290471862 ] 
dist 63=[-.2888744683519901991 ,1.7667091206010858992 ] 
dist 64=[-.08778555471976387846,1.7886537419429401248 ] 
dist 65=[.37985429507519911686,1.7798363374274457499 ] 
dist 66=[.44994387011082136117,1.7711970032984319666 ] 
dist 67=[.99575049927297830831,1.5161640631276234783 ] 
dist 68=[.97224222615278230416,1.4476290387097717911 ] 
dist 69=[.72870109389060214852,1.3886463695874996457 ] 
dist 70=[.3491696983468309214 ,1.3731275464174459558 ] 
dist 71=[-.03448659748768310441,1.3938032765073630973 ] 
dist 72=[-.29443393340781387649,1.3915033037868193296 ] 
dist 73=[-.5079528654117959541 ,1.3522663103583603948 ] 
dist 74=[-.70939106410923025711,1.3337004952681144938 ] 
dist 75=[-.89428133827150054077,1.1369102229776432261 ] 
dist 76=[-.99445779352394208567,1.0862938065963251830 ] 
dist 77=[-1.0508091890444247503 ,1.0162780573241023696 ] 
dist 78=[-1.0632178282319851545 ,.98823580633734487427] 
dist 79=[-.46558102085391309639,.32118183519089251366] 
dist 80=[-.47403938733631869565,.23567578276199294211] 
dist 81=[-.55722418585647464551,.04315858484372823660] 
dist 82=[-.73047334647262291005,.00260602268373507593] 
dist 83=[-.87723944951651266705,-.21028178724428794329] 
dist 84=[-.95915813585502723345,-.2466966435897829321 ] 
dist 85=[-1.0065772173881039303 ,-.22620932761551841439] 
dist 86=[-1.0179259776663275530 ,-.10338237809735445539] 
dist 87=[-.36867279988283258696,.02067789103763920314] 
dist 88=[-.3666455498074301615 ,.1049664294748681754 ] 
dist 89=[-.35801387178738837829,.17453675159061939097] 
dist 90=[-.35208621351483881178,.24018869274259530765] 
dist 91=[-.31327311851766504785,.2966867070598105219 ] 
dist 92=[-.30283083171806505609,.32992934783078605792] 
dist 93=[-.27792961050206439773,.351859670670619241  ] 
dist 94=[-.26880329312439662865,.36346380427067721735] 
dist 95=[-.14392644449980201962,.36881365381737485591] 
dist 96=[-.12432370152656594917,.3675080731953449084 ] 
dist 97=[-.08281726858664930180,.35959564609728962118] 
dist 98=[-.07151595431112588322,.35359398353410555691] 
dist 99=[-.02909662733055133499,.31331229970821666932] 
dist 100=[-.02003352908118686152,.30234583031953265479] 
dist 101=[-.00713976793930078088,.25997846681176276738] 
dist 102=[-.00339838406566975607,.20596855562514311377] 
dist 103=[-.02306511417294962181,.20602365611543782649] 
dist 104=[-.06393910414119345983,.20484909301664511486] 
dist 105=[-.09723307152154690524,.19609333674944526692] 
dist 106=[-.12792791248192991893,.19386571170259172401] 
dist 107=[-.15385352517458389549,.15838810205364964905] 
dist 108=[-.16821688472475211246,.1498407754057957486 ] 
dist 109=[-.17657968513319883314,.14091994548045565741] 
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dist 159=[-.00051593653370266502,.00374706780403724911] 
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dist 174=[-.00289738598097372315,.00207961169484752477] 
dist 175=[-.00088621756921836624,.00049877360347231850] 
dist 176=[-.00088575056354129995,.00033608939215824682] 
dist 177=[-.00100651796796619725,-3.04786845071572179530e-05] 
dist 178=[-.00132222410750370769,-.00010448534758205948] 
dist 179=[-.00158870853464562518,-.00050787425932827741] 
dist 180=[-.00173671321494884102,-.00053270420571178440] 
dist 181=[-.00182493089032170597,-.00039914446313698212] 
dist 182=[-.00184716215114195262,-.00019703108615044893] 
dist 183=[-.00071510813537441897,5.85557692447176942160e-06] 
dist 184=[-.00071216014695671871,.00014249054253477565] 
dist 185=[-.00068113779152876511,.00025413820779776616] 
dist 186=[-.00067647952362516895,.00035782025466276065] 
dist 187=[-.00054375371341992992,.00044604471302913605] 
dist 188=[-.00051242342237944504,.00049632260536364983] 
dist 189=[-.00048912570142935142,.00052750430038044605] 
dist 190=[-.00048352932373818278,.00053991334155749546] 
dist 191=[-4.13570802991350695660e-05,.00054170504357889819] 
dist 192=[1.02488030570567707500e-05,.00053915160265136647] 
dist 193=[.00013028345160989723,.00051782972163675641] 
dist 194=[.00014767030394283052,.00051196209504545183] 
dist 195=[.00022426432552821424,.00042208852986789056] 
dist 196=[.00017218378317780981,.00040021273065410588] 
dist 197=[.00010712450057321405,.00037674772067557234] 
dist 198=[9.04162932562130000000e-06,.00036499797612359522] 
dist 199=[-8.92886036309409507930e-05,.00036495748277420004] 
dist 200=[-.00015533159818007421,.00036259812810650558] 
dist 201=[-.00020910939237932314,.00034860995010006954] 
dist 202=[-.00025874187646737411,.00034325779707652953] 
dist 203=[-.00030076388293547102,.00028859188337188860] 
dist 204=[-.00032432489354363266,.00027497966467889137] 
dist 205=[-.00033972475763589853,.00025590691061171210] 
dist 206=[-.00034339597107805541,.00024853715316764266] 
dist 207=[-.00012515154327326848,7.97386898401058604480e-05] 
dist 208=[-.00012464255109147620,5.75850602189995482060e-05] 
dist 209=[-.00015735277382708095,8.20984546154314953430e-06] 
dist 210=[-.00020277328522724021,-2.60555600454178772800e-06] 
dist 211=[-.00024106590745581189,-5.56249808312834333210e-05] 
dist 212=[-.00026225329176722706,-6.49282353690019640230e-05] 
dist 213=[-.00027457975577998566,-4.97051058098088087900e-05] 
dist 214=[-.00027768692332658753,-1.81073207950838386540e-05] 
dist 215=[-9.69555561084838605880e-05,1.35572593044968025950e-05] 
dist 216=[-9.61657529313158230340e-05,3.48170844083631149250e-05] 
dist 217=[-9.31701066538444984060e-05,5.21233142624308579590e-05] 
dist 218=[-9.14062137762026229540e-05,6.80898899325560190450e-05] 
dist 219=[-8.03595666357813447620e-05,8.16067276442619589970e-05] 
dist 220=[-7.74553491146345070320e-05,8.91860848367274377600e-05] 
dist 221=[-7.10243651189676546260e-05,9.37281063332816070980e-05] 
dist 222=[-6.87857328671291289710e-05,9.51849592915513698220e-05] 
dist 223=[-3.45155141937408140690e-05,9.51006506399072011850e-05] 
dist 224=[-2.93138609795418910710e-05,9.42852831993082537000e-05] 
dist 225=[-1.82638420725743167660e-05,9.13808198930529660600e-05] 
dist 226=[-1.52824504695071389020e-05,8.96848914970681191720e-05] 
dist 227=[-4.19980621646379948950e-06,7.90930363248502502470e-05] 
dist 228=[-1.86956289169069545290e-06,7.63140342474137359840e-05] 
dist 229=[1.20533144848155065590e-06,6.58913105236473760630e-05] 
dist 230=[-4.45914493037598025410e-08,5.11144383936891600120e-05] 
dist 231=[-9.37657607257765594520e-06,5.09522709555358984000e-05] 
dist 232=[-1.56463503532567679620e-05,5.06073335172176590150e-05] 
dist 233=[-2.07547086465127659090e-05,4.83723599723101762940e-05] 
dist 234=[-2.54752603880223035320e-05,4.77997146728977357170e-05] 
dist 235=[-2.94768981146010444310e-05,3.91399689750090153590e-05] 
dist 236=[-3.17307866057143387750e-05,3.70602304187072938980e-05] 
dist 237=[-3.30946584577376562720e-05,3.48318976846169963490e-05] 
dist 238=[-3.35624661748674797250e-05,3.37171080190537278060e-05] 
dist 239=[-3.36251345228071292640e-05,1.19483513943659540030e-05] 
dist 240=[-3.33803333476787264680e-05,1.02620259014785912260e-05] 
dist 241=[-3.28692054725130263260e-05,6.68237441573716957450e-06] 
dist 242=[-3.24796998503420179020e-05,5.71263076490612553170e-06] 
dist 243=[-3.06695914158969521110e-05,2.09035548315840562980e-06] 
dist 244=[-3.04882789518672486700e-05,1.32501238578991414390e-06] 
dist 245=[-3.17499678629962350340e-05,2.73868888764222372350e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 2, 2, 1, 2] 
dist 0=[129.64828335840729283   ,129.64828335840729283   ] 
dist 1=[127.81374275842174669   ,130.17415440134232483   ] 
dist 2=[122.66001177314191659   ,130.13935737777308018   ] 
dist 3=[115.90928041853881641   ,129.85979079132490859   ] 
dist 4=[107.72311934250712513   ,125.03834953326939612   ] 
dist 5=[97.065691904528078821  ,120.70284242511139329   ] 
dist 6=[80.487670488703465025  ,118.29952307427920992   ] 
dist 7=[63.558700090396862766  ,115.92520249070028912   ] 
dist 8=[51.500646793708310286  ,110.88738914964627408   ] 
dist 9=[40.876830588460779368  ,88.436536706161076470  ] 
dist 10=[29.636380339942989180  ,86.665682588606630587  ] 
dist 11=[19.018358442289796524  ,60.376304838969370389  ] 
dist 12=[10.856578416158132753  ,58.068084395011593068  ] 
dist 13=[2.9903363242433169477 ,44.077561867151527257  ] 
dist 14=[-6.4757828764507387793 ,41.728098439139056856  ] 
dist 15=[-15.191833914055595062  ,36.717596981356245495  ] 
dist 16=[-20.079993595855239654  ,35.799059145027757110  ] 
dist 17=[-23.245098809394049252  ,1.2616983645091584715 ] 
dist 18=[-28.318023338299795435  ,-.49434315044931978851] 
dist 19=[-32.540715031386950301  ,-7.9202971499213865949 ] 
dist 20=[-34.371227646060854890  ,-9.1009724681051457524 ] 
dist 21=[-35.159103449739701496  ,-11.344926727021092347  ] 
dist 22=[-35.218587959932102480  ,-10.777856691415135384  ] 
dist 23=[-31.983430811566851161  ,-8.5357534931538362673 ] 
dist 24=[-30.943941952995614769  ,-4.4326466733566042120 ] 
dist 25=[-30.165586128430784227  ,-.78692643118336383104] 
dist 26=[-29.581100933456686216  ,2.8656925910266497370 ] 
dist 27=[-9.7664991962231242069 ,6.2437638537727901558 ] 
dist 28=[-7.3179529843082424270 ,8.8973504718572203761 ] 
dist 29=[-1.4252843307277925293 ,12.193374673412290863  ] 
dist 30=[-.5636300922096634248 ,14.780524533969413290  ] 
dist 31=[7.0125640899750293057 ,17.298049268572977742  ] 
dist 32=[8.2028052160999285104 ,20.326394950957685778  ] 
dist 33=[10.136213765999423347  ,22.996557689924282580  ] 
dist 34=[10.450998601924611775  ,24.094200797670385499  ] 
dist 35=[9.9242197788280681817 ,24.549583715055034662  ] 
dist 36=[8.5152774184090878314 ,24.663204751798117756  ] 
dist 37=[6.5721680855848502749 ,21.892961974813153262  ] 
dist 38=[3.4581270193575219135 ,21.169080970750017275  ] 
dist 39=[.29014042491816789927,20.743950416999871644  ] 
dist 40=[-1.8676902370078242133 ,20.636176469918440053  ] 
dist 41=[-3.6479004492625478337 ,15.393756313964678148  ] 
dist 42=[-5.3188238038451510878 ,14.960858996289412866  ] 
dist 43=[-6.8318560726546518866 ,6.9993332654589334348 ] 
dist 44=[-7.6850585730075101592 ,6.2453651123884112607 ] 
dist 45=[-8.1664781409835070946 ,4.5372304241601197543 ] 
dist 46=[-9.8214083325308313995 ,4.0687806876775029186 ] 
dist 47=[-11.948610777853759476  ,1.9924981721842220859 ] 
dist 48=[-13.080047884152436889  ,1.6002848644470134459 ] 
dist 49=[-13.697659179116255858  ,.70836434875892613247] 
dist 50=[-13.817512402412484521  ,.5216034915152701341 ] 
dist 51=[-12.767166421108948604  ,-3.1454476548418257421 ] 
dist 52=[-12.620371561724898107  ,-2.7762656190748617447 ] 
dist 53=[-11.230665212004367021  ,-2.2721660685083769292 ] 
dist 54=[-10.822205976056004640  ,-1.4677887468086143213 ] 
dist 55=[-10.201581861423026681  ,-.64804778504813330917] 
dist 56=[-9.9586376217035736942 ,-.08282594456440857673] 
dist 57=[-3.7940175905171158614 ,1.0650470047068786150 ] 
dist 58=[-2.9671937166500923676 ,3.3623858073046603718 ] 
dist 59=[-1.0813009094266317956 ,5.2364194570253905593 ] 
dist 60=[-.6851176419679035641 ,6.9672418311510677948 ] 
dist 61=[1.4103067830078420575 ,8.4301920290327420000 ] 
dist 62=[1.4423963486981395347 ,9.2411618437514229123 ] 
dist 63=[1.8842291896252302943 ,9.7135353386333836406 ] 
dist 64=[1.8838452950397775660 ,9.8325081791226117592 ] 
dist 65=[1.8179095016469436998 ,3.0163778927477496151 ] 
dist 66=[1.6475783277058163769 ,3.0521383005887268368 ] 
dist 67=[1.4283311184176301935 ,3.0309843344232025490 ] 
dist 68=[1.1681868408504230627 ,3.0213997375125405159 ] 
dist 69=[.83408217197441881101,2.5801153630495541674 ] 
dist 70=[.32122674511713684708,2.4644750467230592037 ] 
dist 71=[-.19504602870715295983,2.3771763298825486235 ] 
dist 72=[-.54274434897264615744,2.3392260875425132214 ] 
dist 73=[-.82635712127777644529,.50765868513440419198] 
dist 74=[-1.0883012402732354534 ,.28740875411927719466] 
dist 75=[-1.3097322442631458405 ,-.18443238454075232587] 
dist 76=[-1.4327645619898367487 ,-.2391243492525883157 ] 
dist 77=[-1.5047225903672357743 ,-.34347593215383908554] 
dist 78=[-1.5228245953858027792 ,-.36470913792806524296] 
dist 79=[-1.6528225744224451697 ,-.40980640643616265905] 
dist 80=[-1.7271302656363689570 ,-.41107520308685790701] 
dist 81=[-1.7643289021547942068 ,-.39650886296025717708] 
dist 82=[-1.7664418887112658224 ,-.35703135235166541719] 
dist 83=[-1.7167028409262391053 ,-.3057397340942195626 ] 
dist 84=[-1.7021248451778423237 ,-.2442630666369080435 ] 
dist 85=[-1.4178955740869923662 ,-.16489972369529359904] 
dist 86=[-1.3468474294136256746 ,-.04259246011226779323] 
dist 87=[-1.2787556635922176508 ,.08082597849005109119] 
dist 88=[-1.2447543196065628972 ,.16460903654946219692] 
dist 89=[-.37247237499826461594,.23371453546434725588] 
dist 90=[-.28341753252241279537,.36585239464698339247] 
dist 91=[-.08077508483718166051,.56506815522078552875] 
dist 92=[-.03885645494919879577,.74954818445829228401] 
dist 93=[-.01382008767173405365,.90600294225660330482] 
dist 94=[-.00743176010249590261,1.0007626865834045324 ] 
dist 95=[.01393886861318224705,1.0549262995154296946 ] 
dist 96=[.0147323790482094664 ,1.0675311503678466988 ] 
dist 97=[.00841235104794812570,.41339974125972058987] 
dist 98=[-.00904935569648586549,.40695391100238353329] 
dist 99=[-.0318220997271020908 ,.39689298171794874606] 
dist 100=[-.05923232423052713521,.39543961856210533644] 
dist 101=[-.09469678547165719145,.32658895119540851283] 
dist 102=[-.14945000228785046291,.31520297637386905058] 
dist 103=[-.20477137938633590847,.29848633185223330259] 
dist 104=[-.24249572538702209968,.29587951570341997888] 
dist 105=[-.27380680298977795444,.03840007382488016322] 
dist 106=[-.30367465293799633666,.02405621442043967269] 
dist 107=[-.32962506433587896731,-.03201592750720236557] 
dist 108=[-.35235234281530189106,-.03845843850935912199] 
dist 109=[-.36505422929029247109,-.05019202559547763754] 
dist 110=[-.36731870020708088037,-.05236259539333750885] 
dist 111=[-.19776757169011298742,-.05558558042619183410] 
dist 112=[-.2054535380852149587 ,-.05531767804354015380] 
dist 113=[-.20877978453683411439,-.05355941466785525854] 
dist 114=[-.20846144534628768801,-.04936175001423497062] 
dist 115=[-.20304688411596847151,-.04403526854824591596] 
dist 116=[-.20000331332772824774,-.03779466713985127104] 
dist 117=[-.17214688765245272638,-.02982166901519464169] 
dist 118=[-.16483688238273732635,-.01761666311573739943] 
dist 119=[-.15371404737134558099,-.00532233456207743817] 
dist 120=[-.14964623893380622329,.00300591986083253525] 
dist 121=[-.05126452482705350645,.02420542438909164966] 
dist 122=[-.03812978389380594658,.06043038087288443098] 
dist 123=[-.00862459549880893476,.08987783148687030278] 
dist 124=[-.00226181327231583614,.11695802565717310846] 
dist 125=[.02556466707881772356,.13980718086299402043] 
dist 126=[.02598802087228279743,.1524567211019370025 ] 
dist 127=[.02870037115163473259,.1598181412917710961 ] 
dist 128=[.02812430170075284606,.16167229503307984061] 
dist 129=[.02672879053817857154,.04884738274264985165] 
dist 130=[.02388844531520835819,.04886884128140696312] 
dist 131=[.02041163542735969722,.04732890152044604478] 
dist 132=[.01648893636883311806,.04700710804492380743] 
dist 133=[.01156909435456931071,.03876727880859558367] 
dist 134=[.00413315139824486078,.03674811873508575346] 
dist 135=[-.00332406522440098975,.03509629243078382614] 
dist 136=[-.00832851618034290488,.03447158312296135425] 
dist 137=[-.01239722713117402826,.00533225034686251679] 
dist 138=[-.01613951794710914883,.00184824085008692249] 
dist 139=[-.01929733691804005503,-.00414205180391974181] 
dist 140=[-.02104563181424232172,-.00492016247076334137] 
dist 141=[-.02206308969299001149,-.00626395959269250850] 
dist 142=[-.02478030733292728556,-.00652023476813339436] 
dist 143=[-.02651223954294957214,-.00673942652365269509] 
dist 144=[-.02724027796728797566,-.00664710269274841646] 
dist 145=[-.02739850649095808731,-.00638233069592498091] 
dist 146=[-.02729836433850687439,-.00582039647335676613] 
dist 147=[-.02623421222014780149,-.00512538996811457540] 
dist 148=[-.02598115517653445995,-.00433220272291184089] 
dist 149=[-.02129885438798217477,-.00333150393537396714] 
dist 150=[-.02016536886709270051,-.00181253523936333998] 
dist 151=[-.01907976737549294418,-.00028636866210807846] 
dist 152=[-.01858967962745481045,.00074295689446523658] 
dist 153=[-.00465050439500592931,.00194679848122388689] 
dist 154=[-.00320909316957055500,.00570197109182728547] 
dist 155=[5.13827179838040593850e-05,.00875645552303315508] 
dist 156=[.00070470164864076267,.01156962294475410816] 
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dist 180=[-.00304065207642315519,-.00056106174288453266] 
dist 181=[-.00258737492200841679,-.00043539659240671313] 
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dist 183=[-.00229712472251859678,-5.47574302905120581440e-05] 
dist 184=[-.00223406189329460203,7.36201099574312889540e-05] 
dist 185=[-.00073550947323993946,.00040628981518252638] 
dist 186=[-.00053688651768679010,.00095397669863600537] 
dist 187=[-9.31814166891735075190e-05,.00139869768026002511] 
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dist 194=[.00035720517818133183,.00075316321282713528] 
dist 195=[.00030243398237078744,.00072168122184943818] 
dist 196=[.00024167694675468551,.00071697379046532221] 
dist 197=[.00016611242616023115,.00057838661084598968] 
dist 198=[5.25439615493540225690e-05,.00054807194332695904] 
dist 199=[-6.11919778160179894520e-05,.00052047058777239057] 
dist 200=[-.00013742254918118091,.00051468113205685361] 
dist 201=[-.00019932890447375749,9.84994302252030349110e-05] 
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dist 203=[-.00030414445188419100,-5.78964210225430838250e-05] 
dist 204=[-.00033068978380796350,-6.93902353018259163340e-05] 
dist 205=[-.00038282103539094677,-8.79021669740846391560e-05] 
dist 206=[-.00042425596327685724,-9.17896807301432933390e-05] 
dist 207=[-.00044933814598106424,-9.25367273085783181760e-05] 
dist 208=[-.00045796480589835336,-8.98325046988968357920e-05] 
dist 209=[-.00045765759535261138,-8.42929818083907428900e-05] 
dist 210=[-.00045491796010136603,-7.35793662468848544960e-05] 
dist 211=[-.00043566771054806957,-6.06300250525122213700e-05] 
dist 212=[-.00043056677302750812,-4.62124478248939724980e-05] 
dist 213=[-.00035364698270559532,-2.82453573510007737140e-05] 
dist 214=[-.00033506985239616120,-1.20127920358947614000e-06] 
dist 215=[-.00031505723120489873,2.59026418194066715170e-05] 
dist 216=[-.00030500901066705871,4.41077278293906603630e-05] 
dist 217=[-.00011051243471770041,7.79770552995869166140e-05] 
dist 218=[-9.52771741533919735110e-05,.00013345080162167652] 
dist 219=[-6.27745188545044607250e-05,.00017855098237042606] 
dist 220=[-5.39178914207677743980e-05,.00022006911824337385] 
dist 221=[-2.05236766275717788650e-05,.00025515789338439169] 
dist 222=[-1.35273739338060056380e-05,.00027472902769991023] 
dist 223=[-3.21621580365885847080e-06,.00028665836676720565] 
dist 224=[-2.84519919031455665860e-06,.00028973480106589140] 
dist 225=[-5.13330108689514645720e-06,9.17595208957603566290e-05] 
dist 226=[-9.62607096626222036140e-06,8.99420605409029876210e-05] 
dist 227=[-1.50784772910084230250e-05,8.08630780116027988740e-05] 
dist 228=[-2.11773863147558064120e-05,7.94751727123906857030e-05] 
dist 229=[-2.87964513217884937560e-05,7.04591004294995301090e-05] 
dist 230=[-4.02853678410864342570e-05,6.80389912057623082060e-05] 
dist 231=[-5.18088058593151691040e-05,6.26649567503421087430e-05] 
dist 232=[-5.95651664451538874490e-05,6.07688355455537559110e-05] 
dist 233=[-6.59010011425747998180e-05,8.80196672322756878490e-06] 
dist 234=[-7.17841661221481654530e-05,7.56560355123308140960e-06] 
dist 235=[-7.67920253569031695520e-05,2.89686339334389754920e-06] 
dist 236=[-7.96524350430630091340e-05,1.91997522576808569850e-06] 
dist 237=[-8.16327112904478633100e-05,4.64787098891775338100e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 0, 0, 2, 1, 2] 
dist 0=[126.61917291113030686   ,126.61917291113030686   ] 
dist 1=[122.63196520794959726   ,127.91533553473372502   ] 
dist 2=[117.20328663846276500   ,128.08432838653472801   ] 
dist 3=[110.18105003997951884   ,127.59090715935020792   ] 
dist 4=[100.78119084185846560   ,125.80406610220464718   ] 
dist 5=[85.895822025936035680  ,119.10968013917678469   ] 
dist 6=[70.597565343425744619  ,117.39329909076371435   ] 
dist 7=[59.549951101063946739  ,112.69613526579121083   ] 
dist 8=[49.660238643278692053  ,103.93387658605509105   ] 
dist 9=[38.950982009660893471  ,87.327250617502854880  ] 
dist 10=[28.679811008924375833  ,83.700592208257894218  ] 
dist 11=[20.518555797027062747  ,79.524122560159737449  ] 
dist 12=[12.395011196333319550  ,77.783938625386054579  ] 
dist 13=[2.2495200029765566278 ,49.192800026010561715  ] 
dist 14=[-7.2347908776956874891 ,44.532750492995416377  ] 
dist 15=[-12.733644578069480557  ,43.721043832424387975  ] 
dist 16=[-16.386238575570484396  ,16.822290983569722963  ] 
dist 17=[-18.517550193312624510  ,1.8480475057160936601 ] 
dist 18=[-21.457055773331269402  ,-.67034531197960130434] 
dist 19=[-25.961039460754813722  ,-4.9721012871644439291 ] 
dist 20=[-30.069904245896554085  ,-5.7408780108921754966 ] 
dist 21=[-33.348255897597220334  ,-9.1236670979112305629 ] 
dist 22=[-34.552354605742858732  ,-7.7655080618067545377 ] 
dist 23=[-34.948681424253104967  ,-4.4933042474701471803 ] 
dist 24=[-35.000239389174717230  ,-.84854279107355951073] 
dist 25=[-30.766613201904795272  ,1.9955663681438144804 ] 
dist 26=[-29.596036575727471766  ,4.7038884011618084746 ] 
dist 27=[-28.852446091048794433  ,7.8231349130502036645 ] 
dist 28=[-28.533639836983819750  ,10.874125630048342767  ] 
dist 29=[-7.3942640580095872721 ,13.319235039071515713  ] 
dist 30=[-4.8691638149021412752 ,15.744031726751695814  ] 
dist 31=[1.0610055306427152371 ,18.723655715225822696  ] 
dist 32=[1.9750576358221117682 ,21.379375087859338494  ] 
dist 33=[9.1058961295776424994 ,22.520585091086471013  ] 
dist 34=[8.9952166915393374954 ,23.020030861793315457  ] 
dist 35=[7.6712544594987764611 ,23.121322933349780179  ] 
dist 36=[5.8296508264730927234 ,20.772281140142824469  ] 
dist 37=[2.8643828068172702406 ,20.125555249520841484  ] 
dist 38=[-.1540759672105532505 ,19.716933781080819493  ] 
dist 39=[-2.2073517363179094746 ,19.546410585519194754  ] 
dist 40=[-3.8971182821848203622 ,17.663475687917486871  ] 
dist 41=[-5.4746368036238685481 ,15.639024048052627007  ] 
dist 42=[-6.8137695277741905214 ,15.059711769058466753  ] 
dist 43=[-7.5583669392882727058 ,14.109480481712282159  ] 
dist 44=[-7.9929475901281639808 ,13.772330594009699542  ] 
dist 45=[-9.5991584976483038704 ,6.3788009521261334326 ] 
dist 46=[-10.848293875321014328  ,5.4660142186078870885 ] 
dist 47=[-11.821001413343012662  ,3.4149116019210346417 ] 
dist 48=[-12.543575777794895693  ,2.8943635920572040202 ] 
dist 49=[-12.800228224301972158  ,.53330798158660939185] 
dist 50=[-13.446350402122793654  ,.09665822168597540021] 
dist 51=[-14.079574976008802521  ,-.78669353575733997669] 
dist 52=[-14.198169436683450706  ,-.99678089636505079897] 
dist 53=[-11.456794597948953873  ,-1.1182343495888114005 ] 
dist 54=[-10.704367413763214217  ,-.4695997931457095476 ] 
dist 55=[-10.403768159868764933  ,-.02023836984729436331] 
dist 56=[-6.4007422242230472140 ,3.3313229843793946163 ] 
dist 57=[-5.8225875953347810681 ,5.7784611721197164558 ] 
dist 58=[-4.5634790451503128649 ,7.7756435335765601718 ] 
dist 59=[-3.5239442662882060083 ,9.6219817503558632779 ] 
dist 60=[-2.7386824016197463186 ,11.183998589584487544  ] 
dist 61=[-1.1318940749397866973 ,12.059531862297080674  ] 
dist 62=[-.43127273234681637342,12.579889052290856305  ] 
dist 63=[-.25756394084036330917,12.701202685838360243  ] 
dist 64=[.54257555687111297433,1.6218855296611942883 ] 
dist 65=[1.1838364425396824280 ,1.6133516049987048182 ] 
dist 66=[1.0465914147816150419 ,1.5846665557423607199 ] 
dist 67=[.87677463455084573965,1.7308142890573958541 ] 
dist 68=[.65455714946670926707,1.8137915048637830480 ] 
dist 69=[.30930876889759359922,1.8572668690682750220 ] 
dist 70=[-.03942731184296952937,1.8591794521793502667 ] 
dist 71=[-.27551633234905468843,1.8189094701860669823 ] 
dist 72=[-.46927301492498963334,1.7946186278978063307 ] 
dist 73=[-.65004935048381692916,1.5468251458046836212 ] 
dist 74=[-.81701720037713100341,1.4812892492827063628 ] 
dist 75=[-.90816590982030273765,1.3878783305978797343 ] 
dist 76=[-.95947150604702170659,1.3510099886859157813 ] 
dist 77=[-.97089894809480986132,.45970142016220030758] 
dist 78=[-.49697156025635615853,.34379267685820343176] 
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dist 80=[-.99153674741520601433,.02684885127508379251] 
dist 81=[-1.1920355072238627875 ,-.26554665435345891471] 
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dist 84=[-1.3844427296608827767 ,-.18731320929755100186] 
dist 85=[-.47539180016195811193,-.06345828668461984831] 
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dist 87=[-.46469076068527303954,.14573696087937842026] 
dist 88=[-.45655287219670311392,.21496418244595271579] 
dist 89=[-.3999556288250297168 ,.27959634807773686574] 
dist 90=[-.38445880009237700697,.33474529182312178201] 
dist 91=[-.35619962746471522707,.36633380270202107955] 
dist 92=[-.34734609439874455116,.38609619450641675338] 
dist 93=[-.1413370057938213251 ,.39430626198396483806] 
dist 94=[-.11266885320276447503,.3965077819568630754 ] 
dist 95=[-.04899461087867743010,.3933674956868020253 ] 
dist 96=[-.03364758490023486051,.38470488018657919251] 
dist 97=[.03536361768210707982,.37904043585541162643] 
dist 98=[.04004351935356527268,.3424394151669661944 ] 
dist 99=[.02458888498948150522,.33267415797482445588] 
dist 100=[.00451727893948509632,.28370071439519670999] 
dist 101=[-.02653637067471845015,.26745445358677483178] 
dist 102=[-.05790707839871845412,.2664896421643620819 ] 
dist 103=[-.07923959482812185468,.25555408419537961447] 
dist 104=[-.09686986164044577190,.25341328226667467513] 
dist 105=[-.11621402540282203215,.20534654893259906362] 
dist 106=[-.13964223566975095024,.19384240199698093824] 
dist 107=[-.1526207062444061097 ,.18399644477852611358] 
dist 108=[-.16017670102169023424,.18041358413913101227] 
dist 109=[-.16208018596149199355,.03271431784490968672] 
dist 110=[-.14731255236566226973,.02065835525931634716] 
dist 111=[-.14813381732559467584,-.00701937621231472039] 
dist 112=[-.14827346000582722693,-.01198858595274873734] 
dist 113=[-.14752529773664478703,-.04370097232594705579] 
dist 114=[-.14629586586812508106,-.03883600881615299940] 
dist 115=[-.14452439720624532025,-.03310708870087886508] 
dist 116=[-.14206017700749338253,-.02577058964115488936] 
dist 117=[-.06206103004697941057,-.01452288362363076638] 
dist 118=[-.06206564644865698950,-.00318892473968717128] 
dist 119=[-.05991559671939235921,.00449059464230061294] 
dist 120=[-.05960546952564263062,.01081138144438475206] 
dist 121=[-.04851868929807288225,.01675222636621814482] 
dist 122=[-.04584839833827234432,.02185270008382834733] 
dist 123=[-.04399922969564335015,.02483785663490626674] 
dist 124=[-.04358027270834961940,.02678912036408940836] 
dist 125=[-.00456188083151225304,.02778587055857029102] 
dist 126=[-9.41009720346373669060e-06,.02819134983128171334] 
dist 127=[.01054605787073266417,.02816634680583632148] 
dist 128=[.01212204802632148270,.02723706958179978490] 
dist 129=[.01939635181046188467,.02699724989463235125] 
dist 130=[.01673446770452216184,.02825761349225809273] 
dist 131=[.01370088317185753853,.03038611844023233721] 
dist 132=[.00987717259389206976,.03129154787713847768] 
dist 133=[.00407816913860003044,.0315423372074706425 ] 
dist 134=[-.00174365719550796550,.03141337506285721217] 
dist 135=[-.00565813171189657392,.03041730638271802697] 
dist 136=[-.00884832256889542495,.02993820085536815993] 
dist 137=[-.01179487429124527361,.02556241722791900092] 
dist 138=[-.01428945097478485719,.02443850483892815887] 
dist 139=[-.01573624383647568981,.02273066644670810550] 
dist 140=[-.01660111165593583279,.02211385504474334611] 
dist 141=[-.01680148950607287757,.00735517496832980923] 
dist 142=[-.00927443590611636643,.00538770824026377570] 
dist 143=[-.01367111562495138833,.00098475674304215584] 
dist 144=[-.01771012997908462992,2.94715593122661906070e-05] 
dist 145=[-.02111663526971561662,-.00476054595289908307] 
dist 146=[-.02300193245223113693,-.00507886826900227069] 
dist 147=[-.02409886510773440644,-.00433624711984651515] 
dist 148=[-.02437513227741519330,-.00339601948843753403] 
dist 149=[-.00734050731870590441,-.00196537336168419564] 
dist 150=[-.00732308999523418498,-.00052680919627209156] 
dist 151=[-.00704681792126815139,.00044490737047782138] 
dist 152=[-.00699239861227377650,.00124185954809515261] 
dist 153=[-.00571297866719195043,.00198663879609927683] 
dist 154=[-.00540461048026771806,.00262346847956833129] 
dist 155=[-.00514608923914353610,.00299187976723861073] 
dist 156=[-.00505190680605616290,.00322739618494098391] 
dist 157=[-.00070318391677016341,.00333666171105785552] 
dist 158=[-.00018359406575371648,.00337587562335575541] 
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dist 160=[.00120760486346051083,.00326817288146271765] 
dist 161=[.00262161545333021548,.00333806396757589838] 
dist 162=[.00235211549464351141,.00373947614299901685] 
dist 163=[.00189356463035838660,.00398509340623347132] 
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dist 190=[1.26076800375097803680e-05,.00048711520690091259] 
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dist 196=[9.58674474051427174310e-05,.00047731146742409712] 
dist 197=[7.71181500810700000000e-06,.00047784390545771178] 
dist 198=[-8.06544959982263174310e-05,.00047491135466538696] 
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dist 206=[-.00014170134207720737,7.66068077826317585300e-05] 
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dist 210=[-.00034529318137255312,-7.90995851745969829210e-05] 
dist 211=[-.00036155052962626913,-6.23683086502691460850e-05] 
dist 212=[-.00036564903606927007,-4.15582872866627302140e-05] 
dist 213=[-.00012208888638549626,-1.02791201504477282320e-05] 
dist 214=[-.00012126517928046170,2.10512821747440737190e-05] 
dist 215=[-.00011701948606685870,4.20650466419268898110e-05] 
dist 216=[-.00011484746405938814,5.91478108333389264830e-05] 
dist 217=[-9.85238010992170303360e-05,7.48696808022688271230e-05] 
dist 218=[-9.43173006412018540280e-05,8.81526083540395543290e-05] 
dist 219=[-8.70011029376107012470e-05,9.55511952675659959790e-05] 
dist 220=[-8.47193458701489748830e-05,9.99198225793312402080e-05] 
dist 221=[-3.16343584361683692850e-05,.00010117180835617457] 
dist 222=[-2.43453526836463098510e-05,.00010096099993530943] 
dist 223=[-8.26843234868309287270e-06,9.99289901779386463670e-05] 
dist 224=[-4.42711014035698846120e-06,9.73409489299872433340e-05] 
dist 225=[1.12869004009987155430e-05,9.58634820392524144180e-05] 
dist 226=[7.48764815542830290060e-06,8.67045701191298407560e-05] 
dist 227=[3.25184213907179543060e-06,8.43120136121369638980e-05] 
dist 228=[-2.03042708730568971600e-06,7.25994880149117409260e-05] 
dist 229=[-9.98504166746146161980e-06,6.71692268393812184210e-05] 
dist 230=[-1.79582629209769835330e-05,6.67271211205555765500e-05] 
dist 231=[-2.33145267428437688110e-05,6.38105717799182550960e-05] 
dist 232=[-2.76779966796573060220e-05,6.30566304048421228420e-05] 
dist 233=[-3.17092853613240688190e-05,5.16740089021233492860e-05] 
dist 234=[-3.51260451431732603890e-05,4.89364795996601136690e-05] 
dist 235=[-3.70494983569086688340e-05,4.59976936910056430010e-05] 
dist 236=[-3.82121221505430487150e-05,4.45210990933298827700e-05] 
dist 237=[-3.86079785046668249500e-05,1.58693369632511410870e-05] 
dist 238=[-3.86581591741438187960e-05,1.36424681293887795410e-05] 
dist 239=[-3.84482156930177753350e-05,8.90964419707456731160e-06] 
dist 240=[-3.80124556615635304540e-05,7.62566583673756165360e-06] 
dist 241=[-3.75335872143867892630e-05,2.81854145337495686620e-06] 
dist 242=[-4.02392789534043349910e-05,1.80494810639017922970e-06] 
dist 243=[-4.19123495613757540110e-05,3.87965250735139811890e-07] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 1, 0, 2, 1, 2] 
dist 0=[122.47070243846785598   ,122.47070243846785598   ] 
dist 1=[121.33805039704530741   ,123.48527273661882384   ] 
dist 2=[117.85757175897939010   ,124.85544449031073642   ] 
dist 3=[111.51147150634051639   ,127.00110149495876966   ] 
dist 4=[99.740977599646950662  ,128.87757529069492514   ] 
dist 5=[87.239509107710600143  ,129.18259312785066712   ] 
dist 6=[77.984550306084750870  ,128.58107663730674185   ] 
dist 7=[69.477102395826927641  ,126.85324978857525461   ] 
dist 8=[59.930067008252888167  ,106.30078792507543014   ] 
dist 9=[50.573253564145458869  ,102.99342643385235055   ] 
dist 10=[40.943187842559342403  ,93.169737929975975959  ] 
dist 11=[32.650371558731069090  ,91.758989486198798960  ] 
dist 12=[24.152490031536437720  ,71.059192205816369528  ] 
dist 13=[13.199726794034842729  ,66.778189399564447397  ] 
dist 14=[2.8069370201867035499 ,62.728204870709105367  ] 
dist 15=[-3.4690619668047082769 ,61.957730175985096149  ] 
dist 16=[-7.9495988800069853996 ,14.000095907754087196  ] 
dist 17=[-11.188851503154346390  ,8.4393190532847656978 ] 
dist 18=[-13.613385123729808472  ,-3.1271927745080907068 ] 
dist 19=[-14.842917847876507155  ,-3.4273113754229837805 ] 
dist 20=[-21.140543554280524669  ,-2.5466036854814530987 ] 
dist 21=[-25.187806223895878707  ,-1.4030770566336006230 ] 
dist 22=[-27.845543034570761058  ,-.50424827247223436145] 
dist 23=[-29.277437924377413457  ,.30685244110212853355] 
dist 24=[-30.007816656305780366  ,1.1168086589870756314 ] 
dist 25=[-30.042224689558909404  ,1.7915060038126173577 ] 
dist 26=[-29.379832596835792667  ,2.0730241852081540082 ] 
dist 27=[-28.984159526880503610  ,2.1816836234635017600 ] 
dist 28=[-25.009214324756250108  ,2.1806605818747465775 ] 
dist 29=[-23.970955650418273804  ,3.0173397969216530498 ] 
dist 30=[-22.442245171560102266  ,4.6180281271775305962 ] 
dist 31=[-21.864457574757304548  ,5.4969706865962019054 ] 
dist 32=[-7.8720744857761143189 ,6.0087934442940092730 ] 
dist 33=[-6.0187819068627129786 ,7.2128950086255271389 ] 
dist 34=[-1.8428789412197775853 ,11.291509316308525869  ] 
dist 35=[-.96677488104299800269,15.035209254025042828  ] 
dist 36=[-.6436950189141341632 ,18.190336505338284435  ] 
dist 37=[-.88965188607864435261,19.932189754525858589  ] 
dist 38=[-1.0928892670233367732 ,20.939974991068371399  ] 
dist 39=[-1.2936304081738972647 ,21.180443323540801464  ] 
dist 40=[-1.5310327496535200880 ,6.5020992942356458179 ] 
dist 41=[-1.7627832877800770104 ,6.5317575949818892637 ] 
dist 42=[-1.9418356830716863290 ,6.3670320809527747788 ] 
dist 43=[-2.1109734241566371688 ,6.3429354891180645211 ] 
dist 44=[-2.4117042063265723449 ,5.2407054706827721260 ] 
dist 45=[-2.8712155035549312586 ,4.9703822306654792101 ] 
dist 46=[-3.2559919758541424301 ,4.7889580726932704058 ] 
dist 47=[-3.4323519509009912206 ,4.7464715173799380348 ] 
dist 48=[-3.5063614168850417361 ,2.4489269169584172819 ] 
dist 49=[-3.4989914841150168684 ,2.0377872515697296174 ] 
dist 50=[-3.2620626290939116734 ,1.9487819934226909973 ] 
dist 51=[-3.1720663545086938406 ,1.6997134497816911379 ] 
dist 52=[-3.0333372173193434065 ,1.6493224294862076985 ] 
dist 53=[-3.0702221973887684077 ,1.0245555301110277886 ] 
dist 54=[-3.2203704251627614723 ,.91009572733593149921] 
dist 55=[-3.3364530057869038376 ,.78825008758479700411] 
dist 56=[-3.3863410165566241206 ,1.3198900246933160927 ] 
dist 57=[-3.3812134490628650586 ,1.8142479887580111580 ] 
dist 58=[-3.3013864493996878827 ,2.2332389074991829287 ] 
dist 59=[-3.2421027716275999693 ,2.4659464939310194719 ] 
dist 60=[-2.8121014814286921651 ,2.6016535739008172429 ] 
dist 61=[-2.4789295713787549125 ,2.6358636135532341018 ] 
dist 62=[-2.3128782733332272803 ,.8207633070091867913 ] 
dist 63=[-2.2516291998409709407 ,.85673827721596977393] 
dist 64=[-.77567185327295193778,.87101228369483261696] 
dist 65=[-.57964556696917538899,.87480007118938238792] 
dist 66=[-.1396177855290140444 ,1.3125427376024246668 ] 
dist 67=[-.04493336907470709562,1.7149208294172844293 ] 
dist 68=[.27858171784826894974,2.0543722656302078994 ] 
dist 69=[.12380323731568570902,2.2422811402435801163 ] 
dist 70=[.01694320223365213411,2.3516887937988011560 ] 
dist 71=[-.07294841281904421818,2.3792239853077546577 ] 
dist 72=[-.16043355642719113419,.7233160272499929616 ] 
dist 73=[-.24366461489055892123,.72354163853147194591] 
dist 74=[-.34365068360185938653,.69994764688223330342] 
dist 75=[-.40588683566021656259,.69552614069860675983] 
dist 76=[-.45116612343850106223,.57381102935169198628] 
dist 77=[-.48390310278007688516,.54561723768418652894] 
dist 78=[-.50568940756685663087,.5180591352714614738 ] 
dist 79=[-.50990648301679463239,.50968545820083569508] 
dist 80=[-.50309402024635199625,.10799792209483626614] 
dist 81=[-.50003436832855285878,.05903165481702616581] 
dist 82=[-.42385167769980421823,-.05428295324820629682] 
dist 83=[-.40394276514930468315,-.07293984380790994976] 
dist 84=[-.3861975960951830228 ,-.06718581485436121386] 
dist 85=[-.39390868719304271144,.02960588784531364556] 
dist 86=[-.41960764985905898942,.09481435235250640206] 
dist 87=[-.43016638835661610435,.14801906982721314916] 
dist 88=[-.43215432848037725681,.19717450466864401988] 
dist 89=[-.43025250010424828831,.23873061053244736616] 
dist 90=[-.413774797877271317  ,.26177627435500130893] 
dist 91=[-.40893131253618695229,.28449696921080294863] 
dist 92=[-.3385442218395500601 ,.30038378910114007795] 
dist 93=[-.32132182517086710509,.303980780799706231  ] 
dist 94=[-.30214836238046213336,.12070682737325442962] 
dist 95=[-.2927677991449960562 ,.12226917908152236232] 
dist 96=[-.11227615724044692225,.12143125903131384195] 
dist 97=[-.09736387258429578167,.124854401774911464  ] 
dist 98=[-.06527243830636280859,.16892959675257603201] 
dist 99=[-.05645385298793233833,.20959182850923312078] 
dist 100=[-.02272346666420898471,.24401084178578981725] 
dist 101=[-.01577055569537906981,.26329823959937896146] 
dist 102=[-.03011603878805377273,.27590055033639113983] 
dist 103=[-.04507438018391010886,.27879584703889790894] 
dist 104=[-.05909218475054952668,.10064546578922413048] 
dist 105=[-.07109455517829716926,.10005188804669683189] 
dist 106=[-.07805323444665275706,.09688513180324333810] 
dist 107=[-.08251658390641736976,.09497654210052026375] 
dist 108=[-.08461436068252514751,.08226167769737060560] 
dist 109=[-.08541696960038178955,.07890674027201996541] 
dist 110=[-.08487704060130193777,.07265628496599490047] 
dist 111=[-.08323497369172263709,.07071350330178767045] 
dist 112=[-.08206523578487168465,.02852134752867486608] 
dist 113=[-.07433205520025625289,.02259906768635577836] 
dist 114=[-.07224180931395475214,.00962161394052706048] 
dist 115=[-.06604824032998464216,.00633901869155562743] 
dist 116=[-.06410491308634088583,.00516091673384160010] 
dist 117=[-.04776067779515963390,.01225849126193676219] 
dist 118=[-.03635842392290826473,.01704870393662471855] 
dist 119=[-.02769292615829519184,.02096778671639022432] 
dist 120=[-.01614423023795042768,.02734927240032018574] 
dist 121=[-.01553048273093887138,.03583686419144816188] 
dist 122=[-.01518676961105417219,.04300394798262766599] 
dist 123=[-.01267980081307982864,.04697454368933550894] 
dist 124=[-.00689607093040794580,.04929059539307259218] 
dist 125=[.01318729872902162661,.04987181037258759449] 
dist 126=[.01309911855758420696,.01536338988035755558] 
dist 127=[.01266359503626876881,.01544348770257120504] 
dist 128=[.01165320937856481747,.01508409242969877321] 
dist 129=[.01037860331816415098,.0150290174149928202 ] 
dist 130=[.00889390983939032433,.01247160973904806909] 
dist 131=[.00700223321506110426,.01190106124722561328] 
dist 132=[.00411168333138883513,.01137985251126423295] 
dist 133=[.00120151068459778372,.01127206963393766945] 
dist 134=[-.00076820501826404868,.00268532983515737984] 
dist 135=[-.00238755590123749382,.00164428677894209580] 
dist 136=[-.00416818801420780652,-.00078455862571416816] 
dist 137=[-.00603643863311250030,-.00118132274229802968] 
dist 138=[-.00763759666381879410,-.00409119765482987988] 
dist 139=[-.00856981807152878227,-.00453709121479530605] 
dist 140=[-.00917309032255799348,-.00539331382164327180] 
dist 141=[-.00946852243896560813,-.00553385327877487582] 
dist 142=[-.00957466856677910617,-.00593270594511284680] 
dist 143=[-.00955335512696395656,-.00582984761899308333] 
dist 144=[-.00922699432434444687,-.00552774389459100531] 
dist 145=[-.00912918993989142999,-.00481665229428897452] 
dist 146=[-.00758104065342482230,-.00388744102133119177] 
dist 147=[-.00719828974372495421,-.00272339175726897154] 
dist 148=[-.00679129860333539577,-.00096539631145217450] 
dist 149=[-.00658065580374801083,.00079729187907494246] 
dist 150=[-.00257189454461007465,.00198000395116857362] 
dist 151=[-.00225147529257452785,.00294141779839075085] 
dist 152=[-.00155221311433817534,.00382552643433801824] 
dist 153=[-.00135672148045392791,.00457149599411395359] 
dist 154=[-.00058979470706749428,.00527510423335512271] 
dist 155=[-.00043476070839400984,.00572949203836244397] 
dist 156=[-.0001452001922101746 ,.00601883374580141121] 
dist 157=[-7.89652188552878773830e-05,.00608473954379100634] 
dist 158=[.00157232280605731172,.00203877815087804174] 
dist 159=[.00150829788839640753,.00204167670690195785] 
dist 160=[.00137414755483889954,.00197742846742869452] 
dist 161=[.00120872594849820797,.00196779227169234435] 
dist 162=[.00102052638461998847,.00161048489326743785] 
dist 163=[.00078345268244371681,.00152362939738253670] 
dist 164=[.00042396670259057181,.00146365393970845235] 
dist 165=[6.28865206062740440960e-05,.00144899114428958789] 
dist 166=[-.00018052721380445461,.00016665352868412915] 
dist 167=[-.00037966635167265205,1.66586895407518242420e-05] 
dist 168=[-.00056497406494058880,-.00024553500543074615] 
dist 169=[-.00072289803510888264,-.00038373236420325857] 
dist 170=[-.00082484858480518968,-.00060714996233996228] 
dist 171=[-.00093879371189385397,-.00069304424607254037] 
dist 172=[-.00101123163082773768,-.00070666684468137660] 
dist 173=[-.00104397225777357780,-.00073016922636414561] 
dist 174=[-.00105480592368102495,-.00071352359644582980] 
dist 175=[-.00105141682614853694,-.00067738043223115660] 
dist 176=[-.00101919919079643196,-.00060613700157739651] 
dist 177=[-.00100408625876890446,-.00051961397604077899] 
dist 178=[-.00085582197308445897,-.00042279832815488745] 
dist 179=[-.00081777111641616064,-.00030185794317090333] 
dist 180=[-.00076268002184509773,-.00011954322153742329] 
dist 181=[-.00074171463328614991,6.32019812465490258200e-05] 
dist 182=[-.00024134260055987082,.00018585435485537815] 
dist 183=[-.00017619978820862572,.00029835206352055353] 
dist 184=[-3.00119105957915189310e-05,.00044296502740638212] 
dist 185=[1.29141391170398505730e-06,.00057588670600573725] 
dist 186=[.00016152494174101003,.00068802460652614063] 
dist 187=[.00018920412530227937,.00075011813818415361] 
dist 188=[.00020367819256291106,.00078637252290804889] 
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dist 190=[.00020395314599479619,.00026794707277658279] 
dist 191=[.00019527329262492921,.00026700470052480141] 
dist 192=[.00017786517170189893,.00025922777398979105] 
dist 193=[.00015662653648756341,.00025496293965720497] 
dist 194=[.00012400767093609546,.00021950267304469942] 
dist 195=[8.05596423660063412730e-05,.00021023935020698949] 
dist 196=[1.52507700257546047490e-05,.00019522564348894345] 
dist 197=[-5.01478595959545617920e-05,.00019011749976228213] 
dist 198=[-9.39528517344131159630e-05,6.84225135242898117830e-05] 
dist 199=[-.00012949229846690466,5.19707396791760580990e-05] 
dist 200=[-.00016207258370908857,2.43910495934190475550e-05] 
dist 201=[-.00018950234615706340,6.99232604279100779900e-06] 
dist 202=[-.00020459142157571112,-1.22477894748089479710e-05] 
dist 203=[-.00021324862328301436,-2.13837164510697639030e-05] 
dist 204=[-.00021514009302371418,-2.36216741002071856060e-05] 
dist 205=[-.00021400191298020376,-2.42179082023594534520e-05] 
dist 206=[-.00014852870938242115,-2.28512978206155668280e-05] 
dist 207=[-.00014782545420154316,-1.98786165611225226050e-05] 
dist 208=[-.00014136330827504342,-1.40150661939415720730e-05] 
dist 209=[-.00014019550985510314,-6.89152361563840393810e-06] 
dist 210=[-.00011310684491614063,1.08455104820209501280e-06] 
dist 211=[-.00010667947078498320,1.10527136300675269020e-05] 
dist 212=[-.00010133626762151867,2.60865347202524869110e-05] 
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dist 215=[-9.19015445145825155320e-06,5.95688274430580277450e-05] 
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dist 217=[9.79257830535144865080e-06,7.37223026776708162070e-05] 
dist 218=[1.94496615375914869760e-05,7.74002204626857636040e-05] 
dist 219=[2.39187825544527416620e-05,7.96487215531102950180e-05] 
dist 220=[2.48208229211780912680e-05,8.04719811095455200640e-05] 
dist 221=[2.49725507027519094460e-05,8.07205414893116131060e-05] 
dist 222=[2.43560218942396010020e-05,3.75490356731397236740e-05] 
dist 223=[2.31059647700434836600e-05,3.73712199356148864160e-05] 
dist 224=[2.06968048235427828740e-05,3.61160727334273612720e-05] 
dist 225=[1.77876147006110998040e-05,3.55544614543339350330e-05] 
dist 226=[1.38637584230887605220e-05,3.02318379643025705790e-05] 
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dist 228=[1.91659069588869290520e-07,2.68738852573439634720e-05] 
dist 229=[-8.01877998687498723450e-06,2.61331251880184385950e-05] 
dist 230=[-1.35150432676587069840e-05,9.27200808811255624060e-06] 
dist 231=[-1.79715318789593839070e-05,6.07528516158040728420e-06] 
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dist 242=[-1.22519843789560550020e-05,2.26890786919251716230e-06] 
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dist 249=[-6.09433964359863286050e-07,8.58622250928748951120e-06] 
dist 250=[-4.12917343980651477690e-07,8.91396768630001452180e-06] 
dist 251=[-1.06944925187636577300e-07,9.13225323956139967390e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 2, 0, 1] 
dist 0=[113.16375314678062767   ,113.16375314678062767   ] 
dist 1=[111.94683735822095098   ,113.91973134641851308   ] 
dist 2=[108.83595628129693726   ,115.18801519030823762   ] 
dist 3=[103.65453706345951640   ,116.32957568386903444   ] 
dist 4=[94.205934786280942071  ,116.58537994535145087   ] 
dist 5=[84.137666067196012036  ,116.22923374419013449   ] 
dist 6=[76.488933155636476208  ,115.74149392687354672   ] 
dist 7=[69.253011953483350807  ,94.729498037505533029  ] 
dist 8=[60.811422548722884047  ,91.692767230572542147  ] 
dist 9=[52.337769518554927964  ,83.314934599740884107  ] 
dist 10=[44.961052928764619094  ,81.820054528484545580  ] 
dist 11=[37.013106070647637574  ,65.679856580723387216  ] 
dist 12=[26.243845655222647918  ,62.335360431221471910  ] 
dist 13=[15.826459412224856856  ,58.961514422686851335  ] 
dist 14=[9.2741775292317499569 ,56.871376280053304956  ] 
dist 15=[4.2899399853845076530 ,22.096257513336684953  ] 
dist 16=[.12166274571457107262,17.812295396085488383  ] 
dist 17=[-4.9723624761505186959 ,7.8035777835665889723 ] 
dist 18=[-12.470991735281569129  ,6.2863257589717383832 ] 
dist 19=[-18.971839007002496640  ,-6.0516782920972602266 ] 
dist 20=[-23.004264376309725082  ,-6.3142103265924282055 ] 
dist 21=[-25.967682743052682028  ,-6.3561665864083940341 ] 
dist 22=[-28.223564303756470893  ,-3.9911042424907802029 ] 
dist 23=[-29.794001794743645817  ,-1.2033583786080300045 ] 
dist 24=[-30.152858771064036549  ,1.0598623409399716338 ] 
dist 25=[-29.867321947550173303  ,3.2823222703449441453 ] 
dist 26=[-29.818187832720665530  ,5.9231714438822450610 ] 
dist 27=[-25.208768497669542925  ,8.5413156578563781490 ] 
dist 28=[-24.031360288810502659  ,10.682012326518106291  ] 
dist 29=[-23.291798633627297038  ,12.840270916791854873  ] 
dist 30=[-23.094878449588248346  ,15.537863437890963865  ] 
dist 31=[-4.6035623709312302326 ,17.966365585652702024  ] 
dist 32=[-2.4314872328147205436 ,19.058962972447504261  ] 
dist 33=[2.6050686999606043889 ,19.560628101452387198  ] 
dist 34=[2.8136319692623032385 ,19.637347129564556995  ] 
dist 35=[2.3447934736020543165 ,17.893792231891957142  ] 
dist 36=[1.4535172135627307552 ,17.369990275092162622  ] 
dist 37=[.51462732774159259254,17.002616975489649491  ] 
dist 38=[-.14354032760007360245,16.770576921924087196  ] 
dist 39=[-.6995099914357413338 ,14.410383285534067398  ] 
dist 40=[-1.2348196587161677581 ,14.470632970601811628  ] 
dist 41=[-2.5198610003442866134 ,14.338804424473454545  ] 
dist 42=[-5.1219746094391500591 ,14.156054431042151087  ] 
dist 43=[-7.4182622834867336222 ,12.777966234943118623  ] 
dist 44=[-8.8694204174024155550 ,12.382765813512329399  ] 
dist 45=[-9.9513866855476882396 ,11.505403877776661487  ] 
dist 46=[-10.784000828414857180  ,11.185974612288010428  ] 
dist 47=[-11.383830768327613123  ,5.9685366148774796419 ] 
dist 48=[-11.542189146835338155  ,5.2091930315820611610 ] 
dist 49=[-11.510382573372433915  ,3.5574180681898642898 ] 
dist 50=[-11.370788143326755175  ,3.0987253527304373712 ] 
dist 51=[-12.006595654732882358  ,1.3149938318904595313 ] 
dist 52=[-12.958336244932591063  ,.95361145562632354395] 
dist 53=[-13.507264155589085872  ,.29777941384246543464] 
dist 54=[-13.633719692897280591  ,.15328389755889523856] 
dist 55=[-4.7721820369225089375 ,2.1946659598817843017 ] 
dist 56=[-4.2926828285953661865 ,4.0818888726988380068 ] 
dist 57=[-3.2339083132664001171 ,5.6259045860330930311 ] 
dist 58=[-2.9297730839945769332 ,7.0592336940419089586 ] 
dist 59=[-.14588621529661058045,8.2756889387009813915 ] 
dist 60=[.16533724774071228034,9.0072856849674891583 ] 
dist 61=[.46560770741616799802,9.4248132941079575410 ] 
dist 62=[.48986337352328010511,9.5012918133537630990 ] 
dist 63=[.50813771877974081009,2.0810781714479741961 ] 
dist 64=[.48368478529504845573,2.1154275333463154998 ] 
dist 65=[.44127813800447846937,2.1156941006625013573 ] 
dist 66=[.37840066039137226478,2.1153581465159668984 ] 
dist 67=[.29025010861241612527,1.8085491905316756447 ] 
dist 68=[.14756454060301011079,1.7286445144584177767 ] 
dist 69=[.00197759690683119341,1.6815503337428733225 ] 
dist 70=[-.09770741764511627375,1.6686325643236692776 ] 
dist 71=[-.18268421043406434139,.30751399004824009865] 
dist 72=[-.26999742663494974589,.1471948652314825395 ] 
dist 73=[-.34318446158355782043,-.01340672355932864021] 
dist 74=[-.56116600664047590608,-.03154192195102135334] 
dist 75=[-.78598111298426556125,-.06810380324653683634] 
dist 76=[-.92242587213094218755,-.07620857358041996221] 
dist 77=[-1.0176828060608848910 ,-.12670837755144520999] 
dist 78=[-1.0790807387448477891 ,-.13371490140172828215] 
dist 79=[-1.1168907777181057980 ,-.13596587729660309598] 
dist 80=[-1.1215620141249889898 ,-.12652894960800907681] 
dist 81=[-1.1068794808921545681 ,-.11163512583792591453] 
dist 82=[-1.0918802036477711307 ,-.09075467097012472141] 
dist 83=[-.95706216592379955948,-.06201456832770985683] 
dist 84=[-.91967369043826315383,-.01592369006449412737] 
dist 85=[-.86170456245715190698,.03112322978096603641] 
dist 86=[-.84021911580338891315,.06366431276397772183] 
dist 87=[-.31667757245166754364,.12233918445496525466] 
dist 88=[-.24703660803311363796,.31971728931539696468] 
dist 89=[-.08951183516843045767,.48051083627115754394] 
dist 90=[-.05699234395748242575,.62900252564464578649] 
dist 91=[-.04547682219204005341,.75505541505084420354] 
dist 92=[-.04364482059948143872,.82475821566804546917] 
dist 93=[-.02319123009054933975,.86516961079057919877] 
dist 94=[-.02067462627366329771,.87494920289482370441] 
dist 95=[-.02244274449377235251,.2569603185957783833 ] 
dist 96=[-.03043126762769262504,.25874521520595352705] 
dist 97=[-.04154001559230631594,.25377861016563983026] 
dist 98=[-.05569663396977306300,.25294389536116122575] 
dist 99=[-.07446990471789635586,.22220955268394957535] 
dist 100=[-.10390642744790755865,.21567333714766774717] 
dist 101=[-.13376770059124451919,.20211327278918261595] 
dist 102=[-.15423005300037509753,.19719734875573095675] 
dist 103=[-.17130062143208897259,.07497091689360314529] 
dist 104=[-.18770491455750033554,.07016418128459068039] 
dist 105=[-.20357381186209467217,.05223780805971469621] 
dist 106=[-.21622427508874192144,.04783014721371007406] 
dist 107=[-.22245384491295195637,.04210288730425713972] 
dist 108=[-.22320912171291955359,.03999836244126254939] 
dist 109=[-.12872607051205422854,.03831800799675403431] 
dist 110=[-.13441511539748622455,.03846239897877097029] 
dist 111=[-.13724572202995611985,.03972292158979876003] 
dist 112=[-.13729001718250704795,.04279726114524428238] 
dist 113=[-.13402690419820439768,.04671447961777820255] 
dist 114=[-.13230587548627285517,.05132147112662948567] 
dist 115=[-.11349181822990141218,.05721646927863334556] 
dist 116=[-.10857250207879913128,.06624707888327293788] 
dist 117=[-.10191250318178843858,.07533927443612857629] 
dist 118=[-.09915302859627112204,.08147912059225712057] 
dist 119=[-.03201399959822784264,.08650827319581931519] 
dist 120=[-.02373816484281112082,.09119201282906563699] 
dist 121=[-.00509507166022423498,.09518125505698740245] 
dist 122=[-.00112584667017689594,.09745381037609665405] 
dist 123=[.00913043841493191267,.09885987805193673426] 
dist 124=[.00934782588330710756,.09940979465998742200] 
dist 125=[.01086495129986726874,.09929489038516461092] 
dist 126=[.01082227595576358345,.09806179476781531898] 
dist 127=[.01043161431286676225,.03158237011149299116] 
dist 128=[.00947615852919254203,.03162685088954510699] 
dist 129=[.00825829031263743547,.03062365537042273945] 
dist 130=[.00682579918175225258,.03047892052730812219] 
dist 131=[.00499292781094288287,.02491686232383238421] 
dist 132=[.00218559242810902826,.02356704621191182240] 
dist 133=[-.00064001781870838015,.02264890987789139667] 
dist 134=[-.00254555015577200054,.02243864049777891748] 
dist 135=[-.00410334441091352529,.00249621166255519621] 
dist 136=[-.00554879050980026994,.00016769250731336464] 
dist 137=[-.00680916548228209125,-.00186847598320251121] 
dist 138=[-.00956413699454086034,-.00218549945250950854] 
dist 139=[-.01261035057155497982,-.00279948406716995024] 
dist 140=[-.01436712778436304640,-.00292135687072560973] 
dist 141=[-.01548339111711385975,-.00316939947872186636] 
dist 142=[-.01598685697859426523,-.00317094845463924422] 
dist 143=[-.01615476912422850830,-.00308324036951422166] 
dist 144=[-.01610138261398113285,-.00285360259306997572] 
dist 145=[-.01561952216394808807,-.00255692970323795261] 
dist 146=[-.01537695625567786743,-.00220305327414917587] 
dist 147=[-.01316321463774202415,-.00174713158314117540] 
dist 148=[-.01259076812722264684,-.00104531051521869530] 
dist 149=[-.01171993983332615853,-.00033717145865506101] 
dist 150=[-.01140440697815001991,.00014387115731614798] 
dist 151=[-.00382926922499062347,.00195309435532082220] 
dist 152=[-.00281880355071888847,.00473630250945793798] 
dist 153=[-.00055480924624738805,.00699751370588897826] 
dist 154=[-6.43796759540609149970e-05,.00907548975701820736] 
dist 155=[.00143799057343013363,.01082830029702158139] 
dist 156=[.00146380220499287973,.01179847494375579182] 
dist 157=[.00165465132381787855,.01236299440744994878] 
dist 158=[.00162661861155647608,.01250517467656682080] 
dist 159=[.00154975418399206722,.00376769654490710301] 
dist 160=[.00138829718457696873,.00376212576722413621] 
dist 161=[.00118914585861887472,.00362769765368721764] 
dist 162=[.00096261716640536637,.00360073308809766294] 
dist 163=[.00067736977000376683,.00295086963747535059] 
dist 164=[.00024508891899548598,.00279339697756771620] 
dist 165=[-.00018871594396718547,.00266234448600444799] 
dist 166=[-.00048002303453462131,.00261396038755997119] 
dist 167=[-.00071700252378720108,.00037657480039006288] 
dist 168=[-.00093513737013833908,.00010916111449881579] 
dist 169=[-.00111926595854219537,-.00022839040330782148] 
dist 170=[-.00134423284094512753,-.00027382660291872618] 
dist 171=[-.00171108522703144672,-.00035441408060778068] 
dist 172=[-.00191958453763801937,-.00036936083362045176] 
dist 173=[-.00204818258853715041,-.00038679561191526820] 
dist 174=[-.00209780512653227074,-.00038257666214528162] 
dist 175=[-.00210383425361129907,-.00036767702874563071] 
dist 176=[-.00209417523345106412,-.00033472960830187910] 
dist 177=[-.00200831223386618853,-.00029359196261897255] 
dist 178=[-.00198834602053113205,-.00024617114178263398] 
dist 179=[-.00162551401442317341,-.00018605191684935480] 
dist 180=[-.00153814858298647900,-9.44950038862258089370e-05] 
dist 181=[-.00145401537612335632,-2.41499401464552002370e-06] 
dist 182=[-.00141645419950131591,5.97841724955466665580e-05] 
dist 183=[-.00034708353064531220,.00015701991788950032] 
dist 184=[-.00023682240345498496,.00044409476339507095] 
dist 185=[1.20864366770508038840e-05,.00067745374295267398] 
dist 186=[6.21877258198170369370e-05,.00089217120558202125] 
dist 187=[.00014172757363044610,.00107352279929083098] 
dist 188=[.00014496483673515386,.00117440103885578402] 
dist 189=[.00015289716104394379,.00123577854143360920] 
dist 190=[.00014970014195873449,.00125041044239919079] 
dist 191=[.00014151681066831856,.00048364853167860908] 
dist 192=[.00012461214460955175,.00048226394489798351] 
dist 193=[.00010383930038025068,.00046248133689239536] 
dist 194=[8.02965215721995164080e-05,.00045960588817444693] 
dist 195=[5.06985441882173202570e-05,.00037054824415319542] 
dist 196=[5.88321685214450000000e-06,.00034941775452780154] 
dist 197=[-3.90992088864109202570e-05,.00033420200394668237] 
dist 198=[-6.93616135724315164090e-05,.00033076544001456250] 
dist 199=[-9.40503748004118829160e-05,3.84610320519983196370e-05] 
dist 200=[-.00011690509418441835,3.34975084617992049720e-05] 
dist 201=[-.00013629649599754056,1.41945316887944300140e-05] 
dist 202=[-.00015456423756823520,1.02600446373922805930e-05] 
dist 203=[-.00019974487122273436,3.15799005374340000000e-06] 
dist 204=[-.00022530775504274335,1.60139089858518430170e-06] 
dist 205=[-.00024092814793531446,-4.49772447193168583360e-05] 
dist 206=[-.00024663225338894253,-4.40346702241977311240e-05] 
dist 207=[-.00024726789985919748,-4.16590660322189320120e-05] 
dist 208=[-.00024582097803371315,-3.67707310552637638230e-05] 
dist 209=[-.00023711521700382406,-3.07684769741187045790e-05] 
dist 210=[-.00023320968839902851,-2.39696265059932089110e-05] 
dist 211=[-.00019823789058445167,-1.54232578738342652650e-05] 
dist 212=[-.00018935933822596313,-2.48207439570731842730e-06] 
dist 213=[-.00017571067265879664,1.05120012014711283540e-05] 
dist 214=[-.00017088133932536273,1.92686867469062720960e-05] 
dist 215=[-5.80589251357351874970e-05,3.42451002134434487320e-05] 
dist 216=[-4.32663428390307699590e-05,7.59991896858412317260e-05] 
dist 217=[-1.03653437404136044130e-05,.00010989848241670585] 
dist 218=[-2.95310029473046359310e-06,.00014102561985966338] 
dist 219=[2.42746423389256925540e-07,.00016727562644804136] 
dist 220=[6.87543629400578833120e-07,.00018180913329872782] 
dist 221=[1.34929322026106613760e-06,.00019031288925702700] 
dist 222=[6.67252144955465235820e-07,.00019243472676136733] 
dist 223=[-8.51223840315534861790e-07,5.73741386051619399400e-05] 
dist 224=[-3.86813434023820933360e-06,5.71382365712124054450e-05] 
dist 225=[-7.54015084029000568860e-06,5.46478727948662316220e-05] 
dist 226=[-1.16600105253082446540e-05,5.42757735460303181760e-05] 
dist 227=[-1.68141039955038752640e-05,4.37617890002984982190e-05] 
dist 228=[-2.45928666010356621540e-05,4.22861034286584200600e-05] 
dist 229=[-3.23952123539223788480e-05,3.92322385597423084640e-05] 
dist 230=[-3.76430900151948094510e-05,3.87884930193397828850e-05] 
dist 231=[-4.19247537937702185880e-05,1.53410133944669113830e-05] 
dist 232=[-4.58908498409430786640e-05,1.41899609214224365480e-05] 
dist 233=[-4.92592501835322890920e-05,1.00091596342653240200e-05] 
dist 234=[-5.11678293385813496870e-05,8.98972888881761905860e-06] 
dist 235=[-5.24591753333181083180e-05,7.88139034642511862390e-06] 
dist 236=[-5.27721860202642810100e-05,7.58798249343679234520e-06] 
dist 237=[-3.42127817006879398370e-05,7.53118619205117943750e-06] 
dist 238=[-3.48257863602262701880e-05,7.66389415683262451550e-06] 
dist 239=[-3.47612498627919522070e-05,7.95757046928093705400e-06] 
dist 240=[-3.45395384759363840540e-05,8.53999340180099333590e-06] 
dist 241=[-3.30517584409055988350e-05,9.24859230883916090320e-06] 
dist 242=[-3.26586128988864758070e-05,1.00433068744611401530e-05] 
dist 243=[-2.68060461902073081780e-05,1.10373590573321547330e-05] 
dist 244=[-2.53950517145652434110e-05,1.25374939090991707210e-05] 
dist 245=[-2.38648349507253623470e-05,1.40422214013098867070e-05] 
dist 246=[-2.31029505057439450360e-05,1.50545357300679712710e-05] 
dist 247=[-8.31965122167382976830e-06,1.58807507856725105210e-05] 
dist 248=[-7.15952804777606396070e-06,1.66465829164123080840e-05] 
dist 249=[-4.69061201505021448820e-06,1.72973810996572043350e-05] 
dist 250=[-4.01975153817448871030e-06,1.76668616373679368570e-05] 
dist 251=[-1.50172597068285316360e-06,1.94717221132960960490e-05] 
dist 252=[-9.71967142092588382820e-07,2.09550904362048155240e-05] 
dist 253=[-2.17185804403776160230e-07,2.18387644850731043140e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 1, 1, 0, 1] 
dist 0=[107.20972906848043457   ,107.20972906848043457   ] 
dist 1=[101.04344043350756191   ,110.10068739149983261   ] 
dist 2=[94.245517698625916930  ,111.65403234173746898   ] 
dist 3=[88.840558131658853482  ,112.53223812559392812   ] 
dist 4=[83.499191036727985872  ,112.89211575491716305   ] 
dist 5=[76.939105967485627440  ,112.04021864473338583   ] 
dist 6=[70.168470099141719509  ,111.33848309209000345   ] 
dist 7=[63.976772044772411420  ,110.40329247601607283   ] 
dist 8=[57.049549354196067638  ,109.69147041745845988   ] 
dist 9=[47.330747513776362671  ,85.484595723931364784  ] 
dist 10=[37.704289328788724195  ,82.125587230544307938  ] 
dist 11=[31.141379886960565783  ,72.800358159422754882  ] 
dist 12=[25.565883813830352459  ,71.463008592794029186  ] 
dist 13=[19.880780626186368342  ,53.775352689117915843  ] 
dist 14=[14.561614544716743795  ,50.230491685698096182  ] 
dist 15=[10.446779523980615035  ,46.677727462572599678  ] 
dist 16=[.01255778796378965028,46.025158204321407829  ] 
dist 17=[-6.5352057099126132238 ,12.853666482589916261  ] 
dist 18=[-11.246194384267595476  ,6.3690182446795167806 ] 
dist 19=[-14.720274910379779643  ,5.4540482092280684817 ] 
dist 20=[-17.324665558449447327  ,3.4611165032671401476 ] 
dist 21=[-18.565134891346474516  ,3.0278421573270232733 ] 
dist 22=[-20.194788079553615105  ,.58368774436893856051] 
dist 23=[-21.974450591994609799  ,.109689424781072734  ] 
dist 24=[-22.705278221667939577  ,-.78790915581038126971] 
dist 25=[-22.897103465007796645  ,-1.0187019877387104040 ] 
dist 26=[-22.806206909612907738  ,-3.0332519982631179853 ] 
dist 27=[-22.041729002883059043  ,-.28038158423142934704] 
dist 28=[-21.715211181889411558  ,2.3646931328734152993 ] 
dist 29=[-18.440451231890007848  ,4.3896784338007086699 ] 
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dist 228=[6.03354179354378772260e-06,5.33700071294362233200e-05] 
dist 229=[1.89733766017714139330e-05,5.22591029817300965270e-05] 
dist 230=[1.83358911693638959030e-05,4.85434572440716499100e-05] 
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dist 238=[-3.49715741800483895230e-05,2.13079944981651122140e-05] 
dist 239=[-3.55194457627573894840e-05,1.99772294347936715300e-05] 
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dist 241=[-3.51939273116460597500e-05,1.62432651976366009400e-05] 
dist 242=[-3.37014078500898779080e-05,1.54337182617687182370e-05] 
dist 243=[-3.32538428348957272750e-05,1.41378830647092196420e-05] 
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dist 248=[-5.29563969409560658820e-06,1.17130536882561470360e-05] 
dist 249=[-3.98509471659298550200e-06,1.16050070975753337000e-05] 
dist 250=[-2.66435577852428147700e-06,1.14738918611510068410e-05] 
dist 251=[-2.30175946829678730160e-06,1.10359297575411033460e-05] 
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dist 253=[-6.31304989800403463980e-07,9.40287469430561958100e-06] 
dist 254=[-1.70592928569533394100e-07,9.04268219928282542520e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 2, 2, 0, 1, 2] 
dist 0=[123.34356995753540067   ,123.34356995753540067   ] 
dist 1=[122.06823742412994549   ,123.97952585423962373   ] 
dist 2=[119.34993704838809338   ,123.93575825930172184   ] 
dist 3=[112.95673746603532836   ,123.62794652414065205   ] 
dist 4=[105.65700595809268081   ,120.65977201730952036   ] 
dist 5=[99.334388739993502463  ,119.38073720841887054   ] 
dist 6=[90.974580952523617028  ,118.25947513681441650   ] 
dist 7=[77.863286690583076970  ,117.28074320978881845   ] 
dist 8=[68.059910328941927088  ,87.520719866708202972  ] 
dist 9=[58.930765932167782276  ,83.376166943895633097  ] 
dist 10=[48.487078719882439838  ,74.624334162372855766  ] 
dist 11=[37.637198664206149709  ,72.170276127652295162  ] 
dist 12=[22.090362433455188029  ,62.526789661853352778  ] 
dist 13=[11.560718995058963969  ,60.476532488117038982  ] 
dist 14=[2.8144445871859947561 ,56.534251807727849778  ] 
dist 15=[-5.6420698970453258150 ,55.555896371064814082  ] 
dist 16=[-13.158606284937889990  ,9.3474340800216090068 ] 
dist 17=[-18.170694319524086193  ,7.1718677815804968725 ] 
dist 18=[-22.274155418600150819  ,3.8058431832141955226 ] 
dist 19=[-26.186768311320755740  ,3.0448689849226177723 ] 
dist 20=[-29.380305629078803954  ,-12.302398790692352793  ] 
dist 21=[-30.625930908048677900  ,-14.052658228159035019  ] 
dist 22=[-31.086757856249116842  ,-10.644574187173098171  ] 
dist 23=[-31.144129969587937975  ,-5.0052074921100444766 ] 
dist 24=[-27.619174540932804718  ,-.77041671210704064087] 
dist 25=[-26.616856660826180631  ,3.1181655770280357838 ] 
dist 26=[-25.958509148864495905  ,7.3984365151080231331 ] 
dist 27=[-25.631594995236138950  ,11.475970648205587151  ] 
dist 28=[-7.1457464423178442162 ,14.568450254670561064  ] 
dist 29=[-4.9236210606638852262 ,17.472591104994305166  ] 
dist 30=[.32413752634275493234,20.812785746227373555  ] 
dist 31=[1.1222405876936761723 ,23.740460031063652156  ] 
dist 32=[7.5265313718501796470 ,25.009627954197182471  ] 
dist 33=[8.4988727127616973850 ,25.563074433080054285  ] 
dist 34=[10.264290999004912370  ,25.642545570165994383  ] 
dist 35=[10.550078461494395499  ,23.163568715727840123  ] 
dist 36=[13.289422124654974230  ,22.435144203763335711  ] 
dist 37=[13.307226295607174180  ,21.935811479244851569  ] 
dist 38=[10.072492112205881373  ,21.641631134547953391  ] 
dist 39=[4.1317099275218222044 ,15.979869129749719707  ] 
dist 40=[.02760924016511162333,14.189640785136485547  ] 
dist 41=[-3.4263472163170326784 ,13.672276482070430539  ] 
dist 42=[-6.7893837452288337233 ,12.799572594276241182  ] 
dist 43=[-9.7504845244099862743 ,12.497643759163825369  ] 
dist 44=[-11.610727258074377937  ,6.1939894113317763215 ] 
dist 45=[-12.984997021583215599  ,5.4453961368437493304 ] 
dist 46=[-14.019194758587193325  ,3.7713391660208413347 ] 
dist 47=[-14.751403404590817524  ,3.3107721482429904422 ] 
dist 48=[-14.927421553226679889  ,1.3719628202544364341 ] 
dist 49=[-14.867939413772191880  ,.99934834271675244124] 
dist 50=[-14.678427619664667981  ,.22038007842071627706] 
dist 51=[-13.128540003386939832  ,.02181421424364422398] 
dist 52=[-12.668762674247217127  ,-.61581925911912023418] 
dist 53=[-11.867692625172901547  ,-.60440743479692546905] 
dist 54=[-11.595027944610457333  ,-.35179350287442702008] 
dist 55=[-6.0320635319187667622 ,2.6926038425542317353 ] 
dist 56=[-5.3859658407103995513 ,5.1476218933444038907 ] 
dist 57=[-3.9463377596606197463 ,7.1566396337499669642 ] 
dist 58=[-2.9448037287918337536 ,9.0227882888692561737 ] 
dist 59=[-2.3483248936454227648 ,10.656165266421782067  ] 
dist 60=[-.38492618126056296573,11.600907072299783273  ] 
dist 61=[-.15470772431779213159,12.132063410429357005  ] 
dist 62=[.37894582336344652776,12.223969037732643356  ] 
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dist 188=[-3.99159975792866696550e-05,.00166706021418945417] 
dist 189=[1.09507510801192346500e-05,.00175442869182995421] 
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dist 202=[-.00021702493559469421,.00025088976114328483] 
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dist 206=[-.00034786194063234044,8.58015360690184301800e-06] 
dist 207=[-.00034884170458799640,-2.07713102802577293800e-06] 
dist 208=[-.00034684241530522513,-5.44319456576051774760e-05] 
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dist 211=[-.00027946492150051505,-8.09732661399825460480e-05] 
dist 212=[-.00026687756263158481,-8.10271506257217482460e-05] 
dist 213=[-.00024782772410452190,-7.89392057268154832320e-05] 
dist 214=[-.00024097834969460697,-4.36837464304759514870e-05] 
dist 215=[-7.86671720518373799720e-05,4.47858989235701786350e-05] 
dist 216=[-6.29597658468076483840e-05,.00010406084016408908] 
dist 217=[-5.96625875575139034600e-05,.00015218127841171827] 
dist 218=[-5.64920169345019414760e-05,.00019635971206462574] 
dist 219=[-5.57966044623681857580e-05,.00023361066885304780] 
dist 220=[-1.02405069402375099530e-05,.00025422399653128458] 
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dist 222=[7.89419980130214275800e-06,.00026924113479949530] 
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dist 226=[3.06647705366673186800e-05,7.72754848834015949390e-05] 
dist 227=[3.13056170274115919300e-05,6.22697146528128477990e-05] 
dist 228=[3.13999536225818909630e-05,5.90374044288714243270e-05] 
dist 229=[3.03391657653647555280e-05,5.59296861607146071900e-05] 
dist 230=[1.68277852041514690680e-05,5.52469075123446384940e-05] 
dist 231=[-1.73339751046787043160e-06,4.70377410089761106360e-05] 
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dist 234=[-3.36961509385280149990e-05,3.43225108148612028110e-05] 
dist 235=[-4.16215170608569906740e-05,3.32228465342051141460e-05] 
dist 236=[-4.60716041918803045510e-05,1.18719458031733368220e-05] 
dist 237=[-4.87468982715350440630e-05,1.02042949575400363340e-05] 
dist 238=[-4.96251495154680663310e-05,6.66073130586452901480e-06] 
dist 239=[-4.95382766087279057330e-05,5.69964738199670345630e-06] 
dist 240=[-4.92243962877394621520e-05,2.10292500938148360370e-06] 
dist 241=[-4.71057781929435008140e-05,1.34429695957910708370e-06] 
dist 242=[-4.65482128844011145840e-05,2.87030247968728526580e-07] 
dist 243=[-3.82001641029219039530e-05,0                     ] 
dist 244=[-3.61877896842690983570e-05,-1.27331346152285282900e-07] 
dist 245=[-3.40132666545148845650e-05,3.85973939440678445130e-07] 
dist 246=[-3.29264868722233751370e-05,1.35772811671022978960e-06] 
dist 247=[-1.18600561318947813120e-05,8.59015992230886922770e-06] 
dist 248=[-1.02195522009861984200e-05,1.45820707130147063110e-05] 
dist 249=[-6.73324207502750419970e-06,1.94509084800798583900e-05] 
dist 250=[-5.72277650524143696300e-06,2.39290859536507361920e-05] 
dist 251=[-2.14299291896470225510e-06,2.77113133634760612660e-05] 
dist 252=[-1.39022223047950512150e-06,2.98166896015083183580e-05] 
dist 253=[-3.13195302868924442770e-07,3.10635523680506747420e-05] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 2, 2, 1, 0, 2] 
dist 0=[130.76796524359224688   ,130.76796524359224688   ] 
dist 1=[130.05905683433005631   ,130.51642485816814331   ] 
dist 2=[127.00452049067362317   ,130.76796524359224688   ] 
dist 3=[122.53299140970858000   ,129.85979079132491084   ] 
dist 4=[116.62442982627306179   ,121.31418136328820864   ] 
dist 5=[108.63828774745355062   ,118.92568580783431494   ] 
dist 6=[95.900919831030417827  ,117.64082054965866742   ] 
dist 7=[82.308925765666960475  ,114.08772152672736162   ] 
dist 8=[65.352350869333184686  ,91.267897191255020221  ] 
dist 9=[53.210935117604847184  ,87.520229030697325815  ] 
dist 10=[42.449972200688596422  ,83.413409502353743257  ] 
dist 11=[30.966779746484479566  ,81.789971606241255409  ] 
dist 12=[20.059903652050493392  ,48.819784566904419115  ] 
dist 13=[11.576683696725043282  ,43.957288927249529258  ] 
dist 14=[3.3052309794352609736 ,42.812338233150281763  ] 
dist 15=[-6.7843241838079707320 ,33.574456833520898636  ] 
dist 16=[-16.110214295186990050  ,4.990779153851032581  ] 
dist 17=[-21.349839854125399180  ,-.5732182673672783440 ] 
dist 18=[-24.891580796888184505  ,-2.848266905802308498  ] 
dist 19=[-29.276402728021418013  ,-5.9387604718722680690 ] 
dist 20=[-32.826318801429685312  ,-6.4116714158244010786 ] 
dist 21=[-34.245390863613330437  ,-5.3731500573929656869 ] 
dist 22=[-34.773890881505466158  ,-2.6141895355883629023 ] 
dist 23=[-34.767093355109342307  ,.5057467380140349238 ] 
dist 24=[-31.162139849980202619  ,2.9840011583499846920 ] 
dist 25=[-30.057162058795071025  ,5.3803716918308066087 ] 
dist 26=[-29.195982408606175080  ,8.1884234924920043321 ] 
dist 27=[-28.594087007241224183  ,10.959403877849232594  ] 
dist 28=[-9.1480860531656823792 ,13.216100837440962488  ] 
dist 29=[-6.7424438841360560826 ,15.486179682724379354  ] 
dist 30=[-.9898789316524419208 ,18.319142998295760850  ] 
dist 31=[-.1308104063382470299 ,20.847218249587303859  ] 
dist 32=[7.1648291225956756429 ,21.909175184076520374  ] 
dist 33=[8.3064398493341576229 ,22.364504432709096221  ] 
dist 34=[10.228289871507988376  ,22.478190372123274461  ] 
dist 35=[10.581425514787580921  ,20.025140118636748788  ] 
dist 36=[10.550504531215501294  ,19.931687114671227118  ] 
dist 37=[9.0580224830064468412 ,20.025493841255316395  ] 
dist 38=[6.9934710758642122942 ,19.652840261665972691  ] 
dist 39=[3.6792843424504335987 ,19.461947674664564008  ] 
dist 40=[.30667767131599017196,16.539823155836856707  ] 
dist 41=[-1.9904147435684208390 ,15.778891221715049644  ] 
dist 42=[-4.7857109300469487244 ,14.914406815931487241  ] 
dist 43=[-7.2939513844098189494 ,14.482953343136809696  ] 
dist 44=[-8.8730493454349254257 ,6.6522341708875686592 ] 
dist 45=[-10.043573371879514885  ,5.9240216372493074131 ] 
dist 46=[-10.931880180581773392  ,4.2812658162193935504 ] 
dist 47=[-11.567314802528860562  ,3.8281829265480724676 ] 
dist 48=[-11.734495808894444563  ,1.8569227526679056180 ] 
dist 49=[-12.680884151866548162  ,1.4820484350082301711 ] 
dist 50=[-13.280089633299863751  ,.64474394941259455065] 
dist 51=[-13.393756325696893125  ,.45692483795839738414] 
dist 52=[-9.9424426307271262398 ,-3.2959151373435129098 ] 
dist 53=[-9.3757366048530620175 ,-2.9141618139954419069 ] 
dist 54=[-9.1533995272683771910 ,-2.1613694117017060756 ] 
dist 55=[-3.5000864124720743994 ,.96954335559102351629] 
dist 56=[-2.7415643346088254925 ,3.0788065358522058604 ] 
dist 57=[-1.0104312920801070153 ,4.7996926088212591571 ] 
dist 58=[-.64693409607941441762,6.3893869413850784808 ] 
dist 59=[.3451607311662799248 ,7.7331599463506111854 ] 
dist 60=[1.1229500406034612589 ,8.4781202505735195700 ] 
dist 61=[1.2421800620022085230 ,8.9120624654578512513 ] 
dist 62=[1.4520891900444552690 ,9.0213504507906144773 ] 
dist 63=[1.4857367125301261968 ,2.7670816301820559414 ] 
dist 64=[1.9665047942483341903 ,2.8011161463941780856 ] 
dist 65=[1.9686545812046390632 ,2.7843647338936609742 ] 
dist 66=[1.9017474977428831928 ,2.7759408133707922943 ] 
dist 67=[1.7254893534038023540 ,2.3736918242514629396 ] 
dist 68=[1.4978127301081820231 ,2.2680211621827610610 ] 
dist 69=[1.2267629864914435915 ,2.1882422762924160874 ] 
dist 70=[.87812627499163714455,2.1533493216358722286 ] 
dist 71=[.23055899735028616285,1.5788539658548275287 ] 
dist 72=[-.21163425195125953039,.61999371710612562794] 
dist 73=[-.57739988860017714508,.49246169506675248439] 
dist 74=[-.9239477930404187858 ,.2022735739059442403 ] 
dist 75=[-1.2232193299554511742 ,.1395058233677631358 ] 
dist 76=[-1.4013761877691919468 ,-.19476266769682788259] 
dist 77=[-1.5215687960658557995 ,-.25213676641925875989] 
dist 78=[-1.5908212356290574810 ,-.3621431871134579709 ] 
dist 79=[-1.6259121067508648872 ,-.38465355889965534732] 
dist 80=[-1.6281048251242262683 ,-.43351930203125926488] 
dist 81=[-1.5828915912048351165 ,-.43564207297889308402] 
dist 82=[-1.5694444784610445732 ,-.42129483794208093081] 
dist 83=[-1.3083244167560864345 ,-.38123299603741933506] 
dist 84=[-1.2429563123172818351 ,-.32891595816193519652] 
dist 85=[-1.1801053570486589643 ,-.26590711534947282605] 
dist 86=[-1.1484798571851396031 ,-.18438818917136415869] 
dist 87=[-.36491628005013441797,.11496713187251093096] 
dist 88=[-.2668184569864956847 ,.33963364348038188539] 
dist 89=[-.16834971009146916218,.52307554450007016289] 
dist 90=[-.11105093092044802579,.69300065494692496211] 
dist 91=[-.09657070763574734567,.83714247737117563652] 
dist 92=[-.02836854521644953933,.92490401815422449166] 
dist 93=[-.01589928524081169137,.9748094448331395409 ] 
dist 94=[.01079058034680364783,.98642710664021817729] 
dist 95=[.01682833934752973965,.42044175086323198262] 
dist 96=[.03967913371283759835,.42593933085150762361] 
dist 97=[.04034875186137157235,.42463522361631020456] 
dist 98=[.03360140157864041859,.41322363832525576628] 
dist 99=[.01519958244635089550,.40580416592285385583] 
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dist 168=[-.00047747724573199960,.00069152623072869967] 
dist 169=[-.00117331971217760677,.00047935714555674853] 
dist 170=[-.00181906176353329979,-9.08466872882686523260e-07] 
dist 171=[-.00236830535034738817,-9.70571538969135384960e-05] 
dist 172=[-.00268101821898844301,-.00063346314319436139] 
dist 173=[-.00287461770225999341,-.00072291986139802522] 
dist 174=[-.00295094646404426950,-.00087984734193419509] 
dist 175=[-.00296600529012549218,-.00090808879818120866] 
dist 176=[-.00295117136756199499,-.00092902830994833740] 
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dist 179=[-.00238798003923911826,-.00079798086197013884] 
dist 180=[-.00228147428360083890,-.00070364303005060469] 
dist 181=[-.00212029074081315040,-.00059720934004676814] 
dist 182=[-.00206211458912434694,-.00037966914749534702] 
dist 183=[-.00067937018114801830,.00037448344403578227] 
dist 184=[-.00049608958076248977,.00087990110461485707] 
dist 185=[-8.66231206303243822670e-05,.00129030734639095669] 
dist 186=[2.74532352140578020890e-06,.00166720803327611008] 
dist 187=[.00018311943405204080,.00198504840914696294] 
dist 188=[.00036632788151043897,.00216094824723453978] 
dist 189=[.00039317340482052613,.00226331205805657034] 
dist 190=[.00044201730828857350,.00228911647796732369] 
dist 191=[.00044917304162458074,.00069720599658152743] 
dist 192=[.00046680881284197970,.00069494976265690734] 
dist 193=[.00045413699954225028,.00066599950228591418] 
dist 194=[.00042891689665287972,.00066166616511277488] 
dist 195=[.00038063134078889991,.00053390985559872238] 
dist 196=[.00032243370974684451,.00050596745945228049] 
dist 197=[.00025785403448726737,.00048048921529827519] 
dist 198=[.00014626068139876922,.00047513890476608818] 
dist 199=[-1.21138152707251998410e-05,.00033292945634043632] 
dist 200=[-.00011851162247275792,.00011362597289677340] 
dist 201=[-.00020519671440395099,8.48195782942448468830e-05] 
dist 202=[-.00028530058167148726,2.06262438323612104260e-05] 
dist 203=[-.00035320944903732123,6.26372520724296204680e-06] 
dist 204=[-.00039147348868233627,-6.29320257401535041300e-05] 
dist 205=[-.00041464945744797819,-7.51887292232188301630e-05] 
dist 206=[-.00042265034377014230,-9.49861823183116722840e-05] 
dist 207=[-.00042240494894100964,-9.91200423279171945730e-05] 
dist 208=[-.00041988852122178690,-9.99818155229110704640e-05] 
dist 209=[-.00040214723072804503,-9.71891571144945178990e-05] 
dist 210=[-.00039744204159333377,-9.14296248885813150780e-05] 
dist 211=[-.00032646893044270777,-8.02648778332407532550e-05] 
dist 212=[-.00030932489846403174,-6.67621149860746985890e-05] 
dist 213=[-.00029085735211775575,-5.17183421246541758970e-05] 
dist 214=[-.00028158303770411197,-4.42341429106150000000e-06] 
dist 215=[-.00010208953440104473,7.19222373946477700220e-05] 
dist 216=[-8.80275341565052205730e-05,.00012313011716340413] 
dist 217=[-5.80224032269270780600e-05,.00016476369543277239] 
dist 218=[-4.98445531937213384020e-05,.00020309286213543460] 
dist 219=[-1.89991045058166589160e-05,.00023548787613465562] 
dist 220=[-1.25387263386298370410e-05,.00025355876651116299] 
dist 221=[-2.99381862954661199280e-06,.00026459244888190970] 
dist 222=[-3.88755400542918007220e-07,.00026743243087966820] 
dist 223=[4.22851459200040655470e-06,9.68707659541440671700e-05] 
dist 224=[4.89631864766990422420e-06,9.67608446462070923230e-05] 
dist 225=[3.74243047715548584040e-06,9.60406146039329663560e-05] 
dist 226=[1.29349389829244615840e-06,9.25266207680732960810e-05] 
dist 227=[-3.49930629111777016550e-06,9.07750787890937484220e-05] 
dist 228=[-9.31075468921719437780e-06,7.76779747552206971860e-05] 
dist 229=[-1.58048179054113843560e-05,7.43199490466678885380e-05] 
dist 230=[-2.39132976816905869360e-05,6.84534778837484910080e-05] 
dist 231=[-3.61355332187494963670e-05,6.66390316886516403420e-05] 
dist 232=[-4.83924526404943026880e-05,2.46173748723907978700e-05] 
dist 233=[-5.66388727723987852420e-05,1.88396001859792308320e-05] 
dist 234=[-6.33709698938381261560e-05,9.37832494789218824720e-06] 
dist 235=[-7.09015829761488688860e-05,8.06281450811191926320e-06] 
dist 236=[-7.62537477186750234290e-05,3.09289586283758931740e-06] 
dist 237=[-7.94812597963766293910e-05,2.05342589832361062850e-06] 
dist 238=[-8.05635633114595910740e-05,4.99826875010686505780e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[110.46184193865194245   ,110.46184193865194245   ] 
dist 1=[107.18745813118599457   ,111.44110256121993879   ] 
dist 2=[103.23493286829135221   ,112.05487532773670945   ] 
dist 3=[99.671980962381266301  ,112.53169130245604298   ] 
dist 4=[95.750205196406275593  ,112.30288584429875759   ] 
dist 5=[90.358367747732208593  ,109.07582923748104910   ] 
dist 6=[84.470632665413611098  ,107.87454718712658521   ] 
dist 7=[78.414183963919545666  ,106.10221476678481324   ] 
dist 8=[66.246377865893824632  ,105.28784058374645392   ] 
dist 9=[57.116557245884515629  ,81.328117528173765620  ] 
dist 10=[48.597699145583366488  ,77.979692507365419085  ] 
dist 11=[38.841620796479185825  ,68.995617334687204299  ] 
dist 12=[29.159968659336425628  ,67.579391434972308919  ] 
dist 13=[20.921736157462569234  ,51.370572394833910370  ] 
dist 14=[12.211045625345874090  ,48.138583356703785780  ] 
dist 15=[.62353718645266573339,44.474724761100266376  ] 
dist 16=[-10.371656576196280372  ,43.469076039966884791  ] 
dist 17=[-16.732016396483261828  ,19.010311991310251742  ] 
dist 18=[-20.937057285839273041  ,7.7560094642653568059 ] 
dist 19=[-23.348967078252225370  ,4.5119755989696893848 ] 
dist 20=[-24.907562960952801209  ,1.0881435196778502911 ] 
dist 21=[-25.707372151114663773  ,.28686348598023742434] 
dist 22=[-26.366883762658183260  ,-2.0540520140358157086 ] 
dist 23=[-27.600815257281508524  ,-2.4400895556137771753 ] 
dist 24=[-28.160350298479002148  ,-2.2701612173289224232 ] 
dist 25=[-28.275382011879596305  ,-1.3159310418930558697 ] 
dist 26=[-17.564564218526851376  ,-.22461434810005736829] 
dist 27=[-17.033988593738107865  ,.49246770003447076594] 
dist 28=[-16.956541828932899884  ,2.3976868257000829626 ] 
dist 29=[-13.940798373824059815  ,4.8481655726596288755 ] 
dist 30=[-13.216617715962102599  ,7.0300250016263355568 ] 
dist 31=[-12.703306068668920209  ,9.3589187412681962622 ] 
dist 32=[-12.587914607167360842  ,11.401136152509425263  ] 
dist 33=[-2.1026950470911944681 ,12.447579743974536293  ] 
dist 34=[-.87931812364653246995,12.973151889965851301  ] 
dist 35=[-.3111158148432901285 ,13.057949665647191975  ] 
dist 36=[-.67394571677886735725,12.582695411206355646  ] 
dist 37=[-1.0751667243790331197 ,12.313434338298470364  ] 
dist 38=[-1.4557895159177157569 ,11.882454703543590060  ] 
dist 39=[-1.7376147133527943098 ,11.671066450999665477  ] 
dist 40=[-1.9938027118624359484 ,7.6578183959924863394 ] 
dist 41=[-2.6124447620192012369 ,7.7903801045175182280 ] 
dist 42=[-4.6308183839124246203 ,7.7813364910942753911 ] 
dist 43=[-6.5142111225221397150 ,7.5779208771793124608 ] 
dist 44=[-8.1110944666976670561 ,7.4686003103631454001 ] 
dist 45=[-8.9947822276406612464 ,6.4153873543101385645 ] 
dist 46=[-9.5047230656416037016 ,6.1417604170203527636 ] 
dist 47=[-9.6195366878380208350 ,5.7350469813662578576 ] 
dist 48=[-2.8611248348163304589 ,5.5834316100890690067 ] 
dist 49=[-3.0585152521521764100 ,1.9246846647422127597 ] 
dist 50=[-3.1544461764158872028 ,1.4392042324719545363 ] 
dist 51=[-3.1783419564648387480 ,1.4661028969681259413 ] 
dist 52=[-4.1306757500204670882 ,1.8114648088582880496 ] 
dist 53=[-4.9637440622550240168 ,2.2107435131070335275 ] 
dist 54=[-5.4249118704150811949 ,2.5328782065473991856 ] 
dist 55=[-5.6932547848288142291 ,2.6803865736685204145 ] 
dist 56=[-5.7607875101829162372 ,2.7481881291868777939 ] 
dist 57=[-1.7777290300905184167 ,2.7544316654679278041 ] 
dist 58=[-1.7790816300752503663 ,.19888759406284979967] 
dist 59=[-1.7225167663132030037 ,.61475424324106526431] 
dist 60=[-1.7119978438254314087 ,.98469795436045115756] 
dist 61=[-1.4099786076713228030 ,1.2233610190310321863 ] 
dist 62=[-1.3372097208823888378 ,1.4068350418434527145 ] 
dist 63=[-1.2774273901967437925 ,1.5580372033979990008 ] 
dist 64=[-1.2576776487451856490 ,1.6726493523393421786 ] 
dist 65=[-.20940078434263170469,1.7109689866359001088 ] 
dist 66=[-.08445006487783097256,1.7162124241067108577 ] 
dist 67=[.20682773989454481537,1.6993253703589612603 ] 
dist 68=[.2507282767166374706 ,1.5293649019840436928 ] 
dist 69=[.59485808440214529064,1.4766499270946641824 ] 
dist 70=[.64620106134984347008,1.3987898761135433340 ] 
dist 71=[.33688371876880233239,1.3664798141024618129 ] 
dist 72=[-.11909470188543543848,.95339403183103060268] 
dist 73=[-.42678008948684730171,.95931906545745126039] 
dist 74=[-.67818664724981724131,.95596402317026440873] 
dist 75=[-.91086536449900904607,.91858686397770571961] 
dist 76=[-1.1077054708878129058 ,.91000890189928910336] 
dist 77=[-1.2169036748895842120 ,.74489990564263647706] 
dist 78=[-1.2806454379622342634 ,.70504531891388396859] 
dist 79=[-1.2966768591865328560 ,.66763479619734935277] 
dist 80=[-.42827714940786235048,.65137633104677330965] 
dist 81=[-.43622742394718661206,.16296009483796877611] 
dist 82=[-.43664394826909318012,.11267896005128635835] 
dist 83=[-.43408856890351516554,-.00108439658484358028] 
dist 84=[-.39461907422781367768,-.02372651456838910003] 
dist 85=[-.47699240985796255486,-.15049613777582106991] 
dist 86=[-.52288779148520109587,-.17158710223149868756] 
dist 87=[-.55146169818559310602,-.11959756172074148356] 
dist 88=[-.55818034291622054543,-.01122973860223663201] 
dist 89=[-.27035716537035948681,.06260606300730656279] 
dist 90=[-.26786810117710489009,.12376693185355579527] 
dist 91=[-.26072765730002815698,.18183859289162934879] 
dist 92=[-.25649569916522846247,.23205382351526885451] 
dist 93=[-.22994621364135152388,.26203853484503021178] 
dist 94=[-.22296930171821849533,.28236895849811316688] 
dist 95=[-.20310304265494537433,.29427364799447573512] 
dist 96=[-.19661698430989816989,.30067064207151611762] 
dist 97=[-.12056682623292955602,.30049338574142363627] 
dist 98=[-.10745149607225829606,.29463541299440459677] 
dist 99=[-.08095848080053107731,.28958804243781513722] 
dist 100=[-.07381416473012351901,.25476641489070306398] 
dist 101=[-.04791079194861131252,.24515301775720261828] 
dist 102=[-.04168999935566668940,.2268929231557487595 ] 
dist 103=[-.03495868955786137572,.1909957677029165539 ] 
dist 104=[-.03335741603803542696,.10915982529405420709] 
dist 105=[-.04129986838788017392,.10969743259129191032] 
dist 106=[-.06457388379706234556,.10914196298485064294] 
dist 107=[-.0888377043142406857 ,.10543085944736349967] 
dist 108=[-.10945461301755176007,.1037453182503373346 ] 
dist 109=[-.12238070107507199872,.08827522794815851049] 
dist 110=[-.13001300253957543348,.08433811919570672600] 
dist 111=[-.13186428689584255331,.07837574146445900790] 
dist 112=[-.05931685061587145580,.07622757797728787482] 
dist 113=[-.05973564677610145761,.02505129217074110799] 
dist 114=[-.05857291523417474879,.01823772872234158095] 
dist 115=[-.05840476728505080607,.00301294273001671829] 
dist 116=[-.06127308200006816469,-.00029334523152085422] 
dist 117=[-.07302755266803878679,-.01677044882114343188] 
dist 118=[-.07953197261549392439,-.01964407421099318827] 
dist 119=[-.08331610392573631838,-.01934065701023477734] 
dist 120=[-.08426911460901504895,-.00615101948642956040] 
dist 121=[-.02540511806667498444,.00279877799417018160] 
dist 122=[-.02531583389556397970,.01017873916731287268] 
dist 123=[-.02429581087169350927,.01713752611564269539] 
dist 124=[-.02409924686198735472,.02312726068694514838] 
dist 125=[-.01961343609758407322,.02666095034537764647] 
dist 126=[-.01853983832723834704,.02900609791467705050] 
dist 127=[-.01763131652596287032,.03027845465925260247] 
dist 128=[-.01730628842189290896,.03090443683310134362] 
dist 129=[-.00231855355830633521,.03090020381135021182] 
dist 130=[-.00052878403154875378,.03019439323401819606] 
dist 131=[.00362157880754461879,.02975351308782825419] 
dist 132=[.00425694312795530797,.02572248439939312365] 
dist 133=[.00909023540142319330,.02465118895612395057] 
dist 134=[.00980769155595219395,.0230181004627823947 ] 
dist 135=[.00454555444089367195,.02241724939000233065] 
dist 136=[-.00349509300623143485,.01399585310115570610] 
dist 137=[-.00889300756523199818,.01399067788466835500] 
dist 138=[-.01328304917218553626,.01391189169148410124] 
dist 139=[-.01732254482709362740,.01330940144655593381] 
dist 140=[-.02073171914332829665,.01317305576393906963] 
dist 141=[-.02261940240137263456,.01073369070786334016] 
dist 142=[-.02371806632248106038,.01015009568587862932] 
dist 143=[-.02399480441785968672,.00958566746861528414] 
dist 144=[-.00725762761529050134,.00933791677925896935] 
dist 145=[-.00727223160253981207,.00223370668743731999] 
dist 146=[-.00706834927301041801,.00150231970941880890] 
dist 147=[-.00702387600454966624,-.00014492809142609225] 
dist 148=[-.00593617588033200707,-.00047759135549237500] 
dist 149=[-.00713238398032696854,-.00228752876498053770] 
dist 150=[-.00779649341137088350,-.00259156965374981429] 
dist 151=[-.00819039186128315017,-.00199002267334502136] 
dist 152=[-.00829099799350230795,-.00034178058512075215] 
dist 153=[-.00320280402561956015,.00077098181130674374] 
dist 154=[-.00318887711642166227,.00168294885536185392] 
dist 155=[-.00304746489316214926,.00253406941071892873] 
dist 156=[-.00302703015831138683,.00326100665393468045] 
dist 157=[-.00242776630130532848,.00367998778301560245] 
dist 158=[-.00228672401466712700,.00394583895467895523] 
dist 159=[-.00218358931757694453,.00406488160833102800] 
dist 160=[-.00216081222257579901,.00409853606240133599] 
dist 161=[-.00017260645322307111,.00408676745187855193] 
dist 162=[5.88658760451610267470e-05,.00393444064163656358] 
dist 163=[.00059610703349440627,.00389741692997829325] 
dist 164=[.00067446500595460165,.00320261134660004583] 
dist 165=[.00129702057179051552,.00303361244922374182] 
dist 166=[.00138789074553829099,.00287239685097408797] 
dist 167=[.00055855746904113161,.00279880664489485537] 
dist 168=[-.00028111297874302067,.00161212306719480074] 
dist 169=[-.00084496709854653684,.00161166595587125241] 
dist 170=[-.00130387736590585754,.00160083142633882635] 
dist 171=[-.00172690041503833795,.00154044826362757242] 
dist 172=[-.00208459662349532177,.00151505082607650946] 
dist 173=[-.00228463637680678368,.00128208842640919225] 
dist 174=[-.00241018930153373473,.00122352510765921210] 
dist 175=[-.00243898652201824294,.00113505302258236956] 
dist 176=[-.00094813706905149926,.00110335904047829183] 
dist 177=[-.00094764196056909547,.00035543067108452313] 
dist 178=[-.00091366095591058000,.00025641641536470027] 
dist 179=[-.00090870361315854854,3.58065332345282713420e-05] 
dist 180=[-.00090598466055412337,-1.25299024516457041460e-05] 
dist 181=[-.00107701504231715980,-.00024916618275642370] 
dist 182=[-.00117164277379871208,-.00029070390454178299] 
dist 183=[-.00122669335770604253,-.00027158694860907412] 
dist 184=[-.00124056727467383091,-6.50331797219453298020e-05] 
dist 185=[-.00037775242285885172,7.42443652012440172600e-05] 
dist 186=[-.00037579324593965582,.00018813586806993171] 
dist 187=[-.00035846625959546578,.00029404605695391317] 
dist 188=[-.00035592910531851053,.00038426956258457048] 
dist 189=[-.00028492797932628112,.00043588199039510426] 
dist 190=[-.00026937017439106087,.00046814484783022508] 
dist 191=[-.00025564679985772963,.00048154749628774746] 
dist 192=[-.00025283551787966974,.00048490336681751912] 
dist 193=[-4.53944417141515431630e-05,.00048279381342927208] 
dist 194=[-2.04636482617679941130e-05,.00046698376442229960] 
dist 195=[3.66645232870860881500e-05,.00045975127812834397] 
dist 196=[4.64168637625396312080e-05,.00039160580871036910] 
dist 197=[.00011130647776461655,.00037428515543280615] 
dist 198=[.00012138566988646365,.00034806642284927360] 
dist 199=[6.30028937189568762830e-05,.00033857396907656344] 
dist 200=[-6.04477672034658430210e-05,.00022729115074509546] 
dist 201=[-.00014320099027489248,.00022650320509558494] 
dist 202=[-.00021041210201375728,.00022494424901547120] 
dist 203=[-.00027215272123584704,.00021498167441699021] 
dist 204=[-.00032422440935368693,.00021240945942549797] 
dist 205=[-.00035304464501851022,.00017398165791154607] 
dist 206=[-.00036982000508858739,.00016475239261724217] 
dist 207=[-.00037404719019803486,.00015478772473166701] 
dist 208=[-.00011836589818463305,.00014981643953080074] 
dist 209=[-.00011797609701827143,5.32023346313750868930e-05] 
dist 210=[-.00011366070031064516,4.56662805061696172720e-05] 
dist 211=[-.00011247641516952143,2.96806181263952718630e-05] 
dist 212=[-.00010934086407068411,2.53542496111227350400e-05] 
dist 213=[-.00012655722785088642,9.21820584018475458280e-06] 
dist 214=[-.00013612259193953792,5.80517675902115294220e-06] 
dist 215=[-.00014174109252072485,1.16890599387566450740e-06] 
dist 216=[-.00014328487566034760,2.48591748325944905780e-06] 
dist 217=[-6.20521618457376759480e-05,2.11086530035643761850e-05] 
dist 218=[-6.14086435375949765290e-05,3.62852826367903806720e-05] 
dist 219=[-5.97983360214125000750e-05,5.03158979515229332440e-05] 
dist 220=[-5.88876301295116232930e-05,6.22140945330828866590e-05] 
dist 221=[-5.32597270641901941110e-05,6.89238833012276666780e-05] 
dist 222=[-5.17913980983595428840e-05,7.29948480186251075680e-05] 
dist 223=[-4.71691716325885399340e-05,7.44155257214828759140e-05] 
dist 224=[-4.60117678470350553140e-05,7.44615872774057367620e-05] 
dist 225=[-3.05082445775654251050e-05,7.39517643145314472960e-05] 
dist 226=[-2.77119497124601826750e-05,7.13411886571313907950e-05] 
dist 227=[-2.22105363359265245490e-05,7.00126093326447135750e-05] 
dist 228=[-2.07310064230394232900e-05,6.00155113188421592930e-05] 
dist 229=[-1.54593217123255730560e-05,5.74422667080020910790e-05] 
dist 230=[-1.41042353764827572400e-05,5.29105684317784681710e-05] 
dist 231=[-1.28416465539200001030e-05,4.63427931797087196340e-05] 
dist 232=[-1.25776605607996497590e-05,1.91592979620710013600e-05] 
dist 233=[-2.00995811411374513090e-05,1.45988067370298135900e-05] 
dist 234=[-2.69372348546050349180e-05,9.66927910241799448590e-06] 
dist 235=[-3.32366095553707882390e-05,8.32236428416150545210e-06] 
dist 236=[-3.85633601754171821250e-05,3.22179690006669924660e-06] 
dist 237=[-4.15390946855055281320e-05,2.15724802503242603160e-06] 
dist 238=[-4.33919346232955560380e-05,5.39229889710458872640e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 1, 2, 1, 2] 
dist 0=[116.81709926992505431   ,116.81709926992505431   ] 
dist 1=[110.93921539775246564   ,120.72071282978857600   ] 
dist 2=[100.99073497069098686   ,122.81428761292434271   ] 
dist 3=[90.551395790547611977  ,123.88764634450993433   ] 
dist 4=[82.714569904515388700  ,123.74273096381400162   ] 
dist 5=[75.401857399562819723  ,122.88813203696678952   ] 
dist 6=[67.030047299214388132  ,122.15171261150477943   ] 
dist 7=[58.724893622462561489  ,117.51319322628809127   ] 
dist 8=[51.663041970009798083  ,110.61183380433866157   ] 
dist 9=[44.198797124531835280  ,88.239839829223921312  ] 
dist 10=[34.268558439420972937  ,86.879743563364417898  ] 
dist 11=[24.628441579770705328  ,67.237263603200417911  ] 
dist 12=[18.314203421735221389  ,63.193891618910509385  ] 
dist 13=[13.220639366606673903  ,59.339009943306379933  ] 
dist 14=[8.4488724807852106129 ,58.612023695655762938  ] 
dist 15=[4.2282611412059663548 ,32.685684714329778961  ] 
dist 16=[1.3313268688855956222 ,25.143299219208680141  ] 
dist 17=[-4.9191368500930718085 ,4.4142779450101177859 ] 
dist 18=[-12.564559215365240866  ,4.0920341720212661757 ] 
dist 19=[-19.070219214357051685  ,3.5026475546491498053 ] 
dist 20=[-22.873976096869346292  ,3.3643714152934292392 ] 
dist 21=[-25.393087036112261869  ,3.2700605941604287531 ] 
dist 22=[-26.796600028611770236  ,3.2063748503021492716 ] 
dist 23=[-27.535521004562825504  ,2.9960637947707560370 ] 
dist 24=[-27.588099712379470995  ,2.8934875141364366649 ] 
dist 25=[-27.017406092507347480  ,2.5283027685742092810 ] 
dist 26=[-26.661780601909499988  ,2.3663509077190623824 ] 
dist 27=[-23.025540933364508854  ,.10011984071358129474] 
dist 28=[-22.072523104473355278  ,-.36917919161409868974] 
dist 29=[-20.680343107187026588  ,1.2130531795739118786 ] 
dist 30=[-20.148455645692119981  ,3.2232201276106703191 ] 
dist 31=[-7.2308969023575929298 ,5.0830050632783291943 ] 
dist 32=[-5.5221907405086751254 ,7.1767853386314649100 ] 
dist 33=[-4.2988160069866349716 ,10.200726931122667212  ] 
dist 34=[-4.1518211121729945580 ,13.643690923505779030  ] 
dist 35=[-.38771821479574027419,16.547624698032898389  ] 
dist 36=[.07257286335346337331,18.154785208678579647  ] 
dist 37=[1.0874244998319378654 ,19.089881480217590233  ] 
dist 38=[1.2726833852579623433 ,19.325384390262587565  ] 
dist 39=[2.2983225008939748170 ,9.7040701481884102629 ] 
dist 40=[2.4648465858393622787 ,9.6486309090198465569 ] 
dist 41=[2.6593471740418925997 ,5.9223724748865956917 ] 
dist 42=[1.0041403112665298219 ,5.8901649780174229245 ] 
dist 43=[-.43638186875527720373,4.9129819334995256055 ] 
dist 44=[-1.8759629904402652325 ,4.6702665263601879521 ] 
dist 45=[-3.1656726851612660958 ,4.4774640250052408892 ] 
dist 46=[-4.0125353708279238147 ,4.4047119390050470471 ] 
dist 47=[-4.6803510759816934628 ,2.7401548775746791420 ] 
dist 48=[-5.2608459142034108605 ,2.6034546094871752535 ] 
dist 49=[-5.7168386034397452115 ,2.3589257541360320188 ] 
dist 50=[-5.8908504829795165040 ,2.2899549120675799233 ] 
dist 51=[-5.9351498166389621650 ,1.3323344756210724747 ] 
dist 52=[-5.8880616459386703576 ,1.2422623746775475554 ] 
dist 53=[-5.3673646687154272355 ,1.0599266980812112433 ] 
dist 54=[-5.1978332795988929227 ,1.0065436744623971358 ] 
dist 55=[-4.9210583366287043669 ,.78858262280314766704] 
dist 56=[-4.8144403289130694674 ,.73708157734792226136] 
dist 57=[-3.0772286626936912395 ,.70179710802666516512] 
dist 58=[-3.0495762003272038700 ,1.7430741727516279649 ] 
dist 59=[-2.5113208797770004172 ,2.5938533642835715458 ] 
dist 60=[-2.3800727522474058749 ,3.3807183661314788249 ] 
dist 61=[-2.2561041147740203795 ,4.0456726876285143132 ] 
dist 62=[-2.1999501111085031762 ,4.4127628534699468455 ] 
dist 63=[-.580167695780656115  ,4.6242639945950301370 ] 
dist 64=[-.41107549637052824883,4.6718604550327594707 ] 
dist 65=[-.26736016508829460846,1.2538290827119838062 ] 
dist 66=[-.25920439494537904356,1.3105212012992340363 ] 
dist 67=[-.00374650567432897120,1.5892244733919691922 ] 
dist 68=[.02709538187043780066,1.7462423640007453458 ] 
dist 69=[.09507255493568597586,1.8436299651184679240 ] 
dist 70=[.10737843766067222225,1.8660723780145849943 ] 
dist 71=[.17495929049447394617,1.0640841651572838020 ] 
dist 72=[.18595264184638403757,1.0575737923922434775 ] 
dist 73=[.19619033914574352692,.70486699033497590799] 
dist 74=[.01549732157558638391,.70128025170950271062] 
dist 75=[-.15237229080488218411,.57156364817503680265] 
dist 76=[-.31447622951690698834,.540329259295052724  ] 
dist 77=[-.45640527586954425442,.51864149369337558617] 
dist 78=[-.54424722025266964949,.51373354196696359334] 
dist 79=[-.60760386038520061122,.1798317520715936871 ] 
dist 80=[-.65241005373653759479,.17083264211433826326] 
dist 81=[-.68261121308279895466,.15438770943240965297] 
dist 82=[-.68800832203396938569,.14973326703791713222] 
dist 83=[-.68367960515769532972,.07495637886964230967] 
dist 84=[-.67521565975100903198,.06760569558408792600] 
dist 85=[-.59676118048726215697,.05363348114094493676] 
dist 86=[-.57432050217726163861,.05000931474099318204] 
dist 87=[-.5400519547686192942 ,.03784458892300191986] 
dist 88=[-.52690761346986550792,.03450964316241222975] 
dist 89=[-.36426184746812339778,.06371320621863964905] 
dist 90=[-.35812709857803983732,.18674851399308286317] 
dist 91=[-.30780276634418734973,.2870434571087075103 ] 
dist 92=[-.29474443825380393311,.37959576296356332437] 
dist 93=[-.27333363496951852411,.45779743157153606835] 
dist 94=[-.26617272680967696216,.50113474254725307315] 
dist 95=[-.10412678152578220509,.52637155459470501494] 
dist 96=[-.08425401094311491001,.53272976145012868037] 
dist 97=[-.03201807558836986033,.18212173579955235327] 
dist 98=[-.02334133322154370872,.22857670582390040497] 
dist 99=[-.02310898168277385698,.26766063831979196901] 
dist 100=[-.02303017872099470636,.28911529679899780278] 
dist 101=[-.02303467419508318957,.3013663421185000234 ] 
dist 102=[-.02313598998873796465,.30390643103056287361] 
dist 103=[-.02327434224511020977,.12625316369637867156] 
dist 104=[-.02342755020755449575,.12420268844740939243] 
dist 105=[-.02361133738877137911,.08092036080140436632] 
dist 106=[-.02387291139925495493,.08029800275411432516] 
dist 107=[-.03395813936744278183,.06560850330169103945] 
dist 108=[-.05399433181826652906,.06207116670960030360] 
dist 109=[-.07126208468911312030,.05910683526004537679] 
dist 110=[-.08148141441742211614,.05803392070501573046] 
dist 111=[-.08830171970118287698,.03931003306870455743] 
dist 112=[-.09207980987075970613,.03771537532078187894] 
dist 113=[-.09387663409632845368,.03421792913188273285] 
dist 114=[-.09393694620263942198,.03304307898906539463] 
dist 115=[-.09114476921945320428,.01581460369688574174] 
dist 116=[-.09038492204757826155,.01318928410465609235] 
dist 117=[-.07502713023224997198,.00778954489491913425] 
dist 118=[-.07121182657452844935,.00638154909949354549] 
dist 119=[-.06764517575551794888,.00145975728229617213] 
dist 120=[-.06594266667673817967,.00035362891169830113] 
dist 121=[-.04793006493060160067,.00529270293892476770] 
dist 122=[-.04491974117369008035,.01841802174589100267] 
dist 123=[-.03574470509546732485,.02912514066215912257] 
dist 124=[-.03381296996943955688,.03902857229852445280] 
dist 125=[-.03195110979450598163,.04742020631135960563] 
dist 126=[-.03112899453551851728,.05241058353021808671] 
dist 127=[-.00755522790804380053,.05529400476910771792] 
dist 128=[-.00512350601880625248,.05596702757923717878] 
dist 129=[.00035975024333631182,.02191024824789306570] 
dist 130=[.00146410790789468830,.02199694331553841398] 
dist 131=[.00751180329374624352,.02360742819944581684] 
dist 132=[.00852565379277267077,.02582097414798151037] 
dist 133=[.01023063732657942024,.02715037011896534526] 
dist 134=[.01055227565354968793,.02747818643211534267] 
dist 135=[.01063248972629695016,.01605717874731725982] 
dist 136=[.00678455489621954013,.01591422762940954411] 
dist 137=[.00195263380502386293,.01014922136727721277] 
dist 138=[-.00131681635145030903,.01008366085152334390] 
dist 139=[-.00400375905260752171,.00810947209995388372] 
dist 140=[-.00652338661476535000,.00764305539345002459] 
dist 141=[-.00868332312801094349,.00730431697068108156] 
dist 142=[-.00994245526648129719,.00722869278010810899] 
dist 143=[-.01075946015371032946,.00061464225408055754] 
dist 144=[-.01116437346925222165,-.00015537654040944165] 
dist 145=[-.01133337833683996579,-.00194244275923796538] 
dist 146=[-.01131252374739363721,-.00220400497111635245] 
dist 147=[-.01101008626443618606,-.00427460103550119140] 
dist 148=[-.01084458748544443287,-.00457723747272224261] 
dist 149=[-.00932198205416015359,-.00512260721724527162] 
dist 150=[-.00892367961087012408,-.00520209581010196765] 
dist 151=[-.00832017562263081490,-.00448874478954728553] 
dist 152=[-.00809889193170082109,-.00157986820232027215] 
dist 153=[-.00512622432507972747,.00133661706805961457] 
dist 154=[-.00504248138294542069,.00329341275180426908] 
dist 155=[-.00427315452011667404,.00488402095218691259] 
dist 156=[-.00407912396625397958,.00634669191799386639] 
dist 157=[-.00378613274058514531,.00758083216437957527] 
dist 158=[-.00368088469665383152,.00826412866054213772] 
dist 159=[-.00119267019638824096,.00866216816960304859] 
dist 160=[-.00086324849194365019,.00876230961323836950] 
dist 161=[-.00012875464395444543,.00268689702374837297] 
dist 162=[3.19445461451850235970e-05,.00300558123055830664] 
dist 163=[.00082165273523646049,.00357492121867128433] 
dist 164=[.00096009758836493631,.00388994490949534441] 
dist 165=[.00117925143394574222,.00407322265447743153] 
dist 166=[.00122149872877399411,.00411942145578895870] 
dist 167=[.00121995362888676591,.00190777804120664728] 
dist 168=[.00060685752778359103,.00188877992088688542] 
dist 169=[-8.83687133258845726850e-06,.00121957484634122165] 
dist 170=[-.00042374867142673068,.00120824425414528574] 
dist 171=[-.00076304655213238306,.00098165653814240790] 
dist 172=[-.00107854677161329786,.00092762746481513825] 
dist 173=[-.00134727288131616031,.00087877430422031483] 
dist 174=[-.00150087313173133228,.00085953916374734576] 
dist 175=[-.00159671748922061881,.00015454354030425944] 
dist 176=[-.00163614854524058112,7.15842003891334933150e-05] 
dist 177=[-.00164332241209983508,-.00011867751332118216] 
dist 178=[-.00163613355159837481,-.00015109016886356930] 
dist 179=[-.00157261728668314543,-.00036779125400256185] 
dist 180=[-.00155496481491034397,-.00040140906178255378] 
dist 181=[-.00128321601538928002,-.00046143057918947326] 
dist 182=[-.00121693746707894552,-.00047108317929075808] 
dist 183=[-.00114595707232208409,-.00032824740528405598] 
dist 184=[-.00110984198758163208,-3.04413764240726200000e-05] 
dist 185=[-.00071594491144000589,.00026819092045731172] 
dist 186=[-.00070744446627116911,.00046883379726137232] 
dist 187=[-.00057978439957035349,.00063227680472129346] 
dist 188=[-.00054908705786183458,.00078321363698141085] 
dist 189=[-.00051602134663885870,.00091106145837357509] 
dist 190=[-.00049946930991847713,.00098283314295223090] 
dist 191=[-.00017824286970439413,.00103050203038150953] 
dist 192=[-.00015316832276458740,.00104166312859354580] 
dist 193=[-9.99008836669570359630e-05,.00050605139726661965] 
dist 194=[-8.54605915755505723910e-05,.00050369715432648799] 
dist 195=[-3.14546247913950895240e-05,.00049664741801731151] 
dist 196=[-2.00615961169041219900e-05,.00049114453168420662] 
dist 197=[-4.24576671998195002970e-06,.00047101377307837551] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 2, 0, 2, 0, 1] 
dist 0=[124.77324044456272165   ,124.77324044456272165   ] 
dist 1=[120.43429102447493950   ,126.48235831365001664   ] 
dist 2=[113.04034162681600425   ,128.91703038966191036   ] 
dist 3=[100.86857975358831688   ,130.98030877459517261   ] 
dist 4=[88.214667641590003493  ,131.17824243206382909   ] 
dist 5=[78.896516885265909315  ,130.51285493284667357   ] 
dist 6=[70.380342652978367835  ,129.63136554168753561   ] 
dist 7=[60.897914943519344190  ,122.20495095638679083   ] 
dist 8=[51.648695623231655639  ,107.01929597856509134   ] 
dist 9=[44.044978490117944169  ,97.455181364638235967  ] 
dist 10=[36.237733628766373116  ,96.059552622014133925  ] 
dist 11=[26.153203757619952943  ,75.331583091771683282  ] 
dist 12=[16.481368993296493876  ,71.004975187010535522  ] 
dist 13=[10.311066792139020533  ,66.916107923935456648  ] 
dist 14=[5.5136025868330432487 ,66.074983334363512387  ] 
dist 15=[1.3148629629872551313 ,34.063052720587369771  ] 
dist 16=[-4.8372776266682431555 ,11.134630416041220582  ] 
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dist 217=[-4.63968144192294964160e-05,7.49692299855759213730e-05] 
dist 218=[-3.77546900958841071710e-05,.00010958331950591684] 
dist 219=[-3.78405178043870594070e-05,.00014136096982412872] 
dist 220=[1.15192903851387338170e-05,.00016815570592487121] 
dist 221=[1.08384459411747057830e-05,.00018298392147902264] 
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dist 228=[-1.44341080820105503160e-05,4.46690891195409243520e-05] 
dist 229=[-1.83447849965624040770e-05,4.23410296664788251990e-05] 
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dist 232=[-2.68071803156990156630e-05,1.70680427831404837050e-05] 
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dist 236=[-2.97611745318531297320e-05,1.71581392954983318760e-05] 
dist 237=[-3.29454842541084648430e-05,1.70388398078019355930e-05] 
dist 238=[-3.48558402774919753320e-05,1.68692810405472532030e-05] 
dist 239=[-3.54739173710133095080e-05,1.66336228558243446270e-05] 
dist 240=[-3.54017438129199471520e-05,1.62698112499346191110e-05] 
dist 241=[-3.51728191547955121210e-05,1.59753215284882644280e-05] 
dist 242=[-3.36567145511953075580e-05,1.55231401973572488980e-05] 
dist 243=[-3.32506002376815790960e-05,1.52920474104059303060e-05] 
dist 244=[-2.73070955098190075670e-05,1.43210218406525310710e-05] 
dist 245=[-2.58733181558986085810e-05,1.39229516313238172410e-05] 
dist 246=[-2.43010319768107489590e-05,1.36035062491006008630e-05] 
dist 247=[-2.35271092530854842500e-05,1.33273569167670301860e-05] 
dist 248=[-8.52915425111483759920e-06,1.30775404255729767470e-05] 
dist 249=[-7.34009790922738834660e-06,1.29522353451737643700e-05] 
dist 250=[-4.80952038548615530790e-06,1.39944447252173285430e-05] 
dist 251=[-4.12188327957829149690e-06,1.72286855020099497550e-05] 
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dist 253=[-9.97692658094581071720e-07,2.14840038710894722170e-05] 
dist 254=[-2.23347672004795893990e-07,2.24037678505576558680e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 1, 2, 0, 1] 
dist 0=[124.71280737644418950   ,124.71280737644418950   ] 
dist 1=[122.75949702239614544   ,126.29534417184981843   ] 
dist 2=[118.86544738295094412   ,128.70453359806203958   ] 
dist 3=[112.42877810451972204   ,130.78546338460675199   ] 
dist 4=[100.37093040313526017   ,131.06795196883304653   ] 
dist 5=[87.558088864901093465  ,130.45137674692336332   ] 
dist 6=[78.117212147733073295  ,129.65388873741947516   ] 
dist 7=[69.483414295627167918  ,109.39186809533800889   ] 
dist 8=[59.862023336162696795  ,106.17399633702905560   ] 
dist 9=[50.472730894571416203  ,96.469369718210080644  ] 
dist 10=[42.746722182345735081  ,95.075465945201757243  ] 
dist 11=[34.807620586635043064  ,74.183738915314281653  ] 
dist 12=[24.544560298570001980  ,69.837121931394642715  ] 
dist 13=[14.716275836833464973  ,65.771502763947320997  ] 
dist 14=[8.5017707236050649404 ,64.992843431255425241  ] 
dist 15=[-1.6082566342032134032 ,15.666186338549010987  ] 
dist 16=[-7.7414814982892707760 ,9.9402227018863724829 ] 
dist 17=[-12.008138418720266868  ,-1.2271662135550818600 ] 
dist 18=[-14.885036283522714150  ,-2.0667472477419860886 ] 
dist 19=[-20.779775164665282842  ,-2.2085814338453213832 ] 
dist 20=[-25.055642952315597055  ,-1.2247748759847586707 ] 
dist 21=[-27.927624036550240438  ,.01080226659899005198] 
dist 22=[-29.607663377868751766  ,.95453188321788807964] 
dist 23=[-30.551104324911940867  ,1.7837706285869489829 ] 
dist 24=[-30.648452588904822741  ,2.5791530538018222929 ] 
dist 25=[-30.107150866959243106  ,3.2186888869536001813 ] 
dist 26=[-29.717743571338251236  ,3.4362945390892085790 ] 
dist 27=[-25.785194887483655281  ,3.4925484576838804780 ] 
dist 28=[-24.740503194462101821  ,3.5026312761762143377 ] 
dist 29=[-23.198861730123017323  ,2.9117479525852717998 ] 
dist 30=[-22.611338335621934227  ,4.8068261904201421748 ] 
dist 31=[-8.2759378521241279827 ,6.5051462504148127944 ] 
dist 32=[-6.3744803682099009365 ,7.3986183734236917778 ] 
dist 33=[-2.1116592409184756743 ,11.518978423720320967  ] 
dist 34=[-1.4062459052553999854 ,15.366748925749283675  ] 
dist 35=[-1.2286803860594812083 ,18.610925311241339332  ] 
dist 36=[-1.1821797277619027385 ,20.403035459828196054  ] 
dist 37=[-1.1724181350467574978 ,21.440994866327577118  ] 
dist 38=[-1.1991264720656701284 ,21.690947553940483285  ] 
dist 39=[-1.2512275346086792412 ,6.6258110843256293804 ] 
dist 40=[-1.3435183276957435606 ,6.6667974204873804914 ] 
dist 41=[-1.4470146567572388780 ,6.5216994736883743048 ] 
dist 42=[-1.5442819921585702195 ,6.5004143594076016330 ] 
dist 43=[-2.0286507110900350555 ,5.3959634834704537236 ] 
dist 44=[-2.7061032764121686132 ,5.1225353084951102649 ] 
dist 45=[-3.2567815188268343685 ,4.9430270360301079139 ] 
dist 46=[-3.7637719978304233996 ,4.9004100349976156182 ] 
dist 47=[-4.1760276022880541929 ,3.2194647725909000668 ] 
dist 48=[-4.3510618713554091059 ,3.1230716126788354789 ] 
dist 49=[-4.4137804007632803474 ,2.6350203560984941752 ] 
dist 50=[-4.3906498468086473327 ,2.5239427352316236347 ] 
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dist 158=[-8.32889935426595452090e-05,.00734028093582780012] 
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dist 185=[-3.57802388545778246430e-05,.00053640959807802304] 
dist 186=[1.94555595868478314150e-06,.00069632119876601695] 
dist 187=[.00017131989443585052,.00083121416316015866] 
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dist 189=[.00018067999389574247,.00094947008704633075] 
dist 190=[.00017751012364628591,.00096040379584138635] 
dist 191=[.00017003838412122538,.00031368760051037572] 
dist 192=[.00015494219752968310,.00031263737346752885] 
dist 193=[.00013649011167301714,.00030238702704789172] 
dist 194=[.00010539747005378146,.00029833261539007336] 
dist 195=[6.31192381426092114690e-05,.00025188469197430451] 
dist 196=[-3.95599966403376883740e-07,.00024017043449872150] 
dist 197=[-6.39830308334181130320e-05,.00022490633411109687] 
dist 198=[-.00010654994554837557,.00021846879627740491] 
dist 199=[-.00014105737930002542,6.14660340521408878980e-05] 
dist 200=[-.00017264450703316698,4.47791408334172229040e-05] 
dist 201=[-.00019920429736549946,2.04558950192496341970e-05] 
dist 202=[-.00021375035154639605,1.52215612391214654560e-05] 
dist 203=[-.00022200938739795721,8.10664374919826707750e-06] 
dist 204=[-.00022360583420999660,6.13516353056602972880e-06] 
dist 205=[-.00022237701915813515,5.61359715872162068780e-06] 
dist 206=[-.00021941818608480807,6.62074219385120211410e-06] 
dist 207=[-.00017399270330630368,8.91500410595433037450e-06] 
dist 208=[-.00017317308483935919,1.35047217503332525010e-05] 
dist 209=[-.00016535238342654851,1.91007951986525477960e-05] 
dist 210=[-.00016417909913361889,2.53912457248398158650e-05] 
dist 211=[-.00013141989453360478,3.32683208968737837090e-05] 
dist 212=[-.00012371134254406829,4.51645837108087923600e-05] 
dist 213=[-.00011793592990026020,5.70995636610200849280e-05] 
dist 214=[-.00011655479001389860,6.51306096742354589770e-05] 
dist 215=[-2.12911885312984099760e-05,7.16867141705488383540e-05] 
dist 216=[-1.28226405007497310180e-05,7.77656449148161097300e-05] 
dist 217=[6.46947126345818956260e-06,8.29325314370105658860e-05] 
dist 218=[1.00365692474064342970e-05,8.58674933305670314360e-05] 
dist 219=[2.10443605468992256710e-05,8.76756383059177835550e-05] 
dist 220=[2.18251036420213334390e-05,8.83686805689038583900e-05] 
dist 221=[2.19906740822481969050e-05,8.86419965318603454670e-05] 
dist 222=[2.14456149600010435560e-05,8.88543840058529197950e-05] 
dist 223=[2.03326483577751824840e-05,4.29497563999471227110e-05] 
dist 224=[1.81824805864193504200e-05,4.27527336474365502260e-05] 
dist 225=[1.55843814106063482540e-05,4.12128094718353053370e-05] 
dist 226=[1.15633762948751514690e-05,4.06586177907498587430e-05] 
dist 227=[6.18927071725469297190e-06,3.41109957852007445520e-05] 
dist 228=[-1.86900167770262994680e-06,3.24803730314601596570e-05] 
dist 229=[-9.93272174337158787540e-06,3.04058624553326820430e-05] 
dist 230=[-1.53284913055224793940e-05,2.95157118589981897550e-05] 
dist 231=[-1.97009930551736489050e-05,8.70600099732617876940e-06] 
dist 232=[-2.37016304601830576340e-05,8.03520991136706187630e-06] 
dist 233=[-2.70649884830551504600e-05,5.58562100588714202230e-06] 
dist 234=[-2.89070244407766109290e-05,4.99560136073967926620e-06] 
dist 235=[-2.99532044191125992090e-05,4.32316466386973104740e-06] 
dist 236=[-3.01563993489166197920e-05,4.12917054883657385080e-06] 
dist 237=[-3.00004458603626462960e-05,4.06776598688983758730e-06] 
dist 238=[-2.96205503487479867660e-05,4.11057684554488242440e-06] 
dist 239=[-1.49552240485695296170e-05,4.23660723010066454400e-06] 
dist 240=[-1.48024022492105790330e-05,4.50569892206355658680e-06] 
dist 241=[-1.26671174198776597510e-05,4.83911379643944162500e-06] 
dist 242=[-1.25002453588040849990e-05,5.22058213934609333680e-06] 
dist 243=[-1.07047238741674854890e-05,5.70258005911866845880e-06] 
dist 244=[-1.04389266356948884740e-05,6.43519629997997591460e-06] 
dist 245=[-9.37016760016188488740e-06,7.17208523962811337150e-06] 
dist 246=[-9.09719147433606111980e-06,7.67107500077832845020e-06] 
dist 247=[-1.49412641776244669010e-06,8.08186075236964023010e-06] 
dist 248=[-1.29083909752733500520e-06,8.46856488301911528770e-06] 
dist 249=[-5.15000425034083458160e-07,8.80135678378424731700e-06] 
dist 250=[-3.54294050870387122650e-07,8.99810604681730945370e-06] 
dist 251=[-9.58295081665691427900e-08,9.12995079951766867070e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 1, 2, 0, 1] 
dist 0=[124.71294134348043389   ,124.71294134348043389   ] 
dist 1=[122.75961935859990602   ,126.29548675147399820   ] 
dist 2=[118.86551448780231552   ,128.70471942219705605   ] 
dist 3=[112.42876204312415147   ,130.78569755563340569   ] 
dist 4=[100.37079179871331806   ,131.06821500837344802   ] 
dist 5=[87.557827954313808883  ,130.45165623343158924   ] 
dist 6=[78.116869008467689985  ,129.65417446101676568   ] 
dist 7=[69.483004115115680278  ,109.39212557601172649   ] 
dist 8=[59.861551147711940214  ,106.17424030731696380   ] 
dist 9=[50.472206116396934522  ,96.469651446391450529  ] 
dist 10=[42.746167755913372144  ,95.075686574722001699  ] 
dist 11=[34.807048188057295144  ,74.184190456200459802  ] 
dist 12=[24.543981667693687805  ,69.837612290130099237  ] 
dist 13=[14.715697134399520552  ,65.771840335882571180  ] 
dist 14=[8.5011985094297284035 ,64.992980537569396746  ] 
dist 15=[-1.6079848319263929667 ,15.667261650801840869  ] 
dist 16=[-7.7412475576275326028 ,9.9413620726277801794 ] 
dist 17=[-12.007959307736564061  ,-1.2274904394416767718 ] 
dist 18=[-14.884948096154471348  ,-2.0670505535894373810 ] 
dist 19=[-20.781519895381257387  ,-2.2086679795210476877 ] 
dist 20=[-25.057445386796983669  ,-1.2246655377305789797 ] 
dist 21=[-27.929451863197036748  ,.01110707838620466976] 
dist 22=[-29.609478242468457761  ,.95496629362041717449] 
dist 23=[-30.552869405524535312  ,1.7843086748759852908 ] 
dist 24=[-30.650209852529005609  ,2.5797834909615518993 ] 
dist 25=[-30.108706016927129564  ,3.2193952074913639061 ] 
dist 26=[-29.719374801915649734  ,3.4370389515923994403 ] 
dist 27=[-25.785996540748801862  ,3.4933100000241735812 ] 
dist 28=[-24.741138756478443603  ,3.5033854959620199978 ] 
dist 29=[-23.199654502881405723  ,2.9107244168284782253 ] 
dist 30=[-22.612042977240678231  ,4.8058433838412327694 ] 
dist 31=[-8.2741495865401988735 ,6.5042763460990987525 ] 
dist 32=[-6.3724576782713091968 ,7.3980396205989690289 ] 
dist 33=[-2.1111809889693222107 ,11.517762307869964279  ] 
dist 34=[-1.4065393406686023918 ,15.365297817077099474  ] 
dist 35=[-1.2290594299278002328 ,18.609279144535401370  ] 
dist 36=[-1.1826303251678790378 ,20.401287251557685965  ] 
dist 37=[-1.1729400993347527042 ,21.439195165797204055  ] 
dist 38=[-1.1996958954492360109 ,21.689153526400071598  ] 
dist 39=[-1.2518351118563758981 ,6.6292561133501242951 ] 
dist 40=[-1.3441603180902773912 ,6.6701804563357781580 ] 
dist 41=[-1.4476852423234066692 ,6.5249393375357243042 ] 
dist 42=[-1.5449676263974078634 ,6.5035306742886793516 ] 
dist 43=[-2.0393150714566161574 ,5.3987768862011509623 ] 
dist 44=[-2.7170994859356335154 ,5.1252595910585812123 ] 
dist 45=[-3.2679616577684347485 ,4.9453958476534364248 ] 
dist 46=[-3.7749767149245931931 ,4.9024446118139891080 ] 
dist 47=[-4.1871186127451824734 ,3.2202556666280837898 ] 
dist 48=[-4.3617877294133538295 ,3.1238202782255876952 ] 
dist 49=[-4.4241557344442122180 ,2.6355110640831278288 ] 
dist 50=[-4.4006820971295766151 ,2.5243666328598008352 ] 
dist 51=[-4.0495050625030825527 ,2.2359611717582041470 ] 
dist 52=[-3.9276106648222857837 ,2.1515161821013960283 ] 
dist 53=[-3.7619000135098265788 ,1.2349385272575229877 ] 
dist 54=[-3.8910484408889711109 ,1.0772231518270963719 ] 
dist 55=[-3.9484415413143757608 ,.77919632312737557876] 
dist 56=[-3.9399979134721624522 ,1.0412178060219887041 ] 
dist 57=[-3.8511412376950744599 ,1.7030910646857122620 ] 
dist 58=[-3.7857416706090231439 ,2.3174103244339172761 ] 
dist 59=[-3.3401228327969849230 ,2.8377033821860598642 ] 
dist 60=[-2.9837807146656412479 ,3.1267607336441140795 ] 
dist 61=[-2.3869754682059727489 ,3.2953982946941833719 ] 
dist 62=[-2.3238245903970623092 ,3.3377114174179315319 ] 
dist 63=[-.796988408810170951  ,1.0407897151834244167 ] 
dist 64=[-.594840495919287407  ,1.0746416286786943834 ] 
dist 65=[-.1402277815696553593 ,1.3321328950492419542 ] 
dist 66=[-.04324210056657346851,1.7454426290683618871 ] 
dist 67=[.36516242707069669195,2.0941811112138197783 ] 
dist 68=[.24084256625688262629,2.2875507523043614945 ] 
dist 69=[.11372020637260036919,2.4000307520544199272 ] 
dist 70=[.02559312014265918708,2.4282040437524910390 ] 
dist 71=[-.04888450659483690952,.76118549155371553412] 
dist 72=[-.12188685825599439944,.76162212851013115346] 
dist 73=[-.23274275170762002685,.73740146261268068651] 
dist 74=[-.37571761009700647392,.73261131696735417072] 
dist 75=[-.500542391945349367  ,.60297117010754113447] 
dist 76=[-.5771241724297551657 ,.57133392464311260683] 
dist 77=[-.63154638833029947443,.5460314231300898503 ] 
dist 78=[-.66847068336352668414,.53707405097840086445] 
dist 79=[-.69136924297497752101,.09126443125540774059] 
dist 80=[-.69466910334437175432,.03844237246380553757] 
dist 81=[-.68161504521294064731,-.08463534424252421743] 
dist 82=[-.67558043056208911978,-.10344376652798179441] 
dist 83=[-.57304857947487203393,-.13822347900636968177] 
dist 84=[-.5463989683482700877 ,-.05678981832074639270] 
dist 85=[-.51816806619462654584,.02527177215374407563] 
dist 86=[-.50300551231193655212,.08058873375493320801] 
dist 87=[-.41837791755535879611,.12574560554878585995] 
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dist 213=[-9.95919465475081169610e-05,2.55754170687493242140e-05] 
dist 214=[-.00010121204161402652,3.41706916694090787360e-05] 
dist 215=[-.00010086783448773080,4.11843477186584151850e-05] 
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dist 217=[-9.57388370338112718650e-05,5.32003163426197754420e-05] 
dist 218=[-9.46008437012752783280e-05,5.63263515132032110190e-05] 
dist 219=[-7.74571518939581426000e-05,5.82409057438420177550e-05] 
dist 220=[-7.33411192108773645500e-05,5.89493412999436945820e-05] 
dist 221=[-6.89211738777884422360e-05,5.91024380478091677320e-05] 
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dist 224=[-2.02881207401355760730e-05,5.74311020408890965170e-05] 
dist 225=[-1.31937492571333975250e-05,5.51993248620512597060e-05] 
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dist 227=[-4.10656835423087008850e-06,5.61807153227357022540e-05] 
dist 228=[-2.59115840358843362910e-06,6.04284528749453248310e-05] 
dist 229=[-5.25898928648941345350e-07,6.29245909464472998990e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 1, 2, 0, 2] 
dist 0=[128.46305499861838463   ,128.46305499861838463   ] 
dist 1=[126.48241175718991308   ,131.47451375860842143   ] 
dist 2=[121.64069074460923357   ,134.09257028547455352   ] 
dist 3=[113.45700152951014262   ,134.47698496687061339   ] 
dist 4=[100.14730965727949867   ,133.92373293135786028   ] 
dist 5=[86.367381934509750963  ,132.95476390098195243   ] 
dist 6=[76.307020990065607979  ,125.88325156603267336   ] 
dist 7=[67.199756245664032480  ,117.52748287078068988   ] 
dist 8=[57.191927814717416593  ,102.33529098085750909   ] 
dist 9=[47.510499372703718000  ,100.95129036860788139   ] 
dist 10=[39.686053085126110790  ,79.783542953780285780  ] 
dist 11=[31.774575282571545555  ,75.331583091771682949  ] 
dist 12=[21.720799439410684983  ,71.190004866837663205  ] 
dist 13=[12.142118297121899683  ,70.335725436028578856  ] 
dist 14=[6.1155061944779402430 ,42.083790793720203971  ] 
dist 15=[1.5241052228240685958 ,36.559221870813531737  ] 
dist 16=[-6.0322674172133232096 ,1.6483861137860681182 ] 
dist 17=[-12.836514457257467391  ,-2.6068229197004611568 ] 
dist 18=[-20.636702168651390095  ,-3.1721258070848745525 ] 
dist 19=[-25.303293094206894494  ,-2.8231284274871293104 ] 
dist 20=[-28.523259697620646769  ,-1.2542361148864658950 ] 
dist 21=[-30.579807339149922015  ,.55948130114444009942] 
dist 22=[-31.850189272951798926  ,1.8857022342206056230 ] 
dist 23=[-32.048474340035292172  ,3.0217335334449854494 ] 
dist 24=[-31.636757367516708285  ,4.0942808391272279978 ] 
dist 25=[-31.286394613291020982  ,4.9656374719118324465 ] 
dist 26=[-27.142375523184639180  ,5.3097630634902017016 ] 
dist 27=[-26.032296538788972858  ,5.4287717295575521505 ] 
dist 28=[-24.530429935364730938  ,5.4172838305139569109 ] 
dist 29=[-23.898191808221982320  ,4.1728768344886048916 ] 
dist 30=[-8.6477068741963520282 ,4.3533091220098674460 ] 
dist 31=[-6.6902092868646696226 ,6.9251989397441946924 ] 
dist 32=[-2.3319964999111986243 ,11.222404918006710646  ] 
dist 33=[-1.3335085035147742510 ,15.212795428915091982  ] 
dist 34=[-.90224052261569238957,18.599531871963964496  ] 
dist 35=[-.6254160036876186257 ,20.466776987058577272  ] 
dist 36=[-.58015506749430627847,21.542769011391655465  ] 
dist 37=[.81142662404863702581,21.788244166838876929  ] 
dist 38=[.97077942061819789703,8.8943145375227414746 ] 
dist 39=[1.2714417891736814480 ,8.7550089236998794543 ] 
dist 40=[.46531485768266006044,7.6797076036511614210 ] 
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dist 43=[-4.2479929061961750575 ,6.6354792278354168288 ] 
dist 44=[-5.5339640961281043047 ,6.1035500044935832700 ] 
dist 45=[-6.3413752905155064181 ,5.8982838659212892315 ] 
dist 46=[-6.9360452540638785989 ,3.3669883320981544913 ] 
dist 47=[-7.3787133244953907329 ,2.9556217213977982118 ] 
dist 48=[-7.6846362796354739535 ,2.0847116878667924583 ] 
dist 49=[-7.7368927767977695655 ,1.8445963588770166388 ] 
dist 50=[-7.6731478309003300172 ,.92909705643469024025] 
dist 51=[-7.5702572327259372488 ,.73182551127599656838] 
dist 52=[-6.7737636081880430356 ,.41607810698145189253] 
dist 53=[-6.0804503106729483827 ,.33344839712411433708] 
dist 54=[-3.4516053627686019648 ,.19409694784117449155] 
dist 55=[-3.4532744248204273024 ,.15778975746570443898] 
dist 56=[-3.3772144959689098770 ,.15309567925100933158] 
dist 57=[-3.3293548338519457791 ,.1897299552804686996 ] 
dist 58=[-2.8781830149118005010 ,.52727848948615151924] 
dist 59=[-2.7585299946227913627 ,.88906769930594704587] 
dist 60=[-2.5785812063844770171 ,1.2135957811501393562 ] 
dist 61=[-2.5114759103278778241 ,1.4276557629806340356 ] 
dist 62=[-.87756241430132667404,1.5976209608676038497 ] 
dist 63=[-.65983300394922235729,1.7474838614081129700 ] 
dist 64=[-.16957299410994438331,1.8610266980983719857 ] 
dist 65=[-.06490794234015962888,1.8890021451031914088 ] 
dist 66=[-.02636138955062210335,2.2587074390726123914 ] 
dist 67=[-.01176060503198484293,2.4675622792933278060 ] 
dist 68=[-.00823950744063664288,2.5891126702625147403 ] 
dist 69=[.04475486385327209325,2.6197288083272380662 ] 
dist 70=[.05129724575539859629,1.4878388413963753867 ] 
dist 71=[.06185924607578326028,1.4771292316316350940 ] 
dist 72=[.06399393122285358845,.77972719436744084831] 
dist 73=[-.02971232123640713568,.77490552037501701178] 
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dist 88=[-.42379054957433031239,.1001676172229586644 ] 
dist 89=[-.4198214270300669754 ,.27410991673291830023] 
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dist 91=[-.32660231004087431176,.5461880683361772    ] 
dist 92=[-.30926880614003758112,.65634611087075169775] 
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dist 102=[-.07214290150067597107,.17419565337567107192] 
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dist 105=[-.09888726652890513534,.09721190431929343419] 
dist 106=[-.10252949820343445019,.08079963873314873894] 
dist 107=[-.10400604577794476614,.08125508002413300481] 
dist 108=[-.10374663365381823895,.08064786474537593838] 
dist 109=[-.117019233484922672  ,.07966012668845733586] 
dist 110=[-.12605294975173759857,.07860349134152176332] 
dist 111=[-.13058196488893525979,.07731206179075173328] 
dist 112=[-.13235311992966208557,.07616508912096892157] 
dist 113=[-.132201747897421675  ,.07325447940504271831] 
dist 114=[-.12779716005890593136,.07174635991366847739] 
dist 115=[-.12668072751417513973,.06873410060631013113] 
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dist 117=[-.09944030599564108193,.06126655658169796197] 
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dist 120=[-.04939177544832004919,.05565021250544133869] 
dist 121=[-.04861047530976549414,.05395280960339487679] 
dist 122=[-.04140771637474649416,.05327566304696361471] 
dist 123=[-.03956846881473259955,.05486834956021394057] 
dist 124=[-.03679180247157967296,.06651017434324534498] 
dist 125=[-.03578570867698369067,.07351534791020019495] 
dist 126=[-.01184016094352473536,.07749778074589192007] 
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dist 128=[-.00157532681581453319,.03060291713236598088] 
dist 129=[-3.08768183335384012000e-05,.03065806286975028342] 
dist 130=[.00765773756100683415,.03418027398234787804] 
dist 131=[.00899994870248378666,.03722249646504502459] 
dist 132=[.01118786900724283677,.03899296520235420293] 
dist 133=[.01163357649351123692,.03943923812151487274] 
dist 134=[.01173608797907808416,.02202100840054346642] 
dist 135=[.00916836205226575849,.02181799619109459770] 
dist 136=[.00246636442776891631,.01152269254259306799] 
dist 137=[-.00205910733682262889,.01144949856485950583] 
dist 138=[-.00576910738798373814,.00924728182411653665] 
dist 139=[-.00923380896891487267,.00876407130763366390] 
dist 140=[-.01219485221567780526,.00832871343233769802] 
dist 141=[-.01390540942728159745,.00823812483656423087] 
dist 142=[-.01499596220781505936,.00159975234194038160] 
dist 143=[-.01549571370301526807,.00079984157074761318] 
dist 144=[-.01566978371549171944,-.00104055554806681447] 
dist 145=[-.01562161588035471627,-.00135139754467616693] 
dist 146=[-.01516205613810672189,-.00346836640775383735] 
dist 147=[-.01492773134901693777,-.00379517295026316656] 
dist 148=[-.01278747122417380661,-.00439397315507486439] 
dist 149=[-.01223301314269999252,-.00449315773688608626] 
dist 150=[-.01138979518567344634,-.00455047090029465130] 
dist 151=[-.01108380240822512201,-.00214510541394789637] 
dist 152=[-.00691617213454587428,.00188355245985478105] 
dist 153=[-.00683567466906689964,.00458528512485294813] 
dist 154=[-.00561662365209493524,.00678046523828979955] 
dist 155=[-.00532200451553550038,.00879794883402778762] 
dist 156=[-.00500514802693918929,.01049979763639725112] 
dist 157=[-.00484569416901619988,.01144179172666831609] 
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dist 165=[-8.25779022636452401220e-06,.00458996820821189407] 
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dist 187=[-.00059315555903507706,.00086431636915353251] 
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dist 189=[-.00053715385786460442,.00113843410717637786] 
dist 190=[-.00015525934028158529,.00119823090439425255] 
dist 191=[-.00010808154440417253,.00121246708934640817] 
dist 192=[-2.42950088958201421320e-06,.00049248622980344058] 
dist 193=[1.98134189163472151660e-05,.00049068560782434570] 
dist 194=[.00013438484676578637,.00048702766664335008] 
dist 195=[.00015406448265535628,.00053090142619424840] 
dist 196=[.00018564635703575528,.00055661476252427269] 
dist 197=[.00019156208771876186,.00056306776651782917] 
dist 198=[.00019132069766781365,.00034750167042676231] 
dist 199=[9.99580417680014406990e-05,.00033684430280484690] 
dist 200=[-1.64521593897473778280e-05,.00022654386581390162] 
dist 201=[-9.46418337219498741850e-05,.00022390906047528829] 
dist 202=[-.00015832611047749897,.00020769767700840109] 
dist 203=[-.00021714179449993671,.00020302815984283295] 
dist 204=[-.00026697823430860318,.00018666831905378944] 
dist 205=[-.00029500984697289570,.00018304468101354150] 
dist 206=[-.00031192293975670096,.00013989765125763063] 
dist 207=[-.00031761264835367598,.00013080554634457065] 
dist 208=[-.00031735023377417373,.00011420236607575293] 
dist 209=[-.00031522332876325262,.00010971567258988524] 
dist 210=[-.00030280286223123262,9.42785241405193741450e-05] 
dist 211=[-.00029814896307533379,8.94848553708970496680e-05] 
dist 212=[-.00025003071307674251,8.60306897530734898750e-05] 
dist 213=[-.00021508498651877800,8.49195809870484920620e-05] 
dist 214=[-.00017018509933617215,8.45811399521302462480e-05] 
dist 215=[-.00016543699401122453,8.45293560533807286330e-05] 
dist 216=[-.00012000923448695135,8.46767557891721604850e-05] 
dist 217=[-.00011797528772235339,8.51298749161783346420e-05] 
dist 218=[-9.92382036070823872420e-05,.00010308735567225976] 
dist 219=[-9.45761370153118078640e-05,.00013315908278303199] 
dist 220=[-8.75620404158944759990e-05,.00015851605515941688] 
dist 221=[-8.50559206312680256150e-05,.00017254872206360779] 
dist 222=[-2.60354480277385667760e-05,.00018071467243442374] 
dist 223=[-1.81964657249448718510e-05,.00018277644080734935] 
dist 224=[-7.98045597194099807210e-07,9.65531533284873606190e-05] 
dist 225=[3.03024578581410506620e-06,9.56545874864485149700e-05] 
dist 226=[2.13986872451664979200e-05,9.38220043347042720680e-05] 
dist 227=[2.46435852970227676410e-05,9.26784698554691556250e-05] 
dist 228=[2.92245906405581750550e-05,8.54005378031237318050e-05] 
dist 229=[2.97538021611040036180e-05,8.03253027991745452780e-05] 
dist 230=[2.40095383475655678780e-05,4.11347092551841895740e-05] 
dist 231=[1.02424642820634037760e-05,3.99059796919739840520e-05] 
dist 232=[-3.90797185296504429450e-06,3.50992326797941570940e-05] 
dist 233=[-1.34009976875504273300e-05,3.45111471212093698340e-05] 
dist 234=[-2.11214533367729550540e-05,3.08397553575606750500e-05] 
dist 235=[-2.82335152412033812750e-05,2.98762553760645313700e-05] 
dist 236=[-3.42478902169815690950e-05,2.73077357417942245480e-05] 
dist 237=[-3.76097340901784764270e-05,2.63392512505919009810e-05] 
dist 238=[-3.96108289406237035410e-05,1.57287249372762805610e-05] 
dist 239=[-4.02220458732252096330e-05,1.39451328331007953510e-05] 
dist 240=[-4.01357620540175253940e-05,1.02932471139123705500e-05] 
dist 241=[-3.98046746994006218160e-05,9.30896403958710687120e-06] 
dist 242=[-3.84107975455260321360e-05,5.71945578716654635660e-06] 
dist 243=[-3.76082351379565266190e-05,4.88726161982898479470e-06] 
dist 244=[-3.26187597282409807930e-05,3.94989412898984197890e-06] 
dist 245=[-2.88863016653578577570e-05,3.74673649675635275090e-06] 
dist 246=[-2.40779001492769918920e-05,3.75801174209743429210e-06] 
dist 247=[-2.35181921854047991280e-05,3.94890317951366334190e-06] 
dist 248=[-7.73635534381554583650e-06,5.52734771278491963380e-06] 
dist 249=[-6.66316755464879187120e-06,9.43297326764797943860e-06] 
dist 250=[-4.37674620532260569570e-06,1.26077068165820368530e-05] 
dist 251=[-3.75468932286034746530e-06,1.55296010407632751590e-05] 
dist 252=[-1.41501646581123961700e-06,1.79987089099400120260e-05] 
dist 253=[-9.23737359633567552970e-07,1.93755394124119301160e-05] 
dist 254=[-2.12676314107004532970e-07,2.01968808810030530820e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 0, 1, 1, 2] 
dist 0=[106.54055738398189636   ,106.54055738398189636   ] 
dist 1=[103.08801748683103963   ,108.49911294986642798   ] 
dist 2=[96.396331162163711582  ,109.24969888396313986   ] 
dist 3=[89.119169911268855208  ,109.50689743192232424   ] 
dist 4=[83.335296213244799458  ,109.49308134256381953   ] 
dist 5=[77.612364700520620490  ,109.33920975910216319   ] 
dist 6=[70.563791479285081359  ,109.04370971801924358   ] 
dist 7=[63.272049280844871691  ,108.58413789728388628   ] 
dist 8=[56.569671328230068135  ,105.85450566343968729   ] 
dist 9=[49.043305121287070475  ,84.857000014015215710  ] 
dist 10=[38.452036378651108457  ,81.690290484904787278  ] 
dist 11=[28.038881952663756199  ,73.294556828255858928  ] 
dist 12=[21.217930373250224302  ,71.790274461802506200  ] 
dist 13=[15.720310480325244835  ,57.920738737848993338  ] 
dist 14=[10.583990567546461960  ,53.648884119008210535  ] 
dist 15=[6.0554648104172296249 ,49.743594255842734743  ] 
dist 16=[1.9747157759627476060 ,48.332365993865652488  ] 
dist 17=[-3.8482565531835531814 ,18.315009622663803030  ] 
dist 18=[-9.1414123347335035301 ,14.592788175975063683  ] 
dist 19=[-13.711173121319162234  ,5.8441002845608093681 ] 
dist 20=[-16.651127024771135118  ,4.5706321576482994324 ] 
dist 21=[-18.987810184609578016  ,-4.7552539581171091965 ] 
dist 22=[-22.380142604949527403  ,-4.9588039816035878647 ] 
dist 23=[-24.779357726847343122  ,-2.1682527456981054639 ] 
dist 24=[-26.434069101886731283  ,.09801478636098637943] 
dist 25=[-27.477696568509984412  ,2.3129764321123676864 ] 
dist 26=[-27.677255538549167479  ,4.9286427064138363139 ] 
dist 27=[-27.136029695521153558  ,7.5113588867259675250 ] 
dist 28=[-27.050922783084760196  ,9.6039113114426031356 ] 
dist 29=[-22.560884819133750126  ,11.695499428517798944  ] 
dist 30=[-21.446539554402413355  ,14.284073798055794434  ] 
dist 31=[-20.699408564895023724  ,16.606172747408241875  ] 
dist 32=[-20.509989247267691321  ,17.642518576474233116  ] 
dist 33=[-3.6522293853307851411 ,18.125789554377078440  ] 
dist 34=[-1.6764518749750268572 ,18.246708189138544246  ] 
dist 35=[-.5949441865436364509 ,16.464146095941547789  ] 
dist 36=[-.89140107121628581296,15.996180239069118049  ] 
dist 37=[-1.1666087950295509906 ,15.720637463922314114  ] 
dist 38=[-1.4688015226570429432 ,15.650906432389019857  ] 
dist 39=[-1.7512977074332963957 ,12.001410114314744736  ] 
dist 40=[-1.9491478465321674707 ,12.523504684319117946  ] 
dist 41=[-2.1162322754945245606 ,12.783082673712957514  ] 
dist 42=[-3.6357717424779553147 ,12.797196453528245290  ] 
dist 43=[-5.7090581104413275739 ,12.531184340557794313  ] 
dist 44=[-7.0288980382952901974 ,12.358502981834505094  ] 
dist 45=[-8.0239736671675880316 ,10.704684285360873662  ] 
dist 46=[-8.8099025484487684739 ,10.265206415458832338  ] 
dist 47=[-9.3892525419111646411 ,9.6088435844881340584 ] 
dist 48=[-9.5647489068471457211 ,9.3619006703956562524 ] 
dist 49=[-9.5686008369950093576 ,3.3357174584637234764 ] 
dist 50=[-9.4653599568979768857 ,2.5339395616436803815 ] 
dist 51=[-8.4827477532865690946 ,.72335149348865344458] 
dist 52=[-8.1848033970811749862 ,.34147648094880942772] 
dist 53=[-8.5846820559115083689 ,-.17451560740992922604] 
dist 54=[-9.2514159049723608239 ,-.10530425257954297361] 
dist 55=[-9.6600099045672074783 ,.73975952806503064992] 
dist 56=[-9.7397006902740486879 ,2.4681937577536030883 ] 
dist 57=[-2.9416711305514588399 ,3.8792285642384473372 ] 
dist 58=[-2.9563817306226940637 ,5.1836677025197179857 ] 
dist 59=[-2.8853207927999934013 ,6.2866431609836199277 ] 
dist 60=[-2.8750081552006714860 ,6.8981993013209718307 ] 
dist 61=[-2.3778134590739409203 ,7.2544482393547392829 ] 
dist 62=[-2.2549820314932642827 ,7.3442143241939065164 ] 
dist 63=[-2.1745603883851673095 ,2.2594368841657557689 ] 
dist 64=[-2.1556172952731043456 ,2.2916136657872058152 ] 
dist 65=[-.29682885867707926463,2.2875204422155273760 ] 
dist 66=[-.07947678955020972118,2.2818342163360781751 ] 
dist 67=[.01196520531555565557,1.9606188787207948506 ] 
dist 68=[-.04124941336953849390,1.8743245261006437789 ] 
dist 69=[-.08545752396903516227,1.8131770573451481280 ] 
dist 70=[-.12721005975424405598,1.7850677086324611043 ] 
dist 71=[-.16282048597072779815,1.4024828955354657051 ] 
dist 72=[-.18273434190300646196,1.4582342663302316345 ] 
dist 73=[-.44143711110505822457,1.4827053187701833405 ] 
dist 74=[-.72663339756202867739,1.4807360999880982349 ] 
dist 75=[-.97344133649503287022,1.4425442998409999975 ] 
dist 76=[-1.1212426717869566089 ,1.4212028344411512800 ] 
dist 77=[-1.2220209020113309743 ,1.2228541096369882422 ] 
dist 78=[-1.2822406512133675464 ,1.1708872546884633985 ] 
dist 79=[-1.3144736209532747754 ,1.0924367504245193194 ] 
dist 80=[-1.3175902976056955700 ,1.0635269134639672334 ] 
dist 81=[-1.2832354150276631016 ,.3645345467458264332 ] 
dist 82=[-1.2732198441896713503 ,.27142339696665165579] 
dist 83=[-1.0618360765942952127 ,.06221557672874556621] 
dist 84=[-1.0087747606120144659 ,.01726368334619414411] 
dist 85=[-.9812978115908246642 ,.01267488700769517481] 
dist 86=[-1.0706940797373296401 ,.02519630098495318174] 
dist 87=[-1.1227058802087168436 ,.06612203471448300166] 
dist 88=[-1.1357795117378229340 ,.2513153348619107264 ] 
dist 89=[-.34631654636624663013,.40253365408750525835] 
dist 90=[-.34648790510067931232,.54259397300418709563] 
dist 91=[-.33528100745295917851,.66189560137211604738] 
dist 92=[-.33322458397003328236,.7335776948502408944 ] 
dist 93=[-.27434928371888612685,.77405583044652480423] 
dist 94=[-.26011787413533216364,.78356967318372645529] 
dist 95=[-.24840206035864349563,.30786759359987038568] 
dist 96=[-.24426578096786968007,.30966161710436184249] 
dist 97=[-.03886295058268175881,.30281278178701378052] 
dist 98=[-.01432400267223627077,.30181422098821299393] 
dist 99=[-.00744997296607761758,.25021804791848253614] 
dist 100=[-.01917423621238527171,.23737308138664393815] 
dist 101=[-.02881783621056291705,.22912406806158043022] 
dist 102=[-.03785474294307889187,.2271423617944368451 ] 
dist 103=[-.04558047342048584342,.18625352214682145382] 
dist 104=[-.05002079926834284231,.19135522889556512257] 
dist 105=[-.05423839045796369951,.19243732124409411402] 
dist 106=[-.09004139534461084750,.19173214033171688121] 
dist 107=[-.12080218743550253773,.1841794320862207515 ] 
dist 108=[-.13885382900948564058,.18244803987012772982] 
dist 109=[-.1507167007571407291 ,.14927344794352945357] 
dist 110=[-.15691302888475501619,.14126423286830140938] 
dist 111=[-.15977138471552804094,.13374754618752350118] 
dist 112=[-.15963033603525345923,.13047437839881344465] 
dist 113=[-.15569803245660155795,.03229521353161819174] 
dist 114=[-.15340374486786160942,.02223420937264137646] 
dist 115=[-.13223842111213639465,-.00053417579859731179] 
dist 116=[-.12665823232465242413,-.00507305168501765985] 
dist 117=[-.11820668178013436033,-.03046473603393871612] 
dist 118=[-.11509082654245460879,-.02286633561099457663] 
dist 119=[-.11142886204856087931,.01838057777093478495] 
dist 120=[-.11278063985422097251,.04606380012255001698] 
dist 121=[-.04428071119004440853,.06857306507710933702] 
dist 122=[-.04421021994733723059,.08927937436656466223] 
dist 123=[-.04251744065318471332,.10675309280210421021] 
dist 124=[-.04227322398483164076,.11642874049683041258] 
dist 125=[-.03422256349551137629,.12206630094871540667] 
dist 126=[-.03230088765398346176,.12348407873980653214] 
dist 127=[-.03094171772991597679,.03787369342670889378] 
dist 128=[-.03063728342558601628,.03791895808582413210] 
dist 129=[-.00293035555509322409,.03670547025637482152] 
dist 130=[.00029955935340526249,.03652291434201924480] 
dist 131=[.00778998785620678538,.02991272361010150957] 
dist 132=[.00889939875713144705,.02845097572044878839] 
dist 133=[.01742134151964341000,.02712389034197433136] 
dist 134=[.00874927046370546723,.02684856806305038632] 
dist 135=[3.61319734921561377100e-05,.02169675602669764876] 
dist 136=[-.00584011771973687372,.02227045617666705931] 
dist 137=[-.01064988589046228827,.02238064790261807143] 
dist 138=[-.01512914622488005507,.02226736243785973152] 
dist 139=[-.01894872013137347432,.02151262086549052890] 
dist 140=[-.02113956319813443694,.02116745546452119638] 
dist 141=[-.02251634124239882667,.01801761516722436502] 
dist 142=[-.02310413489277373286,.01721492213780911817] 
dist 143=[-.02323490898301470176,.01599565236277119513] 
dist 144=[-.02314263954409423174,.01555742248637494981] 
dist 145=[-.02226434523463266945,.00511694019215677625] 
dist 146=[-.02201710932519433633,.00372622802332230598] 
dist 147=[-.01819058567925760137,.00061873618455460568] 
dist 148=[-.01725503596369996042,-5.73796299092727096860e-05] 
dist 149=[-.01625452229878452392,-.00342124992665142843] 
dist 150=[-.01631146974947260727,-.0004815973840458970 ] 
dist 151=[-.01708553615764611926,.00374827930261408251] 
dist 152=[-.01728048982326607379,.00659128465123805660] 
dist 153=[-.00519421275804244795,.00890815946118146277] 
dist 154=[-.00517624789341856834,.01104917720463822599] 
dist 155=[-.00496836750289325805,.01286352336848733121] 
dist 156=[-.00492828837506070428,.0138834282895237745 ] 
dist 157=[-.00401267192680697435,.01457236904968259507] 
dist 158=[-.00379440493061165663,.01473054772014567249] 
dist 159=[-.00360614639276677751,.00490670098882975949] 
dist 160=[-.00353962135761504544,.00490089235979144706] 
dist 161=[-.00049233687482237303,.00471899629171863975] 
dist 162=[-.00012751099967789926,.00469162637237024279] 
dist 163=[.00071803311227086600,.00380828076002041945] 
dist 164=[.00084873239025077955,.00359654514795387952] 
dist 165=[.00183283640511725633,.00344477992192903116] 
dist 166=[.00137951222290094038,.00340782409840690064] 
dist 167=[.00030889192375808648,.00284926367560132788] 
dist 168=[-.00041203097546338937,.00290811861729186607] 
dist 169=[-.00100107109688808160,.00290728346609802041] 
dist 170=[-.00154808031349453462,.00289085584419273721] 
dist 171=[-.00201359022785588527,.00276653031314357967] 
dist 172=[-.00227905598180844471,.00273747404903097160] 
dist 173=[-.00244394923055575218,.00223427221461937297] 
dist 174=[-.00251016180453228833,.00211362553591650875] 
dist 175=[-.00252456978384078569,.00199457325070788991] 
dist 176=[-.00251226592562052550,.00194055797531119205] 
dist 177=[-.00242936356203858527,.00049539970486967532] 
dist 178=[-.00238969175632793222,.00034976812821556257] 
dist 179=[-.00203996053535496741,2.31612555953902161060e-05] 
dist 180=[-.00195030472031646280,-4.56022287276748089000e-05] 
dist 181=[-.00181084343739789251,-.00040184340409873790] 
dist 182=[-.00176181341481449142,-.00028772187921311744] 
dist 183=[-.00172584923500896071,.00035234995452612952] 
dist 184=[-.00174659021846667413,.00078135653083538707] 
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dist 187=[-.00062588895060366375,.00171964015099854441] 
dist 188=[-.00062163767543268323,.00186903527328919079] 
dist 189=[-.00049908929243398998,.00195603560411528698] 
dist 190=[-.00047020326270154907,.00197804523387009192] 
dist 191=[-.00044888386695814738,.00056290076473867734] 
dist 192=[-.00044394979593880308,.00056136456609624417] 
dist 193=[-.00018408255386513539,.00053848137011885525] 
dist 194=[-.00015045097836792486,.00053517325254601092] 
dist 195=[-7.65580911764623195240e-05,.00044451405783680563] 
dist 196=[-5.75775498201216740700e-05,.00043232043528589377] 
dist 197=[2.06954511738102907780e-05,.00045613148190918661] 
dist 198=[-2.10361219004919763740e-05,.00049433571511430850] 
dist 199=[-.00017669163069926412,.00051733590532838908] 
dist 200=[-.00028123853213889853,.00052496406048879811] 
dist 201=[-.00036638985287620999,.00052486796381428053] 
dist 202=[-.00044503361756740191,.00052019860776553190] 
dist 203=[-.00051167503880105012,.00050592648580351705] 
dist 204=[-.00054917003975667206,.00049751413561003828] 
dist 205=[-.00057180851618273632,.00044481361861603209] 
dist 206=[-.00057946099935223910,.00043095741075213526] 
dist 207=[-.00057869459348083516,.00039394109792225897] 
dist 208=[-.00057407254470913137,.00038000070059390822] 
dist 209=[-.00055429320593086002,.00022701537602575921] 
dist 210=[-.00054279165136435299,.00020128448761226279] 
dist 211=[-.00047105498944357376,.00014862496409479016] 
dist 212=[-.00045224440428738837,.00013443569089702625] 
dist 213=[-.00041526400636959900,8.27290441905799475820e-05] 
dist 214=[-.00039075228535897248,7.07239759259541470070e-05] 
dist 215=[-.00025822194035079823,5.73177513778602943250e-05] 
dist 216=[-.00026110541783030160,9.35616087094848851160e-05] 
dist 217=[-7.41357917643885574480e-05,.00013392078867665422] 
dist 218=[-7.37487959541399436260e-05,.00017095918431189554] 
dist 219=[-7.05321528119027719720e-05,.00020217958262757625] 
dist 220=[-6.98976886976254417230e-05,.00021943704252862774] 
dist 221=[-5.78530579879461139850e-05,.00022945306908095604] 
dist 222=[-5.57802334714567790880e-05,.00023191950803454533] 
dist 223=[-5.12984213537412183830e-05,5.51467313231080730070e-05] 
dist 224=[-4.97515140196661034660e-05,5.48441139371213206210e-05] 
dist 225=[-2.46936586843668689150e-05,5.36300425382084446830e-05] 
dist 226=[-2.09406428508012714560e-05,5.27897434058187845420e-05] 
dist 227=[-1.28712032566487834700e-05,4.72744459998537307020e-05] 
dist 228=[-1.06768034535843293830e-05,5.07725871669065135080e-05] 
dist 229=[-2.39105819348926690980e-06,5.90430427283306489690e-05] 
dist 230=[-6.94825350715498931010e-07,6.36608559628258729360e-05] 
dist 231=[-1.63025215033242298470e-05,6.64032817877075804520e-05] 
dist 232=[-2.71914603029930620090e-05,6.72269353023525037500e-05] 
dist 233=[-3.60582523080220387520e-05,6.70159314827020509780e-05] 
dist 234=[-4.42449589758864542080e-05,6.64575450383540031120e-05] 
dist 235=[-5.11812474205633700710e-05,6.40069933650948264110e-05] 
dist 236=[-5.50830390910778561810e-05,6.26967880576740263220e-05] 
dist 237=[-5.74380135171605126590e-05,5.39607056248191460150e-05] 
dist 238=[-5.82324210131625849510e-05,5.17009470076936783370e-05] 
dist 239=[-5.82327662551826299890e-05,4.74911904403981021040e-05] 
dist 240=[-5.77017689864891022510e-05,4.61965380082562065580e-05] 
dist 241=[-5.62121125728025826900e-05,1.84777723286584700670e-05] 
dist 242=[-5.53313993575992700070e-05,1.45848027747592453940e-05] 
dist 243=[-4.98085786840623186200e-05,6.79070764168271026850e-06] 
dist 244=[-4.83556158848063648140e-05,5.79450588946756612730e-06] 
dist 245=[-4.41643402799819686620e-05,2.08629686042768804980e-06] 
dist 246=[-4.28335144672652914280e-05,1.30016215492983093200e-06] 
dist 247=[-3.27306590537474903430e-05,2.50660724910593920320e-07] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 1, 0, 0, 0, 1] 
dist 0=[110.76383701925225771   ,110.76383701925225771   ] 
dist 1=[107.26133750861479397   ,112.26941061136851180   ] 
dist 2=[103.23106213016935423   ,112.78054053370816131   ] 
dist 3=[99.619359454640955664  ,112.57580078809607805   ] 
dist 4=[95.661403766238320533  ,110.92332481549381843   ] 
dist 5=[90.241854274127543921  ,108.28250732145379058   ] 
dist 6=[84.334574667971518518  ,106.44762061812949000   ] 
dist 7=[78.425605072367428001  ,105.64364846079004985   ] 
dist 8=[71.399360593643771304  ,101.72921918586944238   ] 
dist 9=[61.027606676595899457  ,80.525260509232752928  ] 
dist 10=[50.512981766195374454  ,69.712728606908863953  ] 
dist 11=[42.917215855804208587  ,68.301825520224042021  ] 
dist 12=[36.019888174322780275  ,53.207011024595768549  ] 
dist 13=[28.300097514385022187  ,50.278838801190455011  ] 
dist 14=[20.048687294273967182  ,45.152179657475770035  ] 
dist 15=[11.329013043306407222  ,44.147826046489254973  ] 
dist 16=[-.2409372891106862528 ,19.901322955577744631  ] 
dist 17=[-11.207506117676070608  ,18.998295473383823060  ] 
dist 18=[-17.532878106530641675  ,6.3399073934356176391 ] 
dist 19=[-21.691992418241351134  ,4.5553320981748438150 ] 
dist 20=[-24.031862139223358561  ,1.1422210615838783485 ] 
dist 21=[-25.520170470228593662  ,.34388443359193870632] 
dist 22=[-26.441931890993783738  ,-1.9838383670922128286 ] 
dist 23=[-27.672299533749584557  ,-2.3654179205649705567 ] 
dist 24=[-28.226349261014078099  ,-2.1915894733011618449 ] 
dist 25=[-28.324984817259347181  ,-1.2331999570450413127 ] 
dist 26=[-17.177047578109324718  ,-.13861415457654405982] 
dist 27=[-17.103840485330716763  ,.57882439733371445642] 
dist 28=[-14.099038494693264176  ,1.1435785221884210299 ] 
dist 29=[-13.373822710843315187  ,2.6199922044356910389 ] 
dist 30=[-12.864596117257793031  ,5.1092705167636382582 ] 
dist 31=[-12.748670183249759335  ,7.3169132514665963441 ] 
dist 32=[-2.1747037432836124092 ,9.6601370713827680777 ] 
dist 33=[-.9403187157124687995 ,11.709795212829774997  ] 
dist 34=[.06816176061495754074,12.754655899010113790  ] 
dist 35=[-.33900360835112078751,13.275686547034544601  ] 
dist 36=[-.71342959597621706632,13.354942526952666733  ] 
dist 37=[-1.1241767270238276746 ,12.841508695269566343  ] 
dist 38=[-1.5120017926912433945 ,12.561774528900744344  ] 
dist 39=[-1.7962051450558686769 ,12.114397165937381157  ] 
dist 40=[-2.0516406462156205990 ,11.897144489996674648  ] 
dist 41=[-2.3261421298454777545 ,7.8629780693627031493 ] 
dist 42=[-2.6943388910969799205 ,7.6648328384123489876 ] 
dist 43=[-4.7569920517012627762 ,7.5546508452940129743 ] 
dist 44=[-6.6798421455995623016 ,6.4994007031087811143 ] 
dist 45=[-8.3099204654183304044 ,6.2241283639381897509 ] 
dist 46=[-9.2118008122267473431 ,5.8130964208116563948 ] 
dist 47=[-9.7320838031646953425 ,5.6602316168542098812 ] 
dist 48=[-9.8489243760388318561 ,1.9714568268061526816 ] 
dist 49=[-2.9237526448487129261 ,1.4821720913965108659 ] 
dist 50=[-3.1879168253830873180 ,1.2127570227657665964 ] 
dist 51=[-4.1877661558262184465 ,1.5065244697181121389 ] 
dist 52=[-5.0311964594515880181 ,1.9011451317005960146 ] 
dist 53=[-5.4980606658227116515 ,2.3077367589273295291 ] 
dist 54=[-5.7698348424570356220 ,2.6348395135200972911 ] 
dist 55=[-5.8382535122839228328 ,2.7828510835717344859 ] 
dist 56=[-2.8114295155755543026 ,2.8502093325724098176 ] 
dist 57=[-1.7863619387600990091 ,2.8576587531696321760 ] 
dist 58=[-1.7320069307271785099 ,-.07851277606174348364] 
dist 59=[-1.7211354781280399607 ,.20074479236525565669] 
dist 60=[-1.4256170655673387555 ,.6229993693607130495 ] 
dist 61=[-1.3563541693687893133 ,.99844094514269452287] 
dist 62=[-1.2893765473145087247 ,1.2403561059476415936 ] 
dist 63=[-1.2676155105250106437 ,1.4260035575153567720 ] 
dist 64=[-.27681147115072710716,1.5784227728308636644 ] 
dist 65=[-.15600383162942498688,1.6938167626936940248 ] 
dist 66=[.02123733655460127039,1.7325820378674003257 ] 
dist 67=[.02378852835484697015,1.7378134523490307984 ] 
dist 68=[.02652602075206696439,1.7200152588961759421 ] 
dist 69=[.02607585911517319468,1.5511963170111536079 ] 
dist 70=[.02444895325664720828,1.4984652087718480834 ] 
dist 71=[.02142290669237398552,1.4176788121897014851 ] 
dist 72=[.01690294409587384891,1.3853351901878079373 ] 
dist 73=[-.12874872933788617188,1.0477483275350805948 ] 
dist 74=[-.44410373949371076869,1.0086621221309691965 ] 
dist 75=[-.701730988449602344  ,.99692779897341767902] 
dist 76=[-.94010848954702480675,.82670699318683850085] 
dist 77=[-1.1417429569053991442 ,.78494173119469500672] 
dist 78=[-1.2535708653629587594 ,.73826096615330275391] 
dist 79=[-1.3187250206355373146 ,.71547474212365884137] 
dist 80=[-1.3351434341160079440 ,.27794136989175603011] 
dist 81=[-.4108385288847555462 ,.24134550912599259737] 
dist 82=[-.41868280007292224336,.16241957141846778674] 
dist 83=[-.50885411994879664811,.14069266915084841266] 
dist 84=[-.59321158997524649335,.05732080623566761645] 
dist 85=[-.64052911157694225097,.04021097822775731248] 
dist 86=[-.6718894589604609042 ,.01144032411633172029] 
dist 87=[-.6789341922975919156 ,.01170319221260326678] 
dist 88=[-.33129355351102163392,.01213854727004988303] 
dist 89=[-.21765510506762435855,.01221182428001769266] 
dist 90=[-.20964995841119774073,.02258285007353343788] 
dist 91=[-.20842217317594481286,.07796176633834180318] 
dist 92=[-.16945957332824905972,.13081881545434759497] 
dist 93=[-.16011980797724542902,.17670450554922595379] 
dist 94=[-.15335064899911981814,.2044228012366750183 ] 
dist 95=[-.15165318200377935258,.22360968421396777434] 
dist 96=[-.04246857981316121578,.23564535829313696745] 
dist 97=[-.05128759316425281455,.24251232588696930204] 
dist 98=[-.06019830002585011230,.24338354554535267336] 
dist 99=[-.06625660523031349550,.2376841801804783363 ] 
dist 100=[-.07126119121004877011,.23591107282032357628] 
dist 101=[-.07599012189040756414,.19744632528651282816] 
dist 102=[-.08006287409929843686,.18770971198639909097] 
dist 103=[-.08246330383085865671,.17876590790768630898] 
dist 104=[-.08405106718547076803,.17432545498139830722] 
dist 105=[-.08489855376911395654,.10971448612818679269] 
dist 106=[-.08512940863246835821,.10606950321276240409] 
dist 107=[-.08433910422657388104,.10432574048256733152] 
dist 108=[-.09988722947460734122,.08899306968441137513] 
dist 109=[-.12246392827503297861,.08506587118936555613] 
dist 110=[-.13575491312136162996,.07893811184039282382] 
dist 111=[-.14324003896562941414,.07679237645224319555] 
dist 112=[-.14499728055787967268,.02581520913123701327] 
dist 113=[-.06520957937965068897,.01898406908965431711] 
dist 114=[-.05751498072893314651,.01168297743312393303] 
dist 115=[-.05645695640205069672,.01183820087634254894] 
dist 116=[-.05630225453152338801,.01197899929739141868] 
dist 117=[-.04692414194896351740,.01212866930784875509] 
dist 118=[-.04456420239920892928,.01226586172512867312] 
dist 119=[-.04308839022493030162,.01235770774548896517] 
dist 120=[-.04272776317239014396,.01243797724855168863] 
dist 121=[-.02418389607345877808,.01249673137526338237] 
dist 122=[-.00267439196794878166,.00264714758846478331] 
dist 123=[-.00261150786758557903,.00977078285223363737] 
dist 124=[-.00238289522993688427,.01649346316767794067] 
dist 125=[-.00234995387275444796,.02228350066844652534] 
dist 126=[-.00175228462394198777,.02570544079481971934] 
dist 127=[-.00162337282692765426,.02798388457691405792] 
dist 128=[-.00150961391619612494,.02923541261520182769] 
dist 129=[-.00148709801515596950,.02986248591433640178] 
dist 130=[7.22898458546075704850e-05,.02986592315050689805] 
dist 131=[.00025328364392499731,.02919755836315722608] 
dist 132=[.00066114849129905011,.02877540189370007273] 
dist 133=[.00072543062026270936,.02488406204532054993] 
dist 134=[.00115611866456279356,.02384861435310562783] 
dist 135=[.00122150205475417843,.02227819824238804392] 
dist 136=[.00129974688511145989,.02169672703191792114] 
dist 137=[-.00337565389021465947,.00758244737675339567] 
dist 138=[-.00857468709914433716,.00570623770113408443] 
dist 139=[-.01280347576892389851,.00148238124928075050] 
dist 140=[-.01669522589387556182,.00112407014159460823] 
dist 141=[-.01997999805729828463,.00110116166100684591] 
dist 142=[-.02179912399718179790,.00089058276458955181] 
dist 143=[-.02285942247523284355,.00084211960011908631] 
dist 144=[-.02312588361571398238,.00076973142704735182] 
dist 145=[-.00709892984259025183,.00074514076604132283] 
dist 146=[-.00711543058762026147,.00019416543145747620] 
dist 147=[-.00690529472679420445,.00012165726636218352] 
dist 148=[-.00687355055209030376,-3.66506648689910845650e-05] 
dist 149=[-.00565090818402694786,-7.22189026973999781030e-05] 
dist 150=[-.00537999578460167285,-.00023012205526765062] 
dist 151=[-.00513323452128015003,-.00025870108134882550] 
dist 152=[-.00508213668282554178,-.00029184174918974156] 
dist 153=[-.00113518293021499291,-3.50860571305980365440e-05] 
dist 154=[-.00065758883400737477,.00107205003678730458] 
dist 155=[-.00027071216342628425,.00197937739710414249] 
dist 156=[-.00024928995179073903,.00282610169466368405] 
dist 157=[-.00024600814824164711,.00354922363060758793] 
dist 158=[-.00018712301705780762,.00396587288810637132] 
dist 159=[-.00017440643365694481,.00423006891290751264] 
dist 160=[-.00016221458881138284,.00434798433827016748] 
dist 161=[-.00015933973257188019,.00437966912150577588] 
dist 162=[-3.68379335052287342500e-06,.00436452476801805805] 
dist 163=[1.47456177690495495250e-05,.00420379206017672413] 
dist 164=[5.62415988416977420570e-05,.00415771937431031547] 
dist 165=[6.31435678315030731980e-05,.00344039924797366950] 
dist 166=[.00010717197665537928,.00326443548528583761] 
dist 167=[.00011400455641004381,.00307651759179704930] 
dist 168=[.0001008639392395595 ,.00298022847305054590] 
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dist 173=[-.00242175624975864330,.00024614717853650118] 
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dist 175=[-.00274955781980615414,9.61856107029326644810e-05] 
dist 176=[-.00277947318343569044,9.00587598817306119400e-05] 
dist 177=[-.00092858951056778159,8.77897008358702237070e-05] 
dist 178=[-.00092825642552865377,1.53800329506471297620e-05] 
dist 179=[-.00089529451504749302,8.20405600418450370930e-06] 
dist 180=[-.00089049433953687895,-7.63157410088780016010e-06] 
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dist 182=[-.00068398944723794811,-2.71458284293121824210e-05] 
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dist 190=[-3.89154234452302516180e-05,.00042649914798654104] 
dist 191=[-3.79211269645933519030e-05,.00045822686273885725] 
dist 192=[-3.51194439757493392630e-05,.00047153616231967788] 
dist 193=[-3.40431640752829854270e-05,.00047501322624408228] 
dist 194=[-2.79461360213719358820e-05,.00047299328003449334] 
dist 195=[-2.64190350023439952070e-05,.00045771762084867457] 
dist 196=[-2.41323911081426364950e-05,.00045056810712065164] 
dist 197=[-2.33414682111001572450e-05,.00038406641612491188] 
dist 198=[-2.15216313281792838790e-05,.00036703917928232589] 
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dist 200=[-2.07968740817880454210e-05,.00033217218054019209] 
dist 201=[-5.79313404983534043030e-05,.00010912665080384000] 
dist 202=[-.00013894405014261385,7.96253432290515949350e-05] 
dist 203=[-.00020474023986348262,6.36989600439925405180e-05] 
dist 204=[-.00026517742991065021,6.27701824410356719430e-05] 
dist 205=[-.00031614608620647066,6.17979449977046244160e-05] 
dist 206=[-.00034434723452767855,6.01580144544168311410e-05] 
dist 207=[-.00036074657861411109,5.89781296883621270820e-05] 
dist 208=[-.00036485552489943581,5.73937614210017397280e-05] 
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dist 211=[-.00010934854232525489,5.19966920911435345640e-05] 
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dist 225=[-3.16795589260927719120e-05,6.31790749267440311090e-05] 
dist 226=[-3.25836007863600650010e-05,6.28738593251339744400e-05] 
dist 227=[-3.31885534874817933990e-05,6.01495732823899338350e-05] 
dist 228=[-3.36782654695412055170e-05,5.96330641095534364830e-05] 
dist 229=[-3.41248192182839659560e-05,4.82586552869745469130e-05] 
dist 230=[-3.44986531016906997880e-05,4.42878809092139839390e-05] 
dist 231=[-3.46996685125826040700e-05,4.12776888108336733260e-05] 
dist 232=[-3.48086143772782027260e-05,3.39404602980894828740e-05] 
dist 233=[-3.48169203123864407590e-05,9.11764690333088587200e-06] 
dist 234=[-3.46954483501308640860e-05,8.80784708404641844200e-06] 
dist 235=[-3.42891222530195814190e-05,8.70686296301748314690e-06] 
dist 236=[-3.36046170646536784640e-05,8.58067030381834560110e-06] 
dist 237=[-3.31878453388061604150e-05,8.45597048445268601520e-06] 
dist 238=[-3.09286709310172457730e-05,8.17644950027633740410e-06] 
dist 239=[-3.02303564913874077290e-05,8.01510319462297556930e-06] 
dist 240=[-2.74200894341279954090e-05,7.71152621972760823690e-06] 
dist 241=[-1.49508635109463913120e-05,7.58544333585562830880e-06] 
dist 242=[-1.48888467597897117600e-05,6.96649777021860832350e-06] 
dist 243=[-1.42925530917243833570e-05,6.73923585360108350510e-06] 
dist 244=[-1.41573497575708831670e-05,6.53943925753795880320e-06] 
dist 245=[-1.15948913149345385040e-05,6.39454441908362365530e-06] 
dist 246=[-1.09774194831376993230e-05,6.24963597802938060780e-06] 
dist 247=[-1.02074237255021550240e-05,6.19248671675628305990e-06] 
dist 248=[-7.62722600765008588820e-06,6.22004851942708596970e-06] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 1, 1, 1, 2] 
dist 0=[110.46121040574155246   ,110.46121040574155246   ] 
dist 1=[107.18644536937204852   ,111.44059982107165195   ] 
dist 2=[103.23355874454841975   ,112.05450055091668133   ] 
dist 3=[99.670411391359551100  ,112.53149609173113411   ] 
dist 4=[95.748532080365015204  ,112.30277430531365797   ] 
dist 5=[90.356697453102481026  ,109.07604149149664856   ] 
dist 6=[84.469037140802868346  ,107.87480946226256051   ] 
dist 7=[78.414860554550710983  ,106.10261611617294323   ] 
dist 8=[66.247123777752040181  ,105.28825279756555647   ] 
dist 9=[57.117348622230915252  ,81.328373667697881233  ] 
dist 10=[48.598526666077241406  ,77.979920114852169809  ] 
dist 11=[38.842480563537425353  ,68.995830018059583444  ] 
dist 12=[29.160855230544956182  ,67.579534242442376718  ] 
dist 13=[20.922637222290205144  ,51.370813323212314101  ] 
dist 14=[12.211954770094723406  ,48.138835175885462064  ] 
dist 15=[.62444761910926804307,44.474794141582171038  ] 
dist 16=[-10.370759679696445287  ,43.468939263529230184  ] 
dist 17=[-16.731170097094689066  ,19.012193353410771678  ] 
dist 18=[-20.936296568875298578  ,7.7565427823468559750 ] 
dist 19=[-23.348358233513312587  ,4.5149646112697846320 ] 
dist 20=[-24.907100449991529430  ,1.0909892119271814769 ] 
dist 21=[-25.706973449677803692  ,.28955315968930473264] 
dist 22=[-26.366150962124280921  ,-2.0526871097065701035 ] 
dist 23=[-27.600068181135115094  ,-2.4396333854809350132 ] 
dist 24=[-28.159616504236656179  ,-2.2709008285851489941 ] 
dist 25=[-28.274948283612197714  ,-1.3185449133363785291 ] 
dist 26=[-17.563184249681724626  ,-.22908883014389056928] 
dist 27=[-17.032484861456170884  ,.48685143385723324768] 
dist 28=[-16.955128963434288242  ,2.3971175315501282254 ] 
dist 29=[-13.939097779784639459  ,4.8475267713444762572 ] 
dist 30=[-13.214885921941695431  ,7.0293324321029857325 ] 
dist 31=[-12.701828701060754245  ,9.3581811406903288199 ] 
dist 32=[-12.586767938849093033  ,11.400379192664923995  ] 
dist 33=[-2.1007157684636159816 ,12.446871014242218030  ] 
dist 34=[-.87731754951522995014,12.972465717703113656  ] 
dist 35=[-.31693578578324802792,13.057327146969942191  ] 
dist 36=[-.67782452467739240184,12.582482547937391110  ] 
dist 37=[-1.0757911845943509046 ,12.313331546089025963  ] 
dist 38=[-1.4526032210122025328 ,11.882060645064844732  ] 
dist 39=[-1.7302834578767656093 ,11.670733079001209647  ] 
dist 40=[-1.9813546435692300720 ,7.6543801892515787992 ] 
dist 41=[-2.6141389614961857177 ,7.7870112190732216363 ] 
dist 42=[-4.6338372095604696968 ,7.7779733663585656016 ] 
dist 43=[-6.5172146769738250276 ,7.5749358787377522826 ] 
dist 44=[-8.1140070456801157350 ,7.4654615856312990519 ] 
dist 45=[-8.9974938643581473902 ,6.4138661744502476896 ] 
dist 46=[-9.5071169994013102260 ,6.1405640088573574847 ] 
dist 47=[-9.6213765076709628867 ,5.7335339997816375138 ] 
dist 48=[-2.8574846846711861991 ,5.5820917075879387971 ] 
dist 49=[-3.0547093054850974011 ,1.9263847883849186150 ] 
dist 50=[-3.1505998115605855231 ,1.4408670044619052364 ] 
dist 51=[-3.1851624757694162210 ,1.4616745939163995900 ] 
dist 52=[-4.1337459309043242216 ,1.8553866722466276031 ] 
dist 53=[-4.9671191060074259324 ,2.2514400914165075765 ] 
dist 54=[-5.4283705482845669665 ,2.5697510882492759467 ] 
dist 55=[-5.6967529546959617452 ,2.7130922997934776669 ] 
dist 56=[-5.7643471004993487793 ,2.7781068545580727659 ] 
dist 57=[-1.7713087623500628587 ,2.7859993988635942111 ] 
dist 58=[-1.7726469910689738948 ,.19005327079908503583] 
dist 59=[-1.7174981678135844759 ,.60482287040991828275] 
dist 60=[-1.7061405293416774170 ,.97384740012115017284] 
dist 61=[-1.4081986752424170155 ,1.2120142559940969995 ] 
dist 62=[-1.3354105836166646774 ,1.3952166695159646607 ] 
dist 63=[-1.2759472219045509789 ,1.5463914874349425169 ] 
dist 64=[-1.2540163906030341041 ,1.6612348602816794713 ] 
dist 65=[-.20730897806284709772,1.7003095383829331807 ] 
dist 66=[-.08236113948894139691,1.7061055726248475671 ] 
dist 67=[.02834545177728346258,1.6889348455411365130 ] 
dist 68=[.03239370852308827342,1.5243165637340650597 ] 
dist 69=[.03266451546613399116,1.4727272233181840628 ] 
dist 70=[.03165494681633788245,1.3936571421646228561 ] 
dist 71=[.02898746718633017153,1.3619484772823657829 ] 
dist 72=[-.12528145443677736248,.94948028750866237585] 
dist 73=[-.43502227247203896445,.95551733473577832563] 
dist 74=[-.68809104603151447723,.9521857030258240288 ] 
dist 75=[-.92227668416344827205,.9152287700087535163 ] 
dist 76=[-1.1203740172155747494 ,.90651256002131386234] 
dist 77=[-1.2302428416174914515 ,.74308784766950553823] 
dist 78=[-1.2942555859124050777 ,.70357272735896255676] 
dist 79=[-1.3103832747808344648 ,.6658873582496737155 ] 
dist 80=[-.40325807399368443167,.6490680774137964001 ] 
dist 81=[-.41119441224428857038,.16429470793627716021] 
dist 82=[-.41200864065923557097,.11392680130769131876] 
dist 83=[-.41133327638866000355,1.31141238477330252360e-05] 
dist 84=[-.39724388982355099817,-.00110537155438283553] 
dist 85=[-.47991664019750182049,-.00057177705347440039] 
dist 86=[-.5259598219504822613 ,-6.43287070016204471610e-05] 
dist 87=[-.55449117248438554724,.00030920973346391293] 
dist 88=[-.56115560498311455905,.00055292366763785283] 
dist 89=[-.21855406789920295909,.02200787041217852102] 
dist 90=[-.21820861039406234245,.07647113439318653115] 
dist 91=[-.20985828587086917288,.12847644879381576204] 
dist 92=[-.20864821627687892802,.17363625932484756771] 
dist 93=[-.16897661525955822918,.20093854336821243097] 
dist 94=[-.1595146960924304871 ,.21986424956113382424] 
dist 95=[-.15278810587698560677,.23178872428526902738] 
dist 96=[-.15127186401966118376,.23862920836950251095] 
dist 97=[-.01520549900748723559,.23951153282356232648] 
dist 98=[-.01458114965962516975,.23396488905061587449] 
dist 99=[-.01648937234625322425,.23221884517192907361] 
dist 100=[-.01812639225832223251,.19444319152123132457] 
dist 101=[-.01976537409570530342,.18487132128054873283] 
dist 102=[-.02123323191785865476,.1760593546195793508 ] 
dist 103=[-.02219220275771417301,.17166103111251919597] 
dist 104=[-.02294100938807798893,.1089868351854887268 ] 
dist 105=[-.04501064415558014249,.10951709640470578933] 
dist 106=[-.07265020357933405629,.10896183870962389289] 
dist 107=[-.09829811227556806516,.1052453840062462658 ] 
dist 108=[-.12073997665297136107,.10356953594914512525] 
dist 109=[-.13380768415222497577,.08808365557405594998] 
dist 110=[-.14116337157572470533,.08414584058169713200] 
dist 111=[-.14287621024953062645,.07821048192634124785] 
dist 112=[-.05610084394665842423,.07606218444110915739] 
dist 113=[-.05653289299536437590,.02512228938419575243] 
dist 114=[-.05565271023448652665,.02556482821586578874] 
dist 115=[-.05546835603624933979,.02596205814607485868] 
dist 116=[-.06104289059639936782,.02639135482338356899] 
dist 117=[-.07273019245209066543,.02696248701987573969] 
dist 118=[-.07919782572874291376,.02815150927923288402] 
dist 119=[-.08296116354931673377,.02962916601904393844] 
dist 120=[-.08391003931015376431,.03028857347586969001] 
dist 121=[-.02565082753131818732,.03028743662774131611] 
dist 122=[-.02556392452322642080,.00951039017106325091] 
dist 123=[-.02448868919746010586,.01611995466224916983] 
dist 124=[-.02432894757921069396,.02181387755607177494] 
dist 125=[-.01961621567113491173,.02518126407545455934] 
dist 126=[-.01858302519900872159,.02742614586316362159] 
dist 127=[-.01765322103928748606,.02866490093434400015] 
dist 128=[-.01745968592485390242,.02929056274557824226] 
dist 129=[-.00334597259091735004,.02929698067537087602] 
dist 130=[-.00164624483163255824,.02865083151997533994] 
dist 131=[.00226075031407397134,.02823560121614187551] 
dist 132=[.00292174399292961331,.02443597356213168957] 
dist 133=[.00740267837024865976,.02342301589191198367] 
dist 134=[.00809515187546974810,.02187910694781487250] 
dist 135=[.00434509054904233477,.02130985387846476959] 
dist 136=[-.00328503134959229727,.01539318826211403952] 
dist 137=[-.00840798860901477700,.01538010975683524096] 
dist 138=[-.01257488811542479412,.01528717938839350243] 
dist 139=[-.01640960754992052013,.01463759350595277489] 
dist 140=[-.01964614738992882233,.01446635465477428954] 
dist 141=[-.02143831865597235906,.01187766124677374250] 
dist 142=[-.02248142350729831702,.01125300567066625726] 
dist 143=[-.02274417503760998710,.01058100684910982922] 
dist 144=[-.00688861574601488679,.01024331595889045423] 
dist 145=[-.00690522221526451982,.00371291222116387737] 
dist 146=[-.00671674179496828918,.00319933519591204738] 
dist 147=[-.00667601453590353708,.00210424389096403796] 
dist 148=[-.00737445789393464440,.00180619427922014078] 
dist 149=[-.00855277027475758421,.00068407301182272296] 
dist 150=[-.00920961093524749649,.00044895529072858975] 
dist 151=[-.00960728439094112896,.00010518509301950129] 
dist 152=[-.00971160201809366915,1.03614406036885537100e-05] 
dist 153=[-.00324770571699876579,.00072317806217903825] 
dist 154=[-.00323322184934238708,.00159009934644535939] 
dist 155=[-.00309082736236630392,.00239973011872505395] 
dist 156=[-.00306868649330383144,.00309158018544663234] 
dist 157=[-.00246742991889268848,.00349093895894601656] 
dist 158=[-.00232556922788608611,.00374509468315725350] 
dist 159=[-.00221755201729472620,.00386052614243452919] 
dist 160=[-.00218978108424953464,.00389476308088092945] 
dist 161=[-.00019787236041272550,.00388433287365433263] 
dist 162=[3.52190004783574903250e-05,.00374098437618730306] 
dist 163=[.00057760432208692548,.00370614187400529013] 
dist 164=[.00065623399753312761,.00304639734986089870] 
dist 165=[.00128993800485015140,.00288579394201056927] 
dist 166=[.00132935149951736524,.00273322815593714921] 
dist 167=[.00053429933823556858,.00266375160278855291] 
dist 168=[-.00026308394346484469,.00167193686368012646] 
dist 169=[-.00079861249625625145,.00167014281812821582] 
dist 170=[-.00123453029614893659,.00165908007075316136] 
dist 171=[-.00163644330689562722,.00159261644106607205] 
dist 172=[-.00197633439165222916,.00156937513238632589] 
dist 173=[-.00216708430834190635,.00131121560476878285] 
dist 174=[-.00228631581497309839,.00124755452870110836] 
dist 175=[-.00231373308906039127,.00116340152005714747] 
dist 176=[-.00094782418281793083,.00112899523194798727] 
dist 177=[-.00094647002429001232,.00032832046129411452] 
dist 178=[-.00091702718891628234,.00022877822853290905] 
dist 179=[-.00090715084023133188,6.00962258969176406970e-06] 
dist 180=[-.00086407241831086363,-4.10326034440298693090e-05] 
dist 181=[-.00103149871803794352,-.00028215685902419802] 
dist 182=[-.00112425850719552322,-.00032365076698919836] 
dist 183=[-.00117896699653100526,-.00019727230739962901] 
dist 184=[-.00119243367076585947,2.98483429401881521840e-05] 
dist 185=[-.00048165033182806478,.00018271261919057217] 
dist 186=[-.00047646454857830928,.00030752982739027427] 
dist 187=[-.00046583765123686951,.00042329566494520399] 
dist 188=[-.00045975940897543895,.00052170579503183600] 
dist 189=[-.00042216960219961558,.00057761579590686655] 
dist 190=[-.00041219531035704055,.00061206862383573793] 
dist 191=[-.00037531590862785159,.00062528776135749524] 
dist 192=[-.00036954998901964429,.00062690067527739460] 
dist 193=[-.00026974411430860150,.00062326804645106869] 
dist 194=[-.00024994862859187083,.00060080635360793534] 
dist 195=[-.00021275371118430328,.00059115470052863582] 
dist 196=[-.00020271670299514798,.00050057314334833011] 
dist 197=[-.00016766942839578033,.00047769540637198729] 
dist 198=[-.00015754015353759766,.00044107726446677691] 
dist 199=[-.00014936948947420135,.00035388063336369226] 
dist 200=[-.00014702462106429680,.00026215113307285539] 
dist 201=[-.00014649761427438555,.00026078647003920596] 
dist 202=[-.00019807197492986404,.00025863937423188994] 
dist 203=[-.00025653785549268915,.00024768994726835936] 
dist 204=[-.00030585002650869838,.00024363866726157286] 
dist 205=[-.00033314525838829154,.00020377909795087724] 
dist 206=[-.00034903177088274970,.00019394396384777999] 
dist 207=[-.00035304509960047185,.00017982557455408629] 
dist 208=[-.00019383293749663495,.00017454634974077402] 
dist 209=[-.00019244971964879061,4.96332838718740250960e-05] 
dist 210=[-.00018909367917949623,3.32056387830411102370e-05] 
dist 211=[-.00018702598510636264,-3.36515592385982488180e-06] 
dist 212=[-.00017372452975859145,-1.11782717865133761950e-05] 
dist 213=[-.00016992596827274692,-4.99888721044140728950e-05] 
dist 214=[-.00015607377933012820,-4.74217635591785271530e-05] 
dist 215=[-.00015001099567791442,-2.00217085091934264950e-05] 
dist 216=[-.00011582643131056449,7.82383516891670782000e-06] 
dist 217=[-7.44415111749727420370e-05,2.65291775670633394200e-05] 
dist 218=[-7.37647616425027353610e-05,4.17662757503688175460e-05] 
dist 219=[-7.16180205409777579880e-05,5.58410435629421627660e-05] 
dist 220=[-7.03733080572112489600e-05,6.77682555218290769210e-05] 
dist 221=[-6.26170681297367185080e-05,7.44783956781166065060e-05] 
dist 222=[-6.05837483759548498600e-05,7.85285830497001439890e-05] 
dist 223=[-5.53892855994851560380e-05,7.98943514362429433970e-05] 
dist 224=[-5.34402887503205363510e-05,7.98883825019248972470e-05] 
dist 225=[-3.07392034102915067650e-05,7.92710574843326207790e-05] 
dist 226=[-2.70137964176482413460e-05,7.66674708488341342570e-05] 
dist 227=[-1.93226737302167410300e-05,7.51299232859752953180e-05] 
dist 228=[-1.72503505270332824310e-05,6.54920051527778440610e-05] 
dist 229=[-9.66470041212072786270e-06,6.29578279644337549120e-05] 
dist 230=[-7.94462562875707289340e-06,5.78045740504605912790e-05] 
dist 231=[-5.94653861319887132600e-06,4.93115848564834958380e-05] 
dist 232=[-1.05018678058326781750e-05,2.54406590847789300040e-05] 
dist 233=[-1.81107626525631415250e-05,1.33085246390243702950e-05] 
dist 234=[-2.43020759822584080570e-05,8.84382043019174091200e-06] 
dist 235=[-3.00097177078300945810e-05,7.62183049404542434940e-06] 
dist 236=[-3.48385273586722608930e-05,2.98168430758174976740e-06] 
dist 237=[-3.75403733566270805030e-05,2.01567708150161739980e-06] 
dist 238=[-3.92278579186813162000e-05,5.18586395653770891430e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 0, 2, 1, 0, 2] 
dist 0=[116.49953415306771919   ,116.49953415306771919   ] 
dist 1=[114.73479093619835997   ,117.65953917561650129   ] 
dist 2=[111.50853531606763288   ,118.44176882205108756   ] 
dist 3=[104.53521090144131289   ,118.69321476654966215   ] 
dist 4=[96.839742767001741491  ,118.57027024115857609   ] 
dist 5=[90.739201560794848254  ,117.96292715244911046   ] 
dist 6=[84.715236845234462482  ,116.70729733137089816   ] 
dist 7=[72.668473411641996538  ,115.99217499958192229   ] 
dist 8=[62.975752614267476561  ,94.317177329791195978  ] 
dist 9=[54.021421905151706470  ,91.121144943372804476  ] 
dist 10=[43.898763597141574682  ,82.078221224856859026  ] 
dist 11=[33.929689941769345494  ,80.716716861699981435  ] 
dist 12=[25.570935217843844250  ,62.898885035584756382  ] 
dist 13=[16.841396070937827053  ,59.256739256913928901  ] 
dist 14=[5.3710401733670997022 ,55.551669201450835837  ] 
dist 15=[-5.5094112176651203611 ,54.699541885480734392  ] 
dist 16=[-11.898045907649243283  ,15.455384460588995177  ] 
dist 17=[-16.239201251072648593  ,10.821214760468320544  ] 
dist 18=[-18.965001073423476228  ,6.7522854742409872020 ] 
dist 19=[-20.850581754101985999  ,6.0758596698336204899 ] 
dist 20=[-21.838707288216315421  ,3.4201186620482393524 ] 
dist 21=[-22.681901007839080962  ,2.8495026483034154548 ] 
dist 22=[-25.429767383301323007  ,2.7067833578609998077 ] 
dist 23=[-27.397053143818836341  ,3.0607582167098547487 ] 
dist 24=[-28.779264937706053003  ,3.6619636017287530772 ] 
dist 25=[-29.198525941672258087  ,4.5086960314413369904 ] 
dist 26=[-29.186150896509619385  ,5.6717568640316759490 ] 
dist 27=[-27.920164399977456318  ,7.5372656091612289997 ] 
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dist 185=[6.29666574146266114380e-05,.00051318749555573893] 
dist 186=[8.46206212828602379680e-05,.00054071665552877522] 
dist 187=[.00020610582333906167,.00054713874045431662] 
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dist 195=[5.66028352994258944840e-05,.00040006757869755016] 
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dist 200=[-.00014691362798202683,.00011199522960003760] 
dist 201=[-.00019788395426869732,7.51853571318422998810e-05] 
dist 202=[-.00024493605347529540,6.50545331105909628660e-05] 
dist 203=[-.00028477971367507546,2.62509807329128311350e-05] 
dist 204=[-.00030712969625980449,1.82352092989109430320e-05] 
dist 205=[-.00032182492916823506,5.06336984453005042240e-06] 
dist 206=[-.00032530444032693698,1.87521761711963957760e-06] 
dist 207=[-.00010589078561681693,-8.16806222524065692270e-05] 
dist 208=[-.00010505152321955878,-6.83618542433113303760e-05] 
dist 209=[-.00010131622288396602,-5.35960033257503470950e-05] 
dist 210=[-.00010040095555553739,-3.52364761641737936040e-05] 
dist 211=[-8.28682459414943435370e-05,-7.64792947035364505210e-06] 
dist 212=[-7.85868785226829797470e-05,1.99811307803294735140e-05] 
dist 213=[-7.45478610922167313560e-05,3.85017718419978470780e-05] 
dist 214=[-7.27012726405051651840e-05,5.35455969432979004140e-05] 
dist 215=[-1.30801492113898344200e-05,6.73696044440725197990e-05] 
dist 216=[-5.78787879887100834460e-06,7.90334756477562340850e-05] 
dist 217=[7.20017253961533445650e-06,8.55002047089990053550e-05] 
dist 218=[1.12167380991231333860e-05,8.93201383902662499080e-05] 
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dist 220=[1.23693467770439082530e-05,5.78755689932674802220e-05] 
dist 221=[1.13295653871597428030e-05,6.15393674628477466410e-05] 
dist 222=[9.26007446849135926730e-06,6.29401751606514919570e-05] 
dist 223=[5.29751323179104195020e-06,6.31705021750182960400e-05] 
dist 224=[5.20845987451585106430e-07,6.27728702554516567910e-05] 
dist 225=[-4.78142750884484699180e-06,6.08288291896863424360e-05] 
dist 226=[-1.13787875333948486500e-05,5.96224567279053257260e-05] 
dist 227=[-2.12980785983849376230e-05,5.19431578147073895550e-05] 
dist 228=[-3.12351815455835965580e-05,4.99060494163679109640e-05] 
dist 229=[-3.79033756290629081640e-05,4.59460186567768542200e-05] 
dist 230=[-4.33278608500002503370e-05,4.46737332160797237760e-05] 
dist 231=[-4.83266568657473673030e-05,1.93459671063672087920e-05] 
dist 232=[-5.25547247658141445380e-05,1.57269978389115991700e-05] 
dist 233=[-5.49189266176094981870e-05,7.85479094006865155560e-06] 
dist 234=[-5.63271362181436054260e-05,5.76406139304862154780e-06] 
dist 235=[-5.67593020269529746990e-05,-2.27789120473051830230e-06] 
dist 236=[-5.66064256373155696770e-05,-3.85978372910989998410e-06] 
dist 237=[-5.60486139881474323800e-05,-5.36859650860919892420e-06] 
dist 238=[-5.40627224986336147880e-05,-4.83658654516324836730e-06] 
dist 239=[-1.61140710479823604080e-05,-3.80869068534939112510e-06] 
dist 240=[-1.34973015145671778740e-05,-2.56654102575201739520e-06] 
dist 241=[-1.28488826790029678910e-05,-1.18372220964006501430e-06] 
dist 242=[-1.19575604230484254320e-05,5.39508773816496742530e-07] 
dist 243=[-1.16071038477162762700e-05,3.13341451661383867740e-06] 
dist 244=[-6.86495425510773569460e-06,5.73335431371410058570e-06] 
dist 245=[-6.73684419098227468950e-06,7.48058141327273234190e-06] 
dist 246=[-5.86562301632451115640e-06,8.90480118402011469700e-06] 
dist 247=[-1.82432138495254869280e-06,1.02221997840710884910e-05] 
dist 248=[-6.93921950453206549620e-07,1.13400389507588456860e-05] 
dist 249=[-4.57025012211552499260e-07,1.19718844588173772860e-05] 
dist 250=[-1.08397643607878866830e-07,1.24010383547937695590e-05] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 1, 0, 0, 2] 
dist 0=[113.86732661381317403   ,113.86732661381317403   ] 
dist 1=[111.53462215393721909   ,115.03406603554091914   ] 
dist 2=[105.94237812516782000   ,115.98762062484436069   ] 
dist 3=[99.640612983908157802  ,116.55530437301991188   ] 
dist 4=[94.483927549327162328  ,116.17620390567324815   ] 
dist 5=[89.241103296662767079  ,115.39903296976165330   ] 
dist 6=[82.583352393205112892  ,114.56053544309708296   ] 
dist 7=[70.216520437607004720  ,113.03625118903852798   ] 
dist 8=[60.658797585031457563  ,110.88738914964627388   ] 
dist 9=[51.803237780596948086  ,89.652777192327198502  ] 
dist 10=[41.754235027389223793  ,86.388986101646151881  ] 
dist 11=[31.835897678239381259  ,77.238517371412808766  ] 
dist 12=[23.484611596353908402  ,75.918784470152306699  ] 
dist 13=[14.731876111803616251  ,58.250902921870786383  ] 
dist 14=[3.1900809290829007691 ,54.684511918438208858  ] 
dist 15=[-7.7578857980420393014 ,51.136140344579377130  ] 
dist 16=[-14.154203939516745492  ,50.453234108299215386  ] 
dist 17=[-18.461514447289266141  ,12.658835115868403137  ] 
dist 18=[-21.089719643485687460  ,10.952074200790785308  ] 
dist 19=[-22.862871449833969842  ,4.7121392515755115278 ] 
dist 20=[-23.758136754049446705  ,3.6490444806039634548 ] 
dist 21=[-24.217999674131948936  ,2.2073489328675087172 ] 
dist 22=[-26.057433490132411751  ,1.7791399712626280443 ] 
dist 23=[-28.014684821893762964  ,1.6278945693934950420 ] 
dist 24=[-28.753781469304676856  ,1.9884917544334097555 ] 
dist 25=[-28.966339865722087244  ,2.7534422007498322788 ] 
dist 26=[-28.824552931956188763  ,4.2425920328625765006 ] 
dist 27=[-22.422824396833026794  ,5.7373679599724675162 ] 
dist 28=[-22.253366657101463455  ,6.5275316683344683899 ] 
dist 29=[-18.949447652185023498  ,6.9694370579258486500 ] 
dist 30=[-18.105710874125951931  ,9.1590455856265244171 ] 
dist 31=[-17.250773389141257024  ,11.109185310976785720  ] 
dist 32=[-16.782588415802179752  ,12.071498213971709568  ] 
dist 33=[-4.6994733065536752186 ,12.551453580614102985  ] 
dist 34=[-3.1908065706277083972 ,12.591316381820154427  ] 
dist 35=[.31698057079880382789,11.878973183387921137  ] 
dist 36=[.85007554840047579244,11.571058389901487509  ] 
dist 37=[-.15390105036948030687,11.282042349652525472  ] 
dist 38=[-1.1710829993798197926 ,11.492837814729615152  ] 
dist 39=[-2.0895432972941522809 ,12.311765123148842632  ] 
dist 40=[-2.7026525001632871475 ,12.669291958451520862  ] 
dist 41=[-3.3418991591580893722 ,12.757130098780051336  ] 
dist 42=[-4.9353787710089057688 ,12.711307489390083217  ] 
dist 43=[-6.2924846760322332475 ,12.200827848147784287  ] 
dist 44=[-7.0748575131651799178 ,12.077539949775306930  ] 
dist 45=[-7.5353130314033438540 ,9.8302351271661860330 ] 
dist 46=[-7.6346499775971103647 ,9.2894609662607992073 ] 
dist 47=[-4.6147861537500484358 ,8.7563019985789901934 ] 
dist 48=[-4.9117483210879460128 ,8.5135676633300477765 ] 
dist 49=[-5.1955093759559365790 ,3.5460921127431054566 ] 
dist 50=[-5.5299814395821905659 ,3.1312199827527131106 ] 
dist 51=[-5.8659288370200758928 ,2.2113248111981370484 ] 
dist 52=[-6.1556234572067376987 ,1.9528253791591884734 ] 
dist 53=[-6.8099763649942805846 ,1.6885596972409525745 ] 
dist 54=[-7.4547955077311136893 ,2.2752363817984501995 ] 
dist 55=[-7.8131292698284613557 ,2.7719758994473524659 ] 
dist 56=[-7.8871099492059129815 ,3.0477471045338073629 ] 
dist 57=[.08552033521537143179,3.2085046493180107653 ] 
dist 58=[.18240272095614445154,3.2489709649590115886 ] 
dist 59=[.83504447162769054589,1.0009615651176255452 ] 
dist 60=[.93678805098276228443,1.2400067725509703807 ] 
dist 61=[1.0059066748282308518 ,1.4231718806814841475 ] 
dist 62=[.94415742105875546339,1.5730342169296296556 ] 
dist 63=[.85621562196589798241,1.6862133192213964016 ] 
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dist 211=[-8.08841013465867791620e-05,2.88043742511061151710e-05] 
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dist 222=[1.53216218856751097860e-05,7.27324085648252577410e-05] 
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dist 225=[-2.61285294338915219450e-06,6.94567559610306640490e-05] 
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dist 236=[-5.15003775551602420040e-05,2.01458766403955985870e-06] 
dist 237=[-5.05674246756771464550e-05,5.08656729992137975170e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 1, 1, 2] 
dist 0=[144.38192138417360253   ,144.38192138417360253   ] 
dist 1=[139.38156505557422356   ,145.67054654910790253   ] 
dist 2=[132.50761535829854313   ,145.77124691575116832   ] 
dist 3=[123.88806339610473184   ,145.80551270985286762   ] 
dist 4=[112.50955294395659295   ,144.57496725365171519   ] 
dist 5=[94.665800394521224795  ,133.36403725215571734   ] 
dist 6=[76.424947479984899853  ,130.85497130308819301   ] 
dist 7=[63.461527785485904013  ,122.10786138286639555   ] 
dist 8=[52.083192140465444528  ,120.85169807251589270   ] 
dist 9=[40.126949152743701534  ,98.514765380436228207  ] 
dist 10=[28.894867301161622132  ,93.666385222675313434  ] 
dist 11=[20.380691260704781892  ,89.497531201635016858  ] 
dist 12=[12.292523088717690992  ,88.665775245490806859  ] 
dist 13=[2.7278794713902819186 ,32.587650109760495020  ] 
dist 14=[-6.1116590713635717771 ,29.248914764211210491  ] 
dist 15=[-11.321506869150643764  ,26.942276219502645265  ] 
dist 16=[-14.891901284608335712  ,3.1954025751109389791 ] 
dist 17=[-17.465341666767321816  ,-14.305481322900753371  ] 
dist 18=[-23.452633177377151529  ,-15.591360281613485902  ] 
dist 19=[-27.915745326516910222  ,-14.308022407900341794  ] 
dist 20=[-31.420802354182247757  ,-11.746414686580364662  ] 
dist 21=[-34.024471527971783692  ,-6.9352656255859321042 ] 
dist 22=[-34.906305219402561682  ,-1.8860877502811638134 ] 
dist 23=[-35.057714618537840039  ,1.6256958121184478915 ] 
dist 24=[-34.743106267713888745  ,4.5636166224197571419 ] 
dist 25=[-31.195854390438472268  ,7.3471019158053737025 ] 
dist 26=[-30.117720965463129442  ,9.7100716867346188212 ] 
dist 27=[-28.548749295275486344  ,10.984891036250557722  ] 
dist 28=[-27.893803137079654238  ,11.666226533251878396  ] 
dist 29=[-11.022728010737991866  ,11.790638363275617641  ] 
dist 30=[-8.7755386383003766389 ,11.429159728422978531  ] 
dist 31=[-3.6270498278650917613 ,12.490448714630167792  ] 
dist 32=[-2.5753808790811589424 ,17.113819442712390501  ] 
dist 33=[3.4153878570806019482 ,21.021727796106720694  ] 
dist 34=[3.5337176323913006279 ,23.187882511970830101  ] 
dist 35=[3.3193448844124848968 ,24.449487143499798612  ] 
dist 36=[2.8973877151362626207 ,24.767342287995047647  ] 
dist 37=[2.1028364563339760946 ,7.8029210923086943804 ] 
dist 38=[1.2606738322346963194 ,7.9357007549563453021 ] 
dist 39=[.64925524747049688175,7.9365254515709395435 ] 
dist 40=[.10749470622129159787,7.9215538167932826120 ] 
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dist 43=[-1.3470073743832596663 ,6.3221290642467250201 ] 
dist 44=[-1.9698784295094924193 ,6.2298172638267292300 ] 
dist 45=[-2.5462179302019719939 ,1.4383280286424243759 ] 
dist 46=[-3.0075544184555532119 ,.86447182493385282487] 
dist 47=[-3.4202260795612731843 ,-.49359257742152638421] 
dist 48=[-3.7469002917790151267 ,-.69149939313614967459] 
dist 49=[-3.8672273835879394475 ,-1.5774041215167900079 ] 
dist 50=[-3.9005946307543570308 ,-1.4693880043131678642 ] 
dist 51=[-4.0184695642743333466 ,-1.2915974138075256235 ] 
dist 52=[-4.2253384046630183005 ,-1.0341540627998382116 ] 
dist 53=[-4.3378610622352161255 ,-.61007399646761439439] 
dist 54=[-4.3500635329375316132 ,-.1755393739188295066 ] 
dist 55=[-4.2394515169587987056 ,.12348814698864550762] 
dist 56=[-4.2072921231354924304 ,.434607183719637102  ] 
dist 57=[-3.5097439394182602379 ,.72855954721442541207] 
dist 58=[-3.3347203519952789800 ,1.2459138970348420533 ] 
dist 59=[-3.1741238558438648192 ,1.7570370174051764594 ] 
dist 60=[-3.0968901681288298784 ,2.1870995325620423019 ] 
dist 61=[-.87765611889037842654,2.4204798986779132199 ] 
dist 62=[-.64382879708921161547,2.5493992890898660421 ] 
dist 63=[-.10887847482909398924,2.5778733615193306551 ] 
dist 64=[-.00453115819817642625,1.7596161138255861039 ] 
dist 65=[.5886548469152428267 ,2.1509411325033316547 ] 
dist 66=[.54772522238967381076,2.3866655691566174850 ] 
dist 67=[.48763417975785279404,2.5199426379166861365 ] 
dist 68=[.40358560077929997728,2.5512936484812917985 ] 
dist 69=[.26755875665364421442,1.0214728000059360161 ] 
dist 70=[.12837913940285636015,1.0266724117736878834 ] 
dist 71=[.03179183131342588533,1.0044902852639123514 ] 
dist 72=[-.04993590408977433849,.99922406555463148897] 
dist 73=[-.1302003467838856326 ,.8355755078471840403 ] 
dist 74=[-.20129196300364416654,.79441507065787868297] 
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dist 95=[-.02208560378772504653,.3318552809226924466 ] 
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dist 100=[.04529849374169950565,.39497532425225977014] 
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dist 102=[.00799071267614381053,.14411890346120967446] 
dist 103=[-.00481759224608728320,.14164099441825429606] 
dist 104=[-.03389387110579678424,.139572937402492429  ] 
dist 105=[-.06294877630227733719,.12539763335317729849] 
dist 106=[-.08672273290296924207,.12149209427172334738] 
dist 107=[-.10883103697449712867,.11194741224026726718] 
dist 108=[-.12764575193843129983,.10836429963942519267] 
dist 109=[-.13834592766925940167,.06025831284922192657] 
dist 110=[-.14494613124094747539,.05264488500584471205] 
dist 111=[-.14748589023888836814,.03642773430722519126] 
dist 112=[-.14776416101516987969,.03197225026524776558] 
dist 113=[-.14664307257619680305,.01502373870044881933] 
dist 114=[-.14207524516660495874,.01143204159063760253] 
dist 115=[-.13930738810197189716,.00582883244418607558] 
dist 116=[-.12075489750238031287,.00435610325021997602] 
dist 117=[-.06675698106882725486,.00229517524394062713] 
dist 118=[-.06652208781222768442,.00228698774287950262] 
dist 119=[-.06394578042020973432,.00889755156142455819] 
dist 120=[-.06333271488790934090,.01429880738294097544] 
dist 121=[-.05193304625648015367,.01930639150459573827] 
dist 122=[-.04917244012086865441,.0236274263071110904 ] 
dist 123=[-.04653281406974614728,.02618445696988447116] 
dist 124=[-.04534265974189921292,.02762453792658029165] 
dist 125=[-.01138864651386095781,.02796362110370945143] 
dist 126=[-.00787339509466621948,.01379854019958738060] 
dist 127=[-.00434999933492402661,.02124196372824210455] 
dist 128=[.00167100672452918392,.02809728262735541118] 
dist 129=[.00984801377682781169,.03389077905284668388] 
dist 130=[.00880987635527357388,.03711838717746968113] 
dist 131=[.00757985463706869775,.03912278701341629566] 
dist 132=[.00600009476871562042,.03958969982400831682] 
dist 133=[.00357335814486940696,.01537457673064727136] 
dist 134=[.00112631812744228202,.01535124502678116007] 
dist 135=[-.00053418275300148138,.01476598772844727037] 
dist 136=[-.00190350333096171247,.01468152787160023059] 
dist 137=[-.00319481001993853355,.01188806727882312760] 
dist 138=[-.00430637394476793974,.01122093362947656657] 
dist 139=[-.00496227238018737489,.01074959766094945699] 
dist 140=[-.00539769850745313923,.01064387939222335415] 
dist 141=[-.00563419269363797928,.00103004237258895423] 
dist 142=[-.00575060032794913361,-9.08437767217143705410e-05] 
dist 143=[-.00574986622420949169,-.00269161191594990875] 
dist 144=[-.00561818394540244643,-.0030762227567740963 ] 
dist 145=[-.00622683998537149786,-.00476969263070404857] 
dist 146=[-.00705026880727644026,-.00408165478089316099] 
dist 147=[-.00755975642704793201,-.00330141591723711016] 
dist 148=[-.00776007175052769355,-.00232039786101984297] 
dist 149=[-.00779903541690860890,-.00083519318565791918] 
dist 150=[-.00775984240576726737,.00065487789231423364] 
dist 151=[-.00749676875514807505,.00165524825548004710] 
dist 152=[-.00737706066394089775,.00246887464331262059] 
dist 153=[-.00627711602226277984,.00321759243464064533] 
dist 154=[-.00599693396889561053,.00384951513474339584] 
dist 155=[-.00557340130808466063,.00419946917349067502] 
dist 156=[-.00542041064782496652,.00440343840666530532] 
dist 157=[-.00178473734477256551,.00445469972675167009] 
dist 158=[-.00130297433976460624,.00230679564797410052] 
dist 159=[-.00022673791777840013,.00338485540870343710] 
dist 160=[8.04931613836057125140e-06,.00437485972388367982] 
dist 161=[.00114673223436439293,.00520971511974956300] 
dist 162=[.00100452805181175163,.00567173517046569450] 
dist 163=[.00084131626989413948,.00594059260265725557] 
dist 164=[.00063483785232551949,.00600837454793478139] 
dist 165=[.00032083925680524884,.00183721207085060868] 
dist 166=[5.18239067788666440290e-06,.00183118125227561387] 
dist 167=[-.00020789049330795136,.00175423714294815234] 
dist 168=[-.00038247933979047272,.00174312377312571704] 
dist 169=[-.00054536065073217722,.00140286637105204726] 
dist 170=[-.00068443515890459020,.00132853228453893637] 
dist 171=[-.00076451465043092272,.00126416944289640107] 
dist 172=[-.00081522559527810475,.00125125611395860864] 
dist 173=[-.00083771224421319046,.00023906699642227695] 
dist 174=[-.00084360036069269068,.00011746873011389921] 
dist 175=[-.00084061629096367428,-.00016212099159004015] 
dist 176=[-.00080950605473773853,-.00020945391782304182] 
dist 177=[-.00092580789288149456,-.00042550528672367723] 
dist 178=[-.00102612016708364765,-.00035410868120635097] 
dist 179=[-.00108682845242229503,-.00027343960485455901] 
dist 180=[-.00110768099056348227,-.00017217659693818600] 
dist 181=[-.00110690665096847304,-1.90093770128270040000e-05] 
dist 182=[-.00110027269946970605,.00013468421271874592] 
dist 183=[-.00105366839976341977,.00023804044240285052] 
dist 184=[-.00104134612050219212,.00032232083900111338] 
dist 185=[-.00085519792262994481,.00040028081157521315] 
dist 186=[-.00081025231989728508,.00046639162827667102] 
dist 187=[-.00076188564469102683,.00050372215638152194] 
dist 188=[-.00073757763764023458,.00052939737302194194] 
dist 189=[-.00026719383850286233,.00053515848701600926] 
dist 190=[-.00023032755147874068,.00041074691725095475] 
dist 191=[-.00015168733686307308,.00043129685543482616] 
dist 192=[-.00013026512302401640,.00053166630073927262] 
dist 193=[-4.95224826563731401910e-05,.00061648774443516877] 
dist 194=[-3.26061792115450113590e-05,.00066379034848318187] 
dist 195=[-7.72422926289689065250e-06,.00069256682213559235] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 2, 1, 2] 
dist 0=[135.57153401110967159   ,135.57153401110967159   ] 
dist 1=[130.07066314224870652   ,139.43749207572314221   ] 
dist 2=[122.77453395891396145   ,140.27792922551674544   ] 
dist 3=[112.91755009429429590   ,139.95819994590532122   ] 
dist 4=[97.233071916957058890  ,139.50019576280001704   ] 
dist 5=[81.117162466373932277  ,129.66968125174075066   ] 
dist 6=[69.538310238686004943  ,127.16197509505989890   ] 
dist 7=[59.245263991833744729  ,114.70075796582359334   ] 
dist 8=[48.224144993020235192  ,111.30748062601192229   ] 
dist 9=[37.739593417412678576  ,89.504827897980778538  ] 
dist 10=[29.564905881179131878  ,84.841822795026356184  ] 
dist 11=[21.575469927689241731  ,80.699449417383603622  ] 
dist 12=[11.801148945405138174  ,79.875451226969562460  ] 
dist 13=[2.6352668649633079540 ,40.478864302789765994  ] 
dist 14=[-2.9394636062050522500 ,38.120243646821096234  ] 
dist 15=[-6.9688190911938169777 ,32.277312741092254523  ] 
dist 16=[-10.127689038970076831  ,26.473606591531402946  ] 
dist 17=[-18.829542579350339624  ,-8.8388134317797041882 ] 
dist 18=[-24.177370002149944351  ,-8.9475859563234146809 ] 
dist 19=[-28.040314491193389784  ,-7.4538763002157358693 ] 
dist 20=[-30.848668580556420205  ,-4.2119133194206999672 ] 
dist 21=[-32.814616473268114304  ,-.73071737005216427159] 
dist 22=[-33.330292707115611750  ,1.7179442581502844792 ] 
dist 23=[-33.268455344776302668  ,3.7749309050528161357 ] 
dist 24=[-32.925907690056670801  ,5.7143272122826757861 ] 
dist 25=[-29.182925424466730844  ,7.3359492981751003307 ] 
dist 26=[-28.107464742755936375  ,8.1379002709587784559 ] 
dist 27=[-26.546975064213663835  ,8.5278398074578903667 ] 
dist 28=[-25.912639780983834797  ,8.5359602990696389454 ] 
dist 29=[-10.009081793412947480  ,7.6986216376048739981 ] 
dist 30=[-7.8959890846818985059 ,7.4140244135911473045 ] 
dist 31=[-3.0775642822947018753 ,12.122454174996215046  ] 
dist 32=[-2.0850076286215401991 ,16.461448335601004546  ] 
dist 33=[.87429296564124420291,20.124308325066036417  ] 
dist 34=[.68153594339197060544,22.149272073238959619  ] 
dist 35=[.30815409889143225372,23.322403898722132998  ] 
dist 36=[-.39028796819366444942,23.604039601631099123  ] 
dist 37=[-1.1272322902742850546 ,7.7649014422505280274 ] 
dist 38=[-1.6537243057104017658 ,7.6650762041178296263 ] 
dist 39=[-2.1106160050766428643 ,7.6047273586450244576 ] 
dist 40=[-2.5725740680585730885 ,7.5892172638742256556 ] 
dist 41=[-2.9862527072861818208 ,6.2350162121838983286 ] 
dist 42=[-3.2521981263438343327 ,5.9418880046855994197 ] 
dist 43=[-3.4536803703518742309 ,5.7692640720663967703 ] 
dist 44=[-3.6121967232079974855 ,5.7259229622998297503 ] 
dist 45=[-3.7349341707687925665 ,2.4643333968476666250 ] 
dist 46=[-3.7947557085616622031 ,2.3529442358199091050 ] 
dist 47=[-3.8189277044088021929 ,2.1173739155276511303 ] 
dist 48=[-3.8048503578892993839 ,2.0432132616909748854 ] 
dist 49=[-4.1925880595916980841 ,1.7144348758644591231 ] 
dist 50=[-4.3517564170416091056 ,1.6401023827274503979 ] 
dist 51=[-4.4042949446365735700 ,1.4423002030758036627 ] 
dist 52=[-4.3765929207944555076 ,1.3916655017835629234 ] 
dist 53=[-4.0111528715494216610 ,1.0242960870962022055 ] 
dist 54=[-3.8873278177264624262 ,.94185067088732043886] 
dist 55=[-3.6983810569277468973 ,.83558656317848433103] 
dist 56=[-3.6187274795021413089 ,.795300452165190022  ] 
dist 57=[-3.0992811888105023136 ,.75560718346066333396] 
dist 58=[-2.9738752445030440772 ,1.0444175293228623590 ] 
dist 59=[-2.7850797258571486227 ,1.7026319406439390329 ] 
dist 60=[-2.7139360876612930696 ,2.3131058377958536751 ] 
dist 61=[-.96687573910606682832,2.8299734296764467176 ] 
dist 62=[-.73378539052743275141,3.1168361405933508030 ] 
dist 63=[-.20750096209501198732,3.2840577086545561393 ] 
dist 64=[-.09559237349870568480,3.3261925897080451415 ] 
dist 65=[.49311531945981229861,2.4053413655820663658 ] 
dist 66=[.5939984605392640921 ,2.6298436000640210411 ] 
dist 67=[.60454936665620641316,2.7605209091402975725 ] 
dist 68=[.38283874886541338216,2.7934380219490116496 ] 
dist 69=[.15751020418273242821,.94387540703010816011] 
dist 70=[.00276524935255129350,.90708719319054795073] 
dist 71=[-.12662204068040275524,.88274180144995139008] 
dist 72=[-.25136301241794347584,.87073826076311590394] 
dist 73=[-.36044846799491805979,.69554578593220347829] 
dist 74=[-.42773342976877315094,.66100225245456800335] 
dist 75=[-.47599158055031343844,.6337113135567581558 ] 
dist 76=[-.50960338136724926174,.62303285808632953171] 
dist 77=[-.53183770889518378489,.11041997116529968568] 
dist 78=[-.53554203540047374803,.04913530811489353355] 
dist 79=[-.56247028418960114367,-.09454292820535010843] 
dist 80=[-.59756515075199792802,-.11584485216740943165] 
dist 81=[-.61932850070474335821,-.2880140446383521008 ] 
dist 82=[-.62292092174373381099,-.31384666512352002822] 
dist 83=[-.61115999878821967718,-.22854468039789178214] 
dist 84=[-.60705311170896539869,-.09179196700515278530] 
dist 85=[-.51076444261969296003,.04578632454580039490] 
dist 86=[-.48606725736915307545,.13839619571151935721] 
dist 87=[-.4638769242416323346 ,.21390669066872142953] 
dist 88=[-.45342456622824680458,.28362024499090681813] 
dist 89=[-.37343055108461424542,.34254955770037188901] 
dist 90=[-.35389518397028171472,.37549953724892260145] 
dist 91=[-.33539912747700640468,.39468062791807759314] 
dist 92=[-.32693155218574455022,.39935068491818250032] 
dist 93=[-.08498999905163898636,.31125382631878783987] 
dist 94=[-.05981121055756079985,.3454229749449274936 ] 
dist 95=[-.00268296746285981283,.36467318417015414778] 
dist 96=[.00867329642933812632,.36911625660147442261] 
dist 97=[.07293123400267503968,.23965803408367454059] 
dist 98=[.07844758307764719944,.26319359605547169566] 
dist 99=[.05178848971899795510,.27774397026199612422] 
dist 100=[.01122471853866747485,.28109497974615123012] 
dist 101=[-.02951220186455692966,.14102776709502798609] 
dist 102=[-.05686000103274421198,.13585259223025979661] 
dist 103=[-.07908677802145368955,.12715694769076058755] 
dist 104=[-.09949674255917015475,.12414834322998544426] 
dist 105=[-.11667913489522464253,.08590059358772026997] 
dist 106=[-.12609418666462709686,.08119630246403925564] 
dist 107=[-.13143739510525825957,.07793841288747829126] 
dist 108=[-.13245622601536870266,.07719225027287489352] 
dist 109=[-.13154085808779246241,.00841051904391435815] 
dist 110=[-.12989412766344129141,.00038269355086554961] 
dist 111=[-.12596617728566014487,-.01028665153814559611] 
dist 112=[-.11880631872202599702,-.00769033989667264022] 
dist 113=[-.07687328423129631756,-.00431047092624182907] 
dist 114=[-.07697733664581159008,-.00025002452767426691] 
dist 115=[-.07547176296382889985,.00499848797046977146] 
dist 116=[-.07440334746411024538,.01309557040049066717] 
dist 117=[-.06460636261218415979,.02127267211776242226] 
dist 118=[-.06196830093978968747,.02683944405398853828] 
dist 119=[-.05794667100510630869,.03144915810421652255] 
dist 120=[-.05645496774108067420,.03582781983532274802] 
dist 121=[-.04510635411010727410,.03961869873089594656] 
dist 122=[-.04312120399748384468,.04314238110928913934] 
dist 123=[-.0401229493477407205 ,.04580062423974931431] 
dist 124=[-.03903308387589515618,.04645438905478864660] 
dist 125=[-.01302098555412385607,.05153179850446805350] 
dist 126=[-.00957288522801335441,.05626164709893477802] 
dist 127=[-.00185763955160411952,.05901479840479550598] 
dist 128=[-.00018008481439899123,.05970831249348259274] 
dist 129=[.00821275473232428822,.03707352458352880770] 
dist 130=[.00967564652126998969,.04038462838196753901] 
dist 131=[.0120881634865548113 ,.04231198983078274774] 
dist 132=[.01257329109743106023,.04279760798306668436] 
dist 133=[.01274454811140657805,.01467433241140526599] 
dist 134=[.01189504462371480363,.01393957132310391806] 
dist 135=[.00920502611962760811,.01335543699761759754] 
dist 136=[.00510173155909373440,.01312607050357251394] 
dist 137=[.00097305513298894152,.01009617413862393666] 
dist 138=[-.00181791070427640600,.00957477014894582657] 
dist 139=[-.00410877359426822681,.00910493008763672094] 
dist 140=[-.00625224188353479971,.00900732484608601763] 
dist 141=[-.00808643383889115041,.00178794992814266073] 
dist 142=[-.00914959194723111073,.00091760044056570983] 
dist 143=[-.00983174422397066414,-.00108747978874172017] 
dist 144=[-.01015350653532672668,-.00142507890581358025] 
dist 145=[-.01026088223974414854,-.00374084613075803863] 
dist 146=[-.01023886693681117328,-.00409769411794129903] 
dist 147=[-.00987312245660706456,-.00475755299738316791] 
dist 148=[-.00978250622306662582,-.00486897497868971468] 
dist 149=[-.00805516421759668329,-.00495168157233615200] 
dist 150=[-.00786631246098775088,-.00480538269135640009] 
dist 151=[-.0075419215975802524 ,-.00353239712474404544] 
dist 152=[-.00745489355317007329,-.00143157891538465338] 
dist 153=[-.00613162706525691882,.00067600800110672130] 
dist 154=[-.00581115337657553465,.00209194388180282595] 
dist 155=[-.00546686559701406235,.00324490326676823512] 
dist 156=[-.00529314708442349235,.00430845896846967723] 
dist 157=[-.00194057090024182316,.00520817000247183515] 
dist 158=[-.00167656495950543505,.00571810771482311774] 
dist 159=[-.00111165070095030145,.00603251780352413503] 
dist 160=[-.00095723885892706986,.00610492260457644639] 
dist 161=[-.00037200663614417836,.00439547821129656035] 
dist 162=[-.00025005888598824782,.00473586231372867549] 
dist 163=[-6.32304352872220278140e-05,.00494864266737947566] 
dist 164=[-1.43117319624026321860e-05,.00500197018059366099] 
dist 165=[.00170173007687038682,.00189224396434940142] 
dist 166=[.00154582947356054723,.00179125230675500248] 
dist 167=[.00119473217103079556,.00171394918529429100] 
dist 168=[.00066247925903378712,.00168919420930569566] 
dist 169=[.00012788329588436251,.00131478884390830819] 
dist 170=[-.00023253239785683597,.00124331083908276858] 
dist 171=[-.00052743798988455468,.00117999173816126383] 
dist 172=[-.00080195325417846534,.00115525659532179131] 
dist 173=[-.00103597931979719511,.00016537757162335899] 
dist 174=[-.00117013942386255003,4.61943192359328870300e-05] 
dist 175=[-.00125436259519936438,-.00022950660124083486] 
dist 176=[-.00129013634292295694,-.00027275889067113039] 
dist 177=[-.00129882489466171168,-.00059221196157277754] 
dist 178=[-.00129410086188088770,-.00064009771163284210] 
dist 179=[-.00124650882873322779,-.00072799505405390382] 
dist 180=[-.00123260607684067281,-.00074201860976049902] 
dist 181=[-.00102200675647316881,-.00074706249784082294] 
dist 182=[-.00097028957555367279,-.00066343609824990016] 
dist 183=[-.00091420313346880980,-.00047117036148005648] 
dist 184=[-.00090563833417513996,-.00016115269849000696] 
dist 185=[-.00072173327941361992,.00014943878747823659] 
dist 186=[-.00067873282396168496,.00035767996557471202] 
dist 187=[-.00064645214721723834,.00052684150308190076] 
dist 188=[-.00063909512325573065,.00068227017379544000] 
dist 189=[-.00010988249532952955,.00081337054133361194] 
dist 190=[-6.00726050497575162170e-05,.00088593738785675402] 
dist 191=[5.34448893640051507090e-05,.00092818275781714082] 
dist 192=[7.39286806559231938490e-05,.00093883056231341954] 
dist 193=[.00020148154524060677,.00047882222259016933] 
dist 194=[.00022178984806430424,.00048101489720090547] 
dist 195=[.00025680597532595198,.00048524163027941976] 
dist 196=[.00023609025369539264,.00049223795784273541] 
dist 197=[.00020513242678756813,.00026789403696079622] 
dist 198=[.00017040039208766647,.00026166067735295502] 
dist 199=[.00012695061985974253,.00025353142323115084] 
dist 200=[4.82801408683604105130e-05,.00024865877944530461] 
dist 201=[-3.55678768266393815670e-05,.00021797043297675503] 
dist 202=[-9.18616604479416143580e-05,.00020987757348152084] 
dist 203=[-.00013768232760632451,.00019269269693183756] 
dist 204=[-.00017994653969078460,.00018685255524003407] 
dist 205=[-.00021571791371477185,8.96279987465818948550e-05] 
dist 206=[-.00023575847584756735,7.51719455690447707830e-05] 
dist 207=[-.00024774426623066132,4.42186323164139473270e-05] 
dist 208=[-.00025153374808357448,3.58635495122441348710e-05] 
dist 209=[-.00025127967759927362,4.67841678890387534650e-06] 
dist 210=[-.00024906168710502102,-1.74414372159828494830e-06] 
dist 211=[-.00024158539135673700,-1.04992165171480468330e-05] 
dist 212=[-.00022555803865142197,-1.23772462530279996050e-05] 
dist 213=[-.00013642654957041541,-1.23773776868421497920e-05] 
dist 214=[-.00012921944195681270,-1.06207202286677567700e-05] 
dist 215=[-.00012172236752885959,-7.27977022406673100140e-06] 
dist 216=[-.00011802438372582840,4.16020737673108513830e-06] 
dist 217=[-4.25826992375691320770e-05,3.00435958472916698090e-05] 
dist 218=[-3.68247640523606126670e-05,4.99572233805129021390e-05] 
dist 219=[-2.47122782369505463930e-05,6.70567267002074356910e-05] 
dist 220=[-2.11118186770808660520e-05,8.28199526297231783860e-05] 
dist 221=[-8.27829321836191298900e-06,9.61553631171324750700e-05] 
dist 222=[-5.60814083240631217040e-06,.00010361509500617255] 
dist 223=[-1.45182219143390197100e-06,.00010832991524343192] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 2, 1, 0, 2] 
dist 0=[119.35090765739097169   ,119.35090765739097169   ] 
dist 1=[117.92136773711832972   ,120.38356060871000272   ] 
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dist 177=[-.00145603573522694113,-2.85084658995514161050e-05] 
dist 178=[-.00139153453078751324,-9.87173315181760447170e-05] 
dist 179=[-.00150742300147240927,-.00048117976895574940] 
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dist 191=[-3.81239067576621031470e-05,.00040591565410831497] 
dist 192=[1.07282018695965932160e-05,.00040334964577107576] 
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dist 197=[-6.48779085328087604020e-06,.00033623430105320314] 
dist 198=[-7.13796756784120126770e-05,.00034335547084888550] 
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dist 201=[-.00021473792069010662,.00032848297813504692] 
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dist 205=[-.00025761553542569238,.00024238901877603241] 
dist 206=[-.00025614747506515589,.00023566238408210921] 
dist 207=[-.00024546983490186272,7.82518636973739702360e-05] 
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dist 209=[-.00019944725357071625,1.15708720941260829780e-05] 
dist 210=[-.00019516530422458095,1.28036855304700840070e-06] 
dist 211=[-.00023152653253552154,-4.78726605128178310040e-05] 
dist 212=[-.00025164880473826734,-3.01292093580560000000e-06] 
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dist 217=[-7.57538697271678088990e-05,.00014351787199420038] 
dist 218=[-7.52104341092924563800e-05,.00015457796947997086] 
dist 219=[-6.04262876927354497940e-05,.00016143366003080353] 
dist 220=[-5.77817154887709190670e-05,.00016316859989218032] 
dist 221=[-5.41249606377173807780e-05,4.44173337008876069420e-05] 
dist 222=[-5.34879368435813012660e-05,4.41574593712869607480e-05] 
dist 223=[-2.25840255746365137630e-05,4.34099364902516503040e-05] 
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dist 226=[-6.94006034947278030360e-06,4.88855508637915455420e-05] 
dist 227=[2.52132628084978216970e-06,5.72964322170164654550e-05] 
dist 228=[-2.97265806235186778560e-06,6.19946332412479546120e-05] 
dist 229=[-1.68729203225435932060e-05,6.47873868879760113210e-05] 
dist 230=[-2.62070149346716282770e-05,6.56321274013005564810e-05] 
dist 231=[-3.38078947188110733000e-05,6.54201971831241050110e-05] 
dist 232=[-4.08261192318871243940e-05,6.48993181235222343630e-05] 
dist 233=[-4.67726401945243050120e-05,6.23800018351093100220e-05] 
dist 234=[-5.01181338828762539310e-05,6.12392046278336552660e-05] 
dist 235=[-5.21379534623043693360e-05,5.20403556437612464450e-05] 
dist 236=[-5.28206734559182354600e-05,4.97141342993320193290e-05] 
dist 237=[-5.28334756293398164450e-05,4.58649297181136862800e-05] 
dist 238=[-5.23257389252626488490e-05,4.46124077274503893730e-05] 
dist 239=[-5.11247397327460387510e-05,1.54536659529972722560e-05] 
dist 240=[-5.04115688370204518810e-05,1.14974461652049064520e-05] 
dist 241=[-4.59331150671583335020e-05,6.35488474335126629500e-06] 
dist 242=[-4.47539540245984061920e-05,5.43217287767524396860e-06] 
dist 243=[-4.07925812147078745630e-05,1.98618032402460627400e-06] 
dist 244=[-3.99504453814197394540e-05,1.25797267028061441420e-06] 
dist 245=[-3.02144787393019450580e-05,2.59194311300749231130e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 0, 0, 2] 
dist 0=[116.75520187887645624   ,116.75520187887645624   ] 
dist 1=[110.86282926951667963   ,120.67046493205387693   ] 
dist 2=[100.89258508075297688   ,122.77453395891396201   ] 
dist 3=[90.431486885547637767  ,123.85773654592989329   ] 
dist 4=[82.580192910416040106  ,123.72188993634423023   ] 
dist 5=[75.255874033960353262  ,122.87318741180295450   ] 
dist 6=[66.873668949050320026  ,122.14156449843366740   ] 
dist 7=[58.559963630847636333  ,117.52749208020577217   ] 
dist 8=[51.493826906722530138  ,110.64682940133432172   ] 
dist 9=[44.027706418573599566  ,88.223398407498462588  ] 
dist 10=[34.098487789147489746  ,86.854746662447320536  ] 
dist 11=[24.463372023605306391  ,67.258781300883367081  ] 
dist 12=[18.163065122417140558  ,63.224041157730167533  ] 
dist 13=[13.092383138840893897  ,59.348605951525386614  ] 
dist 14=[8.3611517612212346791 ,58.592318449599022598  ] 
dist 15=[4.1883453534812816168 ,32.854115154853788335  ] 
dist 16=[1.3431532391487624307 ,25.324266916808930349  ] 
dist 17=[-5.1282836594205494587 ,4.2124897400497928634 ] 
dist 18=[-12.789521872366057695  ,3.8840798680346168179 ] 
dist 19=[-19.308570915167475595  ,3.2543756700110293711 ] 
dist 20=[-23.119865916597840164  ,3.1137434769162521893 ] 
dist 21=[-25.643543342109176805  ,2.9985944506053409513 ] 
dist 22=[-27.048643685631786694  ,2.9366906934809813089 ] 
dist 23=[-27.787606671404251376  ,2.7097463289630730071 ] 
dist 24=[-27.837297637882135566  ,2.6042639510814237948 ] 
dist 25=[-27.263651116038908306  ,2.2614945521116535548 ] 
dist 26=[-26.897354075884282603  ,2.0873839133761969559 ] 
dist 27=[-23.258971813700231595  ,-.20396648956512980832] 
dist 28=[-22.303027645645479421  ,-.67173857831997375263] 
dist 29=[-20.880872554829229036  ,1.3313287989173253459 ] 
dist 30=[-20.347391693876929346  ,3.3402213303081642619 ] 
dist 31=[-7.5626696855905878424 ,5.2000399512810854144 ] 
dist 32=[-5.8966338770614263981 ,7.2956579488174407826 ] 
dist 33=[-4.2576997857343771658 ,10.610252326798618646  ] 
dist 34=[-4.1076069148733797565 ,14.058759948633731714  ] 
dist 35=[-1.6608542922354849722 ,16.966364441000131653  ] 
dist 36=[-1.3101239887700635059 ,18.573708302840644307  ] 
dist 37=[-.58826615325925091294,19.506479615262432326  ] 
dist 38=[-.40324272383613157188,19.735697402740177402  ] 
dist 39=[.23917332290308925351,9.7601358369263751351 ] 
dist 40=[.37630438359475104426,9.7332287335852304265 ] 
dist 41=[.49218398853800809695,5.7845893945674318799 ] 
dist 42=[.46414261038948628535,5.7636023712946723153 ] 
dist 43=[-.24659131330385690386,5.3309932249642211811 ] 
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dist 45=[-2.9658747235977031650 ,4.9687513341062479052 ] 
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dist 210=[-.00025996559235843744,6.56742176419276776910e-05] 
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dist 217=[-5.42090558309986670980e-05,3.71639165606046400040e-05] 
dist 218=[-4.68466977767327779110e-05,6.40198185293534263530e-05] 
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dist 222=[-7.02548037890940884820e-06,.00013254997952222006] 
dist 223=[-1.78705559634862103110e-06,.00013851767200625558] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 2, 2, 0, 1, 2] 
dist 0=[128.80352864091710957   ,128.80352864091710957   ] 
dist 1=[127.62534916228358010   ,129.14110940537359070   ] 
dist 2=[123.28855988441023707   ,129.40921971329566398   ] 
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dist 4=[109.85618294149188832   ,121.66257152106156629   ] 
dist 5=[99.930895997603370883  ,119.49118286393932106   ] 
dist 6=[84.317601019857315853  ,117.52226954579267779   ] 
dist 7=[68.309432883622385802  ,116.19349544713977962   ] 
dist 8=[56.808278552874139948  ,90.730660588073591545  ] 
dist 9=[46.572978316127760482  ,87.088805927923127561  ] 
dist 10=[35.583193973965808432  ,82.916131699396211746  ] 
dist 11=[25.100980069526703230  ,81.138675030002009362  ] 
dist 12=[16.870535866619524004  ,48.964109892522673145  ] 
dist 13=[8.7706420859424320954 ,46.757797582706455257  ] 
dist 14=[-1.2165303588368063502 ,41.790758655804338738  ] 
dist 15=[-10.508199301465765959  ,41.074534009721023980  ] 
dist 16=[-15.846946353839648482  ,3.9755078576985833981 ] 
dist 17=[-20.802291854213018749  ,1.0248451720092286825 ] 
dist 18=[-25.558506261614605593  ,-3.4070597586285935156 ] 
dist 19=[-29.988030288623835373  ,-4.2082402508704400936 ] 
dist 20=[-33.561311613320350238  ,-9.9586423205861410399 ] 
dist 21=[-34.915594616997646842  ,-9.6727591385612375450 ] 
dist 22=[-35.405621338044002109  ,-8.1382784187117184490 ] 
dist 23=[-35.526521031175868761  ,-4.6233027871157469681 ] 
dist 24=[-31.175414769049172185  ,-.74038916771310437605] 
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dist 27=[-29.193584859271792399  ,8.3348015132323629196 ] 
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dist 30=[1.6388274815363030551 ,16.459861964618954413  ] 
dist 31=[2.8414243561862109479 ,19.466774578564280285  ] 
dist 32=[9.8698310942804694378 ,22.141088376325104818  ] 
dist 33=[10.239770422372103136  ,23.289926511517671152  ] 
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dist 35=[8.5527893040770194289 ,23.851008047284024425  ] 
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dist 37=[5.0206958862014211418 ,20.830010518476949190  ] 
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dist 44=[-9.9671557598664108036 ,4.9606062261187612192 ] 
dist 45=[-10.738427049236604704  ,3.8567206692916176119 ] 
dist 46=[-12.000219373578580871  ,1.3451638292399606858 ] 
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dist 48=[-13.602580225213503307  ,-.28439084936224462382] 
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dist 50=[-13.692680333713806799  ,.32220005684021906358] 
dist 51=[-13.514139576680293828  ,.98438558948771079943] 
dist 52=[-12.068476341221649579  ,1.8156900186437483758 ] 
dist 53=[-11.641404860722995491  ,2.9105442177084786247 ] 
dist 54=[-10.897461480838280366  ,4.6189945239285164040 ] 
dist 55=[-10.644920554684247445  ,6.3480800841824196460 ] 
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dist 58=[-3.1040615096028851815 ,9.4182496124993833570 ] 
dist 59=[-3.0546695955746063635 ,10.210881787095395153  ] 
dist 60=[-.62038998416381471171,10.677928793070807139  ] 
dist 61=[-.32904481525666678906,10.986742675973357559  ] 
dist 62=[.35920385654206001759,11.151541423069569255  ] 
dist 63=[.45905376252007648316,11.208868189340336508  ] 
dist 64=[1.2994842486683266688 ,2.5356930739170101805 ] 
dist 65=[1.3628640128451186213 ,2.5669421040797070864 ] 
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dist 67=[1.0884166505874730743 ,2.5424241111268615356 ] 
dist 68=[.89850359669033947652,2.2574212697477209981 ] 
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dist 70=[.27082030610068120554,2.1905797655923450179 ] 
dist 71=[-.11346288222666475192,2.1723371103080014831 ] 
dist 72=[-.37264654923876403149,1.8018058433157041549 ] 
dist 73=[-.58434273431163846427,1.7099595929460792742 ] 
dist 74=[-.78018001548181501244,1.6242480675845788923 ] 
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dist 76=[-1.0376473117194304916 ,.43146314018710331553] 
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dist 88=[-.41913421761717400402,.14265075745236602706] 
dist 89=[-.39700316510461484149,.3768937226304474467 ] 
dist 90=[-.38226814406683675806,.5675398781360049097 ] 
dist 91=[-.37880836849075281209,.74312499198724328536] 
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dist 93=[-.00859782341827958299,.97354017426414943821] 
dist 94=[.08126919876610072050,1.0213838753250704386 ] 
dist 95=[.09484725825614638505,1.0333951209577257997 ] 
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dist 100=[.07987163762642273853,.26833240583016494428] 
dist 101=[.05246762571158132825,.2677281697392886285 ] 
dist 102=[.01045999021575689708,.26030005771506718489] 
dist 103=[-.03184252085221811505,.25636698607062887326] 
dist 104=[-.06041927912937638102,.22001963171636359393] 
dist 105=[-.08383753889965866390,.21055563390212488323] 
dist 106=[-.10566602583421272726,.19625320520537571939] 
dist 107=[-.12496802366889522466,.19100984656376343885] 
dist 108=[-.15681720351617140921,.06498966995782151962] 
dist 109=[-.17577587080971152042,.04826900870214004053] 
dist 110=[-.18796786982624326128,.01076124835538011572] 
dist 111=[-.19377901248987639371,.00263919072403691676] 
dist 112=[-.19574487989238200093,-.00568569456344743208] 
dist 113=[-.19520680303692507481,-.00266678077075930896] 
dist 114=[-.20425671877415478336,.00424608488889956551] 
dist 115=[-.20661840563463422194,.01294213485304060861] 
dist 116=[-.15543785630581803522,.02304180335275295583] 
dist 117=[-.14775526875701580879,.03589172216706715042] 
dist 118=[-.13894850309625356552,.05550784393118270286] 
dist 119=[-.13472659247858244041,.07525080118510990326] 
dist 120=[-.04948933625285174245,.08860517468249092971] 
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dist 190=[-9.76897156913997231810e-05,.00163043363956962792] 
dist 191=[-6.94512968461960415380e-05,.00164930206693735156] 
dist 192=[5.20129235333795823710e-05,.00066747194181869757] 
dist 193=[7.47205884931123250470e-05,.00072438172765980585] 
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dist 198=[9.31189627083078410440e-05,.00073416500203214707] 
dist 199=[-4.77583586779698757030e-05,.00072068775655086757] 
dist 200=[-.00020833901951605133,.00061406385459242002] 
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dist 202=[-.00040414804285489945,.00054143087583321581] 
dist 203=[-.00048542024237980670,.00052678915112209212] 
dist 204=[-.00055434309289436091,.00018590894355836655] 
dist 205=[-.00059322648926926979,.00013949767326984559] 
dist 206=[-.00061684156268006456,3.73137552789905627260e-05] 
dist 207=[-.00062514053982540652,1.31586380855427447020e-05] 
dist 208=[-.00062560501707111069,-6.87949107499454385790e-05] 
dist 209=[-.00061971648327347798,-8.05814726333753975330e-05] 
dist 210=[-.00060551294241615796,-9.93472936104427557690e-05] 
dist 211=[-.00057580732572073625,-.00010308368364632647] 
dist 212=[-.00025165397583930915,-.00010320443588211581] 
dist 213=[-.00024047866161903663,-.00010031107117923253] 
dist 214=[-.00022288431883602942,-9.47205315774165430700e-05] 
dist 215=[-.00021681063323908222,-3.24372203013522021400e-05] 
dist 216=[-8.33179131046114216620e-05,4.66499228036080614240e-05] 
dist 217=[-7.96324460391204092320e-05,9.96356765665113910600e-05] 
dist 218=[-7.39779778401325232860e-05,.00014264902499898566] 
dist 219=[-7.19682757154295161360e-05,.00018213835962281230] 
dist 220=[-2.41594701890166342490e-05,.00021543680706706030] 
dist 221=[-1.77789942107637217470e-05,.00023386763273210296] 
dist 222=[-3.48896202834922499640e-06,.00024459838462240897] 
dist 223=[-3.93592875693082970190e-07,.00024731990490930541] 
dist 224=[1.52325972900873952360e-05,6.93309137178438259180e-05] 
dist 225=[1.79468323130744598180e-05,7.56277199776569516040e-05] 
dist 226=[2.25475030629713745820e-05,7.94060239598021182210e-05] 
dist 227=[2.34448273325882203670e-05,8.06303625026797583610e-05] 
dist 228=[2.37056897041116971630e-05,8.05760003977086416010e-05] 
dist 229=[2.19879428203160923710e-05,7.98866808689353928150e-05] 
dist 230=[9.54423456521814594020e-06,7.74874196284349848950e-05] 
dist 231=[-1.07168615682692076890e-05,7.60826081645749793510e-05] 
dist 232=[-3.10083628360708981770e-05,6.73007069905053876950e-05] 
dist 233=[-4.46217891813234858220e-05,6.49944013806462980010e-05] 
dist 234=[-5.56943499408617290170e-05,5.95249697083724627550e-05] 
dist 235=[-6.58967181739312254950e-05,5.75467899115596586780e-05] 
dist 236=[-7.45265363741863647310e-05,3.10023171836051362610e-05] 
dist 237=[-7.93548959411123380220e-05,2.68263965441378132650e-05] 
dist 238=[-8.22351238057993690150e-05,1.80799089387977231560e-05] 
dist 239=[-8.31294123465393357410e-05,1.57238700651644645570e-05] 
dist 240=[-8.29150832860949326800e-05,7.04361467253110199530e-06] 
dist 241=[-8.21843364316678395270e-05,5.14930928850438180130e-06] 
dist 242=[-7.94444968421330165780e-05,2.83342864669394837870e-06] 
dist 243=[-7.36068106320954289760e-05,2.37391680845939852700e-06] 
dist 244=[-2.93263582589740301170e-05,2.44666706204348958260e-06] 
dist 245=[-2.82142661970359548340e-05,2.99440973059989798320e-06] 
dist 246=[-2.59301967190280071060e-05,3.98336557233743847690e-06] 
dist 247=[-2.51703117079920932210e-05,5.80820016406843093100e-06] 
dist 248=[-1.24129012692797042140e-05,9.21783066520216904950e-06] 
dist 249=[-1.06568857734788646790e-05,1.55917653036625362380e-05] 
dist 250=[-6.93101412342816935840e-06,2.07658608498369122410e-05] 
dist 251=[-5.92209526318690547120e-06,2.55163220661255867100e-05] 
dist 252=[-2.15680074964716873880e-06,2.95227035461935311070e-05] 
dist 253=[-1.36030128735161837590e-06,3.17421726382693525420e-05] 
dist 254=[-2.75636307522104670920e-07,3.30466491640914559250e-05] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 0, 0, 0, 2] 
dist 0=[110.45071975277800008   ,110.45071975277800008   ] 
dist 1=[107.17267224121498664   ,111.43140613103233265   ] 
dist 2=[103.21668595936752881   ,112.04715214615449598   ] 
dist 3=[99.652388345789189133  ,112.52602244980256073   ] 
dist 4=[95.730635056544792378  ,112.29858141406582124   ] 
dist 5=[90.340764459286285965  ,109.07800288093084067   ] 
dist 6=[84.456110545745438241  ,107.87807104471669064   ] 
dist 7=[78.401373386691694707  ,106.10466308425329907   ] 
dist 8=[66.230417287240159951  ,105.29085706595886305   ] 
dist 9=[57.099209896757740401  ,81.345867395129792238  ] 
dist 10=[48.580046399022342385  ,77.997122715900467698  ] 
dist 11=[38.825109841465141055  ,69.024423136484724504  ] 
dist 12=[29.145452148200173248  ,67.598724623963423805  ] 
dist 13=[20.910299314363355209  ,51.436769255445794487  ] 
dist 14=[12.204038057686218129  ,48.212788259478355949  ] 
dist 15=[.62388325236280881642,44.525270192329222196  ] 
dist 16=[-10.362826263779339082  ,43.486518969000628998  ] 
dist 17=[-16.714272522702009753  ,19.089624768636746930  ] 
dist 18=[-20.908547206124133575  ,7.9538082346767609200 ] 
dist 19=[-23.304631258985505443  ,4.7425378864723121180 ] 
dist 20=[-24.850026019974716982  ,1.3429200872445765994 ] 
dist 21=[-25.649487892113630578  ,.54634555820389594885] 
dist 22=[-26.604519721921119321  ,-1.7850394671199341996 ] 
dist 23=[-27.837558309966697810  ,-2.1772857862400620163 ] 
dist 24=[-28.395093815671356815  ,-2.0214135012175618872 ] 
dist 25=[-28.522795572893810930  ,-1.0954353246695356805 ] 
dist 26=[-17.315259029618835956  ,-.04045521142337532834] 
dist 27=[-16.820681306838028334  ,.63050389129042801121] 
dist 28=[-16.727943843703289783  ,2.2203680870405250757 ] 
dist 29=[-13.858704881147128361  ,4.6628669508721986254 ] 
dist 30=[-13.163333345369646005  ,6.8394994602862781810 ] 
dist 31=[-12.616795795379796481  ,9.1657045722773181358 ] 
dist 32=[-12.442455883644346226  ,11.206846288209182053  ] 
dist 33=[-2.4643579101428485788 ,12.254464635648989394  ] 
dist 34=[-1.2853159091275993865 ,12.783554231959770288  ] 
dist 35=[.26579500498416587378,12.870209886226417340  ] 
dist 36=[-.04732880681730299063,12.407128287123198863  ] 
dist 37=[-.40104182747555477349,12.141133755198991314  ] 
dist 38=[-.74041163776754317491,11.733740065501813212  ] 
dist 39=[-.99735112231696448416,11.524149640469763696  ] 
dist 40=[-1.2363827672385623921 ,8.0841099109965125167 ] 
dist 41=[-2.4320084713283514213 ,8.2344110813459082890 ] 
dist 42=[-4.4153431469127951768 ,8.2237268491221524844 ] 
dist 43=[-6.2684880859984535175 ,8.0405459998201374518 ] 
dist 44=[-7.8421247554684074968 ,7.9012486775530576910 ] 
dist 45=[-8.7173174156389563949 ,6.9232076233445361477 ] 
dist 46=[-9.2281413155169465370 ,6.6578672997490168213 ] 
dist 47=[-9.3569516576986522804 ,6.1737550423429196005 ] 
dist 48=[-2.9517318231369906206 ,6.0229915001390824122 ] 
dist 49=[-3.1511862480662035175 ,2.8891082783735631280 ] 
dist 50=[-3.2468813117675685252 ,2.5075639192962373556 ] 
dist 51=[-4.1092565350094803142 ,1.6843751961177676166 ] 
dist 52=[-5.1242516682965279601 ,1.4582231162501447760 ] 
dist 53=[-5.9796924843460048321 ,1.4669632250404200692 ] 
dist 54=[-6.4518605067031897726 ,1.6509651226232212068 ] 
dist 55=[-6.7249228484043179446 ,1.7653804930910107928 ] 
dist 56=[-6.7898586973192498919 ,1.8416008578813885250 ] 
dist 57=[-1.3379802024918146275 ,1.8531080754907722135 ] 
dist 58=[-.05026671554002547895,.38249177857763201184] 
dist 59=[.03970966247265820598,.81980326621347326192] 
dist 60=[.19252773552700145222,1.2067599036645891939 ] 
dist 61=[.19713255752834779604,1.4527422946820847657 ] 
dist 62=[.194924578231309452  ,1.6376630536758283602 ] 
dist 63=[.18029719486676107478,1.7825619030315218040 ] 
dist 64=[.15481079964318398735,1.8859933462803892234 ] 
dist 65=[.10887629359856792964,1.9088327426396697100 ] 
dist 66=[.06056805515233978003,1.8983984638593833519 ] 
dist 67=[.02564972438406093235,1.8888491958823821281 ] 
dist 68=[-.00521726733506051379,1.6165270640028607221 ] 
dist 69=[-.03750109886442159073,1.5434350638073177010 ] 
dist 70=[-.06725515378108214290,1.4798186125478377841 ] 
dist 71=[-.08811510073666259288,1.4442963889326590801 ] 
dist 72=[-.10599297864441741738,.4676676760852717575 ] 
dist 73=[-.31865611513598808835,.36327939552539556262] 
dist 74=[-.54660688989092514126,.1202560125148355839 ] 
dist 75=[-.76146889881293838131,.07407573724002705178] 
dist 76=[-.9587863428448621585 ,-.09947189035417385377] 
dist 77=[-1.0657036607341513096 ,-.09145672254059191643] 
dist 78=[-1.1258002693772840456 ,-.07921220995563940147] 
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dist 80=[-.45400661978431175887,-.03962061403467243877] 
dist 81=[-.46186077517235290199,-.00325861120810805023] 
dist 82=[-.46216896860059171596,.0336833018155450698 ] 
dist 83=[-.46223907906164813939,.05882292989367884227] 
dist 84=[-.39591132629045497477,.07954987655313471912] 
dist 85=[-.37884306924535729673,.09899337257176080320] 
dist 86=[-.36819484738596261894,.11608292614796944767] 
dist 87=[-.36547150777670328661,.12631731957572695038] 
dist 88=[-.07732689702947323246,.13202132309663430194] 
dist 89=[-.04315436093985035818,.1329181389933090948 ] 
dist 90=[-.02282589775480976648,.07431277296123917497] 
dist 91=[-.02229102634143142028,.13157891099677711626] 
dist 92=[-.02539451331850080613,.18142038884461646663] 
dist 93=[-.03416942595269767337,.21176652637072830544] 
dist 94=[-.04565520244455272834,.23306422554940791364] 
dist 95=[-.05952096412784686915,.24700515747507759756] 
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dist 97=[-.10520231559090888522,.25674111195668045573] 
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dist 99=[-.15214071276250443564,.24991507854781859604] 
dist 100=[-.16773785475090330975,.22069532326185006227] 
dist 101=[-.18236628092121456467,.21241453726871055257] 
dist 102=[-.19489048447027820679,.19823017099345309778] 
dist 103=[-.2021367315945175384 ,.19345807712446399533] 
dist 104=[-.20676198495138975391,.07669708518911614876] 
dist 105=[-.20888423195371259412,.06068452687008494720] 
dist 106=[-.20918529282976334761,.02472707302351093211] 
dist 107=[-.20715795521366919201,.01650941221091049716] 
dist 108=[-.20215757796416415394,.01111579505777788285] 
dist 109=[-.19912969016648702078,.01195152777159295403] 
dist 110=[-.18760321614254548001,.01325233946906873806] 
dist 111=[-.18984047422085043843,.01506018954999594000] 
dist 112=[-.05776695088627716600,.01754144492506055684] 
dist 113=[-.05817556880272817632,.02151543253680818531] 
dist 114=[-.05718618637920120733,.02557349720743318758] 
dist 115=[-.05691831835852699160,.02838904825008259993] 
dist 116=[-.04793210587535363992,.03077340792592563318] 
dist 117=[-.04563471885375250479,.03312134166800638452] 
dist 118=[-.04387123547998698394,.03543864941982002640] 
dist 119=[-.04313872784650740162,.03770669688535263979] 
dist 120=[-.00809525650013557976,.03879835434276183010] 
dist 121=[-.00389858736979887852,.03894784992063941077] 
dist 122=[-.00286670353461306683,.01253254661519742711] 
dist 123=[-.00280695958406223316,.01953220281701444259] 
dist 124=[-.00257841234570282251,.02554727267365700581] 
dist 125=[-.00254549893808660552,.02907728297389380932] 
dist 126=[-.00191941638962402522,.03139657264463094985] 
dist 127=[-.00178292423398741113,.03260619213159379742] 
dist 128=[-.00166517792165866886,.03312022194923625093] 
dist 129=[-.00164164877467787578,.03310295527797141850] 
dist 130=[4.46939361336530657490e-05,.03203679740819581697] 
dist 131=[.00024044564200537519,.03175828415896964699] 
dist 132=[.00068381052008558345,.02627595639494359429] 
dist 133=[.00075261517872152569,.02492350864876096118] 
dist 134=[.00122870382796777944,.02365023010054458934] 
dist 135=[.00130038192620611088,.02305101286429466250] 
dist 136=[-.00200472938002085526,.00615593337172383737] 
dist 137=[-.00661122769279042317,.00439506793872309422] 
dist 138=[-.01036631579410025134,.00133156407490380286] 
dist 139=[-.01383587720827991958,.00130830482942936487] 
dist 140=[-.01677389962488562564,.00122667621405170203] 
dist 141=[-.01848926929447582952,.00120238059484320377] 
dist 142=[-.01950549298291540463,.00097976993820174040] 
dist 143=[-.01974139145412095590,.00092791262114052282] 
dist 144=[-.00770752168183510073,.00085014855312852761] 
dist 145=[-.00772712434350331060,.00082359195264682436] 
dist 146=[-.00750148749195266575,.00022350296400518707] 
dist 147=[-.00746871656995526230,.00014430976253996414] 
dist 148=[-.00612914045895781903,-2.91526394699989488160e-05] 
dist 149=[-.00580182718171151987,-6.79632101219683459130e-05] 
dist 150=[-.00558214332821432620,-.00024307311154346254] 
dist 151=[-.00553082245246383494,-.00027460017841129375] 
dist 152=[-.00099588426432607607,-.00031331156592972650] 
dist 153=[-.00100662617934031410,.00050786495229473379] 
dist 154=[-.00029957500023793785,.00144714290035430937] 
dist 155=[-.00029418197439874022,.00232572694209431087] 
dist 156=[-.00027266600784376323,.00307747877421718355] 
dist 157=[-.00026910202106136011,.00351326374864027226] 
dist 158=[-.00020740210339212973,.00379297026345066725] 
dist 159=[-.00019371078174676295,.00392513518732680232] 
dist 160=[-.00018083716620789120,.00397476197868734580] 
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dist 162=[-6.91270624046192384900e-06,.00385150619333060689] 
dist 163=[1.33104441064200638640e-05,.00379269157426164775] 
dist 164=[5.90566066638654184050e-05,.00325245044578015536] 
dist 165=[6.65543556297686156040e-05,.00311203055015256889] 
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dist 168=[-.00047770203849004605,.00095682086461523570] 
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dist 170=[-.00171795539725968926,.00015606587311651314] 
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dist 172=[-.00266034544541487804,.00014462505054865780] 
dist 173=[-.00289908007261636795,.00014278944979811920] 
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dist 176=[-.00093964495175508132,9.99590581941997116960e-05] 
dist 177=[-.00093909311243998615,9.73079719458629287140e-05] 
dist 178=[-.00090539437468033602,1.84608060471869059080e-05] 
dist 179=[-.00090035287933721483,1.05192963630167117250e-05] 
dist 180=[-.00073300775881525681,-7.05031029578276489260e-06] 
dist 181=[-.00069615359036277771,-1.07174863212648305480e-05] 
dist 182=[-.00066271548673843301,-2.88852847615432599430e-05] 
dist 183=[-.00065578019740805446,-3.20263339948155356640e-05] 
dist 184=[-.00013595541163096357,6.39618529821512718360e-06] 
dist 185=[-9.18550556679842749320e-05,.00015126989381663089] 
dist 186=[-3.66180914428642840520e-05,.00026964180309881993] 
dist 187=[-3.60280252806083495790e-05,.00037955620811741473] 
dist 188=[-3.37284347058030412430e-05,.00047307620935363075] 
dist 189=[-3.31800770180686251810e-05,.00052635887595882768] 
dist 190=[-2.64836404677458406830e-05,.00055938753566129109] 
dist 191=[-2.49453125821995424040e-05,.00057249525124724054] 
dist 192=[-2.30844215074392042120e-05,.00057434642057862870] 
dist 193=[-2.22899791593478205200e-05,.00057162353071692322] 
dist 194=[-3.71676149906997820230e-06,.00054898403993631669] 
dist 195=[-1.36803038933487482970e-06,.00054275872395649815] 
dist 196=[3.87242080178866987290e-06,.00044744466714760698] 
dist 197=[4.88257672504164454870e-06,.00042424848535147139] 
dist 198=[1.03920293498967497060e-05,.00039936375869300268] 
dist 199=[9.51918128470190000000e-06,.00038674508880965354] 
dist 200=[-9.47307965240303316160e-05,.00014393293257297951] 
dist 201=[-.00016474760050027551,.00012478595358988181] 
dist 202=[-.00022175920497406516,8.36193900017486777570e-05] 
dist 203=[-.00027437326352240320,7.23009970823582913840e-05] 
dist 204=[-.00031891789812389283,2.90168365807236630360e-05] 
dist 205=[-.00034389046238361443,2.12361776927070435830e-05] 
dist 206=[-.00036018934547049778,1.77089569592272065090e-05] 
dist 207=[-.00036408101681425653,1.68522040376650376500e-05] 
dist 208=[-.00012180946682348068,1.54359013568966264610e-05] 
dist 209=[-.00012152575828835110,1.49875967525732382470e-05] 
dist 210=[-.00011673936515871559,4.79902966282541199220e-06] 
dist 211=[-.00011599599299543959,3.42004925199331215430e-06] 
dist 212=[-9.39144454123215266380e-05,3.95448473104914609580e-07] 
dist 213=[-8.86460052470142258170e-05,-3.15094464369837817860e-07] 
dist 214=[-8.47529690903756181330e-05,-2.95501600947483260480e-06] 
dist 215=[-8.37512293438240109440e-05,-3.36303851334088598730e-06] 
dist 216=[-1.82325259641813522680e-05,-3.91006452496314343510e-06] 
dist 217=[-1.83520759296389058810e-05,1.12933265136375664190e-05] 
dist 218=[-1.80780662372804963170e-05,2.58978543881181001010e-05] 
dist 219=[-1.84597220720705761860e-05,3.94350462831494415260e-05] 
dist 220=[-1.92604193132210154330e-05,5.09393038025408919940e-05] 
dist 221=[-2.08214746477414824550e-05,5.74721756348641155880e-05] 
dist 222=[-2.27121223810779386090e-05,6.14947933418178004970e-05] 
dist 223=[-2.48215641453195239180e-05,6.30322797503599833760e-05] 
dist 224=[-2.74528965593845389820e-05,6.32628430814627294110e-05] 
dist 225=[-3.14158143086190917810e-05,6.29383851511583683790e-05] 
dist 226=[-3.53871631402969445790e-05,6.06526764686106510750e-05] 
dist 227=[-3.80520155379512596170e-05,5.97837799167154274570e-05] 
dist 228=[-4.02192536274498348290e-05,5.02965916786382386760e-05] 
dist 229=[-4.22148487870100009280e-05,4.71762069070779755170e-05] 
dist 230=[-4.39011797932624379190e-05,4.29176370214830491660e-05] 
dist 231=[-4.48404906342582371470e-05,4.17159895380699047170e-05] 
dist 232=[-4.53950017041988170980e-05,1.29609002661214825490e-05] 
dist 233=[-4.55534838109430938360e-05,9.86986082421314967280e-06] 
dist 234=[-4.54262001756152546590e-05,9.76863115479813686970e-06] 
dist 235=[-4.49130493606803560670e-05,9.63967377678573866170e-06] 
dist 236=[-4.38900147278357831970e-05,9.46114137676554045820e-06] 
dist 237=[-4.33169456384015185520e-05,9.33121809713223853510e-06] 
dist 238=[-3.98145690488169970850e-05,8.84163925219009329680e-06] 
dist 239=[-3.74324616526887880150e-05,8.65173010196119140780e-06] 
dist 240=[-1.52067596309270310530e-05,8.16193612813947071860e-06] 
dist 241=[-1.51389274311547891260e-05,7.95524667805753267240e-06] 
dist 242=[-1.45584487853630839360e-05,6.86113497458047514970e-06] 
dist 243=[-1.43929190182320769640e-05,6.55526097342661837040e-06] 
dist 244=[-1.19224274432473262030e-05,6.14237987495607648500e-06] 
dist 245=[-1.13186858857062439660e-05,5.97265249856225420950e-06] 
dist 246=[-1.06604297392384479600e-05,5.63204109490258932180e-06] 
dist 247=[-9.54802097616257799020e-06,5.51937317482407111740e-06] 
dist 248=[-2.74255240525515283240e-06,5.51745085403492251510e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 2, 0, 1] 
dist 0=[146.13704010658471626   ,146.13704010658471626   ] 
dist 1=[144.77146170004854858   ,146.22055880796722812   ] 
dist 2=[139.40810734365048633   ,146.48850700280172028   ] 
dist 3=[132.11598567678776402   ,146.68015554232938674   ] 
dist 4=[123.09011929797563305   ,140.87696781097588871   ] 
dist 5=[111.24188384683212751   ,134.90992746832918965   ] 
dist 6=[92.728188875756128134  ,132.46512962732046776   ] 
dist 7=[73.825914328859635489  ,124.01503985380994079   ] 
dist 8=[60.426747727841130519  ,122.64252655025616506   ] 
dist 9=[48.701114121347832042  ,101.04667802742092306   ] 
dist 10=[36.435064785012354958  ,96.314466488528900577  ] 
dist 11=[24.946761650809379593  ,91.832583187892281635  ] 
dist 12=[16.298275998964113721  ,90.529547003877740796  ] 
dist 13=[8.1413814692499165624 ,32.682085890178427793  ] 
dist 14=[-1.4188438346484901334 ,27.760822365821089868  ] 
dist 15=[-10.202748733532035357  ,9.9037434847695093717 ] 
dist 16=[-15.277836875754096353  ,7.4542343966180605352 ] 
dist 17=[-20.502330921178016486  ,-11.177543953945225793  ] 
dist 18=[-26.734756893150434914  ,-13.993703859618311157  ] 
dist 19=[-31.388760182273535490  ,-18.446362575947088951  ] 
dist 20=[-35.057491614978165458  ,-16.939232240338266539  ] 
dist 21=[-37.778863286867882133  ,-14.100701393330357925  ] 
dist 22=[-38.669139011418935341  ,-8.8728876660652499349 ] 
dist 23=[-38.775602097227959963  ,-3.4020168428203060589 ] 
dist 24=[-38.366090862894937093  ,.40676078579244036155] 
dist 25=[-34.484940839017379165  ,3.6034193270902468850 ] 
dist 26=[-33.300674205947344180  ,6.6566606766454798705 ] 
dist 27=[-31.421460896875174087  ,9.2757769709658306603 ] 
dist 28=[-30.705973231407458910  ,10.755551559576065231  ] 
dist 29=[-15.990912339792220920  ,11.618567553184302592  ] 
dist 30=[-14.263313605732996112  ,11.827544493311366895  ] 
dist 31=[-10.342832869081287505  ,15.802629079803749132  ] 
dist 32=[-9.2948744751547300725 ,20.545095806123486552  ] 
dist 33=[-4.5337401493871934948 ,24.889142178817615945  ] 
dist 34=[-3.6461109797016016283 ,27.248149823607273339  ] 
dist 35=[-1.6202454042464389738 ,28.556359356529710189  ] 
dist 36=[-1.2165306979762633193 ,28.799884490263505009  ] 
dist 37=[3.1625803110611746505 ,7.3969496933348429484 ] 
dist 38=[1.4144842770057667892 ,7.5278529241429605197 ] 
dist 39=[-.38099984626138886472,7.5219337141727444920 ] 
dist 40=[-1.6248154773197514506 ,7.4394361547505564499 ] 
dist 41=[-2.6720429958730441055 ,6.7114295766621330942 ] 
dist 42=[-3.6886592869907580691 ,6.4909423621427678842 ] 
dist 43=[-4.5786056320498049795 ,6.0757970720096636891 ] 
dist 44=[-5.1238299030293960754 ,5.9348892930958470926 ] 
dist 45=[-5.5088585194967556186 ,2.6456723732402713336 ] 
dist 46=[-5.7637889774939381878 ,2.1834277504619546241 ] 
dist 47=[-5.9248058476237240628 ,1.1391477964865699774 ] 
dist 48=[-5.9373948014711705915 ,.89319832968535200033] 
dist 49=[-5.8626800405602997589 ,-.3069966808160674650 ] 
dist 50=[-5.7919760290548892194 ,-.3926001638772156880 ] 
dist 51=[-5.2689255951460736411 ,-.3939284723181297900 ] 
dist 52=[-4.8494568090500136802 ,-.3231357398776324252 ] 
dist 53=[-2.5683130784352352474 ,-.1919016672423147337 ] 
dist 54=[-2.5160223403493428125 ,.0503939926840158320 ] 
dist 55=[-1.4469004431879819043 ,.30697014110509593043] 
dist 56=[-1.4729706534120639280 ,.66588331767970544089] 
dist 57=[-1.4782473625382015696 ,1.1156572428642349274 ] 
dist 58=[-1.4482664378273319819 ,1.5337789693301907807 ] 
dist 59=[-1.1661445795368309293 ,1.8881193867806065592 ] 
dist 60=[-.94757665446235332584,2.0849110243104896120 ] 
dist 61=[.02493930946952351477,2.1996943957775254884 ] 
dist 62=[.30311308301288979249,2.2286142392597772248 ] 
dist 63=[.69544710700400338404,1.4812094629209818979 ] 
dist 64=[.71611381939000913322,1.5100392044255101640 ] 
dist 65=[.72357556191861959244,1.5130084252280405563 ] 
dist 66=[.68656072839544119688,1.5135353495686340953 ] 
dist 67=[.62996365732554491625,1.2990023603878788758 ] 
dist 68=[.55245449599594846476,1.2431758983053182462 ] 
dist 69=[.4467331467119219362 ,1.2103363905809048055 ] 
dist 70=[.27814308915696018785,1.2015087315161860673 ] 
dist 71=[.10638374636098742279,.22814946874308476625] 
dist 72=[-.01206860451548526231,.11349663665328038775] 
dist 73=[-.20559407925914437954,-.01630247070052601190] 
dist 74=[-.39093958601431709866,-.03592066778990774047] 
dist 75=[-.55228246616365631353,-.19450849787865761725] 
dist 76=[-.65057911277337621935,-.21878348287055159483] 
dist 77=[-.71965635020103674686,-.26274724819024305863] 
dist 78=[-.76507613795790110467,-.26991389531150670314] 
dist 79=[-.79356364533702046427,-.34286696843318485599] 
dist 80=[-.79751388250468006534,-.34546678616495806166] 
dist 81=[-.78765086812801677903,-.33598060393852825482] 
dist 82=[-.77772255697789629942,-.30788727684893225814] 
dist 83=[-.67998688096032535109,-.27086979459431944101] 
dist 84=[-.65301027980872950496,-.22595329581102599831] 
dist 85=[-.6134494637403702473 ,-.16767405954142142972] 
dist 86=[-.59791242055872728726,-.07761080585591116048] 
dist 87=[-.21439555344154408705,.07413099771428860478] 
dist 88=[-.16384437444740468019,.213399560768176671  ] 
dist 89=[-.04914975186154864431,.32685698316045372862] 
dist 90=[-.02498839165184452795,.43148369567845469342] 
dist 91=[.05522079258680089710,.51989753240601583381] 
dist 92=[.06561659556331032653,.56910323602894659153] 
dist 93=[.08659581783263660562,.59770141633253991867] 
dist 94=[.09022042219463797397,.60478596777947220315] 
dist 95=[.10191499519253384961,.19847334144854787096] 
dist 96=[.10287461337011710663,.19940722958407692961] 
dist 97=[.10073223848623799505,.19621130825239187492] 
dist 98=[.09388067915602384413,.19420617257536776388] 
dist 99=[.08471978826511570903,.1672532813342918767 ] 
dist 100=[.06449490739406333413,.16008511352804073576] 
dist 101=[.0388831998518183151 ,.15141864574779145227] 
dist 102=[-6.70088607938817443000e-05,.14731863729514338101] 
dist 103=[-.03917132845430119743,.06089338072542192680] 
dist 104=[-.06539588677775004026,.05436822957186846676] 
dist 105=[-.08667806475851179017,.04051298819539181391] 
dist 106=[-.10616445050528103732,.03665783289599092221] 
dist 107=[-.12252685471398174492,.02182540578210951937] 
dist 108=[-.13140836749115155725,.01861134782608999576] 
dist 109=[-.13633375588415832483,.01335266485979059634] 
dist 110=[-.13699161871480856894,.01199669586652245039] 
dist 111=[-.11337746581518074922,.00957928812012030143] 
dist 112=[-.11326514075222528094,.00939499128342482420] 
dist 113=[-.10902404445933115026,.01011081517558696201] 
dist 114=[-.10838465508780550316,.01221603692332418573] 
dist 115=[-.08759713407477156337,.01498919538347468385] 
dist 116=[-.08261625097293688273,.01835713907299997138] 
dist 117=[-.07903348994574009487,.02273120703228091367] 
dist 118=[-.07815942995319606805,.02949888822578884978] 
dist 119=[-.01728838829042476494,.03633667945084589469] 
dist 120=[-.01179458731738837445,.04098957304866573888] 
dist 121=[-.00314113609702311060,.04483863506905883209] 
dist 122=[-.00147797588415752173,.04848640533391546346] 
dist 123=[.00726968206216905969,.05163725075188776071] 
dist 124=[.00877074373488677309,.05410303401687901274] 
dist 125=[.01149856978248401001,.05747885312111218980] 
dist 126=[.01200277373998485003,.05831843603897031469] 
dist 127=[.01274325495904248917,.02642198065148494555] 
dist 128=[.01267113418047820293,.02648378054463336269] 
dist 129=[.01224655893817352370,.02569747033209098116] 
dist 130=[.01124291565393392028,.02558399552650619892] 
dist 131=[.00997194597931715669,.02097817006230537903] 
dist 132=[.00848588166074479093,.01985457746285637928] 
dist 133=[.00658914818303240655,.01909964066917034107] 
dist 134=[.00368762883216445559,.01892545321618619076] 
dist 135=[.00076571640770465414,.00220152958320042475] 
dist 136=[-.00172130190261343809,.00074941251066344056] 
dist 137=[-.00493279911748012428,-.00141561690423522418] 
dist 138=[-.00793502440907261994,-.00173479077469451943] 
dist 139=[-.01050278013285096846,-.00434596405438797803] 
dist 140=[-.01198953538715208940,-.00473881823052640921] 
dist 141=[-.01294167172563842855,-.00543190183249769421] 
dist 142=[-.01338714005179383747,-.00554293744227437263] 
dist 143=[-.01355077503224638012,-.00591212038038280711] 
dist 144=[-.01351331876724300718,-.00581144639280853576] 
dist 145=[-.01312525355640020612,-.00554321250432359673] 
dist 146=[-.01292354974465962280,-.00498365555640177034] 
dist 147=[-.01108182109209133965,-.00429456673373734916] 
dist 148=[-.01060342975919807517,-.00351200538865263122] 
dist 149=[-.00987550222156835527,-.00252729771229529174] 
dist 150=[-.00961104313004074743,-.00103559527128867016] 
dist 151=[-.00324766584812593902,.00161884216259085059] 
dist 152=[-.00239858146940381884,.00395867883843266007] 
dist 153=[-.00049462608888851517,.00586000801255933255] 
dist 154=[-8.27435377256796745150e-05,.00760764869064678406] 
dist 155=[.00110647213078086796,.00908194726374951539] 
dist 156=[.00127053921375669179,.00989801938151033127] 
dist 157=[.00156884899950881612,.01037289033791242275] 
dist 158=[.00162192368658434257,.01049249381939531837] 
dist 159=[.00168602209504639560,.00316384657961659927] 
dist 160=[.00166545818609083925,.00316108678753145612] 
dist 161=[.00160280061362866554,.00305236497646572818] 
dist 162=[.00146807722579165468,.00303029516946103622] 
dist 163=[.00130093561126787476,.00248839587710524252] 
dist 164=[.00110954897712047930,.00235662119190097727] 
dist 165=[.00086769319078228873,.00224755479469427196] 
dist 166=[.00050015499911428311,.00220698870276573135] 
dist 167=[.00011120075848144489,.00032535708697548938] 
dist 168=[-.00036837476027187070,.00010044030145274965] 
dist 169=[-.00076020442077971969,-.00027822788787588718] 
dist 170=[-.00112401964499776716,-.00032149044029566833] 
dist 171=[-.00143356699838202712,-.00065513447207757593] 
dist 172=[-.00160994172824634212,-.00070437738072984336] 
dist 173=[-.00171929363706953302,-.00079246712852986686] 
dist 174=[-.00176274772366617591,-.00080557268200579596] 
dist 175=[-.00176949542159647764,-.00085963245262783201] 
dist 176=[-.00176191195045569639,-.00083894355664873166] 
dist 177=[-.00169083101096593708,-.00079466446090950510] 
dist 178=[-.00167418794446387864,-.00070778699504607426] 
dist 179=[-.00136990641586725508,-.00060240808369901445] 
dist 180=[-.00129651187724275481,-.00048466400397545233] 
dist 181=[-.00122597087078203710,-.00033769402990721115] 
dist 182=[-.00119437041007043021,-.00011626967136452153] 
dist 183=[-.00029451020917819826,.00012985243463173470] 
dist 184=[-.00020162799380250419,.00037167130484609938] 
dist 185=[-3.14130588495929594710e-05,.00056828497493381947] 
dist 186=[-5.19188113782152460630e-06,.00074925110723549223] 
dist 187=[.00012657891969132914,.00090212723730146415] 
dist 188=[.00014952142733708084,.00098720979901112455] 
dist 189=[.00018785229904469813,.0010393337504028235 ] 
dist 190=[.00019545434524651429,.00105166330382696990] 
dist 191=[.00019921313913619456,.00040768481354335379] 
dist 192=[.00019540454472952153,.00040668415624084967] 
dist 193=[.00018652419284920951,.00039038632609997355] 
dist 194=[.00016863798341623179,.00038800056175549627] 
dist 195=[.00014679332270741204,.00031332806889839070] 
dist 196=[.00012219422867896161,.00029556624875190889] 
dist 197=[9.13635178964949201170e-05,.00028279853470847045] 
dist 198=[4.47744474416988008970e-05,.00027986531324553940] 
dist 199=[-1.97314302851831859860e-06,2.88544760902927427730e-05] 
dist 200=[-3.52923908084694774450e-05,1.52069636147908945010e-05] 
dist 201=[-8.38197306694954329270e-05,-1.62880570995068306750e-05] 
dist 202=[-.00012876956758184184,-2.15744812078396709630e-05] 
dist 203=[-.00016694802182354610,-5.81483399798465364260e-05] 
dist 204=[-.00018858992294240678,-6.37732353495869758630e-05] 
dist 205=[-.00020186674340044054,-7.42981606697107340580e-05] 
dist 206=[-.00020683224712316193,-7.61188011564452261240e-05] 
dist 207=[-.00020750801643767522,-7.78335169579272632520e-05] 
dist 208=[-.00020636507127080177,-7.56596178125727820400e-05] 
dist 209=[-.00019903774298762338,-7.10991370088698547520e-05] 
dist 210=[-.00019590745028421623,-6.22086028963699025080e-05] 
dist 211=[-.00016599290750812411,-5.14411647339592377030e-05] 
dist 212=[-.00015852974782938808,-3.94276753503526480960e-05] 
dist 213=[-.00014732666254854261,-2.44415087737663845610e-05] 
dist 214=[-.00014321086140354319,-1.87019034047990000000e-06] 
dist 215=[-4.68357370941765220070e-05,2.64319774366032769380e-05] 
dist 216=[-3.40717226869422261890e-05,6.16118264682618993800e-05] 
dist 217=[-1.79031606839276856750e-05,9.01732403166489011770e-05] 
dist 218=[-1.54555246483988874910e-05,.00011639700492504122] 
dist 219=[-6.12735914474861316630e-06,.00013850945787002154] 
dist 220=[-4.19172509132538232010e-06,.00015074608579665213] 
dist 221=[-1.11607021339244896220e-06,.00015786599929258863] 
dist 222=[-3.42713575382891037720e-07,.00015966140154792731] 
dist 223=[3.23291121869432867470e-05,5.11615220032590573460e-05] 
dist 224=[3.12258538556979486890e-05,5.09039058411292793350e-05] 
dist 225=[2.91384081547417199660e-05,4.89716040574839440670e-05] 
dist 226=[2.52153238541452342430e-05,4.83390425591867300030e-05] 
dist 227=[2.05104748419237314400e-05,4.03006478854470859800e-05] 
dist 228=[1.53187370907103422900e-05,3.83186996958870709970e-05] 
dist 229=[8.87906505115124170660e-06,3.59206329400340289830e-05] 
dist 230=[-7.81090643538330794520e-07,3.48419419391363881540e-05] 
dist 231=[-1.04496421801325623160e-05,1.36151596616176853670e-05] 
dist 232=[-1.69227011326465678880e-05,1.19678162750643305630e-05] 
dist 233=[-2.21720355269276300220e-05,8.53710946833367611980e-06] 
dist 234=[-2.69815522268852829050e-05,7.60763910754013829830e-06] 
dist 235=[-3.10297137154388532350e-05,4.16870438950324494140e-06] 
dist 236=[-3.32559136818572370540e-05,3.40326988335804801660e-06] 
dist 237=[-3.45325541708788132140e-05,2.43671981064392028190e-06] 
dist 238=[-3.48102400957048367270e-05,2.18536320212451562080e-06] 
dist 239=[-2.94193450463033261600e-05,2.14491156282503876710e-06] 
dist 240=[-2.92360115748181330640e-05,2.32251726595649477740e-06] 
dist 241=[-2.79816872503984699290e-05,2.68969438723045525740e-06] 
dist 242=[-2.76531438312930852700e-05,3.40204890919931956270e-06] 
dist 243=[-2.26899910926652235350e-05,4.26376608916171370150e-06] 
dist 244=[-2.14934991484542161630e-05,5.22405824938242172020e-06] 
dist 245=[-2.02075400451128173110e-05,6.42131461843221952210e-06] 
dist 246=[-1.95611071371480370320e-05,8.22398582196877153510e-06] 
dist 247=[-7.03646907338437227270e-06,1.00307902646866635350e-05] 
dist 248=[-6.05953895156136113520e-06,1.12444837228996513440e-05] 
dist 249=[-3.97855445465717451540e-06,1.22331355243185792910e-05] 
dist 250=[-3.41249496534838946310e-06,1.41394218534389666650e-05] 
dist 251=[-1.28413860067263295430e-06,1.63854648558964107790e-05] 
dist 252=[-8.37069942793251926960e-07,1.76369953601858133890e-05] 
dist 253=[-1.91755041378653810410e-07,1.83891696762185435940e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 1, 0, 1] 
dist 0=[114.79534189379339682   ,114.79534189379339682   ] 
dist 1=[110.10056953338102284   ,117.53725870609727625   ] 
dist 2=[100.97141803419242558   ,118.90494366883961617   ] 
dist 3=[91.150990646183968031  ,119.83812496508678289   ] 
dist 4=[83.705168247541974876  ,120.84120971589865174   ] 
dist 5=[76.684871464182535765  ,121.55882795880032988   ] 
dist 6=[68.539892329458988774  ,121.36221355930895704   ] 
dist 7=[60.396384256974443182  ,120.47533412278661645   ] 
dist 8=[53.367668874301346244  ,118.44778617110559185   ] 
dist 9=[45.846864142925928340  ,97.062383080759302475  ] 
dist 10=[35.721414199336383167  ,93.721808944248039162  ] 
dist 11=[25.862657455147325667  ,84.094648888419733961  ] 
dist 12=[19.398725983475828543  ,82.713635529465972946  ] 
dist 13=[14.177768259275141860  ,63.317269746203669171  ] 
dist 14=[9.2762959147532583309 ,59.357379721738027114  ] 
dist 15=[.49982743268910324326,55.522521685835109645  ] 
dist 16=[-5.8732898108460886494 ,54.805284772677118071  ] 
dist 17=[-10.383596284834588702  ,11.684358437611448162  ] 
dist 18=[-13.573179158355046545  ,6.6941351451238572754 ] 
dist 19=[-15.936124883007779965  ,2.6930768986790550617 ] 
dist 20=[-17.146989933136078218  ,2.4468541943759627904 ] 
dist 21=[-19.546656709697142753  ,2.0754880042608825329 ] 
dist 22=[-23.074275755437632954  ,1.9761623207277977260 ] 
dist 23=[-25.338222515992964870  ,1.5532278429298310702 ] 
dist 24=[-26.451402663624012238  ,1.4226027453450268469 ] 
dist 25=[-26.927014288479707404  ,1.0378497794898109721 ] 
dist 26=[-26.900069346777088431  ,.87486299763986787024] 
dist 27=[-26.176391566415544466  ,.40536543063407633694] 
dist 28=[-25.810272310688440191  ,2.2444325313980469663 ] 
dist 29=[-22.117297065691008012  ,3.9849840172862213007 ] 
dist 30=[-21.170892546129993914  ,6.0009018782421087874 ] 
dist 31=[-19.787193747575033955  ,7.8136127073613488330 ] 
dist 32=[-19.266711899234802609  ,8.7500464254045721242 ] 
dist 33=[-6.7660662715892589332 ,9.2610259823841169781 ] 
dist 34=[-5.1146694774353867211 ,9.3808215868216955089 ] 
dist 35=[-1.4026456068914648093 ,10.001113388756654385  ] 
dist 36=[-.62389654575780354234,13.315265235989060630  ] 
dist 37=[1.1258826808240723594 ,16.109351062161146223  ] 
dist 38=[1.3015455799637766948 ,17.655237801960679349  ] 
dist 39=[2.2406295731038330443 ,18.554502691034866908  ] 
dist 40=[1.0408535946785693542 ,18.780962541395589702  ] 
dist 41=[-.25087022828287485661,5.8604383230060706000 ] 
dist 42=[-1.5503538243935144796 ,5.8724284266524000382 ] 
dist 43=[-2.7194762244776976795 ,5.7045143965999706826 ] 
dist 44=[-3.4949688749193887122 ,5.6694113616736919769 ] 
dist 45=[-4.1150206305808830938 ,4.6971966305585935277 ] 
dist 46=[-4.6686053559838612020 ,4.4590114983009813560 ] 
dist 47=[-5.1105336486724733435 ,4.2658039053589512401 ] 
dist 48=[-5.2877805503632333811 ,4.1950449019163810589 ] 
dist 49=[-5.3410557071762262814 ,2.1507993094392525528 ] 
dist 50=[-5.3048311832490241500 ,2.0863160093201951167 ] 
dist 51=[-4.8590194529868908004 ,1.1959861581738998355 ] 
dist 52=[-4.7101110210765204638 ,1.1106870863524605702 ] 
dist 53=[-4.4659595524718432979 ,.93754788120426013267] 
dist 54=[-4.3709277358664865935 ,.88718064823390477533] 
dist 55=[-2.9521057623245896307 ,.68245760328458411563] 
dist 56=[-3.0442367585084749635 ,1.5617804784726965931 ] 
dist 57=[-3.0706818660021477204 ,2.3297140391759534399 ] 
dist 58=[-3.0622045870242326894 ,3.0401521794434050087 ] 
dist 59=[-2.9477696407063150398 ,3.6404626660839650822 ] 
dist 60=[-2.9204369955725263131 ,3.9714841899556878162 ] 
dist 61=[-2.3983473121801993958 ,4.1616244491386754440 ] 
dist 62=[-2.2717613894979993402 ,4.2029669665989099709 ] 
dist 63=[-2.1515747888537644745 ,1.1262985651478157563 ] 
dist 64=[-2.0978260580167341129 ,1.1643732020499400969 ] 
dist 65=[-.54374310309841789846,1.1769755340169122499 ] 
dist 66=[-.38178476305802565531,1.1801225375094059575 ] 
dist 67=[-.01521688874356889134,1.0319945393152517016 ] 
dist 68=[.03158082275575168708,1.2615142306455249340 ] 
dist 69=[.09352339716759451064,1.5275281737044249435 ] 
dist 70=[.10501977786785526465,1.6757781718616585611 ] 
dist 71=[.16474493026951363584,1.7685363543747609800 ] 
dist 72=[.02234946144185746651,1.7899755784223899117 ] 
dist 73=[-.13010208386171383972,.69867054780512375268] 
dist 74=[-.2777839304177436842 ,.69815970072512148551] 
dist 75=[-.40736904306172619125,.6726975970373903092 ] 
dist 76=[-.4880420538171394241 ,.6690221726322542459 ] 
dist 77=[-.54677686941639745689,.54332999129755695081] 
dist 78=[-.58934949770732591132,.51324829874649025096] 
dist 79=[-.61866309678967594695,.4920644740122689128 ] 
dist 80=[-.62478231199855331731,.48731086589401939575] 
dist 81=[-.62163399473375366016,.13889520925436652945] 
dist 82=[-.61410542830997412006,.13459763246894849958] 
dist 83=[-.54430422350809445158,.06731187583795428995] 
dist 84=[-.52411546847238654749,.06087738245388157133] 
dist 85=[-.49325346594975310075,.04894962854824352729] 
dist 86=[-.48135622291775757711,.04590798394694963087] 
dist 87=[-.34751344741353649116,.05646927770555472177] 
dist 88=[-.35695680199509678789,.16849364249365747983] 
dist 89=[-.35910416847713164319,.25984082246806739966] 
dist 90=[-.35734192875980550106,.34416834794116369152] 
dist 91=[-.34582249305394091615,.41543156416312215429] 
dist 92=[-.33996502396038579897,.4549281963314478275 ] 
dist 93=[-.2915251725342912811 ,.477930118464824032  ] 
dist 94=[-.27903089142205748387,.48372543410849392884] 
dist 95=[-.25866394840851926961,.14788548969427878912] 
dist 96=[-.25183532542324880222,.14947821052189572059] 
dist 97=[-.09662530873459832448,.14812467935008691739] 
dist 98=[-.06870538163409203713,.16469140218594352503] 
dist 99=[-.02149967227477743519,.20043894361697393478] 
dist 100=[-.02178706702968708661,.22426633042827286959] 
dist 101=[-.02210548439685087405,.25405804965077148716] 
dist 102=[-.02252259417923916951,.27438223455113419203] 
dist 103=[-.02294634336479888307,.28595122290387160869] 
dist 104=[-.02329291284858394184,.28826337537778004838] 
dist 105=[-.03047802931436981158,.08025619704846484769] 
dist 106=[-.04880953214964937839,.08001364489997729797] 
dist 107=[-.06462636785919281850,.07687484364174371641] 
dist 108=[-.07401782452026665035,.07626641839917793422] 
dist 109=[-.08032319512973198538,.06217317324901111686] 
dist 110=[-.08389274427076788835,.05879254847378798726] 
dist 111=[-.08565250805012512188,.05594341973622399458] 
dist 112=[-.08574624211575135788,.05492125427509972365] 
dist 113=[-.08328108471124531633,.03163750294794738983] 
dist 114=[-.08259790113429649257,.03054483200424142746] 
dist 115=[-.06865240111732503013,.01452615245946212189] 
dist 116=[-.06517795495126213795,.01208751119963608655] 
dist 117=[-.06193809311069954516,.00708244207594770657] 
dist 118=[-.06038171840963912791,.00578092876898863517] 
dist 119=[-.04463471212061097543,.00470918627084770837] 
dist 120=[-.04571577089447082366,.01671032679689543285] 
dist 121=[-.04601056738343409609,.02650340048373874708] 
dist 122=[-.04548178985661667267,.03556551017088781540] 
dist 123=[-.04196470912750050153,.04324639482203447833] 
dist 124=[-.04153833130541286947,.04784972457672748349] 
dist 125=[-.03386875274049249260,.05048165813444091225] 
dist 126=[-.03203179781799271164,.05109736288746428521] 
dist 127=[-.0302582347041454283 ,.02002076556950670808] 
dist 128=[-.02947862194159541169,.02011168545830941580] 
dist 129=[-.00709954399117094607,.01961128316769264620] 
dist 130=[-.00479289851296954360,.01953871899279319495] 
dist 131=[.00040459147132120654,.01613444665633651297] 
dist 132=[.00145280488016490043,.01865392251811853931] 
dist 133=[.00717198874835352979,.02242749589034502466] 
dist 134=[.00625802318050980561,.02452322447039439934] 
dist 135=[.00183508378071993595,.02577240674961914456] 
dist 136=[-.00115929872946792192,.02608704801493504251] 
dist 137=[-.00362181767812263533,.01009273205164506073] 
dist 138=[-.00593353940296170872,.01005187540897928816] 
dist 139=[-.00791686115120503961,.00961292588876647528] 
dist 140=[-.00907580700701365685,.00954933410384129946] 
dist 141=[-.00983124808591624970,.00766781926546454300] 
dist 142=[-.01021289124172100209,.00722434228192993738] 
dist 143=[-.01037837605549011411,.00690059369903709040] 
dist 144=[-.01036272215681545951,.00682858617319814445] 
dist 145=[-.01009339416140661374,.00056266707822312881] 
dist 146=[-.00994264324339578095,-.00016664750583025611] 
dist 147=[-.00855558800516278525,-.00185932923415573614] 
dist 148=[-.00819169313163637649,-.00210651282070583926] 
dist 149=[-.00764017398099150305,-.00406791609179108532] 
dist 150=[-.00743763492724799371,-.00145837580916029084] 
dist 151=[-.00496418282479110832,.00121598880047313093] 
dist 152=[-.00507019417411882192,.00301055188928710644] 
dist 153=[-.00507158130018768229,.00446944909344813960] 
dist 154=[-.00503840330863704784,.00581119032239135424] 
dist 155=[-.00485029733738925305,.00694336048080840800] 
dist 156=[-.00477066295096164590,.00757022897055376775] 
dist 157=[-.00403916195491337101,.00793543676101621896] 
dist 158=[-.00385506626873436663,.00802729871695224794] 
dist 159=[-.00357712853164912601,.00246256566298656532] 
dist 160=[-.00347741423926427384,.00246406093831118095] 
dist 161=[-.00112270115651558067,.00238173461893029621] 
dist 162=[-.00081100804267287723,.00236966981620842660] 
dist 163=[-.00011634066570350438,.00220823984102890662] 
dist 164=[3.57443678774211589100e-05,.00284685513519077410] 
dist 165=[.00078155208454343285,.00338524186068443077] 
dist 166=[.00056025193415809776,.00368312677593790203] 
dist 167=[-4.70891932492627512170e-06,.00385642748610454626] 
dist 168=[-.00038555636156234016,.00390010646991541188] 
dist 169=[-.00069711975614973829,.00121146656583451947] 
dist 170=[-.00098701994805706403,.00120485207414720223] 
dist 171=[-.00123406123820931983,.00115189428792010384] 
dist 172=[-.00137547280609859375,.00114119807529092180] 
dist 173=[-.00146397245469004407,.00092557379741615593] 
dist 174=[-.00150095219004781868,.00087428369958329219] 
dist 175=[-.00150831159181913841,.00082821343705627877] 
dist 176=[-.00150196111002615911,.00081045097055368288] 
dist 177=[-.00144419116462170466,.00014432496594080438] 
dist 178=[-.00142804912107641028,6.58689143012465857830e-05] 
dist 179=[-.00117905342114262634,-.00011396404103248829] 
dist 180=[-.00111826135358776679,-.00014464078479986088] 
dist 181=[-.00105319049770886272,-.00030257598199647739] 
dist 182=[-.00102003966894928621,-2.91179655354882900000e-05] 
dist 183=[-.00070315964793848766,.00024513444323348898] 
dist 184=[-.00071476617064157974,.00042943013801518562] 
dist 185=[-.00071248371357144946,.00057958734506844799] 
dist 186=[-.00070764503878308779,.00071830021582908869] 
dist 187=[-.00067642350893677594,.00083582092348333988] 
dist 188=[-.00066836291991540263,.00090183870551560672] 
dist 189=[-.00054751575596244378,.00094605103169102572] 
dist 190=[-.00051848216677065918,.00095630594713966103] 
dist 191=[-.00048719325654153548,.00046912039029930824] 
dist 192=[-.00047154877770877937,.00046728670454073499] 
dist 193=[-.00016773306678706222,.00046117733982102686] 
dist 194=[-.00014403375170851101,.00045606679877978442] 
dist 195=[-9.37340179135253805440e-05,.00043115442394946584] 
dist 196=[-8.01130589137636913280e-05,.00042248224193204538] 
dist 197=[-2.92607215051423021590e-05,.00039749311642371130] 
dist 198=[-1.85162070555475184420e-05,.00042759312554175326] 
dist 199=[-3.80083798908217914710e-06,.00044528724689417961] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 1, 1, 2, 0, 2] 
dist 0=[126.71234644414065738   ,126.71234644414065738   ] 
dist 1=[122.72297567498273284   ,128.00554293749464018   ] 
dist 2=[117.29030753782125054   ,128.17202514688911021   ] 
dist 3=[110.26378555645093304   ,127.68257521781067758   ] 
dist 4=[100.85868971489733395   ,125.90070618146793926   ] 
dist 5=[85.965554859064644961  ,119.15640298575873050   ] 
dist 6=[70.659567979454902291  ,117.44451309626977456   ] 
dist 7=[59.606859663128561644  ,112.72597999763067062   ] 
dist 8=[49.713107928571846807  ,104.02517646483274628   ] 
dist 9=[39.000309396465585438  ,87.378466553223564176  ] 
dist 10=[28.726272897728513561  ,83.743617443664542881  ] 
dist 11=[20.563664353265520878  ,79.573920025832356240  ] 
dist 12=[12.439643104247743549  ,77.847206683299282318  ] 
dist 13=[2.2947678938771936630 ,49.089243764769687001  ] 
dist 14=[-7.1891057099917568872 ,44.442270487256921673  ] 
dist 15=[-12.689145513860668294  ,43.620629775914970899  ] 
dist 16=[-16.344311729699634600  ,16.702375546372822784  ] 
dist 17=[-18.480689959904353221  ,1.7153431197451900989 ] 
dist 18=[-21.386199868752699141  ,-.78742174260113006638] 
dist 19=[-25.890726745604142446  ,-5.0977217236465665082 ] 
dist 20=[-29.999715218547107540  ,-5.8708390303583432159 ] 
dist 21=[-33.279267662914806723  ,-9.1295083924409933916 ] 
dist 22=[-34.488185723711941413  ,-7.7274284689022828056 ] 
dist 23=[-34.887964785877397277  ,-4.3904319373327856984 ] 
dist 24=[-34.935295962557015146  ,-.68137844740945183487] 
dist 25=[-30.739325769731138065  ,2.2046599847248786091 ] 
dist 26=[-29.571602604281976886  ,4.9457167639259469698 ] 
dist 27=[-28.823489839713251530  ,8.0927480786063135176 ] 
dist 28=[-28.489012075746237559  ,11.165509299225642756  ] 
dist 29=[-7.4835145014644857547 ,13.619471328426051060  ] 
dist 30=[-4.9701966527902825669 ,16.045142566817049418  ] 
dist 31=[.94180357953941740595,19.014854001559271345  ] 
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dist 201=[-8.25320184199083900190e-05,.00039624237138488754] 
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dist 225=[7.34242727541858175450e-06,6.92968217109055194210e-05] 
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dist 227=[1.36307998354817069210e-05,7.87362830174792020490e-05] 
dist 228=[1.44771775915182710230e-05,7.98374062363858123780e-05] 
dist 229=[1.47780176870717208850e-05,7.96146641210028880330e-05] 
dist 230=[9.27761449616108445030e-06,7.90088949000855879340e-05] 
dist 231=[-6.16682136836618045700e-06,7.58875891390065964720e-05] 
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dist 233=[-3.20353187836555170360e-05,6.29857928705667869160e-05] 
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dist 238=[-6.09256330990268244230e-05,1.36333470757119413780e-05] 
dist 239=[-6.16944093109897410140e-05,8.90089304474071044650e-06] 
dist 240=[-6.17222621442240749720e-05,7.61720183335837979010e-06] 
dist 241=[-6.11119647773413943860e-05,2.81232574053777305780e-06] 
dist 242=[-5.98157487176437527080e-05,1.79896633303479531460e-06] 
dist 243=[-5.90425684287872348710e-05,3.85072025481668832770e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 2, 0, 1, 0, 2] 
dist 0=[121.04669669386231647   ,121.04669669386231647   ] 
dist 1=[117.49843623609320156   ,122.75960055949440744   ] 
dist 2=[111.58347917442090762   ,124.05671174502257942   ] 
dist 3=[100.46494134415275999   ,125.94076017487413170   ] 
dist 4=[88.619101581945630680  ,127.53673839534949876   ] 
dist 5=[79.809913885001437244  ,127.69364961323132427   ] 
dist 6=[71.672674711476925984  ,127.00445952886919641   ] 
dist 7=[62.481158958476838640  ,126.32485383521202575   ] 
dist 8=[53.436714708609815091  ,104.58721022554597514   ] 
dist 9=[45.869288537205971004  ,101.27764383969782366   ] 
dist 10=[37.979420311002979665  ,91.501365868093242779  ] 
dist 11=[27.626523760266753684  ,90.096386067240595215  ] 
dist 12=[17.661339127625245704  ,69.657573839050387417  ] 
dist 13=[11.309064348362564237  ,65.439587272246965523  ] 
dist 14=[6.3764943013035602166 ,61.429538337782329849  ] 
dist 15=[1.0772140114337050958 ,60.665303661455700185  ] 
dist 16=[-5.1952349963304447588 ,13.646117157631286584  ] 
dist 17=[-9.6202928311727497219 ,8.1952209403157944497 ] 
dist 18=[-12.720879845560161366  ,-1.0076153462073439849 ] 
dist 19=[-15.010388491753160124  ,-.62165560023787416911] 
dist 20=[-20.849355826531835730  ,.01924919619032326275] 
dist 21=[-24.810666576879869703  ,.56618604558541124639] 
dist 22=[-27.408404119185114327  ,1.0740786631817154598 ] 
dist 23=[-28.801015960775441932  ,1.5745762802024395390 ] 
dist 24=[-29.492896655740277550  ,1.9689100567117057647 ] 
dist 25=[-29.517301865232765519  ,2.0655934347890245953 ] 
dist 26=[-28.847467114754314166  ,2.0534206327568396623 ] 
dist 27=[-28.455035237391920231  ,2.0336459637856531515 ] 
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dist 30=[-22.006472213173565634  ,4.3632588909227127201 ] 
dist 31=[-21.439058729783470185  ,6.0560168961612201537 ] 
dist 32=[-7.7210899129499926682 ,6.9570534959761814623 ] 
dist 33=[-5.9177590052059151617 ,7.4646254243183624870 ] 
dist 34=[-1.8736128506163865214 ,11.156130018188358133  ] 
dist 35=[-1.4090559606531473204 ,14.819951978510369825  ] 
dist 36=[-1.1316703932768279329 ,17.907937819447363424  ] 
dist 37=[-1.0644710244497195439 ,19.613304740746897002  ] 
dist 38=[-1.0408195872867185453 ,20.600821024336504642  ] 
dist 39=[-1.0644908238473396445 ,20.838515094790401487  ] 
dist 40=[-1.1108382964644110798 ,6.3446306214733781135 ] 
dist 41=[-1.1778815348787205262 ,6.3719566141287380470 ] 
dist 42=[-1.2693345992143693822 ,6.2075757780378566151 ] 
dist 43=[-1.8760585434203157560 ,6.1837000044521890383 ] 
dist 44=[-2.5303910720882789026 ,5.1045268269445096838 ] 
dist 45=[-3.0663454031723246889 ,4.8403155565763338204 ] 
dist 46=[-3.5665351434199285204 ,4.6627670057292624815 ] 
dist 47=[-3.9763323704810458636 ,4.6216845577638889802 ] 
dist 48=[-4.1538868284335767268 ,2.7310756789159223098 ] 
dist 49=[-4.2204642838341549368 ,2.6146746296436195568 ] 
dist 50=[-4.2013612365450157021 ,2.3236340480430445998 ] 
dist 51=[-3.8786491096976787905 ,2.2282367343863984108 ] 
dist 52=[-3.7643671231972749611 ,1.2373708230873127295 ] 
dist 53=[-3.5890228494480558218 ,1.0703623287980223449 ] 
dist 54=[-3.8107380689901668646 ,.74876644195075012614] 
dist 55=[-3.9253202521736742387 ,.66746514739317480658] 
dist 56=[-3.9703757662931512570 ,.98185194470164354704] 
dist 57=[-3.9571108011961264674 ,1.6168670770903183989 ] 
dist 58=[-3.8614232284282422139 ,2.2064737752778253989 ] 
dist 59=[-3.5952574462502827413 ,2.7058943198120071000 ] 
dist 60=[-2.5167386109285834075 ,2.9831534464838996890 ] 
dist 61=[-2.4091491431714775143 ,3.1447966780848142166 ] 
dist 62=[-2.2477151591727628892 ,3.1855403221274703043 ] 
dist 63=[-2.1880697637210414466 ,.98929839727531629804] 
dist 64=[-.74856682951865022174,1.0250764860724239529 ] 
dist 65=[-.55707452085555453765,1.0374435293257419890 ] 
dist 66=[-.12710049821627365407,1.2731624631404498840 ] 
dist 67=[-.03496836001361613813,1.6647230146743721181 ] 
dist 68=[.09973086217032703180,1.9950357431680009207 ] 
dist 69=[.02499162665950645940,2.1778835334116977944 ] 
dist 70=[-.03841453374113983462,2.2842818010755640681 ] 
dist 71=[-.10092679351162801172,2.3110718260569845337 ] 
dist 72=[-.15643274114077461754,.70622531180127649364] 
dist 73=[-.19206309893265872294,.70630589985990251656] 
dist 74=[-.29950616179405640466,.68322842802143696153] 
dist 75=[-.41676775875002824102,.678679389362939872  ] 
dist 76=[-.48910194864490478276,.55855268103248488777] 
dist 77=[-.54096943033379513367,.5294130239160212165 ] 
dist 78=[-.57705124116124420963,.50544808041376407833] 
dist 79=[-.60018502288094374281,.4969352290498409571 ] 
dist 80=[-.60431423493991590798,.07878829625873903180] 
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dist 211=[-.00019177956216039346,5.11209184590120266780e-05] 
dist 212=[-.00018433333536016158,2.87737338843197928580e-05] 
dist 213=[-.00016921452587532635,2.37180968207617130170e-05] 
dist 214=[-.00014424390975710427,1.76904889159364007240e-05] 
dist 215=[-9.70682590165423598520e-05,1.62917078424791238940e-05] 
dist 216=[-9.66063610743398830600e-05,2.84990325860459057790e-05] 
dist 217=[-9.58109216003626689200e-05,4.14076640910320060260e-05] 
dist 218=[-9.18656707280458845480e-05,5.33587849181507561330e-05] 
dist 219=[-9.02895209599194246410e-05,6.35049126859526529280e-05] 
dist 220=[-7.59745393034827976170e-05,6.92469319794129501970e-05] 
dist 221=[-7.24120984319873808570e-05,7.27570197501909083700e-05] 
dist 222=[-6.69988119504176167450e-05,7.40414378527041319800e-05] 
dist 223=[-6.50854014701398801710e-05,7.42677601771122762820e-05] 
dist 224=[-2.09727948792104904350e-05,7.35929388045198060040e-05] 
dist 225=[-1.80024289433026602640e-05,7.21967390161438264020e-05] 
dist 226=[-1.17016325301387171440e-05,7.13152168064912450290e-05] 
dist 227=[-9.99632753862403066320e-06,6.56748809301147651600e-05] 
dist 228=[-3.63569902319303469700e-06,6.41743425446941710780e-05] 
dist 229=[-2.29034811157093401220e-06,5.84849904513371981720e-05] 
dist 230=[-4.61826533364745837730e-07,5.60003800455475865940e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 1, 1, 0, 1] 
dist 0=[110.78993477715222047   ,110.78993477715222047   ] 
dist 1=[107.26165833969632748   ,112.31320328920176651   ] 
dist 2=[103.20601255346587151   ,112.83550098937135355   ] 
dist 3=[99.578231283346782632  ,112.63660393606093243   ] 
dist 4=[95.608275497790867115  ,110.97560185734053068   ] 
dist 5=[90.179545796923659147  ,108.37080638857839209   ] 
dist 6=[84.265867833141321812  ,106.53407199116170791   ] 
dist 7=[78.355942575260843256  ,105.73131366505352186   ] 
dist 8=[71.332597067310154102  ,101.79563927566448404   ] 
dist 9=[60.969750263297221068  ,80.446127141554273845  ] 
dist 10=[50.464341581716791267  ,69.817935382115471635  ] 
dist 11=[42.872700679220559584  ,68.401894284541237396  ] 
dist 12=[35.976518924417053275  ,53.178969792477973946  ] 
dist 13=[28.254111614419775951  ,50.229528056365521384  ] 
dist 14=[20.014592793763328714  ,45.240456315776088329  ] 
dist 15=[11.296941359804817395  ,44.219674113991811294  ] 
dist 16=[-.26646106033567123121,19.934902009763214106  ] 
dist 17=[-11.224560621362580302  ,19.025605149998903850  ] 
dist 18=[-17.540285893458192113  ,6.5103301073052748649 ] 
dist 19=[-21.687230478312747450  ,4.7379571556853482258 ] 
dist 20=[-24.008627830770980608  ,1.3523108555489399005 ] 
dist 21=[-25.481128934446316999  ,.5596689967808053046 ] 
dist 22=[-26.586732888128622934  ,-1.7546890315140390975 ] 
dist 23=[-27.813419186826879670  ,-2.1406580822110533928 ] 
dist 24=[-28.364329378292843816  ,-1.9791737705693342042 ] 
dist 25=[-28.472870463591116751  ,-1.0470649096974965210 ] 
dist 26=[-17.125937466063822670  ,.01361362328868014268] 
dist 27=[-17.046634279150319949  ,.68845971185831984432] 
dist 28=[-14.092939050317780224  ,1.1969784885204482408 ] 
dist 29=[-13.377450696593006908  ,2.4484001839155301001 ] 
dist 30=[-12.854571850738642967  ,4.9308863361994103687 ] 
dist 31=[-12.715737598713230821  ,7.1340353633080776690 ] 
dist 32=[-2.3143971878190831293 ,9.4748554527396443287 ] 
dist 33=[-1.0942320173760306771 ,11.523479563635912779  ] 
dist 34=[.54718584305222427787,12.569282322400481022  ] 
dist 35=[.19722369349328468606,13.093620576585379393  ] 
dist 36=[-.1303901019988232284 ,13.174455735792471783  ] 
dist 37=[-.4977290215155585764 ,12.671425736236045464  ] 
dist 38=[-.84880326754026059553,12.394488945944993232  ] 
dist 39=[-1.1126069729174749811 ,11.970896014116711563  ] 
dist 40=[-1.3561457186424500068 ,11.755185311650929717  ] 
dist 41=[-1.6276330348529732006 ,8.0097008764998471444 ] 
dist 42=[-2.5114804684035881224 ,7.8079870210541664932 ] 
dist 43=[-4.5385447435236491579 ,7.6912812992048185785 ] 
dist 44=[-6.4318941845684930227 ,6.6294068129502291536 ] 
dist 45=[-8.0394420765893684241 ,6.3512616182883638084 ] 
dist 46=[-8.9333999867188438358 ,5.9216238452983653642 ] 
dist 47=[-9.4551468064339650223 ,5.7672463590179503026 ] 
dist 48=[-9.5867154669645553095 ,2.2292295895200913739 ] 
dist 49=[-3.0231282044462100645 ,1.7660094765172644507 ] 
dist 50=[-3.3558111235773674820 ,.85396344180476241308] 
dist 51=[-4.3787228920684293763 ,1.1329085345111397167 ] 
dist 52=[-5.2392347957473915109 ,1.3646689627252154847 ] 
dist 53=[-5.7109815335673497274 ,1.5844415742617433602 ] 
dist 54=[-5.9794082241445006941 ,1.7731903249520660831 ] 
dist 55=[-6.0326635242207970958 ,1.8918592628132056909 ] 
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dist 57=[-1.7132726237182362701 ,1.9840569896580328192 ] 
dist 58=[-1.6570305407377867117 ,.13707586575671365398] 
dist 59=[-1.6488905787386004296 ,.39546326046682261758] 
dist 60=[-1.3468731064782987783 ,.84092871175033533825] 
dist 61=[-1.2740482883090266050 ,1.2348607598892710227 ] 
dist 62=[-1.2235187378996544923 ,1.4848894277589787361 ] 
dist 63=[-1.2120461487090740599 ,1.6724138065247304059 ] 
dist 64=[-.14756110209897630119,1.8185618713515203458 ] 
dist 65=[-.02337150527153078341,1.9224386347071531824 ] 
dist 66=[.07423734543793305685,1.9452305516940080923 ] 
dist 67=[.04267081061681294324,1.9334905366574226043 ] 
dist 68=[.01453399028621113767,1.9236810252979128458 ] 
dist 69=[-.01522801476478673171,1.6450107811727092237 ] 
dist 70=[-.04284488865439074240,1.5703832636468777234 ] 
dist 71=[-.06250191167830173565,1.5054883883173702164 ] 
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dist 73=[-.09736474869007345423,.83752361521397920895] 
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dist 78=[-1.0842498738542172652 ,.6078099963257863675 ] 
dist 79=[-1.1454630432817272270 ,.59139029659119106664] 
dist 80=[-1.1590165447689117665 ,.19821811683964964223] 
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dist 88=[-.37183125691226047902,.09507055295344508530] 
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dist 90=[-.18638502631732824109,.02801994607386628754] 
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dist 93=[-.1435197779211918686 ,.17423642937293059695] 
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dist 100=[-.01221885216509743355,.24346037133943685228] 
dist 101=[-.01694812393693584243,.21329558583975450484] 
dist 102=[-.02111535261499049335,.20493108712656309053] 
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dist 104=[-.02566901711852272087,.18741219556103410541] 
dist 105=[-.02711917485188607347,.10765658752008783485] 
dist 106=[-.06945350164983384486,.10320183150407092672] 
dist 107=[-.10538163623629138066,.10212066301543130755] 
dist 108=[-.13850350012554151908,.08359694958345081731] 
dist 109=[-.16647936406944367663,.07913465301554587852] 
dist 110=[-.18198319444390621505,.07467946273385945726] 
dist 111=[-.19102675637480585141,.07260031430044456193] 
dist 112=[-.19329525650201527607,.02018981246251376647] 
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dist 114=[-.06008856192417590553,.01246675244386719195] 
dist 115=[-.05889879906304593586,.0153259481569493748 ] 
dist 116=[-.05871432584497018381,.01768388050960243351] 
dist 117=[-.06123271912200522211,.01990276097737778208] 
dist 118=[-.06449641886239027108,.02180576967638814911] 
dist 119=[-.06524032873659699190,.02291416508278891374] 
dist 120=[-.04437761342870819882,.02386948932423069526] 
dist 121=[-.02415738938952608076,.02404259369813130955] 
dist 122=[-.02313893494766744579,.00812660490230146735] 
dist 123=[-.02299189157085837135,.01592618415896225678] 
dist 124=[-.01850469791130005053,.02325788948121598062] 
dist 125=[-.01744367257394612161,.02955289560789248131] 
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dist 127=[-.01650615786614819059,.03564663923376110463] 
dist 128=[-.00142806821531585341,.03687819583220692185] 
dist 129=[.00032798401644461313,.03736906131902019674] 
dist 130=[.00440151606273855828,.03731037979567334176] 
dist 131=[.00499924853501643064,.03608834953478299384] 
dist 132=[.00971199811024801443,.03571282101569737612] 
dist 133=[.01040156281651910279,.02971139277834087820] 
dist 134=[.01163704961119920450,.02822149313872774438] 
dist 135=[.00803204799308971281,.02664127041648229108] 
dist 136=[.0012040179930992301 ,.02581884872374214646] 
dist 137=[-.00565743408176596821,.01207810665825073373] 
dist 138=[-.01028058637640457369,.01163876842806821863] 
dist 139=[-.01405866405614763183,.01144893621934189021] 
dist 140=[-.01756543247779340131,.00970804941238997778] 
dist 141=[-.02054629538366177731,.00926848310382779098] 
dist 142=[-.02237630670612442518,.00860362667546580005] 
dist 143=[-.02350180155830590881,.00836504468680634049] 
dist 144=[-.02376006163336847845,.00270729278034353508] 
dist 145=[-.00796266454528419219,.00195512094181720808] 
dist 146=[-.00798147392774663363,.00027697465917099455] 
dist 147=[-.00774570689409075295,-8.85552553560101861100e-05] 
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dist 149=[-.00882570114606866615,-.00221151913013879983] 
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dist 207=[-.00029362721743170732,.00012460760994696962] 
dist 208=[-.00029764124571032466,3.53114177149958972200e-05] 
dist 209=[-.00013361036144124936,2.44642907589111952000e-05] 
dist 210=[-.00013316959674787258,2.03069475477369923740e-07] 
dist 211=[-.00012829721956755711,-4.92119660752008561780e-06] 
dist 212=[-.00012696193952887119,-3.11277216631598784910e-05] 
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dist 220=[-5.11532198858580854730e-05,5.66873414155755696090e-05] 
dist 221=[-5.00832238028465531140e-05,7.01151081570704766130e-05] 
dist 222=[-4.69770162336000524070e-05,7.76911005903206683730e-05] 
dist 223=[-4.56363474648700230710e-05,8.22924102895796930930e-05] 
dist 224=[-3.83293798101263011540e-05,8.39091214021093801750e-05] 
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dist 228=[-2.97541221313707731480e-05,7.89748183332031013250e-05] 
dist 229=[-2.87964513185030132150e-05,6.53878587086134795400e-05] 
dist 230=[-2.82182062543891997330e-05,6.20726927776791796060e-05] 
dist 231=[-2.80221775850358937470e-05,4.48849815354131498950e-05] 
dist 232=[-2.79385229477155015470e-05,3.48188776484505402960e-05] 
dist 233=[-2.78065810320400758320e-05,3.35672449740730711250e-05] 
dist 234=[-2.76164613633629079290e-05,3.20835628433917606550e-05] 
dist 235=[-2.73019581392511149970e-05,3.16071878747135172060e-05] 
dist 236=[-2.69394544554292897720e-05,2.61780456380160011300e-05] 
dist 237=[-2.65588547666139933650e-05,2.48571028390530571230e-05] 
dist 238=[-2.60999933350504072560e-05,2.31478867632051957270e-05] 
dist 239=[-2.57071915390788659730e-05,2.24394844604609966270e-05] 
dist 240=[-2.47610449512840836950e-05,5.48476726827868284340e-06] 
dist 241=[-2.37155991470080513110e-05,3.34631551667080456090e-06] 
dist 242=[-2.35637267153794625520e-05,2.21007681262053023770e-06] 
dist 243=[-2.32008998245917159840e-05,1.90032712304865269380e-06] 
dist 244=[-2.29383777512082953300e-05,7.30595079779597783860e-07] 
dist 245=[-2.15645813831889157720e-05,4.86277301117552970310e-07] 
dist 246=[-2.11156828485406174000e-05,1.19313948661239530690e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 0, 1] 
dist 0=[130.77336143506606861   ,130.77336143506606861   ] 
dist 1=[129.69461108110434735   ,130.74096082037754185   ] 
dist 2=[125.89167266907676129   ,130.77336143506606861   ] 
dist 3=[120.73473515390623654   ,129.63116684911487288   ] 
dist 4=[114.26869405565836182   ,122.81831092037614525   ] 
dist 5=[105.71610958320211555   ,117.27429927719072320   ] 
dist 6=[92.258486709224269178  ,115.30306673430771756   ] 
dist 7=[78.425947110130042366  ,113.67955091110040427   ] 
dist 8=[68.377232124648309726  ,105.66708376834239367   ] 
dist 9=[59.307956322168212501  ,88.591720931034934934  ] 
dist 10=[49.246146580382896336  ,86.904867234852440960  ] 
dist 11=[31.537432740201090083  ,45.691852316336755739  ] 
dist 12=[18.879464944606629498  ,43.203192071038034233  ] 
dist 13=[8.2719252451749131304 ,38.273689229108305453  ] 
dist 14=[-2.1089897150018895972 ,37.140619534094938605  ] 
dist 15=[-11.395360206339485687  ,29.061594296288566714  ] 
dist 16=[-17.657524877825732911  ,24.794507053409978515  ] 
dist 17=[-22.849559424353475872  ,-.50288014606185445358] 
dist 18=[-27.894305865850062743  ,-1.3940586391417560083 ] 
dist 19=[-32.092310770197017267  ,-8.9517573683933804420 ] 
dist 20=[-33.920363013102180192  ,-8.6724327070234956623 ] 
dist 21=[-34.710941032427047612  ,-7.2056810870928228273 ] 
dist 22=[-34.766318137433830004  ,-3.8527757945964731756 ] 
dist 23=[-31.621160593194414718  ,-.14859292777907088168] 
dist 24=[-30.598498638881256801  ,2.7191830905714690483 ] 
dist 25=[-29.824150215245797394  ,5.4329804257311503845 ] 
dist 26=[-29.227003455429262503  ,8.5383443043666865515 ] 
dist 27=[-9.7843798788255929553 ,11.567236317579057823  ] 
dist 28=[-7.3742070901633838870 ,13.984598141545914804  ] 
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dist 30=[-.72158506569001834288,19.297539840638677416  ] 
dist 31=[5.3566403444361365457 ,21.890677408866911422  ] 
dist 32=[5.6404014254609623280 ,22.967591555604227605  ] 
dist 33=[9.8272407648742802770 ,23.421462554266489673  ] 
dist 34=[10.156715105888144424  ,23.534742296451824087  ] 
dist 35=[12.841873973970109970  ,20.925361109734219551  ] 
dist 36=[12.109237635020128015  ,20.243279017923855661  ] 
dist 37=[10.961689395909760734  ,19.935244405561039544  ] 
dist 38=[9.3709917424984637481 ,19.753616584493561688  ] 
dist 39=[4.6090388631583569081 ,16.864897591925464629  ] 
dist 40=[.98322879351770828249,16.103046845573919262  ] 
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dist 42=[-5.0399007409591520519 ,14.812937706206289048  ] 
dist 43=[-7.6566305376287144710 ,6.8621010895060018478 ] 
dist 44=[-9.3013500292283555513 ,6.1274658432233317209 ] 
dist 45=[-10.517490536720299249  ,4.4604368307738811535 ] 
dist 46=[-11.434920447062449058  ,4.0049183127918981489 ] 
dist 47=[-12.088157569834681581  ,1.9686080518926402680 ] 
dist 48=[-12.751234182214733061  ,1.5852330900406244977 ] 
dist 49=[-13.361028119005859718  ,.7067238730872996726 ] 
dist 50=[-13.476778150545737648  ,.52852282466750158596] 
dist 51=[-10.760393561433468865  ,-3.8826491084055250666 ] 
dist 52=[-10.370181466153353966  ,-3.6881704779468932283 ] 
dist 53=[-9.7769735333701624660 ,-3.3932050128043993767 ] 
dist 54=[-9.5445624085930424570 ,-2.2494654496947430402 ] 
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dist 57=[-1.0438360605383601458 ,5.0143703413520930274 ] 
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dist 59=[.27564021094105098568,8.0746926823270633745 ] 
dist 60=[.38926304313179960273,8.8518137459237994369 ] 
dist 61=[1.1949224167454668127 ,9.3044866731873868951 ] 
dist 62=[1.3179883978721989096 ,9.4184942298881530468 ] 
dist 63=[1.5352844712044592614 ,2.8887882695484216818 ] 
dist 64=[1.5698349141599746243 ,2.9235805584363263980 ] 
dist 65=[2.0348410882604816650 ,2.9044924030919908578 ] 
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dist 67=[1.9603552781386930266 ,2.4740464122435929321 ] 
dist 68=[1.7758679016421583552 ,2.3635416970564049145 ] 
dist 69=[1.5389607686448474844 ,2.2799469072552088774 ] 
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dist 71=[.23857891207583516359,1.6594571810402942940 ] 
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dist 73=[-.60374419444247273061,.63085476003609343995] 
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dist 92=[-.09916436288587292133,.96345882947049916029] 
dist 93=[-.03012798152015662654,1.0154909756498768163 ] 
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dist 100=[.01240349593272277094,.4184175522940755448 ] 
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dist 103=[-.09076332903523630490,.32078683810527845712] 
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dist 105=[-.21600296762182507802,.11894369877160658512] 
dist 106=[-.2690212082126228119 ,.09213971325030555439] 
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dist 109=[-.35828746472801005471,-.03527655342070898690] 
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dist 111=[-.37056811291863321618,-.05467792314503498006] 
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dist 113=[-.19485918207661298332,-.06038979820833365177] 
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dist 119=[-.04923939893111256241,.02320796077960982555] 
dist 120=[-.04421186450668795015,.05797557348400047058] 
dist 121=[-.00831595168377209092,.08623885202433760694] 
dist 122=[-.00220973402701015051,.11223065872138322144] 
dist 123=[.00921929572587722039,.13416168038167905989] 
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dist 130=[.03049971514260794634,.0451204983806668041 ] 
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dist 133=[.02211578596308727677,.03369741568184528386] 
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dist 135=[.00192851134295405297,.02302481850465790457] 
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dist 152=[-.00517120381030070068,.00547199043772552933] 
dist 153=[-.00080633714247378550,.00840461062849141195] 
dist 154=[-.00028437626405266761,.01110562664184861656] 
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dist 196=[.00038709532141251810,.00052641543720439796] 
dist 197=[.00031652529523190460,.00049989726230529698] 
dist 198=[.00015209883087081621,.00049432962327254958] 
dist 199=[-1.27031689499618680640e-05,.00034802728538856520] 
dist 200=[-.00012341543017390175,.00033853731642020227] 
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dist 202=[-.00029695534204669070,8.61169827062397558440e-05] 
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dist 210=[-.00041353563403991104,-9.86257033295421269730e-05] 
dist 211=[-.00033967167624149553,-9.27165523414827458350e-05] 
dist 212=[-.00032183115707396799,-8.12982235723817803640e-05] 
dist 213=[-.00030261247592117580,-6.75003494214099192930e-05] 
dist 214=[-.00029296212086106341,-4.56852901742567000000e-06] 
dist 215=[-.00010617678317089300,7.48686228918952324340e-05] 
dist 216=[-9.15446786613834601990e-05,.00012814910786815191] 
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dist 222=[-1.64703630196337957780e-06,.00027827053443773809] 
dist 223=[2.31877053847009388670e-06,9.79344290380134952120e-05] 
dist 224=[3.30404111346150774250e-06,9.93537268644397294290e-05] 
dist 225=[3.94133562898521904660e-06,9.92207540036034925820e-05] 
dist 226=[2.75763628148975081900e-06,9.84732651632059636020e-05] 
dist 227=[2.59545116342511971710e-07,9.48676317348546952290e-05] 
dist 228=[-4.62047571752614749770e-06,9.30569015732458298490e-05] 
dist 229=[-1.05348921235919000330e-05,7.96781311250759000720e-05] 
dist 230=[-1.71406555967030885240e-05,7.62448562073511178270e-05] 
dist 231=[-2.53865279586718461760e-05,7.01953423316713640140e-05] 
dist 232=[-3.88362522131432293740e-05,6.83409058467023847670e-05] 
dist 233=[-5.14584404391994880930e-05,2.54622100032984149130e-05] 
dist 234=[-6.31092697012077676030e-05,1.95541895190994491230e-05] 
dist 235=[-7.29785433272518703100e-05,9.49803746490413750720e-06] 
dist 236=[-7.85267195528851711320e-05,8.16176411427119568420e-06] 
dist 237=[-8.18709304733409269440e-05,3.11847293051303964800e-06] 
dist 238=[-8.29889647623108006770e-05,2.06270956934131077880e-06] 
dist 239=[-8.29944975445014028200e-05,4.96123820446089408440e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 1, 1, 2] 
dist 0=[101.09897581135439813   ,101.09897581135439813   ] 
dist 1=[97.663702046130109209  ,103.07279047894656373   ] 
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dist 3=[84.602344360276511876  ,103.47737480310119174   ] 
dist 4=[79.157381151181945786  ,103.30205253942240560   ] 
dist 5=[73.715708238459776375  ,103.12776295066024190   ] 
dist 6=[66.933601099945002230  ,103.05668289770907027   ] 
dist 7=[59.871301268355804872  ,103.03303881845604972   ] 
dist 8=[53.303632226089609045  ,100.25637745852405511   ] 
dist 9=[45.866232274234220413  ,82.558269639127845656  ] 
dist 10=[35.323430013892721940  ,79.871733045557224305  ] 
dist 11=[24.961063617391265945  ,74.579316064636406160  ] 
dist 12=[18.238418291855238644  ,73.207548406686858246  ] 
dist 13=[12.892078222424250517  ,68.527534861441441661  ] 
dist 14=[8.0165935197351710607 ,65.320233797836527201  ] 
dist 15=[3.7941542101070712919 ,53.683347350096157649  ] 
dist 16=[-2.0797125346843856898 ,46.235358681607895379  ] 
dist 17=[-8.9959901980005781380 ,15.828556489206624082  ] 
dist 18=[-15.488818367129225431  ,14.662855022598755177  ] 
dist 19=[-21.131497457714622577  ,5.1331330211594456242 ] 
dist 20=[-24.668011825367493164  ,3.4399448522307375825 ] 
dist 21=[-27.313539931788253973  ,.82586845392974362336] 
dist 22=[-29.417622491134076963  ,.17350735689007477731] 
dist 23=[-30.895337361870141423  ,-3.5334512986079581740 ] 
dist 24=[-31.217685985010073921  ,-3.0239719778937486769 ] 
dist 25=[-30.819811945340702186  ,-2.3020779018154576213 ] 
dist 26=[-30.749401838264005896  ,-1.1342860065983132762 ] 
dist 27=[-25.879728900046882195  ,.04029676162908791135] 
dist 28=[-24.645427988453685030  ,.79210809327878625661] 
dist 29=[-23.841979552040644950  ,1.3655376696391386864 ] 
dist 30=[-23.619700992682765030  ,1.8338865116297833126 ] 
dist 31=[-17.904254653644671242  ,2.1964350891100629924 ] 
dist 32=[-16.951519566318346002  ,2.3509869935420529443 ] 
dist 33=[.22017014606851914235,4.2271799791969815481 ] 
dist 34=[.22713759081163027805,7.7664502949794626037 ] 
dist 35=[-.51236344012599683708,10.810984600016585532  ] 
dist 36=[-1.0443513694778399665 ,12.608587239825088067  ] 
dist 37=[-1.5085148283388098009 ,13.806246458810636368  ] 
dist 38=[-1.9802294404803600436 ,14.470256105743266271  ] 
dist 39=[-2.4027476652261528402 ,14.807785116430956860  ] 
dist 40=[-2.6724202819341934509 ,14.818079628610296096  ] 
dist 41=[-2.8737084082090999709 ,14.476761665027004698  ] 
dist 42=[-3.0255977832880597484 ,14.279292817518223393  ] 
dist 43=[-3.1850490668481584116 ,12.271281975337139692  ] 
dist 44=[-3.4168008974692861263 ,11.773815924140307600  ] 
dist 45=[-3.7406863738220157737 ,11.037053203925045817  ] 
dist 46=[-4.2663273612249205496 ,10.755415432768933844  ] 
dist 47=[-4.8687508642152411987 ,3.8365745293657440764 ] 
dist 48=[-5.4977156402244580963 ,2.9168273771548014249 ] 
dist 49=[-6.2546983025862610262 ,.83512328825267735233] 
dist 50=[-8.0306915676794882620 ,.39932606318798724247] 
dist 51=[-9.6192856464753009892 ,-.3164989372195736238 ] 
dist 52=[-10.481182890563614419  ,-.20341910500938066094] 
dist 53=[-10.959258916595690793  ,-.10050029323461098529] 
dist 54=[-11.053605407530716880  ,.01128972362421359617] 
dist 55=[-3.4241867562716156935 ,.11657129351518086275] 
dist 56=[-3.4442749114753424198 ,.19382615355560990049] 
dist 57=[-3.3679302016301061971 ,.26354975914727127778] 
dist 58=[-3.3568379531343568788 ,.33914117749677897466] 
dist 59=[-2.7834142359492560816 ,.40569435541541127604] 
dist 60=[-2.6409823749088228194 ,.43961766722784031362] 
dist 61=[-2.5489404525345902845 ,.45643477500356042155] 
dist 62=[-2.5270675372018893905 ,.45880006144153609292] 
dist 63=[-.35558086472372594487,.44032274412834983404] 
dist 64=[-.10154429316322011079,.43052727857989517695] 
dist 65=[.24058325332193657457,.57647948863714846941] 
dist 66=[.11616521665719267974,.97064334224037436259] 
dist 67=[-.01054703752174843401,1.3090778622586161537 ] 
dist 68=[-.09680203282207501721,1.5074442394867972522 ] 
dist 69=[-.16784067141935236125,1.6375853023884411810 ] 
dist 70=[-.23423267872204338324,1.7052322639683880488 ] 
dist 71=[-.2906191159100871604 ,1.7362526398734079951 ] 
dist 72=[-.32198788430751241707,1.7347064261378749142 ] 
dist 73=[-.34033000220716704701,1.6916803378383975068 ] 
dist 74=[-.34494573590837596954,1.6668587031331761885 ] 
dist 75=[-.11383824321421919012,1.4361942220585888596 ] 
dist 76=[-.12133509739957270686,1.3755174859336438428 ] 
dist 77=[-.12490463240398321069,1.2838850639262333840 ] 
dist 78=[-.12524751161945621031,1.2500440511596546113 ] 
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dist 80=[-.49197846855804644526,.32109371945759414699] 
dist 81=[-.73624915113332293915,.07555530564560323940] 
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dist 83=[-1.1505201530356480160 ,-.01666870107995049062] 
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dist 85=[-1.3165986465537908279 ,.02243526830519522464] 
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dist 87=[-.4066173204183275749 ,.05567810772344039743] 
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dist 90=[-.39190686329181617964,.07906680952401277119] 
dist 91=[-.32288827400115984332,.08335129796352007323] 
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dist 94=[-.28796433854756973734,.08309390301344242406] 
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dist 101=[-.03559089065351555237,.21898759095270825888] 
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dist 104=[-.06288725953152615900,.22579775869677632409] 
dist 105=[-.06634570368635491117,.2170028073319209847 ] 
dist 106=[-.06761639333264673541,.21498735241620659995] 
dist 107=[-.06836371473428726391,.17596693247814593627] 
dist 108=[-.06974555803159998363,.16653673507035909627] 
dist 109=[-.07182884586498200069,.15773026418801372134] 
dist 110=[-.07536238163065566670,.15390641688595106329] 
dist 111=[-.07947401538497425347,.03814618942411885226] 
dist 112=[-.08385344778780256330,.02630849543478620397] 
dist 113=[-.08918495296749378322,-.00049539097182106462] 
dist 114=[-.09707798766214659481,-.00583085869718876345] 
dist 115=[-.11326137256216568804,-.00273905533366328079] 
dist 116=[-.12411909238268201388,.00016230531787343130] 
dist 117=[-.13095977902418691644,.00258315190467538569] 
dist 118=[-.13255501864823132228,.00490972246813825068] 
dist 119=[-.05218403557191759901,.00693974891371578795] 
dist 120=[-.05211573255028132804,.00818401447913470130] 
dist 121=[-.05015251635426133231,.00906683518038463189] 
dist 122=[-.04986942487553102709,.00966280854818196084] 
dist 123=[-.04040893756605304680,.01004718556388165736] 
dist 124=[-.03814725307248457453,.01010384525404015476] 
dist 125=[-.03655383057959317293,.01000374521898162963] 
dist 126=[-.03619653271277829500,.00987342552978674223] 
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dist 129=[.00432747949218227514,.01034593978823237879] 
dist 130=[.00166049744327182969,.01612386423742308720] 
dist 131=[-.00102099535990255797,.02103923120648616461] 
dist 132=[-.00282484230790972369,.02383974424345935713] 
dist 133=[-.00429463692156669048,.02557624380011847570] 
dist 134=[-.00565024456828903879,.02626723966326206499] 
dist 135=[-.00679541571974840789,.02641113281966800427] 
dist 136=[-.00742994394793446598,.02628191076608639784] 
dist 137=[-.00779941598464374858,.02540110716154518444] 
dist 138=[-.00789249780723498400,.02499486114509539309] 
dist 139=[-.00239669737723375952,.02128691153872754372] 
dist 140=[-.00241661792148901318,.02034068531464406460] 
dist 141=[-.00238223074487760853,.01890342107277708575] 
dist 142=[-.00237193865714185018,.01838634834920759588] 
dist 143=[-.00328772349058398985,.00605580797342112084] 
dist 144=[-.00780472710978124423,.00441279691583816523] 
dist 145=[-.01147258092623402313,.00074038572330750487] 
dist 146=[-.01484093670553601978,-5.79632833584132541820e-05] 
dist 147=[-.01768142276416697872,-.00017103441057775364] 
dist 148=[-.01925330729679948952,.00020652226904707156] 
dist 149=[-.02016782690646836887,.00051801112967376555] 
dist 150=[-.02039814637884002074,.00081190734910787342] 
dist 151=[-.00613601711719712820,.00106492867290042407] 
dist 152=[-.00611594810249637016,.00121418444183390916] 
dist 153=[-.00587306131757824628,.00131317705427307986] 
dist 154=[-.00582592813843393976,.00136670494447099622] 
dist 155=[-.00474551377953641629,.00139105927469237559] 
dist 156=[-.00448640934097935322,.00139122375771958949] 
dist 157=[-.00426755473297972211,.00134840917722483545] 
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dist 160=[-.00012808107560001632,.00105174231661326824] 
dist 161=[.00049309398444563833,.00151643632570340303] 
dist 162=[.00020588401902268600,.00221021834342124134] 
dist 163=[-8.26396745234230936490e-05,.00279853905663617712] 
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dist 165=[-.00043514077513721515,.00333174431167827363] 
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dist 240=[-1.95155498959696466430e-05,1.12441307503969481000e-05] 
dist 241=[-2.18388898819555775220e-05,7.32003418306377535080e-06] 
dist 242=[-2.68501392826019894440e-05,6.25710009508317077080e-06] 
dist 243=[-3.10804339910834939050e-05,2.28751251625013631900e-06] 
dist 244=[-3.34318826705727111110e-05,1.44860835358240038540e-06] 
dist 245=[-3.48144708279689964780e-05,2.98303977847185046210e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 0, 2, 2, 0, 1] 
dist 0=[112.89422909974388584   ,112.89422909974388584   ] 
dist 1=[111.47297460477629419   ,113.98748438937139937   ] 
dist 2=[106.92124022479980748   ,115.03676242091119640   ] 
dist 3=[101.66525769210138067   ,115.10402435917035581   ] 
dist 4=[97.222299283953975415  ,113.07810972556573124   ] 
dist 5=[92.575507484330729976  ,112.09257143594497995   ] 
dist 6=[86.496078380395467472  ,110.33180442228627856   ] 
dist 7=[80.009451312193616164  ,109.58845884720552309   ] 
dist 8=[67.547306724504219607  ,86.705937537794042513  ] 
dist 9=[57.985044404442637590  ,83.425732861400107008  ] 
dist 10=[49.122996352140166019  ,76.402755501277512833  ] 
dist 11=[39.063563377701909114  ,73.022215258958118293  ] 
dist 12=[29.133360249030246923  ,56.002108526059935408  ] 
dist 13=[20.769800776084371012  ,52.576695902635403754  ] 
dist 14=[12.002221421640761727  ,48.954779672741474386  ] 
dist 15=[.4382253775782166446 ,48.099302956677452891  ] 
dist 16=[-10.510207359065177463  ,19.540053313948045826  ] 
dist 17=[-16.835064088762218163  ,15.837004299067597564  ] 
dist 18=[-21.006290350586041908  ,14.904156503950679752  ] 
dist 19=[-23.378227823433476492  ,5.5982706720411259267 ] 
dist 20=[-24.902351634698695393  ,4.1740360932472921453 ] 
dist 21=[-25.690234909476258239  ,1.6813628875613810930 ] 
dist 22=[-26.127782022894493212  ,1.1402124602946565863 ] 
dist 23=[-27.528054171302545099  ,-.08904578544229122208] 
dist 24=[-28.513772194127280528  ,-.09581863860436633576] 
dist 25=[-28.893021863737141348  ,.37766948261194973038] 
dist 26=[-28.731877681562610351  ,1.6071938973763764632 ] 
dist 27=[-19.907222214846263542  ,2.9067657821753653127 ] 
dist 28=[-16.595709375093841446  ,3.6612494499846873773 ] 
dist 29=[-15.779639002194366349  ,4.7255393432252833881 ] 
dist 30=[-15.189878232457479482  ,6.9002372342743216263 ] 
dist 31=[-15.017560119269702292  ,9.2203966169855914767 ] 
dist 32=[-2.9137133334912445179 ,11.254660976205416033  ] 
dist 33=[-1.4886674121181050622 ,12.297031676365153878  ] 
dist 34=[1.8321226725673758414 ,12.822288586259508301  ] 
dist 35=[.96622032724318457246,12.906764780972857358  ] 
dist 36=[.15326218758062292763,12.433426197904585528  ] 
dist 37=[-.55989438637731611054,12.165226688080889929  ] 
dist 38=[-1.2966210517559042558 ,11.754570290301271955  ] 
dist 39=[-1.9695247191477181947 ,11.544010208569132468  ] 
dist 40=[-2.4302212274254298911 ,9.5754475869419917662 ] 
dist 41=[-2.8132991144450717533 ,9.5749441915874414296 ] 
dist 42=[-4.4361962060858510708 ,9.3575224482928224164 ] 
dist 43=[-6.2937881625955038739 ,9.2181432894214523666 ] 
dist 44=[-7.8711258292627768868 ,7.9799661144979673627 ] 
dist 45=[-8.7483435099015251190 ,7.6516692612084134506 ] 
dist 46=[-9.2603425285537565543 ,7.1362232312069060311 ] 
dist 47=[-9.3894553772197944260 ,6.9528782259721610439 ] 
dist 48=[-3.2736340222984665712 ,2.8248824127507061391 ] 
dist 49=[-3.1598650011334674788 ,2.2932109648057783393 ] 
dist 50=[-4.0746552606534713321 ,1.0978760892102804765 ] 
dist 51=[-5.3041317938089082050 ,1.1355068342091101927 ] 
dist 52=[-6.3424063122264094876 ,1.6789691545290314934 ] 
dist 53=[-6.9112973923187435163 ,2.1267693197353921374 ] 
dist 54=[-7.2344941083538120188 ,2.5466715319763653077 ] 
dist 55=[-7.2973020386937977467 ,2.9051296979688190555 ] 
dist 56=[-1.9997085088635482798 ,3.1276098823442113742 ] 
dist 57=[-2.0041205872946663216 ,3.2645841130544096464 ] 
dist 58=[-1.9437587715709997752 ,3.2865416144469998273 ] 
dist 59=[-1.9349978457347557653 ,.82200544104068551746] 
dist 60=[-1.5867830833460140094 ,1.2094064604782423352 ] 
dist 61=[-1.5022107995317090292 ,1.4555446172846517998 ] 
dist 62=[-1.4444571759609648436 ,1.6404386691291699345 ] 
dist 63=[-1.4311594106027278394 ,1.7850560785639500670 ] 
dist 64=[-.18213567398458877934,1.8881412497063549842 ] 
dist 65=[-.03630558579008541598,1.9108680550852876489 ] 
dist 66=[.22100350680695109356,1.9000650298812040066 ] 
dist 67=[.10996465847008266156,1.8905191954379737593 ] 
dist 68=[.03238516272080496796,1.6174055035452893088 ] 
dist 69=[-.03375221666629631259,1.5441656328340971850 ] 
dist 70=[-.09943707495387235699,1.4805537813949868106 ] 
dist 71=[-.15803701770443605132,1.4451789579549894439 ] 
dist 72=[-.19609065644190051534,.98929393535317942073] 
dist 73=[-.31762786039345595219,.98643292243370784151] 
dist 74=[-.54594579526766201174,.95760068771781950312] 
dist 75=[-.76090515022700255717,.94293809474884329646] 
dist 76=[-.95832189023165109928,.80774675437134197087] 
dist 77=[-1.0653291379145390751 ,.77278489187810171126] 
dist 78=[-1.1254944216446379049 ,.71977106248872418617] 
dist 79=[-1.1387972844398459766 ,.70049299636935278327] 
dist 80=[-.45508166372506432008,.23802925902286832352] 
dist 81=[-.46285603410303761679,.17647648197085734864] 
dist 82=[-.46310094989389262123,.03858496837396678741] 
dist 83=[-.54767433461903829221,.02328185794346075465] 
dist 84=[-.65439734341849105209,.07379193758031161297] 
dist 85=[-.71346524276305828322,.1150749509834624391 ] 
dist 86=[-.74783376016270990917,.15329694811838901104] 
dist 87=[-.75648842979396189851,.18563637629584276245] 
dist 88=[-.22698011114538252369,.20357769961023418638] 
dist 89=[-.22671916140015893011,.21404204333208190821] 
dist 90=[-.21890296575679803834,.21667881808767939039] 
dist 91=[-.2172077666878178267 ,.12176199263458962797] 
dist 92=[-.17905016421070498272,.1711437697773939047 ] 
dist 93=[-.17005111178873591199,.20119897914038506247] 
dist 94=[-.1613380180264951206 ,.22227945372042523589] 
dist 95=[-.15810222183036436887,.23605297260651583459] 
dist 96=[-.03170118142733150207,.24464932893958781311] 
dist 97=[-.01625242383188769412,.24578832587660829667] 
dist 98=[.01583900836954003017,.24274887749916005391] 
dist 99=[-.00102435758153606676,.23955727325867953176] 
dist 100=[-.01254636076201507536,.20993679651665768458] 
dist 101=[-.02212257975034868742,.20171504493223081341] 
dist 102=[-.03126532651746252111,.18922717264098723745] 
dist 103=[-.03920285531344218868,.18449112979218043949] 
dist 104=[-.04399688442112627467,.13617641801621692266] 
dist 105=[-.06828726225609634874,.13549242998112095563] 
dist 106=[-.10364435552187750318,.13018591053037427621] 
dist 107=[-.13624106343015243647,.12859475877510581289] 
dist 108=[-.16377380815862273383,.10652501516763708415] 
dist 109=[-.17903249016761041236,.10112735856975991299] 
dist 110=[-.18793293780946103754,.09495212520808335875] 
dist 111=[-.19016548074073416097,.09201880951633022165] 
dist 112=[-.05871940919546676408,.03520030055610188229] 
dist 113=[-.05912629526100808269,.03044868452375872514] 
dist 114=[-.05796850397681706936,.02026119362403911860] 
dist 115=[-.06742580503049476496,.01747226667257116454] 
dist 116=[-.07836468494774768371,.02130870205003371223] 
dist 117=[-.08447758689123509448,.02594097620973906194] 
dist 118=[-.08833407109270272574,.03026451263553782369] 
dist 119=[-.08923687413159951498,.03395291749369897268] 
dist 120=[-.02075324254991284792,.03610276482439191666] 
dist 121=[-.02008548978109218099,.03773450595058311436] 
dist 122=[-.01771075962382071634,.03806221779800358334] 
dist 123=[.00408967948872501437,.02287578811629985480] 
dist 124=[.00897076830470492843,.02907455099536602865] 
dist 125=[.00873868041335152250,.03270420162004488427] 
dist 126=[.00810270307581946393,.03507877762488269673] 
dist 127=[.00727437437725695002,.03629597182886764257] 
dist 128=[.00627855627118282434,.03678400025066962000] 
dist 129=[.00499097754340972093,.03672778748444327954] 
dist 130=[.00300430370572946286,.03552820249240345160] 
dist 131=[.00099838128286019351,.03515892550351278058] 
dist 132=[-.00036572777382693710,.02925415355752360279] 
dist 133=[-.00149351257217217467,.02778784021915299675] 
dist 134=[-.00256149637595788417,.02623283744714625731] 
dist 135=[-.00348359196435721260,.02542327394115059337] 
dist 136=[-.00556299776228357748,.01005911231813706977] 
dist 137=[-.01011463154367135087,.00882640502024603435] 
dist 138=[-.01383444976380532365,.00612572040625890980] 
dist 139=[-.01728741587900080194,.00536749031942757700] 
dist 140=[-.02022270581117071595,.00237404892784943560] 
dist 141=[-.02202799835885688831,.00177240120767270610] 
dist 142=[-.02313580942377033608,.00062152897700313356] 
dist 143=[-.02338988074870135796,.00035077606924290716] 
dist 144=[-.00783156213221306368,-.00274871278629778529] 
dist 145=[-.00785068363508914223,-.00193617743824240411] 
dist 146=[-.00761976477476989353,-.00070371362644255702] 
dist 147=[-.00758617617349685443,.00053336354627781003] 
dist 148=[-.00622377466960609148,.00136424152350896225] 
dist 149=[-.00589105901047586702,.00204027908969954140] 
dist 150=[-.00566730743323777738,.00266268256086800364] 
dist 151=[-.00561494818488623960,.00318808963477171770] 
dist 152=[-.00065767386223508316,.00347907080180617611] 
dist 153=[-7.83164334875586226290e-05,.00364850315868502301] 
dist 154=[.00104566087312165509,.00369117036908852128] 
dist 155=[.00109918900808742500,.00236179562184870982] 
dist 156=[.00108884115673723969,.00312492122169080814] 
dist 157=[.00104810926253362943,.00356712452731653872] 
dist 158=[.00095643257408896464,.00385073172063902223] 
dist 159=[.00084151696710554603,.00398427374612917975] 
dist 160=[.00070851047998592999,.00403408591664115594] 
dist 161=[.00053955684219372336,.00402324660180642884] 
dist 162=[.00028191396614507957,.00390876798128845298] 
dist 163=[2.26961816961696849780e-05,.00384855254649912117] 
dist 164=[-.00015251941441464433,.00330224150412455743] 
dist 165=[-.00029632507770279152,.00316010888300193172] 
dist 166=[-.00043085576466448431,.00294293054482523138] 
dist 167=[-.00054595625566608082,.00286430756527847581] 
dist 168=[-.00061263034269731181,.00097677648503568871] 
dist 169=[-.00118762615519688837,.00072534817873129474] 
dist 170=[-.00175359275650919065,.00016179632838774783] 
dist 171=[-.00227385948603400265,3.91697527513789159380e-05] 
dist 172=[-.00271277648507189663,-.00044608778551277312] 
dist 173=[-.00295575953837153383,-.00042228622301097960] 
dist 174=[-.00309729771375043146,-.00037319364023002884] 
dist 175=[-.00313287989273810464,-.00031289254277823329] 
dist 176=[-.00093696271513571248,-.00024458569612269177] 
dist 177=[-.00093634125903903050,-.00015873541121528382] 
dist 178=[-.00090428881605763550,-2.87780426428500874750e-05] 
dist 179=[-.00089802236597774247,.00010164175715161145] 
dist 180=[-.00074061508747113986,.00018933076158939450] 
dist 181=[-.00070429778321062213,.00026080884835220392] 
dist 182=[-.00066697698560333233,.00032687070610413238] 
dist 183=[-.00065466623381884185,.00038284376347762028] 
dist 184=[-.00014171592187902089,.00041426858127502947] 
dist 185=[-7.85965752304350350430e-05,.00043531056978117573] 
dist 186=[2.08228307122581181680e-05,.00043995062659917558] 
dist 187=[2.74910443249403433620e-05,.00038807671370081595] 
dist 188=[2.28897336328142426460e-05,.00048284169623189619] 
dist 189=[1.17114623999348030620e-05,.00053683530529802019] 
dist 190=[-1.10653798375609890840e-05,.00057030679142501905] 
dist 191=[-3.89647056590552202640e-05,.00058359501351840624] 
dist 192=[-7.04838388190746262220e-05,.00058554189516103167] 
dist 193=[-.00011005242535492805,.00058266304100954863] 
dist 194=[-.00016991413862785984,.00056017682397904885] 
dist 195=[-.00023000284805185276,.00055319326151536806] 
dist 196=[-.00027047406759971903,.00045907652350227820] 
dist 197=[-.00030355018696282602,.00043597134784926098] 
dist 198=[-.00033427847768665376,.00040904365957497044] 
dist 199=[-.00036043513718786177,.00039647113537207794] 
dist 200=[-.00037536073540643451,9.25671108432802906930e-05] 
dist 201=[-.00038464253522386840,6.47973931783811062710e-05] 
dist 202=[-.00038839203053012807,2.20083638822265207760e-06] 
dist 203=[-.00038914268341363744,-1.06370408365856682890e-05] 
dist 204=[-.00038651758443308305,-6.61008630284698354700e-05] 
dist 205=[-.00038097951228018002,-6.22116620358793794120e-05] 
dist 206=[-.00037634395544442073,-5.46168900655725489910e-05] 
dist 207=[-.00035705563504658924,-4.54153165312278520030e-05] 
dist 208=[-.00011705045114726221,-3.51458669685060614470e-05] 
dist 209=[-.00011677101994169737,-2.23343024898539583420e-05] 
dist 210=[-.00011240984292281520,-3.03884196697045595500e-06] 
dist 211=[-.00011151214935383456,1.62961943366405965090e-05] 
dist 212=[-9.12952008063520110000e-05,2.92651237203290595810e-05] 
dist 213=[-8.64097156120310715580e-05,3.98059961028224101720e-05] 
dist 214=[-8.22190497156497530330e-05,4.95006702464846370970e-05] 
dist 215=[-8.06102340803413746720e-05,5.76844597259570476350e-05] 
dist 216=[-1.18562086294492804220e-05,6.22264635458443666350e-05] 
dist 217=[-3.60563260541513274810e-06,6.49265668378409489290e-05] 
dist 218=[3.02963651895119615250e-06,6.55950598211316560700e-05] 
dist 219=[3.35316597537319860200e-06,4.27341624710298134270e-05] 
dist 220=[2.49032502485596339640e-06,5.41225748122292270980e-05] 
dist 221=[7.26601860855792959890e-07,6.05840603598690090950e-05] 
dist 222=[-2.68204430930231561890e-06,6.45554170313264317770e-05] 
dist 223=[-6.80113226781925616500e-06,6.60569849068720406190e-05] 
dist 224=[-1.13859624899259989610e-05,6.62833781209149040240e-05] 
dist 225=[-1.70985349003923414720e-05,6.58808737588220030920e-05] 
dist 226=[-2.56956892829688396770e-05,6.37368138426194390380e-05] 
dist 227=[-3.43105773472119398250e-05,6.25219356590540425140e-05] 
dist 228=[-4.00936668240213337570e-05,5.40006450374082821680e-05] 
dist 229=[-4.48001364600551528830e-05,5.17709527615987129550e-05] 
dist 230=[-4.91402423153150184950e-05,4.77186756494606662180e-05] 
dist 231=[-5.28129518964626115750e-05,4.64836391877792976080e-05] 
dist 232=[-5.48694772411181786870e-05,1.83198564820803646490e-05] 
dist 233=[-5.60980616841612167020e-05,1.44046558545564075890e-05] 
dist 234=[-5.64833700288828809150e-05,5.80250976186991603510e-06] 
dist 235=[-5.63462599117455697790e-05,3.67738207845296479270e-06] 
dist 236=[-5.57736557420167555150e-05,-1.93510003702445971410e-06] 
dist 237=[-5.42594922462126649010e-05,-1.52076865102238301580e-06] 
dist 238=[-5.33985326269188663410e-05,-7.05978531626013755300e-07] 
dist 239=[-4.79201758803974570980e-05,2.83139807736535356130e-07] 
dist 240=[-1.01877934414373403170e-05,1.38971744952484453720e-06] 
dist 241=[-1.01373875564799184310e-05,2.77208878468795935150e-06] 
dist 242=[-9.98021073518242681520e-06,4.85633543187529371280e-06] 
dist 243=[-9.86197878904408042150e-06,6.94623902580786004070e-06] 
dist 244=[-9.06101265203545248250e-06,8.35110586069137282240e-06] 
dist 245=[-8.84107058430630624830e-06,9.49649143156622104600e-06] 
dist 246=[-7.92446585407778317190e-06,1.05561346328940991410e-05] 
dist 247=[-5.87627177515797789420e-06,1.14552033612745879060e-05] 
dist 248=[-4.78746175634744039680e-07,1.19630344249624191040e-05] 
dist 249=[-8.84123187885328622310e-08,1.22998812854913356240e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 1, 0, 1] 
dist 0=[113.66273693289488490   ,113.66273693289488490   ] 
dist 1=[111.36333636474169147   ,114.80834278454825709   ] 
dist 2=[105.83399136839160656   ,115.74730578166944999   ] 
dist 3=[99.597754076145068747  ,116.29929081250110739   ] 
dist 4=[94.484807239920597561  ,115.89466414974138015   ] 
dist 5=[89.277249244939002907  ,115.09491295709426970   ] 
dist 6=[82.651394278423778191  ,114.24913346329822752   ] 
dist 7=[70.234288697424345125  ,112.72824814181469512   ] 
dist 8=[60.729325547489886183  ,110.57192212690486001   ] 
dist 9=[51.916394032676310336  ,89.345628838584766279  ] 
dist 10=[41.906114881613365489  ,86.086396320613827642  ] 
dist 11=[32.020074638573416059  ,76.960094313242227791  ] 
dist 12=[23.685901473774622572  ,75.641719412190300999  ] 
dist 13=[14.942078271756426518  ,58.053143785109898248  ] 
dist 14=[3.4000180549197773711 ,54.503981496996398824  ] 
dist 15=[-7.5481121595452689732 ,50.964128216394946053  ] 
dist 16=[-13.935112517309116538  ,50.277672773951584429  ] 
dist 17=[-18.224603432588081888  ,12.716028216598478794  ] 
dist 18=[-20.819207516794896363  ,10.962363604630880793  ] 
dist 19=[-22.567424706069288305  ,4.5920579268222297624 ] 
dist 20=[-23.479275926651833918  ,3.5140054115954140348 ] 
dist 21=[-23.988931396024790878  ,2.0302686631821860031 ] 
dist 22=[-25.965505462024101623  ,1.5980822255389441577 ] 
dist 23=[-27.921976331742113637  ,1.4124529135988062915 ] 
dist 24=[-28.667166630709995670  ,1.7658991314655985012 ] 
dist 25=[-28.883723345768217092  ,2.5296654880080244972 ] 
dist 26=[-28.732841162752214503  ,4.0255876567463482984 ] 
dist 27=[-22.262912742376200596  ,5.5355661033029597054 ] 
dist 28=[-22.175517755162825905  ,6.3580165805002758069 ] 
dist 29=[-18.546906049377403142  ,6.8245145954323944452 ] 
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dist 179=[-.00075542989747928750,-2.82548268210233967540e-05] 
dist 180=[-.00087121316432243811,-7.70314690885065056390e-05] 
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dist 182=[-.00114362408885339809,-.00018460209883370251] 
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dist 195=[-.00016203151520994374,.00052501725474753944] 
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dist 197=[-8.84779585965217803450e-05,.00046381356238958037] 
dist 198=[-7.50961078753311566570e-05,.00043676002685850656] 
dist 199=[-6.01028957415141516470e-05,.00024023605519701767] 
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dist 206=[-.00026706512228922837,.00018263427590992334] 
dist 207=[-.00012784375272621139,.00017015898815012554] 
dist 208=[-.00012739205064888472,.00016515102005144785] 
dist 209=[-.00012293721567822550,4.87794957234259149360e-05] 
dist 210=[-.00012145187663592573,3.42738459115726762390e-05] 
dist 211=[-.00010158183744103270,1.86440650828444899580e-06] 
dist 212=[-.00012814883244342936,-5.05892076099668222860e-06] 
dist 213=[-.00015272935375098135,-4.00060067933416207150e-05] 
dist 214=[-.00016634122366688704,-2.41708280779447668340e-05] 
dist 215=[-.00017431517760664736,6.62044308655271778230e-06] 
dist 216=[-.00017631531730728116,2.73071602355872253880e-05] 
dist 217=[-6.90019587948846609150e-05,4.41613476453887544770e-05] 
dist 218=[-6.82914080631094727150e-05,5.97353937247181693020e-05] 
dist 219=[-6.66766063236609226720e-05,7.29372807727820815220e-05] 
dist 220=[-6.57464080646806173250e-05,8.03726942036582122990e-05] 
dist 221=[-5.99624476425346787960e-05,8.48714214752617730590e-05] 
dist 222=[-5.84478867044599451890e-05,8.64130686992449848980e-05] 
dist 223=[-5.31995140540920570890e-05,8.63914453712367978660e-05] 
dist 224=[-5.22012811122105940250e-05,8.57943104703087481460e-05] 
dist 225=[-3.64474196912692157330e-05,8.26157743926902904940e-05] 
dist 226=[-3.34783863413086302190e-05,8.11694484806096577730e-05] 
dist 227=[-2.77545385030617487140e-05,6.90052054304276738090e-05] 
dist 228=[-2.62107548892929094630e-05,6.59200563615509622160e-05] 
dist 229=[-2.07478714578692406610e-05,6.09627899481718057100e-05] 
dist 230=[-1.92679394605250002740e-05,5.63326786873588396100e-05] 
dist 231=[-1.79500469879722093000e-05,4.12742503969918297070e-05] 
dist 232=[-1.76074974696729082920e-05,4.18015815093521999190e-05] 
dist 233=[-1.75512876236249425000e-05,4.15662170629163997760e-05] 
dist 234=[-1.76386182257107168710e-05,4.12524772560293898080e-05] 
dist 235=[-2.13365085802478979280e-05,3.93398408667274607410e-05] 
dist 236=[-2.37215617629689951570e-05,3.88725475013323902730e-05] 
dist 237=[-2.51665620116021290530e-05,3.16614955471090065800e-05] 
dist 238=[-2.56662219116011804700e-05,2.99411689003474603820e-05] 
dist 239=[-2.57806968836052336880e-05,2.81276737012098647410e-05] 
dist 240=[-2.56962664481986974380e-05,2.72532464145776698650e-05] 
dist 241=[-2.54525484138050066570e-05,6.00729146951366609360e-06] 
dist 242=[-2.51417036267140467820e-05,5.17418629231065192740e-06] 
dist 243=[-2.42932357056758944510e-05,3.39945481545005453920e-06] 
dist 244=[-2.38469149519875930460e-05,2.91678411777825390400e-06] 
dist 245=[-2.27809905637204626210e-05,1.10149487165156177620e-06] 
dist 246=[-2.23122372561791511370e-05,7.20687109006217754370e-07] 
dist 247=[-1.98182436342871568940e-05,1.67203903909191180240e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 2, 0, 0, 1] 
dist 0=[97.584101830247007861  ,97.584101830247007861  ] 
dist 1=[95.318219564845066092  ,98.798209120937700419  ] 
dist 2=[90.953552471146114561  ,98.996571483761338251  ] 
dist 3=[86.119466535376675255  ,98.616561807666737811  ] 
dist 4=[81.983045397782229877  ,97.673338982962429578  ] 
dist 5=[77.607982817109345384  ,97.226708946592427988  ] 
dist 6=[71.813360749715541193  ,96.734833419151703118  ] 
dist 7=[65.590013566033272516  ,96.290602476352245261  ] 
dist 8=[59.498968778133633555  ,92.930064778490240786  ] 
dist 9=[52.355126618730195653  ,74.412010714726209195  ] 
dist 10=[41.924035945627954208  ,73.390913955981242128  ] 
dist 11=[31.560779911751589506  ,70.334084253206716939  ] 
dist 12=[24.684535089912727503  ,69.720104648199244126  ] 
dist 13=[19.046002600456437786  ,65.952924542997442962  ] 
dist 14=[13.619508502320161981  ,59.863109599062467668  ] 
dist 15=[8.7351928646272529923 ,43.578423250585548241  ] 
dist 16=[5.2580586322842488733 ,42.607124073407114193  ] 
dist 17=[2.1332926949366784478 ,24.074276154235822951  ] 
dist 18=[-2.487827001059643258  ,21.603852989663907562  ] 
dist 19=[-8.6799416676224732772 ,15.950802800983888820  ] 
dist 20=[-13.381109830986840811  ,14.882689712115147234  ] 
dist 21=[-18.361004686922773367  ,7.8256714755757909401 ] 
dist 22=[-23.259530194538167861  ,6.5872465735486137872 ] 
dist 23=[-28.239163279408883033  ,4.2794713413434009880 ] 
dist 24=[-31.139026407968606321  ,4.461109624453168962  ] 
dist 25=[-33.058949837429987896  ,6.179464765943639356  ] 
dist 26=[-34.130188987869785644  ,8.359421271955352214  ] 
dist 27=[-34.670552442178398845  ,10.589843501589775152  ] 
dist 28=[-34.477851375259670573  ,12.517063033453837581  ] 
dist 29=[-30.413156965283456937  ,14.552413806990896045  ] 
dist 30=[-26.689840316689690615  ,17.222011961107576431  ] 
dist 31=[-2.5819085747339134617 ,19.635440114192414156  ] 
dist 32=[-2.3173661344351181190 ,20.656442593826752010  ] 
dist 33=[-1.8004329875536359774 ,21.098827304771148157  ] 
dist 34=[-1.6746784429362768665 ,21.209361755395044328  ] 
dist 35=[-.2064008909772148328 ,18.923167937183442089  ] 
dist 36=[.00749062609134080076,18.325247770785869621  ] 
dist 37=[.4201418307729910212 ,17.973911747968834170  ] 
dist 38=[.52011703116492999892,17.884784245758908796  ] 
dist 39=[.77505533070602409242,4.2898371034924308022 ] 
dist 40=[.79906180483477596894,3.9337159808530756210 ] 
dist 41=[-1.8001659185733076480 ,3.9794094450088243354 ] 
dist 42=[-4.5087733516071756047 ,3.9692879078029550580 ] 
dist 43=[-6.9033822312880739865 ,2.9587332414200519267 ] 
dist 44=[-8.4255307530237575106 ,2.8192221363113503366 ] 
dist 45=[-9.5709645188836520818 ,2.8172725243316354735 ] 
dist 46=[-10.471971366919429554  ,3.0010828081344926417 ] 
dist 47=[-11.133104384059794286  ,3.2828325084682200767 ] 
dist 48=[-11.326683728283849960  ,3.6696010005767451432 ] 
dist 49=[-11.325381752218760855  ,4.1975172616340207129 ] 
dist 50=[-11.211624559707972314  ,5.0394199590678636897 ] 
dist 51=[-10.027780769851954011  ,5.8961914482363768960 ] 
dist 52=[-9.6729142013864453107 ,6.4832098510198595179 ] 
dist 53=[-9.1647904596184234248 ,6.9718293614805484595 ] 
dist 54=[-8.7415875248800973263 ,7.4383622981518465147 ] 
dist 55=[-3.2458527007681958362 ,7.8424641526437402848 ] 
dist 56=[-2.5320929415158587187 ,8.0834668151226385561 ] 
dist 57=[-.90648271345740102408,8.2460435479096689136 ] 
dist 58=[-.56218637267123955855,8.3390643803749033668 ] 
dist 59=[-.29118962991572740849,8.3693508566607465604 ] 
dist 60=[-.27006321612820964287,8.2871754599034258817 ] 
dist 61=[-.21641595301174750653,8.1117812175003768012 ] 
dist 62=[-.20767001066264327576,7.7310698518172331033 ] 
dist 63=[-.12467339391953629221,2.5830403514708131854 ] 
dist 64=[-.10941526105209238444,2.6113764358186929787 ] 
dist 65=[-.08796470362115574957,2.5820650577728810988 ] 
dist 66=[-.08173961130674930030,2.5777967395342694686 ] 
dist 67=[.02680944235821865779,2.1689691439614939322 ] 
dist 68=[.04004334507840659876,2.0640272235305408121 ] 
dist 69=[.06571329320782555805,2.0016823316595502728 ] 
dist 70=[.07138049510878240092,1.9861404724509332805 ] 
dist 71=[.08607499464110709251,.31509643609620178145] 
dist 72=[-.08062843447078077152,.17548646532744066398] 
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dist 189=[6.27412853562125378800e-06,.00160655017198601177] 
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dist 191=[6.57022464970114000500e-06,.00062851646182998257] 
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dist 203=[-.00025794930127909652,-3.73651840745676378100e-07] 
dist 204=[-.00029086292732583501,-6.29312032997051094000e-07] 
dist 205=[-.00031085989463777536,-9.07118193897771117900e-07] 
dist 206=[-.00031790452665031314,-8.75359167549180454200e-07] 
dist 207=[-.00031839067097464504,-7.19230837037995612700e-07] 
dist 208=[-.00031643485489393916,-4.00347388165563342500e-07] 
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dist 210=[-.00029994471337819689,9.20473242370530495880e-07] 
dist 211=[-.00025433864246963215,1.78265716396427510860e-06] 
dist 212=[-.00024281708478773229,2.39298903543559433780e-06] 
dist 213=[-.00022538732439282753,2.92083342446124662520e-06] 
dist 214=[-.00021913161015735446,3.45631679389419143610e-06] 
dist 215=[-7.11419075866886169830e-05,4.11937041144568925300e-05] 
dist 216=[-5.15386939141134006440e-05,9.51951270927314333400e-05] 
dist 217=[-7.82105671680834627200e-06,.00013902824217078927] 
dist 218=[-4.25414293415029729610e-06,.00017926342423111993] 
dist 219=[-3.79606943330019910930e-06,.00021318698369139899] 
dist 220=[-3.67099416878797350610e-06,.00023195801204797267] 
dist 221=[-3.61108087194202934490e-06,.00024287912527150984] 
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dist 226=[-4.26422829409170620190e-06,7.05632169688251475070e-05] 
dist 227=[-4.56794237156496066280e-06,5.66917721150732542700e-05] 
dist 228=[-4.78010493713486650270e-06,5.36283649815096776580e-05] 
dist 229=[-4.96041884884644900570e-06,5.08864245006925540170e-05] 
dist 230=[-5.13800072169918944950e-06,5.03128450714004291940e-05] 
dist 231=[-5.29499606711930623780e-06,9.24433496398540739640e-06] 
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dist 234=[-3.07671061132318343520e-05,9.26352295167246723160e-06] 
dist 235=[-3.79639014527722910620e-05,9.14365423699994200370e-06] 
dist 236=[-4.19963367357554423180e-05,9.34477319733858490720e-06] 
dist 237=[-4.44095001932248556320e-05,9.77081188534855969680e-06] 
dist 238=[-4.51766027479016068640e-05,1.06041115301439026730e-05] 
dist 239=[-4.50658243614338581870e-05,1.16143282446321388810e-05] 
dist 240=[-4.47703074178179569450e-05,1.27428999131219460030e-05] 
dist 241=[-4.28201556345909533900e-05,1.41517753589229567370e-05] 
dist 242=[-4.23114954129453147900e-05,1.62750420112774534830e-05] 
dist 243=[-3.46935010007313450980e-05,1.84039307496885552070e-05] 
dist 244=[-3.28599606498528659370e-05,1.98351621437664809290e-05] 
dist 245=[-3.08809810644601512550e-05,2.10022970886752960640e-05] 
dist 246=[-2.98918074143290365830e-05,2.20825831939073539610e-05] 
dist 247=[-1.06902519480683932370e-05,2.29995993955865022850e-05] 
dist 248=[-9.19147785500082885710e-06,2.35184670353827946350e-05] 
dist 249=[-6.00552645785893743370e-06,2.38355416497009223560e-05] 
dist 250=[-5.14099301034315740230e-06,2.39513371014988653020e-05] 
dist 251=[-1.90304954990865487850e-06,2.51768198879316039430e-05] 
dist 252=[-1.22049706599369585080e-06,2.70890321473639141870e-05] 
dist 253=[-2.63806926445251255540e-07,2.82158592577988511520e-05] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 0, 2, 0, 2] 
dist 0=[144.50523491306489684   ,144.50523491306489684   ] 
dist 1=[139.28191143440219312   ,146.01690579499072692   ] 
dist 2=[132.23668308818574168   ,146.14665201082672942   ] 
dist 3=[123.47958960987440107   ,145.89729149794293816   ] 
dist 4=[111.96307323778490771   ,144.22106674688016853   ] 
dist 5=[93.946436406449677433  ,132.79772663213426750   ] 
dist 6=[75.544102972104013989  ,129.60352295122577674   ] 
dist 7=[62.488173654230353131  ,126.28279624774409409   ] 
dist 8=[51.051411621799804539  ,109.69188840063705176   ] 
dist 9=[39.069419330017989241  ,95.039399511166161274  ] 
dist 10=[27.835588281431414374  ,90.906349586574681259  ] 
dist 11=[19.358576793857726636  ,90.078797177482022021  ] 
dist 12=[11.343451701628044383  ,48.361337846012918657  ] 
dist 13=[1.9199904413477531775 ,33.630214660320133337  ] 
dist 14=[-6.7712502560189073854 ,31.019992088872317633  ] 
dist 15=[-11.879732186001877144  ,27.206194338201937319  ] 
dist 16=[-16.647928742008471795  ,23.266236004135432355  ] 
dist 17=[-22.734597591457237379  ,-12.625673570916052990  ] 
dist 18=[-27.310684384429665670  ,-15.413833614272350211  ] 
dist 19=[-30.976007235119033200  ,-14.431180494270485878  ] 
dist 20=[-33.736895637403361642  ,-11.767203952700911092  ] 
dist 21=[-34.719672492878737312  ,-6.8202184787354413799 ] 
dist 22=[-34.936570758471347547  ,-1.6397996105878478608 ] 
dist 23=[-34.637771597604262339  ,1.9560234427169064587 ] 
dist 24=[-31.215444422288096142  ,4.9587099794258924286 ] 
dist 25=[-30.156143037099759937  ,7.7966792657939151501 ] 
dist 26=[-28.615638364024941801  ,10.202655965614770748  ] 
dist 27=[-27.966201024598474083  ,11.496535711810701273  ] 
dist 28=[-11.138690969857023350  ,12.182784407976670177  ] 
dist 29=[-8.8959047778071064931 ,12.309076507675573107  ] 
dist 30=[-3.7501145057240855839 ,12.377104613046237511  ] 
dist 31=[-2.7011252510345970024 ,16.999825587637562546  ] 
dist 32=[1.9334776581889922469 ,20.907943147978945067  ] 
dist 33=[3.3857518351188872692 ,23.074516534874510345  ] 
dist 34=[3.4897890063746861293 ,24.336469320757928149  ] 
dist 35=[3.2736511648549226524 ,24.654426086155569086  ] 
dist 36=[2.8527625989751736307 ,7.7724203572467813076 ] 
dist 37=[2.0631962787315307147 ,7.9206595882908327259 ] 
dist 38=[1.2270157313488400625 ,7.9315900038784945023 ] 
dist 39=[.62063275592548748492,7.9189985793229010755 ] 
dist 40=[.08395812798203381081,6.8409524685110093565 ] 
dist 41=[-.47700878181130811094,6.5484137302868160830 ] 
dist 42=[-.99319054037514117536,6.3463889337647723823 ] 
dist 43=[-1.3529573855269459897 ,6.2542934166521167650 ] 
dist 44=[-1.6591550287294068521 ,1.4651525747144595387 ] 
dist 45=[-2.0864561468798572950 ,.89123664374910719317] 
dist 46=[-2.6775966439313412685 ,-.46708310467277174907] 
dist 47=[-3.1477854876742228937 ,-.6656995100201924929 ] 
dist 48=[-3.5633116335665163408 ,-1.6010079984545755517 ] 
dist 49=[-3.8899167861112636068 ,-1.5527655005014613997 ] 
dist 50=[-4.0095159086838497335 ,-1.4479190037069220504 ] 
dist 51=[-4.2218035862781304321 ,-1.2748245709687913760 ] 
dist 52=[-4.3395938162178078701 ,-1.0239591601588303571 ] 
dist 53=[-4.3534762332635493644 ,-.61051518528207570962] 
dist 54=[-4.2463821244555987170 ,-.18681937019837356988] 
dist 55=[-4.2146352728929951518 ,.14699363956227970972] 
dist 56=[-3.5196881208278735158 ,.46392359852137874508] 
dist 57=[-3.3448780959016558379 ,.75582667003958482203] 
dist 58=[-3.1847981393756103029 ,1.0022085817757548412 ] 
dist 59=[-3.1073676856459222951 ,1.3104529176991501323 ] 
dist 60=[-.88588759031563548124,1.8398462052689408879 ] 
dist 61=[-.65161872648132850607,2.2853503808582557409 ] 
dist 62=[-.11529587378568293101,2.5273575850430899984 ] 
dist 63=[-.01080260746432982046,2.6614089107459691364 ] 
dist 64=[.60905334021080260211,2.6906805616803497400 ] 
dist 65=[.59021494300678806208,2.3896489474549908693 ] 
dist 66=[.54394461957954644491,2.5230968047848852662 ] 
dist 67=[.47838839790355406212,2.5545303006580738005 ] 
dist 68=[.38783840944844396757,1.0180265177093342267 ] 
dist 69=[.24235624130653876086,1.0238307162253666493 ] 
dist 70=[.09381953893794786322,1.0023097191753887043 ] 
dist 71=[-.00887845891209113189,.99780821106774109631] 
dist 72=[-.09539707037500769012,.8328963011780573274 ] 
dist 73=[-.17977611866467128523,.7914904403604458975 ] 
dist 74=[-.25413848290308724077,.76117366941509350318] 
dist 75=[-.30093594573961499874,.7505685201866132762 ] 
dist 76=[-.33557931796597885036,.12507833574774243595] 
dist 77=[-.36174573500892292569,.05095323507896267227] 
dist 78=[-.41331306126799871097,-.1232725547259783149 ] 
dist 79=[-.46221717682010216987,-.14850658430601655558] 
dist 80=[-.49721122210317339307,-.28244755978246689026] 
dist 81=[-.52104341084767024043,-.26092508970402982206] 
dist 82=[-.52565304394762740039,-.2319002937146663715 ] 
dist 83=[-.54263396037214146633,-.19594479939977945299] 
dist 84=[-.54966064506049763135,-.1488739527238135469 ] 
dist 85=[-.548706068260432809  ,-.07572892805075321421] 
dist 86=[-.53060290983350777023,-.00185880693068322871] 
dist 87=[-.52495590686328763087,.04809573602270098920] 
dist 88=[-.43689168762472398169,.08902711762339470940] 
dist 89=[-.41504757558216290002,.12709744509359357682] 
dist 90=[-.39147154300706877673,.15943390925135388116] 
dist 91=[-.37943448325383227973,.21886687750871585499] 
dist 92=[-.12794059898892017424,.28967863143609271476] 
dist 93=[-.09551191979550566041,.34951497085174786894] 
dist 94=[-.02260388909048913355,.38267640228454389489] 
dist 95=[-.00693125481553041907,.40198809015049771163] 
dist 96=[.07356963876623522810,.40685357667674536791] 
dist 97=[.08513916929140811685,.37370076190639467204] 
dist 98=[.07052594669772324514,.39185851835716890858] 
dist 99=[.05348931068198143172,.39643204583788633227] 
dist 100=[.031780254132643326  ,.1359766456480774988 ] 
dist 101=[-.00138319008465852620,.13574864403286054271] 
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dist 127=[.00164655000304053727,.04232037506235361411] 
dist 128=[.01056575229382778633,.04283602365644229551] 
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dist 157=[-.00131374559080621061,.00580914110275252922] 
dist 158=[-.00023086588466375870,.00633315647406956607] 
dist 159=[5.31796173841478635770e-06,.00663842398170391553] 
dist 160=[.00117773156166805563,.00671521884515938259] 
dist 161=[.00138262300644610310,.00570457740312963363] 
dist 162=[.00171495960755765099,.00597511729782658876] 
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dist 169=[-5.51928702004402142430e-06,.00133773131721526851] 
dist 170=[-.00032378688938715222,.00127778677803412781] 
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dist 172=[-.00082621601626306892,.00024152177225421407] 
dist 173=[-.00103248325381803541,.00011917091140063324] 
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dist 176=[-.00125469423750288366,-.00053303069477620287] 
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dist 183=[-.00104821425877368678,-.00025222823981375061] 
dist 184=[-.00086094021633678163,-2.37995421768255890000e-05] 
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dist 186=[-.00076705926619314997,.00035919670022181862] 
dist 187=[-.00074259261104476507,.00048459107967792789] 
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dist 193=[-3.30372177310800740240e-05,.00066789172875673707] 
dist 194=[-7.88034227384487561480e-06,.00069694570091088020] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 0, 1, 1, 2] 
dist 0=[129.51697798754727148   ,129.51697798754727148   ] 
dist 1=[126.85248937323225490   ,130.05905683433005145   ] 
dist 2=[122.84126555913608533   ,129.53285725802879589   ] 
dist 3=[117.34325826783373713   ,128.89023930847908427   ] 
dist 4=[109.80544935142565379   ,127.49584981956579057   ] 
dist 5=[97.678139448452569688  ,118.23466799287344630   ] 
dist 6=[85.117815858851007415  ,116.10787963972901677   ] 
dist 7=[75.852030274933037734  ,108.40684601482794274   ] 
dist 8=[66.502829709416947972  ,105.41694396639604387   ] 
dist 9=[54.545832768720844851  ,88.082665204791094025  ] 
dist 10=[43.905167166006512761  ,84.308774453583891533  ] 
dist 11=[32.483503066277770282  ,80.206922322355728120  ] 
dist 12=[21.593712484609839559  ,78.663892597782221495  ] 
dist 13=[13.053773234373774006  ,46.245018325314044020  ] 
dist 14=[4.6601514739217522799 ,36.989053015947843328  ] 
dist 15=[-5.6730553276866755689 ,32.359323677011749238  ] 
dist 16=[-15.255578411040498911  ,14.660011006192901491  ] 
dist 17=[-20.669050556570049813  ,-.05513818099800549618] 
dist 18=[-24.089060541744880812  ,-2.8915939432115360121 ] 
dist 19=[-25.733549552336392201  ,-4.4934611386492493829 ] 
dist 20=[-29.241247064775181278  ,-3.8267308066430648927 ] 
dist 21=[-32.453753632999420205  ,-1.6089596193563786371 ] 
dist 22=[-33.676841995171988227  ,.97136631455318480813] 
dist 23=[-34.087142626343575857  ,3.0841365686852212284 ] 
dist 24=[-34.053169893978931114  ,5.1777477218004571005 ] 
dist 25=[-30.339396607068500693  ,7.6954995917660492268 ] 
dist 26=[-29.231796923856016893  ,10.211134864926224676  ] 
dist 27=[-28.340309554310511180  ,12.303950302046212085  ] 
dist 28=[-27.742870472656016772  ,14.447606886759097378  ] 
dist 29=[-8.7252061656662946217 ,17.173959221755690533  ] 
dist 30=[-6.3724828581878324920 ,19.622315441961662749  ] 
dist 31=[-.76228558002355509919,20.664691442522332001  ] 
dist 32=[.08252818276432206965,21.120465930030265136  ] 
dist 33=[7.1533059029940774033 ,21.234310117066377357  ] 
dist 34=[8.2574436702135364833 ,18.962933959113131185  ] 
dist 35=[10.144380336230943695  ,18.368578315094279021  ] 
dist 36=[10.474188813007913989  ,18.883820242449855451  ] 
dist 37=[8.9986531973899586825 ,19.489207584801765778  ] 
dist 38=[4.2552438961461354736 ,19.564454667277898524  ] 
dist 39=[.97383571207610193823,19.161458874526976681  ] 
dist 40=[-1.7919388494749371110 ,18.972413251169674666  ] 
dist 41=[-4.4911128711075183477 ,16.071697433626505698  ] 
dist 42=[-6.8714165687642086636 ,15.322049566361977748  ] 
dist 43=[-8.3729491047634188852 ,14.474786781515106101  ] 
dist 44=[-9.4893332392814970315 ,14.051631784858480146  ] 
dist 45=[-10.342636131317243672  ,6.4118856873585742357 ] 
dist 46=[-10.956379888726989706  ,5.7041176591663472167 ] 
dist 47=[-11.122264693728106338  ,4.1109675353054535418 ] 
dist 48=[-11.102294944328189641  ,3.6702087260199954552 ] 
dist 49=[-11.287341643756515174  ,1.7712113764161712430 ] 
dist 50=[-12.349515457476506691  ,1.4087797465235296581 ] 
dist 51=[-12.931591453407911238  ,.60696255384837861506] 
dist 52=[-13.040977896542823299  ,.42062484288992483056] 
dist 53=[-8.6930708577082408195 ,-2.0569163048273810158 ] 
dist 54=[-3.3324381351536515388 ,.91375959309669907076] 
dist 55=[-3.1442956927574638100 ,2.9153090057219938447 ] 
dist 56=[-.97041140243733780781,4.5484909624195606797 ] 
dist 57=[-.62564446025584784721,6.0573708184156780187 ] 
dist 58=[.21764975639652480318,7.3329011373841358917 ] 
dist 59=[.32751951495561140493,8.0400636052414890783 ] 
dist 60=[1.0964822364898472509 ,8.4519976732763712879 ] 
dist 61=[1.2145628300838649288 ,8.5557408306964679628 ] 
dist 62=[1.4220029571731741597 ,2.6242273277393543368 ] 
dist 63=[1.4554089819199305281 ,2.6573168158118849895 ] 
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dist 65=[1.9497592869378060612 ,2.6354373232926780575 ] 
dist 66=[1.8849583987234541272 ,2.2556006858203534438 ] 
dist 67=[1.7115716566525134252 ,2.1556152935127683708 ] 
dist 68=[1.4482890350165276036 ,2.0802409227268099559 ] 
dist 69=[.83765811134508425054,2.0471097476982685491 ] 
dist 70=[.22048384059049511448,1.6052929522546601210 ] 
dist 71=[-.19958816011663197714,1.5673764810304085118 ] 
dist 72=[-.54715550898994086217,.61713000092063092045] 
dist 73=[-.87661219536909090473,.49065430807922785833] 
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dist 75=[-1.3307924012609770758 ,.14048027464567183031] 
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dist 102=[-.08891860026175890659,.30480429705705178855] 
dist 103=[-.15228853013815722672,.2969349891270459475 ] 
dist 104=[-.20440727761082742311,.11110954202324966757] 
dist 105=[-.25333988737950560736,.08550762838884230253] 
dist 106=[-.2953241442106145095 ,.02934489896852081977] 
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dist 108=[-.33586339298344387582,-.03391640999063034842] 
dist 109=[-.34396214713107327856,-.04057613318173092018] 
dist 110=[-.34744392684311173276,-.05283030432063948269] 
dist 111=[-.34511588120257079152,-.05512641602329213688] 
dist 112=[-.17798582661951462417,-.05877195684542725674] 
dist 113=[-.17532823896973864107,-.05855270812023926183] 
dist 114=[-.15100818871334329028,-.05674148641917454106] 
dist 115=[-.14461423213897341294,-.05234074588594840907] 
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dist 118=[-.04509029171232876404,.02113023822050230637] 
dist 119=[-.04335840632680936127,.05289473573597454445] 
dist 120=[-.00770325264843576509,.07871807680914974899] 
dist 121=[-.00212606525667613705,.10246760183741468473] 
dist 122=[.00878231983912993324,.12250719806758584058] 
dist 123=[.01034359896462753096,.13360162670409349298] 
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dist 125=[.02385455017052574331,.14168440330921958341] 
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dist 128=[.03040001936126306290,.04151422167359060033] 
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dist 130=[.02834278580838806667,.03403244693802639427] 
dist 131=[.02534320146112084867,.03226496829777903940] 
dist 132=[.02110431497144294531,.03082198578203860288] 
dist 133=[.01146908308978906275,.03027445813410473274] 
dist 134=[.00178963033902130782,.02257558755423153351] 
dist 135=[-.00473706027467613702,.02198231323768866416] 
dist 136=[-.01007808285039601862,.00759094862337702666] 
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dist 138=[-.01928954369402971955,.00134521095371758325] 
dist 139=[-.02171954064199537725,.00041413855141882471] 
dist 140=[-.02324478436685930526,-.00436423970923435108] 
dist 141=[-.02389204411268051847,-.00519035603807989483] 
dist 142=[-.02403923382383487582,-.00662399831259454840] 
dist 143=[-.02395405894482403626,-.00689591728469112060] 
dist 144=[-.02302612474132338683,-.00714344083389779236] 
dist 145=[-.02280478849808984154,-.00705036306319332990] 
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dist 147=[-.01770723013358412485,-.00618041146840852388] 
dist 148=[-.01675571411061626347,-.00544576767224545805] 
dist 149=[-.01632547550103882032,-.00321146707476776065] 
dist 150=[-.00517134674028186831,.00169996169099961229] 
dist 151=[-.00507990536123981915,.00499651983571618031] 
dist 152=[-.00080706758351820993,.00767818456371233522] 
dist 153=[-.00029603698010442353,.01014828970216000098] 
dist 154=[.00089817198855440532,.01223596038479291919] 
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dist 210=[-.00031092060345320968,-9.19609729009066390850e-05] 
dist 211=[-.00029459659901310724,-8.08784233954093700140e-05] 
dist 212=[-.00027701330518002799,-6.74695556233019312870e-05] 
dist 213=[-.00026818178074477912,-4.24991369546309000000e-06] 
dist 214=[-9.72733808787539036600e-05,6.84553445686043954120e-05] 
dist 215=[-8.38826772097095247060e-05,.00011722256635135320] 
dist 216=[-5.53063379872569999150e-05,.00015687282765864549] 
dist 217=[-4.75167440080896590890e-05,.00019337759605951593] 
dist 218=[-1.81287971337380910260e-05,.00022423156629299988] 
dist 219=[-1.39777729465523745900e-05,.00024144427758257351] 
dist 220=[-2.86747964068498656900e-06,.00025196629058698050] 
dist 221=[-3.86528867521573430840e-07,.00025467100345220541] 
dist 222=[5.36706485858127956740e-06,9.37837171036932463360e-05] 
dist 223=[6.32741801289280209030e-06,9.51965767518807391910e-05] 
dist 224=[7.00906344291972111170e-06,9.50996806590795221490e-05] 
dist 225=[5.85373890997571272140e-06,9.44003550826931909040e-05] 
dist 226=[3.40373122624044811110e-06,9.09310624432546621360e-05] 
dist 227=[-1.38989099815818131550e-06,8.92368253474014417190e-05] 
dist 228=[-7.20189502912372969960e-06,7.62445891796285788090e-05] 
dist 229=[-1.36959624333891417230e-05,7.29221746746186343370e-05] 
dist 230=[-2.32251777042851793410e-05,6.72217255988764543610e-05] 
dist 231=[-3.75620522738245707440e-05,6.54261323060678857540e-05] 
dist 232=[-4.92356676023097545560e-05,2.37201084030561123760e-05] 
dist 233=[-6.00127065562962721710e-05,1.80108874940602661430e-05] 
dist 234=[-6.91429576071988121450e-05,9.39187684792724827830e-06] 
dist 235=[-7.42776992820530905190e-05,8.07606700276200812540e-06] 
dist 236=[-7.73753152743975161840e-05,3.10297345715646516780e-06] 
dist 237=[-7.84168150184841857940e-05,2.06322218743751953070e-06] 
dist 238=[-7.84294410684583998550e-05,5.04617041036277275460e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 1, 1, 1, 0, 1] 
dist 0=[149.68582926576619432   ,149.68582926576619432   ] 
dist 1=[147.94540559886385896   ,149.79532507406667721   ] 
dist 2=[144.80598833929830447   ,149.68582926576619432   ] 
dist 3=[137.59041540895596450   ,146.78084057001441235   ] 
dist 4=[128.35563101337975979   ,144.57496725365171631   ] 
dist 5=[117.74620379053658253   ,135.61144244719235571   ] 
dist 6=[104.28814679113495516   ,125.88817057527246052   ] 
dist 7=[83.730029074238671133  ,123.22067509414908575   ] 
dist 8=[62.905594747237943428  ,120.98759530749928752   ] 
dist 9=[48.384398823911137573  ,105.47408659259433502   ] 
dist 10=[35.923501014353215672  ,55.704220932490755058  ] 
dist 11=[23.275359023471364015  ,39.741044758985279146  ] 
dist 12=[11.673938013156393138  ,36.636915440878370139  ] 
dist 13=[3.1331020835171007608 ,19.410348395094263851  ] 
dist 14=[-7.6737632290738708386 ,16.561528530249109821  ] 
dist 15=[-14.841933934644708296  ,12.059666478143089515  ] 
dist 16=[-20.649650125406910891  ,11.173096773149179798  ] 
dist 17=[-26.064787088073706512  ,-11.101372177007003523  ] 
dist 18=[-30.542982928670118519  ,-22.034051504196786183  ] 
dist 19=[-32.629033371282714293  ,-24.505692663647085523  ] 
dist 20=[-33.562117079196661962  ,-23.170979561699523973  ] 
dist 21=[-33.554387440683482083  ,-20.419608915218827434  ] 
dist 22=[-31.383614669594397677  ,-16.220985936986602478  ] 
dist 23=[-30.531246256379889084  ,-9.1372705300178999227 ] 
dist 24=[-29.304016726734937904  ,-1.8546123553876809488 ] 
dist 25=[-28.715422614692422107  ,3.1383128010580280097 ] 
dist 26=[-12.381217351039557732  ,7.2734817883723183753 ] 
dist 27=[-10.189232196596092690  ,11.160777127667550475  ] 
dist 28=[-5.9845374015777605401 ,14.468266716480617996  ] 
dist 29=[-4.0606942848393076623 ,16.306645225381067343  ] 
dist 30=[.75012016066166081229,19.652967406267341370  ] 
dist 31=[2.6504525996895414700 ,21.821609679650763222  ] 
dist 32=[3.0564093373613801670 ,23.086013196285747453  ] 
dist 33=[5.7245438312953856706 ,23.404712947898202668  ] 
dist 34=[6.2244991206737696647 ,7.4409181917595328416 ] 
dist 35=[6.2519047722669253939 ,7.7560788354091315560 ] 
dist 36=[5.9222233018003445905 ,7.8762196575866582623 ] 
dist 37=[5.3303277532000629370 ,7.8903849186585447983 ] 
dist 38=[4.4520942919394803534 ,7.0196317269580957440 ] 
dist 39=[2.9856241829667943796 ,6.7707982281077056402 ] 
dist 40=[1.4741133269773627130 ,6.6053219312116274354 ] 
dist 41=[.41656238662323641306,6.5185323375943673791 ] 
dist 42=[-.48555547639000816609,1.7565819316190146679 ] 
dist 43=[-1.3814110918058561730 ,1.1825187939844736815 ] 
dist 44=[-2.1802864094202364518 ,.16832666206111591414] 
dist 45=[-2.6982181448114193997 ,-.38367792478064161431] 
dist 46=[-3.0991901479845768171 ,-1.5348676544340449805 ] 
dist 47=[-3.5258614614747771163 ,-1.9117795796256993169 ] 
dist 48=[-3.9141987538147193297 ,-2.0452092064513630925 ] 
dist 49=[-4.1851074621215524844 ,-2.8452399744591401237 ] 
dist 50=[-4.3598586103514227604 ,-2.9925161502102245905 ] 
dist 51=[-4.3919352637989862694 ,-2.7830153201699900015 ] 
dist 52=[-4.3226399011368501352 ,-2.4865955706193319670 ] 
dist 53=[-4.2955332183329724097 ,-2.1046271098512261973 ] 
dist 54=[-3.6274731710714576738 ,-1.5963558231166531564 ] 
dist 55=[-3.4547300655013660192 ,-.79858277615984300766] 
dist 56=[-3.3006431645616378144 ,.00925258369220410269] 
dist 57=[-3.2217108724293710585 ,.55756244494184112877] 
dist 58=[-.97313107746340997023,1.0087065995541757537 ] 
dist 59=[-.73430464965664899288,1.4447577102898079903 ] 
dist 60=[-.19507854158418538703,1.8355259772541441814 ] 
dist 61=[-.07766868371166641184,2.0468012444746169109 ] 
dist 62=[.53030099192708975182,2.1859170385053758505 ] 
dist 63=[.67802655647390429251,2.4174993239945361961 ] 
dist 64=[.77129498359058077767,2.5536417329724317413 ] 
dist 65=[.92582472519463473746,2.5850851372871465037 ] 
dist 66=[.9194248137712706358 ,1.0411984851202472356 ] 
dist 67=[.86163767268233876587,1.0516871548298798974 ] 
dist 68=[.78092729521669021512,1.0400089383807057784 ] 
dist 69=[.67781181504862100124,1.0363846822316676415 ] 
dist 70=[.54096671537140830366,.87845434246840319491] 
dist 71=[.32634635812423629637,.83746586967933561348] 
dist 72=[.10868545101834130713,.80780743902198556645] 
dist 73=[-.04025539845432421202,.79576313846330598848] 
dist 74=[-.1642573097408624273 ,.15525099065014875572] 
dist 75=[-.28297799170730177816,.07882788004657911601] 
dist 76=[-.38627403000677442514,-.10161230766924618648] 
dist 77=[-.44908085352331674396,-.12777195001556196192] 
dist 78=[-.49305423186303124446,-.34347303717949899799] 
dist 79=[-.52163247439859490233,-.37216444519776850311] 
dist 80=[-.54993597540442626565,-.40211259401703754677] 
dist 81=[-.57340195006118890454,-.43752171088108768018] 
dist 82=[-.58437756727476771562,-.42259658506708818049] 
dist 83=[-.58466055237425896694,-.38508845209799090075] 
dist 84=[-.56708481368267767633,-.33704823804311860595] 
dist 85=[-.56225958035905449166,-.28030661166421388881] 
dist 86=[-.46653872716895767891,-.20757698741811255257] 
dist 87=[-.44278335233830975768,-.09606477885627115860] 
dist 88=[-.42031471109988382533,.01618727018026846705] 
dist 89=[-.40949339732730525513,.09185986046249185170] 
dist 90=[-.13856797068920338276,.15368232596014931783] 
dist 91=[-.10467524821732837241,.21096633406675030957] 
dist 92=[-.02822309705370295417,.27770859378033519035] 
dist 93=[-.01186856717547736005,.33443850795241612919] 
dist 94=[.07344683408429391964,.3658709837198218568 ] 
dist 95=[.08811788359020893365,.38854937353404987939] 
dist 96=[.10948954766813833892,.40762364311231203392] 
dist 97=[.11854376667774576297,.41242837442641940299] 
dist 98=[.11854906893019691597,.14848210445362560642] 
dist 99=[.11491378265257304964,.14843249477125395968] 
dist 100=[.09589377436703775152,.14648522967307623704] 
dist 101=[.07403701523659655626,.14444766553570880972] 
dist 102=[.04637829329045736547,.12989554422522902048] 
dist 103=[.00432266979238246132,.12580729551354782804] 
dist 104=[-.03792462563163312753,.11638294329667271522] 
dist 105=[-.06634570368635586362,.11291379527016171288] 
dist 106=[-.08951826774514033555,.06011608950374636475] 
dist 107=[-.11093120177266369712,.05202172335442006015] 
dist 108=[-.12906115459724115969,.03451230794693246254] 
dist 109=[-.13920135536261053224,.02968237679143592166] 
dist 110=[-.14523595130276151037,.01110476777391856145] 
dist 111=[-.14706764918057183228,.00730373882571251176] 
dist 112=[-.14670145297516700301,.00351034629076971157] 
dist 113=[-.1440105972415667786 ,.00277736556349802883] 
dist 114=[-.07059716844269128485,.00103117621242063840] 
dist 115=[-.07043986462022087168,.00074914943251720754] 
dist 116=[-.06790904433643841223,-.00155291188004984566] 
dist 117=[-.06728458713818000303,-.00193950657471653844] 
dist 118=[-.05538595334803685308,-.00257864153300647452] 
dist 119=[-.05248210803094164088,-.00271441253480658451] 
dist 120=[-.04972457068112495197,-.00434225521827657142] 
dist 121=[-.04845931459809669861,.00399525283779680713] 
dist 122=[-.01250659775604970562,.01346477628887395213] 
dist 123=[-.00877309762157109130,.02118559134416762061] 
dist 124=[-.00603426561385168733,.02832134031469640071] 
dist 125=[-.00585024329646479466,.03436490031729289119] 
dist 126=[-.00403704316772993153,.03791055478323933513] 
dist 127=[-.00290624141186802709,.03999705369371365610] 
dist 128=[.01506818526579716910,.04143635064051991040] 
dist 129=[.01581995447606947633,.04193394957141588413] 
dist 130=[.01567411573930107659,.01632732399842645851] 
dist 131=[.01512134457167123505,.01633049927090168851] 
dist 132=[.01388488701987699601,.01576915430697083950] 
dist 133=[.01233732677378908758,.01568817427550761559] 
dist 134=[.01054919913465849011,.01277489559110052609] 
dist 135=[.00827970394385954701,.01207266525243405187] 
dist 136=[.00482080851703232708,.01158729592940255656] 
dist 137=[.00134111013547677847,.01147716732938950849] 
dist 138=[-.00101112525285678187,.00121839601147741261] 
dist 139=[-.00294205403846177291,2.12569585245626619400e-05] 
dist 140=[-.00474929691992741424,-.00275594755262813660] 
dist 141=[-.00629635909818519203,-.00317006433657877382] 
dist 142=[-.00719445306787532678,-.00638557875015111500] 
dist 143=[-.00777251494464556606,-.00685895530775311279] 
dist 144=[-.00804916600570180508,-.00748527372553095782] 
dist 145=[-.00826456201735265533,-.00783293833988265393] 
dist 146=[-.00833236277493322303,-.00790713409662834273] 
dist 147=[-.00829889775928637637,-.00749987439046212989] 
dist 148=[-.00803642310841981972,-.00668906309095858381] 
dist 149=[-.00791050564354812065,-.00570196879410911472] 
dist 150=[-.00675296372668889139,-.00459473429661992013] 
dist 151=[-.00645567826539235818,-.00321000265630436416] 
dist 152=[-.00600598505650337439,-.00112108271523727410] 
dist 153=[-.00584277208649278297,.00097283393563848401] 
dist 154=[-.00194795415588311301,.00237743883443772647] 
dist 155=[-.00143152853922688959,.00351897129023428885] 
dist 156=[-.00027606392383346463,.00456843267319531624] 
dist 157=[-2.45917661911293945180e-05,.00545383538004310492] 
dist 158=[.00123230546561824404,.00594400990615485729] 
dist 159=[.00145149276245223040,.00622949655536775320] 
dist 160=[.00181279640933908232,.00635339057465236718] 
dist 161=[.00187707820362593727,.00642618838750701955] 
dist 162=[.00184452393927283123,.00196935406076024815] 
dist 163=[.00176331635600491881,.00196506151211088617] 
dist 164=[.00159669149567168630,.00188723655507248156] 
dist 165=[.00139226440193376070,.00187600458251522248] 
dist 166=[.00116094665798098911,.00151568269361116713] 
dist 167=[.00087033757010234054,.00143569221417996013] 
dist 168=[.00043047895518826100,.00136860626659540054] 
dist 169=[-1.10863631952723381950e-05,.00135462677966825401] 
dist 170=[-.00030848336083597546,.00026768854216736875] 
dist 171=[-.00055151545909196204,.00013711062217434794] 
dist 172=[-.00077724257761628492,-.00016372943381389023] 
dist 173=[-.00096934043137997533,-.00021441645240318039] 
dist 174=[-.00107885836087086641,-.00056196980728037489] 
dist 175=[-.00114683814314425768,-.00061553984971020160] 
dist 176=[-.00117402303715403131,-.00071376825610190597] 
dist 177=[-.00118961125593875720,-.00073138259685124624] 
dist 178=[-.00119071414607922210,-.00071484872520278334] 
dist 179=[-.00118419725415779507,-.00067260667082677282] 
dist 180=[-.00113538018232237239,-.00058931907235933909] 
dist 181=[-.00112227787929566156,-.00048815649202605853] 
dist 182=[-.00092308886152183523,-.00037493474536386217] 
dist 183=[-.00087484116838522136,-.00023347718392275995] 
dist 184=[-.00082301353570806741,-2.01969468257489700000e-05] 
dist 185=[-.00079685699181052361,.00019362616486671135] 
dist 186=[-.00029190843546005851,.00033724282123646396] 
dist 187=[-.00025223583605898283,.00045419054379388225] 
dist 188=[-.00016733380870710955,.00056212767858819963] 
dist 189=[-.00014411788861841752,.00065351654376400394] 
dist 190=[-5.60866320855061833390e-05,.00070476089889357772] 
dist 191=[-3.77417063765005754670e-05,.00073829290942126645] 
dist 192=[-9.57649805073091168070e-06,.00074628048714009897] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 0, 2, 0, 1] 
dist 0=[124.71822793028463890   ,124.71822793028463890   ] 
dist 1=[122.76746348979886901   ,126.30006741209053863   ] 
dist 2=[118.89776730874007384   ,128.69224354399647266   ] 
dist 3=[112.49731706520498965   ,130.75264231130201113   ] 
dist 4=[100.48912226623251346   ,131.02046539899854470   ] 
dist 5=[87.724990322677828060  ,130.39492516016251037   ] 
dist 6=[78.316584765476334422  ,129.59212704120250839   ] 
dist 7=[69.708938835912011002  ,109.34929135876756268   ] 
dist 8=[60.111166306654111424  ,106.13265257984077499   ] 
dist 9=[50.741472757109527065  ,96.432608570731499343  ] 
dist 10=[43.025654359257885941  ,95.039293587872178248  ] 
dist 11=[35.091583050220413223  ,74.159482920044600979  ] 
dist 12=[24.827628624299052805  ,69.815337462279802564  ] 
dist 13=[14.992382849559959739  ,65.751946127230648253  ] 
dist 14=[8.4744953334950715404 ,64.973620085805155875  ] 
dist 15=[-1.8356308186514418189 ,15.674147989601935603  ] 
dist 16=[-7.9645770604953944046 ,9.9509093605011076586 ] 
dist 17=[-12.225093228985058356  ,-.94824238049753632556] 
dist 18=[-15.091859203865554206  ,-1.7922435892355577181 ] 
dist 19=[-20.746048578268957791  ,-1.9272331282037836304 ] 
dist 20=[-25.019231003192374940  ,-.94078654520347614142] 
dist 21=[-27.889427811949013692  ,.29763347064060088557] 
dist 22=[-29.568481610917613655  ,1.2436691684238025529 ] 
dist 23=[-30.511009863039872586  ,2.0752402644451312240 ] 
dist 24=[-30.608739841603709333  ,2.8735720908775231321 ] 
dist 25=[-30.065081257317900233  ,3.5161990034539913874 ] 
dist 26=[-29.678774041723423243  ,3.7367023094815404120 ] 
dist 27=[-25.735145066241706875  ,3.7902634713810686050 ] 
dist 28=[-24.688752068205760996  ,3.7812253798007080831 ] 
dist 29=[-23.155054823730783710  ,2.8302725366077184304 ] 
dist 30=[-22.566652938047757889  ,4.7216168483427620612 ] 
dist 31=[-8.2244842726057361676 ,6.4162406221701678948 ] 
dist 32=[-6.3281607362830438216 ,7.3098655333574122558 ] 
dist 33=[-2.0466757895855990918 ,11.359853153276612755  ] 
dist 34=[-1.2985721157987612517 ,15.204446820568454886  ] 
dist 35=[-.96545860220569712227,18.447966276135586593  ] 
dist 36=[-.8831182595517802356 ,20.243504645514847058  ] 
dist 37=[.41852622342354187095,21.289088743178456981  ] 
dist 38=[.58366676691709672776,21.552089435012820477  ] 
dist 39=[.89121431066239652015,6.7005380057679066295 ] 
dist 40=[.95620705290516782832,6.7379957028003187589 ] 
dist 41=[.06812954750367148404,6.5950759099200441384 ] 
dist 42=[-1.0409061616105552731 ,6.5631782160858036781 ] 
dist 43=[-2.0441908350791545758 ,5.5090059618251871411 ] 
dist 44=[-2.7185311596341505978 ,5.2560016999584661556 ] 
dist 45=[-3.2673337709567401662 ,5.0186468369809217481 ] 
dist 46=[-3.7737044621738731523 ,4.9369288757615651095 ] 
dist 47=[-4.1860096493398478655 ,1.2795833680972923896 ] 
dist 48=[-4.3618233494921311935 ,1.2294218188971495410 ] 
dist 49=[-4.4250147676625467023 ,.89086734153009749068] 
dist 50=[-4.4027115933408240975 ,.82349597593106386994] 
dist 51=[-4.0587699311347433141 ,.69625887811464700195] 
dist 52=[-3.9387413218531956931 ,.66374128909513780084] 
dist 53=[-3.7501384694654262667 ,.59097415219252037863] 
dist 54=[-3.8448158741730350125 ,.64269467773062027394] 
dist 55=[-3.8910566325587167173 ,.68230879322638625737] 
dist 56=[-3.8829158388679973713 ,1.1642079519280766633 ] 
dist 57=[-3.7532302806892406792 ,1.8200707637554144114 ] 
dist 58=[-3.7118347068803434417 ,2.4260542351276255764 ] 
dist 59=[-3.0932060979357880481 ,2.9373307919407257007 ] 
dist 60=[-2.9398261771607826926 ,3.2174848872215496799 ] 
dist 61=[-2.7698881869745645958 ,3.3759460338587696608 ] 
dist 62=[-2.6855477380419398165 ,3.4044120851706408427 ] 
dist 63=[-1.0780404533541081754 ,.99781434937358814787] 
dist 64=[-.94148951867173297774,1.0769546345591748574 ] 
dist 65=[-.64426832264803178244,1.4800846219364461861 ] 
dist 66=[-.56169190546422160092,1.8530706129002768686 ] 
dist 67=[-.24009602648448037831,2.1694362982478493947 ] 
dist 68=[-.17512270427433397143,2.3545537903361027804 ] 
dist 69=[-.05605719352058268405,2.4737012535140900398 ] 
dist 70=[-.02948964182350096713,2.5000127107814576188 ] 
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dist 201=[-9.89366320292898131380e-05,-4.42076428255526329990e-05] 
dist 202=[-.00011071258379684593,-5.13631407783839164680e-05] 
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dist 210=[-.00014840906972633245,-5.57198121926582413180e-05] 
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dist 212=[-.00011609760120046827,-1.36624892165169872260e-05] 
dist 213=[-.00010934174504162552,1.32982301283636020180e-05] 
dist 214=[-.00010589848507402591,3.13676081528899939510e-05] 
dist 215=[-2.68601695750572569890e-05,4.60408935842564171570e-05] 
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dist 217=[2.16497830705593667730e-06,7.08820722099905748250e-05] 
dist 218=[6.17028088385984925060e-06,7.71720927062364495790e-05] 
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dist 225=[1.77216733193965291150e-05,3.84796207642929947120e-05] 
dist 226=[1.46728549708091540120e-05,3.78499487913264618960e-05] 
dist 227=[1.02954253372479700010e-05,3.23174777755820473570e-05] 
dist 228=[1.08087323690013599980e-06,3.08995827973984940800e-05] 
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dist 233=[-2.77883047754967057600e-05,1.49894923124969142200e-06] 
dist 234=[-2.99175347994159026430e-05,2.83810885880956393850e-07] 
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dist 236=[-3.14173878009489756670e-05,-1.48781562188305199200e-06] 
dist 237=[-3.12667818337653599920e-05,-1.53770265337479982570e-06] 
dist 238=[-3.08008393104144160430e-05,-1.37454687099962821810e-06] 
dist 239=[-1.47045460720076339620e-05,-1.02798563475692006240e-06] 
dist 240=[-1.45453947780275365680e-05,-3.49536567193196229340e-07] 
dist 241=[-1.18813846909009029990e-05,4.73172973850044202380e-07] 
dist 242=[-1.12420170778540749490e-05,1.39259980878003189340e-06] 
dist 243=[-1.05979209471724774910e-05,2.54064187058135628030e-06] 
dist 244=[-1.02973554134833866800e-05,4.27116934515094111930e-06] 
dist 245=[-7.08942011239678517390e-06,6.00658766717848596010e-06] 
dist 246=[-6.90453003014138158440e-06,7.17407979775442036370e-06] 
dist 247=[-2.05077614873262339500e-06,8.12706520537158799970e-06] 
dist 248=[-1.76308792903315318720e-06,9.01077242407640849160e-06] 
dist 249=[-6.76259042307339586350e-07,9.76213512540898222890e-06] 
dist 250=[-4.48933540602578647950e-07,1.01896412768074903780e-05] 
dist 251=[-1.09242801281239577520e-07,1.04761452243223976470e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 0, 0, 0, 1] 
dist 0=[149.84612424952035791   ,149.84612424952035791   ] 
dist 1=[148.10322466385039405   ,149.95273464488830791   ] 
dist 2=[144.95895597970543275   ,149.84612424952035791   ] 
dist 3=[137.77442033254398724   ,146.91579963546197455   ] 
dist 4=[128.55359892817807624   ,144.69712621123945996   ] 
dist 5=[117.95903066136304726   ,135.75357300869342150   ] 
dist 6=[104.51904040006067078   ,125.91038348062068837   ] 
dist 7=[83.987621359204549995  ,123.27393572323268681   ] 
dist 8=[63.189737582108290595  ,121.02976648610528839   ] 
dist 9=[48.686019362730924898  ,105.56721622249304898   ] 
dist 10=[36.238964372622404271  ,55.389865770688075570  ] 
dist 11=[23.602938869890383807  ,39.379364587513659353  ] 
dist 12=[12.011308947631422547  ,36.252822690811208826  ] 
dist 13=[2.7049198103547612869 ,19.079769572798911763  ] 
dist 14=[-8.1334382085017224519 ,16.230534505151641483  ] 
dist 15=[-15.314059248056372067  ,11.844871695721064197  ] 
dist 16=[-21.122348574901103598  ,10.955285098782694490  ] 
dist 17=[-26.521815574695097511  ,-11.201211985849946963  ] 
dist 18=[-30.974788983262895513  ,-22.504590666956493993  ] 
dist 19=[-33.023502109276099760  ,-24.255696205554198875  ] 
dist 20=[-33.928886985253462523  ,-22.972593074939981759  ] 
dist 21=[-33.893284899076618161  ,-20.276624058981906283  ] 
dist 22=[-31.560547424078565471  ,-16.145652151253447308  ] 
dist 23=[-30.667758578270993997  ,-9.1621699080472557381 ] 
dist 24=[-29.465041211088049959  ,-1.9791591643714084166 ] 
dist 25=[-28.855565124607964826  ,2.9484454264101614478 ] 
dist 26=[-12.294079687354768470  ,7.0322385946130709094 ] 
dist 27=[-10.119952492379617567  ,10.875254838863365868  ] 
dist 28=[-5.3457042465805084603 ,14.147533747975912913  ] 
dist 29=[-4.0399351511178703411 ,15.970546404723635761  ] 
dist 30=[1.5617223601517188110 ,19.404645948807955173  ] 
dist 31=[2.7956520308699162353 ,21.568188272127735144  ] 
dist 32=[3.8624037193294274774 ,22.822164695897471814  ] 
dist 33=[5.6959057334681995296 ,23.120620640472567059  ] 
dist 34=[6.4188371799315274609 ,8.0335872679145944245 ] 
dist 35=[6.3284080497933842409 ,8.3417321680794148390 ] 
dist 36=[6.0303155958183605141 ,8.4402634441254820099 ] 
dist 37=[5.4706673249656254282 ,8.3985569721366466487 ] 
dist 38=[4.6306561998259494952 ,7.7801758154424258850 ] 
dist 39=[3.2194775081177926843 ,7.5673408062988032264 ] 
dist 40=[1.4206527587879057541 ,7.1437760243112819243 ] 
dist 41=[-.79662367264634789799,6.9855590853403898035 ] 
dist 42=[-2.3100373734323541438 ,3.5721606818013792760 ] 
dist 43=[-3.5624883899298128543 ,2.9062177608658867746 ] 
dist 44=[-4.7451219044369460088 ,2.3193749602066106697 ] 
dist 45=[-5.7597977725402989734 ,1.4665039917440878405 ] 
dist 46=[-6.3462052161115198655 ,.81980076493948438562] 
dist 47=[-6.7184525695181419951 ,.28986129301952704788] 
dist 48=[-6.8853826968191899322 ,.20134733226043152603] 
dist 49=[-6.9353454129955001995 ,-.42419007605781079343] 
dist 50=[-3.9783482218419355408 ,-.52932231008201018242] 
dist 51=[-4.0225748455455750409 ,-.65959516661367360684] 
dist 52=[-4.0052189080293217181 ,-.65819380400728940943] 
dist 53=[-3.9586626967714560646 ,-.60696870856210083468] 
dist 54=[-3.5079714364666609263 ,-.48928319189694893945] 
dist 55=[-3.3777311657592625905 ,-.30424189501455247723] 
dist 56=[-3.1824458253120642425 ,.21275347128582620374] 
dist 57=[-3.1056003656883805227 ,.84609334852730309296] 
dist 58=[-1.1672806659659884450 ,1.3641351507529161745 ] 
dist 59=[-.90850483238205980952,1.8442010486226713574 ] 
dist 60=[-.31899052592284801026,2.2505355424210639140 ] 
dist 61=[-.19538021354203404548,2.4762430048458081128 ] 
dist 62=[.48232161135531642808,2.6224165468469960537 ] 
dist 63=[.59705426022831198001,2.8749427100242490086 ] 
dist 64=[.80736696042807753066,3.0220075255321928817 ] 
dist 65=[.8250625800757062787 ,3.0589519560884466047 ] 
dist 66=[.8150610385405373228 ,1.7730899307934669019 ] 
dist 67=[.76149603114198107422,1.7720072392505729709 ] 
dist 68=[.68653545286317000638,1.7718132332686656461 ] 
dist 69=[.59061860245792009306,1.5118804257280085073 ] 
dist 70=[.4632505474266725654 ,1.4445943278905276918 ] 
dist 71=[.2634264866426477103 ,1.4053076587543823898 ] 
dist 72=[.06076710406435839742,1.3953990710432236400 ] 
dist 73=[-.07788043089013587173,.73179915769740712874] 
dist 74=[-.19327487279175834714,.15268507907524812742] 
dist 75=[-.30368369012841631469,.08369432144922889870] 
dist 76=[-.46216977352651877901,-.07938735603171674679] 
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dist 78=[-.76274848326292224565,-.26665655569041308469] 
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dist 80=[-.89240265093677092977,-.33049526159567902993] 
dist 81=[-.92338546333500410153,-.3314359474066259061 ] 
dist 82=[-.92720370635502461313,-.31941585375158141731] 
dist 83=[-.91464579985074232042,-.28699393457999438001] 
dist 84=[-.90247164975165274847,-.24492090757602993522] 
dist 85=[-.78969804595419216487,-.19458092212341210399] 
dist 86=[-.75857664779095918141,-.12966282855495259916] 
dist 87=[-.71121983974539500188,-.02971358994098311602] 
dist 88=[-.6933567813523585635 ,.07105689808709816026] 
dist 89=[-.38327468809105691062,.13924172486194180401] 
dist 90=[-.1920048410608703038 ,.25660465254788649384] 
dist 91=[-.09361959244383595919,.39001212299226650243] 
dist 92=[-.04499889920567756929,.51295682480285222487] 
dist 93=[-.03559480726899492773,.61678227191617092135] 
dist 94=[-.01509048054923368407,.67429708165673722243] 
dist 95=[-.00997088821787444255,.70778144747450935889] 
dist 96=[.11598245123074441427,.71621668815187790244] 
dist 97=[.12027793810853341922,.31363831598378215584] 
dist 98=[.12710232543043199835,.21955889359797377948] 
dist 99=[.12615916560731378485,.21539689290333630556] 
dist 100=[.12189078626415030083,.21433219507450854569] 
dist 101=[.11209943832187403742,.17998429715920752053] 
dist 102=[.09978014851292104848,.17126115248637648538] 
dist 103=[.08547322790822976788,.16450695695796519822] 
dist 104=[.06442524713923882234,.16175122081914155203] 
dist 105=[.01433525587339886781,.09225537744447289792] 
dist 106=[-.01959436360879464551,.01397790818914089199] 
dist 107=[-.04751110598537989756,.00213606664012688389] 
dist 108=[-.07373483217591514646,-.01972670813372307602] 
dist 109=[-.09624056991589010090,-.02304578147770750962] 
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dist 164=[.00184293365791667468,.00333755105419161983] 
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dist 167=[.00125346852022218425,.00244979122755779763] 
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dist 169=[-2.93565606475119531730e-05,.00135722620083735698] 
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dist 174=[-.00195196827686454824,-.00077518691919640064] 
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dist 177=[-.00212507892503494297,-.00095027195903717629] 
dist 178=[-.00211446652887777202,-.00097604593056874093] 
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dist 182=[-.00156680878273780327,-.00067293610686563539] 
dist 183=[-.00147459071380267285,-.00041764852224323084] 
dist 184=[-.00142790646753794742,-3.31084353274347700000e-05] 
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dist 187=[-.00030562203042878121,.00082171719571787606] 
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dist 190=[-7.17599935403118622030e-05,.00127246957284037675] 
dist 191=[-1.91750397266081590430e-05,.00133166402092443699] 
dist 192=[-5.99827367309708695740e-06,.00134603886090164118] 
dist 193=[.00022730548109343432,.00076864986475138657] 
dist 194=[.00022834890025277814,.00047626187471277766] 
dist 195=[.00022295192448071437,.00045937336923599501] 
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dist 197=[.00019090212786762236,.00037999319696380959] 
dist 198=[.00016542007324691143,.00036171326853439843] 
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dist 200=[6.66427735647772393920e-05,.00032922879948533511] 
dist 201=[-3.12358211935998020560e-05,.00021177313711136940] 
dist 202=[-.00010984710550515795,.00013523977140404032] 
dist 203=[-.00017269184745755191,.00012188205413522256] 
dist 204=[-.00023119241190865659,9.49538281739241627110e-05] 
dist 205=[-.00028068393515722727,8.76603270721646952690e-05] 
dist 206=[-.00030837418703227128,6.11070182746776823420e-05] 
dist 207=[-.00032488793286688392,5.46779239737432591940e-05] 
dist 208=[-.00033000217168944481,4.75190518148543215050e-05] 
dist 209=[-.00032930302113373947,4.55437198315315514670e-05] 
dist 210=[-.00015212770488893344,4.50473038579180866200e-05] 
dist 211=[-.00014686668401370439,4.57426153397646562090e-05] 
dist 212=[-.00014488323055208289,4.74255374334203851520e-05] 
dist 213=[-.00013701608954740757,5.08514129796759569040e-05] 
dist 214=[-.00011627180003804595,5.50478576478893708680e-05] 
dist 215=[-.00010958709808962128,5.97909484794536107850e-05] 
dist 216=[-.00010571762138519703,6.57482314342872299950e-05] 
dist 217=[-9.88415485133958087930e-05,7.47664246734697879390e-05] 
dist 218=[-3.39789485180123266180e-05,8.38266272955009448060e-05] 
dist 219=[-2.92792599482562899370e-05,8.99510002279157531880e-05] 
dist 220=[-1.92599478667367335830e-05,9.49824922157080259550e-05] 
dist 221=[-1.65320729693502350940e-05,9.97034518720158906050e-05] 
dist 222=[-6.26003371424683064540e-06,.00010375680125638684] 
dist 223=[-4.10558014319092475140e-06,.00010673528323057372] 
dist 224=[-9.60126340780150952350e-07,.00010853756936442005] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 0, 0, 1, 2] 
dist 0=[120.90071811109515366   ,120.90071811109515366   ] 
dist 1=[119.65071704020998183   ,121.51334201188549366   ] 
dist 2=[115.27774192146036868   ,122.06059305576988596   ] 
dist 3=[109.94418270701812812   ,121.76901719427617725   ] 
dist 4=[104.83536815861644993   ,116.75960776718431252   ] 
dist 5=[98.954951377781031599  ,115.10136005681536714   ] 
dist 6=[90.559979930394433401  ,113.31427394866063318   ] 
dist 7=[81.311494575555256147  ,112.24379582318731750   ] 
dist 8=[67.990887571077708612  ,84.605417490669179607  ] 
dist 9=[57.427517574269671723  ,80.519740191481612993  ] 
dist 10=[45.189941898670313956  ,79.105042520988191470  ] 
dist 11=[29.301767588222822527  ,65.839219746312176336  ] 
dist 12=[18.420490005337923888  ,55.053581690003272292  ] 
dist 13=[9.2569927770024245445 ,52.929252859728037198  ] 
dist 14=[.19583164305427547022,48.174296872187719135  ] 
dist 15=[-7.9900129329623236350 ,46.981140273764654610  ] 
dist 16=[-13.678259519499196235  ,16.231243247612942575  ] 
dist 17=[-20.330671254121514960  ,12.661824308262658986  ] 
dist 18=[-25.228700061284073641  ,11.848986629961751213  ] 
dist 19=[-28.907536437582605203  ,-7.1312531372404309850 ] 
dist 20=[-31.573675257909917605  ,-9.2838009725505457981 ] 
dist 21=[-32.435816701198681707  ,-12.448307661774837980  ] 
dist 22=[-32.628853990320735698  ,-13.099141713027363747  ] 
dist 23=[-32.620576963781340503  ,-12.907361021595323837  ] 
dist 24=[-27.659963739343706332  ,-6.3647112660733208287 ] 
dist 25=[-27.092821075266545886  ,-1.2418246126714919181 ] 
dist 26=[-26.780583145928718786  ,3.3672803994559488078 ] 
dist 27=[-8.2728567185563413835 ,8.3163212599804070773 ] 
dist 28=[-6.0348490596867934008 ,12.969356423877332738  ] 
dist 29=[-.73833214248150461084,16.411370815756781691  ] 
dist 30=[.08958399767439621000,19.563198228460173083  ] 
dist 31=[6.5903689561956207543 ,23.073951603856739450  ] 
dist 32=[7.5833461223845144356 ,26.113102135175315249  ] 
dist 33=[9.4222495496918681482 ,27.395053852389709837  ] 
dist 34=[9.7350780705855485861 ,27.931554668697035236  ] 
dist 35=[13.303200835110092838  ,28.003841571963560647  ] 
dist 36=[13.444967687210492144  ,25.162757865381675607  ] 
dist 37=[13.031593786402778563  ,24.336723990479952518  ] 
dist 38=[11.773005517868537284  ,23.776955432079116920  ] 
dist 39=[10.110357546599801719  ,23.459498268906959010  ] 
dist 40=[4.4090024396074279589 ,14.247849489353576542  ] 
dist 41=[-.05307246280204686316,13.377016118120139783  ] 
dist 42=[-3.8023513133658476635 ,13.072076755677562438  ] 
dist 43=[-7.4441498087474661911 ,6.6616167129446672514 ] 
dist 44=[-10.645555564008692692  ,5.9051040173299027110 ] 
dist 45=[-12.648512076935790378  ,4.2055685946566120201 ] 
dist 46=[-14.118836860050119354  ,3.7330582569255033159 ] 
dist 47=[-15.208192625989418518  ,1.7300327831064651306 ] 
dist 48=[-15.969918887703660338  ,1.3450212300700028084 ] 
dist 49=[-16.140204440465872303  ,.51780927654055387058] 
dist 50=[-16.062996703067016328  ,.30661660139681591961] 
dist 51=[-15.851818636824577958  ,-.43820386751392695493] 
dist 52=[-14.151803342994787800  ,-.44585163397271127528] 
dist 53=[-13.650575042585431545  ,-.19311419732161676666] 
dist 54=[-12.782314000424857185  ,.4716898845821258885 ] 
dist 55=[-12.486315174192970286  ,1.3301755875854696515 ] 
dist 56=[-6.4493609756415142770 ,2.8208829134750136945 ] 
dist 57=[-5.7377599870110321411 ,5.4800276851967924780 ] 
dist 58=[-3.3007323889174544980 ,7.6565374610009893692 ] 
dist 59=[-1.3134115485149065299 ,9.6792907097666427749 ] 
dist 60=[-.20702554298917897131,11.492201644187200791  ] 
dist 61=[.34303437044369730139,12.506396431244754276  ] 
dist 62=[.42980349134968545367,13.073589969867650163  ] 
dist 63=[1.0652361410284558657 ,13.172954012911162756  ] 
dist 64=[1.1609102297272498082 ,3.0015231778266014404 ] 
dist 65=[1.3287903588674180422 ,3.0415322225113673795 ] 
dist 66=[1.3538188401859006633 ,3.0228127672008335662 ] 
dist 67=[1.6079646223984283547 ,3.0199699495149127457 ] 
dist 68=[1.5901422606575527740 ,2.5586910570339013967 ] 
dist 69=[1.5221806299409976178 ,2.4392931090974376100 ] 
dist 70=[1.3701693910565858855 ,2.3695200684583683588 ] 
dist 71=[1.0716763059115638812 ,2.3516845361742434182 ] 
dist 72=[.39304830722134040549,1.3229719168168128690 ] 
dist 73=[-.06968147287743075082,1.2397844299038472806 ] 
dist 74=[-.45341927833415952425,1.2084948133505217673 ] 
dist 75=[-.818598756691714223  ,.4376996732821103364 ] 
dist 76=[-1.1350406997698340230 ,.33481002071073723213] 
dist 77=[-1.3253818963892084772 ,.10220409439786629099] 
dist 78=[-1.4562219238068943421 ,.05249087902578552952] 
dist 79=[-1.5365608712053898692 ,-.20904838685794934143] 
dist 80=[-1.5834151123258016155 ,-.25392751130088849097] 
dist 81=[-1.5879350703445602628 ,-.33573883723240874976] 
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dist 85=[-1.2898683590497898795 ,-.35918826725047433754] 
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dist 87=[-1.1771261261907623194 ,-.24798483053387296174] 
dist 88=[-.42406997186012787751,.16774299012188238001] 
dist 89=[-.32348726590050717973,.44710873991982069969] 
dist 90=[-.27915625593900285131,.67451727799624855134] 
dist 91=[-.06564980379273921124,.88400245351374031223] 
dist 92=[-.03950521898985278524,1.0608824515412511837 ] 
dist 93=[.02153866085512302778,1.1588617271266769986 ] 
dist 94=[.03137319654499687152,1.2159501681356910760 ] 
dist 95=[.10451561523331161365,1.2303073091107017210 ] 
dist 96=[.11569207406654992314,.37168701314275919449] 
dist 97=[.13693446371257414698,.37356332391956468231] 
dist 98=[.14052180467719335114,.36543509582839716683] 
dist 99=[.15040086352721294948,.36357685601826162798] 
dist 100=[.1477036115433720627 ,.30510743117052135241] 
dist 101=[.13999657804253619028,.29104707915669126613] 
dist 102=[.12366005077315145316,.27761135237527075344] 
dist 103=[.09530585387255642129,.27281913142080179889] 
dist 104=[.00795237144255332004,.17679678802779500262] 
dist 105=[-.05114807090812436887,.16652821706930203813] 
dist 106=[-.09970609006195505019,.16145853184708040028] 
dist 107=[-.14521243984665702695,.06417152961367046266] 
dist 108=[-.18419865191739046762,.05602656741980568599] 
dist 109=[-.20687554009260285142,.03827126606417285372] 
dist 110=[-.22152552195178626595,.03332276336035260082] 
dist 111=[-.22864990872372522307,.01398519151427658517] 
dist 112=[-.23119983729461014877,.01007612645136610868] 
dist 113=[-.23065222364694344079,.00287337463746985628] 
dist 114=[-.2229043928474267307 ,.00125851696501820721] 
dist 115=[-.22038813279817017569,-.00237367122529736200] 
dist 116=[-.18377295564570907005,-.00104181474197725903] 
dist 117=[-.17467216942721340285,.00280811167579220659] 
dist 118=[-.16447254868183492742,.01099186916371048857] 
dist 119=[-.15946370359211757054,.02111649749994273337] 
dist 120=[-.06379630960072733493,.03712699209927741077] 
dist 121=[-.05584727664442041544,.06647716437871064991] 
dist 122=[-.03472357050382328007,.09043124103697132617] 
dist 123=[-.00387735926713167292,.11261828312020753008] 
dist 124=[-.00027607094882452144,.13144958038126259383] 
dist 125=[.00807302683412035260,.1425781746016206914 ] 
dist 126=[.00932664832975177632,.14968391031794836943] 
dist 127=[.01897440885379145773,.15125057568940623114] 
dist 128=[.02039880624135751704,.04831329895099552593] 
dist 129=[.02292947229205040639,.04837153015669683550] 
dist 130=[.02329592819966479971,.04681588441247006259] 
dist 131=[.02486859161817436444,.04659146383885562147] 
dist 132=[.02426492016264083365,.03806414052028250838] 
dist 133=[.02298168122069947909,.03599695722557202865] 
dist 134=[.02046977140203517380,.03458734138073108529] 
dist 135=[.01432358201674371962,.03426501299738637070] 
dist 136=[.00375873230882872433,.01942194607178466740] 
dist 137=[-.00337122653136022245,.01807807346736190883] 
dist 138=[-.00921258185702703843,.01759095430150592335] 
dist 139=[-.01466176182513355332,.00590060869539517135] 
dist 140=[-.01931496991836865402,.00434159053696643770] 
dist 141=[-.02199637410002560044,.00084899295285467668] 
dist 142=[-.02369743463261804182,9.25901466481727051910e-05] 
dist 143=[-.02445878738483176139,-.00372027410177813590] 
dist 144=[-.02470717366271791097,-.00438307490625313140] 
dist 145=[-.02462281505502341829,-.00548758006997383284] 
dist 146=[-.02388000319685952889,-.00570679477374183208] 
dist 147=[-.02350831887310888921,-.00580768267877376074] 
dist 148=[-.02011733371799372281,-.00570042534230202147] 
dist 149=[-.01924121118766412846,-.00545170791806733490] 
dist 150=[-.01790832538007652628,-.00495163287281204509] 
dist 151=[-.01742567897977293969,-.00334970067322764534] 
dist 152=[-.00584374267911394836,.00299593109764601521] 
dist 153=[-.00429884799167108916,.00725099051337539473] 
dist 154=[-.00402745653490391642,.01070788916796441648] 
dist 155=[-.00057871895191453661,.01388453035003417448] 
dist 156=[-.00016658340704631707,.01656403999583866400] 
dist 157=[.00079222652276812925,.01804712142898147026] 
dist 158=[.00093773974852485101,.01891008087938786121] 
dist 159=[.00206426061308369453,.01912742581443511932] 
dist 160=[.00223168892904377055,.00576161170735395928] 
dist 161=[.00254135444991908321,.00575243501283404268] 
dist 162=[.00258909741645229623,.00554545215816012588] 
dist 163=[.00264256398720742628,.00550401796730462375] 
dist 164=[.00257560798320110741,.00450893431059094835] 
dist 165=[.00243988938316617217,.00426794618381039313] 
dist 166=[.00217839347990147175,.00406724178514471028] 
dist 167=[.00147870414655980557,.00399321909803710101] 
dist 168=[.00018433788342070760,.00236566626098154628] 
dist 169=[-.00068671387206788156,.00223617836296758370] 
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dist 173=[-.00293624742329499824,-2.01779567156659595210e-05] 
dist 174=[-.00313246880249713758,-9.72709868731736236820e-05] 
dist 175=[-.00320778045423062990,-.00052128624427592460] 
dist 176=[-.00321645710538380610,-.00059229234327245675] 
dist 177=[-.00320151782341052091,-.00071301402197390234] 
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dist 182=[-.00222198045104598416,-.00063310858615918903] 
dist 183=[-.00216459091082072570,-.00041400299191460478] 
dist 184=[-.00053702707092948852,.00024029198452969171] 
dist 185=[-.00051357584141097978,.00067913860354081962] 
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dist 187=[-4.43612038053695477100e-05,.00136406334941302536] 
dist 188=[9.70859972397233709660e-06,.00164125811929366063] 
dist 189=[.00013518178773050121,.00179543613861013422] 
dist 190=[.00015361727302851010,.00188913485872355984] 
dist 191=[.00029897259559788442,.00191149967539560336] 
dist 192=[.00032024921268440223,.00073948038694106745] 
dist 193=[.00035855744773161577,.00073731189186807167] 
dist 194=[.00036414456167159945,.00070695647548252965] 
dist 195=[.00037408659067480117,.00070254252948342984] 
dist 196=[.00036322633892434450,.00056628473575149949] 
dist 197=[.00034263608566601391,.00053396229268028621] 
dist 198=[.00030390983097031268,.00051067044771839419] 
dist 199=[.00020279207132372735,.00050540674193167256] 
dist 200=[4.26685181985495842280e-05,.00028815318430326809] 
dist 201=[-6.49710898183844241150e-05,.00026754848867237993] 
dist 202=[-.00015273865039086502,.00026014283730425323] 
dist 203=[-.00023395979658886140,8.47559057550385349410e-05] 
dist 204=[-.00030289646993133370,6.15200016029100757760e-05] 
dist 205=[-.00034188830770044029,9.67954480092420438420e-06] 
dist 206=[-.00036569898607848000,-1.65951989712430455170e-06] 
dist 207=[-.00037435889896782032,-5.75207621800302989170e-05] 
dist 208=[-.00037528386590307782,-6.73076863983987180930e-05] 
dist 209=[-.00037309156859046834,-8.29185918178819476210e-05] 
dist 210=[-.00035977545163424542,-8.60314874802832749420e-05] 
dist 211=[-.00035393169467961994,-8.62024337878061357360e-05] 
dist 212=[-.00030041740740898453,-8.40521051979643189310e-05] 
dist 213=[-.00028686558694817816,-7.98383628862197822520e-05] 
dist 214=[-.00026635804633025287,-7.18151533771325045340e-05] 
dist 215=[-.00025898820440817459,-4.68561964796892693330e-05] 
dist 216=[-8.44231972145977450510e-05,4.82774655682148078310e-05] 
dist 217=[-6.12941700362145386700e-05,.00011201471781366408] 
dist 218=[-5.95892113284059622200e-05,.00016375580374910496] 
dist 219=[-1.10910525631506688040e-05,.00021125606487304007] 
dist 220=[-5.22788332922145081870e-06,.00025130721360512144] 
dist 221=[8.23209586214388687840e-06,.00027346980194556464] 
dist 222=[1.05200305807812373450e-05,.00028636462042922631] 
dist 223=[2.58975345029574861330e-05,.00028961567214432772] 
dist 224=[2.82799773889434863800e-05,8.78359335961067332800e-05] 
dist 225=[3.25750589848837049470e-05,8.74678206149362448280e-05] 
dist 226=[3.32616532442564610340e-05,8.36614521040136450790e-05] 
dist 227=[3.34420233832891481780e-05,8.30741389334607667420e-05] 
dist 228=[3.23368182476798029900e-05,6.69104077031537478410e-05] 
dist 229=[3.02532423421623274440e-05,6.34308724893630404500e-05] 
dist 230=[2.63426451032785106030e-05,6.00858156922909020480e-05] 
dist 231=[1.80679658135709602920e-05,5.93508332714499817380e-05] 
dist 232=[-1.88464067442224994170e-06,3.89760970621983872630e-05] 
dist 233=[-1.52777514074140959090e-05,3.66327146491747242760e-05] 
dist 234=[-2.61783823715866267380e-05,3.54607876334748449420e-05] 
dist 235=[-3.62341119906502141290e-05,1.27282986303853533170e-05] 
dist 236=[-4.47478244721916987870e-05,1.09509059148619172510e-05] 
dist 237=[-4.95255757268648339120e-05,7.16942308152781165460e-06] 
dist 238=[-5.23943792730697501650e-05,6.14229887215280399380e-06] 
dist 239=[-5.33282623718093182420e-05,2.28929805376713367680e-06] 
dist 240=[-5.32249581163437657120e-05,1.47833834182017189730e-06] 
dist 241=[-5.28846057074346701630e-05,3.27640064137363310520e-07] 
dist 242=[-5.06007811507482910910e-05,0                     ] 
dist 243=[-5.00014527031064323510e-05,-3.92920673081423941380e-08] 
dist 244=[-4.10229343301399920100e-05,5.05464510437495515030e-07] 
dist 245=[-3.88595459453563954450e-05,1.54215993378117374380e-06] 
dist 246=[-3.65233161686449081480e-05,3.49493839601789650590e-06] 
dist 247=[-3.53553063109273916840e-05,5.83869057408048524520e-06] 
dist 248=[-1.27083825675955763770e-05,9.19022619223818670340e-06] 
dist 249=[-1.09398086755929615110e-05,1.56303091248926262000e-05] 
dist 250=[-7.15470922432945827970e-06,2.08634274854468416000e-05] 
dist 251=[-6.13093001606476107960e-06,2.56769263790875553120e-05] 
dist 252=[-2.28887116892735922700e-06,2.97426180416048305410e-05] 
dist 253=[-1.48042445367059406280e-06,3.20063535211809698830e-05] 
dist 254=[-3.30001581232253518320e-07,3.33525863690213103090e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 1, 1, 1, 2] 
dist 0=[129.14855001328096697   ,129.14855001328096697   ] 
dist 1=[127.34442759217298481   ,129.66015368126081702   ] 
dist 2=[122.24619609455062327   ,129.63397393281183698   ] 
dist 3=[115.56141177855237777   ,129.36858268868613316   ] 
dist 4=[107.44714231579206167   ,124.59713856015753060   ] 
dist 5=[96.878244150073488878  ,120.30436783917600765   ] 
dist 6=[80.432214288080581609  ,117.92183206666111008   ] 
dist 7=[63.634797108742767359  ,115.57543715958582076   ] 
dist 8=[51.663528211077033031  ,110.57190618074942417   ] 
dist 9=[41.108585928576092394  ,88.109100628985223191  ] 
dist 10=[29.928577796513647466  ,86.340393337156217755  ] 
dist 11=[19.359442822674940709  ,60.422988644797725577  ] 
dist 12=[11.220654584186485245  ,58.121323113990504414  ] 
dist 13=[3.3623325143612259891 ,44.257226040852505674  ] 
dist 14=[-6.1147506423322561221 ,41.927880925433272384  ] 
dist 15=[-14.841009913771057215  ,36.938894908729302353  ] 
dist 16=[-19.718248250913319288  ,36.039463035156818367  ] 
dist 17=[-23.016137171874830866  ,1.3939922090522387657 ] 
dist 18=[-28.104991890284368404  ,-.18770367363771851939] 
dist 19=[-32.337979843340867068  ,-7.8178515230777115037 ] 
dist 20=[-34.143798349977978218  ,-9.0112957035474087043 ] 
dist 21=[-34.924948892959313934  ,-11.338550047923827033  ] 
dist 22=[-35.066020953700568258  ,-10.817854206808497180  ] 
dist 23=[-31.507079754524365612  ,-9.0441276357539932925 ] 
dist 24=[-30.495983846969643680  ,-5.2220731339190943772 ] 
dist 25=[-29.835083038797654397  ,-1.0438296868161341332 ] 
dist 26=[-29.517271221057801409  ,2.1505132664978934279 ] 
dist 27=[-8.3878514436171756327 ,5.1397410817674959206 ] 
dist 28=[-5.8506379092629841694 ,8.5161906455459491946 ] 
dist 29=[.12314443350804749557,11.787442233634936020  ] 
dist 30=[1.0587616513225817510 ,14.366266698141199895  ] 
dist 31=[8.2918618696995619887 ,16.886157316702834125  ] 
dist 32=[9.3878478968626916727 ,19.932196001569991136  ] 
dist 33=[11.438531341072414576  ,22.635099838433373386  ] 
dist 34=[11.787957208449954993  ,23.794845802169173791  ] 
dist 35=[10.703116725132384764  ,24.289208280988862675  ] 
dist 36=[9.0399522594053061019 ,24.343735050056262321  ] 
dist 37=[6.7845927133008548174 ,21.988778812100712350  ] 
dist 38=[3.2059350593492448395 ,21.279302330638420201  ] 
dist 39=[-.42467759852397794258,20.778974675842413558  ] 
dist 40=[-2.8868363302980071467 ,20.455866770209431334  ] 
dist 41=[-4.9075739967817021536 ,14.650460825704104727  ] 
dist 42=[-6.7878087127141610028 ,14.309700567257670792  ] 
dist 43=[-8.3817898085840013151 ,6.8719839819185368225 ] 
dist 44=[-9.2672369387153977478 ,5.9645183674489297979 ] 
dist 45=[-9.7836542665321061661 ,3.9217751509359441806 ] 
dist 46=[-11.332534866938636425  ,3.3906657805795695388 ] 
dist 47=[-12.677607405933530517  ,1.0116268814365281741 ] 
dist 48=[-13.832410481018132477  ,.56779465039547850473] 
dist 49=[-14.485880005857186890  ,-.35213086946529689098] 
dist 50=[-14.605369461030691836  ,-.57940968763251293426] 
dist 51=[-14.327948517173370758  ,-1.2845419041496401527 ] 
dist 52=[-14.140480127890848722  ,-1.2902086093844607246 ] 
dist 53=[-12.634679744786485413  ,-1.0442704129441454673 ] 
dist 54=[-12.191157705472248335  ,-.39976272974560519778] 
dist 55=[-11.400119865520171019  ,.43196186409890692635] 
dist 56=[-11.138382250072403080  ,1.4213309586145752347 ] 
dist 57=[-6.1142175582427420450 ,2.8561485169794582042 ] 
dist 58=[-4.8038916231396564056 ,5.1727762446586057607 ] 
dist 59=[-1.7490094495417090091 ,7.0703357984634360361 ] 
dist 60=[-1.2794489159783349934 ,8.8361711356313925846 ] 
dist 61=[.42615012516518209303,10.423249630470557720  ] 
dist 62=[.52557688159793546902,11.328171018801918376  ] 
dist 63=[1.2577959279372369668 ,11.830600742797616328  ] 
dist 64=[1.3677733801542876988 ,11.918409309834470246  ] 
dist 65=[1.5024359430348523109 ,2.5057280542423503790 ] 
dist 66=[1.3763034966038058584 ,2.5407455064390159431 ] 
dist 67=[1.2102657484884823273 ,2.5285823022088238263 ] 
dist 68=[1.0090116951473859811 ,2.5266793585742786182 ] 
dist 69=[.74801705242151092794,2.1446778805124215658 ] 
dist 70=[.34482431274043410753,2.0457411740359358360 ] 
dist 71=[-.06185713794046935700,1.9878855047070150892 ] 
dist 72=[-.33672903937402192204,1.9730227950384271046 ] 
dist 73=[-.56194008638036708242,1.4203711400612428195 ] 
dist 74=[-.77156034518172638129,1.3843017425900257592 ] 
dist 75=[-.96051957002907357872,.49851144572292835569] 
dist 76=[-1.0665474730246470744 ,.37999529209525269298] 
dist 77=[-1.1262162876246277323 ,.1124483870950828021 ] 
dist 78=[-1.1398098292919127580 ,.05506692005831888978] 
dist 79=[-1.2458807343386363590 ,-.24446570910656712567] 
dist 80=[-1.3610821758197736632 ,-.29599727180615632554] 
dist 81=[-1.4281523811278580902 ,-.38916393542635848667] 
dist 82=[-1.4450440479967471762 ,-.40626850943453628307] 
dist 83=[-1.3073386964129288812 ,-.37512667831341290296] 
dist 84=[-1.2894878930379543991 ,-.32515744749767873225] 
dist 85=[-1.1256200295870042826 ,-.26000419137937927292] 
dist 86=[-1.0807683875349959247 ,-.15894029311773169078] 
dist 87=[-1.0122303864220729122 ,-.05674710384050868566] 
dist 88=[-.9866218566498293841 ,.01289783766461517357] 
dist 89=[-.35714728030623569797,.13986580702660154075] 
dist 90=[-.31658817811923228017,.37361805827288107069] 
dist 91=[-.08323462052089945166,.56391391235993375608] 
dist 92=[-.04247905436219178912,.73923185400954315745] 
dist 93=[.02811036656539842123,.88727006851072536921] 
dist 94=[.03937314125487677853,.96927755891500745719] 
dist 95=[.12325982500956402639,1.0170719199535834848 ] 
dist 96=[.13604308592567370689,1.0290875781101031724 ] 
dist 97=[.1603173173983569659 ,.31036988030141013389] 
dist 98=[.16434936981142749525,.31203778938110637574] 
dist 99=[.17307497884201673068,.30543450260195014293] 
dist 100=[.14059457665766866354,.30393749020188567978] 
dist 101=[.09951648752036831583,.25673053816778438601] 
dist 102=[.03708657466224662906,.25370757455861775743] 
dist 103=[-.02560689927146763289,.23240972090434386038] 
dist 104=[-.06773325152956881008,.22841633409968546294] 
dist 105=[-.10202282086692924094,.18968205519487099779] 
dist 106=[-.13360800201060381062,.18397559753988056853] 
dist 107=[-.16027687061283420534,.07416615445340829075] 
dist 108=[-.17505049476619169476,.06474298678283068436] 
dist 109=[-.1836661923026510024 ,.04426554013741564320] 
dist 110=[-.18582926129971175795,.03857135482633600584] 
dist 111=[-.1908998369574839481 ,.01640497523544961018] 
dist 112=[-.19695508478261503301,.01189861608696901046] 
dist 113=[-.19914161097325704097,.00371769882794956525] 
dist 114=[-.19864193534998217592,.00191206515383526063] 
dist 115=[-.19207201074623311551,-.01670436522043358469] 
dist 116=[-.18977392473266228508,-.01536945737858761077] 
dist 117=[-.15883534807281231522,-.01157189072225323591] 
dist 118=[-.1511039345414949276 ,-.00352808384340395964] 
dist 119=[-.14199984829993638676,.00641509608842476221] 
dist 120=[-.13774414078657706717,.01775508222054557844] 
dist 121=[-.06089802145843775774,.0380454086761080986 ] 
dist 122=[-.04738985713261188347,.06262340445033575250] 
dist 123=[-.00245725804479514215,.08269531206031434590] 
dist 124=[.00187782922308749409,.10130740575375251593] 
dist 125=[.02016356861922529561,.11711883145825961376] 
dist 126=[.02067041757976184545,.12650295404952092205] 
dist 127=[.02205432837488884406,.132642692793437544  ] 
dist 128=[.02164896327903521954,.13397406858961046673] 
dist 129=[.02050943854885925534,.04020297655895044225] 
dist 130=[.01810209528210089945,.04025927852949060676] 
dist 131=[.01512838097345216666,.03898187213318599107] 
dist 132=[.01173993892188772969,.03879737587053312577] 
dist 133=[.00746889579128150067,.03171760799700514507] 
dist 134=[.0009907846435367762 ,.02999945100095698502] 
dist 135=[-.00551446612476297287,.02883019888512967437] 
dist 136=[-.00989344671462910759,.02856192242829874190] 
dist 137=[-.01346815355533829376,.00569459664777610443] 
dist 138=[-.01678052136722050955,.00497138109751241056] 
dist 139=[-.01959281609026431404,.00214277187709734732] 
dist 140=[-.02125121514882311170,.00156952909758523763] 
dist 141=[-.02232765841419293877,.0005109942723144926 ] 
dist 142=[-.02257189296174549184,.00027222348568568495] 
dist 143=[-.01971735532916398058,-.00754061877984850570] 
dist 144=[-.02035842234019072444,-.00744271853327564565] 
dist 145=[-.02057228957204364750,-.00715770687104435144] 
dist 146=[-.02050428852766159978,-.00655079919533029417] 
dist 147=[-.01989086694607121642,-.00579955626339929186] 
dist 148=[-.01958180638435909855,-.00494140199404447816] 
dist 149=[-.01676359682114606866,-.00385822385508982329] 
dist 150=[-.01603476323420634415,-.00221347754353309001] 
dist 151=[-.01492541357670767198,-.00056065312845269794] 
dist 152=[-.01452367278654602129,.00055465223451704456] 
dist 153=[-.00488257024301083418,.00249411715595019078] 
dist 154=[-.00359689398931987684,.00603794555908482997] 
dist 155=[-.00071653732836822304,.00891713017826626850] 
dist 156=[-9.20319231465882036780e-05,.01156301625397359371] 
dist 157=[.00305354228451888029,.01379487674439216290] 
dist 158=[.00360060245626099675,.01503021513962470785] 
dist 159=[.00382161856704741419,.01574906837704022230] 
dist 160=[.00372705891606664168,.01593011737803211598] 
dist 161=[.00352727187581032506,.00479388611561325682] 
dist 162=[.00313691960163481299,.00478687746869075574] 
dist 163=[.00266394830202340227,.00461579077776534077] 
dist 164=[.00213609796347724884,.00458166822859191884] 
dist 165=[.00147761175143068304,.00375653969281437023] 
dist 166=[.00048592886792208889,.00355822119973253755] 
dist 167=[-.00050771727478213840,.00338759530568387530] 
dist 168=[-.00117401146313858227,.00332629976903784365] 
dist 169=[-.00171533525107245939,.00051314437087659440] 
dist 170=[-.00221280148876887930,.00017559781294459335] 
dist 171=[-.00263244169011090311,-.00051016163931504071] 
dist 172=[-.00286476326711425879,-.00061150894484027392] 
dist 173=[-.00300017571132136341,-.00077907994022120566] 
dist 174=[-.00303426366433599926,-.00081310975969097641] 
dist 175=[-.00265275573974899078,-.00082831271816092238] 
dist 176=[-.00271614412475808834,-.00080872906417220133] 
dist 177=[-.00272371636928063584,-.00076479144712429880] 
dist 178=[-.00271092722117571695,-.00067729624184412381] 
dist 179=[-.00260056429128966193,-.00057074399939755252] 
dist 180=[-.00257359227578794751,-.00045113178553144141] 
dist 181=[-.00210894273272084145,-.00030145414578445383] 
dist 182=[-.00199675603113053378,-7.55176660789743954290e-05] 
dist 183=[-.00188511595391418534,.00015111118149204843] 
dist 184=[-.00183278699161972488,.00030354238414897450] 
dist 185=[-.00049838005442746760,.00042790607596936173] 
dist 186=[-.00036545903320258421,.00062189097449394636] 
dist 187=[-6.75201152403649899800e-05,.00091918073026004242] 
dist 188=[-3.28796949372112801480e-06,.00119282137766322955] 
dist 189=[8.58171561352540673700e-05,.00142401003669945911] 
dist 190=[9.35657492313984602810e-05,.00155274247898606761] 
dist 191=[.00010283849133160328,.00163173432696065474] 
dist 192=[9.41763163466785221230e-05,.00165051999703166624] 
dist 193=[7.44592214962692023770e-05,.00071190709010481664] 
dist 194=[3.50229925470992693720e-05,.00069879609688857915] 
dist 195=[-1.30606098396088437890e-05,.00059765568395877556] 
dist 196=[-6.71168101278207728410e-05,.00058215654090702785] 
dist 197=[-.00013481550629030505,.00052734648105502992] 
dist 198=[-.00023707219184984443,.00051327902407014815] 
dist 199=[-.00033968262227133642,.00042384539278867676] 
dist 200=[-.00040878820120704478,.00041905777861610646] 
dist 201=[-.00046527221573664166,4.22220452416632251410e-05] 
dist 202=[-.00051776989621223796,1.86167262602201348880e-05] 
dist 203=[-.00056248438972900414,-6.28285010878918448090e-05] 
dist 204=[-.00058806614496475188,-7.41616720892318037570e-05] 
dist 205=[-.00060723371501962040,-9.26988273562591674260e-05] 
dist 206=[-.00061155347064674693,-9.64760227068237888580e-05] 
dist 207=[-.00030658058247040898,-9.75083612106816538740e-05] 
dist 208=[-.00031383915334261276,-9.51005586386269982420e-05] 
dist 209=[-.00031467323151842234,-9.00309248264957745800e-05] 
dist 210=[-.00031282015660455012,-8.01353608404458782820e-05] 
dist 211=[-.00030185473684879718,-6.81456463705664431690e-05] 
dist 212=[-.00029678061532192614,-5.47601291142881361150e-05] 
dist 213=[-.00025280911827607037,-3.80558267671958111450e-05] 
dist 214=[-.00024160537238654771,-1.28875666679993257770e-05] 
dist 215=[-.00022398203287963738,1.23452941682657594820e-05] 
dist 216=[-.00021788684352774307,2.93065120567740845970e-05] 
dist 217=[-7.64909939603681701550e-05,4.63392851831972059160e-05] 
dist 218=[-5.79717977559434777330e-05,9.95776917563392247420e-05] 
dist 219=[-1.69055022085893401310e-05,.00014280039431761652] 
dist 220=[-7.42824861209843839720e-06,.00018248766345222365] 
dist 221=[1.95242722735627060540e-05,.00021595593400392267] 
dist 222=[2.03857282275900797570e-05,.00023448465616223452] 
dist 223=[2.10284046056482232370e-05,.00024530535659593537] 
dist 224=[1.95070263423638321540e-05,.00024802526106378269] 
dist 225=[1.64605732175066705460e-05,7.53629648629372102830e-05] 
dist 226=[1.06147536835866300200e-05,7.40440323769821579160e-05] 
dist 227=[3.56354472163997487280e-06,6.57108666496399919320e-05] 
dist 228=[-4.26953713112785595950e-06,6.48380626719253854090e-05] 
dist 229=[-1.40200782407681431840e-05,5.81987547842400124110e-05] 
dist 230=[-2.86853879652526670550e-05,5.62550419928304324950e-05] 
dist 231=[-4.33802427608352549250e-05,4.93753563244535977420e-05] 
dist 232=[-5.32482865087354683870e-05,4.85053221489458480010e-05] 
dist 233=[-6.12841331615332088720e-05,1.83390822307460036810e-05] 
dist 234=[-6.87039784673200340280e-05,1.60614311225950068470e-05] 
dist 235=[-7.49905804695064646110e-05,7.65798713683856201980e-06] 
dist 236=[-7.85267195512264365070e-05,5.81556528014663839600e-06] 
dist 237=[-8.08167413375998899030e-05,3.54026591753972592820e-06] 
dist 238=[-8.13797510693251065500e-05,3.04993539273414602150e-06] 
dist 239=[-3.53105490994377839870e-05,3.07544974317384268640e-06] 
dist 240=[-3.60760189969408503980e-05,3.58200371427195391950e-06] 
dist 241=[-3.61395542036286523800e-05,4.52693084706269497300e-06] 
dist 242=[-3.58856248436803022170e-05,6.29324236453257424490e-06] 
dist 243=[-3.47544138798666264980e-05,8.40857785882948869200e-06] 
dist 244=[-3.40698761442599928220e-05,1.07394688017162812350e-05] 
dist 245=[-2.97455639837449319410e-05,1.36286917222060228600e-05] 
dist 246=[-2.86029731162222867080e-05,1.79611142860006051600e-05] 
dist 247=[-2.63079224177831405000e-05,2.22975005166903075120e-05] 
dist 248=[-2.55550817116529306930e-05,2.52024864214520889770e-05] 
dist 249=[-1.24089782029862137020e-05,2.75605750046670317780e-05] 
dist 250=[-1.06544460711807734610e-05,2.97253480540912261920e-05] 
dist 251=[-6.93118694941760244500e-06,3.15507577463941364740e-05] 
dist 252=[-5.92279540872560921740e-06,3.25613003853321265370e-05] 
dist 253=[-2.15859440484739222590e-06,3.31498991031161577080e-05] 
dist 254=[-1.36241686565220544150e-06,3.32998448868492100660e-05] 
dist 255=[-2.76859325398584165940e-07,3.31393991312155059560e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 2, 2, 1, 2] 
dist 0=[130.26214378269582414   ,130.26214378269582414   ] 
dist 1=[129.20639886885447242   ,130.22094869868526316   ] 
dist 2=[125.44574582713912397   ,130.26214378269582414   ] 
dist 3=[120.33916644905784467   ,129.14166487743335805   ] 
dist 4=[113.92817822684799444   ,122.39825601232253383   ] 
dist 5=[105.44349692492851281   ,116.90879114304610272   ] 
dist 6=[92.087244527354024603  ,114.96075007975997346   ] 
dist 7=[78.355813002452054456  ,113.35119464907408752   ] 
dist 8=[68.373956690050489009  ,105.40217188469022621   ] 
dist 9=[59.357927526260023680  ,88.259495204381404840  ] 
dist 10=[49.404241111080935251  ,86.577232476111714430  ] 
dist 11=[31.545917478134474780  ,45.877323690431701667  ] 
dist 12=[18.963412945229452179  ,43.408688755536332627  ] 
dist 13=[8.4149433358092183539 ,38.501253634523239441  ] 
dist 14=[-1.9155873095086189441 ,37.367393555069067073  ] 
dist 15=[-11.162303356040458505  ,29.387329762971631631  ] 
dist 16=[-17.407998609870767605  ,25.143299219208679219  ] 
dist 17=[-22.597775465382872980  ,-.20727515928196985993] 
dist 18=[-27.659296518405834434  ,-1.0960390924234392944 ] 
dist 19=[-31.867827572402241368  ,-8.9360537718079227108 ] 
dist 20=[-33.668817477377318926  ,-8.7031873276860159662 ] 
dist 21=[-34.451941281582863679  ,-7.2921184558925139133 ] 
dist 22=[-34.595641134449851746  ,-4.0205517224949750990 ] 
dist 23=[-31.100019039262889630  ,-.39675670289530834641] 
dist 24=[-30.108167201402548911  ,2.4191193364203851292 ] 
dist 25=[-29.461071641806613876  ,5.0929933579868589573 ] 
dist 26=[-29.152785983324988730  ,8.1655289016174286231 ] 
dist 27=[-8.2871312395104312577 ,11.169525950173789498  ] 
dist 28=[-5.7824691482618044456 ,13.578471663886202001  ] 
dist 29=[.1121114014698007235 ,15.969568863218511741  ] 
dist 30=[1.0373912394190202557 ,18.911294807840304192  ] 
dist 31=[5.6540100893266748496 ,21.536879845396132791  ] 
dist 32=[5.8826555036319631431 ,22.675020404943301839  ] 
dist 33=[11.271613257884859427  ,23.167306779450814410  ] 
dist 34=[11.611183483917855932  ,23.222438550306909306  ] 
dist 35=[14.031162458806348637  ,21.021641038725435653  ] 
dist 36=[13.104035389291023678  ,20.353699232464477350  ] 
dist 37=[11.726245156557580399  ,19.878993410134643600  ] 
dist 38=[8.9022662082029325215 ,19.565435584120434943  ] 
dist 39=[3.4741810322141404680 ,15.934464966703258390  ] 
dist 40=[-.27249817895378118394,15.368222115523074001  ] 
dist 41=[-3.4225324361469208997 ,14.427963398140785052  ] 
dist 42=[-6.4849258577165426621 ,14.092515859734094253  ] 
dist 43=[-9.1785058427829974684 ,6.7369480007333773347 ] 
dist 44=[-10.866117700510161985  ,5.8366799404763270004 ] 
dist 45=[-12.107675415113449417  ,3.8085379602141380176 ] 
dist 46=[-13.032579841656381570  ,3.2851289064257447534 ] 
dist 47=[-13.681478080336949091  ,.92131787005289223818] 
dist 48=[-13.827857367886400517  ,.48203256206951629767] 
dist 49=[-14.233345490435172499  ,-.42794991120884748228] 
dist 50=[-14.351834311916893208  ,-.65200027381813008469] 
dist 51=[-12.143881947576934126  ,-1.3446761184679420753 ] 
dist 52=[-11.719356871158492131  ,-1.3527870374026855152 ] 
dist 53=[-10.957786474387785873  ,-1.1158952886206051464 ] 
dist 54=[-10.706980868767761111  ,-.49152069398549298447] 
dist 55=[-5.9325407431766503994 ,2.7828510835717344866 ] 
dist 56=[-5.4036423608831745508 ,5.0037074319467849297 ] 
dist 57=[-3.8603397364627643613 ,6.8231898121714799394 ] 
dist 58=[-2.7840006708977256887 ,8.5169281050563037214 ] 
dist 59=[-.47723666335512689556,10.043489814550361312  ] 
dist 60=[-.20651325653367938285,10.913175397117074122  ] 
dist 61=[.4207799012993544843 ,11.395330771764751236  ] 
dist 62=[.5191719725857026307 ,11.479568858938849650  ] 
dist 63=[1.2432189517478712177 ,2.3798008363509849480 ] 
dist 64=[1.3173616239282116734 ,2.4138128465527748323 ] 
dist 65=[1.5425641897125973725 ,2.4048466282679686903 ] 
dist 66=[1.5703191045450633384 ,2.4025920985964412550 ] 
dist 67=[1.6159799522019186999 ,2.0696130979413375923 ] 
dist 68=[1.4774627142532603747 ,2.0562300156614181257 ] 
dist 69=[1.2957992798343931086 ,1.8957088639742738170 ] 
dist 70=[.85074496644657363301,1.8792162179701811079 ] 
dist 71=[.30815291715918669829,1.5837704569623301309 ] 
dist 72=[-.06207806284259857795,1.5440558675035038654 ] 
dist 73=[-.36935654538899364673,1.4037742370791450505 ] 
dist 74=[-.66215486769090520456,1.3680158472736276200 ] 
dist 75=[-.91611232705690411885,.48849909381375167544] 
dist 76=[-1.0692705266261579391 ,.37095076298969650494] 
dist 77=[-1.1750357998434894474 ,.10541009724703928752] 
dist 78=[-1.2409425761851264740 ,.04879784677385171728] 
dist 79=[-1.2800627360835308460 ,-.24884093634361780752] 
dist 80=[-1.3392326016045196462 ,-.2998916495596677005 ] 
dist 81=[-1.4054395477951334763 ,-.39228205780640920552] 
dist 82=[-1.4221172684530020839 ,-.40922158259178781029] 
dist 83=[-1.0915883934253206413 ,-.43309761575035361276] 
dist 84=[-1.0488279012913223723 ,-.40804810974385581062] 
dist 85=[-.98079368368339227121,-.35921868435322666397] 
dist 86=[-.95635846718525303566,-.17274981065450836662] 
dist 87=[-.38330168856322504289,.16066207746170100122] 
dist 88=[-.38037788036457606113,.38480510488821668525] 
dist 89=[-.32232138183308227624,.56735273278140340679] 
dist 90=[-.31685908551136333153,.73565563772504752111] 
dist 91=[-.05609940386577777339,.87787445447457667239] 
dist 92=[-.03186884467539806263,.95772054555690778261] 
dist 93=[.04830506089818012914,1.0039819801983018989 ] 
dist 94=[.05913488738213749288,1.0151125053918040442 ] 
dist 95=[.09620399924977931730,.34102536189204477059] 
dist 96=[.1009604519101892221 ,.35422567287460699786] 
dist 97=[.12553618168210105557,.36145534079984746927] 
dist 98=[.12384787471945276075,.36076341103678996415] 
dist 99=[.11341227281224157203,.35509120538186448263] 
dist 100=[.08863435161002694084,.34994881690584260574] 
dist 101=[.04913558946089541661,.31411914031910757637] 
dist 102=[-.03919009349980651724,.30417208898088830117] 
dist 103=[-.12806933578908264925,.28046217273659090561] 
dist 104=[-.18812418963359143373,.2716381946527117163 ] 
dist 105=[-.23738038651786614727,.17251062015666784729] 
dist 106=[-.28339504095103397391,.16813821792750185484] 
dist 107=[-.32271335348195916375,.08583598043384645176] 
dist 108=[-.34538864617981865167,.07450791440079089994] 
dist 109=[-.3597897272391712374 ,.03182180726473613475] 
dist 110=[-.36626392686567211787,.02276977485227067880] 
dist 111=[-.36777992181586255196,.00974719638948148031] 
dist 112=[-.36249720091500180297,.00604382726857598692] 
dist 113=[-.14595442642345081712,.00429350858670415581] 
dist 114=[-.14483084582475961315,.00565657826542100421] 
dist 115=[-.12890290008992695639,.00931587890718518973] 
dist 116=[-.12473193704125659459,.01696282939878553736] 
dist 117=[-.11545123203880922303,.02638329312306681063] 
dist 118=[-.11210554389707243527,.03708462645645960280] 
dist 119=[-.05876687465629433714,.05055168256549598484] 
dist 120=[-.05104487030122090507,.07095331018250465208] 
dist 121=[-.04026724228055613017,.09142829445476171940] 
dist 122=[-.03988502596920043506,.10961508309173623256] 
dist 123=[-.01213113178084587284,.12734199851349609866] 
dist 124=[-.00849133325440796932,.13712089605132965032] 
dist 125=[-.00240474306413430642,.14276422362580987871] 
dist 126=[-.00096067926593151840,.14407239441768065738] 
dist 127=[.02195582814218281609,.03313782363225966363] 
dist 128=[.02359631552679578515,.03426590220031405341] 
dist 129=[.02653453385841702279,.03466849792238286555] 
dist 130=[.02696999057266458769,.03460686963452911700] 
dist 131=[.02641852505620902927,.03339823601988160385] 
dist 132=[.02373338579661352874,.03309531466065678900] 
dist 133=[.02043446283436396105,.02782483199550601556] 
dist 134=[.01669747195386593590,.02739169953854132269] 
dist 135=[.01200097035709324606,.02450932505780771684] 
dist 136=[.00489229927773457502,.02388535379760416733] 
dist 137=[-.00224068677224257277,.02082786995623174627] 
dist 138=[-.00703389424592460880,.02026361853736649507] 
dist 139=[-.01093777793081759681,.00678136809761508011] 
dist 140=[-.01454016152522905667,.00499347409159077189] 
dist 141=[-.01758821500849679563,.00099133724539474033] 
dist 142=[-.01932651477692446771,.00012115975391929943] 
dist 143=[-.02038931702570571325,-.00423883564175514176] 
dist 144=[-.02096341998426393611,-.00499854298521138339] 
dist 145=[-.02196421566184128200,-.00625733318551595386] 
dist 146=[-.02221631730479668992,-.00650921522555240945] 
dist 147=[-.00779176300316440991,-.00661102696410813892] 
dist 148=[-.00775236944039523824,-.00647743864348891010] 
dist 149=[-.00651781013673029528,-.00617643584110464029] 
dist 150=[-.00647895958056037053,-.00526313261143112027] 
dist 151=[-.00574899258018388911,-.00410896878307905782] 
dist 152=[-.00569114761583096170,-.00235344706809630786] 
dist 153=[-.00473775140614495488,-.00058948969609128585] 
dist 154=[-.00468783687229767416,.00060058452335256669] 
dist 155=[-.00093789211190370651,.00157520099829802730] 
dist 156=[-.00048582579764366739,.00248379254866745385] 
dist 157=[.00055628388454537676,.00325927323786609622] 
dist 158=[.00073156775999135962,.00370544108118345604] 
dist 159=[.00193754868940192806,.00398758923845983104] 
dist 160=[.00212326191155204881,.00411191941893364469] 
dist 161=[.00246813938600613179,.00415001934100717073] 
dist 162=[.00252688988906962239,.00413529068588550801] 
dist 163=[.00257479612600928133,.00411939665572832104] 
dist 164=[.00250019979246731981,.00409745989599346503] 
dist 165=[.00234744895153152259,.00392988519886279403] 
dist 166=[.00205209827844851814,.00388468619698700440] 
dist 167=[.00159977707051132590,.00319671972785049224] 
dist 168=[.00054852451830300708,.00302992735343248544] 
dist 169=[-.00050477115296958098,.00285076577007527799] 
dist 170=[-.00121103041937741569,.00276028328622404266] 
dist 171=[-.00178479337078280958,.00101480364805158740] 
dist 172=[-.00231202699540420032,.00087742193051610138] 
dist 173=[-.00275675243461999918,.00058315854001530088] 
dist 174=[-.00300292219457199951,.00050261817506523060] 
dist 175=[-.00314624527850440682,.00019675330748724413] 
dist 176=[-.00318234493444181031,.00013311029193814979] 
dist 177=[-.00257951053162938869,3.43170643285448457860e-05] 
dist 178=[-.00260731553311185457,8.82165776900721421390e-06] 
dist 179=[-.00102748800037228628,-.00088512394400981965] 
dist 180=[-.00101004989591854721,-.00079967778551207711] 
dist 181=[-.00095472465357328558,-.00069552801466187828] 
dist 182=[-.00093569403906475279,-.00057849910510866571] 
dist 183=[-.00081262592578116083,-.00040120859232435615] 
dist 184=[-.00078004948198102713,-.00012357062713940813] 
dist 185=[-.00071857187507036076,.00015464366210640054] 
dist 186=[-.00069925572254202240,.00034134852899812945] 
dist 187=[-.00029107200779011108,.00049321822589160666] 
dist 188=[-.00023346940271085145,.00063311993158512496] 
dist 189=[-.00010750111305478792,.00075139287503326171] 
dist 190=[-7.51736557658017654820e-05,.00081738528323777077] 
dist 191=[5.52082195448323837720e-05,.00085649665422911751] 
dist 192=[8.02724385484171885050e-05,.00086803757105692314] 
dist 193=[.00011788943096105222,.00086640130032670185] 
dist 194=[.00012632933842723295,.00085319134590562914] 
dist 195=[.00012702639590597521,.00056548248693422973] 
dist 196=[.00011999471151833892,.00055902537902737969] 
dist 197=[.00010611585451782121,.00045997363114147407] 
dist 198=[7.30280595387979727010e-05,.00043595516003315384] 
dist 199=[2.14298422956066794760e-05,.00041027892061879471] 
dist 200=[-5.63209493427944832300e-05,.00039724340788090928] 
dist 201=[-.00013425523675350617,.00016623375894595385] 
dist 202=[-.00018658324577031913,.00014724710387058487] 
dist 203=[-.00022917652359495907,8.40475977313676464800e-05] 
dist 204=[-.00028292870757752095,7.24872535880290535630e-05] 
dist 205=[-.00032854150630505183,2.85213347813076953300e-05] 
dist 206=[-.00035406208009823442,1.93816811325493850110e-05] 
dist 207=[-.00037028279908095885,5.06283658031237870090e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 1, 0, 0, 2] 
dist 0=[121.95970602511023050   ,121.95970602511023050   ] 
dist 1=[120.84478627554756286   ,122.95667874154770063   ] 
dist 2=[117.41710571728184520   ,124.29387785702083287   ] 
dist 3=[111.15897357291006860   ,126.37785792622932475   ] 
dist 4=[99.545193082199380383  ,128.19698883876955908   ] 
dist 5=[87.205774112812647791  ,128.48623410549678380   ] 
dist 6=[78.059971987229940768  ,127.87994502552358029   ] 
dist 7=[69.641744257848027526  ,126.13845466035556806   ] 
dist 8=[60.177612271302788925  ,105.62533527913729002   ] 
dist 9=[50.891392601124569430  ,102.31539235487859996   ] 
dist 10=[41.192260188728124957  ,92.637893990177066698  ] 
dist 11=[32.937587087607121332  ,91.138884197627235864  ] 
dist 12=[24.463772030260779200  ,71.071545600493600313  ] 
dist 13=[13.521526010724852582  ,66.910477670823497953  ] 
dist 14=[3.1320107414180366059 ,62.656313303853833684  ] 
dist 15=[-3.1486786261413170859 ,61.566172552462595384  ] 
dist 16=[-7.6404935736490570564 ,15.872451666885188823  ] 
dist 17=[-10.902637137411866226  ,10.489863540354286198  ] 
dist 18=[-13.351183468264070119  ,-1.8888424488107035468 ] 
dist 19=[-16.363306520214493708  ,-3.2486509742168636596 ] 
dist 20=[-23.416325796625844358  ,-2.4589822413793294460 ] 
dist 21=[-27.520301982145830602  ,-1.4066258954453670718 ] 
dist 22=[-30.211037927030670780  ,-.56887138789821558863] 
dist 23=[-31.651243112905187998  ,.19267211226325316813] 
dist 24=[-32.359634560571119519  ,.95718608981277923562] 
dist 25=[-32.360834309744996494  ,1.5936170983255098584 ] 
dist 26=[-31.626612447055562412  ,1.8540703430959291107 ] 
dist 27=[-31.144061583286720522  ,1.9508392159891750113 ] 
dist 28=[-27.005018513131539111  ,1.9479763869713539981 ] 
dist 29=[-25.912509040434035674  ,2.9275117953423688334 ] 
dist 30=[-24.131805450422592917  ,4.5273798815292963893 ] 
dist 31=[-23.525670744906627033  ,5.4080190734421894887 ] 
dist 32=[-11.366620395966270420  ,5.9236597696943969538 ] 
dist 33=[-9.9358869861437687141 ,9.9959111940735693988 ] 
dist 34=[-6.8122747088597525887 ,14.090664621937599001  ] 
dist 35=[-5.9465757602272177683 ,17.867747004568805876  ] 
dist 36=[-2.5727883557176449528 ,21.104853906810083181  ] 
dist 37=[-1.9008499042483850188 ,22.999831138561641751  ] 
dist 38=[-.83398379946882429338,24.072266677899036849  ] 
dist 39=[-.99173944133800526211,24.270529141281955129  ] 
dist 40=[-1.1905606222827551517 ,5.5955985925348314425 ] 
dist 41=[-1.3904335514423811420 ,5.6051563324612490773 ] 
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dist 102=[-.04555658540707083791,.03868459569769699207] 
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dist 151=[-.00110428341091193250,.00280276356060278812] 
dist 152=[-8.82463698224852268350e-05,.00365019251487416260] 
dist 153=[.00013273155982559652,.00436530946395161139] 
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dist 164=[.00041268472653133588,.00142856408825858752] 
dist 165=[6.68947367711383576110e-05,.00141520665869529183] 
dist 166=[-.00016640931879707723,.00015984379278040644] 
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dist 170=[-.00079771936746450215,-.00057859203511132028] 
dist 171=[-.00090886468691390473,-.00066092808877950143] 
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dist 173=[-.00101191279478234832,-.00070082825089387142] 
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dist 181=[-.00072280111762575264,6.00886927333327401680e-05] 
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dist 184=[-3.75150574678651488110e-05,.00044292133621405356] 
dist 185=[-6.55795485690535269030e-06,.00057413468858969903] 
dist 186=[.00014912972073090828,.00068482279817897591] 
dist 187=[.00017623029728941536,.00074609600319333773] 
dist 188=[.00019395207793359017,.00078177596571998182] 
dist 189=[.00019862594078163945,.00079075903674935260] 
dist 190=[.00019529721805761781,.00024165756748847187] 
dist 191=[.00018723694143631541,.00024137529707640519] 
dist 192=[.00017082884370116123,.00023239996890392819] 
dist 193=[.00015073574510645136,.00023106520800378705] 
dist 194=[.00012804255437728708,.00018770562081359948] 
dist 195=[9.94082811003508937220e-05,.00017815931852705678] 
dist 196=[5.60704102104442764870e-05,.00016955472684414351] 
dist 197=[1.25703154046434091910e-05,.00016777968447133825] 
dist 198=[-1.67267093841936743210e-05,3.42152651816416081540e-05] 
dist 199=[-4.06694733789823995830e-05,1.80978893624958974890e-05] 
dist 200=[-6.97397097891133521910e-05,-1.91051738560145272600e-05] 
dist 201=[-9.78897834557031103940e-05,-2.53464679070071961750e-05] 
dist 202=[-.00012182278752039852,-6.85782419133849781720e-05] 
dist 203=[-.00013542679514892545,-7.52251256643459920340e-05] 
dist 204=[-.00014381915652838447,-8.76809755830857473780e-05] 
dist 205=[-.00014706049942562815,-8.98420665697552479800e-05] 
dist 206=[-.00014741552165628089,-9.19304364727133102110e-05] 
dist 207=[-.00014667825325268414,-8.93821048937488685160e-05] 
dist 208=[-.00014078606838986006,-8.18366482860974834790e-05] 
dist 209=[-.00013917874642963535,-6.96283298644541705250e-05] 
dist 210=[-.00011464958339783216,-5.60462036287606031990e-05] 
dist 211=[-.00010868953279563677,-3.88909028820793723620e-05] 
dist 212=[-.00010229006124664143,-1.31003889222441995120e-05] 
dist 213=[-9.90516574750880334830e-05,1.27298541094793733480e-05] 
dist 214=[-3.66622662569140130970e-05,3.00431490911235041840e-05] 
dist 215=[-3.17504493679201864000e-05,4.41035945573659867970e-05] 
dist 216=[-2.12065134485821300940e-05,5.70441926463448803020e-05] 
dist 217=[-1.83126954817591470720e-05,7.05205961286978435340e-05] 
dist 218=[-7.27692767495361950060e-06,8.19261825859980961790e-05] 
dist 219=[-4.98822497505312925090e-06,8.83139769927024685160e-05] 
dist 220=[-1.33573311093381254080e-06,9.24291332727734075520e-05] 
dist 221=[-4.21813259939247458920e-07,9.34263857782935958310e-05] 
dist 222=[2.27519380070459698340e-05,3.41533954304816480830e-05] 
dist 223=[2.16613969670797698050e-05,3.39926173076725981420e-05] 
dist 224=[1.95303807476213795460e-05,3.28630019568349346980e-05] 
dist 225=[1.69476716043355253130e-05,3.23447389633152204620e-05] 
dist 226=[1.36800280971164640800e-05,2.75445718666402794520e-05] 
dist 227=[8.55243246685954805630e-06,2.63194017644424596080e-05] 
dist 228=[8.54808944474017793380e-07,2.44783228803658574340e-05] 
dist 229=[-6.85109944523057245750e-06,2.38080530995671079580e-05] 
dist 230=[-1.20116422854453985460e-05,8.11143450623698005570e-06] 
dist 231=[-1.61979555975947639180e-05,5.65401293669456579870e-06] 
dist 232=[-2.00355588756268940740e-05,4.03490405400269169260e-06] 
dist 233=[-2.32669138956850918030e-05,7.72818623524576609180e-07] 
dist 234=[-2.50460189246708146160e-05,1.02438377563077889310e-07] 
dist 235=[-2.60690124390477454480e-05,-8.49352439769819004690e-07] 
dist 236=[-2.62980777461245261630e-05,-1.08708886762992752380e-06] 
dist 237=[-2.61742975556716869990e-05,-1.13381492836427824640e-06] 
dist 238=[-1.44463674423324690590e-05,-9.93946559360915921420e-07] 
dist 239=[-1.38406874242893631360e-05,-6.93980064295577249710e-07] 
dist 240=[-1.36809060686179160000e-05,-1.04932348349668765180e-07] 
dist 241=[-1.12373706411544097880e-05,6.09915163128223007060e-07] 
dist 242=[-1.06468403722047199150e-05,1.40943460245529971690e-06] 
dist 243=[-1.00158566090929836970e-05,2.40812962084571322610e-06] 
dist 244=[-9.69611611847492961450e-06,3.91388395261310235170e-06] 
dist 245=[-6.23801490859099188730e-06,5.42390902497005147590e-06] 
dist 246=[-3.03621420935888095770e-06,6.43958787631993499680e-06] 
dist 247=[-2.00760140746611767750e-06,7.26840997168223169910e-06] 
dist 248=[-1.72679330714891039370e-06,8.03651731961674348120e-06] 
dist 249=[-6.64890859337446953720e-07,8.68922581131758196590e-06] 
dist 250=[-4.42973306729858978510e-07,9.05985605649099065110e-06] 
dist 251=[-1.09020762027089052610e-07,9.29619587564424388810e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 0, 1, 2] 
dist 0=[124.35545679537362397   ,124.35545679537362397   ] 
dist 1=[122.43001698964231357   ,125.91318482516084700   ] 
dist 2=[118.63018387368338099   ,128.24033437745394560   ] 
dist 3=[112.33626661061300740   ,130.23429716268363381   ] 
dist 4=[100.49899776299093380   ,130.47240588220677224   ] 
dist 5=[87.908270577220327065  ,129.83193142437772967   ] 
dist 6=[78.616241696889188379  ,129.03154514320441645   ] 
dist 7=[70.103260232100072006  ,108.82230405236595206   ] 
dist 8=[60.592691852322553592  ,105.59737304193043194   ] 
dist 9=[51.296731130137706593  ,96.054344085424040348  ] 
dist 10=[43.622093638230618200  ,94.549228592171298630  ] 
dist 11=[35.712498355017683304  ,74.376873153632290248  ] 
dist 12=[25.455955655134008594  ,70.164469473759484479  ] 
dist 13=[15.618409235371904736  ,65.837277319489059609  ] 
dist 14=[8.4034072246234713127 ,64.663440169427348808  ] 
dist 15=[-1.8953286387490089663 ,17.940926201387607002  ] 
dist 16=[-8.0062773075992900254 ,12.414992320696338923  ] 
dist 17=[-12.240803772237048691  ,-.3277266587679680705 ] 
dist 18=[-16.286367870532766746  ,-1.3948340327633433937 ] 
dist 19=[-23.678184593516614589  ,-1.7075695709969956706 ] 
dist 20=[-28.021806296760115062  ,-.88383898128562579817] 
dist 21=[-30.922598326428812286  ,.19203113189927016096] 
dist 22=[-32.584740236255661244  ,1.0297933740620071622 ] 
dist 23=[-33.481003098715031719  ,1.7741816015690277694 ] 
dist 24=[-33.539637293014459339  ,2.4937111538398264686 ] 
dist 25=[-32.857326952250160662  ,3.0707998157565873575 ] 
dist 26=[-32.401361191941019936  ,3.2567922655290979841 ] 
dist 27=[-28.039340600621098340  ,3.2921947626855133326 ] 
dist 28=[-26.887068285302167706  ,3.2825335720076978055 ] 
dist 29=[-25.133332033000178912  ,3.4084772145061156579 ] 
dist 30=[-24.489434480890549535  ,5.2869398577890592122 ] 
dist 31=[-11.713239824315491145  ,6.9735235713420422346 ] 
dist 32=[-10.274920483722580775  ,9.8397628072264754852 ] 
dist 33=[-7.1159981443336426183 ,13.971445867957439882  ] 
dist 34=[-6.2348900541826897685 ,17.790021512759865343  ] 
dist 35=[-2.7680539067903388108 ,21.100860635565409653  ] 
dist 36=[-2.0834774782016819191 ,23.041876356959775552  ] 
dist 37=[-.7536883726507201737 ,24.132396323966568952  ] 
dist 38=[-.43634891797829936435,24.335403829692353655  ] 
dist 39=[.72353749490664547439,6.7014015939406503138 ] 
dist 40=[-.85795734425336269739,6.6773834343182305775 ] 
dist 41=[-2.2024959143941602492 ,6.5679526511531183454 ] 
dist 42=[-3.5299515724913423041 ,6.4755134809075747528 ] 
dist 43=[-4.7079132207291532483 ,5.8416477770280226381 ] 
dist 44=[-5.4600949406748469309 ,5.6683085011089506133 ] 
dist 45=[-6.0286563481601180127 ,5.1904760680630181627 ] 
dist 46=[-6.4789396895726887418 ,5.0106359542826001083 ] 
dist 47=[-6.8053215534778723185 ,2.9896434359582466975 ] 
dist 48=[-6.8824663165262397009 ,2.6485486948259984395 ] 
dist 49=[-6.8467757443356246479 ,1.9392127163316456447 ] 
dist 50=[-6.7605388004375735427 ,1.7443076230277066803 ] 
dist 51=[-6.0581398997729444976 ,1.0095943491308346532 ] 
dist 52=[-5.8505008518328773581 ,.84462750277963698072] 
dist 53=[-4.9990108636297630158 ,.59905237531507355269] 
dist 54=[-3.5073159923983627848 ,.52681038787152614919] 
dist 55=[-.93677507212673542423,.42804922416160873533] 
dist 56=[-.78114942886799044653,.3977127366051318821 ] 
dist 57=[-.65488566520455741693,.38928112226424569243] 
dist 58=[-.69515235796952864025,.7224136102818094213 ] 
dist 59=[-.71839855115301334994,1.0329736548792863897 ] 
dist 60=[-.7242154092031928772 ,1.2374121397284207902 ] 
dist 61=[-.20900501515658766515,1.3992328444466671738 ] 
dist 62=[-.19181572227334656092,1.5409862044334184607 ] 
dist 63=[-.14775918302401699669,1.6488772455926968411 ] 
dist 64=[-.14140800007935809895,1.6763693370886417590 ] 
dist 65=[-.07351369720861642836,1.6767564268376358390 ] 
dist 66=[-.06161328718277348090,1.6768207744076760178 ] 
dist 67=[-.04525748703175493709,1.4327019861636136795 ] 
dist 68=[-.04242264804561816912,1.3694997639696888308 ] 
dist 69=[.04187535763236377107,1.3325928312764002808 ] 
dist 70=[.05194658885653497175,1.3232791288974018175 ] 
dist 71=[.07099556359435064110,.24025421810386931653] 
dist 72=[-.01783685468567901103,.11311318121582681152] 
dist 73=[-.23147575696647980018,.12383830883077185027] 
dist 74=[-.43570448379607861303,.12873142849623174287] 
dist 75=[-.61325257943433416183,.13102860864024162822] 
dist 76=[-.72103236507524928045,.13140685823749450458] 
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dist 188=[-4.62156936986899634070e-06,.00102062991745724720] 
dist 189=[1.85322053791024357640e-06,.00107449990566359426] 
dist 190=[2.54943825293262738960e-06,.00108724511441508644] 
dist 191=[3.94274853041350548260e-06,.00042106661590318330] 
dist 192=[4.18266681049751771650e-06,.00042003322438693404] 
dist 193=[4.93310782213417099080e-06,.00040316740328610220] 
dist 194=[4.85178946448700915110e-06,.00040072769508795111] 
dist 195=[4.27977695656533108680e-06,.00032347106569872789] 
dist 196=[3.02016331077187921260e-06,.00030510609484003913] 
dist 197=[1.66910181085207736690e-06,.00029197637009011917] 
dist 198=[6.62358061824819669560e-07,.00028903338511408218] 
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dist 202=[-.00013261450103384434,2.17269021578408121570e-06] 
dist 203=[-.00017201444818793967,1.85572060397263271810e-06] 
dist 204=[-.00019435074369472032,1.77744849224320943240e-06] 
dist 205=[-.00020805614352467259,3.09406514011032010700e-08] 
dist 206=[-.00021318773376262837,-1.78524290818828842440e-07] 
dist 207=[-.00021390727620606485,-5.37114569887301191180e-07] 
dist 208=[-.00021271962042463167,-6.05348149196333296020e-07] 
dist 209=[-.00020526520736773063,-6.45556410145258856590e-07] 
dist 210=[-.00020194980481990718,-5.34735223340335444880e-07] 
dist 211=[-.00017157316894662912,-3.18892455394754712740e-07] 
dist 212=[-.00016386350513965283,8.47761168419010280450e-08] 
dist 213=[-.00015219728241324947,1.67699130373871675070e-06] 
dist 214=[-.00014799819775754867,2.92270162072589852810e-06] 
dist 215=[-4.84197675204380036660e-05,2.73405812011249973700e-05] 
dist 216=[-3.52248235502748770630e-05,6.37106389489465344000e-05] 
dist 217=[-5.77101334332264188270e-06,9.32382633571181140980e-05] 
dist 218=[-2.05732755897204722760e-06,.00012034906049915352] 
dist 219=[-1.87627938428924632930e-06,.00014320944207294859] 
dist 220=[-1.81228246604579189650e-06,.00015585993589163635] 
dist 221=[6.90170783386230378410e-06,.00016322063766777505] 
dist 222=[6.41862242737966562460e-06,.00016507672003407941] 
dist 223=[5.49587411689434486990e-06,5.02870126480661748850e-05] 
dist 224=[3.75558740792030009020e-06,5.00939695037648033930e-05] 
dist 225=[1.66690693714642799380e-06,4.79350314567188390480e-05] 
dist 226=[-6.39167910734790649580e-07,4.76170636808337681440e-05] 
dist 227=[-3.49981869748187350970e-06,3.82757672294508988490e-05] 
dist 228=[-7.79044892691735063350e-06,3.62743074864640320040e-05] 
dist 229=[-1.20825600800166277630e-05,3.44507609817107555880e-05] 
dist 230=[-1.49490884323713106160e-05,3.40768199532466740640e-05] 
dist 231=[-1.72652542692417292150e-05,1.42136809597994308900e-05] 
dist 232=[-1.93721374242913813220e-05,1.47813229969851548160e-05] 
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dist 235=[-2.54971923714206823680e-05,1.56254949381008375900e-05] 
dist 236=[-2.82334078371702679320e-05,1.56162456976924112730e-05] 
dist 237=[-2.98814405949884398210e-05,1.55508246023185865200e-05] 
dist 238=[-3.04294749212169945330e-05,1.54539593590061783250e-05] 
dist 239=[-3.03849807868599067470e-05,1.53172393938229547370e-05] 
dist 240=[-3.01954005874494376690e-05,1.51019229841598837000e-05] 
dist 241=[-2.89009527842458008870e-05,1.48360911161608204460e-05] 
dist 242=[-2.85604487582199621170e-05,1.45737299029425840090e-05] 
dist 243=[-2.34401312063205900530e-05,1.42380077349160729310e-05] 
dist 244=[-2.22054031486722486090e-05,1.40265230159890817900e-05] 
dist 245=[-2.08743861158562055820e-05,1.32754339198821211110e-05] 
dist 246=[-2.02072966917288743100e-05,1.29561357345887986650e-05] 
dist 247=[-7.27920026511381186360e-06,1.26992777994742836030e-05] 
dist 248=[-6.26840003056740800770e-06,1.24670206689158908010e-05] 
dist 249=[-4.11534623929606505490e-06,1.22733701210133092170e-05] 
dist 250=[-3.52970652634167760050e-06,1.46304553582948824830e-05] 
dist 251=[-1.32787585085969485620e-06,1.69542657702388321860e-05] 
dist 252=[-8.65343921528026140550e-07,1.82490888496252453460e-05] 
dist 253=[-1.98045960269263492050e-07,1.90271957726269228400e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 0, 0, 2, 0, 2] 
dist 0=[129.03042341517223763   ,129.03042341517223763   ] 
dist 1=[126.27252455489902016   ,129.61766354661862432   ] 
dist 2=[122.16070988133624693   ,129.18781766659542032   ] 
dist 3=[116.60041442437159404   ,128.62451985192554860   ] 
dist 4=[109.01597898268188271   ,127.34309101137732778   ] 
dist 5=[96.850456929311336788  ,118.04845887791490266   ] 
dist 6=[84.261935259636142600  ,115.88659526138427130   ] 
dist 7=[74.989489173578471468  ,113.43662802340238353   ] 
dist 8=[66.492082778894421474  ,98.159859417205212524  ] 
dist 9=[56.972628466457088479  ,85.266486369804872792  ] 
dist 10=[47.636574491577892079  ,81.215696824421691354  ] 
dist 11=[39.856302537075459483  ,79.673924941513779429  ] 
dist 12=[26.509351717362524270  ,46.383659947309970202  ] 
dist 13=[14.376484515016957648  ,45.284115662466569465  ] 
dist 14=[4.2841713041804245206 ,35.799426204546099759  ] 
dist 15=[-5.4732326145315953307 ,34.136888075741380698  ] 
dist 16=[-14.124687617795471618  ,27.030982658625728052  ] 
dist 17=[-19.824879487601045585  ,-.39103951940547203873] 
dist 18=[-24.405258474955431317  ,-4.3629101829482582861 ] 
dist 19=[-28.615371026440003447  ,-4.7726360788433800573 ] 
dist 20=[-31.999755484295261686  ,-4.1055177689886097845 ] 
dist 21=[-33.299300964004353329  ,-1.8983263649718470883 ] 
dist 22=[-33.768991879427811367  ,.66923596037580925526] 
dist 23=[-33.838423970783522276  ,2.7736674676445324609 ] 
dist 24=[-29.902498855065051485  ,4.8615610892569123366 ] 
dist 25=[-28.960438687666680334  ,7.3767835567593846746 ] 
dist 26=[-28.106579755402521920  ,9.8929268693259124086 ] 
dist 27=[-27.797024216982527629  ,11.991999334825410216  ] 
dist 28=[-7.4650230739427607357 ,14.147533747975912522  ] 
dist 29=[-4.9593998534867077960 ,16.896630824443727240  ] 
dist 30=[.77499683430818643267,19.379372226389189418  ] 
dist 31=[1.6616695669220861717 ,20.479800645101344862  ] 
dist 32=[4.7625377323212052208 ,20.970967647695714518  ] 
dist 33=[9.6137802329879914941 ,21.029186153588464549  ] 
dist 34=[11.549008807678686121  ,19.130356092080426910  ] 
dist 35=[11.872542738456950276  ,18.545244525835676604  ] 
dist 36=[12.725899570982423849  ,18.122958780279700827  ] 
dist 37=[8.1175091588588171569 ,17.831961328622636865  ] 
dist 38=[3.1813382233788272807 ,17.384468610435112105  ] 
dist 39=[-.22977745817293523465,17.151705417632930933  ] 
dist 40=[-3.1013691286965197743 ,15.218233811366305940  ] 
dist 41=[-5.8984666044738329924 ,14.660429986041648036  ] 
dist 42=[-8.3618123050697454113 ,13.740988548102729296  ] 
dist 43=[-9.9100855753440618726 ,13.415029969517647329  ] 
dist 44=[-11.054690252162433863  ,6.2842283712659071208 ] 
dist 45=[-11.917512801836724596  ,5.4076943847030263091 ] 
dist 46=[-12.528484377282594623  ,3.4375457676949411134 ] 
dist 47=[-12.673790010914633099  ,2.9333021384774010707 ] 
dist 48=[-12.619900868872890883  ,.65872971560001520519] 
dist 49=[-13.066171060638201089  ,.23666014951854824411] 
dist 50=[-13.681563504583327121  ,-.6230995898239919438 ] 
dist 51=[-13.795726360563890740  ,-.82998212788440911169] 
dist 52=[-10.071239876042717488  ,-1.4424731546675957341 ] 
dist 53=[-9.8422419711806280579 ,-.36673466776971401735] 
dist 54=[-5.5127074907734328571 ,2.6347405093173938559 ] 
dist 55=[-5.0421139868747964144 ,4.6630430124406951918 ] 
dist 56=[-4.0055482782136213491 ,6.3246780319915056068 ] 
dist 57=[-3.6552556364313710859 ,7.8711611541371626247 ] 
dist 58=[-2.6723182982482524184 ,9.2421092997543889920 ] 
dist 59=[-2.6514933966165001470 ,10.043489814550360057  ] 
dist 60=[-.43035560342089803697,10.489129226859380463  ] 
dist 61=[-.16996870080543371979,10.566276511664165294  ] 
dist 62=[.43342559945070669369,2.1519333430927887195 ] 
dist 63=[.5272273161975716759 ,2.1847463944598746206 ] 
dist 64=[1.0667577877692037843 ,2.1811992374285663868 ] 
dist 65=[1.3280690516178223762 ,2.2208018625998686316 ] 
dist 66=[1.4180475789050166146 ,2.2364311944566352512 ] 
dist 67=[1.3792111304873928866 ,2.2064645613412085604 ] 
dist 68=[1.2504378279435585074 ,2.1873591321799623697 ] 
dist 69=[.77739325676742782779,1.8718752454674700133 ] 
dist 70=[.28470200737110565505,1.7880577710525332910 ] 
dist 71=[-.05174935020423176144,1.7165789055052071914 ] 
dist 72=[-.33125180573076481194,1.6483475085496511438 ] 
dist 73=[-.59797876977307423087,1.4290964737752037996 ] 
dist 74=[-.82956559263634602134,1.3368429579042793944 ] 
dist 75=[-.9696366614255328278 ,1.3024263666613793974 ] 
dist 76=[-1.0668468451788874603 ,.45997017520699277994] 
dist 77=[-1.2666305461433795713 ,.34745703566725315928] 
dist 78=[-1.3909491850133298857 ,.17792991458218529967] 
dist 79=[-1.4593057473550321985 ,.08053409798947010194] 
dist 80=[-1.4730190448496146685 ,.06180376131559841175] 
dist 81=[-1.2848929626224370974 ,-.29221775034997766494] 
dist 82=[-1.3481075441940694268 ,-.37918321844399692517] 
dist 83=[-1.3640309112190744563 ,-.39510658343282999033] 
dist 84=[-.89577418859534687709,-.3996665450463858971 ] 
dist 85=[-.87350644409502006577,-.1571986649345171985 ] 
dist 86=[-.40620504873497378164,.14588523417998850638] 
dist 87=[-.4038431372780024085 ,.34968447741225741358] 
dist 88=[-.36016911360387740593,.5157009235780452392 ] 
dist 89=[-.31931264321394259099,.66881215188931496024] 
dist 90=[-.305891527294539543  ,.79832119796373271448] 
dist 91=[-.30065200514103423929,.87109931360691662394] 
dist 92=[-.05158687632049869601,.91323085675101195226] 
dist 93=[-.02180145005647148278,.92328154697479823837] 
dist 94=[.04798460440485230215,.30015658363744982251] 
dist 95=[.05835757202348101071,.32231175844458728139] 
dist 96=[.10555166287866800161,.33575193012834630852] 
dist 97=[.13123406419709605983,.34344856046198947462] 
dist 98=[.12988016355924669945,.34305987923537074406] 
dist 99=[.09275664206798284377,.33824934804938309868] 
dist 100=[.03895580095748140225,.33350016429684932364] 
dist 101=[-.04323882223638272074,.29990285108876007045] 
dist 102=[-.12596281171589319455,.29050835130771849708] 
dist 103=[-.18186925295210239307,.26809620248451531656] 
dist 104=[-.22773176846182130304,.25972443515549793338] 
dist 105=[-.27058758973445365689,.17293103819249501233] 
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dist 188=[-5.86179991286533863960e-05,.00110119243436576129] 
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dist 200=[-.00011590703023309705,.00034679711481751235] 
dist 201=[-.00016446437634552499,.00033168100298314998] 
dist 202=[-.00020568675126343849,.00030666207501549039] 
dist 203=[-.00022901893329777402,.00029845837136181356] 
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dist 205=[-.00024852325000036464,9.54515408275874894190e-05] 
dist 206=[-.00024912809395307241,4.61921893260279565660e-05] 
dist 207=[-.00026130914873199589,3.33738908783090591260e-05] 
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dist 209=[-.00033090334247139426,-2.73380580422742897400e-05] 
dist 210=[-.00034551242049989772,-4.21709791120232200600e-05] 
dist 211=[-.00034917229527594488,-4.56458179692924038670e-05] 
dist 212=[-.00018017377021039168,-3.66169622836640136450e-05] 
dist 213=[-.00017525681787435041,1.99269642968956250130e-05] 
dist 214=[-9.68433278904847379600e-05,7.65487353673536638340e-05] 
dist 215=[-8.93636174301456562110e-05,.00011451045301393466] 
dist 216=[-7.47174128693075376360e-05,.00014535595210802184] 
dist 217=[-6.75969323247367004480e-05,.00017372148013995992] 
dist 218=[-5.91656297189033951540e-05,.00019767263181280680] 
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dist 222=[3.98606616399692553700e-06,4.95934602006718711790e-05] 
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dist 225=[2.02568696868764861300e-05,5.31675390620190311290e-05] 
dist 226=[1.42398026969628603280e-05,5.60773246224470557100e-05] 
dist 227=[7.57437140760224905950e-06,5.70327858581852786440e-05] 
dist 228=[-7.10586211074593757960e-07,5.70240956944860344900e-05] 
dist 229=[-1.31586906315476037780e-05,5.65532891230203982020e-05] 
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dist 234=[-5.23824099507360346950e-05,4.20218671277999423220e-05] 
dist 235=[-5.53539626190783779580e-05,4.06593947498905468120e-05] 
dist 236=[-5.71288020075290162620e-05,2.12792607908163337740e-05] 
dist 237=[-5.76849288107657366580e-05,1.82792274822431501500e-05] 
dist 238=[-5.75316845031426247740e-05,1.19549844518999926210e-05] 
dist 239=[-5.70156143013974187980e-05,1.02500118723672590840e-05] 
dist 240=[-5.51429107665703011820e-05,3.94232388895711182730e-06] 
dist 241=[-5.40739208123219000050e-05,2.58869810948262716580e-06] 
dist 242=[-4.74471862763031051630e-05,8.74861795009592196020e-07] 
dist 243=[-4.25684640834796265140e-05,5.21473045990585878970e-07] 
dist 244=[-2.07687170127049356730e-05,5.37801756858029523330e-07] 
dist 245=[-2.01266815821727588870e-05,8.60426703969574912580e-07] 
dist 246=[-7.57873340876329549500e-06,5.47413552899807835000e-06] 
dist 247=[-6.52174108283829139210e-06,9.31822657638223384930e-06] 
dist 248=[-4.27237766184828267160e-06,1.24417765938049367260e-05] 
dist 249=[-3.66119125405677227820e-06,1.53146472115377274350e-05] 
dist 250=[-1.36729281740713482380e-06,1.77410113168040996530e-05] 
dist 251=[-8.84639599831516266440e-07,1.90915822673706509240e-05] 
dist 252=[-1.97420703246197397420e-07,1.98994379338396924520e-05] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 1, 0, 0, 2] 
dist 0=[128.22885192958393512   ,128.22885192958393512   ] 
dist 1=[126.23360302082492984   ,131.26345968315533995   ] 
dist 2=[121.35703428373784206   ,133.91583821602653526   ] 
dist 3=[113.12789600309206912   ,134.33418194779494730   ] 
dist 4=[99.751073520433770436  ,133.80389040786960758   ] 
dist 5=[85.904404114611972161  ,132.85419078151185246   ] 
dist 6=[75.800142399542714809  ,125.88329998195570998   ] 
dist 7=[66.658150513142376775  ,117.61535942351950948   ] 
dist 8=[56.620011621114664970  ,102.19126122670109357   ] 
dist 9=[46.914170835082082469  ,100.82732794822790963   ] 
dist 10=[39.078422734751565179  ,79.600436742012701168  ] 
dist 11=[31.163332874425841573  ,75.139462712575897777  ] 
dist 12=[21.115689085796384506  ,71.048866163937132846  ] 
dist 13=[11.551783825681640041  ,70.258651244750919430  ] 
dist 14=[5.5558786162012174015 ,42.413893748234221869  ] 
dist 15=[1.0121519720551276390 ,37.066498182648268926  ] 
dist 16=[-5.2916053534621702693 ,1.1068012053398055086 ] 
dist 17=[-12.312693123899996391  ,-3.0811198658214528493 ] 
dist 18=[-20.081194083918135921  ,-3.6013575080372500405 ] 
dist 19=[-24.738293037670558548  ,-3.1980403818024555454 ] 
dist 20=[-27.963513403517086878  ,-1.5494066380660638677 ] 
dist 21=[-30.046926676988742656  ,.34337267077026650521] 
dist 22=[-31.356779838768010346  ,1.7212074010278360765 ] 
dist 23=[-31.565064880670147118  ,2.8976202142391208583 ] 
dist 24=[-31.237986662082508739  ,4.0046195933707915629 ] 
dist 25=[-30.863890877016135273  ,4.9031112367082427893 ] 
dist 26=[-27.015310243150190749  ,5.2585546005111158171 ] 
dist 27=[-25.962713178292212474  ,5.3874896969181308935 ] 
dist 28=[-24.411628542678497022  ,5.3976434047662702507 ] 
dist 29=[-23.808935477408870802  ,4.0945818253940455291 ] 
dist 30=[-8.9095391293450075847 ,3.7233623093183537125 ] 
dist 31=[-6.9305712858549042958 ,7.3996654756974628444 ] 
dist 32=[-2.4577436793529355408 ,11.774531131437015214  ] 
dist 33=[-1.5190354012763759339 ,15.798584548374867336  ] 
dist 34=[-1.1543545149584174461 ,19.193130375925540122  ] 
dist 35=[-1.1025375721421131994 ,21.069146285531838839  ] 
dist 36=[-1.1675327381836019307 ,22.156197642765425253  ] 
dist 37=[-1.2680271601182253856 ,22.418589260011668016  ] 
dist 38=[-1.3664952822281918541 ,8.1919539491495874321 ] 
dist 39=[-1.4745703038346973145 ,8.1744735640362662039 ] 
dist 40=[-1.6144277747133670344 ,6.8206792677638915794 ] 
dist 41=[-1.7553758475769273501 ,6.8038452982962970700 ] 
dist 42=[-1.8684465361582677409 ,5.6911429109082853027 ] 
dist 43=[-1.9783109611680455255 ,5.4111882647207849182 ] 
dist 44=[-2.3070735154613049169 ,5.2334081953445207149 ] 
dist 45=[-3.0248781336090350574 ,5.1894509221653880392 ] 
dist 46=[-3.6009936702630117782 ,3.4307628498492880767 ] 
dist 47=[-4.1191531149123226179 ,3.1743540034777845436 ] 
dist 48=[-4.5348392828330620923 ,3.0802163086516313159 ] 
dist 49=[-4.7045807317862703542 ,2.6053131632425893896 ] 
dist 50=[-4.7599109335481800907 ,2.4975416734001938521 ] 
dist 51=[-4.7292054124446159636 ,2.2085780796898809228 ] 
dist 52=[-4.3310779357642027323 ,2.1313510779441965153 ] 
dist 53=[-4.1966429770397724942 ,1.2563811314591785711 ] 
dist 54=[-3.9925177762038474477 ,1.1031298201767031974 ] 
dist 55=[-3.9726848952918280344 ,.81761867458648194562] 
dist 56=[-3.8922591772613518772 ,.74651770661138833736] 
dist 57=[-3.8300338022002599912 ,1.1284073663970015288 ] 
dist 58=[-3.3798833354489785674 ,1.8385706414935879356 ] 
dist 59=[-3.2571309843023359556 ,2.4971970729306986129 ] 
dist 60=[-2.5997053956660592151 ,3.0548265220544748220 ] 
dist 61=[-2.4638566761963363476 ,3.3643092862783631276 ] 
dist 62=[-.8603445650897922009 ,3.5447666521364905593 ] 
dist 63=[-.64826379054874062541,3.5902249147652496581 ] 
dist 64=[-.170737125258024616  ,1.4000592977803463580 ] 
dist 65=[-.06863991444621915462,1.8362552182086826428 ] 
dist 66=[.46104737036670608835,2.2043864646887719370 ] 
dist 67=[.40714519558517054088,2.4084604035453583077 ] 
dist 68=[.2663311064822712202 ,2.5273766938575033713 ] 
dist 69=[.12256423887096063316,2.5571272969587655982 ] 
dist 70=[.02313176857249961743,.95437259233880673559] 
dist 71=[-.06067910585366213030,.94513331437468362692] 
dist 72=[-.14249933442655964283,.7766218922043170872 ] 
dist 73=[-.21467152847704506202,.77167512757315127243] 
dist 74=[-.26022291655193546767,.63870714899155996389] 
dist 75=[-.34752072218713432574,.60594429992563475134] 
dist 76=[-.47737206824798219826,.5793740847685245551 ] 
dist 77=[-.5568488407091642885 ,.56926687687920003405] 
dist 78=[-.61310966294449546724,.13036776474973336424] 
dist 79=[-.65086664934801592521,.07722182707109255296] 
dist 80=[-.67412090007977517046,-.04595338902050268382] 
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dist 83=[-.6603503634188090311 ,-.15406230583992813149] 
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dist 86=[-.50333768108975488125,.09135573086197516423] 
dist 87=[-.4919753420374596628 ,.14195943470834332153] 
dist 88=[-.46178934390174578256,.18871676431358378432] 
dist 89=[-.4569320966286788345 ,.22824477604652575835] 
dist 90=[-.37644287873098261322,.25015842949821574007] 
dist 91=[-.35683248105732276839,.26877080044334847384] 
dist 92=[-.33667724343917123377,.33213243975140241192] 
dist 93=[-.32663688900406692806,.36905150845514555877] 
dist 94=[-.12279422464119791501,.38991680975663467158] 
dist 95=[-.10691076042736033554,.39471124919854452596] 
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dist 97=[-.06301612951748320860,.25593772890097862791] 
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dist 99=[-.01874759373069854423,.28003385814723261737] 
dist 100=[-.00557806985799077352,.29449719607417788147] 
dist 101=[-.00262867206815782736,.29781430593089086421] 
dist 102=[-.00554787675957353703,.12248480724649143817] 
dist 103=[-.01634936788597790130,.12151488049717306325] 
dist 104=[-.02660636942290064124,.01852677381765362198] 
dist 105=[-.03547806400784976007,.00645153345012958227] 
dist 106=[-.04078225226248377589,-.02152294548774036581] 
dist 107=[-.04494900733842136962,-.02587994601867131344] 
dist 108=[-.06137305522538377610,-.03426501777035286550] 
dist 109=[-.07115295020715082870,-.03864730102286983525] 
dist 110=[-.07775491180671085612,-.03833266415421516700] 
dist 111=[-.08156691826490589309,-.03682614243502259273] 
dist 112=[-.08362240080832835288,-.03334511064716159679] 
dist 113=[-.08372715448412644921,-.02895946559843418165] 
dist 114=[-.08207108677822704516,-.02386123881142119395] 
dist 115=[-.08090669978847994976,-.01737401436458774287] 
dist 116=[-.07023299309287031745,-.00747386676674971535] 
dist 117=[-.06736140209137286069,.00248127392572678030] 
dist 118=[-.06298346738602625541,.00918719990110255321] 
dist 119=[-.06136061003334762749,.01466278085985601562] 
dist 120=[-.02165247500534367902,.01973435451243228568] 
dist 121=[-.01634217706629235049,.02405600727333873410] 
dist 122=[-.00436552521576565685,.03577499119649578399] 
dist 123=[-.00179878981642598424,.04677607965664336066] 
dist 124=[.01044783042574800473,.05606256180272813346] 
dist 125=[.01116750049961155389,.06120535109479904583] 
dist 126=[.01112406908474578823,.06419884427039843066] 
dist 127=[.01077833033781351270,.06495289439545316065] 
dist 128=[.00994032487517076566,.01968721176279648815] 
dist 129=[.00887365488865987238,.01975516838623497882] 
dist 130=[.00761994340665954746,.01926335466732927664] 
dist 131=[.00601577852394963189,.01915113330010279255] 
dist 132=[.00355764490964024000,.01594801890210788612] 
dist 133=[.00108076279694656257,.01514835541531832319] 
dist 134=[-.00059796233041748972,.01451207903929482909] 
dist 135=[-.00198032035099952245,.01426133545141012998] 
dist 136=[-.00328083028209949938,.00242786016776464344] 
dist 137=[-.00439836177395624313,.00101194543017989188] 
dist 138=[-.00505442280590572206,-.00230769026865194803] 
dist 139=[-.00680446660587183077,-.00280054744849787106] 
dist 140=[-.00879768028142587044,-.00521158026433984529] 
dist 141=[-.00995255810414262020,-.00576740148132545047] 
dist 142=[-.01069298998850962278,-.00565503004331677881] 
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