8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 2, 0, 1] 
dist 0=[65.799751779602607016  ,65.799751779602607016  ] 
dist 1=[65.562242313463372782  ,65.884100913666822167  ] 
dist 2=[65.005252954343678983  ,65.829656584376310482  ] 
dist 3=[64.106852587397006316  ,65.663168802729452821  ] 
dist 4=[62.506352134638823638  ,65.539042024533690484  ] 
dist 5=[60.512025890427308300  ,64.909236944412948911  ] 
dist 6=[58.041368495907514709  ,64.630541377982228741  ] 
dist 7=[54.745849227984290843  ,64.380648617528963542  ] 
dist 8=[49.458430109385062251  ,64.177155800216960572  ] 
dist 9=[44.056565149913004234  ,63.832557543135296609  ] 
dist 10=[40.304058469388400082  ,63.601041592671986447  ] 
dist 11=[37.037049282575482433  ,63.348243754497916444  ] 
dist 12=[33.573174533502663105  ,63.173784491065170224  ] 
dist 13=[30.242318581306134830  ,38.338294707640974557  ] 
dist 14=[27.506070675729796353  ,36.254059076383552163  ] 
dist 15=[24.592047689143332835  ,31.272595885318560753  ] 
dist 16=[20.457424544421591230  ,30.542318141504510091  ] 
dist 17=[16.554426729586459608  ,23.599166813445946004  ] 
dist 18=[13.465540736977109186  ,22.350559646615728642  ] 
dist 19=[10.376021097457153818  ,20.794818646150553109  ] 
dist 20=[6.4697139058633758133 ,20.488211287541929470  ] 
dist 21=[2.7076435307524352283 ,11.960506965893275722  ] 
dist 22=[.1935565714239317519 ,11.549338248908286940  ] 
dist 23=[-1.8947451920575068423 ,10.748513368287254766  ] 
dist 24=[-3.9573737430084241100 ,10.577244358298283563  ] 
dist 25=[-5.8563622916101520363 ,5.0416080829375381475 ] 
dist 26=[-7.2921355773255814915 ,4.5335122718361401731 ] 
dist 27=[-8.6729122005389905217 ,3.5672142916019172688 ] 
dist 28=[-10.354212374324327208  ,3.4288445312762403358 ] 
dist 29=[-11.920626114083617299  ,-2.3018717337836073128 ] 
dist 30=[-12.842778384928778286  ,-2.7986335774687994304 ] 
dist 31=[-13.479867332719856294  ,-3.7708474803967117357 ] 
dist 32=[-13.906455711640675343  ,-3.9919063614528875273 ] 
dist 33=[-14.205146052450026930  ,-4.6366958237288408548 ] 
dist 34=[-14.330518688896594872  ,-4.7319364008131141551 ] 
dist 35=[-14.356643964110719262  ,-4.1390413484057653515 ] 
dist 36=[-14.339793994723140950  ,-3.2035901296351964793 ] 
dist 37=[-12.993625745930530748  ,-2.1259982574417708214 ] 
dist 38=[-12.769915030774879762  ,-.9656441512225028504 ] 
dist 39=[-12.316511641834547790  ,.4731527844822578206 ] 
dist 40=[-12.177745661591140736  ,2.6617615972708152480 ] 
dist 41=[-11.582302639652029645  ,4.8459920453540688275 ] 
dist 42=[-11.440655960772305478  ,6.2675427694806687472 ] 
dist 43=[-11.083257317578297643  ,7.3988482292292549947 ] 
dist 44=[-10.965107445252774924  ,8.4256358956463581029 ] 
dist 45=[-7.6338735640106287307 ,9.3037221026737353968 ] 
dist 46=[-7.4391324550144347058 ,9.8420388489196117237 ] 
dist 47=[-7.1031313009145109181 ,10.233562726141942004  ] 
dist 48=[-7.0095762782064250268 ,10.526293882263550676  ] 
dist 49=[-4.9814426700164868464 ,10.744208809324899672  ] 
dist 50=[-4.6985114662614290819 ,10.837340133742761548  ] 
dist 51=[-4.0356093001869003687 ,10.857168603194357307  ] 
dist 52=[-3.8886727945372118441 ,10.832582678410686380  ] 
dist 53=[-2.9604862334779779060 ,10.655643574040801421  ] 
dist 54=[-2.7813475301361196429 ,11.068031199261964824  ] 
dist 55=[-2.4412171746077970430 ,11.420700617004452602  ] 
dist 56=[-2.3539129269309565641 ,11.616406487155918861  ] 
dist 57=[.9217721835484543207 ,11.732500290338803079  ] 
dist 58=[1.2697927462791968620 ,11.767361994701475303  ] 
dist 59=[2.0214277276918690917 ,11.749794420167757881  ] 
dist 60=[.24141734327876888017,11.716095527437773084  ] 
dist 61=[-1.8502777549321673642 ,6.1171269145117623932 ] 
dist 62=[-3.2222135062134569966 ,5.8530916739154642083 ] 
dist 63=[-4.3268133838498128707 ,5.1988500572729532358 ] 
dist 64=[-5.3521723067686367527 ,5.0749335122900617123 ] 
dist 65=[-6.2457173474066824152 ,4.0460305685249445797 ] 
dist 66=[-6.8245573916354259992 ,3.8431758612295132748 ] 
dist 67=[-7.2827537041385707200 ,3.5422404584343935552 ] 
dist 68=[-7.6951215756274508985 ,3.4530380836529906156 ] 
dist 69=[-8.0487185139148308261 ,1.6701328565370403454 ] 
dist 70=[-8.2724818018197258827 ,1.4385467121906944230 ] 
dist 71=[-8.4438225974864501510 ,.90351071833870436765] 
dist 72=[-8.5882491794928938641 ,.80478473706697932431] 
dist 73=[-8.7042363145861421334 ,.1130060923397443207 ] 
dist 74=[-8.7621037927107510710 ,-.01005893079435859877] 
dist 75=[-8.7884951108451577314 ,-.23010291273653509151] 
dist 76=[-8.7788981175941265976 ,-.09413513934894971579] 
dist 77=[-2.7534445017201363790 ,.29177211564530426067] 
dist 78=[-2.2604899802503030321 ,.55360332739153591631] 
dist 79=[-1.1356421633537361219 ,.96656943281839135331] 
dist 80=[-.92707591980798428419,1.6575729521763783289 ] 
dist 81=[.46589040946593014764,2.2828911720600595460 ] 
dist 82=[.7071489872541799437 ,2.7284875644367860179 ] 
dist 83=[1.0133359464356245014 ,3.1266884449726457793 ] 
dist 84=[.96274729120164002928,3.5630103172263114326 ] 
dist 85=[.88743715778562984388,4.3626245130969161662 ] 
dist 86=[.793088502062868359  ,4.9041708205926092702 ] 
dist 87=[.66707392728488948055,5.3231391157457668522 ] 
dist 88=[.46552448349650409922,5.6829675669826789907 ] 
dist 89=[.23183598431121191747,5.9762770700301183321 ] 
dist 90=[-.02230804739924133843,6.1299367107606799672 ] 
dist 91=[-.33907491877840730351,6.2104445042712463530 ] 
dist 92=[-.82242586145585124106,6.2217932018402675214 ] 
dist 93=[-1.3073560154186585073 ,2.3895161165189985012 ] 
dist 94=[-1.6304127359982907515 ,2.1879120786175934209 ] 
dist 95=[-1.8954496407032832385 ,1.6919627606010233959 ] 
dist 96=[-2.1490503022736217858 ,1.6176161794970833590 ] 
dist 97=[-2.3745856884338606972 ,1.0731075250527287165 ] 
dist 98=[-2.5277163758582283970 ,1.0420709163289875528 ] 
dist 99=[-2.6564410576411530886 ,.97116542329926166553] 
dist 100=[-2.7846452717309818231 ,.94881914367653513378] 
dist 101=[-2.8917624011421991366 ,.85173922748117651281] 
dist 102=[-2.9364078370272062545 ,.82637566009040780415] 
dist 103=[-2.9533788633698210972 ,.8151823423960890568 ] 
dist 104=[-2.9501959687984821233 ,.82122046303960984249] 
dist 105=[-2.7773170020115346051 ,.83769890860545323913] 
dist 106=[-2.7436110824241544200 ,.86828941424352701599] 
dist 107=[-2.5103336613024713184 ,.91488690795409554882] 
dist 108=[-2.4899465287981199205 ,.99515154512679674448] 
dist 109=[-1.7395934706912606861 ,1.0763521730728080936 ] 
dist 110=[-1.6627324043481300969 ,1.1266731387936665089 ] 
dist 111=[-1.6784350385779658069 ,1.1636929626417842743 ] 
dist 112=[-1.7129106133722245316 ,1.1918709523949190198 ] 
dist 113=[-1.7461622428833585373 ,1.2119141452779213369 ] 
dist 114=[-1.7737303144229590945 ,1.2164986712303076502 ] 
dist 115=[-1.8024669586927075626 ,1.2139785603651555745 ] 
dist 116=[-1.8403643494637673654 ,1.2083428495311570528 ] 
dist 117=[-1.8775087554892718687 ,1.1598671826467542839 ] 
dist 118=[-1.9032264017248742186 ,1.1479077168054395456 ] 
dist 119=[-1.9254814800680108084 ,1.1032536884159794325 ] 
dist 120=[-1.9487842339274529804 ,1.0966901507536863713 ] 
dist 121=[-1.9708830849185823173 ,.97070676044014788332] 
dist 122=[-1.9883139924645155420 ,1.1993212614095147652 ] 
dist 123=[-2.0055533052982293464 ,1.6032809203141088880 ] 
dist 124=[-2.0268531866493248554 ,2.1890239548495883054 ] 
dist 125=[-2.0454776222596705464 ,2.7654729904085928609 ] 
dist 126=[-2.0520389665947121910 ,3.1323647545954652758 ] 
dist 127=[-2.0508844413442614505 ,3.4153807588947121221 ] 
dist 128=[-2.0439184789059885910 ,3.6572330059044440745 ] 
dist 129=[-2.0203793938881459346 ,3.8536470715237727511 ] 
dist 130=[-2.0086795408316780315 ,3.9554049018340686534 ] 
dist 131=[-1.9687079544002128717 ,4.0076624563807411614 ] 
dist 132=[-1.9517739577215098637 ,4.0174485784306570102 ] 
dist 133=[-1.8319251186100866735 ,3.9800288843458330988 ] 
dist 134=[-1.8043306272577264687 ,3.9570505089166040209 ] 
dist 135=[-1.7333274162830906185 ,3.9063094550011387257 ] 
dist 136=[-1.7085972152058341758 ,3.8819246364180377013 ] 
dist 137=[-1.5718544916506620890 ,3.7396209744600332987 ] 
dist 138=[-1.5396803971403913379 ,3.7023534048493238528 ] 
dist 139=[-1.4757661260067874519 ,3.5819371433845787601 ] 
dist 140=[-1.4558559265130359251 ,3.5531085176188177491 ] 
dist 141=[-1.3689096758605192786 ,.31619234793995448396] 
dist 142=[-1.8295149315522401408 ,.23369164109555772081] 
dist 143=[-2.3175538357284042019 ,.05923430851622812401] 
dist 144=[-2.7689336673616730511 ,.01627755679103553190] 
dist 145=[-3.1611010929734644195 ,-.155222339892090313  ] 
dist 146=[-3.4129416637187544403 ,-.18741955497055343589] 
dist 147=[-3.6097252277427708711 ,-.24515005472226582602] 
dist 148=[-3.7822721268227657913 ,-.25713459614390116017] 
dist 149=[-3.9283774739745245979 ,-.27955644644148824799] 
dist 150=[-4.0196843686535876920 ,-.26742509075867060577] 
dist 151=[-4.0881681418806972772 ,-.23617914308208874151] 
dist 152=[-4.1432263313423656386 ,-.17076957245539524428] 
dist 153=[-4.1853161481049633332 ,-.08857207036633682889] 
dist 154=[-4.2020656808036825600 ,.00964722298370920412] 
dist 155=[-4.2034279778263193642 ,.1382257056886745544 ] 
dist 156=[-4.1888570974328626658 ,.34153555938806716954] 
dist 157=[-1.4094000756902214282 ,.58092781577653390379] 
dist 158=[-1.1783748519652287489 ,.8132635253848584022 ] 
dist 159=[-.64737347631217734104,1.0077644227866905479 ] 
dist 160=[-.5545006117189648798 ,1.2009363533718573648 ] 
dist 161=[-.0840718434072279487 ,1.3779984266370286973 ] 
dist 162=[-.00180668704800804406,1.6293967355671030811 ] 
dist 163=[.16694301861496973923,1.8858832155409246776 ] 
dist 164=[.20922840946247868751,2.1946819453934674395 ] 
dist 165=[.53780787203247754459,2.4823401089461805326 ] 
dist 166=[.59185893724140302947,2.6544963168921488636 ] 
dist 167=[.62813547270341383563,2.7746590966694636894 ] 
dist 168=[.60305405644091137421,2.8549144813214069069 ] 
dist 169=[.52858030674845406589,2.9109367297788006841 ] 
dist 170=[.30365992601354564259,2.9344344907952726931 ] 
dist 171=[.02196088385998418316,2.9571179256339798906 ] 
dist 172=[-.41009140283773717028,2.9617205751379471413 ] 
dist 173=[-.8425227288322989048 ,1.6812371703920998197 ] 
dist 174=[-1.1257348445185216830 ,1.6353657779206617746 ] 
dist 175=[-1.3532900197235555923 ,1.5205782651328509405 ] 
dist 176=[-1.5637088387970864744 ,1.4926490568352722355 ] 
dist 177=[-1.7464792261477423993 ,1.2999530622281725666 ] 
dist 178=[-1.8637468493827349096 ,1.2592951273764293718 ] 
dist 179=[-1.9552536041918560719 ,1.1873014672086593939 ] 
dist 180=[-2.0352668833431526125 ,1.1685096773887590167 ] 
dist 181=[-2.1013997114411902016 ,.7840284528882237174 ] 
dist 182=[-2.1707849707502615596 ,.7314546073864728231 ] 
dist 183=[-2.2419073762513597917 ,.6035710912581019804 ] 
dist 184=[-2.2783448328192016722 ,.5814626452222914883 ] 
dist 185=[-2.2990190739320622554 ,.3925988184368885043 ] 
dist 186=[-2.3072607056406919190 ,.3570560454853061184 ] 
dist 187=[-2.3079600448700564366 ,.30555862843248330558] 
dist 188=[-2.2993866076225431194 ,.29069150607135841102] 
dist 189=[-1.9265681154175662754 ,.4391377045453226162 ] 
dist 190=[-1.8754639139458432209 ,.6420539559175354596 ] 
dist 191=[-1.7368503408910911685 ,.8664380671990926268 ] 
dist 192=[-1.7174815777388559999 ,1.0764827265350566871 ] 
dist 193=[-1.6898226886659704864 ,1.2606879827613702017 ] 
dist 194=[-1.6770322736140236423 ,1.3820013868158769203 ] 
dist 195=[-1.6564902592890008927 ,1.4802212087188596266 ] 
dist 196=[-1.6470259263366486840 ,1.5723089143337196027 ] 
dist 197=[-1.3614979521448606706 ,1.6526523276465245036 ] 
dist 198=[-1.3184149044323871402 ,1.7040247289891641134 ] 
dist 199=[-1.2255535796938086829 ,1.7439051466122906543 ] 
dist 200=[-1.1975930200951011086 ,1.7784059477692685832 ] 
dist 201=[-1.0757177883335584638 ,1.8067141829701686123 ] 
dist 202=[-1.0508460238156008527 ,1.8218913444921706543 ] 
dist 203=[-.97958984289415694489,1.8303171075405998815 ] 
dist 204=[-.9693483452241193424 ,1.8316918423647704919 ] 
dist 205=[-.57037957171371770555,1.1889374831125959213 ] 
dist 206=[-.69571502145043485972,1.1758068847750829957 ] 
dist 207=[-.79346245692080581909,1.3716229320061199104 ] 
dist 208=[-.87881054886727700506,1.5505237483927329276 ] 
dist 209=[-.94942827514569079308,1.7044360440716508688 ] 
dist 210=[-.9884171644777666342 ,1.8005698737612439309 ] 
dist 211=[-1.0116157528336220398 ,1.8726047386747914127 ] 
dist 212=[-1.0192463358401651485 ,1.9303834634207587714 ] 
dist 213=[-1.0211454843524640017 ,1.9758051430051727823 ] 
dist 214=[-1.0214823201849083334 ,1.9985466657217561868 ] 
dist 215=[-1.0207343669283463188 ,2.0089887397428668912 ] 
dist 216=[-1.0183086935188789475 ,2.0057368477958031811 ] 
dist 217=[-1.0149973826174341481 ,1.9929506928860255989 ] 
dist 218=[-1.0160910854973910706 ,1.9844176256431789913 ] 
dist 219=[-1.0215119160485178100 ,1.9445171925200381983 ] 
dist 220=[-1.0224830928063177104 ,1.9342489111972634675 ] 
dist 221=[-.78542538072249920054,.83414211163910944036] 
dist 222=[-.87007213231649814212,.73120513380803901271] 
dist 223=[-.94560756530364595792,.50039604521775534281] 
dist 224=[-1.0282433226377710928 ,.45113424458078901136] 
dist 225=[-1.1089121141326778490 ,.5064565585502886693 ] 
dist 226=[-1.2327494993443302308 ,.6296953293586432311 ] 
dist 227=[-1.3866062549717458544 ,.7595414259671086187 ] 
dist 228=[-1.5673702019622171553 ,.9319782514780584411 ] 
dist 229=[-1.7335217550793051738 ,1.1007781465056247682 ] 
dist 230=[-1.8290895500572955358 ,1.2161175451606812975 ] 
dist 231=[-1.8910732286726115163 ,1.3141434839931517522 ] 
dist 232=[-1.9232560192995521583 ,1.4138820557032089344 ] 
dist 233=[-1.9420569221390053510 ,1.5068366877282933256 ] 
dist 234=[-1.9506580517002810326 ,1.5778029314403172118 ] 
dist 235=[-1.9534210753062771436 ,1.6461102815665864745 ] 
dist 236=[-1.9489290274444268960 ,1.7284607614295093073 ] 
dist 237=[-1.8017907934250144153 ,1.9431734703253640267 ] 
dist 238=[-1.8173202048206725577 ,2.2129084671734090538 ] 
dist 239=[-1.8201889863456843265 ,2.4202497194345273183 ] 
dist 240=[-1.8173400401874627618 ,2.5960264768127076473 ] 
dist 241=[-1.7853094089746680932 ,2.7376156289695300713 ] 
dist 242=[-1.7735879964165049159 ,2.8085837802880786649 ] 
dist 243=[-1.7328305403048264395 ,2.8453269906142607981 ] 
dist 244=[-1.7188929727955562751 ,2.8503936570924522275 ] 
dist 245=[-1.5984718441474092542 ,2.8042421537356377889 ] 
dist 246=[-1.5903675074836696451 ,2.7836848776483117388 ] 
dist 247=[-1.5798984408620359361 ,2.7469491350463908937 ] 
dist 248=[-1.5714121758590929213 ,2.7313518330963407571 ] 
dist 249=[-1.5445630050295118479 ,2.6477188412230344407 ] 
dist 250=[-1.5328388093285179538 ,2.6237551082722480075 ] 
dist 251=[-1.5033767678037269812 ,2.5447492084942117150 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 0, 0, 2, 0, 1] 
dist 0=[57.472608721879566780  ,57.472608721879566780  ] 
dist 1=[56.220945275613835114  ,57.955846472944758629  ] 
dist 2=[54.218504736961416531  ,58.633154598687110653  ] 
dist 3=[50.893852653758044012  ,59.375649998604551031  ] 
dist 4=[47.456909625286540949  ,59.791489630464527258  ] 
dist 5=[45.006090841696841798  ,60.047753691403103131  ] 
dist 6=[42.806224740950854980  ,60.153260390964692457  ] 
dist 7=[40.370778273589176281  ,60.117399577455952991  ] 
dist 8=[37.966739379246363544  ,57.063216034878346377  ] 
dist 9=[35.891936791821112364  ,56.546606593825959573  ] 
dist 10=[33.657576121171710968  ,55.781284508235546413  ] 
dist 11=[30.615947542385469284  ,55.512819006245855546  ] 
dist 12=[27.582976809304501136  ,54.830906732594772205  ] 
dist 13=[25.382841425487726095  ,54.557943484960239110  ] 
dist 14=[23.366211724794043293  ,54.353833001838098824  ] 
dist 15=[21.065425454343983405  ,54.169050697527143238  ] 
dist 16=[18.749188559828296038  ,30.246308645407025279  ] 
dist 17=[16.670217014558990420  ,28.278851939502314713  ] 
dist 18=[14.358697864053828997  ,23.623549661780775666  ] 
dist 19=[11.112524159813253892  ,22.941262063230286166  ] 
dist 20=[7.9103929970965456105 ,16.628914870792857632  ] 
dist 21=[5.7746512594941216610 ,15.510686155157256674  ] 
dist 22=[4.0016243368531748208 ,14.079219007367115116  ] 
dist 23=[.98413511542444599878,13.799562596991478528  ] 
dist 24=[-1.3491616132438171898 ,7.7799576339651132260 ] 
dist 25=[-3.3134633575162197069 ,7.0662955603760580133 ] 
dist 26=[-5.2968932311752538934 ,5.7707797979646564420 ] 
dist 27=[-7.1513428120030601160 ,3.2770261396241276245 ] 
dist 28=[-8.6014823698457684638 ,.4963387901491840417 ] 
dist 29=[-10.042453905805131354  ,.1758141757266320763 ] 
dist 30=[-11.862161831095540739  ,-.4427771175586918087 ] 
dist 31=[-13.571054068484272959  ,-.5370291692107052944 ] 
dist 32=[-14.569660681473139937  ,-.42085675829298152003] 
dist 33=[-15.249469980647026768  ,.07969968011063691354] 
dist 34=[-15.683899004974933799  ,.77126737875574700113] 
dist 35=[-15.983696068947604443  ,1.8964655467543673704 ] 
dist 36=[-16.124907092121923063  ,3.0311520561729926192 ] 
dist 37=[-16.180670942924229502  ,3.7608087136196357420 ] 
dist 38=[-16.151685902477558309  ,4.3285947387306082476 ] 
dist 39=[-14.319183558195731970  ,4.8183770649629303504 ] 
dist 40=[-14.031945193449696149  ,5.2176306829394149283 ] 
dist 41=[-13.496622778173676666  ,5.4247699807209157915 ] 
dist 42=[-13.346526007146751807  ,5.5376240734617463697 ] 
dist 43=[-12.783237431224877123  ,5.5611652518475070476 ] 
dist 44=[-12.625433448461244204  ,5.4229567781461481959 ] 
dist 45=[-12.358497879230179350  ,5.3727894088989540517 ] 
dist 46=[-12.273953145939497554  ,5.3225777445126592288 ] 
dist 47=[-6.6326756243094074236 ,5.2778878237423646430 ] 
dist 48=[-4.3537715710960197246 ,5.1919449935099469328 ] 
dist 49=[-4.2279622323215382655 ,5.1380835396622274140 ] 
dist 50=[-4.0449355410107724221 ,5.0552813902010836999 ] 
dist 51=[-3.9852614623649211411 ,6.0236908266540850181 ] 
dist 52=[1.8801542383394154023 ,7.1075669027922578622 ] 
dist 53=[2.3790385627528566559 ,8.1467097813689855300 ] 
dist 54=[3.3466490131465159042 ,9.3968822602655554525 ] 
dist 55=[3.5709875467335930782 ,10.566368603970479634  ] 
dist 56=[4.0584041018916402088 ,11.283528297202498283  ] 
dist 57=[3.9602016712160694856 ,11.807162929291672321  ] 
dist 58=[3.7973975549358484510 ,12.204257078287022563  ] 
dist 59=[3.5022938229111876140 ,12.492640404675935779  ] 
dist 60=[2.8557251674337804283 ,12.582352503213710552  ] 
dist 61=[2.1391730256746039572 ,12.598742204262415581  ] 
dist 62=[.19169434565612406754,12.594402517959254221  ] 
dist 63=[-1.8445746820376106556 ,6.9117371440881041843 ] 
dist 64=[-3.1800596272221029074 ,5.2723640847611176902 ] 
dist 65=[-4.2553153798882732562 ,5.0687231790448707364 ] 
dist 66=[-5.2535756288328559420 ,4.5632300487473098183 ] 
dist 67=[-6.1237177965594925442 ,4.4629410421908085971 ] 
dist 68=[-6.6879468221446490142 ,3.6574347291675554803 ] 
dist 69=[-7.1352630299032648884 ,3.4963133293056276888 ] 
dist 70=[-7.5391041169218298630 ,3.2498486713517086649 ] 
dist 71=[-7.8853958446767739372 ,3.1781542836901276493 ] 
dist 72=[-8.1031464047096458589 ,1.7300579800788708515 ] 
dist 73=[-8.2683139555329628160 ,1.5394065290256846018 ] 
dist 74=[-8.4047854137769497727 ,1.0968782126548299795 ] 
dist 75=[-8.5123214251150614771 ,1.0128794055200690808 ] 
dist 76=[-8.5620316355941353420 ,.42881200309811621684] 
dist 77=[-8.5789381319672607539 ,.32298849036829415299] 
dist 78=[-8.5555877899889114008 ,.13330025530647668328] 
dist 79=[-6.1259292616226729411 ,.15911502765159154077] 
dist 80=[-2.3108945656222090284 ,.50790132068031602407] 
dist 81=[-1.2234335728449255068 ,.74245062138784643151] 
dist 82=[-1.0216779573118832337 ,1.1069550515167123602 ] 
dist 83=[.33005532435559088352,1.7355530673593653377 ] 
dist 84=[.56477386492854457622,2.3023373574556009782 ] 
dist 85=[1.0006398895209187944 ,2.7027819839548550341 ] 
dist 86=[1.0969551593370086275 ,3.5133473722448346586 ] 
dist 87=[1.0305597339755410784 ,4.3299452060897627960 ] 
dist 88=[.93565478355561727938,4.8485583421834225785 ] 
dist 89=[.82937930456169844795,5.2470112907160982700 ] 
dist 90=[.6947997468148397256 ,5.5843404425783050716 ] 
dist 91=[.48705072160989865982,5.8556638249452169186 ] 
dist 92=[.24913366604511123095,5.9908504054833649938 ] 
dist 93=[-.00572494623925541996,6.0555651949926146693 ] 
dist 94=[-.32082315226489145412,6.0629642759517014985 ] 
dist 95=[-.79891614259604283037,4.4654654691152507641 ] 
dist 96=[-1.2781771556956201888 ,2.1825783132427185733 ] 
dist 97=[-1.5979278370443164293 ,1.9875105920360767364 ] 
dist 98=[-1.8608451756614205783 ,1.5122753548640717032 ] 
dist 99=[-2.1134977150061156528 ,1.4386497864631977760 ] 
dist 100=[-2.3390037116582160743 ,.88850867267748742308] 
dist 101=[-2.4936755440272925234 ,.85703017090178888346] 
dist 102=[-2.6254402065242229993 ,.79326553762775154601] 
dist 103=[-2.7595936353688907200 ,.77514399200815711835] 
dist 104=[-2.8726348514393306834 ,.70737998645681399568] 
dist 105=[-2.9202153584193727934 ,.69524348643386252604] 
dist 106=[-2.9396372106359135356 ,.69876304742139298482] 
dist 107=[-2.9404316903064362650 ,.72461593138541192549] 
dist 108=[-2.7939100854714436879 ,.76273954187268930405] 
dist 109=[-2.7500670923349875828 ,.81517148357761592171] 
dist 110=[-2.4572948524846946783 ,.88790916993050451762] 
dist 111=[-2.0584108614927146002 ,1.0069770623366533527 ] 
dist 112=[-1.8125268188169486859 ,1.1263239541240740692 ] 
dist 113=[-1.6497621300730447992 ,1.2001660604295316577 ] 
dist 114=[-1.6246475825233165050 ,1.2544817452637817779 ] 
dist 115=[-1.4174929220981240198 ,1.2959679764563550172 ] 
dist 116=[-1.4343841218498485757 ,1.3257373954330671788 ] 
dist 117=[-1.4513049636399911735 ,1.3333268525724501816 ] 
dist 118=[-1.4715456661357756470 ,1.3329083074641133390 ] 
dist 119=[-1.5016659671523076523 ,1.3307832970081259142 ] 
dist 120=[-1.5327836166700490596 ,1.2600033871530053550 ] 
dist 121=[-1.5569894787843933762 ,1.2437795203359768852 ] 
dist 122=[-1.5807467712187202534 ,1.1986285033456480778 ] 
dist 123=[-1.6100498614286748429 ,1.1829934372154932290 ] 
dist 124=[-1.6405679011061745562 ,1.0022521386231981809 ] 
dist 125=[-1.6691528561869776338 ,1.1826383475917353890 ] 
dist 126=[-1.7016711180267098318 ,1.5271320805942475677 ] 
dist 127=[-1.7478490751134802264 ,2.0243661514661559639 ] 
dist 128=[-1.7919089697098070882 ,2.5127728373008426342 ] 
dist 129=[-1.8159735193681697249 ,2.8220590140748153921 ] 
dist 130=[-1.8298431120549082003 ,3.0588403161998482041 ] 
dist 131=[-1.8332513446327291341 ,3.2580096611375045057 ] 
dist 132=[-1.8295493466461037077 ,3.4173836076028443021 ] 
dist 133=[-1.8230972157459349789 ,3.4954158765279418388 ] 
dist 134=[-1.7977754971065976243 ,3.5341287604350513978 ] 
dist 135=[-1.7834198497792309143 ,3.5369840653145391778 ] 
dist 136=[-1.6918073273826275063 ,3.4726200654966417794 ] 
dist 137=[-1.6696902862649824347 ,3.4469075235345603305 ] 
dist 138=[-1.6084412599575358548 ,3.3920251508716609260 ] 
dist 139=[-1.5892490976608124959 ,3.3683614517263245684 ] 
dist 140=[-1.4584370736295779487 ,3.2369865800147930657 ] 
dist 141=[-1.4276872708837007515 ,3.2037293673525617020 ] 
dist 142=[-1.3737177949667057442 ,3.0929014754318447167 ] 
dist 143=[-1.3581244189207903901 ,3.0707205455066361378 ] 
dist 144=[-1.2401223535413683283 ,.32811857143850253455] 
dist 145=[-1.6177739923294958652 ,.13740448942704772202] 
dist 146=[-2.0449204348892286267 ,.09296832685840310023] 
dist 147=[-2.4390537898443148941 ,-.10851432299564562213] 
dist 148=[-2.7808462407405584951 ,-.14445513712981209021] 
dist 149=[-2.9992038953367770666 ,-.21897115003875459745] 
dist 150=[-3.1685348022944524078 ,-.23614954914507755015] 
dist 151=[-3.3147603236833726189 ,-.29677627453073666026] 
dist 152=[-3.4380299459006976631 ,-.29797450520324364639] 
dist 153=[-3.5157882539452630838 ,-.27859325550909315747] 
dist 154=[-3.5749578619709360008 ,-.22611870027560098181] 
dist 155=[-3.6240719511697172560 ,-.15652527743750032279] 
dist 156=[-3.6628523189408383360 ,-.06885143357677532156] 
dist 157=[-3.6807976227127377066 ,.04868709764815251860] 
dist 158=[-3.6868821902660895981 ,.23741877255041944998] 
dist 159=[-3.6783462068149224772 ,.46098459368519113416] 
dist 160=[-1.1791981299190659124 ,.68421343014138403596] 
dist 161=[-.97375708242866248175,.87134403129635496651] 
dist 162=[-.50206478252286447291,1.0576042792925612686 ] 
dist 163=[-.41710805721537130088,1.2285910894979287064 ] 
dist 164=[-.00763229823865038406,1.3547946605131228517 ] 
dist 165=[.06093558103331814037,1.4721079421671539147 ] 
dist 166=[.20557919136123677981,1.6504032807082352813 ] 
dist 167=[.23869457788826601602,1.9158010084230111664 ] 
dist 168=[.48817331994767028298,2.1632673087738966142 ] 
dist 169=[.53099132430854503486,2.3118019006692333115 ] 
dist 170=[.54600906309537287561,2.4160091521827457037 ] 
dist 171=[.51195626460718156057,2.4866519298724740338 ] 
dist 172=[.3419807441338832261 ,2.5360633636977277309 ] 
dist 173=[.09109244628937512539,2.5555791687002888196 ] 
dist 174=[-.2954866605782209114 ,2.5788931184583402242 ] 
dist 175=[-.6828182248399254994 ,2.5815031041393077520 ] 
dist 176=[-.9367090394089799894 ,1.5076410605678672634 ] 
dist 177=[-1.1409417785705075380 ,1.4001812690191730447 ] 
dist 178=[-1.3301909566719500566 ,1.3756571373588833404 ] 
dist 179=[-1.4948443464799309626 ,1.1909989265228781503 ] 
dist 180=[-1.6009667690487455588 ,1.1522008458350796339 ] 
dist 181=[-1.6843210605958816164 ,1.0888839763962520052 ] 
dist 182=[-1.7581554318204753822 ,1.0708833239620852736 ] 
dist 183=[-1.8198157407668449321 ,.6934340004123838216 ] 
dist 184=[-1.8828305898163618728 ,.6424315461206915614 ] 
dist 185=[-1.9760648585444854560 ,.5221563664574584098 ] 
dist 186=[-2.0348949317426685493 ,.4987511821071890765 ] 
dist 187=[-2.0619829470118910717 ,.3321477542047753271 ] 
dist 188=[-2.0755792763118382847 ,.3010738049234442575 ] 
dist 189=[-2.0805897275670550129 ,.24648017839400322179] 
dist 190=[-2.0802633237947692319 ,.23394902586439153609] 
dist 191=[-2.0725661365689475594 ,.05940463645484145237] 
dist 192=[-1.7171849020037301168 ,.3883093597294207936 ] 
dist 193=[-1.6688919153527952992 ,.6458366216375884709 ] 
dist 194=[-1.5407785171385133324 ,.8542320902811489994 ] 
dist 195=[-1.5172280880601647333 ,1.0494264915538499746 ] 
dist 196=[-1.3840256079474787950 ,1.2206850856889692614 ] 
dist 197=[-1.3716902181216682238 ,1.3336017564440260794 ] 
dist 198=[-1.3496292049310568682 ,1.4251620328379495218 ] 
dist 199=[-1.3411498426932548334 ,1.5112303011543858975 ] 
dist 200=[-1.1037561610932270271 ,1.5860847849236662606 ] 
dist 201=[-1.0680190381261685372 ,1.6329145068127005262 ] 
dist 202=[-.98877155842696374222,1.6680808046317412105 ] 
dist 203=[-.96455261966811084917,1.6964131908512605623 ] 
dist 204=[-.85757053048739338617,1.7181132797053833114 ] 
dist 205=[-.83541264301103873382,1.7268255869401370028 ] 
dist 206=[-.77845204464361154631,1.7276795690100545008 ] 
dist 207=[-.76577013120726745725,1.7224742474596046303 ] 
dist 208=[-.67049833201131627566,.98962150963169959402] 
dist 209=[-.73676664757540939534,1.0563340883158136401 ] 
dist 210=[-.79086099191805921168,1.2178061191081978730 ] 
dist 211=[-.83423547397165044075,1.3639637151193318270 ] 
dist 212=[-.85774448915718865763,1.4887459718428313665 ] 
dist 213=[-.87115080179150036966,1.5649491198973906260 ] 
dist 214=[-.87422964363891180372,1.6200138763415635503 ] 
dist 215=[-.8210036224823938322 ,1.6604725435293556229 ] 
dist 216=[-.8100123345901958624 ,1.6906429347384551198 ] 
dist 217=[-.7994919174476887044 ,1.7046668628240830438 ] 
dist 218=[-.7926979646494893241 ,1.7095245080008715032 ] 
dist 219=[-.8117105330421488471 ,1.7056570056545365791 ] 
dist 220=[-.8260031966936916420 ,1.6900173123210357297 ] 
dist 221=[-.8334264817139726354 ,1.6816932165656454121 ] 
dist 222=[-.83339229740216258338,1.6468671676695703559 ] 
dist 223=[-.74546710990858501317,1.6367023248811386015 ] 
dist 224=[-.83300624366035961993,.66742697315819767502] 
dist 225=[-.90995085397389475931,.57721776088305199605] 
dist 226=[-.99233514372912475545,.37663980366412979494] 
dist 227=[-1.0717047889497400242 ,.4659861128167483268 ] 
dist 228=[-1.1366235767753511494 ,.5728427193352800443 ] 
dist 229=[-1.2032563769532533329 ,.6862922685681506666 ] 
dist 230=[-1.2894627782421502189 ,.8380722052379094537 ] 
dist 231=[-1.3879581498543229203 ,.9871637008557711680 ] 
dist 232=[-1.5338001204515368015 ,1.0898900876394987222 ] 
dist 233=[-1.6181595263714941851 ,1.1781108693280776583 ] 
dist 234=[-1.6734769233974733714 ,1.2693416076356400942 ] 
dist 235=[-1.7034688775035014285 ,1.3552947365963670642 ] 
dist 236=[-1.7213725708054733529 ,1.4224645974894940442 ] 
dist 237=[-1.7284678548084832613 ,1.4886041476078422463 ] 
dist 238=[-1.7289935997320904895 ,1.5704495737858505892 ] 
dist 239=[-1.7231477979202557193 ,1.7330313376337298001 ] 
dist 240=[-1.6451803582041142439 ,1.9869547047718288564 ] 
dist 241=[-1.6401516426274507983 ,2.1832073929904388365 ] 
dist 242=[-1.6349274778314627827 ,2.3514750009658557983 ] 
dist 243=[-1.5931087373336810571 ,2.4884486711763813789 ] 
dist 244=[-1.5802021989182196246 ,2.5598712332388673235 ] 
dist 245=[-1.5434048937328141694 ,2.5975813970124902313 ] 
dist 246=[-1.5473374612888911661 ,2.6048659232935163254 ] 
dist 247=[-1.5092608748436518039 ,2.5817208950842222183 ] 
dist 248=[-1.4960042771307649738 ,2.5661617396866917975 ] 
dist 249=[-1.4818505097961203428 ,2.5383849258043774701 ] 
dist 250=[-1.4722969038977775289 ,2.5253182002948206499 ] 
dist 251=[-1.4464977369811818930 ,2.4511701195147361145 ] 
dist 252=[-1.4345127549637430546 ,2.4300559273501630603 ] 
dist 253=[-1.4106753999167071170 ,2.3560609744785043426 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 0, 1, 0, 0, 1] 
dist 0=[66.082781763872451735  ,66.082781763872451735  ] 
dist 1=[65.543339578033469008  ,66.286986064174547062  ] 
dist 2=[64.626980177293604683  ,66.562932191326116346  ] 
dist 3=[63.230704018981320085  ,66.778731130578836534  ] 
dist 4=[61.212768204792220656  ,66.851452559583032404  ] 
dist 5=[57.814093393349515770  ,66.820325923612373763  ] 
dist 6=[54.278391179973070478  ,66.715047407087862310  ] 
dist 7=[51.713264393897595172  ,66.358376391251350129  ] 
dist 8=[49.363301397681462740  ,65.501636256418848822  ] 
dist 9=[46.686652895523460048  ,62.633855130701506197  ] 
dist 10=[43.998600657805318331  ,61.970076943220197855  ] 
dist 11=[37.457150506336737460  ,60.955446832029765486  ] 
dist 12=[30.660618540491488494  ,60.624123725161242572  ] 
dist 13=[26.068163056176388852  ,59.781639348929688863  ] 
dist 14=[22.203560707690135090  ,59.440229574760501519  ] 
dist 15=[18.313306303837181496  ,57.205941991676315573  ] 
dist 16=[14.696918894982398886  ,52.080048016969866557  ] 
dist 17=[11.925826692670058874  ,31.038085122277181987  ] 
dist 18=[9.2387089252737569734 ,28.749677805812773499  ] 
dist 19=[5.9575593731013832693 ,25.045086796086479799  ] 
dist 20=[2.8570393769002334067 ,24.384739605755573186  ] 
dist 21=[.8911044870145380044 ,24.177080787667350670  ] 
dist 22=[-.6235819132378012935 ,13.963559730773385205  ] 
dist 23=[-2.0356952409455859018 ,12.296513215891440254  ] 
dist 24=[-3.2650333374642463121 ,11.963390772630747490  ] 
dist 25=[-4.0606980010969405152 ,3.0109769785287991207 ] 
dist 26=[-6.0594040486433677889 ,1.9728598515951656571 ] 
dist 27=[-7.8014785669605410495 ,-.29395704969999712155] 
dist 28=[-9.4538399416121263748 ,-.63745693529324299858] 
dist 29=[-11.423243350778543715  ,-2.9679261676832168696 ] 
dist 30=[-13.265436516552892971  ,-3.3104931939198165141 ] 
dist 31=[-14.409683730707771906  ,-3.9591429551033947065 ] 
dist 32=[-15.265642676679810402  ,-4.1906160306154798099 ] 
dist 33=[-15.956291980178414854  ,-5.9428297929169687204 ] 
dist 34=[-16.490998524622683860  ,-5.5480670297435333298 ] 
dist 35=[-16.724101647695451210  ,-4.7020666725841161972 ] 
dist 36=[-16.818791253129427822  ,-3.5238446458104270405 ] 
dist 37=[-16.800481975715006527  ,-1.5892868274788274548 ] 
dist 38=[-11.240723074910237697  ,.71631968910504846257] 
dist 39=[-11.233034210642848866  ,2.3358431448399854208 ] 
dist 40=[-11.194255145359489186  ,3.6845720903215303258 ] 
dist 41=[-10.342580648422241155  ,5.0127602229298922807 ] 
dist 42=[-10.187435258114599738  ,6.2235623589049266581 ] 
dist 43=[-9.8275287398091281787 ,7.1041988190675734480 ] 
dist 44=[-9.7049516870305714767 ,7.9107150687603836104 ] 
dist 45=[-9.1152846929279302206 ,8.8260845101219952277 ] 
dist 46=[-8.9832852520681307194 ,9.6574413462186389386 ] 
dist 47=[-8.6501095343994728795 ,10.128758475544485406  ] 
dist 48=[-8.5493534714871323084 ,10.426407473876820784  ] 
dist 49=[-3.7152217460512329696 ,10.564562451294417605  ] 
dist 50=[-3.2339958798909671163 ,10.634191389157093586  ] 
dist 51=[-2.1694664571865416087 ,10.658465064592561176  ] 
dist 52=[-1.9367322236444992343 ,10.654466461737744542  ] 
dist 53=[-.6892630180913041586 ,10.611689846880248672  ] 
dist 54=[-.4683197710335726161 ,8.3364717068037097203 ] 
dist 55=[.0083184652729836157 ,8.0585489024632915757 ] 
dist 56=[.1174739561552146116 ,7.3693002058216359684 ] 
dist 57=[.111736145582413882  ,7.2268744654397862140 ] 
dist 58=[-.60727998826179384757,6.1322865532140927268 ] 
dist 59=[-1.1828619690858186705 ,5.9130549878612711858 ] 
dist 60=[-1.7620106431950170258 ,5.5594942498675790963 ] 
dist 61=[-2.4952911555702683338 ,5.4624267304521973345 ] 
dist 62=[-3.1959599334111446820 ,3.5347362794446477849 ] 
dist 63=[-3.6450558087529447033 ,3.2791371628902729089 ] 
dist 64=[-3.9947159757366144115 ,2.5277696214450759405 ] 
dist 65=[-4.2988042390755254871 ,-1.2259341523138555048 ] 
dist 66=[-4.5494030163699278279 ,-1.3129332182410335722 ] 
dist 67=[-4.6857296248071925954 ,-1.3280138020950984965 ] 
dist 68=[-4.7641385038485470838 ,-1.3385122693617258068 ] 
dist 69=[-4.7837427348777398626 ,-.97041573983617975057] 
dist 70=[-3.2308723986275029643 ,-.44862607035815475941] 
dist 71=[-3.2659235213450364941 ,-.09706186355676869674] 
dist 72=[-3.2802886877991967836 ,.19595991178834473925] 
dist 73=[-3.2838236845956541400 ,.48431046592915743346] 
dist 74=[-3.2801634625781793088 ,.74642259284920549551] 
dist 75=[-3.2658018691973990318 ,.93481824311029171485] 
dist 76=[-2.6865214787309100967 ,1.1046749038491367369 ] 
dist 77=[-2.6074099688261835426 ,1.2928629708507883461 ] 
dist 78=[-2.4016550536921539615 ,1.5067888121562914257 ] 
dist 79=[-2.3612834639948308483 ,1.8228670896310062631 ] 
dist 80=[-2.0001648571228451820 ,2.1000675933991473260 ] 
dist 81=[-1.9256271220891486867 ,2.2825360362148532773 ] 
dist 82=[-1.8222978706129302010 ,2.4301522972689058237 ] 
dist 83=[-1.7876851726761833645 ,2.5683501895904337606 ] 
dist 84=[-1.0427526242998500080 ,2.6869650146255608064 ] 
dist 85=[-.94445779624202791193,2.7564735109064587853 ] 
dist 86=[-.72471586704823798626,2.8032049948922786056 ] 
dist 87=[-.67417100808637987041,2.8309666253071649941 ] 
dist 88=[-.40700278937395181739,2.8443942882137330966 ] 
dist 89=[-.35848406469031484097,2.8402190845885767063 ] 
dist 90=[-.25234612997809111321,2.8144502258449327456 ] 
dist 91=[-.28080444155956455356,2.7956295366202195442 ] 
dist 92=[-.31972990176972101274,.646731544095208598  ] 
dist 93=[-.44082840387878220531,.63160157156365538238] 
dist 94=[-.58256556180622146751,.19779819327297515564] 
dist 95=[-.68218679490055276361,.14466435865692481763] 
dist 96=[-.94649654693141857425,.02850602193552528697] 
dist 97=[-1.1360604648084346190 ,.00466317158378079605] 
dist 98=[-1.3067020792865140062 ,-.12067297517662241024] 
dist 99=[-1.4955537339168750136 ,-.14159858175303281538] 
dist 100=[-1.6689121688560008904 ,-.18498421929284260272] 
dist 101=[-1.7777613360675063879 ,-.19293731831294606643] 
dist 102=[-1.8599532184866478707 ,-.79022503803644537738] 
dist 103=[-1.9269822833988194641 ,-.82989445986393229147] 
dist 104=[-1.9789487243436897505 ,-.90874849130050178524] 
dist 105=[-2.0010592562073047706 ,-.92266022878902525167] 
dist 106=[-2.0065991355990187026 ,-.96805726620092350416] 
dist 107=[-2.0037612721136792046 ,-.96531713753984363029] 
dist 108=[-1.0611519179222886978 ,-.73817628171218917376] 
dist 109=[-1.0171834434420600248 ,-.54608858335899488257] 
dist 110=[-.94272520068983127112,-.38037409322686536615] 
dist 111=[-.92849155117240845492,-.20799679576513823793] 
dist 112=[-.90261713405108080778,-.04512123764201692080] 
dist 113=[-.89454156171321755474,.08270556753229703547] 
dist 114=[-.86043885236541022166,.20899524241071685752] 
dist 115=[-.85059457004273986043,.36575087985422412815] 
dist 116=[-.82775194186203019147,.51471358519212668787] 
dist 117=[-.81921028987687443766,.60992237426151082675] 
dist 118=[-.16470911156846838419,.68374265469698852315] 
dist 119=[-.10644683877274084065,.74738998664151104364] 
dist 120=[.01656686286272578530,.79939977846092814985] 
dist 121=[.04627630691497153661,.82679712660957785602] 
dist 122=[.16560967621068540393,.8417156168956260654 ] 
dist 123=[.18786795873601883653,.84474725488085352002] 
dist 124=[.22571175960732934887,.83071823479763574186] 
dist 125=[.23360993977169988289,.92994640994872776   ] 
dist 126=[.24283490915541111232,1.0222866908049608375 ] 
dist 127=[.23156819224713305826,1.0775593535478444247 ] 
dist 128=[.20688413178311804186,1.1161898026051387380 ] 
dist 129=[.15751954468802574347,1.1421354390514411243 ] 
dist 130=[.09620260771024490830,1.1591854169541819408 ] 
dist 131=[.02383483870186683508,1.1623253998675996051 ] 
dist 132=[-.07034549042799620672,1.1598421037628481529 ] 
dist 133=[-.21868088876056311851,1.1544560644626849005 ] 
dist 134=[-.38380998049571813127,1.0112577180295682681 ] 
dist 135=[-.53359947265222420781,1.0247821536926455385 ] 
dist 136=[-.65841693161961889856,1.0365556225191378998 ] 
dist 137=[-.78144266273435681911,1.0441290571045835021 ] 
dist 138=[-.89360703926915179525,1.0500336085294590736 ] 
dist 139=[-1.0518597628284995225 ,1.0551371148985913050 ] 
dist 140=[-1.3457943789497547028 ,1.0584615320133076885 ] 
dist 141=[-1.5333536178068991385 ,1.0572672063328054465 ] 
dist 142=[-1.6785671549852045073 ,1.0524917274197642318 ] 
dist 143=[-1.8035791444844593244 ,1.0482691563918092848 ] 
dist 144=[-1.9057741968540575122 ,1.0274290630569954091 ] 
dist 145=[-1.9599692516423021966 ,1.0202590351563778161 ] 
dist 146=[-1.9893028094765683486 ,.99445951528248278739] 
dist 147=[-1.9947685606966975150 ,.9873112117096176162 ] 
dist 148=[-1.9845729639586808109 ,.91120116098441327121] 
dist 149=[-1.9745149779339257828 ,.89537749203810348394] 
dist 150=[-1.9526603692785067402 ,.8545566131049451217 ] 
dist 151=[-1.9414808785771603499 ,.8420469934386981764 ] 
dist 152=[-1.8745585660103790442 ,.81104034725328853209] 
dist 153=[-1.8567410762347067639 ,.94622094751969240894] 
dist 154=[-1.7974446117530447558 ,1.0644250710233764402 ] 
dist 155=[-1.7838670656502848202 ,1.1416701379809229644 ] 
dist 156=[-.68687048838451224196,1.2035481058923072104 ] 
dist 157=[-.67448953730031084036,1.2604553259420442105 ] 
dist 158=[-.43855896984006001305,1.3084621118765788878 ] 
dist 159=[-.4064818054750217781 ,1.3493527132367302183 ] 
dist 160=[-.32684134152136122316,1.5455903079909195833 ] 
dist 161=[-.31492622430789148706,1.6724720137553146684 ] 
dist 162=[-.19359797004766366922,1.7725948855539532708 ] 
dist 163=[-.17094479629503710604,1.8620923872175498890 ] 
dist 164=[-.14372517099548701029,1.9384052299186365505 ] 
dist 165=[-.13767819981385375014,1.9859341157623278619 ] 
dist 166=[-.10189356704691245466,2.0213895235016396568 ] 
dist 167=[-.1941485710840097338 ,2.0495392547410496306 ] 
dist 168=[-.34365285869395679059,2.0707728369032729092 ] 
dist 169=[-.49039119133128624335,2.0786385331551588158 ] 
dist 170=[-.62372996682231955889,2.0782028754074317323 ] 
dist 171=[-.71978603584159073322,2.0712598986082062332 ] 
dist 172=[-.80672014355062274626,.72431235791209033464] 
dist 173=[-.9036738993067219324 ,.61179515080735164265] 
dist 174=[-.9921778693850184378 ,.35232460644119612166] 
dist 175=[-1.0454069263980707783 ,.30571020966116132436] 
dist 176=[-1.0828780008673864930 ,.05433361362579570134] 
dist 177=[-1.1085242684642080593 ,.01430554671241487369] 
dist 178=[-1.1252293506153001885 ,-.06796218987192078924] 
dist 179=[-1.1282520203535051192 ,-.08865556314693639788] 
dist 180=[-1.2282438089545376342 ,-.01472106418658727302] 
dist 181=[-1.3113594450830475432 ,.11942854243826093212] 
dist 182=[-1.3689463227820986276 ,.25385721898659322374] 
dist 183=[-1.4065721167149569124 ,.34167430462768062037] 
dist 184=[-1.4325128754057387849 ,.41196551430379953429] 
dist 185=[-1.4434887257378876580 ,.47648641698038963724] 
dist 186=[-1.4455823723028982609 ,.53217733826250267524] 
dist 187=[-1.4426573183001590793 ,.56724683176045832931] 
dist 188=[-.44278003529005673187,.59384221232020934765] 
dist 189=[-.43645248366815661992,.6157301335967947603 ] 
dist 190=[-.2966090106580863657 ,.63350799696191712613] 
dist 191=[-.27758103628193296751,.64370950760655027165] 
dist 192=[-.23406681732079918188,.65062239033402958831] 
dist 193=[-.22404297181777398325,.74493484837979009702] 
dist 194=[-.16708355421386752234,.83397304651078372275] 
dist 195=[-.156339353889292818  ,.93883834561115303059] 
dist 196=[-.13426086863653189932,1.0353432241225410984 ] 
dist 197=[-.12829662476591092077,1.0910323828636119655 ] 
dist 198=[.05616697098029936042,1.1273767289069187606 ] 
dist 199=[-.03441086891058303150,1.1467159520291786321 ] 
dist 200=[-.11496848548133795452,1.1579819357681117824 ] 
dist 201=[-.2026638522361108164 ,1.1621215926477219003 ] 
dist 202=[-.28799939933250351795,1.1618267218061293789 ] 
dist 203=[-.35914490208036042287,1.1578011958294313090 ] 
dist 204=[-.4333666809972969252 ,.97956390839728155489] 
dist 205=[-.53097436339298222954,.9547393446688851784 ] 
dist 206=[-.62607745248998370668,.93939248888768482829] 
dist 207=[-.6903093340911814173 ,.94395631496001697889] 
dist 208=[-.74409321556720671708,.94329684814743616372] 
dist 209=[-.79752108757279077672,.9393766402607886442 ] 
dist 210=[-.84649722932706038003,.93209302952382571267] 
dist 211=[-.88252447594432987436,.94669165597831811884] 
dist 212=[-.91589539504530841803,.97075575241607924022] 
dist 213=[-.954277470066584194  ,1.0008720805478614569 ] 
dist 214=[-1.1253964519753085478 ,1.0282113445675176091 ] 
dist 215=[-1.2761440764168585208 ,1.0411976081275045120 ] 
dist 216=[-1.3915658804320278082 ,1.0548309174218371334 ] 
dist 217=[-1.4886114489801901959 ,1.0604606004658149998 ] 
dist 218=[-1.5661758357000249165 ,1.0602161715486397230 ] 
dist 219=[-1.6038878021473361362 ,1.0579015370051605034 ] 
dist 220=[-1.6231056886321303530 ,1.0536280255144945839 ] 
dist 221=[-1.6268965902931311904 ,1.0484927499354812013 ] 
dist 222=[-1.5905664248429518906 ,.88571664120867208246] 
dist 223=[-1.5774946437339255952 ,.86666055297149834975] 
dist 224=[-1.5541070526709523109 ,.85396131265174016307] 
dist 225=[-1.5447126967170394962 ,.85019621254581199686] 
dist 226=[-1.4960521029541042225 ,.83787742875773388979] 
dist 227=[-1.4820636405781458603 ,.83221545328223750653] 
dist 228=[-1.4377701316541429864 ,.81584220897805041598] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 0, 2, 1, 1, 2] 
dist 0=[62.132011613856917947  ,62.132011613856917947  ] 
dist 1=[61.927345572462432099  ,62.240147512815971438  ] 
dist 2=[61.592003120998161122  ,62.298125206722043663  ] 
dist 3=[60.747243444087095732  ,62.302376635414630734  ] 
dist 4=[59.086974087749203894  ,62.274439637413668017  ] 
dist 5=[57.041800713623462690  ,62.203898699426714171  ] 
dist 6=[54.660209435513998222  ,62.088124672915968732  ] 
dist 7=[51.572390321901372595  ,61.953868012357596657  ] 
dist 8=[46.707323206504988113  ,61.627202406991187758  ] 
dist 9=[41.755055928590281249  ,61.445825162003349189  ] 
dist 10=[38.318959121042263504  ,61.018940800943324599  ] 
dist 11=[35.330100351508920674  ,60.824753589192490697  ] 
dist 12=[32.163316074867492650  ,59.789845672640191208  ] 
dist 13=[29.117572597761947985  ,58.567507854113168813  ] 
dist 14=[26.611737880402212401  ,35.336819384026028382  ] 
dist 15=[24.016101196654014116  ,34.699959174356937611  ] 
dist 16=[20.611248502572115274  ,28.752489060199037233  ] 
dist 17=[17.271136569357363346  ,27.656032565505014457  ] 
dist 18=[14.933709727312587213  ,26.265093660298368239  ] 
dist 19=[12.876547657771650918  ,25.912744590027231506  ] 
dist 20=[10.655169166393900414  ,17.121445533976619496  ] 
dist 21=[7.0909411449262882471 ,16.034493502137604785  ] 
dist 22=[3.4006629924814844479 ,13.718468437744907185  ] 
dist 23=[.88800379916915518561,13.190249821771063638  ] 
dist 24=[-1.2501895771645867956 ,11.722974176678933949  ] 
dist 25=[-3.4455939968194640810 ,10.390723840039751503  ] 
dist 26=[-5.5197582046687461126 ,9.5330549142512946416 ] 
dist 27=[-7.1744370032826859394 ,9.3292502079368925250 ] 
dist 28=[-8.8470802870400852344 ,4.9079877982897487776 ] 
dist 29=[-10.994391585202343741  ,2.9692799679488391201 ] 
dist 30=[-13.034168767404256945  ,-1.9084390153692883790 ] 
dist 31=[-14.277492968231729260  ,-2.2762198158886822862 ] 
dist 32=[-15.184330975166801459  ,-3.7412808680262352898 ] 
dist 33=[-15.879295097176006479  ,-4.0078248802697954952 ] 
dist 34=[-16.403353477247461119  ,-4.3768929490544317332 ] 
dist 35=[-16.627001182141491725  ,-4.4354864410354746351 ] 
dist 36=[-16.715678893401446177  ,-4.3888527387643560338 ] 
dist 37=[-16.699905520680150707  ,-4.1988162382745907501 ] 
dist 38=[-15.897739797876100973  ,-3.8707628820182845020 ] 
dist 39=[-15.723170064905350523  ,-3.2724296483128124394 ] 
dist 40=[-15.456302012060914256  ,-2.5489367798829549126 ] 
dist 41=[-15.421402204607010261  ,-1.7209423272659945128 ] 
dist 42=[-15.341852381366198491  ,-.65896993623127932642] 
dist 43=[-15.286922899816682218  ,.99872575720762299039] 
dist 44=[-13.899881323977135922  ,3.8038057989844768730 ] 
dist 45=[-13.816254186805101469  ,5.7861717308345532227 ] 
dist 46=[-5.9219743974261861094 ,7.4263561930917937225 ] 
dist 47=[-5.1669893201703437044 ,9.0261064022838289749 ] 
dist 48=[-3.4972861877952029687 ,10.475817492535554395  ] 
dist 49=[-3.1368203698367538510 ,11.517429432771996908  ] 
dist 50=[-1.1938311414128650998 ,12.459010662879674623  ] 
dist 51=[-.85282988715711319333,13.509734022322713270  ] 
dist 52=[-.11768228756982113858,14.449918566937365178  ] 
dist 53=[.04455948100449171551,14.950471922691169173  ] 
dist 54=[1.3397834119467354073 ,15.233028328676053793  ] 
dist 55=[1.2559691639058177757 ,15.303072566038750196  ] 
dist 56=[.83924953913940617835,15.228287513670688017  ] 
dist 57=[.40670092157714143691,15.207998416854003033  ] 
dist 58=[.03449696796130649937,15.194937874102687126  ] 
dist 59=[-.31014614715979047555,14.794572815285385954  ] 
dist 60=[-.65605750632760892863,12.141415086967930150  ] 
dist 61=[-.97507220401527266033,11.348262511267714953  ] 
dist 62=[-1.2340845720143394308 ,.91617791544078405947] 
dist 63=[-1.8341784886980988708 ,.74161440069531544592] 
dist 64=[-2.3133166113683224073 ,-.39633349288624714309] 
dist 65=[-2.7519058302961199796 ,-.59228173171697093418] 
dist 66=[-3.1303936972115482388 ,-.96284936819635136781] 
dist 67=[-3.3697686150226794557 ,-.96912331536570776026] 
dist 68=[-3.9570462127665826454 ,-.90722579460538090076] 
dist 69=[-4.3813229329871100289 ,-.81659837607382457345] 
dist 70=[-4.7039901394203356343 ,-.69260646588373906843] 
dist 71=[-4.9716362553092842726 ,-.52083610182740320876] 
dist 72=[-5.1829484151258844374 ,-.23967791578188800548] 
dist 73=[-5.2808721549018539793 ,.04651202235330023747] 
dist 74=[-5.3256104422168032384 ,.23834263615938149764] 
dist 75=[-5.3247357676244862760 ,.39715703709323339862] 
dist 76=[-4.0506632587417507082 ,.55166877650416634335] 
dist 77=[-4.0362787561821660442 ,.69090016028451186726] 
dist 78=[-1.3965648460917551447 ,.78876324636340474136] 
dist 79=[-1.1756875333726599604 ,.87465012070628870311] 
dist 80=[-.95865213574453787672,1.1981477544233916778 ] 
dist 81=[-.57723177141554464355,1.4404448698130767159 ] 
dist 82=[-.5080301561004753781 ,1.6604639018879295172 ] 
dist 83=[-.4110744386894795228 ,1.9069247911955059121 ] 
dist 84=[-.3945019162568600147 ,2.1332342723583345861 ] 
dist 85=[-.2609476647132988389 ,2.2728807836609889534 ] 
dist 86=[-.2368178756488748539 ,2.3755140846218199628 ] 
dist 87=[-.1992570606983365185 ,2.4541867345855975066 ] 
dist 88=[-.1897502045197771904 ,2.5428754154248796968 ] 
dist 89=[.74810271397990342727,2.6824474458916961151 ] 
dist 90=[.63458424891379988661,2.7907483053094138860 ] 
dist 91=[.5295466432323649983 ,2.8383106225871943942 ] 
dist 92=[.25463981604588798003,2.8593246929642829273 ] 
dist 93=[.02401425526398135746,2.8617152284664672400 ] 
dist 94=[-.17023799185252947137,1.3719560231477408766 ] 
dist 95=[-.36489624402713753863,1.3472428053646475031 ] 
dist 96=[-.54427325629076075165,1.0798851134567446673 ] 
dist 97=[-.67757813984078666045,1.0271109572400014476 ] 
dist 98=[-.80229854728791707714,.96624194461598931308] 
dist 99=[-.94743521152283447753,.94922743492293573208] 
dist 100=[-1.0824028470823865471 ,.43411402109063971691] 
dist 101=[-1.1665625808430578955 ,.36976197499456064358] 
dist 102=[-1.2293756176170580441 ,.23242258176681715155] 
dist 103=[-1.2791987853598362557 ,.19884267646209416653] 
dist 104=[-1.3166435096589272584 ,.05858355940423574187] 
dist 105=[-1.3300796194602035552 ,.03264638078049210437] 
dist 106=[-1.3339215872422451628 ,.03676376774058965322] 
dist 107=[-1.3331220732473650464 ,.06114120422870842479] 
dist 108=[-1.2637737842626684119 ,.09476272493498761171] 
dist 109=[-1.2823702841711235268 ,.13161294392032583646] 
dist 110=[-1.2936189758072134008 ,.260794280409226723  ] 
dist 111=[-1.2945632115894378597 ,.383946172072078004  ] 
dist 112=[-1.2834937495417218606 ,.48623647544464306554] 
dist 113=[-1.2792090022359813738 ,.5864418478942809879 ] 
dist 114=[-1.2091021886235525942 ,.67732493486546308104] 
dist 115=[-1.1904088883855457082 ,.74242842787740778338] 
dist 116=[-1.1726814585243054642 ,.80093719574684778546] 
dist 117=[-1.1618036336636740037 ,.8655092922173310532 ] 
dist 118=[-.96716801636100419808,.92323502008368380481] 
dist 119=[-.96426886776201719107,.95443512829362853765] 
dist 120=[-.94254776843556290236,.97207407466686390155] 
dist 121=[-.93605971351871075216,.9758798033919798994 ] 
dist 122=[-.91301949797463292191,.9741396812880126021 ] 
dist 123=[-.90743225999003563979,.97098735586440811762] 
dist 124=[-.574739464824838163  ,.96606169749103609821] 
dist 125=[-.56372926245288200938,.96121562964300957035] 
dist 126=[-.29796889932916953977,.55415708746616297878] 
dist 127=[-.27772430419554430358,.71094604862113909172] 
dist 128=[-.14440281491901278363,.83622470406826826051] 
dist 129=[-.12022411952008504838,.95096750298998078364] 
dist 130=[-.07540741380166974095,1.0499353105996349050 ] 
dist 131=[-.06492840576739581324,1.1122813680031730167 ] 
dist 132=[.07421021990069107807,1.1596478279759453071 ] 
dist 133=[.09387618615553332228,1.1988572209140568416 ] 
dist 134=[.07558833911564363680,1.2303524127475434794 ] 
dist 135=[.00554190102955666727,1.2469437981390224011 ] 
dist 136=[-.07157560228877742204,1.2557799649441963970 ] 
dist 137=[-.15023825762928839631,1.2563351965007203833 ] 
dist 138=[-.24497050907960740363,1.2515402957568284310 ] 
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dist 142=[-.80295516421205886852,.53567874751205593869] 
dist 143=[-.89788754616506329197,.4725317734666606239 ] 
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dist 145=[-1.0437575702009679360 ,.30003604242022062584] 
dist 146=[-1.0971436588202588063 ,.12838036499539162519] 
dist 147=[-1.1548240104290403349 ,.16653103318346671412] 
dist 148=[-1.2052117737159188030 ,.20777982635048882138] 
dist 149=[-1.2295050313493882104 ,.2423807811409193643 ] 
dist 150=[-1.2408649052664589564 ,.27864686486677353008] 
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dist 152=[-1.2191368818073601754 ,.37813061075905971545] 
dist 153=[-1.2090500488489655891 ,.42910014847377058742] 
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dist 156=[-1.1132070568294024003 ,.72542107281537752861] 
dist 157=[-1.1134499791307359207 ,.91787115913773321182] 
dist 158=[-.98904553006243156378,1.0727041749566757945 ] 
dist 159=[-1.0169296704894812678 ,1.2162096780919340944 ] 
dist 160=[-1.0363430151829613696 ,1.3410857735767904574 ] 
dist 161=[-1.0452559488262127703 ,1.4216110367026921284 ] 
dist 162=[-1.0481521353578403400 ,1.4849121776172641888 ] 
dist 163=[-1.0459463574268640273 ,1.5410882653034646961 ] 
dist 164=[-.91244535853024364156,1.5867267954796377747 ] 
dist 165=[-.89081895203853127593,1.6079946886719469787 ] 
dist 166=[-.85154263513530391562,1.6154576476434440314 ] 
dist 167=[-.84043872119512297224,1.6146476750008968572 ] 
dist 168=[-.79845373210398490234,1.5894962718083943851 ] 
dist 169=[-.78623264150461245253,1.5790027555996533035 ] 
dist 170=[-.76404642717500484309,1.5478403840920108884 ] 
dist 171=[-.75697274927708800967,1.5332586019411010592 ] 
dist 172=[-.23935875207446490864,.8855039644543951945 ] 
dist 173=[-.34197881140222558789,.88354903764582590367] 
dist 174=[-.443770079500289395  ,.78562458273562468487] 
dist 175=[-.50820479343369677888,.77081786015452117267] 
dist 176=[-.55748415715387066244,.72633925780510170518] 
dist 177=[-.59882080506040450273,.72370170128373945908] 
dist 178=[-.63196512559122811838,.71399444918834419246] 
dist 179=[-.64856484718429642086,.71067525885717836322] 
dist 180=[-.65723441617600611285,.70796265426738355883] 
dist 181=[-.65874542496702021449,.70537883840417012585] 
dist 182=[-.64101051077813584122,.55625197498465388983] 
dist 183=[-.63573308001917182831,.53508655120941270635] 
dist 184=[-.65036707235845011912,.49523964322623884647] 
dist 185=[-.660680117590210145  ,.48465158968054755264] 
dist 186=[-.6674029164468193899 ,.44712348900884491364] 
dist 187=[-.66771428195764912026,.43707772591693968854] 
dist 188=[-.66503210507421165506,.42393924903434048797] 
dist 189=[-.66180355621077048494,.41877145313204741187] 
dist 190=[-.31013664417533948146,-.10968120670205335005] 
dist 191=[-.33331410696941128619,-.11001318385942177061] 
dist 192=[-.35407630595366499708,-.10642992446109885527] 
dist 193=[-.36856942643234777821,-.09722893370433428422] 
dist 194=[-.42961349052755394323,-.06624019384316497804] 
dist 195=[-.47686722830584897075,-.01960063542379719478] 
dist 196=[-.51946695602678940057,.02784505136534532400] 
dist 197=[-.56673758235481892604,.08865383668577392685] 
dist 198=[-.60931370271880286343,.14716478822909745758] 
dist 199=[-.63318601691101933428,.18544585883955540368] 
dist 200=[-.64788132969465798597,.21616058489729434568] 
dist 201=[-.65384943747324727245,.24449179368661883435] 
dist 202=[-.65591773676771785411,.2690587710426252253 ] 
dist 203=[-.65505594364164667637,.28475996794149397196] 
dist 204=[-.65188191168664211553,.35672129663373124881] 
dist 205=[-.64933093405353643511,.43038786306394739753] 
dist 206=[-.46466746334952713086,.49176160548997824001] 
dist 207=[-.4440221868770403494 ,.55223896390673438161] 
dist 208=[-.3919336884546585327 ,.60736850211767093957] 
dist 209=[-.38297462881305011327,.64740832454973710246] 
dist 210=[-.29884537209717812399,.68398370009545761722] 
dist 211=[-.28235191935798542149,.72529199607681053334] 
dist 212=[-.26067752791463600726,.76238815779790165221] 
dist 213=[-.25337327757915331323,.78216024965799111621] 
dist 214=[-.10347818735177326455,.79298616679485777303] 
dist 215=[-.08436865309805352960,.79459019886578553746] 
dist 216=[-.08317339992852820094,.79168606342638989994] 
dist 217=[-.13124427025384056908,.78796693478868224135] 
dist 218=[-.18154687861262722404,.77879059964184889584] 
dist 219=[-.32061517187845357808,.77395210283959454412] 
dist 220=[-.50981762014913239748,.66719613070857118332] 
dist 221=[-.63318211609495449155,.65011292443162225365] 
dist 222=[-.73169754289521491821,.61000993076201418707] 
dist 223=[-.82177662819849194302,.59728229648825833736] 
dist 224=[-.89932182593466605556,.53579963885057851309] 
dist 225=[-.94783970008092852431,.52239176195660382382] 
dist 226=[-.98429345016394443254,.49277641873615060447] 
dist 227=[-1.0137156546802730466 ,.48337779478239789482] 
dist 228=[-1.0366319451309533601 ,.37197873400633670871] 
dist 229=[-1.0471331590116842167 ,.33436660247783288609] 
dist 230=[-1.0505355780938017550 ,.00349754917728666528] 
dist 231=[-1.0489696903801413734 ,-.01302155315608611525] 
dist 232=[-1.0350509601667747623 ,-.03442266791006650830] 
dist 233=[-1.0294206206395585007 ,-.07733841613461120293] 
dist 234=[-1.0056506882842919542 ,-.04001421901196773891] 
dist 235=[-1.0000481572634103997 ,.07693031736611173688] 
dist 236=[-.8083224910879292058 ,.21848003366818071799] 
dist 237=[-.80223128079433036117,.43022868062061742791] 
dist 238=[-.69402377516936185606,.64090417201084833737] 
dist 239=[-.67601446833353100022,.77817329977732431205] 
dist 240=[-.63605341079430992173,.88767781463947360172] 
dist 241=[-.62342846248405312025,.98760041232279958096] 
dist 242=[-.56604952669480047055,1.0734674243395184049 ] 
dist 243=[-.55379788743633825195,1.1269043973450097951 ] 
dist 244=[-.52131909108130836068,1.1667115261602941146 ] 
dist 245=[-.51387692034498860583,1.1982095039693056108 ] 
dist 246=[-.42598381147925495266,1.2221301684959313389 ] 
dist 247=[-.41068759518605010951,1.2317113378622799608 ] 
dist 248=[-.37736191284785384146,1.2326186991838779619 ] 
dist 249=[-.36738952573614269731,1.2306470600512562508 ] 
dist 250=[-.32416650015511096797,1.2062732012010084449 ] 
dist 251=[-.31540221386158794009,1.1976801954183032667 ] 
dist 252=[-.29156876734992981251,1.1703765820125024197 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 0, 2, 0, 1] 
dist 0=[56.953662615358354293  ,56.953662615358354293  ] 
dist 1=[56.273670157628419767  ,57.165070234001521284  ] 
dist 2=[55.129462516899527167  ,57.266527886189674799  ] 
dist 3=[53.062779614805665915  ,57.507312056101089175  ] 
dist 4=[50.849727641926392152  ,57.744967723919858541  ] 
dist 5=[49.120976400871894141  ,57.834285889273583163  ] 
dist 6=[47.408119819421542400  ,57.833787711950087154  ] 
dist 7=[45.259005778421278091  ,57.752352840229611190  ] 
dist 8=[42.983256483537829944  ,54.163197484729851942  ] 
dist 9=[40.764699820286749014  ,53.600929436648564633  ] 
dist 10=[38.154539817509418754  ,52.572351632240870905  ] 
dist 11=[34.314502812350158728  ,52.286609891706653239  ] 
dist 12=[30.345766552821679126  ,51.222739342701512658  ] 
dist 13=[27.221493239788132544  ,50.919770702207591247  ] 
dist 14=[24.106138382578708617  ,50.387925309102768042  ] 
dist 15=[20.172973190727296826  ,50.223410856056532752  ] 
dist 16=[15.997269009061910169  ,30.814744286808374436  ] 
dist 17=[11.912828578793854959  ,29.148644147392171447  ] 
dist 18=[7.0971966058756471952 ,28.041714192735119546  ] 
dist 19=[0                     ,27.742599707608967992  ] 
dist 20=[9.8743907454525978337 ,19.387629721052961238  ] 
dist 21=[7.2695834511412236251 ,18.447457955380252054  ] 
dist 22=[3.9200139396977959504 ,17.109477334053675491  ] 
dist 23=[.66309310757719451762,16.737650659949623801  ] 
dist 24=[-1.5721568546696468809 ,10.853442548467727512  ] 
dist 25=[-3.4946887256195406356 ,10.499136146170032361  ] 
dist 26=[-5.5033225229498916980 ,9.0304666081196779860 ] 
dist 27=[-7.4249978872318044062 ,7.2941759369053035799 ] 
dist 28=[-9.0010001461198897849 ,5.1376722906242867566 ] 
dist 29=[-10.635353556637099777  ,4.7777890675918709463 ] 
dist 30=[-12.791699459316995493  ,4.1669346358663800381 ] 
dist 31=[-14.846510478267196764  ,4.0422801024340730882 ] 
dist 32=[-16.075505011348230475  ,.63284844914932665921] 
dist 33=[-16.945441067191397538  ,.26221125230305223948] 
dist 34=[-17.565064455054880476  ,-.45589761707807548969] 
dist 35=[-18.016036235630881155  ,-.62577089505852056053] 
dist 36=[-18.211565500145284428  ,-1.1548536768287797723 ] 
dist 37=[-18.270409755818773861  ,-1.2700953284025164926 ] 
dist 38=[-18.253561740809846867  ,-1.3121983175642747001 ] 
dist 39=[-16.839509442185497777  ,-1.2366696081467882994 ] 
dist 40=[-16.588558968121923161  ,-1.1136164619630528247 ] 
dist 41=[-16.081811420555714942  ,-.95718702061824004215] 
dist 42=[-15.921477296715959221  ,-.74840282487574783841] 
dist 43=[-15.211075602359937862  ,-.41565453265778918859] 
dist 44=[-15.039772093235728431  ,-.02966308913451574047] 
dist 45=[-14.578599656229307877  ,.39204840851589573679] 
dist 46=[-14.442123792301584786  ,.92090546190132154168] 
dist 47=[-12.184515720130738757  ,1.7350539988406520973 ] 
dist 48=[-4.2941229313817585866 ,4.0768856654711035960 ] 
dist 49=[-2.4231994394414662503 ,5.9632191810821061610 ] 
dist 50=[-2.0276910005517550440 ,7.5327591431035681955 ] 
dist 51=[.09037423422978384291,9.1824388366163432460 ] 
dist 52=[.45386798006312550959,10.488743561164439838  ] 
dist 53=[1.2456031670857139912 ,11.552960655478218492  ] 
dist 54=[1.3958511711357265124 ,12.866515406146471391  ] 
dist 55=[2.5623130226748795867 ,14.065859631199780491  ] 
dist 56=[2.7704987399581822684 ,14.749799458617248876  ] 
dist 57=[2.7986735957729059097 ,15.187671247808972394  ] 
dist 58=[2.5899730436992304428 ,15.416555120882005559  ] 
dist 59=[2.2464986930008594694 ,15.544944358636665717  ] 
dist 60=[1.7368058278228168437 ,15.587135161549521500  ] 
dist 61=[1.0089296286533443378 ,15.538472411563847882  ] 
dist 62=[-.2051835577020371758 ,14.870252734090288187  ] 
dist 63=[-1.4384125632100777649 ,4.0142974659214280958 ] 
dist 64=[-2.2426341635094689210 ,1.2915267953451889479 ] 
dist 65=[-2.8854308304934016949 ,1.0570481182972163019 ] 
dist 66=[-3.4747025828689797948 ,.53416843633963933466] 
dist 67=[-3.9836107571812335935 ,.43045883966969485285] 
dist 68=[-4.3058350684117773171 ,-.18072452203348057169] 
dist 69=[-4.5527942326442433182 ,-.28529894272260093252] 
dist 70=[-4.7614996547817713165 ,-.49804640708533546786] 
dist 71=[-4.9356869296962611902 ,-.54979151660893694113] 
dist 72=[-5.0449318885618878713 ,-.92153582129833826194] 
dist 73=[-5.1276759934162069350 ,-.98334504881588464654] 
dist 74=[-5.1960598141762696810 ,-1.0066973759792767144 ] 
dist 75=[-5.2501083698316981035 ,-.95745706633947211881] 
dist 76=[-5.2756186402453074968 ,-.87003488430795766218] 
dist 77=[-5.2851595873740544768 ,-.73439936837080279811] 
dist 78=[-5.2754500056716320830 ,-.53790027720960888914] 
dist 79=[-3.4997032128722302688 ,-.20766514982398695977] 
dist 80=[-1.3473596144978461324 ,.12989575993215238432] 
dist 81=[-.67115091469457265786,.48841855659928643539] 
dist 82=[-.5448334565985951517 ,.79084867071273385232] 
dist 83=[.28315638628055846402,1.0921383482575387756 ] 
dist 84=[.42597565759634788709,1.3688778687902894067 ] 
dist 85=[.69546119704742091827,1.6809120829541446914 ] 
dist 86=[.75577469498235703191,2.2102247008010393763 ] 
dist 87=[.94849471126862538023,2.7139224706794779597 ] 
dist 88=[1.0081606925609601693 ,3.0339309265399228741 ] 
dist 89=[.99687303000746498457,3.2799872409291979193 ] 
dist 90=[.95826343077530472277,3.4886935098184604037 ] 
dist 91=[.87242685994027147216,3.6568704192152096799 ] 
dist 92=[.76309559781890853836,3.7412549862300666424 ] 
dist 93=[.63077043015885463689,3.7819903628758600429 ] 
dist 94=[.45659626480627853646,3.7872035421466543818 ] 
dist 95=[.10862873502466801779,2.4219905313677003686 ] 
dist 96=[-.3394168879969173322 ,1.9346873081609666737 ] 
dist 97=[-.63605163640385764082,1.8722588439530234566 ] 
dist 98=[-.87782061166145333261,1.7093184764855546205 ] 
dist 99=[-1.1070395741613465415 ,1.6796282639515484045 ] 
dist 100=[-1.3099348020980085899 ,1.3949844126411069124 ] 
dist 101=[-1.4467141489011088117 ,1.3370277304730358822 ] 
dist 102=[-1.5609110942445623452 ,1.2617695581792559987 ] 
dist 103=[-1.6737386542769567127 ,1.2350438688092979807 ] 
dist 104=[-1.7729833755314006285 ,.65968316623096643394] 
dist 105=[-1.8330074090142543117 ,.58483277908064012281] 
dist 106=[-1.8756557196340592066 ,.42005567646301917525] 
dist 107=[-1.9056018406824828688 ,.38133967834387528983] 
dist 108=[-1.9250297401768787388 ,.19078361878154701886] 
dist 109=[-1.9257301956574769165 ,.175408696662778355  ] 
dist 110=[-1.9173989994212630171 ,.16756009198178261271] 
dist 111=[-1.9078763706487315614 ,.16819422135409879878] 
dist 112=[-.77391856492017044715,.17203997991067191677] 
dist 113=[-.63098168804692654393,.17892408622811761987] 
dist 114=[-.60593784929246463806,.18908497288986871173] 
dist 115=[-.40385308207736923509,.28482006458495673348] 
dist 116=[-.36674087712425547383,.45872376971276856441] 
dist 117=[-.30900957865143524105,.58612598771010175073] 
dist 118=[-.29407924816687413271,.70353429739880301587] 
dist 119=[-.03505968267696986734,.83758816661701178101] 
dist 120=[.18003771005592562654,.96185171685103680684] 
dist 121=[.27165126240898699718,1.0402139509618812018 ] 
dist 122=[.29274435658021757553,1.0997737892878831486 ] 
dist 123=[.35897094904511603365,1.1490408311461065501 ] 
dist 124=[.45885587946500528286,1.1877786178257039993 ] 
dist 125=[.48657471589096666037,1.2053406025313423985 ] 
dist 126=[.49106630688422738653,1.2115683383440170660 ] 
dist 127=[.61277108347015047778,1.2106631149360967923 ] 
dist 128=[.52253942046199950795,.70738456923987760548] 
dist 129=[.41606993069821275912,.66304649479000049449] 
dist 130=[.32188841690641429636,.61158831276863577507] 
dist 131=[.22026149608189371823,.58405912138765580594] 
dist 132=[.12199724919644637185,.57628457243900005354] 
dist 133=[.04121930769050374179,.56833551167334896925] 
dist 134=[-.04199356821825581586,.56367859688962121855] 
dist 135=[-.14997847279354485399,.43593848968547825534] 
dist 136=[-.25444042551420968009,.41806642540170815734] 
dist 137=[-.32360812205987392451,.38118113569894092751] 
dist 138=[-.38000456499867394366,.37089506715174439165] 
dist 139=[-.43353745546952030683,.33033427087451739656] 
dist 140=[-.48101182484844596217,.32160240953606029438] 
dist 141=[-.51325207550568910039,.30262508835155178154] 
dist 142=[-.54047649131046896363,.29689975708467606296] 
dist 143=[-.56796032957791211334,-.04041285112840253571] 
dist 144=[-.60147533718790648483,-.07073904605003730576] 
dist 145=[-.64606345972767189943,-.13011508525250074325] 
dist 146=[-.68326421067600419218,-.1441181120701634588 ] 
dist 147=[-.72006558876848461675,-.18618692098427931258] 
dist 148=[-.75375460094337838423,-.19324866740904503151] 
dist 149=[-.7785353306817434692 ,-.19050085686586058388] 
dist 150=[-.80151328004913927724,-.17369974855519450116] 
dist 151=[-.82800731998318209307,-.15126250138890988376] 
dist 152=[-.8521370132385217746 ,-.12602781726018936237] 
dist 153=[-.86567978610737331507,-.09398210045378254098] 
dist 154=[-.87404315115812986229,-.04436638234949706844] 
dist 155=[-.87750470003801802161,.02499173410341230513] 
dist 156=[-.87753486979133852334,.16622075150203684713] 
dist 157=[-.87498574014564815499,.30632349063666493482] 
dist 158=[-.86502141321664977808,.47215600665350056391] 
dist 159=[-.85900655190034905213,.71602891746899381319] 
dist 160=[-.82081391674625550454,.95726143871445792412] 
dist 161=[-.8102452336750457018 ,1.1125630572218493730 ] 
dist 162=[-.78890684704223546503,1.2343666783195768499 ] 
dist 163=[-.78140960865483366486,1.3419726321155668820 ] 
dist 164=[-.74478569955809057009,1.4319777830108603873 ] 
dist 165=[-.73591612659215010153,1.4835710306701720405 ] 
dist 166=[-.70724999132761684915,1.5168219486145031283 ] 
dist 167=[-.70186151614969919432,1.5336603497608944536 ] 
dist 168=[-.62985438776063104678,1.5416509105385167360 ] 
dist 169=[-.61570594142845362432,1.5396065865875381754 ] 
dist 170=[-.58292126678212189287,1.5312497363530779812 ] 
dist 171=[-.57205042851013533332,1.5247181264612414782 ] 
dist 172=[-.52070124020988825549,1.4794022348494499996 ] 
dist 173=[-.50930378807024721501,1.4662997593070466424 ] 
dist 174=[-.48228696939787276375,1.4251967836252075325 ] 
dist 175=[-.47715162190103138132,1.4122719128802293751 ] 
dist 176=[-.62510955471876792119,.75961250049314516354] 
dist 177=[-.74434190212219353535,.6978496293538919378 ] 
dist 178=[-.85519818351307210934,.68145570735093054044] 
dist 179=[-1.0245839836188757375 ,.58864057839147631465] 
dist 180=[-1.1778135546717483368 ,.56941384797251770116] 
dist 181=[-1.2781568727365467066 ,.53070704421566853596] 
dist 182=[-1.3587734045807243382 ,.51959172766661555565] 
dist 183=[-1.4333140442932039880 ,.36436217433505687784] 
dist 184=[-1.4974745505245343668 ,.34177186893740321676] 
dist 185=[-1.5366847307499320300 ,.28800399950602979576] 
dist 186=[-1.5650509538452363218 ,.27733392587750929529] 
dist 187=[-1.5859537065128218678 ,.20058525937452022972] 
dist 188=[-1.6004100752261967780 ,.18599645673666796209] 
dist 189=[-1.6030609535563903203 ,.16073849150965587969] 
dist 190=[-1.5975668294830018525 ,.15470483493966008908] 
dist 191=[-1.5926702537716904920 ,.16146726255486259012] 
dist 192=[-.62014284130034945829,.27373110203458452831] 
dist 193=[-.5368570869321756001 ,.40733957861692182214] 
dist 194=[-.3440191555296362637 ,.53681740156100791787] 
dist 195=[-.30913228442266487781,.65339159768289721529] 
dist 196=[-.10606494098494360937,.73552936354502946275] 
dist 197=[-.07219052154642922959,.80799772839320983069] 
dist 198=[-.00613319753185019358,.88600258716262036323] 
dist 199=[.00978644496417547567,.95636596226937520493] 
dist 200=[.17189484226194826889,.99835317748775661614] 
dist 201=[.1963952870629438766 ,1.0275083280218191571 ] 
dist 202=[.22604399359461966569,1.0716836742943189945 ] 
dist 203=[.22846183013767652349,1.0996364822839707151 ] 
dist 204=[.21995448283176333906,1.1186770081456581618 ] 
dist 205=[.19551112150606009849,1.1278752528942642765 ] 
dist 206=[.04802970946464630834,1.1316063030332176844 ] 
dist 207=[-.10400959282725581128,1.1288398470932141745 ] 
dist 208=[-.20532485994814804316,.57026212865148241461] 
dist 209=[-.28866375149441294352,.46785518478370736254] 
dist 210=[-.36899750980761808244,.45111099332372428687] 
dist 211=[-.44103340265718014342,.3443547007342043313 ] 
dist 212=[-.49127291638005139287,.32591004277037402582] 
dist 213=[-.53505460823871187824,.2955413332987508653 ] 
dist 214=[-.58133041270296915516,.28762927467021913818] 
dist 215=[-.65707252377289081425,.13808346495366736559] 
dist 216=[-.73547921068288456813,.11850222077759957797] 
dist 217=[-.7818313098091394971 ,.07204979300011672208] 
dist 218=[-.81348566082491605995,.06475942940672881160] 
dist 219=[-.83326393055333280148,.0874797604204351877 ] 
dist 220=[-.8464236185975433288 ,.12028309947725834133] 
dist 221=[-.85167615413147717807,.15816653009058577863] 
dist 222=[-.85213245529408031742,.20694612929070223156] 
dist 223=[-.85008229121429862769,.28321308581501946824] 
dist 224=[-.77948596828545347544,.35977805264319829712] 
dist 225=[-.8164753740353346519 ,.40974607188745124207] 
dist 226=[-.84044804008288637451,.45722956715451187455] 
dist 227=[-.85286125526974696314,.49970875211704971004] 
dist 228=[-.85951972219507917347,.5345377780763976175 ] 
dist 229=[-.8605354207680121046 ,.55316701985648190744] 
dist 230=[-.85761307445507908437,.56356792970543779523] 
dist 231=[-.85479138934057886349,.5659409546738606989 ] 
dist 232=[-.73789722368026454226,.58375142699880538808] 
dist 233=[-.71926653976192085448,.60576159422070583312] 
dist 234=[-.68154797651028662105,.63477291920686230686] 
dist 235=[-.67024321753661909983,.66919274740748700685] 
dist 236=[-.67531903503178992525,.69215827914240877325] 
dist 237=[-.70581157021655397599,.71108743872390681385] 
dist 238=[-.74781940587058349444,.74053556754530094958] 
dist 239=[-.7878073560976550227 ,.90966686686589104475] 
dist 240=[-.81024240123562273275,1.0156786454051285410 ] 
dist 241=[-.83160079355064560596,1.0955410050090550523 ] 
dist 242=[-.84311957059555093538,1.1603621314078403066 ] 
dist 243=[-.84904224270383388768,1.2112002442377681549 ] 
dist 244=[-.84974072003259890758,1.2352840489993319462 ] 
dist 245=[-.84674163707060672914,1.2465792775537247504 ] 
dist 246=[-.84381780027398489482,1.2465627196684225193 ] 
dist 247=[-.73484211673427765515,1.1902026157701588037 ] 
dist 248=[-.72088494357606233208,1.1763792453839486352 ] 
dist 249=[-.68355247210881212674,1.1516013890012553764 ] 
dist 250=[-.67431174898678631933,1.1430119498724626302 ] 
dist 251=[-.60924510833052015296,1.1031331899441561606 ] 
dist 252=[-.59813953917661171279,1.0915288937706936466 ] 
dist 253=[-.57703476527098883979,1.0598676654063333243 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 0, 2, 0, 0, 2] 
dist 0=[60.693699579623596566  ,60.693699579623596566  ] 
dist 1=[59.661057103306579027  ,61.046596200580341368  ] 
dist 2=[58.235488464916039142  ,61.423085998578286615  ] 
dist 3=[56.364035626823499858  ,61.843821754694422757  ] 
dist 4=[53.804357408706377294  ,62.070687928491982166  ] 
dist 5=[49.630989925839018226  ,62.166955476650434151  ] 
dist 6=[45.340786566556647332  ,62.113256232051722138  ] 
dist 7=[42.314597325292734193  ,61.880085659915095817  ] 
dist 8=[39.630281251918083385  ,61.715038206092944179  ] 
dist 9=[36.704930421663855351  ,60.645016167007459730  ] 
dist 10=[33.842600951144371017  ,60.306101144870869799  ] 
dist 11=[31.409731256511683208  ,59.866038269220420636  ] 
dist 12=[28.820861830142087965  ,59.658809184658465304  ] 
dist 13=[25.335279652395628897  ,59.106666263084763008  ] 
dist 14=[21.876352231139847088  ,58.864738196619073205  ] 
dist 15=[19.245670592352365036  ,57.217367620454635731  ] 
dist 16=[15.724097679860879402  ,53.277004735690122690  ] 
dist 17=[12.938803861414514710  ,36.162158211810181194  ] 
dist 18=[10.153724395944435899  ,34.278189163629117218  ] 
dist 19=[6.6321358281338967716 ,29.751196951586423676  ] 
dist 20=[3.2380425531206473951 ,29.099310070110903585  ] 
dist 21=[.96154995834260797358,22.695443546416188712  ] 
dist 22=[-.93962957091848903516,21.535536367799908552  ] 
dist 23=[-2.8357153283337057942 ,20.147771840084610546  ] 
dist 24=[-4.5948254672902349433 ,19.903772739263543198  ] 
dist 25=[-5.9499223382211451310 ,10.755604385158087467  ] 
dist 26=[-7.2784869058095039046 ,9.6670044943852768137 ] 
dist 27=[-8.9335947462211077538 ,7.3850013587639696446 ] 
dist 28=[-10.483634318247863058  ,6.8752086912613900285 ] 
dist 29=[-11.392756745110873529  ,4.7350418809032211154 ] 
dist 30=[-12.017354696045607946  ,4.3499388374570945077 ] 
dist 31=[-12.429629111905974809  ,3.7715836034110487103 ] 
dist 32=[-12.722061545772415803  ,3.6550459797179958859 ] 
dist 33=[-12.867007500896385969  ,-3.8849425877939267319 ] 
dist 34=[-12.935538127861050899  ,-3.9340031478118826123 ] 
dist 35=[-12.921156622164019546  ,-2.7676223830552997896 ] 
dist 36=[-11.635087309800957956  ,-1.2719478077377529371 ] 
dist 37=[-11.589066054771521316  ,1.0578532844346289685 ] 
dist 38=[-10.831141752897383365  ,3.3980254843489521318 ] 
dist 39=[-10.716691444664532789  ,4.9352653928566758759 ] 
dist 40=[-10.300610690740782709  ,6.1747280857659811090 ] 
dist 41=[-10.746179893781420867  ,7.3273587955975394196 ] 
dist 42=[-11.126806764447598682  ,8.3325844335205361133 ] 
dist 43=[-11.412960844441124441  ,8.9841733134539929471 ] 
dist 44=[-11.648754718291599146  ,9.5000393977464577038 ] 
dist 45=[-11.836942456071219830  ,9.9639602238702887217 ] 
dist 46=[-11.932713405049196431  ,10.355977727325188008  ] 
dist 47=[-11.980346696061608417  ,10.585016630990631412  ] 
dist 48=[-11.976056846296237008  ,10.737991859036313351  ] 
dist 49=[-3.4251628858136363232 ,10.826491413641648415  ] 
dist 50=[-2.4376162086369243618 ,10.866127835256875075  ] 
dist 51=[-2.2531247603663341144 ,10.844629631108124001  ] 
dist 52=[-1.9311697606603568998 ,10.747554436043175303  ] 
dist 53=[-1.8565407074757944132 ,10.678772163833057565  ] 
dist 54=[3.2785023932329790420 ,8.5041140675945116037 ] 
dist 55=[3.0500575794415359143 ,8.8283053183797287238 ] 
dist 56=[2.7174613263326960628 ,9.0698109170053126818 ] 
dist 57=[2.2650756039363422911 ,9.1554092066194811526 ] 
dist 58=[1.6395307854960465606 ,9.1817831769905951951 ] 
dist 59=[.6159861756248075777 ,9.1868270705490601522 ] 
dist 60=[-.42298908689094109437,9.0721298840430782529 ] 
dist 61=[-1.2948805559270937154 ,9.1078562863170884371 ] 
dist 62=[-2.0460971846034400297 ,9.1128145517498722592 ] 
dist 63=[-2.7808472242134763376 ,9.0964573577452515406 ] 
dist 64=[-3.4473035809912955544 ,9.0589000559890872592 ] 
dist 65=[-3.9261088861081783094 ,2.7885263369626763669 ] 
dist 66=[-4.3584564998964218621 ,2.2673593790874185511 ] 
dist 67=[-4.8396263658789277231 ,1.0924314718909545260 ] 
dist 68=[-5.2752742115845172419 ,.8678281819493871743 ] 
dist 69=[-5.5260287144326205432 ,-.54192067756755539127] 
dist 70=[-5.6891445732388916231 ,-.7838479396165548473 ] 
dist 71=[-5.7751529028082901876 ,-1.2547565755935971270 ] 
dist 72=[-5.8207211811338799115 ,-1.3637359149646098766 ] 
dist 73=[-5.8224869491677517556 ,-2.3254172081139308136 ] 
dist 74=[-5.7965834058376059275 ,-2.0789585765912262592 ] 
dist 75=[-6.1962323027579030925 ,-1.0723742011633943168 ] 
dist 76=[-6.5317245032262672780 ,-.05304355033652166964] 
dist 77=[-6.7942400472910167141 ,.62938147793088952596] 
dist 78=[-6.9110887548555225069 ,1.1939898108489978617 ] 
dist 79=[-6.9624386350813277852 ,1.7434276595174395305 ] 
dist 80=[-6.9636705276152609516 ,2.2394276379611404850 ] 
dist 81=[-2.3401590073564973845 ,2.5909113403850288488 ] 
dist 82=[-2.1428030834103528263 ,2.9030251459826327295 ] 
dist 83=[-2.0772950600134092032 ,3.2420160230240054245 ] 
dist 84=[-.74927956067361947413,3.5498592275864832762 ] 
dist 85=[-.58085354776621326552,3.7377439838920841550 ] 
dist 86=[-.20429813436087280908,3.8733597262162914165 ] 
dist 87=[-.12938693153116356107,3.9727208734795924303 ] 
dist 88=[.31274872263675722568,4.0409954449982214961 ] 
dist 89=[.31808287505018302756,4.0536173283690688567 ] 
dist 90=[.25262455344655026877,4.0433796157399411921 ] 
dist 91=[.12108711662032434016,4.0283861013808405906 ] 
dist 92=[-.02062578090343571495,3.4851111562966300405 ] 
dist 93=[-.12667537355386527819,3.5478640547960929071 ] 
dist 94=[-.22610807096296059949,3.5610411541214425980 ] 
dist 95=[-.34154718137056546915,3.5496698795585265135 ] 
dist 96=[-.56952992519229836065,3.5427347249982063978 ] 
dist 97=[-.81952514096259078315,2.2192570336374524620 ] 
dist 98=[-1.0535342661703289384 ,2.0908328532295311688 ] 
dist 99=[-1.3260691308628848222 ,1.7674335172719936386 ] 
dist 100=[-1.5805037340035555774 ,1.7176595597073708050 ] 
dist 101=[-1.7423289161232332667 ,1.2075456857465320325 ] 
dist 102=[-1.8669223462946122098 ,1.1104791712540370835 ] 
dist 103=[-1.9728526811080459589 ,.99363953530031948667] 
dist 104=[-2.0583737097132775414 ,.96407860863392004486] 
dist 105=[-2.1015613402832556866 ,.10746495001940561552] 
dist 106=[-2.1219073384724020646 ,.00319135328842050215] 
dist 107=[-2.1233083500892017048 ,-.22421160061341408346] 
dist 108=[-1.8029895662592736516 ,-.27017497109012225223] 
dist 109=[-1.8740882497689655976 ,-.51276616089350163818] 
dist 110=[-1.9076828716091478968 ,-.55309173055379157817] 
dist 111=[-1.9214144652709275861 ,-.6255527911839303883 ] 
dist 112=[-1.9213334423767345608 ,-.45543101639390757177] 
dist 113=[-.98445064092329591703,-.30866743939913167673] 
dist 114=[-.91454210745294446151,-.15135352246074252938] 
dist 115=[-.74168766361809298209,.06087221710324859896] 
dist 116=[-.71548330527934262021,.26994012843793283055] 
dist 117=[-.45589375458848131989,.41467640959783869012] 
dist 118=[-.40787184541477355299,.53965644500025335965] 
dist 119=[-.34794499200729580758,.66995377689507330814] 
dist 120=[-.33386934760591978799,.79339932875428227185] 
dist 121=[.05304729095080235991,.89107446145692903328] 
dist 122=[.09891350479978808561,.98846015996151906992] 
dist 123=[.16978929792446901697,1.1107931074618423621 ] 
dist 124=[.21752495665165093839,1.2382850891829417486 ] 
dist 125=[.33142985196983149225,1.3419919705821310888 ] 
dist 126=[.34899874593068755769,1.4265837174061267053 ] 
dist 127=[.38102239216221357095,1.5071138592440062748 ] 
dist 128=[.38675880242662277429,1.5787974942808027115 ] 
dist 129=[.48059123872729062206,1.6280890631088643175 ] 
dist 130=[.48776016789759808373,1.6703846856472038378 ] 
dist 131=[.48256093616771690688,1.7141528267625207797 ] 
dist 132=[.45931353054444948015,1.7513991914798710932 ] 
dist 133=[.42645671429970851273,1.7676703858050234666 ] 
dist 134=[.38291271451610310104,1.7716850022610542877 ] 
dist 135=[.14549669864274334694,1.7693371314503291784 ] 
dist 136=[-.12800869269438881619,1.7411530248538927687 ] 
dist 137=[-.40164068985704385374,1.7304506581122148865 ] 
dist 138=[-.72723439744393815194,1.6931157627463082634 ] 
dist 139=[-1.2080336762366848816 ,1.6799208697453546326 ] 
dist 140=[-1.6846654304424204387 ,1.4964290594425378118 ] 
dist 141=[-1.9936387307088660664 ,1.4622100056757087911 ] 
dist 142=[-2.2383956118655859208 ,1.3908191716885461394 ] 
dist 143=[-2.4588607736145541621 ,1.3686083208024524858 ] 
dist 144=[-2.6463572482090661610 ,1.2696727145703594442 ] 
dist 145=[-2.7596001467939962150 ,1.2478372026197296777 ] 
dist 146=[-2.8399532943786822213 ,1.1843736707987667019 ] 
dist 147=[-2.8962543276461748842 ,1.1722559499056086444 ] 
dist 148=[-2.9349232060716665856 ,1.0348128468724631208 ] 
dist 149=[-2.9449388765115718626 ,1.0073215224730485781 ] 
dist 150=[-2.9386316054974826093 ,.95179345432693631859] 
dist 151=[-2.9293325971400229283 ,.93521638200743112978] 
dist 152=[-2.8512851931411456451 ,.86520765854313828471] 
dist 153=[-2.8267752125554830734 ,.84896739829728836449] 
dist 154=[-2.7580930998962088985 ,.80770608907774833409] 
dist 155=[-2.7286557729347938651 ,.79498674595883889151] 
dist 156=[-1.7190055069137458863 ,.8563017946398817629 ] 
dist 157=[-1.6851102401269523958 ,1.2569168359656069839 ] 
dist 158=[-1.6709967859049887350 ,1.6129284284027341632 ] 
dist 159=[-1.6505481909495922906 ,1.9467726417191440930 ] 
dist 160=[-1.6405095779304919302 ,2.2399818869442110826 ] 
dist 161=[-1.3406994604898563246 ,2.4339025166761148044 ] 
dist 162=[-1.2966498326022334727 ,2.5918383593933277070 ] 
dist 163=[-1.1972736386976629405 ,2.7415073267432331284 ] 
dist 164=[-1.1665784106704645678 ,2.8710190925825073635 ] 
dist 165=[-1.0296970525439926266 ,2.9485479163422076267 ] 
dist 166=[-1.0010208515141040833 ,3.0026964215129102692 ] 
dist 167=[-.93207505479978531076,3.0389412483057711609 ] 
dist 168=[-.91285590387821469057,3.0608212878093444262 ] 
dist 169=[-.71540812784495122185,3.0583224571672993068 ] 
dist 170=[-.68249149993140869725,3.0421965391721999130 ] 
dist 171=[-.61160082723989621518,3.0270156464558559793 ] 
dist 172=[-.5910685130392120133 ,2.3405860029363706723 ] 
dist 173=[-.50499101443000045311,2.3047450607251767005 ] 
dist 174=[-.48789587660107739224,2.2901162537703398821 ] 
dist 175=[-.7158232517672331624 ,2.2435810006486844674 ] 
dist 176=[-.996479955035511486  ,2.2223514411252601872 ] 
dist 177=[-1.2086729370776405254 ,.26126473096656619226] 
dist 178=[-1.4109028656281490362 ,.12730767124746575405] 
dist 179=[-1.6518167875188749790 ,.09664291127905625586] 
dist 180=[-1.8750014548843448161 ,-.30273127716822336994] 
dist 181=[-2.0065105719562205166 ,-.35924308884520088176] 
dist 182=[-2.0957738434697575475 ,-.45063676262054601215] 
dist 183=[-2.1504434968843001878 ,-.47120516127680967796] 
dist 184=[-2.1877438675708034685 ,-.48843741886199354493] 
dist 185=[-2.2077215651055814948 ,-.46370384858057292249] 
dist 186=[-2.2209461453660378015 ,-.4099356042316265534 ] 
dist 187=[-2.2434452845708702691 ,-.30265722590695950944] 
dist 188=[-2.2747823560830014926 ,-.17887774680444423081] 
dist 189=[-2.2912134141721079124 ,.05129867562976480268] 
dist 190=[-2.2919107985038201442 ,.2473437010574832928 ] 
dist 191=[-2.2678312893763791134 ,.44747619983109510734] 
dist 192=[-2.2610470458179676741 ,.63439981751035507697] 
dist 193=[-1.2072232500099113522 ,.77775662399836719004] 
dist 194=[-1.1083119500382911004 ,.91635307031807055829] 
dist 195=[-.87579725748208041339,1.0842896588640542923 ] 
dist 196=[-.83871343727797028631,1.2412716409678514070 ] 
dist 197=[-.56551306479000043372,1.3361715745217517279 ] 
dist 198=[-.5145055227032972288 ,1.4035762585656903120 ] 
dist 199=[-.42807205746796750528,1.4508818083176687778 ] 
dist 200=[-.44315432308013837103,1.4849930568045575851 ] 
dist 201=[-.52913657911551718073,1.4997651205878427036 ] 
dist 202=[-.63628142693834012582,1.5031708712728672293 ] 
dist 203=[-.81161675754081102893,1.5447556324413915294 ] 
dist 204=[-.99577834232422112872,1.6379945623111042114 ] 
dist 205=[-1.1118993510136161489 ,1.7303268360036588723 ] 
dist 206=[-1.2001661349425184167 ,1.7918666419284079091 ] 
dist 207=[-1.2732183279411822664 ,1.8273124519990992077 ] 
dist 208=[-1.3307281879017974035 ,1.8493681661424895768 ] 
dist 209=[-1.3569975829298174539 ,1.8574916409031958986 ] 
dist 210=[-1.3696167044498701918 ,1.8569560105816451952 ] 
dist 211=[-1.3726776057736384095 ,1.8514902062554382062 ] 
dist 212=[-1.3297550155364184640 ,1.5959175724102205999 ] 
dist 213=[-1.3172077325918812007 ,1.5554764942893316561 ] 
dist 214=[-1.2929203136061797126 ,1.4782042023334747969 ] 
dist 215=[-1.2835574334845003331 ,1.4559614433882463581 ] 
dist 216=[-1.2353278505967376067 ,1.3679225090380949417 ] 
dist 217=[-1.2227586213522907285 ,1.3450361265967787951 ] 
dist 218=[-1.1810240618589716821 ,1.2971748449994074611 ] 
dist 219=[-1.1722287989879565874 ,1.2812822452070761521 ] 
dist 220=[-1.1747027613218449517 ,.90551260256647996906] 
dist 221=[-1.2289061499781154611 ,.97901185281671722337] 
dist 222=[-1.2594354824019563918 ,1.0495904558089108556 ] 
dist 223=[-1.2784134488530104746 ,1.1313956770683328911 ] 
dist 224=[-1.4296895516279725629 ,1.2612751038045947153 ] 
dist 225=[-1.6912503830075768412 ,1.3975685675448515899 ] 
dist 226=[-1.8522823865835034253 ,1.4787279786997099892 ] 
dist 227=[-1.9701948566106515481 ,1.5348666761204742040 ] 
dist 228=[-2.0597497517919101187 ,1.5713537792952640095 ] 
dist 229=[-2.1278274874016741919 ,1.5954448898685822807 ] 
dist 230=[-2.1600659977002214955 ,1.6021368419224669521 ] 
dist 231=[-2.1724403344823514483 ,1.5997029210210683338 ] 
dist 232=[-2.1724061756895720356 ,1.5943910671127871504 ] 
dist 233=[-1.9961317277649240287 ,1.4310546454982974450 ] 
dist 234=[-1.9630746258793076767 ,1.4024963986764960734 ] 
dist 235=[-1.9037360932923297762 ,1.3419132066801803649 ] 
dist 236=[-1.8855175811262780487 ,1.3223629807235443044 ] 
dist 237=[-1.8101464675298583436 ,1.2320420165040417012 ] 
dist 238=[-1.7879072615648103737 ,1.2123140855493284945 ] 
dist 239=[-1.7384095014505012482 ,1.1510589309810607512 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 1, 2] 
dist 0=[50.459619250091654776  ,50.459619250091654776  ] 
dist 1=[48.911352576078246828  ,51.734562381503768157  ] 
dist 2=[47.119338780060916393  ,52.435057747615589251  ] 
dist 3=[44.802904293273297355  ,52.848868213226382284  ] 
dist 4=[41.160504884741140204  ,52.978780720100746178  ] 
dist 5=[37.454597409494471926  ,52.998714703144266379  ] 
dist 6=[34.884425375586578428  ,52.973494931977041556  ] 
dist 7=[32.649621273374443289  ,52.909436289961123712  ] 
dist 8=[30.282508887605941125  ,52.812214559864308375  ] 
dist 9=[28.005499310374267878  ,52.605664007663492605  ] 
dist 10=[26.130161522788914955  ,52.474052308924518808  ] 
dist 11=[24.185047322097687183  ,52.175608048018597120  ] 
dist 12=[21.628812365121635421  ,52.039161954508232984  ] 
dist 13=[19.116379014216364199  ,51.316667131877262645  ] 
dist 14=[17.345849034999201886  ,51.089640028227390627  ] 
dist 15=[15.773394679389680890  ,49.940706188670529138  ] 
dist 16=[14.051543930605801427  ,47.752513153237480094  ] 
dist 17=[12.355601882880200820  ,32.065118856033616482  ] 
dist 18=[10.885994517991347149  ,30.585615043494715057  ] 
dist 19=[9.2921060315587433944 ,27.159915386351985766  ] 
dist 20=[7.0984332202599848166 ,26.602125311724740230  ] 
dist 21=[4.9438558068695297478 ,22.184389649071170352  ] 
dist 22=[3.5060818649308075072 ,21.411484876323772825  ] 
dist 23=[2.3085415050986296579 ,20.220763672874794573  ] 
dist 24=[1.1147110625959445714 ,19.928950846682254817  ] 
dist 25=[.00562694839555334718,15.364344582730531542  ] 
dist 26=[-.85290404855197849668,14.788478440630492403  ] 
dist 27=[-1.6973125080790263613 ,13.445331974288845045  ] 
dist 28=[-2.7496624920599758550 ,12.280829278303605940  ] 
dist 29=[-3.7607539188942540031 ,8.6409954024886417946 ] 
dist 30=[-5.3919602586018859552 ,8.4354186400719330449 ] 
dist 31=[-7.0559874815927132238 ,7.4640614942457580234 ] 
dist 32=[-8.6602927378599782130 ,6.1429962736386702588 ] 
dist 33=[-10.109914311152619369  ,1.5892461727535917253 ] 
dist 34=[-11.156109396728064134  ,2.1700472363840014177 ] 
dist 35=[-12.110958058355606604  ,2.9108327112571911254 ] 
dist 36=[-13.195856088420413024  ,4.0581570379665294287 ] 
dist 37=[-14.184836229680954734  ,5.1990410136832640186 ] 
dist 38=[-14.756617953858351657  ,5.9142857095792960934 ] 
dist 39=[-15.135010498566408222  ,6.4513258676815443915 ] 
dist 40=[-15.351560540802938154  ,6.8817224195777062077 ] 
dist 41=[-15.475627386970600734  ,7.2232427671256559911 ] 
dist 42=[-15.484556102592670241  ,7.4060226975578825763 ] 
dist 43=[-15.435403656475132974  ,7.5065896387411796023 ] 
dist 44=[-15.380211924812886072  ,7.5206018657698941491 ] 
dist 45=[-6.5226317955645938549 ,6.9089667749747133396 ] 
dist 46=[-6.2950648462615589593 ,6.7894207738017339343 ] 
dist 47=[-5.8526409758803411396 ,6.6512276072436354374 ] 
dist 48=[-5.7311907716152178941 ,7.2067517157071173539 ] 
dist 49=[-5.2741596503561556495 ,8.3551793311304639712 ] 
dist 50=[-5.1607950787232360380 ,9.0978082899735171708 ] 
dist 51=[-4.9538426846034640407 ,9.6849753254784519499 ] 
dist 52=[-4.8948980672440913545 ,10.213302873943356542  ] 
dist 53=[.76155621723814770403,10.664123282599381442  ] 
dist 54=[1.2332163972425852572 ,10.942053774444992680  ] 
dist 55=[2.2963804812177510985 ,11.146877245371173357  ] 
dist 56=[2.4640007909422312200 ,11.305860052508017265  ] 
dist 57=[3.6906515042455909681 ,11.423533463085191381  ] 
dist 58=[3.8856931300667368178 ,11.463460035372621462  ] 
dist 59=[4.2267076205957955611 ,11.454266348128419033  ] 
dist 60=[4.2884646634207205399 ,11.417081169375036944  ] 
dist 61=[2.8751282153742454185 ,5.4307252733207790675 ] 
dist 62=[1.5315224793793833335 ,5.6416876130422500743 ] 
dist 63=[.37537923343185165371,5.7908763714809109377 ] 
dist 64=[-.82349622946783437948,5.8944581138296698020 ] 
dist 65=[-1.9548077562262077134 ,5.9606395416987644866 ] 
dist 66=[-2.8414766254492412496 ,5.9664538345028486891 ] 
dist 67=[-3.7168143446666478285 ,5.9354593754168870739 ] 
dist 68=[-4.8029554051951039468 ,5.9013396503294819792 ] 
dist 69=[-5.8310451383167683176 ,2.9256632805874213177 ] 
dist 70=[-6.4748300193299166274 ,2.6547809431286863704 ] 
dist 71=[-6.9590473286662218664 ,2.0168004159656487333 ] 
dist 72=[-7.3506346477815618309 ,1.9010097121200866735 ] 
dist 73=[-7.6541606303056622742 ,1.0336227064855092934 ] 
dist 74=[-7.7871124870573695430 ,.87592854357225577095] 
dist 75=[-7.8453571315959826305 ,.61181440919884236063] 
dist 76=[-7.8508701507424892817 ,.54983203908943086343] 
dist 77=[-3.2256035484320278681 ,-.45750224809011368217] 
dist 78=[-3.5034093516031825274 ,-.26148654634016866069] 
dist 79=[-3.6998160782527828448 ,.28788571813510600409] 
dist 80=[-3.8357698117625835135 ,.83672378744691317014] 
dist 81=[-3.9348047580411602329 ,1.3414667139082383947 ] 
dist 82=[-3.9839566397547437322 ,1.7149866711797121492 ] 
dist 83=[-4.0058480139757594876 ,2.0629791036246442952 ] 
dist 84=[-3.9996321140251227890 ,2.4659306545183924080 ] 
dist 85=[-.83932816726689735982,2.8397173279641874345 ] 
dist 86=[-.79276912155264319076,3.0713918278673193913 ] 
dist 87=[-.73206676500673432587,3.2428031770194388370 ] 
dist 88=[-.71147892723292154127,3.3762236523385008682 ] 
dist 89=[-.70522050214156699417,3.4746666272579570530 ] 
dist 90=[-.7243403951757783641 ,3.5065675289110450263 ] 
dist 91=[-.7654004522695976767 ,3.5138109741546968988 ] 
dist 92=[-.8471507748687421269 ,3.5138989586860446389 ] 
dist 93=[-.9398584205936019207 ,3.2733903719479660811 ] 
dist 94=[-1.0246120317136437239 ,3.2711575026636629732 ] 
dist 95=[-1.2827723101336829016 ,3.2289193438933029473 ] 
dist 96=[-1.5351786757777936624 ,3.2181936993836366916 ] 
dist 97=[-1.7610069189454017820 ,3.0124290739429781567 ] 
dist 98=[-1.9172811990089698488 ,2.9599564819672297929 ] 
dist 99=[-2.0520456119225964184 ,2.9156490481903747575 ] 
dist 100=[-2.1920757963688921709 ,2.8930125359655293951 ] 
dist 101=[-2.3153260801948107879 ,3.0308079721260854628 ] 
dist 102=[-2.4422988836325983037 ,3.2607545967874718308 ] 
dist 103=[-2.5627818821759747450 ,3.4216747184030418250 ] 
dist 104=[-2.6533273664650035338 ,3.5301202415171796340 ] 
dist 105=[-2.7192225641030532069 ,3.6073778426027521745 ] 
dist 106=[-2.7413913586305280706 ,3.6438757548098664216 ] 
dist 107=[-2.7455162712157002901 ,3.6574803266273282452 ] 
dist 108=[-2.7394507521530984969 ,3.6510835421602853526 ] 
dist 109=[-2.5619328101137268453 ,3.2065469051715335215 ] 
dist 110=[-2.5248945281875315712 ,3.1339493948416895217 ] 
dist 111=[-2.4411773174408881377 ,3.0028602818066413046 ] 
dist 112=[-2.4111729537076632312 ,2.9657614527941572764 ] 
dist 113=[-2.5079550240152377416 ,2.8259809469203725188 ] 
dist 114=[-2.6512731974152327088 ,2.7846126107792970770 ] 
dist 115=[-2.7560210315512710757 ,2.7109235847959856443 ] 
dist 116=[-2.8353088050719336604 ,2.6875814000616636768 ] 
dist 117=[-2.8967790923013733779 ,-.76611560326821942166] 
dist 118=[-2.9304461000419493171 ,-1.0196325304759780652 ] 
dist 119=[-2.9501745853418551221 ,-1.5901436799130590975 ] 
dist 120=[-2.9560325563302959982 ,-1.6785307000642748884 ] 
dist 121=[-2.9525547999704557102 ,-2.0187532857613938794 ] 
dist 122=[-2.9416216720514829681 ,-1.7382725826533515082 ] 
dist 123=[-2.9105537812349174543 ,-1.3771169512700039712 ] 
dist 124=[-3.0001672719686473067 ,-.81235821813151418674] 
dist 125=[-3.1596308054227123919 ,-.2401197802058581729 ] 
dist 126=[-3.2561088727626347119 ,.1508767925118629907 ] 
dist 127=[-3.3247462522653707485 ,.4832489673372498641 ] 
dist 128=[-3.3731491093959732459 ,.82162703144889633238] 
dist 129=[-3.4047382899336540225 ,1.1371896925688302980 ] 
dist 130=[-3.4063037937636404256 ,1.3785491572599191884 ] 
dist 131=[-3.3923587167233935917 ,1.6113286143356539239 ] 
dist 132=[-3.3773152348692144771 ,1.8926672335655116530 ] 
dist 133=[-1.4844116064330574024 ,2.1554097296251728095 ] 
dist 134=[-1.3179375320499786299 ,2.3140067087469169115 ] 
dist 135=[-.92854961264455720026,2.4264032126944323935 ] 
dist 136=[-.85892490208490089503,2.5048429526973691280 ] 
dist 137=[-.34060509083388119521,2.5610787957677814954 ] 
dist 138=[-.24762503523091923703,2.5848983319153790700 ] 
dist 139=[-.09092282985801516610,2.5894972015770746357 ] 
dist 140=[-.05505516696907129051,2.5863136652511544234 ] 
dist 141=[-.05923277010499777913,1.8304343711584004604 ] 
dist 142=[-.33143997280530788566,1.9985272058589451676 ] 
dist 143=[-.56040517726048397079,2.1184200956012417532 ] 
dist 144=[-.78954938137779101032,2.2034983424595523446 ] 
dist 145=[-1.0006914385588356806 ,2.2669358019122833289 ] 
dist 146=[-1.1578467127250706922 ,2.3005069880656041621 ] 
dist 147=[-1.3052286466772300804 ,2.3185603002997859685 ] 
dist 148=[-1.4773855517837288088 ,2.3201016914687935261 ] 
dist 149=[-1.6351806329965796426 ,.54596083825213936246] 
dist 150=[-1.7252743384815100814 ,.50578702885245186726] 
dist 151=[-1.7828494902659852211 ,.43395662347138958846] 
dist 152=[-1.8109305797444841116 ,.41718531401735364474] 
dist 153=[-1.8266265906638645449 ,.37153843323170015069] 
dist 154=[-1.8347966781906674418 ,.36480427429739689862] 
dist 155=[-1.8390048614192661291 ,.37084233218389768899] 
dist 156=[-1.8388914369116744333 ,.39589711465661490812] 
dist 157=[-1.4843676349594148941 ,.46501489869513711959] 
dist 158=[-1.4395476004428057449 ,.6097563582199621923 ] 
dist 159=[-1.3175422812827219722 ,.72484858545244127016] 
dist 160=[-1.2988978869900371070 ,.82922164834434832794] 
dist 161=[-1.1110885015391387157 ,.91844924472479602943] 
dist 162=[-1.2567106586172446018 ,.97312733610190338468] 
dist 163=[-1.4179951748918220012 ,1.0128550559480340217 ] 
dist 164=[-1.6424305676048026078 ,1.0764314007030842703 ] 
dist 165=[-1.8589959804807972614 ,1.1540659254433148893 ] 
dist 166=[-1.9888877836422035856 ,1.2470463896418360084 ] 
dist 167=[-2.0799423541921988945 ,1.3218013799431796689 ] 
dist 168=[-2.1415782521502569724 ,1.3841739232722184617 ] 
dist 169=[-2.1849143148410141105 ,1.4336263690691637330 ] 
dist 170=[-2.2029648709618723544 ,1.4568451999790695156 ] 
dist 171=[-2.2059277047371310956 ,1.4663672676846610404 ] 
dist 172=[-2.2024156515659897425 ,1.4660999975437101764 ] 
dist 173=[-1.9612953838953057847 ,1.4383296155716635401 ] 
dist 174=[-1.9205221011029910537 ,1.4286279344439191659 ] 
dist 175=[-1.8422809982370939133 ,1.3968433882202529108 ] 
dist 176=[-1.8187542560601009150 ,1.3843724268677955279 ] 
dist 177=[-1.7208228387090777841 ,1.2966551399268917765 ] 
dist 178=[-1.6954675784455488436 ,1.2744486480054316599 ] 
dist 179=[-1.6357679745912964167 ,1.2369280984662166598 ] 
dist 180=[-1.6143235828913133786 ,1.2249849576887504249 ] 
dist 181=[-.3432987579038666287 ,.96844733532144961967] 
dist 182=[-.4184878887622320511 ,.99980341378149331696] 
dist 183=[-.4784697901111451181 ,1.2144829382379214620 ] 
dist 184=[-.5332048845481036610 ,1.4519484444099610775 ] 
dist 185=[-.5802564561922270055 ,1.6600423627514259121 ] 
dist 186=[-.6095946132306820217 ,1.7968812007553268158 ] 
dist 187=[-.6315401083828336248 ,1.9074631438292007562 ] 
dist 188=[-.6491120810225219995 ,2.0108146214078132935 ] 
dist 189=[-.6629359550112829947 ,2.0997799832643013714 ] 
dist 190=[-.66993192896289138405,2.1529741650760611105 ] 
dist 191=[-.67329014655089595943,2.1900486971293372750 ] 
dist 192=[-.67259812576085342003,2.2147119161562070041 ] 
dist 193=[-.73240792548445380892,2.2294549322105147589 ] 
dist 194=[-.7923571462274826836 ,2.2271579638882321924 ] 
dist 195=[-.84097406418037823673,2.2155978543784444016 ] 
dist 196=[-.88673330002800056888,2.2049538661429420966 ] 
dist 197=[-.92612951388616430322,.93883332202393352771] 
dist 198=[-.94936203962085733807,.82745116050654461058] 
dist 199=[-.96517556197582912122,.56787503094996197158] 
dist 200=[-.97496998659689859027,.52121576935272436172] 
dist 201=[-.98012979940229730975,.3869553670759856745 ] 
dist 202=[-.97902361933340694754,.4601603038378811781 ] 
dist 203=[-.97160944552163631807,.54274209455416168214] 
dist 204=[-1.0867555913047153747 ,.65950500350357374028] 
dist 205=[-1.2693969718879711674 ,.80511105741318277788] 
dist 206=[-1.3798933052880014685 ,.93565124564350541089] 
dist 207=[-1.4584928763949448337 ,1.0449319105831921143 ] 
dist 208=[-1.5138948278872366001 ,1.1534595920253935174 ] 
dist 209=[-1.5549900544252473813 ,1.2529284194755265792 ] 
dist 210=[-1.5765174059538598450 ,1.3260721818210856558 ] 
dist 211=[-1.5877930760059391990 ,1.3937904019903951122 ] 
dist 212=[-1.5879896647766147884 ,1.4716153699354314630 ] 
dist 213=[-.7526592972491590792 ,1.5422271541880778828 ] 
dist 214=[-.8270331471698876367 ,1.5811711533401679676 ] 
dist 215=[-.8956359039052695436 ,1.6042928584561870889 ] 
dist 216=[-.9740961361748016901 ,1.6117884384169446799 ] 
dist 217=[-1.0526885365366319201 ,1.6101043654446482946 ] 
dist 218=[-1.1218210123712825607 ,1.6055984052160726871 ] 
dist 219=[-1.1971262797461841674 ,1.5811964626578283072 ] 
dist 220=[-1.3003456683879892176 ,1.5718580952709988375 ] 
dist 221=[-1.3984880438462033880 ,1.5211214547040374149 ] 
dist 222=[-1.5626007553097812430 ,1.5580089586032453053 ] 
dist 223=[-1.7709905892419702048 ,1.5768842218448703318 ] 
dist 224=[-1.9592358732316190315 ,1.6477810417028522058 ] 
dist 225=[-2.1196452545746422263 ,1.7110647499855387390 ] 
dist 226=[-2.2170002956052185976 ,1.7441891051486183928 ] 
dist 227=[-2.2866118015730723318 ,1.7614889671227734597 ] 
dist 228=[-2.3363556416599123346 ,1.7620743061510641770 ] 
dist 229=[-2.3716659988062582435 ,1.6039197330243233460 ] 
dist 230=[-2.3837031399440931965 ,1.5754882466490573767 ] 
dist 231=[-2.3809794387634340519 ,1.5339622799096986859 ] 
dist 232=[-2.3755718439573492770 ,1.5714809475850925949 ] 
dist 233=[-2.3246449312396413993 ,1.6015075340858049875 ] 
dist 234=[-2.3078457010637897069 ,1.6128047635496204345 ] 
dist 235=[-2.2496575422255001135 ,1.6132009456890426068 ] 
dist 236=[-2.2319954361746891475 ,1.6099001715264321378 ] 
dist 237=[-1.7451504193195655141 ,1.4386601961603162467 ] 
dist 238=[-1.7825614936245510133 ,1.4091681267342051333 ] 
dist 239=[-1.8032641378435205371 ,1.3504393499619857590 ] 
dist 240=[-1.8065119760833948923 ,1.3322238496141566433 ] 
dist 241=[-1.8001217216479640123 ,1.2528099990712994502 ] 
dist 242=[-1.7934514164306486806 ,1.2335972747207072528 ] 
dist 243=[-1.7633209513294658923 ,1.1825185287618501083 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 0, 2, 0, 1] 
dist 0=[63.105998127009631212  ,63.105998127009631212  ] 
dist 1=[62.306281940062033473  ,63.535666099681190478  ] 
dist 2=[60.725714566937113007  ,63.638823331582618701  ] 
dist 3=[58.760552085836906852  ,63.581272493580603496  ] 
dist 4=[56.425354994793320836  ,63.369267984976602339  ] 
dist 5=[53.368873821918007066  ,63.117739788212436381  ] 
dist 6=[48.523967557756933486  ,62.902404348053579222  ] 
dist 7=[43.585563499465110848  ,62.672003377163782541  ] 
dist 8=[40.155694441250983320  ,62.503319805109406090  ] 
dist 9=[37.169627433882378744  ,62.020032501717020807  ] 
dist 10=[34.002823432962607337  ,61.801287162539531303  ] 
dist 11=[30.956237409777911880  ,61.316188763223916003  ] 
dist 12=[28.449839379188545294  ,61.108990221204130093  ] 
dist 13=[25.854289263600651705  ,60.050516296156402531  ] 
dist 14=[22.451147663204610179  ,58.746917753452207015  ] 
dist 15=[19.114454351734971525  ,33.544436545633167045  ] 
dist 16=[16.783873332372295393  ,32.898280875737372399  ] 
dist 17=[14.737676731462774891  ,26.489106150163320430  ] 
dist 18=[12.536034899529591039  ,25.319986426673752884  ] 
dist 19=[10.393150658277004542  ,23.931414711162318758  ] 
dist 20=[8.5809070817256655918 ,23.679623948182804427  ] 
dist 21=[6.6551759411667045167 ,14.242998100457038690  ] 
dist 22=[4.0576493895477147652 ,13.112234308158383555  ] 
dist 23=[1.2854395407714467134 ,10.750194050039116150  ] 
dist 24=[-1.0817543046529953951 ,10.200375420752489471  ] 
dist 25=[-3.0368365496176056642 ,7.9982050624138881487 ] 
dist 26=[-4.9503683408738114028 ,7.5921862066060640380 ] 
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dist 55=[.65246622195087571293,8.6764581877485581082 ] 
dist 56=[-.23479617250207905707,9.2191580476551720823 ] 
dist 57=[-.97614192554372357784,9.6541871807011329767 ] 
dist 58=[-1.7090073579328682799 ,9.9865570952072386396 ] 
dist 59=[-2.3777243268720224024 ,10.229366552900890278  ] 
dist 60=[-2.8632812372134958549 ,10.306869842672147317  ] 
dist 61=[-3.3063246791045160739 ,10.323719279553650676  ] 
dist 62=[-3.8055451722869894878 ,10.324352402008269833  ] 
dist 63=[-4.2640839102487768458 ,4.0768083018708862325 ] 
dist 64=[-4.5448884230842080535 ,3.9271692527968620279 ] 
dist 65=[-4.7485959476700695555 ,2.7524842376636907426 ] 
dist 66=[-4.8996254215260948510 ,2.5310226490827227700 ] 
dist 67=[-5.0047915062090547825 ,2.1816060953896546095 ] 
dist 68=[-5.3901958685764627075 ,2.0897527497827950840 ] 
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dist 70=[-6.2215434031577303564 ,.20597272055346182255] 
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dist 73=[-6.7737476386114293800 ,-.1434209402732063553 ] 
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dist 77=[-6.9053835792049408516 ,1.3590472129498762804 ] 
dist 78=[-6.8703828849494030700 ,1.7187938656204222308 ] 
dist 79=[-3.0207438099081627344 ,2.0558511797725597444 ] 
dist 80=[-2.6788889280403525867 ,2.2688971814078148545 ] 
dist 81=[-1.8897612838664543053 ,2.4312190485193751000 ] 
dist 82=[-1.7398377577934466922 ,2.5660193173905469579 ] 
dist 83=[-.7212432365448131538 ,2.7541146537099884809 ] 
dist 84=[-.53946256842234371193,3.1744670792760780303 ] 
dist 85=[-.2065022560088002302 ,3.5607875529568795902 ] 
dist 86=[-.13162557851486644453,3.7981727865316782954 ] 
dist 87=[.853654870998374242  ,4.0736210134246458068 ] 
dist 88=[.9922773244713210285 ,4.4231678151432579594 ] 
dist 89=[1.0354290198709657815 ,4.6704622031083191775 ] 
dist 90=[.83390459044198717921,4.8419649729443468292 ] 
dist 91=[.6358638263806334621 ,4.9668216057151514814 ] 
dist 92=[.46794275868750434865,5.0280692186430793775 ] 
dist 93=[.23169382772843041609,5.0543136630744258278 ] 
dist 94=[-.14036443314233804447,5.0465979587792573374 ] 
dist 95=[-.45370072614565317533,2.5733273037806035486 ] 
dist 96=[-.76735690212315390004,2.6913293290104116960 ] 
dist 97=[-1.0559268104302460981 ,2.7972854955556363469 ] 
dist 98=[-1.2692182464870758686 ,2.9142159906358750743 ] 
dist 99=[-1.4674703421032224220 ,3.0289239356004898527 ] 
dist 100=[-1.7688513748068572586 ,3.1259951321325206959 ] 
dist 101=[-2.3108595813809396038 ,3.2284708660176057677 ] 
dist 102=[-3.1028289819892935900 ,3.3647069473587794132 ] 
dist 103=[-3.8819621463856385399 ,3.4917901806367626173 ] 
dist 104=[-4.3727731648730174053 ,3.5577505968978443217 ] 
dist 105=[-4.7454219759096423059 ,3.5913273052685110241 ] 
dist 106=[-5.0532050024727056463 ,3.5925179420164320586 ] 
dist 107=[-5.2965337446526264444 ,3.5691709257441541683 ] 
dist 108=[-5.4120681279919020295 ,3.5526284791063695179 ] 
dist 109=[-5.4687774419319150912 ,3.4906884835625183696 ] 
dist 110=[-5.4774470258626250687 ,3.4624036301319979299 ] 
dist 111=[-5.2887212112840467643 ,3.0740119970187401035 ] 
dist 112=[-5.2357703433465642435 ,3.0068341446536486147 ] 
dist 113=[-5.1409733619800847787 ,2.8295491407504954722 ] 
dist 114=[-5.1061045999375638343 ,2.7879881266711178640 ] 
dist 115=[-4.9364672216965249114 ,2.4581524854093495042 ] 
dist 116=[-4.8872822055865733559 ,2.3867772512118513718 ] 
dist 117=[-4.7439094396723945814 ,2.2987790512274319811 ] 
dist 118=[-4.6940182122331397410 ,2.3069918942608687958 ] 
dist 119=[-2.4961946897248207790 ,2.2634118551070691561 ] 
dist 120=[-2.5789422126732947813 ,2.3012833221034256719 ] 
dist 121=[-2.6575825436637066456 ,2.3582814293599758225 ] 
dist 122=[-2.7200556645261846601 ,2.3997503284607785916 ] 
dist 123=[-2.7824399360594748313 ,2.4278951538240174058 ] 
dist 124=[-2.8606943247100586622 ,2.5356451872988949694 ] 
dist 125=[-2.9312917713642637214 ,3.2210085354567368747 ] 
dist 126=[-2.9631289961892578599 ,3.6547936789531291203 ] 
dist 127=[-2.9724870043610299295 ,3.9865444774600752198 ] 
dist 128=[-2.9693002388208436313 ,4.2648887180207145746 ] 
dist 129=[-2.9216981631855299459 ,4.4870004930707175696 ] 
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dist 131=[-2.8407617838348519633 ,4.6490781062899725848 ] 
dist 132=[-2.8151652289770714571 ,4.6605278132847883725 ] 
dist 133=[-2.4768539701333154664 ,4.5517479539299511856 ] 
dist 134=[-2.4194109676627684530 ,4.5137564270821646330 ] 
dist 135=[-2.2644890412496317359 ,4.4454491674583567420 ] 
dist 136=[-2.2328667462104025745 ,4.4182358292508956088 ] 
dist 137=[-1.9391418195906901675 ,4.2779481867345280741 ] 
dist 138=[-1.8765393854594661131 ,4.2377730191338855753 ] 
dist 139=[-1.8267071948498814290 ,4.1111413049050693853 ] 
dist 140=[-1.8104448487789808363 ,4.0746244239624890616 ] 
dist 141=[-.06907540288878044030,2.1799774288615850999 ] 
dist 142=[-.38195839963822074555,2.1700125619316827759 ] 
dist 143=[-.63979259952130746045,1.1260427406288025867 ] 
dist 144=[-.88915081798436227035,1.0299265639812349849 ] 
dist 145=[-1.1133511421931884941 ,.79974959929633480845] 
dist 146=[-1.2708340722051169279 ,.76062302534578911394] 
dist 147=[-1.4092905386747218612 ,.43526558263926442058] 
dist 148=[-1.5575996623869829667 ,.37551679528216059787] 
dist 149=[-1.6920334148039382003 ,.28652115671001633556] 
dist 150=[-1.7751413488717486914 ,.262349385433163502  ] 
dist 151=[-1.8364127152457261187 ,-.16442350504952123829] 
dist 152=[-1.8837360137411455111 ,-.21811857222479829947] 
dist 153=[-1.9183646587193473587 ,-.33376792195155801723] 
dist 154=[-1.9289944817761484883 ,-.35626902182375835785] 
dist 155=[-1.9278826975433708813 ,-.47194055593857683598] 
dist 156=[-1.9213904467176249491 ,-.4910963175011346182 ] 
dist 157=[-1.4312666140490070165 ,-.52259459921771711067] 
dist 158=[-1.4285119510303232478 ,-.38238817590319317355] 
dist 159=[-.73528057190548419079,-.2143365801970687836 ] 
dist 160=[-.70575904534794652624,-.04269721296230140415] 
dist 161=[-.55175767308473183282,.11764029321189755099] 
dist 162=[-.5720606823252941102 ,.24061020351670665502] 
dist 163=[-.59637161454653791827,.3594794702586398437 ] 
dist 164=[-.62394501947611799467,.50345900408807981271] 
dist 165=[-.65913754695150167127,.63943938400124292558] 
dist 166=[-.71384029453256122452,.7264023805360677211 ] 
dist 167=[-.77107119040099087858,.79391926945646933594] 
dist 168=[-.81634769898149527032,.85233658118566319469] 
dist 169=[-.86144679046067318968,.90028654098325362158] 
dist 170=[-.91796845707221517415,.92605422244077564516] 
dist 171=[-.97736093299305939128,.94046558436179426757] 
dist 172=[-1.0339105582980953201 ,.94312265675116411069] 
dist 173=[-1.0990868798002181236 ,1.0771010834127710180 ] 
dist 174=[-1.1928894281519455548 ,1.3517438388153990083 ] 
dist 175=[-1.2839507877667827687 ,1.6205644185984430292 ] 
dist 176=[-1.3381920422474712380 ,1.7875134249114638512 ] 
dist 177=[-1.3757311517224733610 ,1.9115058015600788042 ] 
dist 178=[-1.4001680998134514692 ,2.0089637908653440745 ] 
dist 179=[-1.4144572942624802393 ,2.0842812175120094946 ] 
dist 180=[-1.4165186378755702959 ,2.1199494985053995214 ] 
dist 181=[-1.4043428636326047697 ,2.1352780653461449998 ] 
dist 182=[-1.4017442661886651178 ,2.1352459528449369595 ] 
dist 183=[-1.3050760991288022614 ,2.0004653316234726172 ] 
dist 184=[-1.2860369228231675126 ,1.9725838104090429949 ] 
dist 185=[-1.2326484486643866900 ,1.9225807035863686270 ] 
dist 186=[-1.2186430219297621951 ,1.9064427784817688376 ] 
dist 187=[-1.1062380438860988319 ,1.8361951137506271732 ] 
dist 188=[-1.1326006269216136514 ,1.8155944011636028676 ] 
dist 189=[-1.4278170600897224213 ,1.7650146344375875129 ] 
dist 190=[-1.6151968899450979602 ,1.7453824072533423580 ] 
dist 191=[-1.7591367973012652865 ,1.1584185581548537806 ] 
dist 192=[-1.8810603869451183986 ,1.1563575408793521389 ] 
dist 193=[-1.9792442603163824679 ,1.1488203920501139417 ] 
dist 194=[-2.0284810720189200838 ,1.1438300771361610431 ] 
dist 195=[-2.0537443190065353688 ,1.1213278580202469860 ] 
dist 196=[-2.0567877914816180214 ,1.1150387625172270464 ] 
dist 197=[-2.0256758033513280398 ,1.0358685203354721144 ] 
dist 198=[-2.0115302841150866798 ,1.0197583422430883214 ] 
dist 199=[-1.9845352292551927944 ,.97408518548529929827] 
dist 200=[-1.9728204060041475170 ,.96334878756225268374] 
dist 201=[-1.9082298565299603208 ,.8671274928528398738 ] 
dist 202=[-1.8622267180837622857 ,.84557165332186985084] 
dist 203=[-1.6398962315733894149 ,.8156955360842389159 ] 
dist 204=[-1.4617321840051104247 ,.80491590005447776967] 
dist 205=[-.96068530611806938468,.73857519358949507226] 
dist 206=[-.95158719548993669695,.93852666978104856165] 
dist 207=[-.27272368505603234833,1.0981484743626235833 ] 
dist 208=[-.21004232386701527193,1.2440244693355041316 ] 
dist 209=[-.07724133320846069586,1.3695578862667315369 ] 
dist 210=[-.04436716742062470554,1.4480306673335386462 ] 
dist 211=[.08744885028400564988,1.5069094242026420569 ] 
dist 212=[.11219720937909840617,1.5542801509811028046 ] 
dist 213=[.15754000751044268295,1.5917020997126089319 ] 
dist 214=[.16729686128784714714,1.6108938153316674494 ] 
dist 215=[.18817901879960352407,1.6203724028580376946 ] 
dist 216=[.1804248947278882872 ,1.6190467939185032393 ] 
dist 217=[.15802189624470965544,1.6108841441986645330 ] 
dist 218=[.10982743524410758307,1.6043341416800011199 ] 
dist 219=[.04886291002418277243,1.5749362553123630156 ] 
dist 220=[-.02448220709109580843,1.5653504303435932170 ] 
dist 221=[-.12079944402755689382,1.3376142383334891278 ] 
dist 222=[-.27340354240774078974,1.3329039293491730854 ] 
dist 223=[-.45541756820603672912,.39431279931401502235] 
dist 224=[-.64525571024451803744,.35476741903352227507] 
dist 225=[-.82073382774148294572,.12799857684734962782] 
dist 226=[-.95231764208256510271,.08789008839893589149] 
dist 227=[-1.0766904304039545012 ,.00483260572634618475] 
dist 228=[-1.2234029802410669020 ,-.01643234867247966111] 
dist 229=[-1.3585609929761632593 ,-.1847074024447241125 ] 
dist 230=[-1.4368413943790521336 ,-.21240443123588942682] 
dist 231=[-1.4882966504216279972 ,-.23635960968700455342] 
dist 232=[-1.5164460070127408948 ,-.22983134020462996187] 
dist 233=[-1.5337556355966335282 ,-.20931554830640341775] 
dist 234=[-1.5420219032863286764 ,-.1695576221613885397 ] 
dist 235=[-1.5450787413947907456 ,-.108169784360092427  ] 
dist 236=[-1.5154071410501823441 ,-.00137003153891421738] 
dist 237=[-.7794566569137491043 ,.10929024652216551596] 
dist 238=[-.77879628949465246762,.18607816471436448639] 
dist 239=[-.14070126478826235291,.25260810108744696604] 
dist 240=[-.0888772840836268235 ,.32234835570822745911] 
dist 241=[.02494606688429593632,.38864580865067660768] 
dist 242=[.04835377903993318845,.44144209982413424778] 
dist 243=[.1746255564208999693 ,.49435536590746694531] 
dist 244=[.19561774768313359238,.56111945643982615083] 
dist 245=[.24193989548637007289,.62487698185684290321] 
dist 246=[.24874024844427352032,.66579676250608349557] 
dist 247=[.3062424843313487471 ,.69774339106629348801] 
dist 248=[.30877590617739874409,.72570611429551691193] 
dist 249=[.29886105455290773453,.74890064925614577602] 
dist 250=[.26938764581113252545,.76182648018499951111] 
dist 251=[.22967205597931290383,.76968010999623183625] 
dist 252=[.17890014082370806822,.77264107871934830114] 
dist 253=[.11040704380283730031,.77204736302763886953] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 1, 0, 0, 1, 0, 2] 
dist 0=[57.314059494164995193  ,57.314059494164995193  ] 
dist 1=[56.231375537769271866  ,57.730948149252373352  ] 
dist 2=[54.475750683963106918  ,58.312742119476839914  ] 
dist 3=[51.546185034890089508  ,58.927886248276677174  ] 
dist 4=[48.503112349579985483  ,59.235200810934282858  ] 
dist 5=[46.294256869860205068  ,59.376352712712693462  ] 
dist 6=[44.270393160068531169  ,59.337069525939690110  ] 
dist 7=[41.965807361722924154  ,59.122989193597868996  ] 
dist 8=[39.652783849888204118  ,55.648040767003195869  ] 
dist 9=[37.595092899558203286  ,54.787443698456253466  ] 
dist 10=[35.326715152398537191  ,54.522441792624367966  ] 
dist 11=[32.172195725745283624  ,53.685362500327121928  ] 
dist 12=[28.997215494836920431  ,53.393434565483687617  ] 
dist 13=[26.646951832655563892  ,53.035760282248334400  ] 
dist 14=[24.445779303895624431  ,52.858576639470392804  ] 
dist 15=[21.865785438802643182  ,52.305789088589368827  ] 
dist 16=[19.231786623421472122  ,28.761406804035528248  ] 
dist 17=[16.814548624179569869  ,25.064436280155918198  ] 
dist 18=[14.085977009554716396  ,23.706417714300188571  ] 
dist 19=[10.207888467373202340  ,23.187955166807311662  ] 
dist 20=[6.3787548332619053586 ,16.661617464798277007  ] 
dist 21=[3.8455634048907162700 ,15.281726098791600978  ] 
dist 22=[1.7683768396019248788 ,14.986401295719739012  ] 
dist 23=[-.23928167954180923029,11.513672418652692329  ] 
dist 24=[-2.0569443925610090544 ,8.2386968702241391525 ] 
dist 25=[-3.3753275387609097470 ,7.7264365529489730061 ] 
dist 26=[-4.5856174194938526104 ,6.3621240573386382118 ] 
dist 27=[-5.9996258557189125182 ,4.7288547297040532451 ] 
dist 28=[-7.8106339239334252292 ,1.7809630694424128202 ] 
dist 29=[-9.2314088986557629376 ,1.1357619220881234059 ] 
dist 30=[-10.647942108845836870  ,1.0379317577316430770 ] 
dist 31=[-12.443865736575310723  ,-2.1969801156250560908 ] 
dist 32=[-14.128502172528295177  ,-2.5009390942090984251 ] 
dist 33=[-15.100783107457072795  ,-2.6567860835822732488 ] 
dist 34=[-15.747919333199585814  ,-1.6148139908323228544 ] 
dist 35=[-16.132747065125867373  ,.07672163257867266800] 
dist 36=[-16.388980016377541966  ,1.7932514737810417416 ] 
dist 37=[-16.521572986603473155  ,2.9351296429853298941 ] 
dist 38=[-16.592710584514488045  ,3.8695464929627405084 ] 
dist 39=[-16.601884076193347599  ,4.7591645988542248054 ] 
dist 40=[-14.361170587360030361  ,5.5471583227497328969 ] 
dist 41=[-14.033207131636909866  ,6.0764605899445386350 ] 
dist 42=[-13.447968232961925293  ,6.5152516199118579554 ] 
dist 43=[-13.294458843843965333  ,6.9423451432776725223 ] 
dist 44=[-12.782826687489789226  ,7.3148017755243639685 ] 
dist 45=[-12.621272812748339988  ,7.5357409038841503208 ] 
dist 46=[-12.500641022890519583  ,7.6867521418048599301 ] 
dist 47=[-12.449795082922778920  ,7.7804056729636046416 ] 
dist 48=[-2.0568503309842500118 ,7.8289620613812443781 ] 
dist 49=[-1.9084471301727318362 ,7.8209729452533673125 ] 
dist 50=[-1.6703515677223276034 ,7.7443339799982714547 ] 
dist 51=[-1.6106461691207739115 ,7.6856517137754070983 ] 
dist 52=[.25629508925488773893,4.8526104215168356890 ] 
dist 53=[.45296378707426103202,5.9653003562765907215 ] 
dist 54=[.90027019885500126775,7.0524782975368594264 ] 
dist 55=[.96560511268579664413,8.3894784465996627758 ] 
dist 56=[1.4960682467118191344 ,9.6546538185531713089 ] 
dist 57=[1.5813839012843982568 ,10.455165160398464449  ] 
dist 58=[1.7106118129372772263 ,11.068871862926146881  ] 
dist 59=[1.7339637113024065157 ,11.588415908189368223  ] 
dist 60=[2.0578954093330074292 ,12.007911269683777896  ] 
dist 61=[2.0963514026466013990 ,12.222271862285971001  ] 
dist 62=[1.3661560792193427626 ,12.327527657639737766  ] 
dist 63=[.51745165984429824241,12.335697969827927944  ] 
dist 64=[-1.1496905022383123849 ,2.3480626405090876438 ] 
dist 65=[-2.2521028375997266575 ,2.3666572602898519786 ] 
dist 66=[-3.1934799738945290250 ,2.3733005886615650474 ] 
dist 67=[-4.1043408427542178689 ,2.3681378895829656316 ] 
dist 68=[-4.9178901844817585460 ,1.0766508227588503236 ] 
dist 69=[-5.4808375710376923209 ,.96948132307609055303] 
dist 70=[-5.9672709177307031344 ,.70915235729455957546] 
dist 71=[-6.4756333368309782265 ,.6711106338255146906 ] 
dist 72=[-6.9287168284743556026 ,.29690334934042047947] 
dist 73=[-7.1946290303757240717 ,.22925994561158424123] 
dist 74=[-7.3741851960069865001 ,.14572715947298840402] 
dist 75=[-7.4827284670892933557 ,.12974985108616028001] 
dist 76=[-7.5384644569744283010 ,-.3861898863992900266 ] 
dist 77=[-7.5423403716542614676 ,-.20154917183821162858] 
dist 78=[-7.4581684311606573564 ,.24692970044084230004] 
dist 79=[-7.4419811261330443956 ,.70183796529638490483] 
dist 80=[-4.1837160100756725296 ,1.0131021186652797882 ] 
dist 81=[-3.8716965673644201544 ,1.3620629511541039342 ] 
dist 82=[-3.1199474328131829248 ,1.7104975117782291289 ] 
dist 83=[-2.9892420764563453351 ,2.0308311386157223332 ] 
dist 84=[-1.9062412799616814380 ,2.2677326526153736514 ] 
dist 85=[-1.7047240343087995236 ,2.6952823643615491255 ] 
dist 86=[-1.4031184397026229384 ,3.1684799854194222014 ] 
dist 87=[-1.3202995845281953426 ,3.7190102365159706073 ] 
dist 88=[-.89241664041336588746,4.2277872233683990892 ] 
dist 89=[-.89746250224017951713,4.5344501636263839214 ] 
dist 90=[-.90193567979058093781,4.7511955614537757217 ] 
dist 91=[-.90680727116094230878,4.9013053585609828256 ] 
dist 92=[-.91109015266330360238,5.0065426762735614827 ] 
dist 93=[-.91320788486715589871,5.0442947038746196593 ] 
dist 94=[-.91412919729032889436,5.0467093986384357087 ] 
dist 95=[-1.4810313148427646238 ,5.0331418669655292462 ] 
dist 96=[-1.9470383392353081417 ,2.5870180991641464185 ] 
dist 97=[-2.3240512374535782680 ,2.4001700340005083283 ] 
dist 98=[-2.6766080002332036039 ,2.3486116982472201954 ] 
dist 99=[-2.9851891497337357056 ,2.0550797386480567656 ] 
dist 100=[-3.1868175973122239678 ,1.9930584611152575965 ] 
dist 101=[-3.3480972680843363044 ,1.8686461466750171626 ] 
dist 102=[-3.4957520994246788046 ,1.8325516206120702803 ] 
dist 103=[-3.6181247111793582788 ,1.7011475959766213748 ] 
dist 104=[-3.6785772389473910989 ,1.7994904142136032918 ] 
dist 105=[-3.7050369956136160275 ,1.8531584900546888879 ] 
dist 106=[-3.7042229480081132660 ,1.8843224070542317075 ] 
dist 107=[-3.6601308826513700497 ,1.8928920108988331483 ] 
dist 108=[-3.6383609908371410008 ,1.8911866172106883085 ] 
dist 109=[-3.5645335945545901924 ,1.8839493731480152686 ] 
dist 110=[-3.5304804635413346517 ,1.8664086942882469005 ] 
dist 111=[-2.4851374075822906798 ,1.8563111560669393284 ] 
dist 112=[-1.4333243256091265685 ,1.7932469826548297944 ] 
dist 113=[-1.3435703825621259427 ,1.7760164100925454164 ] 
dist 114=[-1.1239839181204133887 ,1.7236993582555113153 ] 
dist 115=[-1.0855628137629656219 ,1.7076207699643537572 ] 
dist 116=[-.75819238685992601748,-.49393882345643081364] 
dist 117=[-.83710697010759783069,-.32493166456654625188] 
dist 118=[-1.0706571487701908159 ,-.14580707593345557939] 
dist 119=[-1.2916055960411610817 ,.09325601355844838137] 
dist 120=[-1.4870439091338226767 ,.32759099324527967559] 
dist 121=[-1.6188293169321296262 ,.48787706321954128578] 
dist 122=[-1.7289845178870167774 ,.62422991556467857285] 
dist 123=[-1.8381364081076295919 ,.763137764676098438  ] 
dist 124=[-1.9335876447169137215 ,.89274680626621428819] 
dist 125=[-1.9890881687574017982 ,.99203765041119854905] 
dist 126=[-2.0258550315143652717 ,1.0880295878432617719 ] 
dist 127=[-2.0465730735255333048 ,1.2045278959445924201 ] 
dist 128=[-2.0553500503681794934 ,1.3283361036283837124 ] 
dist 129=[-2.0538247504661638902 ,1.4245965559821691977 ] 
dist 130=[-2.0294307803273033857 ,1.5026954317379924121 ] 
dist 131=[-2.0215240103007659382 ,1.5763802462053130805 ] 
dist 132=[-1.0352783056489186953 ,1.6415535384336647598 ] 
dist 133=[-.94845257367449273549,1.6856865035879562885 ] 
dist 134=[-.77495425656145465147,1.7228466491883246660 ] 
dist 135=[-.74144711862850257916,1.7601950774663771121 ] 
dist 136=[-.50061231351514627562,1.7913557369244075745 ] 
dist 137=[-.45567385922102809205,1.8038222949601128853 ] 
dist 138=[-.37766169662206763433,1.8049852971080073457 ] 
dist 139=[-.35949751047009845733,1.8017120123523012423 ] 
dist 140=[-.18106769784576806209,1.7700310440440839386 ] 
dist 141=[-.46597618189633537838,1.7588383214964100881 ] 
dist 142=[-.80383635555141173464,1.7183080716027407999 ] 
dist 143=[-1.3014372009817108148 ,1.7062005005868800114 ] 
dist 144=[-1.7943738276024462018 ,1.5266757416176075994 ] 
dist 145=[-2.1136328940045275134 ,1.5010019359868112841 ] 
dist 146=[-2.3662257907733637433 ,1.4986636138368268442 ] 
dist 147=[-2.5932224744570577265 ,1.4962103811418568018 ] 
dist 148=[-2.7859083924123568170 ,1.3057138169388294096 ] 
dist 149=[-2.9016334220407624820 ,1.2840418156590258336 ] 
dist 150=[-2.9829642100760819872 ,1.2233100771026424780 ] 
dist 151=[-3.0384535933820118051 ,1.2091656173889467915 ] 
dist 152=[-3.0755661111637554805 ,1.0821121336270084314 ] 
dist 153=[-3.0835882732987750960 ,1.0554056186775964356 ] 
dist 154=[-3.0753801106016281658 ,1.0031503781490579587 ] 
dist 155=[-3.0646775591747795651 ,.98765165448754521232] 
dist 156=[-2.9785257799750490645 ,.92345967140074499588] 
dist 157=[-2.9519102047261604116 ,.90758262534723287238] 
dist 158=[-2.8795863866153601967 ,.86985023787470996975] 
dist 159=[-2.8490662824633708643 ,.8565256572768648293 ] 
dist 160=[-1.1775806991199683609 ,.91512228962603612437] 
dist 161=[-1.2044228080465411888 ,1.3611297303882097397 ] 
dist 162=[-1.2200111099614723633 ,1.7349041035323413585 ] 
dist 163=[-1.2740209494979871328 ,2.0842872966966713220 ] 
dist 164=[-1.4856872454208600846 ,2.3903795699027868570 ] 
dist 165=[-1.6149439962887093129 ,2.5914688567017880835 ] 
dist 166=[-1.7083326856069477440 ,2.7537479020349134054 ] 
dist 167=[-1.7769180330937520212 ,2.9050299563445316302 ] 
dist 168=[-1.8281538530352056870 ,3.0352151265761706852 ] 
dist 169=[-1.8523337586483987113 ,3.1133386652597188268 ] 
dist 170=[-1.8612777082872397755 ,3.1681393938034332226 ] 
dist 171=[-1.8603030636278797329 ,3.2052859550026403386 ] 
dist 172=[-1.6852044653620495902 ,3.2281573739174051792 ] 
dist 173=[-1.6541406759974378183 ,3.2260121714113280591 ] 
dist 174=[-1.5982714329110296662 ,3.2102176100485117453 ] 
dist 175=[-1.5816370593046091429 ,3.1956406987839452639 ] 
dist 176=[-1.5150519530686148564 ,1.3225971414122682263 ] 
dist 177=[-1.4953921951291566233 ,1.1636696305550181316 ] 
dist 178=[-1.4545627848506159570 ,1.0959443762770791266 ] 
dist 179=[-1.4401055588370625150 ,1.0867747320295140768 ] 
dist 180=[-1.0361284253675589251 ,.33115467112406777681] 
dist 181=[-1.2627077083643640971 ,.43997044944104362268] 
dist 182=[-1.4791062720783875886 ,.64622271094925879941] 
dist 183=[-1.7375558231170121886 ,.85065094670928091947] 
dist 184=[-1.9772274258984094571 ,1.0377718676108121136 ] 
dist 185=[-2.1187212026382966074 ,1.1749809324758033510 ] 
dist 186=[-2.2150946051145319960 ,1.3016322013368467671 ] 
dist 187=[-2.2747826633488448730 ,1.4466333625280574819 ] 
dist 188=[-2.3305239367058576643 ,1.5786775396649000860 ] 
dist 189=[-2.3618293715908246270 ,1.6536420440215902829 ] 
dist 190=[-2.3757311446689458632 ,1.7009977138534200596 ] 
dist 191=[-2.3734208022627573076 ,1.7229109757879589182 ] 
dist 192=[-.35372859322470709267,1.7337680694494028556 ] 
dist 193=[-.29034561016776419926,1.7370188712368376819 ] 
dist 194=[-.18670455553413792584,1.7353077306953370320 ] 
dist 195=[-.16100237450346922451,1.7284256120154596732 ] 
dist 196=[-.08111352603547664388,1.3270638283058704935 ] 
dist 197=[-.2852086429052535533 ,1.2792924076634376825 ] 
dist 198=[-.45244943720490906544,1.1532576022643461976 ] 
dist 199=[-.61265994799832742264,1.1335283213292835028 ] 
dist 200=[-.75571086786746419204,1.2885306370226533054 ] 
dist 201=[-.85449949445249245578,1.3866032934746945028 ] 
dist 202=[-.93959263253047986497,1.4558105117618980997 ] 
dist 203=[-1.0280100254318564998 ,1.5035156660733010374 ] 
dist 204=[-1.1077397690067695963 ,1.5377329941109572364 ] 
dist 205=[-1.1581773567296594966 ,1.5531365905899979553 ] 
dist 206=[-1.1967216807385632190 ,1.5576789474790650666 ] 
dist 207=[-1.2290098996203422578 ,1.5554140913710517864 ] 
dist 208=[-1.2547398787099234795 ,1.5539070369932598696 ] 
dist 209=[-1.2671245527385541511 ,1.6218595039142963942 ] 
dist 210=[-1.2720934982771302879 ,1.6624672489531731404 ] 
dist 211=[-1.3000515020759120160 ,1.6762936976150192694 ] 
dist 212=[-1.3620083290697702515 ,1.6803970910789673744 ] 
dist 213=[-1.3913498181446758684 ,1.6822138846353557229 ] 
dist 214=[-1.4058407654439749459 ,1.6827115313077047628 ] 
dist 215=[-1.4085632945958055776 ,1.6815448508009649464 ] 
dist 216=[-1.3729598897109995665 ,1.3571004343397113696 ] 
dist 217=[-1.3612210626102642909 ,1.3108358530582593822 ] 
dist 218=[-1.3386287960106466642 ,1.2274238899225362113 ] 
dist 219=[-1.3295847566613414198 ,1.2057708134201217234 ] 
dist 220=[-1.2819054362148034451 ,1.1335736651207985815 ] 
dist 221=[-1.2693658451748864757 ,1.1117732598903404058 ] 
dist 222=[-1.2267569208719459536 ,1.0939913062241062019 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 0, 2, 2, 0, 1] 
dist 0=[64.200854050441229559  ,64.200854050441229559  ] 
dist 1=[63.928119269367346822  ,64.411821798259768629  ] 
dist 2=[63.050391948931921024  ,64.587449949114128267  ] 
dist 3=[61.939936710376949829  ,64.589160806990402186  ] 
dist 4=[60.753393716976295384  ,64.142578106511641437  ] 
dist 5=[59.282297819606302524  ,63.946167396412198540  ] 
dist 6=[57.035382484732330009  ,63.502766815956452344  ] 
dist 7=[54.456957126095662648  ,63.304358649606010550  ] 
dist 8=[51.661947393176533784  ,59.258419583854825969  ] 
dist 9=[48.167574732506548679  ,58.545210281535079183  ] 
dist 10=[42.796239781417558114  ,58.297767742845944474  ] 
dist 11=[37.366079135945235412  ,57.254987930748461814  ] 
dist 12=[33.636800046048153085  ,56.882050416621361705  ] 
dist 13=[30.432385778995383215  ,56.555636704794715964  ] 
dist 14=[27.098317554457832670  ,54.125736950548174646  ] 
dist 15=[23.929108275705386259  ,48.436193665335971972  ] 
dist 16=[21.383124082504285333  ,30.493035089515234589  ] 
dist 17=[18.801832612065050501  ,29.282011666120636276  ] 
dist 18=[15.491790146596312222  ,26.844697593418409802  ] 
dist 19=[12.285430738936072331  ,26.214940412008348172  ] 
dist 20=[10.118199859201312107  ,23.968767931723134292  ] 
dist 21=[7.9729038991424201056 ,23.485689887119144675  ] 
dist 22=[5.2585230662769163735 ,22.769165908910877459  ] 
dist 23=[1.9354611003656209770 ,22.567046397718906353  ] 
dist 24=[-1.2166724540118817981 ,7.0704877651951363553 ] 
dist 25=[-3.2488892775227602618 ,6.3655960665801577859 ] 
dist 26=[-4.8573963669636992809 ,6.2207420805269296560 ] 
dist 27=[-6.3179896271719968409 ,-.0469698681022598296 ] 
dist 28=[-8.1571535414779801313 ,-1.2448943455498770366 ] 
dist 29=[-9.9011478883233636718 ,-1.8235467350316947652 ] 
dist 30=[-11.549832193835608058  ,-2.7338349463650085619 ] 
dist 31=[-13.506215117634202217  ,-4.2358221617017070471 ] 
dist 32=[-15.330794364372678459  ,-6.7465884972168253590 ] 
dist 33=[-16.453080807839959818  ,-6.9064655455418662183 ] 
dist 34=[-17.279344473252748362  ,-6.7920558872585955584 ] 
dist 35=[-17.921625584198486305  ,-6.2791614648254169109 ] 
dist 36=[-18.399480587619576420  ,-5.5544653143214877266 ] 
dist 37=[-18.569100492477418443  ,-4.5944774029582422611 ] 
dist 38=[-18.620220170134636109  ,-3.2815017943118479803 ] 
dist 39=[-18.624533358088961138  ,-1.1480440597767786197 ] 
dist 40=[-9.7139686647664002553 ,1.4181771562820531645 ] 
dist 41=[-9.5671222231587539697 ,3.2990473591356769720 ] 
dist 42=[-9.1344643934092308093 ,4.8402782525218611904 ] 
dist 43=[-9.0685639751732796706 ,6.3174920284439490201 ] 
dist 44=[-8.1625997680265037174 ,7.6381395226547160381 ] 
dist 45=[-7.9713343046609650270 ,8.5549168535225538118 ] 
dist 46=[-7.7885112604903995827 ,9.3506747610124823598 ] 
dist 47=[-7.7403596595454816826 ,10.188749414645529894  ] 
dist 48=[-5.1883532942940474530 ,10.939601155937251893  ] 
dist 49=[-4.8715123000996204314 ,11.387323034428654948  ] 
dist 50=[-4.1784746295361085384 ,11.698666698635789645  ] 
dist 51=[-3.9945552603988360202 ,11.905032634631870495  ] 
dist 52=[-3.1640053456163366599 ,12.027477110226246924  ] 
dist 53=[-3.0046712528727163996 ,12.045579864823279626  ] 
dist 54=[-2.6254985284296455583 ,11.943882633955399734  ] 
dist 55=[-2.5436222010783366807 ,11.922770810432843944  ] 
dist 56=[-1.7225136463289118224 ,7.0298374379485242861 ] 
dist 57=[-1.5797680659928080049 ,6.5681513087300202005 ] 
dist 58=[-1.3233175145096460354 ,5.4656173672740549996 ] 
dist 59=[-1.2613122725023927706 ,5.2679525384086530935 ] 
dist 60=[-1.0782220552630473161 ,3.7129022694788666370 ] 
dist 61=[-1.5662433181632452575 ,3.4252272160134933705 ] 
dist 62=[-2.2213592207183593635 ,2.6120952829536264658 ] 
dist 63=[-3.0457517431468393652 ,1.5881283268503685715 ] 
dist 64=[-3.8313392824635251259 ,-1.1490042115867286290 ] 
dist 65=[-4.3316898494005225970 ,-1.1676860714407046946 ] 
dist 66=[-4.7177305917221066167 ,-1.1693258137354292080 ] 
dist 67=[-5.0473837977231596868 ,-1.1380975368477829015 ] 
dist 68=[-5.3146279950259955809 ,-1.0909977354019505698 ] 
dist 69=[-5.4517431441163130493 ,-1.0264698604535705896 ] 
dist 70=[-5.5196522704761690101 ,-.9375218318796848116 ] 
dist 71=[-5.5313341272984039425 ,-.7929777322710516024 ] 
dist 72=[-1.0431620388203659127 ,-.60454942528870558717] 
dist 73=[-1.0230995215504373639 ,-.18474608065256552528] 
dist 74=[-.9678364402183219414 ,.16569279054765698098] 
dist 75=[-.9583381849339035214 ,.51157953061471868047] 
dist 76=[-.8540423265746762501 ,.82680225995124669175] 
dist 77=[-.8324667556321957129 ,1.0549619187690642643 ] 
dist 78=[-.8075980490128793230 ,1.2623736000866963341 ] 
dist 79=[-.7989702447403144256 ,1.4948639262250537357 ] 
dist 80=[-.5666367949050566675 ,1.7098785094493681139 ] 
dist 81=[-.53593197839991557974,1.8476019047967260563 ] 
dist 82=[-.47257447889851449452,1.9547168950407430703 ] 
dist 83=[-.45539153014492924592,2.0476695267398092695 ] 
dist 84=[-.38900364174444343263,2.1241489143832055587 ] 
dist 85=[-.37536030059071073341,2.1655744968849634910 ] 
dist 86=[-.34524288913738255071,2.1892041613428439213 ] 
dist 87=[-.33616877685354111798,2.1947267745042862006 ] 
dist 88=[-.29757020323662406665,1.6866015920045588386 ] 
dist 89=[-.28790935533759792931,1.6389574925373755278 ] 
dist 90=[-.27954235347549958766,1.5092722396166020572 ] 
dist 91=[-.27715695089426896351,1.4880870922174643939 ] 
dist 92=[-.40761571169848766287,1.3610841739481341489 ] 
dist 93=[-.5393029656697996093 ,1.3493398018499570791 ] 
dist 94=[-.66699951709643162317,1.3228217527105848950 ] 
dist 95=[-.82209089127186576577,1.3121698809627908588 ] 
dist 96=[-.96717837428523420522,.60615605678057807906] 
dist 97=[-1.0549768110035834344 ,.54028832234306234777] 
dist 98=[-1.1173401553402695895 ,.40026219472232740223] 
dist 99=[-1.1609834005883362388 ,.36379773975684594677] 
dist 100=[-1.1932273689418657863 ,.22091617534574315313] 
dist 101=[-1.2466446428668201793 ,.19357423051858426388] 
dist 102=[-1.3879185632374823031 ,.13967792778312489711] 
dist 103=[-1.5648131604030416940 ,.12653061586565900606] 
dist 104=[-1.7331473970301869267 ,.02593760406197052897] 
dist 105=[-1.8402729684763611332 ,.10190543094405186026] 
dist 106=[-1.9228913582710959862 ,.17890968828991573431] 
dist 107=[-1.9934598059110303776 ,.27722101019183245538] 
dist 108=[-2.0507375925917219361 ,.38143498662371457257] 
dist 109=[-2.0803362550689806561 ,.48198686367720056511] 
dist 110=[-2.0952832092141942242 ,.59889591084007500256] 
dist 111=[-2.0941125408604661093 ,.86849939202100442236] 
dist 112=[-2.0835669126149333275 ,1.2907630490455039910 ] 
dist 113=[-2.0746590623502359428 ,1.5615608779029194425 ] 
dist 114=[-2.0376858288933381579 ,1.7726481000811345794 ] 
dist 115=[-2.0232420968643686325 ,1.9567419902260899922 ] 
dist 116=[-1.8992737521158034718 ,2.1088853997916906058 ] 
dist 117=[-1.8673434898280648353 ,2.1925305348522727619 ] 
dist 118=[-1.8212583433717526030 ,2.2418299690493982338 ] 
dist 119=[-1.8036142516999530620 ,2.2569772571126829434 ] 
dist 120=[-1.3579373493432625956 ,2.2591909328050848898 ] 
dist 121=[-1.2948354904360040922 ,2.2569024604666702651 ] 
dist 122=[-1.1568795550103095995 ,2.2508899161973499225 ] 
dist 123=[-1.1165704349557812625 ,2.2395732288505602868 ] 
dist 124=[-.94574141478167792921,2.2223780072143689032 ] 
dist 125=[-.91201716409853021467,2.2078300355690259779 ] 
dist 126=[-.82394821961034987784,2.1799483453102638749 ] 
dist 127=[-.80908340296677447155,2.1671834175613154977 ] 
dist 128=[-.03103042230656401148,1.2530415149898702855 ] 
dist 129=[-.35286460475622242012,1.3314471386622580853 ] 
dist 130=[-.61826928735124799192,1.3869532768334283982 ] 
dist 131=[-.87515473620135498471,1.4256008372390303756 ] 
dist 132=[-1.1061633329871180662 ,1.4523595701998146709 ] 
dist 133=[-1.2683575192597318465 ,1.4604350693689389645 ] 
dist 134=[-1.4108318078109587115 ,1.4599309073528146909 ] 
dist 135=[-1.5631897994646266422 ,1.4547666155458544128 ] 
dist 136=[-1.7013114782276569044 ,-.28543770884739385376] 
dist 137=[-1.7870021630229643176 ,-.34006776541455164016] 
dist 138=[-1.8505102139761449309 ,-.46150404860478139764] 
dist 139=[-1.9001481761187460618 ,-.48024637935206801296] 
dist 140=[-1.9369404958978602259 ,-.61284814939006149367] 
dist 141=[-1.9492088295963059798 ,-.63292096740238436272] 
dist 142=[-1.9487398675522432863 ,-.66931263802352284718] 
dist 143=[-1.9429323185553166030 ,-.67551856319681214766] 
dist 144=[-1.2692986518226921505 ,-.57445733587316181265] 
dist 145=[-1.3184160518748100482 ,-.37099707717129960031] 
dist 146=[-1.3465756821203638188 ,-.19688592274620297709] 
dist 147=[-1.3534105708670520670 ,-.01792862428565380830] 
dist 148=[-1.3528109136994934634 ,.14988982061121290485] 
dist 149=[-1.3513142724191866322 ,.27957291209615984912] 
dist 150=[-1.3488804226728186237 ,.40582384853624651301] 
dist 151=[-1.3445446595290836895 ,.55995167978284364711] 
dist 152=[-1.0797136174974155491 ,.70534845723399353442] 
dist 153=[-1.0444136071314934240 ,.79677668641831702686] 
dist 154=[-.95539138250067217183,.86595027132870776335] 
dist 155=[-.93672497775368082173,.92258911474478929158] 
dist 156=[-.78874834422646357129,.96721358715302938642] 
dist 157=[-.75846732324987710921,1.0371700708233717740 ] 
dist 158=[-.71131901403973546423,1.1023125235048102762 ] 
dist 159=[-.6975535352799469513 ,1.1641454516455977465 ] 
dist 160=[-.41361079857232996858,1.2173920172208857990 ] 
dist 161=[-.37591187322183320372,1.2482844802520538500 ] 
dist 162=[-.2877879692409717755 ,1.2686601831936300695 ] 
dist 163=[-.27100374283744353882,1.2799552476893044853 ] 
dist 164=[-.15250002225387762129,1.2845292771951811570 ] 
dist 165=[-.13083373089068877134,1.2826796123562172109 ] 
dist 166=[-.09236994642170187268,1.2685297442287773587 ] 
dist 167=[-.08378868949732739101,1.2606127443964489065 ] 
dist 168=[-.01768692678098638337,.75139584166717077278] 
dist 169=[-.09223161928483539805,.77338876234706311487] 
dist 170=[-.18776093847801185358,.79444603409003717559] 
dist 171=[-.32833630704928290655,.81967432838379149748] 
dist 172=[-.4823242284411684464 ,.84557867518306501896] 
dist 173=[-.63028412552093802493,.86932767136210063318] 
dist 174=[-.80187823552621669765,.89597824099920344108] 
dist 175=[-1.0501512921135698048 ,.93344877751805694582] 
dist 176=[-1.2939725942008452395 ,.9693218113601653611 ] 
dist 177=[-1.4478099295108877412 ,.9895987132534821619 ] 
dist 178=[-1.5649084381981778806 ,1.0022630827354833172 ] 
dist 179=[-1.6621740529914888398 ,1.0077742929043049825 ] 
dist 180=[-1.7390387917511653676 ,1.0082205610774252723 ] 
dist 181=[-1.7747566439474251670 ,1.0059665847772848475 ] 
dist 182=[-1.7920433236955456893 ,.99168404516874703398] 
dist 183=[-1.7953775134744084915 ,.9863114941911211783 ] 
dist 184=[-1.7457005359930135675 ,.92497401339358539123] 
dist 185=[-1.7302381275789942457 ,.91212370962247832615] 
dist 186=[-1.6991929426129501129 ,.87298863721839048747] 
dist 187=[-1.6868382715290460400 ,.86509521499192539129] 
dist 188=[-1.6213670855005553281 ,.77553643867037153052] 
dist 189=[-1.6049518417080709695 ,.75545344239177514002] 
dist 190=[-1.5474939984485648630 ,.73272298524262589368] 
dist 191=[-1.5381589078690942093 ,.72249693412537831754] 
dist 192=[-.37810093936740766064,.63565263515689245904] 
dist 193=[-.36435367525554243384,.78292456478651383248] 
dist 194=[-.33548883017311517886,.99781371479562430968] 
dist 195=[-.32710232191043921208,1.1962588071200919426 ] 
dist 196=[-.29221018177790781858,1.3684592294690375275 ] 
dist 197=[-.28483402543903922162,1.4786577639752258949 ] 
dist 198=[-.26616978736843380355,1.5643234663880487518 ] 
dist 199=[-.26169198267988580578,1.6386622448293816613 ] 
dist 200=[.00284577091124701853,1.7016017983847509954 ] 
dist 201=[-.07496079894860210973,1.7417954261005996635 ] 
dist 202=[-.14501125271223246163,1.7729469700350439240 ] 
dist 203=[-.22256849685026657187,1.7998161662035592108 ] 
dist 204=[-.29880076291831767229,1.8218121643641779023 ] 
dist 205=[-.36356737649275906652,1.8335236361109151119 ] 
dist 206=[-.43219533888501962082,1.8399206275499780586 ] 
dist 207=[-.52383157808785879038,1.8407160459842109232 ] 
dist 208=[-.6137560007829936077 ,.90348370891352611204] 
dist 209=[-.6755566863883039613 ,.9377831695769730274 ] 
dist 210=[-.72846028710936063906,.96523370287512186719] 
dist 211=[-.78289659902512649119,.99043123910258459259] 
dist 212=[-.83401521470184952978,1.0121840004956501834 ] 
dist 213=[-.87368618781382473646,1.0258923234157671511 ] 
dist 214=[-.91249150569830239253,1.0362992996296126593 ] 
dist 215=[-.96015955812035516472,1.0448811742977697355 ] 
dist 216=[-1.0975584957855658935 ,1.0505172371434993710 ] 
dist 217=[-1.2629149736131074624 ,1.0491732745771553160 ] 
dist 218=[-1.3910324790434908348 ,1.0434919636698350134 ] 
dist 219=[-1.5014438483275769345 ,1.0389781930699994114 ] 
dist 220=[-1.5917474516889752872 ,1.0075654157875031565 ] 
dist 221=[-1.6396560551618556665 ,.99845611222324438392] 
dist 222=[-1.6655886886418993193 ,.98110002591937842159] 
dist 223=[-1.6708888552163890294 ,.97685762950174958283] 
dist 224=[-1.6618217472536530685 ,.94068293305973121607] 
dist 225=[-1.6528629332162188562 ,.93166976176632643476] 
dist 226=[-1.6368632335489958066 ,.92270766567668892209] 
dist 227=[-1.6288528987914261632 ,.91642117594161720518] 
dist 228=[-1.5819923739411180860 ,.90236485335821840576] 
dist 229=[-1.5687002330014556140 ,.8948810880574356534 ] 
dist 230=[-1.5206717642772913181 ,.88307705814906556836] 
dist 231=[-1.5110289593097783902 ,.94833308239145937113] 
dist 232=[-.14034557385931815386,1.0292237486828255047 ] 
dist 233=[-.08085486810609166643,1.0744553652282505647 ] 
dist 234=[.05384600572479911233,1.1021388803495984745 ] 
dist 235=[.07763747935341457478,1.1130303148775840165 ] 
dist 236=[.1151502085340814007 ,1.1171142559412847680 ] 
dist 237=[.08644887077507359258,1.1176421182051733536 ] 
dist 238=[.04544341598512197045,1.1156663957758612328 ] 
dist 239=[-.07044920774517492175,1.1106941811639227095 ] 
dist 240=[-.29179324284685876946,.91795632784323504255] 
dist 241=[-.43735655037274561428,.89138028864367904667] 
dist 242=[-.55498022726551246803,.82280785007063197325] 
dist 243=[-.66487398818598579948,.80877870141474346642] 
dist 244=[-.76110545176240630615,.74114703786305858962] 
dist 245=[-.82423054715133993478,.73727626020222273596] 
dist 246=[-.87505976098703308348,.7265319792971249796 ] 
dist 247=[-.92224299431356501061,.7211088008403620064 ] 
dist 248=[-.9627796260337375331 ,.6252434911171182886 ] 
dist 249=[-.98709596684259722492,.6095588042683692262 ] 
dist 250=[-1.0041352381815900930 ,.5717704777395549590 ] 
dist 251=[-1.0156448392591018777 ,.5606066141869783865 ] 
dist 252=[-1.0226909617090367193 ,.5000136697156231997 ] 
dist 253=[-1.0219262496222354786 ,.4868777738893387210 ] 
dist 254=[-1.0168502351759324617 ,.4599517668883812674 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 0, 2, 1, 0, 1] 
dist 0=[67.971538867853150723  ,67.971538867853150723  ] 
dist 1=[67.749207736095580077  ,67.953952898304630054  ] 
dist 2=[67.284520631552618680  ,67.971538867853150723  ] 
dist 3=[66.366594696500947617  ,67.583632668326622623  ] 
dist 4=[65.145639252293430141  ,67.078654753852225599  ] 
dist 5=[63.470997452762199693  ,66.820325923612373764  ] 
dist 6=[61.140421122114464455  ,65.397388416986270679  ] 
dist 7=[57.300225507696727095  ,63.423290716101489779  ] 
dist 8=[53.330627413844185829  ,62.999979682390806537  ] 
dist 9=[50.483273282852308063  ,62.123525933918591876  ] 
dist 10=[47.907800986864359518  ,61.795308305762939148  ] 
dist 11=[45.023699449963258144  ,61.387829378025823142  ] 
dist 12=[41.225717287802239685  ,61.181616925618466287  ] 
dist 13=[34.615618975141472143  ,60.481145872495932928  ] 
dist 14=[29.890048595295576433  ,40.311372968816525821  ] 
dist 15=[25.037719432820212530  ,40.081494769463295053  ] 
dist 16=[20.961547177270012826  ,29.828370436393946908  ] 
dist 17=[16.869386845330351342  ,28.546732832580474284  ] 
dist 18=[13.070899210311859102  ,25.968673366673091076  ] 
dist 19=[10.166899513741671672  ,25.309503956193669632  ] 
dist 20=[7.3551915025192430008 ,22.994934225885623824  ] 
dist 21=[3.9243880506383078751 ,22.499277045507774237  ] 
dist 22=[.67617005678623047114,21.852418547988868385  ] 
dist 23=[-1.4069044557379772552 ,21.671505631784404423  ] 
dist 24=[-3.0430408703619829179 ,4.4054985245408645151 ] 
dist 25=[-4.5070736705866274663 ,2.9880959020015565291 ] 
dist 26=[-5.7592802124795613097 ,-.08653462319497034572] 
dist 27=[-6.5503455625473590530 ,-.66726594496205889654] 
dist 28=[-7.1640198871745659920 ,-1.5118201096338648388 ] 
dist 29=[-8.3610772325851211350 ,-3.7945839026046034677 ] 
dist 30=[-9.9218726921736413617 ,-5.5904244969226627740 ] 
dist 31=[-11.785411961482888499  ,-5.7746850805594339939 ] 
dist 32=[-13.530896690031678675  ,-6.9386731421849875238 ] 
dist 33=[-14.620115016830294258  ,-7.0458197205615483916 ] 
dist 34=[-15.441051152675556410  ,-6.8906498502476838816 ] 
dist 35=[-16.114830959366921520  ,-6.3431818165117345865 ] 
dist 36=[-16.645619572443693180  ,-5.5909484327775054651 ] 
dist 37=[-16.895384919067501800  ,-4.6182464181970027190 ] 
dist 38=[-16.999481329389281496  ,-3.3011999214019035782 ] 
dist 39=[-16.998983704293543096  ,-1.0152431789306549202 ] 
dist 40=[-10.027811326196948369  ,1.4667507234881240868 ] 
dist 41=[-9.5088055471560025420 ,3.1219434056576835223 ] 
dist 42=[-9.3776535092255716065 ,4.4853798641996124224 ] 
dist 43=[-9.1360396873322183003 ,5.8037449790415716115 ] 
dist 44=[-9.0609448488917765643 ,6.9899284830220647197 ] 
dist 45=[-5.2425406766225000219 ,7.8262190565531924490 ] 
dist 46=[-4.8297420585761141138 ,8.5656082748267329927 ] 
dist 47=[-3.8965995827052897489 ,9.3654543822818052184 ] 
dist 48=[-3.6887759752117912896 ,10.081901573821031387  ] 
dist 49=[-2.5076558112653845155 ,10.488538831883980301  ] 
dist 50=[-2.2885849279686509178 ,10.746092196427214416  ] 
dist 51=[-1.8407712472886984962 ,10.867431864926800496  ] 
dist 52=[-1.7217623522771596425 ,10.918892866310277382  ] 
dist 53=[-.5167121671696942024 ,10.897683178075869998  ] 
dist 54=[-.3305064439589090094 ,10.833972334793637246  ] 
dist 55=[.0031574734357669179 ,10.783098307203803129  ] 
dist 56=[.0771925072096350925 ,7.3198354970301290817 ] 
dist 57=[.2563460869171866643 ,6.9495744034749122374 ] 
dist 58=[.25765281867894143465,6.0706380626595031291 ] 
dist 59=[-.06343591666251139048,5.8044038992662652111 ] 
dist 60=[-.88703568762238308167,5.5009184221817789799 ] 
dist 61=[-1.5440260411344890455 ,5.4840376854297362352 ] 
dist 62=[-2.2030951067881480247 ,-.54099215761074096664] 
dist 63=[-3.0350145201805540709 ,-.73785912227698818466] 
dist 64=[-3.8288984804744964890 ,-1.1715287350045352993 ] 
dist 65=[-4.3362700020598218971 ,-1.2436111613479838544 ] 
dist 66=[-4.7296728664166951705 ,-1.7092462990033671434 ] 
dist 67=[-5.0689856228746334436 ,-1.7804805913927844001 ] 
dist 68=[-5.3465239302579662866 ,-1.9185560817739444452 ] 
dist 69=[-5.4935303630319162819 ,-1.9400524172161950519 ] 
dist 70=[-5.5726813527153240424 ,-1.6200070816887110088 ] 
dist 71=[-5.5844627957309503237 ,-1.0258565691322722761 ] 
dist 72=[-4.1753571648099866129 ,-.41469565987125041687] 
dist 73=[-4.2059475757574422550 ,-.00415119230313580806] 
dist 74=[-4.2120392765096768990 ,.33673358869180119399] 
dist 75=[-4.2140811205517790095 ,.67011537534115432295] 
dist 76=[-4.2136278268462759564 ,.97185361937042914996] 
dist 77=[-4.2097123701064832462 ,1.1865543914421039734 ] 
dist 78=[-3.3044776678572776162 ,1.3779302708645797300 ] 
dist 79=[-3.1900756301333515338 ,1.5866560659827899133 ] 
dist 80=[-2.8972842003168448992 ,1.7866043039353297995 ] 
dist 81=[-2.8420919046706545640 ,2.0829548418696628433 ] 
dist 82=[-2.3480538468715535366 ,2.4445530141337529573 ] 
dist 83=[-2.2481376891400776913 ,2.6876461204150230206 ] 
dist 84=[-2.1099372055158462990 ,2.8899662547713758248 ] 
dist 85=[-2.0644629363998751552 ,3.0889501322225559104 ] 
dist 86=[-1.1074998036221474840 ,3.2630855571827808622 ] 
dist 87=[-.98254739450453996356,3.3662957969611464631 ] 
dist 88=[-.70215911319850962414,3.4371500637274012609 ] 
dist 89=[-.64102978531991614696,3.4822199622224093380 ] 
dist 90=[-.3001494453423638596 ,3.5072314547544233952 ] 
dist 91=[-.23917804771873179018,3.5056585007538023988 ] 
dist 92=[-.13597794922588605711,3.4768749564365126045 ] 
dist 93=[-.2104419770557830296 ,3.4538103576890680580 ] 
dist 94=[-.28998350926162446327,.47006957889409025949] 
dist 95=[-.39179726295332751773,.45374863952812759266] 
dist 96=[-.58237572068552571051,-.05967615370770776989] 
dist 97=[-.71641286152352087312,-.12053314983908977586] 
dist 98=[-1.0339253140642163070 ,-.2550255783072070813 ] 
dist 99=[-1.2629275615775140635 ,-.27809606376737760886] 
dist 100=[-1.4703753577342639580 ,-.42389831571368247117] 
dist 101=[-1.7019369469862698531 ,-.44640908617227187063] 
dist 102=[-1.9151519693807635155 ,-.491110532798224744  ] 
dist 103=[-2.0494280771606566548 ,-.49771670342089250572] 
dist 104=[-2.1512893430501224440 ,-.89856861332591312951] 
dist 105=[-2.2352093817222443825 ,-.92403302178486005865] 
dist 106=[-2.3009422775724096215 ,-.96820609363758635575] 
dist 107=[-2.3302591387168244074 ,-.97525100501515748517] 
dist 108=[-2.3389880545679788691 ,-.97258303787034216144] 
dist 109=[-2.3369128735504657450 ,-.9510141546919564892 ] 
dist 110=[-1.2575383055393557241 ,-.91237866376249803099] 
dist 111=[-1.1643745257633979343 ,-.70179671943458660203] 
dist 112=[-.93244495461733684545,-.51253292745844854794] 
dist 113=[-.89827948376729035935,-.31350706555234293   ] 
dist 114=[-.80863469579454798963,-.12414340017283458192] 
dist 115=[-.79662312426607366567,.02659693605628175752] 
dist 116=[-.74744734917173054784,.17749924939233013291] 
dist 117=[-.7354587180920027344 ,.36752408937632137572] 
dist 118=[-.70783719130443850886,.54862454941312465865] 
dist 119=[-.69836878846043978489,.66394198052363738227] 
dist 120=[-.07648124518193953499,.75288608061391327472] 
dist 121=[-.02062642220284140670,.82881087083873306452] 
dist 122=[.09398082871276300084,.89075919495287853914] 
dist 123=[.12278027291459729765,.92395025303252734827] 
dist 124=[.2217381148997441006 ,.94243772969217786889] 
dist 125=[.24169311094216177998,.94671359546992356494] 
dist 126=[.26049207584785975104,.94729122369785559947] 
dist 127=[.25645672673460161693,1.0042937824360252608 ] 
dist 128=[.24325184961583783727,1.0913887571438404582 ] 
dist 129=[.21890531307750783061,1.1431059475317513576 ] 
dist 130=[.18181000184321170038,1.1787560294796140578 ] 
dist 131=[.11773886202250147743,1.2017478803847372752 ] 
dist 132=[.04140004544232125917,1.2159465301376144302 ] 
dist 133=[-.04463870730760065062,1.2177870452721007854 ] 
dist 134=[-.15409669304209037494,1.2352637698856761753 ] 
dist 135=[-.32386599294200664494,1.2547404430788359577 ] 
dist 136=[-.5114497137598965733 ,1.2689595222779984716 ] 
dist 137=[-.67747986090833821607,1.2796886026365616199 ] 
dist 138=[-.81558406579479712472,1.2873112372613915959 ] 
dist 139=[-.95131127440507771867,1.2891283807952417316 ] 
dist 140=[-1.0748060031338195474 ,1.2870028750968772722 ] 
dist 141=[-1.2231349713952564507 ,1.2821092343559915351 ] 
dist 142=[-1.5865096491752582085 ,1.2686107863010205272 ] 
dist 143=[-1.8191490379448674343 ,1.2598746163294243375 ] 
dist 144=[-2.0001501952438220288 ,1.2447968226928360254 ] 
dist 145=[-2.1575329694361569090 ,1.2380857222146048411 ] 
dist 146=[-2.2873566925905174883 ,1.2022710122635098778 ] 
dist 147=[-2.3584226921936111206 ,1.1918077387376997659 ] 
dist 148=[-2.3999517206901180142 ,1.1569044662190555146 ] 
dist 149=[-2.4119533034704693338 ,1.1477793115935696367 ] 
dist 150=[-2.4105931913461758273 ,1.0532586569331302385 ] 
dist 151=[-2.4012854615072028637 ,1.0336128480221670180 ] 
dist 152=[-2.3799518182417365531 ,.9855982617993347253 ] 
dist 153=[-2.3674879925779546545 ,.96901634042042540177] 
dist 154=[-2.2892661406988703276 ,1.0349356091963825217 ] 
dist 155=[-2.2678388203962797687 ,1.1959009179453302518 ] 
dist 156=[-2.1989887961590177989 ,1.3363479746422201143 ] 
dist 157=[-2.1805236723865700458 ,1.4275970230795766491 ] 
dist 158=[-.8078628959653250719 ,1.5001004781771440863 ] 
dist 159=[-.79246373801267790006,1.5657739536124921141 ] 
dist 160=[-.53761685670672496704,1.6205872220736654290 ] 
dist 161=[-.50201717164696581019,1.6497696661028524030 ] 
dist 162=[-.41412827058781428591,1.8736060002451221861 ] 
dist 163=[-.39998339384528178756,2.0286484507168476208 ] 
dist 164=[-.26660395153357948726,2.1517181751522697073 ] 
dist 165=[-.24146630455373902731,2.2629817248790283883 ] 
dist 166=[-.20865147671906252455,2.3581153366899070691 ] 
dist 167=[-.19878306238132351738,2.4168423437277212194 ] 
dist 168=[-.17662264781654489762,2.4600354943033382758 ] 
dist 169=[-.31363395783391221381,2.4932020263790203333 ] 
dist 170=[-.50075812211538417561,2.5173083631027545916 ] 
dist 171=[-.68328755937915616805,2.5243588968011649512 ] 
dist 172=[-.84841299770723073258,2.5202524623400273617 ] 
dist 173=[-.96611534420316502139,2.5120722368770377452 ] 
dist 174=[-1.0713691811456053507 ,.91703629107861963813] 
dist 175=[-1.1868401964887418706 ,.78243214867686030545] 
dist 176=[-1.2916677882556804981 ,.47173163195704801793] 
dist 177=[-1.3544661484319972752 ,.41562288025581591237] 
dist 178=[-1.3983725231736278543 ,.10833943357258493642] 
dist 179=[-1.4278406653704599274 ,.05727463693444692281] 
dist 180=[-1.4462335113525109080 ,-.04502598221478019443] 
dist 181=[-1.4493308422800711772 ,-.07022389407319573999] 
dist 182=[-1.5034586926683709382 ,-.13187436853637744075] 
dist 183=[-1.6061885430876918919 ,.05657285084170388360] 
dist 184=[-1.6770323609395194685 ,.24598683441777369079] 
dist 185=[-1.7226631361034423099 ,.37092848188432472396] 
dist 186=[-1.7540656850572954358 ,.47229342547360108649] 
dist 187=[-1.7681539560689105943 ,.56766300844171117068] 
dist 188=[-1.7722286334945969656 ,.65161832588854329448] 
dist 189=[-1.7683035402985870108 ,.70745288784767980132] 
dist 190=[-.49703513758563465844,.75325335426082268349] 
dist 191=[-.48765833393643706831,.7971829058917478281 ] 
dist 192=[-.29581341455921801405,.83522181119987948666] 
dist 193=[-.27029372751869095187,.85752570624084331513] 
dist 194=[-.21003911973216860423,.87252108833308813511] 
dist 195=[-.19905860992070125343,.88140967989593820635] 
dist 196=[-.11632544779961612689,.95754403513283941355] 
dist 197=[-.10117635342187399655,1.0870533761711684702 ] 
dist 198=[-.07602657354093938734,1.2066402989126532133 ] 
dist 199=[-.07000869943653087808,1.2763628762253006073 ] 
dist 200=[.02223530993750953493,1.3227713436589322948 ] 
dist 201=[-.02120378709004603345,1.3493594213313067575 ] 
dist 202=[-.12313937311933985419,1.3659488441687376961 ] 
dist 203=[-.23320827521929080701,1.3724720517882956601 ] 
dist 204=[-.33978730320780008239,1.3728590075134964338 ] 
dist 205=[-.42780313109103179918,1.3686586731226904325 ] 
dist 206=[-.51888738701349619496,1.1693262132266274403 ] 
dist 207=[-.63770738325862096187,1.1750513529188702042 ] 
dist 208=[-.75303281757073845473,1.2005163060200128706 ] 
dist 209=[-.83017829131463737188,1.2098931076872924619 ] 
dist 210=[-.89396853363162884209,1.2121466889052257936 ] 
dist 211=[-.95602196103835856747,1.2091951065595794564 ] 
dist 212=[-1.0120549050723158444 ,1.2018759843719619914 ] 
dist 213=[-1.0518308884363705121 ,1.1969909794104949359 ] 
dist 214=[-1.0872382655926333259 ,1.1130213129660442915 ] 
dist 215=[-1.1258470971052343290 ,1.1611462094946780142 ] 
dist 216=[-1.3521613481234579164 ,1.2060867517145551706 ] 
dist 217=[-1.5225975349317455737 ,1.2374316423767066621 ] 
dist 218=[-1.6522176789381859463 ,1.2666914554292871020 ] 
dist 219=[-1.7596403284560681925 ,1.2778301394494884104 ] 
dist 220=[-1.8446661104607941507 ,1.2813186935007900750 ] 
dist 221=[-1.8849451303318185194 ,1.2800630314733284269 ] 
dist 222=[-1.9048219028076536660 ,1.2750897603602548041 ] 
dist 223=[-1.9084630861843861338 ,1.2696336624227827996 ] 
dist 224=[-1.8468014448668389046 ,1.0773314185259678356 ] 
dist 225=[-1.8289101744744552132 ,1.0554521211249554219 ] 
dist 226=[-1.7968699332447088884 ,.99562946464497271995] 
dist 227=[-1.7849151305321078140 ,.98288729478227889028] 
dist 228=[-1.7260879141918256286 ,.95641910447844757147] 
dist 229=[-1.7090825271744020552 ,.9508335253900002026 ] 
dist 230=[-1.6586469992929981212 ,.9296195637769558284 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 0, 0, 1] 
dist 0=[66.473931274059735732  ,66.473931274059735732  ] 
dist 1=[65.888766029117285826  ,66.770381321774580678  ] 
dist 2=[64.755197046449700785  ,66.789477824798575016  ] 
dist 3=[63.412346135010912628  ,66.581583754037140204  ] 
dist 4=[61.991547107474915995  ,66.435670322838812989  ] 
dist 5=[60.239075721486827689  ,65.947703560995853861  ] 
dist 6=[57.571893911927529599  ,65.695746332048963142  ] 
dist 7=[54.515297222643935581  ,64.300894294539232767  ] 
dist 8=[51.207915273921527859  ,62.374139623370224963  ] 
dist 9=[47.077683695085418435  ,60.704172265417402327  ] 
dist 10=[40.735466358197441685  ,60.365750966247343620  ] 
dist 11=[34.336599139422545776  ,59.807279826447462871  ] 
dist 12=[29.980207968034570621  ,59.682281382993288954  ] 
dist 13=[26.278912489807933104  ,57.909710413509112932  ] 
dist 14=[22.495950182215372209  ,54.588044954060850444  ] 
dist 15=[18.943332872624393054  ,39.784808068269838008  ] 
dist 16=[16.161890207362191942  ,39.570386928315090556  ] 
dist 17=[13.408762111892064661  ,29.432464746482464088  ] 
dist 18=[9.9693551396270487564 ,28.166442770908284020  ] 
dist 19=[6.6826559639726794819 ,25.628856130769678369  ] 
dist 20=[4.5392986908510664527 ,24.981955664492878418  ] 
dist 21=[2.8204564905975890096 ,22.724545177100771894  ] 
dist 22=[1.2287247569972731284 ,22.236704164671479691  ] 
dist 23=[-.16149614232360941711,21.632809311314636966  ] 
dist 24=[-1.0931727722654605190 ,21.485323292377444095  ] 
dist 25=[-2.5581156439781893174 ,4.1248032302441657637 ] 
dist 26=[-4.0313212600314989733 ,2.7093515219386469879 ] 
dist 27=[-5.3023869894890196562 ,-.37045077165199755596] 
dist 28=[-6.1250658714019870733 ,-.94392409231931916007] 
dist 29=[-6.7857470199027149999 ,-3.7303752910269688977 ] 
dist 30=[-8.1027331886723843648 ,-4.2031824352140377908 ] 
dist 31=[-9.6561190660341341425 ,-5.8280952151804460278 ] 
dist 32=[-11.515903384365371172  ,-5.7904128151148860923 ] 
dist 33=[-13.260544325039252166  ,-5.6163362172922651250 ] 
dist 34=[-14.353957944859961164  ,-5.2168547280572128941 ] 
dist 35=[-15.183565955802620514  ,-4.7556206926183215706 ] 
dist 36=[-15.874342856118840753  ,-4.3347158455579831280 ] 
dist 37=[-16.426069657648060957  ,-3.8658570956355162779 ] 
dist 38=[-16.700211864107717027  ,-3.2124700033094353457 ] 
dist 39=[-16.824678127470444380  ,-2.4930405256720964506 ] 
dist 40=[-16.837637913886848200  ,-1.7602413814443926342 ] 
dist 41=[-6.2901369187568520294 ,.30566172434164898663] 
dist 42=[-6.2714162650435664348 ,1.8224047625236475303 ] 
dist 43=[-5.5242724947371819368 ,3.0684077757274162127 ] 
dist 44=[-5.4314858159017054581 ,4.2678129761816264760 ] 
dist 45=[-5.3242142090520930194 ,5.3434214076856931456 ] 
dist 46=[-5.2853347981621402994 ,6.0956535721091545218 ] 
dist 47=[-3.4637502634658436044 ,6.7543033256413971915 ] 
dist 48=[-3.3233857709768483116 ,7.4567150490728953880 ] 
dist 49=[-3.1256609340320914190 ,8.0883372994250057051 ] 
dist 50=[-3.0625318962486199872 ,8.4645895730323702889 ] 
dist 51=[-1.7429105109432829752 ,8.7258508918165294713 ] 
dist 52=[-1.5671743446120574184 ,8.8986226476263932998 ] 
dist 53=[-1.1821703458615370279 ,9.0016234617872505680 ] 
dist 54=[-1.0848954755267781591 ,9.0187615166077640797 ] 
dist 55=[-.63093582782086338929,8.9386581644277556261 ] 
dist 56=[-.54664267564757610586,8.9270100314503738207 ] 
dist 57=[-.34722584373206379201,5.5181824062122209984 ] 
dist 58=[-.30870370812553939643,5.4850175804170979437 ] 
dist 59=[-.48175412332297443781,4.6240664201421660926 ] 
dist 60=[-1.3399175052710287353 ,4.6849997662779193552 ] 
dist 61=[-2.1316089903488891014 ,4.7105321271809382333 ] 
dist 62=[-2.7217787346257049407 ,4.7064488543333184818 ] 
dist 63=[-3.2759440632984356765 ,1.7971749849953386206 ] 
dist 64=[-3.9240892365110281969 ,1.6951917108776513534 ] 
dist 65=[-4.5250945274719552495 ,-.21148602441905179428] 
dist 66=[-4.8912544016612693761 ,-.44692235835771648545] 
dist 67=[-5.1547631998717484172 ,-.98767093686976084701] 
dist 68=[-5.3463240386395556014 ,-1.0678883563983688934 ] 
dist 69=[-5.4846388668785115416 ,-1.4203485211015135858 ] 
dist 70=[-5.5357596439147425935 ,-1.4446428218259979691 ] 
dist 71=[-5.5452778925748671820 ,-1.6573473160766288032 ] 
dist 72=[-5.5291285420276953605 ,-1.4644859478438257164 ] 
dist 73=[-3.6572821514358551814 ,-.9920486639065530784 ] 
dist 74=[-3.6648110594723293526 ,-.66588059259011825087] 
dist 75=[-2.0791452880755935266 ,-.38575487623958484208] 
dist 76=[-2.0816871821267903123 ,.02461061072329859759] 
dist 77=[-2.0710048049644638363 ,.43591419162707856279] 
dist 78=[-2.0589897021240407989 ,.74445602030517671029] 
dist 79=[-1.0052125098338119815 ,1.0359238480023589162 ] 
dist 80=[-.90892703186443743868,1.3791787741061677429 ] 
dist 81=[-.69214878965038657791,1.7010456423696166530 ] 
dist 82=[-.64529313379746122561,1.9072247547130260240 ] 
dist 83=[-.38156152344483636984,2.0676280873244395856 ] 
dist 84=[-.33468302453854028175,2.2069191369048653504 ] 
dist 85=[-.23587689197225915368,2.3215566697089933785 ] 
dist 86=[-.21088836311587144991,2.3836294442329544823 ] 
dist 87=[-.01497221508665110563,2.4189318052836543440 ] 
dist 88=[.01773319045886320319,2.4267950059757183030 ] 
dist 89=[.04804632322630668789,1.4839774958341526213 ] 
dist 90=[.04353759703859728964,1.5116254230766833666 ] 
dist 91=[.02372049715721527033,1.5418652542748811972 ] 
dist 92=[-.08919859823929691318,1.5563308746555255397 ] 
dist 93=[-.19679838246611588665,1.5619646127151605731 ] 
dist 94=[-.27597266220025100664,1.5573348399288841419 ] 
dist 95=[-.34897676837955418063,1.4351771001145465673 ] 
dist 96=[-.43198156763173918371,1.4364361621887338501 ] 
dist 97=[-.50864735716884525863,1.4334240121303149484 ] 
dist 98=[-.5893449289435792843 ,1.4280670485810952159 ] 
dist 99=[-.73988583654075045838,1.4122413951650192442 ] 
dist 100=[-.85837662064814655958,1.4027839021127375773 ] 
dist 101=[-.975754010011193902  ,1.3865158160042049884 ] 
dist 102=[-1.1218838616518808390 ,1.3794012068500960701 ] 
dist 103=[-1.2604062277485135115 ,1.3425457400139781574 ] 
dist 104=[-1.3474583951598698382 ,1.3316562091719241042 ] 
dist 105=[-1.5467404331015376572 ,1.2964240037801675521 ] 
dist 106=[-1.6782661528695286723 ,1.2863572724046298495 ] 
dist 107=[-1.7847666503891379156 ,1.1942382837380844361 ] 
dist 108=[-2.0536091533127197154 ,1.1726318920405375559 ] 
dist 109=[-2.2645142574403713891 ,1.1359085323366173138 ] 
dist 110=[-2.4510390248037244322 ,1.1246604050682961147 ] 
dist 111=[-2.6073000089266205180 ,1.0877641422428450841 ] 
dist 112=[-2.6974743262807615004 ,1.3053910552628126880 ] 
dist 113=[-2.7564129632053481102 ,1.4775042242387356517 ] 
dist 114=[-2.7880719339836548297 ,1.6316915369983155387 ] 
dist 115=[-2.8037551103190775281 ,1.7618980726880402600 ] 
dist 116=[-2.7999552788636832155 ,1.8383665308422913455 ] 
dist 117=[-2.7836767283696947693 ,1.8897951631596028171 ] 
dist 118=[-2.7700011912728927160 ,1.9201217880838509958 ] 
dist 119=[-2.6756900620530732870 ,1.9386425952477910340 ] 
dist 120=[-2.6485108367748886053 ,1.9429929568213283949 ] 
dist 121=[-2.5799290826905954005 ,1.9376889288969732871 ] 
dist 122=[-2.5525028003515133796 ,2.2314776837186890694 ] 
dist 123=[-1.4981528548279269874 ,2.5272275611347675287 ] 
dist 124=[-1.4659169626246962971 ,2.7970999861098995621 ] 
dist 125=[-1.3290524844008303755 ,3.0291053892421181397 ] 
dist 126=[-1.2997368687660961548 ,3.1738009659493166892 ] 
dist 127=[-1.2215487444651634620 ,3.2820189182284124119 ] 
dist 128=[-1.2044332965234929212 ,3.3685172309021151450 ] 
dist 129=[-1.0566438045739625970 ,3.4337200392954094157 ] 
dist 130=[-1.0255865290010580950 ,3.4569863637599225680 ] 
dist 131=[-.97254178377864710761,3.4576544450449220381 ] 
dist 132=[-.95790858909066770883,3.4491220219148006184 ] 
dist 133=[-.91231040957680650772,3.3627734288003659241 ] 
dist 134=[-.89696326892943586149,3.3339070220043930883 ] 
dist 135=[-.8857921315852635204 ,3.2623843998547322935 ] 
dist 136=[-.87986965303425745273,3.2323421424309997081 ] 
dist 137=[-.98313042441147679288,3.0488841032193660924 ] 
dist 138=[-1.4964966544586491456 ,3.0319708984125618588 ] 
dist 139=[-1.9128576830814002017 ,1.4745802701138997914 ] 
dist 140=[-2.3044710043561797522 ,1.3336278142789502646 ] 
dist 141=[-2.6492283232633745469 ,1.0047742276127092389 ] 
dist 142=[-2.8786833565102605512 ,.94299531337393609983] 
dist 143=[-3.0671599373651448730 ,.50425518896648437999] 
dist 144=[-3.2484584902613733603 ,.42456696416420421438] 
dist 145=[-3.4056941186099929320 ,.28367918275821702908] 
dist 146=[-3.4981836119664958096 ,.25265031239460035701] 
dist 147=[-3.5607829328710244444 ,-.23541652859219684106] 
dist 148=[-3.5987821684470476330 ,-.30165426281096060975] 
dist 149=[-3.6179770780914329059 ,-.42599285390219633179] 
dist 150=[-3.6144921376579239564 ,-.45355864852605125829] 
dist 151=[-3.5823388878881192051 ,-.52351493455429125955] 
dist 152=[-3.5584111883945650522 ,-.52470485530930869244] 
dist 153=[-2.3700796201830356629 ,-.37840523296161566196] 
dist 154=[-2.3650043407957152582 ,.06469624201372460789] 
dist 155=[-1.1107923104015601560 ,.43958937949822548048] 
dist 156=[-1.0370441385795059264 ,.81829581678433980914] 
dist 157=[-.51577163519388202282,1.1694898636419010672 ] 
dist 158=[-.42155869288175351827,1.4346370124490924456 ] 
dist 159=[-.30306674388827233678,1.6869698467775100169 ] 
dist 160=[-.32408008143035486127,1.9870473113002657680 ] 
dist 161=[-.36096742189734806288,2.2654360594450437755 ] 
dist 162=[-.42907302472819285074,2.4312540999298228400 ] 
dist 163=[-.50456290766633266206,2.5465695362062882335 ] 
dist 164=[-.57090568366909071781,2.6238460990659088307 ] 
dist 165=[-.64311977387652340493,2.6785482421155893238 ] 
dist 166=[-.74202920948792271141,2.7070214261899442132 ] 
dist 167=[-.8502773546526104178 ,2.7216716194432510096 ] 
dist 168=[-.95974286634771050851,2.7212309493186079616 ] 
dist 169=[-1.0908372508347673857 ,1.4947443299138720203 ] 
dist 170=[-1.2853620383859573606 ,1.7372561974327417016 ] 
dist 171=[-1.4766867586838529818 ,1.9716472741944269813 ] 
dist 172=[-1.5950155666017749941 ,2.1111348085219912893 ] 
dist 173=[-1.6822883857275100418 ,2.2075589849434925256 ] 
dist 174=[-1.7497301987572030470 ,2.2701633596925805857 ] 
dist 175=[-1.7999234297873252082 ,2.3138996844052904600 ] 
dist 176=[-1.8183913835259427262 ,2.3350550180562159591 ] 
dist 177=[-1.8238365496994716000 ,2.3436841559208446804 ] 
dist 178=[-1.8220826121783281079 ,2.3386173931554424742 ] 
dist 179=[-1.7207915345943342506 ,2.0322459744487912449 ] 
dist 180=[-1.6985830614635202984 ,1.9833553130596832091 ] 
dist 181=[-1.6482916199976581540 ,1.8964634178284891668 ] 
dist 182=[-1.6379395936382868960 ,1.8725311798929888924 ] 
dist 183=[-1.6457591428323000983 ,1.7861962269247038981 ] 
dist 184=[-1.8814849930812146792 ,1.7595754991425653527 ] 
dist 185=[-2.1137505494973164160 ,1.7207829488732843431 ] 
dist 186=[-2.2505607588428714734 ,1.7056423213593391078 ] 
dist 187=[-2.3434093733169754748 ,1.7313004027190767392 ] 
dist 188=[-2.4003032906540621804 ,1.8107363472851522209 ] 
dist 189=[-2.4384130612379806670 ,1.8711018498292385078 ] 
dist 190=[-2.4563259265845068723 ,1.8946553987069560446 ] 
dist 191=[-2.4628499925883290914 ,1.9034351322310416874 ] 
dist 192=[-2.4563033755905347905 ,1.9048703187896606993 ] 
dist 193=[-2.1122447962836544586 ,1.8203988746263041739 ] 
dist 194=[-2.0582979120330124354 ,1.7999955883671511993 ] 
dist 195=[-1.9611057013896858011 ,1.7535544375584622269 ] 
dist 196=[-1.9344156013004070666 ,1.7358393731514672399 ] 
dist 197=[-1.8378011045421187749 ,1.6438379874168059806 ] 
dist 198=[-1.8089447551394451738 ,1.6216545699990153451 ] 
dist 199=[-1.7660899808622482891 ,1.5592000145852291201 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 2, 2, 0, 1, 2] 
dist 0=[10.912452776026056659  ,10.912452776026056659  ] 
dist 1=[8.6388541584102944149 ,12.008738442569095476  ] 
dist 2=[5.2037683744812431280 ,14.112003229506715819  ] 
dist 3=[0                     ,16.500658683607430255  ] 
dist 4=[16.365055542440306686  ,18.169782391576029777  ] 
dist 5=[17.172765519733086160  ,19.633947588721704234  ] 
dist 6=[18.311064218030352730  ,21.204651853477646719  ] 
dist 7=[18.594362301630426350  ,22.635039947674898618  ] 
dist 8=[22.463337873078896051  ,23.539030262505666134  ] 
dist 9=[22.923265276967987020  ,24.232469488396563774  ] 
dist 10=[23.424313365580384226  ,24.821989433019112496  ] 
dist 11=[23.138369671470838040  ,25.301039898725607443  ] 
dist 12=[22.430202160762769798  ,25.553312888140983355  ] 
dist 13=[21.329936321706342876  ,25.688280836862535369  ] 
dist 14=[19.410529339915160452  ,25.698879584190670793  ] 
dist 15=[17.405591853121246884  ,25.615134528813041532  ] 
dist 16=[15.963855444364923239  ,16.999841597499311745  ] 
dist 17=[14.660877295599528820  ,16.289742008401279560  ] 
dist 18=[13.209120282112901956  ,14.788802779474160112  ] 
dist 19=[11.774499634356202194  ,14.302354100742085207  ] 
dist 20=[10.539562396519408201  ,12.054903283559989386  ] 
dist 21=[9.2147595468244016284 ,11.548665652742946934  ] 
dist 22=[7.4210468451227645654 ,11.194737444343981389  ] 
dist 23=[5.6419263741956545956 ,10.670909719413471725  ] 
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dist 56=[-.26479480387608048734,7.1032043837777252995 ] 
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dist 58=[.1989338300021151818 ,7.4304987612518643783 ] 
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dist 65=[-2.0425050710535177303 ,-.90848107435361695789] 
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dist 67=[-3.3912955438472518419 ,-2.1263095297735739680 ] 
dist 68=[-3.8283271380119341496 ,-3.3784941216377127113 ] 
dist 69=[-4.2024912683959324424 ,-3.5797240039269353171 ] 
dist 70=[-4.5875670424247511487 ,-3.8623954100171888395 ] 
dist 71=[-4.9320117015970166932 ,-3.9734311104626512889 ] 
dist 72=[-5.1441177758201746918 ,-4.5969464670835101576 ] 
dist 73=[-5.2995247685783298881 ,-4.5489239809305373796 ] 
dist 74=[-5.4177856259647497137 ,-4.3360291109628195535 ] 
dist 75=[-5.5277005983090046877 ,-4.0343703353681268457 ] 
dist 76=[-5.6130950959966307120 ,-3.6323164087711331155 ] 
dist 77=[-5.6366008497341803622 ,-3.0809287431456534347 ] 
dist 78=[-5.6260800744787033001 ,-2.1836731593954464057 ] 
dist 79=[-5.6070516343772845451 ,-1.2661787077339575030 ] 
dist 80=[-2.5061765781253335137 ,-.63406505097578994078] 
dist 81=[-2.2353751764542118303 ,-.09171339540356655025] 
dist 82=[-1.6015407666344540520 ,.4677954137651948572 ] 
dist 83=[-1.4868878094718571465 ,.9935957334078496142 ] 
dist 84=[-.64220660314738928771,1.4015117654005189804 ] 
dist 85=[-.49054989936833718553,1.8000513386174114688 ] 
dist 86=[-.23106264022399779584,2.2884551982237122980 ] 
dist 87=[-.17262537808658037782,2.7471653577079611873 ] 
dist 88=[.73422806735255969141,3.0272773761965486616 ] 
dist 89=[.85549464878530035973,3.2294169664935569069 ] 
dist 90=[1.0716113595286301583 ,3.3771497441986258205 ] 
dist 91=[1.1174691503485197322 ,3.4884560668479952492 ] 
dist 92=[1.1409008269064506726 ,3.5703844726052364536 ] 
dist 93=[1.0661963410589167055 ,3.6288755598286672458 ] 
dist 94=[.89955705529020818766,3.6564542068761492205 ] 
dist 95=[.65783470709493394453,3.6543148791705849830 ] 
dist 96=[.34532683816191658049,.72458645296385662568] 
dist 97=[.07744990041609377712,.65539442112486920494] 
dist 98=[-.19847982308180439762,.5200242260593061748 ] 
dist 99=[-.45752625739925323009,.48604213806374395675] 
dist 100=[-.65807820473729076591,.3765536201270182807 ] 
dist 101=[-.85364950362395562073,.36936021586734134944] 
dist 102=[-1.0928452799923038733 ,.3846862733602840950 ] 
dist 103=[-1.3173688298570812576 ,.4113076461570045419 ] 
dist 104=[-1.4544295547394368320 ,.4491544953963684409 ] 
dist 105=[-1.5533437603731258207 ,.5024245035960107888 ] 
dist 106=[-1.6257335778062502538 ,.5905377238370356652 ] 
dist 107=[-1.6804126208898149114 ,.6940300842670978998 ] 
dist 108=[-1.7086819931638546411 ,.8086239814122272507 ] 
dist 109=[-1.8129270039868705051 ,.95297115737074306445] 
dist 110=[-2.0554758895704219866 ,1.1751112585004743359 ] 
dist 111=[-2.2872441849619136537 ,1.3961353775298272585 ] 
dist 112=[-2.4223977600010866459 ,1.5360251130786059901 ] 
dist 113=[-2.5125132622352130355 ,1.6428460540685885785 ] 
dist 114=[-2.5646075330373503569 ,1.7319797858531001226 ] 
dist 115=[-2.5973837064079241559 ,1.8025483436280886353 ] 
dist 116=[-2.6104237364288773456 ,1.8353204737118662670 ] 
dist 117=[-2.6115301560700989382 ,1.8500325981322345030 ] 
dist 118=[-2.6037317118611323303 ,1.8491855882118257328 ] 
dist 119=[-2.5850920461205870483 ,1.8349837192432292525 ] 
dist 120=[-2.2074661165443230404 ,1.8010134340593703415 ] 
dist 121=[-2.1487473183163569836 ,1.7878915213597311494 ] 
dist 122=[-2.0372102442363536194 ,1.7547456350562006187 ] 
dist 123=[-2.0056110036373388978 ,1.7398291029502049269 ] 
dist 124=[-1.8833641468157503595 ,1.6552256510268061270 ] 
dist 125=[-1.8511280940291884769 ,1.6334177043542552087 ] 
dist 126=[-1.8003628911939241426 ,1.5779170060245076822 ] 
dist 127=[-1.7680757283897627916 ,1.5566991413818315240 ] 
dist 128=[.73119100160149165585,1.0809120531911328116 ] 
dist 129=[.91166337440282128281,1.3718162950689969606 ] 
dist 130=[1.3149000542516534852 ,1.6435065285031354672 ] 
dist 131=[1.3778475243422908784 ,1.8813936802023944282 ] 
dist 132=[1.8275101358455138599 ,2.0374581456899679707 ] 
dist 133=[1.8969400861311060298 ,2.1631718203698442416 ] 
dist 134=[2.0216061397699354168 ,2.2799921621525512488 ] 
dist 135=[2.0432817656113239621 ,2.3802980757869324640 ] 
dist 136=[2.1575635373338265663 ,2.4401351357701462935 ] 
dist 137=[2.0985247171491331823 ,2.4816832112997894557 ] 
dist 138=[1.9633047923261850421 ,2.5090302475912234309 ] 
dist 139=[1.7898467659773041410 ,2.5251053353001430002 ] 
dist 140=[1.5782760638494554386 ,2.5221972142828371942 ] 
dist 141=[1.2987299588772027407 ,2.5100718698339193224 ] 
dist 142=[.8541200676266875107 ,2.4959141678503401927 ] 
dist 143=[.40197391308910685084,2.4832922417634401512 ] 
dist 144=[.0923649670294374788 ,1.0326114683080374267 ] 
dist 145=[-.17146719942146621415,.90484198196612586803] 
dist 146=[-.44101380452948382097,.61001948016094805378] 
dist 147=[-.69290251010337216344,.55491612352066252979] 
dist 148=[-.88629901896833067633,.17524873184304148008] 
dist 149=[-1.0734761412691211772 ,.10773919848797717901] 
dist 150=[-1.3005567256076183565 ,-.01456002903667489952] 
dist 151=[-1.5129498060013248079 ,-.04157297810199117028] 
dist 152=[-1.6415395665246594245 ,-.40746404714182889889] 
dist 153=[-1.7330976740411775986 ,-.45845115291707090241] 
dist 154=[-1.7977737104944225330 ,-.53732368080345702617] 
dist 155=[-1.8453777371719663797 ,-.55568067841367130495] 
dist 156=[-1.8688369596925847377 ,-.53705650263935639167] 
dist 157=[-1.8790554869831517441 ,-.48064883891229760767] 
dist 158=[-1.8835466406214024407 ,-.37115312624092014953] 
dist 159=[-1.8812943868527566208 ,-.2297402135068410972 ] 
dist 160=[-.24541832918249009768,-.05353765402017545197] 
dist 161=[-.20388208498033278898,.09582734844365529328] 
dist 162=[-.12234287079724713414,.24714631714681064905] 
dist 163=[-.10226778948432755254,.38772777607399043024] 
dist 164=[-.03996518736474422162,.49426368071085883371] 
dist 165=[-.03667407316089405385,.5960279601952807455 ] 
dist 166=[-.04820736710908570996,.7175775748575351190 ] 
dist 167=[-.06682961451150110417,.8307119948454416572 ] 
dist 168=[-.09181434564418112500,.8989101336767953753 ] 
dist 169=[-.12619157297116424788,.9471064412604508054 ] 
dist 170=[-.1822773012611113078 ,.9804574929625418302 ] 
dist 171=[-.24786882780062002739,1.0046609518435669480 ] 
dist 172=[-.32016196269524482694,1.0228316282494865421 ] 
dist 173=[-.41104477641566230838,1.0397519495988515379 ] 
dist 174=[-.55078568943002900957,1.1448172380266222428 ] 
dist 175=[-.69010355838197552086,1.2440880691842606955 ] 
dist 176=[-.77929842366623195031,1.2998549147974225813 ] 
dist 177=[-.84865557444973821015,1.3343499923443137833 ] 
dist 178=[-.90884438532477985848,1.3487622980780900998 ] 
dist 179=[-.95836268877464033206,1.3548240167520503856 ] 
dist 180=[-.98515672781228229564,1.3560044493295583263 ] 
dist 181=[-1.0003702244671139538 ,1.3538424859028376589 ] 
dist 182=[-1.0036947051510081921 ,1.3480868755334793078 ] 
dist 183=[-1.0015333538993184019 ,1.3217579358979461409 ] 
dist 184=[-.99738812475330277347,1.0949850926333799827 ] 
dist 185=[-.98938279164761965434,1.0610507252619389407 ] 
dist 186=[-.97960649981003331527,1.0082792512936062030 ] 
dist 187=[-.97294499629353558973,.97894879118586477478] 
dist 188=[-.93578259131120421172,.92369027240990175499] 
dist 189=[-.92562947116407863186,.89519476075929941923] 
dist 190=[-.89806095201034521701,.88209289433884810814] 
dist 191=[-.88718811245711705643,.85517439852198041795] 
dist 192=[-.5876294755805881549 ,-.39224909455782442281] 
dist 193=[-.73936583004581598222,-.4840766822197479837 ] 
dist 194=[-.88288359194577871388,-.54645642143898041658] 
dist 195=[-1.0097969715256699274 ,-.5204591117820866598 ] 
dist 196=[-1.0952953984978067813 ,-.4910018111541188673 ] 
dist 197=[-1.1666646261979671330 ,-.4534489386423621722 ] 
dist 198=[-1.2372136341238044873 ,-.3951558095060521569 ] 
dist 199=[-1.2986538052407816997 ,-.3342387515924677819 ] 
dist 200=[-1.3336867201776211347 ,-.2862164155564154991 ] 
dist 201=[-1.3560164204060811609 ,-.2385488638819797503 ] 
dist 202=[-1.3667830427804989439 ,-.1790419370568354629 ] 
dist 203=[-1.3692712380966694328 ,-.1166256888037702949 ] 
dist 204=[-1.3676004722220720371 ,-.0573491184161814977 ] 
dist 205=[-1.3464766954975055196 ,.0108691342558313626 ] 
dist 206=[-1.3433445276078272755 ,.1089596449734870809 ] 
dist 207=[-1.3166354396512624713 ,.2068896072369781704 ] 
dist 208=[-.70244250406552025749,.2744685985836964218 ] 
dist 209=[-.64360342166550098113,.33263887941014562286] 
dist 210=[-.50482860738503344215,.39303503773343332313] 
dist 211=[-.47908699458876639713,.5181243765684149527 ] 
dist 212=[-.28831191016794570225,.61587407656843508387] 
dist 213=[-.25319354523795200196,.70711904591208172662] 
dist 214=[-.1940235215198734823 ,.81310410294653737945] 
dist 215=[-.1800078441239447273 ,.91086566658712340294] 
dist 216=[.05426351704153025514,.9693059274243691665 ] 
dist 217=[.08527723391757405761,1.0100257961482202092 ] 
dist 218=[.0609871738850768114 ,1.0370965735306465835 ] 
dist 219=[-.0202164221820880161 ,1.0556602604490928452 ] 
dist 220=[-.1055300246254789215 ,1.0624442026446331048 ] 
dist 221=[-.21307044336678011007,1.0623176115319968900 ] 
dist 222=[-.37847083645760109268,1.0600582932768506103 ] 
dist 223=[-.54395506585249425986,1.0461814516720842994 ] 
dist 224=[-.65401080576568671672,.20865015860757299402] 
dist 225=[-.74431282171106718037,.20865485128767944056] 
dist 226=[-.83099929622113073221,.21777695602651591091] 
dist 227=[-.90850612730697123573,.2313711599230860876 ] 
dist 228=[-.96219030625807974857,.2502268118120521648 ] 
dist 229=[-1.0085918577283939342 ,.2764988960632851196 ] 
dist 230=[-1.0570477366727665364 ,.3196777887823999353 ] 
dist 231=[-1.0984148936206544975 ,.3657486457005235137 ] 
dist 232=[-1.1165393822116994871 ,.4035576723106676673 ] 
dist 233=[-1.1243840868526267693 ,.4424719165992757175 ] 
dist 234=[-1.1306303916271287878 ,.4929535861878088480 ] 
dist 235=[-1.1306430445360794229 ,.5468760421522563119 ] 
dist 236=[-1.0997949970315275233 ,.5995169243327176477 ] 
dist 237=[-1.0892722796848629358 ,.6611927959614414252 ] 
dist 238=[-1.0806884425158613387 ,.7511576711493610774 ] 
dist 239=[-1.0728002486677840961 ,.8390405853812557983 ] 
dist 240=[-1.1550922634786345346 ,.8924121114312414093 ] 
dist 241=[-1.2186142193146795348 ,.9388118557535592668 ] 
dist 242=[-1.2641578878084166915 ,1.0726579674961517107 ] 
dist 243=[-1.2977069756250199200 ,1.1901269543545307558 ] 
dist 244=[-1.3133843263339524345 ,1.2676454223567665023 ] 
dist 245=[-1.3189357897717719024 ,1.3305821305165632041 ] 
dist 246=[-1.3221666024043043242 ,1.3898875751148870166 ] 
dist 247=[-1.3210086099559812593 ,1.4394654401099470176 ] 
dist 248=[-1.1852438512594116632 ,1.4635998738327367964 ] 
dist 249=[-1.1617592193166356907 ,1.4829792992148238135 ] 
dist 250=[-1.1194735193729566945 ,1.4924654793445692171 ] 
dist 251=[-1.1070681519519189650 ,1.4926808208425419480 ] 
dist 252=[-1.0582329377628200205 ,1.4716173612244835751 ] 
dist 253=[-1.0438112334672055207 ,1.4620108692967342830 ] 
dist 254=[-1.0149873572834836880 ,1.4364882069735886406 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 1, 1, 1, 0, 1] 
dist 0=[63.218368401008387139  ,63.218368401008387139  ] 
dist 1=[62.249747403143426959  ,63.763170179366675163  ] 
dist 2=[60.422760515597045329  ,63.897910917498718633  ] 
dist 3=[58.449587611328944586  ,63.875994815778424083  ] 
dist 4=[56.897201519599559351  ,63.795219108591735176  ] 
dist 5=[55.353218003813754102  ,63.708639233621236680  ] 
dist 6=[53.413478605121369842  ,63.663522837404698473  ] 
dist 7=[51.363508961975236544  ,63.639875506981468788  ] 
dist 8=[49.379257124189586091  ,62.817704689117263771  ] 
dist 9=[47.059171458634708042  ,57.446346812163904981  ] 
dist 10=[43.667982303209363063  ,56.566461427076993636  ] 
dist 11=[40.181390242148816616  ,55.041262586401965291  ] 
dist 12=[37.480210214663537054  ,54.644003111426955669  ] 
dist 13=[34.831238740249839638  ,53.418003446875929994  ] 
dist 14=[31.552902585023561871  ,53.027646720293342442  ] 
dist 15=[25.134104540525742209  ,52.810386597524993660  ] 
dist 16=[20.644217356950221855  ,51.856247932745694610  ] 
dist 17=[16.866883394390103514  ,34.053528313111740594  ] 
dist 18=[13.064515426337389293  ,33.836259884145586260  ] 
dist 19=[9.5287213976631743229 ,17.267637415929897734  ] 
dist 20=[6.1120910745154001421 ,16.481972932408556754  ] 
dist 21=[3.0261658583047658192 ,9.5962328715188183897 ] 
dist 22=[-.01954207720181526488,8.3955471775660765473 ] 
dist 23=[-2.8158286729468075505 ,6.7657295695717497382 ] 
dist 24=[-4.9056152758857256649 ,6.4101121469076805106 ] 
dist 25=[-6.8837378165787605862 ,.02074670423670792752] 
dist 26=[-9.2341466497828271387 ,-.26155679694466155221] 
dist 27=[-11.427044886259646376  ,-3.9225704003584622148 ] 
dist 28=[-12.776137213920240993  ,-4.4195891979900752874 ] 
dist 29=[-13.769415285906160428  ,-5.1324473701075942498 ] 
dist 30=[-14.541277606769169608  ,-5.2700689660974780615 ] 
dist 31=[-15.131231998549961260  ,-5.2053188924372251092 ] 
dist 32=[-15.398005551339996500  ,-4.8438538725235283244 ] 
dist 33=[-15.508958728179158642  ,-4.2003556098225750448 ] 
dist 34=[-15.496157748281290008  ,-3.0102702346632478432 ] 
dist 35=[-6.5307412654340097878 ,-1.5410493332546301851 ] 
dist 36=[-6.4561545960411291496 ,-.18856666961333670297] 
dist 37=[-6.0545856252817230856 ,.93880258081280090071] 
dist 38=[-5.9595661537614857618 ,2.0483949076968955222 ] 
dist 39=[-5.7411241572581829652 ,3.0577347511115599183 ] 
dist 40=[-5.6673177075120520364 ,3.7855245270653048334 ] 
dist 41=[-4.7458240580511141436 ,4.4448078634398671664 ] 
dist 42=[-4.6039074721277591499 ,5.1812041631623731778 ] 
dist 43=[-4.2553094157380409328 ,5.8588961803211219581 ] 
dist 44=[-4.1845535533445786924 ,6.2840402006056634104 ] 
dist 45=[-3.6441395302751026736 ,6.6049611535896835275 ] 
dist 46=[-3.5363209323991246982 ,6.8666835260587572523 ] 
dist 47=[-3.3650818080939903771 ,7.0693194547376989398 ] 
dist 48=[-3.3174684323691972803 ,7.1543557627716427584 ] 
dist 49=[-2.3615204243817649511 ,7.1784597275245525609 ] 
dist 50=[-2.2268618528663840019 ,7.1654357623237229029 ] 
dist 51=[-1.9525482379714174289 ,4.0843562263751333709 ] 
dist 52=[-1.8776037083951634765 ,3.8151921233778818628 ] 
dist 53=[-1.5857639528302316661 ,3.1558390483402830537 ] 
dist 54=[-1.5241400746979233580 ,3.0503429607358621351 ] 
dist 55=[-1.3840156223358796949 ,2.5118382741399025315 ] 
dist 56=[-1.3406783997972757413 ,2.6437172590503938901 ] 
dist 57=[-1.1432732661499308513 ,2.7432336843944799749 ] 
dist 58=[-1.2453237334648668683 ,2.8254402020956361351 ] 
dist 59=[-1.5772970869098728417 ,2.8908407242349122795 ] 
dist 60=[-1.7836379768672353524 ,2.9231861819016806425 ] 
dist 61=[-1.9365419485905936663 ,2.9377420792536247746 ] 
dist 62=[-2.0554845080065494854 ,2.9363674751580204024 ] 
dist 63=[-2.1469120586181513703 ,-.59308278659098025677] 
dist 64=[-2.1901340944435207015 ,-.56767346281505009872] 
dist 65=[-2.2076796032723685680 ,-.50357335509740258416] 
dist 66=[-2.2074623987952723070 ,-.37048767982422646532] 
dist 67=[-1.7016847191141185734 ,-.15684750480788224231] 
dist 68=[-1.8481867304212426740 ,.04508068235767224962] 
dist 69=[-1.9718484359016053928 ,.21937665884703151279] 
dist 70=[-2.0966510740845806080 ,.4005324930000315698 ] 
dist 71=[-2.2049971717553995532 ,.57135209670058939632] 
dist 72=[-2.2630008850547643427 ,.70444810530779084875] 
dist 73=[-2.2953145567797635177 ,.83489034587703788935] 
dist 74=[-2.3011435047171084597 ,.99514337779185699548] 
dist 75=[-2.2947173516635810427 ,1.1456373191238431562 ] 
dist 76=[-2.2850524631422076924 ,1.2371753770569870461 ] 
dist 77=[-2.2570900561870301947 ,1.3027490514788488584 ] 
dist 78=[-2.2419246702192202631 ,1.3497246290385201286 ] 
dist 79=[-1.3782158560156343899 ,1.3831463690276009786 ] 
dist 80=[-1.2881231692137821353 ,1.3946685407704634741 ] 
dist 81=[-1.0752559001036484964 ,1.3958869652349395845 ] 
dist 82=[-1.0329712203651876991 ,1.3910171466455022244 ] 
dist 83=[-.73505454692911967748,1.2616158088826409624 ] 
dist 84=[-.67889234785293658238,1.3590991058847902605 ] 
dist 85=[-.72504225608552015283,1.4995217150911807909 ] 
dist 86=[-.85219158450621530118,1.6541529893827799571 ] 
dist 87=[-.96270513323005008014,1.7936497261705024919 ] 
dist 88=[-1.0334076778077985873 ,1.8737037662264075038 ] 
dist 89=[-1.0882148411580140491 ,1.9254348134867763875 ] 
dist 90=[-1.1353290569398952765 ,1.9519439483003641857 ] 
dist 91=[-1.1744300301953756835 ,1.9649679169163745497 ] 
dist 92=[-1.1972830535089567228 ,1.9629026743911941688 ] 
dist 93=[-1.2124846497825554350 ,1.9524576073497948481 ] 
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dist 97=[-1.2110991176226147961 ,.30689277206898757253] 
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dist 100=[-1.2920921077528061122 ,.10733424570314477723] 
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dist 102=[-1.5889940682262774188 ,.40139406069840353915] 
dist 103=[-1.7095881905598920229 ,.54119537258556913819] 
dist 104=[-1.8521075761350395696 ,.64917435112405913962] 
dist 105=[-1.9834991223877870485 ,.75422512864076464271] 
dist 106=[-2.0597066197012682310 ,.88234896069020591685] 
dist 107=[-2.1099262567670024582 ,1.0023940960208192393 ] 
dist 108=[-2.1376553470250796437 ,1.0752254588918475905 ] 
dist 109=[-2.1506193182061755636 ,1.1272246599914251462 ] 
dist 110=[-2.1496026295475596871 ,1.1641862853035619033 ] 
dist 111=[-2.1273442856133506690 ,1.1903703121356784426 ] 
dist 112=[-2.1166710524418442252 ,1.1993836116067172086 ] 
dist 113=[-1.9243049831585611797 ,1.4373157498778719097 ] 
dist 114=[-1.8882272297511595506 ,1.7601233385374478180 ] 
dist 115=[-1.7989476192124524963 ,2.0167346187154323782 ] 
dist 116=[-1.7689123660944295832 ,2.2491921551244736514 ] 
dist 117=[-1.6118530987703575031 ,2.4476412111763849608 ] 
dist 118=[-1.5759334544373602204 ,2.5686096829164847265 ] 
dist 119=[-1.5014352577625972092 ,2.6557000986208420075 ] 
dist 120=[-1.4780389338695874542 ,2.7190275340578644096 ] 
dist 121=[-1.1260025064818638213 ,2.7648496710839251619 ] 
dist 122=[-1.0748423176839827864 ,2.7821192663316706842 ] 
dist 123=[-.94109149993214191474,2.7817506051074852984 ] 
dist 124=[-.92179892464356291826,2.7753658087916696573 ] 
dist 125=[-.69400090638412595889,2.7209867170328522687 ] 
dist 126=[-.64948519983472106936,2.7024281672854107324 ] 
dist 127=[-.6028935660445170583 ,2.6315853093124752099 ] 
dist 128=[-.59418424910300830144,2.6139881530512886696 ] 
dist 129=[-.02048397928620494706,.32236935718475916987] 
dist 130=[-.09896288205088192895,.33317868296703749011] 
dist 131=[-.17300965250317634421,.34621454231575353771] 
dist 132=[-.23096834259828949075,.36117995309855496894] 
dist 133=[-.28809298460057504017,.38041696222734421641] 
dist 134=[-.35881668241656391164,.41048799324872793242] 
dist 135=[-.42564283500131230349,.44204173055325722552] 
dist 136=[-.46722412890047353305,.46718947553637806695] 
dist 137=[-.49818043886679209766,.49241355950661500813] 
dist 138=[-.52263123891484902907,.52426492760006751696] 
dist 139=[-.54123438750852670398,.55784356120407668637] 
dist 140=[-.54886498331759396147,.58995234432370980067] 
dist 141=[-.59552790067893984775,.62704510038550170191] 
dist 142=[-.74729177758872550132,.68049590722404922483] 
dist 143=[-.8956717491552574884 ,.73226257189740939271] 
dist 144=[-.98752591000969653764,.76263617972954871637] 
dist 145=[-1.0554024729632998166 ,.78306031175698618427] 
dist 146=[-1.1081328971224507800 ,.79514416224091291746] 
dist 147=[-1.1486641737833199085 ,.8016814734927002162 ] 
dist 148=[-1.1678749332011686766 ,.80185031287134808714] 
dist 149=[-1.1758620322320635158 ,.7956201326034389998 ] 
dist 150=[-1.1758679901248565241 ,.79152337381279624979] 
dist 151=[-1.0933219916808641479 ,.72107502184053375702] 
dist 152=[-1.0769417337532988910 ,.70801188968465597472] 
dist 153=[-1.0474283802671605484 ,.67514522702943461201] 
dist 154=[-1.0380764422391387349 ,.66453694988529719196] 
dist 155=[-.9980602552639703284 ,.60514926963721526771] 
dist 156=[-.9863718447916096125 ,.59159067200887267897] 
dist 157=[-.9585602640720700232 ,.56467816175311222615] 
dist 158=[-.9479556065998595219 ,.55646898985552600686] 
dist 159=[-.32412428244391419492,.17471098543292450551] 
dist 160=[-.32083597013661649356,.24402677788973047683] 
dist 161=[-.3113517940059041793 ,.32270510715961540952] 
dist 162=[-.30817309545238928106,.3967900314538199005 ] 
dist 163=[.07404150569080963249,.46207044716993165571] 
dist 164=[.10059335569237097687,.50562831454614990428] 
dist 165=[.15912581627273257077,.54153098173886167443] 
dist 166=[.16941830649466956358,.57627613585877884905] 
dist 167=[.23305815529874100129,.60664535431726978455] 
dist 168=[.24000740956873610987,.6250923335926481954 ] 
dist 169=[.24462928591449959584,.63830645331615753478] 
dist 170=[.24113409097247094014,.64780023240051056189] 
dist 171=[.23452964317878981908,.65415634694495667582] 
dist 172=[.22470117981591053158,.65485341235036404764] 
dist 173=[.21064782740936784922,.6524038536090326703 ] 
dist 174=[.18718876341286538395,.64980498434476410634] 
dist 175=[.1345067814807380991 ,.38230713423918829265] 
dist 176=[.05756777946307884776,.38178284965298946381] 
dist 177=[-.00811261969170207857,.37935064621373499419] 
dist 178=[-.07539978173527320385,.37739297944013619087] 
dist 179=[-.13839103799900567574,.25095648723791582509] 
dist 180=[-.18693536060861554274,.23778989278514793227] 
dist 181=[-.23408777625467409057,.20445824746215623299] 
dist 182=[-.29152652524389197632,.19929023025492142168] 
dist 183=[-.345359847597499923  ,.14573142117179843526] 
dist 184=[-.37813044310481500797,.13540375493285514579] 
dist 185=[-.4016756572423232577 ,.12319485105483179584] 
dist 186=[-.41870979537699322143,.11997283647249857065] 
dist 187=[-.43151854345418436697,.02502873575416128761] 
dist 188=[-.43820966709246711277,.01331700459145294829] 
dist 189=[-.44168681863363533372,-.01190152074649822318] 
dist 190=[-.44167709245973535251,-.01757030611056293064] 
dist 191=[-.28561990895316011194,-.02627625629654529251] 
dist 192=[-.28622562376088036565,-.02228195477187359350] 
dist 193=[-.28602300487691023064,-.01512189675576995819] 
dist 194=[-.28491047719171956615,-.00178024564146271129] 
dist 195=[-.12102510384244869078,.02588751159619682073] 
dist 196=[-.1099988503842480253 ,.04865852063863562222] 
dist 197=[-.08385905648473292501,.07663611473449180417] 
dist 198=[-.07924790867539125672,.10682231515532414267] 
dist 199=[-.04309411335379524793,.1350070698060380518 ] 
dist 200=[-.03648150566083310205,.15662350042518491912] 
dist 201=[-.02599550245262464525,.17752857710454141292] 
dist 202=[-.02335577073216261363,.20287532209816190551] 
dist 203=[.00271084338991375295,.22658588034156881747] 
dist 204=[-.00647272274420637346,.24096366732030998363] 
dist 205=[-.01675698726998855856,.2512313487673396045 ] 
dist 206=[-.03120397391019664314,.25854552404197526608] 
dist 207=[-.04718610450123794915,.26367354735663350721] 
dist 208=[-.06359475249884265998,.2652202342842295288 ] 
dist 209=[-.08342734231790686641,.26520880836041135932] 
dist 210=[-.11306874373556269231,.2642161693444904856 ] 
dist 211=[-.14233163886818695572,.24383585251609218279] 
dist 212=[-.16065448817587922922,.24029904739106736139] 
dist 213=[-.17443925142067551295,.22906591936660665379] 
dist 214=[-.18559891054658920173,.22742206364027564176] 
dist 215=[-.19442576347216700832,.20239050526621330247] 
dist 216=[-.1989045365539211824 ,.20168578893225298744] 
dist 217=[-.20109045576848523576,.20104705028787420681] 
dist 218=[-.20142278786798289505,.200330629819976541  ] 
dist 219=[-.20659360305337769936,.1582895001541092826 ] 
dist 220=[-.21301218445134434467,.15228794413671144301] 
dist 221=[-.21731935314578109978,.14102742512256407746] 
dist 222=[-.2198583709661016805 ,.13803042230152014691] 
dist 223=[-.22106168182098263828,.12740205655049872073] 
dist 224=[-.22101118122493443793,.12453129111671128724] 
dist 225=[-.21854325262980323155,.12074325871966703763] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 2, 1, 2] 
dist 0=[63.026424609330574131  ,63.026424609330574131  ] 
dist 1=[62.171781139055660068  ,63.488722112567843843  ] 
dist 2=[60.549861129147145122  ,63.587594742838328160  ] 
dist 3=[58.555475451891084317  ,63.410917613165594729  ] 
dist 4=[56.213630765731760043  ,63.251498376303042867  ] 
dist 5=[53.164819949256070295  ,63.044122216347575139  ] 
dist 6=[48.347607385206953023  ,62.899900627408840288  ] 
dist 7=[43.437772697917361524  ,62.312233375698963866  ] 
dist 8=[40.019080072303728777  ,62.098861982250391970  ] 
dist 9=[37.032515479999250821  ,61.466707004124188950  ] 
dist 10=[33.847949657803305310  ,61.189895578557185662  ] 
dist 11=[30.772996305082841848  ,59.640814481887170310  ] 
dist 12=[28.223912930708846338  ,59.201088850094524825  ] 
dist 13=[25.566702874273216832  ,58.960350876363881833  ] 
dist 14=[22.059616241643591701  ,57.860751653723051693  ] 
dist 15=[18.610628218963935681  ,51.411377701948511393  ] 
dist 16=[16.185167152412983034  ,47.251699273200431538  ] 
dist 17=[14.038906460347136021  ,29.423298322960722098  ] 
dist 18=[11.704435659321408657  ,27.138944761819854784  ] 
dist 19=[9.4186649460645907069 ,21.903707717508246483  ] 
dist 20=[7.4663635535062042407 ,21.036016378257471842  ] 
dist 21=[5.3767639209195483943 ,14.485801561656876778  ] 
dist 22=[2.5415969579669201475 ,13.357418744650167080  ] 
dist 23=[-.22438000652537120267,11.517999920507926812  ] 
dist 24=[-2.0377453845738863612 ,11.104911169531450536  ] 
dist 25=[-3.5088673312553945194 ,9.4863922460736104971 ] 
dist 26=[-4.9072250652113647712 ,9.3882287767935036783 ] 
dist 27=[-6.1597398894429753287 ,3.1763849333763054617 ] 
dist 28=[-7.0481299187763305446 ,2.6216918441527089920 ] 
dist 29=[-7.8444294275008036973 ,-.20691961980930231043] 
dist 30=[-8.7291277117194133385 ,-1.3504856893650615518 ] 
dist 31=[-9.5270999631262954700 ,-4.5859829818044512322 ] 
dist 32=[-10.706257152143338339  ,-5.1543946755894366712 ] 
dist 33=[-11.848680668928240936  ,-4.6576582778486573588 ] 
dist 34=[-12.482928953238202702  ,-3.8110915801774341854 ] 
dist 35=[-12.876744806731503120  ,-2.8099878268989914263 ] 
dist 36=[-13.057446874875894883  ,-1.6963895658304588566 ] 
dist 37=[-13.150422890468786899  ,-.29103635674738021807] 
dist 38=[-13.291724348871741913  ,1.8741532148920339868 ] 
dist 39=[-13.630756659371465359  ,4.0423080226311121328 ] 
dist 40=[-13.811463185122180706  ,5.4596713837789102091 ] 
dist 41=[-13.911514567038375627  ,6.5949196218414265244 ] 
dist 42=[-13.928141712353140391  ,7.6379859459004207644 ] 
dist 43=[-10.362666011625997696  ,8.5390836677493407726 ] 
dist 44=[-10.221323710494394276  ,9.1081440484404673497 ] 
dist 45=[-9.7307433829079445440 ,9.5418296899245535474 ] 
dist 46=[-9.5937014224123163029 ,9.9030321972186013826 ] 
dist 47=[-9.4523328266885577538 ,10.195473616867492691  ] 
dist 48=[-9.3864497212062905369 ,10.354856799774359020  ] 
dist 49=[-3.5940811478873911615 ,10.447034375138678268  ] 
dist 50=[-3.4679118268455300150 ,10.471242635410552265  ] 
dist 51=[-2.5554805620552189738 ,10.449487781744572864  ] 
dist 52=[-2.3826517671977330667 ,10.412810289039617428  ] 
dist 53=[-2.0856092718879846629 ,10.154721073240979696  ] 
dist 54=[-2.0143566061189597390 ,9.5591991975011794827 ] 
dist 55=[.54811436247780819345,9.5204784537081776923 ] 
dist 56=[.8139458758396313471 ,9.5335548606589136135 ] 
dist 57=[1.4081988463916143918 ,9.5134277753663325326 ] 
dist 58=[1.5061962616547283099 ,9.4781115297460428014 ] 
dist 59=[2.0834875274923447489 ,8.3558939479367644103 ] 
dist 60=[.9212457524610607147 ,8.7138036796642658187 ] 
dist 61=[-.07720686962844749194,8.9964785181070339602 ] 
dist 62=[-1.1101967834458109565 ,9.1293346634640410654 ] 
dist 63=[-2.0837211571640787117 ,9.1848871483639220238 ] 
dist 64=[-2.8449946828916854169 ,9.1840613138508766869 ] 
dist 65=[-3.5950685886805431640 ,3.4791938746123845929 ] 
dist 66=[-4.5239488696775513812 ,3.5333879587004303303 ] 
dist 67=[-5.4026154767561151285 ,3.5627256436334182732 ] 
dist 68=[-5.9523910130869570321 ,3.5655005854002501242 ] 
dist 69=[-6.3655008684567732532 ,3.5298428001400936311 ] 
dist 70=[-6.6989898524311213121 ,3.5217423842933857637 ] 
dist 71=[-6.9555303679314762213 ,2.0408331188938973319 ] 
dist 72=[-7.0616854899408442027 ,1.8986030172848623751 ] 
dist 73=[-7.1058426139121611816 ,1.5526696759927604864 ] 
dist 74=[-7.1150525006878338327 ,1.4943280126935321236 ] 
dist 75=[-5.3668579648748564514 ,.98558575233223142127] 
dist 76=[-5.4559159686721780104 ,.8904456533869893851 ] 
dist 77=[-5.5052439822551663958 ,.87974423989018085843] 
dist 78=[-5.5098235625510559890 ,1.4073484379100738459 ] 
dist 79=[-5.4600809282840624934 ,1.8900857473406329327 ] 
dist 80=[-5.4432874996002635319 ,2.2432922162662327822 ] 
dist 81=[-3.2042752713954268228 ,2.5684300050138568842 ] 
dist 82=[-2.9870120315385696415 ,2.9392317778638312435 ] 
dist 83=[-2.4553025838375088579 ,3.2796922871479332795 ] 
dist 84=[-2.3668019416324942616 ,3.4838137398281232989 ] 
dist 85=[-2.3292270004111428871 ,3.6267197295532084543 ] 
dist 86=[-2.3297092467688319472 ,3.7230056840574717283 ] 
dist 87=[-1.2200108785744522655 ,3.7873964550868611004 ] 
dist 88=[-1.1575080992674654804 ,3.8030817106747394266 ] 
dist 89=[-1.0301512068422239705 ,3.7969331148533896254 ] 
dist 90=[-1.1040369096174095990 ,3.7803074275315547245 ] 
dist 91=[-1.1827456690236321093 ,3.2542469552679270972 ] 
dist 92=[-1.2593088207774998861 ,3.3658727597611398588 ] 
dist 93=[-1.3488149202352597167 ,3.4451678317225011225 ] 
dist 94=[-1.4791508090005690823 ,3.4703340417060738374 ] 
dist 95=[-1.6120432483816659999 ,3.4722582507829414139 ] 
dist 96=[-1.7117455273820681349 ,3.4588298143780500848 ] 
dist 97=[-1.8060247375897189461 ,1.4534537802022177542 ] 
dist 98=[-1.9172811990089698442 ,1.4266211809661263780 ] 
dist 99=[-2.0306438944902913420 ,1.2055801751025468161 ] 
dist 100=[-2.1333220734151624933 ,1.5206198491945712788 ] 
dist 101=[-2.2476124921714045929 ,1.8883960454263490270 ] 
dist 102=[-2.4072914761709150607 ,2.4232754719456722761 ] 
dist 103=[-2.5602682078536720037 ,2.9480220733795042906 ] 
dist 104=[-2.6478222710686773774 ,3.2753793376389156844 ] 
dist 105=[-2.7040198193150717436 ,3.5201622045988958249 ] 
dist 106=[-2.7319171975171940160 ,3.7155212489308375793 ] 
dist 107=[-2.7424339109152620143 ,3.8676318892445454572 ] 
dist 108=[-2.7388715780516250938 ,3.9398974221820777140 ] 
dist 109=[-2.7094378795083074615 ,3.9723624898933482620 ] 
dist 110=[-2.6930921589808148971 ,3.9725418395012125251 ] 
dist 111=[-2.4355602434736354810 ,3.7484134362901538100 ] 
dist 112=[-2.3890356816392288274 ,3.6991411101075452403 ] 
dist 113=[-2.2696870049704120556 ,3.6111982836898641157 ] 
dist 114=[-2.2352989462011959758 ,3.5820850866610254712 ] 
dist 115=[-2.0169180142206050981 ,3.4525429440499690167 ] 
dist 116=[-1.9681196388475487611 ,3.4143584865994607736 ] 
dist 117=[-1.8779544088721776323 ,3.3173889644606778338 ] 
dist 118=[-1.8522648878934960237 ,3.2790791471101018820 ] 
dist 119=[-1.3086376554201534715 ,.44173774337153033537] 
dist 120=[-1.3009347780050660869 ,.46732794792607955254] 
dist 121=[-1.2705551902921840264 ,.48922152677261819741] 
dist 122=[-1.2636187588534435317 ,.50315957250931668603] 
dist 123=[-.54275144828130240121,.5730058466531157846 ] 
dist 124=[-.47527547294750401236,.64254147075535154533] 
dist 125=[-.32356009912171607241,.70404529509318425373] 
dist 126=[-.29744253489464305833,.74558437482482997258] 
dist 127=[-.27094287375781062175,.78046411872689158344] 
dist 128=[-.26351813126631341648,.82046491538499952131] 
dist 129=[-.00855943121888308811,.95205853688825462375] 
dist 130=[-.01932113932713715733,1.0759076693054473330 ] 
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dist 155=[-2.7491804916679289925 ,1.1406340853402791078 ] 
dist 156=[-2.7389843287330831792 ,1.1302445876426461412 ] 
dist 157=[-2.6688221730182946708 ,1.1116823110743441670 ] 
dist 158=[-2.6485484075659721043 ,1.1032073636011620779 ] 
dist 159=[-2.5691389125612727753 ,1.0967354514036715378 ] 
dist 160=[-2.5559332829344186338 ,1.0913268643805836773 ] 
dist 161=[-.76204174501731983435,.75910992618859297745] 
dist 162=[-.75727123275365411315,.76111670539351601384] 
dist 163=[-.60791433053291113928,.76839383176271752416] 
dist 164=[-.58616403722673206317,.79138693884376811052] 
dist 165=[-.54304452696852913917,.80799012743573025911] 
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dist 167=[-.48432514914675210789,.82856939660469630741] 
dist 168=[-.47327635888989718971,.83003240136841968432] 
dist 169=[-.45079358966232341926,.82722711289758652645] 
dist 170=[-.44393647773954255382,.82440267854813480205] 
dist 171=[.07773256275636712232,.58763847426066500318] 
dist 172=[.12233234504416143117,.61318918235175381378] 
dist 173=[.18694828487239995245,.63225991897328267397] 
dist 174=[.11132203198530702506,.63903203845213387399] 
dist 175=[.03969300050537530429,.64108061750365911174] 
dist 176=[-.01687531424445470862,.64130718978216636759] 
dist 177=[-.07312023770490468180,.46924185743874488705] 
dist 178=[-.14346281194344297426,.51644072625273105723] 
dist 179=[-.21036060576654219163,.55931823966111707749] 
dist 180=[-.25286555620469919891,.58457022132759017626] 
dist 181=[-.28555485636020026273,.60169935836893902538] 
dist 182=[-.3132981744480973447 ,.61217231073571824778] 
dist 183=[-.33589485018832090849,.61842291546129481887] 
dist 184=[-.34805536049820853985,.61884834690660828673] 
dist 185=[-.35487984477368032887,.61645382741096139571] 
dist 186=[-.35639214121014613099,.61344225860004247078] 
dist 187=[-.34238964918163996   ,.41775976623578948934] 
dist 188=[-.33920942815225195903,.3976395795152993952 ] 
dist 189=[-.33486196742809575567,.34638374593423778751] 
dist 190=[-.33266632739215321139,.33848352223883577596] 
dist 191=[-.33301312588935815694,.25494195152717598893] 
dist 192=[-.35546878924354479298,.2387255307709044983 ] 
dist 193=[-.41004398091676703986,.21998143491038977804] 
dist 194=[-.45655482149424445848,.21515790074624003518] 
dist 195=[-.49579300201297839387,.06212858533208703538] 
dist 196=[-.53527952698547469978,.04314361241689813292] 
dist 197=[-.57182557526056941484,.07444235155836211521] 
dist 198=[-.59933110682498752178,.13164904995887881346] 
dist 199=[-.62543386958427802284,.19122293794373409467] 
dist 200=[-.65638110270823745372,.2471713140117845313 ] 
dist 201=[-.68497122469838479742,.31107727577141650727] 
dist 202=[-.70166919797036428252,.40239900951071103646] 
dist 203=[-.71281664656604415139,.49738463882017438669] 
dist 204=[-.71926220064533668638,.56465694090296828997] 
dist 205=[-.72216123778905524717,.61984370009923478263] 
dist 206=[-.72121077820546170741,.67282453903376927595] 
dist 207=[-.7142473576643940365 ,.72021580122852845739] 
dist 208=[-.70954059560112850961,.75310407626029300464] 
dist 209=[-.6760186325231003562 ,.78160763878087095832] 
dist 210=[-.66729921361790791593,.81150689550908114433] 
dist 211=[-.64747713050120278819,.89321786654856108761] 
dist 212=[-.64018676826412815781,.97651518019785392903] 
dist 213=[-.60316069546808540741,1.0463175942717957287 ] 
dist 214=[-.58491994643120570692,1.0865766031317043632 ] 
dist 215=[-.51766941035638617988,1.1128390564761423455 ] 
dist 216=[-.46008211710909692559,1.1268092857973218714 ] 
dist 217=[-.20319501076486026134,1.1342800597113175210 ] 
dist 218=[-.42122271448482396653,1.1346146657861517344 ] 
dist 219=[-.6382082685224576175 ,1.1297965804823331176 ] 
dist 220=[-.77991572870567148788,1.1260003731205618766 ] 
dist 221=[-.8933431518002741183 ,1.0995686321040858833 ] 
dist 222=[-.99751691515998663067,1.0917024854533375897 ] 
dist 223=[-1.0875242101940589593 ,1.0605549035904663935 ] 
dist 224=[-1.1444404448699772165 ,1.0551942472308078727 ] 
dist 225=[-1.1879090485149240139 ,.4831043956945574219 ] 
dist 226=[-1.2242730969847241550 ,.47679895828892298084] 
dist 227=[-1.2527864262359496870 ,.39697372568431603803] 
dist 228=[-1.2649375719933706261 ,.38244328199613598864] 
dist 229=[-1.2675428821308705089 ,.35366747643885423627] 
dist 230=[-1.2660147284094630589 ,.34564078545055142162] 
dist 231=[-1.2421732708747204125 ,.31451706780196669312] 
dist 232=[-1.2333671479472675148 ,.30712715572829300846] 
dist 233=[-1.2074978611211208933 ,.29215595222129998745] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 0, 1, 2, 0, 1] 
dist 0=[58.880472228107855478  ,58.880472228107855478  ] 
dist 1=[58.472428741078366598  ,59.036186019037305967  ] 
dist 2=[57.706701589445120688  ,59.249773001016235232  ] 
dist 3=[56.379610917322860154  ,59.419020701971941844  ] 
dist 4=[54.735778938721408626  ,59.498727382620950082  ] 
dist 5=[52.705228845530345193  ,59.527562031483246799  ] 
dist 6=[49.998583491703700784  ,59.493471095226286303  ] 
dist 7=[45.655028848146796429  ,59.431392243818768598  ] 
dist 8=[41.212872868807593998  ,59.348510961935136598  ] 
dist 9=[38.112435130568709936  ,59.233714972425768301  ] 
dist 10=[35.395348961484857424  ,59.106280843164786112  ] 
dist 11=[32.483757403705761730  ,58.821558191342435923  ] 
dist 12=[29.662634984638090895  ,58.654765924376777348  ] 
dist 13=[27.306586597206118061  ,58.293361081104278734  ] 
dist 14=[24.834406274143432860  ,57.339526315728851314  ] 
dist 15=[21.549112024188343096  ,39.827173085162870218  ] 
dist 16=[18.305702254774913552  ,38.222411585655514656  ] 
dist 17=[16.000533991181252255  ,34.341731899899774791  ] 
dist 18=[13.424314039412201768  ,33.755974848576034617  ] 
dist 19=[9.8470992887784179654 ,28.118229811039291484  ] 
dist 20=[6.3575819607927024421 ,27.072218495007173690  ] 
dist 21=[3.9466053582594245326 ,25.792528264549231920  ] 
dist 22=[1.8567880068836453340 ,25.490269171109323539  ] 
dist 23=[-.35060525109835336212,16.782688326327201321  ] 
dist 24=[-2.4749325517105393970 ,15.706032812137796410  ] 
dist 25=[-4.2336036220718269576 ,13.449938689885330494  ] 
dist 26=[-6.0698148177081078799 ,12.888906607188639396  ] 
dist 27=[-8.5050974166703930907 ,10.692850820189670636  ] 
dist 28=[-10.842701735401751588  ,10.278832784850834474  ] 
dist 29=[-12.288936641966363741  ,9.5065739881787175906 ] 
dist 30=[-13.368275204137140572  ,9.3331600388837782989 ] 
dist 31=[-14.239682197852291819  ,-.760356664762411724  ] 
dist 32=[-14.922108105837464278  ,-1.6388871787321136622 ] 
dist 33=[-15.246068854973569094  ,-3.4345241904795526794 ] 
dist 34=[-15.406936520793022477  ,-3.8508712809490858855 ] 
dist 35=[-15.437273565391110341  ,-5.3587044073425892261 ] 
dist 36=[-15.004717098697751054  ,-5.6445740108435160934 ] 
dist 37=[-14.882271248902228975  ,-5.9014740982933818240 ] 
dist 38=[-15.004763222715041220  ,-5.6731195370225671778 ] 
dist 39=[-16.016434095005821967  ,-4.2459339729177221758 ] 
dist 40=[-16.603323098984711343  ,-2.7895413098852242256 ] 
dist 41=[-16.994314114632560950  ,-1.7841199707684854182 ] 
dist 42=[-17.223406135176600550  ,-.91889883003471985012] 
dist 43=[-17.355950174931284864  ,-.02157086184128431586] 
dist 44=[-17.361182341424022037  ,.85685293924208765954] 
dist 45=[-17.308707442235735319  ,2.8402518712225625134 ] 
dist 46=[-17.244627270363384379  ,4.4906019374055794502 ] 
dist 47=[-2.9461085718687204024 ,6.1164208094141078927 ] 
dist 48=[-1.0136531595562331274 ,7.6010148627301537014 ] 
dist 49=[-.67551475080629487632,8.6878881449013175950 ] 
dist 50=[.01687633504905051931,9.6912362508842530850 ] 
dist 51=[.19086810334091964332,10.842630569947430894  ] 
dist 52=[1.5708148359807426077 ,11.893682454328610315  ] 
dist 53=[1.7954163224985758208 ,12.496589515354121824  ] 
dist 54=[1.7129161193399086629 ,12.886630397729836274  ] 
dist 55=[1.2280860660031829155 ,13.088065140383879064  ] 
dist 56=[.7093297305814117129 ,13.204862610900599828  ] 
dist 57=[.29754437710093329433,13.257141587932695158  ] 
dist 58=[-.04837282830798902078,13.272304248715628254  ] 
dist 59=[-.39324014709850977611,13.137174556773793659  ] 
dist 60=[-.70973273748668414677,-.38299368766979544316] 
dist 61=[-1.1055018370607079888 ,-.46420392218735244486] 
dist 62=[-1.5475962317037603314 ,-.61006307970823432625] 
dist 63=[-1.9639625228771373597 ,-.63960462076542854066] 
dist 64=[-2.3311408553518727497 ,-.97893786724683713064] 
dist 65=[-2.5770380415937356599 ,-1.0266763009214156976 ] 
dist 66=[-2.7808954833494591197 ,-1.0486374285390503668 ] 
dist 67=[-2.9804085159414195740 ,-1.0080350770301399056 ] 
dist 68=[-3.1553925133880811479 ,-.93590788496814428166] 
dist 69=[-3.2613967572371090378 ,-.82385921189334202648] 
dist 70=[-3.3371657143396975510 ,-.66152999996072511635] 
dist 71=[-3.3914905441889488584 ,-.38889961480253493378] 
dist 72=[-3.4279108715664268918 ,-.10918560645085097832] 
dist 73=[-3.4322307968916045527 ,.08139253165051589903] 
dist 74=[-3.4197189311046501613 ,.2425140996524593303 ] 
dist 75=[-3.4052423161241612662 ,.40476874190206804498] 
dist 76=[-1.4956015335772272494 ,.55463812181930395054] 
dist 77=[-1.3279102863883025664 ,.66637071693476358595] 
dist 78=[-1.1513027898857997672 ,.7711626122442037239 ] 
dist 79=[-1.1417083979246902811 ,.8933492043749977472 ] 
dist 80=[-.64265133885576551887,1.0064412725688709186 ] 
dist 81=[-.58000233155878787441,1.0749649562711886494 ] 
dist 82=[-.4515268875737988392 ,1.2639329806301267626 ] 
dist 83=[-.41813635509777860057,1.5662140258383231292 ] 
dist 84=[-.29818827161794276126,1.8493195604521334951 ] 
dist 85=[-.27306423406504525481,2.0211865702422375792 ] 
dist 86=[-.23733018807789391891,2.1440788910231894642 ] 
dist 87=[-.22717969401928355201,2.2318371301636369768 ] 
dist 88=[.67494051214778250633,2.2970428023760272804 ] 
dist 89=[.66552010555616568482,2.3299822841713621161 ] 
dist 90=[.60379667352592911134,2.3455230646216816029 ] 
dist 91=[.47829055693215430022,2.3429544356016392305 ] 
dist 92=[.34312717493111441331,1.0777216410856715198 ] 
dist 93=[.129499915343441603  ,1.1196437377895359719 ] 
dist 94=[-.05387359019763882105,1.1453565348256528563 ] 
dist 95=[-.24142371130716623799,1.1556901452352952822 ] 
dist 96=[-.41673633322442887336,1.1596538390644490308 ] 
dist 97=[-.55130731039953165379,1.1599504403530309964 ] 
dist 98=[-.68148833320894573092,1.1576633303966711868 ] 
dist 99=[-.83930157088409361414,1.1527952240042325822 ] 
dist 100=[-.98682730403972868072,1.1428823657817545001 ] 
dist 101=[-1.0759799357803153274 ,1.1361250595836348176 ] 
dist 102=[-1.1392667301280246051 ,1.1203539690463639021 ] 
dist 103=[-1.1836265113455617365 ,1.1129938865265370438 ] 
dist 104=[-1.2163942977871788697 ,.35493558462322818297] 
dist 105=[-1.2334370321107335110 ,.37968936000312758979] 
dist 106=[-1.2421879164416898026 ,.48179237022471154381] 
dist 107=[-1.2432957199300107286 ,.63932404360300760685] 
dist 108=[-1.3511811119972333397 ,.79635710164442377348] 
dist 109=[-1.4110756423399719138 ,.89646761176904701465] 
dist 110=[-1.4472482228017312768 ,.97377213183193484996] 
dist 111=[-1.4604925851388646174 ,1.0398416325628574936 ] 
dist 112=[-1.4649487692890555351 ,1.0933793421278486548 ] 
dist 113=[-1.4660548418652390655 ,1.1206969827905376989 ] 
dist 114=[-1.4649485216361986216 ,1.1345845055326292345 ] 
dist 115=[-1.4605628251520627514 ,1.1367071978641220522 ] 
dist 116=[-1.1946042671808079321 ,1.1226950107705489646 ] 
dist 117=[-1.1557554077124414036 ,1.1154211997834428684 ] 
dist 118=[-1.1061690635701984862 ,1.1002250439888759235 ] 
dist 119=[-1.1035326147180712356 ,1.0931984295778101341 ] 
dist 120=[-.9956713006794311818 ,1.0528389884830457172 ] 
dist 121=[-.97652421556983566512,1.0423395479481631334 ] 
dist 122=[-.95113230482840609072,1.0064279111137780647 ] 
dist 123=[-.94097376043012679482,.99927867433083455004] 
dist 124=[.30951966478608891658,.52363513262279788269] 
dist 125=[.32278545066785803993,.59152182578326685578] 
dist 126=[.34681548174749684285,.70331153605335337943] 
dist 127=[.35116217192348892341,.8497100716778772338 ] 
dist 128=[.35540907639942242168,.9781891250057992781 ] 
dist 129=[.34677706117681668644,1.0630265604144820978 ] 
dist 130=[.3293030531880370578 ,1.1319876087659506277 ] 
dist 131=[.29524667694433533185,1.1971359769228714649 ] 
dist 132=[.25323093356122032904,1.2535006629249021686 ] 
dist 133=[.20400592532587273562,1.2874224829803041708 ] 
dist 134=[.14017621775303322335,1.3113461106678662979 ] 
dist 135=[.03990108487797074721,1.3278245033944810482 ] 
dist 136=[-.1161039741710046328 ,1.3382279143102498057 ] 
dist 137=[-.22234885413385509799,1.3379165895882230397 ] 
dist 138=[-.30881588498740026222,1.3318183807107649648 ] 
dist 139=[-.39063001470531940908,1.3259380732501063898 ] 
dist 140=[-.46297631686446141926,.56476531215056015911] 
dist 141=[-.51167834450617479592,.49807966460674456012] 
dist 142=[-.55228508256484307149,.43751690439263018641] 
dist 143=[-.59234179095150017916,.42787421950860487679] 
dist 144=[-.62768623478898534188,.21996649246736241158] 
dist 145=[-.64949666842252851498,.19302218926581636737] 
dist 146=[-.66552877837290387136,.13423936528215891788] 
dist 147=[-.67782368838820147515,.1200781597605674666 ] 
dist 148=[-.74061576658258495609,.05390372244650508933] 
dist 149=[-.80759925476786380436,.04211415993743844664] 
dist 150=[-.85553183999521070073,.01436356835598476931] 
dist 151=[-.88985475963951453458,.01004527643083380488] 
dist 152=[-.91546322065430046327,-.07080528843537842768] 
dist 153=[-.92863390662687062023,-.07902570458737613896] 
dist 154=[-.93519074432246696496,-.02949050797908471275] 
dist 155=[-.93441690680727272507,.03822609289187955195] 
dist 156=[-.19690789863741186826,.1015091048410405619 ] 
dist 157=[-.17894337281047439006,.15007380254753259182] 
dist 158=[-.162392449848340329  ,.19704643410922775782] 
dist 159=[-.18033504202605971738,.25398137349379511938] 
dist 160=[-.19781990571437404847,.30738958237951102714] 
dist 161=[-.20964278541590431442,.34029540690602687122] 
dist 162=[-.21955539401545300965,.36441322564735452608] 
dist 163=[-.22941683897510280793,.38276729323848052717] 
dist 164=[-.23845146261296280188,.39682960234314955601] 
dist 165=[-.24506292794624461912,.40382893167249487873] 
dist 166=[-.25113487469260649717,.4069831661884372654 ] 
dist 167=[-.25801200528408427329,.40704669395960337724] 
dist 168=[-.26380268842856571891,.44743764220696524219] 
dist 169=[-.26554051334265345343,.49963381862369995983] 
dist 170=[-.29038089561120186412,.55681151816635375684] 
dist 171=[-.35475438750291354197,.63560252180326589868] 
dist 172=[-.41880603510050317227,.71130839215123394268] 
dist 173=[-.45959734156189113353,.7561795222264030368 ] 
dist 174=[-.49106827817385053715,.78698317461101873432] 
dist 175=[-.51794264269556507383,.80657027200670739901] 
dist 176=[-.5397282502035652699 ,.81975159689114631518] 
dist 177=[-.55090080987979232605,.82500006031608983587] 
dist 178=[-.55641009398144773715,.82543746991829925259] 
dist 179=[-.55699199854004428276,.82362398349396749676] 
dist 180=[-.55186039426181249209,.72344636407747142992] 
dist 181=[-.54906998835660975782,.70705769284343620442] 
dist 182=[-.53921489258088308513,.67561837542590111014] 
dist 183=[-.53463623229419183762,.66635168248386945435] 
dist 184=[-.50445339411616171788,.62860575590238438106] 
dist 185=[-.49653229962502412661,.61885098816004222291] 
dist 186=[-.48251776140826621845,.59694313017636993548] 
dist 187=[-.47817306566734737064,.58931513773770629984] 
dist 188=[-.49442149150918914207,.18841476138955105905] 
dist 189=[-.52256110478040469923,.21966221823206922322] 
dist 190=[-.54944929683568643699,.25367861686343356559] 
dist 191=[-.58158534072459631002,.30026354735116930898] 
dist 192=[-.61785534468678534324,.3465078383103995208 ] 
dist 193=[-.66805109873916432193,.37916636312511561688] 
dist 194=[-.70836774392343623768,.4080573870683124018 ] 
dist 195=[-.74563271893651209806,.43927498081613302974] 
dist 196=[-.77762303141556490546,.46952112738543236286] 
dist 197=[-.79689819875492480404,.49453839045043787265] 
dist 198=[-.81051372954480889414,.52046880480564021187] 
dist 199=[-.81992723197628941985,.5543595994269255029 ] 
dist 200=[-.82589859677817770117,.5980775764894001897 ] 
dist 201=[-.82578320172137300978,.70501355309880320083] 
dist 202=[-.82204312861125560016,.78911406280980845634] 
dist 203=[-.81873769882049632225,.86378944003941167616] 
dist 204=[-.65076757823034941229,.92650495206172395192] 
dist 205=[-.66626083117583248473,.96289829455327091456] 
dist 206=[-.67492394344791870155,.98690751395792864343] 
dist 207=[-.6764997247252992565 ,1.0002239191628673527 ] 
dist 208=[-.62419788328449371365,1.0076696926850849894 ] 
dist 209=[-.6143932374824189583 ,1.0082610476392480813 ] 
dist 210=[-.60246225272117557766,1.0039510125412643303 ] 
dist 211=[-.59683458314507297324,1.0006563980963541639 ] 
dist 212=[-.58630445684853079692,.97609196724987773281] 
dist 213=[-.58174680298430422247,.96874060544696212909] 
dist 214=[-.5784387897768748417 ,.94115955771927648653] 
dist 215=[-.57597992208504761738,.93543045438420614739] 
dist 216=[.02469249514162412858,.56288428373219133388] 
dist 217=[-.01751666083726585086,.57141912378203642608] 
dist 218=[-.07089093149424521470,.5756261316645901076 ] 
dist 219=[-.15331128088280272332,.57527795611031541396] 
dist 220=[-.23596262318764315564,.14212031568752820214] 
dist 221=[-.29474094539465481503,.13070203759959136713] 
dist 222=[-.35027194877335268386,.10981868017219395735] 
dist 223=[-.40423012943131469144,.10483084228234033215] 
dist 224=[-.45291963811742758236,.09028736675079261387] 
dist 225=[-.4874335568645754527 ,.08741088218592701392] 
dist 226=[-.5181072015563447531 ,.08787112539836886032] 
dist 227=[-.55147785010286957017,.09299926983438939501] 
dist 228=[-.58076670636602173874,.1000909264040926508 ] 
dist 229=[-.59515776214652738296,.10838416293820537139] 
dist 230=[-.60256913342384491119,.11912615736982754802] 
dist 231=[-.60401456342299416394,.13598708861881859763] 
dist 232=[-.59221855032375242585,.1554472355600246791 ] 
dist 233=[-.58868549108040369507,.17655830224477676038] 
dist 234=[-.58614070124256364039,.20287960200828262309] 
dist 235=[-.58428753826997417684,.2431245458636964916 ] 
dist 236=[-.50728192268612160701,.28320435543879430363] 
dist 237=[-.54182733821183257505,.33474627145632689572] 
dist 238=[-.56623154948870068627,.40635769999401099498] 
dist 239=[-.58309550435198402382,.47363861510898549146] 
dist 240=[-.59493086965520483831,.5328189939920507098 ] 
dist 241=[-.5992767483795503593 ,.57211716893000415804] 
dist 242=[-.59959132920574868648,.60429705811130105907] 
dist 243=[-.5981699401842567621 ,.63508237771319022664] 
dist 244=[-.53989455183812914784,.66134425846788624346] 
dist 245=[-.52954601828455695618,.67548015802454928423] 
dist 246=[-.50848568174454260215,.68341230833740211186] 
dist 247=[-.5017749765989190806 ,.68492767528191353844] 
dist 248=[-.47153435405042656066,.68275393463739037745] 
dist 249=[-.46445491365350211086,.68040551830488880948] 
dist 250=[-.44412980840281581261,.66875987969133302175] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 0, 0, 1, 2] 
dist 0=[66.825322868099497839  ,66.825322868099497839  ] 
dist 1=[66.367289284904844448  ,66.898111372992979840  ] 
dist 2=[65.503173021315974956  ,66.825322868099497839  ] 
dist 3=[63.811318151663102200  ,66.650321088925927451  ] 
dist 4=[61.712845881987346240  ,66.291108177227228770  ] 
dist 5=[59.225263690439231736  ,65.977835314167342444  ] 
dist 6=[55.971916627854778901  ,65.809721587287037966  ] 
dist 7=[50.815954939492241943  ,65.046341005505684864  ] 
dist 8=[45.555339906362506398  ,64.796439563123519808  ] 
dist 9=[41.884131055612665442  ,64.038612625171480945  ] 
dist 10=[38.668478168076390618  ,63.753125085345580249  ] 
dist 11=[35.226737621008453135  ,61.894831182630792295  ] 
dist 12=[31.896240031914724186  ,61.391990457019026521  ] 
dist 13=[29.124641353759755381  ,60.879181995874236876  ] 
dist 14=[26.226633702169047092  ,58.268629372732906803  ] 
dist 15=[22.391127821992711349  ,51.854858838488801129  ] 
dist 16=[18.616184421380972986  ,28.239234759322894865  ] 
dist 17=[15.959798793825792155  ,26.607341105755847827  ] 
dist 18=[13.608374723353674586  ,26.293287863789057452  ] 
dist 19=[11.050789314882510289  ,18.986891423633254529  ] 
dist 20=[8.5480892017724939277 ,15.420204643709079364  ] 
dist 21=[6.4153547202020447295 ,12.936175219207702517  ] 
dist 22=[4.1380634505494585350 ,12.368783896371927523  ] 
dist 23=[.8909082081365133266 ,10.723018463217183705  ] 
dist 24=[-2.5393871130775933982 ,9.5017612337085997651 ] 
dist 25=[-4.7361943024972138846 ,8.7125090151155261347 ] 
dist 26=[-6.4579130347253495117 ,8.5519622867008780501 ] 
dist 27=[-7.9919507671483068775 ,-.51565017778717572563] 
dist 28=[-9.2998633866708690173 ,-1.2965212326410851786 ] 
dist 29=[-10.119691321970833646  ,-2.8915283651913423981 ] 
dist 30=[-10.749255403243236869  ,-3.2439106458088352515 ] 
dist 31=[-11.299719346777801856  ,-4.5809884556433425496 ] 
dist 32=[-11.733525470742964920  ,-4.8266782497338416153 ] 
dist 33=[-11.897370945106724370  ,-5.0550619931276095991 ] 
dist 34=[-12.043424821641250887  ,-4.9818615330837872992 ] 
dist 35=[-12.348502342331557487  ,-4.8009391979065740157 ] 
dist 36=[-12.803321438459198821  ,-4.4839442012837093854 ] 
dist 37=[-13.111533021695811551  ,-3.1942356665300161282 ] 
dist 38=[-13.304856816350557340  ,-1.5662200397362335693 ] 
dist 39=[-13.416976642284553868  ,.94317136589183424925] 
dist 40=[-13.432102918386391169  ,3.4609165503468085956 ] 
dist 41=[-13.349348849191396508  ,5.1224313147624386759 ] 
dist 42=[-13.322043436573731238  ,6.4711192845498160852 ] 
dist 43=[-7.6243425610805155299 ,7.7412181172191396868 ] 
dist 44=[-6.8925125327107283689 ,8.8604082847051653708 ] 
dist 45=[-6.7450719600489111579 ,9.6072286385445013910 ] 
dist 46=[-6.5417224038861042915 ,10.222967362970073019  ] 
dist 47=[-6.4751318480321991305 ,10.819383228998340812  ] 
dist 48=[-3.4274545185375567692 ,11.333268981833527821  ] 
dist 49=[-3.1441052728070377563 ,11.619767459555346608  ] 
dist 50=[-2.4620336556239344934 ,11.794150264770152549  ] 
dist 51=[-2.3496168625627265033 ,11.860621837936713270  ] 
dist 52=[-1.3747944605984222049 ,11.856016166320054678  ] 
dist 53=[-1.1955002491854621924 ,11.829386469738202272  ] 
dist 54=[-.94096886073675308374,11.540555937784420658  ] 
dist 55=[-.86786404079244859523,10.636050297111875733  ] 
dist 56=[.45502355944776702381,7.7760153503936412026 ] 
dist 57=[.61793657264856441081,7.7591549279258611833 ] 
dist 58=[.98516092763003284485,7.7246300942916066571 ] 
dist 59=[1.0418138715170895282 ,7.9635465529032282768 ] 
dist 60=[.4499047116129742980 ,8.1578093642042247720 ] 
dist 61=[-.41309204955058086042,8.2374793990610538229 ] 
dist 62=[-1.3098993336601433201 ,8.2607050762829223612 ] 
dist 63=[-2.1574539008794683308 ,8.2472605032583556976 ] 
dist 64=[-2.8240215384584597496 ,2.0059888124233678119 ] 
dist 65=[-3.4843113666810065251 ,2.0705066902078271301 ] 
dist 66=[-4.3068656181772838079 ,2.1168119582886591333 ] 
dist 67=[-5.0873496658601366303 ,2.1502353222948334290 ] 
dist 68=[-5.5798334683711995242 ,2.1727404567953024893 ] 
dist 69=[-5.9547533105719993825 ,2.1754924054089367740 ] 
dist 70=[-6.2662694866104461115 ,2.1677798243116316000 ] 
dist 71=[-6.5631570451835106445 ,2.1588966670837393050 ] 
dist 72=[-6.9629581548157046353 ,.96648658066420882253] 
dist 73=[-7.1650414920084586092 ,.86188393861380972005] 
dist 74=[-7.2720547114570187595 ,.61606590623058780967] 
dist 75=[-7.2925228411404665296 ,.92784668284223901711] 
dist 76=[-7.1793514473658538782 ,1.5964343332931232024 ] 
dist 77=[-7.1421062833991464594 ,2.1540233445824512013 ] 
dist 78=[-7.1127026240401414501 ,2.7037615017568549192 ] 
dist 79=[-7.0864485495569133006 ,3.2045686579809069690 ] 
dist 80=[-5.2182947460192611320 ,3.5670123793968263926 ] 
dist 81=[-4.9853436168210645644 ,3.8965485627395433277 ] 
dist 82=[-4.4330175830818140278 ,4.2691700600535805157 ] 
dist 83=[-4.3038638247588138344 ,5.0711261265508466182 ] 
dist 84=[-3.4985551828272889376 ,5.7828444004505065134 ] 
dist 85=[-3.3385996079096777920 ,6.2660134237396155950 ] 
dist 86=[-3.0336007707072604674 ,6.6731607159067010022 ] 
dist 87=[-2.9530181159339224380 ,7.0817083891657644868 ] 
dist 88=[-1.7367728751576150939 ,7.4343544145454188773 ] 
dist 89=[-1.5647970995504871593 ,7.6185427117794056919 ] 
dist 90=[-1.1737723214794400365 ,7.7142784078437847907 ] 
dist 91=[-1.4123406120476186316 ,7.7264046618434617747 ] 
dist 92=[-2.0937375391343210330 ,7.6726042041712260177 ] 
dist 93=[-2.6519628724067434559 ,7.6302539484638330756 ] 
dist 94=[-3.1857613518793436663 ,7.5207129189267423607 ] 
dist 95=[-3.6611564858059940616 ,7.4653489017424282869 ] 
dist 96=[-3.9864701224016869602 ,2.2935191049541800611 ] 
dist 97=[-4.2632453621109533843 ,2.0883597039187024338 ] 
dist 98=[-4.5450753564795451175 ,2.0366169478662033425 ] 
dist 99=[-4.7902995125766195269 ,1.1228086728690956887 ] 
dist 100=[-4.9210841269165689031 ,.99794507877364311254] 
dist 101=[-4.9927481918053440185 ,.75220736459134849457] 
dist 102=[-5.0022359152163516386 ,.86153911864539658584] 
dist 103=[-4.9832303460879439861 ,1.0147389801129638081 ] 
dist 104=[-4.9587388037891710263 ,1.1630914073247822018 ] 
dist 105=[-4.8901752558410215236 ,1.2530878416290127491 ] 
dist 106=[-4.8537494641102806410 ,1.3174164106669044942 ] 
dist 107=[-.86914433783532452219,1.3633758769317449152 ] 
dist 108=[-.89454421082234639516,1.3967417518700932655 ] 
dist 109=[-.90495249352379838115,1.4108308852778991762 ] 
dist 110=[-.90822675313439955122,1.4141288726087697577 ] 
dist 111=[-.90637793348263588954,1.4121995509606477956 ] 
dist 112=[-.8806476309302422144 ,1.2784901319725802856 ] 
dist 113=[-.87325748341936929123,1.3516463516087458916 ] 
dist 114=[-.84966904574515129175,1.4994782091862471177 ] 
dist 115=[-.8419813497142361499 ,1.6334786821610984698 ] 
dist 116=[-.78074164643446767286,1.7159645882355949578 ] 
dist 117=[-.76578098091946057007,1.7763096804917266519 ] 
dist 118=[-.7428653406619194692 ,1.8219989993863166148 ] 
dist 119=[-.7349392223719234411 ,1.8546327386014389282 ] 
dist 120=[-.54631386809826019184,1.8629038404948007691 ] 
dist 121=[-.63960538099057426277,1.8602772757375625252 ] 
dist 122=[-.80597552884045260885,1.8521913656648002461 ] 
dist 123=[-.9622692796640000625 ,.95357676967631349065] 
dist 124=[-1.0997357137001066455 ,.87285534156772353469] 
dist 125=[-1.1910033091539647267 ,.67798700022975495613] 
dist 126=[-1.2657227186144738645 ,.64559935352522269087] 
dist 127=[-1.3371781552665835321 ,.36604602429564825758] 
dist 128=[-1.3988799876550295853 ,.31466576338872238477] 
dist 129=[-1.4346922121770254015 ,.24070819673108118325] 
dist 130=[-1.4583267925461164673 ,.21981220893438934856] 
dist 131=[-1.4714521213324140200 ,-.15408734617933183092] 
dist 132=[-1.4767895481006910534 ,-.20061132576190738466] 
dist 133=[-1.4748362840190712066 ,-.2928753203139859325 ] 
dist 134=[-1.4584680537063137963 ,-.2023601828187765835 ] 
dist 135=[-1.4500050091828686904 ,-.0658729635352371604 ] 
dist 136=[-1.0613465829579464428 ,.07176241981619238639] 
dist 137=[-1.0686883221468793682 ,.16685811796170809667] 
dist 138=[-1.0685989177034729163 ,.24881555312495640207] 
dist 139=[-.46681089531983474593,.36122138990287375211] 
dist 140=[-.47015322087783643029,.50759958234180802919] 
dist 141=[-.47597333463617014744,.61802259097176115345] 
dist 142=[-.48674226180155527366,.72302748215803868489] 
dist 143=[-.49989022670832412226,.8477937754279875764 ] 
dist 144=[-.51519555999449387356,.96341449807123864971] 
dist 145=[-.53500595913021863244,1.0319378713704388556 ] 
dist 146=[-.56612072265530261022,1.0789453644041017804 ] 
dist 147=[-.59883232499619183088,1.1087387567906040705 ] 
dist 148=[-.62500874405573003105,1.1293597392649511637 ] 
dist 149=[-.65136421715903047733,1.1397785537641615835 ] 
dist 150=[-.68478289152694736052,1.1446997142455265443 ] 
dist 151=[-.72008802920615415457,1.1433912347909779422 ] 
dist 152=[-.75396317627766132221,.63573463679249716204] 
dist 153=[-.79318811604126668306,.77954649436750549729] 
dist 154=[-.84982479207969545475,.98654677653416907874] 
dist 155=[-.90474101053273656985,1.1891933947196233506 ] 
dist 156=[-.93710182530903408028,1.3156402921424431613 ] 
dist 157=[-.95903982150159581227,1.4102446159024481727 ] 
dist 158=[-.97238461635957752681,1.4858699528677193586 ] 
dist 159=[-.97911882980205220734,1.5444378584487953405 ] 
dist 160=[-.97951486814723741905,1.5709979029872787916 ] 
dist 161=[-.96809227589202478248,1.5825810145560868901 ] 
dist 162=[-.96618750898491477386,1.5814035735812271806 ] 
dist 163=[-.96010904474555631796,1.5014876961206328175 ] 
dist 164=[-.93408677697541565095,1.4829109753751894143 ] 
dist 165=[-.92709543563081596859,1.4471088299880482667 ] 
dist 166=[-.92268915172228921371,1.4346038995027023981 ] 
dist 167=[-.92067518913420818338,1.3748096816667980445 ] 
dist 168=[-.9333153685822224277 ,1.3592109493839718817 ] 
dist 169=[-.9917583635079895195 ,1.3124961264683651319 ] 
dist 170=[-1.0313670253561886463 ,1.2996965393578806863 ] 
dist 171=[-1.0554949211835128661 ,.7745241585027824291 ] 
dist 172=[-1.0713514498489233225 ,.8700287703900273759 ] 
dist 173=[-1.0779671611132923366 ,.9357257372126824363 ] 
dist 174=[-1.0790646591389596479 ,.9904633461599139500 ] 
dist 175=[-1.2037077068138528865 ,1.0443867475238851305 ] 
dist 176=[-1.3073496855820772800 ,1.0906930534018670225 ] 
dist 177=[-1.3918276454080381403 ,1.1150470091239421598 ] 
dist 178=[-1.4719883819632702346 ,1.1279317377898743191 ] 
dist 179=[-1.5413265909734775188 ,1.1291706910008021162 ] 
dist 180=[-1.5826340801595736923 ,1.1232237222121229578 ] 
dist 181=[-1.6112348823299580430 ,1.1179530401582178189 ] 
dist 182=[-1.6298865143066685464 ,1.1011121963328116915 ] 
dist 183=[-1.6406714758012393149 ,1.0923064333477318922 ] 
dist 184=[-1.6391748019569779266 ,.43240953077759481359] 
dist 185=[-1.6289409852294992843 ,.42372475412977768368] 
dist 186=[-1.6200856810717942622 ,.40066169626772300037] 
dist 187=[-.70306583099754524609,.3950354993613461353 ] 
dist 188=[-.62153459611354212812,.35138081315462243615] 
dist 189=[-.43228219902373190231,.34183271182120531477] 
dist 190=[-.39734384546066034795,.37039074786884445857] 
dist 191=[-.1496929806332300708 ,.46801525533555635069] 
dist 192=[-.1053847944506664591 ,.58304953023451837972] 
dist 193=[-.0267421909270090661 ,.70278660490849537295] 
dist 194=[-.0097014880903527648 ,.84743810341011293476] 
dist 195=[-.01598923809810172061,.98242428894438978981] 
dist 196=[-.07169317007134750915,1.0636072909036668372 ] 
dist 197=[-.12296605393263923688,1.1207551902956187443 ] 
dist 198=[-.18070139860780598168,1.1598671193621146587 ] 
dist 199=[-.26218342460260119283,1.1883520875205702024 ] 
dist 200=[-.34273256277388231715,1.2031095373342776729 ] 
dist 201=[-.39674669020146798899,1.2106068822572170541 ] 
dist 202=[-.44155124928786715779,1.2101309984584635953 ] 
dist 203=[-.48536429528379917793,.19950486598681321632] 
dist 204=[-.52507095364256070779,.17600929519397641422] 
dist 205=[-.56756461108978673364,.13292488239046061337] 
dist 206=[-.663031856459072754  ,.12287163564026848311] 
dist 207=[-.74941129018337005116,.0948873133724938892 ] 
dist 208=[-.81101079960914427184,.0907901809993407249 ] 
dist 209=[-.86612463728153271947,.0942878873686179963 ] 
dist 210=[-.92663399964059569709,.1090551382358695256 ] 
dist 211=[-.98002903563160780485,.1281658003827474390 ] 
dist 212=[-1.0067647464520195330 ,.16600505395487489423] 
dist 213=[-1.0208577285540522909 ,.2228809134844645308 ] 
dist 214=[-1.0238210506924170051 ,.29137845544598305797] 
dist 215=[-1.0060573745473247312 ,.3934450705079395115 ] 
dist 216=[-1.0008048072018045279 ,.49473597803072576379] 
dist 217=[-.99707451835314418397,.5601392802018293112 ] 
dist 218=[-.99445800127327879138,.61163663417523041681] 
dist 219=[-.93039015290064081548,.65745846980806573198] 
dist 220=[-.9832596174503840068 ,.69600257888980533834] 
dist 221=[-1.0186396457439923391 ,.71846994586386964527] 
dist 222=[-1.0392851185274319198 ,.7885991952514925249 ] 
dist 223=[-1.0521566399697770956 ,.8889629148782755585 ] 
dist 224=[-1.0565275569700124737 ,.9558647885343106338 ] 
dist 225=[-1.0554985596038363892 ,1.0109208506092782172 ] 
dist 226=[-1.0524723522414889015 ,1.0640327104109457533 ] 
dist 227=[-.9101536563269440198 ,1.1094578986985103620 ] 
dist 228=[-.8873575595055145395 ,1.1338528746300592371 ] 
dist 229=[-.8429586796530565749 ,1.1474606942505655563 ] 
dist 230=[-.8299214941299562211 ,1.1498579165639426004 ] 
dist 231=[-.7766971307037933593 ,1.1460282281710992391 ] 
dist 232=[-.7633848872640379382 ,1.1418421567847692970 ] 
dist 233=[-.7330352511512722357 ,1.1226710826476564545 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 1, 2, 1, 0, 2] 
dist 0=[62.814578943988990296  ,62.814578943988990296  ] 
dist 1=[62.386827240100919510  ,63.090567301917075162  ] 
dist 2=[60.954819178919228523  ,63.454896782395237914  ] 
dist 3=[59.155945898359894918  ,63.539912524522482508  ] 
dist 4=[56.995671581914209465  ,62.865951504481089434  ] 
dist 5=[54.153344833867919013  ,62.688355123666428149  ] 
dist 6=[49.631152530216749918  ,62.270800768199894096  ] 
dist 7=[45.010573279226152740  ,62.099992771524853687  ] 
dist 8=[41.775357093767682524  ,61.417097243052887557  ] 
dist 9=[38.930318603305883698  ,61.180753009600814032  ] 
dist 10=[35.867506265312190868  ,60.549411799800786544  ] 
dist 11=[32.892687993934798859  ,60.280695704962752361  ] 
dist 12=[30.398821806884713659  ,58.862615426595114021  ] 
dist 13=[27.774746198384505366  ,58.476810780251903964  ] 
dist 14=[24.279651622191501731  ,56.584319833927032454  ] 
dist 15=[20.828191225550496033  ,53.113831984985572350  ] 
dist 16=[18.378117645807251431  ,28.722928304508324261  ] 
dist 17=[16.186486784360513730  ,26.436364703025752456  ] 
dist 18=[13.766652807571583481  ,24.733740950443156692  ] 
dist 19=[11.376485917909643006  ,24.503453372133963465  ] 
dist 20=[9.3028275014333388351 ,14.935733357758338260  ] 
dist 21=[7.0562540641207401998 ,14.094876999911645443  ] 
dist 22=[3.9745135564513638689 ,13.948168964509487769  ] 
dist 23=[.95785222037770159653,10.824751569272870718  ] 
dist 24=[-1.0289061843587690602 ,8.6747340068217301113 ] 
dist 25=[-2.6500165711211350311 ,8.2620117464809109378 ] 
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dist 27=[-6.0532637377050304848 ,7.5964334344937428555 ] 
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dist 30=[-9.7479680843771465483 ,-2.4175393908072944627 ] 
dist 31=[-10.915560628879998099  ,-4.9869014899662638524 ] 
dist 32=[-11.972759826230401062  ,-5.0955576194881837029 ] 
dist 33=[-12.551624901688709296  ,-4.6576261692042084184 ] 
dist 34=[-12.901694725018413314  ,-3.8622580708999641764 ] 
dist 35=[-13.043538145683526512  ,-2.9038085016775818420 ] 
dist 36=[-13.102351986791382067  ,-1.8149338796421620669 ] 
dist 37=[-13.119706160066058464  ,-.4261478477044596698 ] 
dist 38=[-13.113789536864871952  ,1.7288885261283597454 ] 
dist 39=[-13.077949602149708790  ,3.8894946632194861177 ] 
dist 40=[-13.025595658673095285  ,5.3006859501634667823 ] 
dist 41=[-13.159960359058618051  ,6.4293044167808848068 ] 
dist 42=[-13.219018087146829296  ,7.4630481817917180318 ] 
dist 43=[-13.210684124003776694  ,8.3535236991587303570 ] 
dist 44=[-9.5746299949631957856 ,8.9107882983726985191 ] 
dist 45=[-9.4347121599403340173 ,9.3293993815001239040 ] 
dist 46=[-9.2202058023126162782 ,9.6669034144772725195 ] 
dist 47=[-9.1505485192212001973 ,9.9377871552917126232 ] 
dist 48=[-4.6891834223269365981 ,10.090650868743941564  ] 
dist 49=[-4.0098253522603211169 ,10.185969664024167883  ] 
dist 50=[-3.8529792423404249115 ,10.227199842751442037  ] 
dist 51=[-2.9585171069663803780 ,10.229986355807012392  ] 
dist 52=[-2.7889262096844611921 ,10.195414782269432330  ] 
dist 53=[-2.4423778762813545571 ,10.085539034064906248  ] 
dist 54=[-2.3486893148725778256 ,9.7623280041752184843 ] 
dist 55=[2.6821791811332260411 ,9.2974215357020022240 ] 
dist 56=[3.2396744673264522786 ,9.3609128469391039786 ] 
dist 57=[3.2941056158450886722 ,9.3833638966065828321 ] 
dist 58=[3.2216988848727276043 ,9.3802793304412839383 ] 
dist 59=[2.9589430631459679152 ,9.3436010785550454002 ] 
dist 60=[2.2528917746546855019 ,9.1098330714157906378 ] 
dist 61=[1.1142693190609261377 ,9.1803808843894694825 ] 
dist 62=[.13357366741769448738,9.1970711727161200471 ] 
dist 63=[-.88514781738931985723,9.1944436337016767354 ] 
dist 64=[-1.8478292671042171753 ,-.50614043304792146809] 
dist 65=[-2.6050009920695316324 ,-.75612738108476534462] 
dist 66=[-3.3551536368363276135 ,-1.2384241506610847016 ] 
dist 67=[-4.2898574320098178729 ,-1.3490369054284171470 ] 
dist 68=[-5.1768588635464085413 ,-2.3716905893054619663 ] 
dist 69=[-5.7367245573311926452 ,-2.5276862469338637043 ] 
dist 70=[-6.1631092880019839131 ,-2.6307879591201512346 ] 
dist 71=[-6.5176284151726155265 ,-2.5468749384275726935 ] 
dist 72=[-6.7979795161794352213 ,-2.3727877191811294940 ] 
dist 73=[-6.9284883219122832681 ,-2.0806176886202040937 ] 
dist 74=[-6.9880621503029588492 ,-1.6470089577971340696 ] 
dist 75=[-6.9854632784888982621 ,-.90877973370702375375] 
dist 76=[-6.1602048297106423633 ,-.15293031734139387869] 
dist 77=[-6.1586311210195952331 ,.35098482538977240558] 
dist 78=[-6.1290775625475828696 ,.76545165908400145454] 
dist 79=[-6.1073718658967457829 ,1.2330046042589008685 ] 
dist 80=[-4.3058900964085527895 ,1.6738818420101306248 ] 
dist 81=[-4.1072925686382956204 ,1.9917170471214273346 ] 
dist 82=[-3.6084058643142832396 ,2.2795714913625293231 ] 
dist 83=[-3.5215973490575756580 ,2.6008949947616239222 ] 
dist 84=[-2.7239136977217037213 ,2.8953449571811602913 ] 
dist 85=[-2.5680715921688738652 ,3.0760145172505829263 ] 
dist 86=[-2.3583936885690493777 ,3.2924691357554112547 ] 
dist 87=[-2.2898060619488998138 ,3.6414729983634910077 ] 
dist 88=[-.89822768762357432136,3.9567041990490062054 ] 
dist 89=[-.72088609004456905672,4.1478624599204894825 ] 
dist 90=[-.32274995150573477052,4.2843918699776410264 ] 
dist 91=[-.24369290364262111714,4.3817190930938223214 ] 
dist 92=[.23065982122961573326,4.4462526921342761049 ] 
dist 93=[.31234646356828402634,4.4567756380954306247 ] 
dist 94=[.24645140116657997082,4.4372767981582804026 ] 
dist 95=[-.05172505659797156590,4.4202977592441320181 ] 
dist 96=[-.32889711260748818201,1.0143519125941404276 ] 
dist 97=[-.53881919684983072134,.92010603722906199453] 
dist 98=[-.73906534256059010104,.80802442636399229077] 
dist 99=[-.97764884992528063339,.78248585519377227745] 
dist 100=[-1.2191617318945673534 ,-.03550081179131563211] 
dist 101=[-1.3755711802387866912 ,-.13378909198073834642] 
dist 102=[-1.4925901003903853836 ,-.29758583462671729201] 
dist 103=[-1.6259397046444955529 ,-.38972883885008994968] 
dist 104=[-1.9010163377130077577 ,-.61445469096892389397] 
dist 105=[-2.0756190100479130007 ,-.65140859827534778734] 
dist 106=[-2.2096535510955184462 ,-.72193464895393854705] 
dist 107=[-2.3229163042247627692 ,-.736255156974939101  ] 
dist 108=[-2.4138383107707656124 ,-1.0227927801980341568 ] 
dist 109=[-2.4587620973919158925 ,-.91651713082060447087] 
dist 110=[-2.4784901238406186944 ,-.8183685919647208406 ] 
dist 111=[-2.4790745383257421823 ,-.70617756622952700575] 
dist 112=[-1.4468913344455867550 ,-.59402708313020552937] 
dist 113=[-1.3576530419520654319 ,-.49601886430507279884] 
dist 114=[-1.1384712357843281392 ,-.38989639899301758068] 
dist 115=[-1.1006984580454458900 ,-.24535918341603347709] 
dist 116=[-.7712768519345280737 ,-.10231537695583180154] 
dist 117=[-.70913344354542454947,-.00213405381001372064] 
dist 118=[-.61994872358377491776,.08561472630569024599] 
dist 119=[-.59385097226240545822,.1790934015111630675 ] 
dist 120=[-.10459718479380109462,.38927380513438812255] 
dist 121=[-.04344682262584223832,.54366965842790210123] 
dist 122=[.09453451278854093316,.67351180137471478774] 
dist 123=[.11737662132227679272,.80338098291836715069] 
dist 124=[.27745410408174882191,.9230388403215765642 ] 
dist 125=[.30317080058994182769,1.0121767608111443957 ] 
dist 126=[.35009516830879661349,1.0959379169018625708 ] 
dist 127=[.35909757932844280878,1.1941930611801035440 ] 
dist 128=[.39772047990358407593,1.3002079898956249187 ] 
dist 129=[.36898050723703155555,1.3971852235406487357 ] 
dist 130=[.32364598067813882562,1.4765989607182507651 ] 
dist 131=[.24402708878208423441,1.5527434177274370167 ] 
dist 132=[.15726566325901332554,1.6209079191716039060 ] 
dist 133=[.08343024604232825296,1.6684770588168333378 ] 
dist 134=[.00510734937953969169,1.7100452744416786675 ] 
dist 135=[-.09957367531370038699,1.7542625072105505272 ] 
dist 136=[-.21292739008325317732,1.7926073909882158693 ] 
dist 137=[-.32585912799960333729,1.8107409275020946035 ] 
dist 138=[-.45991260493665947274,1.8175314399762634957 ] 
dist 139=[-.65754154836308111421,1.8147365609657691806 ] 
dist 140=[-.86794502730018175853,1.7955535657787547171 ] 
dist 141=[-1.0352155982419854284 ,1.7872436148984133088 ] 
dist 142=[-1.1731791483838438912 ,1.7463937085103028352 ] 
dist 143=[-1.3524660359166380860 ,1.7399295900162526300 ] 
dist 144=[-1.8487941728888766524 ,1.5916355905522146572 ] 
dist 145=[-2.1696444251975184759 ,1.5611684500685019432 ] 
dist 146=[-2.4228080440383853560 ,1.4986636138368268464 ] 
dist 147=[-2.6491257748861345550 ,1.4787004735735003390 ] 
dist 148=[-2.8403788886184640244 ,1.3881078825170103818 ] 
dist 149=[-2.9536674519560329975 ,1.3672845904992273561 ] 
dist 150=[-3.0313616793765176607 ,1.3057912791701720080 ] 
dist 151=[-3.0806306919387236587 ,1.2929820340543672144 ] 
dist 152=[-3.1115464759230132298 ,1.1549872451366540620 ] 
dist 153=[-3.1160264663524566094 ,1.1269914515556537454 ] 
dist 154=[-3.1051536426785287624 ,1.0682667118770648352 ] 
dist 155=[-3.0937695820768411294 ,1.0500263013290540428 ] 
dist 156=[-3.0063727634041984716 ,1.0732833191040551304 ] 
dist 157=[-2.9798964785845155236 ,1.3526361357805586838 ] 
dist 158=[-2.9034355194330006691 ,1.5769592496140594076 ] 
dist 159=[-2.8724920335448851539 ,1.7841956115302937038 ] 
dist 160=[-1.0821891883121746168 ,1.9640926181577940863 ] 
dist 161=[-1.0511332695950360148 ,2.0793594761951019256 ] 
dist 162=[-.98035526762068921699,2.1691404846553080355 ] 
dist 163=[-.9579635790057217363 ,2.2473766661687515389 ] 
dist 164=[-.73221180403972896069,2.3892467925334236931 ] 
dist 165=[-.69596229943744747348,2.5933672006965359984 ] 
dist 166=[-.61465199180385606106,2.7585217545731643245 ] 
dist 167=[-.59234780315178725661,2.9132091181629078167 ] 
dist 168=[-.4874522539920500038 ,3.0466527529506977345 ] 
dist 169=[-.46678361451425184381,3.1270659721372645550 ] 
dist 170=[-.41877236383038728692,3.1838791976207160401 ] 
dist 171=[-.40635784339183583231,3.2231792495552796486 ] 
dist 172=[-.4401211742803144362 ,3.2481246639580259840 ] 
dist 173=[-.71894076199435014876,3.2476753495090631233 ] 
dist 174=[-.99271382329202291875,3.2328510832455886090 ] 
dist 175=[-1.2555266013628019485 ,3.2190752788530508510 ] 
dist 176=[-1.4905064059811124704 ,1.3315773679675965953 ] 
dist 177=[-1.6532561047222199988 ,1.1668046600878606591 ] 
dist 178=[-1.7939257001035040463 ,.78550357033729287128] 
dist 179=[-1.9408306774587159491 ,.72173967811289940691] 
dist 180=[-2.0719238631292065499 ,.30421114401855620838] 
dist 181=[-2.1495209623467565011 ,.22956591566588817798] 
dist 182=[-2.2026342150761391036 ,.08947755510897014557] 
dist 183=[-2.2360608232467730810 ,.05690799957219916891] 
dist 184=[-2.2541941763876626801 ,-.33708629476150140619] 
dist 185=[-2.2557543049456991590 ,-.39386571600149042005] 
dist 186=[-2.2325380139901972918 ,-.47877797506044519129] 
dist 187=[-2.2674990435048992374 ,-.28588455439551726976] 
dist 188=[-2.3068012988257848521 ,.07123463983716961010] 
dist 189=[-2.3279473290977352380 ,.31105947172161941926] 
dist 190=[-2.3425632326577976230 ,.51038118403763421542] 
dist 191=[-2.3407026952379615857 ,.70593619426505369954] 
dist 192=[-.61903144342719204512,.88359101389351313542] 
dist 193=[-.57227864428642914515,1.0115098563834558288 ] 
dist 194=[-.49381505013482034667,1.1272185232907684543 ] 
dist 195=[-.47452539014116174623,1.2561671171477484110 ] 
dist 196=[-.14548830285991440469,1.3736468872750783514 ] 
dist 197=[-.12653799889741314564,1.4436075640672752544 ] 
dist 198=[-.12014619155745635456,1.4920070574497748451 ] 
dist 199=[-.13165974754301671123,1.5234824883275872038 ] 
dist 200=[-.15179635362666759978,1.5432330581133845948 ] 
dist 201=[-.18040161691993511108,1.5458776352328456077 ] 
dist 202=[-.22063510990861944695,1.5396775919843764352 ] 
dist 203=[-.28715375524881648664,1.5807817877057756989 ] 
dist 204=[-.36530634348652515512,1.6134985179310072566 ] 
dist 205=[-.4519455864469033434 ,1.6275414277185596273 ] 
dist 206=[-.5612097714054552708 ,1.6305675463434859964 ] 
dist 207=[-.7349564839997158974 ,1.6278481135002230141 ] 
dist 208=[-.9319808795149837350 ,1.6631800611881094555 ] 
dist 209=[-1.0568653274214889723 ,1.7488860356307619938 ] 
dist 210=[-1.1525526133206959346 ,1.8049675007965127421 ] 
dist 211=[-1.2331105725016455714 ,1.8351383954316516308 ] 
dist 212=[-1.2975596415095831035 ,1.8525410000986616778 ] 
dist 213=[-1.3289884961340280184 ,1.8576864472295684418 ] 
dist 214=[-1.3451263498647651500 ,1.8548357717941313248 ] 
dist 215=[-1.3485837024417582245 ,1.8487987787534774150 ] 
dist 216=[-1.3187681817602993860 ,1.5866834249102372015 ] 
dist 217=[-1.3194367171003847294 ,1.5454478754569164419 ] 
dist 218=[-1.3455666565160121602 ,1.4652082544352839610 ] 
dist 219=[-1.4620610115119938734 ,1.4419250279525449908 ] 
dist 220=[-1.7503430227454750503 ,1.4801710244331950703 ] 
dist 221=[-1.9289966990751260422 ,1.5592328089579299096 ] 
dist 222=[-2.0612011028821407605 ,1.6126532008253750937 ] 
dist 223=[-2.1641954593846447142 ,1.6448714006648439644 ] 
dist 224=[-2.2434588729017158903 ,1.6648952951963071195 ] 
dist 225=[-2.2809993449854668398 ,1.6696734924445276688 ] 
dist 226=[-2.2966801302513356866 ,1.6654246704496954961 ] 
dist 227=[-2.2966447823070667580 ,1.6601287637153791731 ] 
dist 228=[-2.1380771787726143917 ,1.4673702173748860142 ] 
dist 229=[-2.1063205325566374181 ,1.4350302514916599752 ] 
dist 230=[-2.0493425396576653820 ,1.3676694890372094541 ] 
dist 231=[-2.0312398011894049930 ,1.3465673180546675533 ] 
dist 232=[-1.9536552354246842799 ,1.2521833297133671874 ] 
dist 233=[-1.9308612746565898059 ,1.2311469253504475747 ] 
dist 234=[-1.8765133439120740434 ,1.1701629081640826782 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 1, 1, 2, 1, 2] 
dist 0=[56.613522989205693084  ,56.613522989205693084  ] 
dist 1=[55.437000922399751957  ,57.366250666856704963  ] 
dist 2=[53.722560383285553124  ,57.906134474269670511  ] 
dist 3=[50.822159791878392626  ,58.232774060666622065  ] 
dist 4=[47.803898157622530312  ,58.466253926741439710  ] 
dist 5=[45.618861541328489576  ,58.633919049822803083  ] 
dist 6=[43.622393604891420255  ,58.709197902596914750  ] 
dist 7=[41.356914386197997526  ,58.669636665595928556  ] 
dist 8=[39.087189756490919586  ,57.928034870986820336  ] 
dist 9=[37.073624009311542371  ,55.878275607012765891  ] 
dist 10=[34.858172932014131971  ,55.398617867006673841  ] 
dist 11=[31.782052870296674606  ,54.602856825258843953  ] 
dist 12=[28.687178101149926696  ,54.356657026830418412  ] 
dist 13=[26.396650024105323679  ,53.529500626255041997  ] 
dist 14=[24.251452669115340956  ,53.250251354568182298  ] 
dist 15=[21.736582212307331759  ,52.799123029966415742  ] 
dist 16=[19.168249732661912064  ,51.527539768656724378  ] 
dist 17=[16.030144966559318728  ,31.551916334795553998  ] 
dist 18=[12.707402456577424719  ,29.765184976036070680  ] 
dist 19=[10.072095349513014790  ,25.508784308553383669  ] 
dist 20=[6.6068881587773989065 ,24.887145745939751301  ] 
dist 21=[4.0797745749923370275 ,18.993902942359631576  ] 
dist 22=[.8456850003706154618 ,17.936340545257309521  ] 
dist 23=[-1.3326932917940458587 ,16.622118983350914704  ] 
dist 24=[-3.1621508273575932107 ,16.368782453170519267  ] 
dist 25=[-5.0035833654984432158 ,8.4202416121812199444 ] 
dist 26=[-6.7229963906536084272 ,7.4774694020036565395 ] 
dist 27=[-8.0660638852825155533 ,5.4670690247147877597 ] 
dist 28=[-9.4004173594240887298 ,5.0652175330845812987 ] 
dist 29=[-11.086931034254570093  ,3.0701218266626532362 ] 
dist 30=[-12.668654430361682042  ,2.7364308853166357623 ] 
dist 31=[-13.584676966076062767  ,2.1384535287562643656 ] 
dist 32=[-14.199186923141980534  ,2.0270534497157304208 ] 
dist 33=[-14.575360631002633954  ,-2.2520869062184252499 ] 
dist 34=[-14.829904180256056080  ,-1.2424017234329947126 ] 
dist 35=[-14.957641021786842619  ,.39823957947743179971] 
dist 36=[-15.020743513188931106  ,2.0601310615762230465 ] 
dist 37=[-15.015521281444533351  ,3.1547885358520832644 ] 
dist 38=[-13.110134286125037052  ,4.0387467623925542526 ] 
dist 39=[-12.825953546760208289  ,4.8607617033608773129 ] 
dist 40=[-12.310315182729212854  ,5.5757570875333937104 ] 
dist 41=[-12.172155032574099479  ,6.0330598742225109269 ] 
dist 42=[-11.692508672445577225  ,6.3871027699423864662 ] 
dist 43=[-11.547890287852940417  ,6.6903346159044610205 ] 
dist 44=[-11.396865883412304393  ,6.9451511240754912121 ] 
dist 45=[-11.316384688281142045  ,7.1061460190862284635 ] 
dist 46=[-9.7498116613938296787 ,7.2282157896802075839 ] 
dist 47=[-9.6507158031287248081 ,7.3278671061676285027 ] 
dist 48=[-9.6317790702330059058 ,7.4044536156006302746 ] 
dist 49=[-2.7319009094173274259 ,7.4345391119407806039 ] 
dist 50=[-2.3986606768105971469 ,7.4357285027572795793 ] 
dist 51=[-2.3482388325337441873 ,7.4054527054649671388 ] 
dist 52=[1.1957139839719067098 ,6.3509845810414926597 ] 
dist 53=[1.5159220295675739543 ,7.5078755000815093743 ] 
dist 54=[2.2293076568182187387 ,8.5978431843332538990 ] 
dist 55=[2.3405640476081392799 ,9.2801423219105682790 ] 
dist 56=[3.1317437607387066919 ,9.7949278236749630208 ] 
dist 57=[3.2539648637047790304 ,10.216236831098613469  ] 
dist 58=[3.4728464500985333749 ,10.545668200921286217  ] 
dist 59=[2.8908407242349122797 ,10.693713966810742350  ] 
dist 60=[2.0862851890440270281 ,10.753967394013582777  ] 
dist 61=[.77952839751933522427,10.745332743416547725  ] 
dist 62=[-.56979909011589432195,8.2457772571714105470 ] 
dist 63=[-1.5933635581831809632 ,8.2056424005184223666 ] 
dist 64=[-2.4365280768611693237 ,8.1751852795922516089 ] 
dist 65=[-3.2519498681044190016 ,4.3419442829940840929 ] 
dist 66=[-3.9855776630034027247 ,4.3164514160858453116 ] 
dist 67=[-4.5024684192331751033 ,4.2944800945880041404 ] 
dist 68=[-4.9588788880246928492 ,1.9201754638750207321 ] 
dist 69=[-5.4512776161013576407 ,1.7100647000590708807 ] 
dist 70=[-5.8944643603659975150 ,1.2199892419719037679 ] 
dist 71=[-6.1545579457434015539 ,1.1318922066673903149 ] 
dist 72=[-6.3301456666264049443 ,.48371549633267530139] 
dist 73=[-6.4361827812245255319 ,.3675976245272259771 ] 
dist 74=[-6.4953437189162667718 ,.16974760015387741124] 
dist 75=[-6.4990390051636340839 ,.12510991979087607183] 
dist 76=[-6.4500248362601790821 ,-.5679883242631229625 ] 
dist 77=[-6.4196677716587234177 ,-.66034525587852541309] 
dist 78=[-6.1200311049050131784 ,-.68196954716324764937] 
dist 79=[-6.1511147302639234596 ,.0592024467460891985 ] 
dist 80=[-6.1422913547084472902 ,.6794178741412421603 ] 
dist 81=[-2.9814175076593921008 ,1.2945691178840286277 ] 
dist 82=[-2.9557253677853623750 ,1.8576052063407301212 ] 
dist 83=[-2.9587166038064288060 ,2.2699764897002385963 ] 
dist 84=[-1.6501716982224785392 ,2.6500341131319567834 ] 
dist 85=[-1.5761383265281370249 ,3.0842155242785706906 ] 
dist 86=[-.49057187921058270113,3.4843799561672311542 ] 
dist 87=[-.47067296417130765292,3.7287624573784621306 ] 
dist 88=[-.41842159395470352762,3.9053672358084979061 ] 
dist 89=[-.41246874613747999533,4.0351771519519460847 ] 
dist 90=[-.42273007764661856537,4.1266602591764789595 ] 
dist 91=[-.45782569763534290693,4.1503833292517702050 ] 
dist 92=[-.50212371656001383813,4.1493079508618523111 ] 
dist 93=[-.54908821514809696949,4.1418595917335209290 ] 
dist 94=[-.606914785362428474  ,3.3343403141516633393 ] 
dist 95=[-.6945323099069342208 ,3.3342208466422974284 ] 
dist 96=[-.79435877624632365664,3.3271514788648755474 ] 
dist 97=[-.90087996993034547911,2.4942950903596651387 ] 
dist 98=[-1.0324617871811965521 ,2.4016462697060849757 ] 
dist 99=[-1.2322440218997399964 ,2.1775234730486631848 ] 
dist 100=[-1.4304129797029489981 ,2.2015928344840974822 ] 
dist 101=[-1.5555563527062566936 ,2.3516587294604641111 ] 
dist 102=[-1.6508724515357108104 ,2.4556609864784620318 ] 
dist 103=[-1.7300623454439034943 ,2.5237660965145594748 ] 
dist 104=[-1.8157799315527974837 ,2.5709653960781671779 ] 
dist 105=[-1.9008566239403597965 ,2.5915644424979365920 ] 
dist 106=[-1.9525567504821083908 ,2.5966075283866056771 ] 
dist 107=[-1.9894905877833740650 ,2.5914748201767506698 ] 
dist 108=[-2.0156757808878835651 ,2.2786016211904534311 ] 
dist 109=[-2.0327427046948709545 ,2.2273862600493958055 ] 
dist 110=[-2.0333048530104610478 ,2.1318610407041696913 ] 
dist 111=[-2.0246150817146698699 ,2.1041919235980541586 ] 
dist 112=[-2.0160750849480429683 ,1.9951246596036373350 ] 
dist 113=[-1.5995892010784569172 ,1.9652014929179448568 ] 
dist 114=[-1.5487534808439835006 ,1.9041907671649153315 ] 
dist 115=[-1.5318111270348486002 ,1.8836795087876538715 ] 
dist 116=[-1.0968466818659966041 ,.68763887757841812452] 
dist 117=[-1.0779907585119420962 ,.68963874783307429833] 
dist 118=[-1.3005685216911792790 ,.672020916713992961  ] 
dist 119=[-1.5786468356186343525 ,.66586510647144831942] 
dist 120=[-1.8245486487716062828 ,.73735533016008644175] 
dist 121=[-1.9902064383126069183 ,.83535978610301330226] 
dist 122=[-2.1284963142162823046 ,.92486223174731632826] 
dist 123=[-2.2652262054928533995 ,.9902257472507860672 ] 
dist 124=[-2.3848898806095712548 ,1.0503910027189154633 ] 
dist 125=[-2.4551006089093262274 ,1.1192055677762650070 ] 
dist 126=[-2.5024071697726813473 ,1.3066749135254397563 ] 
dist 127=[-2.5307015266179935630 ,1.4879397272590131778 ] 
dist 128=[-2.5445563472467359476 ,1.6415207517890093374 ] 
dist 129=[-2.5430845594667091815 ,1.7971474528786022926 ] 
dist 130=[-2.5173855578926163865 ,1.9418794197969973273 ] 
dist 131=[-2.5049877694384513035 ,2.0519903997715109746 ] 
dist 132=[-1.2449812710419827926 ,2.1576443622925732201 ] 
dist 133=[-1.1287815085789651867 ,2.2845869570514990571 ] 
dist 134=[-.96375798825468354784,2.4027549415874463112 ] 
dist 135=[-1.0793233258214709602 ,2.4733985359168357942 ] 
dist 136=[-1.1821761999734104996 ,2.5226148132983411001 ] 
dist 137=[-1.2942397961653913709 ,2.5552947226683193735 ] 
dist 138=[-1.4033654904922016881 ,2.5747214194323364910 ] 
dist 139=[-1.4945139806879405740 ,2.5737806900163549165 ] 
dist 140=[-1.5897966535353388802 ,2.5578477147910158783 ] 
dist 141=[-1.7154358800269836250 ,2.5433474996082259977 ] 
dist 142=[-2.3292060323387455680 ,2.4402204514474252089 ] 
dist 143=[-2.7435335045601214508 ,2.4119399601356754812 ] 
dist 144=[-3.0685744932015947527 ,2.3443727764702757545 ] 
dist 145=[-3.3558054642582151828 ,2.3183383474254467306 ] 
dist 146=[-3.5960640235084606319 ,2.1822810700057350422 ] 
dist 147=[-3.7337379480161669024 ,2.1492714438211183593 ] 
dist 148=[-3.8223882357307341887 ,2.0660362620181164690 ] 
dist 149=[-3.8671023773690916259 ,2.0353185986347320748 ] 
dist 150=[-3.8891808325860048579 ,1.8453261596882067079 ] 
dist 151=[-3.8875368848846015281 ,1.8152562602609190539 ] 
dist 152=[-3.8682493456945205861 ,1.7769306229085482859 ] 
dist 153=[-3.8545293403766863110 ,1.7599023071426264475 ] 
dist 154=[-3.7577911540440897168 ,1.7248986932275949538 ] 
dist 155=[-3.7294351822430288893 ,1.7095645450902919363 ] 
dist 156=[-3.6195343462520753707 ,1.6977628905286031067 ] 
dist 157=[-3.5998961337859844582 ,1.6877338901184902039 ] 
dist 158=[-.85730679773986469085,.68519883993989554521] 
dist 159=[-.90698515648272082548,.758393877673470389  ] 
dist 160=[-.94579508790685822725,.83773342186334416137] 
dist 161=[-1.0643468433898599834 ,.91686412288440791679] 
dist 162=[-1.2330366541468583168 ,1.0108256414822574948 ] 
dist 163=[-1.4733208371446065929 ,1.1493230538008862884 ] 
dist 164=[-1.7069042095426815912 ,1.2851273553551024452 ] 
dist 165=[-1.8488642350312513060 ,1.3683458046231098562 ] 
dist 166=[-1.9506299589607433126 ,1.4288006519397445726 ] 
dist 167=[-2.0238726225123907169 ,1.4738024689537263118 ] 
dist 168=[-2.0779887310756803585 ,1.5056946895773436278 ] 
dist 169=[-2.1034547499658256110 ,1.5138559667642505744 ] 
dist 170=[-2.1127657513366107299 ,1.5136434582223044570 ] 
dist 171=[-2.1109783987774416831 ,1.5121344031894182108 ] 
dist 172=[-1.8984379773412053004 ,1.4224918145553541622 ] 
dist 173=[-1.8616441430316838557 ,1.4035377845635323110 ] 
dist 174=[-1.7952549359482526191 ,1.3557862094569872943 ] 
dist 175=[-1.7757429796010444366 ,1.3377899035335595275 ] 
dist 176=[-1.6986940759112764411 ,1.2450170497907819260 ] 
dist 177=[-1.6760435709362914877 ,1.2227867583123609847 ] 
dist 178=[-1.6303821565928415142 ,1.1746980816731864041 ] 
dist 179=[-1.6145579298125808734 ,1.1586632637695497959 ] 
dist 180=[.03401886432641492225,.79697552994034315582] 
dist 181=[-.07875457873893632058,.82373629478167491789] 
dist 182=[-.19085080377589022989,.98765917649057296751] 
dist 183=[-.27027911044184860923,1.2142635555857977018 ] 
dist 184=[-.34082431548431561296,1.4141796694471628036 ] 
dist 185=[-.41749025977831638984,1.5480250997211281479 ] 
dist 186=[-.49204090003750069548,1.6588457689874377524 ] 
dist 187=[-.55415173693703029936,1.7669127062094304700 ] 
dist 188=[-.61893367111593013683,1.8617598483630826644 ] 
dist 189=[-.70414546165152330027,1.9198446970341716091 ] 
dist 190=[-.78641900958984117372,1.9620101664635401082 ] 
dist 191=[-.85180486800298561809,1.9933522529389555538 ] 
dist 192=[-.92017589417393852869,2.0152607763706760947 ] 
dist 193=[-.9871063180316360552 ,2.0197939393200029780 ] 
dist 194=[-1.0478562978424847960 ,2.0138752074093858753 ] 
dist 195=[-1.0915707284088141033 ,2.0073027325809459056 ] 
dist 196=[-1.1311082723473929610 ,.88109946958901396183] 
dist 197=[-1.1751948999510440412 ,.78366966448583725718] 
dist 198=[-1.2145138005071620953 ,.5528379770570980298 ] 
dist 199=[-1.2350306590299005024 ,.51415961390210210559] 
dist 200=[-1.2456718088649394115 ,.19833235499508647939] 
dist 201=[-1.2455917140104993216 ,.1415030261685764333 ] 
dist 202=[-1.2392802694434370055 ,.05507044094490701001] 
dist 203=[-1.2345138642603136559 ,.18286594297595340361] 
dist 204=[-1.2109287052216214762 ,.37010990289006135569] 
dist 205=[-1.2049480253058754298 ,.64632429900701043624] 
dist 206=[-1.1180276162988600816 ,.92057754099803125714] 
dist 207=[-1.1436014664609510383 ,1.0999991372026057930 ] 
dist 208=[-1.1606535623055699420 ,1.2439642728933990396 ] 
dist 209=[-1.1638932520954572990 ,1.3767794362785720297 ] 
dist 210=[-1.1590945518710637609 ,1.4919495277104906719 ] 
dist 211=[-1.1563347793519440288 ,1.5655278550953720774 ] 
dist 212=[-.48787092715099614903,1.6225927042020968203 ] 
dist 213=[-.47572922679005166126,1.6718909784836582632 ] 
dist 214=[-.44867265296261306595,1.7104192204339684382 ] 
dist 215=[-.44067289566861895411,1.7245213341685790719 ] 
dist 216=[-.43270240984788826694,1.7268330189498596514 ] 
dist 217=[-.40529703661254687208,1.7221702018504480109 ] 
dist 218=[-.2643368523553624257 ,1.6735025936040411993 ] 
dist 219=[-.17598305150837143711,1.6570713744266952019 ] 
dist 220=[.18407181024053653353,1.6262444845033517469 ] 
dist 221=[-.21216453788825062176,1.6146698836149435036 ] 
dist 222=[-.60871916567648695963,1.5914779893219664962 ] 
dist 223=[-.87029633317501375174,1.5937122322276672802 ] 
dist 224=[-1.0825643016995059550 ,1.5706948867038999052 ] 
dist 225=[-1.2824228593176036622 ,1.5602734243068209044 ] 
dist 226=[-1.4585134477059716176 ,1.5497359166363298096 ] 
dist 227=[-1.5759701611651372044 ,1.5402928588343397869 ] 
dist 228=[-1.6727324192004844391 ,1.2365377641336299668 ] 
dist 229=[-1.7662720771222389804 ,1.1939712050058115066 ] 
dist 230=[-1.8469891574290604171 ,1.0946645599734555098 ] 
dist 231=[-1.8926016833929020554 ,1.0673071448708254384 ] 
dist 232=[-1.9211422835674202123 ,.92323244259790376299] 
dist 233=[-1.9337588199729913077 ,.89349821676981219789] 
dist 234=[-1.9351440116743205425 ,.83056590246806188051] 
dist 235=[-1.9318631958179041454 ,.81185597300910659534] 
dist 236=[-1.9008606328575424230 ,.58720138270712747541] 
dist 237=[-1.8952250885714892024 ,.55314675831294686783] 
dist 238=[-1.5091610713841523597 ,.47539121149034888229] 
dist 239=[-1.5135947264626141402 ,.45668682969597326949] 
dist 240=[-1.5037309243763447242 ,.35424819960421116263] 
dist 241=[-1.4954725775214392364 ,.33462316298637261497] 
dist 242=[-1.4843666068095382450 ,.29342858220322475695] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 2, 1, 2, 0, 1] 
dist 0=[58.471407374121859640  ,58.471407374121859640  ] 
dist 1=[58.134618407471701653  ,58.843729645607139432  ] 
dist 2=[57.161931247407636506  ,59.275195736947629949  ] 
dist 3=[55.823306715291587781  ,59.555252195200877933  ] 
dist 4=[54.069256871247553243  ,59.729279347658931144  ] 
dist 5=[51.671013916883061251  ,59.737241490273419256  ] 
dist 6=[47.760093848519360738  ,59.627780036066408129  ] 
dist 7=[43.738801525657414747  ,59.543513520311039759  ] 
dist 8=[40.899823897084525482  ,58.967995235711155909  ] 
dist 9=[38.377688255332193948  ,58.732910107374093015  ] 
dist 10=[35.621519663758071226  ,58.426238652503751423  ] 
dist 11=[32.918848430310527279  ,58.265922473462345018  ] 
dist 12=[30.525681509923371553  ,57.735250941295842441  ] 
dist 13=[26.566603592176365913  ,57.528077066859907860  ] 
dist 14=[23.179817148441639230  ,56.583292562459785571  ] 
dist 15=[19.680732213534909695  ,54.733822623202457991  ] 
dist 16=[16.369276299499541716  ,38.202090091374275260  ] 
dist 17=[13.731264555677519474  ,36.550275544271578658  ] 
dist 18=[11.075156281211915214  ,32.636392762225842188  ] 
dist 19=[7.6906774231514514186 ,31.990436226195323965  ] 
dist 20=[4.4148346633295731668 ,26.542139049448450511  ] 
dist 21=[2.1921128233741789078 ,25.538475357810862993  ] 
dist 22=[.30761618781281359096,24.117864374927714465  ] 
dist 23=[-1.6181120410698472995 ,23.707671922090095998  ] 
dist 24=[-3.4342057090739180196 ,16.138947996430680889  ] 
dist 25=[-4.8816449744926855014 ,15.180944977952251767  ] 
dist 26=[-6.3457966153379669721 ,13.047556743358864596  ] 
dist 27=[-8.2303286723697768044 ,12.635380568985216056  ] 
dist 28=[-10.015026974355050756  ,10.118616627891343193  ] 
dist 29=[-11.080611903522793135  ,9.6832747469669132647 ] 
dist 30=[-11.833818820695294786  ,8.8338250443910251019 ] 
dist 31=[-12.369691589777702727  ,8.6315301028138978410 ] 
dist 32=[-12.769894897756949314  ,2.2076925841678627762 ] 
dist 33=[-12.980341712705962708  ,1.5514252708638435598 ] 
dist 34=[-13.095750832154909355  ,.23338201586509664836] 
dist 35=[-14.260293039729303226  ,-.09185942520168210799] 
dist 36=[-15.642868754159317494  ,-1.1881484393845509009 ] 
dist 37=[-16.559775548278832820  ,-1.4111465442128077771 ] 
dist 38=[-17.315465839089903427  ,-1.6444358416569701363 ] 
dist 39=[-18.054533706797670945  ,.08761138209961338087] 
dist 40=[-18.674274846402728389  ,1.4629015079405507215 ] 
dist 41=[-18.953390787811731175  ,2.6015720169567919671 ] 
dist 42=[-19.079171607994502150  ,3.7112943372790376405 ] 
dist 43=[-19.085802816906277557  ,4.7145524612514530055 ] 
dist 44=[-18.680085864151676344  ,5.4286171560289261617 ] 
dist 45=[-18.543956132580788338  ,6.0661523786400189134 ] 
dist 46=[-18.435079983431567133  ,6.7641863247542397279 ] 
dist 47=[-18.336360309933880139  ,7.4001207983153680980 ] 
dist 48=[-1.2486817035639698888 ,7.7899174407070505112 ] 
dist 49=[-.67166471113252121917,8.0732361418714684392 ] 
dist 50=[-.56678550776850855361,8.2843153861512354543 ] 
dist 51=[.13397396772858617945,8.4318772371268739513 ] 
dist 52=[.25412563777379797246,8.4617160263418533183 ] 
dist 53=[.47635832798009846   ,8.4480132439213143715 ] 
dist 54=[.5245233039194786109 ,8.4220786922174559279 ] 
dist 55=[1.0594306756318026186 ,8.5882714089530488559 ] 
dist 56=[1.1295864357207908285 ,8.9144221522269085284 ] 
dist 57=[1.2691988676733055756 ,9.0770043403930476735 ] 
dist 58=[1.2963770884917865817 ,9.1510198020817102071 ] 
dist 59=[.9992979000050375218 ,9.1602011243674462170 ] 
dist 60=[-.12583484774362629625,1.4922121223852161644 ] 
dist 61=[-.92423779650501183164,1.5104427652464396961 ] 
dist 62=[-1.5931937740077103264 ,1.5135778190701923113 ] 
dist 63=[-2.2382645957715664563 ,1.4984553235575024888 ] 
dist 64=[-2.8172939770193148828 ,1.4903721917146280039 ] 
dist 65=[-3.2228265353313739074 ,1.4714893555980709278 ] 
dist 66=[-3.5783463695485028628 ,1.4626348658765283772 ] 
dist 67=[-3.9579093397657584262 ,1.4115825923592152141 ] 
dist 68=[-4.3005563029603725037 ,1.3983912511259827443 ] 
dist 69=[-4.5088149293948278780 ,1.3583058688445656401 ] 
dist 70=[-4.6583482145797382738 ,1.3473538917119750541 ] 
dist 71=[-4.7666970998434971626 ,.64030311938764084133] 
dist 72=[-4.8402859431084527465 ,.57074676673312621057] 
dist 73=[-4.8526263738908948014 ,.41896069214176702797] 
dist 74=[-4.8384833208762394872 ,.3832748268858982136 ] 
dist 75=[-4.8182058510634052248 ,.21216487796126180395] 
dist 76=[-2.6142434497237945783 ,.18198975813663140435] 
dist 77=[-2.4123803918991103696 ,.11066871276688514193] 
dist 78=[-1.9169752985738458189 ,.10002846589999349209] 
dist 79=[-1.8394282153840492580 ,.24403010359011858973] 
dist 80=[-1.4937968848623014503 ,.65807033105315374105] 
dist 81=[-1.5278464053351636860 ,.97223492674087831597] 
dist 82=[-1.5388019369804864867 ,1.2726545167278512313 ] 
dist 83=[-1.5411043196737043579 ,1.6319010743602703477 ] 
dist 84=[-1.5406242370182862400 ,1.9679692608769420771 ] 
dist 85=[-1.5380293295543828461 ,2.1759483676729613274 ] 
dist 86=[-1.5318753173888222858 ,2.3294992583937124417 ] 
dist 87=[.16200637480753404826,2.4484716917820995392 ] 
dist 88=[.25861980176685634161,2.5389276750938604586 ] 
dist 89=[.38937917043888088464,2.5787331113018040565 ] 
dist 90=[.40215648591777433197,2.5939518570055323144 ] 
dist 91=[.44461782253326076533,2.5905351723938783599 ] 
dist 92=[.44770700105125841663,1.0109597515548151452 ] 
dist 93=[.43845498986784969489,1.1017027223908456329 ] 
dist 94=[.40987989883874485444,1.2468144912495707412 ] 
dist 95=[.37427945774157479008,1.3829279162403577552 ] 
dist 96=[.2704311416823716168 ,1.4662294551664112554 ] 
dist 97=[.13003054262164388012,1.5266800845172667026 ] 
dist 98=[-.01039084963483961778,1.5716384996281715202 ] 
dist 99=[-.18699688183235324507,1.6031602154463416297 ] 
dist 100=[-.35524742557870226213,1.6104807176107865529 ] 
dist 101=[-.4623546430988270337 ,1.6085302933684041692 ] 
dist 102=[-.54491214738716658808,1.6067762637926538576 ] 
dist 103=[-.6908470027992325659 ,1.5224464656123519919 ] 
dist 104=[-.89535922028982279913,1.5044045018441471101 ] 
dist 105=[-1.0573291911335343381 ,1.4507259635417974036 ] 
dist 106=[-1.2030469947278525622 ,1.4366431104739768184 ] 
dist 107=[-1.3267416552180470892 ,1.3137359077520439114 ] 
dist 108=[-1.4008634563099960862 ,1.2852913129608655552 ] 
dist 109=[-1.4526773893408220233 ,1.2447728128776447936 ] 
dist 110=[-1.4873850933343329080 ,1.2302052543534478994 ] 
dist 111=[-1.5127715078302486768 ,.88502018400002021949] 
dist 112=[-1.5274068377049961159 ,.83731356754844076328] 
dist 113=[-1.5369177310807623071 ,.73225802090613010116] 
dist 114=[-1.5418755107929358138 ,.70278591845923077543] 
dist 115=[-1.5435202651684009049 ,.57454244452644056494] 
dist 116=[-1.5398244710731142739 ,.54971827001227187996] 
dist 117=[-1.5315405115553927128 ,.48820753546165518576] 
dist 118=[-1.5245777744242899456 ,.47661779719827572624] 
dist 119=[-.53677134274309804558,.19126751187734783753] 
dist 120=[-.50972369073869529229,.29596441446800331845] 
dist 121=[-.50311851689431056548,.39309244279082576248] 
dist 122=[-.48779641903593988728,.50313511765284936859] 
dist 123=[-.48253584380355563809,.65938167275100392725] 
dist 124=[.53792854225930025653,.81314765431768013341] 
dist 125=[.60972634529256647346,.93058606238795599637] 
dist 126=[.62349523428395995593,1.0265613643568787150 ] 
dist 127=[.88185215283555438109,1.1177179932886661183 ] 
dist 128=[.91261896056099069788,1.1986750140587967081 ] 
dist 129=[.94492680596558897712,1.2539554912197769117 ] 
dist 130=[.93534611933319981287,1.3009560239748190051 ] 
dist 131=[.8524274005279374418 ,1.3488782220177430601 ] 
dist 132=[.75086062644411530237,1.3892109440689124870 ] 
dist 133=[.65716903950490723595,1.4059301669038328803 ] 
dist 134=[.5479287544927593306 ,1.4116467156039031407 ] 
dist 135=[.38171250918365848037,1.4089728252738376558 ] 
dist 136=[.19701242327089661647,1.3720279995216725378 ] 
dist 137=[.00627014057403671464,1.3586774465693742289 ] 
dist 138=[-.22505004458531061938,1.3409653638991229520 ] 
dist 139=[-.57162879001178484477,1.3320562861911497874 ] 
dist 140=[-.91684606777899655745,1.0735447027364116934 ] 
dist 141=[-1.1427384877253355618 ,1.0361053636847038052 ] 
dist 142=[-1.3240588943484845781 ,.95261237500760094741] 
dist 143=[-1.4914742134004992005 ,.92720116679790526782] 
dist 144=[-1.6367669041894320701 ,.81532568749407668769] 
dist 145=[-1.7298393507290276687 ,.79218800559681113767] 
dist 146=[-1.8023260388396347541 ,.73490514938082432088] 
dist 147=[-1.8655040301107048714 ,.72078593075618097441] 
dist 148=[-1.9163021052790505734 ,.569936839569332866  ] 
dist 149=[-1.9394036360786863716 ,.54417043028463034678] 
dist 150=[-1.9466222565060093681 ,.49071482094981471613] 
dist 151=[-1.9452916296934402648 ,.47559564323482995416] 
dist 152=[-1.9133069923502464331 ,.41471139199912553168] 
dist 153=[-1.9005354430035031895 ,.40173658430772525934] 
dist 154=[-1.8627782131869134990 ,.37142792046599043607] 
dist 155=[-1.8452848461760424758 ,.36241148216685002269] 
dist 156=[-.6978722977334749252 ,.44871200736047664756] 
dist 157=[-.71419286252208491567,.69894948511992319243] 
dist 158=[-.73239583010396556776,.90266138338101824289] 
dist 159=[-.74864751635471566527,1.1185235990456894252 ] 
dist 160=[-.75718176460943903764,1.3110069321117816097 ] 
dist 161=[-.76168624839648032084,1.4421615008229527446 ] 
dist 162=[-.76185805498074731986,1.5532406224514696904 ] 
dist 163=[-.75922616358625017914,1.6656463723245084188 ] 
dist 164=[-.75626549595092400091,1.7649521759722121396 ] 
dist 165=[-.74502098741239109895,1.8237761970627168247 ] 
dist 166=[-.73904814200198633878,1.8640976534525192413 ] 
dist 167=[-.70132472590357575374,1.8895950891754171266 ] 
dist 168=[-.69129112112522901819,1.9035550648833048349 ] 
dist 169=[-.67212411811942729998,1.9036577602945278485 ] 
dist 170=[-.6657746014818383144 ,1.8864816004542240455 ] 
dist 171=[-.6367349651228778276 ,1.8778293337597071693 ] 
dist 172=[-.62912406022933826714,1.3455098250526045464 ] 
dist 173=[-.60773030318368031632,1.3761888042704284447 ] 
dist 174=[-.60090896135602040826,1.3926751135867529119 ] 
dist 175=[-.5535956113222623389 ,1.4011473500523827688 ] 
dist 176=[-.62838119981787613568,1.3998566862131095962 ] 
dist 177=[-.75793370724430201106,1.3927440457247225209 ] 
dist 178=[-.88033889169205400135,1.3867967999844716850 ] 
dist 179=[-1.0246179367054263228 ,1.3449303984751824553 ] 
dist 180=[-1.1580848024535700360 ,1.3327334980595013002 ] 
dist 181=[-1.2373618265664499300 ,1.2965891238004122461 ] 
dist 182=[-1.2919510775212175673 ,1.2834969643691525041 ] 
dist 183=[-1.3269433383609613663 ,-.23820220293141093969] 
dist 184=[-1.3509392100228167540 ,-.27661759098349577134] 
dist 185=[-1.3616650830255813554 ,-.27633372236318978421] 
dist 186=[-1.3646991004275734446 ,-.26100878821797858475] 
dist 187=[-1.3615911431527546087 ,-.22121602888399196793] 
dist 188=[-1.1870645342082012365 ,-.1704126893093971915 ] 
dist 189=[-1.2661301499328633910 ,-.02922955515484305855] 
dist 190=[-1.3430003756899640845 ,.09192817223431072207] 
dist 191=[-1.4099245769965239169 ,.21706236402278259059] 
dist 192=[-1.4493147423009228884 ,.33484454058967661988] 
dist 193=[-1.4760038787162727817 ,.42667699309789607766] 
dist 194=[-1.4922622439025371664 ,.51689180596078536662] 
dist 195=[-1.5005359046034732698 ,.62822307163170157514] 
dist 196=[-1.4993569814163429399 ,.73330710475421764031] 
dist 197=[-1.4858490555505132230 ,.79860308554432015118] 
dist 198=[-1.4767235708790464565 ,.84712471353384366402] 
dist 199=[-.70246366916767992644,.88529806389322987069] 
dist 200=[-.64176695379353675178,.91414812914976666674] 
dist 201=[-.69870106287396245011,.92547866966758938444] 
dist 202=[-.76607417383134866965,.9295146262588820161 ] 
dist 203=[-.86510896141180262715,1.0779343655735462796 ] 
dist 204=[-.96208119566325167936,1.2544048567059784553 ] 
dist 205=[-1.0212261760412151227 ,1.3619249717939887804 ] 
dist 206=[-1.0638546720799559994 ,1.4393290363213609494 ] 
dist 207=[-1.0949442835715271715 ,1.4956626028219199158 ] 
dist 208=[-1.1165987398110779885 ,1.5375490718377854064 ] 
dist 209=[-1.1215916192532265356 ,1.5573207652838024661 ] 
dist 210=[-1.1206731867259429539 ,1.5646456283954257581 ] 
dist 211=[-1.1187492643017352756 ,1.5635986731474530182 ] 
dist 212=[-1.0470593169179780773 ,1.4113498817562165474 ] 
dist 213=[-1.0323066318605066439 ,1.3846787215602334039 ] 
dist 214=[-.99545467617003018004,1.3366345603541517791 ] 
dist 215=[-.98175831540337736496,1.3224261766547518364 ] 
dist 216=[-.91175838172147375223,1.2659654901311464383 ] 
dist 217=[-.89510201985792057868,1.2493210647534514724 ] 
dist 218=[-.85892711528971813725,1.2153211625977108830 ] 
dist 219=[-.84688900211151371792,1.2034189328330014684 ] 
dist 220=[-.41159939179460540461,.20065724731855440457] 
dist 221=[-.48294943761404385036,.21448029624147307999] 
dist 222=[-.56948330896978415283,.24121189715255401771] 
dist 223=[-.65345624187878173459,.27124054469637723524] 
dist 224=[-.77398359074178845212,.29821543753459414093] 
dist 225=[-.85875388144798731056,.32806433848076692369] 
dist 226=[-.93339937236015443588,.36955719223251365789] 
dist 227=[-1.0135377428789589466 ,.41525338385174837445] 
dist 228=[-1.0853549075380395254 ,.46186926952604290929] 
dist 229=[-1.1268063561136693745 ,.51798983807470576329] 
dist 230=[-1.1538719028750356044 ,.6016000370056738276 ] 
dist 231=[-1.1683026458247133734 ,.68397176872168242834] 
dist 232=[-1.1750597472716259011 ,.73515198613531754462] 
dist 233=[-1.1741196822754684037 ,.7731795602351361404 ] 
dist 234=[-1.1643397602575007897 ,.80308526056927133504] 
dist 235=[-1.1567646445438111679 ,.82540575799843616723] 
dist 236=[-.85463739044942084918,.83317580294415924099] 
dist 237=[-.85534124644722424431,.83523899588522462048] 
dist 238=[-.85468134760095151978,.83479509246403931328] 
dist 239=[-.69472016557996441266,.79926024827035872975] 
dist 240=[-.6716902603715583096 ,.79066974077634157782] 
dist 241=[-.63034351503975095543,.76792656361144934067] 
dist 242=[-.61957469618394756963,.75880441305861323307] 
dist 243=[-.58357553037067815883,.71003754311984092636] 
dist 244=[-.57259077983171341219,.69801608422725573449] 
dist 245=[-.56332962146686218611,.67300688177719251135] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 2, 0, 2] 
dist 0=[68.573506666525458566  ,68.573506666525458566  ] 
dist 1=[68.113849033395275654  ,68.798030636979710227  ] 
dist 2=[67.211331846655737265  ,68.769983159841714971  ] 
dist 3=[66.095138747752289018  ,68.563662048574301127  ] 
dist 4=[64.782314536056029864  ,68.436364883191655718  ] 
dist 5=[63.071269754668385842  ,67.746001887689189618  ] 
dist 6=[60.365277835122513271  ,67.632458782477794646  ] 
dist 7=[57.221246239734962769  ,65.254055780356569548  ] 
dist 8=[53.761315911390039637  ,64.382994777112796354  ] 
dist 9=[49.401825145313219258  ,63.683671558332763586  ] 
dist 10=[42.666149251787749923  ,63.359639294172729452  ] 
dist 11=[35.860965787230006970  ,62.974784048841972577  ] 
dist 12=[31.224027444544787696  ,62.895068995343205412  ] 
dist 13=[27.281034816165107129  ,61.065078277085610726  ] 
dist 14=[23.246757194157376046  ,57.572631403561621801  ] 
dist 15=[19.456398336564232901  ,36.224550151806400172  ] 
dist 16=[16.487418684667796938  ,35.964104081821535803  ] 
dist 17=[13.547951687680266988  ,25.813941512402566207  ] 
dist 18=[9.8539231123917249621 ,24.562944394844435685  ] 
dist 19=[6.3056054031094868769 ,21.998837128295531159  ] 
dist 20=[3.9561000776446814139 ,21.341236373386568282  ] 
dist 21=[2.0281702671806659034 ,18.998331137050561918  ] 
dist 22=[.16273823703594294799,18.524381910066026073  ] 
dist 23=[-1.5292679960384367549 ,17.826859974770352890  ] 
dist 24=[-2.7653795557267387827 ,17.643546353883727325  ] 
dist 25=[-3.9121971403798528018 ,3.7188962114253049153 ] 
dist 26=[-5.2491821231916997899 ,2.5648564834368021508 ] 
dist 27=[-6.5394700066537755837 ,.06388087363550568620] 
dist 28=[-7.4844700566951947547 ,-.39824359073306946079] 
dist 29=[-8.2614266968024013426 ,-3.0647493610587642383 ] 
dist 30=[-9.0255039199693576264 ,-3.4959049797510349338 ] 
dist 31=[-9.6812198943970668092 ,-4.3735625740575025174 ] 
dist 32=[-10.025548357824776569  ,-4.5342921378347072324 ] 
dist 33=[-11.204812557409199899  ,-5.5377246603582741622 ] 
dist 34=[-12.001806566810583035  ,-5.6542421053045592218 ] 
dist 35=[-12.588928128639785111  ,-5.4123014389427479454 ] 
dist 36=[-13.048125687810020497  ,-4.6323014454953816647 ] 
dist 37=[-13.393584295208360281  ,-3.7930333458158112347 ] 
dist 38=[-13.526207301703939650  ,-2.6581845835886653304 ] 
dist 39=[-13.571328170336861039  ,-1.4242730549850442598 ] 
dist 40=[-13.566883652512473846  ,-.18938543530162634876] 
dist 41=[-8.8663544155195940095 ,1.2802694965034382957 ] 
dist 42=[-8.8075271110865901394 ,3.4512023163273286473 ] 
dist 43=[-7.3598152739414817946 ,5.6032025140476506158 ] 
dist 44=[-7.1831840954648443813 ,6.9974921397756475657 ] 
dist 45=[-6.8567223118846952127 ,8.1020383038251102405 ] 
dist 46=[-6.7972636102835584906 ,9.0981872292744163554 ] 
dist 47=[-5.7402122213556758236 ,9.9474796802948804056 ] 
dist 48=[-5.5797382322819755162 ,10.466223505950520194  ] 
dist 49=[-5.2499340601825246290 ,10.842242841742054401  ] 
dist 50=[-5.1516236455101493217 ,11.122303979078370431  ] 
dist 51=[-3.7903938836371489495 ,11.327894181733882017  ] 
dist 52=[-3.5916372158605551956 ,11.406789195928070839  ] 
dist 53=[-3.0820063009299775549 ,11.408785952009628294  ] 
dist 54=[-3.0035682701585521129 ,11.386500741126679027  ] 
dist 55=[-2.1569686527309574134 ,11.159722990819295420  ] 
dist 56=[-1.9909619670253814359 ,11.081956003218939827  ] 
dist 57=[-1.8035352426262625940 ,10.810576245928570409  ] 
dist 58=[-1.7553390486905141067 ,10.725447576170618943  ] 
dist 59=[-1.5489211887999705244 ,8.4102218446596805147 ] 
dist 60=[-2.2871746840583747045 ,8.3951644305775397461 ] 
dist 61=[-2.9551245219617191350 ,8.3829239421577608447 ] 
dist 62=[-3.4308396361682362004 ,8.3716446205151578999 ] 
dist 63=[-3.8556797447609045840 ,2.7304064526143605033 ] 
dist 64=[-4.3207627915600005778 ,2.6437245291143152647 ] 
dist 65=[-4.7434072744982815840 ,.91321492744615837418] 
dist 66=[-4.9989943126714323676 ,.69410382356368088324] 
dist 67=[-5.1806409663749161884 ,.19778031789642407168] 
dist 68=[-5.4611424259203848463 ,.10598428958261538968] 
dist 69=[-5.8095038735597395064 ,-.49420957306550899604] 
dist 70=[-6.1184337195190959256 ,-.5965816422936967212 ] 
dist 71=[-6.3814880771731026036 ,-.63294236610504233188] 
dist 72=[-6.5468442033061782985 ,-.43649871867991188733] 
dist 73=[-6.6722722503685403145 ,-.22744728096356402048] 
dist 74=[-6.7759713825676212162 ,-.07853475154316231553] 
dist 75=[-6.8577378520027283894 ,.12592576411799748587] 
dist 76=[-6.8956291272099563775 ,.62020959194551982407] 
dist 77=[-6.9086184181269481551 ,1.0731602388437340121 ] 
dist 78=[-6.8909941507827453799 ,1.4053144003548713858 ] 
dist 79=[-2.2273211945254798979 ,1.7116657811317491273 ] 
dist 80=[-1.8430647712721873282 ,2.0617465315479740015 ] 
dist 81=[-.97062834202179402188,2.3866005313369233386 ] 
dist 82=[-.80544029428334483772,2.5923497544553725896 ] 
dist 83=[-.07295581868518701345,2.7497420988777524834 ] 
dist 84=[-.19521187090812646173,2.8817237752451667082 ] 
dist 85=[-.33624477716865406547,2.9868709701421430529 ] 
dist 86=[-.48853311591596575133,3.0372327104244326824 ] 
dist 87=[-.67749694280661402501,3.5939007615962921534 ] 
dist 88=[-.96469455125960977064,4.0130654670877730394 ] 
dist 89=[-1.2513514443231380098 ,4.3339983849435085228 ] 
dist 90=[-1.4381448610087482755 ,4.6036349999978730393 ] 
dist 91=[-1.5866031125806677826 ,4.8188190337462744328 ] 
dist 92=[-1.7204350084099295311 ,4.9225500786930984272 ] 
dist 93=[-1.8336855270320825358 ,4.9715818320991399712 ] 
dist 94=[-1.9000823605995850684 ,4.9734250939517030032 ] 
dist 95=[-1.9443873379816251823 ,1.1623211136938268129 ] 
dist 96=[-1.9695303637289904918 ,1.1528059817093198326 ] 
dist 97=[-1.9821665597204462554 ,1.0703626165257891774 ] 
dist 98=[-1.9794013897763060426 ,1.0521842989413260281 ] 
dist 99=[-1.9630764485567311994 ,1.0104250610601842324 ] 
dist 100=[-1.9499377297135202282 ,.99615032010344047455] 
dist 101=[-1.8600123807406438244 ,.927232382733367316  ] 
dist 102=[-1.8341046050173500987 ,.91161893774049850875] 
dist 103=[-1.7819150263727731107 ,.87164813872895347828] 
dist 104=[-1.9072046658371174764 ,.8595146317073074499 ] 
dist 105=[-2.0026966463156627447 ,.72484440438831795228] 
dist 106=[-2.0822008540145245142 ,.70023044771684327893] 
dist 107=[-2.1451367542241091971 ,.65669375457869667408] 
dist 108=[-2.1745363077766740378 ,.64535915250372969185] 
dist 109=[-2.1849306759931744569 ,.60739400003179497824] 
dist 110=[-2.1834171406129110999 ,.59559383535907730331] 
dist 111=[-1.7806266094760284936 ,.58370224271186247758] 
dist 112=[-1.8273173961208061791 ,.57700667550134587594] 
dist 113=[-1.8690634223178406439 ,.57105708236511417107] 
dist 114=[-1.8912052950600917664 ,.57116104532510628083] 
dist 115=[-1.9032161308715155307 ,.57498640421149842716] 
dist 116=[-1.9045255273073281398 ,.58479287570176818031] 
dist 117=[-1.8988341497976506441 ,.59761068633150474992] 
dist 118=[-1.8917432041980861930 ,.67728798630828761517] 
dist 119=[-1.8646625805358440514 ,1.0415732585025016971 ] 
dist 120=[-1.8497905824632905739 ,1.5761445846210315348 ] 
dist 121=[-1.7574838138419669898 ,2.1046974709117840965 ] 
dist 122=[-1.7329660701690926440 ,2.4449803515439885624 ] 
dist 123=[-1.6840989706171436672 ,2.7118989074780407812 ] 
dist 124=[-1.6674326514218914058 ,2.9477921786676821110 ] 
dist 125=[-1.5881286482793378316 ,3.1451924228798005163 ] 
dist 126=[-1.5686956393310002560 ,3.2585599650408004964 ] 
dist 127=[-1.5084709076866311986 ,3.3319136276645381309 ] 
dist 128=[-1.4953116035981035218 ,3.3697010324731075065 ] 
dist 129=[-1.3495329256781888822 ,3.3879894370954927022 ] 
dist 130=[-1.3199416861341460048 ,3.3835578461572233905 ] 
dist 131=[-1.2533085523480597685 ,3.3653343429024516698 ] 
dist 132=[-1.2314068769095303051 ,3.3506744375891748095 ] 
dist 133=[-1.1286358703570484408 ,3.2488183332994132302 ] 
dist 134=[-1.1059593641639958343 ,3.2193553233447963568 ] 
dist 135=[-1.0470965661727034522 ,3.1302577376751137319 ] 
dist 136=[-1.0311369318295103128 ,3.0997484112940938855 ] 
dist 137=[-1.0504592506143919502 ,.525353819646893125  ] 
dist 138=[-1.4847881527620228599 ,.50968652295152685542] 
dist 139=[-1.8967603016853114201 ,.44537638615074775584] 
dist 140=[-2.2803034488535820208 ,.43236762110156974621] 
dist 141=[-2.6152609299686508149 ,.39998602236174766442] 
dist 142=[-2.8334271321727941046 ,.3930782318118170993 ] 
dist 143=[-3.0073835797217725317 ,-.05255499506809547093] 
dist 144=[-3.1659920300934890290 ,-.09414677498027792192] 
dist 145=[-3.3018676277554784592 ,-.1737156576985612419 ] 
dist 146=[-3.3851426861764767723 ,-.19202350721396249455] 
dist 147=[-3.4456763049457654243 ,-.24348522935985650556] 
dist 148=[-3.4908325276657825526 ,-.24949189812082063482] 
dist 149=[-3.5225443594948430432 ,-.2410466286461656432 ] 
dist 150=[-3.5294460428789121446 ,-.21073932435910175155] 
dist 151=[-3.5194825610662498234 ,-.17234376086902770638] 
dist 152=[-3.5082988300727915863 ,-.13162906985329430627] 
dist 153=[-1.3204215903399554702 ,-.08151875861529976993] 
dist 154=[-1.1341450328454484088 ,.16620309805118577038] 
dist 155=[-1.1289125953814500673 ,.49233708927030085437] 
dist 156=[-1.1276601816781842078 ,.82320422142662825845] 
dist 157=[-1.1168947514295373889 ,1.1309379137924248132 ] 
dist 158=[-1.1101565729407321456 ,1.3647933049459044804 ] 
dist 159=[.00236244297927221671,1.5888235005119007140 ] 
dist 160=[.03771040766935440630,1.8573642197806496484 ] 
dist 161=[.40407323378315809444,2.1068956502454137790 ] 
dist 162=[.45910307130403113378,2.2550982192447236375 ] 
dist 163=[.5261666298752892641 ,2.3571434544732633476 ] 
dist 164=[.53185218164410107848,2.4225548209301135271 ] 
dist 165=[.51300401394559831223,2.4678123437676978120 ] 
dist 166=[.4583468789671832766 ,2.4974122472206643159 ] 
dist 167=[.36713238137313389554,2.5136501531897701420 ] 
dist 168=[.20246299691780797338,2.5126652277958946245 ] 
dist 169=[.0263035685939996852 ,1.6617948668104939128 ] 
dist 170=[-.24004818704661597826,1.6663495085727360480 ] 
dist 171=[-.46565580971379514909,1.6565914925723262990 ] 
dist 172=[-.6939651089688941105 ,1.6472711593849311224 ] 
dist 173=[-.90594477341134618745,1.6336739847999832704 ] 
dist 174=[-1.0664159833797075296 ,1.6255265765853087185 ] 
dist 175=[-1.2195510254851082384 ,1.3576568413418498325 ] 
dist 176=[-1.4022693193354343572 ,1.3180871517140341100 ] 
dist 177=[-1.5716391782126635823 ,1.2237168223292747812 ] 
dist 178=[-1.6715290646416667368 ,1.1973872369971673398 ] 
dist 179=[-1.7394510829570709764 ,1.0517168729594797820 ] 
dist 180=[-1.7813036788304811087 ,1.0209052818082845266 ] 
dist 181=[-1.8522476549123131810 ,.95821650035068076497] 
dist 182=[-1.9208820171979557838 ,.93977844933648917842] 
dist 183=[-1.9766738496292085066 ,.68034858834036240926] 
dist 184=[-2.0047752197008068229 ,.64251137386391341663] 
dist 185=[-2.0179278769881337050 ,.7324916308965538264 ] 
dist 186=[-2.0162261992133596923 ,.8700132775817172212 ] 
dist 187=[-2.0003433580552431031 ,.9770272233146473612 ] 
dist 188=[-1.9916002503540300175 ,1.0700487631836071501 ] 
dist 189=[-1.9488515370489325026 ,1.1467033899238948696 ] 
dist 190=[-1.9399051823673764787 ,1.1884296408689523698 ] 
dist 191=[-1.6774852490924878414 ,1.2124606650863955531 ] 
dist 192=[-1.6700851080127577693 ,1.2185275584588538440 ] 
dist 193=[-1.4059079834853020974 ,1.2179864497814548875 ] 
dist 194=[-1.3653591001307807095 ,1.2642215585012675027 ] 
dist 195=[-1.2828892680772953927 ,1.2996032130529648242 ] 
dist 196=[-1.2586616399068626664 ,1.3251534412433482644 ] 
dist 197=[-1.1578947334746351650 ,1.4038000924985327066 ] 
dist 198=[-1.1349377021877434312 ,1.5406982551209127127 ] 
dist 199=[-1.0783889393494800821 ,1.6643076267652048087 ] 
dist 200=[-1.0605342865719975204 ,1.7379036364411633411 ] 
dist 201=[.71009618994878614667,1.7888061463097265663 ] 
dist 202=[.63056489346950117437,1.8218913444921706374 ] 
dist 203=[.51901977209941936243,1.8414515130082267395 ] 
dist 204=[.39152200903952555047,1.8442191111708567265 ] 
dist 205=[.22819446208483590011,1.8293764260447879308 ] 
dist 206=[-.02627415904856005613,1.8250865313724756796 ] 
dist 207=[-.28222276424614931999,1.6762236864054619692 ] 
dist 208=[-.45145402165017166151,1.7525250255187409671 ] 
dist 209=[-.58921449582025624724,1.8167238884704501436 ] 
dist 210=[-.71962781206579223807,1.8515142329104743619 ] 
dist 211=[-.83499901337311114798,1.8713584916085140257 ] 
dist 212=[-.91275716043485658977,1.8759369773285051952 ] 
dist 213=[-.9776885753902417254 ,1.8703489383174694954 ] 
dist 214=[-1.0418942537083912886 ,1.8650540775005356474 ] 
dist 215=[-1.0981671432384343500 ,1.8290118866737546498 ] 
dist 216=[-1.1314553564641741718 ,1.8237523115361439544 ] 
dist 217=[-1.1542107280627314449 ,.89190835729560595147] 
dist 218=[-1.1684698442891397510 ,.80313152681442716182] 
dist 219=[-1.1761424179324054053 ,.59973920930029744713] 
dist 220=[-1.1756382900076837868 ,.5584497510075668241 ] 
dist 221=[-1.1654831043279484746 ,.29786205008706014835] 
dist 222=[-1.1586940029514685596 ,.25072698538894917319] 
dist 223=[-1.1799954459421330986 ,.16014419011852961924] 
dist 224=[-1.3359340794027278888 ,.13819783056737010577] 
dist 225=[-1.4789687584787107046 ,.12497357517098908101] 
dist 226=[-1.5616012854285739854 ,.26597141311323389393] 
dist 227=[-1.6156526957284515539 ,.40231227210765599376] 
dist 228=[-1.6446744083177500785 ,.51461702174718115444] 
dist 229=[-1.6620413602730245289 ,.63058410572623345174] 
dist 230=[-1.6696011155159218830 ,.78153479648940500833] 
dist 231=[-1.6714132516387495444 ,.92789719649299196777] 
dist 232=[-1.6658534483027707529 ,1.0255623908627721676 ] 
dist 233=[-1.1030212653956553927 ,1.1060561730977084685 ] 
dist 234=[-1.1593954979088980064 ,1.1839233935211519569 ] 
dist 235=[-1.2156159533232292605 ,1.2539474403336475512 ] 
dist 236=[-1.2646790844342684541 ,1.3031559255593155276 ] 
dist 237=[-1.3177920899226345724 ,1.3464423158878536236 ] 
dist 238=[-1.3901665901040001119 ,1.3928448504320459200 ] 
dist 239=[-1.4587416319837266530 ,1.6657284925418289070 ] 
dist 240=[-1.4966984244034084060 ,1.8644425466486224988 ] 
dist 241=[-1.5194146124735026859 ,2.0145915464684730055 ] 
dist 242=[-1.5271952763163677792 ,2.1372713388237061804 ] 
dist 243=[-1.5262177319021175236 ,2.2337722141898866359 ] 
dist 244=[-1.5221131009441593507 ,2.2794936913114109041 ] 
dist 245=[-1.4997604689884178520 ,2.3012937973145545014 ] 
dist 246=[-1.4907348080977447354 ,2.3023724442889544073 ] 
dist 247=[-1.3451031782125227992 ,2.2072993260731106106 ] 
dist 248=[-1.3191493239222438656 ,2.1829272780151543724 ] 
dist 249=[-1.2492055594298617390 ,2.1392905347974477330 ] 
dist 250=[-1.2326510892610735620 ,2.1238621015555281952 ] 
dist 251=[-1.1428024640519284749 ,2.0510670966805821677 ] 
dist 252=[-1.1365017117456860986 ,2.0298994151948575248 ] 
dist 253=[-1.1082445541818587951 ,1.9707555464246537643 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 0, 0, 2, 0, 2] 
dist 0=[56.756043996568760679  ,56.756043996568760679  ] 
dist 1=[55.239000752632786480  ,57.889730132885740196  ] 
dist 2=[53.149389250480337377  ,58.758021455703590336  ] 
dist 3=[49.729856463420712005  ,59.215584607997298546  ] 
dist 4=[46.207619564840768048  ,59.460009660362614991  ] 
dist 5=[43.707869873411081121  ,59.477531200641472917  ] 
dist 6=[41.475961631788550293  ,59.362784710897386293  ] 
dist 7=[39.022670184416635050  ,59.264748021319436443  ] 
dist 8=[36.610818320871268630  ,58.398789103710573720  ] 
dist 9=[34.544019328697244859  ,56.252862359046396179  ] 
dist 10=[32.330458841389366462  ,55.740168713572413120  ] 
dist 11=[29.332067182617551006  ,55.074511206842416471  ] 
dist 12=[26.347983863879096813  ,54.806233976632323218  ] 
dist 13=[24.191207724051326856  ,54.356385527824120850  ] 
dist 14=[22.221878013781033770  ,54.225454098789734684  ] 
dist 15=[19.985752025491512011  ,53.997421708696904072  ] 
dist 16=[17.740034960776806376  ,52.135630662962242542  ] 
dist 17=[15.731765864150723205  ,29.292073408311074492  ] 
dist 18=[13.504408710839759961  ,27.293100981919215327  ] 
dist 19=[10.382477516275428051  ,22.794554827057806903  ] 
dist 20=[7.3090182179732816329 ,21.958247517135567942  ] 
dist 21=[5.2751130978246881561 ,16.547295457245188250  ] 
dist 22=[3.6035377846814962323 ,15.614163756512812099  ] 
dist 23=[1.9779720314324819725 ,13.860224065262146030  ] 
dist 24=[.4966385230674029510 ,13.465917982318555151  ] 
dist 25=[-.59864491543318692074,9.3377122370834354831 ] 
dist 26=[-1.6267433642488324969 ,8.7321979145604662416 ] 
dist 27=[-3.0103867313529334614 ,6.7798490543617008195 ] 
dist 28=[-5.1830017989573616146 ,1.1921721127914977381 ] 
dist 29=[-7.2460187879569521044 ,1.0873204582779896334 ] 
dist 30=[-8.9087475865860764352 ,-1.9021151138527310916 ] 
dist 31=[-10.605176319058998869  ,-1.7775630478996430941 ] 
dist 32=[-12.804327474438184626  ,-1.5383633673265240710 ] 
dist 33=[-14.896765450078707643  ,-1.1592395637180841886 ] 
dist 34=[-16.167176309494583210  ,-.60944208740377366806] 
dist 35=[-17.087915345154868706  ,.31061200613095317702] 
dist 36=[-17.782803285223195797  ,1.2464383166003237723 ] 
dist 37=[-18.298554213545101405  ,1.8593715735417144103 ] 
dist 38=[-18.503231205966051352  ,2.3491811837535192391 ] 
dist 39=[-18.573374804799882432  ,2.7944879933839863968 ] 
dist 40=[-18.550956042299423620  ,3.1736011421488062974 ] 
dist 41=[-17.610246927451977074  ,3.3996219547883385338 ] 
dist 42=[-17.410365212263758012  ,3.5551044737061921800 ] 
dist 43=[-16.958003746062928258  ,3.6529960640934370624 ] 
dist 44=[-16.795518979477227036  ,3.7233173084853861041 ] 
dist 45=[-15.984590218323121625  ,3.7689585450133352685 ] 
dist 46=[-15.797060582078280341  ,3.8046229135615266028 ] 
dist 47=[-15.263517407500377984  ,3.8354022631419305848 ] 
dist 48=[-15.133281817833667124  ,3.8605282967650437807 ] 
dist 49=[-6.7021727989536246425 ,4.1014138280228009532 ] 
dist 50=[-5.8789466580588149783 ,5.7493922531688281761 ] 
dist 51=[-4.0510489313498797932 ,7.7322518322990671056 ] 
dist 52=[-3.6567089134656894895 ,9.6615314023427019183 ] 
dist 53=[-1.4974503421382350514 ,11.407467582911096532  ] 
dist 54=[-1.1151222770417489861 ,12.658886565012149594  ] 
dist 55=[-1.2991924889734788999 ,13.787559478710571931  ] 
dist 56=[-1.7149492073993428447 ,15.043962023188386714  ] 
dist 57=[-2.0057304262645561541 ,16.169160174325861677  ] 
dist 58=[-2.2595067262974634461 ,16.774294172085258512  ] 
dist 59=[-2.5277410129252970668 ,17.117909769147583476  ] 
dist 60=[-2.7710392752259287752 ,17.200039900965699944  ] 
dist 61=[-2.9254015143051893888 ,17.164894260826819249  ] 
dist 62=[-3.0436066284862975531 ,17.149473624718318678  ] 
dist 63=[-3.1427485420548791611 ,17.134844914870069001  ] 
dist 64=[-3.2216309265765094304 ,17.118395662889781698  ] 
dist 65=[-3.2590614713055249868 ,3.5035665311044803351 ] 
dist 66=[-3.3593175562045542646 ,2.6943175193423780310 ] 
dist 67=[-3.7539500889958252739 ,2.5374204114738988529 ] 
dist 68=[-4.0949847659673263501 ,2.3011985115515095126 ] 
dist 69=[-4.4514551736959777842 ,2.2335839720896258866 ] 
dist 70=[-4.7689915880643742990 ,.92028711866740663532] 
dist 71=[-4.9547169745498630198 ,.75118552582668027878] 
dist 72=[-5.0793672083141075513 ,.35599110754305394479] 
dist 73=[-5.1532158919059409736 ,.60783761613035555988] 
dist 74=[-5.1903500904380371301 ,.86697715929932586852] 
dist 75=[-5.1919020993694606790 ,1.1945079964732074474 ] 
dist 76=[-5.1338006893042230843 ,1.5066807610295346379 ] 
dist 77=[-5.1194780575432821939 ,1.7045874021339888023 ] 
dist 78=[-.43797297274774562824,1.8560098296167407800 ] 
dist 79=[-.13088989251563395816,1.9828384967270143945 ] 
dist 80=[.28405364548681853751,2.0836550359149985282 ] 
dist 81=[.326549056490671012  ,2.1313632174476942630 ] 
dist 82=[.56622051635269197621,2.1537048872476799472 ] 
dist 83=[.30118400434054911095,2.1535961828300577280 ] 
dist 84=[.02829257202460601568,2.2393622992998830698 ] 
dist 85=[-.15875165269574328811,2.5512838412296030944 ] 
dist 86=[-.31799367669708924368,2.8367982205513155834 ] 
dist 87=[-.48003703970614956305,3.0168545316811025372 ] 
dist 88=[-.63068971680213767531,3.1537671587103499396 ] 
dist 89=[-.74451566249425779168,3.2671843055036302134 ] 
dist 90=[-.85270317191560584277,3.3565342495555977619 ] 
dist 91=[-.98087186133425793752,3.3974440497444950103 ] 
dist 92=[-1.0987592231555719017 ,3.4106229762009968169 ] 
dist 93=[-1.1659532851032438516 ,3.4067487644657785364 ] 
dist 94=[-1.2085994229060446813 ,1.6831880861048497948 ] 
dist 95=[-1.2286124800502226392 ,1.5368238844406292085 ] 
dist 96=[-1.2388815144937838852 ,1.1782719788989038152 ] 
dist 97=[-1.2426837444491134368 ,1.1237737633617784318 ] 
dist 98=[-1.2424610180217894474 ,.59678214736301971635] 
dist 99=[-1.2367007696174392700 ,.50022576228304799127] 
dist 100=[-.98254038330616420904,.37707223397786534494] 
dist 101=[-.94765123079293090353,.34791093796893935016] 
dist 102=[-.90335352432215194491,.26448693489074416106] 
dist 103=[-1.0696316633926196777 ,.32413977719959746264] 
dist 104=[-1.1969090569899262859 ,.37631630144290805168] 
dist 105=[-1.3037074160441716654 ,.41027278207945328653] 
dist 106=[-1.3896543262843230610 ,.43727184055226166113] 
dist 107=[-1.4337731322895399972 ,.46171599168383387677] 
dist 108=[-1.4570367357817147178 ,.482381762796303213  ] 
dist 109=[-1.4607904027650040390 ,.49431395075320065655] 
dist 110=[-1.0972837744028336160 ,.50210108648430868688] 
dist 111=[-1.1135370803458717243 ,.50622637847366737749] 
dist 112=[-1.1278120579410852397 ,.50764169650384968055] 
dist 113=[-1.1432766264909570119 ,.50643092787267619453] 
dist 114=[-1.1584460236758652175 ,.50011239912620519185] 
dist 115=[-1.1715282769986469078 ,.49592933648369602824] 
dist 116=[-1.1856434617825307558 ,.49234179619350386457] 
dist 117=[-1.2049211293381340961 ,.59500211518210861907] 
dist 118=[-1.2241647817912979583 ,.6759270459658380473 ] 
dist 119=[-1.2381325202957645110 ,.74808805759658549196] 
dist 120=[-1.2509086128602452539 ,.80889534359362718756] 
dist 121=[-1.2653762759444720971 ,.84453176793470946186] 
dist 122=[-1.2797601801367607348 ,.86847297618457977866] 
dist 123=[-1.2921854926711524426 ,.88262915255154296116] 
dist 124=[-1.3054728143886478183 ,1.0940319200417425395 ] 
dist 125=[-1.3232687326315376568 ,1.4797803748085722189 ] 
dist 126=[-1.3395387357512611491 ,1.8591051275017073176 ] 
dist 127=[-1.3467349102477280224 ,2.1002090244476350781 ] 
dist 128=[-1.3485538060847517521 ,2.2858324837436343149 ] 
dist 129=[-1.3444094013220239824 ,2.4438334490094620904 ] 
dist 130=[-1.3340379407121513379 ,2.5716950522103304110 ] 
dist 131=[-1.3270583236331300735 ,2.6370886809022368904 ] 
dist 132=[-1.3036749686100336437 ,2.6703548623198651286 ] 
dist 133=[-1.2919076351826547330 ,2.6757816650118650956 ] 
dist 134=[-1.2204343501343768843 ,2.6451295872029548749 ] 
dist 135=[-1.2031606836252135343 ,2.6288859435347550370 ] 
dist 136=[-1.1585109424173307358 ,2.5928543426443134279 ] 
dist 137=[-1.1423112656282913154 ,2.5760054485379561307 ] 
dist 138=[-1.0546705591199337727 ,2.4788405169334291096 ] 
dist 139=[-1.0337899839119388807 ,2.4535962441637298108 ] 
dist 140=[-.99188172286055777866,2.3729488109168125233 ] 
dist 141=[-.97863613423644716037,2.3533972524368114509 ] 
dist 142=[-.96722627560857088679,-.13211699519828508132] 
dist 143=[-1.2352204558057723121 ,-.10949206207800706015] 
dist 144=[-1.5596361879018604806 ,-.07741158568615476873] 
dist 145=[-1.8589402838603977399 ,-.03455910136115335667] 
dist 146=[-2.1184669336251651558 ,.02430368705239484571] 
dist 147=[-2.2842105709559973830 ,.12024888415317644936] 
dist 148=[-2.4126741031211655971 ,.24287387695837399889] 
dist 149=[-2.5234920104323733636 ,.37115626069811210152] 
dist 150=[-2.6168195727512829941 ,.47923862905201366326] 
dist 151=[-2.6755131795876031862 ,.58768607824038753296] 
dist 152=[-2.7199710388765582986 ,.68778446767349031919] 
dist 153=[-2.7565078648105092242 ,.76256275734210591696] 
dist 154=[-2.7850749674051050441 ,.83295366666106415184] 
dist 155=[-2.7977390147832871180 ,.91555062752395064249] 
dist 156=[-2.8011541423899687458 ,.99138611008077910072] 
dist 157=[-2.7928240433404501445 ,1.0348057987867964526 ] 
dist 158=[-.89954590504532865842,1.0627010703104668167 ] 
dist 159=[-.74335923055885851392,1.0766107499241413384 ] 
dist 160=[-.4029245273285959760 ,1.0833931535698803644 ] 
dist 161=[-.3489282968614647526 ,1.0828587026367963718 ] 
dist 162=[-.03537029932986958947,1.0775084194920872255 ] 
dist 163=[-.20504370003693433699,1.0732995468521677198 ] 
dist 164=[-.4294251502955957032 ,1.2431625711945468564 ] 
dist 165=[-.5760882952088088628 ,1.4500501812646351673 ] 
dist 166=[-.6935983888147510637 ,1.6430075332676962853 ] 
dist 167=[-.8016904389912870153 ,1.7588971975014674745 ] 
dist 168=[-.8951775566973101623 ,1.8402878282886961341 ] 
dist 169=[-.9544297425320430942 ,1.8956278583683596232 ] 
dist 170=[-.9998274996808501716 ,1.9345916975779939533 ] 
dist 171=[-1.0380506180212053559 ,1.9660478298883003454 ] 
dist 172=[-1.0693124188219719574 ,1.9860404778072446938 ] 
dist 173=[-1.0869418619844626173 ,1.9869688711230205452 ] 
dist 174=[-1.0979257111208734900 ,.34473792746983782099] 
dist 175=[-1.1026780436002482428 ,.32963249550677988016] 
dist 176=[-1.1030498256452714671 ,.23429147186064115742] 
dist 177=[-1.0997640908077000055 ,.21638341984488272168] 
dist 178=[-1.0874751904101717213 ,.1821850918096891166 ] 
dist 179=[-1.0799924913434077247 ,.17361846213417381878] 
dist 180=[-1.1040068351813949002 ,.01648927521877676248] 
dist 181=[-1.2403634760753020949 ,.07610278431445346759] 
dist 182=[-1.3654330278210086956 ,.19784917670828745174] 
dist 183=[-1.4368695156941759442 ,.31910665864121822443] 
dist 184=[-1.4825578315504243029 ,.4304540377948356769 ] 
dist 185=[-1.5049193189637492590 ,.5126697045510167224 ] 
dist 186=[-1.5170915842395499180 ,.5891161073680255712 ] 
dist 187=[-1.5221342071186530816 ,.6774502770385613674 ] 
dist 188=[-1.5229121016733061628 ,.7589194362780510982 ] 
dist 189=[-1.5180683708540882464 ,.8079817247327973834 ] 
dist 190=[-1.2605703030239082711 ,.8425970428825470994 ] 
dist 191=[-1.2257720281442858693 ,.8664380671990926567 ] 
dist 192=[-1.1322166713052207013 ,.8829222808232283253 ] 
dist 193=[-1.1158547823791239994 ,.8881918492774360100 ] 
dist 194=[-.99185942023750510308,.8879501014368688046 ] 
dist 195=[-.98073831613212169307,.91357086660728457264] 
dist 196=[-.96333074391558436518,.9794370731513903717 ] 
dist 197=[-.95638917370523346042,1.0416198102032925961 ] 
dist 198=[-.76633296770986881318,1.0959625866184072782 ] 
dist 199=[-.7384610474722421982 ,1.1305563462964233399 ] 
dist 200=[-.67750155907901481876,1.1572310587049988888 ] 
dist 201=[-.6592959776529091488 ,1.1799876634790243994 ] 
dist 202=[-.580532524295873127  ,1.1984260893747019804 ] 
dist 203=[-.57470364645371993128,1.2078775335754704596 ] 
dist 204=[-.52280093712959437462,1.2125401598334091479 ] 
dist 205=[-.51448794588138814123,1.2118788193572153559 ] 
dist 206=[-.49865188773884292241,.60884748280492850101] 
dist 207=[-.493664009995896645  ,.75133978075550681304] 
dist 208=[-.49723105082431014218,.86414723540988729856] 
dist 209=[-.50597736805890124187,.96562724316733514284] 
dist 210=[-.51001093719770717536,1.0518237333382130681 ] 
dist 211=[-.51015622689989859496,1.1036634157828929373 ] 
dist 212=[-.47754778647760974377,1.1401670716403956432 ] 
dist 213=[-.53781019231943366467,1.1651866849990523682 ] 
dist 214=[-.59057522245569102751,1.1831126213233711501 ] 
dist 215=[-.6467468359676515011 ,1.1913187683982523277 ] 
dist 216=[-.70066338878768259663,1.1939650682286605465 ] 
dist 217=[-.74443332126727701232,1.1907381375959485352 ] 
dist 218=[-.789060892636501825  ,1.1813658996074121469 ] 
dist 219=[-.84639883757210582003,1.1753834881081015439 ] 
dist 220=[-.90164168626286565926,1.1537547728610391956 ] 
dist 221=[-.93791217448968400315,1.1444022887882453572 ] 
dist 222=[-.9671559851859208060 ,.7583397000758077415 ] 
dist 223=[-.9943699001316966836 ,.8215571170945041867 ] 
dist 224=[-1.0181283889873455488 ,.8819279632724055725 ] 
dist 225=[-1.0335888645164877157 ,.9304414522427397459 ] 
dist 226=[-1.0459011593339108125 ,.9794598826323426015 ] 
dist 227=[-1.1078572457107002737 ,1.0418454426369808344 ] 
dist 228=[-1.1647854640210737028 ,1.1100607016355748268 ] 
dist 229=[-1.1929386777407776244 ,1.2759484778096399873 ] 
dist 230=[-1.2072244500540485502 ,1.4044030073849204711 ] 
dist 231=[-1.2088362510660253575 ,1.5149634552804519221 ] 
dist 232=[-1.1885135955885925479 ,1.6052740674498917211 ] 
dist 233=[-1.1807465844596771245 ,1.6529531856722900511 ] 
dist 234=[-1.1738332544265195035 ,1.6784332252012758750 ] 
dist 235=[-1.1429295707030374824 ,1.6837406515372889234 ] 
dist 236=[-1.0095847519188928557 ,1.6728701406563693556 ] 
dist 237=[-.9994903487518222884 ,1.6635178619065652196 ] 
dist 238=[-.9867811155166712462 ,1.6468800613447027550 ] 
dist 239=[-.9799794276218928883 ,1.6387113547014466126 ] 
dist 240=[-.9594202072647757978 ,1.5913926699181407310 ] 
dist 241=[-.9508820912136252958 ,1.5779139846154263236 ] 
dist 242=[-.9334610957329620597 ,1.5297570423298457350 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 0, 2, 0, 0, 2] 
dist 0=[67.029029574738490463  ,67.029029574738490463  ] 
dist 1=[66.241310152391566732  ,67.302930336905720263  ] 
dist 2=[65.054603574139857968  ,67.608535712916553265  ] 
dist 3=[63.387475035352797841  ,67.877743398877997474  ] 
dist 4=[61.047334443282072454  ,67.932029096015376167  ] 
dist 5=[57.173539825225695402  ,67.848507941566440861  ] 
dist 6=[53.168047246950079148  ,67.737859237643250084  ] 
dist 7=[50.301973764537585470  ,67.252628029817274280  ] 
dist 8=[47.718107012874141687  ,66.567392970652208130  ] 
dist 9=[44.839027110654711604  ,63.874505493653654685  ] 
dist 10=[41.985128885578872042  ,63.227310388489518795  ] 
dist 11=[38.955529486268859273  ,62.318042751505073437  ] 
dist 12=[31.973733578294312987  ,61.985485324825514746  ] 
dist 13=[27.241663036062460011  ,61.288317727760573651  ] 
dist 14=[23.244645282519778117  ,60.954670469624174265  ] 
dist 15=[19.197833268206759820  ,58.612987691887481085  ] 
dist 16=[15.422037830581031483  ,53.151529301485100711  ] 
dist 17=[12.507164211797662624  ,31.022567532163761222  ] 
dist 18=[9.6606919887514623249 ,28.623227187694067338  ] 
dist 19=[6.1580393189894046936 ,22.951103963745452406  ] 
dist 20=[2.8366960505259661902 ,22.141354724455035437  ] 
dist 21=[.71411939920963971993,21.953034764933496499  ] 
dist 22=[-.93962957091848904073,13.124376692550550469  ] 
dist 23=[-2.3891702956881905941 ,11.401355935567910124  ] 
dist 24=[-3.5990199935083564094 ,11.083670738152832587  ] 
dist 25=[-4.3199798359086119809 ,1.7509494163439248326 ] 
dist 26=[-5.0252147063399300741 ,.67732986528935413312] 
dist 27=[-6.2732708198963275069 ,-1.6424362685786039445 ] 
dist 28=[-7.6917359512394142642 ,-2.0022741583105689434 ] 
dist 29=[-9.3700769483233146209 ,-3.9331523936550564632 ] 
dist 30=[-10.936699803793906294  ,-4.6185007728426013006 ] 
dist 31=[-11.908833941838625405  ,-5.2947905832118318148 ] 
dist 32=[-12.635978375762622065  ,-5.5747870615121688990 ] 
dist 33=[-13.223736755016882582  ,-5.6447007525415374845 ] 
dist 34=[-13.680417183385966831  ,-5.2082966282020753319 ] 
dist 35=[-13.883866774086049086  ,-4.5663879089972635106 ] 
dist 36=[-13.970562321439748641  ,-3.6541715014606774843 ] 
dist 37=[-13.960632191353694790  ,-2.1388608503811182484 ] 
dist 38=[-10.631513310154088536  ,-.57281445090575872038] 
dist 39=[-10.589468248433674303  ,.66096235944496286024] 
dist 40=[-10.556671972261395657  ,1.6848827974394842060 ] 
dist 41=[-10.103038921464072496  ,2.6871211076614738712 ] 
dist 42=[-10.006127866409528589  ,3.5965630680411329564 ] 
dist 43=[-9.6886011386831982369 ,4.2504383156567567241 ] 
dist 44=[-9.6349077245551728765 ,4.8414713958902480286 ] 
dist 45=[-8.8594217467580943513 ,5.5003866969836475461 ] 
dist 46=[-8.6851042997291924074 ,6.1000190487662449873 ] 
dist 47=[-8.5263578096235314451 ,6.4545822172592839678 ] 
dist 48=[-8.4742296515952008792 ,6.6974421201074040103 ] 
dist 49=[-6.1603943945988155670 ,6.8513750472319255538 ] 
dist 50=[-5.8612829469175757615 ,6.9481772662308771488 ] 
dist 51=[-5.1928000177971882426 ,8.0338375044085418877 ] 
dist 52=[-5.0173306207027312325 ,9.1005485081003637486 ] 
dist 53=[-4.1586655727797344617 ,10.022149044453585017  ] 
dist 54=[-3.9893654751615463096 ,10.608497632469620748  ] 
dist 55=[-3.6129282165399776771 ,11.062034461179712971  ] 
dist 56=[-3.5000963638003032840 ,11.453901064013179551  ] 
dist 57=[-2.4474329392468735356 ,11.766908517041695140  ] 
dist 58=[-2.2772918307750564828 ,11.905759844421292691  ] 
dist 59=[-2.5194952780095971035 ,11.947831976221840714  ] 
dist 60=[-2.9129113537530991345 ,11.938240168722609107  ] 
dist 61=[-3.3563829323357746029 ,11.724473726231411384  ] 
dist 62=[-3.7636327048068290831 ,11.641995415309359508  ] 
dist 63=[-4.0126024506540246733 ,11.423845795239886880  ] 
dist 64=[-4.1927025280056710157 ,11.326552994501577799  ] 
dist 65=[-4.3252874434247500903 ,-.17220890190081062405] 
dist 66=[-4.4946565435316148840 ,-.69769826230798070937] 
dist 67=[-4.7515570908717717931 ,-.73604083524395309328] 
dist 68=[-4.9721046191974912533 ,-.68522696904529011332] 
dist 69=[-5.1092825594582891598 ,-.56194799543616052299] 
dist 70=[-5.2116015963954169262 ,-.42610821413667144869] 
dist 71=[-5.2930378355181971857 ,-.32519223755158917379] 
dist 72=[-5.3547780141507120468 ,-.17525721720982315959] 
dist 73=[-5.3784947572480025243 ,.21348976155167063003] 
dist 74=[-5.3788904925087856453 ,.57244753801135408403] 
dist 75=[-5.3612609295441611863 ,.84013068310198785953] 
dist 76=[-1.8630164261203792009 ,1.0914126588615426679 ] 
dist 77=[-1.5704217979010489723 ,1.3849969747241071109 ] 
dist 78=[-.90492224438932354067,1.6592519004440268018 ] 
dist 79=[-.7780461595706661483 ,1.8334554630252223284 ] 
dist 80=[-.28851484613208791065,1.9672648451739619594 ] 
dist 81=[-.36417192656012416793,2.0804147277383625042 ] 
dist 82=[-.45225469656511570202,2.1712571837664983491 ] 
dist 83=[-.54834708203590475899,2.3983781634052100353 ] 
dist 84=[-.66816031464234469519,2.9024431238887469695 ] 
dist 85=[-.8507463222466911311 ,3.2189039147062904794 ] 
dist 86=[-1.0324640488311984376 ,3.4577509270375174187 ] 
dist 87=[-1.1488000301563216616 ,3.6522393470476573935 ] 
dist 88=[-1.2387898676550246104 ,3.8028745383273290280 ] 
dist 89=[-1.3154916969990787541 ,3.8668176545019608714 ] 
dist 90=[-1.3770652534084585493 ,3.8945663522137723391 ] 
dist 91=[-1.4067394246809222244 ,3.9008314493017791683 ] 
dist 92=[-1.4204397072083398721 ,1.0783289162954407403 ] 
dist 93=[-1.4207060422714117754 ,1.0753922945992622801 ] 
dist 94=[-1.3895522516489368332 ,1.0009857847752509165 ] 
dist 95=[-1.3775217390005354944 ,.9867222630486361343 ] 
dist 96=[-1.3486733454950762233 ,.94184519007290021633] 
dist 97=[-1.3357927913885993111 ,.93496163930863797922] 
dist 98=[-1.2629504801772385263 ,.83142479568298803778] 
dist 99=[-1.3725690980740526025 ,.80877962818663864618] 
dist 100=[-1.5506671275760254533 ,.78886557023818798983] 
dist 101=[-1.6599564520727154130 ,.78390172390089429991] 
dist 102=[-1.7395440913823667446 ,.49476587913449965302] 
dist 103=[-1.7991615730090604229 ,.45698209527666259595] 
dist 104=[-1.8414804480473844703 ,.38431180393297751349] 
dist 105=[-1.8520722864104723516 ,.36587393311790816451] 
dist 106=[-1.8517974588573274567 ,.30371614499337277023] 
dist 107=[-1.8507612646294627296 ,.28834858533892202775] 
dist 108=[-1.6291892898163549410 ,.2746263854159538758 ] 
dist 109=[-1.6747089690095995850 ,.27245576828249437202] 
dist 110=[-1.7142468774627352527 ,.27551966710932967274] 
dist 111=[-1.7330800500202489745 ,.28594156816937250774] 
dist 112=[-1.7403462906730527683 ,.30365495081264220653] 
dist 113=[-1.7381138095165416477 ,.33582397412203234577] 
dist 114=[-1.7193305290336742367 ,.39083456385429836989] 
dist 115=[-1.7110433758166534495 ,.52544260887356281978] 
dist 116=[-1.6734817991743234927 ,.76297115872527653935] 
dist 117=[-1.6655094793009062435 ,1.2363754022881871220 ] 
dist 118=[-1.5135899309455182484 ,1.7053737653707265861 ] 
dist 119=[-1.4833788537294549042 ,2.0087756550221235833 ] 
dist 120=[-1.4203028086572704718 ,2.2484150543680183222 ] 
dist 121=[-1.4001371246422544500 ,2.4630586423326296617 ] 
dist 122=[-1.3080157847483059633 ,2.6447429986206858974 ] 
dist 123=[-1.2874879410425169439 ,2.7529068913877130222 ] 
dist 124=[-1.2252266940082588260 ,2.8277587277892518841 ] 
dist 125=[-1.2144061850164317616 ,2.8765642145843491263 ] 
dist 126=[-1.0718461548729420334 ,2.9080819825288968126 ] 
dist 127=[-1.0440102132569083916 ,2.9139704044558561087 ] 
dist 128=[-.98445004578815615423,2.9049090910846800552 ] 
dist 129=[-.96594078104484351381,2.8947862337372440280 ] 
dist 130=[-.88296002998518308427,2.8150824636006165761 ] 
dist 131=[-.8654744356338940571 ,2.7906816931913555263 ] 
dist 132=[-.81315697780985507959,2.7196883964240997375 ] 
dist 133=[-.80560968697229724341,2.6909932138366124384 ] 
dist 134=[-.85460511267698342416,.20243131547387419928] 
dist 135=[-1.2463919250968785627 ,.18900656916144730835] 
dist 136=[-1.5985649178791924639 ,.12572532256384242994] 
dist 137=[-1.9273928519168162840 ,.11447896741923113692] 
dist 138=[-2.2152185581818310225 ,.08766350770484489421] 
dist 139=[-2.4038366135378271928 ,.08371644275176522414] 
dist 140=[-2.5555218958157480838 ,-.163304988776345201  ] 
dist 141=[-2.6960268490427326841 ,-.18690004317129242142] 
dist 142=[-2.8169393123590839969 ,-.22554143813386832246] 
dist 143=[-2.8904705688931570896 ,-.23397505929677072221] 
dist 144=[-2.9432344227379766790 ,-.24153354985131738504] 
dist 145=[-2.9813028861554595109 ,-.23140169216290722617] 
dist 146=[-3.0069234497357982693 ,-.20927503459368167527] 
dist 147=[-3.0100309236078198476 ,-.16509564256278248923] 
dist 148=[-2.9982434769185150947 ,-.11508838970748271473] 
dist 149=[-2.9880999002409846688 ,-.06970954440118480351] 
dist 150=[-1.1781554022018754325 ,-.01913759871664887223] 
dist 151=[-1.0222343494291120586 ,.1154836685867693586 ] 
dist 152=[-.80578665906641489437,.40018283834388759442] 
dist 153=[-.80402268475849265473,.68876092376362683752] 
dist 154=[-.7921766893783188712 ,.95699402800226236242] 
dist 155=[-.78870688345743207388,1.1605380992267223701 ] 
dist 156=[-.05305251591774635804,1.3552424426384481703 ] 
dist 157=[-.02296838019235171014,1.5882137511811547245 ] 
dist 158=[.32652936166320504508,1.8044708078878413454 ] 
dist 159=[.37740901885433183727,1.9325027437366708976 ] 
dist 160=[.44951602047932515167,2.0201526147595808704 ] 
dist 161=[.46522747462216966735,2.0753279381910106837 ] 
dist 162=[.46023874945575377219,2.1144611301251902193 ] 
dist 163=[.42369410484006363969,2.1464292470129963038 ] 
dist 164=[.35713570373059434136,2.1588057852420449171 ] 
dist 165=[.23242813210254415874,2.1587251296658294806 ] 
dist 166=[.09345939003867651434,1.3740261202891105299 ] 
dist 167=[-.13141838952199472913,1.3767371271464317798 ] 
dist 168=[-.32238161763981919492,1.3629918928832126020 ] 
dist 169=[-.51640898986940798796,1.3543154976258469190 ] 
dist 170=[-.69704829081403307238,1.3403252915983343073 ] 
dist 171=[-.834608898203242414  ,1.3333012137226392342 ] 
dist 172=[-.96666649383752134748,1.1112377053016194984 ] 
dist 173=[-1.1253566297607141233 ,1.0781429769785199228 ] 
dist 174=[-1.2730239473090405754 ,1.0009424533245914766 ] 
dist 175=[-1.3611132303209884325 ,.97797473581742049748] 
dist 176=[-1.4744350819900108147 ,.86363043956333795455] 
dist 177=[-1.5607770517207115996 ,.8393709266027372348 ] 
dist 178=[-1.6275282606700086768 ,.78645358158200477325] 
dist 179=[-1.6848137475897000579 ,.77008106341281742209] 
dist 180=[-1.7309466726189713399 ,.57928092625291472573] 
dist 181=[-1.7532099473354647972 ,.5902578208534781978 ] 
dist 182=[-1.7622165238160139080 ,.7703827339397591500 ] 
dist 183=[-1.7606143886307072309 ,.8849918920485655486 ] 
dist 184=[-1.7405708917154787837 ,.9733073806609118394 ] 
dist 185=[-1.7314374096510824298 ,1.0485483227071929940 ] 
dist 186=[-1.6945760232472483037 ,1.1094192412273440285 ] 
dist 187=[-1.6835458055056196399 ,1.1404128467086902284 ] 
dist 188=[-1.5322499602669263237 ,1.1569060775133454682 ] 
dist 189=[-1.5260900057433347888 ,1.1599394809084055755 ] 
dist 190=[-1.2907234525013027998 ,1.1432978778112032857 ] 
dist 191=[-1.2544350164595006755 ,1.1351536439867621196 ] 
dist 192=[-1.1823582916426287898 ,1.1241885608525302910 ] 
dist 193=[-1.1614393077387106111 ,1.1939126820680506199 ] 
dist 194=[-1.0764155218481287037 ,1.3022341857855965248 ] 
dist 195=[-1.0560987925941157562 ,1.4173211904862881058 ] 
dist 196=[-1.0095438948864377928 ,1.5205919730750300763 ] 
dist 197=[-.99381177622965788971,1.5817789988381786781 ] 
dist 198=[.57537655481617099774,1.6237311939271709738 ] 
dist 199=[.68562249169510855022,1.6502741392421871169 ] 
dist 200=[.60962864795243543458,1.6649826654750002857 ] 
dist 201=[.48736666308892095801,1.6667103371590800117 ] 
dist 202=[.32961485053708429817,1.6500188214161194735 ] 
dist 203=[.08262380571936676223,1.6469594483500537939 ] 
dist 204=[-.16638436997161333128,1.4593207441981505967 ] 
dist 205=[-.33218263466074119207,1.5342199378273305658 ] 
dist 206=[-.46843234862329883629,1.5982236065126389439 ] 
dist 207=[-.59957250124804835391,1.6335325115739090298 ] 
dist 208=[-.71705478946212325019,1.6545159600406716098 ] 
dist 209=[-.79882376144597532107,1.6613748760677509299 ] 
dist 210=[-.86991960711237484957,1.6588767935414814307 ] 
dist 211=[-.94482706486730688244,1.6548429356788907829 ] 
dist 212=[-1.0119287715999047283 ,1.6255063088091175854 ] 
dist 213=[-1.0518879540390381864 ,1.6202773159823468644 ] 
dist 214=[-1.0795337596642643048 ,.82439960750478314488] 
dist 215=[-1.0975185455847254974 ,.74811408783203327616] 
dist 216=[-1.1078739384579749608 ,.57179779747790498846] 
dist 217=[-1.1090765574116805275 ,.53678473285075512154] 
dist 218=[-1.0990287871282593662 ,.30566198628846248113] 
dist 219=[-1.0963346237574694481 ,.26355912628038371234] 
dist 220=[-1.0015439469640453853 ,.1852684835636346119 ] 
dist 221=[-1.1355810207892511190 ,.16685299001403951488] 
dist 222=[-1.2586022581922651244 ,.08290151103524100732] 
dist 223=[-1.3303286061701564104 ,.20721717503428766989] 
dist 224=[-1.3780771366193891612 ,.32689344454586100004] 
dist 225=[-1.4054485143975047010 ,.42461522468588032808] 
dist 226=[-1.4224910719138402201 ,.5247630470698383502 ] 
dist 227=[-1.4290372513431263981 ,.65411740093880805147] 
dist 228=[-1.4291382039174214864 ,.77906882401367536985] 
dist 229=[-1.4248202758756497635 ,.86165396669392542299] 
dist 230=[-.85077969958861354558,.92884894611146495435] 
dist 231=[-.90265833873735617518,.99241020724724257327] 
dist 232=[-.95559607244050375702,1.0486118379905135400 ] 
dist 233=[-1.0036685135196827194 ,1.0864501022077172255 ] 
dist 234=[-1.0572826524958902750 ,1.1180077615122447206 ] 
dist 235=[-1.1323254680201150106 ,1.1606811796573504960 ] 
dist 236=[-1.2043048097240386275 ,1.4109105807313100765 ] 
dist 237=[-1.2456985726108551755 ,1.5670934815901492860 ] 
dist 238=[-1.2725274454776542506 ,1.6839756902559099746 ] 
dist 239=[-1.2864076653468838130 ,1.7774346441601414042 ] 
dist 240=[-1.2920028811365979077 ,1.8502417619897493501 ] 
dist 241=[-1.2907403812290434833 ,1.8847437135082908344 ] 
dist 242=[-1.2765121346932781889 ,1.9002945451501698975 ] 
dist 243=[-1.2699353385503995813 ,1.9002817326434202393 ] 
dist 244=[-1.1551449089457458684 ,1.7961973661604169550 ] 
dist 245=[-1.1341758850566786915 ,1.7730244585646944259 ] 
dist 246=[-1.0789277136922826750 ,1.7315185765716869907 ] 
dist 247=[-1.0639094252067070969 ,1.7176809235072201848 ] 
dist 248=[-.95875508654253612623,1.6556180365298366394 ] 
dist 249=[-.93528073992984343066,1.6374524223207099578 ] 
dist 250=[-.89462671092029989881,1.5905737504445531720 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 2, 1, 2, 0, 2] 
dist 0=[62.003965762320765786  ,62.003965762320765786  ] 
dist 1=[60.677627953119467741  ,62.652409469415815256  ] 
dist 2=[59.003314737427380603  ,62.978835406105393697  ] 
dist 3=[56.965512198424384814  ,63.019374976619057896  ] 
dist 4=[54.267838497945911452  ,62.882281260891247837  ] 
dist 5=[49.958781860417212311  ,62.258621829378158475  ] 
dist 6=[45.549833554964336860  ,61.789008910622087403  ] 
dist 7=[42.453262531687150717  ,61.406730097646937271  ] 
dist 8=[39.720228666376461802  ,61.192284064529322480  ] 
dist 9=[36.762667147102484669  ,60.477381131014094426  ] 
dist 10=[33.880967867228092542  ,60.232988742792429286  ] 
dist 11=[31.450664504427122874  ,59.617024148880728371  ] 
dist 12=[28.880823680434891338  ,59.361589894425888738  ] 
dist 13=[25.441607269480510185  ,58.044322532859912395  ] 
dist 14=[22.037877922825061411  ,57.621465203843626604  ] 
dist 15=[19.609509257347065255  ,55.036518402894097889  ] 
dist 16=[17.424762519456207568  ,32.366674327435420750  ] 
dist 17=[14.993478680079132031  ,26.127955497072986868  ] 
dist 18=[12.581004055831948156  ,24.956220047007721758  ] 
dist 19=[10.470877676039588492  ,23.614769660250781012  ] 
dist 20=[8.1704798580168563917 ,23.381281426202075203  ] 
dist 21=[4.9971389153693839521 ,15.221730048460377617  ] 
dist 22=[1.8853049714507778427 ,12.869424000084622018  ] 
dist 23=[-.16954310821256250823,10.532253458112292097  ] 
dist 24=[-1.8519864439481248146 ,9.9713592822518084094 ] 
dist 25=[-3.4758376819319570996 ,7.8350972059181450259 ] 
dist 26=[-4.9458260542511656454 ,7.4318655147227225115 ] 
dist 27=[-6.0887882163238169579 ,6.8601486297748976005 ] 
dist 28=[-7.6528006633455932613 ,6.7511668835783698726 ] 
dist 29=[-8.7831853786345524429 ,-1.0627278867724690442 ] 
dist 30=[-9.8223380447845070181 ,-3.1816371652663137118 ] 
dist 31=[-11.024078792567149748  ,-4.6771218265940751955 ] 
dist 32=[-12.115929740762851408  ,-4.3385502276581862046 ] 
dist 33=[-12.716374544483328975  ,-3.5946380336951997248 ] 
dist 34=[-13.082631980489773675  ,-2.6869129019768718832 ] 
dist 35=[-13.237597534464367710  ,-1.6418374801034306450 ] 
dist 36=[-13.306921018208381385  ,-.3003025311399710833 ] 
dist 37=[-13.330029636591858182  ,1.7902061420512828320 ] 
dist 38=[-13.327505944707750254  ,3.8872215344245093719 ] 
dist 39=[-13.292740474291940761  ,5.2549016695729892310 ] 
dist 40=[-12.408867132306231528  ,6.3462323414277438179 ] 
dist 41=[-12.648473371121288171  ,7.3412511887108681789 ] 
dist 42=[-12.758871426792294138  ,8.1948859409898035072 ] 
dist 43=[-12.796450447774028730  ,8.7223927700126696609 ] 
dist 44=[-12.787049996781949990  ,9.1106422837353014030 ] 
dist 45=[-9.6301346647611174618 ,9.4088983469181320308 ] 
dist 46=[-9.4166198779798645225 ,9.6434803274054241844 ] 
dist 47=[-9.3458334662407566544 ,9.7777473252555424470 ] 
dist 48=[-4.3308548057517869728 ,9.8638120471277077088 ] 
dist 49=[-4.1598936662437065107 ,9.9060437636182270914 ] 
dist 50=[-3.2985284914686466113 ,9.9162907269848402197 ] 
dist 51=[-3.1343406482858538200 ,9.8809646085991180714 ] 
dist 52=[-2.7679298820277628228 ,9.7984524817035013576 ] 
dist 53=[-2.6702108162495782172 ,9.7458068171884744232 ] 
dist 54=[2.6578095587489527074 ,9.0453038375019288157 ] 
dist 55=[2.7408320904333974391 ,9.1505804424584237176 ] 
dist 56=[3.3151133453776931106 ,9.2311347522805054492 ] 
dist 57=[3.3720116592269513598 ,9.2902340956310135856 ] 
dist 58=[3.2992384056100761830 ,9.3097893193874785325 ] 
dist 59=[3.0321685832295001998 ,9.3043540292790355279 ] 
dist 60=[2.6623111167917497608 ,9.2677145179746006276 ] 
dist 61=[2.1792818490099894959 ,9.3366289517832489549 ] 
dist 62=[1.0682923773978177222 ,9.3546567960255731457 ] 
dist 63=[.09295897567092956339,9.3540359755736243074 ] 
dist 64=[-.91956987867576625545,.93724828869246799147] 
dist 65=[-1.8760451508233843263 ,-.50413379099050218826] 
dist 66=[-2.6277986260397720221 ,-.75190808716660105983] 
dist 67=[-3.3721016215028569567 ,-1.2308290804724744047 ] 
dist 68=[-4.2988776878176765344 ,-1.3408979355468035698 ] 
dist 69=[-5.1780795512225128716 ,-2.3495568313953101680 ] 
dist 70=[-5.7326055314937951457 ,-2.5038465099120243639 ] 
dist 71=[-6.1544529354447284086 ,-2.6039398551715514466 ] 
dist 72=[-6.5043700761266865100 ,-2.5191139564414314146 ] 
dist 73=[-6.7804507565796125233 ,-2.3447849536560078394 ] 
dist 74=[-6.9077431912197589497 ,-2.0534462205239958083 ] 
dist 75=[-6.9654175127861815815 ,-1.6216084153410111682 ] 
dist 76=[-6.9637994700583266542 ,-.8868827636304361196 ] 
dist 77=[-6.2242837714137161672 ,-.13475018033335200857] 
dist 78=[-6.1937720133262563275 ,.36654389733467165761] 
dist 79=[-6.1715233416643127536 ,.77870399362690973913] 
dist 80=[-4.3250075547121270327 ,1.2544508668321385192 ] 
dist 81=[-4.1226757333333193455 ,1.6968065049659881498 ] 
dist 82=[-3.6148242019393222621 ,2.0159144206201231916 ] 
dist 83=[-3.5267623099271980361 ,2.3051374187711460589 ] 
dist 84=[-2.7167087932612543398 ,2.6283212691596296321 ] 
dist 85=[-2.5587034820600415093 ,2.9503589217088712825 ] 
dist 86=[-2.3463620739461961642 ,3.2812502349318516423 ] 
dist 87=[-2.2769355170770436195 ,3.6369538595894137642 ] 
dist 88=[-.87096332426188220624,3.9586458504108412701 ] 
dist 89=[-.69200928783794291907,4.1538822185900833693 ] 
dist 90=[-.29021750094297348881,4.2935163783543339964 ] 
dist 91=[-.21086331704103679811,4.3934220850378649565 ] 
dist 92=[.26741317005496296015,4.4599924217247457454 ] 
dist 93=[.34960827039124146866,4.4712644721365619784 ] 
dist 94=[.28227824848736717888,4.4525747323436341073 ] 
dist 95=[.12823671359499869088,4.4363165599584551561 ] 
dist 96=[-.10325189698360988522,1.5553450542150956625 ] 
dist 97=[-.38286761367136079781,1.0552890069048872503 ] 
dist 98=[-.59382604866652640155,.96082132763025037676] 
dist 99=[-.79427606534203916613,.8480569196954101204 ] 
dist 100=[-1.0319825342144433672 ,.82162739001290175621] 
dist 101=[-1.2549502378235274139 ,-.00102207444875268462] 
dist 102=[-1.3979874085058720040 ,-.10018823435074485837] 
dist 103=[-1.6019657912717145835 ,-.31626544926384282566] 
dist 104=[-1.8780893472784220402 ,-.35884912393042362973] 
dist 105=[-2.0534274758759139516 ,-.58683774097884760859] 
dist 106=[-2.1881078061100314378 ,-.6243921406129347634 ] 
dist 107=[-2.3020600061597053438 ,-.69712191715805584223] 
dist 108=[-2.3936443254163908053 ,-.71230881743226268953] 
dist 109=[-2.4391057698235140163 ,-1.0155978506866691964 ] 
dist 110=[-2.4593817404016937900 ,-.90152795946307122131] 
dist 111=[-2.4601031589310429677 ,-.79708967034319016111] 
dist 112=[-1.4429610871163990032 ,-.6790366576995920367 ] 
dist 113=[-1.3550122622451662936 ,-.5617626854958854324 ] 
dist 114=[-1.1391956507567484374 ,-.46041043771769347347] 
dist 115=[-1.1016210215799634318 ,-.35161368780239868061] 
dist 116=[-.77755491652686227181,-.20462439665552686318] 
dist 117=[-.71635095180366341771,-.05968501414958219103] 
dist 118=[-.62746502232161323602,.04095080391344175665] 
dist 119=[-.60176251058564530788,.14586590165420956959] 
dist 120=[-.12115605555521411545,.37410878013688329243] 
dist 121=[-.06084389694730570158,.52931253364009669382] 
dist 122=[.07490638408835467265,.66036349004977584998] 
dist 123=[.09784150373559862586,.79230070571693952997] 
dist 124=[.18731451483678349993,.9144152315841685194 ] 
dist 125=[.27971534237478851787,1.0063124970651551185 ] 
dist 126=[.32660210949152081397,1.0935779996903150773 ] 
dist 127=[.33590394143199718444,1.1972620175208237073 ] 
dist 128=[.4204000598823780986 ,1.3084116904622569759 ] 
dist 129=[.40302838295616200232,1.4075456132475093658 ] 
dist 130=[.37123441001423259542,1.4886419216522929965 ] 
dist 131=[.32292905613340730552,1.5662582400079094614 ] 
dist 132=[.23968494875007928154,1.6356440159366195063 ] 
dist 133=[.1495220566736077197 ,1.6838960450000462933 ] 
dist 134=[.07360824305067281844,1.7258828074127975069 ] 
dist 135=[-.00621777105530741843,1.7702667926137378361 ] 
dist 136=[-.1120056281833007719 ,1.8085968951771364533 ] 
dist 137=[-.22612467071796548134,1.8264247663680633983 ] 
dist 138=[-.33919739969232185447,1.8326389473731695731 ] 
dist 139=[-.47296205001625396271,1.8298545575820415114 ] 
dist 140=[-.6696420257050350693 ,1.8085575672893764495 ] 
dist 141=[-.87866986447510654349,1.7996661228176290279 ] 
dist 142=[-1.0437751835119553776 ,1.7588509650538933332 ] 
dist 143=[-1.3450581706090698537 ,1.7510661638354743725 ] 
dist 144=[-1.8443721041433691707 ,1.5943918620277055228 ] 
dist 145=[-2.1673025287502933436 ,1.5628380127034004546 ] 
dist 146=[-2.4222772233923975712 ,1.4979182855211860981 ] 
dist 147=[-2.6505073331220048599 ,1.4772996616477294565 ] 
dist 148=[-2.8435870791482487575 ,1.3841172551358198228 ] 
dist 149=[-2.9583446941159759602 ,1.3628490308204558156 ] 
dist 150=[-3.0375246301029249388 ,1.3002991973529342778 ] 
dist 151=[-3.0886867675543514815 ,1.2874020086176839194 ] 
dist 152=[-3.1213803806895556170 ,1.1480937484979843955 ] 
dist 153=[-3.1268861628636710708 ,1.1198674280725959321 ] 
dist 154=[-3.1166719136805010592 ,1.0611027923787270899 ] 
dist 155=[-3.1054935525767488776 ,1.0429763961880388254 ] 
dist 156=[-3.0185170832859741492 ,.96301283855605930818] 
dist 157=[-2.9920175970898891286 ,1.0861840117737358048 ] 
dist 158=[-2.9159520802820264187 ,1.3658870862106014368 ] 
dist 159=[-2.8845451319638154643 ,1.5904487592415938284 ] 
dist 160=[-1.2259365367128148070 ,1.7978340935551575693 ] 
dist 161=[-1.0799405818211267670 ,1.9778117345604941754 ] 
dist 162=[-1.0492146666659122995 ,2.0930444687401308573 ] 
dist 163=[-.97847074674905810905,2.1827013765469223266 ] 
dist 164=[-.9559370763591977662 ,2.3952683946774767097 ] 
dist 165=[-.73503614801338308954,2.6002121229828392155 ] 
dist 166=[-.69922910868697076064,2.7661768731428806206 ] 
dist 167=[-.61941018126167173316,2.9218659677282332606 ] 
dist 168=[-.59689133440186712831,3.0562250228869316088 ] 
dist 169=[-.4951547559776854225 ,3.1371041696064020890 ] 
dist 170=[-.47503565999922500782,3.1941423724042925036 ] 
dist 171=[-.42696955888497894044,3.2333966855558309010 ] 
dist 172=[-.41560160235170099078,3.2581260269841844206 ] 
dist 173=[-.45078284019194101652,3.2572222218732593066 ] 
dist 174=[-.73503488940544599055,3.2420997702746961176 ] 
dist 175=[-1.0106604524032316077 ,3.2279288271520972454 ] 
dist 176=[-1.2750722828491894651 ,1.3426289070148827400 ] 
dist 177=[-1.5113625893129272953 ,1.1777646673799338046 ] 
dist 178=[-1.6748136989768113937 ,.79828090666402924434] 
dist 179=[-1.8158718254042718791 ,.73424387787078060345] 
dist 180=[-1.9628391821906683414 ,.31323534120974933663] 
dist 181=[-2.0938767251070610937 ,.2379202735150094883 ] 
dist 182=[-2.1713915274375478886 ,.09699318089819431165] 
dist 183=[-2.2243875872067622053 ,.06432059707076788863] 
dist 184=[-2.2576192866385842982 ,-.33614439333494613019] 
dist 185=[-2.2755233336384109126 ,-.3936630179964181809 ] 
dist 186=[-2.2769326259582073902 ,-.48091269434182878093] 
dist 187=[-2.2765520863155768049 ,-.50203351928055938902] 
dist 188=[-2.3159342799695050497 ,-.3029389952654886599 ] 
dist 189=[-2.3383132992198738926 ,.06001650162195280480] 
dist 190=[-2.3530704207962238409 ,.30389284295760889814] 
dist 191=[-2.3509840958140818351 ,.50672669983285600059] 
dist 192=[-.86929827313631820305,.70596641517552831284] 
dist 193=[-.61609607977276971171,.88712604976891081262] 
dist 194=[-.56833108531368428393,1.0178394288779525558 ] 
dist 195=[-.48808555365564064094,1.1363520689873396868 ] 
dist 196=[-.46842693127240328599,1.2688431145056444248 ] 
dist 197=[-.13123727123994716821,1.3896677212946743983 ] 
dist 198=[-.12658376898086065678,1.4616440596209003091 ] 
dist 199=[-.13969053816326000282,1.5114676512831105901 ] 
dist 200=[-.16142542098475875347,1.5439281040614330707 ] 
dist 201=[-.19118803647509530198,1.5644462113762155313 ] 
dist 202=[-.23247521543679394545,1.5672137203599808997 ] 
dist 203=[-.30017855558823207256,1.5773401845999109808 ] 
dist 204=[-.37950629261885665036,1.6107113365310673031 ] 
dist 205=[-.46716109918544214619,1.6250757487153745350 ] 
dist 206=[-.57751618424527638012,1.6282403959003126245 ] 
dist 207=[-.7578592247137118314 ,1.6256460873346561693 ] 
dist 208=[-.9551304102608648427 ,1.6771816735869023890 ] 
dist 209=[-1.0800687234583468951 ,1.7645206688834900199 ] 
dist 210=[-1.1756785535356248024 ,1.8217805689019320807 ] 
dist 211=[-1.2559595000622024473 ,1.8528145168842546977 ] 
dist 212=[-1.3200249976802596726 ,1.8708871367152650848 ] 
dist 213=[-1.3509513497736536647 ,1.8764409406086810590 ] 
dist 214=[-1.3666799060094700371 ,1.8738844443326150102 ] 
dist 215=[-1.3701255293036060029 ,1.8678342546484914652 ] 
dist 216=[-1.3377546980587505636 ,1.6031996259694068575 ] 
dist 217=[-1.3265411342649756701 ,1.5615696809925068454 ] 
dist 218=[-1.3196420730857793154 ,1.4808019247833551467 ] 
dist 219=[-1.3449401773293313015 ,1.4574106803833846718 ] 
dist 220=[-1.4673727440769371773 ,1.3635268342136110821 ] 
dist 221=[-1.7531863007360344380 ,1.4810835041057598917 ] 
dist 222=[-1.9301269097544735987 ,1.5610582952471405493 ] 
dist 223=[-2.0608473866479587900 ,1.6152816788222841375 ] 
dist 224=[-2.1622872367655861448 ,1.6483604697740483778 ] 
dist 225=[-2.2402087687098386397 ,1.6691146791018878852 ] 
dist 226=[-2.2771134246162390032 ,1.6741761799136386621 ] 
dist 227=[-2.2923398858961905981 ,1.6701336440323512710 ] 
dist 228=[-2.2923049338407526694 ,1.6647671606468498449 ] 
dist 229=[-2.1294840300226053870 ,1.4748077847212738567 ] 
dist 230=[-2.0972640893020730281 ,1.4427596661941023063 ] 
dist 231=[-2.0394519359858010838 ,1.3758001680333212704 ] 
dist 232=[-2.0211941722487147127 ,1.3547296575196920989 ] 
dist 233=[-1.9434160458620556594 ,1.2600012768558220735 ] 
dist 234=[-1.9205474291930449652 ,1.2389694098015573709 ] 
dist 235=[-1.8666353334528052922 ,1.1772942951985906024 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 0, 1, 1, 0, 1] 
dist 0=[64.497370737656683842  ,64.497370737656683842  ] 
dist 1=[63.863708036601537904  ,64.758977400622376679  ] 
dist 2=[62.834747573830776159  ,64.853396328720266290  ] 
dist 3=[60.994800527634275920  ,64.819528801809085101  ] 
dist 4=[58.770276639998402807  ,64.685490083140775547  ] 
dist 5=[56.205757720062386106  ,64.566511494157313231  ] 
dist 6=[52.896528389096514229  ,63.987741406955330887  ] 
dist 7=[47.698448151276223320  ,63.786851978906867061  ] 
dist 8=[42.411197620445410450  ,63.073680855005432973  ] 
dist 9=[38.745875753932027171  ,62.867329573437928574  ] 
dist 10=[35.560691537742349344  ,60.856602117724368999  ] 
dist 11=[32.190446949872556591  ,60.334866250378045957  ] 
dist 12=[28.951832780456208260  ,59.973764889830148594  ] 
dist 13=[26.292062036505313431  ,59.681382197557400760  ] 
dist 14=[23.541512046790113641  ,52.067595357037727448  ] 
dist 15=[19.940041674183379172  ,50.689782200952988870  ] 
dist 16=[16.411570393750858584  ,43.212677417003071015  ] 
dist 17=[13.952274181735175538  ,29.234891239807323503  ] 
dist 18=[11.799047300241756991  ,26.871474977951523392  ] 
dist 19=[9.4923935619435106359 ,21.429593999038442608  ] 
dist 20=[7.2547143717089778066 ,20.553465059761677507  ] 
dist 21=[5.3764088986969436770 ,14.886861200047082667  ] 
dist 22=[3.3940818827298572669 ,12.674552534874123425  ] 
dist 23=[.73988619813328412449,12.231293226481015845  ] 
dist 24=[-1.8388712824485446180 ,11.644204055367673302  ] 
dist 25=[-3.5200094835636300405 ,11.532677389956938725  ] 
dist 26=[-4.8736274010525872489 ,2.9081550813547391290 ] 
dist 27=[-6.1435447852259022570 ,1.5149910690383027629 ] 
dist 28=[-7.2700983987768926615 ,1.2409065004493023357 ] 
dist 29=[-8.0508739946508887780 ,-1.7653248383839524331 ] 
dist 30=[-8.7321387764754289626 ,-2.1931548187341094053 ] 
dist 31=[-9.4612284505901377319 ,-3.6797067624312769030 ] 
dist 32=[-10.345750147820088327  ,-5.6715066488391764280 ] 
dist 33=[-11.210337440835521670  ,-5.8292870173659952524 ] 
dist 34=[-12.101499834877072085  ,-5.2663783818602204985 ] 
dist 35=[-12.822399849289230366  ,-4.3504838774665397194 ] 
dist 36=[-13.372770902833097515  ,-3.2829809220094435823 ] 
dist 37=[-13.838347380175817551  ,-2.1148886360259414815 ] 
dist 38=[-14.216744195595061129  ,-.6530421293467065985 ] 
dist 39=[-14.418734470886097257  ,1.5865711617472477789 ] 
dist 40=[-14.531402761118893639  ,3.8280053504267985814 ] 
dist 41=[-14.552884070682620814  ,5.2972918389898114973 ] 
dist 42=[-9.7209823583404103002 ,6.4790667809675067521 ] 
dist 43=[-9.1864364326627838103 ,7.5738206444069695662 ] 
dist 44=[-9.0410958683241048168 ,8.5262794582298347286 ] 
dist 45=[-8.5024488365012197338 ,9.1405447520302958708 ] 
dist 46=[-8.3701251413773452951 ,9.6237725046332698866 ] 
dist 47=[-8.1542464655222674139 ,10.053643653238316813  ] 
dist 48=[-8.0905496646621252203 ,10.410797775397582622  ] 
dist 49=[-3.5081366420431227406 ,10.603923030138924854  ] 
dist 50=[-2.8633165303176031158 ,10.713756098888114327  ] 
dist 51=[-2.7562872155660060695 ,10.738442420928933312  ] 
dist 52=[-1.8059295834915921826 ,10.706212856575087245  ] 
dist 53=[-1.6281320399664028289 ,10.570591026216256947  ] 
dist 54=[-1.3820329961859891473 ,9.5455666571004530955 ] 
dist 55=[-1.3077935161513853426 ,9.3099860483938867284 ] 
dist 56=[2.3983615310128530576 ,9.3184834507809449627 ] 
dist 57=[2.8636573876942249076 ,9.2914166244369490011 ] 
dist 58=[2.3988808689138481511 ,7.5089931856956896932 ] 
dist 59=[1.2851794887739934216 ,7.8373178063833519171 ] 
dist 60=[.32386217321962222152,8.0826314447002661560 ] 
dist 61=[-.67783311055706417512,8.2601167025145812318 ] 
dist 62=[-1.6261653994153970769 ,8.3176325160073674357 ] 
dist 63=[-2.3746472362309506375 ,8.3280738564676995298 ] 
dist 64=[-3.1184999019454154381 ,8.3175520880901720608 ] 
dist 65=[-4.0483900337795193194 ,-.6091980411722179339 ] 
dist 66=[-4.9320919577305850460 ,-.94179092537652662938] 
dist 67=[-5.4917050607236609932 ,-1.6474763210971891910 ] 
dist 68=[-5.9199436086072001009 ,-1.7580513750733116412 ] 
dist 69=[-6.2795854131141019824 ,-2.5479161298441496143 ] 
dist 70=[-6.5666944603398890556 ,-2.3846470717981391202 ] 
dist 71=[-6.7055907643305066724 ,-2.1035741895204416068 ] 
dist 72=[-6.7708992366739768897 ,-1.6833739787038467349 ] 
dist 73=[-6.7740023768328296088 ,-.96519722806535512281] 
dist 74=[-5.5113867880386043966 ,-.22919066767804597757] 
dist 75=[-5.6578482794255577826 ,.26214809727927412777] 
dist 76=[-5.7226909040361208486 ,.66694724272850098787] 
dist 77=[-5.7506236751813351106 ,1.0722937327993482810 ] 
dist 78=[-5.7498083365993730486 ,1.4865903631546143562 ] 
dist 79=[-5.7278956206467606331 ,1.7845350770796713395 ] 
dist 80=[-5.7054696846793876061 ,2.0536057002763436670 ] 
dist 81=[-4.1249083378870577501 ,2.3527634003770154816 ] 
dist 82=[-3.9457635385884363684 ,2.6272477217448330983 ] 
dist 83=[-3.4942430751543161489 ,2.7979114458030200567 ] 
dist 84=[-3.4143877302263690648 ,2.9248589366627257764 ] 
dist 85=[-2.6850796059008301728 ,3.0249644427811798400 ] 
dist 86=[-2.5416025138991713679 ,3.0999229005659840361 ] 
dist 87=[-2.3473013229171006641 ,3.2660352578557450908 ] 
dist 88=[-2.2837223213354750965 ,3.5800488062005300696 ] 
dist 89=[-.98398920935581314101,3.8619989819387382048 ] 
dist 90=[-.81745556709726537499,4.0322427407552639412 ] 
dist 91=[-.44354002835195215607,4.1529579693145357570 ] 
dist 92=[-.3677470634533302701 ,4.2373467122906070344 ] 
dist 93=[.08003240078111529127,4.2918109610459782738 ] 
dist 94=[-.16680353199583058573,4.2990068792369917478 ] 
dist 95=[-.36970758789952352524,4.2760604486950722399 ] 
dist 96=[-.57209503731270032092,4.2568617085144612628 ] 
dist 97=[-.82567857495889638626,.77182052804221321064] 
dist 98=[-1.0664621493049130362 ,.53127304438722030726] 
dist 99=[-1.2178050577465304039 ,-.03333574554988827182] 
dist 100=[-1.3320393872063392881 ,-.11648336653003738151] 
dist 101=[-1.4248846142725758192 ,-.27924574601816933936] 
dist 102=[-1.4989020695167575842 ,-.53744629680211341481] 
dist 103=[-1.5380480981926463721 ,-.57505337327329546242] 
dist 104=[-1.6948792096048877060 ,-.73647641637830273609] 
dist 105=[-1.9591342515166128162 ,-.80103255967178645807] 
dist 106=[-2.1265585622721180792 ,-1.0137343303202048330 ] 
dist 107=[-2.2547282239066473944 ,-.94761149381731183478] 
dist 108=[-2.3624077149086686774 ,-.88236252422996039898] 
dist 109=[-2.4483726478172314147 ,-.80166234323800935532] 
dist 110=[-2.4899288210655422305 ,-.7175968559941586135 ] 
dist 111=[-2.5068169649431564467 ,-.63890407214470250769] 
dist 112=[-2.5067770501586639112 ,-.54932859532457877382] 
dist 113=[-1.4304733377466204901 ,-.42183494179915716002] 
dist 114=[-1.3374933760214279207 ,-.29320575241952652842] 
dist 115=[-1.1082078154781489124 ,-.19908579031714634574] 
dist 116=[-1.0704343748717131538 ,-.11243040141768611613] 
dist 117=[-.72444543737395206128,-.01355085516718822772] 
dist 118=[-.659499930307631654  ,.08542266625509194478] 
dist 119=[-.57107721790382687831,.17247358632819668054] 
dist 120=[-.5437996225502090072 ,.26736870556774135756] 
dist 121=[-.09759949798459097039,.44726627388998133516] 
dist 122=[.03670181255559162348,.59437134069232488088] 
dist 123=[.181526751916901777  ,.7156892514344830662 ] 
dist 124=[.20341619743522307839,.83314952722193025969] 
dist 125=[.34632916342459034715,.93888249153256633982] 
dist 126=[.3571918924796909996 ,1.0134471927474115447 ] 
dist 127=[.34353096916006802052,1.0793952797901538437 ] 
dist 128=[.31352348723690260792,1.1507992015453233436 ] 
dist 129=[.25352737162615057468,1.2312237293644628005 ] 
dist 130=[.18563197534118329645,1.3159721819241581602 ] 
dist 131=[.12410587579228808367,1.3857313091658171627 ] 
dist 132=[.05562025454167384824,1.4532290887852387109 ] 
dist 133=[-.04005405071199166202,1.5140703352602792230 ] 
dist 134=[-.14564355931351667549,1.5572646342166898821 ] 
dist 135=[-.2536931163128096316 ,1.5957846482467107543 ] 
dist 136=[-.38404529515318872444,1.6379710304735607200 ] 
dist 137=[-.57861843612725425274,1.6752493987846644056 ] 
dist 138=[-.78773490183585711537,1.6941819813038548673 ] 
dist 139=[-.95891492917858230019,1.7032875470998878965 ] 
dist 140=[-1.1004383149711711688 ,1.7013475451182884775 ] 
dist 141=[-1.2381364647035501133 ,1.6924442475898717052 ] 
dist 142=[-1.3625405162500239397 ,1.6855863733200607563 ] 
dist 143=[-1.4510293652443996754 ,1.6548725731622888604 ] 
dist 144=[-1.5300003349755531511 ,1.6451765804573862279 ] 
dist 145=[-1.8208924347393702730 ,1.5379484247758284429 ] 
dist 146=[-2.1241911682242207542 ,1.5130979178241227986 ] 
dist 147=[-2.3627474632568144603 ,1.4629436525308253266 ] 
dist 148=[-2.5746964481801314262 ,1.4464119174516806143 ] 
dist 149=[-2.7528669887054945029 ,1.3696871365198088700 ] 
dist 150=[-2.8566787488917316322 ,1.3513823566514825876 ] 
dist 151=[-2.9257398007788770608 ,1.2961878718679426161 ] 
dist 152=[-2.9652912459284464933 ,1.2840986278205537392 ] 
dist 153=[-2.9874756489192627570 ,1.1555476865513773445 ] 
dist 154=[-2.9872564389503161609 ,1.1293059838736116915 ] 
dist 155=[-2.9737215355959982660 ,1.2463017773447010850 ] 
dist 156=[-2.9617068693338820111 ,1.4616345682056130054 ] 
dist 157=[-2.8746494163322686512 ,1.6608632494689486116 ] 
dist 158=[-2.8489491523844000378 ,1.8340113261892802034 ] 
dist 159=[-2.7727031789621989228 ,1.9453093796538817620 ] 
dist 160=[-2.7446000207708972169 ,2.0324027609865624621 ] 
dist 161=[-.93518711954086988202,2.1090007891853692512 ] 
dist 162=[-.69523013344900675275,2.1714307287201485754 ] 
dist 163=[-.65823413076314807266,2.2020071809540805402 ] 
dist 164=[-.57292185217704115283,2.2150594649293304284 ] 
dist 165=[-.55240003054854885091,2.3010957975639109284 ] 
dist 166=[-.43654183083205083837,2.4961810880906966954 ] 
dist 167=[-.41404196677544401164,2.6533297984365907025 ] 
dist 168=[-.36796216814003086438,2.7993459568267470439 ] 
dist 169=[-.3552334660207907881 ,2.9250587790778426284 ] 
dist 170=[-.37562946915205408842,3.0012172836484443733 ] 
dist 171=[-.62061600559305693522,3.0555156054174258042 ] 
dist 172=[-.87648303786235390915,3.0940250560189144480 ] 
dist 173=[-1.1229408662277061257 ,3.1193502154050555135 ] 
dist 174=[-1.3438526877126076826 ,3.1210545687172731060 ] 
dist 175=[-1.4978192316511895976 ,3.1080052060656502864 ] 
dist 176=[-1.6319112187860661130 ,3.0964445139019576540 ] 
dist 177=[-1.7735462012762254719 ,1.2454103162199749224 ] 
dist 178=[-1.9004513103972141226 ,1.0851648732606708545 ] 
dist 179=[-1.9757867057829639749 ,.71417906416324109761] 
dist 180=[-2.0276197466358232589 ,.64646910345136669778] 
dist 181=[-2.0607737751195457861 ,.25496389603679222852] 
dist 182=[-2.0793029360004434165 ,.18525026055961266251] 
dist 183=[-2.0815016596164617718 ,.05253051808536609173] 
dist 184=[-2.0606875596939274093 ,.02126171792542940430] 
dist 185=[-2.0568629744862954931 ,-.19447340491767856585] 
dist 186=[-2.0225980802538123880 ,.1234798202515949947 ] 
dist 187=[-2.1121427146402737467 ,.33635224254325839514] 
dist 188=[-2.1677673785995824382 ,.51256101408776603178] 
dist 189=[-2.2057881746495373782 ,.68426585670375428862] 
dist 190=[-2.2251124831021952006 ,.83948111401489470856] 
dist 191=[-2.2353008061115074680 ,.94991398342449582884] 
dist 192=[-2.2345580952732009612 ,1.0484519259909705219 ] 
dist 193=[-.49029276378063657827,1.1562185095419728324 ] 
dist 194=[-.33502760585413030732,1.2538286418938108527 ] 
dist 195=[-.23249079033631454148,1.3118536982398640841 ] 
dist 196=[-.20662398629922221351,1.3518676664122423350 ] 
dist 197=[-.11898617053544107389,1.3776349106024726241 ] 
dist 198=[-.09931778612105348513,1.3930878342094542481 ] 
dist 199=[-.08381748806653262172,1.3950790482167084986 ] 
dist 200=[-.08736355857316358338,1.3857403870519053612 ] 
dist 201=[-.09930726724810682928,1.3808934136523257605 ] 
dist 202=[-.12165347131683504981,1.4485715740253025761 ] 
dist 203=[-.15585835412813383129,1.5125713420920244403 ] 
dist 204=[-.21510366866640360269,1.5544149531874419075 ] 
dist 205=[-.28575837033333402141,1.5832773940386550833 ] 
dist 206=[-.40424666424504677701,1.5954946124328396600 ] 
dist 207=[-.52061649993219650677,1.5978351711914624936 ] 
dist 208=[-.63887036914375921369,1.5946119798425570331 ] 
dist 209=[-.8016144798142465816 ,1.5521591488289355226 ] 
dist 210=[-.93588099540244853413,1.6274169591773742426 ] 
dist 211=[-1.0310411124860212661 ,1.6760600952509805176 ] 
dist 212=[-1.1072715719765850902 ,1.7009753483481055158 ] 
dist 213=[-1.1773737173205978400 ,1.7144315515014610165 ] 
dist 214=[-1.2379983620635744483 ,1.7173615195796499188 ] 
dist 215=[-1.2764246218330374417 ,1.7131428517558842561 ] 
dist 216=[-1.3058758704994781463 ,1.7072847133554379171 ] 
dist 217=[-1.3900723767442298126 ,1.4632861770927188892 ] 
dist 218=[-1.6805812170567848335 ,1.4337766174982592226 ] 
dist 219=[-1.8614708546406276932 ,1.5059513326512718785 ] 
dist 220=[-1.9963393340327989670 ,1.5537958675403358312 ] 
dist 221=[-2.1032687895894646461 ,1.5807862759647987956 ] 
dist 222=[-2.1862402170375224908 ,1.5965792721547403503 ] 
dist 223=[-2.2255392267006075662 ,1.5997582431643785568 ] 
dist 224=[-2.2428355775991472509 ,1.5945750110514047304 ] 
dist 225=[-2.2428006355471345562 ,1.5897353746529005050 ] 
dist 226=[-2.1091810612945027351 ,1.3890177094771979725 ] 
dist 227=[-2.0806083209163947385 ,1.3561996610348116790 ] 
dist 228=[-2.0293596363717635413 ,1.2887737723060779365 ] 
dist 229=[-2.0125645167884339635 ,1.2703903232782810273 ] 
dist 230=[-1.9383913130497216070 ,1.1778675015305590489 ] 
dist 231=[-1.9166803319880767392 ,1.1573995767892080355 ] 
dist 232=[-1.8620575049902732621 ,1.1013216817428072629 ] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 1, 2, 2, 0, 1] 
dist 0=[63.259193294442931954  ,63.259193294442931954  ] 
dist 1=[62.647732722151387138  ,63.460963621349163481  ] 
dist 2=[61.565861102496485412  ,63.654944081449158745  ] 
dist 3=[59.657371723062683093  ,63.815614271301367657  ] 
dist 4=[57.360357345657845949  ,63.854004377206518074  ] 
dist 5=[54.727191367967046268  ,63.809909554193505690  ] 
dist 6=[51.339653403178841870  ,63.694945001600493486  ] 
dist 7=[46.030614040200718118  ,63.405010285760832388  ] 
dist 8=[40.638874516872830315  ,63.234261139299313169  ] 
dist 9=[36.921032667188619751  ,62.757864623316803877  ] 
dist 10=[33.711942179653174423  ,62.529582863683358339  ] 
dist 11=[30.351215813297772535  ,61.252706240577594427  ] 
dist 12=[27.143215421278895449  ,60.857196419962349066  ] 
dist 13=[24.543616316121166439  ,60.433077546965424497  ] 
dist 14=[21.886393211661406141  ,58.293222619696793699  ] 
dist 15=[18.447711537653930252  ,52.834615224704439539  ] 
dist 16=[15.096376227619324598  ,32.242422003625686937  ] 
dist 17=[12.787586772818192047  ,30.017302589612280179  ] 
dist 18=[10.793709830373647783  ,27.747760717214939137  ] 
dist 19=[8.6993966218763436872 ,24.026819942437934119  ] 
dist 20=[6.6908541901215824102 ,18.046794249804922798  ] 
dist 21=[5.0388265012117984506 ,16.293752546630342494  ] 
dist 22=[3.3230408392214371600 ,15.197885898800732829  ] 
dist 23=[1.0584501795259137251 ,14.025054936924896945  ] 
dist 24=[-1.1214061854300910731 ,12.202200003861608889  ] 
dist 25=[-2.4989354512814103974 ,11.213004503113622506  ] 
dist 26=[-3.5619022501098570164 ,11.068270492205944139  ] 
dist 27=[-5.1742318739141847204 ,4.5687741966081842496 ] 
dist 28=[-7.3224628812305891523 ,1.9097128523600023726 ] 
dist 29=[-9.0479603159469036252 ,1.0241814422199418399 ] 
dist 30=[-10.657791962076391961  ,-.1057386669606195601 ] 
dist 31=[-12.078848366673905166  ,-1.6781856431181922447 ] 
dist 32=[-13.258773519513168825  ,-1.9574579728933995391 ] 
dist 33=[-14.365804074457127551  ,-2.4698747438475571338 ] 
dist 34=[-15.166624650352765371  ,-2.5794393655099962483 ] 
dist 35=[-15.768883401718163396  ,-2.8315112392473298924 ] 
dist 36=[-16.213578198933793822  ,-2.7865594367998763712 ] 
dist 37=[-16.384493012017909466  ,-2.6110053740705214405 ] 
dist 38=[-16.440126801947170127  ,-2.2152600765281166426 ] 
dist 39=[-16.423589301787681024  ,-1.7110152774113859109 ] 
dist 40=[-15.888290695978986517  ,-1.1019626228436656651 ] 
dist 41=[-15.831244547626873471  ,-.30051014916894136798] 
dist 42=[-15.772562153523063085  ,.97206390721413186171] 
dist 43=[-14.876937377645121293  ,3.5247791915128012778 ] 
dist 44=[-14.133260186609955680  ,5.6468783747600328456 ] 
dist 45=[-13.959837315016758842  ,7.4000075186810264306 ] 
dist 46=[-13.500889298452760254  ,9.1050152153555272856 ] 
dist 47=[-13.362610040445302038  ,10.646486606191731562  ] 
dist 48=[-6.2517928416689946379 ,11.747237862191793633  ] 
dist 49=[-5.5458340774702479920 ,12.735170179075101473  ] 
dist 50=[-3.9874871687963076591 ,13.826672750551237472  ] 
dist 51=[-3.6405872170954548630 ,14.803944066503258189  ] 
dist 52=[-1.8236903643769173617 ,15.336052552494937538  ] 
dist 53=[-1.5012816425624140380 ,15.643782639836349725  ] 
dist 54=[-.79342187384757298036,15.725489444071139933  ] 
dist 55=[-.64069753658985925038,15.724049773684427252  ] 
dist 56=[-.21679961960810484227,15.700037339474921479  ] 
dist 57=[-.58599774163147811536,15.655172937426180877  ] 
dist 58=[-.8913247525893670068 ,15.580058126104861128  ] 
dist 59=[-1.1909014842820263106 ,11.898879294957613954  ] 
dist 60=[-1.4891948060596864051 ,11.455610923602172391  ] 
dist 61=[-1.7038348717361369555 ,10.361211027912537767  ] 
dist 62=[-1.8977432338366162106 ,10.013406266565864945  ] 
dist 63=[-2.1133860061510567588 ,8.3553706364066918702 ] 
dist 64=[-2.3086060517894065919 ,-.88676698136970083451] 
dist 65=[-2.4210672956727608607 ,-1.1848178686857965536 ] 
dist 66=[-2.7001811420445203195 ,-1.2497972167499040077 ] 
dist 67=[-3.2535615071542032048 ,-1.4722726465212268124 ] 
dist 68=[-3.6069970103326778481 ,-1.2981129893664810735 ] 
dist 69=[-3.8810859876028226433 ,-1.0866007251884956471 ] 
dist 70=[-4.1179218198932004681 ,-.80480266726144201481] 
dist 71=[-4.3122384088568611215 ,-.32954203069131491748] 
dist 72=[-4.4166998095080671637 ,.15203688685547656289] 
dist 73=[-4.4751925764708709593 ,.47606046228825555941] 
dist 74=[-4.4861192248942550383 ,.74577756282648115049] 
dist 75=[-3.6032082282720207810 ,1.0107766144639567534 ] 
dist 76=[-3.6151193656951813055 ,1.2515052525104646864 ] 
dist 77=[-3.6135106405384584722 ,1.4244275271836932540 ] 
dist 78=[-3.6017972960962952744 ,1.5802757797996541210 ] 
dist 79=[-3.5870322510420704362 ,1.7529058276509333391 ] 
dist 80=[-1.1201419088831479382 ,1.9249286030432260006 ] 
dist 81=[-.91312711613732859571,2.1086219387073484449 ] 
dist 82=[-.44671336046721131172,2.3078050218040705171 ] 
dist 83=[-.35660814425531512186,2.4860963786733614899 ] 
dist 84=[.06338988284428821932,2.5864704565633267543 ] 
dist 85=[.09140824075657489596,2.6487756780047579885 ] 
dist 86=[.14891628249050403689,2.6752365155675458747 ] 
dist 87=[-.09382398210574553621,2.6837724408885899800 ] 
dist 88=[-.50358248035069139199,2.6764987392203933493 ] 
dist 89=[-.77999388867072564136,2.6553536931659953986 ] 
dist 90=[-1.0107358594965000851 ,2.6405237125801438436 ] 
dist 91=[-1.2383847828830891353 ,2.7166423068142594042 ] 
dist 92=[-1.4456958091456063689 ,2.8155026088640916630 ] 
dist 93=[-1.5953395083084932010 ,2.8556269399076908872 ] 
dist 94=[-1.7309023897837278072 ,2.8717471991227568165 ] 
dist 95=[-1.8820662196261870164 ,2.8748447310223173526 ] 
dist 96=[-2.0166604699850528606 ,.84422704277498214578] 
dist 97=[-2.0861471330262504096 ,.72391063903452727627] 
dist 98=[-2.1240711079538924090 ,.69527093536873893727] 
dist 99=[-2.1878363176159407804 ,.22083645819344497431] 
dist 100=[-2.2833047133703905954 ,.1559362949219394953 ] 
dist 101=[-2.3407685361528567619 ,.0180809595732950492 ] 
dist 102=[-2.3611683116775122981 ,-.0156349463065321985 ] 
dist 103=[-2.3660548673605621914 ,-.15266565352245010341] 
dist 104=[-2.3616510145629272324 ,-.17824242132519363912] 
dist 105=[-2.3496359149563011887 ,-.22432663630694759894] 
dist 106=[-2.3382230155058732094 ,0                     ] 
dist 107=[-1.6580340077828103185 ,.01268138225432977007] 
dist 108=[-1.6782450141527857026 ,.13777332682862637481] 
dist 109=[-1.6817316016112940932 ,.23343199490592532695] 
dist 110=[-1.6763828838696238401 ,.32557897632997753059] 
dist 111=[-1.6695542564895827597 ,.43666244530161398959] 
dist 112=[-1.1461951675611648683 ,.54129246104525676501] 
dist 113=[-1.0907873709145913862 ,.60770230900101591222] 
dist 114=[-.9498122215840038196 ,.6586459680162661815 ] 
dist 115=[-.92709976904489078984,.70159844055415922374] 
dist 116=[-.69779661487379847993,.73599301553551434781] 
dist 117=[-.65323870737468132304,.75280983205249379766] 
dist 118=[-.59861398091633564365,.76086838516894035274] 
dist 119=[-.58217362458803141439,.82566301213778195983] 
dist 120=[-.1731501787014394367 ,.91778689364398141834] 
dist 121=[-.12216701138242038354,.97519234287665948981] 
dist 122=[-.01069786395333548780,1.0180197428679976398 ] 
dist 123=[.00595809096538802258,1.0520016369111035572 ] 
dist 124=[.10015360431463357065,1.0776084198825484937 ] 
dist 125=[.11603681988873970674,1.0870339872491873821 ] 
dist 126=[.13903129917382064631,1.0884926774334938390 ] 
dist 127=[.09694158750748037921,1.0854586954759550681 ] 
dist 128=[.01993556774478041824,.71944917164186860754] 
dist 129=[-.03564357583520360346,.74502312833051469063] 
dist 130=[-.10960339007675012091,.76798058709350972957] 
dist 131=[-.2376058844012033249 ,.79330767607301163724] 
dist 132=[-.37408542903849671778,.81814912897738320528] 
dist 133=[-.50696914615779267627,.83916512291205859285] 
dist 134=[-.66240079947752985078,.86134614451857138857] 
dist 135=[-.88882971818925023754,.89082814251296559856] 
dist 136=[-1.1116097535652728499 ,.91832540546069757653] 
dist 137=[-1.2524873496240545031 ,.93258824719535510084] 
dist 138=[-1.3600772677867941289 ,.93983544273723242441] 
dist 139=[-1.4500710354416561815 ,.93935089488109879418] 
dist 140=[-1.5216638956165293961 ,.93410285655058943178] 
dist 141=[-1.5558523598630655410 ,.93050414998830722132] 
dist 142=[-1.5728800842980008557 ,.91102186369801046415] 
dist 143=[-1.5760128291982735920 ,.90746107293005004205] 
dist 144=[-1.5376181010378334131 ,.82660097478350213618] 
dist 145=[-1.5246414319435298705 ,.81201884455765949441] 
dist 146=[-1.4997404177436950871 ,.76751784644355095007] 
dist 147=[-1.4897196988858808549 ,.76107276864957330574] 
dist 148=[-1.4368298974681375556 ,.66235760350283249883] 
dist 149=[-1.4228281354556261496 ,.64110276552731624387] 
dist 150=[-1.3755111643379376650 ,.62285697258010754957] 
dist 151=[-1.3656623988532334819 ,.61904403032373960184] 
dist 152=[-.54976449655984892995,.53052383652229555661] 
dist 153=[-.54870019838215400502,.64543944040758736364] 
dist 154=[-.54646951804949024406,.83455254753144417989] 
dist 155=[-.54401040026459455088,1.0104855084919514367 ] 
dist 156=[-.53672100355591429643,1.1640383654832385736 ] 
dist 157=[-.53320022599819692638,1.2638777955113847743 ] 
dist 158=[-.52400488315139941986,1.3432866257852731461 ] 
dist 159=[-.51982047585929499265,1.4153425614090321031 ] 
dist 160=[-.01758282527982953202,1.4772281679413194936 ] 
dist 161=[-.05508460823049193017,1.5160676552774102148 ] 
dist 162=[-.09154895987399137815,1.5453853907487912771 ] 
dist 163=[-.13598825039248194365,1.5692882885597535199 ] 
dist 164=[-.18200541803535010402,1.5878228293467565649 ] 
dist 165=[-.22476622215462887197,1.5957259354499790197 ] 
dist 166=[-.27322294644970122586,1.5973390728407559853 ] 
dist 167=[-.34196236470656417152,1.5921229575443409484 ] 
dist 168=[-.41124235047540339191,.98591774984827735953] 
dist 169=[-.4618572963325601076 ,1.0159100659871631792 ] 
dist 170=[-.50837780381869256702,1.0361370881166833816 ] 
dist 171=[-.56132942925837132295,1.0482590651105205327 ] 
dist 172=[-.61422431923381774268,1.0542049755552365038 ] 
dist 173=[-.66052133884518556674,1.0537071785376584153 ] 
dist 174=[-.71075978856640710617,1.0426902120834635760 ] 
dist 175=[-.77938101006532072111,1.0378988146380333956 ] 
dist 176=[-.90407018120060850034,.97847041263617921511] 
dist 177=[-1.0732646566841807749 ,.96461518251844017029] 
dist 178=[-1.2066033526267956970 ,.93199984791531697004] 
dist 179=[-1.3254638268974243608 ,.92009729254321849122] 
dist 180=[-1.4256168805935956247 ,.92935968010798193139] 
dist 181=[-1.4843345209556716281 ,.94700638286920820229] 
dist 182=[-1.5238264884921284794 ,.95658625473585143393] 
dist 183=[-1.5472921539081470585 ,.9576244985718054454 ] 
dist 184=[-1.5614995298838368653 ,.86307301911475215801] 
dist 185=[-1.5640609514221138386 ,.84673720797178557906] 
dist 186=[-1.5585851005270474021 ,.82325664177307954726] 
dist 187=[-1.5537582522945762506 ,.81452020313590355268] 
dist 188=[-1.5170861291581706790 ,.79315734500278845919] 
dist 189=[-1.5058730238260834107 ,.78442490496000680716] 
dist 190=[-1.4636103121681248701 ,.78777324402779992392] 
dist 191=[-1.4545733357066807181 ,.86037929282697426274] 
dist 192=[-.20399755985865736132,.92615955180972202606] 
dist 193=[-.15592243327567368804,.96227045016414617122] 
dist 194=[-.04541244805902310717,.98349028851335336233] 
dist 195=[-.02640146637014702946,.98987097270314051566] 
dist 196=[-.0360306149061949685 ,.99059402220940647202] 
dist 197=[-.0646869168937241986 ,.98924538778986518064] 
dist 198=[-.1034543364000991662 ,.98612455892472936146] 
dist 199=[-.1660500298061929003 ,.98133580939847690171] 
dist 200=[-.32932820935583731722,.80562118831373284136] 
dist 201=[-.46471436657698671582,.78121027842396416924] 
dist 202=[-.57406815430738964441,.77916277992239837133] 
dist 203=[-.67615331573461538585,.79012169772913480039] 
dist 204=[-.76548713621181944876,.79572966070772946858] 
dist 205=[-.82397651325841963852,.79500724395514284361] 
dist 206=[-.87094744518442119648,.79092547115888251641] 
dist 207=[-.91433459056490626714,.7870650940764126993 ] 
dist 208=[-.95123991340586293786,.6961314251903853615 ] 
dist 209=[-.97235537427254685983,.6807336609368797282 ] 
dist 210=[-.98590211269872205814,.6462495884185765944 ] 
dist 211=[-.99261692931197487998,.6350070365846294260 ] 
dist 212=[-.9944093215953419408 ,.5826013398796389858 ] 
dist 213=[-.99241423500435680454,.5711280435220527038 ] 
dist 214=[-.98021136289588428507,.5408261981796038734 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 2, 2, 2, 0, 2] 
dist 0=[61.480131171593958624  ,61.480131171593958624  ] 
dist 1=[60.436856552744513491  ,61.934249993347059952  ] 
dist 2=[59.251406427624404893  ,62.138099924741694391  ] 
dist 3=[58.229516330582334645  ,62.182108408411965770  ] 
dist 4=[57.129970656864271754  ,62.073180077866742940  ] 
dist 5=[55.634309184004890208  ,61.229093727071259816  ] 
dist 6=[53.994893200303751694  ,60.998839268938403614  ] 
dist 7=[52.321204458358974350  ,60.875538293831788170  ] 
dist 8=[50.298277091449060794  ,60.660358271065152542  ] 
dist 9=[47.264092885919678202  ,53.941464023211340381  ] 
dist 10=[44.111485412769499686  ,52.989206279167752168  ] 
dist 11=[41.615545590955853714  ,51.291307216509975557  ] 
dist 12=[39.116973510288753052  ,50.864355615819611409  ] 
dist 13=[35.953671801856949407  ,49.510595309520094178  ] 
dist 14=[32.595745682065092151  ,49.099569028410215722  ] 
dist 15=[29.053618999398163017  ,48.890869686028410113  ] 
dist 16=[22.713312267653992670  ,48.653408157705159846  ] 
dist 17=[18.431993081334140102  ,37.732442127722732598  ] 
dist 18=[14.166278535695717100  ,19.652065358557570821  ] 
dist 19=[10.374654748120870348  ,14.903755338359641888  ] 
dist 20=[7.2036817612052016625 ,13.878172644985233765  ] 
dist 21=[4.0393947665871892984 ,7.7530272588290974064 ] 
dist 22=[1.1120736334878640993 ,6.3500666867257966035 ] 
dist 23=[-1.1124341583116065308 ,5.4398840764491079715 ] 
dist 24=[-3.2894295752189714643 ,4.3622827811283202327 ] 
dist 25=[-5.8484057048649809629 ,-.07005894013467778921] 
dist 26=[-8.2936253640830129456 ,-3.0655260598694423748 ] 
dist 27=[-9.8377449758914999378 ,-4.2152426564867300845 ] 
dist 28=[-11.021159151948766022  ,-5.0174428889452971492 ] 
dist 29=[-12.025796676341189154  ,-5.8486672932326349808 ] 
dist 30=[-12.841500851100870742  ,-5.9666811166390995547 ] 
dist 31=[-13.270366687590298305  ,-5.7514453540181129416 ] 
dist 32=[-13.499054981040178243  ,-5.3466224156230783295 ] 
dist 33=[-13.541698906997432097  ,-4.2169413566277430413 ] 
dist 34=[-5.1282435064846310468 ,-3.0283512071732828913 ] 
dist 35=[-4.9627061451761170943 ,-2.1738354805421505197 ] 
dist 36=[-4.5591785380579507361 ,-1.4304038084890738358 ] 
dist 37=[-4.3716508104131005783 ,-.6751379100026926121 ] 
dist 38=[-4.1532686235358344254 ,.02565800838557065973] 
dist 39=[-4.0883226752959093437 ,.55220610903660503195] 
dist 40=[-3.3067391597179109187 ,1.0499607426741042515 ] 
dist 41=[-3.1875888659052864109 ,1.6362418346956297674 ] 
dist 42=[-2.9359903115592051948 ,2.1856647522287620100 ] 
dist 43=[-2.8672232907191628257 ,2.5365280613947371771 ] 
dist 44=[-2.5988475283445496774 ,2.8083119952093850677 ] 
dist 45=[-2.5452787978093501506 ,3.0423566069461155610 ] 
dist 46=[-2.4251000216166937878 ,3.2336759066116338922 ] 
dist 47=[-2.3933692355897594848 ,3.3350581532917220043 ] 
dist 48=[-2.2293173637599498586 ,3.4410286978002429182 ] 
dist 49=[-2.1928776001884503780 ,3.9367807251072147039 ] 
dist 50=[-2.1255530599383297076 ,4.3129621868454250873 ] 
dist 51=[-2.1053187747628112985 ,4.6253479199432389346 ] 
dist 52=[-2.0176557113509316035 ,4.8739833560449571346 ] 
dist 53=[-1.9957679204235160506 ,4.9957712972715805952 ] 
dist 54=[-1.9288194313464729598 ,5.0577568777865573806 ] 
dist 55=[-1.9127048262498420194 ,5.0673606717053738256 ] 
dist 56=[-1.7401397910899117070 ,4.9719278819123826898 ] 
dist 57=[-1.7058598456606905606 ,4.9363276513659997022 ] 
dist 58=[-1.6079841720848638123 ,4.8619300610979204139 ] 
dist 59=[-1.5868792592909842659 ,4.8307770486865101197 ] 
dist 60=[-1.3759056879611041169 ,4.6607646001555891092 ] 
dist 61=[-1.4100917082598499144 ,4.6185568808160293295 ] 
dist 62=[-1.4868718419352767870 ,4.4686068145877929455 ] 
dist 63=[-1.5246785893184529254 ,4.4460228507655687153 ] 
dist 64=[-1.5424978129615281353 ,2.2275771799962212422 ] 
dist 65=[-1.5439322449477174421 ,-.11085244764477549459] 
dist 66=[-1.1592869152688279615 ,-.74095941115736951166] 
dist 67=[-1.4283384745277334194 ,-.79591119382193597491] 
dist 68=[-1.6768466268959222650 ,-.90006258388133955755] 
dist 69=[-1.8929571417846692934 ,-.92197215191729752369] 
dist 70=[-2.0327605628339987243 ,-.97224084362877201609] 
dist 71=[-2.1434449053220057695 ,-.9563313560347262387 ] 
dist 72=[-2.2434039698778881200 ,-.90047665410207213413] 
dist 73=[-2.3271854843340123784 ,-.80897991793473832779] 
dist 74=[-2.3733202972190129347 ,-.71189469237080410548] 
dist 75=[-2.4008434422163820767 ,-.63372012600620544884] 
dist 76=[-2.4103281947879568135 ,-.55472209728658001108] 
dist 77=[-2.4076513188488124954 ,-.45429204953842004456] 
dist 78=[-2.4016107736053907066 ,-.34805290470310774784] 
dist 79=[-2.3636435742946862758 ,-.2374204911364023256 ] 
dist 80=[-2.3530840352560615802 ,-.06657085164436555780] 
dist 81=[-1.1411898649570949739 ,.19011628862289228083] 
dist 82=[-1.0267278345320423768 ,.44573440245787318116] 
dist 83=[-.84561443774384633149,.61233522015567668214] 
dist 84=[-.76216639102451214363,.74548816727691445443] 
dist 85=[-.7453150289428062716 ,.96258735889289049853] 
dist 86=[-.61321200291273460578,1.1416809316718257293 ] 
dist 87=[-.58662188261944547046,1.3099620965880139827 ] 
dist 88=[-.545433811686081572  ,1.5070591971228297763 ] 
dist 89=[-.53354133258824567245,1.6885172457937431315 ] 
dist 90=[-.29157149483719919221,1.7944148440224258295 ] 
dist 91=[-.25938209129992519284,1.8650690497934416085 ] 
dist 92=[-.18499950775064825573,1.9059376121230816388 ] 
dist 93=[-.17006535679854775765,1.9321968741633722623 ] 
dist 94=[-.07175995746650670113,1.9445680902819788592 ] 
dist 95=[-.05363776285910174276,1.9491242977262408924 ] 
dist 96=[-.15109524926031221611,1.9441943021156908994 ] 
dist 97=[-.34175276826976847391,1.1861539232253970372 ] 
dist 98=[-.53510458528407683826,.08184142296424615855] 
dist 99=[-.67766851265596162768,.00289776656624938597] 
dist 100=[-.79478243825645095825,-.15948547211131405719] 
dist 101=[-.9074817873481025842 ,-.20029674412608017661] 
dist 102=[-1.0084730993410527607 ,-.34057482554291802737] 
dist 103=[-1.0788823087389536252 ,-.36872144583006113399] 
dist 104=[-1.1402532019738863882 ,-.39478457815028596583] 
dist 105=[-1.2896243136748601121 ,-.38821045011440540273] 
dist 106=[-1.3879439528318744060 ,-.36855792638687298751] 
dist 107=[-1.4606865176559187698 ,-.33327521407324043402] 
dist 108=[-1.5173448230676574559 ,-.27991793559015116626] 
dist 109=[-1.5592227160969685846 ,-.18816104336949976249] 
dist 110=[-1.5730121695322489779 ,-.07905589970501167141] 
dist 111=[-1.5761031940417715762 ,.04350355469588013684] 
dist 112=[-1.5752910973360317663 ,.19908112659525296861] 
dist 113=[-1.5005490031612183052 ,.45340255563619857224] 
dist 114=[-.93523249307665251618,.68050530489310271703] 
dist 115=[-.89498630047707678023,.8353105597305513308 ] 
dist 116=[-.80183982672658187971,.95654425812170137214] 
dist 117=[-.77792066415363942214,1.0632587522764659421 ] 
dist 118=[-.64805452421658668381,1.1768335901563402079 ] 
dist 119=[-.62211948726055607767,1.2641688078140718886 ] 
dist 120=[-.56792407065759229091,1.3363940305288404787 ] 
dist 121=[-.55235520721995018814,1.4066769728755110160 ] 
dist 122=[-.37187149948964241794,1.4667160784261171559 ] 
dist 123=[-.34444253736871090505,1.4980796559911919452 ] 
dist 124=[-.28523265019943987401,1.5143889713186187154 ] 
dist 125=[-.26871173788974600493,1.5157356921707135837 ] 
dist 126=[-.20186961384183257693,1.5066092507265158163 ] 
dist 127=[-.1890505293618507263 ,1.4993982698143574523 ] 
dist 128=[-.15784190234088025795,1.4757417235126695098 ] 
dist 129=[-.15225098550851139406,1.4634700455513827500 ] 
dist 130=[-.24802443834223388231,.24701791652135458661] 
dist 131=[-.42726327264323940491,.06871401920306645952] 
dist 132=[-.58767333090424523586,.04232243589074968774] 
dist 133=[-.75199889788792109288,-.19349165049699416715] 
dist 134=[-.89900270272746905819,-.23402637760455410435] 
dist 135=[-1.0009252786000781631 ,-.29004710356447292425] 
dist 136=[-1.0891211174391329874 ,-.3013462947422645925 ] 
dist 137=[-1.1813732867739123808 ,-.53946862907879526518] 
dist 138=[-1.2638208865535552084 ,-.56769980404853846949] 
dist 139=[-1.3129080626572728172 ,-.6122440375474866201 ] 
dist 140=[-1.3468551206433523293 ,-.62087042784429254814] 
dist 141=[-1.3689096758605193212 ,-.61700287742426838435] 
dist 142=[-1.3815760905904899226 ,-.59424224355865823   ] 
dist 143=[-1.3828326747321688823 ,-.55338428009239684673] 
dist 144=[-1.3703690525671499453 ,-.47734583317710323041] 
dist 145=[-1.3662687604154063715 ,-.28902374552114956428] 
dist 146=[-.73569488571099040278,-.06263311736239167233] 
dist 147=[-.67662410435420558338,.09067145483056995883] 
dist 148=[-.53522526257543555827,.21944714699306353456] 
dist 149=[-.51044322084785821928,.34799729669126974382] 
dist 150=[-.31014692261635944022,.46620018901783600879] 
dist 151=[-.27463452817224575457,.55370246822902236588] 
dist 152=[-.2675051598428273104 ,.63526864666029832538] 
dist 153=[-.20408512430356600454,.72979250136897063701] 
dist 154=[-.11990234628725342699,.8169098219562808367 ] 
dist 155=[-.08069761012682084441,.86893337294120145984] 
dist 156=[-.07279434206755101907,.90509002672497076021] 
dist 157=[-.02624422635149852568,.9289202266483819035 ] 
dist 158=[-.01823955266456603835,.94503309955044227257] 
dist 159=[-.00180647403998842134,.95040720695304703314] 
dist 160=[.00217342910925812996,.94973586694849990886] 
dist 161=[.16564774270706280646,.94719086531398423826] 
dist 162=[.14193602039239430702,.56336163813906671917] 
dist 163=[.04108108668877058856,.60476371810928363915] 
dist 164=[-.04623507169278082691,.64490505658730716344] 
dist 165=[-.13762704065574027936,.68109906022068348101] 
dist 166=[-.22439416560084914097,.70675206168041242549] 
dist 167=[-.2932636250231514778 ,.72956271577567036097] 
dist 168=[-.36206011357432824251,.7544162346691416991 ] 
dist 169=[-.44853759372931881759,.77627354632377913574] 
dist 170=[-.53093432757811580295,.78712981633267254686] 
dist 171=[-.58345409435472990566,.79199173115503559159] 
dist 172=[-.62403538611215248506,.79147242037586200624] 
dist 173=[-.65881215636240178397,.78418032640617310721] 
dist 174=[-.68711245057563190441,.78045279388816655353] 
dist 175=[-.70186102326108297816,.76472057103116476697] 
dist 176=[-.70948374165882093094,.7600841709025254363 ] 
dist 177=[-.83898766904470483636,.74865884531347421899] 
dist 178=[-.99744195893026269801,.81313839425882233904] 
dist 179=[-1.0952276199193022812 ,.85147884418284920255] 
dist 180=[-1.1671085326680309180 ,.87792426058536131671] 
dist 181=[-1.2222274411112714915 ,.89495637716847560248] 
dist 182=[-1.2643286525731104231 ,.9053113686260837319 ] 
dist 183=[-1.2842806245718232753 ,.90661865519033774344] 
dist 184=[-1.2922086598312646416 ,.90142047737220757829] 
dist 185=[-1.2948153752522353630 ,.89775876766630179404] 
dist 186=[-1.2991540960257459711 ,.82503816358796286861] 
dist 187=[-1.2962653448013780841 ,.8112171122911299157 ] 
dist 188=[-1.2923471130611577839 ,.7763351481736280298 ] 
dist 189=[-1.2593295306642463925 ,.76461086669927108793] 
dist 190=[-1.2489413220836434027 ,.70061883132392275611] 
dist 191=[-1.2179240032791196088 ,.68583747579290246357] 
dist 192=[-1.2056074930649978583 ,.65609258665626196543] 
dist 193=[-1.0306162544733064983 ,.64686505488886865113] 
dist 194=[.14794590795182488139,.54392045431599328188] 
dist 195=[.21954962874784599755,.69052868042049971752] 
dist 196=[.37851485490948706736,.83870150241592512498] 
dist 197=[.405899732930378377  ,.96935313216147665721] 
dist 198=[.58232972172425752093,1.0566742859114287102 ] 
dist 199=[.61018098123670145915,1.1288007948486220596 ] 
dist 200=[.66426529214811335545,1.1988415375090259589 ] 
dist 201=[.6746948573961412069 ,1.2599161275974257540 ] 
dist 202=[.72406542952081997921,1.2962766114809927474 ] 
dist 203=[.72037500774020729292,1.3214251257657003833 ] 
dist 204=[.6992324499673226373 ,1.3377744985395948014 ] 
dist 205=[.64879864987555971432,1.3471788693644979127 ] 
dist 206=[.58352801168674327884,1.3464253963964229143 ] 
dist 207=[.50320065055588328265,1.3372548708228469700 ] 
dist 208=[.30559034828536618412,1.3293838875436120485 ] 
dist 209=[.07947730445826936985,.97246410535300190471] 
dist 210=[-.07433432128482905044,.62371461860317972006] 
dist 211=[-.20431844181511378978,.58804845495909742202] 
dist 212=[-.33538428558362101618,.49973056440743249709] 
dist 213=[-.45677786668691017454,.48492734084735275671] 
dist 214=[-.54817954716016196829,.34910235397755237776] 
dist 215=[-.63492382367148940766,.32317153641559004403] 
dist 216=[-.73773894187652278206,.2883069579794819296 ] 
dist 217=[-.83281993813654863919,.27718375818732171693] 
dist 218=[-.88871314375941673474,.05881632345845509414] 
dist 219=[-.9264875294160912341 ,.03148758539304183536] 
dist 220=[-.94929364117310950048,-.03039146259693944413] 
dist 221=[-.9645997147701073158 ,-.04128315122635700335] 
dist 222=[-.97245662464612558737,-.11532590327025213861] 
dist 223=[-.97634471378957578534,-.12773095114648539541] 
dist 224=[-.97581859711085627619,-.12191634488926354263] 
dist 225=[-.68156775828601624806,-.06866441333098156503] 
dist 226=[-.25908630038601884104,.03476333525698563657] 
dist 227=[-.2280729516799323757 ,.12293037726025354532] 
dist 228=[-.15626544325495968738,.21306109977321225674] 
dist 229=[-.14295123423663788421,.29732498153455197325] 
dist 230=[-.04961103408331850918,.36208974930809800087] 
dist 231=[-.03295384954532557140,.42483942367578689969] 
dist 232=[-.03942779511040489522,.50106569351446809074] 
dist 233=[-.06301973599380263986,.5724183807441523482 ] 
dist 234=[-.08592909235271614595,.61572771506459818145] 
dist 235=[-.11268019761853830587,.64670074921478596956] 
dist 236=[-.15159591816604903717,.66884446337631139815] 
dist 237=[-.19525267197105183024,.68486108535315575814] 
dist 238=[-.2409150872340745196 ,.6913928951256780316 ] 
dist 239=[-.29669532625485013661,.69278350622125492203] 
dist 240=[-.38071105569543964466,.69159304043624483682] 
dist 241=[-.46383474082552888695,.67644105740989527932] 
dist 242=[-.51605635066054519427,.70852645718867592118] 
dist 243=[-.55553164202747618664,.72824226493925533741] 
dist 244=[-.58781050763868552106,.73618060487397999627] 
dist 245=[-.61309041980880092937,.73958546716058323901] 
dist 246=[-.62464716193287337077,.74121599227656468112] 
dist 247=[-.63003374053055432929,.74185829552097422199] 
dist 248=[-.63070139587049149445,.74131938436483830168] 
dist 249=[-.6063338720424663961 ,.60233352596007372513] 
dist 250=[-.59993531489506506708,.58233489217551004596] 
dist 251=[-.5876784093088417434 ,.54643352253574987368] 
dist 252=[-.58316295971417730692,.53708657106535141596] 
dist 253=[-.56069685995773670438,.50586467228382388461] 
dist 254=[-.55477580889700480509,.49633218765910482208] 
dist 255=[-.53608944904645818798,.48836132207947660976] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 1, 2, 0, 2] 
dist 0=[63.545529586244875939  ,63.545529586244875939  ] 
dist 1=[62.527739692604751420  ,64.143433491162332613  ] 
dist 2=[61.201726573022090728  ,64.549278197947872656  ] 
dist 3=[59.373128319034032427  ,64.799871805210040871  ] 
dist 4=[56.822895224611486693  ,64.909468055279116755  ] 
dist 5=[52.615812369449992029  ,64.871178787541137862  ] 
dist 6=[48.275704108666536480  ,64.526556835141944540  ] 
dist 7=[45.194381039861960039  ,64.362169536291461068  ] 
dist 8=[42.440665857371930765  ,62.735685082327975685  ] 
dist 9=[39.408509655853413000  ,62.304453430485706327  ] 
dist 10=[36.423805222682523312  ,61.653802404771877783  ] 
dist 11=[33.859433344286882055  ,61.408620332500040740  ] 
dist 12=[31.107492737509228064  ,60.632806752922021790  ] 
dist 13=[27.373615055673461795  ,60.344091910371889305  ] 
dist 14=[23.657089956974913950  ,59.835206025110743034  ] 
dist 15=[20.620663430445926646  ,58.454356914954809608  ] 
dist 16=[16.621883072430006316  ,35.772175325150184128  ] 
dist 17=[12.880945204811179738  ,33.734679011298568658  ] 
dist 18=[9.9760314800415136679 ,28.875177347955378739  ] 
dist 19=[7.1217089118375444297 ,28.159970226552964177  ] 
dist 20=[3.5817080441769716691 ,21.414435451820334477  ] 
dist 21=[.2034005209143436496 ,20.202300683457945210  ] 
dist 22=[-2.0059183959922042893 ,18.681583476087205154  ] 
dist 23=[-3.7895798888599808883 ,18.374471171560927497  ] 
dist 24=[-5.4690535428971821193 ,9.2873041504792275250 ] 
dist 25=[-6.9650191309588495036 ,8.2072745458794980378 ] 
dist 26=[-8.0169796613708318658 ,5.8897483996508748757 ] 
dist 27=[-8.9557066944053780419 ,5.4392984062205666919 ] 
dist 28=[-10.001820446827048084  ,3.0913591525868156326 ] 
dist 29=[-10.936417949492674540  ,2.7056691754787131606 ] 
dist 30=[-11.881098796549702775  ,1.9866091128453600132 ] 
dist 31=[-12.425865726390533854  ,1.8448485732206165946 ] 
dist 32=[-12.746125576370965855  ,-3.5106446771595682998 ] 
dist 33=[-12.847619217692580380  ,-3.9824321191978867137 ] 
dist 34=[-12.868575193277627448  ,-4.8616904714193446099 ] 
dist 35=[-12.867024888546866457  ,-4.1220401562318112241 ] 
dist 36=[-12.850068491287260530  ,-2.4854169407301816984 ] 
dist 37=[-12.809145947471628278  ,.07619934842945985750] 
dist 38=[-10.055174320283855811  ,2.6557013430051396936 ] 
dist 39=[-10.455582662559890325  ,4.3638650182701583820 ] 
dist 40=[-10.806273718858182962  ,5.7564472387365273084 ] 
dist 41=[-10.995588724019269603  ,7.0774029756764864726 ] 
dist 42=[-11.106660993819777898  ,8.2473483333122663170 ] 
dist 43=[-11.144249042281579580  ,9.0376827298750635443 ] 
dist 44=[-11.135020973859399126  ,9.6995181454117616807 ] 
dist 45=[-11.116595788894634226  ,10.356980445013775303  ] 
dist 46=[-10.979044745300532782  ,10.933408326633782616  ] 
dist 47=[-10.954594127418412840  ,11.271994699041213900  ] 
dist 48=[-2.5743422699235656125 ,11.500411749823586195  ] 
dist 49=[-2.4607589290719818689 ,11.637274476203625790  ] 
dist 50=[-1.3317298071027992469 ,11.704015010552483919  ] 
dist 51=[-1.1259836558310514000 ,11.697951525229506879  ] 
dist 52=[-.87414046398809759825,11.570713977193359085  ] 
dist 53=[-.82418846905069768707,11.516019398057308994  ] 
dist 54=[.90523287734451367003,7.7070099817628517537 ] 
dist 55=[1.1028550701581492498 ,7.9896102622432479617 ] 
dist 56=[1.5430935087948168132 ,8.2923486145701309720 ] 
dist 57=[1.6106187855410670954 ,8.5286635658061758355 ] 
dist 58=[1.5061720248761255054 ,8.6345046623710994606 ] 
dist 59=[.7308182930528600051 ,8.6724658575204466515 ] 
dist 60=[-.49989203527881153982,8.6659929361149407045 ] 
dist 61=[-1.9066825918340438201 ,7.8536126497817465059 ] 
dist 62=[-2.8461985201612219534 ,7.8337270009154198408 ] 
dist 63=[-3.6215209085572486032 ,7.7990205410081052642 ] 
dist 64=[-4.3733673029143781121 ,2.7217510947491269283 ] 
dist 65=[-5.0509100853795934088 ,2.7469611738008260490 ] 
dist 66=[-5.5298534819349426259 ,2.7620903814432231396 ] 
dist 67=[-5.9542480052846771420 ,2.7597987874365620747 ] 
dist 68=[-6.4142274724541569509 ,2.7459806382090586940 ] 
dist 69=[-6.8201957551884622119 ,2.7353888360387192478 ] 
dist 70=[-7.0291479049252998575 ,1.0788768676618849401 ] 
dist 71=[-7.1407111660443739512 ,.93575637983561319996] 
dist 72=[-7.1594625071731232789 ,.60593956741515042998] 
dist 73=[-7.0771200326222163079 ,.54531841919455246529] 
dist 74=[-7.0423912312748306046 ,.12324448597261970639] 
dist 75=[-7.0092266609960744190 ,.04867863991192382454] 
dist 76=[-6.9696817162792022746 ,.6310162369948255716 ] 
dist 77=[-6.9192563768459235845 ,2.1455323607946975997 ] 
dist 78=[-6.9755328961309618085 ,3.1516222925076383494 ] 
dist 79=[-6.9804757169622385692 ,3.9752772344933228108 ] 
dist 80=[-4.1260282918943633568 ,4.7622100609997052800 ] 
dist 81=[-3.3159879658496116175 ,5.4628397887492023300 ] 
dist 82=[-3.1560606645928509976 ,5.9423093694480647009 ] 
dist 83=[-2.8532090561416900368 ,6.3504277449527693230 ] 
dist 84=[-2.7741839276544871958 ,6.7665168941525850243 ] 
dist 85=[-1.9792813315444887592 ,7.1281225700959942467 ] 
dist 86=[-1.4016668761248065451 ,7.3189421724442917649 ] 
dist 87=[-1.0199347068092248658 ,7.4208308809568292479 ] 
dist 88=[-.9360531723867494354 ,7.4353425059974406113 ] 
dist 89=[-.4661111704221188983 ,7.3938208770596139585 ] 
dist 90=[-.3813556654164871853 ,7.3541315311543826725 ] 
dist 91=[-.2033306765558788605 ,7.2565513987244722144 ] 
dist 92=[-.1563029236301737735 ,7.2064666316359069842 ] 
dist 93=[-1.0997990194085219290 ,5.0121796938771217292 ] 
dist 94=[-1.8154502659582258512 ,4.9894657370658128430 ] 
dist 95=[-2.4049628481356873556 ,4.9612532045045971139 ] 
dist 96=[-2.9740342168352389696 ,3.5390828941969272497 ] 
dist 97=[-3.4844287264225317188 ,3.3689484519789075277 ] 
dist 98=[-3.8399423308127163279 ,2.9612771145138638714 ] 
dist 99=[-4.1490978224205844450 ,2.8716095895027237794 ] 
dist 100=[-4.4746266899990967845 ,2.2688989510474364496 ] 
dist 101=[-4.7623404450618476402 ,2.1502807007766695372 ] 
dist 102=[-4.9206827389188733684 ,1.9342755854160704666 ] 
dist 103=[-5.0141688311632401457 ,1.8802809672808555877 ] 
dist 104=[-5.0432065961574755035 ,1.2572873534826976169 ] 
dist 105=[-5.0412068956596569509 ,1.2650194109756678487 ] 
dist 106=[-5.0220256996653501408 ,1.2656240029874283046 ] 
dist 107=[-4.9542060948149992497 ,1.2636217311878386735 ] 
dist 108=[-4.6950925278246139225 ,1.2593465787810269417 ] 
dist 109=[-3.2163326986373141191 ,1.2533148965897359501 ] 
dist 110=[-3.2242312153786040962 ,1.0353997167766356911 ] 
dist 111=[-3.2167723660547947964 ,1.0028692276841208181 ] 
dist 112=[-.90743040739907853098,.93971894985238683026] 
dist 113=[-.90293252217954649603,.92205790742786630864] 
dist 114=[-.87105861720221502276,.85404699189717942161] 
dist 115=[-.86172385325191191983,.9391319651119203017 ] 
dist 116=[-.83942977224323322761,1.1973770933940717014 ] 
dist 117=[-.83065639853474274286,1.3796196753632466047 ] 
dist 118=[-.55435820513047296868,1.5406300538071010433 ] 
dist 119=[-.5980315732814966957 ,1.7141987782268006110 ] 
dist 120=[-.73987864283781681967,1.8717744800146666760 ] 
dist 121=[-.8738134799803392164 ,1.9689980348007885015 ] 
dist 122=[-.99209867366816474417,2.0403989187298737112 ] 
dist 123=[-1.0715165705462645847 ,2.0949766479200498351 ] 
dist 124=[-1.1375203822011047984 ,2.1344030968325030706 ] 
dist 125=[-1.2022942690341233309 ,2.1453702823158639685 ] 
dist 126=[-1.2583224924514646592 ,2.1432793521302041995 ] 
dist 127=[-1.2894388098569422720 ,2.1346053618343177010 ] 
dist 128=[-1.3082069848723206673 ,1.1054518555344530574 ] 
dist 129=[-1.3149779220064203614 ,1.0133217347968099784 ] 
dist 130=[-1.3142310110321788619 ,.79000049559061482389] 
dist 131=[-1.3111103937916369326 ,.75351688965854993411] 
dist 132=[-1.2905129623388190638 ,.43047689359753337006] 
dist 133=[-1.2846850793421516640 ,.37102474394232366904] 
dist 134=[-.69186050819217389342,.28776206014156704636] 
dist 135=[-.71828669866517182352,.26346369716973102359] 
dist 136=[-.87874249515137465276,.3221612230959615239 ] 
dist 137=[-.97863701982602230586,.45967088840819033627] 
dist 138=[-1.0530247281422025490 ,.58906929881324336713] 
dist 139=[-1.1117580061332097507 ,.68412295997212667339] 
dist 140=[-1.1571743319650532184 ,.77203841313388047066] 
dist 141=[-1.1784491567703006679 ,.87296360056608720676] 
dist 142=[-1.1875789511608927740 ,.96550149118703924561] 
dist 143=[-1.1872771471667920203 ,1.0199592479487379580 ] 
dist 144=[-.57555214921855588363,1.0568497802402414033 ] 
dist 145=[-.58418411523698469302,1.0793086660393878913 ] 
dist 146=[-.59459709798758213835,1.0936142532062204875 ] 
dist 147=[-.61020760984121679784,1.0979804186928340487 ] 
dist 148=[-.62798420241683940921,1.0959208986350266408 ] 
dist 149=[-.64703199613736278332,1.0932136520102752586 ] 
dist 150=[-.6706498487332110743 ,.1403822588069755802 ] 
dist 151=[-.70665177538875034074,.13346566195246217265] 
dist 152=[-.74407779437462221049,.13315768486098192798] 
dist 153=[-.77337186808211577393,.17179421342706264672] 
dist 154=[-.8483898221036367932 ,.25898192665105271287] 
dist 155=[-.9019219565250963944 ,.40844396543711463628] 
dist 156=[-.9489502620034364914 ,.56592189293908520482] 
dist 157=[-.9992555975916110012 ,.71650370033329411188] 
dist 158=[-1.0428990354515931224 ,.8905721800010219555 ] 
dist 159=[-1.0633532860874882854 ,1.1417467456427641292 ] 
dist 160=[-1.0728626036114558025 ,1.3879453371382786494 ] 
dist 161=[-1.0972908446576383348 ,1.5421667029360086777 ] 
dist 162=[-1.1186527110139432856 ,1.6582567395897955895 ] 
dist 163=[-1.1304233251957537542 ,1.7523471809690170668 ] 
dist 164=[-1.1350600058813052899 ,1.8256970362459960044 ] 
dist 165=[-1.1344092077583961743 ,1.8590498513965457739 ] 
dist 166=[-1.1189957434843534639 ,1.8742166450433161530 ] 
dist 167=[-1.1161489992135994556 ,1.8750192681293306652 ] 
dist 168=[-1.1350963200886069758 ,1.7942002452642387882 ] 
dist 169=[-1.1700972388338401905 ,1.7740668524148150629 ] 
dist 170=[-1.1949158584274511798 ,1.7350480724864778523 ] 
dist 171=[-1.2069570975693782553 ,1.7209367293681836947 ] 
dist 172=[-1.2119154515540863389 ,1.6515148346421281705 ] 
dist 173=[-1.2095280352958510102 ,1.6334964778278120939 ] 
dist 174=[-1.0534538500908789305 ,1.5771779957699050636 ] 
dist 175=[-1.0282856837504441073 ,1.5634089456868115186 ] 
dist 176=[-.9836627428828436897 ,1.4038386626300197002 ] 
dist 177=[-.9713015039655827530 ,1.4038286008789452301 ] 
dist 178=[-1.0272811518867401393 ,1.3837898010228240661 ] 
dist 179=[-1.2377301818723497100 ,1.3747828876386786075 ] 
dist 180=[-1.4221039886636906639 ,1.3499205300614818296 ] 
dist 181=[-1.5432169914414333532 ,1.3382785096678263452 ] 
dist 182=[-1.6409340666161839122 ,.42388261832626185798] 
dist 183=[-1.7319827627449473449 ,.39994996616056839819] 
dist 184=[-1.8104392069677962514 ,.34261217786623161736] 
dist 185=[-1.8579262401760027636 ,.33121167611744354854] 
dist 186=[-1.8917257417905225470 ,.24792272927780032369] 
dist 187=[-1.9155827149004004554 ,.23196136911795542899] 
dist 188=[-1.9311665124176388397 ,.20478238668243254954] 
dist 189=[-1.9319644905046583125 ,.19810171185099327813] 
dist 190=[-1.9237271928149405369 ,.07745785557425817605] 
dist 191=[-1.9163334698067407079 ,.06144404936730078888] 
dist 192=[-.77312092922694051495,.04570625315956179425] 
dist 193=[-.67396792893519999894,.1939760612374640942 ] 
dist 194=[-.44422018628310550431,.32084636925404838599] 
dist 195=[-.40235917662890428949,.45130838266937364848] 
dist 196=[-.34985070725819444835,.57375935546203711653] 
dist 197=[-.41338072707425516753,.66867374057954237717] 
dist 198=[-.47502882979877960897,.76139473125300036674] 
dist 199=[-.51521205602688243696,.92541845999421074481] 
dist 200=[-.54728000348240564689,1.0904390766265205682 ] 
dist 201=[-.57655704922739401512,1.1914365150630194063 ] 
dist 202=[-.60172109835971419395,1.2646669561919342214 ] 
dist 203=[-.61738262969897971346,1.3189265720735705465 ] 
dist 204=[-.62904779722026542211,1.3598057920308726794 ] 
dist 205=[-.63827052742773034275,1.3796622571702704913 ] 
dist 206=[-.64440769024157463416,1.3878809442478556882 ] 
dist 207=[-.64477403077909020645,1.3873498597523724898 ] 
dist 208=[-.64070182379487923432,.24953839901454376137] 
dist 209=[-.63718604726080320594,.2179201955449534891 ] 
dist 210=[-.62580950763699967613,.27232446431937551582] 
dist 211=[-.74190077181509134086,.32586248189246339001] 
dist 212=[-.84738370332975988549,.3884394626193438927 ] 
dist 213=[-.92337109004219711389,.47952936304855486538] 
dist 214=[-.99214454234706668423,.5692139743290759578 ] 
dist 215=[-1.0688524636549926760 ,.62618531850792669184] 
dist 216=[-1.1372126583890687485 ,.6699792611562288619 ] 
dist 217=[-1.1726879847700337660 ,.7071008321153037705 ] 
dist 218=[-1.1919749218777866844 ,.73699252405447093797] 
dist 219=[-1.1957595776930788623 ,.75194727864013975446] 
dist 220=[-1.1832889759525866397 ,.7587905456916788805 ] 
dist 221=[-1.1787310272599947468 ,.7596639836685571761 ] 
dist 222=[-1.1748034454269576607 ,.7498463317776973541 ] 
dist 223=[-1.1707208552108524422 ,.7454524731303691252 ] 
dist 224=[-1.0169562001529676041 ,.7313591766659304749 ] 
dist 225=[-1.0689209647472181616 ,.7245093739770362432 ] 
dist 226=[-1.1031628743122439378 ,.7478460769366054916 ] 
dist 227=[-1.1220574585695402765 ,.8776335584308570994 ] 
dist 228=[-1.1329728531829792478 ,.9918009909046860200 ] 
dist 229=[-1.1353869238557371510 ,1.0675935507412473927 ] 
dist 230=[-1.1320298879220696314 ,1.1296254571296806788 ] 
dist 231=[-1.1285613377379782153 ,1.1889026568232895896 ] 
dist 232=[-.9776973614701424164 ,1.2396081076924130162 ] 
dist 233=[-.9533925000037106332 ,1.2674483643150108530 ] 
dist 234=[-.9042371868561304325 ,1.2838096954256614330 ] 
dist 235=[-.8894215760997925035 ,1.2887278108782642640 ] 
dist 236=[-.8262837858217437634 ,1.2863454214304221141 ] 
dist 237=[-.7968572058862877519 ,1.2828675759668763138 ] 
dist 238=[-.6948413734588766021 ,1.2601650935646142162 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 2, 0, 2, 1, 2] 
dist 0=[58.648216885001325921  ,58.648216885001325921  ] 
dist 1=[57.244503889684961986  ,59.348381617589041302  ] 
dist 2=[55.500413995079182397  ,59.726878035955351221  ] 
dist 3=[53.441254508628043171  ,59.846265207644835639  ] 
dist 4=[50.754051633722631790  ,59.839292809935451783  ] 
dist 5=[46.502295981148342553  ,59.547754268000370618  ] 
dist 6=[42.169160208398672335  ,59.384832640487309992  ] 
dist 7=[39.156904273165898837  ,59.191709737498601831  ] 
dist 8=[36.530884871836263923  ,59.051464820264657174  ] 
dist 9=[33.739571751100510457  ,58.582110128153518218  ] 
dist 10=[31.049477483120808469  ,58.389530265239504900  ] 
dist 11=[28.827277773949644535  ,57.895560223070554832  ] 
dist 12=[26.517229005944748386  ,57.678911861924911783  ] 
dist 13=[23.475742297186097274  ,56.526890564204666274  ] 
dist 14=[20.485792074982164323  ,56.153318049244482797  ] 
dist 15=[18.381189530869411805  ,53.852801222275189143  ] 
dist 16=[16.515553579273072645  ,33.294088273812919972  ] 
dist 17=[14.479400130034668866  ,27.794603146872597437  ] 
dist 18=[12.479344161482186931  ,26.494293506271805192  ] 
dist 19=[10.757219917359078121  ,25.257737592590447778  ] 
dist 20=[8.9000394154393254145 ,25.026418757490827780  ] 
dist 21=[6.3592381242172105430 ,16.137014700528914423  ] 
dist 22=[3.8779343818085946208 ,15.058304796062725024  ] 
dist 23=[2.2582781509259429824 ,13.407116857469839927  ] 
dist 24=[.94984481096771790045,12.262476285496675698  ] 
dist 25=[-.28742683942389591509,10.239321996634656884  ] 
dist 26=[-1.5829075645609494147 ,9.8433398886637704365 ] 
dist 27=[-3.5257762157018865646 ,9.2627688312648869807 ] 
dist 28=[-5.3436466538216159443 ,9.1165249688293312779 ] 
dist 29=[-6.7679496654471002387 ,1.8909001508193609672 ] 
dist 30=[-8.1858306875046091820 ,-1.7428184420389441930 ] 
dist 31=[-9.9797116257190736612 ,-2.8681511809685909806 ] 
dist 32=[-11.671316699242263601  ,-3.5133837573599287033 ] 
dist 33=[-12.680862686938143350  ,-3.4239497591421106291 ] 
dist 34=[-13.393839380940067455  ,-3.2446258577934225429 ] 
dist 35=[-13.899745083996823826  ,-2.9537494719675579638 ] 
dist 36=[-14.271427984303911016  ,-2.5282538376092196189 ] 
dist 37=[-14.447502662675406880  ,-1.8116512712346444639 ] 
dist 38=[-14.517426795870549483  ,-1.0767956796003753984 ] 
dist 39=[-14.510990091509482567  ,-.57826203748300736273] 
dist 40=[-13.307533668341341338  ,-.15946003844282134655] 
dist 41=[-13.102564680924776093  ,.25774002454983521345] 
dist 42=[-13.089169271008807646  ,.64042695055302761695] 
dist 43=[-13.121934382576287736  ,.92175928692508984409] 
dist 44=[-13.108765213270242236  ,1.1821926004764380962 ] 
dist 45=[-12.019820838498378936  ,1.6469286952132824257 ] 
dist 46=[-11.758188786231475673  ,2.9946734951348498566 ] 
dist 47=[-11.669527004824660856  ,4.0912445078093479529 ] 
dist 48=[-3.7387432065662591551 ,5.1308074315300770224 ] 
dist 49=[-3.0474582670331571197 ,6.0536327301990917456 ] 
dist 50=[-1.4910605190209526449 ,6.6844346755810109015 ] 
dist 51=[-1.2007483938715655538 ,7.2220944048628456368 ] 
dist 52=[-.95675909012089804633,7.7733461577807832587 ] 
dist 53=[-.93051328186749427779,8.2602434894823233166 ] 
dist 54=[1.5472031816466228930 ,8.5411162971244332440 ] 
dist 55=[1.4024055558665779026 ,8.7252162821343788520 ] 
dist 56=[1.2677651553797042474 ,8.8258913892414734477 ] 
dist 57=[1.1132657420810108924 ,9.1947770764811253899 ] 
dist 58=[.95903643598064180432,9.5996501055908746569 ] 
dist 59=[.82536091567248972636,9.8794894066031491935 ] 
dist 60=[.68176315196215743052,10.078202323298378125  ] 
dist 61=[.48784791285629406939,10.159184280860558436  ] 
dist 62=[-.04700867767001464603,10.172934553667894283  ] 
dist 63=[-.90298600289097306398,10.158541408781634532  ] 
dist 64=[-1.7519322335139769409 ,3.6750128146762143497 ] 
dist 65=[-2.5293753697428051024 ,2.3998413698686818566 ] 
dist 66=[-3.1001747088800893689 ,2.1614397433785452066 ] 
dist 67=[-3.6279337905948423190 ,1.8281150454770373903 ] 
dist 68=[-4.2337584003736959385 ,1.7287665412873453479 ] 
dist 69=[-4.7922328443976536739 ,.05081942637152255576] 
dist 70=[-5.1311189633176097224 ,-.07302406558830470389] 
dist 71=[-5.3736277287918780550 ,-.087547894096787191  ] 
dist 72=[-5.5476053400813315541 ,-.11052314084727637766] 
dist 73=[-5.6702007208005897581 ,-.11532103836478880866] 
dist 74=[-5.7077234715557214917 ,-.11776419448387607148] 
dist 75=[-5.7088387850079355122 ,-.11147559508826156516] 
dist 76=[-5.7376770686052354499 ,-.09889859508985082171] 
dist 77=[-5.8066707076756709675 ,-.07483824289708842516] 
dist 78=[-5.8418244990810014973 ,-.04836402876180560606] 
dist 79=[-5.8399558946795821023 ,-.02612471675311856752] 
dist 80=[-2.4902646354938904092 ,.10270878884539182674] 
dist 81=[-2.2160907366940939657 ,.53657152675491749946] 
dist 82=[-1.5579443101831993356 ,.86128017518434008434] 
dist 83=[-1.4551533790633349208 ,1.1673774708288627821 ] 
dist 84=[-.75506225015875997732,1.5270606976357396646 ] 
dist 85=[-.75217957352630006442,1.8637591662226503760 ] 
dist 86=[-.1402829134650151611 ,2.0781937251371114908 ] 
dist 87=[-.07947400877248981807,2.2436636003572844279 ] 
dist 88=[.08167174336060111644,2.3850501467822176915 ] 
dist 89=[.10380914352700646517,2.4997601892207309278 ] 
dist 90=[.22279183884152196727,2.5588213621934397314 ] 
dist 91=[.24326872590041569487,2.5883010393445010896 ] 
dist 92=[.27262480160977798158,2.5911486423377981177 ] 
dist 93=[.23427509702658900271,2.5344574216407666374 ] 
dist 94=[.19114731575973669402,2.5795086100871109614 ] 
dist 95=[.15237824691081588179,2.5899222837518913509 ] 
dist 96=[.10943219534805190762,1.6690100136335158357 ] 
dist 97=[.04961423128277900814,1.6344792920900123595 ] 
dist 98=[-.01644332891205982139,1.5695225926881029846 ] 
dist 99=[-.08430406310006548255,1.5504671437936916699 ] 
dist 100=[-.16648826717105497813,1.4745938364017541053 ] 
dist 101=[-.28972721932107091882,1.4537990266155860053 ] 
dist 102=[-.42211573103063922981,1.4116144786373506584 ] 
dist 103=[-.58782668993512435001,1.3975844496401949243 ] 
dist 104=[-.76558437591411692326,1.3360959954436958541 ] 
dist 105=[-.93709340738909000346,1.3166432770835046631 ] 
dist 106=[-1.0779169784543966706 ,1.3045126202062950347 ] 
dist 107=[-1.2230731543328343685 ,1.2994990964065975160 ] 
dist 108=[-1.4119261271679308853 ,1.2993515574042171835 ] 
dist 109=[-1.5984192657607683491 ,1.3066684744486769650 ] 
dist 110=[-1.7441991848513607447 ,1.3207330987150539370 ] 
dist 111=[-2.0264039608501783983 ,1.3474581969373719412 ] 
dist 112=[-2.4791066217546226980 ,1.3753194038902670393 ] 
dist 113=[-2.7659550316494231469 ,1.3939093932115368688 ] 
dist 114=[-2.9858658742412830368 ,1.4090649211645880614 ] 
dist 115=[-3.1715193488033602252 ,1.4232506062813964198 ] 
dist 116=[-3.3206974371847882258 ,1.4355099219274171171 ] 
dist 117=[-3.3950936400223435424 ,1.4429896798151354466 ] 
dist 118=[-3.4315383785599119497 ,1.4482729063935639018 ] 
dist 119=[-3.4357810799294760225 ,1.4517707855323639009 ] 
dist 120=[-3.3861447500885396294 ,1.4533379369733056763 ] 
dist 121=[-3.3643874686556736605 ,1.4509265667876322206 ] 
dist 122=[-3.3109409584106905586 ,1.4450607278659096610 ] 
dist 123=[-3.2864251522166602496 ,1.4382917961696618580 ] 
dist 124=[-3.1462609520727402648 ,1.4175064011845148301 ] 
dist 125=[-3.1100496283920674178 ,1.9933158396253927949 ] 
dist 126=[-3.0111775696817425866 ,2.3880443369794766127 ] 
dist 127=[-2.9763051566210050988 ,2.7019635811340933788 ] 
dist 128=[-1.6752991157916423997 ,2.9868822941701579811 ] 
dist 129=[-1.5295650828091276751 ,3.2307603108598633148 ] 
dist 130=[-1.4988893628566764951 ,3.3809633136392015750 ] 
dist 131=[-1.4097223001680012928 ,3.4910813559679636379 ] 
dist 132=[-1.3955877029930365740 ,3.5750609781898995123 ] 
dist 133=[-1.2060710283254189673 ,3.6368065000513595055 ] 
dist 134=[-1.1694654802496022627 ,3.6582275468117708558 ] 
dist 135=[-1.0969970998356454269 ,3.6565397622687455887 ] 
dist 136=[-1.0761230769587601278 ,3.6477803752074641247 ] 
dist 137=[-.99198017474525841768,3.7030282940536009744 ] 
dist 138=[-.97184481790124320272,3.7586076438095941880 ] 
dist 139=[-.92641906002194830872,3.7912997876517175125 ] 
dist 140=[-.91121783304417498447,3.8067249055017309388 ] 
dist 141=[-.98602606986990561918,3.8006595682955553579 ] 
dist 142=[-1.4759808535607395405 ,3.7686093374908642404 ] 
dist 143=[-1.8989072547576485372 ,3.7454749237231793936 ] 
dist 144=[-2.3148493339781345979 ,1.6385041312371947410 ] 
dist 145=[-2.6829203872300866291 ,1.4497777976375871965 ] 
dist 146=[-2.9312675472312994182 ,1.0128010126615902941 ] 
dist 147=[-3.1389849278548639750 ,.93144861480120139314] 
dist 148=[-3.3449863912994127651 ,.36266417459915891832] 
dist 149=[-3.5255363191442253560 ,.26094030610784270732] 
dist 150=[-3.6317266116388435565 ,.08656165853265441995] 
dist 151=[-3.7035842942232293254 ,.04648292182682242144] 
dist 152=[-3.7471761816949774690 ,-.44182461026222390919] 
dist 153=[-3.7691695631063111666 ,-.51198929999286106332] 
dist 154=[-3.7673460198356976634 ,-.61721800719508219116] 
dist 155=[-3.7303594836024003660 ,-.642978428299504828  ] 
dist 156=[-3.7116384222824953424 ,-.64508011044046494507] 
dist 157=[-2.8881689785328128370 ,-.23155478340497695238] 
dist 158=[-2.9024166137423767712 ,.21142698033970553496] 
dist 159=[-2.9046580597271719667 ,.58472922371583044822] 
dist 160=[-1.1825267600474390623 ,.95943372640715506115] 
dist 161=[-.63212300744993302925,1.3053999587056561540 ] 
dist 162=[-.53198732529564492639,1.5640654800402471697 ] 
dist 163=[-.36795803889041895396,1.8077740300569485748 ] 
dist 164=[-.33147020782671310654,2.0940760375574399794 ] 
dist 165=[-.18752397971882248933,2.3586436748292773816 ] 
dist 166=[-.19968968177000182905,2.5156549453185750124 ] 
dist 167=[-.24016636423720856696,2.6236184330070994042 ] 
dist 168=[-.29100445501422869122,2.6925386601137057078 ] 
dist 169=[-.34450183550245976805,2.7394955969721328982 ] 
dist 170=[-.41008685229178084037,2.7598477281205472549 ] 
dist 171=[-.50914206707179907926,2.7645641360884332380 ] 
dist 172=[-.62188296327173713836,2.7582839645527809670 ] 
dist 173=[-.74206013105746339619,1.9141071957945596725 ] 
dist 174=[-.89045548504042956826,1.9214080009419649227 ] 
dist 175=[-1.1157590633966961763 ,1.9476783818626282313 ] 
dist 176=[-1.3394473539639517776 ,2.1565859872129521298 ] 
dist 177=[-1.4813987429848879370 ,2.2780697662853630203 ] 
dist 178=[-1.5903718298691084947 ,2.3585633596848117375 ] 
dist 179=[-1.6825076173605036669 ,2.4039522534404145372 ] 
dist 180=[-1.7565360283076163821 ,2.4320263133462950637 ] 
dist 181=[-1.7932772125719805357 ,2.4434460975191116013 ] 
dist 182=[-1.8106839900059402742 ,2.4448372092506890831 ] 
dist 183=[-1.8125291440022904470 ,2.4372004225776902873 ] 
dist 184=[-1.7915669273108187686 ,2.0843029963190287908 ] 
dist 185=[-1.8499126596275483658 ,2.0293328680981079333 ] 
dist 186=[-1.8730787393297560269 ,1.9269346773954158257 ] 
dist 187=[-1.8814032701288962285 ,1.8982672330919597551 ] 
dist 188=[-2.1149896319511778187 ,1.7898879081978286710 ] 
dist 189=[-2.4336416802985779773 ,1.8147156573312101954 ] 
dist 190=[-2.6261699243875851561 ,1.9416115516324122727 ] 
dist 191=[-2.7628258152971221566 ,2.0345816305345050636 ] 
dist 192=[-2.8585942572785739414 ,2.1052636019674257541 ] 
dist 193=[-2.9283410291142145374 ,2.1564590610094942567 ] 
dist 194=[-2.9611908670746000096 ,2.1716983249452680974 ] 
dist 195=[-2.9732481625376746610 ,2.1738202268294966434 ] 
dist 196=[-2.9695676142062942918 ,2.1726925875219293608 ] 
dist 197=[-2.6449312029759365404 ,2.0525729624190258926 ] 
dist 198=[-2.5902082805486999473 ,2.0264224670509725290 ] 
dist 199=[-2.4915870544476263921 ,1.9617604406218579601 ] 
dist 200=[-2.4631101638630736074 ,1.9372911133992782217 ] 
dist 201=[-2.3530868772934907813 ,1.8108298373607481176 ] 
dist 202=[-2.3205620682450980154 ,1.7804631800479688951 ] 
dist 203=[-2.2584538800227684687 ,1.7110591951541503243 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 2, 0, 0, 1, 2] 
dist 0=[69.741442823332420370  ,69.741442823332420370  ] 
dist 1=[69.426862742995128745  ,70.069723836968998597  ] 
dist 2=[68.499005558654121786  ,70.363460209072568672  ] 
dist 3=[67.245965322382854808  ,70.393973202792456820  ] 
dist 4=[65.801525791057603020  ,70.252721079210197153  ] 
dist 5=[63.938100912936530498  ,70.137875034422531550  ] 
dist 6=[61.012437272922129358  ,69.471854336829156656  ] 
dist 7=[56.224016372532295327  ,69.344645921889937047  ] 
dist 8=[51.254941581186603530  ,66.825916624513563123  ] 
dist 9=[47.756848076227315411  ,66.227877987735185696  ] 
dist 10=[42.048685972240811966  ,65.513263488737895141  ] 
dist 11=[34.784241453719373754  ,65.186601570730943342  ] 
dist 12=[29.839546501490513522  ,64.704114961023958890  ] 
dist 13=[25.641968189279845510  ,64.384760453719639229  ] 
dist 14=[21.360412320919190937  ,61.911127998478012062  ] 
dist 15=[17.347438966172717518  ,56.005309732849063465  ] 
dist 16=[14.222198653270586717  ,32.336170496190991034  ] 
dist 17=[11.145645536863736884  ,29.776356571040835081  ] 
dist 18=[7.3271054209948760773 ,23.713373218977012802  ] 
dist 19=[3.6925140919736354167 ,22.844832420183247838  ] 
dist 20=[1.3503213849884635421 ,17.685514627592797220  ] 
dist 21=[-.4958734502561110065 ,17.195671530357489473  ] 
dist 22=[-2.1504000860034367688 ,16.551626997799141165  ] 
dist 23=[-3.5571605425270065709 ,16.419352664188799354  ] 
dist 24=[-4.4142963072267485077 ,2.0780339490764812099 ] 
dist 25=[-5.0341418475811609434 ,.91236503675431910637] 
dist 26=[-5.4937427688844985728 ,-1.5756312827267349575 ] 
dist 27=[-5.8551114182091754211 ,-2.0539685344418925190 ] 
dist 28=[-6.2482985393464266681 ,-4.2288437875449445072 ] 
dist 29=[-7.5253445785777974302 ,-4.4187366344287436997 ] 
dist 30=[-8.7277757623607817199 ,-4.4041091826840477686 ] 
dist 31=[-10.151179096218914428  ,-4.3227741505940570891 ] 
dist 32=[-11.482118111387050987  ,-4.1613954535132766576 ] 
dist 33=[-12.315058304177668661  ,-3.9156845732082744043 ] 
dist 34=[-12.947050757912067222  ,-3.4973405338297613242 ] 
dist 35=[-13.474892680441613335  ,-3.0531364822055995199 ] 
dist 36=[-13.898877656359143273  ,-2.7037704254548676403 ] 
dist 37=[-14.115808963086813143  ,-2.3600851607548127215 ] 
dist 38=[-14.223950012854166100  ,-1.9376605274121400416 ] 
dist 39=[-14.227112553681088497  ,-.2054471424437738267 ] 
dist 40=[-8.1849144625340868285 ,1.9085042093061692012 ] 
dist 41=[-8.0374485318557536754 ,3.3153357264474092632 ] 
dist 42=[-7.6515817585203626680 ,4.4710681215826623424 ] 
dist 43=[-7.5711660320969852677 ,5.5834718877631453050 ] 
dist 44=[-6.8914539661539913085 ,6.5808628987863829350 ] 
dist 45=[-6.7510329584838046004 ,7.2778667987112154197 ] 
dist 46=[-6.5407874122971926289 ,7.8875318518974173797 ] 
dist 47=[-6.4760397733439623904 ,8.5366246098852182845 ] 
dist 48=[-4.0169203416016541639 ,9.1100980540786591979 ] 
dist 49=[-3.7398721125072051018 ,9.4181172779702343865 ] 
dist 50=[-3.1201031060146030702 ,9.5907665173519237144 ] 
dist 51=[-2.9806438982074743419 ,9.6245334539406433344 ] 
dist 52=[-2.2099347132364092720 ,9.6024815956042053432 ] 
dist 53=[-2.0660475686065021928 ,9.5553823639952844360 ] 
dist 54=[-1.7703271199085686574 ,9.4810320734956414522 ] 
dist 55=[-1.6904842531095740427 ,9.4336513875654887348 ] 
dist 56=[-1.8339918163049554498 ,7.8255005741050022962 ] 
dist 57=[-3.1420871978835671684 ,7.9667309958682005259 ] 
dist 58=[-4.2223556781932852032 ,8.0320733103801843746 ] 
dist 59=[-5.2698531530188686820 ,8.0376156319655558759 ] 
dist 60=[-6.2126794869122585570 ,7.9571378651476091515 ] 
dist 61=[-6.8755463356408207753 ,7.9140578161790534564 ] 
dist 62=[-7.4586260194947232946 ,7.7983682254065971569 ] 
dist 63=[-8.0833127980673318301 ,7.7429765247568166619 ] 
dist 64=[-8.6372691224697650888 ,1.3160962650834780486 ] 
dist 65=[-8.9382624807136820419 ,1.0873371021885224489 ] 
dist 66=[-9.1110195572980693984 ,.5903860891408700418 ] 
dist 67=[-9.1534805318138015866 ,.4733484000801051568 ] 
dist 68=[-9.1411164588087839666 ,-.0706888356473122975 ] 
dist 69=[-9.0973279685906035453 ,-.1673597005655122237 ] 
dist 70=[-9.0174255358669129787 ,-.3810371563798770490 ] 
dist 71=[-8.9726175634866216529 ,0                     ] 
dist 72=[-5.8473076172848715980 ,.5075070542556692919 ] 
dist 73=[-6.0634045084616971069 ,1.3788867540294451110 ] 
dist 74=[-6.2247894396209229405 ,2.0932718222575220575 ] 
dist 75=[-6.3535203291224260061 ,2.7773202167635499943 ] 
dist 76=[-6.4513100252438584206 ,3.3871979328872958729 ] 
dist 77=[-6.4892367889238055454 ,3.8057878461039157224 ] 
dist 78=[-6.4905820880935097694 ,4.1632875808520255483 ] 
dist 79=[-6.4740205832516599081 ,4.5295426485640949659 ] 
dist 80=[-2.6445116507827742650 ,4.8563408819825605162 ] 
dist 81=[-2.3208719056782107452 ,5.0564808347338014248 ] 
dist 82=[-1.5631714985043420392 ,5.2016727502286236544 ] 
dist 83=[-1.4312400154741224381 ,5.3093160544453670806 ] 
dist 84=[-.42599779957424261713,5.3842843850563337073 ] 
dist 85=[-.24715563890712321682,5.3991561900458670321 ] 
dist 86=[.04746543900842369489,5.3839971150242985619 ] 
dist 87=[.11591062690190994458,5.3608222180229666251 ] 
dist 88=[-.01477125168493615314,2.8404675098357425454 ] 
dist 89=[-.21669128003279694299,3.1852341671129286448 ] 
dist 90=[-.6781346266131144141 ,3.4430238480567552837 ] 
dist 91=[-1.2300127552378245898 ,3.6486260771805865654 ] 
dist 92=[-1.6074087137388637495 ,3.8090954489780220269 ] 
dist 93=[-1.9280592239137220465 ,3.8868695820422131693 ] 
dist 94=[-2.2536522476476397679 ,3.9221891877207284751 ] 
dist 95=[-2.5562314790391902327 ,3.9240975840085177465 ] 
dist 96=[-2.9970694751517945348 ,1.0937018048104109297 ] 
dist 97=[-3.2782963491576179909 ,1.0078372987829645571 ] 
dist 98=[-3.4803843366004951480 ,.83082724449787480514] 
dist 99=[-3.6264566855036449040 ,.78370555613014407329] 
dist 100=[-3.7345117165938273927 ,.60867240831851257377] 
dist 101=[-3.7849844969647376305 ,.5718359372051498285 ] 
dist 102=[-3.8028091440539412006 ,.50688958074679274783] 
dist 103=[-3.7994039471472248540 ,.49179618359894562829] 
dist 104=[-1.7281124234787304672 ,.45556701215618599743] 
dist 105=[-1.6842984197124333274 ,.46191809959898194982] 
dist 106=[-1.6712938125532086110 ,.48842075511637511218] 
dist 107=[-1.3851409545659711241 ,.54928365718156015935] 
dist 108=[-1.6112114892151560285 ,.78253217385304685055] 
dist 109=[-1.8067611855619400656 ,1.0223872002733887996 ] 
dist 110=[-2.0171260048512718126 ,1.2620060960183623072 ] 
dist 111=[-2.3023357102931082240 ,1.4823411783384773828 ] 
dist 112=[-2.5756214047368632738 ,1.6452734027630775862 ] 
dist 113=[-2.7384256687495498372 ,1.7968886347393999440 ] 
dist 114=[-2.8513186955307357472 ,1.9720683961181861244 ] 
dist 115=[-2.9254796207768595140 ,2.1311786530449965138 ] 
dist 116=[-2.9758016086257176423 ,2.2186947015320696058 ] 
dist 117=[-2.9935786154327574159 ,2.2702114135021522842 ] 
dist 118=[-2.9923617272932878779 ,2.2857382644703841244 ] 
dist 119=[-2.9855938188036478798 ,2.2878835119396637952 ] 
dist 120=[-2.6669059972975196531 ,2.2860438178437065022 ] 
dist 121=[-2.6126637321730631423 ,2.2809065571231306425 ] 
dist 122=[-2.5026304084700897743 ,2.2699469866936026916 ] 
dist 123=[-2.4683872212399132014 ,1.7665622770865751485 ] 
dist 124=[-2.3177241035059097290 ,1.6523721656514773448 ] 
dist 125=[-2.2824304176722933628 ,1.6227850780309295320 ] 
dist 126=[-2.1857360762785555105 ,1.6047590993664776002 ] 
dist 127=[-2.1600528328796045877 ,1.5983492992116690252 ] 
dist 128=[-1.8327916665149749093 ,1.2552882471142302014 ] 
dist 129=[-1.9405166626952551361 ,1.4763710866126213998 ] 
dist 130=[-2.0405268828829800988 ,1.8204134792790545203 ] 
dist 131=[-2.1258748548718527177 ,2.1372240481717875774 ] 
dist 132=[-2.1751141544057677299 ,2.4115759547425136232 ] 
dist 133=[-2.2072275817330123035 ,2.5862423440410691925 ] 
dist 134=[-2.2242622035251537247 ,2.7210234563135772350 ] 
dist 135=[-2.2302581714930289116 ,2.8362661548523251220 ] 
dist 136=[-2.2261990301209653545 ,2.9323615774583868540 ] 
dist 137=[-2.2011457285585641253 ,2.9907603040124033169 ] 
dist 138=[-2.1860998070233523465 ,3.0326338446905699124 ] 
dist 139=[-.96624763797292368375,3.0628056758201785659 ] 
dist 140=[-.85490179739971924735,3.0830957754502434005 ] 
dist 141=[-.59980353354476128829,3.0855489832006422838 ] 
dist 142=[-.54959223844809816388,3.0754139992930924936 ] 
dist 143=[-.22521666516513621832,3.0646352812263808831 ] 
dist 144=[-.16727548287902299383,1.0898247794290847831 ] 
dist 145=[-.3290811242439181134 ,1.1798309596669620622 ] 
dist 146=[-.55528172318034397173,1.3784222241820288694 ] 
dist 147=[-.7872305682694586237 ,1.5626072404352322461 ] 
dist 148=[-1.0046002285334001820 ,1.6713383910802422556 ] 
dist 149=[-1.1726410064977113109 ,1.7453820487761878822 ] 
dist 150=[-1.3364206820262500160 ,1.7912036878425128673 ] 
dist 151=[-1.5367916657596983218 ,1.8224250927742946454 ] 
dist 152=[-1.7489389793607936329 ,1.8382308788857834623 ] 
dist 153=[-1.9207515830703504991 ,1.8457369589558452462 ] 
dist 154=[-2.0484446724137225946 ,1.8438530535361090062 ] 
dist 155=[-2.1489715378541488925 ,.08431948797464513137] 
dist 156=[-2.2261517998711955819 ,.04557134951668182230] 
dist 157=[-2.2607100482917286737 ,-.02816354865991531071] 
dist 158=[-2.2749167227175913788 ,.0287805410949278664 ] 
dist 159=[-2.2726471149550800638 ,.3029421899813317955 ] 
dist 160=[-.7773631902266170772 ,.5790952102313922787 ] 
dist 161=[-.8946151030336358793 ,.78739801286063959562] 
dist 162=[-1.0358095359640744585 ,.98875521318767561324] 
dist 163=[-1.1673209295554092135 ,1.1858145017330755347 ] 
dist 164=[-1.2459488476143492223 ,1.3645538699375395525 ] 
dist 165=[-1.3007255737750869303 ,1.4928329888718305158 ] 
dist 166=[-1.3370983306632522421 ,1.6084669556130521440 ] 
dist 167=[-1.3621712444177245223 ,1.7367662469102670598 ] 
dist 168=[-1.3718744415931669121 ,1.8509709596556242892 ] 
dist 169=[-1.3721571177690071010 ,1.9103809363552029210 ] 
dist 170=[-1.3696647906512790421 ,1.9430307777876673932 ] 
dist 171=[-1.2121973172851806456 ,1.9504844318117701897 ] 
dist 172=[-1.1886894546652595335 ,1.9297981751522612470 ] 
dist 173=[-1.1851269983420564034 ,1.9235900232752095524 ] 
dist 174=[-1.1896799205876402003 ,1.9191122506647974331 ] 
dist 175=[-1.1712826195398208922 ,1.9158460632337288791 ] 
dist 176=[-1.1665900670197495331 ,1.5065806063557073342 ] 
dist 177=[-1.1638531261383441140 ,1.5576760730289778653 ] 
dist 178=[-1.1630832721060441867 ,1.5875096517101984692 ] 
dist 179=[-1.2475956399683355975 ,1.5960079782259805948 ] 
dist 180=[-1.4302806897071924810 ,1.5954924551094301629 ] 
dist 181=[-1.5531786966287691099 ,1.5893724696719718153 ] 
dist 182=[-1.6555590355307234070 ,1.5779808430911939063 ] 
dist 183=[-1.7563990369801071696 ,1.5709910623995632969 ] 
dist 184=[-1.8441288825888976121 ,1.3289252128057887415 ] 
dist 185=[-1.8942137119978465232 ,1.2912320715326217415 ] 
dist 186=[-1.9262097064007860377 ,1.2118393869077127702 ] 
dist 187=[-1.9417859232834287639 ,1.1878171967781279712 ] 
dist 188=[-1.9455834530201164315 ,1.0834620826079433273 ] 
dist 189=[-1.9430950737118068294 ,1.0610728546466120375 ] 
dist 190=[-1.9133436429900195298 ,.9987821125136247736 ] 
dist 191=[-1.9081002620221023255 ,.9865941901319351859 ] 
dist 192=[-.80990730288699730666,.89181148515614137984] 
dist 193=[-.88412898037518303811,.96645921785265544132] 
dist 194=[-.93802518583872360968,1.0497696714216986014 ] 
dist 195=[-.97814152996823618567,1.1243992002170896834 ] 
dist 196=[-1.0084031555550946208 ,1.1644186441621277570 ] 
dist 197=[-1.0229858161221657141 ,1.1867986925574150962 ] 
dist 198=[-1.0288553148409554427 ,1.1920073849287850972 ] 
dist 199=[-1.0285771784674304414 ,1.1879155941587041527 ] 
dist 200=[-.9355003044747130072 ,1.1853231992758718202 ] 
dist 201=[-.91881701963344449365,1.1821625864219680800 ] 
dist 202=[-.88937889078096561504,1.1774063861602494960 ] 
dist 203=[-.88062125642490368182,.88968016677577725217] 
dist 204=[-.84619349813159136264,.85428687186097066973] 
dist 205=[-.83562093576483535031,.76681932576711838886] 
dist 206=[-.81463376959377711719,.7490100473817162077 ] 
dist 207=[-.80727806166003686112,.6109516084775862023 ] 
dist 208=[-.84945781007316418441,.5834021041172480102 ] 
dist 209=[-.9115347150519987234 ,.5394542081304930894 ] 
dist 210=[-.97370796529592869485,.5272877918179712950 ] 
dist 211=[-1.0284303809374069157 ,.5938328005869941410 ] 
dist 212=[-1.0607854683718061929 ,.7155742292486049706 ] 
dist 213=[-1.0828880441236133441 ,.80934186940854621914] 
dist 214=[-1.0967116451704987586 ,.90039414158749379181] 
dist 215=[-1.1041203470899983889 ,1.0113047169791426884 ] 
dist 216=[-1.1039099443514449703 ,1.1153052226922034060 ] 
dist 217=[-1.0939328495976830074 ,1.1787928772633910307 ] 
dist 218=[-1.0885289646952872189 ,1.2246431681208805750 ] 
dist 219=[-.17683021092396675456,1.2582864517487595674 ] 
dist 220=[-.22632852148834499811,1.2814367006766157943 ] 
dist 221=[-.2754608911485044812 ,1.2867195404046109445 ] 
dist 222=[-.3367890626655679641 ,1.2833409339896555316 ] 
dist 223=[-.4010969892774150042 ,1.2822288695039772858 ] 
dist 224=[-.55740886240408629658,1.2419274956941570297 ] 
dist 225=[-.72833798917126700061,1.3067118927092414068 ] 
dist 226=[-.87023346745921749239,1.3809846402666117667 ] 
dist 227=[-1.0091873841180626282 ,1.4482735125203565682 ] 
dist 228=[-1.1352623150953860103 ,1.4851996044827176094 ] 
dist 229=[-1.2257833298786261670 ,1.5068781156997448992 ] 
dist 230=[-1.3074068788444005744 ,1.5133452399692228092 ] 
dist 231=[-1.3979893249446951238 ,1.5112523846345028636 ] 
dist 232=[-1.4784573198016363397 ,1.5066060558223995364 ] 
dist 233=[-1.5197342126681743182 ,1.4843151618581775326 ] 
dist 234=[-1.5414819121819825622 ,1.4742275010437560387 ] 
dist 235=[-1.5449935540922412059 ,1.3442242554522565245 ] 
dist 236=[-1.5272434371720623896 ,1.4865901189801157120 ] 
dist 237=[-1.6461982197755632871 ,1.5905456749054332031 ] 
dist 238=[-1.8237235016907874259 ,1.6689302981517902733 ] 
dist 239=[-1.9753085175614990102 ,1.7292225369855448807 ] 
dist 240=[-2.0678596373775860794 ,1.7610098270670519494 ] 
dist 241=[-2.1346949256494927033 ,1.7779343919605136847 ] 
dist 242=[-2.1837019982058654135 ,1.7789423019767205641 ] 
dist 243=[-2.2191386463506630461 ,1.6027341114214491358 ] 
dist 244=[-2.2318426976766294449 ,1.5722455789412303231 ] 
dist 245=[-2.2303019429762432822 ,1.5271801547849819322 ] 
dist 246=[-2.2255560912782216371 ,1.5109684290635856320 ] 
dist 247=[-2.1788347523747029230 ,1.4687703689889029009 ] 
dist 248=[-2.1631800249899549372 ,1.4183674828890631466 ] 
dist 249=[-2.1096221971243528913 ,1.4033019315392108879 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 0, 1, 0, 2] 
dist 0=[67.783334791829745083  ,67.783334791829745083  ] 
dist 1=[67.309009127377085655  ,68.040817612528788833  ] 
dist 2=[66.414180733112893301  ,68.069967994816857009  ] 
dist 3=[65.219610338668618203  ,67.962204017026184390  ] 
dist 4=[63.548527827523114187  ,67.840545057118116255  ] 
dist 5=[61.206098065004900752  ,67.351297750974968373  ] 
dist 6=[57.330979630749964120  ,67.112800245598427280  ] 
dist 7=[53.324019408367816023  ,63.851586788898979454  ] 
dist 8=[50.455085101606375344  ,63.190996178593069790  ] 
dist 9=[47.866279478090198992  ,62.270784987234072192  ] 
dist 10=[44.977549670579570670  ,61.933599664312025078  ] 
dist 11=[42.111256958697256108  ,61.263814809947484831  ] 
dist 12=[39.594022359317343936  ,61.055973470633658608  ] 
dist 13=[32.701995404742442067  ,60.975726616949945378  ] 
dist 14=[28.025560771127400158  ,59.914910374764010294  ] 
dist 15=[24.069749887920253576  ,30.864407680410200401  ] 
dist 16=[20.055160976714839737  ,28.541199406621551955  ] 
dist 17=[16.303356429324009006  ,25.983969318342711577  ] 
dist 18=[13.396864600897070798  ,25.331483595794881138  ] 
dist 19=[10.549024117605615041  ,23.046981843441121036  ] 
dist 20=[7.0314966241927276143 ,22.558931622940915724  ] 
dist 21=[3.6898976733551430621 ,21.938331331992007010  ] 
dist 22=[1.5444990597983292516 ,21.782187860888306234  ] 
dist 23=[-.13811661937223943581,4.9265277011501685556 ] 
dist 24=[-1.6320217213234425106 ,3.5499510840077503146 ] 
dist 25=[-2.8924293005496138236 ,.54310510427892492022] 
dist 26=[-4.0739979241334389753 ,-.00572444752968516216] 
dist 27=[-5.4842852035307816166 ,-3.2437182684374159214 ] 
dist 28=[-7.0534510006919107943 ,-3.3542300808995361326 ] 
dist 29=[-8.5406682175442505347 ,-4.6800313985181673981 ] 
dist 30=[-10.312972435824710859  ,-4.9373578653341518665 ] 
dist 31=[-11.972667786528198495  ,-6.5276566192974580527 ] 
dist 32=[-13.010005591528881537  ,-6.6642512527294130950 ] 
dist 33=[-13.794242798267187924  ,-6.6033053443041771658 ] 
dist 34=[-14.442731802740860867  ,-6.2664461755748420201 ] 
dist 35=[-14.957641021786842619  ,-5.6746644232947553665 ] 
dist 36=[-15.208210259416768711  ,-4.8685402679058395790 ] 
dist 37=[-15.319663777819201781  ,-3.7542530748401255001 ] 
dist 38=[-15.328484413162887764  ,-1.9325111351507537309 ] 
dist 39=[-7.9882107094879318034 ,-.06511968437328705562] 
dist 40=[-7.8426491389666564865 ,1.2968244507063908811 ] 
dist 41=[-7.4854367615134680552 ,2.4201186726705546578 ] 
dist 42=[-7.3880068243375668240 ,3.5084484453652490209 ] 
dist 43=[-6.8127531474259819173 ,4.4888979108397837792 ] 
dist 44=[-6.6914569331900482227 ,5.1819505701486861481 ] 
dist 45=[-6.4518483276244389615 ,5.7963986240546662195 ] 
dist 46=[-6.3829647866528814688 ,6.4634266976426199008 ] 
dist 47=[-3.4585208053553892352 ,7.0658555446818090571 ] 
dist 48=[-3.1520741842224690324 ,7.4226153266673657678 ] 
dist 49=[-2.4726411438864648551 ,7.6677187219585674822 ] 
dist 50=[-2.3227348246186319726 ,7.8246185358585331361 ] 
dist 51=[-1.7608470315899256850 ,7.9189632848455032330 ] 
dist 52=[-1.6962348506649514356 ,7.9310952054727828039 ] 
dist 53=[-1.0537912073005655078 ,7.8786042013010173489 ] 
dist 54=[-.97050614169379389482,7.8477781866635924693 ] 
dist 55=[-.62622251829331108851,7.2795291766893778629 ] 
dist 56=[-.56379219613715029533,7.4631569652598474006 ] 
dist 57=[-.7834505698368138832 ,7.5592383947005000412 ] 
dist 58=[-1.5429499186332931500 ,7.5764813853206402559 ] 
dist 59=[-2.2404836976488512734 ,7.5291746367305219992 ] 
dist 60=[-2.7549029275814431460 ,7.4896940833447070600 ] 
dist 61=[-3.2323708746343498026 ,7.4183133875495979964 ] 
dist 62=[-3.7825793697554400156 ,7.3839427620821825128 ] 
dist 63=[-4.2901709264572325257 ,.15732007352028811913] 
dist 64=[-4.5976801148956334786 ,-.05216183065038829252] 
dist 65=[-4.8168289613722746032 ,-.53968096642499842687] 
dist 66=[-4.9719974249569521150 ,-.61000266675346215651] 
dist 67=[-5.0802143476702562962 ,-1.2260641167491443903 ] 
dist 68=[-5.1120910894347992589 ,-1.3284300989251551723 ] 
dist 69=[-5.1107779860403495102 ,-1.4695211260987762047 ] 
dist 70=[-5.2281737666524131671 ,-1.0742361529176944035 ] 
dist 71=[-5.5704780858584201599 ,-.66311603793086735353] 
dist 72=[-5.7782014553311741457 ,-.37828084824967242888] 
dist 73=[-5.9269402927696875260 ,-.03662270143429231588] 
dist 74=[-6.0338983098495557833 ,.41034105248754100679] 
dist 75=[-6.1057536623556677975 ,.82468651733790290815] 
dist 76=[-6.1144367968480047258 ,1.1365108509409213084 ] 
dist 77=[-6.0935281095523547499 ,1.4320472559682033626 ] 
dist 78=[-6.0651096048410525407 ,1.7814724437068896061 ] 
dist 79=[-2.8463110197550541102 ,2.1072396188130845913 ] 
dist 80=[-2.5602166810023546337 ,2.3084324982577441345 ] 
dist 81=[-1.8872078835871380085 ,2.4563784214359656458 ] 
dist 82=[-1.7672809857939023208 ,2.5697745915087331120 ] 
dist 83=[-.85797202218534961464,2.6542900625164617163 ] 
dist 84=[-.69375840919547213043,2.6870608735548469436 ] 
dist 85=[-.42229267084752899167,2.9507990572469976555 ] 
dist 86=[-.35819375048691283433,3.2087546431636807190 ] 
dist 87=[-.19567814103870724756,3.3897533848080895175 ] 
dist 88=[-.3672670172872769369 ,3.5123504140017835653 ] 
dist 89=[-.50792247274176776622,3.6131881139926477510 ] 
dist 90=[-.64222042950436490627,3.7586067450447589659 ] 
dist 91=[-.76135584646951862339,3.8664748313301833238 ] 
dist 92=[-.84154852868511444479,3.9239943182860286046 ] 
dist 93=[-.90812162546787554588,3.9555150436840440890 ] 
dist 94=[-.97292936290696743483,3.9596599208027261019 ] 
dist 95=[-1.0298804897099815042 ,.96848471308903778007] 
dist 96=[-1.0651361180714724813 ,.91352452494392997781] 
dist 97=[-1.0909849073776101861 ,.82511023633205395547] 
dist 98=[-1.1466382760980586123 ,.80169851487058626381] 
dist 99=[-1.2103048510909512312 ,.75833471549523661692] 
dist 100=[-1.4187642569902410436 ,.75975178309565735012] 
dist 101=[-1.6699852657691384065 ,.78143630298390661948] 
dist 102=[-1.8240301304274163836 ,.83650474929644965984] 
dist 103=[-1.9360612706621305840 ,.90263290707497277837] 
dist 104=[-2.0197127319079760940 ,.96841980021348823875] 
dist 105=[-2.0823550398399353325 ,1.0464376625796821600 ] 
dist 106=[-2.1105794206228462855 ,1.1613290290400885739 ] 
dist 107=[-2.1201475081137362109 ,1.2907831939037510902 ] 
dist 108=[-2.1184924806807003625 ,1.4268718424573132186 ] 
dist 109=[-2.3140920318089069386 ,1.5935180637790562678 ] 
dist 110=[-2.6272428630411979181 ,1.8448328594427341977 ] 
dist 111=[-3.0102021939950189326 ,2.0930430503892240006 ] 
dist 112=[-3.2406206281781595232 ,2.2473001148346963206 ] 
dist 113=[-3.4031241055666948833 ,2.3618318269772126684 ] 
dist 114=[-3.5151413974149675299 ,2.4515966808693625293 ] 
dist 115=[-3.5958636729544113833 ,2.5182082379783333117 ] 
dist 116=[-3.6335085010182440379 ,2.5403881515528815284 ] 
dist 117=[-3.6467870476176045304 ,2.5458229850562954574 ] 
dist 118=[-3.6416122256883100670 ,2.5456701670505943135 ] 
dist 119=[-3.2338887027386278607 ,2.6749878343811303220 ] 
dist 120=[-3.1659861277387104662 ,3.1030265978723030116 ] 
dist 121=[-3.0423871705138574027 ,3.4357710998893359368 ] 
dist 122=[-3.0067508305760076845 ,3.7245092804720712320 ] 
dist 123=[-2.8687136835189419274 ,3.9621865739449860827 ] 
dist 124=[-2.8287266608994752799 ,4.0912548615466976235 ] 
dist 125=[-2.7516326237351896362 ,4.1652651321992816455 ] 
dist 126=[-2.7259462586090272422 ,4.1833272896739264068 ] 
dist 127=[-2.0074849006069771493 ,4.1780487467607129935 ] 
dist 128=[-1.9504313494815419035 ,4.1593234568953146734 ] 
dist 129=[-1.7940103207227129407 ,4.1261663727352914213 ] 
dist 130=[-1.7693721768593790794 ,4.1075773114166359752 ] 
dist 131=[-1.7310476538424975073 ,3.9937192658719363004 ] 
dist 132=[-1.7162732158471135969 ,3.9613633069160843291 ] 
dist 133=[-1.6914645258024521168 ,3.8398858939388500912 ] 
dist 134=[-1.6810288694109195245 ,3.8180057443698798114 ] 
dist 135=[.16748879708183489397,2.3177538417752157146 ] 
dist 136=[-.08448114173191831618,2.3487942666537870604 ] 
dist 137=[-.29421734265642824718,2.3658183370827561199 ] 
dist 138=[-.50050882109115105191,2.3658572425719828097 ] 
dist 139=[-.68825959551042169541,2.3450995060373509285 ] 
dist 140=[-.82404201197663819451,2.3341509304450719976 ] 
dist 141=[-.94747886326236981791,1.1917196216887676679 ] 
dist 142=[-1.0859894414949993506 ,1.0864287238403657243 ] 
dist 143=[-1.2134729002758210440 ,.83606809254216329818] 
dist 144=[-1.2929238245097211611 ,.79228450091624429541] 
dist 145=[-1.3522503511879815206 ,.4438475678525277666 ] 
dist 146=[-1.3994550316935554259 ,.38006159034224244828] 
dist 147=[-1.4351422318970421617 ,.28037101790843552031] 
dist 148=[-1.4485239525840971565 ,.25482882752817483692] 
dist 149=[-1.4514435995728409603 ,-.183181773442690942  ] 
dist 150=[-1.4474750763269192983 ,-.23931392531461867962] 
dist 151=[-1.4901911778378163013 ,-.35607083177429861632] 
dist 152=[-1.5453376457679468349 ,-.38239717447920516025] 
dist 153=[-1.5858395083298050415 ,-.28851136204664181624] 
dist 154=[-1.6031761020665571722 ,-.16295619583111987115] 
dist 155=[-1.6078918131447007760 ,-.04260136906379312945] 
dist 156=[-1.6058028820455389829 ,.05480880138857702072] 
dist 157=[-.49330959036333188432,.15385095021343819102] 
dist 158=[-.48994250128026513419,.28071976233836410469] 
dist 159=[-.49326835885816486849,.40276338709108080296] 
dist 160=[-.506608460658837863  ,.48256090805654007977] 
dist 161=[-.52534315897452836741,.54653084777459930678] 
dist 162=[-.55018657005111696922,.6054432034895907464 ] 
dist 163=[-.58421734430487172598,.65646398460798694542] 
dist 164=[-.6395991369777564842 ,.68895857111901906589] 
dist 165=[-.69851729644765958615,.71405969810579084276] 
dist 166=[-.74665355337242332533,.73559521821803626086] 
dist 167=[-.79601207475631590522,.75313282913674620207] 
dist 168=[-.8598039409814247951 ,.80104808320101360456] 
dist 169=[-.9278241427848998431 ,.8518440713721846185 ] 
dist 170=[-.99404798078442937028,.96555212240359322862] 
dist 171=[-1.0714949747777318941 ,1.1481354157830345648 ] 
dist 172=[-1.1842817794946304970 ,1.4104166999596987769 ] 
dist 173=[-1.2943104070895375711 ,1.6664678422723039046 ] 
dist 174=[-1.3607546123379424491 ,1.8241987968521388046 ] 
dist 175=[-1.4078504039551302214 ,1.9398226983686620393 ] 
dist 176=[-1.4406995359174514079 ,2.0279019695199148419 ] 
dist 177=[-1.4621311375689847615 ,2.0949263101274535406 ] 
dist 178=[-1.4663915837875485032 ,2.1265575299328851485 ] 
dist 179=[-1.4592584195261805574 ,2.1387999331782087672 ] 
dist 180=[-1.4568519000665351565 ,2.1386483456282478252 ] 
dist 181=[-1.3608948954194914898 ,1.9707665437017053415 ] 
dist 182=[-1.3415400231089441428 ,1.9389936633608550974 ] 
dist 183=[-1.2956833284065099634 ,1.8817471053467052764 ] 
dist 184=[-1.4999408348991693796 ,1.8640454830123719740 ] 
dist 185=[-1.6594962517931219439 ,1.7901263469344094469 ] 
dist 186=[-1.7993408073182836313 ,1.7684980361134895614 ] 
dist 187=[-1.9155029495854170158 ,1.7192931259972485097 ] 
dist 188=[-1.9805848712518657084 ,1.7009648987837284703 ] 
dist 189=[-2.0205996642126917169 ,1.0139016294884702062 ] 
dist 190=[-2.0367652334532669820 ,1.0076547225799163114 ] 
dist 191=[-2.0415953628918464238 ,.90853242153305651836] 
dist 192=[-2.0363906407174308540 ,.88947350727959314775] 
dist 193=[-2.0235406674867400005 ,.84246745953961461619] 
dist 194=[-2.0151353785159072440 ,.82818850099545879717] 
dist 195=[-1.9594990556864682775 ,.74795282433882478011] 
dist 196=[-1.9437865977118663134 ,.73012250233885221871] 
dist 197=[-1.8860333201745261340 ,.69461880403416802667] 
dist 198=[-1.8747762684069119486 ,.68396188936324598919] 
dist 199=[-.84627384615506123476,.67235110047281587664] 
dist 200=[-.83713526751435058216,.90283409668443475809] 
dist 201=[-.79792864812506365401,1.0885415938595450406 ] 
dist 202=[-.78749266777819332187,1.2611680982753675916 ] 
dist 203=[-.76163905975676973   ,1.4117547182176728742 ] 
dist 204=[-.75195256128737274898,1.5095436714689243571 ] 
dist 205=[-.11845660941669319998,1.5871908071096676494 ] 
dist 206=[-.06116092024731575781,1.6574304896474908808 ] 
dist 207=[.05672690709663778228,1.7162999373588543841 ] 
dist 208=[.08654967726288649818,1.7485903848991174721 ] 
dist 209=[.19003253410367121401,1.7675318448330787222 ] 
dist 210=[.210912044181673409  ,1.7731509936807931465 ] 
dist 211=[.23248739822520857113,1.7697650476100143531 ] 
dist 212=[.23048440902148744076,1.7648417979374862473 ] 
dist 213=[.21904174833578146874,1.7347298777728435151 ] 
dist 214=[.19540987614850892521,1.7270600357238040780 ] 
dist 215=[.00763233053099020434,1.2190831604659540235 ] 
dist 216=[-.22871347103027437355,1.2434651357249808920 ] 
dist 217=[-.42772646357044322822,1.2585638984984301073 ] 
dist 218=[-.62725919757864394243,1.2603771761852939943 ] 
dist 219=[-.81136588502927330752,1.2551945789168237316 ] 
dist 220=[-.94884344372989624956,1.2488075427806158270 ] 
dist 221=[-1.0782175891056730002 ,.10416310996604670266] 
dist 222=[-1.2299992997499849881 ,.08317088770813574159] 
dist 223=[-1.3696524317942153225 ,-.14805991366820921406] 
dist 224=[-1.4506447895423635152 ,-.18239831573540655258] 
dist 225=[-1.5040160117597558679 ,-.23231745001596058566] 
dist 226=[-1.5334862866962091808 ,-.24501192884323753531] 
dist 227=[-1.5518503685328266659 ,-.24428285386757323462] 
dist 228=[-1.5609183290549335963 ,-.22275356188787816643] 
dist 229=[-1.5648950709128459290 ,-.18190659104836587254] 
dist 230=[-1.5629504976227821688 ,-.1041177904597292455 ] 
dist 231=[-1.0029673910271556950 ,-.02121017093312484088] 
dist 232=[-1.0006438280908679681 ,.04005595243796960242] 
dist 233=[-.98389995213222883598,.09708085261631113480] 
dist 234=[-.97807009842014577007,.16306926757637166304] 
dist 235=[-.95298881317659931758,.22960588641212953638] 
dist 236=[-.94850790556977269285,.28881710422996320933] 
dist 237=[-.41512619077319981051,.35388174442128145419] 
dist 238=[-.36383421663742943461,.44376725439957645276] 
dist 239=[-.25081264148862729099,.53336944591037065245] 
dist 240=[-.22484879090348334824,.5973035510825630691 ] 
dist 241=[-.09429756139175136657,.66058977192361942551] 
dist 242=[-.04907555107761894603,.74429550895746556868] 
dist 243=[.04828106571018532762,.82225824748855305364] 
dist 244=[.12050519375188492894,.9125496914811772656 ] 
dist 245=[.44374874076711712733,.99485614250938875616] 
dist 246=[.53623498188781295135,1.0409667587271778903 ] 
dist 247=[.59748021611660093828,1.0693036762237593262 ] 
dist 248=[.52629989398157303327,1.0807103711460481108 ] 
dist 249=[.43900234989841246118,1.0854474712335085147 ] 
dist 250=[.33736899735481846907,1.0871786425172554911 ] 
dist 251=[.20598258450211094283,1.0810318173244054963 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 2, 0, 2] 
dist 0=[67.769707949564500490  ,67.769707949564500490  ] 
dist 1=[66.747521957587582650  ,68.507153293082100822  ] 
dist 2=[65.228473921343955863  ,68.889516989200160410  ] 
dist 3=[63.053638314587477698  ,69.084815982160877622  ] 
dist 4=[59.413300727441743526  ,69.075730818914051811  ] 
dist 5=[55.634309184004890206  ,68.955742072589163173  ] 
dist 6=[52.905778494646989654  ,68.801905722459738210  ] 
dist 7=[50.421670428625433313  ,67.835543169956994748  ] 
dist 8=[47.618099017412574211  ,65.646032574309894303  ] 
dist 9=[44.819390742333798020  ,63.895014236314420271  ] 
dist 10=[42.354336321439679163  ,63.117523599199476516  ] 
dist 11=[39.657461009772316414  ,61.980413163004784894  ] 
dist 12=[35.932576850985413117  ,61.597644427388655794  ] 
dist 13=[30.979339689429921602  ,60.789308693328226632  ] 
dist 14=[26.042589621537085004  ,60.556886985685321486  ] 
dist 15=[21.856650887570430809  ,58.671514268283097940  ] 
dist 16=[17.593141710483761300  ,55.122990821601975734  ] 
dist 17=[13.599651470944407253  ,28.208396078769486841  ] 
dist 18=[10.491937138385853397  ,25.650629546737866323  ] 
dist 19=[7.4342257635635315868 ,24.483952525036066719  ] 
dist 20=[3.6405521707739703621 ,24.370552540697498312  ] 
dist 21=[.0295957643497810751 ,10.911927890925056745  ] 
dist 22=[-2.2985670080617630844 ,9.5421205998737894749 ] 
dist 23=[-4.1351712963303212791 ,7.6852316303470927873 ] 
dist 24=[-5.7836061122851646217 ,7.2867265852529487847 ] 
dist 25=[-7.1865948543159119369 ,-1.5026656138247552707 ] 
dist 26=[-8.0432617078953301221 ,-2.5362194796372520501 ] 
dist 27=[-8.6643678160347746012 ,-3.9784789340330847669 ] 
dist 28=[-9.1268653846525707149 ,-4.2224147688420731260 ] 
dist 29=[-10.552273446348068354  ,-5.5380065616308751999 ] 
dist 30=[-11.662627176550776938  ,-5.5383355358199131986 ] 
dist 31=[-12.511962103851265417  ,-5.4436532656640104000 ] 
dist 32=[-13.231889488171510496  ,-5.2045392322794972336 ] 
dist 33=[-13.816916696142786418  ,-4.8990448416038165202 ] 
dist 34=[-14.127290438937519678  ,-4.5300468833088714416 ] 
dist 35=[-14.297177287567129256  ,-3.4228441200853977613 ] 
dist 36=[-14.320933998628973659  ,-1.6070242051446118537 ] 
dist 37=[-5.8754042237724543763 ,.2418871530079714870 ] 
dist 38=[-5.7115264458607235368 ,1.4813957912903670867 ] 
dist 39=[-5.5351568185267562500 ,2.5084028948298621440 ] 
dist 40=[-5.4804590816707272112 ,3.5100180529025848268 ] 
dist 41=[-4.1063103108378495859 ,4.4157709118906565467 ] 
dist 42=[-4.0486516211620930164 ,5.0605688497533754844 ] 
dist 43=[-3.9018821311036019106 ,5.6364695665435414594 ] 
dist 44=[-3.8669049511579953077 ,6.2675837466228211564 ] 
dist 45=[-3.4656098715982572279 ,6.8351473108013659329 ] 
dist 46=[-3.3951249845665512444 ,7.1575969457112043849 ] 
dist 47=[-3.2342348747907659772 ,7.3620415804954581881 ] 
dist 48=[-3.1819253687153106768 ,7.4588527447232397657 ] 
dist 49=[-2.9371634858776362116 ,7.5013139290526708212 ] 
dist 50=[-2.8813727862596710230 ,7.4889208418389754943 ] 
dist 51=[-2.7610332335263817793 ,7.4424914271101265860 ] 
dist 52=[-2.7218383146953779231 ,7.4062474907114650837 ] 
dist 53=[-2.1821975404543147513 ,5.5820340209440121693 ] 
dist 54=[-2.0986928850216348050 ,5.5548868008372689546 ] 
dist 55=[-2.5704311109551034885 ,5.5106573317183799407 ] 
dist 56=[-3.3717032460893766547 ,5.4853556862798833944 ] 
dist 57=[-4.0997759540045507998 ,5.3501602338056804561 ] 
dist 58=[-4.6227412733673113271 ,5.3088668689390501212 ] 
dist 59=[-5.0940014829577390290 ,5.1714778844679653507 ] 
dist 60=[-5.6159360370152268160 ,5.1328629823793007045 ] 
dist 61=[-6.0849593872949875737 ,3.4682964706545803892 ] 
dist 62=[-6.3452283908870290960 ,3.4642870955794136627 ] 
dist 63=[-6.5017291719507137033 ,3.4366349792442574558 ] 
dist 64=[-6.5569194287302650620 ,3.4174902743366717728 ] 
dist 65=[-6.5688289590175204787 ,-.3181181263508876940 ] 
dist 66=[-6.5527252699383652570 ,-.3926721566804517193 ] 
dist 67=[-6.5131339357895702359 ,-.5432990497324749359 ] 
dist 68=[-6.4818781555569572082 ,0                     ] 
dist 69=[-4.4295397206771806829 ,.3190367501991530196 ] 
dist 70=[-4.5878950017138928136 ,.96866074993369543471] 
dist 71=[-4.7056337314400437355 ,1.5047580866197037991 ] 
dist 72=[-4.7985847150351114218 ,2.0237353236312294947 ] 
dist 73=[-4.8684139737022230467 ,2.4900528972530463886 ] 
dist 74=[-4.8938965252737066871 ,2.8161564190456822990 ] 
dist 75=[-4.8917819008538698389 ,3.1010239080511476968 ] 
dist 76=[-4.8789439198625630064 ,3.4029069420491073189 ] 
dist 77=[-3.0290268411386040137 ,3.6740342438040296609 ] 
dist 78=[-3.0227056284784882827 ,3.8362503718986624641 ] 
dist 79=[-3.0080703351373129427 ,3.9492887168264243102 ] 
dist 80=[-2.9940252604908672124 ,4.0242877535116332731 ] 
dist 81=[-.74404914805829792531,4.0688351978007759640 ] 
dist 82=[-.55409890144266515876,4.0743725021940528283 ] 
dist 83=[-.13976715954944298808,4.0378268407708056887 ] 
dist 84=[-.04948065292548076931,4.0257825002320662761 ] 
dist 85=[.39006903815139982381,2.2592813522323892892 ] 
dist 86=[-.11065874994030569296,2.5210952646248473713 ] 
dist 87=[-.53630814164859676831,2.7162326415374509581 ] 
dist 88=[-.96893162740650762595,2.8707175279117819519 ] 
dist 89=[-1.3712908308707690843 ,2.9906474332177084816 ] 
dist 90=[-1.6762468133859689462 ,3.0479601042098794347 ] 
dist 91=[-1.9673025735563167370 ,3.0731842317768183004 ] 
dist 92=[-2.3142246337782607521 ,3.0736962815884675010 ] 
dist 93=[-2.6352420615480087158 ,2.9597708308903725610 ] 
dist 94=[-2.8229924179281347407 ,3.0004494284680973228 ] 
dist 95=[-2.9484909603073150484 ,3.0146725759849632189 ] 
dist 96=[-3.0212579635935638280 ,3.0090071405085924149 ] 
dist 97=[-3.0688221634232939161 ,.3242087718326657409 ] 
dist 98=[-3.0938144450484970945 ,.29445447026886551757] 
dist 99=[-3.1069712159444859692 ,.24119135602960334821] 
dist 100=[-3.1073330459991104109 ,.22917678685352666162] 
dist 101=[-1.5752106189348275086 ,.20107584444743300021] 
dist 102=[-1.6980295977174055232 ,.207590493398977995  ] 
dist 103=[-1.8001149270015934645 ,.23090765317557901562] 
dist 104=[-1.9002725349545792970 ,.28319152000977291679] 
dist 105=[-1.9859414008447854804 ,.34991501247580962668] 
dist 106=[-2.0302378171617455386 ,.43081552265856969777] 
dist 107=[-2.0526300492326570828 ,.53735872647073087185] 
dist 108=[-2.0548442364444768004 ,.70634385314811912595] 
dist 109=[-2.0385449009738842055 ,.87645042837392253429] 
dist 110=[-2.0273297688480449602 ,.98746338769797562878] 
dist 111=[-2.0565143213942144669 ,1.0761180150085463130 ] 
dist 112=[-2.0942894389541208314 ,1.1955750848098706215 ] 
dist 113=[-2.1169856598404244604 ,1.3476523679852278533 ] 
dist 114=[-2.1233515623206978409 ,1.4822222338268541597 ] 
dist 115=[-2.1190066758687732708 ,1.6294651404898158777 ] 
dist 116=[-2.1129320065301684990 ,1.8321129236244786168 ] 
dist 117=[-1.8386819071240324688 ,2.0252218056265400002 ] 
dist 118=[-1.7946759413426368848 ,2.1344206628390507190 ] 
dist 119=[-1.7064834879827092255 ,2.2028862470745951763 ] 
dist 120=[-1.6801086442733778356 ,2.2335118601621747630 ] 
dist 121=[-1.5690687330932809862 ,2.2489930233991594656 ] 
dist 122=[-1.5427593011015440660 ,2.2570448118624397985 ] 
dist 123=[-1.4772402977830786511 ,2.2612147787940664776 ] 
dist 124=[-1.4551428633210657529 ,2.2612020470347640913 ] 
dist 125=[.74278257709820244505,1.8248271739286655715 ] 
dist 126=[.75373663987231265485,1.7622170133399866583 ] 
dist 127=[.46794381589897290065,1.5638723532444916189 ] 
dist 128=[.02131966552247439383,1.5082427356369255524 ] 
dist 129=[-.42826163753226658367,1.7022834624544578897 ] 
dist 130=[-.72584851512767593865,1.8272143030120843603 ] 
dist 131=[-.96839596708086497933,1.9252220679781397563 ] 
dist 132=[-1.1984419048492351414 ,2.0118614589277581482 ] 
dist 133=[-1.4021956650070232999 ,2.0847331416822106782 ] 
dist 134=[-1.5398720228939809416 ,2.1278186578453592995 ] 
dist 135=[-1.6551959863662444437 ,2.1572654462854864502 ] 
dist 136=[-1.7697938732981706037 ,2.1757290276439908075 ] 
dist 137=[-1.8705454243890395828 ,2.1856916234494158565 ] 
dist 138=[-1.9306401447615897333 ,2.1816157546644141244 ] 
dist 139=[-1.9723269946359542713 ,2.1686209045224165944 ] 
dist 140=[-1.9996528863200563552 ,2.1583170143019277119 ] 
dist 141=[-2.0155818909814912249 ,.86010704837364429649] 
dist 142=[-2.0152792663466880544 ,.74660402683824922218] 
dist 143=[-2.0007813883491047480 ,.48484726117944944504] 
dist 144=[-1.9880704388096995885 ,.43643335400890938529] 
dist 145=[-.93213388490045145663,.1002825325415056790 ] 
dist 146=[-.83622689652592069636,.0407054130867506362 ] 
dist 147=[-.94502686616635269925,.1753447451345598618 ] 
dist 148=[-1.1433481859888911915 ,.3871369864387543477 ] 
dist 149=[-1.3290117623598013734 ,.58431991681966010923] 
dist 150=[-1.4418526873257673932 ,.73440550114244149004] 
dist 151=[-1.5227538090496798672 ,.87838057864768321888] 
dist 152=[-1.5810049859736658034 ,1.0511893069979511633 ] 
dist 153=[-1.6241903173210820731 ,1.2119501421825725377 ] 
dist 154=[-1.6449897727284374499 ,1.3078699028626267070 ] 
dist 155=[-1.6533383459511282793 ,1.3744362287090923670 ] 
dist 156=[-1.6519370986987356818 ,1.4181165775593110932 ] 
dist 157=[-.25015102167092392856,1.4492279011719338636 ] 
dist 158=[-.21192877047636601151,1.4656599290666542407 ] 
dist 159=[-.13747165067723437084,1.4744457316645910789 ] 
dist 160=[-.1191621568375896993 ,1.4750563310584698478 ] 
dist 161=[-.0603252176081334773 ,1.0561955593854233226 ] 
dist 162=[-.0463419747453695718 ,1.1425086906068761001 ] 
dist 163=[-.0602853664362106154 ,1.2189382977393849104 ] 
dist 164=[-.1867992292126065032 ,1.3016586444112413621 ] 
dist 165=[-.3054446000967944035 ,1.3743064502240585531 ] 
dist 166=[-.3971930747615394137 ,1.4105561636765699019 ] 
dist 167=[-.4865987046440286849 ,1.4295207953478217703 ] 
dist 168=[-.5959002833654972974 ,1.4332147060971355932 ] 
dist 169=[-.6985243015662750881 ,1.4084219593515315177 ] 
dist 170=[-.7612955067605178164 ,1.4007370353946097146 ] 
dist 171=[-.8067551007121023651 ,1.3950008646138903264 ] 
dist 172=[-.8403282417748707129 ,1.3904468822210128971 ] 
dist 173=[-.8653961345049868459 ,1.2165729451065480248 ] 
dist 174=[-.8769297891433531104 ,1.2742360949704691408 ] 
dist 175=[-.8844496827621764194 ,1.3113007994732810966 ] 
dist 176=[-1.0112530527219102897 ,1.3298099045608780454 ] 
dist 177=[-1.1440086989065380577 ,1.3393920249352923726 ] 
dist 178=[-1.2383595169592119127 ,1.3408492636862147695 ] 
dist 179=[-1.3173597639211294508 ,1.3366252270711716367 ] 
dist 180=[-1.3958291431689105786 ,1.3318959188324006748 ] 
dist 181=[-1.4639245575626546197 ,1.1389871475613641939 ] 
dist 182=[-1.5015437864897175461 ,1.1085948220185820670 ] 
dist 183=[-1.5239646285632980726 ,1.0478846195917731940 ] 
dist 184=[-1.5314357401446655330 ,1.0299597938692653139 ] 
dist 185=[-1.5301169056561484502 ,.9555455807306488265 ] 
dist 186=[-1.5259143216323359180 ,.9378960249326881118 ] 
dist 187=[-1.5029334901845741128 ,.90763859930140382321] 
dist 188=[-1.4940411205568475052 ,.89837078667690840035] 
dist 189=[-.9770638943250062753 ,.84966067777686499279] 
dist 190=[-.96125826369361118249,.83780771680086519939] 
dist 191=[-.93182563542279273503,.80581897090100710659] 
dist 192=[-.92252969996383885757,.7955991984269212553 ] 
dist 193=[-.63388480579177206766,.51140080980816765562] 
dist 194=[-.63235488991026469118,.52718739183937623702] 
dist 195=[-.6312822903055920045 ,.67821726985881541503] 
dist 196=[-.63056229960589685379,.82281748512786688635] 
dist 197=[-.49566216707371745029,.95185357872491537969] 
dist 198=[-.47678728456536835187,1.0407981263475499147 ] 
dist 199=[-.44219915209917589436,1.1172251797634653974 ] 
dist 200=[-.43323642259545220942,1.1963288735545342913 ] 
dist 201=[-.40313706720261193174,1.2661367476788288934 ] 
dist 202=[-.39444239661407049947,1.3054828105933377571 ] 
dist 203=[-.38707412340263000303,1.3299692250457649742 ] 
dist 204=[-.38431239959854365825,1.3405021826631391737 ] 
dist 205=[.0104216056444958406 ,1.3429116659154446005 ] 
dist 206=[-.0410315437446051959 ,1.3401312221436683231 ] 
dist 207=[-.0990202433334454813 ,1.3242235265118705665 ] 
dist 208=[-.1809304039676017742 ,1.3152574401965314904 ] 
dist 209=[-.2622946196964107225 ,.77474092660034781677] 
dist 210=[-.3181060794430824556 ,.72035470502996139158] 
dist 211=[-.3657767748693076242 ,.59111623486941107513] 
dist 212=[-.4674550605316240234 ,.64876836131981012976] 
dist 213=[-.59532138739714384853,.71842320009096090279] 
dist 214=[-.68825381790640776893,.7627938103352195174 ] 
dist 215=[-.77320319235504101667,.79705560103849729371] 
dist 216=[-.86922545234946980679,.82638533328685331455] 
dist 217=[-.95708737807067718844,.85023319106193687273] 
dist 218=[-1.0094850684085513662 ,.86262737175800929898] 
dist 219=[-1.0458320928524477159 ,.86898353382563566594] 
dist 220=[-1.0696672471351433137 ,.86874554535412019834] 
dist 221=[-1.0851290358772915089 ,.0914954068281035736 ] 
dist 222=[-1.0880747773278139414 ,.1695615540409947020 ] 
dist 223=[-1.0855288185068691005 ,.2641168154998825102 ] 
dist 224=[-1.0806089111845151207 ,.4056296305436026186 ] 
dist 225=[-.90498871874118496324,.55602526188353109063] 
dist 226=[-.96156230324887898554,.6644640623004951233 ] 
dist 227=[-1.0103302945449709608 ,.75400095814717700355] 
dist 228=[-1.0610513184819054344 ,.8408789408810801754 ] 
dist 229=[-1.1042340801466785353 ,.9191707098060421368 ] 
dist 230=[-1.1229320234330699400 ,.9744578721041253437 ] 
dist 231=[-1.1312665108468238347 ,1.0233628527138520619 ] 
dist 232=[-1.1331105750771131009 ,1.0761965049568561666 ] 
dist 233=[-1.0951942841794611384 ,1.1223333618290770364 ] 
dist 234=[-1.0852860966585914396 ,1.1445253543943432898 ] 
dist 235=[-1.0792835193599825607 ,1.1547512678287817368 ] 
dist 236=[-1.0770628356566329596 ,1.1551094289146338691 ] 
dist 237=[-.8013446984806417161 ,1.1344459262204381376 ] 
dist 238=[-.7655934441711061435 ,1.1251301945685593556 ] 
dist 239=[-.6660610223530537237 ,1.1130840613371439043 ] 
dist 240=[-.5467747970171174138 ,1.1062526521415483178 ] 
dist 241=[-.7301698692448267407 ,1.1240066509474774571 ] 
dist 242=[-.9143446897246302066 ,1.2246041583293356734 ] 
dist 243=[-1.0625469112988239015 ,1.2969093367015603518 ] 
dist 244=[-1.1999452844633916645 ,1.3492762109724389350 ] 
dist 245=[-1.3195205440639268284 ,1.3883756133450668808 ] 
dist 246=[-1.3966287419952918895 ,1.4077585304953090026 ] 
dist 247=[-1.4572301422591867524 ,1.4163678504309626341 ] 
dist 248=[-1.5109621863318963459 ,1.4124935276567739258 ] 
dist 249=[-1.5545443065852737293 ,1.1827434215812075298 ] 
dist 250=[-1.5746588675678556745 ,1.1497397470026332206 ] 
dist 251=[-1.5813934801660771934 ,1.0373418583073963614 ] 
dist 252=[-1.5805503726080454309 ,.8600680796213125364 ] 
dist 253=[-1.5550127851972892650 ,.3385748089203229583 ] 
dist 254=[-1.5445576282239367719 ,.3274920991344592250 ] 
dist 255=[-1.5142467044635379417 ,.3011492309883835560 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 2, 0, 0, 0, 0, 1] 
dist 0=[51.878329496077489627  ,51.878329496077489627  ] 
dist 1=[50.899868978195591562  ,52.322035460762275077  ] 
dist 2=[49.805206331507601158  ,52.546805576239031041  ] 
dist 3=[48.897617162621056907  ,52.650700645523420378  ] 
dist 4=[47.951179959176408000  ,52.665505842394112775  ] 
dist 5=[46.701710899847179149  ,52.365592796270158952  ] 
dist 6=[45.350593550954835109  ,52.230080652126417174  ] 
dist 7=[43.998493279098887863  ,52.093199913278129301  ] 
dist 8=[42.384937630591109130  ,51.968975369380164527  ] 
dist 9=[39.990158450372810530  ,47.961133405586155771  ] 
dist 10=[37.516859097962978390  ,47.361997815688734103  ] 
dist 11=[35.571745089354714121  ,46.214321758132933546  ] 
dist 12=[33.622119247077477517  ,45.895466428388190364  ] 
dist 13=[31.166710633016357340  ,44.677483150490623890  ] 
dist 14=[28.566551392030155159  ,44.368344384077400941  ] 
dist 15=[25.908772560449109098  ,43.766241174284569931  ] 
dist 16=[20.899207408549310696  ,43.580239769706152895  ] 
dist 17=[17.479946685998134970  ,32.396513569510468975  ] 
dist 18=[14.389050328474874535  ,24.949651243557605420  ] 
dist 19=[11.487806408386647048  ,21.509048833894181599  ] 
dist 20=[8.7538078988595202380 ,20.909409583819430934  ] 
dist 21=[6.5262447862502309070 ,16.479501169167563418  ] 
dist 22=[4.3006431215598244238 ,15.688343712724839070  ] 
dist 23=[1.4874424916503150344 ,14.391995931386279855  ] 
dist 24=[-1.2262671439822556851 ,14.087359861584560439  ] 
dist 25=[-3.0550677844703883126 ,9.1595213918938853672 ] 
dist 26=[-4.5931607797489573343 ,8.5224829090916254830 ] 
dist 27=[-6.1465683447690309990 ,7.1359381332426931587 ] 
dist 28=[-7.6022570184455056463 ,6.8652313527309591122 ] 
dist 29=[-8.7509619447464186870 ,5.3348553940902727066 ] 
dist 30=[-9.9046408902401845053 ,5.0744120082547406699 ] 
dist 31=[-11.382087585731694426  ,4.5474673063973754483 ] 
dist 32=[-12.767834799675480308  ,4.4198402726375039942 ] 
dist 33=[-13.555425962636468141  ,3.4290128264289034582 ] 
dist 34=[-14.066489896646034729  ,3.2668573097634674725 ] 
dist 35=[-14.346369307208228093  ,3.0060976094060690196 ] 
dist 36=[-14.519363347420270101  ,2.9416712622306681414 ] 
dist 37=[-14.602488487833584593  ,2.7995280411274215836 ] 
dist 38=[-14.639505510954583395  ,2.7696057558000601640 ] 
dist 39=[-14.639622360220886569  ,2.7708619242421543536 ] 
dist 40=[-14.675530115557088169  ,2.8101617099274090251 ] 
dist 41=[-14.572512886945784983  ,2.8594609868191377617 ] 
dist 42=[-14.505756399307842452  ,2.9009566432325195540 ] 
dist 43=[-14.331315515780561051  ,2.9424762296965826286 ] 
dist 44=[-14.245875094770023418  ,2.9925421189553021888 ] 
dist 45=[-13.744272945807876280  ,3.0428627050256429598 ] 
dist 46=[-13.612963737295123101  ,3.1384445281521565463 ] 
dist 47=[-13.260635183772029847  ,3.2133493302842261118 ] 
dist 48=[-13.128260898465929378  ,3.2447099883128613740 ] 
dist 49=[-3.0016264030120576922 ,3.2405520095557015976 ] 
dist 50=[.27563809319150489934,2.2741168314799304814 ] 
dist 51=[.58592076400353035786,3.1177785812663517777 ] 
dist 52=[2.3271088925038269722 ,4.3305220446656992934 ] 
dist 53=[2.6145144539804022477 ,5.2571394750580848737 ] 
dist 54=[3.2228949111038630042 ,6.1522203397361638453 ] 
dist 55=[3.3282139574271577773 ,7.2391709700966200057 ] 
dist 56=[4.0363999631578398249 ,8.2618085251588484048 ] 
dist 57=[4.1122619612931072538 ,8.9001898482798654978 ] 
dist 58=[4.0364823510336473845 ,9.3799283068425866966 ] 
dist 59=[3.7356910866128071496 ,9.7692792683732955145 ] 
dist 60=[3.3150803138193239362 ,10.071287861009659016  ] 
dist 61=[2.7610990779797574823 ,10.202370261699016686  ] 
dist 62=[2.0046742793086398032 ,10.253980363437474028  ] 
dist 63=[.77623679342965700522,10.240896954976857742  ] 
dist 64=[-.46832230924247695558,4.9981113248636860824 ] 
dist 65=[-1.4247598291364611309 ,4.9774040688106584383 ] 
dist 66=[-2.2293653733220803375 ,1.6656308401810679384 ] 
dist 67=[-3.0081629955573640870 ,1.3830475345622001951 ] 
dist 68=[-3.7093509384627392079 ,.74940631855235863683] 
dist 69=[-4.2043725429246057338 ,.62388393591985700034] 
dist 70=[-4.6425436597402877714 ,-.12849114934947752713] 
dist 71=[-5.1169826879586371207 ,-.25803834208650361121] 
dist 72=[-5.5446106807861144108 ,-.51875971643073270551] 
dist 73=[-5.7960401306107174447 ,-.5817443393999064756 ] 
dist 74=[-5.9663942166209933426 ,-1.0721654114189139358 ] 
dist 75=[-6.0705496013513807698 ,-1.1517382525741272739 ] 
dist 76=[-6.1299776789133954966 ,-1.1918946650728964925 ] 
dist 77=[-6.1345599586851159043 ,-1.1387319011752150670 ] 
dist 78=[-6.0916489609568184405 ,-1.0382267305460866253 ] 
dist 79=[-6.0628237509132332907 ,-.87694281731531405086] 
dist 80=[-4.1278780505258578788 ,-.64082812369656969342] 
dist 81=[-4.1191300264676754606 ,.00298685852477350865] 
dist 82=[-2.9560577295227556394 ,.58278143279560108553] 
dist 83=[-2.8627665073740898970 ,1.1576668773044554365 ] 
dist 84=[-1.9952224542641456035 ,1.6837234327524642424 ] 
dist 85=[-1.8307063890488508581 ,2.0687813691981521086 ] 
dist 86=[-1.6125403458819095030 ,2.4234308795515604067 ] 
dist 87=[-1.5425530084577318199 ,2.8282306927680041830 ] 
dist 88=[-.17415522812040971551,3.2014890526880582439 ] 
dist 89=[-.00399899646837016658,3.4303382325709356639 ] 
dist 90=[.37979246027369521006,3.5967947786925467497 ] 
dist 91=[.44675973240741893212,3.7211815667420881010 ] 
dist 92=[.89899766270776478737,3.8094697198602938454 ] 
dist 93=[.90149667308736916714,3.8319322030479213478 ] 
dist 94=[.81456369971141042268,3.8316049627639346148 ] 
dist 95=[.64062239273733583811,3.8289759873162549678 ] 
dist 96=[.45442919857632993367,2.5415002609646984514 ] 
dist 97=[.31862060276903788698,2.5325671001579374918 ] 
dist 98=[-.07367414933009320962,1.9325493001913005783 ] 
dist 99=[-.36987725835021341185,1.8618022213128196664 ] 
dist 100=[-.61348578327090458857,1.6792389125460349840 ] 
dist 101=[-.8480987189248080118 ,1.6474449710506619083 ] 
dist 102=[-1.0582092942436625959 ,1.3382873686753908439 ] 
dist 103=[-1.2040880591281067493 ,1.2765257665743607334 ] 
dist 104=[-1.3304495585324466903 ,1.1975197889877200748 ] 
dist 105=[-1.4627089221200249262 ,1.1695448059017776740 ] 
dist 106=[-1.5820073890036601999 ,.57823059732764295253] 
dist 107=[-1.6566781767924483192 ,.50217384205331673   ] 
dist 108=[-1.7127461320562225463 ,.33508584504148129521] 
dist 109=[-1.7578651453344868728 ,.29702012383763651241] 
dist 110=[-1.7923723973271351873 ,.1067880924596867467 ] 
dist 111=[-1.8061282687036650615 ,.07364376395724294195] 
dist 112=[-1.8073248253262452444 ,-.00306219733669729041] 
dist 113=[-1.8037521909379071990 ,-.01491029941428223424] 
dist 114=[-.91068106520284804307,-.57748382098206094762] 
dist 115=[-.88403906406130291161,-.39103331471890819686] 
dist 116=[-.70749085214555627664,-.23220309393255035784] 
dist 117=[-.67307944896717543288,-.07015595873652774740] 
dist 118=[-.60915523394550673059,.08102919710944842742] 
dist 119=[-.59304620852927414451,.19654575417663292067] 
dist 120=[-.34128022784865713106,.3077662867700311441 ] 
dist 121=[-.30605881224905230448,.44182869796318378002] 
dist 122=[-.23199134353670525101,.5682438934204657208 ] 
dist 123=[-.21260010697352532358,.64896593317681518913] 
dist 124=[-.14159361284844071379,.71149313989930930243] 
dist 125=[-.1276071883413674464 ,.76533346849241397655] 
dist 126=[-.10531899087603278941,.81925629361421205477] 
dist 127=[-.10010097759384969291,.98184878410909080512] 
dist 128=[.69787063432303237538,1.1468890681880606338 ] 
dist 129=[.64224546418950404408,1.2562955514299322480 ] 
dist 130=[.58013940191668311959,1.3444780835792249774 ] 
dist 131=[.53004394791548061979,1.4266542384471704992 ] 
dist 132=[.47935975774578000796,1.4986087008608080467 ] 
dist 133=[.41488503617467620498,1.5460051239868413381 ] 
dist 134=[.34674416682975920727,1.5844627600738949071 ] 
dist 135=[.28142631204983156719,1.6207515753740747993 ] 
dist 136=[.20585315011060086278,1.6495837819404502153 ] 
dist 137=[.09679638538894338977,1.6582876875533401119 ] 
dist 138=[-.01389728492797537224,1.6573977882471610926 ] 
dist 139=[-.09600727625969184009,1.6518495570558394109 ] 
dist 140=[-.17271874923486573478,1.6024132120623929484 ] 
dist 141=[-.26189148572559425939,1.5865138620679094851 ] 
dist 142=[-.49474391403139923475,1.5552253125087813657 ] 
dist 143=[-.93086040997722239692,1.5434872243330448612 ] 
dist 144=[-1.3640518555302643399 ,1.2786866403863821069 ] 
dist 145=[-1.6464806773028345273 ,1.2375259074724217258 ] 
dist 146=[-1.8720380037068631343 ,1.1500774067886690735 ] 
dist 147=[-2.0783625706558632326 ,1.1240131734158248354 ] 
dist 148=[-2.2560859833881497453 ,1.0119149557119013021 ] 
dist 149=[-2.3675518874040741105 ,.98858566437261737204] 
dist 150=[-2.4516483763520338172 ,.92377695788236792878] 
dist 151=[-2.5201975457184778410 ,.91246877328900580479] 
dist 152=[-2.5726451835946216028 ,.78391565389506254766] 
dist 153=[-2.5925100638785930335 ,.75845041021283213891] 
dist 154=[-2.5945920209232893753 ,.71208433439273873913] 
dist 155=[-2.5890175093756842871 ,.69970283533529782303] 
dist 156=[-2.5277210256237475615 ,.65627550731838134093] 
dist 157=[-2.5067496653237944017 ,.64362604395454751751] 
dist 158=[-2.4537607233011651794 ,.62788297051333611728] 
dist 159=[-2.4311827640825257947 ,.62097228383631883038] 
dist 160=[-1.1376255024097189781 ,.70944276854493058792] 
dist 161=[-1.1293470198050339096 ,1.0924545794910661754 ] 
dist 162=[-.94017775588763777852,1.4030349749051146585 ] 
dist 163=[-.91066015136262038352,1.6950476332592479375 ] 
dist 164=[-.84746227973452880964,1.9520398609138637420 ] 
dist 165=[-.828461353988258489  ,2.1229265139113564801 ] 
dist 166=[-.74586921742621089793,2.2631189016681498555 ] 
dist 167=[-.72883729237463772882,2.3976755807952348309 ] 
dist 168=[-.68036223504284100248,2.5144225019514729980 ] 
dist 169=[-.67285817634051024577,2.5835721515446156526 ] 
dist 170=[-.57389725451615954735,2.6309661015176537042 ] 
dist 171=[-.55478035980870846761,2.6609268188952413790 ] 
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dist 177=[-.44539245114185131387,1.7480483126678048101 ] 
dist 178=[-.48158315003839467022,.80406632065702710164] 
dist 179=[-.75604778122662505792,.75024077102594418175] 
dist 180=[-.97969015800499673842,.37146629011360425462] 
dist 181=[-1.1917924811669108653 ,.30303827918176577433] 
dist 182=[-1.3797140479912153536 ,.18111653055706975027] 
dist 183=[-1.5068998656049182382 ,.15421510087601439271] 
dist 184=[-1.6513719299365436588 ,-.25182569837458951554] 
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dist 188=[-1.9501706991165921908 ,-.47326702600389723034] 
dist 189=[-1.9727695679614812579 ,-.46541376538797606408] 
dist 190=[-1.9856187263907704611 ,-.43347239429196288261] 
dist 191=[-1.9884741909254219093 ,-.36041988873076218632] 
dist 192=[-1.9110526849804158618 ,-.26862193571885668904] 
dist 193=[-1.9036872450878652087 ,-.07162432265923784674] 
dist 194=[-.99165939715013974308,.09680763662855197131] 
dist 195=[-.9115993267232463484 ,.26977977381821788575] 
dist 196=[-.72255114089657536495,.43197749827874228828] 
dist 197=[-.68730446667901354995,.55743254873234896379] 
dist 198=[-.42651088913829137698,.7025968206299092474 ] 
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dist 202=[-.40395358123423318913,1.2284899546300922086 ] 
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dist 206=[-.75548272182959678411,1.4253144757193949917 ] 
dist 207=[-.91339676097475560793,1.4374960745026070379 ] 
dist 208=[-1.0692893772168147185 ,1.5136335550389992115 ] 
dist 209=[-1.1665833389325565914 ,1.6091654429896658883 ] 
dist 210=[-1.2393710040845592650 ,1.6735522729215114809 ] 
dist 211=[-1.2975095509808762832 ,1.7121085819425236992 ] 
dist 212=[-1.3418299032914980832 ,1.7375218952542155038 ] 
dist 213=[-1.3594980231380167115 ,1.7494770148606592859 ] 
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dist 215=[-1.3671991692664644932 ,1.7490022249864841544 ] 
dist 216=[-1.3063414557544948234 ,1.4967387803116146597 ] 
dist 217=[-1.2916270057813342699 ,1.4575034867464437208 ] 
dist 218=[-1.2587522746389038058 ,1.3868329213212870917 ] 
dist 219=[-1.2462936607886310556 ,1.3675374640744901231 ] 
dist 220=[-1.1818453545550606692 ,1.2982563548587245534 ] 
dist 221=[-1.1663538265410771528 ,1.2775248141479019044 ] 
dist 222=[-1.1210150436097490609 ,1.2480809531168171836 ] 
dist 223=[-1.1095452571980482906 ,1.2365170161819239735 ] 
dist 224=[-.97973278856989376692,.89889604838292342999] 
dist 225=[-1.1692438562931038808 ,1.0183971559997311996 ] 
dist 226=[-1.3602103961375844321 ,1.1349250388554178950 ] 
dist 227=[-1.4759836074032952224 ,1.2052525693606870674 ] 
dist 228=[-1.5586251832444930801 ,1.2550564798598037874 ] 
dist 229=[-1.6174263611046527439 ,1.2897161341851066872 ] 
dist 230=[-1.6609340788154808460 ,1.3135630560094261136 ] 
dist 231=[-1.6825678157570970512 ,1.3202352505739367280 ] 
dist 232=[-1.6922810161548268976 ,1.3193094233330466722 ] 
dist 233=[-1.6904873678195594217 ,1.3141072259660692039 ] 
dist 234=[-1.5037576854356218972 ,1.2054922898328512763 ] 
dist 235=[-1.4724399210686390607 ,1.1849125114720160373 ] 
dist 236=[-1.4189431563206849798 ,1.1388311817761150907 ] 
dist 237=[-1.3782257995041333844 ,1.1230709086358778184 ] 
dist 238=[-1.2807101758767872674 ,1.0469075830962176401 ] 
dist 239=[-1.2629739301700061792 ,1.0296455035670742687 ] 
dist 240=[-1.2295516128171706015 ,.98227395929279252625] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 0, 2, 2, 0, 1] 
dist 0=[58.263349539414126705  ,58.263349539414126705  ] 
dist 1=[57.877220084286596675  ,58.487332508948547359  ] 
dist 2=[57.190468228426582740  ,58.650641896637499026  ] 
dist 3=[55.766081258838405135  ,58.794411176820522994  ] 
dist 4=[53.973373701127700511  ,58.914359196227688286  ] 
dist 5=[51.815892784357940991  ,58.982421520056054941  ] 
dist 6=[48.974060985152744595  ,59.024922939453495121  ] 
dist 7=[44.448691337519837744  ,59.042557216370384935  ] 
dist 8=[39.829968698194542288  ,59.042158756566567160  ] 
dist 9=[36.615291144786562509  ,59.012685889740022919  ] 
dist 10=[33.807732516777223684  ,58.955458056462306563  ] 
dist 11=[30.814422583776084982  ,58.844575022349564351  ] 
dist 12=[27.923408542102991873  ,58.707302683118480566  ] 
dist 13=[25.524078627732735385  ,58.557305747826344378  ] 
dist 14=[23.019750434753479683  ,57.256135265300387876  ] 
dist 15=[19.708977822503317105  ,53.918246782065056888  ] 
dist 16=[16.448219831395334135  ,39.272122326547243801  ] 
dist 17=[14.143342706776075501  ,37.643817075292282366  ] 
dist 18=[12.090475481611959823  ,33.722753112568257125  ] 
dist 19=[8.8009605688668095720 ,33.122479922425293539  ] 
dist 20=[6.3778760710304322905 ,27.478754568148859716  ] 
dist 21=[4.2572718786468815677 ,26.434318358233569377  ] 
dist 22=[1.9857246944412895763 ,25.123346489911655236  ] 
dist 23=[-.21914215836928356395,24.792628593001111062  ] 
dist 24=[-2.0740059903309467779 ,16.275978534920287227  ] 
dist 25=[-4.0362061428655516699 ,15.219444377156112762  ] 
dist 26=[-6.6709504487450971878 ,12.983078899974914086  ] 
dist 27=[-9.2125690299843744877 ,12.450619656801482707  ] 
dist 28=[-10.802973121047866077  ,10.193035040253293193  ] 
dist 29=[-12.010192576049939128  ,9.7821136992125181008 ] 
dist 30=[-13.020634359572617012  ,8.9620949435276501325 ] 
dist 31=[-13.835890828204647625  ,8.7641777095271964581 ] 
dist 32=[-14.263376624761638423  ,-.4982603805603203537 ] 
dist 33=[-14.493521972031672844  ,-1.3258081152756317150 ] 
dist 34=[-14.543812235697622991  ,-3.0075520527350703854 ] 
dist 35=[-14.469862832459254214  ,-3.4083473962454782549 ] 
dist 36=[-14.401219714091986601  ,-4.7902964397006783528 ] 
dist 37=[-14.271287375365035786  ,-5.0585203641137435521 ] 
dist 38=[-14.511790829214612274  ,-5.2758426728386317382 ] 
dist 39=[-15.538697170731486179  ,-4.3089413401892381630 ] 
dist 40=[-16.464769537358031503  ,-2.7434964196974717254 ] 
dist 41=[-16.984208918280677490  ,-1.6646659711953259037 ] 
dist 42=[-17.308184831173028748  ,-.73780962811817054015] 
dist 43=[-17.453428946512760975  ,.68023049310325340065] 
dist 44=[-17.512617194976262573  ,2.5943371638879380085 ] 
dist 45=[-17.492697845222776757  ,4.1866044365415152788 ] 
dist 46=[-17.418248775304243355  ,5.7540928965204976275 ] 
dist 47=[-17.364945639823881584  ,7.1843528560071599121 ] 
dist 48=[-1.1877006434687181964 ,8.2291135717033871604 ] 
dist 49=[-.52459746648947289575,9.1910534015397221619 ] 
dist 50=[-.36054315754839478058,10.290930714029971545  ] 
dist 51=[1.1330270185884097146 ,11.295356422395381153  ] 
dist 52=[1.3658548760474512060 ,11.876386099167615015  ] 
dist 53=[1.6481414502441455730 ,12.258355870450212943  ] 
dist 54=[1.6789777016841361651 ,12.468293428621100063  ] 
dist 55=[1.2312113972345888356 ,12.594532962732174405  ] 
dist 56=[.59552594801567864329,12.642507826336516290  ] 
dist 57=[.12708847994099607336,12.642427685661207013  ] 
dist 58=[-.26356831747185784995,12.603545820500040531  ] 
dist 59=[-.64859558070412712182,-.15273211774861377659] 
dist 60=[-.99922973162889456194,-.52180697775230530377] 
dist 61=[-1.2527470570569169291 ,-.84920555646821436523] 
dist 62=[-1.4830255098143143330 ,-1.0129877089341099105 ] 
dist 63=[-1.7715003287519653520 ,-1.0480152801212105986 ] 
dist 64=[-1.9833777064073196317 ,-1.4903443119959330109 ] 
dist 65=[-2.1636406496073078675 ,-1.5482595659980422258 ] 
dist 66=[-2.3475846820333938067 ,-1.5829699606579224148 ] 
dist 67=[-2.5110411409301631010 ,-1.5390832647573181461 ] 
dist 68=[-2.6095774683904534506 ,-1.4573387674901785080 ] 
dist 69=[-2.6793816253136004483 ,-1.3270329916731572300 ] 
dist 70=[-2.7281878941198872936 ,-1.1366615125990641939 ] 
dist 71=[-2.7597657275703640296 ,-.81537224642068103407] 
dist 72=[-2.7624907011207164283 ,-.48487253203611669859] 
dist 73=[-2.7497011517800360638 ,-.2577654487135238703 ] 
dist 74=[-2.7341239106082952783 ,-.06362254085136942254] 
dist 75=[-1.3341986959582081327 ,.13542556931292623997] 
dist 76=[-1.2074544140043679330 ,.32162617957689325132] 
dist 77=[-.92920597215158237646,.46453661856265465521] 
dist 78=[-.86599103306898200989,.60265447260558805857] 
dist 79=[-.85283051115545365913,.76974268832346442786] 
dist 80=[-.38326355090752829804,.92676064890052852694] 
dist 81=[-.25911052873873398203,1.0543439158022869008 ] 
dist 82=[-.23088191841620629698,1.2853057362770484981 ] 
dist 83=[-.04260168013591086741,1.5006152601282169423 ] 
dist 84=[.09591795661306224793,1.6302362799431042183 ] 
dist 85=[.12197846673831127287,1.7215921474865026329 ] 
dist 86=[.16271234043171853912,1.7842842829162221793 ] 
dist 87=[.17201713627147408175,1.8298866732674229044 ] 
dist 88=[.47756340932422262613,1.8530771152644810560 ] 
dist 89=[.45435590596835125426,1.8642291287363234528 ] 
dist 90=[.39321449376139775611,1.8618046740448214834 ] 
dist 91=[.32367714442262014832,.94218012178082066777] 
dist 92=[.16913490206962380778,.98267643023075012369] 
dist 93=[.01832223799661345422,1.0026124251857954738 ] 
dist 94=[-.1379313159022536991 ,1.0121145930937683771 ] 
dist 95=[-.28526130369918195777,1.0130002845360214753 ] 
dist 96=[-.40048810516420462838,.96332935394052463635] 
dist 97=[-.51400197339185961538,.95219110336379248867] 
dist 98=[-.65450927959132604689,.93386431248231835574] 
dist 99=[-.7873374359596442682 ,.92721035638927016937] 
dist 100=[-.87022582971523500047,.90100701779359000688] 
dist 101=[-.93224426858305470921,.89245238062697314103] 
dist 102=[-.98183162624395332365,.87310777950483453391] 
dist 103=[-1.0201584161308775593 ,.86561385849891331177] 
dist 104=[-1.0372536105187593654 ,.59391885188105199044] 
dist 105=[-1.0446381378348240274 ,.67991292888007087062] 
dist 106=[-1.1318832220911118627 ,.80930000207978456573] 
dist 107=[-1.2772104157496837301 ,.93703025589951150415] 
dist 108=[-1.3627959093407265964 ,1.0164116855969714062 ] 
dist 109=[-1.4208984135723709802 ,1.0753581281365205671 ] 
dist 110=[-1.4565851107638928211 ,1.1215788040687266135 ] 
dist 111=[-1.4806234209578402956 ,1.1564632951033221036 ] 
dist 112=[-1.4922528221693074650 ,1.1701965605681138979 ] 
dist 113=[-1.4970210398965795855 ,1.1749469094152440422 ] 
dist 114=[-1.4936783192592491190 ,1.1740052966603007472 ] 
dist 115=[-1.2797461471741910348 ,1.1109846111084910188 ] 
dist 116=[-1.2465020765466122147 ,1.0967886067596475496 ] 
dist 117=[-1.1870711771320949065 ,1.0662176167659268774 ] 
dist 118=[-1.1709195376423578780 ,1.0551158106506130077 ] 
dist 119=[-1.1136044382522850168 ,.9991907878089920756 ] 
dist 120=[-1.0960821888086265557 ,.9860257463276679175 ] 
dist 121=[-1.0730056561506976223 ,.94494538467467743629] 
dist 122=[-1.0631168470476726470 ,.93684461532937958908] 
dist 123=[.27585203423651540554,.54506767182995581906] 
dist 124=[.37667991388214166221,.6379026315047195064 ] 
dist 125=[.45435931398778951078,.70550512852215154657] 
dist 126=[.48052740044491069991,.79264487288994420754] 
dist 127=[.48512201794183165626,.92822573726473692216] 
dist 128=[.49764759319520453025,1.0192231286891035269 ] 
dist 129=[.49031331344450747055,1.0948152490238290702 ] 
dist 130=[.47343344021401988046,1.1689460854077734784 ] 
dist 131=[.43916562556704182293,1.2340789514488912272 ] 
dist 132=[.36383352743179036813,1.2737776963710492497 ] 
dist 133=[.26703102045003588781,1.3023792564129670847 ] 
dist 134=[.14365247118620715361,1.3232424824552676272 ] 
dist 135=[-.04790116763406370420,1.3374937768562529746 ] 
dist 136=[-.24032737724365924273,1.3397187662733671193 ] 
dist 137=[-.36718781506862053027,1.3352691554351802686 ] 
dist 138=[-.47004802726266922789,1.3301875741053584431 ] 
dist 139=[-.5667400730601431379 ,.65375280221579448571] 
dist 140=[-.65182281824819956684,.54677293172596377091] 
dist 141=[-.70837529501537066997,.52499215971739070475] 
dist 142=[-.75474598995878235726,.49184613319519389137] 
dist 143=[-.79921608276191463547,.48196934088628665109] 
dist 144=[-.83770259363205341211,.27803433850919186602] 
dist 145=[-.86020533140058870485,.25107796743808415427] 
dist 146=[-.87527022428044524733,.18855414629135363086] 
dist 147=[-.88408633194260313108,.17638301956337897754] 
dist 148=[-.88819832808846786913,.09387548114600211178] 
dist 149=[-.88719009659686158791,.07886655538204049012] 
dist 150=[-.87836031397234031495,.05145070454858881813] 
dist 151=[-.87274545828435341156,.04514967384734874591] 
dist 152=[-.85202123500318473903,.00594766625948391791] 
dist 153=[-.85991315613675817501,.03209883087540414749] 
dist 154=[-.86152383478531131899,.11077791384872177023] 
dist 155=[-.26063091709781313816,.20267211908840244053] 
dist 156=[-.24729763140765379513,.28703811255336157768] 
dist 157=[-.22518869563009158809,.34928059604622041263] 
dist 158=[-.21946088249896845496,.40709952980684308913] 
dist 159=[-.20660278117895092111,.47382281881317646204] 
dist 160=[-.20523664125636429467,.53548477378107672343] 
dist 161=[-.20818314385198647929,.57311528390273213623] 
dist 162=[-.21778697445965502124,.60026926550081633984] 
dist 163=[-.22981741032479053025,.62014116302942417533] 
dist 164=[-.24244236862159936931,.63428726663106489651] 
dist 165=[-.25789499389338939734,.63860225205298194206] 
dist 166=[-.28120282821176217144,.63889613766802198079] 
dist 167=[-.30771042731380191332,.63700154125529832949] 
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dist 169=[-.370727153824823481  ,.55290700947314719502] 
dist 170=[-.42350834981135957165,.65614922163956595452] 
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dist 172=[-.50877374198047614235,.81748288800787872174] 
dist 173=[-.53376529760940053569,.86165783304177515283] 
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dist 175=[-.5704441320263260321 ,.91804342325058393108] 
dist 176=[-.57758059085452212666,.92830355358080562497] 
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dist 189=[-.51689439081182630784,.25629296962965687625] 
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dist 192=[-.75961421957422670159,.41374046946535481675] 
dist 193=[-.8035386267191602199 ,.45222233086139678026] 
dist 194=[-.8424016749663250529 ,.48487329605822174989] 
dist 195=[-.87542162011064824034,.51800701120287065628] 
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dist 198=[-.92383999018983351562,.59477780701872405987] 
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dist 201=[-.93709303029157497127,.82261863681088107813] 
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dist 203=[-.66994420827917524348,.98165840613050354389] 
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dist 207=[-.65193802935730976997,1.0969832446386600308 ] 
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dist 209=[-.6199529280756101134 ,1.0893960357349349872 ] 
dist 210=[-.61425758826229366062,1.0800309890439899727 ] 
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dist 212=[-.60297632845164175456,1.0445821404853359136 ] 
dist 213=[-.598747750769280711  ,1.0360226837632059676 ] 
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dist 215=[-.59086812189791570992,.99832685752711331221] 
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dist 218=[-.11226903120447416008,.63060813675336854361] 
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dist 220=[-.26287339784235252959,.14045517898243784952] 
dist 221=[-.32703960933049629296,.10331150919076118923] 
dist 222=[-.39016455772167794234,.09341449457214860672] 
dist 223=[-.44763720779539092469,.05618585216476763500] 
dist 224=[-.48925611808932673998,.04875983400570167853] 
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dist 226=[-.56976983591187319345,.03115486982706555314] 
dist 227=[-.60795449692652423263,.02115333583470795304] 
dist 228=[-.62816246065464975959,.02139676537308772709] 
dist 229=[-.6393156785058438433 ,.02567453432242727021] 
dist 230=[-.64168353758917090158,.03656406284281890462] 
dist 231=[-.63771640619048308072,.05084135279394257114] 
dist 232=[-.63581104438382679037,.06863359539197104830] 
dist 233=[-.63380572002021857192,.09237231670495432653] 
dist 234=[-.63114569575208406866,.13037111004719077566] 
dist 235=[-.50451879298571450798,.21828787289471608218] 
dist 236=[-.49690821671796708039,.3076982808912868869 ] 
dist 237=[-.51326171692837426181,.38005514681925323546] 
dist 238=[-.52333099579347049488,.4478460132704585779 ] 
dist 239=[-.5295108075841248873 ,.50734456963648706655] 
dist 240=[-.53034978138751637949,.54662315324575239527] 
dist 241=[-.52864163370301385946,.57853214151793127495] 
dist 242=[-.52629358703177846754,.60863309247883231973] 
dist 243=[-.4723848050317466895 ,.63438691584196020798] 
dist 244=[-.46290461355847504152,.64895520884215550755] 
dist 245=[-.44174965172151930272,.6580902642843458328 ] 
dist 246=[-.43474522276591367787,.66217118412015724055] 
dist 247=[-.40170044691618346482,.66268269601438053296] 
dist 248=[-.39437880693580559598,.66138635489226287408] 
dist 249=[-.37455860507455952327,.65162170125498050715] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 2, 2, 2, 0, 2] 
dist 0=[51.261006108897789384  ,51.261006108897789384  ] 
dist 1=[49.794852933655728757  ,52.046976298257325537  ] 
dist 2=[48.221047045734741288  ,52.499426455668410550  ] 
dist 3=[47.005290134146321871  ,52.634124499706446681  ] 
dist 4=[45.818023015821586491  ,52.705490289375208705  ] 
dist 5=[44.357914604883275762  ,52.737035876116079263  ] 
dist 6=[42.832630334485620848  ,52.734890285008044603  ] 
dist 7=[41.385134461507875161  ,52.707396243452293933  ] 
dist 8=[39.715991199304291543  ,52.602659634980108767  ] 
dist 9=[37.305785973922475223  ,48.675152786140058382  ] 
dist 10=[34.844431289622650827  ,48.083321302708174464  ] 
dist 11=[32.971032778157966825  ,47.025669964435476065  ] 
dist 12=[31.167543942873802434  ,46.745075605071433180  ] 
dist 13=[28.985175792643565517  ,45.775142080489221696  ] 
dist 14=[26.723031872585524318  ,45.481807563616310454  ] 
dist 15=[24.600936737654580657  ,45.134240345886304977  ] 
dist 16=[22.172085486005985645  ,44.970123121774963029  ] 
dist 17=[18.685044477698189266  ,30.066998042491655184  ] 
dist 18=[15.205346858189001930  ,23.976337768103101173  ] 
dist 19=[12.801271442421000705  ,20.157391803526305703  ] 
dist 20=[10.720107278578582881  ,19.605988522409601469  ] 
dist 21=[8.5620178636920132098 ,14.408156272276321578  ] 
dist 22=[6.2817695197945420350 ,13.485370392359465424  ] 
dist 23=[3.2396241034653191304 ,12.336245656973851012  ] 
dist 24=[.28631161731055890604,12.132811495799936329  ] 
dist 25=[-1.7314645939612860764 ,8.5995526499312462279 ] 
dist 26=[-3.4570735567682420113 ,4.6372453514233774209 ] 
dist 27=[-5.2442695102903159904 ,2.9608400006854068281 ] 
dist 28=[-6.9447529794473332090 ,2.6441542268464556088 ] 
dist 29=[-8.3248715409272301949 ,.99371281325026354767] 
dist 30=[-9.7438045779486151703 ,.72475681557131977242] 
dist 31=[-11.601007214535027809  ,.26815569815611070942] 
dist 32=[-13.362462099496223215  ,.18611618023058181922] 
dist 33=[-14.399165238533168429  ,.30349091462082399646] 
dist 34=[-15.113610068889603579  ,.47989472728718453826] 
dist 35=[-15.586823226610858959  ,.62054132493705802746] 
dist 36=[-15.922127847268369704  ,.75702946830706355186] 
dist 37=[-16.084898784203630886  ,.91794128187008959782] 
dist 38=[-16.156007023172897309  ,1.0779390566155643937 ] 
dist 39=[-16.133246122666709524  ,1.2112811638751142693 ] 
dist 40=[-14.422196502391503260  ,1.3485833255052358652 ] 
dist 41=[-14.150874862212829901  ,1.5247755397266602583 ] 
dist 42=[-13.653205069144942383  ,1.6923701151413222750 ] 
dist 43=[-13.514066231499916762  ,1.7956445968930366186 ] 
dist 44=[-12.998093118409697073  ,1.8709756660733300402 ] 
dist 45=[-12.847989072959885099  ,1.9275069577976983919 ] 
dist 46=[-12.608774930623843293  ,1.9680872509370889787 ] 
dist 47=[-12.526371050657468377  ,1.9800740183853700186 ] 
dist 48=[-6.5271741639864354332 ,1.9744434503379249880 ] 
dist 49=[-6.2504982838986723988 ,2.1749926611939493868 ] 
dist 50=[-.49822355333824180193,3.4359265046847090716 ] 
dist 51=[-.14526498207601772269,4.6963874084940267859 ] 
dist 52=[1.7814106229914127827 ,5.7597567882549283690 ] 
dist 53=[1.6721070635601166641 ,6.8308826788728334405 ] 
dist 54=[1.5476391817485969407 ,7.8239517230364587755 ] 
dist 55=[1.4171611484648408372 ,9.0168007211298575473 ] 
dist 56=[1.2583869455025549887 ,10.174860836577388322  ] 
dist 57=[1.0209539555821715842 ,10.882573342102254062  ] 
dist 58=[.77762603573373234262,11.396237140324649210  ] 
dist 59=[.59524227912961129332,11.779764627140990883  ] 
dist 60=[.42332219513796755712,12.061098645098233795  ] 
dist 61=[.22154718019455004552,12.166855831537068665  ] 
dist 62=[.01654947111906389246,12.194033703219613244  ] 
dist 63=[-.16834926804066316204,12.161687807081944518  ] 
dist 64=[-.83059146202508302923,6.0179386551016564963 ] 
dist 65=[-1.7088604270681708234 ,3.8351792412950010944 ] 
dist 66=[-2.4210210330686742614 ,3.6035358875944813666 ] 
dist 67=[-3.0909951543037002581 ,3.0514280492030718503 ] 
dist 68=[-3.6813465759998098864 ,2.9443328558213301215 ] 
dist 69=[-4.0759075742952638562 ,2.1543413841910488878 ] 
dist 70=[-4.4021553569575289702 ,2.0042698306565848203 ] 
dist 71=[-4.7200500130501037318 ,1.7524805587100567838 ] 
dist 72=[-4.9991228331057847984 ,1.6901860125242818306 ] 
dist 73=[-5.1704981668428625097 ,.57147852403581246497] 
dist 74=[-5.2957914871347216079 ,.42411070038270760477] 
dist 75=[-5.3909638976170033759 ,.18442458909472082121] 
dist 76=[-5.4595403759767672527 ,.20415671558338040677] 
dist 77=[-5.4786997580525734324 ,.23682050471153005325] 
dist 78=[-5.4660138978599802312 ,.27506601938206746555] 
dist 79=[-5.4511272307267213798 ,.31710664034830519487] 
dist 80=[-5.1323063862770111214 ,.36988153781172926207] 
dist 81=[-2.0127162718327873361 ,.45099950929952063649] 
dist 82=[-1.3795917106442702396 ,.53708719789937782359] 
dist 83=[-1.2657754527265646395 ,.93376800631921037025] 
dist 84=[-.43570763253152412488,1.4384202730291996764 ] 
dist 85=[-.28801131186365175877,1.8960907925621864899 ] 
dist 86=[-.03284082718470802027,2.2240440529291035983 ] 
dist 87=[.02328862046185488553,2.5190273144002828945 ] 
dist 88=[.52685596062381665307,2.8452196910222819718 ] 
dist 89=[.44834900928081636758,3.1431110123093911781 ] 
dist 90=[.36173526966186407916,3.3252151209050553907 ] 
dist 91=[.28644332107538096391,3.4570077281910996161 ] 
dist 92=[.20522291496939864302,3.5542080552353657200 ] 
dist 93=[.09494640763146631588,3.6215037877776452464 ] 
dist 94=[-.02526391784341416551,3.6357533314744618852 ] 
dist 95=[-.14611911821994851529,3.6276046874933430621 ] 
dist 96=[-.36887728022506436661,3.6194861054446130900 ] 
dist 97=[-.87953688309155410044,2.4377807049588707727 ] 
dist 98=[-1.3883390118186143674 ,2.3476142118716749718 ] 
dist 99=[-1.7164675833789183843 ,2.3241389278062998413 ] 
dist 100=[-1.9743885291897622420 ,2.2532374073834372220 ] 
dist 101=[-2.2031427197817983245 ,2.2313598192217451499 ] 
dist 102=[-2.3950589124135128946 ,2.0607776757660617277 ] 
dist 103=[-2.5060392324722509745 ,2.0199231434992116509 ] 
dist 104=[-2.5787654400089878929 ,1.9561628534833178165 ] 
dist 105=[-2.6180938923448493130 ,1.9348725437614040772 ] 
dist 106=[-2.6417119987254016381 ,1.4277916443929207622 ] 
dist 107=[-2.6517720151995612325 ,1.3565397281621403783 ] 
dist 108=[-2.6538291324469878704 ,1.1964216274642813657 ] 
dist 109=[-2.6455228432336458392 ,1.1529838130046928504 ] 
dist 110=[-2.6312454146657495311 ,.94589688935083813604] 
dist 111=[-2.6166473143132178583 ,.90520391161311594652] 
dist 112=[-2.5827122189564810465 ,1.0284442647025437188 ] 
dist 113=[-2.5659072128685691696 ,1.1585605387002501536 ] 
dist 114=[-2.0902323340628648011 ,1.2602387463108788455 ] 
dist 115=[-2.1171872760512162689 ,1.3491992939026439974 ] 
dist 116=[-2.1306733776705205251 ,1.4227863969504795879 ] 
dist 117=[-2.1360975459846339753 ,1.4631501732339516509 ] 
dist 118=[-2.1367175664687591721 ,1.4867263321760878308 ] 
dist 119=[-2.1309894078867619467 ,1.4933516754607785150 ] 
dist 120=[-1.7787121546321271911 ,1.5988993643413025787 ] 
dist 121=[-1.7711439275834389690 ,1.7840866031368357538 ] 
dist 122=[-1.8473681364406542909 ,1.9526728619455557733 ] 
dist 123=[-1.9161892692193050612 ,2.0565177134249026947 ] 
dist 124=[-1.9926987731394357432 ,2.1326092814340433135 ] 
dist 125=[-2.0680642569400157915 ,2.1904883080578092370 ] 
dist 126=[-2.1323087696842905032 ,2.2320844431645677320 ] 
dist 127=[-2.2005217541256551782 ,2.2432238024900423276 ] 
dist 128=[-2.2916955350647543840 ,2.2412951741281503516 ] 
dist 129=[-2.3769093487876504414 ,2.7006681285063117521 ] 
dist 130=[-2.4213454161290529027 ,3.0406136003395245346 ] 
dist 131=[-2.4442472062407436725 ,3.2988202369492315237 ] 
dist 132=[-2.4448045667341083096 ,3.5122899760305374643 ] 
dist 133=[-2.4305387272150236203 ,3.6810748478266099337 ] 
dist 134=[-2.4198185959334472436 ,3.7610262386853819219 ] 
dist 135=[-2.3766154910960492363 ,3.8003233763663177584 ] 
dist 136=[-2.3591819301227052791 ,3.8069318601809826723 ] 
dist 137=[-2.1047673120198961685 ,3.6798229073460407453 ] 
dist 138=[-2.0604471134350378147 ,3.6436824843430358946 ] 
dist 139=[-1.9409032572117259369 ,3.5785880352394873384 ] 
dist 140=[-1.9144825580581199161 ,3.5544535488316237835 ] 
dist 141=[-1.6850844860870397265 ,3.4361068643315646687 ] 
dist 142=[-1.6354430884464691920 ,3.4021046537803415742 ] 
dist 143=[-1.5781270881532706018 ,3.3014937436347076117 ] 
dist 144=[-1.5681848293647318462 ,3.2680116691070100020 ] 
dist 145=[-1.1253212422101235747 ,-.08918393798621110601] 
dist 146=[-.80220974057925848185,-.23482145005617772523] 
dist 147=[-.84487652694427588593,-.56450647329026328226] 
dist 148=[-.88362505187351647682,-.61782372884256138788] 
dist 149=[-1.0716287924530715575 ,-.58778291010338633366] 
dist 150=[-1.2234467669036182539 ,-.50612745778163820968] 
dist 151=[-1.3593020287512958083 ,-.42850806796481623913] 
dist 152=[-1.5085182393363856660 ,-.33916101466010040932] 
dist 153=[-1.6441618893336452204 ,-.21071913558027544845] 
dist 154=[-1.7258758114495993277 ,-.08049082463664439141] 
dist 155=[-1.7835776476809117640 ,.01598615201522980873] 
dist 156=[-1.8234342293469491541 ,.13114537394229568736] 
dist 157=[-1.8489358577692563675 ,.33342921659483020593] 
dist 158=[-1.8538792498901144739 ,.54956942083873227426] 
dist 159=[-1.8427662000165006124 ,.76072726666958870796] 
dist 160=[-1.8401529547724479859 ,1.0082692606154578325 ] 
dist 161=[-1.3934435167078786089 ,1.3695562274730243818 ] 
dist 162=[-1.4280492707266047724 ,1.7253221017272695836 ] 
dist 163=[-1.4451981131288594320 ,1.9508414029537356139 ] 
dist 164=[-1.4527799901628523441 ,2.1237209781862549308 ] 
dist 165=[-1.4508451468936402458 ,2.2694993763800151268 ] 
dist 166=[-1.4387656677992174421 ,2.3863794980742791476 ] 
dist 167=[-1.4326141458267595086 ,2.4439805581600817368 ] 
dist 168=[-1.4002235505313773695 ,2.4732866513093378032 ] 
dist 169=[-1.3953724078704999892 ,2.4772879792093043013 ] 
dist 170=[-1.2764503964959110612 ,2.4311189425447960646 ] 
dist 171=[-1.2543552983645624970 ,2.4127028331861039695 ] 
dist 172=[-1.1889710944925142340 ,2.3778614473629306492 ] 
dist 173=[-1.1776246538825185583 ,2.3632563926382205071 ] 
dist 174=[-1.0363085281415682707 ,2.2844824871858690809 ] 
dist 175=[-1.0055927020753297016 ,2.2632692598834316005 ] 
dist 176=[-.97386680261325852851,2.1904607762397298905 ] 
dist 177=[-.96232285238986992358,2.1753683961803179035 ] 
dist 178=[-.84896104502862091984,.77064226433286430734] 
dist 179=[-1.0497793928015505871 ,.82602580941047990773] 
dist 180=[-1.2659975995359240368 ,.88792624128884131868] 
dist 181=[-1.5452392822658884309 ,.94913735151294402586] 
dist 182=[-1.7904825313447080482 ,1.0017696855033660381 ] 
dist 183=[-1.9526957881341375301 ,1.0580971552557648384 ] 
dist 184=[-2.0848323806588171872 ,1.1340469924163222044 ] 
dist 185=[-2.2100966719123656338 ,1.2089418827576797260 ] 
dist 186=[-2.3191060137295669887 ,1.2610600081047027221 ] 
dist 187=[-2.3864003796076192472 ,1.3063702688613168456 ] 
dist 188=[-2.4358924791849079654 ,1.3541063329321410906 ] 
dist 189=[-2.4738881022328495855 ,1.3996248781882157053 ] 
dist 190=[-2.5014986665798623039 ,1.4360877786275638489 ] 
dist 191=[-2.5095647586371344963 ,1.4728193296558711769 ] 
dist 192=[-2.5048478228745194467 ,1.5194068310456626718 ] 
dist 193=[-2.4976843788584898887 ,1.5619924771886250068 ] 
dist 194=[-.64573507257352730431,1.5827601010388333258 ] 
dist 195=[-.69903133938453600875,1.5914705050699009863 ] 
dist 196=[-.75054726266939178952,1.5902012909756228240 ] 
dist 197=[-.79686183206292080078,1.5730852890657261547 ] 
dist 198=[-.82940870552276455729,1.5650128507635289627 ] 
dist 199=[-.85804507140345471103,1.5324482336481209758 ] 
dist 200=[-.8887598811092911567 ,1.5224019808362293102 ] 
dist 201=[-.91547612594374623723,1.3637933643968438106 ] 
dist 202=[-.92816127805071560559,1.4908099780116461955 ] 
dist 203=[-.93297600847484038348,1.5786557122462563687 ] 
dist 204=[-.93266183206910606165,1.6379945623111041911 ] 
dist 205=[-.91956197234943800234,1.6737662269191030486 ] 
dist 206=[-.91385661841506005407,1.6968216502112305165 ] 
dist 207=[-.89675636947982925946,1.7054349086754985040 ] 
dist 208=[-.88866359283299655936,1.7051016696134055632 ] 
dist 209=[-.09480424763276887902,1.7006031351823006366 ] 
dist 210=[-.25016706992005586337,.98417914129153578443] 
dist 211=[-.45484364355156390071,1.1093684144210441595 ] 
dist 212=[-.62726828567328014368,1.2204398175496732600 ] 
dist 213=[-.80026383420883090198,1.3136681654332020409 ] 
dist 214=[-.95995730095981703561,1.3676801209579384205 ] 
dist 215=[-1.0793198238447764373 ,1.4032031970298971668 ] 
dist 216=[-1.1917574665643592324 ,1.4226780894419044251 ] 
dist 217=[-1.3238278938973699996 ,1.4338819266698477537 ] 
dist 218=[-1.4451935870172035934 ,1.4364112115165698560 ] 
dist 219=[-1.5149298530343889651 ,1.4330673697599438626 ] 
dist 220=[-1.5600633072575662196 ,1.4281035005412574869 ] 
dist 221=[-1.5832875161974229939 ,1.4038797182354453769 ] 
dist 222=[-1.5958143269397478025 ,1.3949103781109243286 ] 
dist 223=[-1.5982749234769361851 ,1.3613208616352097798 ] 
dist 224=[-1.5938285400187596969 ,1.3520796369294677612 ] 
dist 225=[-1.5884325023128092343 ,.50541755239121554714] 
dist 226=[-1.3614689876896418348 ,.42652888613532762487] 
dist 227=[-1.3285192863303538327 ,.31170031628199461418] 
dist 228=[-1.2404858607428090280 ,.40411606930531969218] 
dist 229=[-1.2228493959023899826 ,.49248013518359174807] 
dist 230=[-1.0594120319125084052 ,.57125252754659032589] 
dist 231=[-1.0249183682876562810 ,.6254062818223925915 ] 
dist 232=[-.97860988799586331498,.67178265757421298267] 
dist 233=[-.96219582634299059904,.71952973802913999825] 
dist 234=[-.59793107479260574179,.7617197674885716079 ] 
dist 235=[-.54951975222121756232,.78592904611839440304] 
dist 236=[-.4427675005288420921 ,.80154941307797040495] 
dist 237=[-.41610681844689862763,.80947956408446522199] 
dist 238=[-.18872286772275719826,.81229518052537075313] 
dist 239=[-.14645285512058704961,.81144402497843120626] 
dist 240=[-.02901429755175075178,.80120104542723166957] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 2, 2, 0, 2] 
dist 0=[64.166811885007362717  ,64.166811885007362717  ] 
dist 1=[62.914223120133237694  ,64.915901526619469164  ] 
dist 2=[60.646358133319724181  ,65.173581338887866811  ] 
dist 3=[58.233162500105630583  ,65.255951840721618956  ] 
dist 4=[56.400222663910814634  ,65.305220598580582222  ] 
dist 5=[54.639640388599721632  ,65.339128822296557368  ] 
dist 6=[52.514942307273318081  ,65.360427498712714674  ] 
dist 7=[50.315264929310953887  ,65.367568756033731726  ] 
dist 8=[48.255007291934746829  ,64.597620939434657494  ] 
dist 9=[45.898664244900558743  ,59.407686756437047484  ] 
dist 10=[42.516307954523036034  ,58.541890290909379582  ] 
dist 11=[39.064878759211663275  ,57.064174760907132583  ] 
dist 12=[36.432451602412329262  ,56.665289592022799845  ] 
dist 13=[33.889929414519704703  ,55.449454541715444834  ] 
dist 14=[30.797083493452473374  ,55.043068684135178275  ] 
dist 15=[25.009536759112345788  ,54.795417164485194967  ] 
dist 16=[20.218267463192160362  ,53.837010228460453348  ] 
dist 17=[16.184061965627402362  ,32.004431420243552754  ] 
dist 18=[12.119437778893767594  ,31.907155122162467465  ] 
dist 19=[8.3389550242646251101 ,17.706953907610924220  ] 
dist 20=[5.4393742462172581649 ,16.861331818898068498  ] 
dist 21=[2.6254639197755392785 ,9.7376710717926227306 ] 
dist 22=[-.81286566917202821466,8.4967527867623490669 ] 
dist 23=[-4.0615588872735795235 ,6.7293476490552057942 ] 
dist 24=[-6.1182806859988092223 ,6.2796739626563186530 ] 
dist 25=[-7.6985377318568690523 ,-1.3626972547690632688 ] 
dist 26=[-9.0448599071935959756 ,-1.8402643490127242043 ] 
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dist 36=[-5.2115435934982280680 ,-.5041735338363448340 ] 
dist 37=[-4.5779753111542468609 ,.32198050173483652387] 
dist 38=[-4.4488819562015642101 ,1.1417780153607671071 ] 
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dist 40=[-4.1461726657051384955 ,2.4363094895883995258 ] 
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dist 56=[-1.8126273272240155846 ,4.3406438790247657973 ] 
dist 57=[-2.1433234713770890490 ,4.2391859134016327834 ] 
dist 58=[-2.5363543866745830909 ,4.2064731915717850917 ] 
dist 59=[-2.8988091025005086605 ,4.1335654957060317124 ] 
dist 60=[-3.1076179547900609624 ,4.1037437328799713680 ] 
dist 61=[-3.2430831647520776002 ,3.9431734975315080585 ] 
dist 62=[-3.3131219300526315460 ,3.9039532843267333537 ] 
dist 63=[-3.3547481884407127661 ,3.7777403657385240027 ] 
dist 64=[-3.3769348514762145180 ,3.7524471591795726102 ] 
dist 65=[-3.3890805776526907125 ,-.62863821019761545678] 
dist 66=[-3.3906766503783947352 ,0                     ] 
dist 67=[-2.0057161617597404756 ,-.0503335494223732049 ] 
dist 68=[-2.4462403127430383576 ,.3249715016857249662 ] 
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dist 73=[-3.6497980413124214444 ,1.6325643873142214778 ] 
dist 74=[-3.7489608582750047678 ,1.8457051607087014052 ] 
dist 75=[-3.8216574268324469262 ,2.0401978150880148135 ] 
dist 76=[-3.8772623332343464954 ,2.1550272354490735698 ] 
dist 77=[-3.9176624159605686546 ,2.2330954831077740883 ] 
dist 78=[-3.9296799142471953630 ,2.2809935706326953053 ] 
dist 79=[-3.9232491427233054454 ,2.3099372742583389668 ] 
dist 80=[-3.9109453997332729086 ,2.3124299366737541492 ] 
dist 81=[-1.4611278492277359582 ,2.3030091814486545420 ] 
dist 82=[-1.2539275975963064169 ,2.2904177120427742365 ] 
dist 83=[-.77695463565390336976,1.4548010586584691956 ] 
dist 84=[-.68954460323749923024,1.3677561097206690735 ] 
dist 85=[-.53498904185223700704,1.2008546946955657061 ] 
dist 86=[-.77583981384517408719,1.4643283193944532566 ] 
dist 87=[-.99684979820308293413,1.7149848205340510583 ] 
dist 88=[-1.1591859854973815939 ,1.8739738208281951536 ] 
dist 89=[-1.3090493175745251507 ,2.0407822782432473589 ] 
dist 90=[-1.4803102949959417593 ,2.2580963292080532973 ] 
dist 91=[-1.6369431965604085309 ,2.4202688138767869493 ] 
dist 92=[-1.7284752008093563785 ,2.5490845584810696250 ] 
dist 93=[-1.7894984719876357923 ,2.6483983337044124897 ] 
dist 94=[-1.8244857880940504681 ,2.6928925215592488570 ] 
dist 95=[-1.8450281634633611830 ,2.7116735332732304377 ] 
dist 96=[-1.8484528183217977737 ,2.7087784802887661529 ] 
dist 97=[-1.8414676824676120494 ,.3784936975269865276 ] 
dist 98=[-1.8343529328536993575 ,.30283268564489765384] 
dist 99=[-1.2724533378786191066 ,.13884750155335598475] 
dist 100=[-1.3925233166621225706 ,.10156219814705360903] 
dist 101=[-1.4992740518399258961 ,-.07374374443243712738] 
dist 102=[-1.6154334000210520418 ,-.10456917454478962948] 
dist 103=[-1.7181787200125666147 ,-.09252183474670404805] 
dist 104=[-1.7714259036430788576 ,-.02948236450820864152] 
dist 105=[-1.7999625031156089724 ,.05330290095215533935] 
dist 106=[-1.8050671027378434063 ,.18434806974371433336] 
dist 107=[-1.7863641921065038517 ,.32218856509961433963] 
dist 108=[-1.7778905386875001369 ,.43208471579957215241] 
dist 109=[-1.7693417401977425839 ,.54226965803849226129] 
dist 110=[-1.7585245165715544624 ,.68127622122661396648] 
dist 111=[-1.2740472260746198690 ,.82776449971657357794] 
dist 112=[-1.2610455011838749972 ,.96780139152676461817] 
dist 113=[-1.3042420421233390748 ,1.1296208022314840315 ] 
dist 114=[-1.3219692709802760927 ,1.3630071266567739896 ] 
dist 115=[-1.3287716718111522325 ,1.5898661297936882247 ] 
dist 116=[-1.3283513967822662165 ,1.7256538753072618248 ] 
dist 117=[-1.2855680268133453652 ,1.8204643161106858996 ] 
dist 118=[-1.2718793472608201310 ,1.8838743920319437316 ] 
dist 119=[-1.2613527071540255811 ,1.9297422439704672061 ] 
dist 120=[-1.2524461996376642357 ,1.9545765849045303190 ] 
dist 121=[-.96940109586360138586,1.9687234283088415793 ] 
dist 122=[-.92953369624733416686,1.9719488566710964874 ] 
dist 123=[-.85059520636619197063,1.6795943400739802784 ] 
dist 124=[-.82909188791427341362,1.6352203959367956667 ] 
dist 125=[-.74822060777752465125,1.4841916118638769880 ] 
dist 126=[-.72912163508460280615,1.2470954755975334597 ] 
dist 127=[-.69398746396403611024,.94054692141229827601] 
dist 128=[-.68430439542691232249,.933412768225239579  ] 
dist 129=[-.7165907808273501562 ,.62477943771621892224] 
dist 130=[-.9239055832124687192 ,.65379437067247219859] 
dist 131=[-1.1088569595997866822 ,.78960330468928840656] 
dist 132=[-1.2361505227032762191 ,.91602793099400090747] 
dist 133=[-1.3452900785405011161 ,1.0264891383926193814 ] 
dist 134=[-1.4578335012860780879 ,1.0986134291071280353 ] 
dist 135=[-1.5582565510573730390 ,1.1563496478119184280 ] 
dist 136=[-1.6190519298519586420 ,1.2094110884562889912 ] 
dist 137=[-1.6623252169248370242 ,1.2542092922457452669 ] 
dist 138=[-1.6928560148260796041 ,1.2789805698143795330 ] 
dist 139=[-1.7127755364842136414 ,1.2937893068294234231 ] 
dist 140=[-1.7146302633415440234 ,1.2988441887538561874 ] 
dist 141=[-1.7070757662629951248 ,1.2972450321592321430 ] 
dist 142=[-1.6975386836136568702 ,1.2940386706361547492 ] 
dist 143=[-.83557928419678061023,1.2728826826221204932 ] 
dist 144=[-.7575253289041639686 ,1.2677225254725123685 ] 
dist 145=[-.57246959388305295178,.61631970622139431984] 
dist 146=[-.53987807491048608417,.55523458063723289698] 
dist 147=[-.30503053122083656509,.4134336711009947867 ] 
dist 148=[-.40129558286992020008,.50687406307039759623] 
dist 149=[-.53063995662881463927,.62448547841446954011] 
dist 150=[-.62687398774325785484,.76596306036264169108] 
dist 151=[-.71711655171208597452,.89808397152973223538] 
dist 152=[-.82256232635398896212,.97837550932798317494] 
dist 153=[-.91973030403309031922,1.0358818413846862925 ] 
dist 154=[-.97695058706018729877,1.0771236051315184145 ] 
dist 155=[-1.0157725298240105716 ,1.1076963051731536609 ] 
dist 156=[-1.0395418525054023351 ,1.1226474852658710919 ] 
dist 157=[-1.0552995111175162061 ,1.1289808202856296688 ] 
dist 158=[-1.0621604653520761802 ,1.1278721474587054677 ] 
dist 159=[-1.0638121940102133566 ,.3229449849895061087 ] 
dist 160=[-1.0610620902980691207 ,.3165091000037542364 ] 
dist 161=[-.14227887616797364277,.47849970485741546946] 
dist 162=[-.12833632537342042631,.58628029178312737372] 
dist 163=[-.11274052361665186909,.67477014052056221149] 
dist 164=[-.1246367225176821410 ,.75980948008541842417] 
dist 165=[-.1896778376684688801 ,.83590660052453492472] 
dist 166=[-.2706043642671037449 ,.88872547124352770908] 
dist 167=[-.3472852214183969672 ,.93449684596267043608] 
dist 168=[-.3953927680357077599 ,.9824806558722142054 ] 
dist 169=[-.4316741041902684336 ,1.0235529852445323106 ] 
dist 170=[-.4611853098971168613 ,1.0417541131849229166 ] 
dist 171=[-.54761009489605320252,1.0499864798658599103 ] 
dist 172=[-.64319788457191503253,1.0512957865679811050 ] 
dist 173=[-.75181633773155484747,1.0190887517647147746 ] 
dist 174=[-.90633147653193841668,1.0099446042013592035 ] 
dist 175=[-1.0566839168271874381 ,1.0037537834660109575 ] 
dist 176=[-1.1486983218830900666 ,1.0000014126396064141 ] 
dist 177=[-1.2154271725794549791 ,.93709739691932922916] 
dist 178=[-1.2649138698215964827 ,1.0001278370040500950 ] 
dist 179=[-1.3018579999823354816 ,1.0434356079209303304 ] 
dist 180=[-1.3185526081687042883 ,1.0709983502735468659 ] 
dist 181=[-1.3240535664668991767 ,1.0898109113675910797 ] 
dist 182=[-1.3231405759146101627 ,1.0982163499215878932 ] 
dist 183=[-1.2082997993105868105 ,1.1005847698825328341 ] 
dist 184=[-1.2389350424400734261 ,1.0980081768601263853 ] 
dist 185=[-1.2869090303436924337 ,.9531405637970526365 ] 
dist 186=[-1.3107103659958335557 ,.9298736323124444293 ] 
dist 187=[-1.3213196037931153569 ,.8871126327430780502 ] 
dist 188=[-1.3221267411478428398 ,.8749990812066618227 ] 
dist 189=[-1.3058637163702933566 ,.8288328635751894593 ] 
dist 190=[-1.2976266996191112176 ,.8157400079399905826 ] 
dist 191=[-1.2766456627173414884 ,.7914142510953628549 ] 
dist 192=[-1.2667459176678844140 ,.7836454973986732729 ] 
dist 193=[-.4044479741890715505 ,.69624985579821787946] 
dist 194=[-.39173826149790901717,.84293983674474865647] 
dist 195=[-.35841232590364205714,.97245345629931470055] 
dist 196=[-.35246872290309246309,1.0593105224046408682 ] 
dist 197=[-.29385061029252119192,1.1313769143273470143 ] 
dist 198=[-.28191796520907603128,1.2018905422982755371 ] 
dist 199=[-.26684838577741773093,1.2634146395837321133 ] 
dist 200=[-.26133244242527257802,1.2996217620286416602 ] 
dist 201=[-.14182437667206105073,1.3241441469167768613 ] 
dist 202=[-.12631043082056487652,1.3390577305222282472 ] 
dist 203=[-.09245010973653712414,1.3466179540201388180 ] 
dist 204=[-.08425506880434968507,1.3456683458782178265 ] 
dist 205=[-.04602796243097414824,1.3331519026519254507 ] 
dist 206=[-.03920805035994772060,1.3253715039704208678 ] 
dist 207=[-.10847468396919413764,.63478250486846010569] 
dist 208=[-.18855145496170913626,.5716040771043422457 ] 
dist 209=[-.25742640235025586214,.42354625990603344313] 
dist 210=[-.32882503259888233123,.39651347197920605783] 
dist 211=[-.40975602033836845697,.34953707921694314734] 
dist 212=[-.50826528390045335029,.38317247643787746582] 
dist 213=[-.60207766178771468302,.4141099575415323018 ] 
dist 214=[-.71374066732505976452,.43705455238749121682] 
dist 215=[-.81749089613638632726,.45849528645480531665] 
dist 216=[-.87973915541928111968,.48343368736734571794] 
dist 217=[-.92337995626616915959,.50622854278676662698] 
dist 218=[-.95290465569542848702,.51911831257523747601] 
dist 219=[-.97404195234555270755,.52719714392364990534] 
dist 220=[-.98422544181878724867,.53080028241772405911] 
dist 221=[-.98831466532834835002,.53124363378611778303] 
dist 222=[-.98660185313082144519,.53041295625396410262] 
dist 223=[-.25354842807485340461,.52175709554112139651] 
dist 224=[-.35803742819791782916,.52046781867625134923] 
dist 225=[-.46193419610683747759,.57033254738543280406] 
dist 226=[-.52994212555042032747,.6491005787706541806 ] 
dist 227=[-.58454341015505255178,.71989535361968699375] 
dist 228=[-.63496125677965481057,.76957101626128122836] 
dist 229=[-.67870267683540673183,.81318683268518167804] 
dist 230=[-.70667173658482443057,.85980956269608238127] 
dist 231=[-.72838476020975991146,.90025069357662766468] 
dist 232=[-.7471707890560059216 ,.91920851701578804677] 
dist 233=[-.76122508744933698689,.92842460951787026294] 
dist 234=[-.7643175557083228997 ,.93000567546704345945] 
dist 235=[-.7630390542897098635 ,.90658713453210002469] 
dist 236=[-.7616844140014307718 ,.89969309979229294826] 
dist 237=[-.7245728141729759524 ,.89482117168819125267] 
dist 238=[-.7140530415284616891 ,.8914503730173885966 ] 
dist 239=[-.7061232244218907475 ,.89395545447838248623] 
dist 240=[-.7009796446592919303 ,.96076022448542258954] 
dist 241=[-.69207908088070725838,1.0079754260259775721 ] 
dist 242=[-.7995291836367676262 ,1.0406491670005260528 ] 
dist 243=[-.89407778053527223501,1.0640370561459164703 ] 
dist 244=[-.95690665576509285886,1.0742121074179310986 ] 
dist 245=[-1.0083983127791025034 ,1.0766343088280489298 ] 
dist 246=[-1.0577234223428658955 ,1.0751385003169741195 ] 
dist 247=[-1.0995469023162184352 ,.9585449160646868098 ] 
dist 248=[-1.1211151769673958137 ,.9271383100471807451 ] 
dist 249=[-1.1319305400579924072 ,.7747247549538995900 ] 
dist 250=[-1.1325776675451683768 ,.7608083739884194914 ] 
dist 251=[-1.1241670081854372546 ,.7396700791693820119 ] 
dist 252=[-1.1185681480226646991 ,.6927787187192700736 ] 
dist 253=[-1.0999986152398288744 ,.4593993867796935163 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 2, 2, 1, 0, 2] 
dist 0=[56.558763135924929915  ,56.558763135924929915  ] 
dist 1=[55.521962556566952724  ,56.963576988748093973  ] 
dist 2=[53.836855913170854243  ,57.543087066746144747  ] 
dist 3=[51.033347937952105272  ,58.146667952495106957  ] 
dist 4=[48.122861269383828079  ,58.432683839260375478  ] 
dist 5=[46.010563803317954317  ,58.541367010856301244  ] 
dist 6=[44.075148386761124107  ,58.509813760229786472  ] 
dist 7=[41.870798011150849200  ,58.172725840244763443  ] 
dist 8=[39.657640315233398605  ,55.217897325604927861  ] 
dist 9=[37.686921713624778508  ,54.389052732359016334  ] 
dist 10=[35.512529619040053107  ,54.144145178365583051  ] 
dist 11=[32.485848334717484313  ,53.249910397504421190  ] 
dist 12=[29.437358015857957422  ,52.965917860627658472  ] 
dist 13=[27.175700974034601252  ,52.458990262662338256  ] 
dist 14=[25.052146373287305078  ,52.290652757394961817  ] 
dist 15=[22.554809497047281650  ,51.418295057048267513  ] 
dist 16=[20.000135557742367807  ,29.971005559621125457  ] 
dist 17=[17.647222707648972618  ,25.785968403781554299  ] 
dist 18=[14.984146576423645177  ,25.170719970279859270  ] 
dist 19=[11.190047517035684593  ,23.496364649930813616  ] 
dist 20=[7.4382049749635841976 ,18.334740589026885625  ] 
dist 21=[4.9437898497286994937 ,17.031108107282350036  ] 
dist 22=[2.8844851697556117444 ,16.768971585191716860  ] 
dist 23=[.87077583367141918184,10.694258331430381190  ] 
dist 24=[-.96786584793628467354,8.0205151502237407656 ] 
dist 25=[-2.3394850289629593745 ,7.1236540321199622521 ] 
dist 26=[-4.1369086680558998616 ,5.8289087753250642385 ] 
dist 27=[-5.9305113289232427743 ,4.2670530436470561607 ] 
dist 28=[-7.5956313941809972482 ,3.3022094500537178435 ] 
dist 29=[-8.8808645452667945726 ,2.6864191527837550481 ] 
dist 30=[-10.143722118241460063  ,2.5647658025148998916 ] 
dist 31=[-11.721411182148077280  ,-2.3869634851430269047 ] 
dist 32=[-13.193479114290017249  ,-2.6863668449830915650 ] 
dist 33=[-14.034685149693129922  ,-2.0216740306696302651 ] 
dist 34=[-14.585561669486540862  ,-1.0948480445496573936 ] 
dist 35=[-14.896706022158103459  ,.42454737627976752289] 
dist 36=[-15.094428491627970623  ,1.9658127394134546187 ] 
dist 37=[-15.191292802441803780  ,2.9800827098250665847 ] 
dist 38=[-15.236604218410890033  ,3.7976502964918514996 ] 
dist 39=[-15.226779617008432035  ,4.5549172649689916403 ] 
dist 40=[-13.162888470662571130  ,5.2110871867605002491 ] 
dist 41=[-12.860395598583351756  ,5.6256421681084463972 ] 
dist 42=[-12.305130487774037460  ,5.9404722623040397812 ] 
dist 43=[-12.156875493309539661  ,6.1989881850996400322 ] 
dist 44=[-11.640624015184282761  ,6.4132044342875603146 ] 
dist 45=[-11.489849280501452274  ,6.5514165353184216512 ] 
dist 46=[-11.328252298933080820  ,6.6593525174258968475 ] 
dist 47=[-11.246037410815116172  ,6.7529334367339538095 ] 
dist 48=[-3.0544559625242023362 ,6.8290656610554027400 ] 
dist 49=[-2.9245767545892243404 ,6.8674375778624620302 ] 
dist 50=[-2.6253623982175537846 ,6.8848918903581939727 ] 
dist 51=[-2.5560693398236122704 ,6.8775706402249202693 ] 
dist 52=[1.2687733843044991824 ,7.0781249991352268495 ] 
dist 53=[1.6060068324780791534 ,7.4264617970870288881 ] 
dist 54=[2.3572349066244482745 ,7.7089396436223948152 ] 
dist 55=[2.4742765722087326362 ,7.9379565687443258976 ] 
dist 56=[3.3068608239116630728 ,8.7418995557440567681 ] 
dist 57=[3.4353734761749638721 ,9.4235444630539587306 ] 
dist 58=[3.6654888902839253803 ,9.9376130061292986662 ] 
dist 59=[3.7054131409057774653 ,10.358007546282495587  ] 
dist 60=[3.5009120119912325520 ,10.686521738714330796  ] 
dist 61=[2.8952376301203148807 ,10.833831050384707520  ] 
dist 62=[2.0712931774294733407 ,10.893262715158261200  ] 
dist 63=[.73621113714125972268,10.884305685157895165  ] 
dist 64=[-.64073729512019155857,4.5742585527615537900 ] 
dist 65=[-1.6834657309453999067 ,4.5693416679631534530 ] 
dist 66=[-2.5419432857497202158 ,4.5428105702888523521 ] 
dist 67=[-3.3714412610383407084 ,4.5199601959811186529 ] 
dist 68=[-4.1172890157671937228 ,2.0016014678742544900 ] 
dist 69=[-4.6420845986891058514 ,1.7790833826976179243 ] 
dist 70=[-5.1047654610952396993 ,1.2609567614550777529 ] 
dist 71=[-5.6028622658014314293 ,1.1673470082949177301 ] 
dist 72=[-6.0507194100950436100 ,.48503882828589905254] 
dist 73=[-6.3129818467310574393 ,.36297962382935769983] 
dist 74=[-6.4893355673044937638 ,.15280400463834848776] 
dist 75=[-6.5944429439293311132 ,.10604833767486026248] 
dist 76=[-6.6520534197922108056 ,-.61229996837849709504] 
dist 77=[-6.6547146968882273409 ,-.70856625663889757074] 
dist 78=[-6.6032296888607398805 ,-.88184800077083176166] 
dist 79=[-6.5710067131206149229 ,-.4463196275269566357 ] 
dist 80=[-4.0289073878250172163 ,.09227562546374062608] 
dist 81=[-3.7762182445408989643 ,.56021369603716414296] 
dist 82=[-3.1542122455053848444 ,1.0291510131782393368 ] 
dist 83=[-3.1376419754244533357 ,1.4615022821141365058 ] 
dist 84=[-2.1091291358152560518 ,1.9472087883311978905 ] 
dist 85=[-1.9309727146243947666 ,2.3701873491644808033 ] 
dist 86=[-1.6885387360014502213 ,2.7596270842910517768 ] 
dist 87=[-1.6129789186015290836 ,3.2039579987725232643 ] 
dist 88=[-.38241090452989452513,3.6132140904650606214 ] 
dist 89=[-.37230558705468602449,3.8627586557968903894 ] 
dist 90=[-.37952930551727142848,4.0426336496861490802 ] 
dist 91=[-.41232617423872365736,4.1739867036756122358 ] 
dist 92=[-.45517400351341369   ,4.2661116600110536775 ] 
dist 93=[-.50248515260267635417,4.2895087975320877453 ] 
dist 94=[-.56203940244407163715,4.2875911055189616741 ] 
dist 95=[-.7154077635770470790 ,4.2787233300925651397 ] 
dist 96=[-.9908045374559863229 ,2.3843105224209082645 ] 
dist 97=[-1.2135869792592735067 ,2.3205206083481195526 ] 
dist 98=[-1.4219545122426568176 ,2.3067511477744556079 ] 
dist 99=[-1.6043975192858133415 ,2.1418166912592788301 ] 
dist 100=[-1.7237738288943927643 ,2.2532374073834372113 ] 
dist 101=[-1.8194474806666249592 ,2.3983471119332482527 ] 
dist 102=[-1.9073374931134118269 ,2.4975952196493295594 ] 
dist 103=[-1.9823090102556387290 ,2.5600012279511554445 ] 
dist 104=[-2.0264536693785192911 ,2.6020659170516535829 ] 
dist 105=[-2.0562688350025288274 ,2.6201616180901269706 ] 
dist 106=[-2.0740916833249953312 ,2.6241570742529611830 ] 
dist 107=[-2.0826602132088361854 ,2.6179855512744638986 ] 
dist 108=[-2.0791550974748943641 ,2.2810846214625082278 ] 
dist 109=[-2.0701556607206146233 ,2.2269574752268219099 ] 
dist 110=[-2.0845116077540514084 ,2.1260231085057603629 ] 
dist 111=[-2.0833124055306277194 ,2.0971467438575019235 ] 
dist 112=[-1.6770332112742172838 ,1.9850041977453531169 ] 
dist 113=[-1.6523441230788864799 ,1.9542148732004258671 ] 
dist 114=[-1.5999466497091164578 ,1.8937820773381620242 ] 
dist 115=[-1.5817836759232201011 ,1.8740288253339369267 ] 
dist 116=[-1.2233639124123847583 ,.67375714655703261117] 
dist 117=[-1.1790016304183141583 ,.69863925143549519863] 
dist 118=[-1.3103155002977241546 ,.71256310734855236062] 
dist 119=[-1.5895442832702765147 ,.71590141170431774842] 
dist 120=[-1.8364376165254193791 ,.70897144753574065458] 
dist 121=[-2.0027232056238166618 ,.7060373460893804114 ] 
dist 122=[-2.1414953461777129799 ,.77952314309787914697] 
dist 123=[-2.2786359397522902917 ,.87726654942760680666] 
dist 124=[-2.3986309107672240066 ,.96553280226688724897] 
dist 125=[-2.4690069673672873868 ,1.0282989494329771098 ] 
dist 126=[-2.5163896130478239977 ,1.0843809810495309067 ] 
dist 127=[-2.5446590106319239258 ,1.1460335408026034624 ] 
dist 128=[-2.5584266702163283766 ,1.3284888964023323386 ] 
dist 129=[-2.5569069481417454617 ,1.5097783956671585696 ] 
dist 130=[-2.5309273966961351171 ,1.6635662681695265779 ] 
dist 131=[-2.5185055983341341883 ,1.8197064989944440617 ] 
dist 132=[-1.2524595568159159810 ,1.9651120944822482754 ] 
dist 133=[-1.1356812847875164174 ,2.0760681744861615701 ] 
dist 134=[-.86060866601750008992,2.1828546826264194083 ] 
dist 135=[-.82608520484915219942,2.3116171938806175099 ] 
dist 136=[-.9933835234383131416 ,2.4317146174682641742 ] 
dist 137=[-1.1117591220762956618 ,2.5039273533284010999 ] 
dist 138=[-1.2166823256782450936 ,2.5547464424305089286 ] 
dist 139=[-1.3303411837583230170 ,2.5894895812567003246 ] 
dist 140=[-1.4406313894013522801 ,2.6111112063807026675 ] 
dist 141=[-1.5321323627757412686 ,2.6104468460438228641 ] 
dist 142=[-1.6272409175219572514 ,2.5974583208034451032 ] 
dist 143=[-1.7519447081125021008 ,2.5841768438659683951 ] 
dist 144=[-2.3892405163553323558 ,2.4883118212357412256 ] 
dist 145=[-2.8096344553301764387 ,2.4610430695147616212 ] 
dist 146=[-3.1391506219201748693 ,2.3956926531267626415 ] 
dist 147=[-3.4298445641108805373 ,2.3701130517845322325 ] 
dist 148=[-3.6726444567149334801 ,2.2351947304888793649 ] 
dist 149=[-3.8111170641654402473 ,2.2022216775001690626 ] 
dist 150=[-3.8994425815754756424 ,2.1185957483031672566 ] 
dist 151=[-3.9422166501745812448 ,2.0875767547163845907 ] 
dist 152=[-3.9620257501348929817 ,1.8689607657248128857 ] 
dist 153=[-3.9587433940642132172 ,1.8395756449235289501 ] 
dist 154=[-3.9379704703674505289 ,1.8026804998373747955 ] 
dist 155=[-3.9236434917684357023 ,1.7858311121211261036 ] 
dist 156=[-3.8240418256080232458 ,1.7512575806989543564 ] 
dist 157=[-3.7950754165442649024 ,1.7356179418783352520 ] 
dist 158=[-3.6821196870251753454 ,1.7231107309379879751 ] 
dist 159=[-3.6627282747991665846 ,1.7116474636578442785 ] 
dist 160=[-.94778684141829373212,.84726108166470713429] 
dist 161=[-1.0712225588309165438 ,.92684333265556624451] 
dist 162=[-1.2416796198374721754 ,1.0213044916095310028 ] 
dist 163=[-1.4845469841390791556 ,1.1604968010701756792 ] 
dist 164=[-1.7206689402221807106 ,1.2969675467939012993 ] 
dist 165=[-1.8642182783543327287 ,1.3805721435630213373 ] 
dist 166=[-1.9671795345530731409 ,1.4412812806434359149 ] 
dist 167=[-2.0413898354616945016 ,1.4864234932374381356 ] 
dist 168=[-2.0962684297569086581 ,1.5183758046304894549 ] 
dist 169=[-2.1221115537198888372 ,1.5264709823008283522 ] 
dist 170=[-2.1315888589660248879 ,1.5261681567797589975 ] 
dist 171=[-2.1298337096157913877 ,1.5246225596534249073 ] 
dist 172=[-1.9163649685764101916 ,1.4340329586110523908 ] 
dist 173=[-1.8793587031043039136 ,1.4149003334801030171 ] 
dist 174=[-1.8126228385839183429 ,1.3666402113210909561 ] 
dist 175=[-1.7929985991594218697 ,1.3484516512311234550 ] 
dist 176=[-1.7154777027087356249 ,1.2546858075015359595 ] 
dist 177=[-1.6926644694388608096 ,1.2322171291523366803 ] 
dist 178=[-1.6466457255629682621 ,1.1837730201790704033 ] 
dist 179=[-1.6306819153006733521 ,1.1676565807564399608 ] 
dist 180=[.18591688119439070573,.80411449158545416124] 
dist 181=[.10829400927985952132,.83210657668488748918] 
dist 182=[.02402457405199299352,.99450743846046445096] 
dist 183=[-.09109707884971081342,1.2229689440220166940 ] 
dist 184=[-.20526372633862427674,1.4244761312473969837 ] 
dist 185=[-.28572631054799043202,1.5593045708833849866 ] 
dist 186=[-.35674299584095139659,1.6708496062402909433 ] 
dist 187=[-.43323442168486464969,1.7794757772741247515 ] 
dist 188=[-.50720973149681761805,1.8748002570577845536 ] 
dist 189=[-.56819327429283063266,1.9332827211902844322 ] 
dist 190=[-.631230594035428862  ,1.9758629228455907862 ] 
dist 191=[-.71340469694436681978,2.0077505405945468402 ] 
dist 192=[-.79254470006813659592,2.0302455595974169616 ] 
dist 193=[-.85642311500885268705,2.0353568042201790560 ] 
dist 194=[-.92383514397545679824,2.0297081861907796880 ] 
dist 195=[-.98990216117822979745,2.0234723887446912341 ] 
dist 196=[-1.0499193052315554565 ,.88179115209639043822] 
dist 197=[-1.0931955102926438458 ,.78331221152041186128] 
dist 198=[-1.1324280788680359167 ,.55000409470466403524] 
dist 199=[-1.1763133516397690951 ,.51100259871596806362] 
dist 200=[-1.2155296734205870459 ,.19194191662275460832] 
dist 201=[-1.2361355164257199946 ,.13457129302773854188] 
dist 202=[-1.2470230200613660086 ,.04749302295926573227] 
dist 203=[-1.2474679760273110230 ,.02496227159126106862] 
dist 204=[-1.2415973206078378121 ,.03537861895991401745] 
dist 205=[-1.2371230758693899425 ,.19304276124390821733] 
dist 206=[-1.2131640141562158541 ,.38020749626853539767] 
dist 207=[-1.2080144845427140512 ,.65607288431308324209] 
dist 208=[-1.1740867515914015035 ,.92991746048051423092] 
dist 209=[-1.1773092280148210159 ,1.1090218650139817118 ] 
dist 210=[-1.1718766524064132492 ,1.2526775669814029124 ] 
dist 211=[-1.1693920986831544426 ,1.3851148596118486637 ] 
dist 212=[-.52450546199998602658,1.4998938183943172380 ] 
dist 213=[-.51064491161697231248,1.5731097447918111128 ] 
dist 214=[-.48344410917226818225,1.6297650507043239408 ] 
dist 215=[-.47549477833647928298,1.6784841004228005344 ] 
dist 216=[-.44495468457593054739,1.7164207590445757618 ] 
dist 217=[-.43795204833693144945,1.7300639793350632815 ] 
dist 218=[-.3947942136446124047 ,1.7320533354087917133 ] 
dist 219=[-.31924744346013809698,1.7271904202915946983 ] 
dist 220=[.18765464170959335189,1.6775495537854343670 ] 
dist 221=[.23918620488625502947,1.6608965313864081994 ] 
dist 222=[.17867952889853667982,1.6298556388048230845 ] 
dist 223=[-.21964513555947436785,1.6182770591025049479 ] 
dist 224=[-.61824242880814519811,1.5857949735292375632 ] 
dist 225=[-.88110556945829630013,1.5754295428854172740 ] 
dist 226=[-1.0943496638238820186 ,1.5648075664113724957 ] 
dist 227=[-1.2950147453079683275 ,1.5553526685320234365 ] 
dist 228=[-1.4717398695337832907 ,1.2505922619863120372 ] 
dist 229=[-1.5894865727604766401 ,1.2078328472093405316 ] 
dist 230=[-1.6863417648781685553 ,1.1079306696117061040 ] 
dist 231=[-1.7797298410057586031 ,1.0804636995029676013 ] 
dist 232=[-1.8602316308273372069 ,.93501447899823459611] 
dist 233=[-1.9056829129593124997 ,.90497412114755219766] 
dist 234=[-1.9340714764359086019 ,.84164396636205135142] 
dist 235=[-1.9465093827590442042 ,.8228591009399433129 ] 
dist 236=[-1.9477130264138616338 ,.59435555879335656717] 
dist 237=[-1.9443226690978192416 ,.55984172460632658177] 
dist 238=[-1.9107315814378032167 ,.48070463172878604495] 
dist 239=[-1.8277411965031215353 ,.46199527236977099819] 
dist 240=[-1.4996617116947690381 ,.35681405929398439127] 
dist 241=[-1.4917702704313076745 ,.3366738372929963307 ] 
dist 242=[-1.4811464725333749988 ,.29516867400509523986] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 2, 2, 1, 0, 1] 
dist 0=[54.167778072245186969  ,54.167778072245186969  ] 
dist 1=[53.753308574023101217  ,54.815853365674779198  ] 
dist 2=[52.746231727429796720  ,55.484649886202534421  ] 
dist 3=[51.120575148792121027  ,55.790773968081568656  ] 
dist 4=[48.459087117122914584  ,55.903174471335192584  ] 
dist 5=[45.705667974054210974  ,55.892120211409832875  ] 
dist 6=[43.712845678489976802  ,55.490648211101083024  ] 
dist 7=[41.891085218928731828  ,54.932332754667947683  ] 
dist 8=[39.820760331034305713  ,53.209248496486147121  ] 
dist 9=[37.743226465878515232  ,53.021109205972042700  ] 
dist 10=[35.892611482651050032  ,52.225813824669899399  ] 
dist 11=[33.849213446221582467  ,51.991965971102559143  ] 
dist 12=[31.001638578888782391  ,51.439141444210917225  ] 
dist 13=[28.129987652989198608  ,51.227993248924622505  ] 
dist 14=[25.990326553313035604  ,50.201185816157754569  ] 
dist 15=[23.971425117025378772  ,49.078187930856153973  ] 
dist 16=[21.581839821125232126  ,29.487464139169398143  ] 
dist 17=[19.128232726463996459  ,28.969317006993600868  ] 
dist 18=[16.853360092279694290  ,24.126799783098648863  ] 
dist 19=[14.266240882433653663  ,23.452977339783135369  ] 
dist 20=[10.564961017384895326  ,23.288691436806852457  ] 
dist 21=[6.9113871775483364931 ,21.506167415180054634  ] 
dist 22=[4.5146872268650381077 ,13.492920553748344586  ] 
dist 23=[2.5713309692601632235 ,12.518947971759673793  ] 
dist 24=[.7286200690216030005 ,10.518634080732167626  ] 
dist 25=[-.91697475693855199196,10.009762130647200068  ] 
dist 26=[-2.6620224008208145957 ,8.8920297839099637689 ] 
dist 27=[-4.6225397977135100273 ,7.8551115794013798308 ] 
dist 28=[-6.4935940036894612573 ,7.3568526905531451339 ] 
dist 29=[-8.0196044380501608339 ,7.2428948082640510991 ] 
dist 30=[-9.5939595819628351546 ,-1.7843663401655558048 ] 
dist 31=[-11.659529002672198662  ,-3.1684133988468800618 ] 
dist 32=[-13.625897563311834410  ,-4.8083486256979857150 ] 
dist 33=[-14.804201536909067196  ,-5.1536515232859314776 ] 
dist 34=[-15.640313858984886830  ,-5.3457218473092937248 ] 
dist 35=[-16.239007733754340294  ,-4.8496325255494442657 ] 
dist 36=[-16.679934180662770203  ,-3.9573387902863805785 ] 
dist 37=[-16.885199282660764740  ,-3.0251410263446702207 ] 
dist 38=[-16.960466416005081044  ,-2.3696670121937492548 ] 
dist 39=[-16.954033792367749313  ,-1.7954158904286576407 ] 
dist 40=[-15.572196101584227828  ,-1.1866047952984885081 ] 
dist 41=[-15.332531148409830327  ,-.60609435519677545555] 
dist 42=[-14.877561291733611378  ,-.14448220991548389571] 
dist 43=[-14.739978276493396378  ,.31626338123647386358] 
dist 44=[-14.170909409357403455  ,.89346519278725864973] 
dist 45=[-14.017715765355068003  ,1.5642810285630883189 ] 
dist 46=[-13.674006575893313331  ,3.9093023175185467605 ] 
dist 47=[-13.552154606332483834  ,5.4869306247799729376 ] 
dist 48=[-4.2437554437211659740 ,6.8034886440839140264 ] 
dist 49=[-3.4205422048755900821 ,8.1067967059968478240 ] 
dist 50=[-1.6099345914578355066 ,9.3009897869941289502 ] 
dist 51=[-1.2364742004874957591 ,10.182173222851670225  ] 
dist 52=[.80530886445274615498,11.002499599667370579  ] 
dist 53=[1.1520619634609354928 ,11.953907085843686008  ] 
dist 54=[1.0059069649774062892 ,12.824830629049234316  ] 
dist 55=[.86606638246957896845,13.323995137192353928  ] 
dist 56=[.70774115174602565781,13.646427827918641946  ] 
dist 57=[.55097019198130539008,13.812070404801803301  ] 
dist 58=[.41724447028784138144,13.894119534672230025  ] 
dist 59=[.27554315198133055184,13.882890062841809173  ] 
dist 60=[.08689671578704747168,13.819399263610864488  ] 
dist 61=[-.09724931596165749725,13.692902381751334858  ] 
dist 62=[-.2210554839704083496 ,12.243961211889687286  ] 
dist 63=[-.32391542298117960998,11.746243029346546513  ] 
dist 64=[-1.1712570063835143563 ,1.2328365867298493552 ] 
dist 65=[-2.0038480552995594133 ,1.2585555235646049275 ] 
dist 66=[-2.6747241692007223233 ,1.2871213649607100124 ] 
dist 67=[-3.2987424091105907550 ,1.3230195653920458419 ] 
dist 68=[-3.8437575773902924097 ,1.3778833748850062023 ] 
dist 69=[-4.1994986876677886330 ,1.4309118587922468453 ] 
dist 70=[-4.4843226927387401971 ,1.4594682044749694806 ] 
dist 71=[-4.7464841712587407964 ,1.4751836119515370067 ] 
dist 72=[-4.9720351271487296978 ,1.4770320451367705798 ] 
dist 73=[-5.1108069502949116642 ,1.4717079423914645713 ] 
dist 74=[-5.2126099100970401239 ,1.4658220064521757941 ] 
dist 75=[-5.2906207278605882082 ,1.4442781637509645684 ] 
dist 76=[-5.3474328419032349603 ,1.4325574439937081611 ] 
dist 77=[-5.3646359963843786337 ,1.2723650009626179750 ] 
dist 78=[-5.3561853160994605765 ,1.2441661411875956738 ] 
dist 79=[-5.3394264041405554201 ,1.1746484320378716108 ] 
dist 80=[-2.0886410232671047087 ,1.1534063644048781420 ] 
dist 81=[-2.0159871343123341344 ,1.0336750367635546257 ] 
dist 82=[-1.9944362913002728720 ,1.0068635344132887753 ] 
dist 83=[-1.9408008366259047027 ,.95388891143348852376] 
dist 84=[-1.9197839090941047456 ,1.0068535949178360443 ] 
dist 85=[.04380883037606305622,1.4235821182785070304 ] 
dist 86=[.3084388666414680658 ,1.8342712149346044563 ] 
dist 87=[.36654696067887414334,2.3428027223401906303 ] 
dist 88=[.9276833533614968995 ,2.8235149253167940423 ] 
dist 89=[.918818603646218479  ,3.1232433603544709456 ] 
dist 90=[.88526264520720244336,3.3471325746420756015 ] 
dist 91=[.82730335913002455573,3.5253396838907458394 ] 
dist 92=[.72111892131027891312,3.6624597700559489742 ] 
dist 93=[.6039047404666427923 ,3.7224633463097764100 ] 
dist 94=[.50195888870956248634,3.7474248921511448531 ] 
dist 95=[.3919876208344909342 ,3.7447653706367895128 ] 
dist 96=[.24276765610804320852,2.1027423279782462101 ] 
dist 97=[.00502592910137473941,2.1269696259588820397 ] 
dist 98=[-.27074396874985940563,2.1323476173069207722 ] 
dist 99=[-.5476045012277643733 ,2.1261864850297656198 ] 
dist 100=[-.80307098019222076969,2.1193430525509808428 ] 
dist 101=[-.99352148543394107282,.89647639741639605031] 
dist 102=[-1.1723247031376561082 ,.79076551942204337355] 
dist 103=[-1.3813474827034079782 ,.5438110587968935081 ] 
dist 104=[-1.5746752183252000869 ,.49991505642987220466] 
dist 105=[-1.6908825651415883253 ,.17293637879760208698] 
dist 106=[-1.7725714624309206599 ,.14477295500475914985] 
dist 107=[-1.8282222396238447784 ,.139536204356031965  ] 
dist 108=[-1.8670154878060633043 ,.15107756276014835363] 
dist 109=[-1.8814694125944305484 ,.17094429590159977199] 
dist 110=[-1.8822251547152060091 ,.19891254711391849555] 
dist 111=[-1.8778172416920717770 ,.23812423000714180028] 
dist 112=[-1.5750739149773862497 ,.41243146800744602158] 
dist 113=[-1.5742618714499760026 ,.56939210827878957204] 
dist 114=[-1.5533554826014639087 ,.69694079113123090713] 
dist 115=[-1.5490032573467363534 ,.81716329583547462606] 
dist 116=[-1.4456135126623898789 ,.92303528948153890395] 
dist 117=[-1.4194692938579635828 ,.99334953904053606463] 
dist 118=[-1.4001001256530727807 ,1.0508603209248665611 ] 
dist 119=[-1.3919281160104108436 ,1.1056645272515250555 ] 
dist 120=[-.98230007101310137166,1.1525090861776674342 ] 
dist 121=[-.92769663792394496495,1.1782736995496575096 ] 
dist 122=[-.81965301710847543436,1.1934238779163437376 ] 
dist 123=[-.79115358154450491752,1.1979365592511385684 ] 
dist 124=[-.6885423414943084574 ,1.1951994804887029437 ] 
dist 125=[-.66453492735875004784,1.0645213571759850506 ] 
dist 126=[-.62978786415794325356,1.0422171374497381108 ] 
dist 127=[-.61879338330894124826,.92899544460116937161] 
dist 128=[-.25848704977703375516,.59657831379712601606] 
dist 129=[-.2981883913579280542 ,.77585830786110990195] 
dist 130=[-.34257251678539101258,.91871342017339489759] 
dist 131=[-.39877503014309874704,1.0488569513898445982 ] 
dist 132=[-.48561226289403624793,1.1606012223511549206 ] 
dist 133=[-.57226806388566262911,1.2300570344931281273 ] 
dist 134=[-.62774586478138003857,1.2817265373411904678 ] 
dist 135=[-.67086605340554033535,1.3225180880224601426 ] 
dist 136=[-.70823209983272901538,1.3548361176252399427 ] 
dist 137=[-.73891467982512160924,1.3727021620947128573 ] 
dist 138=[-.75537635155453778684,1.3833861171828067710 ] 
dist 139=[-.76452113150231470101,1.3870503348293252139 ] 
dist 140=[-.76601726107830325249,1.3859300466921929927 ] 
dist 141=[-.76335663567810199787,1.3811384591017217314 ] 
dist 142=[-.76051934885958572699,1.3659775851587317820 ] 
dist 143=[-.74788216249030575264,1.3571473908495705143 ] 
dist 144=[-.74282104376404945471,.96839025467517784021] 
dist 145=[-.6982416798595718447 ,.91247966150910021438] 
dist 146=[-.68666092754803311603,.8984987418475470069 ] 
dist 147=[-.67031682217890560258,.86462427176651708   ] 
dist 148=[-.66386895958284074972,.85244927176380165743] 
dist 149=[-.65068200114683116199,-.00235665678339977017] 
dist 150=[-.75894324989296372863,-.07377272398205314292] 
dist 151=[-.88945914579109635449,-.09102775966497717128] 
dist 152=[-1.0111707012775927829 ,-.249142407296671864  ] 
dist 153=[-1.0843105815967608982 ,-.27369683301957063792] 
dist 154=[-1.1357428495683659411 ,-.29659916945979542188] 
dist 155=[-1.1708595022436464641 ,-.2915782509116562804 ] 
dist 156=[-1.1957967590707017597 ,-.27411142534304038066] 
dist 157=[-1.2066213351971710409 ,-.23944196210673125515] 
dist 158=[-1.2091636129466408802 ,-.18560730405374245782] 
dist 159=[-1.2073184833189422756 ,-.09168852741190102074] 
dist 160=[-1.1986079294383232333 ,.02186195629232493158] 
dist 161=[-1.2062628494614216553 ,.14990399490952860604] 
dist 162=[-1.2053177495371242831 ,.25779940217490343704] 
dist 163=[-1.1993368742961180942 ,.36609113532365015361] 
dist 164=[-1.1942059740976659915 ,.46607328859951989046] 
dist 165=[-.48532979910592651041,.54082218058694517734] 
dist 166=[-.42359081624997702621,.61124697396402671322] 
dist 167=[-.28032450172245916561,.69398064121066742573] 
dist 168=[-.25441878759644353863,.77000554241287789775] 
dist 169=[-.06766983570882349778,.81366929772009784812] 
dist 170=[-.03445794313463678915,.8419001694097478447 ] 
dist 171=[.02351296170081057809,.85636364182327683946] 
dist 172=[.03610568334007228194,.86481086383377005226] 
dist 173=[.01853042126357986299,.86904331007265898819] 
dist 174=[-.04873454324747297979,.87099203338877711232] 
dist 175=[-.15301836234522721966,.87033031395404157424] 
dist 176=[-.25737279394791515272,.82856471598622942455] 
dist 177=[-.3249196132011658263 ,.85282417696219684195] 
dist 178=[-.37829700122151296466,.86490944519774116992] 
dist 179=[-.42613066752343688562,.87036918908511949125] 
dist 180=[-.46661697897661021299,.86977734306386809781] 
dist 181=[-.49068636203122035246,.53110739234760502715] 
dist 182=[-.50728928271877695362,.52272161428603578955] 
dist 183=[-.5226378541940250500 ,.51847641703344007489] 
dist 184=[-.5587893179876300021 ,.37081047418052636294] 
dist 185=[-.61763525956181368764,.35075968841988125683] 
dist 186=[-.66668296596445604942,.31065512415410184223] 
dist 187=[-.71030300205313546033,.2998965844620370756 ] 
dist 188=[-.75780272695093440937,.26000544862985959096] 
dist 189=[-.79951613645740672889,.25090558531397482143] 
dist 190=[-.82005434124522701376,.23491410502948820958] 
dist 191=[-.83076645115399794108,.23082561907495233618] 
dist 192=[-.83328158999731937535,.1493079246464010831 ] 
dist 193=[-.81637429817978945842,.1792308208052056856 ] 
dist 194=[-.81187258012707269942,.2120214463736572327 ] 
dist 195=[-.80907062982069489562,.2531245406498897098 ] 
dist 196=[-.80786536509680871269,.3162070134192301032 ] 
dist 197=[-.70352390011095161933,.3791069824790107983 ] 
dist 198=[-.74508121892144562623,.43485085390325037363] 
dist 199=[-.77351456832157227973,.53269903317552310429] 
dist 200=[-.79137459575563679014,.62490555108386429351] 
dist 201=[-.80304797815452823768,.70619523283253922739] 
dist 202=[-.8068038859386238304 ,.76049617496831784112] 
dist 203=[-.80566028349466649066,.80531373314396495816] 
dist 204=[-.80366227557623466462,.84877412130976184076] 
dist 205=[-.7095446507546068444 ,.88609366313478030834] 
dist 206=[-.6937982755889320525 ,.90641561545210675978] 
dist 207=[-.6620134443073255753 ,.9181365625046471184 ] 
dist 208=[-.6522369605105660516 ,.92114744913884668492] 
dist 209=[-.6097457828855479240 ,.91906186346776143519] 
dist 210=[-.5997545091022749874 ,.91618106828826572804] 
dist 211=[-.5730279328779866978 ,.90108748510261023698] 
dist 212=[-.5654500126069423967 ,.89598494817520247292] 
dist 213=[-.28118084302370737792,.39987077189699181405] 
dist 214=[-.26303636157241147076,.4250988403654355438 ] 
dist 215=[-.25768068356851598207,.44907623308733574732] 
dist 216=[-.14759628819414635653,.46980062106974522246] 
dist 217=[-.13305253839452894058,.48205149090352570521] 
dist 218=[-.1131720841374990772 ,.49042427570033856994] 
dist 219=[-.15126699824383895693,.49567590599734590369] 
dist 220=[-.19056578692254145515,.49850941121887088256] 
dist 221=[-.22690622460750408939,.49802731683111351217] 
dist 222=[-.26796829666730800324,.49432138044032457463] 
dist 223=[-.32610419358674453517,.49138032478140122747] 
dist 224=[-.39664664789634072731,.40455965644022316005] 
dist 225=[-.46111878202623644475,.38763796607856227226] 
dist 226=[-.51509515338114293943,.38271355729942969082] 
dist 227=[-.5687047901754965989 ,.37191215862038388589] 
dist 228=[-.61784191301858499054,.36798616357173154305] 
dist 229=[-.65397702074884553184,.2412705305725585537 ] 
dist 230=[-.68743377841220632389,.27681491171267854977] 
dist 231=[-.72588644783439239908,.32736484930341515256] 
dist 232=[-.76077634787749609452,.37838302146023482843] 
dist 233=[-.78002092285198363692,.41579593923981301177] 
dist 234=[-.79144958957670153697,.45032765207670060945] 
dist 235=[-.79516147729880721414,.48985425768010714957] 
dist 236=[-.79434052604811750448,.52946627366001758128] 
dist 237=[-.79211939242899010518,.56433977135615836015] 
dist 238=[-.7800860643000289469 ,.60235140813361874488] 
dist 239=[-.77547544185290396775,.65448308878357094798] 
dist 240=[-.7004734275100048808 ,.70406061925857883295] 
dist 241=[-.73340955043672165539,.7718848734006878627 ] 
dist 242=[-.78683428708616073994,.8747926315450550995 ] 
dist 243=[-.82776536116551767394,.9677664539154526263 ] 
dist 244=[-.85946840498257779603,1.0470013479922635417 ] 
dist 245=[-.87608381174814999177,1.0951057667836467694 ] 
dist 246=[-.88479157327900780236,1.1295197677921778657 ] 
dist 247=[-.88506310661499671921,1.1541451516445457465 ] 
dist 248=[-.80498913742176621906,1.1716417293499909343 ] 
dist 249=[-.79063558661131244681,1.1776193427635406856 ] 
dist 250=[-.76969440055874856968,1.1762942690040702993 ] 
dist 251=[-.76191267396572962768,1.1736314350735516515 ] 
dist 252=[-.74145986929578804734,1.1484849475575894370 ] 
dist 253=[-.73296308259343495428,1.1401845698319911636 ] 
dist 254=[-.7250668374021129979 ,1.1114689198693338993 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 0, 2, 0, 1, 2] 
dist 0=[59.466206386342061835  ,59.466206386342061835  ] 
dist 1=[59.033426899324055808  ,59.845062279470291781  ] 
dist 2=[57.684479708289917955  ,60.309672439667781075  ] 
dist 3=[55.959005506492561974  ,60.479075588554639847  ] 
dist 4=[53.849980040211761607  ,60.517293152600722909  ] 
dist 5=[51.053238018059828605  ,60.458061341842590875  ] 
dist 6=[46.581902744161034870  ,60.315542860344821738  ] 
dist 7=[42.012892278107023270  ,60.207516906545116125  ] 
dist 8=[38.826050143264191070  ,59.708840216349689253  ] 
dist 9=[36.036897988998473490  ,59.496252982654563397  ] 
dist 10=[33.055422901129096419  ,59.314895003949467662  ] 
dist 11=[30.172337609824637379  ,59.142362508781687398  ] 
dist 12=[27.775716103061250134  ,58.950343328965320046  ] 
dist 13=[25.271440306549566440  ,58.808524653546992559  ] 
dist 14=[21.957921678971746177  ,57.719415926635564956  ] 
dist 15=[18.694227305432625040  ,55.422310739058019423  ] 
dist 16=[16.388567711165201911  ,36.713091946466457791  ] 
dist 17=[14.336637381414017604  ,34.892042364910267540  ] 
dist 18=[12.085665155444456438  ,30.547132202044170584  ] 
dist 19=[9.8689434432657658487 ,29.888225316635120278  ] 
dist 20=[6.6110693047199381087 ,23.811922821100416227  ] 
dist 21=[4.0334634761843932366 ,22.708065373942353794  ] 
dist 22=[1.7868384434655363311 ,21.290891941982063334  ] 
dist 23=[-.60430296849842949962,20.951678948951194488  ] 
dist 24=[-2.9150273439829458261 ,12.516709867315647672  ] 
dist 25=[-4.8411000387386444970 ,11.489481699456164470  ] 
dist 26=[-6.8624723513056492315 ,9.2804022420621441028 ] 
dist 27=[-9.5550256487174528311 ,8.8236444353758280558 ] 
dist 28=[-12.142158199641448290  ,6.5181452692388039449 ] 
dist 29=[-13.742673502294122991  ,6.1309057289227992790 ] 
dist 30=[-14.935750350452131076  ,5.3347373886743976507 ] 
dist 31=[-15.894944225700620478  ,5.1809070842677489817 ] 
dist 32=[-16.645904608847960702  ,-1.3592147306094308994 ] 
dist 33=[-17.006810036121088294  ,-1.9574949123158069820 ] 
dist 34=[-17.184340243760312459  ,-3.1459213874093653857 ] 
dist 35=[-17.202298911606025800  ,-3.4273609157442689338 ] 
dist 36=[-16.621033182217259995  ,-4.3109029452349652397 ] 
dist 37=[-16.468767324674989297  ,-4.4900154819322203740 ] 
dist 38=[-16.185745788577112829  ,-3.5128640048913491467 ] 
dist 39=[-16.084008775762049910  ,-2.2311924695792764458 ] 
dist 40=[-15.597101077289826960  ,-1.3480526217340179102 ] 
dist 41=[-15.460084548101960495  ,-.59008338163292509871] 
dist 42=[-15.072481747262146339  ,.1925213502106219848 ] 
dist 43=[-14.935458146299910134  ,.92891964376817145574] 
dist 44=[-13.628070678427540431  ,1.5026826970166778440 ] 
dist 45=[-13.579361703991793343  ,3.1031734832520327814 ] 
dist 46=[-13.467205245115437745  ,4.9661255594720053461 ] 
dist 47=[-13.408809874604708164  ,6.8150407647412792122 ] 
dist 48=[-.19207187652960148445,8.5118494921460709276 ] 
dist 49=[.1897247977317826296 ,9.7679417065226717156 ] 
dist 50=[.99415563148866672389,10.941132096293638562  ] 
dist 51=[1.1757713061403241288 ,12.307262039178324475  ] 
dist 52=[1.4154873676214572641 ,13.560583899270462021  ] 
dist 53=[1.1976025014490307909 ,14.283658119169196794  ] 
dist 54=[.80239579350339172634,14.756780775284408800  ] 
dist 55=[.39157496452394735312,15.012666704892940005  ] 
dist 56=[.03886070803698051732,15.167652262591053294  ] 
dist 57=[-.30051315720650470962,15.238036070809837686  ] 
dist 58=[-.64303041044324889197,15.259976983591195007  ] 
dist 59=[-.96004104174344205223,15.221375893226295725  ] 
dist 60=[-1.1977304475465645504 ,7.2253822871821488839 ] 
dist 61=[-1.4221523079290071447 ,7.2217477881187273754 ] 
dist 62=[-1.6862929777291334772 ,7.2043128630281306389 ] 
dist 63=[-1.9304490236831006709 ,7.1733303792227815364 ] 
dist 64=[-2.0751778587531146396 ,2.1744433715318758556 ] 
dist 65=[-2.1744448921908904503 ,1.7591145822226449412 ] 
dist 66=[-2.2372758220104606821 ,.82248672847395659378] 
dist 67=[-2.2798620585315444815 ,.64484417691902770271] 
dist 68=[-2.2983903676227201880 ,-.47943406756618418058] 
dist 69=[-2.3028440395101893726 ,-.50135748763865202114] 
dist 70=[-2.7823822957922233340 ,-.23157898520152678111] 
dist 71=[-3.4917213113171308825 ,.04344010864400174956] 
dist 72=[-4.1633570251981667376 ,.22904678131803605382] 
dist 73=[-4.5856131458481189941 ,.39568504897477865482] 
dist 74=[-4.9054624332768064398 ,.60068565452339267101] 
dist 75=[-5.1685336105884882883 ,.78554576716943567876] 
dist 76=[-5.3745403887796816075 ,.91582371494892115987] 
dist 77=[-5.4667230771585634704 ,1.0306067448197781483 ] 
dist 78=[-5.5073105636859487154 ,1.1536688674526489892 ] 
dist 79=[-5.5074696442760656552 ,1.2656895211808407458 ] 
dist 80=[-.46023590656710573311,1.3364458069960672805 ] 
dist 81=[-.39328930248056112485,1.3902665362710213082 ] 
dist 82=[-.37642435426645656248,1.4347720697687271772 ] 
dist 83=[-.30029511470618049888,1.4697204179294741217 ] 
dist 84=[-.28633308284916132198,1.4854428573997096409 ] 
dist 85=[-.25256879924854398051,1.7011208420136750896 ] 
dist 86=[-.24695692324634636589,1.9364336545361626854 ] 
dist 87=[-.19014073556769437153,2.1999231841290059027 ] 
dist 88=[-.18149584562887302612,2.4409986280828617657 ] 
dist 89=[-.1829692788771523349 ,2.5869112862954020399 ] 
dist 90=[-.19822017832889777802,2.6907940545175766172 ] 
dist 91=[-.22077472665811191652,2.7642145651218412164 ] 
dist 92=[-.25141355896565812452,2.8134403387225815849 ] 
dist 93=[-.29359918576191224192,2.8236543996971034457 ] 
dist 94=[-.36223796334166153002,2.8143846280672768544 ] 
dist 95=[-.43658375092072469284,2.8085633724398924761 ] 
dist 96=[-.50520556552810457393,1.7553959278348462847 ] 
dist 97=[-.55816978708706271298,1.6531256897529308768 ] 
dist 98=[-.62787194840348231552,1.3943738891860364062 ] 
dist 99=[-.70755951996934609323,1.3554330049352870332 ] 
dist 100=[-.78446982665794033693,.94380878677009843958] 
dist 101=[-.87402756934532539766,.86540511000427194206] 
dist 102=[-1.0042200053789961688 ,.77405103560083452713] 
dist 103=[-1.1321166691414228800 ,.75311448873665600821] 
dist 104=[-1.2125253254806172285 ,.04867004928273890439] 
dist 105=[-1.2735687707370050317 ,-.03656459033641562490] 
dist 106=[-1.3441301149711811868 ,-.22051859177678358437] 
dist 107=[-1.4134838724169642532 ,-.25933278616008128907] 
dist 108=[-1.4680691769542336315 ,-.21194885228045913749] 
dist 109=[-1.4929654308559277154 ,-.15198143225348707809] 
dist 110=[-1.5028408532160716291 ,-.06549856591341144748] 
dist 111=[-1.5017719367846445687 ,.02221922641578445219] 
dist 112=[-.72997672237178440507,.08711947155896837717] 
dist 113=[-.67348409492757532137,.14757370111296649745] 
dist 114=[-.53386108267977252531,.2175706402750094816 ] 
dist 115=[-.51333356314511979513,.28816846803029521795] 
dist 116=[-.30487726683327281064,.35102957062329991169] 
dist 117=[-.26663081373367857024,.42015578889982363969] 
dist 118=[-.22016043254420470228,.51576003434705808738] 
dist 119=[-.21090149056858844861,.61117474002575588355] 
dist 120=[.09488526898183949336,.68266544818787021165] 
dist 121=[.13049460143447022986,.74111738154023705867] 
dist 122=[.20947147886727860498,.79693828549117412063] 
dist 123=[.22170004096988044067,.84669953924294895934] 
dist 124=[.30689244966387383187,.88097599277004727897] 
dist 125=[.31962243523111071605,.91042722586238570374] 
dist 126=[.34312756900672448355,.94093819566896968862] 
dist 127=[.34697214292630654444,.9668880680151836662 ] 
dist 128=[.38588512581476197723,.97814215065711588943] 
dist 129=[.29752674386251516162,.98160049374148900248] 
dist 130=[.16971444473759710761,.98043393969563050088] 
dist 131=[.02922741823707534320,.96016483299970645384] 
dist 132=[-.11369853505406402577,.95254118774702470848] 
dist 133=[-.28549374845396612366,.935536552043847614  ] 
dist 134=[-.54114595979929020428,.9283625803419157421 ] 
dist 135=[-.79524929736062166289,.78593231391482752147] 
dist 136=[-.96086745626428948734,.76304200079896749477] 
dist 137=[-1.0930617171098053263 ,.71374383503385480543] 
dist 138=[-1.2138355435877840891 ,.69870974236491636329] 
dist 139=[-1.3177424696202274862 ,.63240867633554674573] 
dist 140=[-1.3826544524909840784 ,.61867962238254674137] 
dist 141=[-1.4313142178604644111 ,.57905988146570797764] 
dist 142=[-1.4703920201306126468 ,.57305686217470801576] 
dist 143=[-1.5001274526458826676 ,.49054550896513988114] 
dist 144=[-1.5115198174485445165 ,.47108943904791113443] 
dist 145=[-1.5125169684185829294 ,.43928795427746831514] 
dist 146=[-1.5094936526280264207 ,.43030498115727715262] 
dist 147=[-1.4755900463700399190 ,.39501564773320217287] 
dist 148=[-1.4639252168471596170 ,.38650152914351863012] 
dist 149=[-1.4318893899243630956 ,.3686399330175252356 ] 
dist 150=[-1.4178571651385012782 ,.36296559124395513988] 
dist 151=[-1.0846267164951930953 ,.41041638209983287768] 
dist 152=[-1.1193073794400684710 ,.6155150413363362999 ] 
dist 153=[-1.1338519356450604094 ,.79221645240117422776] 
dist 154=[-1.1391796053556237693 ,.96342511006339608314] 
dist 155=[-1.1370889040224099241 ,1.1146140569942624873 ] 
dist 156=[-1.1064387603061493245 ,1.2160501960862002614 ] 
dist 157=[-1.0952751768310427878 ,1.3002591589405391715 ] 
dist 158=[-1.0827835412351529746 ,1.3827304624630944121 ] 
dist 159=[-1.0753016489825562689 ,1.4547707470936039740 ] 
dist 160=[-.85529918305524331455,1.4973706497095361389 ] 
dist 161=[-.82395456256902672331,1.5264784816547099839 ] 
dist 162=[-.75409957518203676592,1.5446981475821759302 ] 
dist 163=[-.73295728391600487178,1.5544819836055728548 ] 
dist 164=[-.64034988221493568498,1.5535818477820715825 ] 
dist 165=[-.6213197652054126507 ,1.5405234806350525491 ] 
dist 166=[-.57427599612334898199,1.5308721047957484303 ] 
dist 167=[-.56292176182494777808,1.4922493879154517739 ] 
dist 168=[-.44209604595918476245,1.5359398099545403853 ] 
dist 169=[-.42136358703786533491,1.5561766927256997133 ] 
dist 170=[-.37941179607327324617,1.5630834143544900774 ] 
dist 171=[-.51615867755192599542,1.5624134576826179610 ] 
dist 172=[-.62531468493794997347,1.5374523638680689804 ] 
dist 173=[-.728874846378366277  ,1.5271620306937185283 ] 
dist 174=[-.85156789112228604999,1.4980410268966130963 ] 
dist 175=[-.96518405809486296024,1.4845830806083599444 ] 
dist 176=[-1.0325372600325180128 ,-.15975031830248197564] 
dist 177=[-1.0787573195154893676 ,-.2156382387942103929 ] 
dist 178=[-1.1080755191334582769 ,-.22729727407571875074] 
dist 179=[-1.1282565427603323089 ,-.25115388229739266226] 
dist 180=[-1.1380289022915924203 ,-.24626655667071988121] 
dist 181=[-1.1690584458929705134 ,-.22778370327779914305] 
dist 182=[-1.2587066933772318262 ,-.18597428764736822958] 
dist 183=[-1.3496386942568109496 ,-.13229879389537562602] 
dist 184=[-1.4299700063511089813 ,-.01517317806418692257] 
dist 185=[-1.4773327197546416550 ,.08497359804145880940] 
dist 186=[-1.5095211029362312934 ,.1878322647811395226 ] 
dist 187=[-1.5293213579606563293 ,.28429503148166058608] 
dist 188=[-1.5395969535868101166 ,.35892945294618926384] 
dist 189=[-1.5395474219246761928 ,.43171044844729317384] 
dist 190=[-1.5239019389370752405 ,.52078075559947824841] 
dist 191=[-1.5178895850451686594 ,.6044847684864486247 ] 
dist 192=[-.780312678020474259  ,.65586025600742023264] 
dist 193=[-.71168452523264094824,.69328796903949168621] 
dist 194=[-.54942662829787498165,.72135533896910459682] 
dist 195=[-.52008513115545514528,.74226538317622918243] 
dist 196=[-.4335302582634855302 ,.75114233124013919332] 
dist 197=[-.4915161304104370895 ,.75394755655735000169] 
dist 198=[-.57823208514895657622,.83918553211100760661] 
dist 199=[-.66377060296058469536,.95300784335813124851] 
dist 200=[-.71705936100894378094,1.0211341460602187687 ] 
dist 201=[-.75681476808920045493,1.0687047600496703960 ] 
dist 202=[-.78836935823965664782,1.1005283412799835273 ] 
dist 203=[-.81215218225971555655,1.1229502742390144626 ] 
dist 204=[-.82090612649036176947,1.1330162368594542509 ] 
dist 205=[-.82368899856329202586,1.1359415479368047293 ] 
dist 206=[-.82365481457167245241,1.1339064021221983566 ] 
dist 207=[-.78942138210812227101,1.1083533564485964770 ] 
dist 208=[-.78099700726739526518,.97717802619086648519] 
dist 209=[-.75958216772411652545,.93623650431142483009] 
dist 210=[-.75105160851493679115,.92440218759254678014] 
dist 211=[-.70562092093911303705,.87808673736179719492] 
dist 212=[-.69445338891055301679,.86509068038864772074] 
dist 213=[-.66912264896223904146,.83917616721709798528] 
dist 214=[-.66026235996492269327,.83049027784153575943] 
dist 215=[-.48968571844104833649,.34030821085729483458] 
dist 216=[-.57888077072285581964,.38010311956160220435] 
dist 217=[-.6350128125456746544 ,.41331889128738128296] 
dist 218=[-.70168074724493785666,.44800977444378746571] 
dist 219=[-.81568149986968620529,.49368708702735255348] 
dist 220=[-.89507165127926371747,.54281125057167135359] 
dist 221=[-.96415183809301567063,.59125024706943430854] 
dist 222=[-1.0370244041245297634 ,.64835867952974431449] 
dist 223=[-1.1017135042106048765 ,.73206298728294059503] 
dist 224=[-1.1381495224536690207 ,.81393634290943071179] 
dist 225=[-1.1607926011872492437 ,.86374072097191774885] 
dist 226=[-1.1996255978647527192 ,.89948136432520817477] 
dist 227=[-1.2465086626972535747 ,.92525558081819301255] 
dist 228=[-1.2813488559500102497 ,.94311575318960927894] 
dist 229=[-1.2978394999291537541 ,.94728811777433205943] 
dist 230=[-1.3040170539930509204 ,.94642409185782978774] 
dist 231=[-1.3030985888281707120 ,.94419527553103055184] 
dist 232=[-1.1745817919883159162 ,.88013917569689114569] 
dist 233=[-1.1521428230886034773 ,.86719054883085509045] 
dist 234=[-1.1118206383475770204 ,.83548747894335916374] 
dist 235=[-1.0999380651158918578 ,.82388922363487702584] 
dist 236=[-1.0529681894663525379 ,.76520555456615505095] 
dist 237=[-1.0390433279094967904 ,.75136017278391097982] 
dist 238=[-1.0109828510744620797 ,.72015837942948426359] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 0, 1, 0, 1, 1, 2] 
dist 0=[54.768089243429485796  ,54.768089243429485796  ] 
dist 1=[54.418281261323839549  ,54.947765215686309529  ] 
dist 2=[53.200843862578157836  ,55.394280518761269547  ] 
dist 3=[51.211397065376268780  ,56.320707611474831908  ] 
dist 4=[47.638889242815895130  ,57.205481783153398756  ] 
dist 5=[43.683892046320780785  ,57.486578939268381991  ] 
dist 6=[40.167690185344140644  ,57.540126842210237854  ] 
dist 7=[36.292011259782004637  ,57.515658357546676557  ] 
dist 8=[30.902427409527198885  ,55.505882662730303034  ] 
dist 9=[24.940882318135835090  ,55.082849524474759646  ] 
dist 10=[18.781807756795916902  ,53.932733923172707520  ] 
dist 11=[11.288531698476356912  ,53.534461639538602408  ] 
dist 12=[0                     ,51.077571484351281570  ] 
dist 13=[29.182030976783886520  ,50.482681932110859423  ] 
dist 14=[25.572613192782937937  ,49.394899693825475645  ] 
dist 15=[22.908653694207229693  ,49.067786066473480157  ] 
dist 16=[20.424761372916507602  ,33.358824420324047134  ] 
dist 17=[17.533068497651955610  ,31.693526323691545763  ] 
dist 18=[14.593951358685652105  ,27.905205059691055438  ] 
dist 19=[11.919744919135305358  ,27.141910649508805059  ] 
dist 20=[8.9201237195595857409 ,22.397486421391345623  ] 
dist 21=[4.6800926458298310597 ,21.862256873842857170  ] 
dist 22=[.5054048836571529839 ,19.903328272217421049  ] 
dist 23=[-2.2335642045391426459 ,19.503189413631340736  ] 
dist 24=[-4.4546872618491607807 ,15.325381537669289129  ] 
dist 25=[-6.5608644260244863434 ,14.696956187043266106  ] 
dist 26=[-8.4414061276941789797 ,13.891567158035180865  ] 
dist 27=[-9.7613604435638275484 ,13.226878053284800057  ] 
dist 28=[-10.929111115929188602  ,9.9325531411310002560 ] 
dist 29=[-12.202039949032230700  ,8.3117044813130645531 ] 
dist 30=[-13.338075936693895436  ,2.6546937117269871721 ] 
dist 31=[-13.959142193984602426  ,.8239004078292760188 ] 
dist 32=[-14.956148530911835962  ,-8.4076178099830982358 ] 
dist 33=[-16.874337476818517940  ,-7.4853719978048902749 ] 
dist 34=[-18.308358271167135273  ,-6.3446819736694117629 ] 
dist 35=[-19.467969764209165834  ,-5.0120372253324478480 ] 
dist 36=[-20.377380926188755595  ,-3.2889569529970741047 ] 
dist 37=[-20.811653873140746069  ,-.5904341459296519930 ] 
dist 38=[-21.026851036939107251  ,2.1266833733876283223 ] 
dist 39=[-21.060596879620305757  ,3.9242123709320355192 ] 
dist 40=[-20.435581657997875487  ,5.3874372398285642809 ] 
dist 41=[-20.262841720866841593  ,6.7714466056304234047 ] 
dist 42=[-19.936300624790942433  ,7.9944794438591411475 ] 
dist 43=[-19.815517756823320454  ,8.8157809788389910476 ] 
dist 44=[-19.222484524838696996  ,9.4983500369884551883 ] 
dist 45=[-19.059221903123752112  ,10.168188628000478360  ] 
dist 46=[-18.577684289431627853  ,10.751535732149251052  ] 
dist 47=[-18.427132150141580006  ,11.089159171262257095  ] 
dist 48=[-7.3175865794044452220 ,11.311131890320817540  ] 
dist 49=[-6.2987419369163288459 ,11.433149650859516645  ] 
dist 50=[-4.0046009510670823850 ,11.481867369945359758  ] 
dist 51=[-3.5511948177857338124 ,11.469799422919794032  ] 
dist 52=[-.7971453849615187777 ,11.315644411307066800  ] 
dist 53=[-.6892630180913041587 ,11.262842974192651461  ] 
dist 54=[.2836500675535620379 ,12.183175000562212779  ] 
dist 55=[-1.1995699029148903578 ,13.772245052730635080  ] 
dist 56=[-2.4275433267423811995 ,15.229003721817139785  ] 
dist 57=[-3.6229156269030846064 ,16.069246204535657784  ] 
dist 58=[-4.7015270411363396880 ,16.619306428059544635  ] 
dist 59=[-5.4639121543571753926 ,16.918103306090891221  ] 
dist 60=[-6.1385196232036799061 ,17.098286905770099028  ] 
dist 61=[-6.8671440939861219578 ,17.174881151352371428  ] 
dist 62=[-7.5286272198532126846 ,17.190746563296778064  ] 
dist 63=[-7.9354773735614264617 ,17.134844914870069006  ] 
dist 64=[-8.2327120111136827802 ,-1.4511143510199469964 ] 
dist 65=[-8.4569864960786401389 ,-2.4351772507885850988 ] 
dist 66=[-8.6165170541159205557 ,-4.6720715543571780033 ] 
dist 67=[-8.6555119086610463234 ,-5.0096166443689053845 ] 
dist 68=[-8.6426024004396227447 ,-4.6637018842080849370 ] 
dist 69=[-8.7543171852991053341 ,-3.2799034736669625666 ] 
dist 70=[-9.5120916355993485776 ,-1.8629816502412279812 ] 
dist 71=[-10.266634019615910285  ,-.8882291071013248738 ] 
dist 72=[-10.934674201342665103  ,-.05373954687900569786] 
dist 73=[-11.347411733178216350  ,.80382651162294494056] 
dist 74=[-11.651611010466234339  ,1.6072889383604710033 ] 
dist 75=[-11.886629690852588064  ,2.2260128006375067386 ] 
dist 76=[-12.058852036000958177  ,2.8259251034481624767 ] 
dist 77=[-12.112522674838779044  ,3.5543527422228672442 ] 
dist 78=[-12.090778794148359706  ,4.2362795144390302691 ] 
dist 79=[-12.059471324163823133  ,4.6507559797137358086 ] 
dist 80=[-5.0326087929675154712 ,4.9473726775865491665 ] 
dist 81=[-4.4286767507473076364 ,5.1593175447690395192 ] 
dist 82=[-3.0240963725909752521 ,5.3169187437713182835 ] 
dist 83=[-2.7689185242827398038 ,5.3968150148799544644 ] 
dist 84=[-.93013943355886491317,5.4348035043427947089 ] 
dist 85=[-.6028118214036270204 ,5.4285410741559882190 ] 
dist 86=[-.0288396511454057527 ,3.8789567473557043199 ] 
dist 87=[.0953444872179605258 ,4.9843844516579872489 ] 
dist 88=[.3397730160666092011 ,6.0265703664792701534 ] 
dist 89=[-.1027223205049634051 ,6.6704819435906169430 ] 
dist 90=[-.5231033624973562300 ,7.1442860870845162650 ] 
dist 91=[-.85671047195932516883,7.5080068008849680341 ] 
dist 92=[-1.1897188714457826858 ,7.7861471547872910501 ] 
dist 93=[-1.6077383626672127782 ,7.9186293378760084120 ] 
dist 94=[-2.0054354168664270236 ,7.9713909322326051144 ] 
dist 95=[-2.2574068801943580339 ,7.9720588065927654232 ] 
dist 96=[-2.4502706715815400120 ,1.7617484461048280471 ] 
dist 97=[-2.6122465706063028222 ,1.9305249763250005767 ] 
dist 98=[-2.7415962202483928399 ,2.1168998481948292256 ] 
dist 99=[-2.8043559072705070998 ,2.3076058785752149275 ] 
dist 100=[-3.0754683167091936897 ,2.5374785766234076315 ] 
dist 101=[-3.6741032524695841451 ,2.8800232752573425466 ] 
dist 102=[-4.2546227669786471540 ,3.2164128295845156592 ] 
dist 103=[-4.6059125877723577225 ,3.4217212955637745516 ] 
dist 104=[-4.8560222351692991886 ,3.5696789006470152883 ] 
dist 105=[-5.0329142266494743085 ,3.6773284641422528098 ] 
dist 106=[-5.1622456173925374346 ,3.7530112165136692350 ] 
dist 107=[-5.2226150365820677125 ,3.7734804756079621253 ] 
dist 108=[-5.2439884548235106891 ,3.7723631470676653428 ] 
dist 109=[-5.2382061085273730714 ,3.7619665707177595860 ] 
dist 110=[-4.6770777917196818584 ,3.4986732226095166842 ] 
dist 111=[-4.5816653245542702188 ,3.4453525591727837226 ] 
dist 112=[-4.4075130232748946286 ,3.3202028573636863623 ] 
dist 113=[-4.5759856012642655509 ,3.2751852287375302724 ] 
dist 114=[-4.6786970874819148823 ,3.0498541658810028064 ] 
dist 115=[-4.7105695709570102567 ,2.9971206924300034761 ] 
dist 116=[-4.7151716445138248006 ,3.1004708407151348422 ] 
dist 117=[-4.7090642576875812253 ,3.2080202952875798953 ] 
dist 118=[-4.6940725680849054452 ,3.2785200474876207785 ] 
dist 119=[-4.6716883054715328633 ,3.3164169717195220201 ] 
dist 120=[-3.8571275728462991135 ,3.3351118901653945491 ] 
dist 121=[-3.7357300011451233413 ,3.3300147575494459122 ] 
dist 122=[-3.4997671581817775819 ,3.5640751231944755965 ] 
dist 123=[-3.4338077896406921261 ,3.8918913110489602327 ] 
dist 124=[-3.1799898241403899445 ,4.1612540322533275049 ] 
dist 125=[-3.1167045007590545995 ,4.4205062699816778054 ] 
dist 126=[-2.9932643376237370992 ,4.6464001950416508933 ] 
dist 127=[-2.9556091286902103854 ,4.7826982403068253156 ] 
dist 128=[1.5447286726495078408 ,4.8792136264013270141 ] 
dist 129=[1.8690292319234729910 ,4.9464091603937524510 ] 
dist 130=[2.5900590898601349883 ,4.9894729881182425871 ] 
dist 131=[2.7032203071377035888 ,4.9897242940226789192 ] 
dist 132=[2.6424166393108246308 ,4.9678347267308933700 ] 
dist 133=[1.7873494782382037125 ,4.9452140442992791149 ] 
dist 134=[.9167237084049636413 ,4.0743018450529270848 ] 
dist 135=[.3201261685894811926 ,4.2617486880482893517 ] 
dist 136=[-.1886839949073824557 ,4.4195751313588865252 ] 
dist 137=[-.7091395058328996610 ,4.5122512612570337892 ] 
dist 138=[-1.1958467091216298081 ,4.5748053255860320979 ] 
dist 139=[-1.5700400891420899024 ,4.6124650619361693269 ] 
dist 140=[-1.9326539650563046376 ,4.6311868093405217187 ] 
dist 141=[-2.3731723290443803174 ,4.6222438297223653145 ] 
dist 142=[-2.7854379232773327479 ,4.5892306295675289963 ] 
dist 143=[-3.0353553809923931677 ,4.5646989651189025421 ] 
dist 144=[-3.2136638392826494778 ,1.8372032758020653491 ] 
dist 145=[-3.3402907881132230670 ,1.5967061975072910825 ] 
dist 146=[-3.4343349812044690120 ,1.0457450542834485990 ] 
dist 147=[-3.4826768203699131147 ,.9404367482633711935 ] 
dist 148=[-3.5066973468692189996 ,.24366292924945793026] 
dist 149=[-3.5037318735051361167 ,.12038612948271532661] 
dist 150=[-2.1555905185847544823 ,-.10958111195173664923] 
dist 151=[-2.5803868310429993751 ,-.16198903474947187848] 
dist 152=[-2.9774804439094866753 ,-.0502844211046780063 ] 
dist 153=[-3.2175818198044888207 ,.2206642013785233743 ] 
dist 154=[-3.3881790313036510815 ,.4732517214373926182 ] 
dist 155=[-3.5080202289453276247 ,.6660866735822096008 ] 
dist 156=[-3.5953836229437849969 ,.8516446419343847347 ] 
dist 157=[-3.6364265945047829187 ,1.0752094706482883034 ] 
dist 158=[-3.6513212822300337538 ,1.2845928391361796369 ] 
dist 159=[-3.6468361679283045155 ,1.4135856724455586674 ] 
dist 160=[-.54125946244427960097,1.5081128199033669966 ] 
dist 161=[-.643575304302147168  ,1.5800212479179455780 ] 
dist 162=[-.76182539969957363112,1.6594649578887787496 ] 
dist 163=[-.89027905764132966052,1.8446242951367776890 ] 
dist 164=[-1.0505084824584310238 ,2.0466117858256322299 ] 
dist 165=[-1.2955002183347203882 ,2.3238931707438388921 ] 
dist 166=[-1.5391559749429427367 ,2.5897642126298545069 ] 
dist 167=[-1.6940548786379947955 ,2.7462369796962654066 ] 
dist 168=[-1.8132369233886496014 ,2.8522824028309258758 ] 
dist 169=[-1.9144261903534751374 ,2.9169877629317001247 ] 
dist 170=[-1.9960041576456212961 ,2.9592518753120254157 ] 
dist 171=[-2.0369600686715433691 ,2.9757705151754155922 ] 
dist 172=[-2.0559216370125260200 ,2.9765812703872040315 ] 
dist 173=[-2.0584610319501834352 ,2.9689900442974202855 ] 
dist 174=[-2.0325888115644340256 ,2.5832456110237480329 ] 
dist 175=[-2.0207423428797464820 ,2.5212708036525880806 ] 
dist 176=[-1.9839757988321062515 ,2.4028252288158485139 ] 
dist 177=[-1.9661205991099166448 ,2.3683897024250618839 ] 
dist 178=[-1.8614172324137144357 ,2.2305217470014098023 ] 
dist 179=[-1.8338602552912383848 ,2.2322177500842500058 ] 
dist 180=[-1.7787106715972212317 ,2.1926645390700944343 ] 
dist 181=[-1.7601174483415883357 ,2.1804327346362681545 ] 
dist 182=[-1.7509761305684265654 ,2.1713270424359741537 ] 
dist 183=[-1.7697654899883665768 ,2.1641433326766555274 ] 
dist 184=[-1.7784364130526441831 ,1.6886488921754848027 ] 
dist 185=[-1.9576530097603689406 ,1.6219472691076316322 ] 
dist 186=[-2.2386481779493225053 ,1.4961401092179963626 ] 
dist 187=[-2.4253833013920504447 ,1.4628991591949749921 ] 
dist 188=[-2.5784679075236715723 ,1.3459392687783636147 ] 
dist 189=[-2.7252260562357516547 ,1.3147704083965321644 ] 
dist 190=[-2.8522196238327978431 ,1.2760573349365641109 ] 
dist 191=[-2.9264612399681340148 ,1.2600997885229421510 ] 
dist 192=[-2.9761339582834497909 ,-.6438276918892586139 ] 
dist 193=[-3.0051211931948072003 ,-.7013992246888070953 ] 
dist 194=[-3.0185313565163501596 ,-.5545387433275383143 ] 
dist 195=[-3.0151192715540973448 ,-.4065115282977145546 ] 
dist 196=[-2.9855784567021758127 ,-.2295581299227797954 ] 
dist 197=[-2.9669774001745602486 ,.0327008472855991237 ] 
dist 198=[-1.8594848813871258988 ,.2961274651271482628 ] 
dist 199=[-1.9818071180623189019 ,.47774020467421428594] 
dist 200=[-2.0892075091318757209 ,.63387368091812172562] 
dist 201=[-2.1484826362039356318 ,.79565634277997521678] 
dist 202=[-2.1837406095358369809 ,.94832639954324909716] 
dist 203=[-2.1953359969234595874 ,1.1605070313292406030 ] 
dist 204=[-2.1945705158100232456 ,1.3717635043068202095 ] 
dist 205=[-2.1878441431823418069 ,1.6232223324908982694 ] 
dist 206=[-2.1619721652596085670 ,1.8567802175455355542 ] 
dist 207=[-2.1466007343893336153 ,1.9966278559228468455 ] 
dist 208=[-1.3000781859056768357 ,2.0943457127858607720 ] 
dist 209=[-1.2133221033822942937 ,2.1598408125080513358 ] 
dist 210=[-1.0064568318958042053 ,2.2065963278450640917 ] 
dist 211=[-.9672028194886921994 ,2.2295600083868598707 ] 
dist 212=[-.6726889943254642069 ,2.2394533011549069500 ] 
dist 213=[-.6519363705243073722 ,2.2353228967766113916 ] 
dist 214=[-.9772298395115645965 ,1.3345763091892636987 ] 
dist 215=[-1.1924399906418096876 ,1.4852838972425347294 ] 
dist 216=[-1.3689789963133032670 ,1.6225627533435099987 ] 
dist 217=[-1.5527320271635131307 ,1.7043273212060846243 ] 
dist 218=[-1.7173022753695375786 ,1.7609403213224853059 ] 
dist 219=[-1.8318070457328655184 ,1.7978810722931949930 ] 
dist 220=[-1.9313431359529737720 ,1.8211947473995106147 ] 
dist 221=[-2.0362040063266670199 ,1.8243922412711626517 ] 
dist 222=[-2.1263081919613796367 ,1.8176878662870283587 ] 
dist 223=[-2.1669794508012278840 ,1.8090392573742234420 ] 
dist 224=[-2.1861890373548487890 ,.6579973982598717717 ] 
dist 225=[-2.1906784830320594603 ,.7455803873808661523 ] 
dist 226=[-2.1246971963638431101 ,.8420517942194154567 ] 
dist 227=[-2.1075843712857821567 ,.9404797425194373922 ] 
dist 228=[-2.0973332607258998838 ,1.0589881466184528017 ] 
dist 229=[-2.0938009155161126441 ,1.2355634312091409774 ] 
dist 230=[-2.0550065404629304571 ,1.4095616358399172365 ] 
dist 231=[-2.2066367926083128141 ,1.5177911531842842506 ] 
dist 232=[-2.3137516270143134949 ,1.5983558041898218550 ] 
dist 233=[-2.3877680172241094751 ,1.8364075883441459816 ] 
dist 234=[-2.4406109531737227974 ,2.0597885818299762762 ] 
dist 235=[-2.4632680436362192428 ,2.2091264847698714512 ] 
dist 236=[-2.4680979224570138318 ,2.3325150801264852919 ] 
dist 237=[-2.4646431673312864367 ,2.4523845520691579015 ] 
dist 238=[-2.1991829949194176750 ,2.5546897834928120988 ] 
dist 239=[-2.1576627572640055995 ,2.6080153808392039801 ] 
dist 240=[-2.0676489815978818491 ,2.6355652433722287017 ] 
dist 241=[-2.2026162705862066811 ,2.6377503162500217521 ] 
dist 242=[-2.3383075176213216602 ,2.6212433321350881669 ] 
dist 243=[-2.4383320817616910035 ,2.6086740439476631363 ] 
dist 244=[-2.5137200216502648011 ,2.6293357498172780143 ] 
dist 245=[-2.5511394073231934437 ,2.7762731812974511189 ] 
dist 246=[-2.5678257117862273348 ,2.8899201410895129454 ] 
dist 247=[-2.5665600442612681333 ,2.9875106031479852695 ] 
dist 248=[-2.3107121574320064957 ,3.0653365890279992280 ] 
dist 249=[-2.2661368896683927629 ,3.1001448335726158760 ] 
dist 250=[-2.1909010116148116460 ,3.1100436388075044517 ] 
dist 251=[-2.1677231373493888892 ,3.1073040390522101104 ] 
dist 252=[-2.0863428372031640050 ,3.0538608465475869178 ] 
dist 253=[-2.0595195321287061919 ,3.0330359819661910065 ] 
dist 254=[-2.0147683502816017841 ,2.9701375442977895422 ] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 0, 1, 2, 0, 1] 
dist 0=[62.855350541375695872  ,62.855350541375695872  ] 
dist 1=[62.218875847422965478  ,63.283581014007469769  ] 
dist 2=[61.130045036170570202  ,63.540543116297006322  ] 
dist 3=[59.731008132728445132  ,63.665316213519942559  ] 
dist 4=[57.855838402119563051  ,63.621737040163586803  ] 
dist 5=[55.268925491767367526  ,63.377399035466874796  ] 
dist 6=[51.028116884652826559  ,63.198697413027570701  ] 
dist 7=[46.659562352594062975  ,62.020329003622685092  ] 
dist 8=[43.562616239460959850  ,61.660826301590998034  ] 
dist 9=[40.798919719100875192  ,61.150146251930194148  ] 
dist 10=[37.760972625500237130  ,60.934368030029687580  ] 
dist 11=[34.772852490666989092  ,60.272279674637415229  ] 
dist 12=[32.208036271953255457  ,60.013583231581433439  ] 
dist 13=[29.457315549667769390  ,59.537794873121027737  ] 
dist 14=[25.726695134992541204  ,59.073941776346169519  ] 
dist 15=[22.013350219868822690  ,37.000197108380209251  ] 
dist 16=[18.190231105865095693  ,35.082683236039999208  ] 
dist 17=[14.555491150266083405  ,30.482202113895433850  ] 
dist 18=[11.701390642051120122  ,29.813896284419268383  ] 
dist 19=[8.8667559907996543786 ,23.328117024620706573  ] 
dist 20=[5.3088075626016467432 ,22.154245096705957121  ] 
dist 21=[1.8922940653305474219 ,20.729274946252963452  ] 
dist 22=[-.3781308400250254604 ,20.462956443375492422  ] 
dist 23=[-2.2513522578334940387 ,11.299664672473035976  ] 
dist 24=[-4.0824977719035456747 ,10.207202540303077011  ] 
dist 25=[-5.7581106081436031991 ,7.9021600434307386215 ] 
dist 26=[-7.4308178959418622830 ,7.4025014536962562101 ] 
dist 27=[-8.9791619399231787024 ,5.1864979272188370807 ] 
dist 28=[-10.007128401242838491  ,4.7969391442034660423 ] 
dist 29=[-10.975751348346064370  ,4.1531291688221519355 ] 
dist 30=[-11.730361896395486878  ,4.0232442330020306571 ] 
dist 31=[-12.406351218394562493  ,-3.0943744971528134670 ] 
dist 32=[-12.807824960559302965  ,-3.6915531720293736161 ] 
dist 33=[-13.056651060056636476  ,-4.8505271084391026636 ] 
dist 34=[-13.166078359853385996  ,-5.1117205099302083690 ] 
dist 35=[-13.191252227339559118  ,-5.8465682727460884835 ] 
dist 36=[-13.167708585706029635  ,-5.9354342625333225043 ] 
dist 37=[-12.992330627801800622  ,-4.9419092110179384215 ] 
dist 38=[-12.923829308580466298  ,-2.4592210704853014333 ] 
dist 39=[-11.031040864957925380  ,.05220116861443906609] 
dist 40=[-11.368701618259983394  ,1.7442522223130005983 ] 
dist 41=[-11.604950544800805181  ,3.1561452763521958563 ] 
dist 42=[-11.768222787587327139  ,4.5502513079409288049 ] 
dist 43=[-11.874644769799904354  ,5.8225786563854414140 ] 
dist 44=[-11.888983288805827761  ,6.7488003717419906928 ] 
dist 45=[-11.856067775708679718  ,7.5970472699231462656 ] 
dist 46=[-11.816797930551995297  ,8.5584211803404540963 ] 
dist 47=[-.46806545782613874316,9.4371129818748634194 ] 
dist 48=[-.19078398492249426037,9.9555173346111021670 ] 
dist 49=[.35200638375398648098,10.308271614909971517  ] 
dist 50=[.48147962882002277452,10.526034970665154355  ] 
dist 51=[.87805143522698135672,10.662849567883982925  ] 
dist 52=[.95269405251837085662,10.692706718463871402  ] 
dist 53=[.94114060494719658498,10.664535362786963493  ] 
dist 54=[.80940715526445958764,10.625241955582030136  ] 
dist 55=[.65246917116432581278,8.9524227762545452699 ] 
dist 56=[.54036288088933426832,9.1006434363230386977 ] 
dist 57=[.44016309183848464242,9.2072024089908012935 ] 
dist 58=[.33066221055784305729,9.3245727211102744209 ] 
dist 59=[.2241406814566412335 ,9.4022088776076701783 ] 
dist 60=[-.1117677562159823577 ,9.4067505693373547108 ] 
dist 61=[-1.4508752883035695530 ,9.3382685905061863364 ] 
dist 62=[-2.3388285073742719052 ,9.3029859007046039150 ] 
dist 63=[-3.0646271744537420472 ,3.1164570528400414369 ] 
dist 64=[-3.7569220734303386102 ,2.6002101425827244043 ] 
dist 65=[-4.3731692386534380854 ,1.4226642189123407472 ] 
dist 66=[-4.7956299968730064980 ,1.2054814520151293119 ] 
dist 67=[-5.1563581987512046446 ,-.25351640312765312883] 
dist 68=[-5.5383000918929187975 ,-.37467243609132783302] 
dist 69=[-5.8984059297706889236 ,-.39680132566217042751] 
dist 70=[-6.1002229560818299211 ,-.40026142948327789962] 
dist 71=[-6.2246376953212999350 ,-.43207953179444442083] 
dist 72=[-6.2759293776286138046 ,-.42904844020499730163] 
dist 73=[-6.2882338051353552869 ,-.41651370731127423669] 
dist 74=[-6.2726913370354766792 ,-.38782328861963180225] 
dist 75=[-6.4838994105599254650 ,-.35107808883048406911] 
dist 76=[-6.5935182650048221047 ,-.30641218958809056511] 
dist 77=[-6.6420684229799784742 ,.4601601305910284410 ] 
dist 78=[-6.6525366192879317544 ,1.2715885509268066515 ] 
dist 79=[-2.9570887642095143315 ,1.9491267404713375890 ] 
dist 80=[-2.8419370596276093498 ,2.6184732098506241271 ] 
dist 81=[-2.0204606552009974015 ,3.2291866994791129589 ] 
dist 82=[-1.8655879299278464665 ,3.6729120637572404959 ] 
dist 83=[-1.5944482337838061058 ,4.0782155385004747995 ] 
dist 84=[-1.5311296163827133752 ,4.5357407835582808983 ] 
dist 85=[-.59624631647445852553,4.9493182487718491259 ] 
dist 86=[-.59284651361598874343,5.1793472984086112270 ] 
dist 87=[.02321272978356775705,5.3185324176492871499 ] 
dist 88=[.09538820321920514302,5.3697552387644832403 ] 
dist 89=[.41992118287730065742,5.3857964457240704769 ] 
dist 90=[.47773319363015097924,5.3846574026707861197 ] 
dist 91=[.59056332821004003451,5.3708244315340213154 ] 
dist 92=[0                     ,5.3441501556186848950 ] 
dist 93=[.0482403249899701049 ,2.9928928820988473384 ] 
dist 94=[-.5613013580788324429 ,2.9846961011853908968 ] 
dist 95=[-1.0642584992746189226 ,2.5676981614269746182 ] 
dist 96=[-1.5513103119633156484 ,2.5429278181603530764 ] 
dist 97=[-1.9892707090391533337 ,2.4549476320033655347 ] 
dist 98=[-2.2964480413175563116 ,2.4405484630274291835 ] 
dist 99=[-2.5658579912925251836 ,2.2074063759267487293 ] 
dist 100=[-2.8532078145029492744 ,2.1545832393699970274 ] 
dist 101=[-3.1136175607559654069 ,2.1088050836592711415 ] 
dist 102=[-3.2755832294222942944 ,2.0944778267200977134 ] 
dist 103=[-3.3960725051544253041 ,1.7637344066819467885 ] 
dist 104=[-3.4910474613651202144 ,1.7255448265650496410 ] 
dist 105=[-3.5620843790650677250 ,1.6447039764806397725 ] 
dist 106=[-3.5870930676619817534 ,1.6185372317438990033 ] 
dist 107=[-3.5870498115522591475 ,1.4976322047854465301 ] 
dist 108=[-3.5773194787733134158 ,1.4709946714993622631 ] 
dist 109=[-2.1754154378551345600 ,1.3892100684774547750 ] 
dist 110=[-2.2479889696507909788 ,1.3761480889486268319 ] 
dist 111=[-2.3059227634339013205 ,1.1888942834001390518 ] 
dist 112=[-2.3296238354397506613 ,1.1526467454104643339 ] 
dist 113=[-2.3355863219803600094 ,1.0782284192870546251 ] 
dist 114=[-2.3313225710119119938 ,1.0561101752006172725 ] 
dist 115=[-2.2754307673081292139 ,.96305008780983211318] 
dist 116=[-2.2554573102765643602 ,.94198409357417204402] 
dist 117=[-2.2128380612866687845 ,.88957152771031956332] 
dist 118=[-2.1954405988606860615 ,.87365488261098614371] 
dist 119=[-2.1106868181978832806 ,.71325013507395759175] 
dist 120=[-2.1369825620801601840 ,1.0588353938978980432 ] 
dist 121=[-2.1508258713018104824 ,1.3388500669230699167 ] 
dist 122=[-2.1512986868155599634 ,1.6017564703423326702 ] 
dist 123=[-2.1431803338391331529 ,1.8328783851051978415 ] 
dist 124=[-2.1353612337447261381 ,1.9861070012946390605 ] 
dist 125=[-2.1010266081356648569 ,2.1113083359914346503 ] 
dist 126=[-2.0877421392973779924 ,2.2306323747783121071 ] 
dist 127=[-.93059731612096737337,2.3335994999710634053 ] 
dist 128=[-.82416174674792083997,2.3935537561626279953 ] 
dist 129=[-.57881216322541941401,2.4333654422575578635 ] 
dist 130=[-.5322157428213172657 ,2.4559828357568791410 ] 
dist 131=[-.2152303892973530138 ,2.4657688876760394106 ] 
dist 132=[-.1584133200972087038 ,2.4625441423146411599 ] 
dist 133=[-.0549707122716012353 ,2.4367365738336930537 ] 
dist 134=[-.0316938584573503375 ,2.4214452752051159956 ] 
dist 135=[.2377148029976820457 ,1.5351054267684400768 ] 
dist 136=[-.0721983338012687523 ,1.6325652121242920551 ] 
dist 137=[-.33466613335662381894,1.6983344063672579713 ] 
dist 138=[-.60021131697465931061,1.7379276498832714931 ] 
dist 139=[-.84671400379238179104,1.7643695155532524003 ] 
dist 140=[-1.0332231151819399806 ,1.7776695220679897717 ] 
dist 141=[-1.2111042255549300855 ,1.7838862028090733989 ] 
dist 142=[-1.4231907121595206353 ,1.7820730602494157521 ] 
dist 143=[-1.6198028606556660720 ,.2333678595455493714 ] 
dist 144=[-1.7359584948619894661 ,.20309920370148084793] 
dist 145=[-1.8151765898929587756 ,.15696183633847039946] 
dist 146=[-1.8644488917629141290 ,.14473391653642010536] 
dist 147=[-1.8983783188493096872 ,.1319298310598872044 ] 
dist 148=[-1.9163946899340160396 ,.1402276686526162014 ] 
dist 149=[-1.9261669755556840788 ,.1617391322693733637 ] 
dist 150=[-1.9272097158439731824 ,.2067950209686405371 ] 
dist 151=[-1.8241414621304666499 ,.2584132413938054088 ] 
dist 152=[-1.8540638183182182013 ,.3061059412050898342 ] 
dist 153=[-1.8672027344750559079 ,.3599322551390913077 ] 
dist 154=[-1.8704148171778099232 ,.4360271554847009197 ] 
dist 155=[-1.8049162933425893920 ,.52312517667705800371] 
dist 156=[-1.7882448783503762338 ,.6473782480674129663 ] 
dist 157=[-1.7785358470701242631 ,.7678408986987982592 ] 
dist 158=[-1.7758039392211262922 ,.9142651905128593719 ] 
dist 159=[-1.5553294994787196218 ,1.0513481790678271934 ] 
dist 160=[-1.6501097914217921730 ,1.1578592870564629069 ] 
dist 161=[-1.7143244856976481185 ,1.3891129055293663274 ] 
dist 162=[-1.7533704450203071430 ,1.6073563905606737220 ] 
dist 163=[-1.7788821276100805176 ,1.7999641557272235209 ] 
dist 164=[-1.7891133025164841561 ,1.9289644733513453283 ] 
dist 165=[-1.7900734371419974058 ,2.0358125244802233616 ] 
dist 166=[-1.7853314520092684080 ,2.1400647545171244141 ] 
dist 167=[-1.5455833551929165345 ,2.2286963221069707265 ] 
dist 168=[-1.5071900401833314426 ,2.2732358177146011241 ] 
dist 169=[-1.4346714265523585236 ,2.2939341271899547273 ] 
dist 170=[-1.4137881449637105157 ,2.2960468995617413724 ] 
dist 171=[-1.3314901189378156670 ,2.2700966493168893778 ] 
dist 172=[-1.3095618330947481916 ,2.2560146031794459953 ] 
dist 173=[-1.2644285682678285387 ,2.2216977668478643008 ] 
dist 174=[-1.2493968704021499278 ,2.2054323984842995836 ] 
dist 175=[-1.1978595144736047951 ,1.2936159298724019640 ] 
dist 176=[-1.1854586884388227937 ,1.2551203792026106564 ] 
dist 177=[-1.1595019359378595235 ,1.1849090655780514640 ] 
dist 178=[-1.1495823398763312937 ,1.1659982069557325094 ] 
dist 179=[-1.0980110546099145776 ,1.0989111572962030550 ] 
dist 180=[-1.0855681598166195908 ,1.0794045480997160825 ] 
dist 181=[-1.0435145491922904311 ,1.0536264258103612088 ] 
dist 182=[-1.0366240847646953866 ,1.0429685611813762133 ] 
dist 183=[-.62406678415347080681,.34282525030809989035] 
dist 184=[-.5986135142351112666 ,.31811681910320795831] 
dist 185=[-.74635921520656363074,.26764448574504930344] 
dist 186=[-.91370454113349777696,.25421568934441474006] 
dist 187=[-1.0635565567833716586 ,.20444751146423861005] 
dist 188=[-1.1677745571263134954 ,.19377768490953833715] 
dist 189=[-1.2583148872959254962 ,.1748624205669489336 ] 
dist 190=[-1.3536049281537548336 ,.17036650658795227798] 
dist 191=[-1.4382257920479927853 ,-.1045419061754882795 ] 
dist 192=[-1.4862059203900025647 ,-.0422050156955697132 ] 
dist 193=[-1.5164374469899628977 ,.0141511749137084570 ] 
dist 194=[-1.5302583741604294189 ,.0769138140882224226 ] 
dist 195=[-1.5346699826394347445 ,.1388343776716515906 ] 
dist 196=[-1.5318603096391009177 ,.1918341121361681643 ] 
dist 197=[-1.5161639636577807717 ,.2483473909770549926 ] 
dist 198=[-1.5056179479069201650 ,.3242874982491958489 ] 
dist 199=[-.92053440745777860322,.3987951693747512689 ] 
dist 200=[-.86104642011122199924,.4495952450518088086 ] 
dist 201=[-.83263711513939697903,.49266698417597578949] 
dist 202=[-.85064177656905736227,.53634461512755568712] 
dist 203=[-.86364192826770861761,.6434201595759301812 ] 
dist 204=[-.86728111290986658041,.74589490799408839451] 
dist 205=[-.86603102130115114369,.83898775991268176728] 
dist 206=[-.86320713418525660776,.94336366025657756181] 
dist 207=[-.0680574550750900940 ,1.0389334477635137997 ] 
dist 208=[-.0298022952384884082 ,1.0968975028748031859 ] 
dist 209=[.0102326094206016891 ,1.1383023507527436241 ] 
dist 210=[-.0778811932145206581 ,1.1678143445377447045 ] 
dist 211=[-.1739450594982933792 ,1.1877375776229746221 ] 
dist 212=[-.2705572030306738995 ,1.1919757770235073442 ] 
dist 213=[-.3858732432035855843 ,1.2388274310469019773 ] 
dist 214=[-.5565485055037507305 ,1.3022643851384540969 ] 
dist 215=[-.73659341317930566576,1.3572927953167810728 ] 
dist 216=[-.86798770350352185006,1.3830845781332763997 ] 
dist 217=[-.97641382423259295768,1.3949448914455733382 ] 
dist 218=[-1.0815231081964323592 ,1.3946121122877035157 ] 
dist 219=[-1.1761886678641701168 ,1.3651487579686790733 ] 
dist 220=[-1.2429548210138813394 ,1.3530597584698206638 ] 
dist 221=[-1.3019313548551367311 ,1.3417457763873384064 ] 
dist 222=[-1.3655240328258184590 ,1.3328411878066227672 ] 
dist 223=[-1.4209942782838492065 ,1.0585784367011590904 ] 
dist 224=[-1.4475704719477482980 ,1.0199807064825818320 ] 
dist 225=[-1.4594607575538480348 ,.9321672639690398195 ] 
dist 226=[-1.4597746679089222824 ,.9063313723962303890 ] 
dist 227=[-1.4960709607198411555 ,.6679512769058350353 ] 
dist 228=[-1.5891010971240047914 ,.6243186128219417203 ] 
dist 229=[-1.6632196998930356962 ,.4611426205289479947 ] 
dist 230=[-1.7306964497978891659 ,.6143637701297270980 ] 
dist 231=[-1.7863913986913139741 ,.9737794657740857973 ] 
dist 232=[-1.8135124453288213020 ,1.2091150305362385255 ] 
dist 233=[-1.8248464361224946955 ,1.3981306495596254719 ] 
dist 234=[-1.8244922539282448983 ,1.5727794801121848675 ] 
dist 235=[-1.8019702002512324203 ,1.7243770841819564435 ] 
dist 236=[-1.7913980239823222422 ,1.8214432063546890140 ] 
dist 237=[-1.7365209768295577674 ,1.8969498109092916196 ] 
dist 238=[-1.6235437671321997139 ,1.9625485386643907453 ] 
dist 239=[-.6283528704921601217 ,2.0151629367237468331 ] 
dist 240=[-.6010993531422472473 ,2.0388758657699455319 ] 
dist 241=[-.5442346571601934494 ,2.0459119511017858165 ] 
dist 242=[-.5280635444243373661 ,2.0443662318052480214 ] 
dist 243=[-.4624696184647290734 ,2.0094942306267445178 ] 
dist 244=[-.4485954789845623268 ,1.9957582480070069273 ] 
dist 245=[-.4156217259241584657 ,1.9553952699821475900 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 1, 0, 2, 0, 1] 
dist 0=[65.850206696513387008  ,65.850206696513387008  ] 
dist 1=[65.366651967600406755  ,65.940424716456449417  ] 
dist 2=[64.470810454835464891  ,65.850206696513387008  ] 
dist 3=[62.734621776657982454  ,65.720827337328128829  ] 
dist 4=[60.580228334728265196  ,65.382226594814981377  ] 
dist 5=[58.014764016955298741  ,65.054114607851835203  ] 
dist 6=[54.653813087670666570  ,64.822524058734219764  ] 
dist 7=[49.323590776312425649  ,64.634375017076907467  ] 
dist 8=[43.891650906500660587  ,64.225764188312472300  ] 
dist 9=[40.124534378592428371  ,63.996969745082388436  ] 
dist 10=[36.851268640604923427  ,63.589532590471834481  ] 
dist 11=[33.390696710180518594  ,63.420501958535709078  ] 
dist 12=[30.068874474740315274  ,62.615263758965743860  ] 
dist 13=[27.349260555774721963  ,62.266683256969632218  ] 
dist 14=[24.545321921065279067  ,59.802882754281212805  ] 
dist 15=[20.886254023702090007  ,32.185147853299164708  ] 
dist 16=[17.308378851881382526  ,29.814208657746379672  ] 
dist 17=[14.828263894338796092  ,24.339362012328467625  ] 
dist 18=[12.671324484005254263  ,23.441446639617734486  ] 
dist 19=[10.383300442791751922  ,22.285825598603841869  ] 
dist 20=[8.1766868401835226963 ,15.227010838585635808  ] 
dist 21=[6.3441115312540228752 ,13.311246026897695238  ] 
dist 22=[4.4262162589384407117 ,12.856709324745698902  ] 
dist 23=[1.2638061260531484691 ,10.136311660782095397  ] 
dist 24=[-1.2213237563805060750 ,6.3846646873279552332 ] 
dist 25=[-3.2684357733551152568 ,5.9789333710939826377 ] 
dist 26=[-5.2624796619374469372 ,5.2512523665631356326 ] 
dist 27=[-7.0805298530126991420 ,5.1131173012579798075 ] 
dist 28=[-8.4257825780459173550 ,-.3035037030882356472 ] 
dist 29=[-9.6916294431220919471 ,-.6721256954978104434 ] 
dist 30=[-11.194532123965775509  ,-2.1931548187341094210 ] 
dist 31=[-12.580679950114932218  ,-3.5417503805532695736 ] 
dist 32=[-13.380435593718597421  ,-4.4246757358212197585 ] 
dist 33=[-13.913965910698112625  ,-4.0915301294479846921 ] 
dist 34=[-14.235483113388848424  ,-3.5363680689925939226 ] 
dist 35=[-14.443247987794226302  ,-2.6594413528891749747 ] 
dist 36=[-14.521531060878777560  ,-1.6491141648421144216 ] 
dist 37=[-14.523598021543789910  ,-.5613743009292304384 ] 
dist 38=[-14.493023620283337984  ,.78709365953076317294] 
dist 39=[-12.896091838467079630  ,2.8377497617936742838 ] 
dist 40=[-12.643593604029317797  ,4.8829304745314040798 ] 
dist 41=[-12.132418784897657462  ,6.2097706607210886204 ] 
dist 42=[-11.980382724851520673  ,7.2608218854307497991 ] 
dist 43=[-11.346001415090024127  ,8.2062335400570893565 ] 
dist 44=[-11.196698306436126386  ,9.0085551030987405965 ] 
dist 45=[-10.839705637505451447  ,9.4890022616744425147 ] 
dist 46=[-10.716982565155946996  ,9.8247308694635800633 ] 
dist 47=[-7.1496108030234865741 ,10.049966849191889423  ] 
dist 48=[-5.1908545638349911767 ,10.205598757318706356  ] 
dist 49=[-4.9158378722568624864 ,10.263730531879495334  ] 
dist 50=[-4.2832687224317126695 ,10.261857573398001005  ] 
dist 51=[-4.1283273758908905143 ,10.231160540433109998  ] 
dist 52=[-3.2698523082732791947 ,10.048854831869542963  ] 
dist 53=[-3.1024392604467788511 ,9.9831298924044910002 ] 
dist 54=[-2.7552665936811475107 ,9.7014798010098700657 ] 
dist 55=[-2.6578144012275842380 ,10.513186123190649144  ] 
dist 56=[.9308711371202781565 ,11.053077084729397727  ] 
dist 57=[1.3011037678964031155 ,11.412845977487471948  ] 
dist 58=[1.9974463778541036824 ,11.621783705572846916  ] 
dist 59=[.49982283781936499115,11.749700325062500667  ] 
dist 60=[-1.1009024005071537748 ,11.786029132609596516  ] 
dist 61=[-2.1624130407335199432 ,11.762634158387774870  ] 
dist 62=[-3.0299745237894805449 ,11.732892281713929570  ] 
dist 63=[-3.8571135311690663585 ,4.9980221419646641423 ] 
dist 64=[-4.5930026074357471050 ,3.9729789368374605100 ] 
dist 65=[-5.0966172253247353799 ,3.7710909702878890534 ] 
dist 66=[-5.5256837757521183928 ,3.4745022485502291270 ] 
dist 67=[-6.2913132609223994989 ,3.3857231367244469702 ] 
dist 68=[-6.8626960124417487829 ,1.6088193944672714712 ] 
dist 69=[-7.3125802286889296154 ,1.3785352398116062702 ] 
dist 70=[-7.7133773888658841762 ,.84790923432011608953] 
dist 71=[-8.0557973748457585740 ,.74948376375455552583] 
dist 72=[-8.2728152845625953815 ,.06861754576091279984] 
dist 73=[-8.4394053281730912960 ,-.05209006321840331427] 
dist 74=[-8.5806046187914100065 ,-.27003941325755830094] 
dist 75=[-8.6946186742884184936 ,-.10795604146390496789] 
dist 76=[-8.7527347388667559171 ,.25465527578798237117] 
dist 77=[-8.7810553302343581333 ,.50159103195716553771] 
dist 78=[-8.7761854237351170775 ,.87707760574353479731] 
dist 79=[-2.7059990066503564290 ,1.5470973841640886649 ] 
dist 80=[-2.2109225868619659228 ,2.1540591291026554451 ] 
dist 81=[-1.0820558338482718734 ,2.5876245753988409209 ] 
dist 82=[-.87283269395109918362,2.9761391049490023117 ] 
dist 83=[.5218433867451452998 ,3.4034561842917837500 ] 
dist 84=[.76305846499493984374,3.7952648090951571133 ] 
dist 85=[.68766725057119013144,4.0421604743824745324 ] 
dist 86=[.56273743470328096171,4.2296516866588302300 ] 
dist 87=[.36496837743112156611,4.3845045355979552044 ] 
dist 88=[.1364825622848212257 ,4.8895829059343051933 ] 
dist 89=[-.11090222916483731955,5.3111273925142654102 ] 
dist 90=[-.41849524485885064064,5.6747312138784569982 ] 
dist 91=[-.88701098058795544515,5.9723008445056776716 ] 
dist 92=[-1.3566644009516292921 ,6.1304675927308766190 ] 
dist 93=[-1.6687854903954882356 ,6.2165199859082571461 ] 
dist 94=[-1.9239984155828088488 ,6.2278869199773622255 ] 
dist 95=[-2.1667558069512756424 ,1.5845457798457779281 ] 
dist 96=[-2.3816527341770643409 ,1.1147592570761033803 ] 
dist 97=[-2.5257759915838876065 ,1.0864865783449859214 ] 
dist 98=[-2.6449825814381910800 ,1.0214566857471180100 ] 
dist 99=[-2.7605109136723520627 ,1.0005044128338283354 ] 
dist 100=[-2.8555790393934256249 ,.90763416200917921409] 
dist 101=[-2.8932065660134134044 ,.88325654787820969635] 
dist 102=[-2.9055355563595373272 ,.86885283291378501615] 
dist 103=[-2.8997812110453404236 ,.87010237007761478716] 
dist 104=[-2.7952785279147531025 ,.88036117995001851357] 
dist 105=[-2.7596698883030155791 ,.90328054723306193311] 
dist 106=[-2.7240910028667646244 ,.93969583448866317632] 
dist 107=[-2.6338308528460750576 ,1.0037251665253106052 ] 
dist 108=[-2.5168245774009123830 ,1.0686642419497673080 ] 
dist 109=[-2.5187995903265911836 ,1.1086981083471556683 ] 
dist 110=[-2.5149305062145798606 ,1.1378636443442277716 ] 
dist 111=[-1.7091589502323259856 ,1.1594830252675825291 ] 
dist 112=[-1.7463633700874083482 ,1.1743224003742220440 ] 
dist 113=[-1.7764206330088869121 ,1.1764560230891538738 ] 
dist 114=[-1.8070437026442990252 ,1.1723326479014780499 ] 
dist 115=[-1.8464899877215807942 ,1.1667153337260609438 ] 
dist 116=[-1.8847079179521290970 ,1.1218453093559518649 ] 
dist 117=[-1.9104161511005968671 ,1.1101339687914783814 ] 
dist 118=[-1.9318666158882953872 ,1.0698912108479558625 ] 
dist 119=[-1.9530715209623364468 ,1.0611352969261177466 ] 
dist 120=[-1.9724090753514837024 ,.95376073696594584004] 
dist 121=[-1.9863894233047580802 ,1.1465916521036728644 ] 
dist 122=[-1.9990221684065063110 ,1.5478829901193601615 ] 
dist 123=[-2.0129503719299422012 ,2.1304984327764145011 ] 
dist 124=[-2.0241256947003593509 ,2.7041491325516671938 ] 
dist 125=[-2.0257716964083196254 ,3.0696858862719362254 ] 
dist 126=[-2.0206303459145605103 ,3.3521426662373252379 ] 
dist 127=[-2.0129290257002668522 ,3.5943717796216871499 ] 
dist 128=[-1.9830885137673616505 ,3.7917296023023410522 ] 
dist 129=[-1.9704840143560880800 ,3.8951898674225872099 ] 
dist 130=[-1.9279978368200215932 ,3.9495541672265979636 ] 
dist 131=[-1.9114636747224089246 ,3.9598930814657770291 ] 
dist 132=[-1.7877449855070662837 ,3.9313774528706279613 ] 
dist 133=[-1.7597541076280886701 ,3.9101730222987895170 ] 
dist 134=[-1.6887131859185372216 ,3.8629617212768592401 ] 
dist 135=[-1.6637132452073646320 ,3.8395575136474286875 ] 
dist 136=[-1.5301220233909201528 ,3.7012019494349812120 ] 
dist 137=[-1.4987617000300456029 ,3.6646646618877056092 ] 
dist 138=[-1.4351187277605515471 ,3.5471466506848039031 ] 
dist 139=[-1.4150525215175639663 ,3.5180962200310292676 ] 
dist 140=[-1.3396349973010739418 ,1.1861312803512490271 ] 
dist 141=[-1.7979717555570950066 ,1.1478148389279013470 ] 
dist 142=[-2.2796680925224804102 ,1.1350526326330512852 ] 
dist 143=[-2.7254902412617936027 ,.27419788687865441976] 
dist 144=[-3.1130409906736269382 ,.19520177484552507716] 
dist 145=[-3.3622929119192292233 ,.02919557026038694763] 
dist 146=[-3.5574814824091920143 ,-.01234321379473944535] 
dist 147=[-3.7293755792349015956 ,-.17133063336879385004] 
dist 148=[-3.8751253435522863554 ,-.2017050115263821489 ] 
dist 149=[-3.9660229918653620141 ,-.2518327617041970778 ] 
dist 150=[-4.0339799012323775140 ,-.26284874617891553961] 
dist 151=[-4.0882135597727886113 ,-.27351897355317095305] 
dist 152=[-4.1293522140743205370 ,-.25755352462260924712] 
dist 153=[-4.1450698833305985726 ,-.2233241101293263423 ] 
dist 154=[-4.1451456544097107261 ,-.15532155731936161137] 
dist 155=[-4.1309008694656244862 ,-.07098669042510355099] 
dist 156=[-1.6981682911759167195 ,.02839907559060200959] 
dist 157=[-1.6920793833456765219 ,.25936364716352367452] 
dist 158=[-1.6849780593436390868 ,.62523494260847189086] 
dist 159=[-.5670251810133342230 ,.99714983015111643514] 
dist 160=[-.09955151630872571969,1.3435463220535957744 ] 
dist 161=[-.01769005697267870711,1.6076244483933574460 ] 
dist 162=[.14934509346832942552,1.8614312756405743516 ] 
dist 163=[.19102941562719965341,2.1668549751039783720 ] 
dist 164=[.52456587690274538599,2.4512909275469550665 ] 
dist 165=[.57888445315614834989,2.6213771823260873990 ] 
dist 166=[.6185445216663810229 ,2.7399210477765802352 ] 
dist 167=[.59666615773047555039,2.8187536863046084259 ] 
dist 168=[.54535149213229963027,2.8737198806306951016 ] 
dist 169=[.45460288693554881555,2.8970615719108270978 ] 
dist 170=[.3178072679961634090 ,2.9163772061989607911 ] 
dist 171=[.0828162685474408549 ,2.9221639641657018502 ] 
dist 172=[-.1592666581045777715 ,2.0007037122419487462 ] 
dist 173=[-.4722753172772635530 ,1.9889562134254715179 ] 
dist 174=[-.7405352368330922907 ,1.9801407987453193064 ] 
dist 175=[-1.0099500926540329964 ,1.6655236307061322362 ] 
dist 176=[-1.2587984057098603115 ,1.6195728933245518726 ] 
dist 177=[-1.4450207192030460172 ,1.5051943269732038674 ] 
dist 178=[-1.6206461739338265554 ,1.4769972586814709656 ] 
dist 179=[-1.8272264050553368732 ,1.2867504376720320959 ] 
dist 180=[-2.0172018490940193976 ,1.2466260753179089837 ] 
dist 181=[-2.1265923628705802594 ,1.1746019414050671168 ] 
dist 182=[-2.1976843699228298662 ,1.1555647318127992620 ] 
dist 183=[-2.2348888730495797340 ,.7803669818498323520 ] 
dist 184=[-2.2564376527639051809 ,.7289232056661482323 ] 
dist 185=[-2.2650777341559019525 ,.6026467180715164053 ] 
dist 186=[-2.2659021271998125732 ,.5816787965970630831 ] 
dist 187=[-2.2577205287163284270 ,.3919613859842361657 ] 
dist 188=[-2.1644013411433012749 ,.4729585299052226915 ] 
dist 189=[-2.1275473475987248523 ,.6425032918835051790 ] 
dist 190=[-2.1160695187036858528 ,.8374673710584027848 ] 
dist 191=[-1.7262900035366282441 ,1.0432979497704461879 ] 
dist 192=[-1.7029627158857066527 ,1.2240877508998928813 ] 
dist 193=[-1.6909219270901429060 ,1.3436483515955688629 ] 
dist 194=[-1.6719838823127313597 ,1.4410010209238953470 ] 
dist 195=[-1.6627483979300256534 ,1.5332060380485820610 ] 
dist 196=[-1.3787137920552203649 ,1.6138681987207458468 ] 
dist 197=[-1.3357311514653056238 ,1.6651769839562846699 ] 
dist 198=[-1.2436348827076888037 ,1.7047014317239959873 ] 
dist 199=[-1.2159536288368641476 ,1.7383549014224029365 ] 
dist 200=[-1.0957499474851609226 ,1.7655670354926596749 ] 
dist 201=[-1.0709505924709962156 ,1.7793959694505515367 ] 
dist 202=[-1.0007785912987243887 ,1.8042300265134055840 ] 
dist 203=[-.98968399964814918206,1.8317249961726046711 ] 
dist 204=[.00699649092692100375,1.8365074125713265479 ] 
dist 205=[-.12754464459303739434,1.8308980948440258198 ] 
dist 206=[-.33365312108680333898,1.8240782916447449443 ] 
dist 207=[-.539265152814729084  ,1.5368503826941575885 ] 
dist 208=[-.67182591358660233901,1.6927247323499689223 ] 
dist 209=[-.77597522836898111238,1.7906671783134996854 ] 
dist 210=[-.86825629151092787093,1.8647406209797846927 ] 
dist 211=[-.94559979473173587714,1.9253987398143947845 ] 
dist 212=[-.99016408223941532503,1.9736193671002046187 ] 
dist 213=[-1.0191513717165433993 ,1.9980785898053606983 ] 
dist 214=[-1.0343585933203440428 ,2.0097715918801179639 ] 
dist 215=[-1.0434741748424271675 ,2.0070674068545851238 ] 
dist 216=[-1.0481628693664181396 ,1.9953316952718514181 ] 
dist 217=[-1.0504927107743735616 ,1.9871207905222649353 ] 
dist 218=[-1.0502012850400261789 ,1.9471915080320415301 ] 
dist 219=[-1.0482489845501072091 ,1.9375554251583957485 ] 
dist 220=[-1.0439553187221384314 ,.84995602594734172606] 
dist 221=[-1.0445757108632934842 ,.74794144150993024466] 
dist 222=[-1.0441387831645146319 ,.51865149487070631606] 
dist 223=[-.84285165272304996534,.46996473817098226481] 
dist 224=[-1.0601430607845856893 ,.19134826156694303445] 
dist 225=[-1.2223964553807530283 ,.20389049109642132872] 
dist 226=[-1.3750853223060298329 ,.3538478288257561605 ] 
dist 227=[-1.5542252051986280147 ,.5004414683337023941 ] 
dist 228=[-1.7187528938968112896 ,.6237444787665932792 ] 
dist 229=[-1.8131536086499175743 ,.7533372940700912902 ] 
dist 230=[-1.8740836268450955376 ,.9250219129647673960 ] 
dist 231=[-1.9050950136246322830 ,1.0928940410356469961 ] 
dist 232=[-1.9229779156465426225 ,1.2072798561811835739 ] 
dist 233=[-1.9315362146573221972 ,1.3041527258056808750 ] 
dist 234=[-1.9348893162769194433 ,1.4021677874198364267 ] 
dist 235=[-1.9320039260585976218 ,1.4931686916572743657 ] 
dist 236=[-1.6559226204062720969 ,1.5620635373846205482 ] 
dist 237=[-1.6937407767331140594 ,1.6278210040721931268 ] 
dist 238=[-1.7397332943415883941 ,1.7063091008131371104 ] 
dist 239=[-1.7808717074379734238 ,1.9323132890709027173 ] 
dist 240=[-1.7993267554026298653 ,2.1965404531470865814 ] 
dist 241=[-1.8046590569713296014 ,2.3993281329360143238 ] 
dist 242=[-1.8023894525689727277 ,2.5706775617961096979 ] 
dist 243=[-1.7744789838129761101 ,2.7082714388198176075 ] 
dist 244=[-1.7635544927297467616 ,2.7764093709897055090 ] 
dist 245=[-1.7245705815918190680 ,2.8114681760668739005 ] 
dist 246=[-1.7110761610047584842 ,2.8171100291579246857 ] 
dist 247=[-1.5611882535736521419 ,2.7644034879699518908 ] 
dist 248=[-1.5552278852434957674 ,2.7431336667330584312 ] 
dist 249=[-1.5462832267586824629 ,2.7051115532517633046 ] 
dist 250=[-1.5384697326370010967 ,2.6893483598385122880 ] 
dist 251=[-1.5127179930554832711 ,2.6060433471126316651 ] 
dist 252=[-1.5015781604562752332 ,2.5821374851886982081 ] 
dist 253=[-1.4718417598875717251 ,2.5046239907021967314 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 0, 1, 1, 2] 
dist 0=[60.657309704839660237  ,60.657309704839660237  ] 
dist 1=[60.371715102542183808  ,60.893264784538008945  ] 
dist 2=[59.896146332336545441  ,61.170338535006832203  ] 
dist 3=[59.071794485019209558  ,61.405239419089651840  ] 
dist 4=[57.393408021602406687  ,61.472837805472631004  ] 
dist 5=[55.335315706064126698  ,61.430390437760550909  ] 
dist 6=[52.994762893497976540  ,61.344346711724183735  ] 
dist 7=[49.994595296506331125  ,60.933092497734835424  ] 
dist 8=[45.302433443150984287  ,60.775500001686152482  ] 
dist 9=[40.534052425785211401  ,60.171598160146351800  ] 
dist 10=[37.229426540112442614  ,60.007505306253397202  ] 
dist 11=[34.357846708579974955  ,58.194533118297046349  ] 
dist 12=[31.318500059813396321  ,57.734156520167811289  ] 
dist 13=[28.396048692478702287  ,55.944252303245039978  ] 
dist 14=[25.991037108895741455  ,52.736688335215985987  ] 
dist 15=[23.498608331494768389  ,32.897373212936275269  ] 
dist 16=[20.226636376649757202  ,31.864193534049376224  ] 
dist 17=[17.014466451929722254  ,30.652961109108649600  ] 
dist 18=[14.760601691057475762  ,30.375500854454235317  ] 
dist 19=[12.770344616063424311  ,21.222934963315980540  ] 
dist 20=[10.610549508029868074  ,20.082435164441495813  ] 
dist 21=[8.4973099075583633261 ,17.733542199907955353  ] 
dist 22=[6.2891830036909283710 ,17.125032809466305160  ] 
dist 23=[2.8147674051354427450 ,14.918480287540489500  ] 
dist 24=[.46062985146764541261,14.476192765400634694  ] 
dist 25=[-1.5310618398339195097 ,13.726383319523597546  ] 
dist 26=[-3.5584887305158109836 ,13.556492094505649187  ] 
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dist 231=[-.44256378305523749943,.13935037158597602919] 
dist 232=[-.44963755158866697041,.1513695368611794701 ] 
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dist 252=[-.42162830991502220415,.55974802166020430551] 
dist 253=[-.40741736868541725801,.55156808413207674444] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 0, 0, 0, 1] 
dist 0=[55.065148224860709633  ,55.065148224860709633  ] 
dist 1=[53.689152587762605102  ,55.999977149470481434  ] 
dist 2=[51.349143107214252156  ,56.578538443197838161  ] 
dist 3=[48.901097974478847615  ,56.965512198424384804  ] 
dist 4=[47.093785293818024626  ,57.135476813457802152  ] 
dist 5=[45.407652950843867719  ,57.179262738876607013  ] 
dist 6=[43.443551047366569314  ,57.117364574980431882  ] 
dist 7=[41.448756223302902625  ,56.895518912103054889  ] 
dist 8=[39.640185684766197203  ,56.213872752468664360  ] 
dist 9=[37.620019970323342004  ,52.304248319358001119  ] 
dist 10=[34.780605509679200368  ,52.035243136738703525  ] 
dist 11=[31.914869772480836545  ,51.033815251671003479  ] 
dist 12=[29.789652805788199803  ,50.733287113033376347  ] 
dist 13=[27.798234227043909572  ,50.205412602038024362  ] 
dist 14=[25.466621418133650768  ,50.036425004944863651  ] 
dist 15=[23.092517428083743650  ,49.397073188664206662  ] 
dist 16=[20.847372957093680034  ,48.319324002691124057  ] 
dist 17=[18.220420931692181229  ,26.151888387738794821  ] 
dist 18=[14.450969568850607545  ,26.033720400187875684  ] 
dist 19=[10.708356881511615384  ,18.043008313828919973  ] 
dist 20=[8.1885179032281613458 ,17.228259321734970104  ] 
dist 21=[6.0732847827796501937 ,15.147076918185211437  ] 
dist 22=[3.9471069211649962350 ,14.891706822727078241  ] 
dist 23=[1.9680298515358059820 ,9.8633045722784641224 ] 
dist 24=[.44045924601224166954,9.4825910055796959060 ] 
dist 25=[-1.0541129733891997602 ,6.9723788626515867512 ] 
dist 26=[-3.0429376759427553221 ,5.9132752992763735955 ] 
dist 27=[-4.7263229505005381213 ,2.2851443846434972995 ] 
dist 28=[-6.3835277921754715306 ,1.9703154351590005016 ] 
dist 29=[-7.9084459625880789157 ,1.3800848377268860143 ] 
dist 30=[-9.0645046686461035133 ,1.2636389447471809730 ] 
dist 31=[-10.181722272290228939  ,-.11197423345479689327] 
dist 32=[-11.553570438343621908  ,.42176121391256815255] 
dist 33=[-12.823883826758969164  ,1.1892051997347821123 ] 
dist 34=[-13.535763309897841734  ,2.4681892170217850456 ] 
dist 35=[-13.985878132916068996  ,3.7679734338604990106 ] 
dist 36=[-14.209209599053340239  ,4.6185869562404118642 ] 
dist 37=[-14.333640768660235948  ,5.2977361534678007437 ] 
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dist 39=[-14.404334772430858956  ,6.4384629525274132819 ] 
dist 40=[-14.377830394075040463  ,6.7494161565543911114 ] 
dist 41=[-12.330108246797492212  ,6.9611700155647341711 ] 
dist 42=[-12.032698024823099125  ,7.0897420019552906838 ] 
dist 43=[-11.470352918665984699  ,7.1735019662443820178 ] 
dist 44=[-11.318423262155724708  ,7.2066527474048360461 ] 
dist 45=[-10.771249652944315188  ,7.2077851900431648132 ] 
dist 46=[-10.623340485752920264  ,7.1792322339409711061 ] 
dist 47=[-10.423178605580258842  ,7.0944397127374395349 ] 
dist 48=[-10.346489545975128251  ,7.0469960322887404041 ] 
dist 49=[-6.0245792449338872876 ,6.8874084246270601218 ] 
dist 50=[-5.9769650531160146668 ,6.8131764174268088364 ] 
dist 51=[.16763793364848154308,6.7325017544826718862 ] 
dist 52=[.46867782075337744549,7.1527311262556170844 ] 
dist 53=[2.1324360102017102519 ,7.4532715295138819557 ] 
dist 54=[2.4071713210489945132 ,7.6698080932334747507 ] 
dist 55=[2.9953584669145123294 ,7.8357756155161024833 ] 
dist 56=[3.0920454909418518982 ,7.9345124644431668061 ] 
dist 57=[3.7529156308880293754 ,8.3453850971444703301 ] 
dist 58=[3.8218208142432291518 ,8.9466436793941650584 ] 
dist 59=[3.7460102636856571889 ,9.3922912048805496504 ] 
dist 60=[3.4546505830329257194 ,9.7428964077357825913 ] 
dist 61=[3.0488138373729069260 ,10.006245484178079449  ] 
dist 62=[2.5161091209062683352 ,10.103577561525114485  ] 
dist 63=[1.6940586419049925467 ,10.134829943281451123  ] 
dist 64=[.61114882027772523109,10.134306806577728078  ] 
dist 65=[-.58272760086375005865,1.0298634285594730453 ] 
dist 66=[-1.5587342425334799003 ,.83043313480423949168] 
dist 67=[-2.3866593774876398743 ,-.41081820445634257294] 
dist 68=[-3.1920944068111902790 ,-.62405932287368688112] 
dist 69=[-3.9199695543037192729 ,-1.0417312762420852967 ] 
dist 70=[-4.4385078113689601628 ,-1.1392351219829122704 ] 
dist 71=[-4.9023415950586230411 ,-1.9816338421139713967 ] 
dist 72=[-5.4120274708290554471 ,-2.1130457670040136348 ] 
dist 73=[-5.8719874798822841132 ,-2.1890904979651024607 ] 
dist 74=[-6.1374514139840079450 ,-2.1082860951607029722 ] 
dist 75=[-6.3111048575167854510 ,-1.9498781861360104118 ] 
dist 76=[-6.4047679369951743823 ,-1.6909486417282836389 ] 
dist 77=[-6.4538254530102745671 ,-1.3096879314897128280 ] 
dist 78=[-6.4495006795995948994 ,-.66333849865946736631] 
dist 79=[-6.4179445454752797668 ,-.00237553749944936712] 
dist 80=[-6.3871033555421990816 ,.43719969426395440756] 
dist 81=[-4.2737855008778128695 ,.82705240836372638998] 
dist 82=[-4.0514932966229681953 ,1.2838931692973608264 ] 
dist 83=[-3.4969359163843861449 ,1.7003376568788982141 ] 
dist 84=[-3.4029969558252025527 ,2.0025339816291416168 ] 
dist 85=[-2.5340694791196994625 ,2.3071847247786114839 ] 
dist 86=[-2.3665348080315801515 ,2.7026012225052553447 ] 
dist 87=[-2.1428407595254404209 ,3.0575520473575862145 ] 
dist 88=[-2.0701161319287327975 ,3.4490060326056609908 ] 
dist 89=[-.61849224427105588653,3.8060633934357265233 ] 
dist 90=[-.43540677814100041819,4.0238247679115010199 ] 
dist 91=[-.02377250771841970889,4.1808427166111316112 ] 
dist 92=[.05398280874950966617,4.2956071325159561241 ] 
dist 93=[.54155439500405441403,4.3742392838711716603 ] 
dist 94=[.59215663712888948471,4.3906461471701271661 ] 
dist 95=[.50016612104758547621,4.3779377954832697188 ] 
dist 96=[.14356561634266252182,4.3683958152416453381 ] 
dist 97=[-.15539595176616487031,1.7655398017637208659 ] 
dist 98=[-.45267636292854944918,1.7202861479440865957 ] 
dist 99=[-.7251038134166876306 ,1.2631515597434299530 ] 
dist 100=[-.92494458698411157471,1.1753306764476528680 ] 
dist 101=[-1.1093172699399560415 ,1.0678230879823527510 ] 
dist 102=[-1.3200502153889633697 ,1.0375887075094690229 ] 
dist 103=[-1.5155301665179977280 ,.2514921326186101861 ] 
dist 104=[-1.6390741911711831330 ,.15450094189294657664] 
dist 105=[-1.7332417452473353912 ,-.05766474901402464093] 
dist 106=[-1.8115770733615751492 ,-.10153762594318521547] 
dist 107=[-1.9420145060957151014 ,-.33246762739112041025] 
dist 108=[-2.0559012435510622086 ,-.37107543500277698821] 
dist 109=[-2.1481974428000523106 ,-.45279097185751954825] 
dist 110=[-2.1954879727339286868 ,-.46690701733751325186] 
dist 111=[-2.2187565706313292290 ,-.89161738011288237613] 
dist 112=[-2.2203987007007108908 ,-.73385320662072956209] 
dist 113=[-1.3512536522266369949 ,-.59505806995888768756] 
dist 114=[-1.2760585166590796745 ,-.44649058484487692212] 
dist 115=[-1.0928771485964132776 ,-.30356670000472645072] 
dist 116=[-1.0583575437842182546 ,-.18726337631161236114] 
dist 117=[-.78528637304485595922,-.06851001793432365457] 
dist 118=[-.73322458648727480916,.08420577236230669270] 
dist 119=[-.65040003915824108675,.23131878300954577346] 
dist 120=[-.62854104707526167011,.32773788882532332339] 
dist 121=[-.22833243834771115767,.4052819350144126923 ] 
dist 122=[-.17643529243082783299,.47712847070460060042] 
dist 123=[-.06200700922035961341,.53970156356435959689] 
dist 124=[-.03945914789090069519,.6787398563101109325 ] 
dist 125=[.08673113718217361290,.81214348150160621712] 
dist 126=[.10732720697470487742,.91875768618063643127] 
dist 127=[.15114774411295481357,1.0260394804134679091 ] 
dist 128=[.15782251559903386973,1.1621528263471809680 ] 
dist 129=[.48614431289924213863,1.3035968020066745485 ] 
dist 130=[.45166292380418541882,1.4127268907310617903 ] 
dist 131=[.40894049686791117296,1.5014142550926512923 ] 
dist 132=[.3588502322952422385 ,1.5853048309933233453 ] 
dist 133=[.29394549518645411476,1.6596256198997195971 ] 
dist 134=[.19211931318382725481,1.7101262929041211596 ] 
dist 135=[.08534840232929650285,1.7528217492234551473 ] 
dist 136=[.00070985773028827916,1.7959978292679767733 ] 
dist 137=[-.08372324968849456610,1.8321593964729576793 ] 
dist 138=[-.18969316204328651166,1.8468638573438773991 ] 
dist 139=[-.30114014640640514377,1.8487784240659960403 ] 
dist 140=[-.40743460958664834837,1.8460663956486449515 ] 
dist 141=[-.53013142753777843286,1.8109564689659264971 ] 
dist 142=[-.7070280963160224917 ,1.7984286031323730201 ] 
dist 143=[-.89306269350060147886,1.7597928603476407793 ] 
dist 144=[-1.2285587622780854873 ,1.7431933850286433161 ] 
dist 145=[-1.7243834681201390822 ,1.5358166518742431933 ] 
dist 146=[-2.0460880023511287484 ,1.4982349654157454412 ] 
dist 147=[-2.3012610722296961874 ,1.4196692192927962301 ] 
dist 148=[-2.5316837843244100473 ,1.3954932435834982848 ] 
dist 149=[-2.7280635736106585290 ,1.2888281809694119604 ] 
dist 150=[-2.8474373972695629954 ,1.2655001798888979537 ] 
dist 151=[-2.9330720771741013082 ,1.1986428793777076986 ] 
dist 152=[-2.9948684833078887544 ,1.1857639761231307068 ] 
dist 153=[-3.0382901234289642883 ,1.0440816582870850016 ] 
dist 154=[-3.0506247703985892095 ,1.0156242626680279563 ] 
dist 155=[-3.0454613422525904873 ,.95942569902644696351] 
dist 156=[-3.0362402283050077100 ,.94296632465048152366] 
dist 157=[-2.9563336640148764631 ,.87546722355557167808] 
dist 158=[-2.9309427196530431626 ,.85914266405929300182] 
dist 159=[-2.8613126130609883091 ,1.1059871393076676133 ] 
dist 160=[-2.8315640726819686537 ,1.3700377560936727312 ] 
dist 161=[-1.1528522431923234647 ,1.5817183856481675004 ] 
dist 162=[-1.1244116214470784985 ,1.7766808077191863798 ] 
dist 163=[-.99782122530035431203,1.9455166752440679183 ] 
dist 164=[-.97135293554832507523,2.0529782489977311665 ] 
dist 165=[-.90548201632229901159,2.3213332958010513608 ] 
dist 166=[-.88881812917591838898,2.5218767957958351009 ] 
dist 167=[-.70947085649331397049,2.6851810534007110385 ] 
dist 168=[-.67894997845793645985,2.8398953104914400546 ] 
dist 169=[-.61423563272781349818,2.9737290432127717350 ] 
dist 170=[-.59557319804317251542,3.0537410015049050469 ] 
dist 171=[-.51816270106208780587,3.1094970951150318142 ] 
dist 172=[-.5022745026362274841 ,3.1465710376324369725 ] 
dist 173=[-.46171851243130076777,3.1687149681273179584 ] 
dist 174=[-.45316529323317329501,3.1660292565102142731 ] 
dist 175=[-.49297431569750020007,3.1485716897203865100 ] 
dist 176=[-.7968580562089579946 ,3.1325239310329445536 ] 
dist 177=[-1.0675073285303819607 ,1.3496430459301111334 ] 
dist 178=[-1.3259723794662071537 ,1.1919118563426924568 ] 
dist 179=[-1.5561683827983240574 ,.84585223470841689762] 
dist 180=[-1.7140540942179625898 ,.78302957650331796623] 
dist 181=[-1.8488828685051753429 ,.3584914287933655298 ] 
dist 182=[-1.9871068614345272363 ,.28222930704686500445] 
dist 183=[-2.1096103168013756125 ,.14236173869649382233] 
dist 184=[-2.1817302516476856552 ,.11056305944777003933] 
dist 185=[-2.2306101562061133147 ,-.31462250876637908275] 
dist 186=[-2.2604081618305830447 ,-.37439534706364449963] 
dist 187=[-2.2755893190228772818 ,-.47328154323954906545] 
dist 188=[-2.2758994264714852299 ,-.49494995002487663642] 
dist 189=[-2.2709515845653035003 ,-.51816584009171179808] 
dist 190=[-2.2967399619189360954 ,-.39242051063574689426] 
dist 191=[-2.3116567560601602167 ,-.01345577112164464892] 
dist 192=[-2.3106183153780171056 ,.24197313173589866914] 
dist 193=[-.87689082108001634505,.45528866111721411526] 
dist 194=[-.83963794902467455394,.66626507843787250094] 
dist 195=[-.5640906130212741064 ,.85904568618446115092] 
dist 196=[-.51266631467766967698,.99977882144347623767] 
dist 197=[-.42590180882635185426,1.1290399070604311586 ] 
dist 198=[-.40502597895870265327,1.2760586251339986496 ] 
dist 199=[-.15727195688185651941,1.4108426882642624592 ] 
dist 200=[-.17978931582310394899,1.4913005699980678140 ] 
dist 201=[-.21058474020895325214,1.5472021185024721589 ] 
dist 202=[-.2462884801427880508 ,1.5840333165749336100 ] 
dist 203=[-.29235753778718414369,1.6082349148097999550 ] 
dist 204=[-.36449689104639376817,1.6137574188476230669 ] 
dist 205=[-.45386180192726261107,1.6106384576747832914 ] 
dist 206=[-.55695596274295133069,1.6039591833221680747 ] 
dist 207=[-.68340537682052931229,1.5314492177110420764 ] 
dist 208=[-.8744276318098249164 ,1.5298190374350434632 ] 
dist 209=[-1.0636174200199877597 ,1.6829913521786445353 ] 
dist 210=[-1.1827561941516680736 ,1.7757609698465331055 ] 
dist 211=[-1.2731382493128564551 ,1.8371391062763220845 ] 
dist 212=[-1.3476188049634238989 ,1.8715665957694998878 ] 
dist 213=[-1.4060013140233163977 ,1.8925289827717409456 ] 
dist 214=[-1.4321693823498747644 ,1.9001912739264358485 ] 
dist 215=[-1.4444464521934354358 ,1.8995710122282521870 ] 
dist 216=[-1.4474199847509061230 ,1.8936624976252896242 ] 
dist 217=[-1.3996561352993513730 ,1.6246588883747032652 ] 
dist 218=[-1.3861327474741821896 ,1.5824326174071118587 ] 
dist 219=[-1.3590795151849370149 ,1.5020590638376977670 ] 
dist 220=[-1.3486469774475222969 ,1.4791044585313361566 ] 
dist 221=[-1.2944439186332888558 ,1.3892477241628433703 ] 
dist 222=[-1.4148667534272647591 ,1.3657034972140812471 ] 
dist 223=[-1.6674879111277765183 ,1.4086086543568037840 ] 
dist 224=[-1.8226671318646029610 ,1.4896844971890739849 ] 
dist 225=[-1.9358781920380107369 ,1.5457691122412302908 ] 
dist 226=[-2.0210863129423383095 ,1.5822301478937843688 ] 
dist 227=[-2.0855701343258960984 ,1.6062373657724157464 ] 
dist 228=[-2.1161105214722157922 ,1.6126443824725966304 ] 
dist 229=[-2.1275763212677319869 ,1.6100084065151625727 ] 
dist 230=[-2.1274232095287469658 ,1.6044218264530419314 ] 
dist 231=[-1.9463468632438205335 ,1.4422221111270833430 ] 
dist 232=[-1.9129987471380250866 ,1.4137223992332268692 ] 
dist 233=[-1.8531488972858501964 ,1.3527510976950680827 ] 
dist 234=[-1.8349602828912175611 ,1.3329513596083855647 ] 
dist 235=[-1.7605484858311839844 ,1.2409366135859542159 ] 
dist 236=[-1.7385492219632268134 ,1.2208408349663651251 ] 
dist 237=[-1.6907152205117998434 ,1.1591440799498606015 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 1, 2, 1, 1, 2] 
dist 0=[66.741062254561466311  ,66.741062254561466311  ] 
dist 1=[66.046667904496529114  ,66.982817264800287123  ] 
dist 2=[64.969756864113545875  ,67.253510976068606240  ] 
dist 3=[63.424612712347719629  ,67.467931134472307054  ] 
dist 4=[61.238526605223505442  ,67.467072470500308542  ] 
dist 5=[57.602459234653954614  ,67.346554152827713207  ] 
dist 6=[53.834637787995192687  ,67.209248959674196828  ] 
dist 7=[51.122394600370759288  ,66.774194569276361550  ] 
dist 8=[48.660121065636835190  ,65.879773825738852842  ] 
dist 9=[45.890113490935172101  ,62.874501459340853623  ] 
dist 10=[43.128655644705752680  ,62.175766693452981990  ] 
dist 11=[39.116199741729228816  ,61.182750993586154706  ] 
dist 12=[32.330364173179498819  ,60.833407269983488531  ] 
dist 13=[27.721902120133391006  ,60.136615834079491949  ] 
dist 14=[23.818915956261226471  ,59.796282235546729760  ] 
dist 15=[19.850092918840021554  ,57.392374711320360148  ] 
dist 16=[16.135850604338524070  ,51.816995628259178916  ] 
dist 17=[13.249455230734856676  ,29.580996327189347637  ] 
dist 18=[10.412678761063078716  ,27.179840047833436019  ] 
dist 19=[6.8966723336923604260 ,23.906850612081894440  ] 
dist 20=[3.5503535806496019084 ,23.303319614037411701  ] 
dist 21=[1.3911196151857412071 ,23.152721255763692062  ] 
dist 22=[-.31470168988383750738,11.778863842294487674  ] 
dist 23=[-1.8507071978188497252 ,10.084921320889486106  ] 
dist 24=[-3.1621508273575932095 ,9.7929397956151301027 ] 
dist 25=[-3.9713818199985090324 ,.75232308063680441691] 
dist 26=[-4.8634835979652962514 ,-.28173840909472137117] 
dist 27=[-6.4856965813879265144 ,-2.4752905346070431983 ] 
dist 28=[-8.0259589947991801792 ,-2.8342279433799063732 ] 
dist 29=[-9.8651269760312270117 ,-4.6611263124712117304 ] 
dist 30=[-11.588790742754435300  ,-5.1240015221655314924 ] 
dist 31=[-12.667619407103755495  ,-5.7987878628692031739 ] 
dist 32=[-13.484798430104745654  ,-6.1742098073476059222 ] 
dist 33=[-14.163140106819495553  ,-5.9952305048969756386 ] 
dist 34=[-14.703601595188442036  ,-5.6553787788464768204 ] 
dist 35=[-14.969951095320533806  ,-4.9689077905205996334 ] 
dist 36=[-15.091457279316077808  ,-3.9078522053103673812 ] 
dist 37=[-15.104408324163434654  ,-2.1574191532660794548 ] 
dist 38=[-8.6374855614957421509 ,-.3602844584640991425 ] 
dist 39=[-8.5400702111337500881 ,.94912287991266155661] 
dist 40=[-8.4987629821646096497 ,2.0311377871988693828 ] 
dist 41=[-7.3233697188171862243 ,3.0825459194394825202 ] 
dist 42=[-7.1496285495933083500 ,4.0315274840588457108 ] 
dist 43=[-6.7476875845184225499 ,4.7050830231219893373 ] 
dist 44=[-6.6337044662841544458 ,5.3049740885458102323 ] 
dist 45=[-6.0709573833205627629 ,5.9602594243376713450 ] 
dist 46=[-5.9566340148631456441 ,6.5539536346041071204 ] 
dist 47=[-5.6999320119014279399 ,6.9081680219615038076 ] 
dist 48=[-5.6211019271307100561 ,7.1547063236134518949 ] 
dist 49=[-2.6822695938327987301 ,7.3187665406443509341 ] 
dist 50=[-2.4621251480071705329 ,7.4215175687083114252 ] 
dist 51=[-2.4017291087011922419 ,7.4384325653029981127 ] 
dist 52=[-1.6040814093020593917 ,7.3939821502374376425 ] 
dist 53=[-1.4884779027492240972 ,7.3715235122952769036 ] 
dist 54=[-1.2082542857055251008 ,6.5144602411442137710 ] 
dist 55=[-1.1574129558638450073 ,6.5097639595962105736 ] 
dist 56=[-.73639476849921424731,6.4413735905848468400 ] 
dist 57=[-1.2641296863678601662 ,6.6317349128670803592 ] 
dist 58=[-1.9148343124929967694 ,6.8151673023492275178 ] 
dist 59=[-2.3972199335418630512 ,6.9126180132037273310 ] 
dist 60=[-2.8473728657628602604 ,6.9308856794448093008 ] 
dist 61=[-3.3695723447321699572 ,6.8730129924502395058 ] 
dist 62=[-3.8525296591790239795 ,6.8423035116477067638 ] 
dist 63=[-4.1461885644398999081 ,6.8083461831908393768 ] 
dist 64=[-4.3567213682028568741 ,6.7727389817268267988 ] 
dist 65=[-4.5081453582606981284 ,-.63365634638715488244] 
dist 66=[-4.6154318158122456766 ,-1.2061433996601819237 ] 
dist 67=[-4.6499222756625567004 ,-1.3006474718520248756 ] 
dist 68=[-4.9322038457746894711 ,-1.3658818473685265480 ] 
dist 69=[-5.1329125007665865865 ,-1.0312566756217101670 ] 
dist 70=[-5.2766796682713125214 ,-.68151339624832822919] 
dist 71=[-5.3800809116561983789 ,-.43776095687264469105] 
dist 72=[-5.4495061655864491865 ,-.13827383006308870642] 
dist 73=[-5.4577221526962898835 ,.26237821448060447673] 
dist 74=[-5.4619897798804078004 ,.63489544668892239505] 
dist 75=[-5.5812484484600763200 ,.91702168040931209676] 
dist 76=[-5.6654021761245199280 ,1.1861188407134612272 ] 
dist 77=[-5.7205421969575140053 ,1.5067123261539177606 ] 
dist 78=[-5.7240332821040314678 ,1.8062711895362853992 ] 
dist 79=[-5.7006522522006365685 ,1.9914888775512203760 ] 
dist 80=[-5.6752955039901228175 ,2.1279237056898720671 ] 
dist 81=[-2.4464415122391305374 ,2.2329199336018699711 ] 
dist 82=[-2.1625444090553586955 ,2.3119112052760914162 ] 
dist 83=[-1.5058594477584693403 ,2.3446421023420671529 ] 
dist 84=[-1.3831181326793896510 ,2.7440300346107548193 ] 
dist 85=[-.53241710606432379381,3.0000733721196121358 ] 
dist 86=[-.38081008160243930084,3.1833581816678083574 ] 
dist 87=[-.34111432776228514934,3.3146259136360444226 ] 
dist 88=[-.45509744012800534932,3.4122388400642629298 ] 
dist 89=[-.5629449913609414547 ,3.4612854775161593057 ] 
dist 90=[-.65788647410510139314,3.5247932019564841803 ] 
dist 91=[-.72040655010033679674,3.7328702764798460661 ] 
dist 92=[-.77074955242164081118,3.8812572258312712205 ] 
dist 93=[-.81711716996506163769,3.9910101671053505338 ] 
dist 94=[-.85716858955386009267,4.0449929115177958668 ] 
dist 95=[-.88233760791669994511,4.0683422701880278008 ] 
dist 96=[-.92015633674874972476,4.0638893255346457117 ] 
dist 97=[-.99813715837153153895,.88700890794873692152] 
dist 98=[-1.0619667095132013615 ,.92346368114851796169] 
dist 99=[-1.0960158703652832203 ,.9936150356231155107 ] 
dist 100=[-1.1148064578405187895 ,1.0724175492814158029 ] 
dist 101=[-1.2480267513740163424 ,1.1433689580618745776 ] 
dist 102=[-1.3623284900481666698 ,1.2220307938474119757 ] 
dist 103=[-1.4565359128719573600 ,1.3315669543813953558 ] 
dist 104=[-1.6331350198800114214 ,1.4522457490215677674 ] 
dist 105=[-1.8901443500453934083 ,1.5753378378752789080 ] 
dist 106=[-2.0928007885556003212 ,1.7234477099507814232 ] 
dist 107=[-2.5167125843471866590 ,1.9438934513394912200 ] 
dist 108=[-2.9286331841104893422 ,2.1604761490306986584 ] 
dist 109=[-3.1794919997941803236 ,2.2931718953568854023 ] 
dist 110=[-3.3600290168566194795 ,2.3894505987520424752 ] 
dist 111=[-3.4914141750186708046 ,2.4607815925844786736 ] 
dist 112=[-3.5890415675312587162 ,2.5107837623213128281 ] 
dist 113=[-3.6349011982937985884 ,2.5225961584700664347 ] 
dist 114=[-3.6515740341947585021 ,2.5201112474218368600 ] 
dist 115=[-3.6492166274438845408 ,2.5179048085594278173 ] 
dist 116=[-3.2984726052492712978 ,2.3683038678170566679 ] 
dist 117=[-3.2369540565751541372 ,2.3366132013232594643 ] 
dist 118=[-3.1253327147246342366 ,2.4244025580971194768 ] 
dist 119=[-3.0921555023517353851 ,2.8217875139158262203 ] 
dist 120=[-2.9591591269364794943 ,3.1313110195668113267 ] 
dist 121=[-2.9205250977166580104 ,3.4009627286259001120 ] 
dist 122=[-2.8397818355877264341 ,3.6237128048608055420 ] 
dist 123=[-2.8112957433912048830 ,3.7461515435754949605 ] 
dist 124=[-2.1724189854203585573 ,3.8183498665960324950 ] 
dist 125=[-2.1439355495976628866 ,3.8407020482430153092 ] 
dist 126=[-1.8117989750498039222 ,3.8413863268479778114 ] 
dist 127=[-1.7586206857214469767 ,3.8271506182918688012 ] 
dist 128=[-1.6129726553151028237 ,3.7993369243188271174 ] 
dist 129=[-1.6009153160795071603 ,3.7829588189417284388 ] 
dist 130=[-1.5723202281513520026 ,3.6801135245317754947 ] 
dist 131=[-1.5582205670185551200 ,3.6509167343614227769 ] 
dist 132=[-1.5373042346900226453 ,3.5386068701870604877 ] 
dist 133=[-1.5274418459817556278 ,3.5198965405091498662 ] 
dist 134=[.17339133301836553803,1.6562112025236712923 ] 
dist 135=[-.05060354835980207290,1.7717117202920855108 ] 
dist 136=[-.23706812097627279285,1.8862903568472588596 ] 
dist 137=[-.42048785559689617457,1.9866699094923421995 ] 
dist 138=[-.58742972384166038297,2.0455272546356663900 ] 
dist 139=[-.70816928978668870287,2.0851448142631823263 ] 
dist 140=[-.81793575680372299027,2.1087706750523425703 ] 
dist 141=[-.94111222938425651887,2.1202715770668680488 ] 
dist 142=[-1.0545979098817859150 ,2.1191690678189763804 ] 
dist 143=[-1.1257091520184767689 ,2.0974519807564151161 ] 
dist 144=[-1.1792596352588374585 ,2.0877466086160955418 ] 
dist 145=[-1.2226931295807805354 ,1.0541552164041100878 ] 
dist 146=[-1.2561948678731645739 ,.95863006364378386871] 
dist 147=[-1.2701261243395582592 ,.73271140843704419847] 
dist 148=[-1.2739939418983996147 ,.69245699856620293689] 
dist 149=[-1.2718046883992041882 ,.38172623957087656649] 
dist 150=[-.77178077378955372712,.3249764557725859764 ] 
dist 151=[-.91363109531539488891,.23334892334058164311] 
dist 152=[-1.0811487406135335312 ,.21079301894026988505] 
dist 153=[-1.2367196657602425733 ,-.16788233739632045892] 
dist 154=[-1.3309135906429924584 ,-.08095144584312013934] 
dist 155=[-1.3980077645470894667 ,.00535463317995519410] 
dist 156=[-1.4454746381543810711 ,.09397990134269359992] 
dist 157=[-1.4798207502822010525 ,.20867526223247534543] 
dist 158=[-1.4945742368427989998 ,.31956444910258762901] 
dist 159=[-1.4978974182926533816 ,.39300992471215005605] 
dist 160=[-1.4961861148479788197 ,.45294168104206954907] 
dist 161=[-.39742875156301964157,.50992964470271446566] 
dist 162=[-.38851365373557031599,.56053594392754838012] 
dist 163=[-.38695956636253963111,.59501538176957772853] 
dist 164=[-.39506078972530112778,.62423438118208278635] 
dist 165=[-.4087327358705748165 ,.65386399705701694649] 
dist 166=[-.42939942884883079606,.68005995373892149269] 
dist 167=[-.45910741528277863714,.71667354057455073245] 
dist 168=[-.50884428765429916185,.75976997219147501053] 
dist 169=[-.56227420217038525221,.80294815337160413728] 
dist 170=[-.60671316795981031514,.84280556958761379527] 
dist 171=[-.65298447767379148283,.87265227634942466257] 
dist 172=[-.71372272807390281238,.90084232190552519757] 
dist 173=[-.77895331297777078534,.9340892156572288148 ] 
dist 174=[-.84314377953982705935,.9647460036492100409 ] 
dist 175=[-.91872855711541136861,1.0420804447931122048 ] 
dist 176=[-1.0294096625437728128 ,1.2628653997321825256 ] 
dist 177=[-1.1376522253960767882 ,1.4780056209111886775 ] 
dist 178=[-1.2035094433598316577 ,1.6096886563218543720 ] 
dist 179=[-1.2507894850701636699 ,1.7052123825936411959 ] 
dist 180=[-1.2849284468354378878 ,1.7761070323473583586 ] 
dist 181=[-1.3082877722893629306 ,1.8293901660219104442 ] 
dist 182=[-1.3134565604493828324 ,1.8546576037158155187 ] 
dist 183=[-1.3105145671140509922 ,1.8641966367747742703 ] 
dist 184=[-1.4177751169868464336 ,1.8635840612554915296 ] 
dist 185=[-1.5402705048106061795 ,1.6960511501793225821 ] 
dist 186=[-1.6425225246418585240 ,1.6659309167308529762 ] 
dist 187=[-1.7007552970899711053 ,1.6119406190075642141 ] 
dist 188=[-1.7377951428693452413 ,1.5957695728702834438 ] 
dist 189=[-1.7555048787830837811 ,1.5307006000899869540 ] 
dist 190=[-1.7633173840324801720 ,1.5113743132361083622 ] 
dist 191=[-1.7608748206108966289 ,1.4708236562896626839 ] 
dist 192=[-1.7512336864669946893 ,1.4563245649492747934 ] 
dist 193=[-1.7443417938353210508 ,.68840407438022374207] 
dist 194=[-1.6968112338259423777 ,.63001736430846567835] 
dist 195=[-1.6830996272092395457 ,.61694087571000555264] 
dist 196=[-1.6350464811352356653 ,.58623455036359854728] 
dist 197=[-1.6237285862026328546 ,.57588881312351256082] 
dist 198=[-.79446626236860194246,.58300120717358414309] 
dist 199=[-.79386817599009642193,.79782773817257671093] 
dist 200=[-.79188943982489575773,.97128671326797866767] 
dist 201=[-.69328089792125099294,1.1331488792170738304 ] 
dist 202=[-.67725641897760457994,1.2747756420160882536 ] 
dist 203=[-.64587539019654824461,1.3675142258645064152 ] 
dist 204=[-.63654773762018533079,1.4420178463943806296 ] 
dist 205=[-.59787161628382267762,1.5109042038920534120 ] 
dist 206=[-.58828544173505613847,1.5692508468779272411 ] 
dist 207=[-.56556496619999295191,1.6017107346238703388 ] 
dist 208=[-.55754986369334835878,1.6213608119395222366 ] 
dist 209=[-.04341967595231114123,1.6286078720760706930 ] 
dist 210=[.00300908314960488309,1.6273117644036124468 ] 
dist 211=[.09668054005256123565,1.6234055357163125543 ] 
dist 212=[.11978600600697386162,1.5970777753513952744 ] 
dist 213=[.19604414450669128155,1.5902963812427910654 ] 
dist 214=[.03233685348148666662,.75814847734502497206] 
dist 215=[-.18177915833570161751,.80115029833444811265] 
dist 216=[-.36206078505947804721,.88215584151912609428] 
dist 217=[-.5427935937238124233 ,.9574112206801009553 ] 
dist 218=[-.70954225805227686088,1.0021416123762427028 ] 
dist 219=[-.83404015266595400249,1.0329969791895250046 ] 
dist 220=[-.9511825562895307614 ,1.0529019533324757625 ] 
dist 221=[-1.0885896179098606697 ,1.0650249690891527212 ] 
dist 222=[-1.2151589567195477602 ,1.0665953605485164072 ] 
dist 223=[-1.2890688155251984505 ,1.0605711817147597408 ] 
dist 224=[-1.3384114377610472357 ,1.0564310183198054140 ] 
dist 225=[-1.3669800661339772285 ,-.22605774914642465043] 
dist 226=[-1.3853403432343823260 ,-.23584007403708711085] 
dist 227=[-1.3939612025063002773 ,-.22173631270162732482] 
dist 228=[-1.3970812351642481221 ,-.1909814483358127981 ] 
dist 229=[-1.3934988096808904020 ,-.12953637514969260417] 
dist 230=[-.87554940894164954067,-.06314659676035744772] 
dist 231=[-.90451503572104055548,-.01266709144007074257] 
dist 232=[-.92673582974630958218,.03572512042825953514] 
dist 233=[-.94320289255382011373,.09378798747060683761] 
dist 234=[-.94921648223864837472,.15347973694613916961] 
dist 235=[-.94903928727342495545,.20836926230256052887] 
dist 236=[-.9470291030014190865 ,.27014185094659463384] 
dist 237=[-.92611516663148492447,.35728995889488458594] 
dist 238=[-.91906117665781364824,.44496618627652236771] 
dist 239=[-.89782488906651396579,.50884518377553529199] 
dist 240=[-.8888136166828921369 ,.56739520162878106423] 
dist 241=[-.44372678442859463299,.63381354633798287111] 
dist 242=[-.39864138349723590771,.700037728967408489  ] 
dist 243=[-.29937964020008936201,.7578128275151043341 ] 
dist 244=[-.24568344789754193712,.82034305022561070003] 
dist 245=[-.06394705759572694733,.90553480918239408246] 
dist 246=[.65070190915498705086,.98629151468916620319] 
dist 247=[.68822571968555926146,1.0311300477971978369 ] 
dist 248=[.6928744740643711973 ,1.0581503868647135221 ] 
dist 249=[.68576336758957318653,1.0678301623442516209 ] 
dist 250=[.66143227874434816986,1.0711608195773000877 ] 
dist 251=[.61987990410062852069,1.0728548315092233112 ] 
dist 252=[.54407241565672205211,1.0736696372594470568 ] 
dist 253=[.4522439267414943856 ,1.0673626232165851924 ] 
dist 254=[.34678334728241503439,.85759927045774317648] 
dist 255=[.21135810968816793088,.82715390183127077617] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 0, 0, 0, 2] 
dist 0=[54.955519647167661930  ,54.955519647167661930  ] 
dist 1=[53.635602553260861270  ,55.804653812389017047  ] 
dist 2=[51.325750576838115961  ,56.234981878144022135  ] 
dist 3=[48.897617162621056907  ,56.497147933710287482  ] 
dist 4=[47.105530373325725809  ,56.674839585443315570  ] 
dist 5=[45.434154180501399636  ,56.863561662436568762  ] 
dist 6=[43.488082102228117832  ,57.030352796179428674  ] 
dist 7=[41.512093244829322834  ,57.078088679970175039  ] 
dist 8=[39.721374686396812226  ,56.705990976227891508  ] 
dist 9=[37.721815523855054508  ,53.614848470678264286  ] 
dist 10=[34.912202465234515733  ,53.067735940924897643  ] 
dist 11=[32.076947137936954403  ,52.098280447667818218  ] 
dist 12=[29.975046191545300391  ,51.829664569829228921  ] 
dist 13=[28.006193329784564327  ,50.848140096998261753  ] 
dist 14=[25.599296686236528671  ,50.547637124060746130  ] 
dist 15=[23.114748228236695274  ,50.064327636906703982  ] 
dist 16=[20.670731895037714793  ,49.579975418063002683  ] 
dist 17=[17.342570544103600121  ,29.210301705090476961  ] 
dist 18=[13.928849327545296787  ,27.457104089024138461  ] 
dist 19=[10.577160197634972178  ,23.295288976227018414  ] 
dist 20=[8.0386729674130591350 ,22.685006074717780672  ] 
dist 21=[5.6642262416718280692 ,16.976295742781553299  ] 
dist 22=[2.4912502613186792491 ,15.956586574108438355  ] 
dist 23=[-.5612060148298574593 ,14.670744943563602451  ] 
dist 24=[-2.6006553870464107508 ,14.416961745329824025  ] 
dist 25=[-4.2958356917341405527 ,6.9263551357372655550 ] 
dist 26=[-5.9742593944011601865 ,6.0409420618364350889 ] 
dist 27=[-7.5248123189649429301 ,4.1371524324533463831 ] 
dist 28=[-8.7102953514134592357 ,3.7799631810567441886 ] 
dist 29=[-9.8653467565876038129 ,1.8450547996757632451 ] 
dist 30=[-11.296399358660027181  ,1.5328484014515832828 ] 
dist 31=[-12.626505260367861829  ,.94882681785948419147] 
dist 32=[-13.378568552403734692  ,.83479155916994722845] 
dist 33=[-13.862210436936137688  ,1.0659305501069388826 ] 
dist 34=[-14.118768763258324624  ,2.3756129545870686268 ] 
dist 35=[-14.271960886489718527  ,3.7064216930200929204 ] 
dist 36=[-14.341689856091619237  ,4.5779944815351731744 ] 
dist 37=[-14.367509139533347883  ,5.2747419299572195126 ] 
dist 38=[-14.343620202278161110  ,5.9089000533290204242 ] 
dist 39=[-12.363112965153114990  ,6.4493372372131200591 ] 
dist 40=[-12.073215224649047003  ,6.7725043960188069457 ] 
dist 41=[-11.527945127859875169  ,6.9958383166566257457 ] 
dist 42=[-11.380410360337354184  ,7.1381368254800784240 ] 
dist 43=[-10.849791521975538105  ,7.2349790240008593044 ] 
dist 44=[-10.704257394783004957  ,7.2771380707949845251 ] 
dist 45=[-10.509794563997140921  ,7.2860065598603197263 ] 
dist 46=[-10.433529382256007769  ,7.2585946836847094715 ] 
dist 47=[-8.8420313082557823552 ,7.1882240412548447310 ] 
dist 48=[-8.7975451249057605251 ,7.1425622518647303855 ] 
dist 49=[-5.9059142785302999969 ,6.9905200603878893572 ] 
dist 50=[-5.8459643371879709043 ,6.9145711551078714771 ] 
dist 51=[2.0963567302904364865 ,5.2627626796767532639 ] 
dist 52=[2.3733428459913570842 ,6.0707848981960397061 ] 
dist 53=[2.9641344957408205627 ,6.7562609894668442546 ] 
dist 54=[3.0637494905857744813 ,7.3357981735130119269 ] 
dist 55=[3.7442005650209735470 ,8.3143290966173513430 ] 
dist 56=[3.8184657691158363548 ,8.9201247909490773716 ] 
dist 57=[3.7472425509878727055 ,9.3695378090491366674 ] 
dist 58=[3.4605944445079035142 ,9.7237988800681495124 ] 
dist 59=[3.0591815668218263130 ,9.9904229852071907465 ] 
dist 60=[2.5299213248047613762 ,10.090004862743152911  ] 
dist 61=[1.8069574108183195149 ,10.122645734259226280  ] 
dist 62=[.63258359159617437798,10.121966164115758460  ] 
dist 63=[-.55732556181718893098,8.0389042780761908963 ] 
dist 64=[-1.5268727044529799176 ,8.0058979126175940672 ] 
dist 65=[-2.3509923766689429929 ,2.5129490799317012526 ] 
dist 66=[-3.1529106477870593661 ,2.0540353302972029879 ] 
dist 67=[-3.8777099085127830315 ,1.0205511182749838386 ] 
dist 68=[-4.3942031346431669418 ,.82138726526171194982] 
dist 69=[-4.8563471599197674444 ,-.41618156028463782755] 
dist 70=[-5.3643754740483126404 ,-.62873370761553348111] 
dist 71=[-5.8229917683696809526 ,-1.0455336282112942222 ] 
dist 72=[-6.0880188472897555774 ,-1.1429426029716595208 ] 
dist 73=[-6.2618092980513690021 ,-1.9793244957340601140 ] 
dist 74=[-6.3564195053098341263 ,-2.1100503647312942717 ] 
dist 75=[-6.4065039467802774007 ,-2.1844122358694487120 ] 
dist 76=[-6.4026358182241752509 ,-2.1027368669497417422 ] 
dist 77=[-6.3716511858589219546 ,-1.9436307010725882103 ] 
dist 78=[-6.3407753545628253028 ,-1.3620159259636603572 ] 
dist 79=[-6.2396392846134595212 ,-.25209287133006054089] 
dist 80=[-6.2461380773419447610 ,.49278603624023591243] 
dist 81=[-3.4632298567142827522 ,1.1110765068769559777 ] 
dist 82=[-3.3699940513656016540 ,1.7161198532974077208 ] 
dist 83=[-2.5059034928410300403 ,2.2645887480860607411 ] 
dist 84=[-2.3393633334240259658 ,2.6572456796875263130 ] 
dist 85=[-2.1174210069789208644 ,3.0100813812099485622 ] 
dist 86=[-2.0451436762043401493 ,3.3997459566661929345 ] 
dist 87=[-.60247224175694578435,3.7553596245563133348 ] 
dist 88=[-.42061052155630103438,3.9723851574540553600 ] 
dist 89=[-.01192876011120044183,4.1290420792664750711 ] 
dist 90=[.06530104786910649404,4.2438590017988946764 ] 
dist 91=[.54856005624475385155,4.3228018775246716603 ] 
dist 92=[.58754519518519759095,4.3394096395741738978 ] 
dist 93=[.50222711564987387838,4.3278054646990074641 ] 
dist 94=[.33438920851851165002,4.3184385939544498235 ] 
dist 95=[.15492229780981022734,3.3225369607022352801 ] 
dist 96=[.02321328266629155797,3.3055857115445282634 ] 
dist 97=[-.09786829466296975193,2.1890745396094807501 ] 
dist 98=[-.23506773052030685838,2.0756571219439196147 ] 
dist 99=[-.53222660845033025948,1.7888105480587368950 ] 
dist 100=[-.79464846555202679988,1.7433495188588235901 ] 
dist 101=[-1.0409163548017147813 ,1.2846027270771414816 ] 
dist 102=[-1.3286396537403678046 ,1.1963815737661958541 ] 
dist 103=[-1.5975650194144126636 ,1.0882556256291160091 ] 
dist 104=[-1.7688676411914110871 ,1.0575724744326760515 ] 
dist 105=[-1.9010600687677725911 ,.26646432619208165586] 
dist 106=[-2.0139885574945771898 ,.16872878664938315666] 
dist 107=[-2.1055672985802022939 ,-.04509023725403182903] 
dist 108=[-2.1526027383470025951 ,-.08944272503100868203] 
dist 109=[-2.1759064383305615387 ,-.32249765431719753047] 
dist 110=[-2.1776404754471675152 ,-.36150353229098484691] 
dist 111=[-1.9406034496460886829 ,-.44439053473166995845] 
dist 112=[-1.9397562567304264176 ,-.45858832784098342695] 
dist 113=[-1.0811239608306438270 ,-.86497912342937607404] 
dist 114=[-1.0471932104309268126 ,-.69072980960119887294] 
dist 115=[-.7819438201671498054 ,-.51695645581045030983] 
dist 116=[-.73129809037444573395,-.36574423384870814918] 
dist 117=[-.64973305726612282079,-.20256980674596830692] 
dist 118=[-.62846564490668267045,.01894152310451153814] 
dist 119=[-.24014532571493219755,.23776954270945504227] 
dist 120=[-.18955501536692176371,.39026118285330436723] 
dist 121=[-.0782695764636689665 ,.52299216437437731369] 
dist 122=[-.05593410633158821680,.66303580309073867774] 
dist 123=[.06607715087828873789,.79674314905083730213] 
dist 124=[.08618436266279896521,.904228262438464475  ] 
dist 125=[.12856868710282317912,1.0129602465244466116 ] 
dist 126=[.13554180151096745175,1.1516876290453089716 ] 
dist 127=[.51718039977936207127,1.2954422863064742051 ] 
dist 128=[.52165613314829260423,1.4052731663216431567 ] 
dist 129=[.52373186010755331133,1.4944997669799790447 ] 
dist 130=[.51341246470684086132,1.5788467266550273397 ] 
dist 131=[.49396784726359788437,1.6535331517130039681 ] 
dist 132=[.4572019232033539618 ,1.7042112125603476283 ] 
dist 133=[.41234811141867815366,1.7469790648555313368 ] 
dist 134=[.36062890303721240808,1.7901020882172882175 ] 
dist 135=[.29415534789244296725,1.8261420202655052659 ] 
dist 136=[.19043752106419873227,1.8406454255181904167 ] 
dist 137=[.08190401858982927727,1.8424787557125894693 ] 
dist 138=[-.00378864660270967667,1.8396056342846370602 ] 
dist 139=[-.09470319853542946572,1.8035354267218582068 ] 
dist 140=[-.37736990911530480367,1.7907527186916437012 ] 
dist 141=[-.71397680305366798707,1.7525464656411197697 ] 
dist 142=[-1.2113435919626411004 ,1.7352904089442920389 ] 
dist 143=[-1.7045775180238409306 ,1.5240516146109832570 ] 
dist 144=[-2.0247026814232275599 ,1.4860790928716617656 ] 
dist 145=[-2.2787370823195989625 ,1.4065768100436388168 ] 
dist 146=[-2.5083271146308246516 ,1.3821663596519954973 ] 
dist 147=[-2.7041356467791053474 ,1.2746386532951373278 ] 
dist 148=[-2.8234136658701582910 ,1.2512141101149664993 ] 
dist 149=[-2.9092820069077857887 ,1.1841778391184832809 ] 
dist 150=[-2.9718213995396669318 ,1.1713902944491329234 ] 
dist 151=[-3.0160813702394178562 ,1.0298431925656249865 ] 
dist 152=[-3.0290300556177332285 ,1.0014601062753194279 ] 
dist 153=[-3.0243844736174924931 ,.94564935537543258097] 
dist 154=[-3.0154061080732780147 ,.92938435324903283233] 
dist 155=[-2.9366198770134846227 ,.86316673944745541163] 
dist 156=[-2.9114716253469029112 ,.84702171457455291824] 
dist 157=[-2.8427673940924435988 ,.80997163617847959758] 
dist 158=[-2.8134075292204832529 ,.79728879406031850745] 
dist 159=[-1.5630418957988175542 ,.86719525086183383691] 
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dist 162=[-1.2374172873593442975 ,2.0015477686717621808 ] 
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dist 164=[-1.1173914731454839270 ,2.5019232143072762455 ] 
dist 165=[-.99185199042206923834,2.6642987735569351015 ] 
dist 166=[-.96564165992592386601,2.8183442394059180618 ] 
dist 167=[-.89996570695689318853,2.9516472640379387606 ] 
dist 168=[-.88374317997600093233,3.0312813555301749623 ] 
dist 169=[-.70742032417693464934,3.0866998054299627369 ] 
dist 170=[-.67726655673457698122,3.1234035354013600486 ] 
dist 171=[-.61370648654824660484,3.1451854980875886913 ] 
dist 172=[-.59543555343889027723,3.1425329534509766388 ] 
dist 173=[-.52008495427381229146,3.1246759484298760400 ] 
dist 174=[-.50444042120773632848,3.1084787543675462515 ] 
dist 175=[-.46526063372194938428,2.1916541917889606680 ] 
dist 176=[-.45618810283619731272,2.1702349410902694866 ] 
dist 177=[-.49780163446540506794,.84666831925845318191] 
dist 178=[-.80354897345131253403,.78427800286163438208] 
dist 179=[-1.0742647088961422394 ,.36157407905954182776] 
dist 180=[-1.3326811156740682860 ,.28560842829058181891] 
dist 181=[-1.5627586520118542064 ,.14654478382717562487] 
dist 182=[-1.7204322878199822406 ,.11498572796744216456] 
dist 183=[-1.9285544221719733925 ,-.31045052203117224654] 
dist 184=[-2.0654679955949671834 ,-.37014408603799889128] 
dist 185=[-2.1587929792776892128 ,-.46967764808126251369] 
dist 186=[-2.2167408367176102753 ,-.49129216255917419352] 
dist 187=[-2.2565616689993229646 ,-.51627153765930640936] 
dist 188=[-2.2811966071849284212 ,-.49420324620697450599] 
dist 189=[-2.2960983702307165645 ,-.44255794183457148186] 
dist 190=[-2.2956119380771627326 ,-.33721416321906020168] 
dist 191=[-2.2549115454770215765 ,-.21402962605879952073] 
dist 192=[-2.2478397811528651878 ,.02107132094302410350] 
dist 193=[-1.1892473911864893669 ,.22146323724125344827] 
dist 194=[-1.0899594300917757174 ,.4262756219493009229 ] 
dist 195=[-.87390825671704666283,.61772104408991577773] 
dist 196=[-.83623138318288898376,.76479437684746432018] 
dist 197=[-.55778887527702819152,.90722052126643795767] 
dist 198=[-.50588966617683187891,1.0801305452468555638 ] 
dist 199=[-.41822867551907814952,1.2419283211295182836 ] 
dist 200=[-.39719615010009309745,1.3400292836247827878 ] 
dist 201=[-.3009217934650804573 ,1.4146293054222904556 ] 
dist 202=[-.37326842972542382914,1.4962076394503660160 ] 
dist 203=[-.46506862830809961419,1.5528997776250741748 ] 
dist 204=[-.56746412620980522245,1.5902756900370960941 ] 
dist 205=[-.69295724351174251964,1.6149291198031478217 ] 
dist 206=[-.88242419061216618992,1.6208717034190073738 ] 
dist 207=[-1.0700294155219071750 ,1.6792098528340951365 ] 
dist 208=[-1.1880952013927158268 ,1.7727191689239901370 ] 
dist 209=[-1.2775757830052845742 ,1.8347156740514791563 ] 
dist 210=[-1.3511559529848134882 ,1.8697557119981704106 ] 
dist 211=[-1.4087314632144612022 ,1.8912627018594885443 ] 
dist 212=[-1.4343705806661244279 ,1.8992723390590321550 ] 
dist 213=[-1.4462777019786491456 ,1.8989207064943327582 ] 
dist 214=[-1.4490784832170317553 ,1.8930842993930880514 ] 
dist 215=[-1.3998610349751569622 ,1.6250424394387660624 ] 
dist 216=[-1.3861471591531836896 ,1.5829368171307698219 ] 
dist 217=[-1.3584583709471621628 ,1.5029579344156655350 ] 
dist 218=[-1.3478064849750996729 ,1.4801365029218585252 ] 
dist 219=[-1.2924251018062739370 ,1.3909833418126077549 ] 
dist 220=[-1.2787376401484587682 ,1.3675158628121472233 ] 
dist 221=[-1.2314154587630280530 ,1.3202271266410750438 ] 
dist 222=[-1.2362424752859725716 ,1.3048490577600270535 ] 
dist 223=[-1.2542325348339200236 ,1.1219159732152290074 ] 
dist 224=[-1.4109446211826448050 ,1.2622903060223272968 ] 
dist 225=[-1.6605123790711237031 ,1.3986162529599180354 ] 
dist 226=[-1.8136802684955627872 ,1.4799158084170899224 ] 
dist 227=[-1.9252625942405641094 ,1.5363015115800409604 ] 
dist 228=[-2.0089434235790768923 ,1.5732471473927510415 ] 
dist 229=[-2.0721573643037113327 ,1.5977192501613504019 ] 
dist 230=[-2.1020957854041787500 ,1.6043487102634343928 ] 
dist 231=[-2.1133349108722274074 ,1.6019250728730190414 ] 
dist 232=[-2.1130347263587555015 ,1.5963408196631726763 ] 
dist 233=[-1.9300064339434453678 ,1.4375665841201453516 ] 
dist 234=[-1.8965190988294753000 ,1.4095098954480587097 ] 
dist 235=[-1.8364162072579894697 ,1.3493400269293228431 ] 
dist 236=[-1.8182182483534669094 ,1.3297268568389989990 ] 
dist 237=[-1.7440698676266509871 ,1.2383086120171433791 ] 
dist 238=[-1.7221374256839137407 ,1.2182848546738081752 ] 
dist 239=[-1.6748577056671404849 ,1.1571881879086818950 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 0, 1, 1, 2] 
dist 0=[65.700201954628155301  ,65.700201954628155301  ] 
dist 1=[65.000819069605051364  ,66.087824830704940371  ] 
dist 2=[63.692226876597207512  ,66.151739451914653705  ] 
dist 3=[62.176772450955401771  ,66.061047157979374411  ] 
dist 4=[60.651384728589124548  ,65.938255041608612876  ] 
dist 5=[58.824380183306795752  ,65.551783782115441219  ] 
dist 6=[56.104375362446956709  ,65.340900687337822121  ] 
dist 7=[53.012819713703193814  ,64.159426231372240107  ] 
dist 8=[49.702076590047011708  ,62.435777237723101425  ] 
dist 9=[45.590603377647546966  ,60.254197244920278131  ] 
dist 10=[39.301514346074853956  ,59.928564487632063495  ] 
dist 11=[32.965808936107887682  ,59.218113178579081340  ] 
dist 12=[28.668050394496644822  ,58.999650277047330003  ] 
dist 13=[25.032072844554699457  ,57.395935819924409903  ] 
dist 14=[21.338640567460596737  ,54.353996710806800294  ] 
dist 15=[17.881388118990573182  ,41.533345016175636681  ] 
dist 16=[15.188183725474302840  ,41.216239585332825966  ] 
dist 17=[12.532022574165164664  ,31.653427652111768992  ] 
dist 18=[9.2220330191060027536 ,30.423824305088203045  ] 
dist 19=[6.0532266644671558590 ,27.914695544698111576  ] 
dist 20=[3.9605094805403717696 ,27.255705508794885769  ] 
dist 21=[2.2478650537531943468 ,24.834600867365945979  ] 
dist 22=[.59644606077813307851,24.329422250632793411  ] 
dist 23=[-.8995078020565336693 ,23.422143729483395808  ] 
dist 24=[-1.9919504257372527912 ,23.207419988860495890  ] 
dist 25=[-3.0063499938660873947 ,5.9333409543363452746 ] 
dist 26=[-4.1921341891168474290 ,4.4512603067819867463 ] 
dist 27=[-5.3887707860722670368 ,1.2385722815325681436 ] 
dist 28=[-8.1044230094502984985 ,.60322364123004668583] 
dist 29=[-10.583725319930193257  ,-1.6219172622855943597 ] 
dist 30=[-12.412722761206706447  ,-2.0300043313756904611 ] 
dist 31=[-14.120604652710798512  ,-4.6355396001848476997 ] 
dist 32=[-16.116394100340150124  ,-4.8279886502086403296 ] 
dist 33=[-17.961798840677781937  ,-6.1626740905240028055 ] 
dist 34=[-19.069179537545131538  ,-6.3143012573528650703 ] 
dist 35=[-19.851701404458785995  ,-6.1825399175195039309 ] 
dist 36=[-20.399792310379403767  ,-5.6348092322454275721 ] 
dist 37=[-20.781137869145198505  ,-4.8661312413645556846 ] 
dist 38=[-20.897650626434374443  ,-3.8522801139266797554 ] 
dist 39=[-20.897808693239323381  ,-2.4674601831455923767 ] 
dist 40=[-20.826871258843260771  ,0                     ] 
dist 41=[-10.285145103338955108  ,2.0656007502428048395 ] 
dist 42=[-10.169807538482313070  ,3.5886008547876642802 ] 
dist 43=[-9.5951485448737132208 ,4.8437923921865559263 ] 
dist 44=[-9.4624440604009059086 ,6.0593493369836512723 ] 
dist 45=[-9.1521369711593957804 ,7.1548858320114387951 ] 
dist 46=[-9.0456836681667846701 ,7.9313612896278254861 ] 
dist 47=[-4.5117248969195224258 ,8.6224002727275820919 ] 
dist 48=[-4.0505944871653786132 ,9.3772524312867745636 ] 
dist 49=[-3.0283196990175420496 ,10.052531656519594819  ] 
dist 50=[-2.8017233678766681792 ,10.426045025313760318  ] 
dist 51=[-1.5896473516510144091 ,10.650100727060426024  ] 
dist 52=[-1.3723215682970142772 ,10.728756440355149975  ] 
dist 53=[-.90502909414730667298,10.746599161560656879  ] 
dist 54=[-.79100608385139607071,10.728010812741699555  ] 
dist 55=[.14936334629999557299,10.679475759825754017  ] 
dist 56=[.30717880040943221375,10.634376292123504819  ] 
dist 57=[.49963253141083705659,7.7989520469244783313 ] 
dist 58=[.53308815206611278647,7.4755218817069500511 ] 
dist 59=[-.01689563628459765425,6.6882032467443416244 ] 
dist 60=[-.41409905584867446493,6.5303136247298948772 ] 
dist 61=[-.73987478492760459992,5.3381523554748930545 ] 
dist 62=[-1.0524822305202628859 ,4.7610736075183057275 ] 
dist 63=[-1.3320497535060262335 ,-.64415418286895466979] 
dist 64=[-1.5260435365587569545 ,-.77961573864435003639] 
dist 65=[-1.6942300005978259009 ,-1.0790896350949689806 ] 
dist 66=[-1.8708755638755833232 ,-1.1242751956456142813 ] 
dist 67=[-2.0299702525849162869 ,-1.4464478389817217293 ] 
dist 68=[-2.1281463085508537321 ,-1.4948572240165813884 ] 
dist 69=[-2.2004405604545201628 ,-1.5809796047486033590 ] 
dist 70=[-2.2562702533683087903 ,-1.5950096008057236965 ] 
dist 71=[-2.2972561694883464905 ,-1.6490489504413773360 ] 
dist 72=[-2.3103286214179473652 ,-1.5807373552215655678 ] 
dist 73=[-2.3086788593976445780 ,-1.3728129648576973059 ] 
dist 74=[-2.3016212745293688678 ,-1.0308702344152633822 ] 
dist 75=[-1.8064928720007849564 ,-.68065616525114090979] 
dist 76=[-1.8041116077145986097 ,-.43972843232964844238] 
dist 77=[-1.7953331667741345991 ,-.23338761853652399323] 
dist 78=[-1.7887231108625096484 ,-.02109742376960699149] 
dist 79=[-.65822028003698172268,.17808982311242329534] 
dist 80=[-.56203466998956035617,.33218446184820648921] 
dist 81=[-.34257343995688614214,.48238323980813660137] 
dist 82=[-.30172388556939919882,.66605002096812522384] 
dist 83=[-.02894338283585728465,.83874082132992637565] 
dist 84=[.01860597219187503944,.94516626954401594658] 
dist 85=[.10674458407438802208,1.0232111086108709682 ] 
dist 86=[.12631568642868807515,1.0827008178205383164 ] 
dist 87=[.35303697842620606015,1.1287325549133156058 ] 
dist 88=[.38556766464347368389,1.1530975103471973649 ] 
dist 89=[.42454969057289273383,1.1757393082022552402 ] 
dist 90=[.42584585934950335578,1.2290096622171633572 ] 
dist 91=[.41205633557110123254,1.2694510995916097112 ] 
dist 92=[.35838177604723430852,1.2880288042652209238 ] 
dist 93=[.28556848555315615056,1.2950964064100348401 ] 
dist 94=[.20854542627778175288,1.2944465688290713028 ] 
dist 95=[.10762984837782738556,.32912802478114351444] 
dist 96=[.03286311575610329681,.31098974205339747638] 
dist 97=[-.03190941893378798963,.2805684250206018998 ] 
dist 98=[-.12016052315453290887,.27296695449711458411] 
dist 99=[-.20618192577117613587,.13539489705519991039] 
dist 100=[-.26970786419012387346,.11723826074918284731] 
dist 101=[-.32881846736728583045,.07654257030008416454] 
dist 102=[-.397234734869909084  ,.06864698546334117685] 
dist 103=[-.46101340962443805442,.02060529973630331874] 
dist 104=[-.5016220688415375179 ,.01237071732769614979] 
dist 105=[-.5329749375934260525 ,-.00394084249177419492] 
dist 106=[-.55981711708025646171,-.00778115586199000002] 
dist 107=[-.58162783769563386249,-.0396360730265083968 ] 
dist 108=[-.59289902538642913557,-.04503879299761363576] 
dist 109=[-.59855206313873423819,-.01232709252924557922] 
dist 110=[-.5989276653014845816 ,.07489149097230881007] 
dist 111=[-.53321598451672866959,.16304498761049777442] 
dist 112=[-.53221557079102872132,.22149360186982733638] 
dist 113=[-.52374094423143732922,.26923485997013639141] 
dist 114=[-.52209012038249757618,.31467596342961800598] 
dist 115=[-.48655960935168341324,.355010961061737316  ] 
dist 116=[-.47776182059237787856,.38238158112435207137] 
dist 117=[-.47102059940872619019,.40540960860153986933] 
dist 118=[-.46831886481386038106,.42841577777650431116] 
dist 119=[-.33408915377593207855,.44845586677490751191] 
dist 120=[-.31620125224325117936,.45965307198568960955] 
dist 121=[-.28090777247609289992,.46646175019002362724] 
dist 122=[-.27161839950365646282,.46900483229373204432] 
dist 123=[-.238294163870973296  ,.46887537976928940685] 
dist 124=[-.23045823938012916309,.46778601050030174614] 
dist 125=[-.21935007906565671903,.46065711026463255243] 
dist 126=[-.21574555476294898969,.45847008496783874788] 
dist 127=[.12264917523849206671,.44871873167215024893] 
dist 128=[.15000610083382944326,.46976794704172188069] 
dist 129=[.21142773796465088239,.48758669297042454661] 
dist 130=[.2206115563884726619 ,.50563778090265920466] 
dist 131=[.28833543931745973572,.52077093401358203341] 
dist 132=[.25486002511355223684,.52694680537604092411] 
dist 133=[.21615950404211459507,.52906713660278225811] 
dist 134=[.1554428633190533541 ,.5280177363773861963 ] 
dist 135=[.08782248510853116708,.51342727108250520754] 
dist 136=[.01777852139229759917,.50823501369266449819] 
dist 137=[-.06731760700803212641,.50233743316614014725] 
dist 138=[-.1949873563691293639 ,.49889199578476668312] 
dist 139=[-.32220578994733852112,.39813075618464843   ] 
dist 140=[-.40550311259574690635,.38496993292917818179] 
dist 141=[-.47242652177179668355,.38419981809951988237] 
dist 142=[-.53432752066283417818,.38297664028463319457] 
dist 143=[-.58812963072424932995,.29842885637226138899] 
dist 144=[-.62274622070492367847,.28945242004889333881] 
dist 145=[-.64988276979688481205,.26809028542002954957] 
dist 146=[-.67384787355682251588,.26220110428715180706] 
dist 147=[-.69328999186431628709,.20255824795114178952] 
dist 148=[-.70238360307610618803,.19261796388026384129] 
dist 149=[-.70563279030761381128,.17154416235094806026] 
dist 150=[-.7052581549750901148 ,.16553167236408556681] 
dist 151=[-.69482539065355657138,.1408580165325008997 ] 
dist 152=[-.69043847075263846402,.13584057923515272904] 
dist 153=[-.67697115809014742659,.12328698118361002778] 
dist 154=[-.67061509610948418903,.120589162621188158  ] 
dist 155=[-.2313450911848613176 ,.16162586818165983628] 
dist 156=[-.23596274828445465375,.25038175588312704823] 
dist 157=[-.23816761477497197756,.32242929934221810571] 
dist 158=[-.23842997571362629916,.39079066653344034597] 
dist 159=[-.09008935360128448993,.45987595347887797873] 
dist 160=[-.08356113890841264154,.50695134049048362891] 
dist 161=[-.07467048698551608278,.54682321566488051546] 
dist 162=[-.07240201441239601203,.58717533157778540313] 
dist 163=[-.06480172901435155243,.62286924812152554479] 
dist 164=[-.06281304681498458846,.64415986577147697834] 
dist 165=[-.06126802798252842908,.65893652812226048701] 
dist 166=[-.06110838567468071067,.66864552931955596906] 
dist 167=[-.06164020023255048238,.67433269447284162364] 
dist 168=[-.06314932757660692660,.67450143723440212039] 
dist 169=[-.06565931684503880307,.66947567871564616777] 
dist 170=[-.07018368526892815785,.66589521506674680081] 
dist 171=[-.07564388807979781003,.33137362906514379839] 
dist 172=[-.08188695015971531605,.30074463645028112392] 
dist 173=[-.08988544015874266308,.22837546039227956634] 
dist 174=[-.14509020084650148417,.2154383912990393719 ] 
dist 175=[-.20695487529583247329,.2147050622807176112 ] 
dist 176=[-.25386053269542590005,.23239793291687108958] 
dist 177=[-.29868482638483825694,.24536620799864751644] 
dist 178=[-.35224682236224934032,.25524832591459443311] 
dist 179=[-.40194015128776036301,.26264557658908414854] 
dist 180=[-.43133315454954856058,.26570042380161982147] 
dist 181=[-.45141792398477453589,.26670898303563295171] 
dist 182=[-.46398325358626681983,.26620363706548054013] 
dist 183=[-.4726775619851658655 ,.24892145905023679646] 
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dist 188=[-.1387673139641451563 ,.22118084544205149954] 
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dist 190=[-.13453627933332654327,.21078225414498659982] 
dist 191=[-.1155792454382165802 ,.12876966325075100271] 
dist 192=[-.14361957927771158221,.15961375491912772733] 
dist 193=[-.16594162263934929134,.18952855964946857974] 
dist 194=[-.18674266295577815985,.22590849115944929986] 
dist 195=[-.2134343282585366473 ,.25998068722904194084] 
dist 196=[-.23139145327160148758,.28069059214718425393] 
dist 197=[-.24635789726454266269,.29553649412552806465] 
dist 198=[-.26111833282646798811,.30621821139424921694] 
dist 199=[-.27398658017173965041,.31401686433980292319] 
dist 200=[-.28140445223499712943,.31736190720343896236] 
dist 201=[-.28623713026904371533,.31821175213309207028] 
dist 202=[-.28879257683977947694,.36456412407019103797] 
dist 203=[-.31904133695332764913,.42392687529266805755] 
dist 204=[-.33885749935320170344,.46008930087120277183] 
dist 205=[-.35321284032606582514,.48611861055640902448] 
dist 206=[-.3638181172965181866 ,.50505841879880008494] 
dist 207=[-.37125542781870975319,.51913394028514872264] 
dist 208=[-.3730035054519265412 ,.52575818787874553561] 
dist 209=[-.37273119495445449907,.52818255919594048046] 
dist 210=[-.37234267483843714457,.52783168453071238034] 
dist 211=[-.3499727264477375899 ,.47676795196427284685] 
dist 212=[-.34526792942949018176,.46781438269496191003] 
dist 213=[-.33327753369577385392,.45163765985304924836] 
dist 214=[-.32874702525495881348,.44684228133468915715] 
dist 215=[-.30535353387672856015,.42770854895373189804] 
dist 216=[-.29973907887195260746,.42210405878640936007] 
dist 217=[-.28794675506338315278,.41052985010649898935] 
dist 218=[-.28409147679067219448,.40646174571932596652] 
dist 219=[-.06501420117675080664,.22204311355538156238] 
dist 220=[-.10975009156605523934,.22317217998410335652] 
dist 221=[-.14633370153267292403,.22378697192287769218] 
dist 222=[-.18125643415807502486,.22385890831036094956] 
dist 223=[-.2123573549621114717 ,.06352040929393675199] 
dist 224=[-.23369546236422133226,.06411510816446372219] 
dist 225=[-.25192868276587743693,.06555431190638254166] 
dist 226=[-.27064419366632191878,.06851322536142595817] 
dist 227=[-.28723601571569264827,.07221044485322772915] 
dist 228=[-.29699752368680813103,.07659516619192053960] 
dist 229=[-.30360781719544943953,.08231184815617731512] 
dist 230=[-.30762852603046364994,.09132258265343126345] 
dist 231=[-.30966858814279039705,.10079396479005551414] 
dist 232=[-.30972236678790305693,.10834848685373364673] 
dist 233=[-.30635789384379009896,.11592928765889185174] 
dist 234=[-.30549176867637566069,.12550610408284546792] 
dist 235=[-.184717085702541364  ,.13560925314490408126] 
dist 236=[-.18575530523755387164,.14529004328848283134] 
dist 237=[-.18573809025069456907,.15649690033110337943] 
dist 238=[-.18531484305301387914,.17268824246957974756] 
dist 239=[-.1625001757674745783 ,.18844923037821440371] 
dist 240=[-.15919454999724780034,.1979395258842898801 ] 
dist 241=[-.14948730326849312481,.20463691402452349397] 
dist 242=[-.14808900242360901102,.20925664029607817874] 
dist 243=[-.12825003793133189127,.21222927743793927618] 
dist 244=[-.12684925698433779834,.21279985021061740538] 
dist 245=[-.1257570415813352768 ,.21164573404389890867] 
dist 246=[-.12480280844393789975,.21127889590959674683] 
dist 247=[-.09638320337853575984,.19717877604834362512] 
dist 248=[-.09234844417886947549,.19435568000163693473] 
dist 249=[-.08438182180706232560,.18457157143827938091] 
dist 250=[-.08220608763436322052,.16935185948254658288] 
dist 251=[-.07399897365546994699,.14376811614415637427] 
dist 252=[-.07204997598427765304,.14396168427799682476] 
dist 253=[-.06841960376892688086,.14275925282540980717] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 0, 0, 1, 2] 
dist 0=[57.260737247992927201  ,57.260737247992927201  ] 
dist 1=[56.880028281836304027  ,57.520648632926177803  ] 
dist 2=[55.464273058788609380  ,58.454085840750122023  ] 
dist 3=[53.222916548994905416  ,59.452135292703641765  ] 
dist 4=[49.546544045846969982  ,59.969941029399558312  ] 
dist 5=[45.761398022826450159  ,60.235081357439413338  ] 
dist 6=[43.085792178264723755  ,60.250643443118437569  ] 
dist 7=[40.709044610778275914  ,57.994118979693756768  ] 
dist 8=[38.116865116490906210  ,57.570818997440637838  ] 
dist 9=[35.582723740294105331  ,56.985812527327747234  ] 
dist 10=[33.437606800983127179  ,56.749590179492129896  ] 
dist 11=[31.165142073601815610  ,56.157680301599170327  ] 
dist 12=[28.122537312213891642  ,55.898289868724170734  ] 
dist 13=[25.117838308395644535  ,55.630648262733661444  ] 
dist 14=[22.996602798046292371  ,55.457400561064010021  ] 
dist 15=[21.114467619796235621  ,32.396679088842592142  ] 
dist 16=[19.064082376560157073  ,30.473879166097816253  ] 
dist 17=[17.059660596405299062  ,25.885256626565563373  ] 
dist 18=[15.360826656679550393  ,25.224241638595937495  ] 
dist 19=[13.558026159718529562  ,19.375082039382501630  ] 
dist 20=[11.138200075723613362  ,19.233884200726620823  ] 
dist 21=[8.3755087584876567859 ,16.330213111401108629  ] 
dist 22=[4.8368162556612040859 ,16.086701669231285877  ] 
dist 23=[1.4223311652066320957 ,7.8365827029759527264 ] 
dist 24=[-.87219246584733063252,7.1878932161484789739 ] 
dist 25=[-2.7925822391823013475 ,6.4241922259539461770 ] 
dist 26=[-4.7138168856519252473 ,5.7500597883021485098 ] 
dist 27=[-6.4992765953629320314 ,2.8569799788398368615 ] 
dist 28=[-7.8783797097466774024 ,2.1862889680719827847 ] 
dist 29=[-9.2333397966807722531 ,.9942584477277895627 ] 
dist 30=[-10.924294264629282301  ,.8853878922209176981 ] 
dist 31=[-12.508441128871133468  ,-.5941083765488254384 ] 
dist 32=[-13.437015585851473755  ,-.7031147103363610316 ] 
dist 33=[-14.073527423397158867  ,-1.0053974807920591639 ] 
dist 34=[-14.489857552116201231  ,-1.0433729966701729105 ] 
dist 35=[-14.780082988506572728  ,-1.0046684281736887084 ] 
dist 36=[-14.912021001417863479  ,-.85621255493051256482] 
dist 37=[-14.956936712322410890  ,-.68490546296008194635] 
dist 38=[-14.935098170011511524  ,-.55479573521126359773] 
dist 39=[-13.401634352482667749  ,-.43281198777687699894] 
dist 40=[-13.155997397220925343  ,-.29321503157272909973] 
dist 41=[-12.686875902141962255  ,-.15527566608125968767] 
dist 42=[-12.551264090012303802  ,-.03956753771155211244] 
dist 43=[-12.017055074687318684  ,.08106348882780403187] 
dist 44=[-11.875169204293843988  ,.23894478799677526822] 
dist 45=[-11.592916994234807808  ,.39223296987007712238] 
dist 46=[-11.502113496186948600  ,1.9095103787781469953 ] 
dist 47=[-3.6822759565007322631 ,3.5997726893157795711 ] 
dist 48=[-3.6349520575872762770 ,4.7121254251871498200 ] 
dist 49=[-3.3296655861104382444 ,5.6136797907686315709 ] 
dist 50=[-3.2638848824374740602 ,6.4627802002575385152 ] 
dist 51=[-3.1432441677385060793 ,7.2129438419525354060 ] 
dist 52=[-3.1102672017012554835 ,7.7197202269105691327 ] 
dist 53=[.99015870267080171124,8.1453219031143937990 ] 
dist 54=[1.0112351309596008979 ,8.5716213288409369809 ] 
dist 55=[1.0271042046488780471 ,9.3543291692771188752 ] 
dist 56=[1.0125840898737009974 ,9.9528353427049492501 ] 
dist 57=[.98553689889047278539,10.376872014928231521  ] 
dist 58=[.94407443847561973359,10.674718803932959587  ] 
dist 59=[.88480083615948842479,10.885187624138344047  ] 
dist 60=[.78660981780324302619,10.960383979679398080  ] 
dist 61=[.68238482584982027809,10.968959539580907053  ] 
dist 62=[-.6816797777832733701 ,10.941829338986999767  ] 
dist 63=[-2.6220389471729499643 ,5.9918870429079366118 ] 
dist 64=[-3.9101969691327838249 ,5.6677271736976848564 ] 
dist 65=[-4.9644042421255940535 ,4.9090006326812714413 ] 
dist 66=[-5.9716599734167943096 ,4.7388287520718363706 ] 
dist 67=[-6.8691088776384919659 ,3.6777919947780281951 ] 
dist 68=[-7.4853755080417558883 ,3.4722253951124845455 ] 
dist 69=[-8.0125910992446747665 ,3.0795556010133025787 ] 
dist 70=[-8.5549232708969789717 ,2.9779539229615055869 ] 
dist 71=[-9.0275965763970132276 ,1.5288726017050154124 ] 
dist 72=[-9.2769582551261595243 ,1.3226480513091855028 ] 
dist 73=[-9.4102936404016006747 ,.8739499421653979917 ] 
dist 74=[-9.4317056693131971968 ,.82811091492948431001] 
dist 75=[-9.3790919662331811421 ,.79581240778624855689] 
dist 76=[-9.3278722989478379672 ,.78453024199411918497] 
dist 77=[-9.2179316182946302975 ,.61054261574148118846] 
dist 78=[-9.1622789861641417313 ,.58316304270837282521] 
dist 79=[-2.8766055327821092891 ,.5171149139324379626 ] 
dist 80=[-2.5301382079678807990 ,1.3270714322386834086 ] 
dist 81=[-1.7154976161104842477 ,2.0297273051799775338 ] 
dist 82=[-1.5763796346744861021 ,2.6962833203019859265 ] 
dist 83=[-.92629237708910876342,3.2866938918229729295 ] 
dist 84=[-.92188611699845029853,3.6856605012073220444 ] 
dist 85=[-1.1614026116552344214 ,4.0199167604674540088 ] 
dist 86=[-1.3477132929506728146 ,4.3522604194749618743 ] 
dist 87=[-1.5143142702620076725 ,4.6477135194247174834 ] 
dist 88=[-1.6966185889249701752 ,4.8348282502838244203 ] 
dist 89=[-1.8741759837385957668 ,4.9780804645771715403 ] 
dist 90=[-2.0218642136692713342 ,5.0985475427138186328 ] 
dist 91=[-2.1753949807323516074 ,5.1948647452243762366 ] 
dist 92=[-2.3762649966248038176 ,5.2417704155940083230 ] 
dist 93=[-2.5710068609309670311 ,5.2613512258431797091 ] 
dist 94=[-2.7001125329341048095 ,5.2486511299357002121 ] 
dist 95=[-2.8054275483419859966 ,1.9925843661537691814 ] 
dist 96=[-2.9053207585179815450 ,1.7232212491457844371 ] 
dist 97=[-2.9937277517417840590 ,1.0980237007910225270 ] 
dist 98=[-3.0532554525888654251 ,1.0385437492547734467 ] 
dist 99=[-3.1029008057571163009 ,.86633435814447991945] 
dist 100=[-3.1519265253481239923 ,.82913012291825141796] 
dist 101=[-3.1905454491804269086 ,.76160376654380772166] 
dist 102=[-3.1986943671985123591 ,.74494782988623617401] 
dist 103=[-3.1885531329881074580 ,.69729469766135458635] 
dist 104=[-3.1772333082919505833 ,.75898569096676866924] 
dist 105=[-3.0865613507229820729 ,.83606059114998292214] 
dist 106=[-3.0587274359463094472 ,.89728782804281151072] 
dist 107=[-2.9734014435536838226 ,.95841255873491681809] 
dist 108=[-2.9424563696325543763 ,1.0350571496829238999 ] 
dist 109=[-2.5442678533461428446 ,1.1077155584655064865 ] 
dist 110=[-2.4715886987594991072 ,1.2143143657629231556 ] 
dist 111=[-2.8123820301739274870 ,1.3959051023407944136 ] 
dist 112=[-3.0192653551801406176 ,1.5144486184396084152 ] 
dist 113=[-3.1674540111600384148 ,1.6091053217170033437 ] 
dist 114=[-3.2740806066044483137 ,1.6954366730232207154 ] 
dist 115=[-3.3509619394670898201 ,1.7694175231745990630 ] 
dist 116=[-3.3804707020152082565 ,1.8148172745065653140 ] 
dist 117=[-3.3862178717664853769 ,1.8477758996133498577 ] 
dist 118=[-3.3784947277544473325 ,1.8721310618959560360 ] 
dist 119=[-3.0965554012723038996 ,1.8868169709871137546 ] 
dist 120=[-3.0442689921870517665 ,1.8873865839293329276 ] 
dist 121=[-2.9360198696519292755 ,1.8700373932040064357 ] 
dist 122=[-2.9005343863990295006 ,1.8625301896979115093 ] 
dist 123=[-2.7358265791527044396 ,1.7586414054489261194 ] 
dist 124=[-2.6979700195721806832 ,1.7306193621923174964 ] 
dist 125=[-2.5827464377176949802 ,1.7015618469125927314 ] 
dist 126=[-2.5607506653853934855 ,1.6852274564740092939 ] 
dist 127=[-1.6587767314585827178 ,1.3883267546277879029 ] 
dist 128=[-1.6527806576315878623 ,1.6831361189435440242 ] 
dist 129=[-1.6264991000497379215 ,2.0756843582141528497 ] 
dist 130=[-1.6162053414058954106 ,2.4347314008034010310 ] 
dist 131=[-1.5800627460909623686 ,2.7439666414076479807 ] 
dist 132=[-1.5679232366212021363 ,2.9378059776992285954 ] 
dist 133=[-.57948790413570145112,3.0838925184763491706 ] 
dist 134=[-.48824042098637755951,3.2026341700176426058 ] 
dist 135=[-.28777952769378393739,3.3002013896565511413 ] 
dist 136=[-.2430275642565944138 ,3.3618185432622309945 ] 
dist 137=[-.01551713400756389476,3.4088044440550685100 ] 
dist 138=[.02390323569868145679,3.4480018330269029484 ] 
dist 139=[.11383759866247752128,3.4791228578092046162 ] 
dist 140=[.12830923867497630889,3.4938894346616036574 ] 
dist 141=[.24872325204321582131,3.4994879189816301478 ] 
dist 142=[.26816377490566424748,3.4940352169376552503 ] 
dist 143=[.00629938127829344974,1.7133762277847559449 ] 
dist 144=[-.33011289310638606203,1.7454845815260366451 ] 
dist 145=[-.61649155063680514392,1.7650466148924143328 ] 
dist 146=[-.90870731168862444462,1.7715622673986948801 ] 
dist 147=[-1.1816425329225366116 ,1.7697623980892118791 ] 
dist 148=[-1.3911073623868248500 ,1.7645080869570366170 ] 
dist 149=[-1.5938036017931221158 ,-.28977707620707761757] 
dist 150=[-1.8397376996797349903 ,-.34306718875507932515] 
dist 151=[-2.0698834970006001164 ,-.45520837131590688263] 
dist 152=[-2.2095967085087810952 ,-.47794909840266609491] 
dist 153=[-2.3095626523058915017 ,-.54939349173835012662] 
dist 154=[-2.3811475450752413924 ,-.4823154607440454213 ] 
dist 155=[-2.4318928574713425925 ,-.38881282470204481239] 
dist 156=[-2.4859122419624774132 ,-.26574830961851215044] 
dist 157=[-2.5147880514834204535 ,-.0977353891962540753 ] 
dist 158=[-2.5197999631717862071 ,.1750685534203438727 ] 
dist 159=[-1.7373486394692167891 ,.4508247176521727693 ] 
dist 160=[-1.7625620288096368732 ,.69816908491759218475] 
dist 161=[-1.7758625369893351305 ,.93217772855938677594] 
dist 162=[-1.7771150767591015760 ,1.1634388648406232800 ] 
dist 163=[-1.7697811167200494254 ,1.3746756355694332985 ] 
dist 164=[-1.7639973736447385893 ,1.5288071209794954024 ] 
dist 165=[-1.5243475052305980367 ,1.6703256003316760760 ] 
dist 166=[-1.4885645782693045382 ,1.8312506464104906754 ] 
dist 167=[-1.3933690269731035237 ,1.9763996539377867168 ] 
dist 168=[-1.3732416332738919258 ,2.0549871851526231891 ] 
dist 169=[-1.1964605313666738474 ,2.1000011367024883797 ] 
dist 170=[-1.1588475745319944355 ,2.1112185289178972411 ] 
dist 171=[-1.1057570114708360489 ,2.1085457634853508070 ] 
dist 172=[-1.0878128719762874553 ,2.1077736678640099416 ] 
dist 173=[-.6911326299220417734 ,2.1072418798813268453 ] 
dist 174=[-.6380187034553566996 ,2.1069023135333575442 ] 
dist 175=[-.5192443438880174055 ,1.6629061148195707872 ] 
dist 176=[-.7368662351842694797 ,1.6673408510997281414 ] 
dist 177=[-.9616925828427553388 ,1.6740771995763697715 ] 
dist 178=[-1.1737948774368558683 ,1.6704581337662114789 ] 
dist 179=[-1.3609442788777398940 ,1.6603808266045570868 ] 
dist 180=[-1.4862335712066776288 ,1.6527373769999162687 ] 
dist 181=[-1.5899402273003266711 ,1.3561574483443431610 ] 
dist 182=[-1.6909960084973363981 ,1.3462795384974844597 ] 
dist 183=[-1.7793197045692576038 ,1.1145942738643416708 ] 
dist 184=[-1.8322388499517594006 ,1.0792126688261158890 ] 
dist 185=[-1.8692469689706574753 ,.9981327594154076055 ] 
dist 186=[-1.8941043605877847209 ,.9731957363590858613 ] 
dist 187=[-1.9091926212096579183 ,.8579520250324423142 ] 
dist 188=[-1.9084847959375456658 ,.8336175427898576130 ] 
dist 189=[-1.8977687278876301176 ,.7776312702435118769 ] 
dist 190=[-1.8875501347746366630 ,.7597801558590908466 ] 
dist 191=[-1.1489451658699546300 ,.38014577456324907613] 
dist 192=[-1.1892092581893609309 ,.42761769926708074227] 
dist 193=[-1.2183985547231253091 ,.47639047357551215636] 
dist 194=[-1.2299158396905633728 ,.52116985104543027587] 
dist 195=[-1.3025861295469163610 ,.57149687115927130145] 
dist 196=[-1.3495946259699246582 ,.64239682011821789604] 
dist 197=[-1.3784634509336374664 ,.71054800320708278572] 
dist 198=[-1.3900483840187697022 ,.74991037978699465567] 
dist 199=[-1.3938791878451288727 ,.77563057916380669236] 
dist 200=[-1.3918154323073846923 ,.78936602952674293205] 
dist 201=[-1.3850477351111830035 ,.79751333628341236772] 
dist 202=[-1.3794413658603785656 ,.8009435274263279561 ] 
dist 203=[-1.3511196235396866871 ,.80156359599681901909] 
dist 204=[-1.3415781515757561174 ,.79872638955033295308] 
dist 205=[-1.3075967942716404036 ,.67316698048651803002] 
dist 206=[-1.2982161075425562909 ,.65393260733625853175] 
dist 207=[-.70012006224517347645,.61852096943516326536] 
dist 208=[-.69295138175577830714,.64633170127851177218] 
dist 209=[-.66759109384979533012,.68935051156827070166] 
dist 210=[-.65924182905251367595,.75438466839899403864] 
dist 211=[-.64490166760303298655,.91658118031424527064] 
dist 212=[-.63994736713761566223,1.0380607677136821036 ] 
dist 213=[-.06511254348443301072,1.1527465217122371297 ] 
dist 214=[-.17515911438608058968,1.2878435787793603621 ] 
dist 215=[-.27540572193737608245,1.4122219118438324899 ] 
dist 216=[-.38818380928781923275,1.4841501607119430041 ] 
dist 217=[-.5000868817663050532 ,1.5313017403323725851 ] 
dist 218=[-.5968444206239980558 ,1.5568432791448417732 ] 
dist 219=[-.7008316960177345460 ,1.5715413787135240054 ] 
dist 220=[-.8415753857018509726 ,1.5754358224473453707 ] 
dist 221=[-.9805736811570085331 ,1.5721584704420135258 ] 
dist 222=[-1.0775995941271360880 ,1.5671687464877981117 ] 
dist 223=[-1.1622604266902225466 ,1.5409511396631602519 ] 
dist 224=[-1.2519362074012791978 ,1.5725151293694667025 ] 
dist 225=[-1.3377492001655326340 ,1.5973377329035245438 ] 
dist 226=[-1.4070027730358825492 ,1.6086148666229487707 ] 
dist 227=[-1.4772520246295700279 ,1.6121048027133655388 ] 
dist 228=[-1.5670391157605457619 ,1.6078050619493733482 ] 
dist 229=[-1.6495682142624456356 ,1.5951105200095891438 ] 
dist 230=[-1.8936138342522184005 ,1.5856576505070769003 ] 
dist 231=[-2.0980251245242590488 ,1.5636051886846867619 ] 
dist 232=[-2.2764925393769940003 ,1.5680900151678358345 ] 
dist 233=[-2.4241709167499050849 ,1.6490414740958514404 ] 
dist 234=[-2.5057660160562468470 ,1.6918634076314259214 ] 
dist 235=[-2.5544109273797528816 ,1.7148617003706752112 ] 
dist 236=[-2.5706524884793864055 ,1.7184313575042389759 ] 
dist 237=[-2.5725117429880627548 ,1.6189275424818710093 ] 
dist 238=[-2.5637861642526173073 ,1.5976333118393432781 ] 
dist 239=[-2.5457523056823426721 ,1.5731380414763648495 ] 
dist 240=[-2.5349710655420070454 ,1.5601190110214284116 ] 
dist 241=[-2.4659011251742963955 ,1.5341107139877668527 ] 
dist 242=[-2.4465267173624009672 ,1.5206654973607891505 ] 
dist 243=[-2.3704629133075159664 ,1.5084400489255562751 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 0, 2, 0, 0, 2] 
dist 0=[66.297078461235339907  ,66.297078461235339907  ] 
dist 1=[65.651100605040122675  ,66.522115120569012895  ] 
dist 2=[64.635338797394531430  ,66.774604481904176733  ] 
dist 3=[63.163218759720737723  ,66.964228509260737556  ] 
dist 4=[61.072400600669101743  ,66.942676163370079962  ] 
dist 5=[57.586118781063069199  ,66.810634197589284526  ] 
dist 6=[53.966394537867888716  ,66.665890416168986158  ] 
dist 7=[51.342679488060410725  ,66.258159581879047324  ] 
dist 8=[48.941693041190074727  ,65.301559193681146278  ] 
dist 9=[46.211197865892533951  ,62.235331357393514860  ] 
dist 10=[43.471791963444080760  ,61.530522455891976060  ] 
dist 11=[39.267976971699731786  ,60.524329440152726261  ] 
dist 12=[32.653572360400698684  ,60.175403998272523854  ] 
dist 13=[28.162920956143521388  ,59.491036264330724157  ] 
dist 14=[24.359861215621334729  ,59.154697012678050168  ] 
dist 15=[20.490874659976140685  ,56.774477814075932205  ] 
dist 16=[16.866288295269315471  ,51.264818312394885027  ] 
dist 17=[14.038906460347136023  ,29.404058221164185644  ] 
dist 18=[11.247533883928083370  ,27.043727453051998154  ] 
dist 19=[7.7662376660709346217 ,24.833641771778253499  ] 
dist 20=[4.4343797740983670546 ,24.057259355185315276  ] 
dist 21=[2.2394596071389125408 ,23.856934538688772614  ] 
dist 22=[.45035091890928425145,12.008766982636396058  ] 
dist 23=[-1.2613657837490225416 ,10.318010813802797944  ] 
dist 24=[-2.8013839557899685947 ,9.9899178671274394288 ] 
dist 25=[-4.4510638710203150198 ,1.8706343735327105275 ] 
dist 26=[-6.7269052589239236466 ,.40262668458268337451] 
dist 27=[-8.4101961492422215474 ,-1.6880714258869429526 ] 
dist 28=[-9.9875831384793080158 ,-2.0515189341358393845 ] 
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dist 34=[-16.363136499598772741  ,-4.9895617783680655074 ] 
dist 35=[-16.519184813257622517  ,-4.2951779135970633752 ] 
dist 36=[-16.563235465881550065  ,-3.3043323013808923507 ] 
dist 37=[-16.536384940445422429  ,-1.6543285773208056499 ] 
dist 38=[-9.2071677599940520542 ,.6873053286458961233 ] 
dist 39=[-9.1792125455446510087 ,2.3498152728829606741 ] 
dist 40=[-9.1594635162705814173 ,3.7202694176029341436 ] 
dist 41=[-7.6642015406206784106 ,5.0464570161991899360 ] 
dist 42=[-7.5042525535692594966 ,6.2398395480066744085 ] 
dist 43=[-7.4311643456923182736 ,7.0806920113249134908 ] 
dist 44=[-6.6488691866288149657 ,7.8232620342577746919 ] 
dist 45=[-6.2239080157379747516 ,8.6248042550881580325 ] 
dist 46=[-6.1175596589335930462 ,9.3466458192371056359 ] 
dist 47=[-5.9860160419939605101 ,9.7712467006245226692 ] 
dist 48=[-5.9343803893672473305 ,10.059188355941920861  ] 
dist 49=[-2.6264627536523634531 ,10.235568468949428668  ] 
dist 50=[-2.2601558631017269940 ,10.336393367485675842  ] 
dist 51=[-2.1720693194594900443 ,10.343773313608649290  ] 
dist 52=[-1.3467411055986883914 ,10.271451225310923388  ] 
dist 53=[-1.2065483625813687037 ,10.220490311937915078  ] 
dist 54=[-.96222359274540288241,6.3771285512922583918 ] 
dist 55=[-.90503022535903822998,5.9941004162918745380 ] 
dist 56=[-.76150275521327636439,5.0755109321100052692 ] 
dist 57=[-.74651697681492755767,5.2585222811196289623 ] 
dist 58=[-.79671179416086795346,5.6240344583227492697 ] 
dist 59=[-1.2631292488904710387 ,5.8982726357977898942 ] 
dist 60=[-1.7256429504732388610 ,6.1203532978211718781 ] 
dist 61=[-2.3019691045383817087 ,6.2924594126566790914 ] 
dist 62=[-2.8480899836204908824 ,6.3671727259262935884 ] 
dist 63=[-3.1901460974508205759 ,6.3946436962061311420 ] 
dist 64=[-3.4473035809912955814 ,6.3872801773674918681 ] 
dist 65=[-3.6548236528623330946 ,-.71856662925360893304] 
dist 66=[-3.8159324433350855384 ,-.99259675316553802121] 
dist 67=[-3.8879931586203935654 ,-.88961670823719407491] 
dist 68=[-3.9197225262844016495 ,-.77685964657371032971] 
dist 69=[-3.9199695543037193071 ,-.68101998858667768011] 
dist 70=[-3.2031313657402122283 ,-.45671018467844726817] 
dist 71=[-3.4844412458437129204 ,-.13017123114446781975] 
dist 72=[-3.7847974836267744896 ,.14662598616285777645] 
dist 73=[-4.0526818478828481295 ,.42664631767460287317] 
dist 74=[-4.2044493127755619237 ,.68623049109822969902] 
dist 75=[-4.3001676675370584039 ,.88154419587424994351] 
dist 76=[-4.3444259152925568368 ,1.0665934656884429450 ] 
dist 77=[-4.3609876116760743251 ,1.2852613337406999720 ] 
dist 78=[-4.3527101532997247185 ,1.4881528691706175988 ] 
dist 79=[-4.3173613483641071149 ,1.6102909809973131939 ] 
dist 80=[-4.2920114324539002105 ,1.6963330432494186664 ] 
dist 81=[-2.7426835539543186235 ,1.7552697450250807931 ] 
dist 82=[-2.5816454204224938129 ,1.7969728975884384175 ] 
dist 83=[-2.1894974697745245049 ,1.8142877799337508015 ] 
dist 84=[-2.1186310658257077809 ,1.8170307292794404245 ] 
dist 85=[-1.5337653666459023242 ,1.8139894041554455310 ] 
dist 86=[-1.4222836808944602407 ,2.0895415841650788978 ] 
dist 87=[-1.2549899456026013982 ,2.3430227912764482787 ] 
dist 88=[-1.2078522032659099027 ,2.6240186424308238058 ] 
dist 89=[-.70522050214156697106,2.8796610898307636756 ] 
dist 90=[-.80874098218229558699,3.0320168096723191030 ] 
dist 91=[-.87853642011633071292,3.1376263123537743339 ] 
dist 92=[-.93671666500688808883,3.2067974325687330684 ] 
dist 93=[-.99390460944207992391,3.2501615028100908714 ] 
dist 94=[-1.0439931442341865053 ,3.2563765609503469877 ] 
dist 95=[-1.0738589294297854236 ,3.2410652528046560131 ] 
dist 96=[-1.1546805332137366621 ,3.2268785477780405242 ] 
dist 97=[-1.2824197667166001924 ,.6962657235017484118 ] 
dist 98=[-1.4062379229393059680 ,.6003008863165048985 ] 
dist 99=[-1.5567601242266637800 ,.5802746796463687910 ] 
dist 100=[-1.6977817428328673723 ,.5377174799577512453 ] 
dist 101=[-1.7837026393487864046 ,.5255126332427131794 ] 
dist 102=[-1.8455670782426650385 ,-.37861984328307588603] 
dist 103=[-1.8906246029428064241 ,-.30253007576186888491] 
dist 104=[-1.9213529261291937453 ,-.19275200292547156638] 
dist 105=[-1.9272516103280093117 ,.02499718278876344517] 
dist 106=[-1.9216579016999469531 ,.29498688105293472438] 
dist 107=[-1.9160599676814576434 ,.70604476327630086977] 
dist 108=[-1.9308660645602586507 ,1.1158696014189967436 ] 
dist 109=[-1.9801613288133529331 ,1.3809422546452692676 ] 
dist 110=[-1.9950241819499075838 ,1.5901507261824189643 ] 
dist 111=[-1.9966853025774451387 ,1.7771440213390103580 ] 
dist 112=[-1.9933157549888995441 ,1.9350333114886202481 ] 
dist 113=[-1.5522824837259983169 ,2.0281510766101977983 ] 
dist 114=[-1.4965094999613492774 ,2.0914439467660110786 ] 
dist 115=[-1.4802467009191992752 ,2.1303663060143625900 ] 
dist 116=[-1.1066009428777216678 ,2.1562839230996468425 ] 
dist 117=[-1.0536613645724826817 ,2.1677042783300693526 ] 
dist 118=[-.93011765983472840233,2.1706659274697007675 ] 
dist 119=[-.90070013090368632418,2.1633634233598633806 ] 
dist 120=[-.72751438925665634517,2.1487305507913670292 ] 
dist 121=[-.69352959864722988047,2.1370412659322546829 ] 
dist 122=[-.62601046319943834091,2.1022904385513935944 ] 
dist 123=[-.60767479768175410865,2.0849499053328974258 ] 
dist 124=[-.30887399362578629513,.94690210517557113098] 
dist 125=[-.38202469321647921129,.95610333284288558155] 
dist 126=[-.63422603899465125521,.96199236835677921871] 
dist 127=[-.87883882500071130651,.97100447485096897801] 
dist 128=[-1.0991744518478622553 ,.9714472096791873457 ] 
dist 129=[-1.2545426409796231117 ,.88275849118838771648] 
dist 130=[-1.3917297661309933448 ,.97859360604051725882] 
dist 131=[-1.5395495722031958301 ,1.0622216207235783537 ] 
dist 132=[-1.6735191123590978611 ,1.1508944492222892165 ] 
dist 133=[-1.7554608981115246718 ,1.2358639134612733205 ] 
dist 134=[-1.8148098226746800497 ,1.3047119741443309063 ] 
dist 135=[-1.8586579315683402486 ,1.3748242756216415067 ] 
dist 136=[-1.8890732417771527701 ,1.4648301672020787680 ] 
dist 137=[-1.8948395315080163336 ,1.5515522543088947581 ] 
dist 138=[-1.8908858283557206048 ,1.6085598792493363791 ] 
dist 139=[-1.8825315337931438206 ,1.6546042869680001360 ] 
dist 140=[-1.1323233112541901219 ,1.6975843183246996634 ] 
dist 141=[-1.2089947043896838343 ,1.7351717626257435199 ] 
dist 142=[-1.2669264658627966378 ,1.7596972641998347335 ] 
dist 143=[-1.3221305497024720231 ,1.7792649592141880945 ] 
dist 144=[-1.4427055404340803430 ,1.7970623294850326315 ] 
dist 145=[-1.8837001081221959209 ,1.8097739340261032981 ] 
dist 146=[-2.1648216981735120634 ,1.8090532418165034863 ] 
dist 147=[-2.3821085290957264380 ,1.8004072215385928912 ] 
dist 148=[-2.5684679686812572322 ,1.7927895430919267188 ] 
dist 149=[-2.7202482832371403486 ,1.7381000187743297897 ] 
dist 150=[-2.7996014252773750773 ,1.7219670167863251994 ] 
dist 151=[-2.8415918558228395500 ,1.6752134441477291928 ] 
dist 152=[-2.8499254008536361133 ,1.6571037013419160888 ] 
dist 153=[-2.8260871029611735087 ,1.4343812668222037339 ] 
dist 154=[-2.8093104781579013837 ,1.3976352438125636282 ] 
dist 155=[-2.7793684145706815948 ,1.2965487966431012382 ] 
dist 156=[-2.7651727876527345284 ,1.2807416769313669080 ] 
dist 157=[-2.6843493610847471212 ,1.2621056162944197060 ] 
dist 158=[-2.6613113415921264811 ,1.2525344212128560170 ] 
dist 159=[-2.5804280710284265742 ,1.2321281872349077002 ] 
dist 160=[-2.5626829560544307042 ,1.2233024699204209983 ] 
dist 161=[-.09198073237528189682,.74245274435368849277] 
dist 162=[.00624901004176748217,.77544189730373533972] 
dist 163=[.06743540863745761675,.82218269216854821315] 
dist 164=[-.02962429782158851091,.86931924889604152625] 
dist 165=[-.09836309109609850887,.90388448554267964877] 
dist 166=[-.18595676203652329586,.93579528493476594917] 
dist 167=[-.34580442702366123374,.97233824392960057619] 
dist 168=[-.51590144323676776925,1.0089629456216853476 ] 
dist 169=[-.68104933753532417421,1.0411960580790999149 ] 
dist 170=[-.87387776488825271506,1.0782396348056592311 ] 
dist 171=[-1.1543993988991176550 ,1.1243985714444546930 ] 
dist 172=[-1.4301466471624201393 ,1.1699832608785227123 ] 
dist 173=[-1.6039308361821721340 ,1.1950864731946426609 ] 
dist 174=[-1.7359772632908688319 ,1.2099211685546817508 ] 
dist 175=[-1.8452279244398368932 ,1.2145478174071260528 ] 
dist 176=[-1.9314452539672315420 ,1.2123879241441178778 ] 
dist 177=[-1.9716080239907112601 ,1.2093403444273386711 ] 
dist 178=[-1.9911778848658557590 ,1.1875115654046780421 ] 
dist 179=[-1.9952466185297994051 ,1.1837302464838670581 ] 
dist 180=[-1.9317521588459817849 ,1.0857387220412438716 ] 
dist 181=[-1.9133416734036035721 ,1.0676862428883341341 ] 
dist 182=[-1.8789514649191374442 ,1.0130991744898754409 ] 
dist 183=[-1.8659147892939673099 ,1.0041645345290767215 ] 
dist 184=[-1.8002288931687926096 ,.88324472449990509434] 
dist 185=[-1.7822858638569437069 ,.85692976284971667174] 
dist 186=[-1.7258671413845790416 ,.8316340609171602656 ] 
dist 187=[-1.7108014904803326280 ,.82363827235821689015] 
dist 188=[-.5915324419265380057 ,.68995902587196477254] 
dist 189=[-.61763573169678299113,.82217890211724474155] 
dist 190=[-.63071869214035059661,1.0127579530695335845 ] 
dist 191=[-.63686420564629560674,1.2330820497417535581 ] 
dist 192=[-.63765914016135793621,1.4255244229495724683 ] 
dist 193=[-.60755138584801274443,1.5509318693905248888 ] 
dist 194=[-.67524979889122785253,1.6510005193551113865 ] 
dist 195=[-.73421427248465668102,1.7423644466801711982 ] 
dist 196=[-.79652096097520420509,1.8211867885671823541 ] 
dist 197=[-.85606312628777170986,1.8712263819255246552 ] 
dist 198=[-.90399874551050902713,1.9096649398760212970 ] 
dist 199=[-.95252061746377938541,1.9422107654485557372 ] 
dist 200=[-1.0144004792389169429 ,1.9684008116550735629 ] 
dist 201=[-1.0738138047950996677 ,1.9814863651037444421 ] 
dist 202=[-1.1124957443676961852 ,1.9874554083906156511 ] 
dist 203=[-1.1433226066894022039 ,1.9852582745984915860 ] 
dist 204=[-1.1714001864450531205 ,.68129786351740260361] 
dist 205=[-1.1954896724338303821 ,.57468520587670761653] 
dist 206=[-1.2104066886625750565 ,.32608745995680068493] 
dist 207=[-1.2214266925041957091 ,.26956263341127335275] 
dist 208=[-1.2299688914423547281 ,.40038200236583490124] 
dist 209=[-1.2351878430909774477 ,.52975215125984656826] 
dist 210=[-1.2329509771294568623 ,.61554638880382747989] 
dist 211=[-1.2258440074941032773 ,.68568292753145001314] 
dist 212=[-1.2205499810596144016 ,.75259319233673008273] 
dist 213=[-1.2019974996486973161 ,.81214965236600220258] 
dist 214=[-1.2477711043732964745 ,.85295137948472191244] 
dist 215=[-1.2771277201199869429 ,.8877505496821272095 ] 
dist 216=[-1.2964442636460192003 ,.9233627085123633769 ] 
dist 217=[-1.3021677576422008344 ,.9533564499274266101 ] 
dist 218=[-1.3002771400441763381 ,.96574333783879532614] 
dist 219=[-1.2964241227446035479 ,.97027113562481500793] 
dist 220=[-.39037405052202509863,.96891331079201421277] 
dist 221=[-.35103043455109877542,.94032164644168839104] 
dist 222=[-.26431574617600234447,.93028276787673894279] 
dist 223=[-.21746358038473150395,.9205958972062986683 ] 
dist 224=[-.38120573114028138605,.91391114367476687082] 
dist 225=[-.62098000465835133732,.94258650033124032506] 
dist 226=[-.77710354161112428289,1.0275501090327058574 ] 
dist 227=[-.90153327050573891092,1.1258432387597829313 ] 
dist 228=[-1.0148800164452108560 ,1.2153827662806250726 ] 
dist 229=[-1.1121465725070742180 ,1.2654282811385416010 ] 
dist 230=[-1.1724319346252791013 ,1.2960280186236531256 ] 
dist 231=[-1.2170505650701140007 ,1.3079980496473555326 ] 
dist 232=[-1.2518220203291775309 ,1.3120510663078866546 ] 
dist 233=[-1.2786485823652597073 ,1.3110692936290224603 ] 
dist 234=[-1.2915748908661869464 ,1.3062140464007087770 ] 
dist 235=[-1.2967685484377438994 ,1.3006812011598461438 ] 
dist 236=[-1.2943682889119554338 ,1.0910018207387679342 ] 
dist 237=[-1.2831289218911349867 ,1.0611007385138917906 ] 
dist 238=[-1.2771630619547870631 ,.98481102995357560524] 
dist 239=[-1.2496489285210398187 ,.96779139494255828275] 
dist 240=[-1.2433143860627560378 ,.83639574197169935148] 
dist 241=[-.52954511448190025086,.80888314591522447915] 
dist 242=[-.46248590548898822934,.76500306555071245491] 
dist 243=[-.45320369911789491117,.75224568543915795772] 
dist 244=[-.51847291943654266637,.48391107645710936462] 
dist 245=[-.55832888302094920819,.44779685986428587029] 
dist 246=[-.58711319633065002712,.363280983849410575  ] 
dist 247=[-.60821761185177769415,.34644341266514114911] 
dist 248=[-.62363166062114737124,.23140191104254468664] 
dist 249=[-.62971829640936332624,.21002066245895841848] 
dist 250=[-.63116499891131142744,.17129877986807045061] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 2, 2, 1, 0, 1] 
dist 0=[59.722253821601320042  ,59.722253821601320042  ] 
dist 1=[59.112992543845690789  ,60.677814501907335837  ] 
dist 2=[57.636603165282069151  ,61.691899127152949462  ] 
dist 3=[55.283802427150606972  ,62.205161789986317844  ] 
dist 4=[51.455676995386603631  ,62.449961735361486316  ] 
dist 5=[47.515274506696540049  ,62.460651130868082236  ] 
dist 6=[44.714259490153120759  ,62.185783910804636639  ] 
dist 7=[42.209818739932311619  ,61.686026973769602194  ] 
dist 8=[39.453350287183067042  ,58.866602045996297594  ] 
dist 9=[36.744020679178341523  ,58.614598832508449894  ] 
dist 10=[34.427767375013445520  ,57.862901362475440611  ] 
dist 11=[31.954520140215487211  ,57.575784942361905187  ] 
dist 12=[28.618491334412369504  ,57.152480368318836016  ] 
dist 13=[25.313883946636781802  ,56.969832030510924912  ] 
dist 14=[22.966022032449415307  ,56.384140542242877835  ] 
dist 15=[20.867919723320853638  ,55.212912382274616645  ] 
dist 16=[18.560189030633310652  ,27.720481770382985720  ] 
dist 17=[16.292169944226822346  ,25.684067019477929168  ] 
dist 18=[14.352459335044319361  ,20.393299459271981421  ] 
dist 19=[12.279855515030716545  ,19.516655090078472088  ] 
dist 20=[9.4810870818434439558 ,19.194949365432981722  ] 
dist 21=[6.7329748935148343835 ,16.163203600755669905  ] 
dist 22=[4.8623804236959636311 ,10.389552652042544012  ] 
dist 23=[2.4267874295964130144 ,10.011508850237099002  ] 
dist 24=[-.96605261057889766184,5.1273900070294609052 ] 
dist 25=[-3.1983303681255326144 ,4.4586257759948474443 ] 
dist 26=[-5.0149979186984635301 ,3.5811472238297340509 ] 
dist 27=[-6.7491086061712449074 ,2.3088997940161423953 ] 
dist 28=[-8.3086341312438719927 ,1.2167656079249984986 ] 
dist 29=[-9.4291804494058934381 ,.4983931810639398571 ] 
dist 30=[-10.452656695911384335  ,-.1363279557650690488 ] 
dist 31=[-11.626739538378048294  ,-.2435697399924325951 ] 
dist 32=[-12.689801282991013230  ,-.1372798023784016385 ] 
dist 33=[-13.270088079877393706  ,.0698106349818041657 ] 
dist 34=[-13.618848963186772381  ,.39948597919617105192] 
dist 35=[-13.755617335916570239  ,.87790809734483869188] 
dist 36=[-13.806084558410578603  ,1.6784159482231590974 ] 
dist 37=[-13.809040537455280110  ,2.4916077693153632685 ] 
dist 38=[-13.781626960827209232  ,3.0208734847978369833 ] 
dist 39=[-13.728969473338351228  ,3.4399808064710304001 ] 
dist 40=[-11.751471782406219063  ,3.8144213474117653576 ] 
dist 41=[-11.461745105227840651  ,4.1287431033457501307 ] 
dist 42=[-10.881014151916115584  ,4.3083573125496283969 ] 
dist 43=[-10.717497096180086167  ,4.4226728839754913129 ] 
dist 44=[-10.077823445151105316  ,4.4768099180799981093 ] 
dist 45=[-9.9270796490373266779 ,4.5002100519265356743 ] 
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dist 47=[-9.5293073335914928736 ,4.9877558622715027075 ] 
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